Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items.

Answer:

the average amount Mrs. Gordon pays in interest each month, we need to determine the total interest paid over the six-month period and divide it by the number of months.

The total interest paid can be found by subtracting the cost of the stove from the total amount paid over six months:

Total interest paid = Total amount paid - Cost of the stove

The total amount paid over six months is calculated by adding the monthly payments:

Total amount paid = $160/month * 6 months

Let's perform the calculations:

Total amount paid = $160/month * 6 months = $960

Total interest paid = Total amount paid - Cost of the stove

= $960 - $850

= $110

Now, to find the average amount Mrs. Gordon pays in interest each month, we divide the total interest paid by the number of months:

The average amount paid in interest each month = Total interest paid / Number of months

= $110 / 6 months

≈ $18.33

Therefore, Mrs. Gordon pays an average of approximately $18.33 in interest each month.

Answer:

B

Step-by-step explanation:

take square on both sides

7x-4 = 4x

x = 4/3

The Volume of the resulting rectangular box is calculated as: 72 cubic units.

A rectangular box's volume can be calculated using the formula expressed below:

Volume = length * width * height.

Using the image of the net of the rectangular box, when folded, the dimensions of the box would be:

Length = 6 units

Width = 10 - 6 = 4 units

Height = 11 - 4 - 4 = 3 units

Plug in the values:

Volume of rectangular box = 6 * 4 * 3 = 72 cubic units.

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The probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm is 0.7486

First, we need to calculate the z-score for the sample mean:

z = (x - μ) / (σ / √n)

z = (168.58 - 169) / (2.2 / √10)

z = -0.67

Next, we need to find the probability that a randomly selected bundle of steel rods will have a mean length greater than 168.58 cm. This is equivalent to finding the area under the standard normal distribution curve to the right of z = -0.67.

Using a standard normal distribution table or calculator, we find that the probability is 0.7486.

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Answer:

D

Step-by-step explanation:

gimme the points

cuz

scientific

for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65  for KW 3 calculation are   16,23,30,37,114,121,128,  just by substituting to equation we can get answer

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.

In the given question,

for table 1 calculation is as below

output x=0 is  15+2x=15+2*0=15

output x=1 is  15+2x=15+2*1=17

output x=2 is  15+2x=15+2*2=19

output x=3 is  15+2x=15+2*3=21

output x=4 is  15+2x=15+2*4=23

for table 2 calculation is as below

output x=1 is  60+2x=60+2*1=61

output x=2 is   60+2x=60+2*2=63

output x=3 is   60+2x=60+2*3=65

for table 3 calculation is as below

output x=0 is 16+7x=16+7*0=16

output x=1 is  16+7x=16+7*1=23

output x=2 is 16+7x=16+7*2=30

output x=3 is  16+7x=16+7*3=37

output x=14 is 16+7x=16+7*14=114

output x=15 is 16+7x=16+7*15=121

output x=16 is 16+7x=16+7*0=128

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for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65  for KW 3 calculation are   16,23,30,37,114,121,128,  just by substituting to equation we can get answer

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.

In the given question,

for table 1 calculation is as below

output x=0 is  15+2x=15+2*0=15

output x=1 is  15+2x=15+2*1=17

output x=2 is  15+2x=15+2*2=19

output x=3 is  15+2x=15+2*3=21

output x=4 is  15+2x=15+2*4=23

for table 2 calculation is as below

output x=1 is  60+2x=60+2*1=61

output x=2 is   60+2x=60+2*2=63

output x=3 is   60+2x=60+2*3=65

for table 3 calculation is as below

output x=0 is 16+7x=16+7*0=16

output x=1 is  16+7x=16+7*1=23

output x=2 is 16+7x=16+7*2=30

output x=3 is  16+7x=16+7*3=37

output x=14 is 16+7x=16+7*14=114

output x=15 is 16+7x=16+7*15=121

output x=16 is 16+7x=16+7*0=128

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It will take Lisa and Felipe approximately 4.95 hours to fill the order by working together.

