Q8.
(a)
Work out the value of
(√2)^4

Answer:

No, Beth is not correct. One of the x-values, 2, corresponds to two y-values.

The surface area of the triangular prism be 108 ft²

The volume of the triangular prism be 48 ft³.

Given, a triangular prism (base is a right triangle).

Triangle legs are 3 ft and 4 ft, hypotenuse is 5 ft, height of prism is 8 ft.

Now, the surface area of the triangular prism is,

Surface Area = 2×Area of the base triangle + Side rectangle 1 +Side rectangle 2 + Side rectangle 3

Surface Area = 2×(1/2×3×4) + 5×8 + 3×8 + 4×8

Surface Area = 12 + 40 + 24 + 32

Surface Area = 108 ft²

Now, Volume of the triangular prism be,

Volume = Area of the base triangle × height

Volume = 1/2×3×4×8

Volume = 48 ft³

Hence, the surface area of the triangular prism be 108 ft²

and the volume of the triangular prism be 48 ft³.

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The ratio of the density of cube A to the density of cube B as required in the task content is; 81 : 128.

It follows from the task content that the ratio of the density of cube A to cube B is to be determined.

Recall that the density of an object is given as its mass to volume ratio.

Therefore, given that the volumes are equal; it can be inferred that the density and mass are directly proportional.

Ultimately, the required density ratio can be estimated from the given masses as;

Density of A : Density of B = 81 : 128.

Consequently, the required ratio is; 81 : 128.

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The number of containers that are needed to hold all the gravel in one truck is 3.

The first step is to convert the capacity of the truck from cubic yards to tons. In order to do this multiply the unit of conversion by the capacity of the truck in cubic yards.

Multiplication is the mathematical process used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.

1 cubic yards = 1.48 tons

1.48 x 22.5 = 33.3 tons

The next step is to determine the number of containers that can be on the truck. To do this, divide the converted capacity of the truck by the capacity of each container.

Division is the mathematical operation that is used to determine the quotient of two or more numbers. The sign that is used to represent division is ÷.

Number of containers = total capacity of the truck in tons / capacity of one container

Number of containers = 33.3 / 11.1 = 3 containers

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By using the formula for the gradient, we can solve a simple equation to find that the value of x is 9.

For a segment whose endpoints are:

P = (x₁, y₁) and Q = (x₂, y₂)

The gradient of the line PQ is:

G = (y₂ - y₁)/(x₂ - x₁)

So it is like the slope of a linear equation.

In this case, the endpoints are:

P = (5, 7)

Q = (x, 15)

And the gradient is equal to 2, so we have G = 2, then we can write the equation:

2 = (15 - 7)/(x - 5)

We can solve this to get:

2*(x - 5) = (15 - 7)

2x - 10 = 8

2x = 10 + 8

2x = 18

x = 18/2 = 9

The value of x is 9.

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Answer:    A cruise ship maintains a speed of 22 knots (nautical miles per hour) sailing from San Juan to Barbados, a distance of 600 nautical miles. To avoid a tropical storm, the captain heads out of San Juan at a direction of

20

∘

off a direct heading to Barbados. The captain maintains the 22-knot speed for 9 hours, after which time the path to Barbados becomes clear of storms. (a) Through what angle should the captain turn to head directly to Barbados? (b) Once the turn is made, how long will it be before the ship reaches Barbados if the same 22-knot speed is maintained? (a) The captain should head through an angle of (Do not round until the final answer. Then round to one decimal place as needed.) (b) The time it will take for the ship to reach Barbados is hours (Do not round until the final answer. Then round to one decimal place as needed.)

Answer:

  x = 9

Step-by-step explanation:

Apparently, you want the solution to (10x -27) = 7x.

Subtract 7x from both sides to get ...

  3x -27 = 0

Divide by 3, and you have ...

  x -9 = 0

Add 9 to show the value of x:

  x = 9

The solution to the given equation is x=9.

__

Additional comment

There is no information here that relates the given equation to b, so we cannot help you find b.

The mean height of the team  rounded  to 1 decimal place is 200.0.

The height of this new player is 206.

