Using pythagoras theorem, the values given in the question 9, 40 and 41 represents a right angle triangle
Pythagoras TheoremThis theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. The sides of this triangle are named the perpendicular, base and hypotenuse. In this case, the hypotenuse is always longest side, as it is opposite to the angle 90°
Mathematically Pythagoras theorem is given as;
x² = y² + z²
x = hypothenusey = legz = legLet's substitute the values into the formula and check if the values are a right angle triangle.
41² = 40² + 9²
1681 = 1600 + 81
1681 = 1681
The values 9, 40, 41 represents a right angle triangle
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Let f(x) be a 4th-degree polynomial function with zeroes 1,-1, and 3-i. If f(0)=20, write the equation in:
a) Factored form
b) Standard form
The polynomial expression are P(x) = (x - 1)(x + 1)[(x - 3)² + 1] and P(x) = x⁴ - 6x³ + 9x² + 6x - 10
How to determine the polynomial expression?Factored form
The given parameters are
Degree = 4Zero = 1,-1, and 3-iThere are complex numbers in the above zeros
This means that, the other zero is
Zeros = 3 + i
The equation of the polynomial is then calculated as
P(x) = Leading coefficient * (x - zero)^multiplicity
So, we have
P(x) = (x - 1) * (x + 1) * (x - (3 + i)) * (x - (3 - i))
This gives
P(x) = (x - 1) * (x + 1) * (x - 3 - i) * (x - 3 + i)
Evaluate the products
P(x) = (x - 1) * (x + 1) * [(x - 3)² - (i)²]
So, we have
P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]
P(x) = (x - 1)(x + 1)[(x - 3)² + 1]
The standard form
In (a), we have
P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]
Expand
P(x) = (x² - 1) * (x² - 6x + 9 + 1)
So, we have
P(x) = (x² - 1) * (x² - 6x + 10)
Remove the brackets
P(x) = x⁴ - 6x³ + 10x² - x² + 6x - 10
Evaluate the like terms
P(x) = x⁴ - 6x³ + 9x² + 6x - 10
Hence, the equation is P(x) = x⁴ - 6x³ + 9x² + 6x - 10
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The wholesale price for a chair is $169. A certain furniture store marks up the wholesale price by 16%. Find the price of the chair in the furniture store. Round your answer to the nearest cent, as necessary.
Need Help!
The price of the chair in the furniture store is $94.
How to calculate the price of the chair in the furniture store?Given that the wholesale price for a chair is $169 and that a certain furniture store marks up the wholesale price by 16%.
The price of the chair in the furniture store will be:
= $169 + (16% × $169)
= $169 + $27.04
= $196
The price is $194.
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Helllo sir please tell me what is linear equation in one variable
The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
What is a variable?It is a symbol standing in for an unknown numerical value in an equation.
The general form of a one variable linear equation is given by
ax+b = 0
where a and b are two integers, and x is the variable
The one-variable linear equation has only one solution.
Hence, the equation in the form ax+b = 0 is known as a one-variable linear equation.
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Jin went to the grocery store and bought bottles of soda and bottles of juice. Each
bottle of soda has 25 grams of sugar and each bottle of juice has 15 grams of sugar.
Jin purchased a total of 16 bottles of juice and soda which collectively contain 300
grams of sugar. Graphically solve a system of equations in order to determine the
number of bottles of soda purchased, x, and the number of bottles of juice
purchased, y.
Answer: x = 6, y = 10; as a point, that would be (6, 10).
Step-by-step explanation:
To do it graphically, you would just graph the equations 25x + 15y = 300 and x + y = 16. Then, you would find the intersecting point.
To do this, you should convert to point-slope format.
15y = -25x + 300 and x + y = 16
1) y = -5/3x + 20 and 2) y = -x + 16
Now, for equation 1, you start at the y-intercept (0, 20) and for every increase of 1 on the x-axis, you decrease -5/3 on the y-axis. To graph this in the software, you click on the point (0, 20) and on another point on the line y = -5/3x + 20. (Any will do, but it should be an integer. (3, 15) works.)
Do the same for equation 2. Start at the y-intercept (0, 16) and decrease 1 for every increase of 1 on the x-axis.
Look for the point(s) where the lines intercept. It is (6, 10). If you have the time, you can verify this algebraically.
at 95% confidence, what is the margin of error? if required, round your answer to four decimal places. g
At 95% confidence interval for a sample of size 100 where p = 0.15 , the margin of error is 0.0700 .
In the question ,
it is given that ,
the sample size is = 100 and
the value of p is ⇒ 0.15 .
we have to find the "margin of error"(E) for the 95% confidence interval ,
we know that the z value for the 95% confidence interval is = 1.96
the formula for margin of error is :
E = Z×√p(1-p)/n .
