If (a, b, c) is a solution to the system of equations above, what is the value of c?
•-26
•-6
•6
•It cannot be determined from the information given

Complete  Question

In a random sample of  ten  people, the mean driving distance to work was  23.1 miles and the standard deviation was  6.6 miles. Assume the population is normally distributed and use the​ t-distribution to find the margin of error and construct a  99​%  confidence interval for the population mean Interpret the results.  Identify the margin of error.

Answer:

The  99% confidence interval is  [tex]16.32< \mu <29.88[/tex]

The interpretation is that there is 99% confidence that the true mean lies within the limits

The margin of error is  [tex]E = 6.783[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 23.1[/tex]

     The standard deviation is  [tex]\sigma = 6.6 \ miles[/tex]

    The  sample size is  n = 10

Generally the degree of freedom is mathematically represented as

     [tex]df = n-1[/tex]

=>  [tex]df = 10-1[/tex]

=>  [tex]df =9[/tex]

Given that the confidence level is 99% , the n the level of significance is mathematically evaluated as

         [tex]\alpha = 100 - 99[/tex]

         [tex]\alpha =1\%[/tex]

        [tex]\alpha =0.01[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] with a df of  9  from from the student t-distribution table the value is  

          [tex]t _{\frac{\alpha }{2} , df } = 3.250[/tex]

Generally the margin of error is mathematically represented as

           [tex]E = t_{\frac{\alpha }{2} , df } * \frac{\sigma }{\sqrt{n} }[/tex]

          [tex]E = 3.250 * \frac{6.6 }{\sqrt{10} }[/tex]

         [tex]E = 6.783[/tex]

The 99% confidence interval is

      [tex]\= x - E < \mu < \= x + E[/tex]

=>   [tex]23.1 - 6.78 < \mu <23.1 + 6.78[/tex]

=>  [tex]16.32< \mu <29.88[/tex]

The interpretation is that there is 99% confidence that the true mean lies within the limits

Answer:

25 CAN be written as a fraction.

=> 250/10 = 25

Square root of 14 is 3.74165738677

It is NOT POSSIBLE TO WRITE THIS FULL NUMBER AS A FRACTION,  but if we simplify the decimal like: 3.74, THEN WE CAN WRITE THIS AS A FRACTION

=> 374/100

-1.25 CAN be written as a fraction.

=> -5/4 = -1.25

Square root of 16 CAN also be written as a fraction.

=> sqr root of 16 = 4.

4 can be written as a fraction.

=> 4 = 8/2

Pi = 3.14.........

It is NOT POSSIBLE TO WRITE THE FULL 'PI' AS A FRACTION, but if we simplify 'pi' to just 3.14, THEN WE CAN WRITE IT AS A FRACTION

=> 314/100

.6 CAN be written as a fraction.

=> 6/10 = .6

Answer:

The equation 1+0=1

Step-by-step explanation:

Other options are not eligible because

1 option -Natural numbers cannot be closed under subtraction

2 option-The equation is not having proper rational numbers, they are decimals

3 option-Whole numbers cannot be closed under subtraction

Thank you!

Answer:

B = 6

Step-by-step explanation:

2x^2 + 4xy − 48y^2

Factor out 2

2(x^2 + 2xy − 24y^2)

What 2 numbers multiply to -24 and add to 2

-4 *6 = -24

-4+6 = 2

2 ( x+6y)( x-4y)

Answer:

[tex]\huge\boxed{B=6}[/tex]

Step-by-step explanation:

They are two way to solution.

Factor the polynomial on the left side of the equation:

[tex]2x^2+4xy-48y^2=2(x^2+2xy-24y^2)=2(x^2+6xy-4xy-24y^2)\\\\=2\bigg(x(x+6y)-4y(x+6y)\bigg)=2(x+6y)(x-4y)[/tex]

Therefore:

[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)\\\Downarrow\\2(x+6y)(x-4y)=2(x+By)(x-4y)\to\boxed{\bold{B=6}}[/tex]

Multiply everything on the right side of the equation using the distributive property and FOIL:

