A drawing has a scale of 1:40
On the drawing, a kitchen is a rectangle measuring 14 cm by 22 cm
A bedroom has an actual area of 500 000 cm?
How much smaller, in cm2, is the kitchen than the bedroom?

Answer:

2 units

Step-by-step explanation:

From one crest (high point) to the next crest  point is one period....

  this covers 2 units on this graph

Answer: is there an image to go along with the question

Step-by-step explanation:

Answer:

d. All of the above are true

Step-by-step explanation:

All of the following statements,

a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.

b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative.

C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant.

are true

The two-sample z-test statistic for evaluating the null hypothesis that the percentage of students who support capital punishment did not change from 1970 to 2005 is -4.08 (rounded to two decimal places).

To calculate the two-sample z-test statistic, we need to compare the proportions of students who support capital punishment in 1970 and 2005. The null hypothesis states that the percentage of students who support capital punishment did not change.

Let p1 be the proportion of students who support capital punishment in 1970, and p2 be the proportion in 2005. We can calculate the sample proportions as p1 = 590/1000 = 0.59 and p2 = 350/1000 = 0.35.

The formula for the two-sample z-test statistic is given by z = (p1 - p2) / sqrt((p(1 - p)(1/n1 + 1/n2))), where p is the pooled proportion and n1 and n2 are the sample sizes.

To calculate p, we compute the pooled proportion as p = (p1n1 + p2n2) / (n1 + n2) = (0.591000 + 0.351000) / (1000 + 1000) = 0.47.

Substituting the values into the formula, we have z = (0.59 - 0.35) / sqrt((0.47*(1 - 0.47)(1/1000 + 1/1000))) = -4.08.

Therefore, the two-sample z-test statistic for evaluating the null hypothesis is -4.08 (rounded to two decimal places).

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To find the point on the hyperbola xy = 8 that is closest to the point (3, 0), we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Let's denote the coordinates of the point on the hyperbola as (x, y). Substituting the given coordinates (3, 0) and the equation of the hyperbola xy = 8 into the distance formula, we get:

Distance = √[(x - 3)² + (y - 0)²]

Now, we need to minimize this distance. Since the distance is squared, we can minimize the square of the distance, which is:

Distance² = (x - 3)² + y²

To minimize this expression, we can take its derivative with respect to x and y and set them equal to zero. Let's differentiate Distance² with respect to x and y:

d(Distance²)/dx = 2(x - 3)

d(Distance²)/dy = 2y

Setting these derivatives equal to zero, we have:

2(x - 3) = 0 => x = 3

2y = 0 => y = 0

Therefore, the point on the hyperbola xy = 8 that is closest to the point (3, 0) is (3, 0).

Note that the distance from (3, 0) to any point on the hyperbola xy = 8 is always the same, which means the hyperbola is equidistant from the point (3, 0).

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Answer:

\(g(2)=11\)

Step-by-step explanation:

\(g(2)=5(2)+1=10+1=11\)

Answer:

(a) is a line an appropriate model :)

Step-by-step explanation:

Therefore, the integral ∫x^3√(81 - x^2) dx, with the trigonometric substitution x = 9sin(θ), simplifies to - 29524.5(1 - x^2/81)^2 + 29524.5(1 - x^2/81)^3 + C.

To evaluate the integral ∫x^3√(81 - x^2) dx using the trigonometric substitution x = 9sin(θ), we need to express the integral in terms of θ and then perform the integration.

First, we substitute x = 9sin(θ) into the expression:

x^3√(81 - x^2) dx = (9sin(θ))^3√(81 - (9sin(θ))^2) d(9sin(θ))

Simplifying the expression:

= 729sin^3(θ)√(81 - 81sin^2(θ)) d(9sin(θ))

= 729sin^3(θ)√(81 - 81sin^2(θ)) * 9cos(θ)dθ

= 6561sin^3(θ)cos(θ)√(81 - 81sin^2(θ)) dθ

Now we can integrate the expression with respect to θ:

∫6561sin^3(θ)cos(θ)√(81 - 81sin^2(θ)) dθ

This integral can be simplified using trigonometric identities. We can rewrite sin^2(θ) as 1 - cos^2(θ):

∫6561sin^3(θ)cos(θ)√(81 - 81(1 - cos^2(θ))) dθ

= ∫6561sin^3(θ)cos(θ)√(81cos^2(θ)) dθ

= ∫6561sin^3(θ)cos(θ) * 9|cos(θ)| dθ

= 59049∫sin^3(θ)|cos(θ)| dθ

Now, we have an odd power of sin(θ) multiplied by the absolute value of cos(θ). We can use the trigonometric identity sin(2θ) = 2sin(θ)cos(θ) to simplify the expression further:

= 59049∫(1 - cos^2(θ))sin(θ)|cos(θ)| dθ

= 59049∫(sin(θ) - sin(θ)cos^2(θ))|cos(θ)| dθ

Now, we can split the integral into two separate integrals:

