The points (-7,4) and (r,19) lie on a line with slope 3. Find the missing coordinate r.
Answer:
r = -2
Step-by-step explanation:
We can use the slope formula to find r.
m = ( y2-y1)/(x2-x1)
3 = ( 19-4)/(r- -7)
3 = 15/(r+7)
Multiply each side by (r+7).
3 ( r+7) = 15
Divide each side by 3.
r+7 = 15/3
r+7 = 5
Subtract 7 from each side.
r+7-7 = 5-7
r = -2
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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In Problems 1 through 6 you are given a homogeneous system of first- order linear differential equations and two vector-valued functions, X(1) and x(2) a. Show that the given functions are solutions of the given system of differential equations. b: Show that X = Cx(T) + C2x(2) is also a solution of the given system for any values of C1 and C2. C. Show that the given functions form a fundamental set of solutions of the given system.
The given functions form a fundamental set of solutions of the given system.
The solution of the given system of differential equations is shown below.a) To prove that the given functions X(1) and x(2) are the solutions of the given system of differential equations, we must substitute these functions into the given system to show that they satisfy the equations.In the given system, we have the following equations:
X_1' (t) = 2X_1 (t) - X_2 (t)
X_2' (t) = 4X_1 (t) - 2X_2 (t)
Now, let's substitute the given vector-valued functions X(1) and x(2) into the above equations and check if they satisfy these equations.
a. For X(1) = [1, 2]e^2t
Substituting X(1) into the given system, we get:
X_1' (t) = [1, 2] * 2e^2t = 2X_1 (t) - X_2 (t)
X_2' (t) = [1, 2] * 4e^2t = 4X_1 (t) - 2X_2 (t)
Therefore, the given function X(1) is a solution to the given system of differential equations.
b. To prove that X = C1x(1) + C2x(2) is also a solution of the given system for any values of C1 and C2, we need to X into the given system of equations and check if it satisfies the equations.
So, we have:
X = C_1[1, 2]e^2t + C_2[1, -1]e^-t
X_1 = C_1e^2t + C_2e^-t
X_2 = 2C_1e^2t - C_2e^-t
Differentiating X_1 and X_2 with respect to t, we get:
X_1' = 2C_1e^2t - C_2e^-t
X_2' = 4C_1e^2t + C_2e^-t
Substituting X_1 and X_2 into the given system, we get:
X_1' (t) = 2(C_1e^2t - C_2e^-t) = 2X_1 (t) - X_2 (t)
X_2' (t) = 4(C_1e^2t + C_2e^-t) = 4X_1 (t) - 2X_2 (t)
Therefore, the given function X = C1x(1) + C2x(2) is also a solution of the given system for any values of C1 and C2.
c. To show that the given functions form a fundamental set of solutions of the given system, we need to prove that they are linearly independent and that their Wronskian is non-zero.
We know that the vectors [1, 2] and [1, -1] are linearly independent, therefore the functions x(1) and x(2) are also linearly independent.
Also, the Wronskian of x(1) and x(2) is given by:
W(x1, x2) = | x1 x2 |
| x1' x2' |
Substituting x(1) and x(2) into the above equation, we get:
W(x1, x2) = | e^2t e^-t |
| 2e^2t -e^-t |
Simplifying the above equation, we get:
W(x1, x2) = 3e^(3t) ≠ 0
Therefore, the given functions form a fundamental set of solutions of the given system.
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2. The point (3,w) is on the graph of the line y = 2x + 7. What is the
value of w?
Answer:
We are given that the point (3,w) lies on the line y = 2x + 7. This means that if we substitute x = 3 into the equation y = 2x + 7, we will get the value of y at x = 3, which is equal to w.
Substituting x = 3 into the equation y = 2x + 7, we have:
y = 2(3) + 7
y = 6 + 7
y = 13
Therefore, the value of w is 13.
Step-by-step explanation:
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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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.
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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Which equation is equivalent to pq=r?
Responses
A) p=logR q
B) p=logQ r
C) q=logR p
D) q=logP r
The equation is equivalent to pq=r is option (C) q=logR p
To determine which equation is equivalent to pq=r, we can use logarithmic properties. Taking the logarithm of both sides of the equation, we get
log(pq) = log(r)
Using the property that log(a×b) = log(a) + log(b), we can simplify the left side of the equation
log(p) + log(q) = log(r)
Now, we can compare this expression to each of the answer choices
A) p = logR q
Substituting this into the equation, we get
log(p) + logR(q) = log(r)
This is not equivalent to our expression, so A is not the correct answer.