[tex]2(x+By)(x-4y)=\bigg((2)(x)+(2)(By)\bigg)(x-4y)\\\\=(2x+2By)(x-4y)=(2x)(x)+(2x)(-4y)+(2By)(x)+(2By)(-4y)\\\\=2x^2-8xy+2Bxy-8By^2=2x^2+(2B-8)xy-8By^2[/tex]

Compare polynomials:

[tex]2x^2+4xy-48y^2=2x^2+(2B-8)xy-8By^2[/tex]

From here we have two equations:

[tex]2B-8=4\ \text{and}\ -8B=-48[/tex]

[tex]1)\\2B-8=4[/tex]        add 8 to both sides

[tex]2B=12[/tex]         divide both sides by 2

[tex]B=6[/tex]

[tex]2)\\-8B=-48[/tex]          divide both sides by (-8)

[tex]B=6[/tex]

The results are the same. Therefore B = 6.

Answer:

15

Step-by-step explanation:

3 + 3+ 4+ 5+ 5+ 5+ 6+ 7+ 7=45

You would then divide that my 9(the amount of numbers) to get three

(3 + 3+ 4+ 5+ 5+ 5+ 6+ 7+ 7)/9

=3

If you are adding a number the numbers would be

3 + 3+ 4+ 5+ 5+ 5+ 6+ 7+ 7+?/10

Its ten because now you would have 10 numbers.

You know it equals 6, so you ask yourself: What divided by 10 would give you 6 or this equation:

( 3 + 3+ 4+ 5+ 5+ 5+ 6+ 7+ 7+?)/10=6

(45+?)/10=6

multiply both sides of the equal sign by 10

10(45+?)/10=6*10

The 10 on the bottom of the left side cancels out.

(45+?)=60

Subtract 15 from both sides of the equal sign

45+?-45=60-45

?=15

Answer:

x=9.6

Step-by-step explanation:

The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.

The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.

Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:

[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]

Answer:

a

   The  correct option is  B

b

   The  correct option is  D

Step-by-step explanation:

From the  question we are told that

     The level of significance is  [tex]\alpha = 0.05[/tex]

      The p-value is  [tex]p = 0.2761[/tex]

Considering question b

      Given that the  [tex]p< \alpha[/tex] then the null hypothesis is  rejected

Considering question b

Given that the original claim is The standard deviation of pulse rates of a certain group of adult males is more than 11 bpm

Then the null hypothesis is   [tex]H_o : \sigma = 11[/tex]

The  reason why the null hypothesis is write like this above is because a null hypothesis expression can not contain only a > or a < but only allows = [tex]\le , \ and \ \ge[/tex]

  and  the alternative hypothesis is  [tex]H_a : \sigma > 11[/tex]

Now given that the null hypothesis is rejected, it mean that there is sufficient evidence to support original claim

Answer:

Step-by-step explanation:

The sequence of the problem above is an arithmetic sequence

For an nth term in an arithmetic sequence

F(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

To find the equation first find the common difference

0.65 - 0.5 = 0.15 or 0.80 - 0.65 = 0.15

The first term is 0.5

Substitute the values into the above formula

That's

f(n) = 0.5 + (n - 1)0.15

f(n) = 0.5 + 0.15n - 0.15

The final answer is

Hope this helps you

Answer:

Step-by-step explanation:

Took the math test on edge

Answer:

The 90 % confidence limits are (-2.09, 8.09).

Since the calculated values do not lie in the critical region we accept our null hypothesis.

Step-by-step explanation:

The null and alternative hypothesis are given by

H0: σ₁²= σ₂² against Ha: σ₁² ≠ σ₂²

Confidence interval for the population mean difference is given by

(x`1- x`2) ± t √S²(1/n1 + 1/n2)

Where S ²= (n1-1)S₁² + S²₂(n2-1)/n1+n2-2

Critical value of t with n1+n2-2= 50+ 35-2= 83 will be -1.633

Now calculating

S ²=34* (12.8)²+ (14.6)²*49/83= 192.96

Now putting the values in the t- test

(75.1 -72.1) ± 1.633 √ 192.96(1/35 +1/50)

=3 ±  5.09

=-2.09, 8.09  is the 90 % confidence interval for the difference

The 90 % confidence limits are (-2.09, 8.09).

Since the calculated values do not lie in the critical region we accept our null hypothesis.

