A spherical snowball is melting. Its radius decreases at a constant rate of 3 cm per minute from an initial value of 100 cm. How fast is the volume decreasing 5 minutes later? give your answer in cubic centimeters per minute.

The Length of the line segment RS is 9 units

In geometry, the line that is bounded by two distinct points is known as a Line segment. In simple words, we can say that a line segment is part of a straight line that connects two distinct points.

To find the length of the line segment we can use the distance formula

Where (x₁, y₁) and (x₂, y₂) are endpoints of Line segments  

Here we have

R ( 6,5) and S (6,-4)    

And we need to find the length of the line segment RS

Length of Line segment RS = distance between two points

= √ [ (6 - 6)² + (-4 - 5)²]  

= √ [ (-9)²]  

= 9 units

The Length of the line segment RS is 9 units

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a) The hypothesis are given as follows:

b) The significance level is of α = 0.1.

c) The test statistic is of: t = -2.69.

d) The p-value is of: 0.018

e) The decision is to reject the null hypothesis.

At the null hypothesis, it is tested if there is not enough evidence that SUVs sustain less damage, that is, the mean is equal or greater than zero, hence:

[tex]H_0: \mu_d \geq 0[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the SUVs sustain less damage, that is, the mean if less than zero, hence:

[tex]H_1: \mu_d < 0[/tex]

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

The sample of the differences is given as follows:

447, -893, -2373, 271, -1680, -1916, -1676.

Using a calculator from the above sample, the values of these parameters are given as follows:

[tex]\overline{x} = -1117, \mu = 0, s = 1100, n = 7[/tex]

Hence the test statistic is of:

t = (-1117 - 0)/(1100/sqrt(7))

t = -2.69.

Using a t-distribution calculator, considering a left-tailed test, as we are testing if the mean is less than a value, with 7 - 1 = 6 df and t = -2.69, the p-value is of 0.018.

Since this p-value is less than the significance level of 0.1, the decision is to reject the null hypothesis.

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On solving the 3 variable equation you will get the answer x=6, y=1, and z=2. It is solved by elimination method.

What is elimination method?

The elimination method involves removing a variable from a system of linear equations by employing addition or subtraction along with multiplication or division of the variable coefficients.

Now, consider the first two equations.
-3x + 3y +2z = -11
3x + 5y - 5z = 13

Multiply the upper eqation with 5 and lower eqation with 2 to make coefficient of z equal.

-15x + 15y + 10z = -55
6x + 10y - 10z = 26

Add these two equations to eliminate z.

-9x + 25y = -29                   ... (1)

Now, consider second and third eqation from the the eqation given in the question.
3x + 5y - 5z = 13
5x - 6y - z = 22

Multiply the upper equation with 5 to make coefficient of z equal in both the equations.

3x + 5y - 5z = 13
25x - 30y - 5z = 110

Now, subtract the lower equation from the upper equation.
3x + 5y - 5z = 13
-25x + 30y + 5z = -110

To get the following equation:
-22x + 35y = -97                   ... (2)

Now, consider equation (1) and (2).
-9x + 25y = -29
-22x + 35y = -97

Multiply the upper equation with 35 and lower equation with 25.

-315x + 875y = -1015
-550x + 875y = -2425

Now, subtract these two equations to get the following equation:

235x = 1410
x = 6

Substitute the value of x in equation (1).

-9x + 25y = -29
-9 (6) + 25y = -29
25y = 25
y = 1

Now, substitute the value of x and y in following eqation:

-3x + 3y + 2z = -11
-3(6) + 3(1) + 2z = -11
-15 + 2z = -11
2z = 4
z =2

Hence, on solving the 3 variables equation, you will get the answer x=6, y=1, and z=2.

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The coefficients of the expression are 6, 1.

The constant of the expression is 9.

The error Jake might have made is that: D. Jake did not include the coefficient 1.

In Mathematics, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.

Based on the algebraic expression provided, we can reasonably infer and logically deduce that there are two (2) coefficients and these include 6 as the coefficient of b and 1 as the coefficient of y.

This ultimately implies that, the error Jake made was not including the coefficient 1 for y.

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Complete Question:

On a math test a student, Jake, has to identify all the coefficients and constants of the expression 9 + 6b + y. Jake says that 6 is a coefficient and 9 is a constant. Identify all the coefficients and constants of the expression. What error might Jake have made?

