Given the two functions, which statement is true?
fx = 3^4, g(x) = 3^x + 5

Given The Two Functions, Which Statement Is True?fx = 3^4, G(x) = 3^x + 5

Answers

Answer 1

Answer:

third option

Step-by-step explanation:

Given f(x) then f(x) + c represents a vertical translation of f(x)

• If c > 0 then shift up by c units

• If c < 0 then shift down by c units

Given

g(x) = [tex]3^{x}[/tex] + 5 ← this represents a shift up of 5 units

Thus g(x) is the graph of f(x) translated up by 5 units

Answer 2

Answer:

[tex]\boxed{\sf{Option \: 3}}[/tex]

Step-by-step explanation:

g(x) is translated up 5 units compared to f(x). In a vertical translation, when the graph is moved 5 units up, 5 is added to the function. When the graph is moved 5 units down, 5 is subtracted from the function. The graphs are shifted  in the direction of the y-axis.

Given The Two Functions, Which Statement Is True?fx = 3^4, G(x) = 3^x + 5

Related Questions

cooks are needed to prepare for a large party. Each cook can bake either 5 Large cakes or 14 small cakes per hour . The kitchen is available for 3 hours and 29 large cakes and 260 cakes need to be baked . How many cooks are required to bake the required number of cakes during the time the kitchen is available?​

Answers

it was all about equating some values

to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

Let's determine the number of cooks required to bake the required number of cakes during the available time.

We have the following information:

- Each cook can bake either 5 large cakes or 14 small cakes per hour.

- The kitchen is available for 3 hours.

- We need to bake 29 large cakes and 260 cakes in total.

First, let's calculate the number of large cakes that can be baked by one cook in 3 hours:

1 cook can bake 5 large cakes/hour × 3 hours = 15 large cakes.

Next, let's calculate the number of small cakes that can be baked by one cook in 3 hours:

1 cook can bake 14 small cakes/hour × 3 hours = 42 small cakes.

Now, let's calculate the number of large cakes that can be baked by all the cooks in 3 hours:

Total number of large cakes = Number of cooks × Large cakes per cook per 3 hours

We need to bake 29 large cakes, so:

29 = Number of cooks × 15

Number of cooks = 29 / 15 ≈ 1.93

Since we can't have a fraction of a cook, we need to round up to the nearest whole number. Therefore, we need at least 2 cooks to bake the required number of large cakes.

Similarly, let's calculate the number of small cakes that can be baked by all the cooks in 3 hours:

Total number of small cakes = Number of cooks × Small cakes per cook per 3 hours

We need to bake 260 small cakes, so:

260 = Number of cooks × 42

Number of cooks = 260 / 42 ≈ 6.19

Again, rounding up to the nearest whole number, we need at least 7 cooks to bake the required number of small cakes.

Since we need to satisfy both requirements for large and small cakes, we choose the larger number of cooks required, which is 7 cooks.

Therefore, to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

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Which property is not used to simplify the following expression 2* (x+5)+7x=(2x+10)+7x

Answers

Distributive property

Hence, the commutative property of addition is not used.

What is an expression?

A mathematical expression is in form of variables and constants separated by their arithmetic operation.

As we know that, there are three types of properties they are associative property which is [tex](a+b) + c = a + (b+c)[/tex],

Distributive property which is [tex]a(b+c) = ab + ac[/tex],

Commutative property which is [tex]a + b = b + a[/tex].

Here given that,

[tex]2 (x+5)+7x=(2x+10)+7x[/tex]      

[tex](2x+10)+7x=(2x+10)+7x[/tex]         ( distributive property of multiplication)

[tex](2x+7x)+10=(2x+7x)+10[/tex]        ( it is associative property of addition)

[tex](8x)+10=(8x)+10[/tex]        ( it is a commutative property)

Hence, the commutative property of addition is not used.

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The image of (5,-4) reflected across the y-axis is

A. (-5, 4)
B. (-5, 4)
C. (5, 4)
D. (5, 4)

The image of (3,-2) reflected across the line x - 1 is

A. (-1, -2)
B. (3,0)
C. (0, -2)
D. (-2, -1)

Answers

Answer:

Number 1: A

Number 2:D

Step-by-step explanation:

Solve the polynomial x² - 7x + 12 = 0 Show each step used to find the solutions.

