Find the surface area and volume of each 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

The apple mean weight's 95% confidence interval is;

CI = (119.14, 125.86) (119.14, 125.86)

The confidence interval above should be understood as;

We have a 95% confidence that each apple's average weight, across all of the apples they send, falls between 119.14 and 125.86 grams.

Ours is given;

12 for the standard deviation.

Sample size: 49; n

x = 122.5 is the indicated mean weight.

The current confidence interval formula is;

CI = x⁻ ± z(σ/√n)

Tables indicate that z = 1.96 at a 95% confidence level.

Thus;

CI = 122.5 ± 1.96(12/√49)

CI = 122.5 ± 3.36

CI = (122.5 - 3.36), (122.5 + 3.36)

CI = (119.14, 125.86)

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we know that [tex]r[/tex]

area of the circle is equal to

A=  [tex]\pi[/tex] × [tex]r^{2}[/tex]

solve for [tex]r[/tex]

[tex]r[/tex] = [tex]\sqrt{\frac{A}{\pi } }[/tex]

for A=60cm2

[tex]r[/tex] = [tex]\sqrt{\frac{60}{\pi } cm}[/tex]

we know that

[tex]\sqrt{60\\}[/tex] = [tex]\sqrt{2^{4} }[/tex] × 3 × 5

=2[tex]\sqrt{15}[/tex]

so,

[tex]\sqrt{\frac{60}{\pi } }[/tex] = 2 [tex]\sqrt{\frac{15}{\pi } }[/tex]

2[tex]\sqrt{\frac{15}{\pi } } = 2\frac{\sqrt{15} }{\pi }[/tex]  × [tex]\frac{\sqrt{\pi } }{\sqrt{\pi } }[/tex]

= 2 [tex]\frac{\sqrt{15\pi } }{\pi }[/tex]cm

this means the answer is-

2 [tex]\frac{\sqrt{15\pi } }{\pi } cm[/tex]

The probability to take 5 classes is 0.1, while the probability to take at least one class is 0.6, the probability to take 2 or 3 classes is 0.23 and the expectation of the distribution is 1.37.

The distribution given is

X                  PIX)

0                  0.4

1                   0.25

2                  0.15

3                  0.08

4                  0.02

5                  ???  

1.

We know that the sum of all the probabilities in a probability distribution is always equal to 1.

Let the probability of X = 5 be p

Hence,

0.4 + 0.25 + 0.15 + 0.08 + 0.02 + p = 1

or, 0.9 + p = 1

or, p = 1 - 0.9

or, p = 0.1

Hence the probability to take 5 classes is 0.1.

2.

We need to find P(X ≥ 1)

= 1 - P(X = 0)

From the distribution we know that P(X = 0) is 0.4

Therefore, P(X ≥ 1)

= 1 - 0.4

= 0.6

Hence, the probability to take at least one class is 0.6

3.

The probability to take 2 or 3 classes in a semester

= P( X = 2)  +  P(X = 3)

= 0.15  +  0.08

= 0.23

4.

The expectation of any distribution

= ∑xp(x)

where,

x is the random variable

p(x) is the probability of the random variable

Therefore,

E(X) = 0 X 0.4  +  1 X 0.25  +  2 X 0.15  +  3 X 0.08  +  4 X 0.02  +  5 X 0.1

= 0  +  0.25  +  0.30+  0.24  +  0.08  +  0.50

= 1.37

Therefore the expectation is 1.37

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The change in temperature is 15°

How to find Change in temperature ?

        t₂ = t₁ + final temperature

We have given,

In morning, when Rae woke up the temperature is (t₁) = -20°

At dinner time, the temperature is = 35°

t₂ = t₁ + 35

t₂ = (-20) + 35

t₂ = 15°

Hence, the change in temperature is 15°

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Answer:

1

Step-by-step explanation:

because the 1 is actually invisible

its called invisible math

y=mx+b

Kinematic parameters is the way by which coefficient of restitution change with angle of impact.

