Suppose there are approximately 220 calories in 3 servings of a particular brand of cereal and 362 calories in 5 servings of the same cereal. Find the rate of change.

Answer:

3.61%

Step-by-step explanation:

Mathematics, calculator

Answer:

Step-by-step explanation:

If we are looking for the probability that the battery lasts between 7 and 8 years, we find the z-score for the probability that it lasts less than 8 years, and then subtract from it the z-score for the probability that it lasts less than 7 years. This subtraction will give you what's left: the span in between 7 and 8 years. To find the z-score:

[tex]z=\frac{x_i-\mu}{\sigma}[/tex] Therefore,

P(x < 8) has a z-score of

[tex]z=\frac{8-5}{1.2}=1.667[/tex] The p-value that accompanies this z-score is .99379 (which translates to 99.379% of the data falling below 8 years) and

P(x < 7) has a z-score of

[tex]z=\frac{7-5}{1.2}=2.5[/tex] The p-value that accompanies this z-score is .95224 (which translates to 95.224% of the data falling below 7 years).

Subtract the p-value of 2.5 from the p-value of 1.667 to get

.99379 - .95224 = .04155 = 4.16%, choice A.

The distance between points W and X is exactly 5 units.

To know this, we need to see between which pair of two points we have 5 units.

By looking at the number line, we can see that the pair of points that is 5 units apart is W and X.

We have:

Taking the difference, we get: X - W = -3 - (-8) = 5

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Answer:

108 children and 115 adults were admitted

Step-by-step explanation:

Create a system of equations where c is the number of children admitted and a is the number of adults admitted:

c + a = 223

3.5c + 6.8a = 1160

Solve by elimination by multiplying the top equation by -3.5:

-3.5c - 3.5a = -780.5

3.5c + 6.8a = 1160

Add the equations together and solve for a:

3.3a = 379.5

a = 115

So, 115 adults were admitted.

Find how many children were admitted by subtracting 115 from 223, the total number of people admitted:

223 - 115

= 108

108 children and 115 adults were admitted.

Answer:

I'm pretty sure it is 3 hours.

Step-by-step explanation:

Well, when you add 9 plus 6, you get 15. Then you divie 45 by 15, which gives you three. Hope this helps. Good luck :D

Answer:

a = sqrt(7)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

where a and b are the legs and c is the hypotenuse

a^2 +3^2 = 4^2

a^2 +9 = 16

a^2 = 16-9

a^2 = 7

Taking the square root

a = sqrt(7)

Answer:

[tex]\displaystyle [CQF]=5[/tex]

Step-by-step explanation:

Note that [tex][n][/tex] refers to the area of some polygon [tex]n[/tex].

Diagonal [tex]\overline{AC}[/tex] forms two triangles, [tex]\triangle ABC[/tex] and [tex]\triangle ADC[/tex]. Both of these triangles have an equal area, and since the area of parallelogram [tex]ABCD[/tex] is given as [tex]210[/tex], each triangle must have an area of [tex]105[/tex].

Furthermore, [tex]\triangle ADC[/tex] is broken up into two smaller triangles, [tex]\triangle ADF[/tex] and [tex]\triangle ACF[/tex]. We're given that [tex]\frac{DF}{FC}=2[/tex]. Since [tex]DF[/tex] and [tex]FC[/tex] represent bases of [tex]\triangle ADF[/tex] and [tex]\triangle ACF[/tex] respectively and both triangles extend to point [tex]A[/tex], both triangles must have the same height and hence the ratio of the areas of [tex]\triangle ADF[/tex] and [tex]\triangle ACF[/tex] must be [tex]2:1[/tex] (recall [tex]A=\frac{1}{2}bh[/tex]).

Therefore, the area of each of these triangles is:

[tex][ACF]+[ADF]=105,\\[][ACF]+2[ACF]=105,\\3[ACF]=105,\\[][ACF]=35 \implies [ADF]=70[/tex]

With the same concept, the ratio of the areas of [tex]\triangle AQE[/tex] and [tex]\triangle DQE[/tex] must be [tex]2:1[/tex] respectively, from [tex]\frac{AE}{ED}=2[/tex], and the ratio of the areas of [tex]\triangle DQF[/tex] and [tex]\triangle CQF[/tex] is also [tex]2:1[/tex], from [tex]\frac{DF}{FC}=2[/tex].

Let [tex][DQE]=y[/tex] and [tex][CQF]=x[/tex] (refer to the picture attached). We have the following system of equations:

[tex]\displaystyle \begin{cases}2y+y+2x=70,\\y+2x+x=35\end{cases}[/tex]

Combine like terms:

[tex]\displaystyle \begin{cases}3y+2x=70,\\y+3x=35\end{cases}[/tex]

Multiply the second equation by [tex]-3[/tex], then add both equations:

[tex]\displaystyle \begin{cases}3y+2x=70,\\-3y-9x=-105\end{cases}\\\\\rightarrow 3y-3y+2x-9x=70-105,\\-7x=-35,\\x=[CQF]=\frac{-35}{-7}=\boxed{5}[/tex]

Answer:

64 = 2^6

Step-by-step explanation:

The conversion method for log is:

log (b) a = x

then you rearrange it into:

a = b^x

(these are all variables, so you can insert the numbers)

Answer:

300

Step-by-step explanation:

Is means equals and of means multiply

90 = 30% *n

90 = .3n

Divide each side by .3

90/.3 = n

300 = n

Answer:

[tex]30[/tex]

Step-by-step explanation:

[tex]6(3 + 2) \\ = 6(5) \\ = 30[/tex]

Step-by-step explanation:

It is read thus Y^3+X^2-7

The equation form from the given statement would be Y^3 + X^2 - 7.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.

