3) How many cubic feet of water can the
following in-ground swimming pool hold?
6 ft
8 ft
/8 ft
6 ft
6 ft
8 ft
144f

Answer:

Step-by-step explanation:

a = BC - DC

\(\frac{60}{BC}\) = tan 28°

BC = \(\frac{60}{tan28}\) ≈ 112.8 m

DC = \(\frac{60}{tan54}\) ≈ 43.6 m

a ≈ 112.8 - 43.6 = 69.2 m

Answer:

Slope=2

y intercept= Length of spring without any weight

15 lbs= 38 inches

Step-by-step explanation:

slope=

18-12/5-2= 6/3 = 2

y intercept= 0=x and x=amount of weight

equation= 2x+8=y

2(15)+8=38

Answer: 174.09

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 Pint is equal to 0.5 quart. To convert pints to quarts, multiply the pint value by 0.5 or divide by 2. For example, to convert 5 pints to quarts, multiply 5 by 0.5, that makes 2.5 quarts is 5 pints. pints to quarts formula. quart = pint * 0.5. quart = pint / 2. 1 Pint = 0.5 Quart.

Answer:  4.50356 quarts

Step-by-step explanation:

Answer:

206

Step-by-step explanation:

The formula for this problem would be -310 + 13(8) which = 206

Answer:

slope = \(\frac{1}{3}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{1}{3}\) x + 4 ← is in slope- intercept form

with slope m = \(\frac{1}{3}\)

The shopkeeper made a profit of $40 from each scooter.

What is Profit & Loss?

The shopkeeper bought 70 scooters for $7000.

So, the cost price of one scooter = 7000/70 = $100

The profit percentage is 40%.

The formula for Profit can be given as,

Profit = (Profit Percentage × Cost Price)/ 100

⇒ Profit = (40 × 100)/100

⇒ Profit = $40

Therefore, she made a profit of $40 from each scooter.

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Answer:

3,696

Step-by-step explanation:

7x24x22 equals 3,696

24x7=168

168x22=3,696

Answer:

1440

Step-by-step explanation:

6 x 8 = 48

48 x 30 = 1440

Step-by-step explanation:

(1 + i)¹⁴ = (1 + i)²×(1 + i)¹² = ((1 + i)²)⁷

(1 + i)² = 1 + 2i - 1 = 2i

((1 + i)²)⁷ = (2i)⁷ = 2⁷×i⁷ = 128×i²×i²×i²×i =

= 128×-1×-1×-1×i = -128i

Answer:

Its2 for every 3

Step-by-step explanation:

Answer:

2/4 +6/8 =5/4

Step-by-step explanation:

(a) The probability that all 4 missiles will fire is 0.2098 and (b) The probability that at most 2 will not fire is 0.0099.

Here we need to use the concept of combinations to get our required answer.

Here we have been given that 4 out of 14 missiles are defective.

Hence 10 missiles are working.

A sample of 4 missiles was chosen

Hence the simple can be chosen in ¹⁴C₄ ways

a)

The probability that all 4 missiles will fire is

¹⁰C₄/¹⁴C₄

= 0.2098

b)

The probability that at most 2 will not fire is

1 - the probability of including all three defective missiles

= 10³C₃/¹⁴C₄

= 0.0099

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(a) Probability all 4 fire: 0.3297. (b) Probability at most 2 not fire: 0.9591.

(a) To track down the chance that all of the 4 rockets will fire, we actually need to do not forget the quantity of methods we can select 4 operating rockets out of the eleven that are not unsuitable, isolated by the all out range of approaches we will select four rockets out of the whole component.

The amount of ways of selecting four operating rockets out of the eleven that aren't improper is given by way of the combination recipe:

C(eleven,four) = 330

The absolute quantity of methods of selecting four rockets out of the entire part is given via:

C(14,4) = 1001

Subsequently, the chance that each one of the four rockets will hearth is:

P(all four hearth) = C(11,four)/C(14,4) = 330/1001 ≈ zero.3297

(adjusted to 4 decimal spots)

(b) To find the likelihood that at most 2 rockets might not fire, we need to remember every one of the potential conditions in which 0, 1, or 2 poor rockets are selected, and afterward song down the likelihood of every case and upload them up.

