Students are painting the backdrop for the school play. the backdrop is 15 feet wide and 10 feet high. Every 16 inches on the scale drawing represents 5 feet on the backdrop. What is the area of the scale drawing?

15 points

I believe that the answer is $175

Answer:

$112

Step-by-step explanation:

140 divided by 5 is 28, which means 1/5 of 140 is 28. You take that 28 times 4 to get 4/5 of 140 which comes out to be 112. Brainliest please!

Answer:$271

Step-by-step explanation:

$125x12= 1500+250=1750

1750-1479=271

Answer:

200 miles

Step-by-step explanation:

8x25=200

The actual distance will be 200 miles

The question states that

The distance between two cities is 8 inches

Actual distance would be

8 * 25 = 200

So the actual distance would be 200 miles

I believe the estimate should be higher

Answer:

A. No, the estimate should be higher.

Step-by-step explanation:

Intersection of the first two lines:

[tex]\begin{cases}5x - 2y + 3 = 0\\4x - 3y + 1 = 0\end{cases}[/tex]

Multiply the first equation by 4 and the second by 5:

[tex]\begin{cases}20x - 8y + 12 = 0\\20x - 15y + 5 = 0\end{cases}[/tex]

Subtract the two equations:

[tex](20x - 8y + 12)-(20x - 15y + 5)=0 \iff 7y+7=0 \iff y=-1[/tex]

Plug this value for y in one of the equation, for example the first:

[tex]5x - 2\cdot (-1) + 3 = 0\iff 5x+5=0 \iff x=-1[/tex]

So, the first point of intersection is [tex](-1,-1)[/tex]

We can find the intersection of the other two lines in the same way: we start with

[tex]\begin{cases}x=y\\x=3y+4\end{cases}[/tex]

Use the fact that x and y are the same to rewrite the second equation as

[tex]x=3x+4 \iff 2x=-4 \iff x=-2[/tex]

And since x and y are the same, the second point is [tex](-2, -2)[/tex]

So, we're looking for a line passing through [tex](-1,-1)[/tex] and [tex](-2, -2)[/tex]. We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be [tex]y=x[/tex]

In the attached figure, line [tex]5x - 2y + 3 = 0[/tex] is light green, line [tex]4x - 3y + 1 = 0[/tex] is dark green, and their intersection is point A.

Simiarly, line [tex]x=y[/tex] is red, line [tex]x = 3y + 4[/tex] is orange, and their intersection is B.

As you can see, the line connecting A and B is the red line itself.

To answer the student’s question, solve for points of intersection of given pairs of equations, use these points to calculate the slope, and then apply the point-slope or two-point form to determine the equation of the line.

To find the equation of a line that passes through the points of intersection of two sets of equations, we first need to determine the coordinates of these intersection points. We have two given sets of equations: 5x - 2y + 3 = 0 and 4x - 3y + 1 = 0, as well as x = y and x = 3y + 4. To solve for the intersection points, we can use substitution or elimination method for the pairs of equations separately.

Once we have found the two points of intersection, we use these points to determine the slope of the line (using the slope formula ∆y /∆x). After that, we apply the point-slope form or the two-point form of the equation of a line to find the equation that contains both points. The final step would be to simplify the equation to its standard form.

However, the question seems to include extraneous information, as the equation provided for a specific line, y = 9 + 3x, does not directly pertain to the given task of determining the equation of the line through the points of intersection. It does illustrate that a line's equation can be represented in the form y = mx + b, where m represents the slope, and b represents the y-intercept.

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Answer:

[tex]\large\boxed{0.000008=8\cdot10^{-6}}[/tex]

Step-by-step explanation:

The scientific notation:

[tex]a\cdot10^k[/tex]

where 1 ≤ a < 10 and k ∈ Z.

0.000008

You must move the comma 6 places to the right.

[tex]0\underbrace{.000008}_{6\rightarrow}=8\cdot10^{-6}[/tex]

[tex]0.000008=\dfrac{8}{1,000,000}=8\cdot10^{-6}[/tex]

To express the diameter of a human red blood cell in scientific notation, we can write it as 8.0 × 10^-6 meters.

