Answer:

1.120.68 cubic units

2.128 square units

3.192 square units

Step-by-step explanation:

First find the height of the pyramid.

Apply Pythagorean relationship where the base is a square, find the hypotenuse

a²+b²=c²---------apply this on the square base to find the length of the diagonal then divide by 2 to get the length from one square base to the center of the pyramid. With this length and the slant height, you can find the height of the pyramid.

8²+8²=c²

64+64=c²

128=c²

√128=c

11.31=c

c/2= 5.7

Finding height of the pyramid

8²-5.7²=h²

64-32=h²

32=h²

√32=h

5.7=h

Finding volume of the pyramid

v=a²*h/3 where a is the length of the edges=8 and h is the height of the pyramid= 5.7

v=8²* 5.7/3

v=64*1.889 =120.68 cubic units

2.

Lateral area of the pyramid is calculated by finding the product of the slant height of the pyramid and half the perimeter of the base.

L.S.A=1/2p*l where p is perimeter of the base and l is the slant height

slant height =8

Perimeter of the base= 8*4 =32

Half the perimeter of the base= 32/2=16

Lateral area= 16*8=128 square units

3. The total surface area of the pyramid is given by;

T.S.A=1/2p*l +B where B is area of the base

Area of the base=8*8=64

Lateral area= 128

T.S.A= 128+64 =192 square units

You are dealt one card from a 52-card deck. Find the probability that you are dealt a king or a black card.

Answer:

a probability of 1/26

Step-by-step explanation:

In a standard 52 deck of cards 26 are black and 4 are kings

Now we can take the chances of black cards being drawn multiplied by a king.

What is the probability of getting either a spade or a queen when drawing a single card from a deck of 52 cards?

Answer:

4/13

Step-by-step explanation:

There are 13 spades and 3 non-spade queens. So the probability is P = 16/52 = 4/13.

A tent company has a tent design that is a triangular prism. The following is a net of the design. If a = 74 inches, b = 75 inches, c = 48 inches, and d = 70 inches, how much fabric is needed to make the tent

Answer:

15,236 2q in

Step-by-step explanation:

step 1

1/2 bh = 1/2 (44 in)(64 in)

= 1/2 (2,816 sq in)

= 1,408 sq in.

2 x 1,408 sq in = 2,816 sq in.

step 2

end rectangle area

lw = (68 in)(69 in)

= 4,692 sq in

2 x 4,692 sq in = 9,384 sq in

Now find the area of the middle rectangle

lw - (69 in) (44 in) = 3,039 sq in.

then add all the areas together

2,816 + 9,384 + 3,036 = 15,236 sq in

A light bulb consumes 1440 watt hours per day. How many watt hours does it consume in 3 days and 12 hours?

Answer: it consumes 5040 watt hour in 3 days and 12 hours

Step-by-step explanation:

light bulb consumes 1440 watt hours per day. The number of hours in a day is 24. This means that the consumption of the light bulb per hour would be

1440/24 = 60 watt hour.

The consumption for 12 hours would be

60 × 12 = 720 watt hour.

The consumption for 3 days would be

3 × 1440 = 4320 watt hour

The total consumption in 3 days and 12 hours would be

4320 + 720 = 5040 watt hour

Answer:

5040 watts i think

Step-by-step explanation:

1440 X 3 = 4320 24 / 12 = 2

1440 / 2 = 720

4320 + 720 = 5040

In a jar there are 3 yellow candies, 3 blue candies, and 2 orange candies. What percent of the jar is filled with orange candies?

Answer: 25 percent of the jar is filled with orange candies

Step-by-step explanation:

In the jar, there are 3 yellow candies, 3 blue candies, and 2 orange candies. This means that the total number of candies inside the jar would be the sum of the yellow, blue and orange candies. It becomes

3 + 3 + 2 = 8 candies.

The percent of the jar filled with orange candies would be expressed as

number of orange candies/total number of candies × 100

It becomes

2/8 × 100 = 25%

A factory bought a new machine. It is not configured well yet, so the probability of defects is 0.05. Estimate the probability that there are at most 2 spoiled details in the random sample of 20.

