Below is a scale drawing of a stage that Syla is designing. A rectangle with length 8 centimeters and width 5 centimeters. Using the scale 1 cm : 7 m, Syla calculated the width, or the shorter side of the stage, to be 35 m. She decides to change the scale to 1 cm : 10 m. What is the width of the new stage?

Answer:

2-6

Step-by-step explanation:

To set up an iterated double integral equivalent to the given expression, we need to define the region B bounded by the curve y = 4 - x² and the x-axis. The iterated double integral will allow us to calculate the integral of the function f(x, y) over this region.

To set up the iterated double integral, we first need to determine the limits of integration for both x and y. The region B is bounded by the curve y = 4 - x² and the x-axis. The curve intersects the x-axis at x = -2 and x = 2. Therefore, the limits of integration for x will be -2 to 2.

For each value of x within the limits, the corresponding y-values will be determined by the curve equation y = 4 - x². So, the limits of integration for y will be given by the function y = 4 - x².

The iterated double integral will then be expressed as ſſ f(x, y) dA, where the limits of integration for x are -2 to 2 and the limits of integration for y are 0 to 4 - x².

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Answer:

9 4/21

Step-by-step explanation:

I think it's the answer

The estimated length of the diagonal of a square with area 100 cm square is 14 cm.

The length of the diagonal of a square with area 100 cm square can be estimated using the formula d = 1.4x2, where d is the length of the diagonal and x is the area of the square. Substituting x with 100 cm square, we get:

d = 1.4(100)^(1/2)

d = 1.4(10)

d = 14 cm

Therefore, the estimated length of the diagonal of a square with area 100 cm square is 14 cm.

The formula d = 1.4x2 can be derived using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In a square, the diagonal is the hypotenuse of two right-angled triangles formed by the sides of the square. If we let s be the length of the sides of the square, then we can write the Pythagorean theorem as: s^2 + s^2 = d^2

Simplifying this equation, we get: 2s^2 = d^2

Taking the square root of both sides, we get: d = (2s^2)^(1/2)

Since the area of the square is x = s^2, we can substitute s^2 with x to get: d = (2x)^(1/2)

Simplifying this equation, we get:

d = x^(1/2) * 2^(1/2)

To estimate the value of d, we can substitute 1.4 for 2^(1/2) and get:

d = 1.4x^(1/2)

This formula allows us to estimate the length of the diagonal of a square when we know its area.

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Answer:

11

Step-by-step explanation:

11

since it asks the absolute value of -11 it

will be 11 because in absolute value-for negatives it always positive.

Answer:

see attached

Step-by-step explanation:

Answer:

The correct option is;

b) Vertically stretches by a factor 2 then flip over horizontal axis

Step-by-step explanation:

In the function y = -2×cos(x - pi), given that the maximum value of the cosine function is 1 and that the value of the cosine function ranges from +1 to -1, we have that a factor larger than 1, multiplying a cosine function vertically stretches the function and a negative factor flips the function over the horizontal axis by transforming the y-coordinate value from y to -y

Therefore, the factor of -2, vertically stretches the the function by a factor of 2 then flip over horizontal axis.

Answer:

True

Step-by-step explanation:

mark brainliest

Answer:

370 stores

Step-by-step explanation:

Given data

initial number of stores P= 200

r= 8%

t= 1999-2007=  8 years

Let us apply the compound interest expression to find the final amount of stores

A= P(1+r)^t

A= 200(1+0.08)^8

A= 200(1.08)^8

A= 200*1.85

A=370

Hence the number of stores in 2007 is 370 stores

Answer:

Sam can do the job in 20 min. So he can do the whole job at the rate of 1 job in 20 minutes.

So he does 1/20 of the job per minute.

.

Rob can do the job in 30 min. His rate is 1/30 of the job per minute.

.

Working together how does it take?

.

1/20*x + 1/30*x = 1 job done

, where x = minutes.

.

Step-by-step explanation:

=======================================================

Work Shown:

Use that given info to say the following:

P(LC given S) = P(LC and S)/P(S)

P(LC and S) = P(LC given S)*P(S)

P(LC and S) = 0.31*0.226

P(LC and S) = 0.07006

P(LC and S) = 0.07

This problem is an example of using conditional probability.

I used "and" in place of the intersection symbol \(\cap\)

Saying P(LC and S) is the same as P(S and LC). The order doesn't matter.

Answer:

try -8 + 34 to get your answer because -8 - 34 wont work

Step-by-step explanation:

Answer:

x=26°, y=26°, z=26°

Step-by-step explanation:

x+74=100 (the sum of linear pair)

x=100-74

x=26

x=y=26 (alternate angle)

y=z=26 (vertically opposite angle V.O.A)

Answer: 0.1"/minute

Step-by-step explanation:

Volume of a sphere is:  V = (4/3)πr³

In one minute, the volume increases by 2032 in^3.  Set the starting volume at a point 1 minute from the target of 342342 in^3:  (342342 - 2032) =  340310 in^3.

