simplify : 3/5x+x , find the answer ?​

First we divide the figure into 3 rectangles and find the volume of each one. This is:

Then, the volume for rectangle 1:

Given, depth of 30 in

The volume formula is

Volume for rectangle 2:

Volume rectangle 3 = Volume rectangle 1:

Therefore, the volume of the figure is:

Next, we have:

1 yard = 3 ft

So 1 cubic yard is given by

Hence:

Round up the nearest yard = 20 cubic yard

Answer: 20 cubic yards

Answer: F

Step-by-step explanation:

Answer: correct answer is A

Step-by-step explanation:

Remember that the coordinates (−2,−5π3) tell us the radius r=−2 and the angle θ=−5π3. So the point should be on the circle labeled 2 and form an angle of −5π3 with the negative x-axis. Point A is the correct point.

The vector in component form whose tail is the point (−1,5), and whose head is the point (8,−6) is (-9, 11)

A vector is a physical quabntity thet has both magnitude and direction.

To find  the component form of the vector whose tail is the point (−1,5), and whose head is the point (8,−6), we proceed as folows

Since we have the points (-1, 5) and (8, -6) and we want the head to be at (8, -6),

Let A = (8, -6) and B = (-1, 5)

So, AB = B - A

= (-1, 5) - (8, -6)

= (-1 - 8), (5 - (-6))

= (-9, 5 + 6)

= (-9, 11)

So, the vector in component form is (-9, 11)

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Answer:

1. x = {1.5, 0.2}  

2. x = 1

Step-by-step explanation:

Step-by-step explanation:

Area=23ft²

Side=√23ft²

Side=4.8ft

Answer:

• Area formula of a square:

\({ \tt{area = side \times side}} \)

• let s represent dimensions of each side of a square:

\({ \tt{23 = s \times s}} \\ \\ { \tt{ {s}^{2} = 23}} \\ \\ { \tt{s = \sqrt{23} }} \\ \\ { \tt{length = 4.8 \: ft}}\)

Answer:

-72x - 53y + 287 = 0.

Step-by-step explanation:

To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.

The line mirror equation is given as 4x + 7y + 13 = 0.

The reflection of a point (x, y) in the line mirror can be found using the formula:

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

where A, B, and C are the coefficients of the line mirror equation.

For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.

Now, let's find the equations of the image of the circle.

The original circle equation is x² + y² + 16x - 24y + 183 = 0.

Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)

= (x - 8y - 8(4x + 7y + 13)) / 65

= (x - 8y - 32x - 56y - 104) / 65

= (-31x - 64y - 104) / 65

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)

= (y - 14x + 8(Ax + By + C)) / 65

= (y - 14x + 8(4x + 7y + 13)) / 65

= (57x + 35y + 104) / 65

Therefore, the equation of the image of the circle is:

(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0

Simplifying the equation, we get:

-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0

-72x - 53y + 287 = 0

So, the equation of the image of the circle is -72x - 53y + 287 = 0.

9514 1404 393

Answer:

  45

Step-by-step explanation:

Let x and y represent the tens and ones digits, respectively. The 5 times the sum of digits is 5(x+y). The value of the digit-reversed number is (10y+x), so the required relation is ...

  5(x +y) = (10y +x) -9

The other relationship between the digits is given as ...

  4y = 1/2(10x)

A graphing calculator shows the solution to these equations is (x, y) = (4, 5).

The two-digit number is 45.

__

Additional comment

You can solve these equations in any of a variety of ways. Using a graphing calculator to find integer solutions is fast and easy, so is one of my favorites. Here, the coefficients on one equation are not easy multiples of those in the other, so substitution and/or elimination can get messy. In this situation, I like to use the "cross-multiplication" method, which starts with the equations in general form:

From the coefficients of these equations, differences of cross products are formed:

Then the solutions are the solutions to 1/d1 = x/d2 = y/d3:

(x, y) = (4, 5)   ⇒   the number is 45.

__

This method is one of several variations of Cramer's Rule, the general solution of systems of linear equations using matrix methods.

We can conclude the proof of inequality : 3 (m + n)! ≥ m! + n! below.

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Mathematically, we can write -

\($n! = n \times (n-1) \times \dots \times 1\)

Given is the inequality -

3 (m + n)! ≥ m! + n!

We have -

3 (m + n)!

3 {(m + n)(m + n - 1)(m + n - 2) ....... (3)(2)(1)}

3 {m² + mn - m + nm + n² - n}(m + n + 2) ...... (3)(2)(1)

3 {m² + n² - m - n + 2mn}(m + n + 2) ........ (3)(2)(1)

3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1)

Now, for (m! + n!) --

(m! + n!) = m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)

It can be seen that -

3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1) ≥

m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)

Hence, it can be seen that -

3 (m + n)! ≥ m! + n!

