The nearest hundredth, we get:
C ≈ 12.56 feet.
What is the value of 2r of a circle?Circle circumference (or perimeter) = 2R
where R denotes the circle's radius. 3.14 is the approximate (up to two decimal points) value of the mathematical constant. Again, Pi () is a special mathematical constant that represents the circumference to diameter ratio of any circle.
The circumference of a circle is calculated as follows:
C = 2πr
where C is the circumference, (pi) is a constant close to 3.14, and r is the radius of the circle.
When the given values are substituted, the following results are obtained:
C = 2(3.14)(2) \s= 12.56
We get the following when we round to the nearest hundredth:
C ≈ 12.56 feet.
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Can anyone solve this problem please? Thanks!
The trapezoid has a surface area of 480 square units.
What is the measurement for a trapezoid's area?So, a trapezoid measured in feet offers an area in square feet; one measured in millimetres gives an area in square centimetres; and so on. If it's simpler for you, you can add the lengths of the bases and then divide the total by two. Keep in mind that multiplication by 12 is equivalent to dividing by 2.
We must apply the formula for a trapezoid's area to this issue in order to find a solution:
[tex]A = (1/2) * (a + b) * h[/tex]
where h is the trapezoid's height (or altitude) and a and b are the lengths of its parallel sides.
The values for a, b, and h are provided to us, allowing us to change them in the formula:
A = (1/2) * (20 + 60) * 12
A = (1/2) * 80 * 12
A = 480 square units
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Halla los números desconocidos de estas operaciones
A)872+. +173=2000
B)9180:. =102
C). -99=706
Con los mismos números y las mismas operaciones podemos obtener diferentes resultados,coloca los paréntesis de manera que se obtengan los resultados indicados. A)3+5x7-2=40
B)3+5×7-2=54
C)3+5×7-2=28
ES PARA HOY PORFAVOR☹,PUEDEN HACER EN UNA HOJA O ESCRIBIR ASI PERO EXPLIQUEN BIEN!!!!!!AYUDA SI NO SABEN NO RESPONDAD
In equation A the missing number is 955, In equation B the missing number is 90 and In equation C the missing number is 805.
A) To find the missing number in the equation 872 + ? + 173 = 2000, we need to subtract 872 and 173 from 2000, which gives us:
2000 - 872 - 173 = 955
Therefore, the missing number is 955.
B) To find the missing number in the equation 9180 ÷ ? = 102, we need to divide 9180 by 102, which gives us:
9180 ÷ 102 = 90
Therefore, the missing number is 90.
C) To find the missing number in the equation ? - 99 = 706, we need to add 99 to 706, which gives us:
706 + 99 = 805
Therefore, the missing number is 805.
To obtain the indicated results with the same numbers and operations, we need to use parentheses to change the order of operations.
A) 3 + (5x7) - 2 = 40
B) (3 + 5) × 7 - 2 = 54
C) 3 + (5 × (7-2)) = 28
Equations are used extensively in various fields of science, engineering, economics, and finance, to name a few. It is formed by placing an equal sign between the two expressions. Equations are used to solve problems and find unknown values.
An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that need to be found, while the constants are known values that are already given. Solving an equation involves manipulating the expressions on both sides of the equal sign using mathematical operations to isolate the variable on one side and constants on the other. The final solution obtained is the value of the variable that satisfies the equation..
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Complete Question: -
Find unknown numbers of these operations
A ) 872 +. + 173 = 2000
B ) 9180:. = 102
C ). -99 = 706
With the same numbers and the same operations we can obtain different results, place the parentheses so that the indicated results are obtained.
A ) 3 + 5 x 7-2 = 40
B ) 3 + 5 × 7-2 = 54
C ) 3 + 5 × 7-2 = 28
IT'S FOR TODAY PLEASE ☹, CAN DO IN A LEAF OR WRITE ASI BUT EXPLAIN WELL!!!!!!HELP IF THEY DON'T KNOW NO RESPOND
I need help with this
sum area = -3x - 6y + 12 and product area = -36x - 72y.
what is rectangle?
A rectangle is a geometric shape that is defined as a four-sided flat shape with four right angles (90-degree angles) and opposite sides that are parallel and equal in length.