Answers

Answer:

x=4 and x=3

Step-by-step explanation:

The first step to find all factors of 12

1,2,3,4,6,12

and their negative form

-1,-2,-3,-4,-6,-12

we must add two of these numbers to get -7

and the two numbers that add up to -7 are -3 and -4

we can simply plot them into the polynomial (x-3)(x-4)

since x-3=0

we add three to both sides to get x=3

and since x-4=0

add four to both sides

we get x=4

and now check out work which

we can use First out in last (foil) method

(x-3)(x-4)

first

x^2

out

-4x

in

-3x

last

12

now we simplify to get x^2-7x+12

so it x=4 x=3 works

Answer:

x² - 7x + 12 = 0

doing middle term factorization

x²-4x-3x+12=0

taking common from each two term

x(x-4)-3(x-4)=0

taking common

(x-4)(x-3)=0

either

x-4=0

:. x=4

or

x-3=0

x=3

:.x=4,3

a
A solid metal cone of base radius a cm and height 2a cm is melted and solid
spheres of radius are made without wastage. How many such spheres can be
made?​

Answers

volume of a cone

.

.

.

volume of sphere

.

.

number of spheres that can be made......

.

.

hence a hemisphere can be formed

What is the constant of variation, k, of the line y=kx through (3,18) and (5,30)? 3 6

Answers

Answer:

6

Step-by-step explanation:

The constant of variation is the slope

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

  = (30-18)/(5-3)

   =12/2

   = 6

The value of constant of variation, k, is,

⇒ k = 6

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Here, the constant of variation, k, of the line y = kx through (3,18) and (5,30)

Since, The constant of variation is the slope,

Hence, We get;

k = (y₂ - y₁)/(x₂ - x₁)

 = (30 - 18)/(5 - 3)

  = 12/2

  = 6

Thus, the value of constant of variation, k, is,

⇒ k = 6

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The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. A 2-row table with 10 columns. The first row is labeled time (seconds), x with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.6. The second row is labeled height (meters), h with entries 100, 98.8, 95.1, 89.0, 80.4, 69.4, 55.9, 40.0, 21.6, 0. A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table? According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground. According to the line of best fit, the object was dropped from a lower height. The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds. The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.

Answers

Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.

The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

What is the line of best fit?

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

We have a line of best fit:

h = –21.962x + 114.655

As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.

Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

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2000 people attended a baseball game. 1300 of the people attending supported the home team, while 700 supported the visiting team. What percentage of people attending supported the home team?

Answers

Answer:

Percentage of home team supporters =65%

Percentage of visiting team supporters =35%

Step-by-step explanation:

Total attendees=2,000 people

Home team supporters=1,300

Visiting team supporters=700

What percentage of people attending supported the home team?

Percentage of people attending who supported the home team = home team supporters / total attendees × 100

=1,300/2,000 × 100

=0.65 × 100

=65%

Visiting team supporters = visiting team supporters / total attendees

× 100

=700/2000 × 100

=0.35 × 100

=35%

Alternatively,

Visiting team supporters = percentage of total attendees - percentage of home team supporters

=100% - 65%

=35%

100 pointer and will mark brainliest thank you. Hi! I ask that you provide a digital scatter plot image of this graph and predict the line of best fit and make sure to sketch it on the graph aswell. Thank you. Arm Span (inches) Height (inches) 58 60 49 47 51 55 19 25 37 39 44 45 47 49 36 35 41 40 46 50 58 61 And then provide the answers to these questions about the scatter plot which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way. Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined. What does the slope of the line represent within the context of your graph? What does the y-intercept represent Test the residuals of two other points to determine how well the line of best fit models the data. Use the line of best fit to help you to describe the data correlation. Using the line of best fit that you found, approximate how tall is a person whose arm span is 66 inches According to your line of best fit, what is the arm span of a 74-inch-tall person

Answers

I used arm span as the x-axis and height as the y-axis; arm span is the independent variable because height is typically dependent on arm span. Although the opposite could be argued for.

The equation of the line of best fit is y= 12+(7/9)x. To get the slope I used the points (37,39) and (19,25). The slope is therefore 14/18=7/9. The slope represents that height increases by 7/9 inches when arm span increases by 1 inch. The y-intercept 12 represents roughly the height when arm size is very small. I tested the residuals of the points (47,49) and (58,61). The respective predictions are 48.556 and 57.111. The respective residuals are then (49-48.556)=0.444 and (61-57.111)=3.889. It seems that the line models the data well until the x values get larger, where the performance decreases. The line of best fit with its positive slope indicates that there is a positive correlation with arm span and height.

