Find the equation of the exponential function represented by the table below:
Y
8
0
1
2
3
3
12
48
192

Volume is a three-dimensional scalar quantity. The volume of the rectangular prism is 200 in³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the rectangular prism of the length of 8 inches, the width of 2 inches, and the height of 12 1/2 inches can be written as,

The volume of the rectangular prism = 8in × 2in × 12.5in

                                                               = 200 in³

Hence, The volume of the rectangular prism is 200 in³.

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Answer:

There were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.

Let x be the number of 50-cent coins in the bag,

And y be the number of 20-cent coins.

From the problem,

we know that y = x - 5,

Since there were 5 fewer 20-cent coins than 50-cent coins.

We can also set up an equation for the total value of the coins in the bag,

⇒ 0.5x + 0.2y = 24.20

Now we can substitute y = x - 5 into the equation,

⇒ 0.5x + 0.2(x - 5) = 24.20

Simplifying, we get,

⇒ 0.7x - 1 = 24.20

⇒ 0.7x = 25.20

⇒ x = 36

So there were 36 50-cent coins in the bag.

Using y = x - 5,

We can find that there were 31 20-cent coins.

Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).

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Answer:

6

Step-by-step explanation:

Answer:

2 or A

Step-by-step explanation:

Correct on edge22

The ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

We have ABCD is a parallelogram.

BE is perpendicular to FC

FA is perpendicular to FC

As we know in the parallelogram ABCD:

AB ≅ DC

AD ≅ CB

As the DC is extended to F

So, AB ≅ FE

And BE is perpendicular to FC

       FA  is perpendicular to FC  (given)

∴ FA ≅ BE

∴ ABEF is a parallelogram.

Thus, the ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.

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Answer:

Step-by-step explanation:

The two relations can be translated to a system of linear equations in two variables. These can be solved in any of the usual ways.

__

Let d and m represent the amounts David and Mary saved last month, respectively.

The first relation tells us

  d/m = 3/5   ⇒   5d = 3m   ⇒   5d -3m = 0

The second relation tells us that adding 3 times what David had last month to 2 times what Mary had last month will give a total that is 154 greater than the sum of their funds last month.

  d +m + 154 = 3d +2m   ⇒   2d +m = 154

__

We can add 3 times the second equation to the first to eliminate m.

  (5d -3m) +3(2d +m) = (0) +3(154)

  11d = 462 . . . . . . . . simplify

  d = 42 . . . . . . . . . divide by 11

Using the second equation, we can find Mary's savings:

  m = 154 -2d

  m = 154 -2(420 = 70

David saved $42 last month; Mary saved $70.

For the given linear system equations, the value for the variables are: x=-2, y=4, and z=-5 - Option C.

System of Linear Equations

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

2x+y-5z=4 (1)

x+3y+z=5  (2)

3x-y-4z=-11 (3)

First, you should sum equations 1 and 2. The results will be:

3x+4y-4z=9 then you have a new equation (4).

3x-y-4z=-11 (3)

3x+4y-4z= 9(4)

Now, you should multiply equation (3) by -1, then you will have:

-3x+y+4z=+11 (3)

3x+4y-4z=9 (4)

After that, you should sum the previous equations: (3) and (4).

5y=20

y=4

For find z, you should multiply equation 2 by -2. After that, you should sum equations 1 and 2.

2x+y-5z=4 (1)

-2x-6y-2z=-10  (2)

Thus, you will have:

-5y-7z=-6, like y=4 you have

-5*4-7z=-6

-20-7z=-6

-7z=14

z=-2

If z=-2 and y=4 from equation 2, you can find x.

x+3y+z=5

x+3*4-2=5

x+12-2=5

x+10=5

x=5-10

x=-5

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Answer:

C. All real numbers

By finding the minimum of the given function, we conclude that the lowest average temperature that year is 57°F.

We know that the average temperature is given by the equation:

f(x)=31cos(0.0055πx)+88

And it is in Fahrenheit degrees.

To get the lowest average temperature, we just need to find the minimum of the above function.