The ratio of a boulder's velocities or energy prior to and following its impact with the slope is represented by the coefficient of restitution, which is a dimensionless number. Different definitions of the coefficient of restitution have been put forth in earlier studies, but it has not been determined which definition is better suitable for predicting rockfall.

The determination of suitable values for the coefficients of restitution, which often change with the kinematic parameters and terrain conditions, is essential for the accuracy of a computer program modelling a rockfall trajectory. Using small-scale laboratory testing, the effects of the impact angle with regard to the slope on the coefficients of restitution have been identified and analyzed. to determine the validity of the current conclusion based on limited laboratory testing.

This study conducted a medium-scale laboratory test employing spherical limestone polyhedrons impacting concrete slabs to determine how the impact angle affects the coefficients of restitution when the test scale is changed. A 3D motion capture system measures the velocities before and after the collision during free fall tests. Several general laws apply when taking into account the impact angle's effect, regardless of the test scales and conditions, according to the results comparison between our test and the existing small-scale tests. The normal coefficient of restitution (Rn), the kinematic coefficient of restitution Rv, and the kinetic energy coefficient of restitution Re will all decrease as the impact angle increases.

In contrast, it will cause Rt's tangential coefficient of restitution to increase. The impact of the impact angle is significantly influenced by the rotation. The normal coefficient of restitution Rn and tangential coefficient of restitution Rt are always higher when more kinetic energy is converted to rotational energy.

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The test statistics value is 0.380

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

Standard deviation  It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

For example: To find the standard deviation, you have to add up all the numbers in the data set, then divide by how many numbers there are, and that will get you your answer.

Formula:

t=(mean-time)/(standard deviation/√(number of students) )

=( 12 - 11.8) / (1.9 / √13 )

= 0.380

This is test statistics value.

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Answer:

Foot: 18.416666666666668

Yard: 6.1388888888888892836

Answer:bgvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvddddddddddddddddddddddddddd

Step-by-step explanation:

Answer:

Step-by-step explanation:

well it will be 16 because a square has 4 sides so you multiply by the grams that would be 4. 4*4= 16

Amount of money present in Juan's account when she is 18 years old is $2,284.73

When Juan is 12 years old ;

Given P = principal = $ 2000

r = interest rate = 2.3 %

t = number of periods = 2

To start, multiplying R percent by 100 gives us 2.3%/100, or 0.023 each year.

Simply converting time into years, 2 months divided by 12 months each year equals 0.166667 years.

How to resolve our equation

A = 2000(1 + (0.023 × 0.166667)) = 2007.666682

A = $2,007.67

Simple interest on a principal of $2,000.00 at a rate of 2.3% annually for 0.166667 years (2 months)

Juan when she is 18 years old

time = 18 - 12 = 6 years

rate = 2.3 %

Principal = $2,007.67

Accrued money = A = $2,284.73

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The number of bananas Bruce can eat in 4 weeks is 70 bananas

From the question, we are to calculate the number of bananas Bruce can eat in 4 weeks.

From the given information,

Bruce can eat 2 1/2 bananas per day

First, we will determine the number of days there are in 4 weeks

NOTE: There are 7 days in 1 week

If there are 7 days in 1 week

Then,

There are 4 × 7 days in 4 weeks

4 × 7 = 28 days

That is, 4 weeks = 28 days

Now, we will determine the number of bananas Bruce can eat in 28 days

If Bruce can eat 2 1/2 bananas per day

Then,

Bruce can eat 28 × 2 1/2 bananas in 28 days

28 × 2 1/2 = 28 × 5/2

= 14 × 5

= 70

Hence, Bruce can eat 70 bananas in 4 weeks

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Answer:

70

Step-by-step explanation:

Bruse can eat 2 1/2 bananas in one day so:

1day=2 1/2bananas.

if 1wk=7days

4wks=x =28days

1day=2 1/2 bananas

28da

28×2 1/2

=28×5/2=70

answer=70bananas

Equation of the line that passes through (7, 10) and is perpendicular to the line y =x-9 is y = -x+17.

