The hypotenuse of a right triangle measures 8 cm and one of its legs measures 4 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

66.6% = 0.6666... = [tex]\frac{2}{3}[/tex]

Answer:

Fraction = 2/3

Step-by-step explanation:

Given information,

→ Percentage = 66.6%

→ Decimal = 0.6

→ Fraction = ??

Then the required fraction is,

→ Percentage ÷ 100

→ 66.6/100

→ 2/3

Hence, the fraction is 2/3.

Answer:

x = 12

Step-by-step explanation:

Angles in a triangle add up to 180 degrees.

This means that 6x - 19 + 3x + 7 + 84 = 180

6x - 19 + 3x + 7 + 84 = 180

==> combine like terms

9x + 72 = 180

==> subtract 72 from both sides

9x = 108

==> divide both sides by 9

x = 12

The missing side lengths are (m = 4[tex]\sqrt{6}[/tex] , n =  6[tex]\sqrt{2}[/tex]).

According to given triangle, Using triangular formula;

tan 30 = [tex]\frac{2\sqrt{6} }{n}[/tex]

⇒[tex]\frac{1}{\sqrt{3} }[/tex]  = [tex]\frac{2\sqrt{6} }{n}[/tex]

⇒ n = [tex]6\sqrt{2}[/tex]

  n = [tex]6\sqrt{2}[/tex]

Similarly,

sin 30 = [tex]\frac{2\sqrt{6} }{m}[/tex]

⇒ [tex]\frac{1}{2}[/tex] = [tex]\frac{2\sqrt{6} }{m}[/tex]

⇒ m = [tex]4\sqrt{6}[/tex]

   m = [tex]4\sqrt{6}[/tex]

so,

    m = [tex]4\sqrt{6}[/tex] and n = [tex]6\sqrt{2}[/tex]

So, the correct option is D.

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Answer:

27

Step-by-step explanation:

The cat weighs 7 kg.

The rabbit weighs 3 kg.

The dog weighs 17 kg.

You can check these answers by adding them together.

A cat plus the rabbit is 10 kg.

The rabbit and the dog is 20 kg.

The dog and cat is 24 kg.

The level of a independent variable known to as the "Control group" is designed to portray a neutral state.

The cause is the independent variable. Its value is unaffected by the other study variables.

You plan a study out whether variations in the room's temperature have an impact on students' math test results.

Consequently, "control group" refers to a level of such an independent variable that is meant to stand in for "no treatment" or a neutral circumstance.

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The three consecutive even integers are -2, 0 and 2.

Let the three consecutive even integers be x, x+2 and x+4.

Since the product of the first two is taken, the result is four less than the square of the third one. This will be:

x(x + 2) = (x + 4)² - 4

x² + 2x = x² + 8x + 16 - 4

x² + 2x = x² + 8x + 12

Collect like terms

x² - x² + 2x - 8x - 12

-6x - 12 = 0

-6x = 12.

Divide

x = -12/6

x = -2

x + 2 = -2 + 2 = 0

x + 4 = -2 + 4 = 2

They're -2, 0, and 2.

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Probability that the product of the numbers on the top faces is prime is  1/2(1/6)⁴.

In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution. Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.

Given,

12 fair dice rolled,

Probability that the product of the numbers on the top faces is prime:

⁶C₅ × (1/6)⁵ × ³C₁/⁶C₁

6 × (1/6)⁵ × 3/6

1/2(1/6)⁴

Probability that the product of the numbers on the top faces is prime is  1/2(1/6)⁴.

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Answer:

[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]

Step-by-step explanation:

When adding or subtracting fractions that have different denominators, first rewrite the fractions as equivalent fractions with the same denominator.  To do this, find the lowest common multiple (LCM) of the denominators.

The given subtraction is:

[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}[/tex]

The LCM of the denominators 2 and 8 is 8.  Therefore, we need to rewrite the first fraction as an equivalent fraction with 8 as its denominator.  To do this, multiply its numerator and denominator by 4:

[tex]\implies \sf \dfrac{1}{2} \times\dfrac{4}{4}=\dfrac{4}{8}[/tex]

Therefore:

[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}[/tex]

To subtract fractions with the same denominator, simply subtract the numerators. (The denominator stays the same).

[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}=\dfrac{4-1}{8}=\dfrac{3}{8}[/tex]

Final solution

[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]

A 90% confidence interval for the average speed of all drivers on interstate 94 is (73.69, 76.31)

Given that,

Imagine asking a sample of 16 people how quickly they travel on Interstate 94. You determine the average speed to be 75 mph and the variance to be 9 mph after gathering your sample.