Substituting the values of z , p and n ,
we get ,
E = 1.96×√0.15(1-0.15)/100
= 1.96×√0.15(0.85)/100
= 1.96×√0.1275/100
= 1.96×√0.001275
= 1.96×0.03570
Simplifying further ,
we get ,
= 0.06995899
rounding to the four decimal places ,
≈ 0.0700
Therefore , the required margin of error is 0.0700 .
The given question is incomplete , the complete question is
At 95% confidence, for a sample of size 100 where p = 0.15 . What is the Margin Of Error ? if required, round your answer to four decimal places.
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(a) Calculate the simple interest collected by a bank if $1500 is loaned for 3 years at 8% per annum.
(b) What amount of money did the borrower actually pay the bank?
(c) What amount of money was paid monthly?
Answer:
Step-by-step explanation:
(a)Given:
Principal Amount=$1500
Time = 3 years
Rate of Interest = 8% per annum
Find:
Simple Interest=?
According to the formula of simple interest
Simple Interest=Principal x Time x Rate of Interest
i.e., SI=PRT
SI= 1500 X 3 X 8/100
SI= $360
Therefore, the simple interest for the principal amount of the loan $1500 in 3 years at a rate of 8% per annum will be $360.
(b) According to the formula:
Total Amount= Principal Amount + Simple Interest
i.e., Total Amount = $1500+$360
Total Amount = $1860
Therefore, the loan amount the borrower will pay the bank is $1860.
The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to
clean 2 hamster cages.
Complete the table.
Minutes
15
Cages cleaned 2 4
Graph the data from the table.
Cages cleaned
20
18
16
14
12
10
8
30 55
•
90
8 10
The complete table will be;
Minutes 15 30
Cages cleaned 2 4
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.
Now,
Since, The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.
Hence, By definition of proportion we get;
Let the time to clean 4 hamster cages = x
So, We get;
⇒ 15 / 2 = x / 4
⇒ 15×4 / 2 = x
⇒ 30 = x
⇒ x = 30
Thus, It take 30 minutes to clean the 4 hamster cages.
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rate change of (0, -9) and (7, 5)
show that the picture and board aren't mathematically similar (diagram below)
Answer:
See below
Step-by-step explanation:
If the figures were similar the corresponding sides would be proportional.
[tex]\frac{10}{12}[/tex] = [tex]\frac{8}{10}[/tex] This statement would be true if the sides were proportional, but it is not true. Cross multiply.
10(10) ≠ (8)(12)
100≠96
PLEASE HELP WITH THIS PROBLEM
Answer:
y -2 = 2(x +7)y -2 = -1/2(x +7)Step-by-step explanation:
You want equations of lines parallel and perpendicular to y = 2x -1 through the point (-7, 2).
SlopeThe given equation is written in slope-intercept form:
y = mx + b
where m = 2, and b = -1.
The slope of the line is m, the x-coefficient. For the given line, the slope is 2.
A parallel line will have the same slope: 2.
A perpendicular line will have the opposite reciprocal slope: -1/2.
Point-slope equationWhen you have a point and slope, it is useful to use the point-slope form of the equation for a line:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
For both of the desired lines, the point is (h, k) = (-7, 2). Using this point and the above slopes, we have ...
equation of parallel line: y -2 = 2(x +7)equation of perpendicular line: y -2 = -1/2(x +7)Write the linear equation in slope intercept form
The given linear equation (1/3)x+ y=2 in the slope-intercept form is
y=(-1/3)x+2.
Explain about slope-intercept form?Where m is the slope and b is the y-intercept, the slope-intercept form is represented as y = mx+ b. By utilizing y=mx+ b, a line is typically simple to graph. The point-slope form and standard form of linear equations are further types. Example 1: A line with a slope of 1/2 and a y-axis crossing at (0, -3). Calculate the line's equation. It is y = x/2 - 3 that determines the line's equation. Example 2: Determine the equation utilizing the y-y-intercept axis's and the horizontal line's slope intercept formula (0, 8).
Finding the slope between two points on a line and then solving for the y-intercept in the slope-intercept equation y=mx+ b allow us to build an equation for that line.
Given linear equation is:
(1/3)x+ y=2
The following is the slope-intercept form of the given linear equation:
y=(-1/3)x+2
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In circle C, mCG= 148°, mCD = 86°, and m∠EPF = 116°. What is the measure of arc FG?
Answer:
The measure of arc FG is 148°
Step-by-step explanation:
Since the measure of an arc is equal to the measure of the central angle that subtends it, and the measure of central angle CG is 148°, the measure of arc FG is 148°. This is because the arc FG is subtended by the central angle CG.
