Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. Other battery models, produced by similar processes, have normally distributed life spans. The 98% confidence interval for the population mean life of the new model is _________. Group of answer choices

Answer:

He should pay $2,790.7.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time, in years.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

In this question:

Rate of 10%, so I = 0.1.

9 months, so [tex]t = \frac{9}{12} = 0.75[/tex]

How much should he pay for a note that will be worth $3,000 in 9 months?

We have to find P for which T = 3000. So

[tex]T = E + P[/tex]

[tex]3000 = E + P[/tex]

[tex]E = 3000 - P[/tex]

Then

[tex]E = P*I*t[/tex]

[tex]3000 - P = P*0.1*0.75[/tex]

[tex]1.075P = 3000[/tex]

[tex]P = \frac{3000}{1.075}[/tex]

[tex]P = 2790.7[/tex]

He should pay $2,790.7.

Answer:

x =-5

Step-by-step explanation:

Answer:

x=-5

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

It would be a cone with a radius of 4 units rotating around y-axis.

Answer:

$160

Step-by-step explanation:

In the monthly payment option she would pay $80 per month, therefore in a year (12 months) she would pay:

$80*12 =  $960

We can see that this amount is greater than the $800 she would pay in the lump sum payment option.

The money she would save is:

$960 - $800 = $160

She would save $160 yearly with the lump sum payment option.

Answer:

Step-by-step explanation:

The point estimate is the sample proportion.

Considering the sample,

Sample proportion, p = x/n

Where

x = number of success = 137

n = number of samples = 200

p = 137/200 = 0.685

From the information given,

Population proportion = 62% = 62/100 = 0.62

The correct options are

A) Yes, the sample size is greater than 30.

B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.

Answer:

x > -4

Step-by-step explanation:

— 3х + 7 < 19

Subtract 7 from each side

— 3х + 7-7 < 19-7

-3x < 12

Divide each side by -3, remembering to flip the inequality

-3x/-3 > 12/-3

x > -4

Just like any of your two-step equations, in this inequality,

start by isolating the x term which in this case is -3x by

subtracting 7 from both sides.

This gives us -3x < 12.

Solving from here, we divide both sides by -3.

However, when solving inequalities, you need to watch out.

When you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign.

Please give this idea your full attention. Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when dividing both sides of an inequality by a negative.

So we end up with x > -4.

Answer:

acute and scalene

Step-by-step explanation:

Answer:no entiendo esta en ingles

Step-by-step explanation:

Answer:

765,795 = 96%

Step-by-step explanation:

confidence interval = 0.04  

The Za/2 theorem = 1/2 = 0.04/2 = 0.02= /x = 720z

If ; 0.02 = 2.05  then the interval is 780-2.05 x 40/√30 x 780+2.05 x 30/√30 = 765,795 = 96%

We see 40/ √30 which is found in equation of finding the sample mean at point /x = 720z

σ 40/ n√30 = 7.3029674334 and is simply a fraction of /x 720z

By normal distribution we find

The 96% confidence interval for the population mean of all bulbs = 765,795

As 765, x 1.04 = 795 = 765, 795

To find Sampling mean.

The Sampling Distribution of the Sample Mean. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).

Confidence Level z*-value

80% 1.28

90% 1.645 (by convention)

95% 1.96

96% 2.05

98% 2.33

99% 2.58

Answer:

4 pizza's

Step-by-step explanation:

hope this helps :)

Answer:

The probability of spinning a 3 out of the 6 options is 1/6.

Answer: 1/6

Step-by-step explanation:

Im assuming the p stands for probability. There is a total of 6 slices, the 3rd slice takes up 1/6th of the circle

Answer: Cylinder

Step-by-step explanation:

Two bases first: that rules out cone and rectangular pyramid.

One lateral face: the only one with that is cylinder.

Hope that helped,

-sirswagger21

The figure which has two bases and one lateral face that is rectangular is, ''Cylinder.''

Any triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The shape have two bases and one lateral face that is rectangular.

We know that;

In a Cylinder,

It is a three-dimensional solid that contains two parallel bases connected by a curved surface.

And, The bases are usually circular in shape. The perpendicular distance between the bases is denoted as the height “h” of the cylinder and “r” is the radius of the cylinder.

Thus, The figure which has two bases and one lateral face that is rectangular is, ''Cylinder.''

