Sarah started her day with a full bag of Apple after making apple pie where she used three apples she noticed that she had 12 apples remain in the bag how many apples did Sarah begin the day with?

The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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Answer:

300

Step-by-step explanation:

3 :  15 :: 60 : x

Product of extremes  = Product of  means

3 * x = 15 * 60

    \(x = \frac{15 * 60}{3}\\\\x = 5*60\\\\x = 300\)

Or Do in this way

\(\frac{3}{15}=\frac{60}{x}\\\\\)

\(\frac{3*20}{15*20}=\frac{60}{x}\)

x = 15* 20 = 300

Answer:

300

Step-by-step explanation:

here this probally will help

Answer:

5, 3

Step-by-step explanation:

Answer:

y = 3/5x - 5

Step-by-step explanation:

y intercept is -5

slope is rise / run = 3/5

The cost of installing a fence around an 80 ft. wide and 120 ft. deep rectangular lot, with the fence priced at $3.25 per linear foot, will be $1,300.

To determine the cost of installing a fence around a rectangular lot, you need to calculate the total length of the fence required and then multiply that by the cost per linear foot. The given dimensions of the lot are 80 feet wide and 120 feet deep.
First, calculate the perimeter of the rectangular lot. The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length (or depth) and W is the width. In this case, the perimeter is P = 2(120) + 2(80) = 240 + 160 = 400 feet.
Next, multiply the total length of the fence by the cost per linear foot, which is $3.25. So, the cost of installing the fence is 400 feet × $3.25 per linear foot = $1,300.

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The range of Axel's training zone, assuming a moderate exercise intensity, would be approximately 123 to 164 beats per minute (BPM).

To calculate this range, we use the Karvonen formula, which takes into account Axel's resting heart rate (RHR) and desired training intensity. Assuming a moderate-intensity workout, we can use a target heart rate range of 60% to 80% of his MHR.

Target Heart Rate = ((MHR - RHR) x %Intensity) + RHR

Assuming a resting heart rate of 65 BPM and moderate intensity of 60% to 80% of his MHR, Axel's target heart rate range would be approximately 123 to 164 BPM.

Therefore, the range of Axel's training zone would be approximately 123 to 164 BPM.

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The probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.

What is probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Given:

The probability that a person who makes reservations on a certain flight and does not show up for the flight is p=0.05.

The probability that a person who makes reservations on a certain flight and does show up for the flight is 1-p=1-0.05=0.95.

The airlines sell 160 tickets for a flight with only 155 seats.

Let X be a random variable that denotes the number of persons who show up for the flight and it follows a binomial distribution with parameters n = 160 and p = 0.95.

Hence, X~ Binom (n = 160, p = 0.95).

Here,

np=160×0.95=152>5

n(1-p)=160×0.05 = 8.1>5

Hence, both np and n(1-p) are greater than 5, the binomial distribution can be approximated to normal distribution.

The probability that a seat will be available for every person holding a reservation and planning to fly is calculated as follows:

P(X ≤ 155) = (P < 155 + 0.5)

                 \(=P(x < 155.5)\\\\=P(\frac{X-np}{\sqrt{np(1-p)}} < \frac{155.5 - (160 \times 0.95}{\sqrt{160\times 0.95 \times 0.05}})\\\\=P(Z < \frac{155.5-152}{2.7568})\\\\=P(Z < 1.27)\\\\=0.8980\)

Hence the probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.

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Answer: 29.2%

Step-by-step explanation:

The total surface area is 196.9 million square miles and out of this, land occupies 57.5 million square miles.

The probability that a meteorite would hit land is the percentage of and out of the entire planet area:

= Land area/ Total earth surface area

= 57.5/ 196.9

= 29.2%

Answer:

36 cm³

Step-by-step explanation:

V = lwh

you can separate the figure into a 2 ×2 × 3 rectangular prism on left which gives you a volume of 12

the remaining portion is 2 × 2 × 6 which gives a volume of 24

12 + 24 = 36 cm³

Answer:

the second choice

Step-by-step explanation:

2 has to be divided into 8 parts in total which is shown by option B

Anaiah currently spending  $150 on these goods

*He is not spending his entire income  

*His marginal utility per dollar spent is not the same for both goods

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

consumption of eggplant

= 20 price of eggplant

= 3

consumption of kiwi is

= 30 price of eggplant

= 3

Formula:

Spending

= price of eggplant*consumption of eggplant + price of kiwi*consumption of kiwi

= 3*20+3*30

= 150

Utility per one dollar spent on the 20th eggplant

=  160

Marginal utility per dollar spent on the 30th kiwi

= 190 utils.

