Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?

StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction

Step-by-step explanation:

the volume of a 3D object is always calculated in some way by multiplying the 3 dimensions with each other.

so, if every dimension is then changed by a factor f (4 in our case), then the volume changes by f×f×f = f³, as the factor has to be included in the calculation for each dimension. and as they are multiplied with each other, so are the scaling factors in each case.

in our case the prism is dilated by the factor 4.

that means that every side length, every height, ..., each dimension is increased by the factor 4.

and therefore, the volume increases by the factor 4³ = 64.

so, the volume of the new image is

244 × 64 = 15,616 cm³

Volume changes by f × f × f = f³

Volume increases by the factor of 4³ = 64

The volume of the new image exists 244 × 64 = 15616 cm³.

The volume of a 3D object exists always computed in some form by multiplying the 3 dimensions by each other.

The volume changes by f × f × f = f³, as the factor, contains to be included in the calculation for each dimension and as they exist multiplied with each other, so exist the scaling factors in each case.

Here, the prism exists dilated by factor 4 which indicates that every side length, every height and each dimension exists increased by factor 4.

Volume increases by the factor of 4³ = 64

The volume of the new image exists 244 × 64 = 15,616 cm³.

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The solution to the system of inequalities is (-3.375, 1.75)

The system of inequalities is given as:

3y > 2x+12

2x+y ≤ -5

Next, we plot the graph of the system using a graphing tool

From the graph, both inequalities intersect at

(-3.375, 1.75)

Hence, the solution to the system of inequalities is (-3.375, 1.75)

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The probability of getting tails on the coin and an even number on the number cube is 1/4

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The sample space of a coin is:

S = {H, T}

The sample space of a die is:

S = {1, 2, 3, 4, 5, 6}

The above means that:

A coin has 2 faces, one of which is the tail.

So, we have:

P(Tail) = 1/2

A number cube has 6 numbers, 3 or which are even.

So, we have

P(Even) = 3/6

The required probability is

P = P(Tail) * P(Even)

This gives

P = 1/2 * 3/6

Evaluate

P = 1/4

Evaluate the quotient

P = 0.25

Hence, the probability of getting tails on the coin and an even number on the number cube is 1/4 or 0.25

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The outcome of the product is 4 + 2/24, so the correct option is B.

Here we want to solve:

(4 + 2/3)*(7/8)

Using the distributive property of the product we get:

4*(7/8) + (2/3)*(7/8)

28/8 + 14/24

Now we can multiply the first fraction by (3/3) (it does not change the fraction).

(3/3)*28/8 + 14/24

84/24 + 14/24 = 98/24  

Now we can rewrite it as:

98/24 = (96/24) + (2/24)  =4 + 2/24

Then the correct option is B.

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maths questions can be solved using unitary method.

Answer:

(a) The total number of girls in the class are 48

(b) The total number of students that like maths are 80

(c) The total number of boys like maths are 45

Solution:

According to the question, [tex]\frac{3}{5}[/tex] of total students are boys

number of boys = [tex]\frac{3}{5}[/tex] × 120 = 72

Also, According to the question, [tex]\frac{2}{3}[/tex] of total students like maths

number of students = [tex]\frac{2}{3}[/tex] × 120 =80

(a) The total number of girls in the class = total number of students - total number of boys

total number of girls in the class = 120 - 72 = 48

(b) The total number of students that like maths are 80

(c) The total number of boys like maths = total number of students that like maths - total number of girls that like maths

total number of boys like maths = 80 - 35 = 45

What is unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

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Answer:

Answer

Answer in decimal

11.8998

The surface area of the composite figure is 444m²

Given a composite figure which is shown in the question.

The  area of ​​a shape (in square units) is the number of unit squares required to cover the entire area without gaps or overlaps. If a hologram has planes, those faces are called faces. Area is the sum of the areas of the faces.

Firstly, we will find the area of front and end triangles by using the formula

Area=(1/2)×b×h and we will multiply this area by 2 because we are finding the area of two same triangles.

Here, h=6 and b=16 and substitute these values in the formula, we get

A₁=2×(1/2)×16×6

A₁=2×8×6

A₁=96m²

Now, we will find the area of the left and right side rectangles which joined both the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=10 and b=5 and substitute these values in the formula, we get

A₂=2×10×5

A₂=100m²

Further, we will find the area of the front and end side rectangles that joined both by the base of the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=16 and b=4 and substitute these values in the formula, we get

A₃=2×16×4

A₃=128m²

Furthermore,  we will find the area of the left and right side rectangles which joined by the front and end rectangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=4 and b=5 and substitute these values in the formula, we get

A₄=2×4×5

A₄=40m²

Now, we will find the area of the base of the composite figure which is rectangle.

