A data set includes 103 body temperatures of healthy adult humans having a mean of 98.1degreesf and a standard deviation of 0.56degreesf. construct a 99​% confidence interval estimate of the mean body temperature of all healthy humans. what does the sample suggest about the use of 98.6degreesf as the mean body​ temperature?

The unit of measure used to express the volume of a prism is  cubic units correct option is c.

Volume refers to the amount of space occupied by a three-dimensional object. A prism, being a three-dimensional shape with length, width, and height, necessitates a measurement that encapsulates all three dimensions.

Prisms have a base shape that repeats through their height. Calculating volume involves finding the space enclosed within this repeating shape. By multiplying the area of the prism's base by its height.

Cubic units represent the volume of an object, akin to how square units represent area. They measure the number of unit cubes needed to fill the three-dimensional space within the prism. This measurement allows for precise quantification of space in a three-dimensional context.

complete the question

Which unit of measure can be used to express the volume of the prism?

a) unit squares

b) square units

c) cubic units

 d)  units

Answer:

3,247,695

Step-by-step explanation:

We want the coefficient of  the term with  x^8

So  Use Newton's Binomial Expansion formula

Formula is  (x + y) ^n  =   Sum for i=0 to n     (n choose i)   x^(n-i)*y^i

here   (x^2  + 3) ^ 12

( 12 choose i) *  (x^2)^(12-i) * (3)^i

i needs to equal 8  for us to get  x^8

(12 choose 8) * (x^2)^(12-8) * (3^8)

= (12 choose 8) * x^8  * (3^8)

so  a = (12 choose 8) * [tex]3^{8}[/tex]

a =  (12! /(8! * 4!) ) * [tex]3^{8}[/tex]

a = ( 12*11*10*9/  4*3*2*1)  * [tex]3^{8}[/tex]

a =  (11*5*9) * [tex]3^{8}[/tex]

a = 11*5*9 * 6561

a = 3,247,695

Answer:

The answer is A

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

edg

Answer:

4

Step-by-step explanation:

i just got it right

Answer:

B. a decrease in their water bill of $3.16.

Step-by-step explanation:

Monthly service charge =$10.10

Volume charge = $1.58 for every 100 cubic feet of water.

Total monthly cost = 1.58x + 10.10

If the Johnson family used [tex]200ft^3[/tex] less water this month than last month, then they can expect a reduction in their bill by the Volume charge for  [tex]200ft^3[/tex].

Volume Charge per [tex]100ft^3[/tex] of water = $1.58

Therefore: Volume Charge for [tex]200ft^3[/tex] of water = 2 X $1.58=$3.16

Therefore, the Johnson family can expect a decrease in their water bill of $3.16.

The correct answer is B) a decrease in their water bill of $3.16.  

Given the equation: y = 1.58x + 10.10

Johnson family used 200 cubic feet less water.

200 cubic feet = 2 hundreds of cubic feet.

Change in water usage: [tex]\(\Delta x = -2\)[/tex]

Calculate the change in the water bill:

[tex]\(\Delta y = 1.58 \times \Delta x\)[/tex]

[tex]\(\Delta x = -2\): \(\Delta y = 1.58 \times (-2)\)[/tex]

[tex]\(\Delta y = -3.16\).[/tex]

The water bill will decrease by $3.16.

Correct answer: B. a decrease in their water bill of $3.16.

Answer:

Step-by-step explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 3

θ = π/6

2π = 360 degrees

π = 360/2 = 180

Therefore,

θ = 180/6 = 30 degrees

Therefore,

Length of arc = 30/360 × 2 × 3.14 × 3

Length of arc = 1.6 to the nearest tenth

Final answer:

To find the length of the intercepted arc on a circle with radius 3 and a central angle of π/6, calculate using the formula s = rθ. The result is approximately 1.6 units after rounding to the nearest tenth.

Explanation:

The question asks to find the length of the intercepted arc given a central angle of measure θ=π/6 on a circle with radius r = 3 and to round the answer to the nearest tenth. To calculate the arc length (θ), we use the formula s = rθ, where θ is measured in radians. Given θ=π/6 and r=3, the arc length s is therefore 3*(π/6)= π/2. To get a numerical answer, substitute π with approximately 3.14159, resulting in s = (3*3.14159)/6 which simplifies to s ≈ 1.57. Rounding to the nearest tenth gives us an arc length of 1.6 units.

