A $750 gift was shared equally by 5 people. After spending $90 of her share, Clarissa divided the amount remaining into 2 equal parts. What amount of money is now in each part of Clarissa's money?

Answer:

Step-by-step explanation:

Given function:

x-coordinate of the vertex is:

The axis of symmetry is the vertical line that passes through the vertex:

The interval can the researcher be 95% certain that the sample mean will fall within $258.13 and $271.87.

Central limit theorem states that the distribution of a sample variable approximates a normal distribution as the sample size become larger, assuming that all samples are identical in size and regardless of the population's actual distribution shape.

We know the formula for Central limit theorem is,

Sample standard deviation = (standard deviation) / \(\sqrt{n} \\\) = σ/\(\sqrt{n}\)

Here population mean (μ) = $265

standard deviation = $40.93

sample size = 130

for confidence level 95% the formula is,

CI = μ ± 1.96 * (σ/\(\sqrt{n}\))

⇒ CI = 265 ± 1.96 * (40/\(\sqrt{130}\))

        = 265 ± 1.96 * 3.51

        = 265 ± 6.87

⇒ 265 + 6.87 =271.87  and 265 - 6.87 = 258.13

Therefore sample mean will fall within $258.13 and $271.87.

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Answer:

k ≤ 7

Step-by-step explanation:

The correct option is a) $5161.24

To evaluate the expression P(1+rt) with the given values:

P = 1575

r = 0.055

t = 168/365

First, let's calculate rt:

rt = 0.055 * (168/365)

= 0.0252836 (rounded to 7 decimal places)

Now, substitute the values into the expression P(1+rt):

P(1+rt) = 1575 * (1 + 0.0252836)

= 1575 * 1.0252836

= 1615.85846 (rounded to 5 decimal places)

The result is approximately $1615.86.

Therefore, the correct option is a) $5161.24

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Answer: I. True

II. True

III. True

Step-by-step explanation:

Uniform probability distributions, this are probability distributions which have equally likely outcomes. There are two known types of uniform distributions:

1. discrete

2. continuous.

In the first type of distribution, each outcome is discrete. In a continuous distribution, outcomes are continuous this means they are usually infinite.

Answer:

A.30

Step-by-step explanation:

^ABC = 180⁰-60⁰=120⁰

=> 4x⁰=120⁰

=> x = 30⁰

Answer:

2

Step-by-step explanation:

there are 10 numbers, adding up to 20 in total

20÷10 =2

The space p^1 is the one-point compactification of the real line, which means that it is the real line with an additional point added at infinity. The space s^1 is the unit circle in the complex plane, which can be thought of as the set of complex numbers with absolute value 1.

The covering map from p^1 to s^1 is given by projecting each point in the upper half of the complex plane onto the unit circle, and projecting each point in the lower half of the complex plane onto the unit circle with opposite orientation. This covering map is familiar because it is closely related to the exponential function, which maps the real line to the unit circle in the complex plane. In fact, the exponential function can be used to construct the covering map explicitly.
Another familiar example of a covering map between p^1 and s^1 is the map that sends each point in p^1 to its argument (i.e. its angle with respect to the positive real axis), viewed as an element of the circle group. This covering map is also closely related to the exponential function, and can be used to compute the winding number of closed curves on the unit circle.
Overall, the space p^1 and its covering maps to s^1 are important examples in topology and complex analysis, and arise in many different contexts.

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The probability of getting a z-score greater than 0.15 is approximately 0.5693.

The probability of getting more than 2100 nails in a bag is approximately 0.5693.

The number of nails in a bag is a discrete random variable, so it's not appropriate to use a normal distribution to model it.

Also, the mean of 8.9 and standard deviation of 5.56 are for a single nail, not for a bag of 225 nails.

To answer the question, we need more information on the distribution of the number of nails in a bag.

Assuming that the distribution is approximately normal, the mean of the number of nails in a bag would be 225 * 8.9 = 2009 and the standard deviation would be the square root of 225 * (5.56)^2 = 59.11.

