The base of a rectangular prism is 20 cm 2. If the volume of the prism is 100 cm 3, what is its height?

Answer:

Step-by-step explanation:

Corresponding true average energy expenditure of shovel with conventional blade and true average energy expenditure of shovel with perforated blades form matched pairs.

The data for the test are the differences between the true average energy expenditures of the shovels.

μd = true average energy expenditure of shovel with conventional blade minus true average energy expenditure of shovel with perforated blades.

Conventional perforated diff

0.0011 0.0011 0

0.0014 0.0010 0.0004

0.0018 0.0019 -0.0001

0.0022 0.0013 0.0009

0.0010 0.0011 -0.0001

0.0016 0.0017 -0.0001

0.0028 0.0024 0.0004

0.0020 0.002 0

0.0015 0.0013 0.0002

0.0023 0.0017 0.0006

0.0017 0.002 -0.0003

0.0020 0.0013 0.0007

0.0014 0.0013 0.0001

Sample mean, xd

= (0 + 0.0004 - 0.0001 + 0.0009 - 0.0001 - 0.0001 + 0.0004 + 0 + 0.0002 + 0.0006 - 0.0003 + 0.0007 + 0.0001)/13 = 0.0002077

xd = 0.0002077

Standard deviation = √(summation(x - mean)²/n

n = 13

Summation(x - mean)² = (0 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2+ (0.0009 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2 + ( - 0.0001 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (0 - 0.0002077)^2 + (0.0002 - 0.0002077)^2 + (0.0006 - 0.0002077)^2 + (- 0.0003 - 0.0002077)^2 + (0.0007 - 0.0002077)^2 + (0.0001 - 0.0002077)^2 = 0.00000158923

Standard deviation = √(0.00000158923/13

sd = 0.00035

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 13 - 1 = 12

The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (0.0002077 - 0)/(0.00035/√13)

t = 2.14

We would determine the probability value by using the t test calculator.

p = 0.027

Since alpha, 0.05 > than the p value, 0.027, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the true average energy expenditure using the conventional shovel does not exceed that using the perforated shovel.

Answer:

Fastest wind speed ever recorded

That is, however, a patch on the top speed ever reached by an aircraft, a record held by the Lockheed Blackbird, which tickled 2,193mph in 1976

Step-by-step explanation:

Answer:

[tex]7x^2-2x-2[/tex]

Step-by-step explanation:

[tex]-3x^2+9+10x^2-11-2x[/tex]

Combine like terms:

[tex]10x^2-3x^2-2x+9-11[/tex]

Simplify:

[tex]7x^2-2x-2[/tex]

Hope this helps!

Answer: 7x^2 - 2x - 2

Step-by-step explanation:

in this expression, all you have to do is combine like terms. those are -3x^2 and 10x^2, 9 and -11.

-3x^2 + 9 + 10x^2 - 11 - 2x     rearrange to make easier

-3x^2 + 10x^2 - 2x + 9 - 11     combine like-terms

7x^2 - 2x - 2

Answer:

its probably a. x>-53

my appolgies if it's wrong

Answer:

14, 32

Step-by-step explanation:

45,15,44,17,40,20,31,25

this is combination of 2 series:

In the first series we can see the pattern as:

In the second series we can see the pattern as:

The series will continue as:

Answer:

see below

Step-by-step explanation:

[tex]\frac{x-c}{d} > y[/tex]

x - c > dy

x > dy + c

Answer:

So C doesn't have symmetry so that rules out a

b does though

J doesn't work so that rules out c

F doesn't work so that rules out d

B is answer

Answer:

B. is the rotational symmetry

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

rational number means comparison between two numbers

eg: 1:3 or 1/3 or 0.333

irritional number does not

The one of the numbers is an irrational number that is A) 134 / 675

Rational numbers are numbers which can be written in the form of [tex]\dfrac{a}{b}[/tex]where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.

Irrational numbers are those real numbers which are not rational numbers.

Noted that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

For example

: 1:3 or 1/3

or 0.333

But irrational number does not.

The rational number means the comparison between two numbers

A) 134 / 675 = 0.19

B) 3.

C) 7.676767…

D) 8.12131415…

So,  A) 134 / 675

This is an irrational number

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Answer:

a=5

b=15

Step-by-step explanation:

By following the pattern on the table we can see that the x is increasing by 1 and the y is increasing by 3 each time. Therefore, the next set of numbers would be (5,15).