Note that y 160<190

Currently spending= 150

& budget = 180

150<180

According theory of choice consumer need the maximize the utility so answer is

Answer -:

*He is not spending his entire income

*His marginal utility per dollar spent is not the same for both goods

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The hash of the given message is 135.

In computing, a message digest is a fixed-sized string of bytes that represents the original data's cryptographic hash. This hash is used to authenticate a message, guaranteeing the integrity of the data in the message.

Here, it is given the message m = 23  

The formula to calculate hash is him) - (m*7;2 MOD 7793.

So, let's calculate the hash : him) - (m*7;2 MOD 7793(him) - (23*7;2 MOD 7793

⇒ (8*23) - (49 MOD 7793)

⇒ 184 - 49= 135.

So, the hash of the given message is 135.

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9514 1404 393

Answer:

  13

Step-by-step explanation:

The distance between the points is the magnitude of their difference.

  |(-2-3i) -(3+9i)| = |-5 -12i| = √(5² +12²) = 13

The distance between the point is 13 units.

(a) The density of \(X^2\) is given by \(P(X^2=k) = (1-p)^{k-1}p\), where \(k\) is a positive integer. (b) The density of \(X+3\) is given by \(P(X+3=k) = (1-p)^{k-4}p\), where \(k\) is a positive integer.


(a) To compute the density of \(X^2\), we note that \(X^2\) takes values \(1, 4, 9, 16, \ldots\) with respective probabilities \(p, (1-p)p, (1-p)^2p, (1-p)^3p, \ldots\). This is because \(X^2\) is obtained by squaring the values of \(X\), which follow a geometric distribution.
(b) To compute the density of \(X+3\), we consider that \(X+3\) takes values \(4, 5, 6, \ldots\) with respective probabilities \(p, (1-p)p, (1-p)^2p, (1-p)^3p, \ldots\). This is because \(X+3\) represents the sum of \(X\) and a constant, which doesn’t affect the geometric distribution of \(X\).

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Answer:3.86

Step-by-step explanation:

Answer:

3.86cm

Step-by-step explanation:

46.81   ÷   3.142 = 14.898154042011457670273711012094

√14.898 = 3.859

3.859 rounded is 3.86cm

Answer:

a. 25%

b. 5%

Step-by-step explanation:

a. Take 60000 divided by 240000, then times 100% = 25%

So the solution for a is 25%

b. Take 12000 divided by 240000, then times 100% = 5%

So the answer for b is 5%

The area of the picture frame 72 cm². Therefore, option C is the correct answer.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Given that, a bigger outer rectangle has sides of 12 cm and 10 cm.

So, the area of a outer rectangle = 12×10

= 120 cm²

An inner rectangle has sides of 8 cm and 6 cm

The area of a inner rectangle = 8×6

= 48 cm²

The area of the picture frame = 120-48

= 72 cm²

Therefore, option C is the correct answer.

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Answer: C | 72 square centimeters

Step-by-step explanation:

The answer is C. 72 square centimeters. The area of the picture frame can be found by subtracting the area of the inner rectangle from the area of the outer rectangle. The area of the outer rectangle is 120 square centimeters (12 x 10). The area of the inner rectangle is 48 square centimeters (8 x 6). Therefore, the area of the picture frame is 120 - 48 = 72 square centimeters.

The monthly payment on a 30-year, $205,000 loan with a 5.0% interest rate would be $1,073.51, with $926.23 of that being interest.

To calculate the monthly payment on a 30-year, $205,000 loan with a 5.0% interest rate, you first need to calculate the monthly interest rate. This can be done by dividing the annual interest rate (5.0%) by 12: 5.0% / 12 = 0.416%.

Next, you need to calculate the monthly payment by using this formula: Monthly Payment = \(Loan Amount x [Interest Rate / (1 – (1 + Interest Rate)^-N)]\)

In this example, the loan amount is $205,000, the interest rate is 0.416%, and N is 360 (the number of payments over 30 years). Plugging this into the formula gives us:

\(Monthly Payment = $205,000 x [0.416% / (1 – (1 + 0.416%)^-360)]]\)]

This gives a monthly payment of $1,073.51. To calculate the interest portion of the payment, multiply the loan amount by the monthly interest rate (0.416%): $205,000 x 0.416% = $926.23. Thus, the interest portion of the monthly payment is $926.23.

