Tran planned a rectangular pool and made a scale drawing using centimeters as the unit of measurement. He originally planned for the length of the pool to be 40 m but decided to change it to 32 m. If the length of the pool in his scale drawing is 8 cm, which statement about the change of scale is true?
One cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.
One cm represented 40 m in the first scale, but now 1 cm represents 32 m in the second scale.
One cm represented 1 m in the first scale, but now 1 cm represents 5 ft in the second scale.
One cm represented 4 m in the first scale, but no

You can form various dollar amounts using just two-dollar bills and five-dollar bills.

For example, using one two-dollar bill and one five-dollar bill, you can form $7.

By increasing the number of bills, you can form amounts like $10 (using five two-dollar bills or two five-dollar bills), $12 (using six two-dollar bills), $14 (using one five-dollar bill and four two-dollar bills), and so on.

In general, you can form any amount that is a multiple of 2 or 5, or a combination of both, using these bills.

The dollar amounts of money that can be formed using just two-dollar bills and five-dollar bills are $2, $4, $5, $7, $9, $10, $12, $14, $15, $17, $19, $20, $22, $24, $25, $27, $29, $30, $32, $34, $35, $37, $39, $40, $42, $44, $45, $47, $49, $50, and so on.

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                                        "Complete question "

Which amounts of money can be formed using just two-dollar bills and five-dollar bills? Prove your answer using strong induction. 5. Give a recursive definition of the set of even integers.

Answer:

9 inch by 15 inch

Step-by-step explanation:

45/5=9 in

75/5=15 in

Answer:

second option

Step-by-step explanation:

Let's find A ∪ B. ∪ (union) means all of the numbers in the sets so A ∪ B = {1, 2, 3, 4, 5, 6}. Now we need to find C ∩ {1, 2, 3, 4, 5, 6}. ∩ (intersection means the common elements between the sets so the answer is {2, 3}.

The control limits for the mean chart are 7.76821 (LCL) and 8.34595 (UCL), while the control limits for the range chart are 0 (LCL) and 0.86566 (UCL).

To calculate the exact control limits for the mean and range charts, we will use the formulas provided:

Calculate the mean and range for each sample:

Sample 1:

Mean = (7.98 + 8.34 + 8.02 + 7.94 + 8.44 + 7.68 + 7.81 + 8.11) / 8 = 8.055

Range = 8.44 - 7.68 = 0.76

Sample 2:

Mean = (8.33 + 8.22 + 8.08 + 8.51 + 8.41 + 8.28 + 8.09 + 8.16) / 8 = 8.275

Range = 8.51 - 8.08 = 0.43

Sample 3:

Mean = (7.89 + 7.77 + 7.91 + 8.04 + 8.00 + 7.89 + 7.93 + 8.09) / 8 = 7.9475

Range = 8.09 - 7.77 = 0.32

Sample 4:

Mean = (8.24 + 8.18 + 7.83 + 8.05 + 7.90 + 8.16 + 7.97 + 8.07) / 8 = 8.055

Range = 8.24 - 7.83 = 0.41

Sample 5:

Mean = (7.87 + 8.13 + 7.92 + 7.99 + 8.10 + 7.81 + 8.14 + 7.88) / 8 = 7.9925

Range = 8.14 - 7.81 = 0.33

Sample 6:

Mean = (8.13 + 8.14 + 8.11 + 8.13 + 8.14 + 8.12 + 8.13 + 8.14) / 8 = 8.1325

Range = 8.14 - 8.11 = 0.03

Calculate the overall mean and overall average range:

Overall Mean = (8.055 + 8.275 + 7.9475 + 8.055 + 7.9925 + 8.1325) / 6 = 8.05708

Overall Average Range = (0.76 + 0.43 + 0.32 + 0.41 + 0.33 + 0.03) / 6 = 0.37833

Construct the control charts:

Mean Chart:

Upper Control Limit (UCL) = Overall Mean + (A2 * Overall Average Range)

Lower Control Limit (LCL) = Overall Mean - (A2 * Overall Average Range)

For a sample size of 8, A2 = 0.729.

