A backpacker parked his car and hiked a distance of 1.2 km on the first day. On the second day, he continued hiking away from his car with an average speed of 2.3 km/hr. Write the equation that can be used to find the backpacker's distance in km (d) from his car as a function of time in hours (t) as he hiked on the second day.
d(t) =

Answer:

The amount invested at 8% is $11,908 and the amount invested at 5% is $11,895

Step-by-step explanation:

Let

x ----> the amount invested at 8%

(23,803-x) ----> the amount invested at 5%

Remember that

[tex]8\%=8\100=0.08[/tex]

[tex]5\%=5\100=0.05[/tex]

we know that

The interest earned  from the amount invested at 8% is equal to the interest earned from the amount invested at 5% plus $357.89

so

The linear equation that represent this situation is

[tex]0.08x=0.05(23,803-x)+357.89[/tex]

solve for x

Apply distributive property right side

[tex]0.08x=1,190.15-0.05x+357.89[/tex]

Group terms

[tex]0.08x+0.05x=1,190.15+357.89[/tex]

Combine like terns

[tex]0.13x=1,548.04[/tex]

[tex]x=\$11,908[/tex]

[tex]\$23,803-x=\$23,803-\$11,908=\$11,895[/tex]

therefore

The amount invested at 8% is $11,908 and the amount invested at 5% is $11,895

Answer:

For x: We subtract the exponents,

this way. 0 - 2 = -2

For y: We subtract the exponents,

this way. -3 - -1 = -2

x -² y -²

Answer: 10.0

Step-by-step explanation: In this problem, we are asked to round 10.034 to the nearest tenth. It's important to understand that the tenths place is 1 place to the right of the decimal point. So the digit in the rounding place is 0.

Next, look at the digit to the right of the rounding place which in this case is 3. Since the digit to the right of the rounding place, 3, is less than 5, we round down.

This means that the digit in the rounding place, 0, stays the same and we change all digits to the right of the rounding place to 0.

So 10.034 rounded to the nearest tenth is 10.000 or just 10.0 since we can drop zeroes at the end of a decimal.

Answer:

14 bags

Step-by-step explanation:

multiply 4*3.5 to get 14

The rate at which the area of the triangle changes when the height is 22 cm and the base is 10 cm is 14 cm²/min.

Using the formula for a triangle's area, A = (1/2) × base × height, we can determine rate of the triangle's area changes.

We can describe the rate of change of the base as db/dt = -1 cm/min (negative because it is shrinking) given that the base is shrinking at a rate of 1 cm/min.

The height is increasing at a rate of 5 cm/min, so the rate of change of the height can be expressed as dh/dt = 5 cm/min.

We must determine dA/dt for h = 22 cm and b = 10 cm in order to determine the rate at which the triangle's area changes at these two points.

We can start by differentiating the area formula with respect to time (t):

dA/dt = (1/2) × (db/dt × h + b × dh/dt)

Substituting the given values:

dA/dt = (1/2) × (-1 cm/min × 22 cm + 10 cm × 5 cm/min)

Simplifying:

dA/dt = (1/2) × (-22 cm/min + 50 cm/min)

= (1/2) × 28 cm/min

= 14 cm/min

Therefore, the rate at which the area of the triangle changes when the height is 22 cm and the base is 10 cm is 14 cm/min.

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The rate at which the area of the triangle changes is 2 cm²/min. This is found by applying the chain rule of differentiation to the triangle area formula, substituting the given values and rates, and simplifying.

The subject of this question is rate of change in context of the Triangle Area Formula: 1/2 * base * height. Given that the base is shrinking at a rate of 1cm per minute (1 cm/min) and the height is increasing at a rate of 5 cm/min, we can express this rate of change in the formula. A negative sign is used for the base because the base length is decreasing.