Answer: 0.8749

Step-by-step explanation:

Given, The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20.

Let x be the time taken by Tim to install a satellite dish.

Then, the probability that Tim will takes less than 150 minutes to install a satellite dish.

[tex]P(x<150)=P(\dfrac{x-\text{Mean}}{\text{Standard deviation}}<\dfrac{150-127}{20})\\\\=P(z<1.15)\ \ \ [z=\dfrac{x-\text{Mean}}{\text{Standard deviation}}]\\\\=0.8749\ [\text{By z-table}][/tex]

hence, the required probability is 0.8749.

Answer:

H0: μc ≤ μs    Ha :μc > μs    

Step-by-step explanation:

The null and alternate hypotheses can be stated as

H0: μc ≤ μs    Ha :μc > μs    one tailed test

Where

μc =  Mean of college students watching movies in a month

μs  =  Mean of school students watching movies in a month

For one tailed test of α =0.05   the value of Z= ± 1.645

The critical region will be Z >  ± 1.645

It is of importance to note that by rejecting the null hypothesis and accepting the alternate hypothesis we are automatically rejecting all values of mean that are greater than 7.1

====================================================

Explanation:

Both AB and XY are the first two letters of ABC and XYZ respectively. So we have one fraction of AB/XY = 2/7.

AC and XZ are the first and last letters of ABC and XYZ respectively. We can form another fraction AC/XZ. I'm dividing in the same order of small over large to keep things consistent. As you can probably guess, the order of the letters ABC and XYZ are important so we see how the angles match up and how the proportional sides match up.

Because the triangles are similar, the two fractions formed earlier are equal to one another.

The equation we need to solve is AB/XY = AC/XZ

-----

AB/XY = AC/XZ

2/7 = 3/N ... plug in given values

2N = 7*3 .... cross multiply

2N = 21

N = 21/2 .... divide both sides by 2

N = 10.5

ZX is 10.5 units long.

Answer:

For the functions to coincide, the value of k in y = (kx)3 must be smaller than in y = kx3. This is because the value of y changes more rapidly when k is cubed inside the parentheses. The behavior of the functions is similar since a vertical stretch is similar to a horizontal compression.

Step-by-step explanation:

PLATO

(1,1) is your answer.

Work is shown below.

Any questions? Feel free to ask.

Answer: (1,1)

Step-by-step explanation:

Answer:

235.6 units^3

Step-by-step explanation:

The formula for the volume of the oblique cone is the same as for the volume of a right circular cone:  V = (1/3)(base area)(height).

Here that comes to        V = (1/3)(π)(5 units)^2*(9 units), or

V = 75π units^3, or approximately 235.6 units^3

Answer:

235.5 cubic units

Step-by-step explanation:

Answer:

Table in option C represents the linear relationship as the equation, [tex] y = 2x + 6 [/tex]

Step-by-step explanation:

The equation given seems to be wrong. The equation should be [tex] y = 2x + 6 [/tex], because, taking a look at the tables given, the table in option C is the only table that has values that conforms to the equation, [tex] y = 2x + 6 [/tex].

In table C, when x = 2 using the equation, [tex] y = 2x + 6 [/tex], thus,

[tex] y = 2(2) + 6 = 4 + 6 = 10 [/tex].

When x = 3,

[tex] y = 2(3) + 6 = 6 + 6 = 12. [/tex]

Theredore, the equation, [tex] y = 2x + 6 [/tex], represents the relationship between the X and y variables in the table in option C.

Answer:

A

Step-by-step explanation:

we just substitute the value of "a" given in the above expression we get

21-2(3)

21-6=15

Answer:

a. 15

Explanation:

Step 1 - Input the value of 'a' in the expression.

21 - 2a

21 - 2(3)

Step 2 - Multiply two and three

21 - 2(3)

21 - 6

Step 3 - Subtract six from twenty one

21 - 6

15

Therefore, the value of the expression 21 - 2a if a = 3 is a. 15.

Answer:

Yes because no same x-value resulted in different y-values.

Answer:

Yes

Step-by-step explanation:

Answer:

1.

d. (-14) + (-8)

2.

a. (-14) + 8

Step-by-step explanation:

(-14) - 8 is equal to (-14) + (-8) because we still add two negative values so the result wouldn't change.

