Jolene makes rocking horses to sell at craft fairs. she sells each rocking horse for the same amount. The chart shows the total cost of different numbers of her rocking horse.

Answer:

yes it is correct

Step-by-step explanation:

option 1  

Answer:

Your answer is correct! 9:1

Step-by-step explanation:

Old Area = side x side

? = 2 x 2

     4cm

New Area-

Step 1: Triple the sides

2 x 3 = ?

    6cm

Step 2: Find the area

6 x 6 = ?

  36cm

The ratio of the new area to the old area is:

                     36 : 4

But wait! You can simply it!

36 / 4 = 9

4 / 4 = 1

So the new ratio would be:

                     9 : 1

Hope this helps!

Good Luck!

:)

Answer:

y=4x+9

Step-by-step explanation:

The slope intercept form is \(y=mx+b\)

So m=4 and we plug it into the equation \(y=4x+b\)

Since there are x point is -1 and y point is 5 we plug those in replacing the corresponding variables \(5=4(-1)+b\)

So the equation becomes \(5=4+b\)

We add 4 to both sides \(5=4+b\\+4=+4\) so 9 equals b

Then we rewrite the whole equation as \(y=4x+9\)

Answer: -152

Step-by-step explanation:

(-4)(-19)(-2)=

(-4)*(38)=

-152

The error of posting $50 as $500 can be detected by comparing the recorded amount to the expected amount. Here are the steps to detect this error:

1. Calculate the expected amount: Determine the correct amount that should have been posted. In this case, the expected amount is $50.

2. Compare the recorded amount with the expected amount: Check the posted amount and compare it to the expected amount. If the recorded amount shows $500 instead of $50, then an error has occurred.

3. Identify the discrepancy: Recognize that the recorded amount of $500 is significantly higher than the expected amount of $50.

4. Investigate the source of the error: Look for the cause of the error. It could be a data entry mistake, a typo, or a misunderstanding.

5. Take corrective actions: Once the error is detected, rectify it by posting the correct amount of $50. Additionally, ensure that the source of the error is addressed to prevent similar mistakes in the future.

By following these steps, the error of posting $50 as $500 can be detected, corrected, and prevented from happening again.

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Answer:

it is 6 inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula you will want to use for this is one that allows a certain number of compoundings of the interest per year. This is a specific one for compounding continuously, and there is one for finding simple interest. Here is the one we want:

\(A(t)=P(1+\frac{r}{n})^{nt}\) where A(t) is the amount in the account after the compounding occurs over the number of years specified, P is the initial amount in the account, r is the interest rate in decimal form, n is the number of times per year the compounding occurs, and t is the amount of time the money is in the account in years. For us:

P = 300,

r = .04,

n = 4 (quarterly means 4 times), and

t = 10

Filling in:

\(A(t)=300(1+\frac{.04}{4})^{(4)(10)}\) and

\(A(t)=300(1+.01)^{40}\) and

\(A(t)=300(1.01)^{40}\) and

A(t) = 300(1.488863734) so

A(t) = $446.66 or $447

Answer: rounded it to $447

Step-by-step explanation: i think :)

The coordinate that is represented by the graph is: (1, M).

The constant speed that represents the miles per hour a car travelled can be calculated using a point on the graph as:

k = y/x.

The coordinate of the point would be an x-coordinate of 1, while the y-coordinate of that point on the graph is the value of k, which is y/x.

Given the graph where:

Constant speed = k = M miles per hour.

This implies that the coordinate on the graph would be expressed as (1, M).

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The store that offers the best discount is store B

The graph that completes the question is added as an attachment

For store A, we have the following equation

y = 0.3x

On the graph of store B, we have the following points

(x, y) = (60, 24)

So, the equation is

y = 24/60x

Evaluate

y = 0.4x

The discounts for both stores are 0.3 and 0.4, respectively

0.4 is greater than 0.3

Hence, store B offers the best discount

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Answer:

b.