Remember that the minimum of the cosine function is:

cos(x) = -1

Then the lowest value of the above function is:

f(x₀) = 31*(-1) + 88 = 57

From this, we conclude that the lowest average temperature that year is 57°F, so the correct option is A.

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Answer:

  133 miles

Step-by-step explanation:

The limited budget gives rise to an inequality that can be solved for the maximum number of miles.

__

The rental cost for m miles will be the sum of the fixed charges and the product of the mileage charge and the number of miles.

  cost = 19.95 +0.15m

We want this to be no greater than 40, so we have the inequality ...

  40 ≥ 19.95 +0.15m

This two-step inequality can be solved in the usual way:

  20.05 ≥ 0.15m . . . . . step 1, subtract 19.95 from both sides

  133.667 ≥ m . . . . . . . step 2, divide by the coefficient of the variable

The maximum whole number of miles Gabrielle can drive is 133.

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

Assuming that conditions have been met for the interval, we use the formula [tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex] where [tex]\bar{x}[/tex] represents the sample mean, [tex]t[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] is the sample size.

The critical value of [tex]t[/tex] for an 80% confidence level with degrees of freedom [tex]df=n-1=25-1=24[/tex] is equivalent to [tex]t=1.317836[/tex]

Thus, we can compute the confidence interval:

[tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}\\\\CI=32.64\pm1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\\\\CI\approx\{30.17,35.11\}[/tex]

Therefore, we are 80% confident that the true mean age of all customers is between 30.17 and 35.11 years.

Part B

The margin of error is [tex]\displaystyle t\frac{s}{\sqrt{n}}=1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\approx2.47[/tex]

Given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

Note that: Area of a circle is expressed as;

A = πr²

Where r is radius and π is constant pi ( π = 3.14 )

Given that;

A = πr²

A = 3.14 × ( 35cm )²

A = 3.14 × 1225cm²

A = 3846.5cm²

Therefore, given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

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Answer:

10:

7/4π = 5.5(1decimql place)

11:

50π = 157.1(1 decimal place)

Step-by-step explanation:

the equation is (angle/360) X πr^2

Step-by-step explanation:

please mark me as brainlest

Answer:

Step-by-step explanation:

a)  Sum of nine and two ⇒ 9 + 2

Four multiplied by (9+2) :  

       4* (9+2)

[tex]b) \dfrac{(18-6)}{4}[/tex]

[tex]c) \dfrac{45}{3*(3+2)}[/tex]

2) a) Multiply the sum of five and eight by 6

   b) There 5 story books in 6 red bags and 8 art books in 6 blue bags. How many books are there?

3) a) 7*(8-3)

      Multiply the difference of eight and three by 7.

The functions in order from least to greatest according to their average rates of change are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]

The rate of change is calculated using:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

For function g at the interval [2,3], we have:

[tex]m = \frac{g(3) - g(2)}{3- 2}[/tex]

This gives

[tex]m = \frac{20 - 4}{3- 2}[/tex]

[tex]m =16[/tex]

For function h at the interval [0,2], we have:

[tex]m = \frac{h(2) - h(0)}{2- 0}[/tex]

Where:

h(2) = 3(3)^2 - 9 = 18

h(0) = 3(3)^0 - 9 = -6

This gives

[tex]m = \frac{18 + 6}{2 - 0}[/tex]

[tex]m = 12[/tex]

For function f at the interval [1,2], we have:

[tex]m = \frac{f(2) - f(1)}{2- 1}[/tex]

This gives

[tex]m = \frac{12 - 6}{2 - 1}[/tex]

[tex]m = 6[/tex]

Hence, the functions are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]

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Answer:

A.264

Step-by-step explanation:

((Area Of triangle*height)=Volume

Area of triangle is the base of the triangle multiplied by height of triangle divided by 2

((8*6)/2)*11=264

Answer:

x = 23.0

Step-by-step explanation:

To solve, you have to make the equation:

[tex]cos(64)=\frac{9}{x}[/tex]

Now multiply x to both sides:

[tex]cos(64)*x=9[/tex]

Next divide both sides by cos(64):

[tex]x=\frac{9}{cos(64)}[/tex]

x = 22.9675486404

Round to the tenth:

x = 23.0

Hope it helps and have a nice day!

The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.

