While riding her bike to the ocean and back home 6 times, Kelly timed herself at 48min, 56min, 41min, 49min, 43min, and 59min. She had set a goal of averaging 51 minutes for her rides. How many minutes will she need to spend on her seventh ride to attain her goal?

Answer:

(f◦​g)(−1​) = -14

Step-by-step explanation:

First solve for g(x). g(x) = -1 - 6 = -7. Then plug -7 into f(x). f(x) = (-7)(2) = -14

I'm not sure what the question means by "use S = n^2"...

At any rate, the given sum

1 + 3 + 5 + … + 301

is simply the sum of the first 151 odd positive integers, which we can write in the form 2n - 1 for n between 1 and 151. That is,

\(1+3+5+\cdots+301 = \displaystyle\sum_{n=1}^{151}(2n-1)\)

We can expand the sum as

\(\displaystyle 2\sum_{n=1}^{151}n - \sum_{n=1}^{151}1\)

Next, recalling that

\(\displaystyle \sum_{i=1}^n1 = 1+1+1+\cdots+1 = n \text{ and }\sum_{i=1}^ni=1+2+3+\cdots+n = \frac{n(n+1)}2\)

it follows that

\(1+3+5+\cdots+301 = 2\cdot\dfrac{151\cdot152}2 - 151 = 151\cdot(152-1) = 151^2 = \boxed{22,801}\)

(Probably "S = n^2" means "sum of n odd integers = n ²")

Given:

The complex number is:

\(z=1+i\sqrt{3}\)

To find:

The argument of the given complex number.

Solution:

If a complex number is \(z=x+iy\), then the argument of the complex number is:

\(\theta=\tan^{-1}\dfrac{y}{x}\)

We have,

\(z=1+i\sqrt{3}\)

Here, \(x=1\) and \(y=\sqrt{3}\). So, the argument of the given complex number is:

\(\theta =\tan^{-1}\dfrac{\sqrt{3}}{1}\)

\(\theta =\tan^{-1}\sqrt{3}\)

\(\theta =\tan^{-1}\left(\tan \dfrac{\pi}{3}\right)\)

\(\theta =\dfrac{\pi}{3}\)

Therefore, the argument of the given complex number is \(\theta =\dfrac{\pi}{3}\).

Answer:

21x²

Step-by-step explanation:

hopefully A is a typo

Answer: A (if it's just a typo)   or   \(21x^{2}\)

Step-by-step explanation:

Since it's the same variable and same exponent, you just need to add the whole numbers and put the same variable and exponent.

12 + 9 = 21

\(21x^{2}\)

Answer:C

Step-by-step explanation:

Answer: 0.41

Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).

41 over 100 as a decimal point would be 41 divided by 100

Which produces the equivalent decimal, 0.41

P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)

0.41 = 41%

so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)

Best of luck in 5th grade :)

Answer:

the answer is 5+4× and ur welcome

Answer: 4x + 5

Step-by-step explanation:

sorry if that's

not the answer you're looking for.

Answer:

Hi there!

Your answer is:

width=15

Length=25

Step-by-step explanation:

L=2w-5

P=80

Perimeter formula

L+L+W+W=P

(2w-5)+(2w-5)+w+w=80

6w-10=80

+10

6w=90

/6

w=15

Plug in width in length formula

L=2w-5

2(15)-5

30-5

L=25

Therefore, Kallie will need to use a total of 6 teaspoons of water conditioner for all the water in 12 fish tanks.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign, with the expression on the left being equal to the expression on the right. Equations are used to represent various relationships and situations in mathematics and other fields, and are solved to find the values of variables that make the equation true.