(-14) - (-8) is equal to (-14) + 8 because there's two negative sign in front of 8 and two negative values multiplied makes a positive result.

Answer:

1. D  

2. A

Step-by-step explanation:

1.  It asks you what expression has the same value as (-14)-8.  All you need to do is find other equations that have the same value as that.  So the equation is -14-8.  IF a negative is outside a parenthesis with a positive number inside like -(+5), it is going to be -5.  If it's both negative: -(-5), it will be +5.  If it is both positive: +(+5), it is going to be +5.  

IMPORTANT!

- and + = -

- and - = +

+ and + = +

What we are looking for: -14-8

So choice A is (-14)+8 which is simplified to -14+8.  So, this one isn't right.

Choice B: 14-(-8)= 14+8.  So, it's incorrect.

Choice C: 14+(-8)= 14-8.  Again, it's not -14-8 so it's not right.

Choice D: (-14)+(-8)= -14-8.  This equation matches the one we are looking for!  So it's correct!

2. Same thing as number 1.  Let's simplify the equation it wants us to find first.  

(-14)-(-8)= -14+8

So -14+8 is what we are looking for.

Choice A: (-14)+8= -14+8.  It matches!  So it is correct.  Let's look at the other options anyway.

Choice B: 14-(-8)= 14+8.  Nope.  Not right.

Choice C: 14+(-8)= 14-8 because - always beats +.  So, this one is also incorrect.

Choice D: (-14)+(-8)= -14-8.  Oops, this is also wrong.  So choice A is the right answer.

Keep in mind, when you start getting questions like this with numbers inside the parenthesis as well, you want to remember the same rules for positive and negative, but also multiply the numbers together:

(When there is a number outside and inside a parentheses, multiply them.)

2(5)=10, CORRECT!    2+(5) is not 2 times 5.  It's whatever is closest to the parentheses, in this case being the positive sign.  So + and 5 is just 5!

IMPORTANT!

-2(-5)= - and - is positive, so positive (2 times 5).  Positive 10.

-2(+5)= - and + is negative, so negative (2 times 5). Negative 10.

+2(+5)= + and + is positive, so positive (2 times 5).  Positive 10.

Answer:

x = 1

Step-by-step explanation:

First, move all the variables to one side by subtracting 5x on both sides:

5x + 2 = 12x - 5

2 = 7x - 5

Add 5 to both sides:

7 = 7x

1 = x

Answer:

x=1

Step-by-step explanation:

5x + 2 =12x- 5

Subtract 5x from each side

5x-5x + 2 =12x-5x- 5

2 = 7x-5

Add 5 to each side

2+5 = 7x-5+5

7 = 7x

Divide each side by 7

7/7 = 7x/7

1 =x

Answer:

Step-by-step explanation:

x² - 5x - 36

To factor the expression rewrite -5x as a difference

That's

x² + 4x - 9x - 36

Factor out x from the expression

x( x + 4) - 9x - 36

Factor out -9 from the expression

x( x + 4) - 9( x+ 4)

Factor out x + 4 from the expression

The final answer is

Hope this helps you

Answer:

[tex] \boxed{(x - 9) \: (x + 4) }[/tex]

Option A is the correct option.-

Step-by-step explanation:

( See the attached picture )

Hope I helped!

Best regards!

Answer:

Section I test scores are more dispersed that that of section II.

Step-by-step explanation:

Consider the data collected from the arithmetic test given to two sections of a school.

Section I: Mean = 45, Standard  Deviation = 6.5

Section II: Mean = 45,  Standard deviation = 3.1

The mean of both the sections are same, i.e. 45.

So there is no comparison that can be made from the center of the distribution.

The standard  deviation for section I is 6.5 and the standard  deviation for section II is 3.1.

The standard deviation is a measure of dispersion, i.e. it tells us how dispersed the data is from the mean or how much variability is present in the data.

The standard  deviation for section I is higher than that of section II.

So, this implies that section I test scores are more dispersed that that of section II.