Here we have the functions:

[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]

f(x) is quadratic, and g(x) is exponential.

Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards.  So first and second options are false.

Also, g(x) never intersects the x-axis, so third option is false.

Finally, the y-intercepts of the given functions are:

[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]

So the y-intercepts are equal, meaning that the correct option is D.

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Answer:

Both f(x) and g(x) have the same y-intercept of (0, 1).

Step-by-step explanation:

I got it right on the test.

The point at which three or more lines intersect is the point of concurrency.

The point were three lines meet or intersect is a point of concurrency.

In other words, a point of concurrency is where three or more lines intersect in one place.

This point of concurrency is a single point shared by three or more lines.

Perpendicular bisectors, and altitudes are concurrent in every triangle.

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Answer:

concurrency

Step-by-step explanation:

Look above for more

The midpoint theorem simply states that the line segment that joins the two sides of the triangle is parallel to the third side.

Your information is incomplete. Therefore, an overview of the theorem will be given. It should be noted that the midpoint theorem states that the line drawn through the mid point of one side of the triangle is parallel to another side.

To find the midpoint, one can measure the distance between the two end points and divide the results by 2.

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     If the question should read as the following, then I hope my answer will help;       -3 +7 _ -10 - 2

Answer: A. >

Step-by-step explanation:

  Given:

-3 + 7 _ -10 - 2

  Simplify both sides by combining like terms:

4 _ -12

  Compare, knowing that 4 is greater than -12:

4 _ -12

4 > -12

             A. >

Answer:

Train A = 466

Train B = 60

Step-by-step explanation:

Answer:

130 degrees

Step-by-step explanation:

3:40, it has traveled 6 * 40 = 240 degrees  which is 110 degrees from vertical The difference is 240 - 110 = 130 degrees, which is the final answer.

Hope This Helped

If these coordinates are translated two units down, we will subtract 2 units from the y axis to have A(2, -1), B(0, -3) and C(2, -3)

Translation is a transformation technique of changing the position of an object on the xy-plane.

Given the following coordinate of a triangle expressed as:

A(2, 1)

B(0, -1)

C(2, -1)

If these coordinates are translated two units down, we will subtract 2 units from the y axis to have:

A(2, -1)

B(0, -3)

C(2, -3)

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Answer:

  0.513671875 = 263/512 inches

  easier to use: depends on the measurement tool

Step-by-step explanation:

The model dimension is found by multiplying the actual dimension by the scale factor.

__

  model frame dimension = actual frame dimension × 1/64

  = (32.875 inches)/64 = 0.513671875 inches

In fractional form, this is ...

  (32 7/8) / 64 = (263/8) / 64 = 263/512 . . . inches

__

It is unlikely that a casual hobbyist will have access to tools that measure with a resolution finer than 0.0001 inches. More common would be a measurement resolution of 0.001 inches. Using such tools, the rounded decimal value 0.5137 or 0.514 inches would be more useful than the fractional measurement.

It is possible that an optical measuring device could be available that would present its result as a fraction of an inch. If such a tool were used, the fractional measurement value would provide an appropriate point of comparison.

In short, the measurement easiest to work with depends on the tool being used to make the measurement.

Answer:

this is one of systematic sample and correct option is d

Answer:

your answer will be 85 1/3ins

Step-by-step explanation:

16x 5 1/3 = 85.3333333333

then I took the 85 and the 1/3

and just put em together

The statement that matches the vector operation shown on the coordinate grid is v + w = u.

In order to add two vectors a and b graphically by using the tail and tip method, we must draw the tail of b at the tip of vector a.

Then we must draw a line that goes from the tail of vector a to the tip of vector b.

This line represents the sum of a + b.

In the given problem, we notice that the tail of the vector w is on the tip of the vector v.

The line that joins the tail of vector v with the tip of vector w is vector u.

Therefore we can say that v + w = u

The statement that matches the vector operation shown on the coordinate grid is v + w = u.

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Answer:

230 degrees

Step-by-step explanation:

draw a horizontal line from x and use congruent rule to have a full 360 degree circle. You can now subtract 60 and 70 from 360 degrees leaving you with 230 degrees as x