To find the rate of change in the area, use the chain rule of differentiation, leading to the formula (-1/2 * height * db/dt) + (1/2 * base * dh/dt). When the height is 22 cm and the base is 10 cm, substituting these values along with the rates at which the base and height are changing, the formula becomes (-1/2 * 22cm * 1 cm/min) + (1/2 * 10cm * 5 cm/min). Simplify to find that the area of the triangle is changing at 2 cm²/min.

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Answer:

I have to say the first one sorry responded late  

GIVE BRAINIEST:

plz give me brainliest i almost got caught in class WHILE HELPING!!!

Answer:

i think its the first one

Step-by-step explanation:

The cost of two pounds of cherries is $8.58. So, the unit rate that describes the cost per pound of cherries is $4.29 and this can be determined by using the unitary method.

Given :

The cost of two pounds of cherries is $8.58.

The unitary method can be used to determine the unit rate that describes the cost per pound of cherries. In the unitary method, there are two values that have to be found that is a single unit and a necessary unit.

Given that the cost of two pounds of cherries is $8.58 then the cost of unit rate is:

[tex]=\dfrac{8.58}{2}\times 1[/tex]

Multiply 8.58 by 1 in the above expression.

[tex]=\dfrac{8.58}{2}[/tex]

Divide 8.58 by 2 in the above expression.

= $4.29

The cost of two pounds of cherries is $8.58. So, the unit rate that describes the cost per pound of cherries is $4.29.

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Answer:

1/3

Step-by-step explanation:

Because parallel lines have the same slopes.

The relative frequencies using percentages are as follows:

A => 12.5%

B => 27.5%

C => 35%

D => 17.5%

E => 7.5%

Step-by-step explanation:

To find the relative frequency, the specific frequency is divided by the total frequency. To find in the percentages, the division is multiplied by 100

So,

Total frequencies = 5+11+14+7+3 = 40

So,

[tex]Relative-frequency\ of\ A = \frac{5}{40} *100\\= 0.125*100\\=12.5\%\\Relative-frequency\ of\ B = \frac{11}{40} * 100\\= 0.275*100\\=27.5\%\\Relative-frequency\ of\ C = \frac{14}{40} * 100\\=0.35*100\\=35\%\\Relative-frequency\ of\ D = \frac{7}{40} * 100\\=0.175*100\\=17.5\%\\Relative-frequency\ of\ E= \frac{3}{40} * 100\\=0.075*100\\=7.5\%[/tex]

Hence,

The relative frequencies using percentages are as follows:

A => 12.5%

B => 27.5%

C => 35%

D => 17.5%

E => 7.5%

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The relative frequencies of the five classes are 12.5%, 27.5%, 35%, 17.5%, 7.5%.

A frequency table grades have five classes (A, B, C, D, F) with frequencies of 5,11,14,7, and 3 respectively.

Using percentages, what are the relative frequencies of the five classes.

The relative frequency, the specific frequency is divided by the total frequency.

The sum of all the frequencies is called relative frequency.

= 5 + 11 +14 +7 +3 = 40

Then,

The relative frequency of the first class is,

[tex]= \dfrac{5}{40} \times 100\\ \\ = 0.125 \times 100\\ \\ =12. 5 \rm \ Percent[/tex]

The relative frequency of the second class is,

[tex]= \dfrac{11}{40} \times 100\\ \\ = 0.275 \times 100\\ \\ =27. 5 \rm \ Percent[/tex]

The relative frequency of the third class is,

[tex]= \dfrac{14}{40} \times 100\\ \\ = 0.35 \times 100\\ \\ =35 \rm \ Percent[/tex]

The relative frequency of the fourth class is,

[tex]= \dfrac{7}{40} \times 100\\ \\ = 0.175 \times 100\\ \\ =17. 5 \rm \ Percent[/tex]

The relative frequency of the fifth class is,

[tex]= \dfrac{3}{40} \times 100\\ \\ = 0.075 \times 100\\ \\ =7. 5 \rm \ Percent[/tex]

Hence, the relative frequencies of the five classes are 12.5%, 27.5%, 35%, 17.5%, 7.5%.

