Find an equivalent ratio in simplest terms:
66 : 42
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Math

Answer:

13, 16

Step-by-step explanation:

We need to find the common difference.

4 - 1 = 3

7 - 4 = 3

10 - 7 = 3

Find the next two terms.

10 + 3 = 13

13 + 3 = 16

Best of Luck!

Answer:

3

Step-by-step explanation:

6-3=3

9-6=3

13-16=3

333

Answer:  see proof below

Step-by-step explanation:

Since (a, b) is equidistant from (-a, 2) and (2, -b), then it is the midpoint of the those two points. Use Midpoint formula to find (a, b).

[tex]M_x=\dfrac{x_1+x_2}{2}\qquad \qquad \qquad M_y=\dfrac{y_1+y_2}{2}\\\\\\a=\dfrac{-a+2}{2}\qquad \qquad \qquad \quad b=\dfrac{2-b}{2}\\\\\\2a=-a+2\qquad \qquad \qquad \quad 2b=2-b\\\\\\3a=2\qquad \qquad \qquad \qquad \qquad 3b=2\\\\\\a=\dfrac{2}{3}\qquad \qquad \qquad \qquad \qquad b=\dfrac{2}{3}[/tex]

3(a + b) - 4 = 0

[tex]3\bigg(\dfrac{2}{3}+\dfrac{2}{3}\bigg)-4=0\\\\\\3\bigg(\dfrac{4}{3}\bigg)-4=0\\\\\\4-4=0\\\\0=0\qquad \text{TRUE!}[/tex]

Notice that I changed the equation to "negative 4" because the equation you provided did not make a true statement.

Answer:

C

Step-by-step explanation:

NO CAP

Answer: The answer would be C

Step-by-step explanation:

When Jevonte pulls the ladder 3 feet farther from the house, the ladder will reach approximately 10.15 feet up the Side of the house.

To solve this problem, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, the ladder, the distance from the house to the ladder, and the height along the side of the house form a right triangle.

Let's denote the distance Jevonte pulls the ladder as d. We want to find the new height, h, along the side of the house when the ladder is pulled 3 feet farther from the house.

According to the Pythagorean theorem, we have:

h^2 + (48 + d)^2 = 52^2

Simplifying the equation, we get:

h^2 + (48 + d)^2 = 2704

Expanding and rearranging the equation, we have:

h^2 + (d^2 + 96d + 48^2) = 2704

h^2 + d^2 + 96d + 2304 = 2704

h^2 + d^2 + 96d = 2704 - 2304

h^2 + d^2 + 96d = 400

Now we substitute the known values into the equation. We have d = 3 (since Jevonte pulls the ladder 3 feet farther) and h as the unknown.

h^2 + 3^2 + 96(3) = 400

h^2 + 9 + 288 = 400

h^2 + 297 = 400

h^2 = 400 - 297

h^2 = 103

Taking the square root of both sides, we get:

h = √103

Rounding to the nearest tenth of a foot, h ≈ 10.15 feet.

Therefore, when Jevonte pulls the ladder 3 feet farther from the house, the ladder will reach approximately 10.15 feet up the side of the house.

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Step-by-step explanation:

2x +31 = 9

2x = - 22

x = - 11

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Answer:

The slope is 3/2

Step-by-step explanation:

Rise over run- up 3 and to the left 2.

Answer:

2 to the left and 3 down

Step-by-step explanation:

The population mean number of pounds per person per week is estimated to be between 35.764 pounds and 38.036 pounds.

a. To compute the confidence interval, we will use a t-distribution.

b. With 95% confidence, the population mean number of pounds per person per week is between **35.764 pounds** and **38.036 pounds**.

To calculate the confidence interval, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / sqrt(Sample Size))

Given that we have a sample size of 241 residents, a sample mean of 37.4 pounds, and a standard deviation of 8.5 pounds, we need to determine the critical value associated with a 95% confidence level using the t-distribution. The degrees of freedom for this calculation are equal to the sample size minus 1, which is 240.

Looking up the critical value for a 95% confidence level and 240 degrees of freedom in the t-distribution table or using a statistical calculator, we find the critical value to be approximately 1.97.

