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sample size of 6945 parents.

To determine the sample size, we can use the formula:

n = ((z*σ)/E)^2

where:

z = the z-score associated with the confidence level (98% confidence level corresponds to a z-score of 2.33)

σ = the population standard deviation (given as 35.8 dollars)

E = the margin of error (10 dollars)

Substituting the given values, we get:

n = ((2.33*35.8)/10)^2

n = (83.414)^2

n = 6944.4

Rounding up to the nearest A, we get a sample size of 6945 parents.

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Victor will pay $13,500 in interest over the 36-month term of his line of credit.

To calculate the interest that Victor will pay on his 36-month line of credit for $15,000 at an interest rate of 2.5%, we can use the formula for simple interest:

I = P × r × t

Where I is the interest, P is the principal (the amount borrowed), r is the interest rate per period, and t is the number of periods.

Here, P = $15,000, r = 0.025 (since the interest rate is 2.5%), and t = 36 months.

I = P × r × t

Substituting values into the formula, we get:

I = 15,000 × 0.025 × 36

I = $13,500

Therefore, he will pay $13,500 in interest over the 36-month term of his line of credit.

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Answer:

$53.46

Step-by-step explanation:

The answer is 53.46 because 2.97 multiplied by 18 is 53.46

the volume of the solid below the paraboloid z = 48 - \(3x^2 - 3y^2\) in polar coordinates is 640π cubic units.

To find the volume of the solid below the paraboloid given by the equation z = 48 - \(3x^2 - 3y^2\) using polar coordinates, we need to express the equation in terms of polar variables.

In polar coordinates, we have x = rcosθ and y = rsinθ, where r represents the distance from the origin and θ is the angle with the positive x-axis.

Substituting these values into the equation of the paraboloid, we get:

z = 48 - 3(rcosθ\()^2\) - 3(rsinθ\()^2\)

z = 48 - 3\(r^2(cos^2\)θ + \(sin^2\)θ)

z = 48 - \(3r^2\)

Now, the volume of the solid can be expressed as a triple integral in polar coordinates:

V = ∬D (48 - 3\(r^2\)) r dr dθ

The region D in the xy-plane corresponds to the projection of the solid. Since the solid extends infinitely in the z-direction, the limits of integration for r and θ will be the same as the limits for the entire xy-plane.

Assuming we integrate over the entire xy-plane, the limits of integration will be:

0 ≤ r < ∞

0 ≤ θ < 2π

Now, we can evaluate the triple integral:

V = ∫₀²π ∫₀ᴿ (48 - 3r^2\(r^2\)) r dr dθ

To find the value of R, we need to determine the radius at which the paraboloid intersects the xy-plane. In this case, when z = 0:

0 = 48 - 3r^2

3r^2 = 48

r^2 = 16

r = 4

Therefore, the limits of integration become:

0 ≤ r ≤ 4

0 ≤ θ < 2π

Now, we can calculate the volume:

V = ∫₀²π ∫₀⁴ (48 - 3\(r^2)\) r dr dθ

Integrating with respect to r first:

V = ∫₀²π [(24\(r^2 - r^4/2\))] from 0 to 4 dθ

V = ∫₀²π [(\(24(4)^2 - (4)^4/2\))] dθ

V = ∫₀²π [(384 - 64)] dθ

V = ∫₀²π (320) dθ

V = 320∫₀²π dθ

V = 320(θ) from 0 to 2π

V = 320(2π - 0)

V = 640π

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1)The slope of the line is C) 13. 2)It would be inefficient since it is not the most optimal use of resources.the correct option is C. 3)The equilibrium price and quantity are D) $25 and 10 dozens of roses per day, respectively.

1) Y = 13X + 38, where Y is a function of X.

The slope of the line is 13.

Therefore, the correct option is C.

2) Kolin catches 25 fish and gathers 70 fruits. If we consider the combination, then it would be inefficient since it is not the most optimal use of resources.

Therefore, the correct option is C.

3) Using the given figure, we can see that the point where the demand and supply curves intersect is the equilibrium point. At this point, the equilibrium price is $25 and the equilibrium quantity is 10 dozens of roses per day.

