Carlos and Aisha take the same bike route home from school each day. Aisha lives 3 miles from school and Carlos lives 1 mile further along the path. Sometimes Aisha bikes all the way to Carlos' place before going home. Write an absolute value equation that represents how far Aisha bikes after school each day.

I'm assuming the integral is

\(\displaystyle \int \frac{dx}{x (\ln(x^2))^5}\)

We have

\(\ln(x^2) = 2 \ln|x| \implies (\ln(x^2))^5 = 32 (\ln|x|)^5\)

Then substituting \(y=\ln|x|\) and \(dy=\frac{dx}x\), the integral transforms and reduces to

\(\displaystyle \int \frac{dx}{x(\ln(x^2))^5} = \frac1{32} \int \frac{dy}{y^5} \\\\ ~~~~~~~~ = \frac1{32} \left(-\frac1{4y^4}\right) + C \\\\ ~~~~~~~~ = -\frac1{128(\ln|x|)^4} + C\)

which we can rewrite as

\(128 (\ln|x|)^4 = 8\cdot2^4(\ln|x|)^4 = 8 (2\ln|x|)^4 = 8 (\ln(x^2))^4\)

and so

\(\displaystyle \int \frac{dx}{x (\ln(x^2))^5} = \boxed{-\frac1{8(\ln(x^2))^4} + C}\)

$2100 was invested at 2% and $2900 ($5000 - $2100) was invested at 3%.

Let x be the amount invested at 2% and y be the amount invested at 3%. We know that x + y = $5000 and the interest earned is $129. We can use the formula for simple interest, I = Prt, where I is the interest earned, P is the principal (or initial amount invested), r is the interest rate, and t is the time period.

Thus, we have:

0.02x + 0.03y = $129 (1)

x + y = $5000 (2)

We can solve for one of the variables in terms of the other from equation (2), such as y = $5000 - x. Substituting this into equation (1), we get:

0.02x + 0.03($5000 - x) = $129

Simplifying and solving for x, we get:

0.02x + $150 - 0.03x = $129

-0.01x = -$21

x = $2100

Therefore, $2100 was invested at 2% and $2900 ($5000 - $2100) was invested at 3%.

Know more about simple interest here:

https://brainly.com/question/30964674

#SPJ11

Answer:

8n+7

Step-by-step explanation:

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

To know more about point , visit:

https://brainly.com/question/26310043

#SPJ1

Given, the coin is tossed three times.

Sample space: {HHH, HTH, THH, TTH, HHT, HTT, THT, TTT}

Number of positive outcomes = 8

Probability of

(1) A: Getting at least two heads

P(A) = P(Getting 3 heads) + P(Getting 2 heads)

        = \(\frac{3}{8} +\frac{1}{8}\)                           Since, P(event) = \(\frac{No. of favourable outcomes}{Total no. of possible outcomes}\)

P(A)  = \(\frac{1}{2}\)            

(2) B: Getting exactly two heads

P(B) = \(\frac{3}{8}\)

(3) C: Getting at most one head

P(C) = P(Getting zero head) + P(Getting 1 head)

       = \(\frac{1}{8} + \frac{3}{8}\)

       = \(\frac{4}{8}\)

P(C) = \(\frac{1}{2}\)

To learn more about probability of events:

https://brainly.com/question/26497828

Part A: The student was supposed to divide before subtracting

Part B: The student was supposed to simplify the parentheses before finding the exponents

Part C: The simplification of the expression gives -16.

From the question, we are to simplify the given expression

The given expression is

(∛64 - 16 ÷ 2)(2 - 4)²

Part A:

The mistake the student made was not applying the PEMDAS rule

P - Parentheses

E - Exponent

M - Multiplication

D - Division

A - Addition

S - Subtraction

Since division comes before subtraction, the student was supposed to divide before subtracting

Part B:

The student mistake was trying to simplify the exponent before simplifying the parentheses. The student was supposed to simplify the parentheses before finding the exponents.