Using the model, a person with arm span 66 inches has a height of 12+(7/9)*66= 63.333 inches. A person with 74 inches height has an estimated arm span of 62*9/7= 79.714 inches.

The equation of best  fitted line is given as follows

[tex]\rm y = 0.955x+ 3.787 \\with \; R^2 = 0.951[/tex]

The y  intercept 3.787 represents the  height of that is independent of Arm span.

The height of the person whose arm span is 66 inches is 66.817 inch.

The arm span of a person whose height is 74 inches is 73.52 inch

According to the given data the arm span  and heights are given in inches

Using Microsoft excel we can draw the scatter plot of both the variables such that arm span is on X axis and Height is on Y axis

The  image for the excel work done showing calculations and scatter plot  is attached.

Now we can fit the linear tread line and  to find out the equation of fitted line just tick on the " show equation" line option of trend line fitting

The equation of best  fitted line is given as follows

[tex]\rm y = 0.955x+ 3.787 .....(1) \\with \; R^2 = 0.951[/tex]

Slope of line of best fit = 0.955

So we can conclude that height (Y) is related to Arm span according to equation (1)

Equation (1) shows the equation of line of best fit for the given data

The y  intercept 3.787 represents the  height of that is independent of Arm span.

So the height of the person whose arm span is 66 inches is given following

[tex]\rm y = 0.955 \times 66+ 3.787 \\y = 66.817 \; inch[/tex]

Similarly the arm span of a person whose height is 74 inches

[tex]\rm 74 = 0.955x +3.787 \\x = 73.52 \; inches[/tex]

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Sharon tried to solve an equation step by step.

9
9
15
5


=−3(e−2)
=−3e+6
=3e
=e


Step 1
Step 2
Step 3


Find Sharon's mistake.
Choose 1 answer:
Choose 1 answer:

Answers

Answer:

step 2

Step-by-step explanation:

9 = -3(e - 2)

9 = -3e + 6

9-6 = -3e

3 = -3e

divide both sides by -3

-1 = e

What is the solution to this equation? 2x + 4 = 16

Answers

Answer:

x=6

Step-by-step explanation:

2x+4=16

2x+4-4=16-6

2x=12

x=6

Proof:

2x+4=16

2(6)+4=16

12+4=16

16=16

Hope this helps ;) ❤❤❤

Answer:

find out what x is and it is 6 it is 6 because 2 times 6 is 12 and 12 plus 4 is 16

Step-by-step explanation:

Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of -0.12. See the figure below. There is $28.96 in credit remaining on the card after minutes of calls. How much credit was there after 21 minutes of calls?

Answers

Answer:

Credit remaining after 21 minutes = $30.4

Step-by-step explanation:

Credit remaining on a phone card is a linear function of the total calling time.

When graphed, let the linear function representing the line is,

y = mx + b

Where 'm' = slope of the line

b = y-intercept

From the graph,

Slope of the line = -0.12

y = -0.12x + b

If this line passes through a point (33, 28.96),

28.96 = -0.12(33) + b

b = 28.96 + 3.96

b = 32.92

Therefore, the linear function is,

f(x) = -0.12x + 32.92

where x = calling time

Credit left in the card after 21 minutes,

f(21) = -0.12(21) + 32.92

      = -2.52 + 32.92

      = $30.4

Scott start his banking account with 150 and is spending $7 per day on lunch . How would one describe the graph of this model?

Answers

Answer:

So this is giving us the slope the slope is y=-7x+150

Step-by-step explanation:

It is giving us the Y intercept which is $150  because thats how much he starts out with

It is giving us the slope -7 dollars because he is spending that everyday

The mean number of rushing yards for one NFL team was less than 99 yards per game. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

Answers

Question options :

A. There is sufficient evidence to reject the claim

u < 99.

B. There is sufficient evidence to support the claim

u < 99.

C. There is not sufficient evidence to reject the claim

u < 99.

D. There is not sufficient evidence to support the claim

u< 99.

Answer:

B. There is sufficient evidence to support the claim

u < 99.