Case 1: No defective rockets are selected

The amount of ways of selecting four working rockets out of the eleven that are not faulty is given through the mixture recipe:

C(11,four) = 330

Subsequently, the chance of choosing no defective rockets is:

P(0 inadequate) = C(eleven,4)/C(14,four) ≈ 0.3297

Case 2: One defective rocket is chosen

The quantity of ways of selecting three operating rockets out of the eleven that are not poor is given with the aid of the combo equation:

C(eleven,three) = 165

The amount of ways of selecting 1 damaged rocket out of the three that are available is given through the mix equation:

C(three,1) = 3

Subsequently, the all out number of approaches of selecting 1 insufficient and three running rockets is:

C(eleven,three) × C(3,1) = 495

Thusly, the probability of choosing one deficient rocket and three running rockets is:

P(1 deficient) = C(eleven,three) × C(three,1)/C(14,4) ≈ 0.4655

Case three: Two poor rockets are selected

The amount of approaches of choosing 2 poor rockets out of the three which might be handy is given through the combination recipe:

C(3,2) = 3

The amount of ways of choosing 2 running rockets out of the 11 that aren't faulty is given via the mix recipe:

C(11,2) = 55

In this way, the all out number of methods of selecting 2 broken rockets and 2 working rockets is:

C(3,2) × C(eleven,2) = one hundred sixty five

Subsequently, the chance of choosing two incorrect rockets and two operating rockets is:

P(2 insufficient) = C(3,2) × C(11,2)/C(14,four) ≈ 0.1638

Subsequently, the likelihood that at maximum 2 rockets might not fireplace is:

P(at maximum 2 don't fire) = P(zero imperfect) + P(1 blemished) + P(2 deficient) ≈ 0.9591

(adjusted to 4 decimal spots).

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Answer: 0.25

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

multiply by the recipricol

3x 4/3

3's cancel eachother out

answer is 4

Based on the number of pounds of butter that Hall has and the number of cups needed per fasnachts, the number of fasnachts Hall will be able to make is 36 fasnachts

First, find out the number of cups of butter than Hall has:

= 9 pounds x 2 cups per pound

= 18 cups

Then, find out the number of 3/4 cups in this amount of butter:
= 18 cups / 3/4

= 18 x 4/3

= 24 cups

The number of fasnachts that Hall can make are:

= 24 x 1.5 frozen fasnachts per cup

= 36 fasnachts

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Answer: 1/50

Step-by-step explanation:

Step 1: We need to multiply the numerator and denominator by 100 since there are 2 digits after the decimal.

0.02 = (0.02 × 100) / 100

= 2 / 100 [ since 0.02 × 100 = 2 ]

Step 2: Reduce the obtained fraction to the lowest term

Since 2 is the common factor of 2 and 100 so we divide both the numerator and denominator by 2.

2/100 = (2 ÷ 2) / (100 ÷ 2) = 1/50

Answer:

\(\displaystyle g(f(1)) = 20\)

Step-by-step explanation:

We are given the two functions:

\(f(x)=6x+2 \text{ and } g(x)=2x+4\)

And we want to find:

\(g(f(1))\)

First, find f(1):

\(\displaystyle \begin{aligned} f(1) &= 6(1) + 2 \\ &= 6 + 2 \\ &= 8 \end{aligned}\)

Substitute:

\(g(f(1))=g(8)\)

Find g(8):

\(\displaystyle \begin{aligned} g(8) &= 2(8) + 4 \\ &= 16 + 4 \\ &= 20 \end{aligned}\)

In conclusion:

\(\displaystyle g(f(1)) = 20\)

The expected win of a coin flip, on average, is $1.25. This means that if you were to play this game repeatedly, you can expect to win an average of $1.25 per flip.

To calculate the expected win of a coin flip, we multiply the outcome of each flip by its corresponding probability and sum them up.

In this case, flipping heads has a probability of 3/4 and results in a win of $2, while flipping tails has a probability of 1/4 and results in a loss of $1.

Expected win = (Probability of heads × win for heads) + (Probability of tails × loss for tails)

= (3/4 × $2) + (1/4 × -$1)

= $1.50 - $0.25

= $1.25

Therefore, the expected win of a coin flip, on average, is $1.25.

This means that if you were to play this game repeatedly, you can expect to win an average of $1.25 per flip.

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The 90% confidence interval estimate of the difference between the two population means is given by:

(-0.57, 4.57).

For each sample, the mean and the standard error are given as follows:

Then, for the distribution of differences, the mean and the standard error are given as follows:

The rule for the bounds of the confidence interval is given as follows:

Mean ± Critical Value x Standard Error

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 6 + 6 - 2 = 10 df, is t = 1.8125.

Then the bounds of the interval are obtained as follows:

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Answer:

I can't see the picture. Sorry

Step-by-step explanation:

The percent decrease in the mower's price to the nearest tenth of a percent is 25.3%.

We have,

We need to calculate the initial discount given by the 23% off sale:

Discount

= 0.23 x $425

= $97.75

After the first discount, the mower's price is:

New price

= $425 - $97.75

= $327.25

Then, the store manager discounted it by another $10, so the final price is:

Final price

= $327.25 - $10

= $317.25

The total decrease in price is:

= $425 - $317.25

= $107.75

The percent decrease in the mower's price is:

Percent decrease

= (107.75 / 425) x 100%

= 25.3%

Therefore,

The percent decrease in the mower's price to the nearest tenth of a percent is 25.3%.

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Amelia made a mistake in Step 2. She should have squared the expression (r+2) before taking the square root of both sides.