Answer:

middle is 2.5 ft

right is 4375 ft

left is 1875 ft

Step-by-step explanation:

Here is the full question:

When a species has several variants of a phenotype passed on from generation to generation, we can form a hypothesis about the genetics of the trait based on Mendelian theories of genetic inheritance. For example, in a two-gene dominant epistatic model, the first gene masks the effect of the second gene, leading to the expression of three phenotype variants. Crossing the dominant and recessive homozygote lines would result in a second generation represented by a mix of dominant, intermediate, and recessive phenotype variants in the expected proportions: and respectively, also called a 12:3: 1 ratio.

Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2: 131 white squash, 34 yellow squash, and 10 green squash. Are these data consistent with a 12: 3: 1 dominant epistatic model of genetic inheritance( white being dominant)?

The null hypothesis for the chi-square goodness-of-fit test is                

Answer:

The null  hypothesis for the chi-square goodness-of-fit test is :

[tex]\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }[/tex]

Step-by-step explanation:

The objective of this question is to state the null hypothesis for the  chi-square goodness-of-fit test.

Given that:

There are three colors associated with this model . i,e White , yellow and green and they are in the ratio of 12:3:1

The total number of these color traits associated with this model = 12 + 3 + 1 = 16

Thus ;

The null  hypothesis for the chi-square goodness-of-fit test is :

[tex]\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }[/tex]

Answer:

30

Step-by-step explanation:

It is an equalateral triangle

Answer:

y-1 = 3(x-2)

Step-by-step explanation:

The point slope form of a line is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y-1 = 3(x-2)

Answer:

Step-by-step explanation:

€150 ($1.3687 / €1) = $205.30

$250 − $205.30 = $44.70

Answer:

A: 44.70 US dollars

Step-by-step explanation:

Answer:

El tejado tenía un ancho de 31.4 m.

Step-by-step explanation:

Tenemos un techo rectangular, con un largo de 29.7 m y un ancho x, que debemos calcular.

Entonces, la superficie del tejado es:

[tex]S=29.7x\;\,\text{[m}^2\text{]}[/tex]

Las locetas tienen una superficie de 25x19 cm,  de las cuales 1/5 se pierde en la colocación. La superficie eficaz que ocupa cada loceta una vez colocada es:

[tex]S_L=(25\cdot19)\cdot(1-1/5)=475\cdot(0.8)=380\;\text{cm}^2[/tex]

Entonces, si se utilizaron 24552 locetas para cubrir todo el techo, podemos expresar la superfice del techo como:

[tex]S=24552\;\text{locetas}\;\cdot380\dfrac{\text{cm2}}{\text{loceta}}\cdot \left(\dfrac{1\text{m}}{100\text{cm}}\right)^2=\dfrac{24552\cdot380}{10000}\;\text{m2}=932.976\;\text{m2}[/tex]

Podemos calcular x igualando este último resultado con la primer ecuación:

[tex]S=29.7x=932.976\\\\x=932.976/29.7=31.413\approx31.4[/tex]

Answer:

8

Step-by-step explanation:

The other patterns go with the two factors on top (2 x 3 = 6 and 3 x 3 = 9).

So, 2 x 4 = 8

Answer:

10x-15a

Step-by-step explanation:

Answer:

A 16 inches diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let r be the radius and [tex]\theta[/tex] be the angle of a circle.

According with the graph, the area of the sector is given by

[tex]A=\frac{1}{2}r^2\theta[/tex]

The arc length of a circle with radius r  and angle  [tex]\theta[/tex] is r [tex]\theta[/tex]

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.

Thus the perimeter has length

[tex]2r+r\theta=32 \:in[/tex]

We need to express the area as a function of one variable, to do this we use the above equation and we solve for [tex]\theta[/tex]

[tex]2r+r\theta=32\\\\r\theta=32-2r\\\\\theta=\frac{32-2r}{r}[/tex]

Next, we substitute this equation into the area equation

[tex]A=\frac{1}{2}r^2(\frac{32-2r}{r})\\\\A=\frac{1}{2}r(32-2r)\\\\A=16r-r^2[/tex]

The domain of the area is

[tex]0<r<12[/tex]

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

[tex]\frac{d}{dr} A=\frac{d}{dr}(16r-r^2)\\\\A'(r)=\frac{d}{dr}(16r)-\frac{d}{dr}(r^2)\\\\A'(r)=16-2r16-2r=0\\\\-2r=-16\\\\\frac{-2r}{-2}=\frac{-16}{-2}\\\\r=8[/tex]

To check if r=8 is a maximum we use the Second Derivative test

if [tex]f'(c)=0[/tex] and [tex]f''(c)<0[/tex] , then f(x) has a local maximum at x = c.