We will find the area by using the formula Area=l×b.

here, l=16 and b=5 and substitute these values in the formula, we get

A₅=16×5

A₅=80m²

So, the surface area of the given composite figure will be

Surface area=A₁+A₂+A₃+A₄+A₅

Surface area=96m²+100m²+128m²+40m²+80m²

Surface area=444m²

Hence, the surface area of the given composite figure is 444m².

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Answer:

acute angle and angle between zero and 90 degrees right angle and 90 degree angle obtuse angle and angle between 90 and 180

Answer:

what kind of people are the best division

The given analytical tools:

a. The single sample z-test analysis is appropriate for the data where the sample size is large and all data points are independent. Where the standard deviation is given(known).

b. The single sample t-test analysis is appropriate for the data where the sample size is small and the population variation or standard deviation is unknown.

This is a type of hypothesis test where the sample means and the population means are compared when the population variance or the standard deviation are given(known).

z = (X - μ)/(σ/√n)

Where X - sample mean, μ - population mean, σ - population standard deviation, and n - sample size.

Here the sample size is large and all data points are independent.

This is a type of parametric hypothesis test where the sample means and the population means are compared when the population variance or the standard deviation are not given(unknown).

t = (X - μ)/(s/√n)

Where X - sample mean, μ - population mean, s - sample standard deviation, and n - sample size.

Here the sample size is small.

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by taking the quotient between the volume in the pot and the volume of each serving, we conclude that there are 12 servings.

The number of servings is given by the quotient between the volume in the pot and the volume of each serving, so we have:

N = (3/4)*/(1/16) = 12

So there are 12 servings in the pot.

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Answer:

The slope is -3, in a y=mx+b equation the x coefficient is the slope

9 hundredths is greater than 8 thousandths by 82 thousandths

From the question, we are to determine how much greater 9 hundredths is than 8 thousandths

9 hundredths = 9/100 = 0.09

8 thousandths = 8/1000 = 0.008

Then,

0.09 - 0.008 = 0.082

= 82/1000

≡ 82 thousandths

Hence, 9 hundredths is greater than 8 thousandths by 82 thousandths

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The maximum possible length of the rectangular front of the building is 23 feet

The complete question is attached

Let the length of the rectangular front be x and the height be y.

So, we have:

x = 2y

The building has 4 congruent sides.

So, the area of the 4 sides is

A = 4 * (x * y)

This gives

A = 4 * (x * 2x)

Evaluate

A = 8x²

For the triangular roof, we have:

Slant height, l = y

Base, b = x

So, the area of the 4 triangular faces is

A = 0.5 * 4 * xy

This gives

A = 2xy

Recall that:

x = 2y

Make y the subject

y = 1/2x

So, we have:

A = 2x * 1/2x

A = x²

The cost of designing the buildings is

C = 25 * 8x² + 50 * x²

C = 200x² + 50x²

C = 250x²

This gives

250x² = 500000

Divide both sides by 250

x² = 2000

Square both sides

x = 45

Recall that:

y = 1/2x

This gives

y = 1/2 * 45

y = 23

Hence, the maximum possible length of the rectangular front of the building is 23 feet

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Answer:

B 6.5

Step-by-step explanation:

The area of a whole circle is

a = [tex]\pi[/tex][tex]r^{2}[/tex]  A whole circle is 360 degrees.  We only have part of a circle.  We were also given the diameter and we need the radius.  The radius is half of the diameter.

a = [tex]\frac{30}{360} \pi 5^{2}[/tex]

a= 6.5 rounded.

A whole circle exists 360 degrees. The radius exists half of the diameter.

[tex]$$a = (30/360) $\pi 5^2[/tex]

a = 6.5 rounded.

The area to the nearest tenth of a square centimeter, of the sector formed by the 30° angle exists at 6.5 rounded.

The diameter of the circle exists double the radius of the circle. Therefore the area of the circle formula utilizing the diameter exists equivalent to π/4 times the square of the diameter of the circle. The formula for the area of the circle, utilizing the diameter of the circle

π/4 × [tex]$$diameter^2[/tex].

Given: diameter of the circle = 10 cm

then the radius of the circle is half of the diameter

Radius of the circle  = 10/2 = 5 cm

Area of circle = [tex]$$\pi $r^2[/tex]

Where r be the radius of the circle

A whole circle exists 360 degrees. The radius exists half of the diameter.

