Question 3
On problem #10, which variable will be the easiest to isolate in order to solve the system using
substitution?
A: x, in the top equation
B: y. in the top equation
C: x, in the bottom equation
D: y, in the bottom equation

The difference between groups and the sample size makes the results of a study statistically significant.

Statistical significance is a measure of the likelihood that the results of a study are not due to chance. In order for a result to be statistically significant, it must meet two criteria:

The difference between groups must be large enough to be unlikely to occur by chance. This is typically assessed using a statistical test such as a t-test or an ANOVA.

The result of the test is expressed as a p-value, which represents the probability of obtaining the observed results if there were no true difference between groups. A p-value of less than 0.05 (or 5%) is generally considered to be statistically significant.

The sample size must be large enough to reduce the possibility of sampling error. A larger sample size generally increases the power of a study, making it more likely to detect a true effect.

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The percentage of people who filed their taxes during the week of tax day is 10%

I can estimate how many people filed their taxes during the week of April 15th using a percentage of 100 is a/b * 100.

A percentage is a portion of a sum divided into 100 equal parts.

Calculate (Number of persons who submitted their taxes during the week of April 15th / total people who filed their taxes that year) times 100 to get the percentage of people who filed during that week.

Let :

a represents the total number of taxpayers during the week of April 15th.

b represents the total number of taxpayers for that year.

The original equation is reduced to

a/b× 100

As an illustration, 100 individuals submitted their taxes the week of April 15th and

Let's say that year, 1000 persons filed their taxes.

= 100/1000 = 10%

Thus, 10% of Americans submitted their taxes during the week of April 15th, or 100 out of 1,000.

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The smaller square has sides that are 10 cm long. The larger square has sides that are 50% longer, or 15 cm long. The scale factor from the smaller to larger square is 1.5, which is the ratio of the larger square's side length to the smaller square's side length.

The ratio of the areas of the smaller to larger square is (10 cm)^2/(15 cm)^2 = 0.44. This means that the larger square has an area that is 2.27 times greater than the smaller square. The scale factor and ratio of areas are important concepts in geometry and can be used to find the relationship between the sizes of different shapes.

Let's solve problem step by step.

1. One square has sides 10 cm long.

2. A second square has sides 50% longer. To find the length of the larger square's sides, multiply the original length by 1.5 (since it's 50% longer): 10 cm * 1.5 = 15 cm.

3. The scale factor from the smaller to the larger square, written as a decimal, is the ratio of their sides: 15 cm / 10 cm = 1.5.

4. To find the ratio of the areas, square the scale factor: (1.5)^2 = 2.25. So, the ratio of the areas of the smaller to the larger square, written as a decimal, is 1/2.25 ≈ 0.44.

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The 90% confidence, 95% confidence and 99% confidence have a z critical value of 1.65, 1.96 and 2.58 respectively.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

From the normal distribution table:

The z critical value for 90% confidence, 95% confidence and 99% confidence is 1.65, 1.96 and 2.58 respectively.

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Answer:

90% confidence:

1.645

95% confidence:

1.960

99% confidence:

2.576

Step-by-step explanation:

EDGE2022

Answer:

<X = 36

<Y = 72

<W = 108

<Z = 144

Step-by-step explanation:

Since this shape is a quadrilateral, all angles add up to 360

x + 3x + 4x + 2x = 360

10x = 360

x = 36

<X: x

36

<W: 3x

3(36) = 108

<Y: 2x

2(36) = 72

<Z: 4x

4(36) = 144

Answer:

The slope of the line passing through the points (1, -1) and (4, 8) is 3.

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the following formula:

\(slope = (y2 - y1) / (x2 - x1)\)

Here, the given points are (1, -1) and (4, 8). So,

\(slope = (8 - (-1)) / (4 - 1) = 9 / 3 = 3\)

Therefore, the slope of the line passing through the points (1, -1) and (4, 8) is 3.

The confidence level for the given interval of 13.45 to 14.15 days is 95%, which means that we can be 95% confident that the true mean survival time falls within this range.