The diameter of a human red blood cell is approximately 0.000008 meters. To express this number in scientific notation, we can use the concept of significant figures. In this case, the leading zeros are not significant, so we can write the number as 8.0 × 10-6 meters. This scientific notation represents the size of a human red blood cell.

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The correct equation is . n + 45.60 - 15.75. Option C is correct.

Let n represent William's balance before writing the check (unknown).

He wrote a check for $45.60, so this amount needs to be subtracted from his original balance.

After writing the check, his balance became -$15.75. Since a negative balance indicates he owes money, we can represent this with -15.75.

To find his original balance (n), we need to add the amount he subtracted (check amount) and then consider the ending balance.

Therefore, the equation that accurately represents the situation is:

n (original balance) + $45.60 (check amount) - $15.75 (ending balance) = n + 45.60 - 15.75

complete question:

On Wednesday, William wrote a check in the amount of $45.60. This brought his balance down to -$15.75. Suppose n represents William's balance before he wrote the check.

Which equation can be used to represent this situation?

A. n-15.75-45.60

B. п-15.7545.60

C. n+45.60 -15.75

D. n-45.60-15.75

Answer:

[tex]\boxed{\bold{-5cd}}[/tex]

Step By Step Explanation:

[ Step One ] Expand [tex]\bold{-d\left(2c-4\right)}[/tex]

[tex]\bold{-2cd+4d}[/tex]

[ Step Two ] Rewrite Equation

[tex]\bold{-3cd-2cd+4d-4d}[/tex]

[ Step Three ] Simplify [tex]\bold{-3cd-2cd+4d-4d}[/tex]

[tex]\bold{-5cd}[/tex]

Answer:

The Answer is -5CD when simplified

Step-by-step explanation:

1) Distributive property

-3cd - d ( 2c - 4 ) - 4d

Turns to:  3cd -2cd + 4d - 4d  Multiplying to negative give you a positive.

2) combine like terms

-3cd - 2cd = -5cd

4d - 4d = 0

3) Answer

-5cd is your answer

Hopes this helps!

All angles are the same and all side lengths are equal/congruent

Congruent triangles are triangles that have the same size and shape, with corresponding sides and angles that are equal. They can be proven congruent using criteria such as SSS, SAS, and ASA.

**Congruent triangles** are triangles that have the same size and shape. In other words, all corresponding sides and angles of congruent triangles are equal. There are several ways to prove that triangles are congruent, such as the Side-Side-Side (SSS) Criteria, Side-Angle-Side (SAS) Criteria, Angle-Side-Angle (ASA) Criteria, and more. For example, if two triangles have the same length for each corresponding side, they are congruent.

Answer:

15. 31.42 cm^2

16. 25.73 m^2

17. Fly A

Step-by-step explanation:

15.

The blue shaded region is a sector of a circle. The formula for area of sector = [tex]\frac{\theta}{360}*\pi r^2[/tex]

Where  [tex]\theta[/tex] is the central angle and r is the radius

For the diagram, we have 80° arc and 180° arc as the "white" area. Since the whole circle is 360°, the shaded region arc is 360 - (80+180) = 100°. this is  [tex]\theta[/tex] and the radius is 6.

Plugging in it in the formula we get:

Area of shaded region = [tex]\frac{\theta}{360}*\pi r^2\\=\frac{100}{360}*\pi(6)^2\\=31.42[/tex] cm^2

16.

We can say that area of shaded region = area of parallelogram - area of circle

Now,

Area of Parallelogram = b * h

where

b is the base (it is 6+3=9) and h is the height (diameter of the circle is the height = 6)

Area of Parallelogram = 9 * 6 = 54

Area of Circle = πr^2   where r is the radius, which is 6/2=3

Area of Circle = π(3)^2 = 9π

Now,

Area of Shaded Region = 54 - 9π = 25.73 m^2

17.