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Answer:10,300 gallons H2O

Step-by-step explanation:

Volume = L*W*D

Vol Pool = 25.5*15*6 = 2295 ft^3

60% of 2295 ft^3 = 1377 ft^3

(1377 ft^3)*(7.48 gal/ft^3) = 10,300 gallons H2O

Answer:

Omg I remeber that wait  let me think

Step-by-step explanation:

Step-by-step explanation:

the third one is the nonlinear function

hope this helps

Answer:

32% is 0.32

6% is 0.06

93% is 0.93

150% is 1.5

12.5% is 0.125

Hope this helps!

Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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Answer:

I'm going to say A

Step-by-step explanation:

For sure the next would be blue but this is just my guess.

The most likely next step in the series is Option A, where a blue ray is added 90 degrees to the left along with the existing rays.

It appears that the pattern involves adding a ray 90 degrees to the left and alternating colors between red and blue. The first figure is a 180 degrees line with arrows on both sides of red color.

Based on this pattern, the most likely next step would be to add a blue ray 90 degrees to the left, while keeping the existing rays and alternating colors. Therefore, the next step would be Option A, where the figure is blue in color with a ray added to the left along with the already present rays.

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P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.

1) The statement is true. Suppose (x^,y^) is an extreme point of P. To show that x^ is an extreme point of Q, we need to prove that for any two distinct points x_1, x_2 in Q, the line segment connecting x_1 and x_2 lies entirely in Q. Since Q is the projection of P onto x-space, it means that for any x in Q, there exists y in R^k such that Ax + By ≥ b.

Now, let's assume x_1 and x_2 are two distinct points in Q. Since they belong to Q, there exist corresponding y_1 and y_2 in R^k such that Ax_1 + By_1 ≥ b and Ax_2 + By_2 ≥ b. Since P is a polyhedron, the set of points that satisfy Ax + By ≥ b is a convex set. Therefore, the line segment connecting x_1 and x_2, denoted by [x_1, x_2], lies entirely in P. Since the projection of a convex set onto a subspace is also a convex set, [x_1, x_2] lies entirely in Q. Thus, x^ is an extreme point of Q.

2) The statement is false. Suppose x^ is an extreme point of Q. It does not necessarily imply the existence of a corresponding y^ such that (x^, y^) is an extreme point of P. This is because the projection Q onto x-space may not capture all the extreme points of P. It is possible for multiple points in P to project to the same point in Q, making it impossible to uniquely determine y^.

3) The statement is true. If x^ is an extreme point of Q and P does not contain a line, then there exists a corresponding y^ such that (x^, y^) is an extreme point of P. Since P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.

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Answer:

first 7 then 3  5  4  6

Step-by-step explanation:hope it helps

The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.

The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.

It is calculated simply by dividing the standard deviation by the square root of the sample size. That is \(SE = \frac{σ }{\sqrt{n}}\)

where , n --> sample size

σ --> population standard deviations

Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.

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Complete question:

standard error of an estimator is not affected by the multiple choice question.

a) population standard deviation

b) sample size

c) population size

Answer:

Step-by-step explanation:

If the parent function is f(x) = x² and the transformed function is g(x) = a(x)²

For a > 1, then the transformed function g(x) will be vertically stretched by a factor of 'a'

For 0 < a < 1, then the transformed function will be vertically compressed or shrink by a factor of 'a'

For a function f(x) = x² when transformed to f(5x) = (5x)²

g(x) = 25x²

Therefore, graph of the parent function f(x) will be vertically stretched by 25 units.

\(\left \{ {{2y-x=-9} \atop {y=2x-3}} \right. \iff \left \{ {{2(2x-3)-x=-9} \atop {y=2x-3}} \right. \iff \{ {{4x-6-x=-9} \atop {y=2x-3}} \right. \\\)

\(\{ {{3x=-9+6} \atop {y=2x-3}} \right. \iff \{ {{3x=-3} \atop {y=2x-3}} \right. \iff \{ {{x=-1} \atop {y=2x-3}} \right. \\\)

\(\{ {{x=-1} \atop {y=2(-1)-3}} \right \iff \{ {{x=-1} \atop {y=-2-3}} \right \implies \bf \{ {{x=-1} \atop {y=-5}}\)

\(\implies (x, \ y) = (-1, \ -5)\)