The coefficient(s) of the expression is/are __

Use a comma to separate answers as needed.)

The constant(s) of the expression is/are __

(Use a comma to separate answers as needed.)

What error might Jake have made?

A. Jake said 9 is a coefficient. It is actually a constant.

OB. Jake said 6 is a constant. It is actually a coefficient.

OC. Jake did not include the constant 1.

OD. Jake did not include the coefficient 1.

Regarding the data from the table, it is found that:

a) The percentage of students who failed, given that they completed the review, is of 15.38%.

b) The percentage of students who failed, given that they did not complete the review, is of 42.86%.

c) There is an inverse association between failing the exam and completing the exam review.

A percentage is calculated applying proportions, as it is a fraction of a total amount, obtained as the division of the number of desired outcomes by the number of total outcomes and multiplied by 100%.

For item a, the outcomes are given as follows:

Hence the percentage is:

p = 10/65 x 100% = 15.38%.

For item b, the outcomes are given as follows:

Hence the percentage is:

p = 15/35 x 100% = 42.86%.

Regarding the association between failing the exam and completing the exam review, it is an inverse association, as the percentage of those who failed completing the review is way less than the percentage of those who failed without completing the review.

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The examples of unit rates include miles per hour, blinks per second, calories per serving, and steps per day.

A unit rate is the price for one unit of something. This is written as a ratio with a denominator of one. For instance, if you ran 70 yards in 10 seconds, you averaged 7 yards per second. Both ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but only the latter is a unit rate.

The denominator of a unit rate is always 1. To find the unit rate, divide the denominator by the numerator so that the denominator equals 1.

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Answer: 4,300 gallons of water

215 x 4 = 860 gallons of water using the dishwasher

215 x 6 x 4 = 5,160 gallons of water by hand

5,160 - 860 = 4,300 gallons of water saved by using the dishwasher.

- Your welcome, keep it up champ.

The probability to take 5 classes is 0.1, while the probability to take at least one class is 0.6, the probability to take 2 or 3 classes is 0.23 and the expectation of the distribution is 1.37.

1.

We know that in a probability distribution,  the sum of all the probabilities is always equal to 1.

Let the probability of X = 5 be a

Hence,

0.4 + 0.25 + 0.15 + 0.08 + 0.02 + a = 1

or, 0.9 + a = 1

or, a = 1 - 0.9

or, a = 0.1

Hence the probability to take 5 classes is 0.1.

2.

We need to find P(X ≥ 1)

= 1 - P(X = 0)

we already know from the table that P(X = 0) is 0.4

Hence, P(X ≥ 1)

= 1 - 0.4

= 0.6

Hence, the probability to take at least one class is 0.6

3.

The probability to take 2 or 3 classes in a semester = P( X = 2)  +  P(X = 3)

= 0.15  +  0.08

= 0.23

4.

We know that the expectation of any distribution

= ∑xp(x)

where,

x is the random variable

p(x) is the probability of the random variable

Therefore,

E(X) = 0 X 0.4  +  1 X 0.25  +  2 X 0.15  +  3 X 0.08  +  4 X 0.02  +  5 X 0.1

= 0  +  0.25  +  0.30+  0.24  +  0.08  +  0.50

= 1.37

Therefore the expectation of the given distribution is 1.37

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The correct statement about the given negative numbers is none of these

Negative numbers

A number whose value is always less than zero and it has a minus (-) sign before it is known as negative number.

Given,

Four numbers are listed.

-√50,- 36/5, - 7.05, - 2.3n

Here we need to find the correct statement that describes given numbers.

In order to find the correct statement we have to convert all the number into the same decimal form.

So, first number is written as,

-√50 = -7.07

Then the decimal form of the second number is

-36/5 = -7.2

The value is

=> -2.3n here we have to place any value for n but we have take the value of 1, then we get

=> -2.3(1) = -2.3

So, this one is rapidly decreasing based on the value of n.

Now, we have the decimal equivalent for all the four numbers.

Then we looking into the given statements we have identified that the statement none of these

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For the given expression, the values are a = 3, b = 3, c = 5 and d=2

What are prime number?

What is prime factorization?