For the first figure (rectangle) we could let the height be h (since not given). So area of yellow region would be 4h (area of rectangle is base * height)

And area of whole ruler would be 8*h = 8h

So probability of landing in yellow region would be  [tex]\frac{4h}{8h}=\frac{1}{2}=0.5[/tex]

For 2nd figure, the yellow region has area of π(2)^2 = 4π ( radius of yellow circle is 2 and area of circle is πr^2)

Area of whole circle is  π(4)^2 = 16π

So probability of landing in yellow region would be  [tex]\frac{4\pi}{16\pi}=\frac{1}{4}=0.25[/tex]

Hence, Fly A is more likely to land in a yellow region.

Answer:

Answer: part a is 4.8 and part b is 3.125

Step-by-step explanation:

PART A.  60/25 = 2.4 (inches)

PART B.  25/4 = 6.26 (miles)

Hope this helps! Please mark me as brainliest if it did.

Answer: D.

Step-by-step explanation: it’s D because when you do the volume of mode A, you get 48 units. When you do the volume of model B you get 40 units. Use the formula V=length x width x height!

To find the diameter of a cone with a given volume and height, use the volume formula, substitute the given values, and solve for the radius. The calculated diameter of this cone is approximately 4.90 meters.

To find the diameter of a cone given its volume and height, we can use the formula for the volume of a cone: V = (1/3)πr²h, where V is the volume, r is the radius of the base, and h is the height of the cone. Given that the volume (V) is 20π cubic meters and the height (h) is 10 meters, we can substitute these values into the formula and solve for r.

First, rearrange the formula to solve for r: r = √((3V)/(π×h)). Substitute V = 20π and h = 10 into the equation to get r = √((3×20π)/(π×10)) = √(6) meters. Therefore, the diameter of the cone, which is twice the radius, is 2×√(6) meters, or approximately 4.90 meters.

The diameter of the cone is  [tex]\[ d = 4\sqrt{3} \][/tex]

To find the diameter of the cone, we first need to determine the radius of the cone's base. The volume V of a cone can be calculated using the formula:

[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]

where r is the radius of the base and h is the height of the cone. Given that the volume V is [tex]\(20\pi\)[/tex] cubic meters and the height  [tex]\(h\) is \(10\)[/tex] meters, we can set up the equation:

[tex]\[ 20\pi = \frac{1}{3} \pi r^2 \cdot 10 \][/tex]

[tex]\[ 60 = r^2 \cdot 10 \] \[ \frac{60}{10} = r^2 \] \[ r^2 = 6 \][/tex]

Taking the square root of both sides gives us the radius r:

[tex]\[ r = \sqrt{6} \][/tex]

Since the radius is half the diameter, we can find the diameter d by multiplying the radius by 2:

[tex]\[ d = 2r \] \[ d = 2\sqrt{6} \] \[ \sqrt{6} = \sqrt{2 \cdot 3} \] \[ \sqrt{6} = \sqrt{2} \cdot \sqrt{3} \] \[ \sqrt{6} = \sqrt{2} \cdot \sqrt{3} = 2\sqrt{3} \][/tex]

Thus, the diameter d of the cone is:

[tex]\[ d = 2 \cdot 2\sqrt{3} \][/tex]

[tex]\[ d = 4\sqrt{3} \][/tex]

Answer:

16

Step-by-step explanation:

Answer:

[tex](g\circ f)(0)=16[/tex]

Step-by-step explanation:

The given functions are

[tex]f(x)=-3x+4[/tex] and [tex]g(x)=x^2[/tex]

We first find the composition; [tex](g\circ f)(x)[/tex]

[tex](g\circ f)(x)=g(f(x))[/tex]

[tex](g\circ f)(x)=g(-3x+4)[/tex]

[tex](g\circ f)(x)=(-3x+4)^2[/tex]

We now plug in x=0, to obtain;

[tex](g\circ f)(0)=(-3(0)+4)^2[/tex]

[tex](g\circ f)(0)=(4)^2[/tex]

[tex](g\circ f)(0)=16[/tex]

1.MAD Calculation: A possible set of data values that yield a mean of 20 and a MAD of 10 is: 10, 20, 20, 20, 30, 40.