Step-by-step explanation:

Answer:

84 ft

Step-by-step explanation:

Since this is a right triangle we can use trig functions

sin theta = opp side / hypotenuse

sin 50 = y / 110  where y is the height above the ground

110 sin 50 = y

84.26488 = y

To the nearest foot

84 ft

Answer:

84 feet

Step-by-step explanation:

Since you are given an angle and the length of hypotenuse, you can use the trigonometric function sine.  

sinθ = opposite length / hypotenuse length

sin (50) = x / 110

sin(50) * 110 = x

~84 feet

The problem involves a line segment divided into two parts in a specific ratio. The ratio of the length of the lesser part to the length of the greater part is found to be (√2 - 1).

Let the length of the whole line segment be x, and let y be the length of the greater part. Then the length of the lesser part is (x - y).

According to the problem statement, the ratio of the lesser part to the greater part is the same as the ratio of the greater part to the whole. Mathematically, we can write this as:

(x - y)/y = y/x

Simplifying this equation, we get:

x^2 - y^2 = y^2

x^2 = 2y^2

Taking the square root of both sides, we get:

x = y√2

Therefore, the value of the ratio of the lesser part to the greater part is:

(x - y)/y = (√2 - 1)

So, the answer will be (√2 - 1).

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Answer:

3/10 of the total distance to her grandmother's house was traveled on Sunday

Step-by-step explanation:

Carly's family traveled distance of Saturday = \(\frac{3}{10}\)

Remaining distance =\(1-\frac{3}{10}=\frac{7}{10}\)

They traveled 3/7 of the remaining distance on Sunday.

So, Distance traveled on Sunday =\(\frac{3}{7}(\frac{7}{10})\)

Distance traveled on Sunday =\(\frac{3}{10}\)

Fraction of the total distance to her grandmother's house was traveled on Sunday =\(\frac{3}{10}\)

Hence 3/10 of the total distance to her grandmother's house was traveled on Sunday

The index form is simplified to -12x4y²4z

Index forms are described as mathematical forms of writing numbers or variables that are large or small in a more convenient way.

Other names for index forms are;

They are are numbers with power or exponents of variables or numbers.

From the information given, we have that;

( -3x³y²z)4​

To simply, expand the bracket, we have;

-12x4y²4z

Hence, the expression is -12x4y²4z

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a )The equation of the new parallel line is   x - y = 3

b ) The equation of the new perpendicular line is   x + y = -1

The given line passes through the points (0, 3 ) and (-3, 0).

Here,

\((x _{1}, y _{1}) = (-3, 0)\\\\(x _{2}, y _{2}) = (0, 3)\)

The slope of the line = m

\(m =\frac{y_{2}- y _{1}}{x _{2}- x_{1}} \\\\m = \frac{3-0}{0+3} \\\\m = \frac{3}{3} = 1\)

The slope of the given line is 1

a ) The new line passes through the point (1, -2) and is parallel to the given line .

           \(y- y_{1} = m (x- x_{1}) -- (1)\)

          y + 2 = 1 (x -1 )

          y  +2 = x - 1

           x - y -1 -2 = 0

           x - y - 3 =0

           x - y = 3

The equation of the new parallel line is   x - y = 3

b ) The new line passes through the point (1, -2) and is perpendicular to the given line .

           \(y- y_{1} = m (x- x_{1}) -- (1)\)

          y + 2 = -1 (x -1 )

          y  +2 = - x + 1

           x + y -1 +2 = 0

           x + y + 1 = 0

           x + y = -1

The equation of the new perpendicular line is   x + y = -1

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Answer:

A triangle has nagle 35, 120 degrees, and 35 degrees

Step-by-step explanation:

Answer:

The Triangle that has 115 32 33 or B

Step-by-step explanation:

115+32+33=180 All triangle angles measure 180.