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Answer:

last Monday is 27

Step-by-step explanation:

perfect square: 4, 9 , 16

2nd Thursday is a day >5 and < 14 day from the begining of the month, therefore the only day fit the criteria is 9th of the month.

last Monday is 27

Sun Mon Tue Wen Thu Fri Sat

                                  9     10  11

12    13      14     15     16     17  18

.........................................................

26    27

To find the date of the last Monday of the month, calculate the number of days between the second Thursday and the last Monday by considering the number of weeks in the month.

To find the date of the last Monday of the month, we need to determine the number of days between the second Thursday and the last Monday.

Let's assume that the second Thursday is on the 9th of the month.

Since there are 7 days in a week, the last Monday will be 9 + (7 * (number of weeks in the month) - 1).

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Answer:

x=3/2

Step-by-step explanation:

4x+18=24

4x=24-18

4x=6

x=6/4

simplify

x=3/2

Answer: 4x+18=24

First move 18 to other side (24-18), left with 4x=6

Divide both sides by 4 to be left with x=6/4 & reduce that fraction down to 3/2

Step-by-step explanation:

The amount given to them is GHS300.00

Step-by-step explanation:

A man gave an amount of money to his three sons Yao, Esi and Ampa in the ratio of  their years

We need to find the amount given to them

Let us use the ratio method to solve the problem

∵ Yao is 15 years old

∵ Esi is 10 years old

∵ Ampa is 5 years old

∴ The ratio between them is

→  Yao    :    Esi    :    Ampa

→  15       :    10     :    5

Simplify the terms of the ratio by divide each term by 5

∴ The ratio between their ages in the simplest form is

→  Yao    :    Esi    :    Ampa

→  3         :    2      :    1

∵ Esi had GHS100.00

→  Yao    :    Esi    :    Ampa    :   Total

→  3         :    2      :    1             :   6 ( 3 + 2 + 1 = 6)

→             :  100     :                  :    x

Use the cross multiplication to find x

∵ 2(x) = 100(6)

∴ 2x = 600

- Divide both sides by 2

∴ x = 300

∵ x represents the total money given to them

∴ The amount given to them is GHS300.00

The amount given to them is GHS300.00

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Answer:

GHS300.00.,//.:.  

15 years!%

10 years!)

5 years%

GHS100.00!))>))                                  

......................................................

that is the answer i got but it could be wrong

:| :)

Answer:

36 movies

Step-by-step explanation:

16/4=4 this shows that there are 4 4s in 16.

Because every 4 video games 9 movies are rented so 4*9=36 for the answer

Answer:22%

Step-by-step explanation:

You paid approximately 27.12% gratuity on a $59 bill by leaving a $16 tip on a $75 payment.

To find out the percentage gratuity paid, you can first calculate the gratuity amount by subtracting the bill amount from the total paid:

Gratuity = Total paid - Bill amount

Gratuity = $75 - $59

Gratuity = $16

Now, to find the percentage gratuity, divide the gratuity amount by the bill amount and then multiply by 100:

Percentage Gratuity = (Gratuity / Bill amount) * 100

Percentage Gratuity = ($16 / $59) * 100

Percentage Gratuity ≈ 27.12%

So, you paid approximately a 27.12% gratuity.