Based on the given information, we know that a random sample of 25 rats exposed to 10Sv of radiation has a mean lifetime of x=13.8 days. We also know that the LD100 is 14 days, and that the lifetimes for this level of exposure follow a normal distribution with unknown mean and standard deviation 0.75.

The report states that a confidence interval for the true mean survival time extends from 13.45 to 14.15 days, which means that we can be 95% confident that the true mean survival time falls within this range. This is because the confidence level for this interval is 95%.

To calculate this, we can use the formula:

Confidence level = 1 - alpha

where alpha is the significance level, which is typically set to 0.05 for a 95% confidence level. This means that there is a 5% chance that the true mean survival time is outside the given interval.

In conclusion, the confidence level for the given interval of 13.45 to 14.15 days is 95%, which means that we can be 95% confident that the true mean survival time falls within this range.

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Answer:

x^2 +14x+49

Step-by-step explanation:

Area = length * width

        = ( x+7) * ( x+7)

       FOIL

    first: x^2

    outer: 7x

   inner: 7x

    last: 7*7 = 49

Add them together

x^2 +7x+7x + 49

Combine like terms

x^2 +14x+49

Step-by-step explanation:

on the first step, where the student subtracted the two equations, when they subtracted 3y - y, they got 4y, but they were supposed to get 2y.

If they did it right it would look like this

 2x + 3y = 8

-(2x  +  y = 16)

0x + 2y = -8

y = -4

2x - 4 = 16

2x = 20

x = 10

Solution (10,-4)

You must find the error, I will correct their work.

This is a system of linear equations. To solve it, you can use the substitution method. First, you can solve the first equation for x and substitute it into the second equation:

2x + 3y = 8

2x = 8 - 3y

x = (8 - 3y) / 2

2((8 - 3y) / 2) + y = 16

8 - 3y + 2y = 16

5y = 8

y = 8 / 5

Then, you can substitute y into the first equation:

2x + 3(8 / 5) = 8

2x = 8 - 24 / 5

2x = 16 / 5

x = 16 / 10

Therefore, the solution to the system of linear equations is x = 16/10 and y = 8/5.

Here is a sample correction to this (paraphrase):

When you tried to solve the system of linear equations, you likely made a mistake when solving one of the equations for a variable or when substituting the values into the equations. To ensure that you get the correct solution, you should double-check your work and make sure that the values you get satisfy the original equations.

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Answer:

the given expression is equivalent to

Step-by-step explanation:

\(2(x - 3) {}^{2} \\ 2( {x}^{2} - 2.x.3 + {3}^{2} ) \\ using \: formula \: (x - y) {}^{2} = x {}^{2} - 2.x.y + y {}^{2} \\ 2(x {}^{2} - 6x + 3) \\ 2 {x}^{2} - 12x + 6\)

Answer:

690 sq in

Step-by-step explanation:

SA = LA + 2B     where LA is the lateral area and B is the area of the base

The triangular base has an area of

B = 1/2bh 1/2(5)(12) = 30

LA = ph  where p is the perimeter of the base and h is the height of the prism

LA = (12 + 5 + 13)(21) = 30(21) = 630

SA = 630 + 2(30) = 630 + 60 = 690 sq in

The optimal dimensions for the garden to maximize the area are 30 feet by 18 feet, with fencing costing $2 per foot on three sides and $3 per foot on the fourth side.

To determine these dimensions, we start by setting up the equation based on the given information. The cost of fencing for three sides is equal to 2 times the sum of the length and width of the garden, while the cost of fencing for the fourth side is 3 times the length of the garden. Since the total cost of fencing should not exceed $120, we can set up the equation:

2(l + w) + 3l = 120

Simplifying this equation, we get:

5l + 2w = 120

Next, we aim to maximize the area of the garden, which is given by the formula A = lw. We can solve for one variable in terms of the other using the equation obtained above. Substituting the value of w in terms of l into the area equation, we have:

A = (120 - 2w)/5 * w

A = (120w - 2w^2)/5

To find the maximum area, we can take the derivative of the area equation with respect to w and set it equal to zero. Solving this equation, we find w = 30. Substituting the value back into the equation, we get l = 18.

