You are at an altitude of 250 feet in a hot-air balloon. You turn the burner on high and rise at a rate of 20 feet per minute for 5 minutes. Your altitude h after you have risen for t minutes is given by the function h = 250+ 201. (a) Make a table to show the altitude as a function of the number of minutes you have traveled. (b) Graph your data points-make sure to label the units on your axes. (c) Does it make sense to connect the points on the graph? Explain. 400 Altitude # of minutes ( in feet) 350 300 1 250 1.5 200 150 3 100 4 50 1 2 4 5 6 3. 2. Question Name: Date: Page 5 of 6 7. You are at an altitude of 250 feet in a hot-air balloon. You turn the burner on high and rise at a rate of 20 feet per minute for 5 minutes. Your altitude h after you have risen for t minutes is given by the function h = 250 + 20t. (a) Make a table to show the altitude as a function of the number of minutes you have traveled. (b) Graph your data points-make sure to label the units on your axes. (c) Does it make sense to connect the points on the graph? Explain. 400 Altitude # of minutes ( in feet) 350 300 1 250 1.5 200 150 3 100 4 50 5 1 3 4 5 (d) After 5 minutes, you turn the burner to low. This gives just enough heat to keep the balloon from falling but not enough to make it rise any higher. Plot a point on the graph to show how high the balloon is after 6 minutes. (e) Does it make sense to connect the point plotted in part (d) to the rest of the graph? Explain. (f) What is the domain of the function? (g) What is the range of the function? Transcribed Image Text:Name: Date: Page 5 of 6 7. You are at an altitude of 250 feet in a hot-air balloon. You turn the burner on high and rise at a rate of 20 feet per minute for 5 minutes. Your altitude h after you have risen for t minutes is given by the function h = 250 + 20t. (a) Make a table to show the altitude as a function of the number of minutes you have traveled. (b) Graph your data points-make sure to label the units on your axes. (c) Does it make sense to connect the points on the g

The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The table represents a quadratic function C(t).

 t          C(t)

−2           1

−1           4

0           5

 1           4

2            1

From the table, the coordinate of the vertex will be at (0, 5). Then the equation is given as,

C(t) = a(t - 0)² + 5

C(t) = at² + 5

The equation is passing through the point (1, 4), then we have

4 = a (1²) + 5

4 = a + 5

a = - 1

The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.

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Probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%

If the length of the life of an instrument produced by the machine has a normal distribution with a mean of 12 months and a standard deviation of 2 months, then the random variable X representing the length of the life of the instrument is also normally distributed.

To find the probability that X assumes a value greater than 12 months, we need to use the cumulative distribution function (CDF) of the normal distribution. The CDF is given by the formula:

F(x) = (1/2) * [1 + erf((x - μ) / (σ * sqrt(2)))]

where μ is the mean, σ is the standard deviation, and erf(z) is the error function.

Plugging in the given values, we get:

F(12) = (1/2) * [1 + erf((12 - 12) / (2 * sqrt(2)))] = (1/2) * [1 + erf(0)] = (1/2) * [1 + 0] = 1/2

Since the CDF gives us the probability that X assumes a value less or equal than x, we need to subtract F(12) from 1:

P(X > 12) = 1 - F(12) = 1 - 1/2 = 0.5

So the probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%.

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Answer: it D :)

Step-by-step explanation:

Answer:

x=0, y=1

Step-by-step explanation:

Answer:

your answer would be A

Step-by-step explanation:

it is kinda confusing but if you are reflecting off the x axis, you change the y, and if you are reflecting off the y axis, you would change the x

hope this helps and have a nice day!

Answer:

option d is correct answer

Step-by-step explanation:

equation y=-7 and slope zero

as equation of staight line y= MX+c

The we can say that the slope of the line is undefined and the {y} - intercept is -7.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is that Zoran graphed the line shown in the image.

The line is parallel to the {x} axis. So, it has no slope. Or, we can say that the slope of the line is undefined. It intersects the line at y = -7, at the {y} - axis. So, the {y} - intercept will be {y} = -7.

Therefore, the we can say that the slope of the line is undefined and the {y} - intercept is -7.