B) p = logQ r
Substituting this into the equation, we get
log(logQ r) + log(q) = log(r)
This is also not equivalent to our expression, so B is not the correct answer.
C) q = logR p
Substituting this into the equation, we get
log(p) + logR(q) = log(r)
This matches our expression, so C is the correct answer.
D) q = logP r
Substituting this into the equation, we get
log(p) + log(q) = log(logP r)
This is not equivalent to our expression, so D is not the correct answer.
Therefore, the correct option is (C) q=logR p
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Find the area of the shaded region.
80°
5 cm
A=[?] cm2
Enter a decimal rounded to the nearest tenth.
From the given information provided, the area of the shaded region inside the circle is 22.58
The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane.
The space enclosed by the sector of a circle is called the area of the sector.
the radius of the circle is 5cm.
area of arc = radius² × θ/2
area of the arc is = 5² × 4π/9 = 25 × 4/9 = 34.88
area of the triangle inside circle = a×b × sin(y)/2
area of triangle = 5×5 × sin(80°)/2 = 25 × 0.492
area = 12.3
area of the shaded region is = 34.88 - 12.3 = 22.58
Hence, the area of the shaded region is 22.58
Question - Find the area of the shaded region in the circle if the angle of the arc is 80 degree radius is 5cm.
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If G is a group with subgroups A, B of orders m, n, respectively, where m and n are relatively prime, prove that the subset of G, AB = {abla E Ab E B}, has mn distinct elements.
The number of distinct elements of AB = m n.
Given that G is a group with subgroups A and B of orders m and n, respectively, where m and n are prime, we need to prove that the subset of G, AB = {abla E Ab E B}, has m n distinct elements. Step-by-step. Let, G is a group with subgroups A and B of orders m and n, respectively. Since, m and n are relatively prime, then we have gcd(m, n) = 1.By Lagrange's Theorem, the order of any subgroup of G divides the order of G.
Hence, the order of G is equal to the product of the orders of A and B, i.e. |G| = |A| * |B| = m * n Let, a and a' be two distinct elements of A and b and b' be two distinct elements of B. Thus, a and a' generate distinct subgroups of G, i.e. ≠ and b and b' generate distinct subgroups of G, i.e. ≠ .Now, the number of distinct elements of AB = {abla E Ab E B} is equal to |A||B| since any two elements ab and a'b' of AB will be distinct if either a and a' are distinct or b and b' are distinct or both are distinct. Hence, the number of distinct elements of AB = m n.
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a tank is being filled with water at the rate of 2 3 450t gallons per hour with t > 0 measured in hours. if the tank is originally empty, how many gallons of water are in the tank after 5 hours?
The rate of filling water in the tank is 23450t gallons per hour.
Let's assume that the time taken to fill the tank is t hours.
The volume of water filled into the tank at time t is given by the expression V(t) = 23450t.
The tank is originally empty, which means its volume = 0 gallons.
After 5 hours,
t= 5 hours
The volume of water filled in is given by [tex]V(5) = 23450 * 5= 1,17,250[/tex] gallons of water.
Therefore, 1,17,250 gallons of water are filled in the tank after 5 hours.
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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
Subtract the given equation
3x-(4x-11)
Answer:
3x - (4x - 11) = 3x - 4x + 11 = -x + 11
Step-by-step explanation:
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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For what values of c does the quadratic equatrion x^2-2x+c=0 have two roots of the same sign
The roots have positive or same signs when c>0.
Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.
[tex]b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2[/tex]
Roots of quadrant equation have Samsame sign if product of roots >0.
[tex]\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0[/tex]
Roots of quadratic equation have positive sign if product of roots<0.
c>0.
Combining results, we get:-
roots have positive signs when:-
c>0.
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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:
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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Question 9(Multiple Choice Worth 2 points)
(Irrational Numbers LC)
Describe in words where √63 would be plotted on a number line.
O Between 3 and 4, but closer to 3
O Between 3 and 4, but closer to 4
O Between 2 and 3, but closer to 2
O Between 2 and 3, but closer to 3
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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Which box plot represents data that contains an outlier?
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 3 to 8. A line divides the box at 7. 5.
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 10, and the box ranges from 6 to 8. 5. A line divides the box at 7. 5.
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 2 to 7. A line divides the box at 4.