A random sample of 100 people was taken. eighty-five of the people in the sample favored candidate a. we are interested in determining whether or not the proportion of the population in favor of candidate a is significantly more than 80%. the test statistic is?
Answer:
Step-by-step explanation:
Sorry if this is different, but based on what I read, here is the answer.
100 x 0.85 = 85
therefor it is 85%, which is significantly more than 80%
a surveyor followed a property's legal description by starting at a point of beginning, then following the indicated directions between natural and artificial landmarks to arrive back at the point of beginning, using the method called a) lot-and-block. b) torrens. c) metes and bounds. d) rectangular survey.
The method which the surveyor followed was the method of metes and bounds.
The surveyor followed a property's legal description by starting at a point of beginning, then following the indicated directions between natural and artificial landmarks to arrive back at the point of beginning, using the method called metes and bounds.
Metes and bounds are the natural markers that define the limits or boundaries of a piece of property. Rivers, roads, stakes, and other natural or artificial markers are examples of metes and bounds landmarks.
A system or method of representing land, real property (as opposed to personal property), or real estate is known as metes and bounds. The technique has been used in England for centuries and is still used to define general boundaries there.
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Erica takes out a loan to purchase a car. She borrows 12,000 at 12% annual percentage rate. Complete the statements. The graph is [Drop Down 1]. Erica's loan is a [Drop Down 2] loan. The equation which models this loan is [Drop Down 3]. If Erica pays off the loan in six years, she will have paid [Drop Down 4].
An increasing exponential function is modeled as follows:
A(t) = A(0)(1 + r)^t.
The parameters of the exponential function are given as follows:
A(0) is the initial value of the exponential function.r is the growth rate of the exponential function, as a decimal.She borrows 12,000 at 12% annual percentage rate, hence the initial value and the growth rate are given as follows:
A(0) = 12,000, r = 0.12.
Then the function that describes her loan is given as follows:
A(t) = 12000(1.12)^t.
After six years, the value of the loan is calculated as follows:
A(6) = 12000(1.12)^6 = $23,686.
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a poll shows that of all voters approve of the mayor's work. on three separate occasions a pollster selects a voter at random. what is the probability that on exactly one of these three occasions the voter approves of the mayor's work?
The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:
0.189 = 18.9%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The values of these parameters in the context of this problem are given as follows:
n = 3, p = 0.7.
Then the probability of exactly one success is calculated as follows:
P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.
Missing InformationThe proportion of voters that approve the mayor's work is of 70%.
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What is the slope of the line that passes through (–3, 2) and (10, –2)
The slοpe οf the line is –4/13
Slοpe οf the line:The slοpe fοrmula is used tο calculate the slοpe οf a straight line passing thrοugh twο given pοints. It is alsο knοwn as the gradient fοrmula. The slοpe fοrmula is as fοllοws: slοpe = (change in y) / (change in x)
where "change in y" represents the difference between the y-cοοrdinates οf the twο pοints and" change in x" represents the difference between the x-cοοrdinates οf the twο pοints. Hence slοpe fοrmula can be given as slοpe = (y₂ - y₁) / (x₂ - x₁)
Here we have
The line passes thrοugh (–3, 2) and (10, –2)
Take (x₁, y₁) = (–3, 2) and (x₂, y₂) = (10, –2)
Using the fοrmula, m = (y₂ - y₁)/(x₂ - x₁)
Slοpe οf the line (m) = (–2 –2 )/(10 –(–3))
= (–4 )/(10 + 3)
= –4/13
Hence,
The slοpe οf the line is –4/13
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Q9.
Rachel, Samina and Tom share £600 between them.
2
Rachel gets 2/5 of the £600
ima
Samina gets 1/4 of the money that is left over.
Tom gets the rest of the money.
Tom says,
"I would have got more money if we had shared the £600 equally between us."
Is Tom correct?
You must show how you get your answer.
No. Tom is not correct.
If the money were split equally everyone would've gotten £200.
But, if everyone went by the mentioned distribution, then,
Rachel would get = 2/5 x 600 = £280
Remainder money = 600 - 280 = £320
Samina would get = 1/4 x 320 = £80
Tom would get the remaining money = 600 - (280 + 80)
= 600 - 360
= £240
Since, £240 > £200, Tom would be incorrect in saying he would have had more money if he had split the money equally.
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Please help meee !!!??
its A
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What is the total cost of the rental is Dana drives the car for 15 miles?