What is mean Average?

The mean average, of a data set is the sum of all  the numbers divided by the total number of values.

Formular for calculating mean Average:

Mean Average = {Sum of all the values} ÷ {Total numbers of values}

From the question the height of the  players are as follows:

(height) 198,199,200,201,202)

a) Mean Average =(198 +199 +200 +201 +202)

                                             5

                          =1000

                                5

                           =200.0

b) The new player joins the  team to make the Mean Average 201. hence the height of the new player will be calculated using:

Mean Average = {Sum of all the values} ÷ {Total numbers of values}

201 =(198 +199 +200 +201 +202 + x )

                                             6

201  = 1000+ x

               6

crossmultiply to solve for X:

201 *6 =1000+ x

1,206 = 1000+ x

making x subject of the formular we have:

x = 1,206 - 1000

x = 206

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The system of inequalities has been solved graphically and one possible solution is buying 4 apples and 12 peaches.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of apples purchased and number of peaches purchased by Alang and his children, and then translate the word problem into algebraic equation as follows:

Since apples for $2 each and peaches for $0.50 each, the cost of fruits is given by:

2x + 0.5y ≤ 20

Also, they must buy a minimum of 16 apples and peaches altogether:

x + y ≥ 16

Therefore, a possible solution when x = 4 is given by:

x + y ≥ 16

4 + y ≥ 16

y ≥ 16 - 4

y ≥ 12

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In the situation,  60 births per every 1,000 women ages 15 to 44 years, the statistics used is descriptive statistics.

What is descriptive statistics?

Suppose there is a population and suppose there is a sample of the population. If the inference is made on the sample alone and not on the whole population, the statistics used is called descriptive statistics.

Here, the sample is 60 births per every 1,000 women ages 15 to 44 years.

And the inference is made only about those 60 births per every 1,000 women ages 15 to 44 years, and not on the whole population of women aged between 15 to 44 years. So the statistics used in this case is descriptive statistics.

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Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Step-by-step explanation:

Point Form:

[tex](\frac{2}{3} ,-\frac{5}{3}) , (-1, -5)[/tex]

Equation Form:

x= [tex](\frac{2}{3}[/tex], [tex]-\frac{5}{3} )\\[/tex] , y= [tex]-\frac{5}{3}[/tex]

x = -1 , y =-5

Hope this answer your question... sorry I couldnt help more, if it didnt.

The height of the pyramid is 99.1875 meters when the Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.

Given that,

The Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.

We have to find what would the height be if you gave the base sides of 280m using the same material.

We know that,

Volume of Great Pyramid of Cheops = Volume of the  pyramid  with the base sides of 280m

Volume of Great Pyramid of Cheops is 1/3×(side of the base)²×(height of the pyramid)

Side of the base is 230 meters.

Height of the pyramid is 147 meters.

Volume of the  pyramid  with the base sides of 280m is 1/3×(side of the base)²×(height of the pyramid)

Side of the base is 280 meters.

Height of the pyramid is h meters.

Volume of Great Pyramid of Cheops = Volume of the  pyramid  with the base sides of 280m

1/3×(230)²×(147)=1/3×(280)²×h

h = 99.1875 meters.

Therefore, the height of the pyramid is 99.1875 meters while the Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.

The complete question is:

The Great Pyramid of Cheops is a square-based pyramid, the base has sides of 230m, and the height is 147m.

Using the same material, what would the height be if you give the base sides of 280m.

Please give the answer to the nearest meter.

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Answer:

60

Step-by-step explanation:

5 x8 = 40 40 + 20 = 60

Answer:

The factor is the sleep medication

The levels are the 4 different treatments, or medications

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

to make the 11 denominator turn into 22 they had to multiply by 2

So we multiply the numerator by 2 too

9x2=18

Hopes this helps please mark brainliest

Answer:

If you would like to solve the equation 9/11 = x/22, you can calculate this using the following steps:

Steps to find ?

9/11 = x/22    /*22

x = 9/11 * 22

x = 18

The correct answer should be 18 through my calculations

14.375 grams of the radioactive isotope will be left after 3 half-lives.

