Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms. 2 similar triangles. Triangle 1 has side lengths 3, 4, blank. Triangle 2 has side lengths 9, 12, blank. a. StartFraction 3 Over 4 EndFraction = StartFraction 9 Over 12 EndFraction = StartFraction 3 Over 4 EndFraction b. StartFraction 3 Over 9 EndFraction = StartFraction 4 Over 12 EndFraction = StartFraction 1 Over 3 EndFraction c. StartFraction 3 Over 12 EndFraction = StartFraction 4 Over 9 EndFraction = StartFraction 1 Over 4 EndFraction d. StartFraction 4 Over 3 EndFraction = StartFraction 12 Over 9 EndFraction = StartFraction 4 Over 3 EndFraction Please select the best answer from the choices provided A B C D

To measure the height of a stack of 1,000 ponies:
1. Decide on the unit of measurement (meters, feet, etc.).
2. Prepare a suitable measuring tool.
3. Arrange the ponies in a stable stack.
4. Position the measuring tool vertically alongside the stack and measure from the base to the highest point.
5. Record the measurement in the chosen unit.

To measure the height of a stack of 1,000 ponies, you can use the following steps:
1. Determine the unit of measurement: Before measuring the height, it is important to decide on the unit of measurement that you will be using. Common units for measuring height include meters, feet, or centimeters.
2. Prepare a measuring tool: Depending on the unit of measurement you have chosen, you will need a suitable measuring tool. For example, if you are using meters, you can use a measuring tape or a ruler marked in meters. If you are using feet, a yardstick or measuring tape marked in feet would be appropriate.
3. Arrange the ponies: Make sure the stack of ponies is stable and secure. You can align them in a straight line or stack them on top of each other.
4. Measure the height: Position your measuring tool vertically alongside the stack of ponies. Start from the base of the stack and measure up to the highest point. Ensure that your tool is perpendicular to the ground and the stack of ponies for accurate measurement.
5. Record the measurement: Once you have determined the height, write down the measurement in the chosen unit. For example, if the stack of ponies measures 3 meters, record it as 3m.
It is important to note that the accuracy of your measurement may depend on factors such as the alignment and stability of the ponies in the stack. Also, consider rounding your measurement to an appropriate level of precision based on the measuring tool you are using.

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Answer:

2,4,6,8,10

Step-by-step explanation:

Because the bar never reaches the top, each individual bar is worth 2 each so the scale only works up to 10

Answer:

4,8,12,16,20

Step-by-step explanation:

bottom box 4 then going Upto 2o

The correct answer is A. no; since np<5, the normal distribution should not be used.  This is because np<5, which violates the condition for using the normal distribution approximation to the binomial distribution. In this case, np=15 which is less than 5, and therefore, the binomial distribution should be used. If np is greater than or equal to 5, a normal approximation to the binomial distribution can be used.

The binomial distribution can be used to model the probability of a certain number of successes in a fixed number of independent trials, where the probability of success in each trial is the same. However, if the number of trials is large and the probability of success is small, the binomial distribution can be approximated by a normal distribution.

In this case, we have

n = 100 trials and p = 0.15

probability of success in each trial.

Therefore, np = 15, which is less than 5. According to the rule of thumb, if np < 5 or n(1-p) < 5, the normal distribution approximation is not valid, and the binomial distribution should be used.

Since the probability of success is small (0.15), and the number of trials is relatively large (100), we could use a normal approximation to the binomial distribution. However, since np < 5, we cannot use the binomial probability formula directly. Instead, we would need to use a continuity correction and the standard normal distribution to estimate the probability. Therefore, option A is the correct answer.

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Answer:

£2.52

Step-by-step explanation:

we first need to calculate 100% which is the cost price. by selling at £2.34 she makes a profit of 30%

thus £2.34 represents 130%. we calculate 100%:

(100 X £2.34)/130

= £1.8

if she increases the profit to 40% if the cost price the new selling price will be :

(140 X 1.8)/100 = £2.52

Answer:

1/2 gallon

Step-by-step explanation:

There are 5 gallons from 10 trees, so divide

5 ÷ 10 = 1/2

or create a fraction 5/10 and simplify by dividing by 5/5

5/10 ÷ 5/5 = 1/2

The value of the indefinite integral \(\int [z^2 + \frac{1}{(1-z)^8}]dz\) will be \([ \frac{(z)^3}{3} - \frac{1}{7(1-z)^7}] + c\).