Solution is as given below :

90% Confidence Interval for μ is

μ = X ± tₐ/2 (n-1) 5/[tex]\sqrt{n}[/tex]

μ = 75  ± (1.75) * 3/[tex]\sqrt{16}[/tex]

μ = (73.69, 76.31)

Consequently, a 90% confidence interval for the interstate 94 average speed of all drivers is μ = (73.69, 76.31)

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The expression for the cost of each scarf is s/4.

According to the question,

We have the following information:

Let s be the total amount Heidi spent for scarves. each of the 4 scarves that she bought cost the same.

Now, the cost of 1 scarf can be easily found by dividing the total cost of the scarves by the number of scarves.

(If we would have to find the cost of 15 scarves then first we would have used division and then multiplication.)

So, we have the following expression:

4 scarves = s

Cost of one scarf = s/4

Hence, the expression for the cost of each scarf is s/4.

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Answer:22.5

Step-by-step explanation:

Answer:

9/34

Step-by-step explanation:

I find when multiplying fractions, its easier to separate them into the numerator and denominator.

So we have 12 x 3, and 17 x 8

12 x 3 = 36

17 x 8 = 136

So we have 36/136

Simplified, that is 9/34

The surface area of the triangular prism is  936 cm².

In geometry, a triangular prism is a three-sided prism.

Therefore, the surface area of the triangular prism can be calculated as follows:

surface area of triangular prism = bh + L(x + y + z)

where

Therefore,

surface area of triangular prism = 24 × 18 + 7(18 + 30 + 24)

surface area of triangular prism = 432 + 7(72)

surface area of triangular prism = 432 + 504

surface area of triangular prism = 936 cm²

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Darryl receive $579.44  in dividends every year .

In the question ,
it is given that

Darryl's portfolio

number of shares of Essentia Inc. = 66

dividend received from each share in a year = $1.79 per share

So , amount of dividend received from Essentia Inc. = 66 × 1.79

= $118.14

number of shares of SFT Legal = 95

dividend received from each share in a year = $2.62 per share

So , amount of dividend received from SFT Legal = 95 × 2.62

= $248.9

number of shares of Grath Oil = 180

dividend received from each share in a year = $1.18 per share

So , amount of dividend received from Essentia Inc. = 180 × 1.18

= $212.4

So , total dividend Darryl receives = $118.14 + $248.9 + $212.4

= $579.44

Therefore , amount of dividend received by Darryl each year is $579.44  .

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Answer:

12 tables per classroom.

Step-by-step explanation:

We will assume that the teacher uses all of the 4/5 oz of paint.  We can find how many samples of 1/30 oz are contained in the 4/5 oz by dividing:

(4/5)÷(1/30) = (4/5)*(30/1)

(4/5)*(30/1)  = (120/5)

(120/5) = 24 samples of 1/30 oz paint in (4/5) oz total paint.

Each of the 2 Pre-K classrooms have the same number of tables, so we can divide 24 samples by 2 to find the number of tables in each classroom,

*24 samples/2 classrooms) = 12 tables/classroom

Answer:

Option D: 160 square feet

Step-by-step explanation:

Area of the lawn

= (7 feet × 8 feet) + (13 feet × 8 feet)

= 56 square feet + 104 square feet

= 160 square feet

To select the community, there are 20 ways available.

What is Combination?

A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant.

Solution:

Since 2 particular students are to be included,

we have to arrange 3 students from 6 students.

nCr = n! / (n-r)!*r!

6C2 = 6!/ (6-3)! 3!

6C2 = 6*5*4*3!/ 3! * 3*2

6C2 = 5*4 = 20

Thereofre, there exists 20 ways of doing the above mentioned.

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The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).

A rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).

For a dilation with a scale factor of 2, we have:

Point A (-8, 1)   →   (-8 × 2, 1 × 2)  = Point A' = (-16, 2)

By applying a rotation of 180° to the given point, the coordinates of its image is given by:

(x, y)                           →               (-x, -y)

Points A' = (-16, 2)   →  Points A' = (-(-16), -(1)) = (16, -1).

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Complete Question:

What is the image point of (-8, 1) after the transformation D₂ о R180°?

Answer is :

The chosen at random is 25 - 44 years old is  = 26 %.  

Probability determines how likely it is that a stated event would

occur. This event would occur. This probability lies between 0 and 1.

The probability that a person chosen at random is at least

15 years = sum of percentages of people at least 15 years old :

14 + 13 + 13 + 15 + 12 + 13 = 80%

the probability that a person chosen at random is 25 - 44 years old :

13% + 13% = 26%

Therefore The probability is 26%.

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Jade and Jordan both have a total of 35 trading cards altogether.

Given, Jade has 28 trading cards. He has 4 times as many trading cards as Jordan.

As, Jade has 28 trading cards

Let Jordan has 'x' trading cards.