We can then determine the change in the radius for the initial (340310 In^3) and end (342342 in^3) points as the sphere reaches its maximum size:

Initial:  The radius for a 340310 in^3 sphere is 43.3".

Finish:  The radius for a 342342 in^3 sphere is 43.4".  {Wow]

It took an increase in radius of 0.1" to add the final 2032 in^3 of volume to the sphere.  That occurred in one minute, so the rate of change of the radius is 0.1"/minute.

The equation in the form of subtraction is c=458-247.

What is an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The definition of an equation in algebra is a mathematical statement demonstrating the equality of two mathematical expressions. For instance, the equation 3x + 5 = 10 consists of the two equations 3x + 3 and 10, separated by the 'equal' sign.

An equation is given as 247+c=458.

Subtract 247 from both sides of the equation to isolate c.

247+c-247=458-247

c=458-247

So, the equation in the form of subtraction is c=458-247.

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If Caroline has 6.8 L of lemonade to serve 20 people. Caroline can pour 340 milliliters of lemonade into each glass.

To find out how many milliliters of lemonade Caroline can pour into each glass, we need to convert the volume of lemonade from liters to milliliters and then divide it equally among the 20 guests.

1 liter is equal to 1000 milliliters. So, Caroline has 6.8 L * 1000 mL/L = 6800 mL of lemonade.

To divide it equally among 20 guests, we divide the total volume of lemonade by the number of guests:

6800 mL / 20 = 340 mL.

Therefore, Caroline can pour 340 milliliters of lemonade into each glass.

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Answer:

\(\textsf{A)} \quad \dfrac{m\overline{AC}}{m\overline{DF}}=3\)

Step-by-step explanation:

In similar triangles:

Given ΔABC ~ ΔDEF with a scale of 3 : 1 then:

    \(\bullet \quad \overline{AB} = 3\overline{DE}\)

    \(\bullet \quad \overline{BC} = 3\overline{EF}\)

    \(\bullet \quad \overline{AC} = 3\overline{DF}\)

Therefore:

\(\dfrac{m\overline{AC}}{m\overline{DF}}=3\)

The closer the correlation coefficient is to +1, the more closely the data points will be clustered around the straight line.

The correlation for which the data points would be clustered most closely around a straight line is a strong positive correlation. In this type of correlation, as one variable increases, the other variable also increases at a consistent rate, resulting in a straight line when the data points are plotted. The closer the correlation coefficient is to +1, the more closely the data points will be clustered around the straight line.

For the following correlations, the data points would be clustered most closely around a straight line when the correlation coefficient is closest to 1 or -1. A positive correlation near 1 indicates a strong positive relationship, while a negative correlation near -1 indicates a strong negative relationship. In both cases, the data points will be tightly clustered around a straight line.

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a correlation coefficient of +0.95 or -0.95 would result in the data points being clustered most closely around a straight line.

The strength and direction of the correlation determine how closely the data points cluster around a straight line. In general, a stronger correlation indicates that the data points are more closely clustered around a straight line.

Therefore, for the following correlations, the data points would be clustered most closely around a straight line in the case of a correlation coefficient of +0.95 or -0.95. These correlation coefficients indicate a strong positive or negative linear relationship between the variables, respectively. The data points would be tightly clustered around a straight line with little scatter, indicating a high degree of linear association between the variables.

Correlation coefficients of +0.70, -0.70, and 0.10 indicate moderate positive, moderate negative, and weak positive correlation, respectively. While these correlations also show some degree of clustering around a straight line, it would not be as tight and pronounced as with correlation coefficients of +0.95 or -0.95.

In summary, a correlation coefficient of +0.95 or -0.95 would result in the data points being clustered most closely around a straight line.

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Answer:

it is now at 108

Step-by-step explanation:

10% of 120 is 12 120-12=108

The radius of Earth is 3,960 mi then  (a) Arc length = 7.32 units. (b) Area of sector = 11.01 sq units. (c) Distance along arc on Earth's surface with central angle of 5 minutes ≈ 1.15 miles.

The area of sector, arc length and distance along arc on earth's surface with central angle

(a) To find the arc length of a circle with radius r and central angle θ (in radians), we use the formula:

arc length = rθ

First, we need to convert the central angle from degrees to radians:

140° = (140/180)π radians

≈ 2.44 radians

Then, we can plug in the values for r and θ:

arc length = (3)(2.44)

≈ 7.32

Therefore, the arc length is approximately 7.32 units.

(b) To find the area of a sector of a circle with radius r and central angle θ (in radians), we use the formula:

area of sector = (1/2)r^{2θ}

Again, we need to convert the central angle from degrees to radians:

140° = (140/180)π radians

≈ 2.44 radians

Then, we can plug in the values for r and θ:

area of sector = (1/2)(3)²{2.44}

≈ 11.01

Therefore, the area of the sector is approximately 11.01 square units.