The area of a rectangle is given by the product of its length and width. Assuming that the length of the rectangle is given by -3x - 6y and its width is 12, we can express the area in terms of a sum and a product as follows:
Sum:
Area = length x width
Area = (-3x - 6y) + 12
Area = -3x - 6y + 12
Product:
Area = length x width
Area = (-3x - 6y) x 12
Area = -36x - 72y
Note that the product expression is not equal to the sum expression. This is because we used different assumptions for the length of the rectangle in each case.
Therefore, sum area = -3x - 6y + 12 and product area = -36x - 72y.
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The dwarf lantern shark is the smallest shark in the world. At birth, it is about 55 millimeters long. As an adult, it is only 3 times as long. How many centimeters long is an adult dwarf lantern shark? centimeters
Answer: 165
Step-by-step explanation:
55 x 3 = 165
A local winery wants to create better marketing campaigns for its white wines by understanding its customers better. One of the general beliefs has been that higher proportion of women prefer white wine as compared to men. The company has conducted a research study in its local winery on white wine preference. Of a sample of 400 men, 120 preferred white wine and of a sample of 500 women, 170 preferred white wine. Using a 0.05 level of significance, test this claim.INPUT Statistics required for computation170 = Count of events in sample 1500 = sample 1 size120 = Count of events in Sample 2400 = sample 2 size0.05 = level of significance0 = hypothesized differenceOUTPUT Output valuesSample 1 Proportion 34.00%Sample 2 Proportion 30.00%Proportion Difference 4.00%Z α/2 (One-Tail) 1.645Z α/2 (Two-Tail) 1.960Standard Error 0.031Hypothesized Difference 0.000One-Tail (H0: p1 − p2 ≥ 0)Test Statistics (Z-Test) 1.282p-Value 0.900One-Tail (H0: p1 − p2 ≤ 0)Test Statistics (Z-Test) 1.282p-Value 0.100Two-Tail (H0: p1 − p2 = 0)Test Statistics (Z-Test) 1.276p-Value 0.202Group of answer choicesThis is a one-tail test and the data does support the claim that higher proportion of women prefer white wine as compared to men.This is a one-tail test and the data does not support the claim that higher proportion of women prefer white wine as compared to men.This is a two-tail test and the data does support the claim that higher proportion of women prefer white wine as compared to men.This is a two-tail test and the data does not support the claim that higher proportion of women prefer white wine as compared to men.Question 2. Based on the study results presented in the last question, what is the upper bound for the proportion differences between women and men for a 95% confidence interval?(Note: Please enter a value with 4 digits after the decimal point. For example, if you computed an upper boundary of 23.456% or .23456, you would enter it here in decimal notation and round it to four digits, thus entering .2346).
Answer:
235.65
Step-by-step explanation:
g in acid base reactions, the hydrogen ions from the acid and the hydroxide ions from the base neutralize each other. khp has one ionizable hydrogen; this means that one mole of sodium hydroxide neutralizes one mole of khp. from experiment 1, calculate the exact molarity of the sodium hydroxide. (hint: use the mass of khp and do a stoichiometry problem.....) tip: khp is not the chemical formula. khp stands
In the following question, among the conditions given, the statement is said to be, the exact molarity of the NaOH solution is 0.0960 M.
The question is asking to calculate the exact molarity of the sodium hydroxide from Experiment 1.
KHP stands for potassium hydrogen phthalate, and one mole of sodium hydroxide (NaOH) will neutralize one mole of KHP. To solve the problem, use the mass of KHP and a stoichiometry problem.
First, calculate the number of moles of KHP:
Moles KHP = (Mass KHP (g) / Molar Mass KHP (g/mol))
Then, calculate the moles of NaOH:
Moles NaOH = (Moles KHP * Mole Ratio NaOH/KHP)
Finally, calculate the molarity of NaOH:
Molarity NaOH = (Moles NaOH / Volume NaOH (L))
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Write as a single power of 3:
27divided by 9a
Answer:
Step-by-step explanation:
27/9a
= 3^3/3^2 a
= 3/a
Suppose that a phone originally sold for $800 loses 3/5 of its value each year after it is released. After 2 years, how much is the phone worth?A. $800B. $1333C. $128D. $288
The phone is worth $128 after 2 years, which is option C.
What is exponential decay ?