Given equation, y = x-9

Slope = m = 1

Slope of line perpendicular to given line = -1/m

                                                                    = -1/1

                                                                    = -1

Let the equation of line be y = mx + c

Passes through A(7,10)

10 = -1(7) + c

10 = -7 + c

c = 10 + 7

  = 17

Hence, equation is y = -x+17

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If Latanya receives 60 rewards points just for signing up. She earns 9.5 points for each visit to the movie theater. She needs 117 points for a free movie ticket. Then 6 visits Latanya has to make to earn a free ticket.

What is slope intercept form of line?

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given that,

Latanya has 60 rewards points just for signing up.

For each visit to theatre she earns 9.5 points.

To get free ticket she needs 117 points.

We need to find how many visits she has to do to get free ticket.

We use Linear equation to solve this

Let y = total number of rewards points

x = number of visits to the movie theater

m=Points for each visit

y=mx+b

117=9.5x+60

Subtract 60 on both sides

117-60=9.5x

57=9.5x

x=6

Hence she has to make 6 visits to earn a free ticket.

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Answer:

6   x=6

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

1/4 + 1/2 ÷ 3/8

0.25 + 0.5 ÷ 3/8

0.25 + 1.33

= 1.58

approximately 2

The ratio of BE/BC is 1:3.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

In triangle ABC, the ratio of FA and CF is 1:2.

Since, the point G is the midpoint of BF,

Implies that G divides  BF in ratio 1:1.

By using mass point geometry,

The ratio of BE/BC=1:3

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Answer:

f ≤ 4

Step-by-step explanation:

f/4 + 6 ≤ 7

f/4 ≤ 7 - 6

f/4 ≤ 1

f ≤ 4

Answer:

 F<4

________

________

The solution is

The Hypotenuse = FD

Side Opposite of ∠F = MD

Side Adjacent of ∠F = MF

Side Opposite of ∠D = MF

Side Adjacent of ∠D = MD

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

The triangle FMD and the ∠M is a right angle

So , ∠M = 90°

From the figure , we can deduce that

The Hypotenuse = FD

Side Opposite of ∠F = MD

Side Adjacent of ∠F = MF

Side Opposite of ∠D = MF

Side Adjacent of ∠D = MD

Hence , the required solution is based on trigonometric relations

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Answer: t = 5d t = 1/5d

Step-by-step explanation:

The equation that models the amount of time that is left on the cd is 80 - m.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the blank CD can hold 80 minutes of music you have burned m minutes of music onto the cd. The time left will be:

= Total minutes - Time used

= 80 - m

This illustrates the equation.

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Answer:

Step-by-step explanation:

x=-4 that should be the answer i don't really know how too explain but i did this 2 years ago

Answer:

Step-by-step explanation:

The distance between the cars increasing 2 hours later is 65mph

Let’s say, the velocity in the west is x, the velocity in the south is y, and the distance between them is s at any time t. Since the west and south directions are perpendicular to each other, this will be for a right-angled triangle.

So, we have [tex]x^2 + y^2 = s^2[/tex] --------------(1)  

(please note all of them are changing as t increases.)

So, x=u×t and y=v×t,

so using (1), we can write

[tex][(u\times t)^2 + (v\times t)^2] = s^2[/tex]

[tex]s= \sqrt{(u^2 + v^2)}* t[/tex]

Using the value of u and v,

get [tex]\sqrt{(u^2 + v^2)}[/tex]= 65

So, s= 65 t

ds/dt = 65 mph

There fore the distance between the cars increasing 2 hours later is 65mph

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The measure of ∠A is 106°.

Quadrilateral ABCD is inscribed in this circle.