Therefore, the correct option is D. The equilibrium price and quantity are $25 and 10 dozens of roses per day, respectively.

Note that this is the point of intersection between the demand and supply curves, which represents the market equilibrium.

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Answer:

2x + 20

Step-by-step explanation:

\(12 + 4x -2x + 8\\\rule{150}{0.5}\\4x - 2x + 12 + 8\\\\\\\rightarrow\text{4x and -2x are like terms. 12 and 8 are also like terms.}\\\\\\\boxed{2x + 20}\)

Hope this helps.

Answer:

Dot number 2. Makayla invests her money 2 years longer.

Step-by-step explanation:

Calvin 400$ with 5% interest compounded monthly will get you to 666.0294029241$ after 13 months or 1 year and 1 month

Makayla 300$ with 6% interest quarterly

1st year 378.743088$(4 quarters)

2nd year 478.1544223592$(+4 quarters)

3rd year 603.6589415506$(+4 quarters)

3rd year and 1 quarter 639.8784780436$

Answer:

So the second option is the answer: Makayla invests her money 2 years longer.

Step-by-step explanation:

Formula for compound interest: \(A=P(1+\frac{r}{n})^{nt}\)

Calvin:

\(A=658.80\)

\(P=400\)

\(r=0.05\)

\(n=12\)

\(t=?\)

Makayla:

\(A=613.04\)

\(P=300\)

\(r=0.06\)

\(n=4\)

\(t=?\)

Lets solve for \(t\).

1)  Divide both sides of the equation by \(P\).

\(\frac{A}{P} =(1+\frac{r}{n})^{nt}\)

2)  Take the natural log of both sides.

\(ln(\frac{A}{P}) =ln((1+\frac{r}{n})^{nt})\)

3)  Rewrite the right side of the equation using properties of exponents.

\(ln(\frac{A}{P}) =nt*ln(1+\frac{r}{n})\)

4)  Divide each side of the equation by \(n*ln(1+\frac{r}{n})\)

\(\frac{nt*ln(1+\frac{r}n)}{n*ln(1+\frac{r}n)}=\frac{ln(\frac{A}{P})}{n*ln(1+\frac{r}n)}\)

5)  Cancel the common factor \(n\) on the left side of the equation.

\(\frac{t*ln(1+\frac{r}n)}{ln(1+\frac{r}n)}=\frac{ln(\frac{A}{P})}{n*ln(1+\frac{r}n)}\)

6)  Cancel the common factor of \(ln(1+\frac{r}{n})\).

\(t=\frac{ln(\frac{A}{P)}}{n*ln(1+\frac{r}{n})}\)

Now we have an equation for \(t\) that we can use to answer your question.

For Calvin:

\(t=\frac{ln(\frac{658.80}{400)}}{12*ln(1+\frac{0.05}{12})}\)

\(t=10\)

For Makayla:

\(t=\frac{ln(\frac{613.04}{300)}}{3*ln(1+\frac{0.06}{3})}\)

\(t=12\)

So the second option is the answer: Makayla invests her money 2 years longer.

Note: This question took me 2 minutes to answer but typing it took 30. lol

The answer to this question is option b) -.80. The correlation coefficient (r) ranges from -1 to +1. The closer the value of r is to -1 or +1, the stronger the correlation between the two variables. A value of 0 indicates no correlation.

A correlation coefficient of 0.40 indicates a moderate positive correlation. Therefore, to find a stronger correlation than 0.40, we need to look for values of r closer to +1. Option b) -.80 is the only value listed that is closer to -1 than 0.40 is to +1, indicating a strong negative correlation.

t's important to note that correlation does not imply causation. A strong correlation between two variables does not necessarily mean that one causes the other. It is possible for two variables to be correlated due to a third variable that affects both. Additionally, correlation only measures linear relationships between variables and does not account for non-linear relationships.