Exponential decay is a decrease in a quantity over time where the rate of decay is proportional to the current value. In this case, the value of the phone decreases by 3/5 each year after it is released. This means that the value after one year is 2/5 of the original value, and the value after two years is (2/5) times (2/5) of the original value. Exponential decay is a common phenomenon in many areas of science and mathematics, including radioactive decay, population growth and decay, and financial investments.
Calculating the worth of the phone :
The phone is not worth the same amount after 2 years, as it loses 3/5 of its value each year. We need to calculate its worth after 2 years.
Let's use the formula for exponential decay: [tex]A = A_0(1 - r)^t[/tex], where A is the final amount, [tex]A_0[/tex] is the initial amount, r is the decay rate, and t is the time elapsed.
In this case, the initial amount is $800, the decay rate is 3/5, and the time elapsed is 2 years. Substituting these values into the formula, we get:
[tex]A = 800(1 - 3/5)^2[/tex]
[tex]A = 800(2/5)^2[/tex]
[tex]A = 800(4/25)[/tex]
[tex]A = 128[/tex]
Therefore, the phone is worth $128 after 2 years, which is option C.
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If all other factors are held constant, which of the following results in an increase in the probability of a Type II error? a. The true parameter is farther from the value of the null hypothesis. b. The sample size is increased. c. The significance level is decreased d. The standard error is decreased. e. The probability of a Type II error cannot be increased, only decreased
If all other factors are held constant, then the true parameter is farther from the value of the null hypothesis which is an increase in the probability of a Type II error.The correct option is A.
The true parameter is farther from the value of the null hypothesis.
When the true parameter is farther away from the value of the null hypothesis, it increases the probability of a Type II error. This is because the null hypothesis will have a harder time rejecting the true parameter.
The other factors - increasing sample size, decreasing significance level, and decreasing standard error - all result in a decreased probability of a Type II error.
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Analyze the proportion below and complete the instructions that follow. Use a model to find the missing value in the proportion. A. 4 B. 5 C. 10 D. 22 Please select the best answer from the choices provided A B C D
Step-by-step explanation:
The area of a rectangle is 1,872 ft2. The ratio of the length to the width is 9:13. Find the perimeter of the rectangle.
176 ft
You want to make a scale drawing of your bedroom to help arrange your furniture. You decide on a scale of 3 in. = 2 ft. Your bedroom is a 12 ft by 14 ft rectangle. What should the dimensions of your drawing be?
18 in. by 21 in.
If 5/y + 7/x=24 and 12/y + 2/x=24, find the ratio of x to y.
5/7
Simplify the ratio 8ft/12in. Use the conversion 12 in. = 1 ft.
8/1
Analyze the proportion below and complete the instructions that follow.
2x+5/3 = x-5/4
-7
If a+b/2a-b = 5/4 and b/a+9 = 5/9, find the value of b.
30
Analyze the ratio below and complete the instructions that follow.
$30:$6
Simplify the ratio.
5:1
If 14/3 = x/y then 14/x =
3/y
Analyze the diagram below and complete the instructions that follow.
In the diagram, AB:BC is 3:4 and AC = 42. Find BC.
24
Analyze the diagram below and complete the instructions that follow.
If AB:BC is 3:11, solve for x.
9
If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, which of the following is false?
b/a = c/d
Analyze the diagram below and complete the instructions that follow.
Find the ratio of the width to the length of the rectangle, then simplify the ratio. Use the conversion 100 cm = 1 m.
3/4
Simplify the ratio 3 gal./24 qt. Use the conversion 4 qt = 1 gal.
1/2
The area of a rectangle is 4,320 ft2. The ratio of the length to the width is 6:5. Find the length of the rectangle.
72 ft
Analyze the diagram below and complete the instructions that follow.
Given that CB/CA = DE/DF, find BA.
10.5
Analyze the proportion below and complete the instructions that follow.
2/3 = 8/x
3, 8
Analyze the diagram below and complete the instructions that follow.
Are the polygons shown here similar? Justify your answer. The images are not drawn to scale.
Yes, PQR ~TSV with a scale factor of 1:√3
All __________ are similar.
squares
Analyze the diagram below and complete the instructions that follow.
Determine which 2 triangles are similar to each other. The images are not drawn to scale.
GHI ~ JKL
Analyze the diagram below and complete the instructions that follow.
Pentagon PQRST ~ pentagon XYZVW. Find the value of b. The images are not drawn to scale.
3
Analyze the diagram below and complete the instructions that follow.