The prime factorization of 600 is given by

600 = 2 * 2 * 2 * 3 * 5 * 5

       = 2³ * 3 * 5²

Compare this to the given expression.

Hence, the values are a = 3, b = 3, c = 5 and d=2

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keeping in mind that a line with an undefined slope is a vertical line, Check the picture below.

The value of tan W is 5/12

From the question, we have

tan W = 15/36

= 5/12 =0.41

Divide:

Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

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Answer:

32 cm²

Step-by-step explanation:

By using property of logarithms, We get the answer

In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x

Given,

In the question:

The equation is :

In  [tex]\frac{x^{2} -1}{x^7}[/tex] , x > 1

To solve by using by using property of logarithms to expand the expression as a sum, difference, and / or constant multiple of logarithms.

Now, According to the question:

We know that:

The property of logarithms is:

[tex]log_{a}{\frac{m}{n} } = log_{a}m - log_{a}n[/tex]

The given equation is :

In  [tex]\frac{x^{2} -1}{x^7}[/tex] , x > 1

In  [tex]\frac{x^{2} -1}{x^7}[/tex] = In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex]

Again, Using the another property of logarithms.

[tex]log_am^x = nlog_am[/tex] {x∈ R}

In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In [tex](x^2 -1)[/tex] - 7 In x

In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In [ (x + 1)(x - 1)] - 7In x

In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x

{Log (mn) = [tex]log_{a}m - log_{a}n[/tex]}

Hence, By using property of logarithms, We get the answer

In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x

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Answer: -19x + 10

Step-by-step explanation:

1. Remove parenthesis

-10x + 2 - 9x + 8

2. Collect like terms

(-10x - 9x) + (2 + 8)

3. Simplify

-19x + 10

The factored form of n2 + n is:  n(n+1).

Given data:

n²+n

Now let find the factored form of n²+n

n²+n

Rewrite in factored form

n(n+1)

Hence,

n²+n = n(n+1)

Therefore n(n+1) is the factored form.

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Answer:

Step-by-step explanation:

1(x1)+ (-4)x2+ (-10)x3 = -40                               Eq 1

0   +    (1)x2 +   3(x3)   = 14                               Eq 2

0  +   (-2)x2 + (-5)x3  =  -23                             Eq 3

from the 2nd equations we get

x2 + 3*x3 = 14

x2 = 14 - 3*x3

plug this into equation 3

(-2)*(14-3*x3) + (-5)x3 = -23

now solve for x3  :)

-28+6*x3-5*x3 = -23

-28 +x3 = -23

x3 = 5

nice !

now find x2

x2 = 14-3*(5)

x2 = -1

now find x1

x1 + (-4)*(-1) + (-10)*5 = -40

x1 +4 -50=-40

x1 = 6

X = [ 6 ; (-1) ; 5 ]

The birth weight of elephants at the 99% confidence level is 3820 pounds

What is the standard deviation?

Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.

The average birth weight of elephants is 200 pounds     = 200

The deviation of 60 pounds.                                               = 1500

The birth weight of elephants is at the 85th percentile.      z = 99%= 1.645

Now from the formula of z-score:-

[tex]z=\sqrt{\frac{x-\mu}{\sigma} }[/tex]

[tex]1.64 =\sqrt{\frac{x-200}{1500} }\\[/tex]

[tex]1.645^{2} =\frac{x-200}{1500}[/tex]

2.68 = (x-200)/1500

2.68×1500=x-200

4020-200=x

3820=x

Hence the birth weight of elephants at the 99% level percentile is 3820 pounds

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Claribel needs to pay $875 for 17 months to gym, $25 for one time membership fee and $50 for 17 months.

A set or group of equations that you solve all at once is referred to as a "system" of equations. A linear equation can be represented as Ax + By +C = 0, Where A, B are coefficient and C is the constant. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.

To find the amount for Claribel, we have to find the monthly fee and one time membership fee for the gym.

Let x be one time membership fee for the gym and y be the monthly fees, so the system of equations will be,

x + 6y = 325

x + 9y = 475

Now, subtracting the above equations, we get

3y = 150

y = 50

Now, putting the value of y in first equation, we get

x + 6(50) = 325

x+300 = 325

x = 25

Now, finding the amount for Claribel,

One time membership fee + 17(Monthly Fee) = Total Amount

Putting the values,

Total Amount = 25 + 17(50)

= 25 + 850

=$ 875

Therefore, Claribel needs to pay $875 for 17 months to gym.