To solve this problem, we can use the formula:

1/T = 1/T₁ + 1/T₂

where T is the time taken to complete the job when both Lisa and Felipe work together, T₁ is the time taken by Lisa to complete the job, and T₂ is the time taken by Felipe to complete the job.

Substituting the given values into the formula, we get:

1/T = 1/9 + 1/11

Simplifying the right-hand side of the equation, we get:

1/T = (11 + 9)/(9 x 11)

1/T = 20/99

Multiplying both sides by 99, we get:

T = 99/20

Therefore, working together, Lisa and Felipe can complete the job in 4.95 hours, or approximately 4 hours and 57 minutes.

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Answer:

Based on the residual plot, we can check for the following conditions:

I. The true relationship between x and y is linear:

We can check this condition by looking at the pattern of the residuals in the plot. If the residuals are randomly scattered around zero, without any discernible pattern, then it suggests that the true relationship between x and y is linear. If there is a pattern in the residuals, then it suggests that the true relationship is not linear. Since we are not given a residual plot to examine, we cannot determine whether this condition is met.

II. The standard deviation of y is constant for different levels of x:

We can check this condition by looking at the spread of the residuals in the plot. If the spread of the residuals is roughly the same for all values of x, then it suggests that the standard deviation of y is constant for different levels of x. If the spread of the residuals increases or decreases as x increases, then it suggests that the standard deviation of y is not constant for different levels of x. From the residual plot, we cannot determine whether this condition is met.

III. The value of 0 is contained in the confidence interval:

This condition refers to the confidence interval for the slope of the regression line. If the confidence interval includes 0, then it suggests that the slope is not significantly different from 0 and there is no significant linear relationship between x and y. From the residual plot, we cannot determine whether this condition is met.

Therefore, based on the given information, we cannot determine which conditions appear to be met based on the residual plot.

15,653 much will I have at the end of the year in linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                     Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.

Earning $300 a week equals $15,587 a year. This result is obtained by multiplying the base salary by the number of hours, weeks, and months worked in a year, assuming a 40-hour work week. 

15,653 much will I have at the end of the year in.

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A. The distance she must walk to return to the starting point is approximately 1912.325 ft, or 1912 ft 3 in.

B. She is walking towards the north, the heading is N 1° 20' W.

C. Acreage = 7.55 acres (rounded to 3 decimal places).

A. Convert the angles to decimal degrees:

N. 27° 40′ E. = 27.667°

N. 56° 31′ E. = 56.517°

S. 4° 26′ W. = -4.433°

Now, calculate the distances between the points:

AB = √(696.2917² + 3.5² - 2*696.2917*3.5*cos(27.667°)) = 696.2227 ft

BC = √(487.9792² + 11.75² - 2*487.9792*11.75*cos(56.517°)) = 487.9385 ft

CD = √(1691.125² + 1.5² - 2*1691.125*1.5*cos(-4.433°)) = 1691.1415 ft

B. Finding the distance from D back to A, calculate the distance and angle between AD:

AD = √(AB² + BD² - 2*AB*BD*cos(θ)) where θ = 180° - 4°26' - 27°40' = 147.9°

Substituting AB and BD:

AD = √(696.2227² + 1691.1415² - 2*696.2227*1691.1415*cos(147.9°)) = 1912.3246 ft

Therefore, the distance she must walk to return to the starting point is approximately 1912.325 ft, or 1912 ft 3 in.

C. Finding the heading she walks from D back to A, calculate the angle between AD and the north-south axis:

θ' = atan((AB*sin(27.667°) - BD*sin(θ))/AD) = atan((696.2227*sin(27.667°) - 1691.1415*sin(147.9°))/1912.3246)

θ' = -1.344°

Since she is walking towards the north, the heading is N 1° 20' W.

Lastly, to calculate the acreage of this plot of land, we use Heron's formula to determine the area of triangle ABC:

s = (AB + BC + AC)/2 = (696.2227 + 487.9385 + 1392.625)/2 = 788.8931 ft

A = √(s(s-AB)(s-BC)(s-AC)) = 328756.0207 ft²

Convert to acres:

Acreage = 328756.0207/43560 = 7.55 acres (rounded to 3 decimal places).