If ABC ~ XYZ, find XY. The images are not drawn to scale.
24
ABC is a right triangle. The legs of ABC are 9 ft and 12 ft. The shortest side of XYZ is 13.5 ft, and ABC ~ XYZ How long is the hypotenuse of XYZ?
22.5 ft
For the function f(x)=x^2+4x-12 solve the following. F(x) ≤0
The solution to the inequality f(x) ≤ 0 is the interval [-6, 2]. In other words, the values of x that satisfy the inequality are those that lie between -6 and 2, inclusive.
To solve the inequality f(x) ≤ 0, we need to find the values of x for which the function f(x) is less than or equal to zero.
We start by factoring the quadratic expression f(x) = x^2 + 4x - 12:
f(x) = (x + 6)(x - 2)
Setting this expression to zero, we get:
(x + 6)(x - 2) = 0
This gives us two solutions: x = -6 and x = 2.
Now, we need to determine the sign of f(x) in the intervals between these two solutions. We can use a sign chart to do this:
x f(x)
-∞ +
-6 0
2 0
+∞ +
From the sign chart, we see that f(x) is positive for x < -6 and for x > 2, and it is negative for -6 < x < 2.
To summarize, the solution to the inequality f(x) ≤ 0 for the function f(x) = x^2 + 4x - 12 is the interval [-6, 2].
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What will be the exponent of the product of 8.9 x 1012 and 4.7 x 10-2 in Scientific Notation?
the exponent of the product of 8.9 x 10¹² and 4.7 x 10⁻² in scientific notation is 11.
define exponentialExponential refers to a mathematical function or relationship in which a variable (such as x) is raised to a constant power (such as 2, 3, or e) to produce a result. The term "exponential" can also be used more broadly to describe any situation in which something grows or changes at an increasingly rapid rate over time, often with a compounding effect.
First, we multiply the two numbers:
(8.9 x 10¹²) x (4.7 x 10⁻²) = 41.83 x 10¹⁰
41.83 x 10¹⁰ = 4.183 x 10¹¹
Therefore, the exponent of the product of 8.9 x 10¹²and 4.7 x 10⁻² in scientific notation is 11.
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Jackson owns a heating and cooling company. He is going to install a new furnace into a customer's house, but he must determine the volume of airflow
needed in order to select the best size of furnace. Find the volume of the house sketched below, where H1-10 ft., H2=9 feet, L=30 feet, and W=20 feet.
Volume of a rectangular prism is V=WLH (width x length x height) Volume of a triangular Prism is:
V =
a.ch
A
A target has a bull's-eye with a d X
O mathwarehouse.com
h (in this case a-9, c= 20, h= 30)
15
[tex]8700[/tex] cubic feet of airflow are required for the entire home. Jackson may utilize this information to determine the best furnace size for the customer's requirements.
Volume explain: What is it?Volume is the quantity of space an object occupies, whereas capacity is a measurement of the substance—such as a solid, liquid, or gas—that an object can hold. While capacity may be measured in virtually any other unit, such as liters, gallons, pounds, etc., volume was determined in cubic units.
What are volume and what is its unit?Volume, which is measured in cubic units, is the three dimensional space inhabited by material or surrounded by a surface. The cubic centimeter (m3), a derived unit, is the SI unit for volume.
Volume of the first section with height [tex]H1=10[/tex] ft:
[tex]V1 = WLH1 = (20 ft)(30 ft)(10 ft) = 6000[/tex] cubic feet
Volume of the second section with height [tex]H2=9[/tex] ft:
[tex]V2 = (1/2)WLH2 = (1/2)(20 ft)(30 ft)(9 ft) = 2700[/tex]cubic feet
Total volume of house,
[tex]V total = V1 + V2 = 6000[/tex] cubic feet + [tex]2700[/tex] cubic feet [tex]= 8700[/tex] cubic feet
Therefore, the volume of airflow needed for the house is [tex]8700[/tex] cubic feet.
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find the values of a and b such that
x^2- +5=(x-a)^2+b
The value οf a = 1/2 and b = 19/4 in the equatiοn x² - x + 5 = (x-a)² + b.