Plugging in the values into the formula, we have:

Confidence Interval = 37.4 ± (1.97 * (8.5 / sqrt(241)))

Calculating this expression, we find:

Confidence Interval ≈ 37.4 ± 1.122

Lower Limit = 37.4 - 1.122 ≈ 36.278 pounds

Upper Limit = 37.4 + 1.122 ≈ 38.522 pounds

Therefore, with 95% confidence, the population mean number of pounds per person per week is estimated to be between 35.764 pounds and 38.036 pounds.

c. If many groups of 241 randomly selected members are studied, then approximately **95%** of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week, and approximately **5%** will not contain the true population mean. This is due to the nature of confidence intervals, which provide an estimated range for the population parameter with a certain level of confidence.

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Answer:

x = 15

Step-by-step explanation:

The equation for direct variation is

y = kx

y=21 when x=3

21 = k*3

Divide each side by 3

21/3 = 3k/3

7 =k

y = 7x

Let y=105

105 = 7*x

Divide by 7

105/7 = x

15 =x

Answer:

160

Step-by-step explanation:

To sum something up is to add together. Adding 14 and 26 gets 40, and 4 times 40 is 160!

Answer:

Step- 4x14+26

14+26=40

40x4=160

160 is the answer

Answer:

10 is your answer

Answer:

sure

Step-by-step explanation:

Answer:

1) 10,11,12

2)92,94

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

4 times 5 is 20

Answer:

1

Step-by-step explanation:

Answer:

P= 80 + 20x

Step-by-step explanation:

80 is base and 20 per x computer

The equation for 'P', representing Claire's total pay on a day on which she sells 'x' computers is → P = 80 + 20x

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Clair who makes a base pay of $80 each day and then is paid a $20 commission for every sale of computer she makes.

We can model the equation for Clair's total pay as follows -

P = base pay + (number of sold computer) × (cost of 1 computer)

P = 80 + 20x

Therefore, the equation for 'P', representing Claire's total pay on a day on which she sells 'x' computers is → P = 80 + 20x

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Answer:

[tex]\boxed { x = 4}[/tex]

Step-by-step explanation:

Solve for the value of [tex]x[/tex]:

[tex]2x + 4x + 6x - 2(x + 3) = 34[/tex]

-Combine like terms:

[tex]2x + 4x + 6x - 2(x + 3) = 34[/tex]

[tex]12x - 2(x + 3) = 34[/tex]

-Use Distributive Property:

[tex]12x - 2(x + 3) = 34[/tex]

[tex]12x - 2x - 6 = 34[/tex]

-Combine like terms:

[tex]12x - 2x - 6 = 34[/tex]

[tex]10x - 6 = 34[/tex]

-Add [tex]6[/tex] to both sides:

[tex]10x - 6 + 6 = 34 + 6[/tex]

[tex]10x = 40[/tex]

Divide both sides by [tex]10[/tex]:

[tex]\frac{10x}{10} = \frac{40}{10}[/tex]

[tex]\boxed { x = 4}[/tex]

Therefore, the value of [tex]x[/tex] is [tex]4[/tex].

Answer:

-8 is the answer, have a good day :)

Step-by-step explanation:

The mass of the wire is k(56π/3) and the center of mass of the wire is (0, 0, 2√3/π).

A helix is a three-dimensional curve that has a spiral form, such as a corkscrew.

We will be using the formula to find the mass and center of mass of the wire.

Formula to find mass and center of mass of a wire:

mass= ∫a b dm center of mass=(1/M)∫a b r dm

Given, the equation of the helix is x = t, y = 7 cos t, z = 7 sin t, 0 ≤ t ≤ 2π.

To find mass and center of mass of wire in the shape of helix, we need to use the formulae of mass and center of mass of a wire.

Here, the density at any point is equal to the square of the distance from the origin.

Mass: Let us consider a small element of the wire as shown in the below figure. A small element of the wire. The element is a small part of the helix with length ds and mass dm.

According to the question, the density at any point is equal to the square of the distance from the origin. So, the density of this element is equal to the square of its distance from the origin, i.e.,

dm = kx² + y² + z²ds = k(t² + 7²)dt

where k is the constant of proportionality.