2. Five Students' Test Scores: Mean = 85, Median = 85, Range = 10, MAD ≈ 3.33.

3. Survey Data: Students' mean sleep = 7.7 hours; Teachers' mean sleep = 6.7 hours.

let's go through each question step by step:

1. MAD Calculation:

The Mean Absolute Deviation (MAD) is the average of the absolute deviations from the mean of a dataset. Given that the MAD of the set of six data values is 10 and the mean is 20, we need to find the data values that satisfy these conditions.

Let's denote the data values as (x_1, x_2, x_3, x_4, x_5, x_6).

The mean is given as:

[tex]\[ \text{Mean} = \frac{x_1 + x_2 + x_3 + x_4 + x_5 + x_6}{6} = 20 \][/tex]

Multiplying both sides by 6 gives us:

[tex]\[ x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 120 \][/tex]

Now, we need to find a set of values that satisfy this equation and also have a Mean Absolute Deviation of 10.

The Mean Absolute Deviation (MAD) formula is:

[tex]\[ \text{MAD} = \frac{|x_1 - \text{Mean}| + |x_2 - \text{Mean}| + |x_3 - \text{Mean}| + |x_4 - \text{Mean}| + |x_5 - \text{Mean}| + |x_6 - \text{Mean}|}{6} \][/tex]

Given MAD = 10, and Mean = 20, we have:

[tex]\[ 10 = \frac{|x_1 - 20| + |x_2 - 20| + |x_3 - 20| + |x_4 - 20| + |x_5 - 20| + |x_6 - 20|}{6} \][/tex]

Multiplying both sides by 6, we get:

[tex]\[ 60 = |x_1 - 20| + |x_2 - 20| + |x_3 - 20| + |x_4 - 20| + |x_5 - 20| + |x_6 - 20| \][/tex]

Now, we need to find a set of six values that satisfy both equations.

There are multiple possible sets of values that satisfy these equations. One such set could be:

[tex]\[ x_1 = 10, \ x_2 = 20, \ x_3 = 20, \ x_4 = 20, \ x_5 = 30, \ x_6 = 40 \][/tex]

You can verify that these values satisfy both the mean and the MAD conditions.

2. Five Students' Test Scores:

Given:

- Five students scored 80 on a test,

- Five students scored 85, and

- Five students scored 90.

A. The mean:

[tex]\[ \text{Mean} = \frac{(5 \times 80) + (5 \times 85) + (5 \times 90)}{15} = \frac{400 + 425 + 450}{15} = \frac{1275}{15} = 85 \][/tex]

B. The Median:

Since there are an odd number of data points (15), the median will be the 8th value when the data is arranged in ascending order. Since each score (80, 85, 90) appears 5 times, the median is 85.

C. The Range:

The range is the difference between the highest and lowest values:

[tex]\[ \text{Range} = 90 - 80 = 10 \][/tex]

D. The MAD:

To find the MAD, we first calculate the deviations from the mean for each data point, take their absolute values, and then find their mean.

[tex]\[ \text{MAD} = \frac{|80 - 85| + |80 - 85| + \ldots + |90 - 85|}{15} \][/tex]

[tex]\[ = \frac{5|80 - 85| + 5|85 - 85| + 5|90 - 85|}{15} \][/tex]

[tex]\[ = \frac{5(5) + 5(0) + 5(5)}{15} = \frac{50}{15} \approx 3.33 \][/tex]

3. Survey Data:

Given:

Students: 7, 6, 8, 9, 8, 9, 10, 10, 10

Teachers: 6, 6, 4, 5, 7, 8, 7, 8, 8, 8

A. Mean of students' data set:

[tex]\[ \text{Mean} = \frac{7 + 6 + 8 + 9 + 8 + 9 + 10 + 10 + 10}{10} = \frac{77}{10} = 7.7 \][/tex]

B. Mean of teachers' data set:

[tex]\[ \text{Mean} = \frac{6 + 6 + 4 + 5 + 7 + 8 + 7 + 8 + 8 + 8}{10} = \frac{67}{10} = 6.7 \][/tex]

The means tell us that, on average, students get slightly more sleep per night compared to teachers.