What dο yοu mean by algebra?The part οf mathematics in which letters and οther general symbοls are used tο represent numbers and quantities in fοrmulae and equatiοn is called algebra.
x² - x + 5 = (x-a)² + b
x² - x + 5 = x² + a² - 2xa + b
-x + 5 = -2xa + a² + b
By matching cοrrespοnding terms,
2a = 1 and a²+ b = 5
a= 1/2 and a²+ b = 5
Substituting value οf "a"
(1/2)² + b = 5
1/4 + b = 5
b = 5- 1/4
b = 19/4
Thus, a = 1/2 and b = 19/4.
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smart mugs are the next generations of hot drinks dispensers tha om with built in technology to keep drinks at the perfect temperature for hours on end initial cost of a smart mug was aed 896, because of high demand in market the cost increased by 12% find the new price of the mug
PLS QUICK ITS DUE 1 HOUR!!
With a [tex]12[/tex]% price rise, the smart mug now costs AED [tex]1003.52[/tex].
Price and sell price: what are they?The sale price is the price an user pays to purchase a thing or a commodity. It is a cost that is higher than the market cost and also includes a portion of the profit. The cost price refers to the price paid by the seller for the item or service.
How would you define price?Price is the process of figuring out how much a something or service is worth. Price establishes a customer's cost, although it can or cannot be linked to the price a firm pays to manufacture a good or service.
We need to multiply the initial price by [tex]1.12[/tex] which represents a [tex]12[/tex]% increase in decimal form,
New price [tex]=[/tex] Initial price [tex]*[/tex] (1 [tex]+[/tex] Percent increase in decimal form)
New price[tex]= 896 * (1 + 0.12)[/tex]
New price [tex]= 896 * 1.12[/tex]
New price [tex]= 1003.52[/tex]
Therefore, the new price of the smart mug is AED [tex]1003.52[/tex] after a [tex]12[/tex]% increase.
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why can't we use mean when a data set has one or two values that are much higher than all of the others
The reason we can't use the mean when a data set has one or two values that are much higher than all of the others is that it skews the average, making it not representative of the rest of the data.
What is the mean?The mean is a numerical measure of the central tendency of a data set. It is calculated by dividing the sum of all the values in a data set by the number of data points.
A data set is a collection of observations or measurements that are analyzed to obtain information. It can be represented graphically, in tabular form, or in any other format. The data set may be a sample or the entire population.
If a data set has one or two extremely high or low values, it can significantly impact the mean. These values are known as outliers. The outliers can cause the mean to be higher or lower than the actual middle value of the data.
Hence, in such cases, the median is a better choice for finding the central tendency of the data. The median is the middle value of the data set, and it is less affected by outliers than the mean. The mode, which is the value that occurs most frequently in the data set, is also a measure of central tendency that is less sensitive to outliers than the mean.
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There is a 0.99962 probability that a randomly selected 28-year-old female lives through the year. An insurance company wants to offer her a one-year policy with a death benefit of $500,000. How much should the company charge for this policy if it wants an expected return of $400 from all similar policies?
In order to expect a return on $400 from across all policies of a similar nature, the insurance firm should charge the policy for about $501.88.
How then do we return a value?Return[expr] leaves control structures that are present during a function's definition and returns the value expression for the entire function. Even if it comes inside other functions, yield takes effect as quickly as it is evaluated. Functions like Scan can use Return inside of them.
Since p is the chance that the 28-year-old woman survives the year and is given as 0.99962, we can enter this number into the equation for n as follows: n = 400(0.99962)/500,400 n 0.799
In light of this, the insurance provider should impose a premium of: Premium = 400/n
$501.88 is the premium ($Premium = 400/0.799)
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Consider a hash table, a hash function of key % 10. Which of the following programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation? O c1 = 1 and 2 = 0 O c1 = 5 and c2 = 1 O c1 = 1 and c2 - 5 O c1 = 10 and 2
D: "[tex]c_{1} = 10[/tex] and [tex]c_{2} = 2[/tex]" are programmer-defined constants for quadratic probing that cannot be used in a quadratic probing equation. Option D is correct answer.
The quadratic probing equation is defined as:
h (k, i) = (h′(k) + [tex]c_{1}[/tex] * i + [tex]c_{2}[/tex] * i^2) mod m,
where h′(k) is the hash value of key
k and m is the size of the hash table.
The constants [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are programmer-defined constants that are used to compute the new hash index when a collision occurs in the hash table.
The given hash function is h(k) = k % 10.