With these values, we can use a standard normal distribution to find the probability of getting more than 2100 nails in a bag:

z = (2100 - 2009) / 59.11 = 0.15

Note: This calculation assumes that the distribution is approximately normal, and that the mean and standard deviation of a single nail are accurate. These assumptions might not hold in practice, so the answer should be taken with caution.

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(a) The probability that both score more than 175 is 0.12 and (b) the probability that Thomas scores more than 175 and Sarah scores higher than Thomas is 0.04

If the occurrence of one event say A does not affect the occurrence of event B, then the two events are said to be independent such that;

P (A ∩ B) = P (A) × P (B)

a:

consider; event A represents Sarah scoring more than 175 and event B represents Thomas scoring more than 175

Thus, P(A) = Probability that Sarah scores more than 175 = 0.6

P(B) = The probability that Thomas scores more than 175 = 0.2

Since the scores are independent, therefore the probability that both Sarah and Thomas score more than 175 is,

P (A ∩ B) = (0.6) × (0.2)

P (A ∩ B) = 0.12

b:

If the occurrence of one event say A affects the occurrence of another event say B, then the two events are said to be dependent on each other such that;

P (A ∩ B) = P (B) × P (A|B)

As; P(B) = The Probability that Thomas scores more than 175 = 0.2

and P(A|B) = Sarah scores more than Thomas given that Thomas scores more than 175 = 0.2

Therefore;

P (A ∩ B) = (0.2) × (0.2) = 0.04

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A sample size of 32 is necessary if the width of the 95% interval is to be 0.38.

To compute the confidence intervals (CI) for the true average porosity of coal seams, we can use the t-distribution since the sample sizes are relatively small (less than 30) and the true standard deviation is unknown. The formula for the confidence interval is:

CI = sample mean ± t_critical * (sample standard deviation / √(sample size))

where t_critical is the critical value of the t-distribution for the desired confidence level and degrees of freedom (sample size - 1).

(a) For the 95% CI of the true average porosity of the first seam with a sample mean of 4.85 and a sample size of 19, the t_critical value for a 95% confidence level with 18 degrees of freedom is approximately 2.101 (you can find this value from t-distribution tables or using a calculator/software). The sample standard deviation is not the true standard deviation, so we use the sample standard deviation instead, which is 0.71.

CI (95%) = 4.85 ± 2.101 * (0.71 / √19)

CI (95%) ≈ 4.85 ± 0.296

So, the 95% confidence interval for the true average porosity of the first seam is approximately (4.554, 5.146).

(b) For the 98% CI of the true average porosity of the second seam with a sample mean of 4.56 and a sample size of 13, the t_critical value for a 98% confidence level with 12 degrees of freedom is approximately 2.681.

CI (98%) = 4.56 ± 2.681 * (0.71 / √13)

CI (98%) ≈ 4.56 ± 0.365

The 98% confidence interval for the true average porosity of the second seam is approximately (4.195, 4.925).

(c) To find the necessary sample size for a 95% confidence level and a CI width of 0.38, we rearrange the CI formula:

Sample size = [(t_critical * sample standard deviation) / (CI width / 2)]^2

Given t_critical for a 95% confidence level and a sample standard deviation of 0.71:

Sample size = [(1.96 * 0.71) / (0.38 / 2)]^2 ≈ 31.52

Since the sample size must be a whole number, we round up to 32. Therefore, a sample size of 32 is necessary to achieve a 95% confidence interval with a width of 0.38.

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Answer:

$41.40
2.5x + 4.2y

Step-by-step explanation:

Cost for each large box = $4.20

Cost for each small box = $2.50

How much would it be to get 3 smalls and 8 larges?
Total cost = 3(2.5) + 8(4.2) = 7.5 + 33.6 = 41.1
So the cost of 3 small boxes and 8 large boxes would be $41.40.

How much is it for x small boxes and y large boxes?
Write an expression to represent the situtation with two variables, x and y.

2.5x + 4.2y

Answer: 18.6

Step-by-step explanation: 15^2= 225

11^2=121, so then we added 225+121= 346, then square root it, and the answer is 18.60, so we need to do it to the nearest tenth is 18.6

It is true that the objective function and the restrictions in a linear programming problem must be linear functions of the choice variables.