UCL = 8.05708 + (0.729 * 0.37833) = 8.34595

LCL = 8.05708 - (0.729 * 0.37833) = 7.76821

Range Chart:

Upper Control Limit (UCL) = D4 * Overall Average Range

Lower Control Limit (LCL) = D3 * Overall Average Range

For a sample size of 8, D3 = 0 and D4 = 2.282.

UCL = 2.282 * 0.37833 = 0.86566

LCL = 0 * 0.37833 = 0

Therefore, the control limits for the mean chart are 7.76821 (LCL) and 8.34595 (UCL), and the control limits for the range chart are 0 (LCL) and 0.86566 (UCL).

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--The given question is incomplete, the complete question is given below " Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped. Management is concerned about whether the filling process for tubes of caulking is in statistical control. Several samples of eight tubes were taken, each tube was weighted, and the weights in the following table were obtained.

Assume that only six samples are sufficient and develop the control charts for the mean and the range. "--

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Answer:

8 and 2

Step-by-step explanation:

If you add them together you get 10. (8 + 2 = 10)

If you multiply them you get 16. (8 x 2 = 16)

Have a great day! (I'd love brainiest if you could give it to me!)

Answer:

the pattern is going by 3s and u would multiply 3 by each number

Answer:

This question is so complex

Step-by-step explanation:

kfdsjbdsnmvn sdbvjhsbadjvm dashbnvdjnzcxshjd

Answer:

1) 3,3

2) 4,5

3) 6,1

4) 1/36

There are 36 possible outcomes when you roll a dice. Rolling two 3s is only one of the possible outcomes. Therefore, the fraction 1/36 can represent this probability.

Answer:

y = \(\frac{3}{2}\) x - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = \(\frac{3}{2}\) , thus

y = \(\frac{3}{2}\) x + c ← is the partial equation

To find c substitute (8, 4) into the partial equation

4 = 12 + c ⇒ c = 4 - 12 = - 8

y = \(\frac{3}{2}\) x - 8 ← equation of line

The equation of a line that has a slope of 3/2 and passes through (8, 4) can be written as:

\(y - 4 = \frac{3}{2} (x - 8)\) (point-slope form) or

\(y = \frac{3}{2}x - 8\) (slope-intercept form).

Given:

a point on a line: (8, 4)

slope of the line: 3/2

The equation of the line can be written in either point-slope form or slope-intercept form.

First, let's write the equation in point-slope form since we know one of the points and the slope.

Where,

\(y - 4 = \frac{3}{2} (x - 8)\) =>> point-slope form.

\(y - 4 = \frac{3}{2} (x - 8)\)

\(y - 4 = \frac{3}{2}x - 12\)

\(y - 4 + 4 = \frac{3}{2}x - 12 + 4\\\\y = \frac{3}{2}x - 8\)(slope-intercept form)

Therefore, the equation of a line that has a slope of 3/2 and passes through (8, 4) can be written as:

\(y - 4 = \frac{3}{2} (x - 8)\) (point-slope form) or

\(y = \frac{3}{2}x - 8\) (slope-intercept form).

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Answer:

Katie made more money. Her hourly rate was $9.25 per hour.

Step-by-step explanation:

a. The equation is y =2x -5 is non - directly proportional because there is a constant term of -5 which makes the equation non-linear.

b. The equation is \(\frac{2}{5}\)x = y is directly proportional because the constant of proportionality exist is \(\frac{2}{5}\).

Given that,

We have to find for each equation whether x and y are directly proportional and if so, then find the constant of proportionality.

We know that,

a. The equation is y =2x -5

The equation does not show direct proportional because the variables y and x are not directly proportional.

There is a constant term of -5 which makes the equation non-linear.

b. The equation is \(\frac{2}{5}\)x = y

The equation  \(\frac{2}{5}\)x = y shows direct proportional because the variables x and y are directly proportional.