Therefore, the optimal dimensions for the garden are 30 feet by 18 feet to maximize the area, with the given cost of fencing.

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After solving, the height of the cylinder is 6 meters.

The surface area of a cylinder is 24π m².

The distance around the base of the cylinder is 3π meter.

The diameter of a base of the cylinder is 4 meter.

Now the radius of the cylinder = diameter/2

The radius of the cylinder = 4/2

The radius of the cylinder = 2 meter.

The formula of surface area of cylinder:

S = 2πrh

From the question:

2πrh = 24π

Now putting the value of r

2π × 2 × h = 24π

4πh = 24π

Divide by 4π on both side, we get

h = 6

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The complete question is:

The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meter and the diameter of a base of the cylinder is 4 meter. What is the height of the cylinder? Enter your answer, in a simplified fraction, in the box.

Answer:

E

Step-by-step explanation:

28=28

14*2=28

4*28

they are both equal

The expression for the number of games Holly now has in standard form is 37 - 6x, where x represents the number of games she gave away.

The expression for the number of games Holly has after starting with 3x3 games, buying 7x4 games, giving away x games, selling 5x games, and donating 9 games can be written in standard form.

Let's break down the given information step by step:

Holly starts with 3x3 games, meaning she has a total of 3 * 3 = 9 games.

She buys another 7x4 games, which adds 7 * 4 = 28 games to her collection.

She gives away x games, resulting in a decrease in the total number of games by x.

She sells 5x games, further decreasing her collection by 5x.

Finally, she donates another 9 games, resulting in a decrease of 9 games.

To express the total number of games Holly has after all these actions in standard form, we can add or subtract the respective quantities:

Total number of games = (9 + 28) - x - 5x - 9

Simplifying the expression, we have:

Total number of games = 37 - 6x

Therefore, the expression for the number of games Holly now has in standard form is 37 - 6x, where x represents the number of games she gave away.

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The appropriate alternative hypothesis is the opposite of null hypothesis that there is a difference in mean SSHA scores between men and women.

The alternative hypothesis is the opposite of the null hypothesis, which is typically stated as there being no difference between the two groups. In this example, the null hypothesis is that there is no difference in mean SSHA scores between men and women. The alternative hypothesis is then that there is a difference in mean SSHA scores between men and women. This can be stated as "There is a difference in mean SSHA scores between men and women". This is the appropriate alternative hypothesis for this test of significance.

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The amount of fabric that is needed for the tent is 18350 in² (optionC)

A prism is a solid shape that is bound on all its sides by plane faces. The surface area of a prism is expressed as ;

SA = 2B +pH

where B is the base area , p is the perimeter of the base and H is the height of the prism.

Base area =1/2bh

= 1/2 × 50× 70

= 25 × 70

= 1750in²

Perimeter of the base = 74+74+50

= 198 in

height = 75in

Therefore SA = 2×1750 +198 × 75

= 3500 + 14850

= 18350 in²

therefore the amount of fabric that will be needed nis 18350 in²

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Answer:

Option (3)

Step-by-step explanation:

Given function is,

f(x) = x⁴ + x³ - 2x²

     = x²(x² + x - 2)

     = x²(x² + 2x - x - 2)

     = x²[x(x + 2) - 1(x + 2)]

     = x²(x + 2)(x - 1)

So the factored form of the polynomial function is,

f(x) = x²(x + 2)(x - 1)

For x - intercepts,

F(x) = x²(x + 2)(x - 1) = 0

x = -2, 1

This function has even multiplicity = 2 at x = 0.

Therefore, graph of the function will touch the x-axis at x = 0

And at other roots x = -2, 1 has odd multiplicity = 1, so the graph will cross the x-axis.

Option (3) will be the correct option.

The volume of grain in the silo when it is 60% filled is approximately 1178.1 cubic yards.

A closed surface or object's volume is determined by its three dimensions and is represented mathematically.

The following formula determines a cylinder's volume:

V = πr²h

where r is the radius of the cylinder and h is the height.