The initial mass of the isotope = 115 gm

after each half-life, the amount of the isotope is reduced to half

therefore,

after the first half-life, the mass of the isotope will become = 115/2

                                                                                          = 57.5 gram

now after the second half live, the mass will again be reduced to half of the previous mass = 57.5/2

                              = 28.75 gram

similarly, after the third half-life, the mass will be half of the previous mass  = 28.75/ 2

           = 14.375 gram

OR

simply we can write that

weight after 3 half-lives will be = 115/ 2³        

                                                = 115 / 8

                                                = 14.375 grams.

So the mass after 3 half-lives is 14.375 grams.

A risky form of a chemical element that releases radiation as it breaks down and will become extra stable. Radioisotopes may additionally arise in nature or be made in a laboratory. In medication, they may be used in imaging exams and in treatment. additionally known as a radionuclide.

Atoms of equal detail with extraordinary numbers of neutrons are known as isotopes. Many elements have one or extra isotopes which might be radioactive. Their nuclei are risky, so they destroy down, decay, and emit radiation.

whilst utilized in cautiously controlled clinical programs, radioactive isotopes are safe and no longer almost as frightening as we first imagined. The radiation from those isotopes has a quick half of lifestyles and handiest give off low stages of radiation. Radioactive isotopes are not constantly risky, though. a few most effective ones supply tiny amounts of radiation. There are radioactive isotopes in nature all around us. maximum of them cause us very little damage.

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The unit rate or miles per gallon for Blue car is 35.6 miles and for Red car is 36 miles. Red car could travel the greater distance on 1 gallon of gasoline.

44 1/2 = 44 + 1/2

         = (88+1)/2

         = 89/2

1 1/4 = 1 + 1/4

       = (4+1)/5

       = 5/4

28 4/5 = 28 + 4/5

           = (140+4)/5

           = 144/5

Distance blue car covers in 5/4 gallons of fuel = 89/2

     Distance blue car covers in 1 gallon of fuel = (89/2) / (5/4)

                                                                             = (89*4)/(2*5)

                                                                             = 178/5  

                                                                             = 35.6

Distance red car covers in 4/5 gallons of fuel = 144/5

     Distance red car covers in 1 gallon of fuel = (144/5) / (4/5)

                                                                             = (144*5)/(4*5)

                                                                             = 144/5  

                                                                             = 36

Hence, Red car could travel the greater distance on 1 gallon of gasoline by 0.4 miles.

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J and K have values of 0.38 and 0.50, respectively with sampling distribution for the sample variance.

Given data;

The sampling distribution for the sample variance using the distribution;

(I) To find the value of J,

(II) To find the value of K,

We know;

⇒ ∑P(s²) = 1

⇒ J + K + 0.12 = 1

   J + K = 0.88

   K = 0.88 - K

Now K = 0.5;

J = 0.88 - 0.5

  = 0.38

Therefore, the values of J and K are 0.38 and 0.50 respectively.

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Answer:
a - 67
b - 58
c -  125
d - 23
e - 90

Step-by-step explanation:

Solve for b first

90 - 32 = 58

Then you can solve for a

180 - 58 - 55 = 67

Now solve for c

180 - 55 = 125

Now you can solve for d

180 - 125 - 32 = 23

e is equal to 32 + b, so it is 90.

Answer:

64

Step-by-step explanation:

16 ÷ 12 = 1.33 (rounded to 2 decimal places)

1.33 = scale factor

1.33² = area scale factor

1.33² × 36 = 64 (rounded to a whole number)

The graph of the linear function y - 6 = 4(x - 4) is the bottom right graph.

The point-slope representation of a linear function is given as follows:

y - y* = m(x - x*).

In which the coefficients of the equation are defined as follows:

In this problem, the equation is:

y - 6 = 4(x - 4).

From this equation, the slope is of:

m = 4.

This means that the linear function is increasing, and thus, both the left graphs are not correct.

The coordinates of the point that the function passes through are given as follows:

(4, 6).

The only function that passes through this point is the bottom right function, hence it is the correct graph of y - 6 = 4(x - 4).