Therefore, we can conclude that 3 (m + n)! ≥ m! + n!.

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Answer: Yellow Greed

Step-by-step explanation: Maths

Answer:

the length is 96 meters

Step-by-step explanation:

384/4=96

Answer:

Step-by-step explanation:

The given expression is

\(36,700 - (5,000 + 500m)=0\)

Where \(m\) is months.

We need to solve for the variable.

\(36,700-5,000-500m=0\\31,700=500m\\m=\frac{31700}{500} \approx 63.4\)

Therefore, Michael needs to save $63.40, approximately.

Answer:

The number representing describing the value of his signing bonus = 5,000.

Step-by-step explanation:

Total debt = $36,700

He pays $500 every month from his monthly salaries, since m = months.

The $5,000 is the amount of his signing bonus, which puts entirely towards paying off his debt.

It is like the fixed payment.  While the 500m is the variable payment per month.

So, at the end of any number of months, you can easily calculate the remaining debt using the expression, 36,700 - (5,000 + 500m)

Answer: 2/3-6=9 is equal to = − 2(2x+6)

Answer:

x = 45 over 2  or  22.5

Step-by-step explanation:

Answer:

If a person is randomly selected from this group, the probability that they have both high blood pressure and high cholesterol is P=0.25.

Step-by-step explanation:

We can calculate the number of people from the sample that has both high blood pressure (HBP) and high cholesterol (HC) using this identity:

\(N(\text{HBP or HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP and HC})\\\\\\ N(\text{HBP and HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP or HC})\\\\\\ N(\text{HBP and HC})=15+25-30=10\)

We can calculate the probability that a random person has both high blood pressure and high cholesterol as:

\(P(\text{HBP and HC})=\dfrac{10}{40}=0.25\)

Mr. Arnett will pay $207 for all the trail mix bought by his children.

Here, we are given that Mr. Arnett allowed each of his children to fill their own bag as follows-

Child                 Ava   Grayson   Mason   Tyler

Amount of

Trail Mix (oz)      15        14            10            7

Further, cost of trail mix = $4.50 per pound

The total amount of trail mix collected by all 4 children will be-

15 + 14 + 10 + 7

= 46

Thus, in total the children put 46 pounds of trail mix in their bags.

Hence, the total cost will be-

46 × 4.5

= 207

Thus, Mr. Arnett will pay $207 for all the trail mix.

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Answer:

21°

Step-by-step explanation:

In an sosceles trapezoid, the lower base and upper base angles are congurent

⇒ ∠HGF = ∠EFG

⇒ 9y + 3 = 8y + 5

⇒ 9y - 8y = 5 - 3

⇒ y = 2

⇒ ∠HGF = 9(2) + 3

= 18 + 3

= 21

The measure of angle HGF in the given isosceles trapezoid EFGH is calculated to be 21 degrees.

This problem deals with the properties of an isosceles trapezoid, which is a type of quadrilateral. In an isosceles trapezoid, opposite angles are equal. In this case, angle EFG and angle HGF would be equal to each other given the shape is an isosceles trapezoid. So, their measures should be equal.

Here, the measure of angle HGF is given as (9y + 3)°, and the measure of angle EFG is (8y + 5)°. Setting these equal to each other to find the value of y, we get 9y + 3 = 8y + 5. By simplifying, we get the value of y is 2. Substituting the found value of y in angle HGF we get, 9*2+3 = 21 degrees.

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Answer:

The z-score for this data is Z = -0.26.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

This is based on knowledge that in the U.S., the mean PAL is 1.65 and the standard deviation is 0.55.

This means that \(\mu = 1.65, \sigma = 0.55\)

A study took a random sample of 51 people who lived in low income neighborhoods and found their mean PAL to be 1.63.

This means that \(n = 51, X = 1.63\)

Using a one-sample z test, what is the z-score for this data

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{1.63 - 1.65}{\frac{0.55}{\sqrt{51}}}\)

\(Z = -0.26\)

The z-score for this data is Z = -0.26.

Answer:

Step-by-step explanation:

(a) To find the linear cost function C(x), we need to consider the fixed cost and the marginal cost. The fixed cost is $100, and the marginal cost is $8 per pair of earrings.

The linear cost function can be represented as C(x) = mx + b, where m is the slope (marginal cost) and b is the y-intercept (fixed cost).

In this case, the slope (m) is $8, and the y-intercept (b) is $100. Therefore, the linear cost function is:

C(x) = 8x + 100.

(b) The average cost function (AC) can be found by dividing the total cost (C(x)) by the number of units produced (x):

AC(x) = C(x) / x.

Substituting the linear cost function C(x) = 8x + 100, we have:

AC(x) = (8x + 100) / x.

(c) To find C(5), we substitute x = 5 into the linear cost function:

C(5) = 8(5) + 100

= 40 + 100

= 140.