Answer:

Determinant = -12

Step-by-step explanation:

rewrite the system as

-2 =  2x - 3y  + 0z

0 =  0x +  y - 2z

1 =  -3x + 2y   - z

then the coefficient matrix is

{  [2,  -3,   0]

  [0,   1,    -2]

  [-3,  2,   -1]  }

to find determinant

{  [2,  -3,   0]    ,   2,    -3

  [0,   1,    -2]   ,    0,     1

  [-3,  2,   -1]  },     -3,     2

determinant  =   2*1*-1  +  (-3 * -2 * -3)  +   (0*0*2)  -  0  -  (2*-2*2)  - 0

determinant = -2  - 18  + 0  - 0 + 8 =   -12

They spent $111 on shopping

Step-by-step explanation:

Let the amount they spent be 'a'

Leilas amount = $134

Diannes amount = $180

After they spent same amount on shopping dianne had 3 times as much money as Leila

180 - a = 3(134 - a)

180 - a = 402 - 3a

3a - a = 402 - 180

2a = 222

a = $111

They spent $111 on shopping

Answer:

B. f(x) = 884 • [tex]1.22^{x}[/tex]

Step-by-step explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one. Please have a look at the attached photo

My answer:

Given that:

The following functions could model this situation is:

B. f(x) = 884 • [tex]1.22^{x}[/tex] where:

884 is a profit its first year

1.22 growth rate in revenue

x  represents the number of years in operation

Hope it will find you well.

Answer:

1 1/4

Step-by-step explanation:

For the strawberries, we will have to multiply 3 by 1/4 to get the total amount of strawberries used.

1/4 * 3 = 3/4

For the blueberries, we will have to multiply 2 by 1/4 to get the total amount of blueberries used.

1/4 * 2 = 2/4

Simplify that to get 1/2

Now we need to add 3/4 and 1/2

3/4 + 1/2 = 5/4

Simplify that and we get our answer;

1 1/4

Answer: 144

Step-by-step explanation: To find a value of c that would make this a perfect square, take -24 and divide it by 2 to get -12. Next, simply square -12 to get 144.

x^2 - 24x + 144 can be factored into (x - 12)(x - 12)

Answer:

144 is the correct answer

Answer: The exterior angle, D, is supplementary to the adjacent interior angle, C. Together, they form a straight line, measuring 180°. The measure of the remote interior angles, A and B are equal to the measure of the exterior angle D.

Step-by-step explanation: I just did the assignment.

Answer:

Sample answer: The exterior angle, D, is supplementary to the adjacent interior angle, C. Together, they form a straight line, measuring 180°. The measure of the remote interior angles, A and B are equal to the measure of the exterior angle D.

Step-by-step explanation:

Each sphere of ice has a radius of 2cm

one tray makes 6 spheres

What is the total volume of ice the tray can make at one time?

Total volume of each sphere is 33.51 cm^3

The tray can hold 6 of these at a time

33.5 * 6

201 cm^3 total volume of ice that the tray can make at one time

Written in pi 

64  cm^3

Read more on Brainly.com - https://brainly.com/question/8790068#readmore

Answer: Its 64[tex]\pi[/tex]!!!

Step-by-step explanation:

The known acute angle of the triangle is 46 degrees, so the unknown acute angle of that triangle is 90-46 = 44 degrees. In other words, the two acute angles of any right triangle must add to 90, so 46+44 = 90.

The 44 degree angle is adjacent to angle ADC, and it adds to angle ADC to form 180 degrees.

If x is the measure of angle ADC, then

44+(angleADC) = 180

44+x = 180

x = 180-44

x = 136

angle ADC = 136 degrees

For any parallelogram, the opposite angles are always congruent. Therefore, angle ABC is equal to angle ADC = 136, making ABC = 136 as well.

Answer: C. 136 degrees

Step-by-step explanation:

From the diagram, angle C is a right angle because it is formed by a perpendicular line. It means that

Angle BCD + 46 = 90

angle BCD = 90 - 45 = 44 degrees

The opposite angles in a parallelogram are equal while the adjacent angles are supplementary. Angle ABC and angle BCD are supplementary and the sum of supplementary angles is 180 degrees. Therefore,

Angle ABC + 44 = 180

Angle ABC = 180 - 44

Angle ABC = 136 degrees

Answer:

turn the percentage into a decmial and then multiply the money

To simplify the expression, first rewrite the fractions:[tex]\( \frac{2y}{y - 3} \) and \( \frac{2(y - 3)}{y + 3} \)[/tex]. Then, divide the first fraction by the reciprocal of the second, yielding[tex]\( \frac{2y}{y - 3} \).[/tex]

let's simplify the expression:

[tex]\[ \frac{\frac{2y}{y - 3}}{\frac{4y - 12}{2y + 6}} \][/tex]

First, we'll simplify the fractions within the larger fractions:

[tex]\[ \frac{2y}{y - 3} = \frac{2y}{y - 3} \times \frac{(y - 3)}{(y - 3)} = \frac{2y(y - 3)}{(y - 3)^2} = \frac{2y^2 - 6y}{y^2 - 6y + 9} \][/tex]

[tex]\[ \frac{4y - 12}{2y + 6} = \frac{4(y - 3)}{2(y + 3)} = \frac{2(y - 3)}{y + 3} \][/tex]

Now, we'll divide the first fraction by the second fraction. This is equivalent to multiplying by the reciprocal:

[tex]\[ \frac{\frac{2y^2 - 6y}{y^2 - 6y + 9}}{\frac{2(y - 3)}{y + 3}} = \frac{2y^2 - 6y}{y^2 - 6y + 9} \times \frac{y + 3}{2(y - 3)} \][/tex]

Now, let's cancel out common factors:

[tex]\[ = \frac{2y(y + 3)}{(y - 3)(y + 3)} \times \frac{y + 3}{2(y - 3)} \][/tex]

[tex]\[ = \frac{2y}{y - 3} \][/tex]

So, the simplified expression is [tex]\( \frac{2y}{y - 3} \).[/tex]

Answer:

1/8

Step-by-step explanation:

1/4 divided by 2

Final answer:

Each friend received 1/8 of the original pie after equally sharing 1/4 that was left over.

Explanation:

Marge and Kimo equally shared 1/4 of a pie that was left over. To determine the fraction of the original pie that each friend got, we divide that 1/4 by two, since there are two people sharing it. So, each friend received 1/8 of the original pie.

Step-by-step explanation:

Answer:

The width of the framing material is 3 inches

Step-by-step explanation:

we know that

The area of the frame and photograph combined is given by the expression

[tex]156=(7+2x)(6+2x)[/tex]

solve for x

Expanded the expression

[tex]156=42+14x+12x+4x^2\\4x^2+26x+42-156=0[/tex]

[tex]4x^2+26x-114=0[/tex]

solve the quadratic equation by graphing

using a graphing tool

The solution is x=3 in

see the attached figure

therefore

The width of the framing material is 3 inches

The width of the framing material is [tex]\( x = 3 \)[/tex] inches

Given:

- Length of the photograph = 7 inches

- Width of the photograph = 6 inches

- Width of framing material = x inches

- Area of frame and photograph combined = 156 square inches

The total length of the framed photograph would be [tex]\( 7 + 2x \)[/tex] inches, and the total width would be [tex]\( 6 + 2x \)[/tex] inches.

So, the area of the framed photograph is the product of its total length and total width:

[tex]\[ \text{Area of framed photograph} = (7 + 2x)(6 + 2x) \][/tex]

Given that the area of the framed photograph is 156 square inches, we set up the equation:

[tex]\[ (7 + 2x)(6 + 2x) = 156 \][/tex]

Expanding and simplifying:

[tex]\[ 42 + 14x + 12x + 4x^2 = 156 \][/tex]

[tex]\[ 4x^2 + 26x + 42 = 156 \][/tex]

[tex]\[ 4x^2 + 26x - 114 = 0 \][/tex]

Now, let's solve this quadratic equation for x . We can simplify it by dividing all terms by 2:

[tex]\[ 2x^2 + 13x - 57 = 0 \][/tex]

Using the quadratic formula:

[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

Where:

- a = 2

- b = 13

- c = -57

Plugging in the values:

[tex]\[ x = \frac{{-13 \pm \sqrt{{13^2 - 4(2)(-57)}}}}{{2(2)}} \][/tex]

[tex]\[ x = \frac{{-13 \pm \sqrt{{625}}}}{{4}} \][/tex]

[tex]\[ x = \frac{{-13 \pm 25}}{{4}} \][/tex]

So, we have two possible solutions for x:

[tex]\[ x_1 = \frac{{-13 + 25}}{{4}} = 3 \][/tex]

[tex]\[ x_2 = \frac{{-13 - 25}}{{4}} = -9 \][/tex]

Since the width of the framing material cannot be negative, we discard [tex]\( x_2 \).[/tex]

Therefore, the width of the framing material is [tex]\( x = 3 \)[/tex] inches.