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The number of seconds it takes for such an object to fall to the

ground from a height of 800 feet is 50 seconds

According to the question,

When an object (with negligible wind resistance) is dropped, its height, h, in feet at a certain time is given by the model

h = - 16t+s

where s is the height from which the object was dropped

t is the number of seconds it has fallen

We have to find the number of second it takes to reach ground when fall from height 800 feet

given,

s = 800

h = 0 (ground height = 0)

using the model h = - 16t+s

0 = -16t + 800

800 = 16t

t = 800/16

t = 50 seconds

Hence, the object will take 50 seconds to reach ground when drop from 800 feet

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The missing number in the bracket is 19. The correct option is d. 19

From the question, we are to determine the missing number in the bracket.

The given sequence is

(1,2) (2,5) (3,10) (?,362)

Now, to determine the missing number, we will study the given sequence.

Let the missing number be x

From the sequence, we can observe that

1² + 1 = 2

2² + 1 = 5

3² + 1 = 10

and

x² + 1 = 362

Now, we will solve the equation for x

x² + 1 = 362

Subtract 1 from both sides of the equation

x² + 1 - 1 = 362 - 1

x² = 361

Therefore,

x = √361

x = 19

Hence, the missing number is 19

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To find the constant of proportionality of a given relationship, divide the given ratios:

8​ grams of yeast for every 500​ grams of flour

⇒ 8/500

⇒ 0.016

We can find the constant that is greater than 1 by reversing the values:

500​ grams of flour for every 8​ grams of yeast

⇒ 500/8

⇒ 62.5

Greater than 1: 62.5

Less than 1: 0.016

The ball must be thrown up at an initial velocity of approximately 24.658 feet per second.

Free fall motion is an uniformly accelerated motion due to gravity. In this question we need to determine the initial velocity of a ball (v), in feet per second, such that the ball reaches a height of 37 feet up. The initial velocity can be found by means of the following equation:

v'² = v² + 2 · g · (h' - h)

Where:

If we know that v' = 0 ft / s, g = - 9.807 ft / s², h = 6 ft and h' = 37 ft, then the minimum initial velocity of the ball is:

v² = v'² - 2 · g · (h' - h)

v = √[v'² - 2 · g · (h' - h)]

v = √[(0 ft /s)² - 2 · (- 9.807 ft / s²) · (37 ft - 6 ft)]

v ≈ 24.658 ft / s

The ball must have an initial velocity of approximately 24.658 feet per second.

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At a profit of $30 per bike and $1950 operating cost per month the store needs to sell 65 bikes to break even.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The store pays an average of ​$60 per bike. The average selling price of each bicycle is ​$90.

∴ The profit per bike the bicycle store make is $(90 - 60) = $30.

Also, the bicycle store costs ​$1950 per month to operate,

Assuming no. of bikes the store needs to sell to break even is x.

∴ 30x = 1950.

x = 195/3.

x = 65.

The store needs to sell 65 bikes to break even the cost.

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Answer:

Answer option C

Step-by-step explanation:

it is a line that ends so it’s C

Answer: 1 -1/20

Step-by-step explanation:

Based on the given conditions, formulate: 42 divided by 40

Cross out the common factor: 21/20

Convert to mixed fraction: 1- 1/20

By taking a common denominator, we can find out that the simplified expression of the given expression is [tex]\frac{6c+4}{c^{2} }[/tex] .

The given expression is -

[tex]\frac{6}{c}+\frac{4}{c^{2} }[/tex] ---- (1)

We have to simplify the expression.

From equation (1), we have the given expression as -

[tex]\frac{6}{c}+\frac{4}{c^{2} }[/tex]

Establishing common denominator [tex]c^{2}[/tex], we have

[tex]\frac{6c}{c^{2} }+\frac{4}{c^{2}}[/tex]

Combining the numerator and common denominator, we have

[tex]\frac{6c+4}{c^{2} }[/tex]

Thus, the simplified expression of the given expression is [tex]\frac{6c+4}{c^{2} }[/tex] which is obtained by taking a common denominator.

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