For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.

We have been given a statement as;

"A number y cubed plus x squared decreased by 7".

So, the equation form would be

Y^3 + X^2 - 7

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The complete question is

"A number y cubed plus x squared decreased by 7". write the expression.

Answer: I believe the answer to your question is 4

Step-by-step explanation:

Let's check

a be positive tiles and b be negative tiles

Sum

Answer:

A

Step-by-step explanation:

The tangent- tangent angle x is half the difference of the measures of the intercepted arcs.

minor arc = 360° - 254° = 106° , then

x = [tex]\frac{1}{2}[/tex] (254 - 106)° = [tex]\frac{1}{2}[/tex] × 148° = 74° → A

The value of angle x will be 74°. Then the correct option is A.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

We know that the sum of the minor arc and major arc made by a tangent in a circle will be 360 degrees.

Then the measure of the minor arc will be

⇒ 360° - 254°

⇒ 106°

We know that the angle made by the tangent is half of the major arc to the minor arc.

x = (254° - 106°) / 2

x = 148° / 2

x = 74°

The value of angle x will be 74°.

Then the correct option is A.

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Answer:

21.28 and 967.46

Hope it helps have a good night :)))))))))))))))))

Answer:

117.33333 feet per second

Step-by-step explanation:

Answer:

-7α + 28 = 7

-7α + 28 - 28 = 7 - 28

-7α = -21

α = -21/-7

α = 3

Answer:

i think its 58,660

Step-by-step explanation:

Answer:

58,660

Step-by-step explanation:

Answer:

18. [tex] x = 8 [/tex]

19. [tex] c = 9 [/tex]

20. [tex] d = \sqrt{10} [/tex]

21. 83 1/3 ft

22.

a. decay

b. growth

c. decay

Step-by-step explanation:

18.

[tex] \sqrt{x + 1} + 12 + 10 = 25 [/tex]

[tex[ \sqrt{x + 1} = 3 [/tex]

Square both sides.

[tex] x + 1 = 9 [/tex]

[tex] x = 8 [/tex]

19.

[tex] a^2 + b^2 = c^2 [/tex]

[tex] (\sqrt{75})^2 + (\sqrt{6})^2 = c^2 [/tex]

[tex] 75 + 6 = c^2 [/tex]

[tex] 81 = c^2 [/tex]

[tex] c = 9 [/tex]

20.

[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

[tex] d = \sqrt{(3 - 4)^2 + (-9 - (-6))^2} [/tex]

[tex] d = \sqrt{(-1)^2 + (-3)^2} [/tex]

[tex] d = \sqrt{1 + 9} [/tex]

[tex] d = \sqrt{10} [/tex]

21.

Max: 5 ft tall; 3 ft shadow

Building: x ft tall; 50 ft shadow

5 ft is to 3 ft as x ft is to 50 ft

5/3 = x/50

3x = 250

x = 250/3

x = 83 1/3

Answer: 83 1/3 ft

22.

Exponential function:

y = a(b)^x

b is the number in parentheses raised to exponent x.

If b > 1, it is growth.

If b is between 0 and 1, it is decay.

Look at each case.

a. 0.85 is between 0 and 1: decay

b. 1.025 > 1: growth

c. 0.682 is between 0 and 1: decay

Answer:

A. Average

Step-by-step explanation:

The mean is when we take the sum of all the numbers, and divide it by the total amount, giving us the average value of the group.

Answer:

Average

Step-by-step explanation:

It is average because ,the total number of tally is divided by the number of people or item

Answer:

∠ RQP or ∠ PQR

Step-by-step explanation:

When naming the angle the vertex always goes in the middle of the 2 legs

Answer:

∠Q

∠RQP

∠PQR

Step-by-step explanation:

Brainliest, please!

[tex]\\ \sf\longmapsto Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \sf\longmapsto Slope=\dfrac{4-12}{9-15}[/tex]

[tex]\\ \sf\longmapsto Slope=\dfrac{8}{6}[/tex]

[tex]\\ \sf\longmapsto Slope=\dfrac{4}{3}[/tex]

Basically, everything except choice A.

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

Explanation:

All exponential functions can be written into the form y = a*b^x

The b term determines if we have growth or decay.

If 0 < b < 1, then we have decay. If b > 1, then we have growth.

------------

For choice A, we have b = 1.7 which satisfies b > 1. This represents growth. So we cross choice A off the list.

Choice B looks almost identical since it appears b = 1.7 here as well, but note the negative exponent. It might help to rewrite choice B into y = 3( 1.7^(-2) )^x and note how b = (1.7)^(-2) = 0.346 approximately. This represents decay.