Here,

First, we need to determine the total amount of water in all 12 fish tanks. Since each fish tank is filled with 20 quarts of water, the total amount of water in all 12 fish tanks is:

12 fish tanks * 20 quarts per fish tank = 240 quarts of water

To convert quarts to gallons, we divide by 4 (since there are 4 quarts in a gallon):

240 quarts / 4 quarts per gallon = 60 gallons of water

Now, we can use the given conversion factor to determine how many teaspoons of water conditioner are needed for 60 gallons of water. Since for every 10 gallons of water, Kallie uses 1 teaspoon of water conditioner, for 60 gallons of water, she will use:

60 gallons / 10 gallons per teaspoon = 6 teaspoons of water conditioner

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The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;

C² = a²+b²

Where:

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When you multiply the same number with different exponents together, you add the exponents together.

3^2 + 3^x = 3^7

Adding the two together you have 3^(2 + x = 7)

Solve for x: 2 + x = 7

Subtract 2 from both sides:

x = 5

Answer:

Roots are basically the x-intercepts (of a parabola)

Step-by-step explanation:

When you are doing quadratic equations, whenever the line touches the x-intercept, it is called a root.

Answer:

Y = -5

Step-by-step explanation:

Answer:

anime girl

Step-by-step explanation:

anime girl

The average number of students who are afraid of spiders and snakes is 15. (Option C).

To calculate the average number of students who are afraid of spiders and snakes, you need to add the number of students afraid of spiders and the number of students afraid of snakes, and then divide by 2 (since there are two categories being considered: spiders and snakes).

Average = (Number of students afraid of spiders + Number of students afraid of snakes) / 2

Given the information:

Number of students afraid of spiders = 18

Number of students afraid of snakes = a little more than 11 (let's consider 12 for calculation)

Average = (18 + 12) / 2 = 30 / 2 = 15

So, the average number of students who are afraid of spiders and snakes is 15.

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Answer:

Take the square root of both sides

Step-by-step explanation:

I'm going to assume your questions looks like this

\(x^{2} =\frac{9}{16}\)

To solve this you just take the sqareroot of both sides which should get you

-3/4, 3/4=x

1.) Probability of getting 1: 0.12 or 12%.

2.) Probability of getting 2: 0.16 or 16%.

3.) Probability of getting 3: 0.25 or 25%.

4.) Probability of getting 4: 0.18 or 18%.

5.) Probability of getting 5: 0.15 or 15%.

6.) Probability of getting 6: 0.14 or 14%.

To calculate the probability of getting a specific number on a fair die, we divide the number of times that number appears by the total number of rolls. In this case, the die was rolled 100 times, and the results are given as follows:

Number: 1 2 3 4 5 6

Times: 12 16 25 18 15 14

To find the probability of getting each number, we divide the corresponding number of times by the total number of rolls (100):

Probability of getting 1 = 12 / 100 = 0.12.

Probability of getting 2 = 16 / 100 = 0.16.

Probability of getting 3 = 25 / 100 = 0.25.

Probability of getting 4 = 18 / 100 = 0.18.

Probability of getting 5 = 15 / 100 = 0.15.

Probability of getting 6 = 14 / 100 = 0.14.

Therefore, the probabilities of getting each number on a fair die, based on the given results of 100 rolls, are approximately:

1: 0.12 or 12%,

2: 0.16 or 16%,

3: 0.25 or 25%,

4: 0.18 or 18%,

5: 0.15 or 15%,

6: 0.14 or 14%.

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Answer:

43.6 has 3 significant figures.

Answer:

1/2

Step-by-step explanation:

that's the answer because 2/8-1/4 is 1/2

Answer:

A BCG

Step-by-step explanation:

Answer:

(1) 4x + 28 (2) 18x- 27

Step-by-step explanation:

the first question 4(x + 7) can be simplified by multiplying the number outside the parenthesis (4) by both of the values inside:

4x + 28 or the last answer choice

in the second question you can use the same method:

9 (2x) = 18x

9 ( -3) = -27

therefore the correct answer choice is 18x - 27

hope this helps :)

The surface area of a rectangular prism is 48 5/6 mi².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]

Surface area of rectangular prism = 2[14 + 15/2 + 35/12]

Surface area of rectangular prism = 48 5/6 mi².