Part C:

Simplifying the expression

(∛64 - 16 ÷ 2)(2 - 4)²

Simplify the cube root

(4 - 16 ÷ 2)(2 - 4)²

Divide

(4 - 8)(2 - 4)²

Simplify the parenthesis

(-4)(-2)²

Simplify the exponent

(-4)(4)

Evaluating

-16

Hence, the simplification of the expression gives -16.

Learn more on Simplifying an expression here: https://brainly.com/question/11812662

#SPJ1

The minimum cost will be at (2.5 , 3) and the minimum cost be $25.

Given, a landscaping contractor plans to use the least expensive combination of two brands of fertilizer.

A package of Brand X costs $16 and contains 12 oz of phosphates and 10 oz of nitrates.

A package of Brand Y costs $7 and contains 10 oz of phosphates and 5 oz of nitrates.

The lawn requires at least 60 oz of phosphates and 40 oz of nitrates.

Let the number of Brand X packages be, x

the number of Brand Y packages be, y

According to the question,

12x + 10y ≥ 60 = 6x + 5y ≥ 30

10x + 5y ≥ 40 = 2x + y ≥ 8

x ≥ 0

y ≥ 0

Z = 16x + 7y

On solving the equations, we get

6x + 5y = 30

6x + 3y = 24

On subtracting, we get

2y = 6

y = 3

and x = 2.5

So, minimum cost will be at (2.5 , 3) and the minimum cost be

Z = 16(2.5) + 7(3)

Z = 4 + 21

Z = 25

Hence, the minimum cost will be at (2.5 , 3) and the minimum cost be $25.

Learn more about Linear Programming Problems here https://brainly.com/question/14309521

#SPJ1

Answer:

21 or 26

Step-by-step explanation:

Answer:

b=A/h

Step-by-step explanation:

To isolate b, you need to divide both sides by h. Therefore:

A=bh

b=A/h

Hope this helps!

Answer:

A/h =b

Step-by-step explanation:

A = bh

Divide each side by h

A/h = bh/h

A/h =b

Yes, there is a relationship between advertisement expenditures and sales revenues. The fitted regression model is: Sales = 1591.28 + 3.59(Advertisement).

1. To construct a scatter plot, plot the advertisement expenditures on the x-axis and the sales revenues on the y-axis. Each data point represents one observation.
2. Use Excel to fit a linear regression line to the data by following the steps outlined in the textbook.
3. The fitted regression model is in the form of: Sales = Intercept + Slope(Advertisement). In this case, the model is Sales = 1591.28 + 3.59
4. The slope of 3.59 tells us that for every $1,000 increase in advertisement expenditures, there is an estimated increase of $3,590 in sales.
5. To determine if the slope is significant, perform a hypothesis test or check if the p-value associated with the slope coefficient is less than the chosen significance level.
6. The intercept of 1591.28 represents the estimated sales when advertisement expenditures are zero. In this case, it is not meaningful as it does not make sense for sales to occur without any advertisement expenditures.
7. The value of the regression coefficient, r, represents the correlation between advertisement expenditures and sales revenues. It ranges from -1 to +1.
8. The value of the coefficient of determination, r^2, tells us the proportion of the variability in sales that can be explained by the linear relationship with advertisement expenditures. It ranges from 0 to 1, where 1 indicates that all the variability is explained by the model.
9. To predict sales when the business spends $950,000 in advertisement, substitute this value into the fitted regression model and solve for sales. This will help determine if the model underestimates or overestimates sales.

To learn more about expenditures

https://brainly.com/question/30063968

#SPJ11

Answer:

17.5

Step-by-step explanation:

Answer:

4.1 inches

I would appreciate Brainliest, but no worries.