Answer:

Step-by-step explanation:

add a picture of the question please

Solution:- A shopkeeper with a basket of eggs finds that if he sells 3 eggs at a time there is only one egg left if he sells four eggs at a time there is again 1 egg left however if the trader sells 7 is at a time there is no egg left is the capacity of the basket is 108

LCM of 3 and 4 = 3×4 = 12

The capacity of the basket is 100.

So, there may be:-

= 12 × 8 +1

= 96 + 1

= 97 eggs.

But, 97 is not divisible by 7.

Again, there may be:

12 × 7 +1 = 85 eggs.

12 × 6 +1 = 73 eggs.

12 × 5 +1 = 61 eggs.

12 × 4 +1 = 49 eggs.

Among these numbers 85 , 73 and 61 are not divisible by 7. But 49 is divisible by 7.

So, the number of eggs in the basket is 49.

[Answer = 49]

Answer:

1/2

Step-by-step explanation:

3 * 1/6 = 3/6

Which can simplify to 1/2 if you divide the top and bottom by 2.

The product 3x1/6 simplifies to 1/2.

To simplify the product 3x1/6, we need to perform the multiplication and express the result in its simplest form.

First, let's calculate the product:

3 x 1/6 = 3/1 x 1/6 = 3/6

Now, we can simplify the fraction 3/6 by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3 in this case:

3/6 ÷ 3/3

The divided by six by three by three

= (3 ÷ 3) / (6 ÷ 3)

=3/3×3/6

= 1/2

Therefore, the product 3x1/6 simplifies to 1/2.

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Answer:

Step-by-step explanation:

sistemul digestiv

Answer x^-5

Step-by-step explanation: since (- 5/6)*6=-5

The answer is x^-5

795

first u multiple the 15 with 8 & 45 then u add

Center (0,0)

radius - 5

Hope this help

The correct choice is A(-1,3)

See the attached figure

Answer:

9.) A. integers

Step-by-step explanation:

rational numbers can't have negatives

whole numbers can't have fractions

negative numbers can't have positives

---hope this helps!!

Answer:

Last option

y ≤ 1/2 x - 1

Step-by-step explanation:

The graph is linear inequality. Since the graph is a solid line so the inequality symbol is either ≥ or ≤.

The colored grey is shaded below the line, so the symbol is ≤.

So either  y≤1/2x-1 or  y≤2x-1

Now we have to find the slope to see which equation is the right one.

(2,0) and (0,-1)

Slope = (0 + 1) /(2-0) = 1/2 and b = y intercept = -1

So equation:

y ≤ 1/2 x - 1

The correct inequality that represents the graph is y≤2x-1.

In this question, we are asked to determine which inequality best represents the graph. From the given options, the correct choice is b. y≤2x-1. This choice represents a graph where y is less than or equal to 2x minus 1. To verify this, we can examine some points on the graph.

For example, let's test the point (0,0). Substituting these values into the inequality, we get 0 ≤ 2(0) - 1, which simplifies to 0 ≤ -1. Since this statement is true, the point (0,0) lies on the graph. Similarly, we can test other points to confirm that the inequality correctly represents the graph.

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Answer:

3160

Step-by-step explanation:

Answer:

3160

Step-by-step explanation:

Hello, thanks for using Brainly!

We are solving 6x6-4+9.

We will do three steps in this case.

First is 6x6, 6x6 is 30.

So now we must keep in our head we have 30 as our first number.

Now, let's -4 from 30. 30-4 is 26.

We just did step 2. Boom!

So, we have 26 as our second number. Let's do our third step.

If we have 26, we need to add 9 to that. To quickly find that we know that 26+10 is 36. That is adding ten, we need 9 so minus 1 from 36 we get 35.

Our final answer is 35.

Answer:

The answer is the first graph in the second raw

Step-by-step explanation:

* Lets study the dilation:

- A vertical stretching is the stretching of the graph away

 from the x-axis

- A vertical compression is the squeezing of the graph

 toward the x-axis.

- if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically

 stretched by multiplying each y-coordinates by k.

- if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed

 by multiplying each y-coordinates by k.