Step-by-step explanation:

We construct the n*ll and alternative hypotheses to support our claim

The n*ll hypothesis :H0

The alternative hypothesis : Ha

N*ll hypothesis =H0: u=99

Alternative hypothesis =Ha: u<99

So if n*ll hypothesis (H0) u=99 is rejected, then we accept the alternative hypothesis that u<99

we can therefore have sufficient evidence to support our claim that u<99

what is the prime factorization of 55^5 x 65 x 9^15 and why? A. 3^15 * 5^6 *11^5*13 B. 3^30 *5^6 *11^5 *13 C.3^30 * 5^6 *11 * 13 D. 3^30 *5^5*11^5*13

Answers

Answer:

B

Step-by-step explanation:

1. Lets focus on 55^5

55^5 = 11^5 * 5^5

2. now on 65

65 = 5 * 13

3. now on 9^15

9^15=(3^2)^15 = 3^30

4. combine all three parts

11^5 * 5^5 * 5 * 13 * 3^30 = 11^5*5^6*13*3^30

so our answer is B

In designing an experiment involving a treatment applied to 4 test​ subjects, researchers plan to use a simple random sample of 4 subjects selected from a pool of 31 available subjects.​ (Recall that with a simple random​ sample, all samples of the same size have the same chance of being​ selected.) Answer the question below.
What is the probability of each simple random sample in this​case?

Answers

Answer:

The probability is  [tex]p(n ) = 3.18*10^{-5}[/tex]

Step-by-step explanation:

From the question we are told that

     The population size is  N =  31

      The sample size  n =  4  

 

Generally the number of way by which the n  can be selected from N is mathematically represented as

          [tex]\left N} \atop {}} \right. C_n = \frac{N! }{(N-n)!n!}[/tex]

=>       [tex]\left 31} \atop {}} \right. C_4 = \frac{31! }{(31-4)!4!}[/tex]

=>       [tex]\left 31} \atop {}} \right. C_4 = \frac{31 * 30 * 29 * 28* 27! }{27! * 4*3 * 2 * 1 }[/tex]

=>        [tex]\left 31} \atop {}} \right. C_4 = \frac{ 755160 }{ 24}[/tex]

=>        [tex]\left 31} \atop {}} \right. C_4 = 31465[/tex]

The number of ways of selecting a particular sample size is  is   [tex]k = 1[/tex]

Therefore the probability of each simple random sample in this​ case is mathematically evaluated as  

           [tex]p(n ) = \frac{1}{31465}[/tex]  

           [tex]p(n ) = 3.18*10^{-5}[/tex]

20 applicants are interviewed for a job. The interviewer creates an ordered list (first to last) of the best 6 applicants. How many ways are

Answers

Answer:

38,760 different ways.

Step-by-step explanation:

The question is incomplete. Here is the complete question.

20 applicants are interviewed for a job. The interviewer creates an ordered list (first to last) of the best 6 applicants. How many ways are there for the interviewer to create the list?

Since the question deals with selection, we will apply the combination rule. Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

According to the question, if the the interviewer is to select 6 applicants from a pool of 20 applicants that are interviewed for a job, this can be done in 20C6 number of ways.

20C6 = 20!/(20-6)!6!

20C6 = 20!/14!6!

20C6 = 20*19*18*17*16*15*14!/14!*6*5*4*3*2

20C6 =  20*19*18*1716*15/6*5*4*3*2

20C6 = 27,907,200/720

20C6 = 38,760 different ways.

Hence, the interviewer can create the list in 38,760 different ways.

what is the definition of a sequence

Answers

Answer:

the process of combining things in a particular order, or discovering the order in which they are combined: A common sign of dyslexia is that the sequencing of letters when spelling words may be incorrect. biology specialized.

Step-by-step explanation:

the diameter of Earth's moon is on average 3.8 x 10^8m. Use the formula A=4π² to find the approximate surface area. (Use 3.14 for the value of π)

Answers

Answer:

The answer is

[tex]A = 4.53 \times {10}^{17} \: {m}^{2} [/tex]

Step-by-step explanation:

Since the Earth's moon is a sphere

Surface area of a sphere from the question is given by

A = 4πr²

where r is the radius

To find the radius using the diameter we use the formula

radius = diameter / 2

[tex]radius \: = \frac{3.8 \times {10}^{8} }{2} [/tex]

[tex]radius = 1.9 \times {10}^{8} \: m[/tex]

π = 3.14

Substitute these values into the above formula

That's

[tex]A = 4 \times 3.14 \times ({1.9 \times {10}^{8} })^{2} [/tex]

We have the final answer as

[tex]A = 4.53 \times {10}^{17} \: {m}^{2} [/tex]

Hope this helps you

There are two pitchers of lemonade in the fridge there are 1.5 gallons of lemonade in 1 pitcher and 9 quarts of lemonade in the other pitcher how many cups of lemonade are there in the fridge

Answers

Answer:

52 cups

Step-by-step explanation:

1 gallon = 4 quarts

1.5 gallons = 6 quarts

6 + 9 = 13 quarts of lemonade in the fridge.