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Answer:

[tex]40[/tex].

Step-by-step explanation:

The range of a set of numbers is the difference between the maximum and minimum numbers.

In this set of number, [tex]50[/tex] is the maximum while [tex]10[/tex] is the minimum. Hence, the range would be [tex]50 -10= 40[/tex].

Answer:

D

Step-by-step explanation:

if x=11, -4(11)=-44. 47-44=3 and 3<7 which is true.

Answer:

x=2/3

Step-by-step explanation:

when the three turned into a 2 it removed one third, so we need to remove one third from 1, which gives us 2/3.

Basically, if a rectangle side goes from x to y, we figure out the percent decrease, and subtract that percent from the other side to find the variable we need to find on the other rectangle

Answer:

[tex]\dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]

Step-by-step explanation:

Given expression:

[tex](a^{10}b^{0}cde^{3})^{-2}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{1}{(a^{10}b^{0}cde^{3})^{2}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \dfrac{1}{a^{(10 \times 2)}b^{(0 \times 2)}c^2d^2e^{(3 \times 2)}}[/tex]

Simplify:

[tex]\implies \dfrac{1}{a^{20}b^{0}c^2d^2e^{6}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^0=1:[/tex]

[tex]\implies \dfrac{1}{a^{20}(1)c^2d^2e^{6}}[/tex]

[tex]\implies \dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]

Answer: D

Step-by-step explanation: She should make rows of 3 until she has 47 rows. She will have 1 left over. Because 47*3 = 141 plus the left over 142

Answer:

1 [tex]\frac{1}{4}[/tex] miles

Step-by-step explanation:

the routes from Lexington to Somerville are

Lexington → Brookfield → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{7}{8}[/tex] = [tex]\frac{3+7}{8}[/tex] = [tex]\frac{10}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex] = 1 [tex]\frac{1}{4}[/tex] miles

the other route is

Lexington → Brookfield → Yardley → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{3+4+4}{8}[/tex] = [tex]\frac{11}{8}[/tex] = 1 [tex]\frac{3}{8}[/tex] miles

the shortest distance is

Lexington → Brookfield → Somerville , a distance of 1 [tex]\frac{1}{4}[/tex] miles

Answer:

B) 20%

Step-by-step explanation:

Exponential equation:

An exponential equation is given by:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which A(0) is the initial amount and r is the growth rate, as a decimal.

In this question:

[tex]P(t) = 85(1.2)^t[/tex]

Growth rate:

We want to find r, so:

[tex]1 + r = 1.2[/tex]

[tex]r = 1.2 - 1 = 0.2[/tex]

The growth rate is of 0.2 = 2%, and the correct answer is given by option B.

Answer:

a(n) = 1 + 7(n-1)

Step-by-step explanation:

Answer:

BD = 2

Step-by-step explanation:

here's your solution

==> in ∆ABC and ∆ ABD

==> angle C = angle D. [ = to 90° ]

==> AB is common side

==> angle BAC = angle BAD. [ BA is angle bisector]

==> hence both traingle are congruent

==> so, BD = BC. [ by C.P.C.T ]

==> BC = 2. [ Given ]

==> BD = 2

hope it helps

Answer:

Subtraction property of equality

Step-by-step explanation:

Answer:

the bottom right could NOT

the fourth option is the answer (. ^ ᴗ ^.)

Step-by-step explanation:

[tex] \bf \red { Area: \; \boxed{ 24 } units^2} [/tex]

Formula of area of a parallelogram is :

○ b denotes base

○ h denotes height

Here,

→ Area of the parallelogram = 6 units × 4 units

→ Area of the parallelogram = 24 units²

[tex] \therefore [/tex] Area of the parallelogram is 24 units².

[tex] \bf \purple { Perimeter: \; \boxed{ 22 } units} [/tex]

Since, opposite sides of a parallelogram are equal. So,

○ First side = 6 units

○ Second side = 5 units

○ Third side = 6 units

○ Fourth side = 5 units

→ Perimeter = ( 6 + 5 + 6 + 5 ) units

→ Perimeter = ( 12 + 10 ) units

→ Perimeter = 22 units

[tex] \therefore [/tex] Perimeter of the parallelogram is 22 units.