The constant of proportionality is \(\frac{2}{5}\) exist.

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Answer:

x = 20

Step-by-step explanation:

You can use Pythagorean theorem which is \(a^2 + b^2 = c^2\)

a = 12

b = 16

and c would be x.

12^2 + 16^2 = c^2

144 + 256 = c^2

400 = c^2

square root

c = 20 or x = 20

Coach Yellsalot can create 792 different starting lineups of 5 players without including both Bob and Yogi, considering the combinations and permutations of the remaining players.

To calculate the number of possible lineups, we can use combinations and permutations.

First, let's consider the combinations of 5 players out of the remaining 10 players (excluding Bob and Yogi). This can be calculated using the formula for combinations, denoted as C(n, r), where n is the total number of players and r is the number of players in the lineup. In this case, we have C(10, 5) = 252 possible combinations.

Now, since the order of players does not matter in a lineup, we need to consider the permutations of the lineup combinations. The number of permutations can be calculated using the formula for permutations, denoted as P(n, r), where n is the total number of players and r is the number of players in the lineup. In this case, we have P(10, 5) = 30240 possible permutations.

However, we need to exclude the cases where both Bob and Yogi are in the lineup. This means we need to subtract the number of lineups that include both players from the total permutations. There are P(8, 3) = 336 possible permutations of the remaining 8 players (excluding Bob and Yogi) in a lineup of 3 players.

Therefore, the total number of starting lineups without both Bob and Yogi is P(10, 5) - P(8, 3) = 30240 - 336 = 29904.

Thus, Coach Yellsalot can make 792 different starting lineups of 5 players without including both Bob and Yogi.

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Answer:

We've learned that the circumference is the distance around the circle and the diameter is the distance across the circle going through the center. ... To find the circumference given the diameter, you multiply the diameter by pi. To find the diameter given the circumference, you divide the circumference by pi.

Answer:

a) y= x+7

The slope is 1 and the y intercept is 7

b) y = -3x

The slope is -3 and the y intercept is 0

Step-by-step explanation:

The slope intercept form of the equation of a line is

y = mx+b where m is the slope and b is the y intercept

a) y= x+7

The slope is 1 and the y intercept is 7

b) y = -3x

The slope is -3 and the y intercept is 0

The integral ∫x^3e^xdx evaluates to x^3e^x - 3x^2e^x + 6xe^x - 6e^x + C. The integral ∫csc(2x)cos(3x)dx simplifies to 2ln|sin(2x)| + C.

The integral ∫x^3e^xdx and ∫csc(2x)cos(3x)dx can be evaluated using integration techniques. The first integral can be solved using integration by parts, while the second integral requires applying trigonometric identities and substitution.

To evaluate the integral ∫x^3e^xdx, we use integration by parts. This technique involves splitting the integrand into two functions and applying a specific formula:

∫u * dv = u * v - ∫v * du

Let's assign u = x^3 and dv = e^xdx. Taking the derivatives and antiderivatives, we have du = 3x^2dx and v = ∫e^xdx = e^x.

Using the integration by parts formula, we obtain:

∫x^3e^xdx = x^3 * e^x - ∫(3x^2 * e^x)dx

Now, we have a new integral to evaluate: ∫(3x^2 * e^x)dx. We can apply integration by parts again to solve this integral. Let's assign u = 3x^2 and dv = e^xdx. Calculating the derivatives and antiderivatives, we get du = 6xdx and v = ∫e^xdx = e^x.

Applying the integration by parts formula once more, we have:

∫(3x^2 * e^x)dx = 3x^2 * e^x - ∫(6x * e^x)dx

Now, we have another integral to solve: ∫(6x * e^x)dx. This integral can be evaluated using integration by parts for the third time. Assigning u = 6x and dv = e^xdx, we calculate du = 6dx and v = ∫e^xdx = e^x.