[tex]$$a = (30/360) $\pi 5^2[/tex]

simplifying the above equation we get

[tex]$$a = 25$\pi$ /$12[/tex]

a = 6.5 rounded.

The area to the nearest tenth of a square centimeter, of the sector formed by the 30° angle exists at 6.5 rounded.

Therefore, the correct answer is option (B) 6.5

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Answer:

D

Step-by-step explanation:

The red line starts with a filled in circle that mean that the number -12 is included.  The graph is saying that x can be -12 or any number above -12.  The line under the > is telling you that 12 is included.

The graphed function, F(x), has a value greater than 0 over the intervals (-0.7, 0.76) and (0.76,  ∞) . F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞) is the correct statement [Fourth choice].

About a Graphed Function

The function graph of an object F stands for the set of all points in the plane that are (x, f(x)). The graph of f is also known as the graph of y = f. (x). The graph of an equation is thus a specific example of the graph of a function. A graphed function is a function that has been drawn out on a graph.

It is evident from the attached graph that the supplied function exceeds 0 for the following range:

-0.7 < F(x) < 0.76

And, 0.76 < F(x) < ∞

As a result, the intervals for which the given graphed function, F(x) is greater than 0 are as follows,

(-0.7, 0.76) and (0.76, ∞)

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Answer:

250,000 Meters

Step-by-step explanation:

1 Km = 1000 meters

250x1000= 250,000 meters

Answer:

D. [tex]\displaystyle{\dfrac{5^8}{9^8}}[/tex]

Step-by-step explanation:

The law of exponent defines that:

[tex]\displaystyle{\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}}[/tex]

In word, you simplify the expression by expanding an exponent to both numerator and denominator.

So from the expression [tex]\displaystyle{\left(\dfrac{5}{9}\right)^8}[/tex], you expand the exponent 8 in both numerator and denominator then you'll end up with D choice!

If you have any questions then please let me know in comment!

Answer: y=8x+6

Step-by-step explanation:

The slope is

[tex]\frac{70-54}{8-6}=\frac{16}{2}=8[/tex]

So, the slope is 8.

Since the y-intercept is 6, the equation is y=8x+6.

Answer: The height of the ball at time t is given as h = -16t² + 14t + 6 while the height of the receiver hand at time t is given as h = -16t² + 10t + 8

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

A quarterback throws a football toward a receiver from a height of 6 ft. The initial vertical velocity of the ball is 14 ft/s. At the same time that the ball is thrown, the receiver raises his hands to a height of 8 ft and jumps up with an initial vertical velocity of 10 ft/s.

The height of the ball at time t is given as h = -16t² + 14t + 6 while the height of the receiver hand at time t is given as h = -16t² + 10t + 8

Answer:

6

10

8

Step-by-step explanation:

The average height is [tex]5feet[/tex] and [tex]11.5[/tex] inches if Allen is [tex]5 feet 9 inches[/tex] tall and Terrel is [tex]6 feet 2 inches[/tex] tall.

How to find the average height ?

Allen height is [tex]5feet ,9inches[/tex]

Terrel height is [tex]6feet,2inches[/tex]

And we know that [tex]1feet=12inches[/tex]

So Allen height is

[tex]=5*12+9\\=60+9\\=69 inches[/tex]

And Terrel height is

[tex]=6*12+2\\=72+2\\=74inches[/tex]

Average of the Allen and Terrel height is

[tex]\frac{69+74}{2\\} \\=143/2\\=71.5inches[/tex]

And average height in feet is  [tex]5feet,11.5inches[/tex]

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Answer:

16

Step-by-step explanation:

We can use the binomial distribution formula to find the probability of flipping three coins tails, four coins tails, and five coins tails. This is because the probability of P(x=3) is going to give the same result if we had defined the entire set, counted how many had 3, and then divided that by the entire set. So we can use this to find how much % of the data set is going to have at least 3.

So the binomial distribution formula is defined as: [tex]P_x=(^n_x)p^x(1-p)^{n-x}[/tex], where n=number of trials, x=how many successes (in this case it will be 3, 4, and 5) and p=probability of success.

The binomial coefficient is defined as: [tex](^n_x)=\frac{n!}{k!(n-x)!}[/tex].

So let's define the variables.

x = 3, 4, 5 since we want to find the probability of getting at least 3. This means we want the probability of getting 3, 4, or 5 tails, and then we simply add up these probabilities.

n = 5, since Paul is flipping the coin 5 times

p = 0.5 since the probability of flipping tails is 0.50

So let's plug the information in!