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Answer:

\( - 10(n + 6) \\ - 10n + 60 \: \: \: answer\)

Step-by-step explanation:

please mark me brainliest

Answer:

4/9

Step-by-step explanation:

Answer:

4 9/10 or 49/10

Step-by-step explanation:

49 over 10

49

10

=4 and 9 over 104

9

10

=4.9

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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Answer:

\(y=x-1\)

Step-by-step explanation:

The line of symmetry of an isosceles triangle is perpendicular to its base.

Given vertices of the isosceles triangle:

By sketching the triangle with the given points, we can see that AB is its base.  (See attached graph).

To find the equation for the line of symmetry, first find the slope of the line AB.  To do this, use the coordinates of points A and B and the slope formula.

Define the points:

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-2}{3-7}=-1\)

As the line of symmetry is perpendicular to line AB, its slope is the negative reciprocal of the slope of line AB.

Therefore, the slope of the line of symmetry = 1.

The line of symmetry will pass through point C (4, 3).

Therefore, substitute the found slope and the coordinates of point C into the point-slope formula:

\(\implies y-y_1=m(x-x_1)\)

\(\implies y-3=1(x-4)\)

\(\implies y-3=x-4\)

\(\implies y=x-1\)

Therefore, the equation of the given isosceles triangle's axis of symmetry is:

\(y = x - 1\)

If we graph the points

then we will get AC=CB

That means C is the point from where the axis of symmetry passes

Foot of perpendicular is midpoint of AB

Midpoint of AB

Find equation of C and foot of perpendicular

Slope

Equation

Answer:

Yes

no

no

yes

Step-by-step explanation:

I hope it's serving

:v

\([Hello,BrainlyUser]\)

Answer:

$20

Step-by-step explanation:

20% More = Markup

20% = .20

$25 * .20 = 5 ( Markup Price)

$25 - 5 = $20

Hence, last month the cost of the cat was $20.

[CloudBreeze]

The sum to infinity of the function is -3/2

from the question, we have the following parameters that can be used in our computation:

\(\sum\limits^{\infty}_{1} {3^n} \,\)

From the above sequence, we have

First term, a = 3

Common ratio, r = 3

The sum to infinity of the function is calculated as

Sum = a/(1 - r)

So, we have

Sum = 3/(1 - 3)

Evaluate

Sum = -3/2

Hence, the sum is -3/2

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Question

Calculate the sum to infinity of the function for

\(\sum\limits^{\infty}_{1} {3^n} \,\)

Therefore ,There is sufficient evidence to support the claim that the results contradict Mendel's theory.

Mendelian inheritance is the term used to describe certain patterns of how features are passed down from parents to offspring. Gregor Mendel, an Austrian monk, developed these broad patterns through his countless pea plant studies in the 19th century.

Here,

n=307+77+98+18=500

k=4

O1=307

O2=77

03=98

04=18

\(\alpha =0.05\)

The null hypothesis claims that the population proportions are the same as those indicated (9:3:3:1).

\(H_{0}\): P1=9/16, P2=3/16,P3=3/16 & P4=1/16

In contrast to the null hypothesis, the alternative hypothesis states:

\(H_{\alpha }\): At least one of the peas is different.

E1=nP1=4297*9/16=281.25

E2=nP2=4297*3/16=93.75

E3=nP3=4297*3/16=93.75

E4=nP4=4297*1/16=31.25

The  subtotals are the squared differences between the observed and expected frequencies, divided by the expected frequency.

Next, the sum of the  subtotals represents the test-value: statistic's

\(x^{2} =\)∑\(\frac{O-E}E^{2}\)=\(\frac{(307-281.25)^{2}}{281.25} + \frac{(77-93.75)^{2}}{93.75} + \frac{(98-93.75)^{2}}{93.75} + \frac{(18-31.25)^{2}}{31,25}\)

=11.16

The number of categories has shrunk by 1 to reflect the degrees of freedom:

The P-value is the likelihood of getting the test statistic's value or a more extreme result. The number (or range) in the column heading of the chi-square distribution table in the appendix that contains the \(x^{2}\) value in the row df=k-1=4-1=3

0.01<P<0.025

If the P-value is less than or equal to the significance level, then the null hypothesis is rejected:

P<0.05=>Reject \(H_{0}\)

Therefore, The claim that the outcomes defy Mendel's theory is sufficiently supported by the available data.