Applying the integration by parts formula for the final time, we get:

∫(6x * e^x)dx = 6x * e^x - ∫(6 * e^x)dx

The integral ∫(6 * e^x)dx is straightforward to evaluate, as it does not contain x terms. The result is 6e^x.

Combining all the results from the integration by parts calculations, we have:

∫x^3e^xdx = x^3 * e^x - 3x^2 * e^x + 6x * e^x - 6e^x + C

where C is the constant of integration.

Now, let's move on to the integral ∫csc(2x)cos(3x)dx. This integral involves trigonometric functions and can be solved by applying trigonometric identities and substitution.

We can rewrite the integral as:

∫csc(2x)cos(3x)dx = ∫(1/sin(2x)) * cos(3x)dx

To simplify the expression, we use the identity csc(x) = 1/sin(x) and rewrite the integral as:

∫(1/sin(2x)) * cos(3x)dx = ∫(1/sin(2x)) * cos(3x) * (sin(2x)/sin(2x))dx

Expanding the expression, we have:

∫(cos(3x) * sin(2x))/(sin(2x) * sin(2x))dx

Canceling out the sin(2x) term in the numerator and denominator, we get:

∫

cos(3x)/sin(2x)dx

Now, we can substitute u = sin(2x) to simplify the integral. Taking the derivative of u, we have du = 2cos(2x)dx. Rearranging the terms, we get dx = du/(2cos(2x)).

Substituting these values into the integral, we have:

∫cos(3x)/sin(2x)dx = ∫(cos(3x)/(u/2)) * (du/(2cos(2x)))

Simplifying the expression, we get:

∫2cos(3x)du/u

Now, the integral has been transformed into a simpler form. We can integrate with respect to u:

∫2cos(3x)du/u = 2∫cos(3x)du/u

The integral of cos(3x)du/u can be evaluated as:

2∫cos(3x)du/u = 2ln|u| + C

Finally, substituting back u = sin(2x), we obtain:

∫csc(2x)cos(3x)dx = 2ln|sin(2x)| + C

where C is the constant of integration.

In summary, the integral ∫x^3e^xdx can be evaluated using integration by parts, resulting in x^3e^x - 3x^2e^x + 6xe^x - 6e^x + C. The integral ∫csc(2x)cos(3x)dx can be simplified using trigonometric identities and substitution, resulting in 2ln|sin(2x)| + C.

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Answer:

54

Step-by-step explanation:

Mon - 2 pages read

Tues - 2x3 = 6 pages

Wed - 6x3 = 18 pages

Thurs - 18x3 = 54 pages read

Answer:

24

Step-by-step explanation:

-3(1(-8))

1x(-8) = -8

-3 x -8 =24

Step-by-step explanation: WELL...

1,200 divided by 3 is 400

SO....

                           Each person will have 400 soccer cards.

a) The solution for b in the equation 2b × 3 = 6 is b = 1.

b) The solution for b in the equation 32 - 3b = 2 is b = 10.

c) The solution for b in the equation 6 + 7b = 41 is b = 5.

d) The solution for b in the equation 100/5b = 2 is b = 10.

a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.

2b × 3 = 6

(2b × 3) / 2 = 6 / 2

3b = 3

b = 3/3

b = 1

Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.

c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.

6 + 7b - 6 = 41 - 6

7b = 35

b = 35/7

b = 5

Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.

b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.

32 - 3b - 32 = 2 - 32

-3b = -30

b = (-30)/(-3)

b = 10

Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.

d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.

(100/5b) × 5b = 2 × 5b

100 = 10b

b = 100/10

b = 10.

Therefore, the solution for b in the equation 100/5b = 2 is b = 10.

In summary, the solutions for b in the given equations are:

a) b = 1

c) b = 5

b) b = 10

d) b = 10

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Answer:

\((-\frac{2}{7},-\frac{65}{7} )\)

Step-by-step explanation:

By steps in the image:

Step 1:

To eliminate, you need one of the coefficients to be the same in both equations. We will use the term "-6x" found in the first equation.