A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 3 to 9, and the box ranges from 5 to 7. A line divides the box at 6,
The box plot represents the data set 2, 4, 6, 8, 10, 12 is option (a) A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 3 to 8. A line divides the box at 7. 5.
A box-and-whisker plot is a graphical representation of a data set that displays the distribution of the data, as well as its quartiles and any outliers. The plot is made up of a rectangular box, which represents the middle 50% of the data, with a line in the box representing the median. Two lines, called whiskers, extend from the box to represent the range of the data outside of the box, excluding any outliers. Outliers are any values that fall outside of the whiskers.
In the given options, the box-and-whisker plot that represents the data set 2, 4, 6, 8, 10, 12 is the one that has a box ranging from 4 to 10, with a median line dividing the box at 7. This means that 50% of the data falls between 4 and 10, with the median value being 7. The whiskers range from 2 to 12, indicating that the data set has a minimum value of 2 and a maximum value of 12.
Therefore, the correct option is (a) A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 10. A line divides the box at 7.
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The given question is incomplete, the complete question is:
Which box plot represents the data set 2, 4, 6, 8, 10, 12?
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 10. A line divides the box at 7.
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 8. A line divides the box at 6.
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 9. A line divides the box at 6.
A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 6 to 10. A line divides the box at 8.
Answer: (B)
Correct Answer 100%! Pls, give me brainliest. Thank You!
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.
A snow making machine priced at $1800 is on sale for 25% off. The sales tax rate is 6. 25%. What is the sale price including tax? If necessary, round your answer to the nearest cent
The sale price including tax is $ 2390.625.
Given that,
The price of the snow machine= $ 1800
Discount percentage= 25%
Sales tax rate = 6.25%
Hence, Sale price = Price + Discount percentage of price
= 1800 + 25/100 × 1800
= 1800 + 450
= 2250.
Sale price including tax = Sale price + Tax rate
= 2250 + 6.25/100
= 2250 + 140.625
= $ 2390.625.
Hence, the sale price including tax is $ 2390.625.
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Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks. If Terri does not make any calls, what would her bill be?
Answer:
$10
Step-by-step explanation:
We Know
Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks.
Let C be the total cost, and x be the number of minutes she talks; we have the equation.
C = 0.05x + 10
If Terri does not make any calls, what would her bill be?
C = 0.05(0) + 10
C = $10
So, her bill will be $10
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 percent of the discount: a $30 board game on sale for 21
well, we know the discount is just 30 - 21 = 9, so hmm if we take 30(origin amount) to be the 100%, what's 9 off of it in percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 30 & 100\\ 9& x \end{array} \implies \cfrac{30}{9}~~=~~\cfrac{100}{x} \\\\\\ 30x=900\implies x=\cfrac{900}{30}\implies x=30[/tex]
sebi rides his bike at a constant rate of 10 mph by a linear equation to represent how far he travels
The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.
what is linear equation ?The basic form of a linear equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. Many real-world situations, such as the connection between a product's price and the number of sales, or the relationship between a person's age and height, can be modelled using linear equations.
given
Let t be the number of hours and d be the number of miles that Sebi goes. Since Sebi consistently travels at 10 mph on his bicycle, we can apply the following equation:
Distance is determined by rate and duration.
When we change the numbers, we obtain:
d = 10t
The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.
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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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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.
The store sells a television for $1000. customers can choose to receive 10% discount and pay it off at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years with no interest. which option is better
Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Option 1 is the better choice as it has a lower total cost.
What is simple interest?Simple interest is a type of interest that is calculated on the original principal amount of a loan or investment. It is a fixed percentage of the principal amount that is paid by the borrower or earned by the lender over a specific period of time.
According to question:To compare the two options, we need to calculate the total cost of each option and compare them.
Option 1: 10% discount and pay off with 4% simple interest
The discount reduces the price of the television to $1000 x 0.9 = $900. If the customer chooses to pay it off at 4% simple interest, the total cost would be:
Total cost = $900 + ($900 x 0.04 x 3) = $972
Option 2: Full price and pay off in 3 years with no interest
The total cost of this option would be simply the full price of $1000 paid over 3 years, so:
Total cost = $1000 / 3 = $333.33 per year x 3 years = $1000
Comparing the two options, we see that Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Therefore, Option 1 is the better choice as it has a lower total cost.
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The complete question is: The store sells a television for $1000. customers can choose to receive 10% discount and pay it off at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years with no interest. which option is better?
Option 1 with the discount and 4% simple interest.
Option 2 with no discount and no interest.
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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