The method of choosing the best result from a linear function is known as linear programming. Making a few straightforward assumptions is the easiest way to accomplish linear optimization. As the goal function, the linear function is referred to. Real-life relationships can be quite challenging. However, such interactions can be represented using linear programming, which facilitates analysis of such relationships.

When the need of a mathematical model are represented by linear relationships as, the optimal result can also be obtained using a technique known as the linear programming (LP), sometimes known as linear optimization. A particular type of mathematical programming is linear programming.

Formally speaking, linear programming is the method for optimizing a linear objective function under the restrictions of the linear equality and linear inequality. Convex polytopes, a set defined as the total intersection of a finite number of half spaces, each of which is determined by the linear inequality, make up viable region.

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Answer:

12*x-(9*x)

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The probability of picking out a certain colour = 12/48 = 1/4

So, this means that every 4 socks you pick out you can be sure of having one of each colour. If you need to find a pair, then you pick out 8.

Hope this helps

Answer:

x=30 because if you look across from x the angle is 30 degrees.

Step-by-step explanation:

Answer:

The first one is c, I’m pretty sure, the second one is a white block, and I don’t fully understand the last question but I’m pretty sure you’re correct

Step-by-step explanation:

Answer:

C. (0,-3)

Blank

D. (4,-5)

Step-by-step explanation:

(-1,-5)is point before translation (+1,+2)

(0,-3) after translation

Ok second one

90 degree counterclockwise rotation about the origin rule

A(x,y) becomes A'(-y,x)

n=(-5,-4) ok so -4 becomes positive 4

(4,-5)

Hope this helps!!

The total sale of the bedding set including 5% sale tax is $69.66

An equation is an expression that shows the relationship between two or more variables and numbers.

Discount = 20% of 86 = 0.2 * 86 = 17.2

Selling price of bed = 5% of 17.2 = 0.05 * 17.2 = 0.86

Total sale = 86 - 17.2 + 0.86 = 69.66

The total sale of the bedding set including 5% sale tax is $69.66

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5/9 of 54 are the ones which have chocolate, so we need to multiply the fraction by 54

5/9 * 54 = 30

Since 30 pieces of candy have chocolate, then 24 don't have it. 2/3 of the last number are the ones which have gum, multiply 2/3 by 24 to get the answer:

2/3 * 24 = 16.

The answer is: 16 pieces of candy have gum

Answer:

Step-by-step explanation:

Let number of chocolate cakes = c

Number of lemon cakes = l

Total cakes = 27

c + l = 27 ---------------(I)

Total slices = 170

7c + 6l = 170  ---------------(II)

Multiply equation (i) by (-7) and then add. So, c will be eliminated and we can find the value of  l

(I) * (-7)        -7c - 7l = -189

(II)                7c + 6l = 170     {Now add}

                         - l    = -19

l = 19

Plugin l = 19 in equation (I)

c + 19 = 27

c = 27 - 19

c = 8

Number of chocolate cakes = 8

Number of lemon cakes = 19

Answer: A. Not a function. B. Is a function. C. Not a function. D. Not a function.

Step-by-step explanation:

Answer:

D. Add 8x to both sides of the inequality

Step-by-step explanation:

Answer:

it's D :)

Step-by-step explanation:

The identity for addition for rational numbers is zero which is the option b.

Given addition of rational numbers.

We are required to find the identity for the addition of rational numbers.

Rational numbers are those numbers which can be written in the form of p/q and q cannot be equal to zero because if q is equal to zero the whole fraction will become infinity. The numbers whih cannot be written as p/q are known as irrational numbers.

From the all option zero is the identity for addition for rational numbers. This  means if a is a rational number. Then a+0=0+a=a.

Hence the identity for addition for rational numbers is zero which is the option b.

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Answer: 3 square inches

Step-by-step explanation:

   See attached for how I broke the shape up. Since each square is equal to 1 square inch, and the shape is about 3 squares, the answer should be;

O 3 square inches

Please note that different people may estimate differently.

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Answer:

6xy(2x²-3y)

Step-by-step explanation:

factorized completely