(c) The distance along an arc on the surface of Earth that subtends a central angle of 5 minutes can be found using the formula:

distance = (radius of Earth) × (central angle in radians)

First, we need to convert the central angle from minutes to degrees:

5 minutes = (5/60)°

= 1/12°

Then, we can convert the angle from degrees to radians:

1/12° = (1/12)(π/180) radians

≈ 0.000291 radians

Finally, we can plug in the value for the radius of Earth:

distance = (3960) × (0.000291)

≈ 1.15

Therefore, the distance along the arc on the surface of Earth that subtends a central angle of 5 minutes is approximately 1.15 miles.

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Answer:

Undefined

Step-by-step explanation:

When computing the given expressions for f(x) = 3x - 1, we find that f(3 + 1) = 15, f(3) + f(1) = 8, f(3-1) = 5, f(3) = 8, f(1) = 2, and f(3-1) = 5.

To find f(3 + 1), we substitute the value of 3 + 1 into the expression for f(x): f(3 + 1) = 3(3 + 1) - 1 = 12 - 1 = 11.

Next, to calculate f(3) + f(1), we substitute the values of 3 and 1 into the expression for f(x) separately and add them together: f(3) + f(1) = (3 * 3 - 1) + (3 * 1 - 1) = 8.

For f(3-1), we substitute the value of 3 - 1 into the expression for f(x): f(3-1) = 3(3-1) - 1 = 5.

Since f(3) and f(1) are both defined as 3x - 1, they have the same value: f(3) = f(1) = 8.

Finally, to compute f(3) f(1), we multiply the values of f(3) and f(1) together: f(3) f(1) = (3 * 3 - 1)(3 * 1 - 1) = 5.

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To determine the 90% confidence interval for the mean repair cost of VCRs, we need to find the critical value for constructing the interval. The sample data consists of 1414 randomly selected VCRs, with a sample mean repair cost of $55.95 and a sample standard deviation of $18.89.

The critical value is determined based on the desired confidence level and the sample size. In this case, we want a 90% confidence interval, which means we need to find the critical value that leaves 5% in the tails of the distribution (since the remaining 90% will be in the interval).

Using a standard normal distribution table or a calculator, the critical value for a 90% confidence level is approximately 1.645 (rounded to three decimal places). This value represents the number of standard deviations away from the mean that includes 90% of the distribution.

In the next step, we will use this critical value along with the sample mean, standard deviation, and sample size to calculate the confidence interval for the mean repair cost of the VCRs.

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Answer:

slope: 1/3

y-intercept: 3

Answer:

392

Step-by-step explanation:

h(1) = 14

h(n) = h(n-1)*28

h(2) = ?

Use the equation h(n) = h(n-1)*28 to find the value of h(2):

h(n) = h(n-1)*28 at n = 2

h(2) = h(2-1)*28 = h(1)*28 = 14*28 = 392

Answer:

The answer above is correct. You are probably mistaking this problem for a different on. In this problem you are given the equation h*(n-1)*28. The question you want the answer for has the equation 28/(h*(n-1))

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Hope you have a great day! <3

The expected number of days until a value higher than 2 is obtained from a standard normal distribution is approximately 43.86 days. This calculation is based on the probability of selecting a value higher than 2, which can be derived from the cumulative distribution function of the standard normal distribution.

The expected number of days until a value higher than 2 is obtained from a standard normal distribution can be calculated using the concept of the expected value. In this scenario, the expected number of days can be interpreted as the average number of days it takes to obtain a value higher than 2.

To calculate the expected number of days, we can consider the probability of selecting a number below or equal to 2 on any given day. The standard normal distribution has a mean of 0 and a standard deviation of 1. The area under the curve of the standard normal distribution up to 2 is approximately 0.9772. This means that the probability of selecting a value below or equal to 2 is 0.9772.

Therefore, the probability of selecting a value higher than 2 on any given day is 1 - 0.9772 = 0.0228. This implies that, on average, it would take approximately 1/0.0228 = 43.86 days to obtain a value higher than 2.

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The distance that she runs from one corner of the field to another is given as follows:

147.1 yards.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The distance in this problem is the diagonal of a rectangle, which is the hypotenuse of a right triangle in which the length and the width are the sides, hence:

d² = 85² + 120²

d = sqrt(85² + 120²)

d = 147.1 yards.

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The relationship between the ratios of sin x° and cos yº is that they are reciprocals. The correct answer is option c. The ratios of sin x° and cos yº are reciprocals of each other.

In trigonometry, sin x° represents the ratio of the length of the side opposite the angle x° to the length of the hypotenuse in a right triangle. Similarly, cos yº represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Since the hypotenuse is the same in both cases, the ratios sin x° and cos yº are related as reciprocals. This means that if sin x° is equal to 12/13, then cos yº will be equal to 13/12. The reciprocals of the ratios have an inverse relationship, where the numerator of one ratio becomes the denominator of the other and vice versa.

It's important to note that the signs of the ratios can vary depending on the quadrant in which the angles x° and yº are located. However, the reciprocal relationship remains the same regardless of the signs.

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The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

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