What is the missing length?? Of this triangular prism

Answer:

It would take [tex]2.7[/tex] seconds, correct to 1 decimal place/nearest tenth.

Step-by-step explanation:

Step 1: Understanding the formula

The formula is given as [tex]h=16t^{2}[/tex], where [tex]h[/tex] represents the height, and [tex]t[/tex] represents the time.

Step 2: Substituting and solving

The question asks for the time that would take when the height is [tex]117~\text{feet}[/tex].

So, substitute [tex]117[/tex] for [tex]h[/tex] in the formula, since [tex]h[/tex] denotes the height:

[tex]h=16t^{2}\\117=16t^{2}[/tex]

Now, let's solve the equation to find the time, [tex]t[/tex]:

[tex]117=16t^{2}\\\\\text{Divide by 16 on both sides of the equation:}\\\frac{117}{16}=\frac{16t^{2}}{16}\\\\\text{Simplify:}\\7.3125=t^{2}\\\\\text{Square root both sides of the equation:}\\\sqrt{7.3125}=\sqrt{t^{2}}\\\\\text{Calculate:}\\2.7 \approx t\\\\\text{Rearrange the equation:}\\t\approx2.7[/tex]

So, it takes about [tex]2.7[/tex] seconds to travel [tex]117[/tex] feet, according to the formula.

The number of field goals the team made in the game is equal to b. 3

The number of field goals the team made can be determined using an algebraic expression. An algebraic expression can be defined as an expression or equation that consists of both letters and numbers in it.

If the team scored 14 points from touchdowns and made x goals which are worth three points each, then an algebraic expression can be given as;

3(x) + 14 = 23

Solving for x;

3x = 23 - 14

3x = 9

x = 9 ÷ 3

x = 3

Hence, the team made a total of 3 field goals that are worth three points each.

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Answer:

10 and 5[tex]\sqrt{6}[/tex]

Step-by-step explanation:

these cannot be solved as they are not equations, but can be simplified

using the rule of radicals

[tex]\sqrt{ab}[/tex] ⇔ [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex]

then

2[tex]\sqrt{25}[/tex] = 2 × 5 = 10

[tex]\sqrt{150}[/tex]

= [tex]\sqrt{25(6)}[/tex]

= [tex]\sqrt{25}[/tex] × [tex]\sqrt{6}[/tex]

= 5[tex]\sqrt{6}[/tex]

Answer:

Step-by-step explanation:

You want the repeating decimal cost ...

  [tex]\$3.\overline{23}[/tex]

written as a fraction and as a mixed number.

One can convert the repeating decimal to a fraction by multiplying it by a power of 10 equal to the number of repeating digits.

This cost number (C) has 2 repeating digits (23), so we want to multiply it by 10^2:

  [tex]100C=10^2\times3.23\overline{23}=323.\overline{23}[/tex]

Now, we can subtract the original cost to cancel the repeating decimal fraction:

  [tex]100C -C = 323.\overline{23}-3.\overline{23}=320[/tex]

Dividing by the coefficient of C, we have the fraction we want:

  [tex]C=\boxed{\dfrac{320}{99}}[/tex]

This is expressed as a mixed number by figuring the quotient and remainder.

  [tex]\dfrac{320}{99}=\boxed{3\dfrac{23}{99}}[/tex]

Answer: x= -18

Step-by-step explanation:

Your equation would be (x/9)+6=4

Subtract 6 by both sides.

Multiply 9 by both sides.

Then you should get -18.

Answer:

40

Step-by-step explanation:

Go through PEMDAS

Exponents: 4∧0 = 1 and 1³ = 1

Multiply: 4 × 5 = 20 × 2 = 40

Add: 1 + 40 = 41

Subtract: 41 - 1 = 40

Answer:

No solution.

Step-by-step explanation:

3(x+1)+4=2x-2+x

-> distribute

3x+3+4=2x-2+x

-> simplify (add constants & x terms)

3x+7=3x-2

-> variable cancels out

7=-2

-> this is not true

Untrue statement; no solution.

Put empty parenthesis/brackets: [,] / (,) or simply put "no solution."

Using proportions, it is found that the value of x would be 28.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We have been given two triangle, we need to find the value of x.

Then using proportions;

12/(x-7) = 8 / 14

Cross multiplication;

12 (14/8) = x - 7

3 (14/2) = x - 7

21 = x - 7

x = 21 + 7

x = 28

Therefore, the value of x is 28.

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Answer:

10% of 25 is 5/2 or 2½ as a fraction and 2.5 as a decimal. Let's find 10% of 25.

Step-by-step explanation:

Answer:

1 is 2 and 2 is 2

Step-by-step explanation:

10 miles per hour is the average journey speed.

Given that,

Some pupils choose to ride bikes. They move at a 15 mph average speed for the first two hours, and then they stop for lunch for an hour. The pupils ride at a 10 mph speed for an additional hour.

Average speed is ( total distance ) / ( total time )

During the 1st 2 hrs:

distance = speed * time

distance = 15 *2 = 30 miles

During the last hour:

distance = speed * time

distance = 10 *1 = 10 miles

Average speed = 30+10 / 2+1+1 = 40/4 = 10 mil/hr

Therefore, their average speed for the trip is 10 mil/hr

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The perimeter of the rectangle given its dimensions is 24x - 4.

A rectangle is a two-dimensional quadrilateral with four right angles that sum up to 360 degrees. A rectangle has two diagonals of equal length that bisect each other at right angles.

The perimeter of  rectangle is the sum of the lengths of the four sides of the rectangle.