Given that:

\(\begin{aligned} I &= \int \left [z^2 + \dfrac{1}{(1-z)^8}\right] dz \end{aligned}\)

The indefinite integral, also known as an antiderivative, represents the family of functions whose derivative is equal to the given function. It is denoted by the symbol ∫.

Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.

Let 1 - z = u, then -dz = du and 1 - u = z. Then we have

\(\begin{aligned} I &= -\int \left [(1-u)^2 + \dfrac{1}{u^8}\right] du\\I &= \left [ \dfrac{(1-u)^3}{3} - \dfrac{1}{7u^7}\right] + c \\I &= \left [ \dfrac{(z)^3}{3} - \dfrac{1}{7(1-z)^7}\right ] + c\end{aligned}\)

The value of the indefinite integral \(\int [z^2 + \frac{1}{(1-z)^8}]dz\) will be \([ \frac{(z)^3}{3} - \frac{1}{7(1-z)^7}] + c\).

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We integrate each component separately over the given limits of t. Evaluating the integral for each component will yield the final result of the line integral of F along the line segment C from (0, 0, 0) to (4, 3, 2).

A line integral is a way to calculate the work done by a force along a curve. In this case, we have the vector field F = xeyz and the curve C, which is the line segment from (0, 0, 0) to (4, 3, 2). The line integral of F along C can be written as ∫CF · dr, where dr is the differential vector along the curve.

To evaluate this line integral, we parameterize the curve C. Since C is a line segment, we can use a linear parameterization. Let's denote the parameter as t, ranging from 0 to 1. We can express the coordinates of C as x = 4t, y = 3t, and z = 2t.

Next, we need to find the differential vector dr along curve C. Taking the derivatives of the parameterized equations with respect to t, we obtain dx = 4dt, dy = 3dt, and dz = 2dt. Hence, dr = (dx, dy, dz) = (4dt, 3dt, 2dt).

Substituting these values into the line integral, we have ∫CF · dr = ∫CF(x, y, z) · (4dt, 3dt, 2dt). Simplifying the expression, we get ∫C(4xeyz dt, 3xeyz dt, 2xeyz dt).

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The value of the fraction expression after rationalise the denominator will be √33.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ [(6 + √3)(6 - √3)] / √33

Simplify the expression, then we have

⇒ [(6 + √3)(6 - √3)] / √33

⇒ [6² - (√3)²] / √33

⇒ [36 - 3] / √33

⇒ 33 / √33

⇒ √33

The value of the fraction expression after rationalise the denominator will be √33.

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The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

36.5

Step-by-step explanation:

Answer:

292 divided by 8 is 36.5

However, 8 divided by 292  is 0.02739726027

Step-by-step explanation:

We know this by dividing, plus if you want to double check answers, go ogle is always there for you!

Answer:

translation

Step-by-step explanation:

translation move with same shape and size

Answer:

translation

Step-by-step explanation:

move the same ship and size

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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The required cost of the meal given as a hot dog is of $6 and the hamburger is of $8.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Let's call the cost of a hot dog meal "x" and the cost of a hamburger meal "y".

From Mrs. Hammond's purchase, we know that:

x + 3y = 30   -- - - - - -(1)

From Mr. Weber's purchase, we know that:

3x + 3y = 42 - - - - - -(2)

We can use substitution to solve for one of the variables in terms of the other. If we substitute the first equation into the second equation:

3x + 3y = 42

3x + 3(30 - x)/3 = 42

3x + 30 - x = 42

2x = 12
x = 6

now,
6 + 3y = 30
3y = 24
y = 8

Thus, the required cost of the meal given as a hot dog is of $6 and a hamburger is $8.

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Answer:

G is correct

H is correct

M is correct

K is 131

Step-by-step explanation:

Angles in a straight line add up to 180 degrees

Answer:

g: 43

h: 137

m: 49

K: 131

Step-by-step explanation:

i got it right

The formula to calculate the standard deviation (σ) of a binomial distribution is σ = √[n * p * (1 - p)] where n is the number of trials and p is the probability of success in each trial.

Substituting the given values, we get:

σ = √[10 * 0.70 * (1 - 0.70)]

σ = √[10 * 0.70 * 0.30]

σ = √2.1

σ ≈ 1.45

Therefore, the standard deviation of the binomial distribution with n = 10 and p = 0.70 is approximately 1.45.

Hence, the answer is 1.45.

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The number that makes the equation 0.54 + 17/100 = x/100 + 17/100 true is 54.

To solve this equation, we want to isolate x on one side of the equation.