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Answer:

d = 2

Step-by-step explanation:

Using the formula

A=pq/2

Dont forget to click THANKS

Answer:

For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:

Null hypothesis (H0): [tex]\mu \geq 2000[/tex]

Alternative hypothesis (H1): [tex]\mu <2000[/tex]

And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 200 or no

Step-by-step explanation:

For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:

Null hypothesis (H0): [tex]\mu \geq 2000[/tex]

Alternative hypothesis (H1): [tex]\mu <2000[/tex]

And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 2000 or no

Answer:

the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.

Step-by-step explanation:

With the statement we can make a system of 2x2 equations, where:

"x" is the area of the first field

"y" is the area of the second field

However,

x + y = 56 => x = 56 - y

3/4 * x + 2/3 * y = 40

replacing we have:

3/4 * (56 - y) + 2/3 * y = 40

42 - 3/4 * y + 2/3 * y = 40

-0.0833 * y = 40 - 42

y = -2 / -0.0833

y = 24

now for x:

 x = 56 - 24

x = 32

This means that the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.

Answer:

x=-2,y=-4

Step-by-step explanation:

By dividing to lowest terms

5x – 5y = 10= x-y=2.......(1)

6x – 4y = 4=3x-2y=2........(2)

By elimination method

Multiply equation (1) by 3 so as to correspond with equation (2)

3(x-y)=3(2)

3x-3y=6..........(3)

Multiply equation (2) by 1 so as to correspond with equation (1)

1(3x-2y)=1(2)

3x-2y=2..........(4)

Then equation (3)-equation (4)

(3x-3y=6)

-

(3x-2y=2)

__________

-y=4

y=-4

Substitute y=-4 into equation(1)

x-(-4)=2

x+4=2

x=-2

Therefore x=-2,y=-4

Answer:

Maths keeps one mentally active. The total surface of a hemisphere = 3(pi)r^2. So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.

Step-by-step explanation:

hope this helps you :)

Answer:

The total surface of a hemisphere = 3(pi)r^2.

So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.

Answer:

3.14

Step-by-step explanation:

We find the total circumference of a circle with radius 2 to be

2 * pi * r

= 2 * 3.14 * 2

= 12.56

We divide by 4 to get the perimeter of the quarter circle

12.56/4 = 3.14

Answer:

Class width = 20

Approximate lower class limit of the first class = 110

Approximate Upper class limit of the first class = 119

Step-by-step Explanation:

The class width of the histogram attached below can be gotten by finding the difference between successive lower class limits.

Thus, class width = 130 - 110 = 20

The approximate lower class limit of the first class is the lowest score we have in the first class = 110

The approximate upper class limit of the first class is the closest highest score that fall within the first class and is below the lower limit of the second class. Thus approximate upper class limit of the first class = 129

Answer:

77

Step-by-step explanation:

80*0.2 + 84*0.3 + 74*0.4 + 60*0.1 = 76.8 = 77

Answer:

1) Antonio's statement

2) <A = 123

Step-by-step explanation:

1) Antonio's statement is incorrect. This is because the opposite angles of a quadrilateral add up to 180°. Erin was incorrect because the opposite angles of this quadrilateral are unequal.

2) 2x+7+5x-2 = 180° (opposite angles of quadrilateral)

Now

7x+5 = 180

7x = 175

x = 25

<A = 5x-2

= 5(25)-2

= 125-2

= 123

Answer:  The answer has one solution:

_______________________________

      →  x = 1 ;   y =  -4 ;  or, write as:  [1, -4].

_______________________________

Step-by-step explanation:

_______________________________

Given:

  y  =  - 1x – 3

  y  =   -7x + 3 ;

_______________________________

    -1x – 3  =   -7x + 3  ;  Solve for "x" ;

Add:  " +1x" ; and add " +3 " ;  to Each Side of the equation:

Subtract " 1x " ; and Subtract " 1 " ; from Each Side of the equation:

   -1x  + 1x  – 3  + 3  =  -7x  + 1x + 3 + 3 ;

         to get:  

             0  =  -6x + 6

          ↔  -6x + 6 = 0 ;

Now, subtract " 6 " from Each Side of the equation:

                -6x + 6 – 6  = 0 – 6  ;

       to get:

               -6x = -6 ;

Now, divide Each Side of the equation by " -6 ";  

      to isolate "x" on one side of the equation;

      & to solve for "x" ;

              -6x /-6  =  -6/-6 ;

      to get:

                x = 1 .