* Notice that the "roots" on the graph stay in their same

 positions on the x-axis.

* Lets check our question:

∵ f(x) = 3g(x)

∵ f(x) = k.g(x)

∴ It is a vertical stretching or vertical compression

∵ k = 3 > 1

∴ It is vertical stretching with scale factor = 3

* That means we will multiply each y-coordinates in g(x) by 3

∴ The graph of f(x) will be away from x- axis and narrow to y- axis

∴ The answer is the first graph the second raw

Example: If g(x) = x²

                ∴ f(x) = 3x²

* Look to the graph:

- The red is the graph of g(x)

- The blue is the graph of f(x)

- f(x) = 3g(x)

Answer: the answer is b

Step-by-step explanation:i did the test yourself on algebra nation

To solve the equation 3/8c -2 = 3/2c -12 for c, first clear the fractions by multiplying the entire equation by 8. Then, use algebraic operations to isolate and solve for c, yielding the solution c = 80/9 or about 8.89.

The given algebraic equation is 3/8 c−2= 3/2 c−12. Our goal is to solve for c. Here's how:

So, the solution to the equation 3/8c - 2 = 3/2c -12 is c = 80/9 or about 8.89.

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To solve the equation:3/8 c−2= 3/2 c−1. We can solve the equation by combining like terms, eliminating fraction denominators, and distributing.

After simplifying,80/9.

Let's solve the equation:3/8 c−2= 3/2 c−1.

We can solve the equation by combining like terms, eliminating fraction denominators, and distributing.

Steps to solve:

1. Combine multiplied terms into a single fraction:

3/8 c−2= 3/2 c−12

2. Find common denominator:

3/8 c + (8/8) −2= 3/2 c−12

3. Combine multiplied terms into a single fraction:

3/8 c + (8 *(−2) /8) −2= 3/2 c−12

4. Combine fractions with common denominator:

(3c + 8 *(−2) /8) = 3/2 c−12

5. Multiply the numbers:

(3c -16) /8) = 3/2 c−12

6.Combine multiplied terms into a single fraction:

(3c -16) /8) = 3/2 c−12

7. Find common denominator:

(3c -16) /8) = 3/2 c +(2/2) (-12)

8.Combine multiplied terms into a single fraction:

(3c -16) /8) = 3/2 c +(2*-12)/2

9.Multiply the numbers:

(3c -16) /8) =(3c -24) /2)

10. Eliminate fraction denominators:

8*(3c -16) /8) = 8*(3c -24) /2)

11. Cancel multiplied terms that are in the denominator:

3c−16=4(3c−24)

12. Distribute:

3c−16=12c−96

13. Add/subtract to both sides:

3c−16+16=12c−96+16

14. Simplify:

3c=12c−80

15. Add/subtract to both sides:

3c−12c=12c−80−12c

16. Simplify:

−9c=−80

17.Divide both sides of the equation by the same factor:

−9c/-9=−80/-9

18.Simplify:

c=80/9.

Answer:

C= 2π*4

C= 4*2= 8*3.14

C= 25.12

Step-by-step explanation:

Answer:

5.5%

Step-by-step explanation:

100%-20%=80%

80%×$75=$60

3.30/60×100%=5.5%

the sales tax rate is 5.5%

Final answer:

The sales tax rate on Sunil's discounted concert ticket is found by calculating the discounted ticket price and then dividing the sales tax paid by this discounted price, resulting in a sales tax rate of 5.5%.

Explanation:

To find the sales tax rate, we need to calculate the discounted price of the concert ticket and then use the amount of sales tax paid to determine the rate. Initially, Sunil receives a 20% discount on a $75 ticket.

The calculation for the discount amount is $75 × 0.20 = $15. Thus, Sunil's discounted ticket price is $75 - $15 = $60.

Now, knowing Sunil paid $3.30 in sales tax for the discounted ticket, we can find the sales tax rate by dividing the sales tax amount by the discounted ticket price:

$3.30 ÷ $60 = 0.055, or 5.5% when converted to a percentage. Therefore, the sales tax rate is 5.5%.