Starting with:

0.54 + 17/100 = x/100 + 17/100

We can first simplify the left side by finding a common denominator for 0.54 and 17/100:

0.54 = 54/100

54/100 + 17/100 = 71/100

Now, we can simplify the right side by combining like terms:

x/100 + 17/100 = (x + 17)/100

Substituting these simplifications back into the original equation, we get:

71/100 = (x + 17)/100

To isolate x, we can multiply both sides by 100:

71 = x + 17

Subtracting 17 from both sides, we get:

x = 54

Therefore, the number that makes the equation true is 54.

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The question is -

Enter the number that makes the equation true.

0.54 + 17/100 = x/100 + 17/100

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The Correct choice is : D

\( \dfrac{i}{j} = \dfrac{h}{k} \)

The value of f(0.025) is approximately ±2.086 for an f-curve with df = (20, 5).

The t-distribution is a way of describing a set of observations where most observations fall close to the mean, and the rest of the observations make up the tails on either side. It is a type of normal distribution used for smaller sample sizes, where the variance in the data is unknown.

To find f(0.025) for an f-curve with df = (20, 5), we need to use a t-distribution table.

First, we need to determine the critical value for a two-tailed test with a significance level of 0.05 and 20 degrees of freedom (df).

Looking at the t-distribution table, we find that the critical value is approximately ±2.086.

Next, we can use the formula for the t-distribution to calculate f(0.025):
f(0.025) = t(0.025, 20) = ±2.086

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The coordinates of the equilibrium point are (70, 2600).

To find the equilibrium point, we need to set the consumer willingness to pay equal to the producer willingness to accept. In other words, we need to find the value of x that makes D(x) equal to S(x).

Given:

D(x) = 4000 - 20x

S(x) = 850 + 25x

Setting D(x) equal to S(x), we have:

4000 - 20x = 850 + 25x

To solve this equation, we can combine like terms:

45x = 4000 - 850

45x = 3150

Now, divide both sides by 45 to isolate x:

x = 3150 / 45

x = 70

So the equilibrium quantity is 70 units.

To find the equilibrium price, we substitute this value of x back into either D(x) or S(x). Let's use D(x) = 4000 - 20x:

D(70) = 4000 - 20(70)

D(70) = 4000 - 1400

D(70) = 2600

Therefore, the equilibrium price is $2600 per unit.

The coordinates of the equilibrium point are (70, 2600).

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The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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We want to find the dimensions of the poster such that the area of the whole poster is minimized .These are: Length = 325.2cm and

Width = 17cm

We can assume that the poster is a rectangle, and we know that a rectangle of length L and width W has an area:

A = L*W

Here we do know that the top and bottom margins are 9 cm each.

The side margins are 6cm each.

Then the measures of the printed areas are:

W' = W - 2*6cm = W - 12cm

L' = L - 2*9cm = L - 18cm

And we know that the area of the printed part is 1536 cm^2, then we can write:

A'  = (W - 12cm)*( L - 18cm) = 864 cm^2

      W*L - 12cm*L - 18cm*W + 216cm^2 = 1536 cm^2

      W*L = 12cm*L + 18cm*W + 1320cm^2

And W*L is equal to the area, so what we need to minimize is:

A =  12cm*L + 18cm*W + 1320cm^2

Here we can see that the dependence of the area is larger on W than on L, so what we need to minimize is W.

We will take the smallest value of W such that the given margins are allowed.

That value would be such that:

W - 12cm > 0

W > 12cm

this could (and to be strict, should) be something like 16.0001cm, but let's use 17cm just to use whole numbers, we will get:

W = 17cm

Then to get the length we solve:

W*L = 12cm*L + 18cm*W + 1320cm^2

17cm*L = 12cm*L + 18cm*17cm + 1320cm^2

5cm*L = 1560cm^2

L = 325.2cm

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Viksim, this is the solution:

• Alex's base salary = $ 2,200

• Alex's commision = 10% of total vacuum cleaners or 0.1

• Total sales one month = $ 4,300

In consequence,

• Total salary = Base salary + Commission

• Total salary = 2,200 + (0.1 * 4,300)

• Total salary = 2,200 + 430

• Total salary = 2,630

Alex earned $ 2,630 of total salary

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer:

\(\frac{3}{5n}\)

Step-by-step explanation:

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

ax²+bx+c

Rewrite the division as a fraction.

(3÷5)⋅1/n

Multiply 3÷5 by 1.