Yes, because (−1, −5) is below the line

The statement says:

y is less than or equal to negative three fourths times x minus 1:

[tex]y\leq -\frac{3}{4}x-1[/tex]

To know whether (−1, −5) is a solution to the inequality, let's substitute x and y-values into the inequality:

[tex]y\leq -\frac{3}{4}x-1 \\ \\ -5\leq -\frac{3}{4}(-1)-1 \\ \\ -5\leq -\frac{1}{4} \\ \\ -20\leq -1 \ True![/tex]

Given that the point lies on the shaded region, which is below the line, then the correct statement is:

Yes, because (−1, −5) is below the line

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Answer:

D

Step-by-step explanation:

If you Break the bigger ones into smaller ones they will seem more attainable. Writing down your goals will help you remember. Taking care of resell will help you attain your goals faster and easier

Answer:

The value of home after t years is $249,000 [tex](0.929)^{\textrm t}[/tex]

Step-by-step explanation:

Given as :

The original value of home = p = $249,000

The value of home depreciate every year at rate = r = 7.1%

Let The value of home after t years = A

Now, According to question

The value of home after t years = original value of home × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, A = p × [tex](1-\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, A = $249,000 × [tex](1-\dfrac{\textrm 7.1}{100})^{\textrm t}[/tex]

Or, A = $249,000 × [tex](0.929)^{\textrm t}[/tex]

So,The value of home after t years = A = $249,000 [tex](0.929)^{\textrm t}[/tex]

Hence,The value of home after t years is $249,000 [tex](0.929)^{\textrm t}[/tex] . Answer

There is no specific requirement in the question, but I'm assuming you need to compute the time needed for Alexis reach 1,000,000 Instagram followers

Answer:

[tex]t= 462.82\ days[/tex]

Step-by-step explanation:

Exponential Growth

When the number of observed elements grows as the previous value multiplied by a constant ratio, we have exponential growth. The formula to model such situations is

[tex]\displaystyle f(x) = f_o(1 + r)^t[/tex]

Where [tex]f_o[/tex] is the initial value of f, 1 + r is the constant ratio, and t is the time expressed in half days (12 hours)

The initial value is 100 Instant followers, thus:

[tex]\displaystyle f(x) = 100(1.01)^t[/tex]

We need to know when the number of followers will reach 1,000,000. Setting up the equation

[tex]\displaystyle 100(1.01)^t=1,000,000[/tex]

Simplifying by 100

[tex]\displaystyle (1.01)^t=10,000[/tex]

Taking logarithms

[tex]\displaystyle t\ log(1.01)=log\ 10,000[/tex]

[tex]\displaystyle t\ log(1.01)=4[/tex]

Solving for t

[tex]\displaystyle t=\frac{4}{log(1.01)}=925.63[/tex] periods of 12 hrs

[tex]t= 462.82\ days[/tex]

Alexis will reach 1,000,000 followers in approximately 462.82 days.

To calculate how long it will take Alexis to reach 1,000,000 followers, we can use the following equation:

f(t) = f(1+r)^t

We know that Alexis currently has 100 followers (f=100), and she wants to reach 1,000,000 followers (f=1,000,000). We also know that her follower growth rate is 1% every 12 hours (r=0.01).

To solve for the time (t) it will take Alexis to reach 1,000,000 followers, we can use the following steps:

Divide both sides of the equation by f(1+r):

f(t)/f(1+r) = (1+r)^t

Take the natural logarithm of both sides of the equation:

ln(f(t)/f(1+r)) = t * ln(1+r)

Divide both sides of the equation by ln(1+r):

t = ln(f(t)/f(1+r)) / ln(1+r)

Substitute the known values into the equation:

t = ln(1,000,000/100) / ln(1+0.01)

Solve for t:

t = 462.82 days

Therefore, it will take Alexis approximately 462.82 days to reach 1,000,000 followers.

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Answer:

x=12,y=10

Step-by-step explanation:

let two nos are  x and y

so x-y=2.............(1)

xy=120................(2)

(x+y)^2=(x-y)^2+4xy

(x+y)^2=2^2+4(120)

(x+y)^2=4+480=484

x+y=[tex]\sqrt{484}[/tex]

x+y=22.................(3)

adding  (1) and (3),

x+y=22

x-y=2

2x=24

x=12,y=10  answer

Answer:

yo   m om        s  u  c   k        c o c  k

Step-by-step explanation:

So first we have to know what (fog)(x) means. Whenever we have the notation (fog)(x) or (gof)(x) or whatever variables (hof)(c) it means that we put the function closest to the x in the other function.

