Jacob splits the cost of snacks, which was 12.24, with two friends. Before they ate, another friend joined them and paid Jacob for his fourth of a cost. how much does Jacob need to refund each of the other two friends so that everyone pays the same amount?

There is a 38.51% probability that a randomly chosen applicant will score between 550 and 650 which is derived through standard normal distribution method.

It is given to us that the scores of the applicants for graduate school are normally distributed with -

Mean(μ) = 560

and, Standard deviation (σ) = 90

We have to find out the probability of a randomly chosen applicant will score between 550 and 650.

We have to use the standard normal distribution method in order to find out the required probability.

According to standard normal distribution curve method,

Z = (X-μ)/σ

=> Z = (550-560)/90 and, Z = (650-560)/90

=> Z = -0.11 and Z = 1.00

The probability will be with respect to the corresponding z-tables which is equal to = (0.3413+0.0438)

= 0.3851

Thus, the probability of a randomly chosen applicant will score between 550 and 650 is 0.3851 or 38.51%.

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You started out with a 0 dollar investment. You would've have spent $5 after one day. After two days. When x is the duration of the day, f (x) = 5 x. Only positive integers would be allowed in the range.

A whole number, as opposed to a fraction that might be affirmative, negative, or zero, is an integer.

Like an integer is nothing more than a collection of numbers, there is no specific formula for it. Even so, there are several rules to keep in mind while adding, subtracting, and performing other mathematical operations on integers: A positive integer will always be produced when adding two positive integers.

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The speed will be calculated by the formula by the product of frequency and wavelength.

The speed of sound is the distance travelled by a sound wave per unit of time as it propagates through an elastic medium. At 20 degrees Celsius, the speed of sound in air is approximately 343 metres per second or one kilometre in 2.91 seconds or one mile in 4.69 seconds.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

The speed of the sound will be calculated by the multiplication of frequency and wavelength.

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An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

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The transformations which have been performed on the graph of f(x)=x√3 to obtain the graph of g(x)=−2x√3−1 is g(x) = -2f(x) - 1.

We are given that;

The functions f(x)=x√3 and g(x)=−2x√3−1

Now,

To obtain the graph of g(x) from the graph of f(x), the following transformations have been performed:

A reflection over the x-axis, which changes the sign of f(x) to -f(x).

A vertical stretch by a factor of 2, which multiplies f(x) by 2.

A vertical translation down by 1 unit, which subtracts 1 from f(x).

g(x) = -2f(x) - 1.

Therefore, by transformation the answer will be g(x) = -2f(x) - 1.

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The probability of rolling a 1 three out of the four rolls with a fair 6-sided die is 20/1296 or approximately 0.0154.

To find the probability of rolling a 1 three out of the four rolls with a fair 6-sided die, we need to consider the number of favorable outcomes (rolling a 1 three times) and the total number of possible outcomes.

The probability of rolling a 1 on a single roll is 1/6, as there is one favorable outcome (rolling a 1) out of six possible outcomes (numbers 1 to 6 on the die).

Since we want to roll a 1 three out of the four rolls, we can calculate the probability using the binomial probability formula:

P(X = k) = (nCk) * p^k * q^(n-k)

Where:

n is the total number of trials (4 rolls)

k is the number of successful outcomes (rolling a 1, which is 3 in this case)

p is the probability of success on a single trial (1/6)

q is the probability of failure on a single trial (5/6)

Using the formula:

\(P(X = 3) = (4C3) * (1/6)^3 * (5/6)^(4-3)\)

Simplifying the expression:

\(P(X = 3) = 4 * (1/6)^3 * (5/6)\)

\(P(X = 3) = 4/6^4 * 5/6\)

P(X = 3) = 20/1296

Therefore, the probability of rolling a 1 three out of the four rolls with a fair 6-sided die is 20/1296 or approximately 0.0154.

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Step-by-step explanation:

a=32(alternate angles are equal)

b=a=32

c=17(all sides of rhombus are equal in length)

d=17(all sides of rhombus are equal in length)

e=90

f=90(diagonals intersect at right angles)

Solution

Hypotheses:

- The population mean is 132. In order to test the claim that the mean is 132, we should check for if the mean is not 132.