Choice C has b = 1/3 = 0.33 approximately which is also decay.

Finally, choice D has b = 2^(-1) = 1/(2^1) = 1/2 = 0.5 which is also decay.

Choices B through D have b values such that 0 < b < 1.

------------

Check out the graph below. It visually confirms the answers mentioned earlier. A growth function goes uphill as we move to the right, while a decay function moves downhill while moving to the right.

I used GeoGebra to make the graph.

Answer:

If you like my answer than please mark me brainliest

Part (a)

Since we want segment AT to be an altitude, this means that point A is somewhere on segment RI such that angle TAI is 90 degrees. In other words, segments AT and RI are perpendicular. Check out the diagram below.

We'll need to find the slope of line RI, so we'll need the slope formula

R = (x1,y1) = (-2,-2)

I = (x2,y2) = (4,1)

m = slope of line RI

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

m = (1-(-2))/(4-(-2))

m = (1+2)/(4+2)

m = 3/6

m = 1/2

m = 0.5

The slope of line RI is 1/2 or 0.5

Now let's use point R(-2,-2) along with that slope we just found to find the equation of line RI.

Turn to point slope form

y - y1 = m(x - x1)

y - (-2) = 0.5(x -(-2))

y + 2 = 0.5(x + 2)

y + 2 = 0.5x + 1

y = 0.5x + 1 - 2

y = 0.5x - 1

This is the equation of line RI. We'll use it later.

----------

We found that the slope of line RI was 1/2.

The negative reciprocal involves us flipping the fraction and flipping the sign to get -2/1 or simply -2.

The perpendicular slope is -2. This is the slope of altitude AT.

We want line AT to go through T(-2,4), so we'll use this point along with the perpendicular slope we just found to calculate the equation of line AT.

We'll turn to the point slope form

y - y1 = m(x - x1)

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

y - 4 = -2(x + 2)

y - 4 = -2x - 4

y = -2x - 4 + 4

y = -2x

The equation of the line that goes through points A and T is y = -2x.

----------

To summarize so far, we have these two equations

Apply substitution to solve for (x,y) to find the intersection point. This will determine where point A is located.

y = 0.5x - 1

-2x = 0.5x - 1

-2x-0.5x = -1

-2.5x = -1

x = -1/(-2.5)

x = 0.4

Then we can determine y like so

y = -2x

y = -2(0.4)

y = -0.8

Therefore, point A is located at (0.4, -0.8). Both coordinate values are exact. In fraction form, we can say that the point is (2/5, -4/5), but I find decimals easier to work with in this instance.

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

Part (b)

To find the length of segment AT, we can find the distance from A to T. As you can probably guess, we'll use the distance formula.

A = (x1,y1) = (0.4, -0.8) ... found back in part (a)

T = (x2,y2) = (-2, 4) ... given

[tex]d = \sqrt{ (x_2-x_1)^2+(y_2-y_1)^2 }\\\\d = \sqrt{ (-2-0.4)^2+(4 - (-0.8))^2 }\\\\d = \sqrt{ (-2-0.4)^2+(4 + 0.8)^2 }\\\\d = \sqrt{ (-2.4)^2+(4.8)^2 }\\\\d = \sqrt{ 5.76+23.04 }\\\\d = \sqrt{ 28.8 }\\\\d \approx 5.36656\\\\d \approx 5.37\\\\[/tex]

The distance from point A to point T is approximately 5.37 units. This means that segment AT is roughly 5.37 units long.

Answer:

5

(40+24)=64

64÷8=8

(2^2-1)=3

8-3=5

[tex]\begin{gathered} {\underline{\boxed{ \rm {\red{Area \: of \: triangle \: = \: \frac{1}{2} \: \times \: base \: \times \: height }}}}}\end{gathered}[/tex]

[tex] \rm \large \longrightarrow \: Area \: of \: triangle \: = \: \frac{1}{2} \: \times \: 9.6 \:in \: \times \: 3.9 \: in[/tex]

[tex] \rm \large \longrightarrow \: Area \: of \: triangle \: = \: \frac{1}{2} \: \times \: 37.44 \: {inches}^{2} [/tex]

[tex] \rm \large \longrightarrow \: Area \: of \: triangle \: = \: \frac{1}{ \cancel2} \: \times \: \cancel{37.44} \: {inches}^{2} \: \: ^{\bf{\red{ 18.72 \: {inches}^{2} }}} [/tex]

[tex] \rm \large \longrightarrow \: Area \: of \: triangle \: = \: 18.72 \: {inches}^{2} [/tex]

Answer:

Hello,

Step-by-step explanation:

In order to cut off ( pour couper court)

all multiple of 20 are divisible by 20, so they are not primes.

Answer:

She used 1/8 or 12.5% more flour than sugar

Step-by-step explanation:

flour: 5/8

sugar: 1/2 = 4/8

[tex]\frac{5}{8} - \frac{4}{8} = \frac{1} {8} = 0.125[/tex]

0.125 = 12.5%

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

for it to be a function every x value must have at most 1 y value, therefore it is option A as this requirement is met