Perimeter of a rectangle = 2 x (length + width)

2 x [(12x - 7) + 5)

2 x (12x - 2)

24x - 4

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The equation of the line perpendicular to y=5/6x+7/6 that passes through the point (-7,5) is y = (-6/5)x -17/5 .

In the question ,

it is given that the required line is perpendicular to  y=5/6x+7/6 .

on comparing it with the slope intercept form of the line , we get

slope(m₁)= 5/6

So, the slope of the perpendicular(m₂)  line will be

m₂= -1/m₁

m₂= -6/5

hence,  slope(m₂) of the perpendicular line = -6/5

Given that the perpendicular line is  passing through (-7,5)

substituting the values in slope intercept form (y=mx+c) of the line , we get

5 = (-6/5)(-7) + c

5 = 42/5 + c

c = 5-42/5

= (25-42)/5

= -17/5

y intercept = -17/5

so , the equation of the perpendicular line is y = (-6/5)x -17/5   .

Therefore , the equation of the line perpendicular to y=5/6x+7/6 that passes through the point (-7,5) is y = (-6/5)x -17/5 .

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what in your opinion is the moral in the story ?

Answer:

Step-by-step explanation:

3 cups for 15 packets would be 5 packets for each cup. So 1 cup is 5 packets of trail mix. Which means 5×90= 45

The answer is 45.

we know that

The parent function is

The transformation is to shift 1 unit to the left

so

The rule of this translation is given by

(x,y) -----> (x-1,y)

so

the equation for the transformed function is

Answer:

  128

Step-by-step explanation:

You want the total number of bedrooms in a mix of 1-, 2-, and 3-bedroom apartments.

The total number will be the sum of the products ...

  1 × number of 1-bedroom apartments = 1 × 32 = 32

  2 × number of 2-bedroom apartments = 2 × 24 = 48

  3 × number of 3-bedroom apartments = 3 × 16 = 48

That total is ...

  32 +48 +48 = 128

There are 128 bedrooms in the apartment building.

3 < x < 44

=============================================================

Explanation:

For triangles ABC and DEF we have these two pairs of congruent sides

In between sides AB and BC is angle ABC = 82

In between sides DE and EF is angle DEF = 2x-6

Since AC > DF, this must mean angle ABC is larger than angle DEF. This is because the longer a side is, the larger the opposite angle will be.

Therefore, this leads to angle ABC > angle DEF

--------------------------------------------------

This is what the steps will look like

angle ABC > angle DEF

angle DEF < ABC

0 < angle DEF < angle ABC

0 < 2x-6 < 82

0+6 < 2x-6+6 < 82+6

6 < 2x < 88

6/2 < 2x/2 < 88/2

3 < x < 44

x is between 3 and 44, excluding both endpoints.

Likert scales are designed to be ordinal in measurement.

What is Likert scale and why is it used ?

The Likert scale is a psychometric scale that is used in survey questions that are based on it. It is one of the most popular sorts of survey questions. Respondents in a Likert scale survey are given precise options based on whether they "agree" or "disagree" with a particular survey question rather than just selecting "yes" or "no."

Likert scale survey questions are crucial for gauging a respondent's attitude or view toward a certain topic and are therefore a vital component of market research. Likert scales are commonly used to gauge respondents' levels of agreement with diverse claims using a five-, seven-, or nine-point scale. The Likert Scale was created by organizational psychologist Rensis Likert to evaluate the degree of agreement or disagreement on a symmetric agree-disagree scale. In general, a series of statements is used, each intended to look at a construct from a little different angle. The effectiveness of this method lies in the fact that it can be applied to both social science and marketing constructs.

Therefore, likert scales are designed to be ordinal in measurement.

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Considering the relative frequencies in this problem, the association between scoring 21 points and winning the game is as follows:

There is a strong, positive association.

The relative frequency of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

From the table given at the end of the answer, we have that when the team scored at least 21 points, an interval composed of 28 games, the team won 25 games and lost only 3, hence the relative frequency of wins when the team scores at least 21 points is of:

25/28 = 0.8929 = 89.29%.

Due to this high frequency of wins, there is a strong and positive association between scoring 21 points and winning the game

The table with the team's results is given by the image at the end of the answer.

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If the difference between the total surface area and curved surface area of a hemisphere is 154 cm2, then its volume is 718.66 cm³

In general, the term "hemisphere" refers to the lower half of the earth, such as the northern or southern hemispheres. A hemisphere, however, is a 3D figure that is created by splitting a sphere into two equal halves, each with one flat side, and is known as such in geometry.

In everyday life, we encounter a variety of objects that have a hemisphere shape, such as a cherry that is shaped like a hemisphere when cut in half or a grapefruit that has a hemisphere shape when cut in half.

The difference between the total surface area and curved surface area of a hemisphere is 154cm.

Total Surface Area of Hemisphere = 3πr²

And Curved Surface Area of Hemisphere = 2πr²

It is Given that

Total Surface Area of Hemisphere - Curved Surface Area of Hemisphere. = 154.

Substituting the values, we get,

⇒ 3πr² - 2πr² = 154

⇒ πr² = 154

⇒ r² = 154/π

⇒ r² = 154 × (7/22)

⇒ r² = 7 × 7

⇒ r = 7.

Now, lets find the volume which is

Volume of Hemisphere = 2/3πr³

V = 2/3π(7)³

V = 2/3(22)(7)²

V = 2156/3

V = 718.66 cm³

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Answer: 5.4

Step-by-step explanation:

[tex]29.16 < 30 < 30.25 \implies 5.4 < \sqrt{30} < 5.5[/tex]

The probability of the outermost ring is 55.6%

Answer:

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