Answer:

see explanation

Step-by-step explanation:

If f(x) and [tex]f^{-1}[/tex] are inverse functions, then

f([tex]f^{-1}[/tex])(x) = x

Thus substitute x = [tex]f^{-1}[/tex] (x) into f(x)

f([tex]\frac{x+6}{5}[/tex] )

= 5 ([tex]\frac{x+6}{5}[/tex] ) - 6

= x + 6 - 6

= x

Thus f(x) and [tex]f^{-1}[/tex] (x) are inverse functions

Answer:

1.-0.25     2..0173   3. .1/16    4. 1/7     5.2.2

Step-by-step explanation:

You want to put all numbers in fractions to see which numbers are smallest

Answer:

8 3/4

Step-by-step explanation:

The decimal 3.5 as an improper fraction is 35/10.

Answer:

[tex]8\frac{3}{4}[/tex]

Step-by-step explanation:

To write as a mixed number means that you will have a whole number and a fraction together. To find the mixed fraction version, see how many times the denominator (bottom) fits into the numerator (top) evenly.

4, 8, 12, 16, 20, 24, 28, 32, 36

1   2  3   4    5    6    7    8     9

4 can go into 35 '8' times without being greater than the numerator. 8 is the whole number. Now subtract the original numerator by the product of 4 and 8, which is 32:

[tex]35-32=3[/tex]

3 is the new numerator. Keep the same denominator. Insert all values:

[tex]\frac{35}{4}=8\frac{3}{4}[/tex]

:Done

Answer:

33 web pages (at least)

Step-by-step explanation:

We can set up an inequality to represent this, where x represents the number of web pages made.

1.5x > 1.25x + 8

1.5x represents the number of hours it will take normally, and 1.25x + 8 represents the time with the new software. 1.5x (amount of hours using old software) needs to be larger than the time it takes with the new software.

Solve for x:

1.5x > 1.25x + 8

0.25x > 8

x > 32

So, the designer would have to make at least 33 pages.

The number of web pages would the designer have to make in order to save time using the new software will be 33 web pages (at least).

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

We can set up an inequality to represent this, where x represents the number of web pages made.

1.5x > 1.25x + 8

The time with the new software is represented by 1.25x + 8 and the normal time is represented by 1.5x. The number of hours spent using the old software must be 1.5 times greater than the time spent using the new product.

Solve for x:

1.5x > 1.25x + 8

0.25x > 8

x > 32

Therefore, the number of web pages would the designer have to make in order to save time using the new software will be 33 web pages (at least).

To know more about inequality follow

https://brainly.com/question/24372553

#SPJ2

Answer:

[tex]\large \boxed{{y=18}}[/tex]

Step-by-step explanation:

[tex]1(y+3)=2(y+-4)+- 7[/tex]

Expand brackets.

[tex]y+3=2y-8+- 7[/tex]

Simplify.

[tex]y+3=2y-15[/tex]

Add -y and 15 on both sides.

[tex]y+3-y+15=2y-15-y+15[/tex]

Simplify.

[tex]3+15=2y-y[/tex]

[tex]18=y[/tex]

Answer:

18

Step-by-step explanation:

● 1 (y+3) = 2 (y+(-4) )+ (-7)

When you multiply by 1 you get the same result.

● y+3 = 2 (y+(-4))+(-7)

When you have a + sign with a - sign write -.

● y+3 = 2(y-4)-7

Multiply 2 by (y-4) and simplify

● y+3 = (2y-8)-7

● y+3 = 2y -8-7

● y+3 = 2y -15

Add 15 to both sides

● y +3+15 = 2y-15 +15

● y + 18 = 2y

Sibstract y from both sides

● y +18 - y = 2y -y

● 18 = y

Answer:

H₀: μ = 93.29 vs. Hₐ: μ ≠ 93.29.

Step-by-step explanation:

In this case we need to test whether the claim made by BC financial aid is true or not.

Claim: The average textbook at BC bookstore costs $93.29.

A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.  

It is a hypothesis of no difference.

It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.

Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.

The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.

It is also known as the research hypothesis and is denoted by Hₐ.

The hypothesis to test this claim can be defined as follows:

H₀: The average textbook at BC bookstore costs $93.29, i.e. μ = 93.29.

Hₐ: The average textbook at BC bookstore costs different than $93.29, i.e. μ ≠ 93.29.