Answer:

6/30=0.2 so 0.2 miles per minute

8/0.2=40 minutes

You can also check 30/6=5 so the conversion is 5

8 x 5 = 40 minutes.

Step-by-step explanation:

Hope this helps can I have brainliest

If on rainy days, Francesca likes to ride the stationary bike at the gym. Yesterday, she rode for 30 minutes and covered 6 miles. Today, she plans to ride 8 miles.  If she rides at the same rate, how many minutes will it take Francesca to ride today will be 40 minutes

First step is to formulate

8×30÷6

Now let determine the how many minutes will it take Francesca to ride today

Number of minutes=8×30÷6

Number of minutes=8×6

Number of minutes=40 minutes

Inconclusion if on rainy days, Francesca likes to ride the stationary bike at the gym. Yesterday, she rode for 30 minutes and covered 6 miles. Today, she plans to ride 8 miles.  If she rides at the same rate, how many minutes will it take Francesca to ride today will be 40 minutes.

Learn more here:

https://brainly.com/question/17023521

Answer: 54

Step-by-step explanation:

Answer:

The teacher will have to give out 54 pencils

Step-by-step explanation:

there 9 children in the class. each student gets 6 pencils.

9 times 6 = 54

Answer:

9x8=72 and 25+2=27

Step-by-step explanation:

1x9=9

2x9=18

3x9=27

4x9=36

5x9=45

6x9=54

7x9=63

8x9=72

brainleist please i really need it

Answer:

50%

Step-by-step explanation:

no matter how many times it is flip you will get heads or tails.

Answer:

50%

Step-by-step explanation:

two sides 1/2= 50%

Answer:

D. The data points are close to the mean

Step-by-step explanation:

given data

mean absolute deviation = 0.1

Answer:

We use Simultaneous Equation to express the problem

From the equation, a bag of popcorn will cost $5

Step-by-step explanation:

We can represent drink with d and bad of popcorn with p

If Tristan spent $38.75 on 5 drinks and 2 bags of popcorn, the we can interpret it as

5d + 2p = 38.75 ....................... eqn 1

And if Noah spent $37.25 on 3 drinks and 4 bags of popcorn, we can interpret it also as

3d + 4p = 37.25 ........................ eqn 2

This is now a Simultaneous Equation

Since we are to state the price of a bag of popcorn, then we can use the elimination method to eliminate d and solve for p

To do this, Multiply eqn 1 by 3 and eqn 2 by 5

(5d + 2p = 38.75)*3

(3d + 4p = 37.25)*5

The we will have

15d + 6p = 116.25 .......................... eqn 3

15d + 20p = 186.25 ...................... eqn 4

If we subtract eqn 3 from eqn 4, we will have

14p = 70

Divide both sides by 14 to get the value of p, and we will have

p = 70/14

p = 5

Therefore a bag of popcorn equals to $5

Answer:

The area of a cover that will fit on the larger tank is 6 square inches

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its Volumes is equal to the scale factor cubed

Let

z ---> the scale factor

so

[tex]z^3=\frac{64}{8}=8[/tex]

[tex]z=2[/tex]

step 2

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ---> the scale factor

x ---> the area of a cover that will fit on the larger tank

y ---> the area of a cover that will fit on the smaller tank

so

[tex]z^2=\frac{x}{y}[/tex]

we have

[tex]z=2\\y=1.5\ ft^2[/tex]

substitute the given values

[tex]2^2=\frac{x}{1.5}[/tex]

solve for x

[tex]x=4(1.5)=6\ ft^2[/tex]

The area of the cover that will fit on the larger aquarium is approximately 12 square feet, calculated by multiplying the area of the smaller cover by the square of the scaling factor for linear dimensions (≈ 2.83) due to the difference in volume.

To find the area of a cover that will fit on the larger aquarium, we begin by understanding that the area scales by the square of the linear dimensions.

Since the volume of the larger aquarium is 64 gallons and the smaller one is 8 gallons, the volume scales by a factor of 64/8 = 8. Taking the square root of 8 gives us the scaling factor for the linear dimensions, which is sqrt(8) ≈ 2.83. The larger tank's cover will therefore need to increase by this scaling factor squared for its area.

To calculate the area of the larger tank's cover, we multiply the area of the smaller cover by this scaling factor squared: 1.5 ft2 * 2.832 ≈ 12 ft2. Thus, the cover for the larger tank should be approximately 12 ft2 in area. This demonstrates the concept that area is proportional to the square of the linear dimensions when scaling similar shapes.