The diameter of the silo is 10 yards, so the radius is 5 yards. The height of the silo is 25 yards.

To find the volume of the silo, we need to first calculate its total capacity, which is the volume of a completely filled cylinder:

V_total = πr²h

V_total = π(5²)(25)

V_total = 625π

To find the volume of grain in the silo when it is 60% filled, we need to find 60% of the total capacity:

V_grain = 0.6V_total

V_grain = 0.6(625π)

V_grain ≈ 1178.1 cubic yards (rounded to the nearest tenth)

Therefore, the volume of grain in the silo when it is 60% filled is approximately 1178.1 cubic yards.

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Answer:

20°

Step-by-step explanation:

A right triangle equals 90°.

So, you can subtract the angle that you already know.

90°

-50°

-----------

40°

Since the other two angles are congruent you can divide 40° into two parts.

40°

÷2

-----------

20°

So, each unknown measurement of the triangle is 20°.

The average temperature last Sunday is 1.08T or (1 + 8/100)T.

Temperature simply means the hotness and coldness of a body.

In this case, last Sunday, the average temperature was 8 percent higher than the average temperature two Sundays ago.

This will be expressed as:

= T + (8% × T)

= T + (0.08 × T)

= T + 0.08T

= 1.08T

The temperature is 1.08T.

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Answer:

14.90 $ 527.86- 349.11 = 178.75 divided by 12 pta members is 14.89 rounded would be 14.90 the answer depends if u want to round it

Step-by-step explanation:

sub to imaginefn in utube

Answer: 4.15$

Step-by-step explanation: I think im correct.

Subtract the flat rate from the total, then divide by price per mile for total miles:

40.03 - 6.75 = 33.28

33.28/3.20 = 10.4 miles.

Lupita drove 10.4 Miles for her trip.

Explanation:

40.03 - 6.75 = 33.28 dollars left

33.28 ÷ 3.20 = 10.4 Miles

Answer:

The value of (y+6) is greater in 4(y+6).

Step-by-step explanation:

This is because the higher number of y's there are, the higher number you have to divide by, therefore in the end the number is smaller.

Answer:

4π (approx. 12.57) inches

Step-by-step explanation:

Equation to find circumference of a circle is πd, where d is the diameter of the circle.

d = 2r (radius)

d = 4

Circumference = πd

Circumference = 4π (inches)

Circumference ≈ 12.57 (inches)

The general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

We are given the differential equation: d²y/dx - 36y = cosh(3x).

In this case, the homogeneous equation is d²y/dx - 36y = 0.

The characteristic equation associated with the homogeneous equation is obtained by replacing the derivatives with their corresponding algebraic expressions. In our case, we have r² - 36 = 0. Solving this quadratic equation, we find the roots to be r = ±6.

Since the roots are distinct and real, the general solution for the homogeneous equation is given by:

\(y_h = C_1e^{6x} + C_2e^{-6x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

The term cosh(3x) can be written as a linear combination of exponential functions using the identities:

\(cosh(ax) = (e^{ax} + e^{-ax})/2, \\\\sinh(ax) = (e^{ax} - e^{-ax})/2.\)

Therefore, \(cosh(3x) = (e^{3x} + e^{-3x})/2.\)

Now, we assume the particular solution has the form:

\(y_p = A_1e^{3x} + A_2e^{-3x}\)

where A₁ and A₂ are undetermined coefficients.

Substituting these derivatives into the original differential equation, we get:

\((9A_1e^{3x} + 9A_2e^{-3x}) - 36(A_1e^{3x} + A_2e^{-3x}) = (e^{3x} + e^{-3x})/2.\)

To satisfy this equation, the coefficients of the exponential terms on both sides must be equal. Therefore, we have the following system of equations:

9A₁ - 36A₁ = 1/2,

9A₂ - 36A₂ = 1/2.

Solving these equations, we find A₁ = -1/70 and A₂ = -1/70.

Thus, the particular solution is:

\(y_p = (-1/70)e^{3x} + (-1/70)e^{-3x}\)

Finally, the general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

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