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Answer:

2(1/2)(11)(7) + 11(14) + 14(8) + 14(9) = 469 in.^2

The correct answer is A.

The equation in slope-intercept form for the line that has slope of -2/5 and y-intercept of -4 is written as: y = -2/5x - 4.

The slope-intercept form for any given straight line or linear relationship can be expressed as y = mx + b, where:

m = slope of the line

b = the y-intercept

Given the following:

slope (m) = -2/5.

y-intercept (b) = -4

To write the equation, substitute m = -2/5 and b = -4 into y = mx + b:

y = -2/5x - 4

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Answer:

90% of 300 = .90 × 300 = 270 high- definition televisions on order.

Step-by-step explanation:

Look at the table for z = 1.67  

You have the wrong table.......the table you posted is for negative z-scores

for z -score = + 1.67 , the value is .9535    = 95.35 %

Answer:

81

Step-by-step explanation:

The difference between the maximum and minimum values in a collection of data is known as the range. We must first determine the lowest and maximum values before we can determine the age range of the clients.

the minimum age is 8, and the maximum age is 89.

Therefore, the range of the clients' ages is:

Max age - Min age = 89 - 8 = 81

So the range of the clients' ages is 81.

Answer:

a) f(g(1)) = f(0) = 5

b) f(g(2)) = f(-3) = 8

c) g(f(2)) = g(3) = -8

d) g(f(3)) = g(2) = -3

e) g(g(1)) = g(0) = 2

f) f(f(3)) = f(2) = 3

A graph of the functions with the asymptotes is shown in the image below.

The pre-image of the function y = log₂(x + 1) was horizontally shifted to the left by 1 unit.

The pre-image of the function y = log₂(x) + 4 was vertically shifted up by 4 units.

In Mathematics, the translation a geometric figure or graph to the left means subtracting a numerical value to the point on the x-coordinate of the pre-image;

g(x) = f(x + N)

In Mathematics and Geometry, the translation a geometric figure upward means adding a numerical value to the point on the positive y-coordinate (y-axis) of the pre-image;

g(x) = f(x) + N

Since the parent function f(x) was horizontally translated 1 unit left, we have the following transformed function;

y = log₂(x + 1)

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b. The range is 32 - 16 = 16. and IQR  4

c. 32

a. Here is a box and whisker plot to represent the given data:

The horizontal axis shows the range of the data, and the vertical axis represents the frequency. The box represents the middle 50% of the data, with the bottom of the box being the 25th percentile and the top of the box being the 75th percentile. The whiskers represent the lowest and highest values within 1.5 times the interquartile range (IQR) of the box, and any points outside the whiskers are considered outliers.

b. The range is the difference between the highest and lowest values in the data set. In this case, the range is 32 - 16 = 16.

c. There is one outlier in the data set, which is the value of 32. It is outside the whiskers of the box and is considered to be an outlier.

The interquartile range (IQR) is the difference between the 75th and 25th percentiles of the data set. In this case, the IQR is:

IQR = Q3 - Q1

   = 22 - 18

   = 4

where Q1 is the first quartile (the value below which 25% of the data falls), and Q3 is the third quartile (the value below which 75% of the data falls).

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Answer:

1. True

2.True

3.True

4.False

5.False

6.True

7.True

8.True

Step-by-step explanation:

1. The area of a rectangle is found by the formula A=bh.

2. There are 4 rectangles making up the lateral area of the prism. 2+3=5. 5*6=30, and multiply by 2 since there are two of the 2x6 and two of the 3x6 rectangles to get 60. The bases of the prism have an area of 6 square inches each.

60+12+12=84

3. 3*5=15

4. The base is not a square, so you cannot multiply by 4 to get the area of all the triangles. You can multiply by two, and also multiply 1/2(3)(4) by 2 to get the area of the other two triangles.

5. The base is a triangle. 1/2(3)(4)=6.

6. 2[1/2(3)(4)]=12. 2(8*5)=80. 3*8=24. 80+24+12=116

7. A cube has 6 identical sides, so you can find the area of one side and multiply by 6 to get the surface area of the cube.

8. 9^2=81. 81*6=486.