Answer:

a. $49

b. $74.28

c. No

Step-by-step explanation:

The computation is shown below:

a. The store price is

= Purchase price + markup

= $35 + $35 × 40%

= $35 + $14

= $49

b. The price paid is

Since there is a markup of 40% and when it is added to 100% of cost so the selling price is 140% of the cost or 1.40 of the cost

Now the price paid is

$104 = 1.40 × cost

So, the cost is

= $104 ÷ 1.40

= $74.28

c. Now the markup is

= $100 - $75

= $25

The markup percentage is

= $25 ÷ $75

= 33.33%

No the store does not markup the price by 40%

The relation between mode, mean and median is:

mode=3median-2mean

Now, to find mean:

2mean=3median-mode

mean=7/2 = 3.5

Let we wish to evaluate the mean  μ of a population. In real practice we would typically take just one sample. Imagine still that we take sample after sample, all of the same size n, and compute the sample mean x¯ every time.

The sample mean x is a random variable: it differs from sample to sample in a way that cannot be predicted with sureness. We will write X¯ when the sample mean is idea of as a random variable and write x for the values that it takes.

The random variable X¯ has a mean, denoted  μX¯, and a standard deviation, denoted  σX¯. Here is an example with such a small population and small sample size that we can indeed write down every single sample.

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Answer:

6 days

Step-by-step explanation:

Relation :

6 tractors took 10 days. Now, we have 10 tractors. This means the number of tractors has increased by 10/6 = 5/3. Therefore, the number of days will become 3/5 of the original time.

Solving :

Answer:

1 feet

Step-by-step explanation:

15-14

Answer:

The answer is 58°.

Step-by-step explanation:

☆m<D and m<G are supplementary angles, meaning they equal 180°.

☆The equation: \(2w + 5w - 23 = 180\)

☆Let's solve it.

\(2w + 5w - 23 = 180 \\ 7w - 23 = 180 \\ \frac{ \: \: \: \: \: \: \: \: \: + 23 = + 23}{ \frac{7w}{7} = \frac{203}{7} } \\ w = 29\)

☆m<D and m<F is congruent, meaning they equal the same.

☆Solving for D is basically solving for F.

☆We found the value of w so let's plug it in into 2w.

\(m < d \\ 2w\\ 2(29) \\ 58\)

☆m<D equals 58, so m<F equals 58.

Answer:

if the ratio is 7/10 then do 10/400 and it will be 28 days

Step-by-step explanation:

Answer:

12 cans were damaged

EXPLANATION:

Cause When You Divide 4 To Divide 40, It Gives You 100% Calculation, And Subtract 30% from 100% it gives you 70%, which is 28 cans of food

(a) By plugging in different values for x1, we can plot the indifference curves passing through the given points (2, 2), (1, 2), and (4, 2).

(b) The shape of the indifference curves shows convexity.

(c) The property used to determine this is the non-satiation property of preferences.

(d) The Walrasian demand may not always be single-valued.

(e) Receiving the voucher makes the consumer better-off .

(f) The cash payment allows the consumer to maximize utility by making trade-offs

For 4x1 + x2 = x1 + 2x2, rearranging the equation gives x2 = 3x1, representing the linear part of the indifference curves.

For x1 + 2x2 = 4x1 + x2, rearranging the equation gives x2 = 3x1, representing the kink in the indifference curves.

By substituting different values for x1, we can plot the indifference curves. They will be upward sloping straight lines with a kink at x2 = 3x1.

(b) Properties of the preferences deduced from the shape of indifference curves and utility function:

Diminishing Marginal Rate of Substitution (MRS): Indifference curves are convex, indicating diminishing MRS. The consumer is willing to give up less of one good as they consume more of it, holding the other good constant.

Non-Satiation: Indifference curves slope upwards, showing that the consumer prefers more of both goods. They always prefer bundles with higher quantities.

Convex Preferences: The kink in the indifference curves indicates convexity, implying risk aversion. The consumer is willing to trade goods at different rates depending on the initial allocation.

(c) UMP does not have a solution when Pk = 0 and X -> R2+. This violates the assumption of finite resources and prices required for utility maximization. The property used is non-satiation, as a consumer will always choose an infinite quantity of goods when they are available at zero price.