Therefore, the hash value of any key will be between `0` and `9`.Now, let's check which of the given programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation:
Option A: `c1 = 1 and c2 = 0`This option can be used in the quadratic probing equation. It means that linear probing is being used.
Option B: [tex]c_1 = 5[/tex] and [tex]c_2 = 1[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 5i + i^2) mod m`.
Option C: [tex]c_1 = 1[/tex] and [tex]c_2 = 5[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + i + 5i^2) mod m`.
Option D: [tex]c_1 = 10[/tex] and [tex]c_2 = 2[/tex] This option cannot be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 10i + 2i^2) mod m`.
Since [tex]c_{1}[/tex] is greater than or equal to `m`, this equation will always result in a hash index that is greater than or equal to `m`. Therefore, it is not possible to use `[tex]c_{1}[/tex]= 10` in the quadratic probing equation. Hence, the correct option is D.
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What is an equation for the quadratic function represented by the table shown?
(0,-1),(2,3),(4,-1),(6,-13)
The equation of the quadratic function represented by the given table is y = -x² + 4x - 7.
What is a quadratic function?A quadratic function is a function of the form:\sf(x) = ax^2 + bx + c\swhere a, b, and c are constants and x is the parameter. The graph of a quadratic function is a parabola, which is an Inverted curve. Whether the parabola opens up (if a > 0) or down (if a 0) depends on the sign of the coefficient a.
The width of the parabola is also determined by the coefficient a. The parabola is narrow if |a| is greater than 1. (i.e. it has a small width relative to its height). The parabola is wide if |a| is greater than 1.
The standard form of the quadratic equation is given as:
y = ax² + bx + c
Substitute the value of x and y from the table:
3 = a(2)² + b(2) + c
4a + 2b + c = 3........(1)
For point (4, -1):
-1 = a(4)² + b(4) + c
16a + 4b + c = -1..........(2)
For (6, -13):
-13 = a(6)² + b(6) + c
36a + 6b + c = -13..........(3)
From 1 we have:
c = 3 - 4a - 2b
Substitute the value of c in equation 2 and 3:
16a + 4b + 3 - 4a - 2b = - 1
12a + 2b = - 4........(4)
36a + 6b + 3 - 4a - 2b = -13
32a + 4b = -16.......(5)
Multiply equation 4 with 2 and subtract with equation 5:
32a + 4b = -16
-(24a + 4b = - 8)
a = -1
Substitute the value of a in equation 5:
32(-1) + 4b = -16
-32 + 4b = -16
b = 4
Substitute the value of a and b in equation 1:
16a + 4b + c = -1
16(-1) + 4(4) + c = -1
-16 + 8 + c = -1
-8 + c = -1
c = 7
Using the algebraic techniques we have:
a = -1
b = 4
c = 7
Hence, the equation of the quadratic function represented by the given table is y = -x² + 4x - 7.
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pls help Are the following lines parallel, perpendicular, or neither?
y = 2/3x − 4
y = −3/2x − 7
Responses
Parallel
Perpendicular
Neither
Answer:
Perpendicular.
Step-by-step explanation:
To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So we can rewrite the given equations in this form
y = 2/3x - 4 ==> slope = 2/3
y = -3/2x - 7 ==> slope = -3/2
Two lines are parallel if and only if their slopes are equal. Therefore, since the slopes of the two lines are different (2/3 and -3/2), they cannot be parallel.
Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the product of their slopes is -1. Therefore, we can check if the product of the slopes of the two lines is -1
(2/3) * (-3/2) = -1
Since the product of the slopes is -1, the two lines are perpendicular.
Therefore, the answer is: perpendicular.
Sophie invested $92,000 in an account paying an interest rate of 6 1/8% compounded
continuously. Damian invested $92,000 in an account paying an interest rate of 6 5/8%
compounded monthly. After 14 years, how much more money would Damian have in
his account than Sophie, to the nearest dollar?
Answer:
Step-by-step explanation:
To solve this problem, we need to use the formula for compound interest:
A = P*e^(rt)
where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).