To find out the measure of LA:

We are given that, 'Quadrilateral ABCD is inscribed in the circle'.

So, we get that,

'ABCD is a cyclic quadrilateral' that is The sum of the opposite interior angles is 180°.

Thus, we have,

∠A +∠C = 180°

i.e. ∠A + 74° = 180°

i.e. ∠A = 180° - 74°

i.e. ∠A = 106°

Thus, the measure of ∠A is 106°.

Hence the answer is the measure of ∠A is 106°.

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The number of each type of shirt that Marcus bring to the fair is 80 long-sleeved T-shirts  and 120 short-sleeved T-shirts .

Let x =Number of long-sleeved T-shirts

Let y = Number of short-sleeved T-shirts

Hence,

x + y = 200

1/2x + 1/3y = 80

Using linear Combinations Method:

6[1/2x + 1/3y = 80]

x +y =200

3x + 2y =480

So,

-2(x +y = 200)

3x + 2y = 480

-2x -2y=-400

3x + 2y = 480

x            = 80 (Long sleeved)

Solve for y

80 + y =200

y = 200 -80

y = 120 (Short sleeved)

Therefore he brought  80 and 120  T-shirts .

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The equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.

We are given:

The perimeter of the 1 triangle = 24

The perimeter of the 2 triangle = 30

The perimeter of the 3 triangle = 36

As we can see in the given figures two sides with lengths of 9 are fixed and the side with a length of 6 is varying.

So, we can write this as,

P = 6n + 18, where n = number of triangles.

Now, check the equation formed by substituting the values;

Substitute n = 1, and we get;

P = 6(1) + 18

P = 6 +18

P = 24 True.

Substitute n = 2, and we get;

P = 6(2) + 18

P = 12 +18

P = 30 True.

Substitute n = 3, and we get;

P = 6(3) + 18

P = 18 + 18

P = 36, true.

So, it is true for all the figures.

Thus, the equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.

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The percentage of three types of tickets collected at the gate:

ai) student's ticket as a percent: 48%, as a fraction: 48/100, and as a decimal: 0.48.

aii)Adult's ticket as a percent:28%, as fraction:28/100, and as decimal: 0.28.

aiii) Senior's( 65 and older) ticket: 14%, as fraction:14/100 and as decimal: 0.14.

b)Tickets for children under 5years is: 10%, as fraction:10/100, and as decimal: 0.10.

what is percentage?

This is a number written as a ratio of a hundred or as a fraction of a hundred. it is represented with "%".

How to calculate the percentages:

.As a fraction: Write it as a ratio of a hundred.

ticket type for

i) students48% =48/100

ii)Adult       28%=28/100

iii)Senior's( 65 and older)14% =14/100

.As a decimal: Write it as a ratio of hundred then divide by hundred.

ticket type for:

i) students48% =48/100=0.48

ii)Adult       28%=28/100=0.28

iii)Senior's( 65 and older)14% =14/100=0.14

b)To calculate the percentage of tickets of children under 5 years:

Percent(% )means 100

Therefore,

100 - student ticket %- Adult's ticket % - Senior's( 65 and older) ticket%

100- 48 - 28 - 14 = 10%

Thus for children under 5 years,

i)As percent is:10%,

ii)as fraction:10/100

iii)decimal: 0.10.

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the decision rule for rejecting the null hypothesis is, to reject H₀ if t > 1.363.

Right-tailed test: H0µ = k H1:>k P-value = P(z>z x) This indicates the probability of obtaining a test statistic as high as or higher than z x. If the P-value is less than α, we reject H0(null hypothesis) and conclude that the data are statistically significant at the level α. We do not reject H0 if the P-value is greater than α.

H0: µ  = 5.3 , H1: µ> 5.3

it is a right-tailed test

n = 12

α = 0.10

therefore the decision rule for rejecting the null hypothesis is, Reject H0 if t> 1.363.

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