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A formula for the sequence 2.3, 2.8, 3.3, 3.8, ... is a_n = 1.8 + 0.5 n.

First, let us understand the arithmetic progression:

Arithmetic Progression (AP) is a number sequence in which the difference between any two consecutive numbers is a constant value.

We can find the common difference (d) by subtracting any two consecutive terms of arithmetic progression.

The nth term of an arithmetic progression is given by:

a_n = a + (n - 1)d

where

a = first term of an arithmetic progression

n = nth term of an arithmetic progression

d = common difference

We are given the following sequence;

2.3, 2.8, 3.3, 3.8, ...

We need to write a formula for the given sequence.

Let us find the common difference;

d = 2.8 - 2.3 = 0.5

a = 2.3

substitute the values in the above formula;

a_n = 2.3 + (n - 1) * 0.5

a_n = 2.3 + 0.5 n - 0.5

a_n = 1.8 + 0.5 n

So, the formula for the given sequence is a_n = 1.8 + 0.5 n.

Thus, a formula for the sequence 2.3, 2.8, 3.3, 3.8, ... is a_n = 1.8 + 0.5 n.

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The number of signatures that Sadie and Cora have is 40 signatures.

Sadie has 10 and she is collecting signatures at an average rate of 3 per day. This will be:

10 + 3d

Cora has 20 and is averaging 2 signatures every day. This will be:

= 20 + 2d

The equation will be:

10 + 3d = 20 + 2d

Collect like terms

3d - 2d = 20 - 10

d = 10

Therefore, the number of signature will be:

= 10 + 3d

= 10 + 3(10)

= 10 + 30

= 40

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Answer:

D. Normality of the estimator (e.g., sample mean)

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The question was incomplete. Check below the complete question.

Which of the following is the necessary condition for creating confidence intervals for the population mean? A. Known population parameter B. Normality of the population C. Known standard deviation of the estimator D. Normality of the estimator (e.g., sample mean)

Step-by-step explanation:

The y intercept is the y value when x=0,

So plug in x=0,

[tex]5(0) - 2y = 20[/tex]

[tex] - 2y = 20[/tex]

[tex]y = - 10[/tex]

According to the concept of difference, the amount of time spend on answering the phone call is 50 minutes.

Difference:

Difference means the result of one of the important mathematical operations, which is obtained by subtracting two numbers and it tells us by how much a number differs from the other.

Given,

On Saturday mornings, Eddie volunteers at the hospital where his mother works. One Saturday, he answers phone calls at the information desk while the receptionist is away. The he spends 40 minutes delivering flowers to patients' rooms. In all, Eddie volunteers at the hospital for 90 minutes that day.

Here we need to find the amount of time spend on answering the phone calls.

While we looking into the given question, we have identified the following things,

Total amount of time spend by Eddie = 90 minutes

Time spend in delivering flowers = 40 minutes

So, the time spend by answering the phone calls is calculated as the difference between the total time and the flower delivering time

=> 90 - 40

=> 50

Therefore, he spent 50 minutes on answering the phone calls.

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Check the picture below.

[tex]\textit{Sum and Difference Identities} \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ cos(105^o)\implies cos(60^o+45^o)\implies cos(60^o)\cdot cos(45^o)-sin(60^o)\cdot sin(45^o) \\\\\\ \cfrac{1}{2}\cdot \cfrac{\sqrt{2}}{2}~~ - ~~\cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{2}}{4}~~ - ~~\cfrac{\sqrt{6}}{4}\implies {\Large \begin{array}{llll} \cfrac{\sqrt{2}-\sqrt{6}}{4} \end{array}}[/tex]

There is currently $62.65 billion in the fund.

Given that;

If the FDIC must use 7.6% of its $67.8 billion insurance reserve to pay for several bankrupt banks,

To get how much money is left in the fund, we need to;

The total insurance fund = $67.8 billion

To cover several failed banks = 7.6% = 0.076

Therefore, the money left = $67.8 * 0.076

                                           = $5.15

So, the final amount left in the fund = $67.8 - $5.15

                                                           = $62.65

Hence, the money left in the fund is $62.65 billion.

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