For Sophie's account, we have:
P = $92,000
r = 6 1/8% = 0.06125 (as a decimal)
t = 14 years
A = 92000*e^(0.06125*14)
A = $219,499.70 (rounded to the nearest cent)
For Damian's account, we have:
P = $92,000
r = 6 5/8% = 0.06625/12 = 0.005521 (as a monthly decimal rate)
t = 14*12 = 168 months
A = 92000*(1+0.005521)^168
A = $288,947.46 (rounded to the nearest cent)
Now we can subtract Sophie's final amount from Damian's final amount to find the difference:
Difference = $288,947.46 - $219,499.70
Difference = $69,447.76
Therefore, Damian would have about $69,448 more in his account than Sophie, to the nearest dollar.
Describe the error in finding the distance between A(6, 2) and B(1,−4)
The error is the substitution of coordinates. Coordinates are ordered pairs of points that help us locate any point in a 2D plane or 3D space.
Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identifies a specific point's precise location on a grid. This grid is referred to as a coordinate plane.
The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by
[tex]AB = \sqrt{(x_{1} , x_{2})^{2} + (y_{1} - y_{2})^{2} }[/tex]
Observe that the x-coordinate of B is subtracted from the x-coordinate of A. This goes with the y-coordinates.
Therefore, the error is the substitution of coordinates.
The correct computation is
[tex]AB = \sqrt{(6-1)^{2} + [2 - (-4)]^{2} }[/tex]
[tex]= \sqrt{5^{2} + 6^{2} }[/tex]
[tex]= \sqrt{25 + 36} \\[/tex]
[tex]= \sqrt{61}[/tex]
≈ 7.81
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The complete question is as follows:
Describe and correct the error in finding the distance between A(6, 2) and B(1, -4). AB = √[(6 - 2)² + {2 - (-4)}²] = √(4² + 5²) = √(16 + 25) = √41 ≈ 6.4.
Given the triangle, find the length of X. Give your answer in simpliest radical form.
Answer:
x = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the cosine ratio in the lower right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} } }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 4[tex]\sqrt{2}[/tex]
what are the roots of 2x^2+10x+9=2x
The roots of the equation 2x² + 10x + 9 = 2x does not exist i.e no real roots
Calculating the roots of the equationTo find the roots of the given quadratic equation 2x² + 10x + 9 = 2x, we can start by rearranging the equation to the standard form of a quadratic equation
2x² + 10x + 9 - 2x = 0
Simplifying the left-hand side, we get:
2x² + 8x + 9 = 0
Now, we can use the quadratic formula to find the roots of the equation:
x = (-b ± √(b² - 4ac)) / 2a
where a = 2, b = 8, and c = 9.
Substituting these values into the formula, we get:
x = (-8 ± √(8² - 4(2)(9))) / 2(2)
Simplifying the expression under the square root, we get:
x = (-8 ± √-8) / 4
The square root of -8 is not a real number
So, the equation has no real root
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Help due soon !!!!!!!!!
An expression for the length of the rectangle in terms of A is [tex]$\boxed{L=x+5}$[/tex]
How to find the expression?We are given that the area of a rectangle is [tex]$A=x^2+x-15$[/tex], and we want to find an expression for the length of the rectangle in terms of A.
Recall that the area of a rectangle is given by the formula: [tex]$A=L\cdot W$[/tex], where L is the length and W is the width. We can use this formula to write L in terms of A and W as [tex]$L=\frac{A}{W}$[/tex].
We know that the rectangle has a length and a width, so we need to find an expression for the width W in terms of A. We can rearrange the given formula for A to solve for W:
[tex]&& \text{(substitute }L=x+5\text{)}[/tex]
[tex]W&=\frac{x^2+x-15}{x+5} && \text{(divide both sides by }x+5\text{)}[/tex]
Now that we have an expression for W in terms of A, we can substitute it into our expression for L to get:
[tex]L&=\frac{A}{W}[/tex]
[tex]&=\frac{x^2+x-15}{\frac{x^2+x-15}{x+5}} && \text{(substitute the expression we found for }W\text{)}\&=x+5[/tex]
Therefore, an expression for the length of the rectangle in terms of A is [tex]$\boxed{L=x+5}$[/tex]
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a 3-digit pin number is selected. what it the probability that there are no repeated digits? the probability that no numbers are repeated is
The probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]
The probability that there are no repeated digits in a 3-digit pin number is 0.72.
Formula used:
[tex]P(n,r)=\frac{n!}{(n-r)!}\\ Probability=\frac{Number of favourable outcomes}{Total number of events in the samples pace}[/tex]
There are 10 digits (0,1,2,3,4,5,6,7,8,9) to choose from.