1 quart = 4 cups

13 quarts = 4 × 13 = 52 cups

52 cups of lemonade are in the fridge.

I would really appreciate it if you would mark me brainliest!

Have a blessed day!

Answer:

60 cups

Step-by-step explanation:

1 gal = 16 cups

1 quart = 4 cups

               16 cups

1.5 gal x ------------- = 24 cups

                  1 gal.

                 4 cups

9 quarts x ----------- = 36 cups

                  1 quart

number of cups of lemonade in the fridge = 24 cups + 36 cups = 60 cups

Henry is investing at a continuously compounded annual interest rate of 4.5%. How many years will it take for the balance
to triple? Round your answer up to the nearest whole number, and do not include the units in your answer.

Answers

Answer:

1 year

Step-by-step explanation:

Hello,

Continuously compounding with an annual interest rate of 4.5% means multiplying the initial investment by (for t tears).

[tex]\displaystyle e^{(1+4.5\%)t}=e^{\left( 1.045\cdot t \right) }[/tex]

So we need to find t so that:

[tex]\displaystyle e^{\left( 1.045\cdot t \right) }=3\\\\1.0.45t=ln(3)\\\\t=\dfrac{ln(3)}{1.045}=1.051304...[/tex]

Rounding to the nearest whole number gives 1 year.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

25

Step-by-step explanation:

Trust me

Use inductive reasoning to predict the most probable next number in each list.
9, 13, 21, 33, 49, 69, ?

Answers

Answer:

  93

Step-by-step explanation:

First differences increase by 4 each time. The given numbers are a quadratic sequence that can be described by 2n² -2n +9. The 7th term would be 93.

_____

First differences are ...

  13-9 = 4, 21-13 = 8, 33-21 = 12, 49-33 = 16, 69-49 = 20

Second differences are ...

  8-4 = 4, 12-8 = 4, 16-12 = 4, 20-16 = 4

When second differences are constant, the sequence can be represented by a second-degree polynomial function. The leading coefficient is half the value of the second differences.

Find the principal invested if $495 interest was earned in 3 years at an interest rate of 6%.

Answers

Answer: $2750

Step-by-step explanation:

Formula to calculate interest : I = Prt , where P = Principal amount , r = rate of interest ( in decimal) , t= time.

Given:  I= $495

t= 3 years

r= 6% = 0.06

Then, according to the above formula:

[tex]495 = P (0.06\times3)\\\\\Rightarrow\ P=\dfrac{495}{0.18}\\\\\Rightarrow\ P=2750[/tex]

Hence, the principal invested = $2750

IQ scores have a mean of 100 and a standard deviation of 15. What percentile corresponds to an IQ score of 115? Explain the steps you took to find the percentile.

Answers

Answer:

The percentile that corresponds to an IQ score of 115 is 34.13 %

Step-by-step explanation:

Here, we want to find the percentile that corresponds to an IQ score of 115.

To calculate this percentile, we start with making observations. From the question, we are told that the mean score is 100 while the standard deviation is 15.

Now we want to find the percentile for a score if 115. For a score of 115, we can see that the difference between this score and the mean is 15 which is exactly equal to the standard deviation.

What this means is that the score is within +1 SD of the mean.

For a score of within +1 SD of the mean, the percentile is 34.13%

A score at the mean is the 50th percentile, a score which is 1 SD above or below the mean has a percentile value of 34.13%

Please, I will like you to check the attachment to see how percentiles are valued given the number of standard deviations a particular value is from the mean.

Write and equation for each situation and solve. Your car gets 25 miles per gallon in the city if you travel 300 miles how many gallons of gas will you use?