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Answer:

30

Step-by-step explanation:

If A||B then the sum of given angles must be equal to 180°

2x + 50 + 5x - 80 = 180 add like terms

7x - 30 = 180 add 30 to both sides

7x = 210 divide both sides by 7

x = 30

a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.

b. Super Vision raises the rates 23% after a new customer's first year,  a customer who switched from Super Vision save $180 in the second year.

c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.

a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.

Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:

$46 (home phone) + $36 (Internet) + $56 (cable television) = $138

Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:

$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month

Therefore, during the first year, the customer could save:

$38 (monthly savings) * 12 (number of months) = $456

b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:

$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123

To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month

Therefore, in the second year, the customer would save:

$15 (monthly savings) * 12 (number of months) = $180

c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:

$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14

To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14

In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.

Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.

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It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed,  then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.

To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.

We can set up a proportion to find the time:

(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)

Let's solve for the time taken for 146 km:

(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)

Substituting the given values:

(time taken for 146 km) = 32 minutes * (146 km / 48 km)

Calculating the value:

(time taken for 146 km) ≈ 32 minutes * 3.042

(time taken for 146 km) ≈ 97.344 minutes

Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.

To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:

Additional time = 97.344 minutes - 32 minutes

Additional time ≈ 65.344 minutes

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53 years for the Population of the United States to reach 300 million people according to this model.

The recursive formula of the population of the United States is given by ao = an1.015a - 1

Let's solve this to get a formula that is not recursive.a0 = a0 givena1 = 1.015a0 - 1a2 = 1.015a1 - 1 = 1.015 (1.015a0 - 1) - 1 = 1.0152 a0 - 1.015 - 1a3 = 1.015a2 - 1 = 1.015(1.015²a0 - 1.015 - 1) - 1 = 1.015³ a0 - 1.015² - 1.015 - 1a4 = 1.015a3 - 1 = 1.015(1.015³a0 - 1.015² - 1.015 - 1) - 1 = 1.015⁴ a0 - 1.015³ - 1.015² - 1.015 - 1an = 1.015na0 - 1.015n-1 - 1.015n-2 - ... - 1.015 - 1We can rewrite this asan = a0(1.015)

where a0 is the population of the United States in 1910 (92.2 million people) .

Now, we need to write an exponential function to find the population of the United States as a function of time in years since 1910.P(t) = 92.2(1.015)

To find the number of years it takes for the population to reach 300 million people, we need to solve the equation92.2(1.015)t = 300

Dividing both sides by 92.2, we get1.015t = 3.2596

Taking the natural logarithm of both sides, we get ln(1.015) = ln(3.2596)t = ln(3.2596)/ln(1.015) ≈ 53.2

Therefore,  approximately 53 years for the population of the United States to reach 300 million people according to this model.

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This would be the average value of R(x) between 10 m and 50 m :

\(\displaystyle \frac1{50\,\mathrm m - 10\,\mathrm m} \int_{10\,\rm m}^{50\,\rm m} kx^2 \, dx\)

The average intensity of radiation between 10 meters and 50 meters from the source is 1033.33 k.

It is the reverse of differentiation.

The intensity of radiation at a distance x meters from a source is modeled by the function given by

R(x)=kx²

where k is a positive constant.

The average intensity of radiation between 10 meters and 50 meters from the source will be

\(\rm Average \ intensity = \dfrac{1}{50 - 10} \int_{10}^{50} \ kx^2 \ dx\\\\\\Average \ intensity = \dfrac{k}{50 - 10} [ \dfrac{x^3}{3} ]_{10}^{50}\\\\\\Average \ intensity = \dfrac{k}{40} [ \dfrac{50^3}{3} - \dfrac{10^3}{3} ]\\\\\\Average \ intensity =1033.33k\)

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Explanation

Step 1

subtract 7 in both sides

Step 2

divide both sides by 2

so, the answer is x=-5/2