A circle is a two-dimensional shape that is defined as the set of all points in a plane that are at a constant distance, called the radius, from a given point, called the center. It can be thought of as a closed curve or a line forming a closed loop. The distance around the circle is known as its circumference, and it is equal to 2 times pi times the radius, where pi is an irrational number approximately equal to 3.14159. The area enclosed by a circle is given by the formula A = pi times the radius squared. Circles have many important applications in mathematics, geometry, and physics, and they are used to represent many real-world objects, including wheels, gears, planets, and celestial objects.

Amelia made a mistake in Step 2. She should have squared the expression (r+2) before taking the square root of both sides.

The correct solution process is:

Step 1: A = π (r+2)²

Step 2: ±√(A/π) = r+2

Step 3: (± √(A/π)) - 2 = r

In Step 2, we first divide both sides by pi, and then take the square root of both sides. In Step 3, we subtract 2 from both sides to isolate r. This process correctly solves for the radius of the original circle based on the given area covered in oil.

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The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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Option C represents a modified Hardy-Weinberg equation that incorporates the effects of natural selection on a population. The equation is given as:

$(p-3s)^2 + 2(p-s)q + q^2 = 1$

In this equation, various terms are included to express the impact of natural selection. Let's break down the equation and understand its components.

$p$ represents the frequency of the dominant allele in the population, while $q$ represents the frequency of the recessive allele. These frequencies are determined based on the initial allele frequencies in the population.

The term $(p-3s)^2$ represents the expected frequency of the homozygous dominant genotype in the next generation. The factor $3s$ denotes the selection coefficient, where $s$ represents the frequency of homozygous recessive individuals who do not survive due to natural selection. By subtracting $3s$ from $p$, we account for the reduction in the frequency of the dominant allele due to selection.

The term $2(p-s)q$ represents the expected frequency of the heterozygous genotype in the next generation. This term incorporates both the initial frequency of the heterozygous individuals, represented by $(p-s)$, as well as the transmission of alleles through reproduction, given by $q$. The factor of 2 accounts for the two possible combinations of alleles in the heterozygous genotype.

Finally, $q^2$ represents the expected frequency of the homozygous recessive genotype in the next generation. This term considers the transmission of the recessive allele, represented by $q$, and its squared value accounts for the homozygous recessive genotype.

The equation is set equal to 1, as the frequencies of all genotypes should sum to 1 in a population.

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Answer:

7/10 x 3/6 = 21/60

21/60 in its simpliest form =  7/20

Answer:7/20

Step-by-step explanation:

7/10 * 3/6

7/10*3/6=7/20

21/60 divided by 3/3=7/20

So 7/10*3/6=7/20

Answer:

Step-by-step explanation:

The "unit rate" is the slope of the line, or the ratio of change in y to change in x.

__

The "unit rate" of the relationship in the table can be found from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (16 -8)/(14 -7) = 8/7

The slopes of the various lines are conveniently found using the fact that they all terminate on grid points with y=6, and they all go through the origin. Their slope is the ratio of 6 to the x-coordinate of the termination point:

  line 1: 6/2 = 3 . . . . slope not < 2

  line 2: 6/3 = 2 . . . . slope not < 2

  line 3: 6/4 = 3/2 . . . . slope < 2, > 8/7

  line 4: 6/5 . . . . slope < 2, > 8/7

  line 5: 6/6 = 1 . . . . slope not > 8/7

Lines 3 and 4 have slopes in the required range.

_____

Alternate solution

We can find the values of x corresponding to the limits on slope when y = 6. This lets us compare the given lines to the desired range of slope in a fairly direct way.

For the proportional relations shown,

  y = mx

Then x = y/m, and we have, for y=6, ...

  x = 6/2 = 3 . . . . upper limit on slope

  x = 6/(8/7) = 42/8 = 5 1/4 . . . . lower limit on slope

The lines that terminate at points with y=6 and 3 < x < 5 1/4 are ...

  lines 3 and line 4

Answer:

line 3, line 4 :)

Step-by-step explanation:

Answer:

Can you please post a picture?!

Step-by-step explanation:

Answer: Henge

Step-by-step explanation:

I got you boys ;)

The hypothesis test to conduct in this situation is a two-sample test for

means, specifically a paired-sample t-test.

This is because the same group of workers is being tested twice, under

two different conditions: without exercise breaks and with exercise breaks.

The two sets of data are dependent because they are coming from the

same group of individuals, and the goal is to determine if there is a

statistically significant difference in their well-being between the two

conditions.

A paired-sample t-test is appropriate because it can compare the means of

two related samples, and it takes into account the correlation between the

data points in each sample.

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Answer:

y= 32x

Step-by-step explanation:

Use slope formula

192-128/6-4= 64/2

M=32x

Find y-intercept (if any)

128=32(4)+b

128=128+b

B=0