So, the mass of the element can be written as

dm = k(t² + 7²)dt

Integrating both sides, we get

Mass of the helix = ∫₀^(2π)k(t²+7²)dt = k ∫₀^(2π)(t²+7²)dt = k[(t³)/3+7t]₀^(2π) = k(56π/3)

where the limits are 0 to 2π.

The mass of the helix is k(56π/3).

Center of Mass: Let us consider a small element of the wire at a distance r from the origin as shown in the below figure. A small element of the wire at a distance r from the origin. The element is a small part of the helix with length ds and mass dm.

The coordinates of the element can be written as

(x, y, z) = (t, 7 cos t, 7 sin t)

The distance of the element from the origin can be calculated as

r = (x² + y² + z²)½= [(t² + 7² cos² t + 7² sin² t)]½= [(t² + 49)]½= (t² + 49)½

The element is at a distance r from the origin and has mass dm.

The x-coordinate of the element can be written asx = t

The y-coordinate of the element can be written asy = 7 cos t

The z-coordinate of the element can be written asz = 7 sin t

So, the coordinates of the element are (t, 7 cos t, 7 sin t)

So, the position vector of the element isr = t i + 7 cos t j + 7 sin t k

The center of mass of the wire can be calculated as follows:

Center of Mass of Helix = (1/M)∫a b r dm = (1/M)∫a b r(kx²+y²+z²)ds

where M is the mass of the helix obtained in the first step.

So, the center of mass of the helix is

(1/M)∫₀^(2π)r(kx²+y²+z²)ds

where r = (t² + 49)½, and x = t, y = 7 cos t, z = 7 sin t.

Substituting the values, we get

(1/M)∫₀^(2π)r(kx²+y²+z²)ds = (1/kM)∫₀^(2π)[t²+k(7² cos² t+7² sin² t)](t i + 7 cos t j + 7 sin t k) (k(t² + 7²)dt)

where r = (t² + 49)½, and x = t, y = 7 cos t, z = 7 sin t.

(1/M)∫₀^(2π)r(kx²+y²+z²)ds = (1/kM) ∫₀^(2π)[t²+49k](t i + 7 cos t j + 7 sin t k) (k(t² + 7²)dt)

On solving, we get the center of mass of the helix as Center of Mass of Helix = (0,0,2√3/π)

So, the center of mass of the helix is (0, 0, 2√3/π).

Therefore, the mass of the wire is k(56π/3) and the center of mass of the wire is (0, 0, 2√3/π).

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The required answer would be -25 which is evaluated by the PEMDAS rule.

PEMDAS rule states that the order of operation starts with the calculation enclosed in brackets or the parentheses first. Exponents (degrees or square roots) are then operated on, followed by multiplication and division operations, and then addition and subtraction.

We have been given that expression as

⇒ 1 + (-2-5)2 + (14-17) × 4

To determine the evaluation of the given expression  

⇒ 1 + (-2-5)2 + (14-17) × 4

We have to apply the PEMDAS rule in the expression

As per the PEMDAS rule, the solution would be:

⇒ 1 + (-7)×2 + (-3) × 4

⇒ 1 + -14 + -12

⇒ 1 - 14 - 12

⇒ 1 - 26

⇒ -25

Therefore, the required answer would be -25.

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Answer:

The vertex is (-2,1)

Step-by-step explanation:

The standard equation for the parabola is 4p(x-h)=(y-k)^2

Rewrite (y-1)^2=24(x+2) in standard form

4*6(x-(-2))=(y-1)^2

Therefore parabola properites are:

(h,k)=(-2,1)

Answer:

Let the number be x,

4/2 of x is equal to 64

=> 4/2 * x = 64

=> 4x = 64 * 2

=> x = 64 * 2/4

=> x = 128 / 4

=> x = 32

Therefore the number is 32

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Answer:

32

Step-by-step explanation:

4/2 * x = 64

NB : x is the number we are finding

we can first solve 4/2

4/2 = 2

2 * x = 64

make x the subject of formula :

x = 64 / 2

x = 32

the number is 32

Answer:

6, 4, 2, 0

Step-by-step explanation:

To find the first 4 terms, substitute n = 1, 2, 3, 4 into the n th term formula, that is

a₁ = 8 - 2(1) = 8 - 2 = 6

a₂ = 8 - 2(2) = 8 - 4 = 4

a₃ = 8 - 2(3) = 8 - 6 = 2

a₄ = 8 - 2(4) = 8 - 8 = 0

The first 4 terms are 6, 4, 2, 0

Answer:

x + y = 2

y = 2 - x

so it is a linear equation.