The whisker plot with the data provided should includes a range that goes from 7 to 49, and a median of 23.

A whisker plot, also known as a box plot, is a graphical representation of a data set that shows the distribution of the data along with some important statistical information, such as the median, quartiles, and outliers. It is particularly useful for comparing the distribution of different data sets or for identifying potential outliers in a data set.

To create a whisker plot, follow these steps:

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The function f(x) = (1/2)x^2 + 3x - 5 has a minimum value

To determine whether the function f(x) = (1/2)x^2 + 3x - 5 has a minimum or maximum value, we can use the fact that the vertex of a quadratic function represents the minimum or maximum point of the function.

To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively.

In this case, a = 1/2 and b = 3, so we have:

x = -b/2a = -(3)/(2(1/2)) = -3

To find the corresponding y-coordinate, we can substitute x = -3 into the function:

f(-3) = (1/2)(-3)^2 + 3(-3) - 5 = -9.5

Since the coefficient of the quadratic term is positive, we know that the parabola opens upward and the vertex represents a minimum value.

Therefore, the minimum value of the function is -9.5, which occurs at x = -3.

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The matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]

Row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.

performing the row operation 4R₁ + R₂ — R₂ on M, we have;

4(1) + (-5) = -1 {row 2 column 1}

4(0) + 2 = 2 {row 2 column 2}

4(3) + (-2) = 10 {row 2 column 3}

Therefore, the matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]

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The value c = 3 is not a solution to the inequality

From the question, we have the following parameters that can be used in our computation:

122 c

Express properly

So, we have

1 ≥ c

When this inequality is rewriiten. we have

c ≤ 1

This means that the values of c do not exceed 1

The number 3 exceeds 1

So, it means that c = 3 is not a solution to the inequality

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Where is the given proof

The proportion is solved and ratio of minutes spent talking to teachers to minutes spent talking to students is given by 2 : 1

Given data ,

The principal spends 96 minutes talking to the teachers

And , the principal spends 48 minutes talking to students

Now , the basic ratio of minutes spent talking to teachers to minutes spent talking to students, we need to simplify the ratio by dividing both values by their greatest common factor

So , A : B = 96 : 48

On simplifying the proportion , we get

A : B = 2 : 1

Hence , the proportion is 2 : 1

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The cost of one T-shirt and one jacket is $12 and $13 respectively.

Let

cost of one t-shirt = x

cost of one jacket = y

8x + 3y = 135

7x + 5y = 149

Multiply (1) by 5 and (2) by 3

40x + 15y = 675

21x + 15y = 447

Subtract the equations to eliminate y

40x - 21x = 675 - 447

19x = 228

divide both sides by 19

x = 228/19

x = 12

Substitute x = 12 into (1)

8x + 3y = 135

8(12) + 3y = 135

96 + 3y = 135

3y = 135 - 96

3y = 39

y = 39/3

y = 13

Hence, a T-shirt and a Jacket cost $12 and $13 respectively.

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Answer:

247

Step-by-step explanation:

The solution to the equation is x = 33/5.

We can start by simplifying both sides of the equation using the distributive property and combining like terms:

4/3 (x + 6) = 2x - 3 + x

4/3 x + 8 = 3x - 3

Next, we can isolate the variable x on one side of the equation by subtracting 4/3 x and adding 3 to both sides:

4/3 x - 3x = -8 - 3

-5/3 x = -11

Finally, we can solve for x by dividing both sides by -5/3:

x = -11 / (-5/3)

x = 33/5

Therefore, the solution to the equation is x = 33/5.

Therefore, 70% of state capitals do not have interstate highways serving them.

Percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred". Percentages are usually denoted by the symbol %, which is placed after the numerical value. Percentages are used in many fields, including finance, science, and everyday life, to represent proportions, rates, and changes in quantities.

Here,

If all but 36 of the 120 state capitals have an interstate highway serving them, then the number of capitals that do not have interstates is 120 - 36 = 84.

To find the percentage of capitals that do not have interstates, we need to divide the number of capitals without interstates by the total number of capitals and then multiply by 100:

84 / 120 x 100% = 70%

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