Answer:

Pr(at most 2 are defective) = 0.38

Step-by-step explanation:

probability of defective = 0.05

probability of not defective =1- 0.05 = 0.95

Pr(at most 2 are defective) = pr (0 defective) + pr (1 defective) + pr (2defective)

pr (0 defective) = (0.05^0) * (0.95^20) = 0.36

pr (1 defective) = (0.05^1) * (0.95^19) = 0.019

pr (2 defective) = (0.05^2) * (0.95^18) = 0.0025 * 0.397 = 0.00099

Pr(at most 2 are defective) = 0.36 + 0.019 + 0.00099

Pr(at most 2 are defective) = 0.37999 = 0.38

Answer:

P(x2)=1- P(x

A family has j children with probability pj , where p1 = .1, p2 = .25, p3 = .35, p4 = .3. A child from this family is randomly chosen. Given that the child is the eldest child in the family, find the conditional probability that the family has

Answer:

A) the conditional probability that the has only 1 child = 0.24

B) The conditional probability that the family has only 4 children = 0.18

Step-by-step explanation:

To answer the questions, we first start with defining each event. Let E be the event that the child selected is the oldest and let Fj be the event that the family has j children.

From this, we can deduce that the probability that the child is the oldest, given that there is j children is ; P(E | Fj ) = 1/j.

In addition, we know P(Fj ) = pj as given in the problem. In answering the 2 questions, we seek the probability P(Fj | E). Thus, by the Bayes’s formula;

P(Fj | E) = P(EFj )/P(E) which gives;

P(Fj | E) = {P(E | Fj )P(Fj )} / {Σ(4,i=1)P(E | Fj )P(Fj )}

= (1/j)/ Σ(4,i=1)(1/j)pj

= ((pj)/j) / {p1 + (p2)/2 + (p3)/3 +(p4)/4}

Therefore, the conditional probability that the family has only 1 child; P(F1 | E) = p1 / {p1 + (p2)/2 + (p3)/3 +(p4)/4} = 0.1/ (0.1 + (0.25/2) +(0.35/3) + (0.3/4) = 0.1/0.4167 = 0.24

The conditional probability that the family has only 4 children =

{(p4)/4} / {p1 + (p2)/2 + (p3)/3 +(p4)/4} = (0.3/4)/ (0.1 + (0.25/2) +(0.35/3) + (0.3/4) = 0.075/0.4167 = 0.18

An environmental group at a local college is conducting independent tests to determine the distance a particular make of automobile will travel while consuming only 1 gallon of gas. They test a sample of five cars and obtain a mean of 28.2 miles. Assuming that the standard deviation is 2.7 miles, find the 95 percent confidence interval for the mean distance traveled by all such cars using 1 gallon of gas.

Answer:

Step-by-step explanation:

Confidence Interval

When the population standard deviation is known, the formula for a confidence interval for a population mean is:

Where n is the sample size and z is the corresponding z-value from the standard normal distribution for the selected confidence level. The value of z for a 95% confidence interval is z=1.96. The rest of the values are

Calculating the confidence interval

Or, equivalently

Can y = sin(t2) be a solution on an interval containing t = 0 of an equation y + p(t) y + q(t) y = 0 with continuous coefficients? Explain your answer.

Answer:

Step-by-step explanation:

y = sin(t^2)

y' = 2tcos(t^2)

y'' = 2cos(t^2) - 4t^2sin(t^2)

so the equation become

2cos(t^2) - 4t^2sin(t^2) + p(t)(2tcos(t^2)) + q(t)sin(t^2) = 0

when t=0, above eqution is 2. That is, there does not exist the solution. so y can not be a solution on I containing t=0.

387 in base 10 to base 5

Answer: 387 in base 10 to base 5 is 3022

Step-by-step explanation:

To convert 387 in base 10 to base 5, we would take the following steps

Firstly , we would divide the number to be converted by 5. The remainder forms the last digit of the number in base 5 while the quotient is divided again to get a new quotient and remainder. The new remainder forms the next digit to the left of the last digit. It continues till it gets to zero. Therefore,

387/5 = 77 remainder 2(last digit)

77/5 = 15 remainder 2(next digit to the left of the last).

15/5 = 3 remainder 0(next digit to the left)

3/5 = 0 remainder 3(next and final digit to the left)

Therefore, 387 in base 10 to base 5 is 3022

Answer:

3022

Step-by-step explanation:

To convert a number from base 10 to base 5, divide the number repeatedly by 5, keeping track of each remainder, until you get a quotient that is equal to zero

Next, write all the remainders in reverse order.