_______________________________

Now, let us solve for "y" ;  

We are given:  

 y =  -x – 3  ;

Substitute our solved value for "x" ; which is:  " 1 " ; for " x " ; into this given equation; to obtain the value for " y " :

 y =  -x – 3  ;

    =  -1  – 3  

 y =   - 4 .

_______________________________

Let us check our answers by plugging the values for "x" and "y" ;

" 1 " ; and " -4 "; respectively);  into the second given equation; to see if these values for " x " and " y"  ; hold true:

Given:   y  =    - 7x  +  3 ;

           →  -4   =?  -7(1) + 3 ??  ;

           →  -4   =?   -7   + 3  ??  ;

           →  - 4 =?   -4 ?? ;

           →  Yes!

_______________________________

The answer has one solution:

      →  x = 1 ;   y =  - 4 ;  or, write as:  [1, -4 ].

_______________________________

Hope this is helpful!  Best wishes!

_______________________________

Answer:

The quarterly growth rate in revenues is significantly different from 1.2%.

b. 2,666,858

Step-by-step explanation:

Given that:

The regression equation can be represented as :

[tex]log_{10} \hat Y= 6.102+0.012 X - 0.129 Q_1 - 0.054 Q_2 + 0.098 Q_3[/tex]

In testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.02.

The null and alternative hypothesis can be stated as;

[tex]H_0:[/tex]    The quarterly growth rate in revenues is not significantly different from 1.2%.

[tex]H_a:[/tex]   The quarterly growth rate in revenues is significantly different from 1.2%.

The decision rule is to reject the null hypothesis if the p-value is less than 0.05.

From above ; the p-value = 0.02 which is less than 0.05.

Conclusion:

Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e

The quarterly growth rate in revenues is significantly different from 1.2%.

b.

Since [tex]Q_1=Q_2=Q_3 = 0[/tex] ; X = 27

Thus ;

[tex]log_{10} \hat Y= 6.102+0.012 X - 0.129 Q_1 - 0.054 Q_2 + 0.098 Q_3[/tex]

[tex]log_{10} \hat Y= 6.102+0.012 (27)[/tex]

[tex]\hat Y=10^{ 6.102+0.012 (27) }[/tex]

[tex]\hat Y =[/tex] 2666858.665

[tex]\hat Y =[/tex]  2,666,858

Answer:

π

Step-by-step explanation:

For a circle, arc length is equal to the radius times the angle.

s = rθ

s = (1) (π − 0)

s = π

Answer:

all real numbers

Step-by-step explanation:

The domain is the input values

All values for x are valid as inputs to the function

Answer:

c

Step-by-step explanation:

when the absolute value of slope gets smaller, the graph of line gets less steeper.

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

[tex]\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min[/tex]

So it will take them approximately 51.43 minutes to complete the project together.

Answer:

2/3

Step-by-step explanation:

We can find the slope by using the slope formula

m= (y2-y1)/(x2-x1)

  = (-4-2)/(-1-8)

  = -6/ -9

  = 2/3

Answer:

the answer is 6!!!!!!

Step-by-step explanation:

The missing value in the table is 5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

An intravenous fluid is infused at the rate shown in the table

Minutes         Milliliters

3                            4

?                             12

2.                            3

?                             6

3                             9

9                             24

Slope=24-9/9-3

=15/3

=5

Now 5=12-4/x-3

5=8/x-3

5x-15=8

5x=23

x=23/5

x=4.6

x=5

The missing number is 5.

Hence, the missing value in the table is 5

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Answer:

Step-by-step explanation:

The formula is y = mx + b

m being the slope, rise over run. And b being the y-intercept. Right off the bat we can visually see the y-intercept is -4.

To find slope, we need to take two sets of coords and apply the slope fomula. The slope fomula is change in y divided by the change in x. The function itself is straight, so that means the slope will be the exact same no matter which points you choose.

(4, -1) and (8, 2) are coords on the line. Do 2 - (-1) to get 3. then do 8 - 4 to get 4. Finally, we just gotta do 3/4 which is simply [tex]\frac{3}{4}[/tex].

We have the slope of 3/4 and we have the y-intercept of -4. Just plug it in the standard formula of y = mx + b to get:

[tex]y=\frac{3}{4} x-4[/tex]

Answer:

s(r(-4)) = -164

Step-by-step explanation:

r(x) = 2x - 1

s(x) = -2x^2 - 2

r(-4) = 2(-4) - 1 = -8 - 1 = -9

s(r(-4)) = s(-9) = -2(-9)^2 - 2 = -2*81 - 2 = -162 - 2 = -164

Hope this helps!