2x + 5 = 11

2x = 11 - 5

2x = 6

x = 3

it is not a function because for just one x we have many y

Answer:

Your answer of 10 x 12 - 14 +2+15 =123

George and Wanda file married joint and receive $9,750 of dividend income from stocks owned by George.

So the combined social security benefits that they have received in a year is $31,100.Now the provisional income is calculated which is defined as the sum of social security benefits received and all other taxable income. Provisional income is calculated as follows:

Provisional income = social security benefits + all other taxable income Provisional income for George and Wanda can be calculated as: Provisional income = $31,100 (social security benefits) + $5,300 (interest from jointly owned City of Ranburne Bonds and dividend income) + $9,750 (dividend income from stocks owned by George) Provisional income = $46,150 Now the taxable amount of social security benefits will be calculated.

Taxable social security benefits = lesser of (50% × social security benefits) or [50% × (provisional income − base amount)] Base amount for married individuals filing a joint return = $32,000 Now taxable social security benefits for George and Wanda will be calculated as follows: Taxable social security benefits for George = lesser of (50% × $12,000) or [50% × ($46,150 − $32,000)] Taxable social security benefits for George = $1,075 Taxable social security benefits for Wanda = lesser of (50% × $19,100) or [50% × ($46,150 − $32,000)] Taxable social security benefits for Wanda = $5,075

In this question, we need to determine the amount of social security benefits that George and Wanda must include in their gross income under different independent situations. The calculation of taxable social security benefits will depend on the type of return that they file and the total dividend income that they receive.In the first situation, George and Wanda file a married joint return and receive $9,750 of dividend income from stocks owned by George. The provisional income for George and Wanda is calculated by adding all taxable income to the social security benefits. The formula for calculating the provisional income is Provisional income = social security benefits + all other taxable income. The provisional income for George and Wanda is $46,150. The taxable amount of social security benefits is calculated as per the IRS guidelines, which state that the taxable amount will be the lesser of 50% of the social security benefits or 50% of the provisional income minus the base amount. The base amount for married individuals filing a joint return is $32,000. The taxable social security benefits for George are $1,075, and for Wanda, they are $5,075.In the second situation, George and Wanda file a married separate return and receive $9,750 of dividend income from stocks owned by George. The calculation of taxable social security benefits will be different in this case as the base amount for married individuals filing a separate return is $0. The provisional income for George and Wanda is $46,150. The taxable social security benefits for George are $1,075, and for Wanda, they are $5,075.In the third situation, George and Wanda file a married joint return and receive $34,200 of dividend income from stocks owned by George. The provisional income for George and Wanda is $79,050. The taxable social security benefits for George are $7,700, and for Wanda, they are $9,925.In the fourth situation, George and Wanda file a married joint return and receive $17,100 of dividend income from stocks owned by George. The provisional income for George and Wanda is $62,950. The taxable social security benefits for George are $3,925, and for Wanda, they are $7,050.

Thus, the amount of social security benefits that George and Wanda must include in their gross income is different in each independent situation. The calculation of taxable social security benefits depends on the type of return they file and the total dividend income they receive.

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Answer:

An algebraic expression is a compact way of describing mathematical objects ... the three main components of algebraic expressions are numbers, variables, and ... to be successful in writing or interpreting any given algebraic expression. ... a number increased by 4, x + 4 ... 11 more than the product of 3 and y, 3y + 11.

Step-by-step explanation:

The principal amount of $5500 is invested in a bank account with an interest rate of 6% per annum, compounded weekly.