= 59049∫sin(θ)|cos(θ)| dθ - 59049∫sin(θ)cos^2(θ)|cos(θ)| dθ

Integrating each term separately:

= - 59049∫sin^2(θ)cos(θ) dθ - 59049∫sin(θ)cos^3(θ) dθ

Using the trigonometric identity sin^2(θ) = 1 - cos^2(θ), and substituting u = cos(θ) for each integral, we can simplify further:

= - 59049∫(1 - cos^2(θ))cos(θ) dθ - 59049∫sin(θ)cos^3(θ) dθ

= - 59049∫(u^3 - u^5) du - 59049∫u^3(1 - u^2) du

= - 59049(∫u^3 du - ∫u^5 du) - 59049(∫u^3 - u^5 du)

= - 59049(u^4/4 - u^6/6) - 59049(u^4/4 - u^6/6) + C

Substituting back u = cos(θ):

= - 59049(cos^4(θ)/4 - cos^6(θ)/6) - 59049(cos^4(θ)/4 - cos^6(θ)/6) + C

= - 29524.5cos^4(θ) + 29524.5cos^6(θ) + C

Finally, substituting back x = 9sin(θ):

= - 29524.5cos^4(θ) + 29524.5cos^6(θ) + C

= - 29524.5(1 - sin^2(θ))^2 + 29524.5(1 - sin^2(θ))^3 + C

= - 29524.5(1 - x^2/81)^2 + 29524.5(1 - x^2/81)^3 + C

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Answer:

square root of ten so b.

Step-by-step explanation:

The probability of not picking a red marble is 0.2.

The probability of picking a yellow or green marble is 0.5

The probability of drawing an even number of a number greater than 4 is  1.

The probability of getting heads and an even number is 1.

The probability of drawing a 2 or a 4 is 0.25.

Probability determines how likely it is for an event to happen. The chances of the event occurring lies between 1 and 0.

The probability of not picking a red marble = (number of all the marbles - red marbles) / total marbles

4/20 = 0.2

The probability of picking a yellow or green marble = (number of yellow marbles / total number of marbles) + (number of green marbles / total number of marbles)

2/20 + 8/20 = 10/20 = 0.5

The probability of drawing an even number of a number greater than 4 = (number of even numbers / total numbers) + (numbers greater than 4 / total numbers)

5/10 + 5/10 = 1

The probability of getting heads and an even number is = (side that is head / total sides) x (even numbers on a die / total numbers on a die)

1/2 x 3/6 = 1

The probability of drawing a 2 or a 4 = 1/8 + 1/8 = 2/8 = 0.25

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We cannot evaluate (g⁰g⁻¹)(0) because g⁻¹(0) is undefined.

To calculate (g⁰g⁻¹)(0), we need to determine the value of g⁰(g⁻¹(0)).

First, let's find g⁻¹(x):

g(x) = 4/(x + 2)

To find the inverse function, we'll swap 'x' and 'g(x)' and solve for 'x':

x = 4/(g(x) + 2)

Solving for g(x):

g(x) + 2 = 4/x

g(x) = 4/x - 2

Now, let's substitute this result into the expression (g⁰g⁻¹)(0):

(g⁰g⁻¹)(0) = g(g⁻¹(0))

Let's find g⁻¹(0):

g⁻¹(0) = 4/0 - 2 (division by zero is undefined)

Since division by zero is undefined, the value of g⁻¹(0) does not exist.

Therefore, we cannot evaluate (g⁰g⁻¹)(0) because g⁻¹(0) is undefined.

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Answer:

−87.5

Step-by-step explanation:

3×5−4×7×5+2×4×5−5÷2=-87.5

Answer:

x=15 y=24

Step-by-step explanation:

This is because the rule is x goes up 3 y goes up 4

(9,12)->(x,20)

it skips one, so instead of adding 3 we add six

x=15

(15,20)->(18,y)

you follow the rule and 4.

Y=24

Answer:

She earns $180 at the grocery store and $144 at the nursery is for the first part. Is the second part simplifying? Because if so it would be $20g and $19n.

Answer:

$294

Step-by-step explanation:

grocery store: 9 hours at $20=20 x 9= $180 altogether

nursery: 6 hours at $19 an hour= 3 x 19= $57 x 2= $114 altogether

180 + 114= $ 294

as for part B= I don't know what that means

Answer:

SSS

Step-by-step explanation:

Answer:

8.875 km

Step-by-step explanation:

1km = 1000 metres

so 8875 metres = 8875/1000 = 8.875 X 1km = 8.875km

Answer: 8,875 metres= 8.875 kilometres

Answer:

1. 78, 51, 51

or

2. 78, 78, 24

Step-by-step explanation:

180-78=102

102/2=51

180-78-78=24

When b is 3, the value of the expression \(2b^3 + 5\) is 59.

To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.

Given that b = 3, we substitute this value into the expression:

\(2(3)^3 + 5\)

First, we evaluate the exponent, which is 3 raised to the power of 3:

2(27) + 5

Next, we perform the multiplication:

54 + 5

Finally, we add the two terms:

59

Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.