Final answer:

By using the ratio of 4:5 for the amounts that Jamie and her sister save, we calculate that since Jamie has $20, her sister has $25 in her account.

Explanation:

To find out how much money Jamie's sister has in her account, we need to first understand the ratio of the amounts they save. For every four dollars that Jamie saves, her sister saves five dollars. This gives us a ratio of 4:5.

Since Jamie has $20 in her account, we can determine how many times four dollars fits into twenty dollars to find out how many 'units' of savings Jamie has made. We do this by dividing 20 by 4, which equals 5. So, Jamie has saved 5 units of 4 dollars each.

Knowing that each unit for Jamie's sister is $5, we calculate the total amount for her sister by multiplying 5 units with the sister's $5, which equals $25. Therefore, Jamie's sister has $25 in her account.

Final answer:

For every $4 Jamie saves, her sister saves $5. Jamie has $20, which is equal to 5 units of $4. Therefore, Jamie's sister has saved 5 units of $5, which amounts to $25.

Explanation:

The question asks how much money Jamie's sister would have in her account, given that Jamie has $20 and for every four dollars that Jamie saves, her sister saves five dollars. To find the amount Jamie's sister has saved, we use the ratio of their savings. Since Jamie has $20 and saves $4 for every $5 her sister saves, we can calculate the amount Jamie's sister has saved using the following steps:

First, determine how many 'four dollar' units Jamie has saved. She has saved $20, so that's $20/$4 = 5 units.

Since Jamie's sister saves $5 for each of these units, we multiply the number of units by $5 to find her savings, which is 5 units * $5/unit = $25.

Therefore, Jamie's sister has $25 in her account.

Answer: 0.72

Step-by-step explanation: I’ve drawn the triangle out and have assumed that 21 is adjacent and 29 is the hypotenuse. In that case, 21/29 = 0.724

The zeros of the function f(x) = (x + 4)(x – 7) are x = -4 and x = 7. These values are where the function intersects the x-axis and can be expressed as points (-4, 0) and (7, 0) on a graph.

To find the zeros of the function f(x) = (x + 4)(x – 7), we need to determine the values of x that make f(x) equal to zero. This means each factor in the product must be set equal to zero and solved for x individually.

Setting the first factor equal to zero gives us x + 4 = 0, which simplifies to x = -4.

Similarly, setting the second factor equal to zero gives us x – 7 = 0, which simplifies to x = 7. Thus, the zeros of the function are x = -4 and x = 7.

These can be written as the ordered pairs (-4,0) and (7,0) when we consider them as points on the Cartesian plane where the function intersects te x-axis.

The correct choice from the options provided would be -4 and 7, which corresponds to the first option.

It is not necessary to provide the y-coordinates when identifying the zeros of a function, as by definition, they are points where the y-value is zero.

Given:

The given triangle is a right angled triangle.

One of the angle is 64° and the length of one of the leg is x.

The length of the hypotenuse is 28.

We need to determine the value of x.

Value of x:

The value of x can be determined using the trigonometric ratio.

Thus, we have;

[tex]cos \ \theta=\frac{adj}{hyp}[/tex]

where [tex]\theta= 64[/tex], adj = x and hyp = 28

Substituting the values, we get;

[tex]cos\ 64=\frac{x}{28}[/tex]

Multiplying both sides by 28, we have;

[tex]cos \ 64 \times 28=x[/tex]

 [tex]0.438\times 28=x[/tex]

       [tex]12.264=x[/tex]

Rounding off to the nearest hundredth, we get;

[tex]12.26=x[/tex]

Therefore, the value of x is 12.26

Answer:

Therefore it will take 28 years.

Step-by-step explanation:

To find the years, we use the following formula,

[tex]A=P(1+r)^n[/tex]

A= Total balance after n years

P= Initial amount.

r= Rate of interest per year.

n = Time in years.

Given that, Josh's grandparents put $3,000 into a college saving account when he was born. The account earn 6% interest per years.

Here A=$15,000,P=$3,000, r=6%=0.06 ,n=?

[tex]\therefore 15,000=3,000(1+0.06)^n[/tex]

[tex]\Rightarrow (1.06)^n=\frac{15,000}{3,000}[/tex]

[tex]\Rightarrow (1.06)^n=5[/tex]

Taking ln both sides

[tex]\Rightarrow ln(1.06)^n=ln(5)[/tex]

[tex]\Rightarrow n=\frac{ln(5)}{ln(1.06)}[/tex]

[tex]\Rightarrow n\approx 28[/tex]

Therefore it will take 28 years.