[tex]\boxed{ \sf { AREA \; FORMULA }} [/tex]

[tex]\boxed { \sf { A = Base \times Height }} [/tex]

Answer:

9 = 1st number

21 = 2nd number

Step-by-step explanation:

given that :

1st number = x __eq_i

2nd number (in terms of the first number) = 2x + 3 __eq_ii

1st number + 2nd number = 30 __eq_iii

input eq_i and eq_ii in eq_iii

x + 2x + 3 = 30

3x + 3 = 30

3x = 30 - 3

x = 27 ÷ 3

x = 9

9 = 1st number

input the value of x in eq_ii

2x + 3

2(9) + 3

18 + 3

21 = 2nd number

hope that helps.

Answer:

Its between A and B

Step-by-step explanation:

I think its B Tho

Answer:

Its always ily, but never stwywimc

Step-by-step explanation:

On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is 500

obtained is 400

so, percentage - 400/500 X 100 = 80%

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The slope of the lines that passes trough the points (-2,-1) and (-4,-7) is m = 3 , (2,-3) and (6,-13) is m = -2.5 , (-3,4) and (-3,-8) is m = undefined , (-5,7) and (3,-1) is m = -1 .

What is slope ?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b).

           m=Δy/Δx

           m=(y2−y1)/(x2−x1)

           m=(−7−−1)/(−4−−2)

           m=−6/−2

           m = 3

          m=Δy/Δx

          m=(y2−y1)/(x2−x1)

          m=(−13−−3)/(6−2)

          m=−10/4

          m=−5/2

          m = -2.5

           m=Δy/Δx

           m=(y2−y1)/(x2−x1)

           m=(−8−4)/(−3−−3)

           m=−12/0

          m is undefined

            m=Δy/Δx

            m=(y2−y1)/(x2−x1)

            m=(−1−7)/(3−−5)

            m=−8/8

            m = -1

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Answer:

6 hours

Step-by-step explanation:

70miles divided by 4 hours equals 17.5mph

106miles divided by 17.5 mph = 6 hours

Answer:

6 hours

Step-by-step explanation:

105miles ÷ 70miles=1.5

4×1.5= 6

Answer:

Given that Figure A and Figure B are similar polygons, the scale factor of Figure A to Figure B = 5/2.

Recall:

Similar Polygons have corresponding side lengths whose ratio are equal. That is, their pairs of corresponding sides are proportional.

The ratio of any of their corresponding side length = scale factor

Given the two pairs of similar polygons, the scale factor of figure A to figure B will be calculated as follows:

A side length of Figure A = 10

Corresponding side length of Figure B = 4

Scale factor of Figure A to Figure B = 10/4 = 5/2

Step-by-step explanation:

Answer:

The p-value of the test is 0.1738, which means that for a level of significance above this, there is evidence of a change from the status quo.

Step-by-step explanation:

A high school has found over the years that out of all the students who are offered admission, the proportion who accept is 70%. Test if there is a change from status quo.

At the null hypothesis, we test if the proportion is 70%, that is:

[tex]H_0: p = 0.7[/tex]

At the alternate hypothesis, we test if there is a change from status quo, that is, the proportion is different from 70%. So

[tex]H_a: p \neq 0.7[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

70% is tested at the null hypothesis:

This means that [tex]\mu = 0.7, \sigma = \sqrt{0.7*0.3}[/tex]

Suppose they offer admission to 210 students and 156 accept.

This means that [tex]n = 210, X = \frac{156}{210} = 0.7429[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.7429 - 0.7}{\frac{\sqrt{0.7*0.3}}{\sqrt{210}}}[/tex]

[tex]z = 1.36[/tex]

P-value of the test and decision:

The p-value of the test is the probability that the sample proportion differs from 0.7 by at least 0.7429 - 0.7 = 0.0429, which is P(|z| > 1.36), which is 2 multiplied by the p-value of z = -1.36.

Looking at the z-table, z = -1.36 has a p-value of 0.0869

2*0.0869 = 0.1738

The p-value of the test is 0.1738, which means that for a level of significance above this, there is evidence of a change from the status quo.