Therefore, the total number of possible 3-digit pin numbers with no repeated digits is
[tex]P(10,3)=\frac{10!}{(10-3)!}\\P(10,3)= \frac{10!}{7!}\\P(10,3)=720[/tex]
The total number of possible 3-digit pin numbers [tex]= 10 * 10 * 10 = 1000[/tex].
Thus, the probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]
Therefore, the probability that there are no repeated digits in a 3-digit pin number is 0.72.
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What is 6x+2y=-4 in slope-intercept form
Answer:
y = -3x - 2
Step-by-step explanation:
To write the equation 6x + 2y = -4 in slope-intercept form, we need to solve for y.
First, we can isolate the y-term by subtracting 6x from both sides:
6x + 2y = -4
2y = -6x - 4
Next, we can divide both sides by 2 to isolate y:
2y/2 = (-6x - 4)/2
y = -3x - 2
So the slope-intercept form of the equation 6x + 2y = -4 is y = -3x - 2.
LMN is a straight angle. Find m LMP and m NMP
From the given information provided, the value of angle LMP and angle NMP is 77 and 103 degrees respectively.
Since LMN is a straight angle, it measures 180 degrees.
We are given the measures of LMP and NMP, and we are told that LMP + NMP = LMN. Therefore, we can set up an equation:
LMP + NMP = LMN
(-16x + 13) + (-20x + 23) = 180
Simplifying and solving for x, we get:
-36x + 36 = 180
-36x = 144
x = -4
Now that we have found the value of x, we can substitute it back into the expressions for LMP and NMP to find their measures:
LMP = -16x + 13 = -16(-4) + 13 = 77 degrees
NMP = -20x + 23 = -20(-4) + 23 = 103 degrees
Therefore, the measures of LMP and NMP are 77 degrees and 103 degrees, respectively, and the measure of LMN is 180 degrees.
Question - LMN is a straight angle. LMP = -16x + 13 NMP = -20x + 23 LMP + NMP = LMN What are the measures?
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Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A sampling distribution is normal only if the population is normal. Choose the correct answer below. A. The statement is true. B. The statement is false. A sampling distribution is normal only if n≥30. C. The statement is false. A sampling distribution is normal if either n≥30 or the population. D. The statement is false. A sampling distribution is never normal.
A sampling distribution is normal only if the population is normal. This statement is false because A sampling distribution is normal only if n≥30.
If the underlying population is normally distributed, the sampling distribution (such as the sample mean distribution, also known as the xbar distribution) is also normally distributed. Even though the population is not normally distributed, the x(bar) distribution is approximately normal if n > 30, due to the central limit theorem. Some textbooks may use values above 30, but after a certain threshold the x(bar) distribution is effectively "normal".
Option B is close, but misses the normal population part. n > 30 is not necessary if we know the population is normal.
A sampling distribution is the probability distribution of a statistic obtained from a large number of samples drawn from a particular population. The sampling distribution for a given population is the frequency distribution of a range of different outcomes that can occur in the population.
In statistics, a population is the entire basin from which a statistical sample is drawn. A population can refer to an entire population of people, objects, events, hospital visits, or measurements. Thus, a population can be said to be a global observation of subjects grouped by common characteristics.
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PLEASE HELP!!! WILL MARK BRANLIEST!!!
Answer:
The point z = 3+4i is plotted as a blue dot, and the two square roots are plotted as a red dot and a green dot. The magnitudes of z and its square roots are shown by the radii of the circles centered at the origin.
Step-by-step explanation:
qrt(z) = +/- sqrt(r) * [cos(theta/2) + i sin(theta/2)]
where r = |z| = magnitude of z and theta = arg(z) = argument of z.
Calculate the magnitude of z:
|r| = sqrt((3)^2 + (4)^2) = 5
And the argument of z:
theta = arctan(4/3) = 0.93 radians
Now, find the two square roots of z:
sqrt(z) = +/- sqrt(5) * [cos(0.93/2) + i sin(0.93/2)]
= +/- 1.58 * [cos(0.47) + i sin(0.47)]
= +/- 1.58 * [0.89 + i*0.46]
Using a calculator, simplify this expression to:
sqrt(z) = +/- 1.41 + i1.41 or +/- 0.2 + i2.8