- Thus, the Hypotheses are:

Test statistic:

- The test statistic has to be a t-statistic because the sample size (n) is less than 30.

- The formula for finding the t-statistic is:

- Applying the formula, we have:

Critical value:

- The critical value t-critical, is gotten by reading off the t-distribution table.

- For this, we need the degrees of freedom (df) which is gotten by the formula:

- And then we also use the significance level of 0.1 and the fact that it is a two-tailed test to trace out the t-critical. (Note: significance level of 0.1 implies 10% significance level)

- This is done below:

- The critical value is 1.729

P-value:

- To find the p-value, we simply check the table for where the t-statistic falls.

- The t-statistic given is 1.5747. We simply check which values this falls between in the t-distribution table. It falls between 1.328 and 1.729. We can simply choose a value between 0.1 and 0.05 and multiply the result by 2 since it is a two-tailed test.

- However, we can also use a t-distribution calculator, we have:

- Thus, the p-value is 0.13183

Final Conclusion:

- The p-value is 0.13183, and comparing this to the significance level of 0.1, we can see that 0.13183 is outside the rejection region.

- Thus, the result is not significant and we fail to reject the null hypothesis

Answer:

n-8=19

Step-by-step explanation:

Answer:

y = 2

Step-by-step explanation:

Using the sine ratio and the exact value

sin45° = \(\frac{1}{\sqrt{2} }\) , then

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{\sqrt{2} }{y}\) = \(\frac{1}{\sqrt{2} }\) ( cross- multiply )

y = (\(\sqrt{2}\) )² = 2

Answer:

1 m/s/s.

Step-by-step explanation:

Acccelaration = rate of change of speed

= (40 - 30) /10

= 10/10

= 1 m/s/s.

If the flourishing-flowers charges $60 for each standard "flower-arrangement", then the equation to represent the cost is "y = 60x + 125".

The number-of-arrangements be = "x",

The cost of flowers for x number of standard floral arrangements can be calculated as "sum" of "cost of each arrangement" and the "one-time delivery and set up fee".

The cost of each standard floral arrangement is given to be = $60, and The delivery and set-up fee is = $125,

The total cost of flowers for "x" arrangements can be expressed in equation as :

y = $60x + $125.

Therefore, the required equation is "y = 60x + 125".

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The length of a wave does not directly determine its depth. The depth of a wave is influenced by various factors, including the shape and size of the seafloor,

The temperature and salinity of the water, and the strength and direction of the current. Therefore, without additional information about these factors, it is impossible to accurately determine the depth of a wave based solely on its length. I suggest seeking the advice of an expert in oceanography or physics for a more comprehensive explanation.

The length of a wave is the distance between two successive points in the same phase, such as from crest to crest or trough to trough. In your case, the wave length is given as 30 feet. However, without additional information about the wave, we cannot determine its depth solely based on its length.

Depth refers to the vertical distance from the surface to the lowest point of a wave (trough), and it's not directly related to the wave length. Therefore, we cannot accurately choose an option (a, b, c, or d) for the depth based on the provided information.

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Answer:

C

Step-by-step explanation:

Answer:

RS= 17

Step-by-step explanation:

l hope l can help You

Answer:

Step-by-step explanation:1.1c

The expression for the price last month is 1.1c, and the cell phone was $438.9 last month

The given parameters are:

The price last month would be:

Price = Initial price * (1 + Increment)

This gives

Price = c * (1 + 10%)

Evaluate

Price = 1.1c

We have:

c = 399

So, the expression becomes

Price = 1.1 * 399

Evaluate

Price = 438.9

Hence, the cell phone was $438.9 last month

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Answer:

x = 138

Step-by-step explanation:

Exterior angle thm:

68 + 70 = x

x = 138

Answer:

9 for both I  think

Step-by-step explanation:

possbily each workout plan takes half of the trained hours so basicly (6h ÷2plans=3) (12h÷2plans=6) then just add 3 and 6 and get your answer (i might be wrong tho)

The family size has the lowest price compared to the family price per ounce which the amount is $0.21 / ounce.