(3÷5)/n

Rewrite the division as a fraction. (3/5)/n

Multiply the numerator by the reciprocal of the denominator.

(3/5⋅(1/n)

Multiply 3/5 and 1/n.

3/5n

The calculation; (9.04-8.23+21.954+81.0) * 3.1416 should have three significant figures.

To determine the number of significant figures in a calculation, we follow these rules:

1. When adding or subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places.

2. When multiplying or dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures.

Let's calculate the expression:

(9.04 - 8.23 + 21.954 + 81.0) * 3.1416

First, perform the addition and subtraction:

(0.81 + 21.954 + 81.0) * 3.1416

= 103.764 * 3.1416

Next, perform the multiplication:

325.8512544

To determine the number of significant figures, we look at the original numbers involved in the calculation.

9.04 has three significant figures.

8.23 has three significant figures.

21.954 has five significant figures.

81.0 has three significant figures.

3.1416 has five significant figures.

Among these numbers, the number with the fewest significant figures is 81.0 with three significant figures.

Therefore, the result of the calculation, 325.8512544, should have three significant figures to match the least precise value.

In scientific notation, the result would be expressed as 3.26 x 10^2.

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The given calculation would yield a result with five significant figures because we base our significant digits off of the least precise term within the parentheses, which is 81.0. The result is then rounded according to this rule.

In the case of the calculation (9.04-8.23+21.954+81.0) * 3.1416, it's important to first consider the rule for significant figures in calculations - the result should be reported with the smallest number of decimal places in the numbers used in the calculation. The number 81.0 has two numbers after the decimal point, therefore, our final answer should have two numbers after the decimal point. When you calculate the inside of the parentheses, the result is 103.764. Multiplying that by 3.1416 would approximately yield 325.854. Rounding this to the least precise measurement (which is to two decimal places due to 81.0) would give us 325.85 which has five significant figures, effectively limiting our calculated value to five significant figures.

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The correct answer is A. True

A linear equation represents a line in the xy-plane. In the form of y = mx + b, where m is the slope and b is the y-intercept, a linear equation defines a straight line relationship between x and y. Each x value corresponds to a unique y value on the line.

By plotting the points that satisfy the equation, a line can be formed. The slope determines the steepness or direction of the line, while the y-intercept represents the point where the line intersects the y-axis.

Therefore, a linear equation does determine a line in the xy-plane.

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True. A linear equation determines a line in the xy-plane.

A linear equation is an equation that describes a straight line in the xy-plane. It is an equation of the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. The slope-intercept form of a linear equation is commonly used to graph lines.

The equation y = mx + b shows that for every value of x, there is a corresponding value of y that lies on the line. The slope, m, determines the steepness of the line, while the y-intercept, b, represents the point where the line crosses the y-axis.

Therefore, it is true that a linear equation determines a line in the xy-plane.

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Thomas Johnson's annual disability benefit is $1,103.66 and his monthly disability benefit is $91.97.

percentage, a relative value indicating hundredth parts of any quantity.

We know that Disability Benefit = (Average Monthly Earnings x Benefit Rate x Years of Service) / 12

Average Monthly Earnings is the final average salary divided by 12

Benefit Rate is 2.00%, or 0.02

Years of Service is the number of years Thomas has contributed to Social Security

Let us find Average Monthly Earnings:

Average Monthly Earnings = $37,850 / 12 = $3,154.17

Now calculate Thomas Johnson's annual disability benefit:

Annual Disability Benefit = ($3,154.17 x 0.02 x 22) / 12 = $1,103.66

Now,  Monthly Disability Benefit = $1,103.66 / 12 = $91.97

Therefore, Thomas Johnson's annual disability benefit is $1,103.66 and his monthly disability benefit is $91.97.

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Answer:

A. 2x - (4x + 3) = 12

Step-by-step explanation:

A. 2x - (4x + 3) = 12

B. -4(4y+)+y=3

C. 2 (4x+3) - y

D. -4x+4 x-3=3

Given equation:

-4x+y = 3. (1)

2x - y = 12. (2)

From (1)

y = 3 + 4x

Substitute y = 3 + 4x into (2)

2x - y = 12 (2)

2x - (3 + 4x) = 12

Or

2x - (4x + 3) = 12

2x - 4x - 3 = 12

- 2x = 12 + 3

- 2x = 15

x = 15/-2

x = -7.5

Substitute x = -7.5 into (1)

-4x+y = 3 (1)

-4(-7.5) + y = 3

30 + y = 3

y = 3 - 30

y = -27