(d) Walrasian demand depends on relative prices:

If p1 = p2 > 4, the maximizing bundle lies on the linear portion of indifference curves, where x2 = 3x1.

If 4 < p1 = p2 < 1/2, the maximizing bundle lies on the linear portion of indifference curves but at lower x1 and x2.

If p1 = p2 < 1/2, the maximizing bundle lies at the kink point where x1 = x2.

Walrasian demand may not be single-valued due to the shape of indifference curves and the kink point, allowing for multiple optimal solutions based on relative prices.

(e) Given p1 = p2 = 1 and w = $60, the initial budget set is x1 + x2 = 60. With a $10 voucher for good 1, the new budget set becomes x1 + x2 = 70. Since p1 = 1, the consumer spends the voucher on good 1, resulting in x1 = 20 and x2 = 40. Receiving the voucher improves the consumer's welfare by allowing more consumption of good 1 without reducing good 2.

(f) If given the choice between a $10 cash payment and a $10 voucher for good 1 only, the consumer would choose the cash payment. It provides flexibility to allocate the funds based on individual preferences. The answer remains the same even if the assistance were $30, as the cash payment still allows optimal allocation based on preferences. Cash payment offers greater utility-maximizing options compared to the voucher, which restricts choices.

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The height of the water increasing at the rate of   \(\frac{1}{12} \frac{m}{min}\) .

What is a function?

In mathematics, a function is a unique arrangement of the inputs (the domain) and their outputs (the codomain), where each input has exactly one output and the output can be linked to the input.

We need a function to connect the two variables when there are associated rates; in this instance, it is unmistakably volume and height. The equation is:

\(V=\) \(\pi r^{2}h\)

Although radius is mentioned in the formula, it is not a variable in this issue because it is constant. We might change the value in

V=\(\pi(6m)^{2}h\)

We must implicitly differentiate wrt (with respect to) time because the rate in this problem is tied to time

\(\frac{dV}{dt} =(36m^{2} )\)  \(\pi\frac{dh}{dt}\)

In the problem, we are given  \(3\frac{m^{2} }{min}\)   which is  \(\frac{dV}{dt}\) .So we substitute this in:

\(\frac{dh}{dt} =\frac{3m^{3}}{min(36m^{2} )\pi }\)

\(=\frac{3}{36\pi} \frac{m}{min}\)

\(=\frac{1}{12} \frac{m}{min}\)

Hence, the height of the water increasing at the rate of  \(\frac{1}{12} \frac{m}{min}\) .

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Answer:

1

Step-by-step explanation:

Add all values / the number of values

The coordinates of the point that corresponds to -π/3 on the unit circle are (x, y) = (1/2, √3/2)

A unit circle is a circle in which the value of the radius is equal to 1 unit.

The coordinates of a point with angle Ф on a unit circle are given by

To find the coordinates of the point that corresponds to -π/3 on the unit circle, since we have the coordinates of a point on a unit circle as

substituting Ф = -π/3 into both equations, we have that the x - coordinate is

Also, we have that the y - coordinate is

So, the coordinates of the point are (x, y) = (1/2, √3/2)

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Ii is the estimated value of the integral at the ith iteration, and I is the overall estimated value of the integral. We can stop the algorithm when the standard deviation σ is less than 0.01.

The standard deviation (SD, also written as the Greek symbol sigma or the Latin letter s) is a statistic that is used to express how much a group of data values vary from one another.

To estimate the integral I = ∫[1 to 0] \(e^{(x^2)\) dx using Monte Carlo simulation, we can use the following algorithm:

To stop when the standard deviation of the estimator is less than 0.01, we can keep track of the estimated value of the integral and the number of points generated at each iteration of the algorithm. We can compute the standard deviation of the estimator using the formula:

σ = √((1/N) * Σ[i=1 to N] (Ii - I)²)

where N is the number of iterations, Ii is the estimated value of the integral at the ith iteration, and I is the overall estimated value of the integral. We can stop the algorithm when the standard deviation σ is less than 0.01.

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