Basically for (fog)(x) this means put g(x) in f(x)

For (hof)(c) this means put f(c) in h(c)

For (gof)(x) this means put f(x) in g(x)

So now we can proceed with the problem.

f(x) = x^2 - 2 (I assume you wrote x squared) and g(x) = x - 3. Find (fog)(x)

So we are going to put g(x) in f(x). So wherever there is an x in f(x) we are gonna replace that with x -3:

f(g(x)) = (x-3)^2 - 2

If we want we can foil this out:

(x-3)(x-3) - 2

x^2 - 6x + 9 -2

or x^2 - 6x + 7

So: (fog)(x) = x^2 - 6x + 7

*If you meant 2x the process is the same but will give you a different answer*

Jake runs fastest

Step-by-step explanation:

The given is:

We need to find who runs fastest

To solve the problem we must to find the unit rate of each one in feet per second

∵ Jake runs 334 feet and 26 seconds

- To find the unite rate divide 334 feet by 26 seconds

∴ Jake's rate = 334 ÷ 26 = 12.85 ft./s

∵ Katie runs 1 mile in 596 seconds

- Change the mile to feet

∵ 1 mile = 5280 feet

∴ Katie runs 5280 feet in 596 seconds

- To find the unite rate divide 5280 feet by 596 seconds

∴ Katie's rate = 5280 ÷ 596 = 8.86 ft./s

∵ Stephanie runs 580 feet in one minute

- Change the minute to seconds

∵ 1 minute = 60 second

∴ Stephanie runs 580 feet in 60 seconds

- To find the unite rate divide 580 feet by 60 seconds

∴ Stephanie's rate = 580 ÷ 60 = 9.67 ft./s

∵ Emily's rate is 10 ft./s

∵ Jake's rate is 12.85 ft./s

∵ Katie's rate is 8.86 ft./s

∵ Stephanie's rate is 9.67 ft./s

- The fastest one who has the greatest rate

∵ Jake's rate is the greatest

∴ Jake runs the fastest

Jake runs fastest

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Answer:

The actual length of the helicopter is 23 feet.

Step-by-step explanation:

Given:

On a scale drawing, a helicopter is 2.3 feet long.

The scale on the drawing shows a ratio of 1 foot to 10 feet.

Now, to find the actual length of the helicopter.

Let the actual length of helicopter be [tex]x[/tex].

On scale drawing length of helicopter = 2.3 feet.

The scale on the drawing shows a ratio = 1:10.

Now, as ratios are given so by setting proportion we solve it:

[tex]\frac{2.3}{x} =\frac{1}{10}[/tex]

By cross multiplying we get:

⇒ [tex]2.3\times 10=x[/tex]

⇒ [tex]23=x[/tex]

⇒ [tex]x=23\ feet.[/tex]

Therefore, the actual length of the helicopter is 23 feet.

The average rate of change for the function on the interval from x = -2 to x = 2 is 1.

The average rate of change for a function on an interval is calculated by finding the slope of the line connecting the two endpoints of the interval. In this case, the interval is from x = -2 to x = 2.

To find the slope, we need to find the change in y values divided by the change in x values. In other words, we need to find the difference in f(x) values divided by the difference in x values.

Substituting the given function into the equation, we have:

slope = (f(2) - f(-2)) / (2 - (-2)) = (-3(2) + 2 - (-3(-2) + 2)) / (2 + 2)

= (-6 + 2 + 6 + 2) / 4

= 4 / 4 = 1.

Therefore, the average rate of change for the function on the interval from x = -2 to x = 2 is 1.

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Answer:

x=9

Step-by-step explanation:

To solve, simplify the equation them isolate x.