387₁₀ = 3022₅

Check:

387 = 3×5³ + 0×5² + 2×5¹ + 2×5⁰

387 = 3×125 + 0×25 + 2×5 + 2×1

387 = 375 + 0 + 10 + 2

387 = 387

OK.

It has been conjectured by the U.S. Census Bureau that "approximately 60% of foreign-born people who live in the U.S. are not naturalized citizens." In a national random sample of 70 foreign-born people who live in the U.S., on average, how many people would you expect to get that are not naturalized citizens? Select the best answer below.a. 28 peopleb. 42 peoplec. 4.10 peopled. None of these.

Answer:

Option B) 42 people

Step-by-step explanation:

We are given the following in the question:

Percentage of people who live in the U.S. that are not naturalized citizens = 60%

Sample size, n = 70

We have to given an estimate for people who are not naturalized citizens.

Thus, 42 people are not naturalized citizens.

Option B) 42 people

Find the area under the standard normal distribution curve for the following intervals. a. Between z = 0 and z = 2.0 b. To the right of z = 1.5 c. To the left of z = −1.75 d. Between z = −2.78 and z = 1.66

Answer:

a)

And we can use the following excel code to find the probability:

"=NORM.DIST(2,0,1,TRUE)-NORM.DIST(0,0,1,TRUE)"

b) 1.5) =1-P(Z" alt=" P(Z>1.5) =1-P(Z" align="absmiddle" class="latex-formula">

And we can use the following code and we got:

"=1-NORM.DIST(1.5,0,1,TRUE)"

1.5) =1-P(Z" alt=" P(Z>1.5) =1-P(Z" align="absmiddle" class="latex-formula">

c)

And we can use the following code and we got:

"=NORM.DIST(-1.75,0,1,TRUE)"

d)

And we can use the following excel code to find the probability:

"=NORM.DIST(1.66,0,1,TRUE)-NORM.DIST(-2.78,0,1,TRUE)"

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Part a

We want this probability:

And we can use the following excel code to find the probability:

"=NORM.DIST(2,0,1,TRUE)-NORM.DIST(0,0,1,TRUE)"

Part b

For this case we want this probability:

1.5)" alt=" P(Z>1.5)" align="absmiddle" class="latex-formula">

And we can use the complement rule and we have:

1.5) =1-P(Z" alt=" P(Z>1.5) =1-P(Z" align="absmiddle" class="latex-formula">

And we can use the following code and we got:

"=1-NORM.DIST(1.5,0,1,TRUE)"

1.5) =1-P(Z" alt=" P(Z>1.5) =1-P(Z" align="absmiddle" class="latex-formula">

Part c

We want this probability:

And we can use the following code and we got:

"=NORM.DIST(-1.75,0,1,TRUE)"

Part d

We want this probability:

And we can use the following excel code to find the probability:

"=NORM.DIST(1.66,0,1,TRUE)-NORM.DIST(-2.78,0,1,TRUE)"

The area under the standard normal distribution curve for the interval between z = 0 and z = 2.0 is; 0.47725

How to use the normal distribution table?A) P(0 < z < 2)

From online p-value from two z-score calculator, we have;

p-value = (0.97725 - 0.5000) = 0.47725

B) P(z > 1.5)

From online p-value from z-score calculator, we have;

p-value = 0.0668

C) P(z < 1.75)

From online p-value from z-score calculator, we have;

p-value = 1 - 0.040059

p-value = 0.9599

D) P(-2.78 < z < 1.6)

From online p-value from two z-score calculator, we have;

p-value = 0.94882

Read more about Normal Distribution table at; brainly.com/question/4079902

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Find four square roots of 2833 modulo 4189. (The modulus factors as 4189 = 59 · 71. Note that your four square roots should be distinct modulo 4189.)Hoffstein, Jeffrey. An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) (p. 112). Springer New York. Kindle Edition.

Answer:

Step-by-step explanation:

Let us proceed to find square roots of modulo 59 and 71:

≡ 2833 mod 59 ≡ 1 mod 59 (1)

≡ 2833 mod 71 ≡ 64 mod 71 (2)

By inspection, we find that = ± 1 and = ± 8 works

Now, using Chinese remainder to solve the simultaneous congruence,

≡

The first congruence yields

Then putting this back into the second equation, we get

≡ ⇒ ≡ ⇒ ≡

But

≡ ;

Hence,

≡ ⇒ ≡

This shows that is a third square root. From this, we immediately get the fourth square root, namely ≡ .