Answer:

6

Step-by-step explanation:

the formula for the sphere's volume is \(\frac{4}{3} *\pi *r^3\)

so when you set that equal to 288\(\pi\), you get 6 as the radius

The sample space for rolling a fair seven-sided die is S = {1, 2, 3, 4, 5, 6, 7}.

Given that,

A fair seven sided die is rolled.

We have to find the sample space of the rolling.

A sample space is a set of all the possible outcomes in a random experiment. It is usually denoted by the letter, S.

The subset of the sample space are events.

The die has the numbers marked from 1 to 7.

So when we roll the die,

The possible numbers are 1, 2, 3, 4, 5, 6, 7

Sample space = {1, 2, 3, 4, 5, 6, 7}

Hence the sample space is {1, 2, 3, 4, 5, 6, 7}.

Learn more about Sample Space here :

https://brainly.com/question/30206035

#SPJ1

200000J/200KJ

Step-by-step explanation:

using k.e=1/2(mv2)

k.e=1×1000×20²/2

k.e=400000/2

k.e=200000J/200KJ

Answer:

The smallest number of bags the groundskeeper must buy to cover the field is 165 bags.

Given:

A groundskeeper needs grass seed to cover a circular field, 290 feet in diameter.

A store sells 50 pound bags of grass seed. One pound of grass seed covers about 400 square feet of field.

To find:

The smallest number of bags the groundskeeper must buy to cover the field.

Solution:

Diameter of the field = 290 feet, radius = 145 feet

Area of the circular field = \pi r^{2}=πr

2

= \pi \times 145 \times 145π×145×145 = 66018.5

No of bags to be brought = \frac{66018.5}{400}

400

66018.5

= 165 bags.

Step-by-step explanation:

first answer pic

second answer

Answer:

13

Step-by-step explanation:

3 2/3 + 4 + 5 1/3

2/3 + 1/3 = 1

5 + 4 + 3 = 12

12 + 1 = 13

Hope this helped!

Mark Brainleist if you can please!

Answer:

43° and 47°

Step-by-step explanation:

→ Let one angle be x and second angle be x + 4°

As we know the sum of complementary angle is 90°

So,

x + x + 4° = 90°

2x + 4° = 90°

x = 86°/2

x = 43°

Therefore , 1st angle is 43° and 2nd angle is 47°

Answer:

\(\huge\boxed{\sf 43 \textdegree, \ 47 \textdegree}\)

Step-by-step explanation:

Let the first angle be x, and the second angle be x + 4

Given that, they are complementary angles, they add up to 90 degrees.

x + x + 4 = 90

2x + 4 = 90

Subtract 4 to both sides

2x = 90 - 4

2x = 86

Divide 2 to both sides

x = 86/2

x = 43°

The second angle:

= x + 4

= 43 + 4

= 47°

\(\rule[225]{225}{2}\)

A. \(\frac{v}{3} = 20 -v\\\)

B. \(3(n +4) = 28\)

Answer:

additive inverse properties

200 is your response.

Step-by-step explanation:

Answer:

Welp here is the answer to your question, 372/35 in exact form. in mixed number form it is 10 22/35

Answer:

I'm guessing C

Step-by-step explanation:

I don't think this is the correct way to answer it. But I litterly rotated it in my brain and got 7.5....

Answer:

120 miles

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

2 divided by .5 = 4 ( 4 half’s equal 2 )

4 times 30 miles = 120 ( each for represents 30 )

By simplifying the expression (-4-√7)² we get the value as 23+8√7 in decimals we get 44.12.

Given that,

The expression is (-4-√7)²

We need to find the value and simplify the expression.

Take the expression.

(-4-√7)²

We know that (a+b)²=a²+2ab+b²

The expression is in the form of (a+b)² substitute the formula.

(-4)²+2(-4)(-√7)+(-√7)²

Now do the square

16+2(-4)(-√7)+7

Now do the multiplication.

16+8√7+7

Now do the addition.