In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.

It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.

It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.

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the probability of rolling an odd number and then rolling an even numberprobability is 1/4.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
It is based on the idea that if something happens, it will happen. The theoretical probability is mainly based on the reasoning behind probability. For instance, the theoretical chance of getting a head when tossing a coin is 12.
Mathematics' study of random events is known as probability, and there are four main types of probability: axiomatic, classical, empirical, and subjective.
Probability of odd number= 3/6 = 1/2.

similarly, the probability of even number= 3/6 = 1/2.

since, both events are independent of each other as trials are independent.

so, required probability= [P(even number)* P(odd number)]

therefore, the required probability= 1/2 * 1/2 = 1/4.

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The surface area of a square pyramid with base length of 3 ft. and height of 6 ft. is 45 square ft. (option A)

The formula for the surface area of a square pyramid is given by:

A = a² + a  √(a² + 4h²)

Where:

A = surface area

a = base length

h = height of the pyramid

In the given problem, the side length of the base = W = L = 3 ft.

Hence,

a = 3 ft.

h = 6 ft.

Plug these parameters into the formula:

A = 3² + 3 x √(3² + 4x6²)

A = 9 + 3 x √153

A = 45 ft². (option (A)

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If the CAPM (Capital Asset Pricing Model) is valid, we would expect the estimated coefficient, g0, to be zero.

In the CAPM, the excess return of a stock (ri - rf) is modeled as a linear function of the stock's beta (bi), representing the systematic risk, and the nonsystematic variance (s2(ei)). The constant term in the regression equation, g0, represents the expected excess return when the beta and nonsystematic variance are both zero.

According to the CAPM, the expected excess return for a stock with zero systematic risk (beta) and zero nonsystematic variance should be equal to the risk-free rate (rf). Therefore, in the regression equation, the expected value of g0 would be zero.

So, if the CAPM is valid and the regression equation is estimated correctly, we would expect the estimated coefficient, g0, to be close to zero.

In practice, the estimated coefficient g0 is often found to be significantly different from the market risk premium. This is because the CAPM is a simplified model of the capital markets. It ignores factors such as investor risk aversion and transaction costs. As a result, the estimated coefficient g0 should be interpreted with caution.

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The net growth of of population of butterflies led to 560 butterflies.

We know that the population of butterflies is 500.

The population experiences a net growth of 12%.

The net growth can be defined as increase in number of individuals in a population .

So, the gain in the population of butterflies = 12% of 500= (12/100) × 500= 60 Butterflies

So, the new population of butterflies after the gain is 500 + 60 = 560 Butterflies.

This can be calculated by another method which is

112% of 500= (112/100)*500 = 560 butterflies

Hence, the required answer is 560 butterflies.

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Answer:

The answer is "d"

-3(4x-2)-2x

-12x+6-2x

-12x-2x+6

-14x+6

Hence, the answer is D.

Answer:

The would-be option number D

Step-by-step explanation:

Distribute - 3 through the parentheses

\(-12x+6-2x \\-14+6\)

The graph is a straight line that starts at the point (0, 20) and increases by 10 units on the y-axis for every 1 unit increase on the x-axis. This represents the linear relationship between the number of T-shirts ordered and the Total cost.

The total cost of ordering the shirts:

\[c(x) = 10x + 20\]

In this equation, $x$ represents the number of T-shirts ordered, and $c(x)$ represents the total cost in dollars. The cost per shirt is $10, and there is a flat shipping fee of $20 per order.

To graph this equation, we can plot points on a coordinate plane, where the x-axis represents the number of T-shirts ($x$) and the y-axis represents the total cost ($c$) in dollars. We can choose a few values for $x$ and calculate the corresponding values of $c$ using the equation.

Let's choose some values of $x$ and calculate the corresponding values of $c$:

- If $x = 0$, there are no T-shirts ordered, so the total cost is $c(0) = 10(0) + 20 = 20$.

- If $x = 1$, there is one T-shirt ordered, so the total cost is $c(1) = 10(1) + 20 = 30$.

- If $x = 2$, there are two T-shirts ordered, so the total cost is $c(2) = 10(2) + 20 = 40$.

We can plot these points on the graph and connect them to create a straight line. Here's how the graph looks:

        |

   50   +-----------------------------------------------------------

        |

   40   +                    * (2, 40)

        |

   30   +           * (1, 30)

        |

   20   +  * (0, 20)

        |

        +-----------------------------------------------------------

              0        1        2

The graph is a straight line that starts at the point (0, 20) and increases by 10 units on the y-axis for every 1 unit increase on the x-axis. This represents the linear relationship between the number of T-shirts ordered and the total cost.

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Answer:

A (7,2)

Solution is in the photo :)

Answer:

4 1/6 miles of walking and eating per hour

Step-by-step explanation:

The unit rate here is

 50 miles

----------------- = 4 1/6 miles of walking and eating per hour

    12 hrs

Answer:

y = 31.5x

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

A. $329.04

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