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​

Answer:

B.

Step-by-step explanation:

Irrational as π is irrational.

Answer:

50 km per hour

Step-by-step explanation:

distance = 100km

time= 2hrs

average speed 100/2

50 km per hour

Answer:

7

Step-by-step explanation:

The middle 2 numbers are 6 and 8. Add them both up and divide them by 2. Gets you 7.

Answer:

B

Step-by-s??????????tep explanation:

By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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The y-intercept of the line is (0 -6). The given function has no vertical and horizontal asymptotes

A linear equation is an equation that has a leading degree of 1. Given the equation

g(x) = 4x - 6

The y-intercept occurs at a point where x = 0

g(0) = 4(0) - 6

g(0) = -6

Hence the y-intercept of the line is (0 -6)

The given function has no vertical and horizontal asymptotes

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The solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

To simplify the equation 3(x-6) - 1/2(8x+10) = -25, we can start by applying the distributive property and then combining like terms.

First, let's distribute the 3 and the -1/2 to the terms inside the parentheses:

3(x-6) - 1/2(8x+10) = 3x - 18 - (4x + 5)

Now, let's simplify further by combining like terms:

3x - 18 - 4x - 5 = -x - 23

So, the simplified equation is -x - 23 = -25.

To solve for x, we can isolate the variable by adding 23 to both sides of the equation:

-x - 23 + 23 = -25 + 23

This simplifies to:

-x = -2

Finally, we can solve for x by multiplying both sides of the equation by -1:

(-1)(-x) = (-1)(-2)

This gives us:

x = 2

Therefore, the solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

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The estimated standard error for the sample mean with a mean of m = 40 and a standard deviation of s = 10 is 2.

To find the estimated standard error for a sample with n = 25 scores, a mean of m = 40, and a standard deviation of s = 10.

Step 1: Identify the sample size (n), mean (m), and standard deviation (s).
n = 25
m = 40
s = 10

Step 2: Calculate the standard error using the formula: standard error (SE) = s / √n
SE = 10 / √25

Step 3: Simplify the equation.
SE = 10 / 5

Step 4: Calculate the standard error.
SE = 2

The estimated standard error for the sample mean is 2.

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They can be parallel (0 common points), can intersect (1 common point) or overlap (infinitely many common points).

Answer:

Check the "explanation" section

Step-by-step explanation:

These are the 3 ways that two lines can relate to one another:

Parallel means they never intersect. They are at the same distance from one another so they never intercept each other.

The intersection of these two lines is at a right angle of 90°.

One line can be two lines. It's just that we can't see the second one since they combined to form one line. And they have an infinite number of common points and x- (or y-) intercepts.

Therefore, these are the ways.

Answer:

14-23

Step-by-step explanation:

12

Answer:

x = 60

Step-by-step explanation:

X/2-5=25

Add 5 to each side

X/2-5+5=25+5

x/2 = 30

Multiply each side by 2

x/2*2 = 30*2

x = 60

Answer:

60

Step-by-step explanation:

x/2 - 5 =25 /×2

x - 10 =50

x=50 +10

x=60

To summarize, the equivalent expression to the cube root of 343 multiplied by 9 to the power of y and 12 to the power of z and 6 is 7 x 9y x 12z x 2 x 3.

To find the equivalent expression to the cube root of 343 multiplied by 9 to the power of y and 12 to the power of z and 6, we can simplify the expression as follows:

1. The cube root of 343 can be simplified to 7 because 7 x 7 x 7 equals 343.

2. We can rewrite 9 to the power of y as 9y.

3. We can rewrite 12 to the power of z as 12z.

4. We can rewrite 6 as 2 x 3.

Putting it all together, the equivalent expression is 7 x 9y x 12z x 2 x 3.

To summarize, the equivalent expression to the cube root of 343 multiplied by 9 to the power of y and 12 to the power of z and 6 is 7 x 9y x 12z x 2 x 3.

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