Note that the square roots:

are all distinct modulo 4189.

Find the probability that a randomly selected card from a Euchre deck is a jack or a spade. (Enter the fraction reduced to the lowest possible fraction on the left hand side of "=" symbol and the final answer on the right hand side simplified to the lowest possible fraction.)

Answer:

3/8

Step-by-step explanation:

There are 24 cards in a euchre deck with 4 Jack and 6 spade

P (J U S) = 4/24 + 6/24 - 1/24 = 1/6 + 1/4 - 1/24 = 3/8

Find the minimum sample size necessary to be 99% confident that the population mean is within 3 units of the sample mean given that the population standard deviation is 29.

Answer:

The minimum sample size required is 207.

Step-by-step explanation:

The (1 - α) % confidence interval for population mean μ is:

The margin of error of this confidence interval is:

Given:

*Use a z-table for the critical value.

Compute the value of n as follows:

Thus, the minimum sample size required is 207.

Find the probability that a randomly selected multiple birth for women 15-54 years old involved a mother who was at least 40 years old. P(at least 40

Age Number of Multiple Births

15–19 100

20–24 467

25–29 1620

30–34 2262

35–39 1545

40–44 328

45–54 105

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

Total. 6427

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

Answer:

Probability of selecting a mother who is at least 40 years old is 0.067.

That means there are 6.7% of the the total mothers who are at least 40 years old.

Step-by-step explanation:

The question is looking for probability of a mother at least 40 years.

It means 40 years and above.

From the table, the number of mothers who fall into this category = 328 +105 = 433

So, the probability would be = 433/6427 = 0.067

Therefore, converting to percentage, we have 6.7%

Answer:3/8

Step-by-step explanation:

Total number of women with ages from 15 to 54years (15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54)= 40

Total number of women with age 40 years and above = 15

Probability of picking a mother of age greater than 40 = 15/40 which is equal to 3/8.

Find a possible exponential function in y = a · bx (y=a(b)^x) form that represents the situation described below. Has an initial value of 2 and passes through the point (3, 128).

Answer:

y = 2 · 4ˣ

Step-by-step explanation:

Initial value of 2 means that a = 2.

y = 2 · bˣ

It passes through the point (3, 128), so:

128 = 2 · b³

64 = b³

b = 4

y = 2 · 4ˣ

Karen, 28 years old and a single taxpayer, has a salary of $33,000 and rental income of $33,000 for the 2019 calendar tax year. Karen is covered by a pension through her employer. AGI phase-out range for traditional IRA contributions for a single taxpayer who is an active plan participant is $64,000 – $74,000. a. What is the maximum amount that Karen may deduct for contributions to her traditional IRA for 2019?

Answer:

$4,800

Step-by-step explanation:

The maximum contribution for traditional IRA in 2019 = $6000

Given that;

karen has a salary of $33,000 and rental income of $33,000; then total income = $66,000

AGI phase-out range for traditional IRA contributions for a single taxpayer who is an active plan participant is $64,000 – $74,000.

PhaseOut can be calculated as:

=

= 0.2 * 6000

= 1200

Therefore, the maximum amount that Karen may deduct for contributions to her traditional IRA for 2019 = The maximum contribution for traditional IRA in 2019 - PhaseOut

= $6000 - $1,200

= $4,800

Let's say you take an exam worth 240 points and your score marked the 78th percentile of all the exam scores. Based on this you can conclude that ______% of exam takers had scores equal to or better than yours.

Here, we are required to determine what percentage of exam takers had scores equal to or better than mine.

The correct answer is therefore, 22%

First, a percentile is a statistical term used to represent each of the 100 equal groups into which a population can be divided according to the distribution of values of a particular variable, (in this case the scores).

Therefore, according to the definition above, Since my score marked the 78th percentile, we can conclude that only (100 - 78)% of the exam takers had scores equal to or better than mine.

The correct answer is therefore, 22%

Read more:

brainly.com/question/15876171

Answer:

28%

Step-by-step explanation:

78th percentile means 78% scored less than/equal to you.

100 - 78 = 22%

how strong is the relationship between the score on the first exam and the score on teh final exam in an elementary statistics course? ehre are data for eight students form such a course

Answer: Invalid question

Step-by-step explanation: Hello friend, kindly make available the remaining details of the question.

Regards

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