8(2x- 6) = 96   Distribute over brackets by multiplying

16x - 48 = 96   Add 48 to both sides

16x = 144         Divide both sides by 16

x = 9                Final answer

Answer:

a² – 3ab + 5b²

Step-by-step explanation:

M – (4ab – 3b²) = a² – 7ab + 8b²

M = a² – 7ab + 8b² + 4ab – 3b²

M = a² – 3ab + 5b²

Answer:

image

Step-by-step explanation:

image

Answer:

29

Step-by-step explanation:

Use definition of conditional probability:

[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)},[/tex]

where

A = the student is a freshman,

B = the student is a male

From the table,

[tex]P(B)=\dfrac{4+6+2+2}{4+6+2+2+3+4+6+3}=\dfrac{14}{30}=\dfrac{7}{15}\\ \\P(A\cap B)=\dfrac{4}{4+6+2+2+3+4+6+3}=\dfrac{4}{30}=\dfrac{2}{15}[/tex]

So,

[tex]P(A|B)=\dfrac{\frac{2}{15}}{\frac{7}{15}}=\dfrac{2}{7}\approx 0.29=29\%[/tex]

Answer:

36 ounces

Step-by-step explanation:

The common relationship between 24 ounces and 8 ounces is that 8 times x= 24.

24 divided by 8 is 3. Applying this same technique, we can figure out that 12 times 3 is 36.

Answer: 36 oz of oil

Ratio of oil to vinegar: 3:1

Step-by-step Explanation:

1)  The oil to vinegar ratio of the recipe is calculated my dividing the amount of oil (oz) by the amount of vinegar (oz)

         24 ÷ 8 = 3

      This 3 means you have 3 parts oil for every 1 part vinegar, ratio being: [tex]\frac{3}{1}[/tex]

2)

[tex]\frac{3}{1}[/tex] ⇒ [tex]\frac{?}{12}[/tex]

             To get the denominator from 1 to 12 you must multiply by 12.

            You must do the same to the numerator (top of fraction) meaning you mus multiply 3 (The ratio's nominator) by 12.

                     3 × 12 = 36

3)

The answer is 36 oz of oil

Answer Check:

To Check answer you can do 36 ÷ 12

And if it equals 3 than we know that the ounces of oil (36) over the ounces of vinegar (12) give us a ratio of 3:1  Which is the same ratio as used in the recipe. (24:8)

This is a simplified method of this problem.

Answer:

Practical Domain is the set of x values which are from zero to 230.

The maximum he can earn is $510.

Step-by-step explanation:

Domain is the set of x values. In this equation it is the number of videos sold that could be between zero and 230 ( considering the maximum number of people buying videos are 230).

It can be written as v lies between zero and 230 or in other words [0,230].

The maximum he can earn is

E(v)=50+2v

E(230)=50+2(230)

50+ 460= 510$

The figure/drawing isn't needed to answer this question.

The question tells us ABCD ~ WXYZ, which means trapezoid ABCD is similar to WXYZ.

Point A corresponds to point W, B corresponds with X, C corresponds with Y, and D corresponds with Z (first, second, third, and last letters correspond with each other according to the similarity statement).

Now let's check each answer choice and see which applies to these similar trapezoids:

Let me know if you need any clarifications, thanks!

Answer:

c kd kjdkwj

Step-by-step explanation:

jc kjkd ndjfhcajhd,cm sdnfj vkdshf vndc jdsfhbv

Answer:($7.76/4)x 13

Step-by-step explanation: There is no way to start from the price of 4 glue sticks. So, you have to find the unit rate. The unit rate is the cost of 1 of the items. For example, if 8 apples was $5.65, you have to find out what 1 apple cost so you can buy as many apples you want, not just 8. After finding the unit rate, multiply the unit rate by 13. Back to the apple example, if I did not want 8 apples but 15, and I want to know what the price is before I go up to the counter to buy it, I would multiply the unit rate by how much I want.

Also, the answer to ($7.76/4)x 13 is $25.22. The unit rate was $1.94.