To get this, multiply the entire second equation by 6 and simplify using the distributive property. The new equation is:

\(6x-6y=54\)

Step 2:

Now you need to subtract the first equation and the new version of the second equation. By doing this, the "-6x" in both equations will cancel each other out.

Step 3:

Solve for x in the given equation by:

Step 4:

Solve for y by:

Solution:

\((-\frac{2}{7},-\frac{65}{7} )\)

:Done

Answer:

c 116

Step-by-step explanation:

Answer:

The answer is c

Step-by-step explanation:

Answer:

16x25x15=6000

4+11÷2=9.5

Step-by-step explanation:

1) 16x25x15 is 16 times 25 times 15, which is 6000

2) This question requires BIDMAS/BODMAS. As you start with the multiplication (Brackets Indices Multi Divide Add Subtract) 11÷2 = 5.5, 5.5+4=9.5

Answer:

w^2*(w+4)*(w^2+10)

Step-by-step explanation:

w^5+4w^4+10w^3+40w^2

w^2*(w^3+4w^2+10w+40)\w^2*(w^2*(w+4)+10(w+4))

w^2*(w+4)*(w^2+10)

I'm assuming there's an =0 at the end of this?

You need to factor to get an answer, so:

\(w^5+4w^4+10w^3+40w^2=0\\w^4(w+4)+10w^2(w+4)=0\\(w^4+10w^2)(w+4)=0\\w^2(w^2+10)(w+4)=0\\w=0\\w^2+10=0\\w^2=-10\\w=\sqrt{-10}=10i\\ w+4=0\\w=-4\\w=0,10i,-4\)

If your teacher doesn't want any imaginary numbers, then your answer would be limited to w=0 and 4. (exclude the 10i if you don't want imaginary numbers)

The values of "l" and "r" that maximize the area of the rectangular region are approximately 326.5 ft and 105.6 ft, respectively.

To find the values of "l" and "r" that maximize the area of the rectangular

region of the racetrack, we need to use optimization techniques.

Let's start by breaking down the rectangular region into its two

components: a rectangle and two semicircles.

Let "l" be the length of the rectangle and "r" be the radius of the

semicircles. Then we can express the area of the rectangular region as:

A = l(1056/5 - 2r)

the length of the track is 1056 ft, or 1/5 of a mile. Since there are two

semicircular ends, the length of the rectangle is equal to the length of

the track minus the combined length of the two semicircles, which is 2r.

To find the values of "l" and "r" that maximize the area of the rectangular

region, we need to find the critical points of the function A(l, r). To do this,

we can take partial derivatives of A with respect to both "l" and "r", and

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∂A/∂l = 1056/5 - 2r = 0

∂A/∂r = -2l + (2112/5 - 4πr) = 0

Solving the first equation for "r", we get:

r = 528/5

Substituting this value of "r" into the second equation and solving for "l", we get:

l = (2112/5 - 4πr)/2

l ≈ 326.5 ft (rounded to the nearest foot)

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Answer:

38

Step-by-step explanation:

2 + ( (15 + 3) * 2)

2 +  (18 * 2)

2 + (36)

= 38

Answer:

38

Step-by-step explanation:

2 + [(15 + 3) × 2]

= 2 + [ 18 × 2]

= 2 + 36

= 38

The values of the given expression having exponent with negative fractional base i.e. \(-2^{(3/2)^2}\\\) is evaluated out to be 16/9.

First, we need to simplify the expression inside the parentheses using the rule that says "exponents with negative fractional base can be rewritten as a fraction with positive numerator."

\(-2^{(3/2)^2}\) = (-2)² × (2/3)²

Now, we can simplify the expression  further by solving the exponent of (-2)² and (2/3)²:

(-2)² × (2/3)² = 4 × 4/9 = 16/9

Therefore, the value of the given expression \(-2^{(3/2)^2}\\\)  is 16/9.

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The question is :

What is the value of the expression \(-2^{(3/2)^2}\) ?