Now, as Jade has 4 times as many trading cards as Jordan.

So, 28 = 4x

4x = 28

x = 7

So, Jordan has 7 trading cards.

Now, they both have a total of 35 trading cards altogether.

Hence, Jade and Jordan both have a total of 35 trading cards altogether.

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If EOF = 26 and FOG= 38, then the measure of BOG would be 64 degrees.

What is a measure of angle?

An angle is measured in degrees, thus the term "degree measure." Because one complete revolution equals 360 degrees, it is divided into 360 parts. Each stage of the revolution represents a degree.

The given data:

A measure of EOF = 26 and a measure of FOG = 38.

Then we can say that OF is an angle bisector of angle EOG.

Then the measure of BOG = EOF + FOG

                                            = 26 + 38

                                            =  64 degrees.

Hence, If EOF = 26 and FOG= 38, then the measure of BOG would be 64 degrees.

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x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

What is, axis of symmetry, vertex and x - intercept?

A vertical line that splits the parabola into two equal half is the axis of symmetry. The equation x = - b/2a tells us where the line of symmetry lies. The parabola's vertex, which is a point (x, y), is where it crosses its axis of symmetry.

A line's x-intercept is the location at which the x-axis is crossed.

Consider, the given equation,

[tex]f(x) = \frac{1}{4}(x - 1)(x + 7)[/tex]

Let,

[tex]y = \frac{1}{4}(x - 1)(x + 7)[/tex]             ..(1)

To find x - intercept, plug y = 0 in above equation,

[tex]\frac{1}{4}(x - 1)(x + 7) = 0\\ (x - 1)(x + 7) = 0\\(x - 1) = 0, (x + 7) = 0\\x = 1, x = -7[/tex]

Therefore, x = 1 and x = -7 are the x - intercepts.

Since, the x-coordinate of the vertex is at the midpoint of the x-intercepts.

So,

[tex]x = \frac{-7+1}{2} = \frac{-6}{2} = -3[/tex]

Plug x = -3 in equation (1)

[tex]y = \frac{1}{4}(-4)(4) = -4[/tex]

Therefore, the vertex is, (-3, -4).

The x - coordinate of the vertex is the axis of symmetry.

Therefore, axis of symmetry is x = -3.

Hence, x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

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Graph will shift in both horizontal and vertical direction by 4 units.

What is straight line?

An unending, one-dimensional figure with no width is a straight line. It consists of an infinite number of points connected on either side of a point. There is no curvature in a straight line. It might be angled, vertical, or horizontal.

What is general equation of a Straight Line?

The general equation of a straight line can be given as ax + by + c = 0, where

What do you mean by function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain. The usual way to refer to a function is as fn(x), where x is the input.

We have function,

fn(x) = x + 5

when the graph is translated by 4 units, we can write it as;

g(x) = fn(x) + 4

the graph will shift in both horizontal and vertical direction by 4 units as it can be seen in the graph.

Therefore, graph will shift in both horizontal and vertical direction by 4 units.

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Answer:75

Step-by-step explanation:

since there are 15 students and they each need 5 plates you just do 15x5 and get 75

The first four terms of the sequence would be -

9, 12, 15, 18

Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -

3, 6, 9, 12, 15

x, x + 2, x + 4, x + 6

We have the following sequence -

f(n) = 3n + 6

We can write the first four terms as -

f(1) = 3 x 1 + 6 = 9

f(2) = 3 x 2 + 6 = 12

f(3) = 3 x 3 + 6 = 15

f(4) = 3 x 4 + 6 = 18

Therefore, the first four terms of the sequence would be -

9, 12, 15, 18

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Answer:

Using formula to calculate the circumference of wheel: c=d/n

where

D is the distance bike travel

n is the number of times rotation

C is the circumference of the wheel

As per the statement:

Lin’s bike travels 100 meters when her wheels rotate 55 times.

here, n = 55 rotation and D = 100 meter.

then by definition:

meter c=100/55=20/11

Therefore, the circumference of her wheel is 1 9/11

As per the given equation of the parabola, the directrix of the parabola is equal to y = -2.5.

What is directrix?

A directrix in mathematics is a curve which is associated with the process generating a geometric object, such as:

Directrix - conic section

Directrix - generatrix

Directrix - rational normal scroll

The equation of a quadratic function, with vertex (h,k), is:

y = (a)(x - h)² + k

In which, a is the leading coefficient.

The directrix is: y = k + 4a.

In this problem, the equation of parabola is given as:

y = (1/8)(x-2)² - 3

The coefficients in the given equation are a = 1/8 = 0.125,

h = 2, k = -3,

Hence the directrix is given by:

y = -3 + 4 x 0.125

y = -3 + 0.5

y = -2.5.

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