The second derivative is

[tex]\frac{d}{dr} A'(r)=\frac{d}{dr} (16-2r)\\\\A''(r)=-2[/tex]

Because [tex]A''(r)=-2 <0[/tex]  the largest slice is when r = 8 in.

The diameter of the pizza is given by

[tex]D=2r=2\cdot 8=16 \:in[/tex]

A 16 inches diameter will reward you with the largest slice of pizza.

last option

The previous transformation could be classified as a

✔ reflection across the y–axis

.

Step-by-step explanation:

Answer:

D. [3, -1, -1, 3, 4, 4, 1, 1]

Reflection across the y–axis

Step-by-step explanation:

Please mark as Brainliest!

Answer: 368 ways

Step-by-step explanation: To find the total number of probabilities, you multiply all the factors together to get total outcome. 16 * 23 = 368

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

We have,

Given:

Total number of components (n) = 1000

Number of defective components (d) = 350

a.

P(A) is the probability that the first component drawn is defective:

P(A) = d/n = 350/1000 = 0.35

b.

P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:

Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.

P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349

c.

P(A ∩ B) is the probability that both the first and second components drawn are defective:

P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122

d.

P([tex]A^c[/tex] ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:

[tex]P(A^c)[/tex] is the probability that the first component drawn is not defective:

[tex]P(A^c)[/tex] = 1 - P(A) = 1 - 0.35 = 0.65

Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.

P([tex]A^c[/tex] ∩ B) = P([tex]A^c[/tex]) * P(B) = 0.65 * (350/999) ≈ 0.228

e.

P(B) is the probability that the second component drawn is defective:

P(B) = Number of defective components / Total number of components

= 350/1000

= 0.35

f.

P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:

P(A|B) = P(A ∩ B) / P(B)

= (0.35 * 0.349) / 0.35

= 0.349

g.

To determine if A and B are independent, we need to compare

P(A) * P(B) with P(A ∩ B).

P(A) * P(B) = 0.35 * 0.35 = 0.1225

P(A ∩ B) = 0.122

Since P(A) * P(B) = P(A ∩ B), A and B are independent events.

It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.

The occurrence or non-occurrence of A does not impact the probability of B.

Thus,

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

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Answer:

615.44

Step-by-step explanation:

The area in terms of π is 196π

196 * 3.14 = 615.44

Answer:

615.75

Step-by-step explanation:

Area equals pi times r times 2

A equals 3.14 times 14 times 2

Answer:

$7875

Step-by-step explanation:

1 Month      4000 Paid

2 Months    2000 Paid

3 Months     1000 Paid

4 Months     500 Paid

5 Months      250 Paid

6 Months       125 paid

Total = $7875 Paid

Hope this helped ;)

Answer:

90° and 180°

Step-by-step explanation:

An obtuse angle is any angle larger than 90° and smaller than 180°

Answer:

13.53% probability that no customers arrive in a five-minute period

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given time interval.

They arrive at a rate of two every five minutes

This means that [tex]\mu = 2[/tex]

What is the probability that no customers arrive in a five-minute period?

This is P(X = 0).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]

13.53% probability that no customers arrive in a five-minute period

Answer:

Step-by-step explanation:

This problem brothers is the probability of mutually exclusive events,

Given the sample space of 80 separate events, the probability of of one event happening is

Pr(each event)= [tex]\frac{1}{80}[/tex]

Answer:

step 3 is wrong

Step-by-step explanation:

i know it because i did the unit test review

Answer:

D

ヾ(•ω•`)o

Step-by-step explanation:

Answer:

2) Strong Negative Correlation

Step-by-step explanation:

With the value of r we have both the information about the sign of the relationship and the strength of this relationship.

As the value of r is negative, we can conclude that the correlation between x and y is negative.

Also, as the absolute value of r is close to 1, we can conclude that this relationship is strong.

The strength can also be seen in the value of r2, which is also close to 1, but this value does not give information about the sign.

The value of the slope a, being negative, can also tell us that the relation between x and y is a negative correlation.

Answer:

C.

Step-by-step explanation:

1/2r = 2π/Cb