23+8√7

We can write the √7 value

23+8(2.64)

Multiply 8 and 2.64

23+ 21.12

Now adding

44.12

Therefore, By simplifying the expression (-4-√7)² we get the value as 23+8√7 in decimals we get 44.12.

To learn more about expression visit: https://brainly.com/question/14083225

#SPJ1

A graphical plot with sales on the Y axis and time on the X axis is a:

a. Scatter diagram.

Using a single variable on each axis, the scatter diagram plots pairings of numerical data in an effort to identify any relationships between them. A line or curve will be formed by the points if the variables are correlated. The points will hug the line closer the more highly correlated the data is. You may also visualise the strength of any relationship. If the researcher believes there may be a correlation, a line of greatest fit can also be drawn on the graph.

Data points are shown on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.

Thus, correct option: a

To know more about Scatter diagram refer to:

https://brainly.com/question/6592115

#SPJ4

The area under the standard normal curve to the left of z = 2.06 is approximately 0.9803.

The normal distribution function, also known as the Gaussian distribution or bell curve, is a probability distribution that is symmetric, bell-shaped, and continuous. It is defined by two parameters: the mean (μ) and the standard deviation (σ).

The normal distribution is widely used in statistics and probability theory due to its many desirable properties and its applicability to various natural phenomena. It serves as a fundamental distribution for many statistical methods, hypothesis testing, confidence intervals, and modeling real-world phenomena.

To find the area under the standard normal curve to the left of z = 2.06, you can use a standard normal distribution table or a calculator with a normal distribution function. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

Using a standard normal distribution table, the area to the left of z = 2.06 can be found by looking up the corresponding value in the table. However, since the standard normal distribution table typically provides values for z-scores up to 3.49, we can approximate the area using the available values.

The closest value in the standard normal distribution table to 2.06 is 2.05. The corresponding area to the left of z = 2.05 is 0.9798. This means that approximately 97.98% of the area under the standard normal curve lies to the left of z = 2.05.

Since z = 2.06 is slightly larger than 2.05, the area to the left of z = 2.06 will be slightly larger than 0.9798.

Therefore, rounding the answer to four decimal places, the area under the standard normal curve to the left of z = 2.06 is approximately 0.9803.

To know more about function visit:

https://brainly.com/question/31062578

#SPJ11

The equation for Garage A can be expressed as A = 12 + 4t, and the equation for Garage B as B = 7 + 5t.

A = 12 + 4t

B = 7 + 5t

12 + 4t = 7 + 5t

4t - 5t = 7 - 12

-t = -5

t = 5 hours

To learn more about a linear equation refer to:

https://brainly.com/question/2030026

#SPJ1

Answer:

4

Step-by-step explanation:

Length time width times high , 8x8=16 square rooted equals 4

The correct option is: the volume of the stone 6 in3

To find the volume of a square pyramid, we use the formula:

V = (1/3) * B * h

where B is the area of the base and h is the height of the pyramid. Since the stone is in the shape of a square pyramid, its base is a square.

Let's say that the length of one side of the square base is x. Then, the area of the square base is:

B = x^2

Since the stone is in the shape of a square pyramid, all four triangular faces are congruent. Therefore, the height of the pyramid can be found by multiplying the slant height of one of the triangular faces by a factor of 1/2. Let's say that the slant height of each triangular face is y.

Then, the height of the pyramid is:

h = (1/2) * y

The volume of the stone is:

V = (1/3) * B * h

V = (1/3) * x^2 * [(1/2) * y]

V = (1/6) * x^2 * y

We're not given any specific measurements for the sides or heights of the stone, so we can't calculate an exact volume. However, if we assume that the length of one side of the base is 3 inches and the slant height is 4 inches, we can calculate the volume as follows:

V = (1/6) * (3 in)^2 * (4 in)

V = 6 in^3

Therefore, the correct option is: the volume of the stone 6 in3

learn more about volume here

https://brainly.com/question/28058531

#SPJ11