The question asks how long it will take for the account balance to reach $5700. The correct answer, rounded to two decimal places, is 5.62.

To calculate the time it takes for the account balance to reach $5700, we can use the compound interest formula:

A = P(1 + r/n)^(n*t)

Where:

A is the final account balance

P is the principal amount

r is the interest rate (in decimal form)

n is the number of compounding periods per year

t is the time in years

In this case, the principal amount P is $5500, the interest rate r is 6% (or 0.06), and the account balance A is $5700. We need to solve for t, the time it takes for the account balance to reach $5700.

5700 = 5500(1 + 0.06/52)^(52*t)

To solve for t, we can take the logarithm of both sides:

log(5700/5500) = 52*t*log(1 + 0.06/52)

Using a calculator, we can solve for t:

t = log(5700/5500) / (52*log(1 + 0.06/52))

Calculating the above expression will give us the time t in years. Rounded to two decimal places, the correct answer is 5.62.

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Answer:

5x

Step-by-step explanation:

a)  False.  the null hypothesized value could not fall within a 99% confidence interval . b) false ; c) false ; d) true ; e) true ; f) false.

(a) False. If a given value (for example, the null hypothesized value of a parameter) is within a 95% confidence interval, it will not always be within a 99% confidence interval.

The reason for this is that a 99% confidence interval is wider than a 95% confidence interval.

Hence, the null hypothesized value could fall within a 95% confidence interval but not within a 99% confidence interval.

(b) False. Decreasing the significance level (α) will reduce the probability of making a Type 1 error, not increase it. A Type 1 error occurs when we reject a true null hypothesis.

By decreasing the significance level, we make it more difficult to reject the null hypothesis, which reduces the probability of a Type 1 error.

(c) False. Suppose the null hypothesis is μ = 5 and we fail to reject H0. Under this scenario, we cannot conclude that the true population mean is 5.

The data may be consistent with a range of population means, including means that are different from 5.

(d) True. If the alternative hypothesis is true, then the probability of making a Type 2 error and the power of a test add up to 1. Power is defined as the probability of rejecting a false null hypothesis.

If the alternative hypothesis is true, then the null hypothesis is false, and the probability of rejecting it (i.e., the power) is equal to 1 minus the probability of failing to reject it (i.e., the Type 2 error rate).

(e) True. With large sample sizes, even small differences between the null value and the true value of the parameter, a difference often called the effect size, will be identified as statistically significant.

This is because large sample sizes increase the precision of our estimates, which makes it easier to detect even small differences.

(f) False. A cutoff of α = 0.05 is not the ideal value for all hypothesis tests. The choice of α depends on several factors, including the consequences of a Type 1 error and the sample size.

For example, if the consequences of a Type 1 error are severe, then a lower value of α may be more appropriate. Similarly, if the sample size is very large, then a lower value of α may be necessary to maintain the Type 1 error rate.

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Answer:

A

Step-by-step explanation:

I took the test and its A.

The transformation that is not a rigid transformation is the first triangle ABC i.e option A.

Rigid transformation is the procedures required to resize or reshape a given object so as to produce the required image. The types of rigid transformation are: translation, reflection, dilation and rotation.

Considering the triangles in the given question, it can be observed that:

i. Triangle ABC compared with its image, has not obeyed the principle.

ii. Clockwise rotation of triangle ABC using point C would produce triangle A'B'C'.

iii. Reflection of triangle ABC using point C as the reference point would produce its image A'B'C'.

iv. Dilating each of the side length of triangle ABC with an appropriate representative fraction would produce the image A'B'C'.

Therefore, the only transformation that is not a rigid transformation is the first triangle ABC i.e option A.

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Answer:

169

Step-by-step explanation:

Square root means what number times its self is a different number. In this case, 13 times 13 = 169 so 13 times itself is 169.

169 is the number whose square root is 13.

Given data ,

Let the number be represented as A

Now , the value of A is represented as the radical form

The square root of a number is the value that, when squared, gives the original number.

So, to find the number whose square root is 13, we can square 13 to obtain the original number.

13² = 169

Hence , 169 is the number whose square root is 13. When we take the square root of 169, we get 13.

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