[tex]P_{x\ge3} = P_3 + P_4 + P_5[/tex]

[tex]P_3=\frac{5!}{3!2!}*0.5^30.5^2 = 0.3125[/tex]

[tex]P_4=\frac{5!}{4!1!}*0.5^4*0.5^1=0.15625[/tex]

[tex]P_5 = \frac{5!}{5!0!}0.5^50.5^0 = 0.03125[/tex]

Now let's add up all these probabilities to get:

[tex]0.3125 + 0.15625 + 0.03125 = 0.5[/tex]

This means 50% of the time Paul will flip three or more tails.

To translate this to the number of ways, we need to find how many combinations there are which can generally be defined as: [tex]options^{length}[/tex] and in this case options = tails and heads so 2, and the length is 5. So we get: [tex]2^5 = 32[/tex]

Now multiply the 32 by the 0.5 and you get 16, which is the amount of ways he can flip at least three tails

Answer:

16

Step-by-step explanation:

The number of half page advertisements that Michael purchased is 4 while the full page advertisements is 11.

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

Let the number of half page ads be represented by h

Let the number of full page ads be represented by f.

Total number of advertisements = 15

h + f = 15 ....... (i)

h = 15 - f

Therefore, the system of equations to represent the situation will be:

60h + 100f = 1340 ........ (ii)

Put the value of h into equation (ii)

60(15 - f) + 100f = 1340

[tex]\Rightarrow[/tex]  900 - 60f + 100f = 1340

Collect like terms

    100f-60f  = 1340-900

[tex]\Rightarrow[/tex]              40f = 440

[tex]\Rightarrow[/tex]                   f = 11

The number of full-page advertisements that Michael purchased is 11.

Since h + f = 15

[tex]\Rightarrow[/tex]    h + 11 = 15

[tex]\Rightarrow[/tex]       h = 15 - 11

[tex]\Rightarrow[/tex]      h = 4

The number of half page advertisements that Michael purchased is 5.

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Using it's concept, the relative frequency of business majors in the sample is of 0.16 = 16%.

A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 337 students, of which 30 + 24 = 54 students are business majors, hence the relative frequency is:

r = 54/337 = 0.16 = 16%.

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The domain of the exponential function given is the set of all real numbers while the range of the exponential function is the set of all real numbers greater than zero.

As with other exponential functions, it follows that the domain of the exponential function given is the set of all real numbers while the range of the exponential function is the set of all real numbers greater than zero.

Additionally, by observation, the function has a positive variable correlation, hence;

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[tex]\large\bold\blue{ANSWER:-}[/tex]

Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.

Answer:

Step-by-step explanation:

This is a geometric means problem where the height (length AC of 4) is the geometric mean between the base BC and the base DC. The proportion is

[tex]\frac{12.8}{4} =\frac{4}{CD}[/tex] . Cross multiply to get

12.8CD = 16 and divide both sides by 12.8 to get that

CD = 1.25

That means that the length of the whole thing, BD, is

12.8 + 1.25 = 14.05

Using a system of equations, it is found that she has 9 picture books.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

The ratio of the number of picture books encyclopedias, and fairy tale books Annette had is 3:4:5, hence:

[tex]\frac{x}{y} = \frac{3}[4}, \frac{x}{z} = \frac{3}{5}, \frac{y}{z} = \frac{4}[5}[/tex]

She gave half of her encyclopedias to her brother and he gave her 5 books of fairytales. Now she has 14 more books of fairy tales than encyclopedias, hence:

z + 5 - 0.5y = 14.

z - 0.5y = 9

From the ratios, we have that:

[tex]y = \frac{4}{3}x, z = \frac{5}{3}x[/tex]

Hence we solve for x to find the number of picture books:

[tex]z - \frac{y}{2} = 9[/tex]

[tex]\frac{5}{3}x - \frac{2}{3}x = 9[/tex]

x = 9.

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The area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another

Let the side of a square be x.

So,

Area of square = [tex]x^{2}[/tex]

A =[tex]x^{2}[/tex]

Differentiating with respect to time we get,

dA/dt = 2x dx/dt

When area = 9 [tex]cm^{2}[/tex] the side becomes 3 cm

At x = 3cm and dx/dt = 5 cm/s (Given)

dA/dt = 2.3.5 = 30 [tex]\frac{cm^{2} }{sec}[/tex]

Thus the area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]

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