The total cost of the rental if Dana drives the car for 15 miles is $90.2
How to determine the total cost?From the question, we have the following parameters that can be used in our computation:
C = 73.25 + 1.13m
Where
m = number of miles
This means that
m = 15
SO, we have the following equation
C = 73.25 + 1.13 * 15
Evaluate
C = 90.2
Hence, the total cost is $90.2
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"Dana and her family are going to Six Flags Great America the sum- mer after her Sophomore year. She is excited, because she will be doing all driving: After doing some complicated analysis, she calcu; lates that it will cost a certain amount per mile to pick up everyone and drive to the park, plus flat amount for everyone's admission tickets. The equation below models the total cost, €,and the variable m represents the number of miles driven: C = 73.25 + 1.13m
On a team,8 girls and 5 boys devoted a total of 87 points. The difference between the number of points scored by the 8 girls and the number of points scored by the 5 boys is 57. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and boy
Answer:
Girls: 7 points each
Boys: 11 points each
Step-by-step explanation:
Josiah began earning an allowance each day. At the end of 6 days he buys a video game that costs $150 and has $102 left over. How much money does he earn each day in allowance
Answer:
42
Step-by-step explanation:
150+102=252
252/6=42
50 points please help asap
The domain is set of all real numbers and the range is y ≥ -4
How to determine the domain and the range of the function?From the question, we have the following parameters that can be used in our computation:
The equation is given as
g(x) = |x + 4|
The domain
The above equation is an absolute value equation
An absolute value equation can take any value as its input
This means that the domain is the set of all real numbers
When represented as an interval, we have
The domain is (-∝, ∝)
Also, we have
-∝ < x < ∝
Hence, the domain is the set of all real numbers
The range
Here, we have
g(x) = |x + 4|
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
Vertex = (-4, 0)
Remove the x value
y = -4
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
[-4, ∝)
Another representation is
y ≥ -4
So, the range is y ≥ -4
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maria has type b blood. she can safely receive blood transfusions from people with blood types o and b. what is the probability that a randomly chosen person from the united states can donate blood to maria?
The probability that a randomly chosen person from the united states can donate blood to maria is 0.50
considering blood to be of types A,B,AB and O
further all blood groups are equi probable
Probability of blood type A = probability of blood type B = probability of blood type AB = probability of blood type O = x
Probability of blood type A + probability of blood type B + probability of blood type AB + probability of blood type O = 1
⇒ 4x = 1
⇒ x = 1/4
Probability that a random person will have blood of type B or O = x+x
= 1/4 + 1/4
= 1/2
= 0.50
Hence we get the required answer.
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Luis typically eats 4 1/4 ounces of fruit each day. Today he ate his usual amount. Write each answer as a fraction and as a decimal. Use bar notation is necessary.
Answer:
Fraction: 4 1/4 = 17/4
Decimal: 17/4 = 4.25
Step-by-step explanation:
-2(2x-3)=-22 i dont get it
Jaime y rocío están pintando una pared con cubos de pintura idénticos. Si Jaime ha gastado 2/5 de su pintura y rocío,3/5. ¿Quién ha gastado más? ¿Qué cubo de pintura estará más lleno?
Answer:
Step-by-step explanation:
Rocio ha gastado mas. El cubo de Jaime esta mas lleno.
Rocio gasto otro poco mas porque 3 esta mas grande que 2
the quadtratic expression -3x^2 +6x + 72 will equal zero when x equals
The values of x is x = 6 Or x = - 4 when the expression - 3x² + 6x + 72 will be zero.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Here in the problem, we have to find the roots of the quadratic equation
- 3x² + 6x + 72 = 0.
3x² - 6x - 72 = 0.
x² - 2x - 24 = 0.
x² - 6x + 4x - 24 = 0.
x(x - 6) + 4(x - 6) = 0.
(x - 6)(x + 4) = 0.
x = 6 Or x = - 4 are the values of x when the expression will be zero.
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Given:NP=MP,NP PL prove NPL≈MPL
two stores sell identical sandwich rolls in different size packages, store A sells a six pack for $5.28 store B sells a four pack for $3.40, which store offers the better per-roll price
Store B offers better $0.85 per-roll price than store A.
What is division?One type of operation is division in mathematics. The phrases or numbers are divided into the same number of components during this operation.
Given, two stores sell identical sandwich rolls in different size packages.
Store A sells a six-pack for $5.28.
To find the unit price,
we take division of 5.28 with number 6.
The unit price of sandwich roll for store A,
= 5.28 / 6
= $0.88
To find the unit price of sandwich roll for store B,
we take division of 3.40 with number 4.
= 3.40 / 4
= $0.85
And $0.85 < $0.88.
Therefore, Store B offers better per-roll price.
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