To compare the box of cereal price we need to know the price per ounce first. It can be written as

Price per ounce = price /  total ounces

From the text above, we know that :

large size price = $3.34

large size ounces = 15

family size price = $5.14

family size ounces = 24

By substituting the parameter we can get the price per ounce of large size and family size

Large size

Price per ounce = price /  total ounces

Price per ounce = 3.34 / 15

Price per ounce = $0.22 / ounce

Family size

Price per ounce = price /  total ounces

Price per ounce = 5.14 / 24

Price per ounce = $0.21 / ounce

Hence, the family size has the lowest price compared to the family price per ounce which the amount is $0.21 / ounce.

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Answer:

$20,240

Step-by-step explanation:

Multiply 22,000 by 0.92% since if you subtract 0.08 which is equivalent to 8% from 1, you would need that percentage to get to your final answer which is $20,240.

Another option is to do the same thing except multiply 22,000 by 0.08% in which $1,760 is being cut off as it decreases.  Subtract that number from $22,000 to get the same answer mentioned earlier.

Answer:

$20,240

Step-by-step explanation:

This is a simple interest formula.

$22,000*(8%/100%) = $1760

$22,000-$1760 = $20,240

Answer:

not possible

Step-by-step explanation:

\(a^{2} + b^{2} = c^{2}\)

25 + 196 = 400

221=400

The range is ( 290, 230).

In statistics, the standard deviation is a measure of the amount of variation. The low standard deviation indicates that the values tend to be close to the expected value of the set, while a high standard deviation indicates that the values are spread out over a wide range.

According to the question,

The middle 50% of the pregnancies are within two standard deviations of the mean: 260 ± 2*15

               = ( 260 + 2*15 , 260 - 2*15)

               = ( 260 + 30, 260-30)

               = ( 290, 230)

Hence the range is ( 290, 230).

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The slope of a line parallel to the line having equation 10x+12y=-120 is -5/6.

What is the slope of a line parallel to another line?

Parallel lines are coplanar and they never intersect.

Slope is a measure of the angle of a line from the horizontal.

Since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel.

According to the given question:

Given equation of line is 10x+12y=-120

Converting this to slope-intercept form we get

y = -5/6 x + 10

Clearly slope of this line is -5/6

Any line parallel to this line will have the same slope

Therefore the slope of a line parallel to the given line is -5/6

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An equation to find the fraction of punch that is either pineapple juice or orange juice is 1/6 + 1/9 = 5/8.

In Mathematics, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided about the pineapple juice and orange juice, an equation that can be used for determining the fraction of punch that is either pineapple juice or orange juice is as follows;

Fraction = 1/6 + 1/9

Fraction = 3/18 + 2/18

Fraction = 5/18

In this context, we can reasonably infer and logically deduce that exactly 5/18 of the punch is either pineapple juice or orange juice.

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Complete Question:

About 1/6 of a fruit punch is pineapple juice. About 1/9 of the punch is orange juice. Write and solve an equation to find the fraction of the punch that is pineapple juice or orange juice.

Answer:

0.5(−y−2)+y=1

(0.5)(−y)+(0.5)(−2)+y=1

−0.5y+−1+y=1

(−0.5y+y)+(−1)=1

0.5y+−1=1

0.5y−1=1

0.5y−1+1=1+1

0.5y=2

0.5y /0.5 = 2/0.5

y=4

Step-by-step explanation:

I hope this is help you

Answer:

\(0.5( - y - 2) + y = 1 \\ - 0.5y - 1 + y = 1 \\ - 0.5y + y = 1 + 1 \\ 0.5y = 2 \\ y = \frac{2}{0.5} \\ y = 4\)

Answer:

9/1

Step-by-step explanation:

45/5 = 9

The  total distance it flies, rounded to the nearest mile is: d. 1,692 miles .

First distance= 550 miles (given)

Second distance=483 miles (given)

Now let find the third distance

Let x represent the third distance

Hence:

x/sin79 = 550/sin55

x= 659.1

Now let calculate the total distance

Total distance=550+483+659.1

Total distance= 1692.1

Total distance= 1692 miles (rounded)

Therefore the correct option is d.

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