Answers

if. 25 miles : 1 gallon

300 miles. : ?

if more less divides

300/25×1

=12 gallons of gas will be used

slope of -4/3x with point (7,20) find equation

Answers

Answer:

y= -4/3x+10 2/3

Step-by-step explanation:

To do this, just put the equation in point slope form and then rearrange it to y=mx+b, or slope intercept form. Slope point form is arranged like this, y-y1=m(x-x1). Now, just insert in the variables (x1=x coordinate of point, y1= y coordinate of point, m=slope). So your equation is now y-20=-4/3(x-7), which simplifies to y-20=-4/3x-9 1/3. Now rearrange it so that y in by itself, and all like terms are combined, making it look like this: y=-4/3x+10 2/3. Now its in slope intercept form and you've got your answer.

I hope my explanation wasn't confusing and that my answer helped.

Simplify the expression (6^4)^2

Answers

When raising a power inside parentheses to another power, multiply the numbers:

(6^4)^2 = 6^(4x2) = 6^8

Simplified = 6^8

6^8 = 1679616

Answer:

[tex] \boxed{ \purple{ {6}^{8} }}[/tex]

Step-by-step explanation:

[tex] \mathsf{ ( { {6}^{4}) }^{2} }[/tex]

It is the example of Power to power law of indices.

Multiply the exponents

⇒[tex] \mathsf{ {6}^{4 \times 2} }[/tex]

Multiply the numbers

⇒[tex] \mathsf{ {6}^{8} }[/tex]

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

[tex] \mathsf{\orange{ \underline{ power \: to \: power \: law \: of \: indices}}}[/tex]

If [tex] \mathsf{ ({x}^{a} )^{b}} [/tex] is an algebraic term then [tex] \mathsf{( {x}^{a} ) ^{b} = {x}^{a \times b} }[/tex]

i.e When an algebraic term in the index form is raised to another index , the base is raised to the power of two indices.

Hope I helped!

Best regards!!

Sketch a graph to envision the following scenario. Place time on the x-axis. A rock climber is 25 feet above sea level. After 8 seconds he is at sea level. (He did not fall). What is the slope of the line depicted (no units)

Answers

Answer:

Please refer to the attached graph.

Slope = -3.125

Step-by-step explanation:

Given

Time is placed on x axis.

Initially, height of rock climber is 25 feet above sea level.

[tex]t_1 =0\ sec[/tex]

[tex]h_1[/tex] = 25 feet

After 8 seconds, he is at sea level.

[tex]t_2 =8\ sec[/tex]

[tex]h_2[/tex] = 0 feet

To find:

Graph of the given points and Slope of the line depicted.

Solution:

Kindly refer to the attached graph.

Here, we have been given two points to be plotted on the xy coordinate plane.

1st point is (0, 25): Time is 0 and height above sea level is 25 ft

2nd point is (8, 0): Time is 8 seconds and height above sea level is 0 ft (i.e. he comes to sea level)

First of all, mark these points and join them with a straight line.

Please refer to attached graph.

Slope of a line is given as:

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

Here,

[tex]y_2 = 0\\y_1 = 25\\x_2 = 8\\x_1 = 0[/tex]

Using the formula:

[tex]m=\dfrac{0-25}{8-0}\\\Rightarrow m=-\dfrac{25}{8} = \bold{-3.125}[/tex]

A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.

Answers

Answer:

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

Step-by-step explanation:

Given

[tex]Sections = 10[/tex]

[tex]n(Gray) = 5[/tex]

[tex]n(Blue) = 5[/tex]

Required

Determine P(Gray and Blue)

Using probability formula;

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

Calculating P(Gray)

[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]

[tex]P(Gray) = \frac{5}{10}[/tex]

[tex]P(Gray) = \frac{1}{2}[/tex]

Calculating P(Gray)

[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]

[tex]P(Blue) = \frac{5}{10}[/tex]

[tex]P(Blue) = \frac{1}{2}[/tex]

Substitute these values on the given formula

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

The average person lives for about 78 years. Does the average person live for at least 1,000,000 days? (Hint: There are 367 days in each year.)
what i

Answers

Answer:

[tex]\large \boxed{\sf No}[/tex]

Step-by-step explanation:

There are 365 days in 1 year.

The average person lives for about 78 years.

Multiply 78 by 365 to find the value in days.

[tex]78 \times 365= 28470[/tex]

The average person lives for about 28470 days.

Answer: No

Explanation:

78 x 367 = 28,626 days

And 28,626 days < 1,000,000 days

So an average person cannot live 1,000,000 days

Hope this helps!
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