Interpretation: C(5) = 140 means that when the artist produces 5 pairs of earrings, the total cost (including fixed and variable costs) is $140.

(d) To find C(50), we substitute x = 50 into the linear cost function:

C(50) = 8(50) + 100

= 400 + 100

= 500.

Interpretation: C(50) = 500 means that when the artist produces 50 pairs of earrings, the total cost (including fixed and variable costs) is $500.

(e) The horizontal asymptote of C(x) represents the cost as the number of units produced becomes very large. In this case, the marginal cost is constant at $8 per pair of earrings, indicating that as the number of units produced increases, the cost per unit remains the same.

Therefore, the horizontal asymptote of C(x) is $8, indicating that the average cost per pair of earrings approaches $8 as the number of units produced increases indefinitely.

In practical terms, this means that for every additional pair of earrings produced beyond a certain point, the average cost will stabilize and remain around $8, regardless of the total number of earrings produced.

The amount in year 6 is $1282.5.

What is simple interest?

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Given,

rate of interest = 7%

time = 1 year

Amount on first year = $950

First we will calculate simple interest for 5 years, because amount is available for 1 year.

SI =PRT

SI = 950(7/100)1

SI = $332.5

Therefore, the amount after 6 years = 950+332.5

=$1282.5

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Let:

Using the distance formula:

so:

Square both sides:

Expand (x - 6)²:

Factor:

The factor of 11 that sum to -12 are -11 and -1, so:

Answer:

x = 1 and x = 11

Answer:

19%

Step-by-step explanation:

285÷15 which equals 19 meaning Tom needs to lose 19%

About 88.49% of cellphone plans have charges that are less than $83.60.

To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.

z = (x – μ) / σ

where x = 83.60, mean, μ =  62 and standard deviation, σ = 18

Thus, the z-score of $83.60 is:

z = (83.60 - 62) / 18 = 1.2

Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).

Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.

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Answer:

y - 11 = -8(x - 1)

Step-by-step explanation:

We are told Hamid’s instruments read 11 ft above his marker 1 hour before.

Where y is tide level and x is time.

Thus, x1 = 1 and y1 = 11

Since graph of yesterday's data is y = -8x - 2,then in slope intercept form, the equation parallel is;

y - y1 = m(x - x1)

m is -8.

Thus; y - 11 = -8(x - 1)

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer:

Third option

Step-by-step explanation:

the difference between the areas of the square and the 4 circles:

the square is 8 inches per side

\((8)^{2} -4\pi (2)^{2} =64-4\pi (4)=(64-16\pi)in^{2}\)

Hope this helps

The remaining area of the square is,

⇒ (64 - 4π) in.²

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

Four circles, each with a radius of 2 inches, are removed from a square.

Now, We get;

Side of square = 8 inches

Hence, The remaining area of the square is,

⇒ (8 x 8 - π × 2²)

⇒ (64 - 4π) in.²

Thus, The remaining area of the square is,

⇒ (64 - 4π) in.²

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Answer:  I belive it is 360 inches cubed. I could be wrong

Step-by-step explanation:

The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

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A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

Answer:

Step-by-step explanation:

Kaylee held 1000 shares after the split. The post-split price per share was $17.06.

Explanation:

Before the split, Kaylee held 500 shares of the stock, and each share was worth $34.12. So, her total investment was 500 x $34.12 = $17,060.

After the 2-for-1 split, each share is split into 2 shares. So, the total number of shares she holds becomes 500 x 2 = 1000.

To find the post-split price per share, we divide the pre-split price by 2.

Post-split price per share = $34.12 / 2 = $17.06.

Answer:

P = $98.77

Step-by-step explanation:

FV = p (1+i)^n -1

            i

pv = 700,000

i = .075/12 = .00625

n = (66 - 15)* 12 = 612

700,000 = P (( 1 + .00625)^ 612 -1 /.00625

4375 = P (1.00625)^612 -1)

P = $98.77

Answer:

page 1:

51 years

$98.78

639546.64 (i think)

Page 2:

213 months

17.8 years

321 months

26.8 years

1128.9 months

88.8 years

I would probably choose the second plan because it's rather unlikely that i live past 90

Step-by-step explanation:

page 1

Let's assume the payments are at the end of the month

66-15= 51 years

effective rate: .075/12=.00625

\(700000=x\frac{(1+.00625)^{51*12}-1}{.00625}\\x=98.77973387\)

which i guess we can round to 98.78

700000-98.78*(51*12)= 639546.64

This number is really really high and so maybe you want to double check it

page 2

effective rate: .051/12=.00425

\(700000=5000\frac{1-(1+.00425)^{-n}}{.00425}\\.405=(1+.00425)^{-n}\\log_{1.00425}.405=-n\\n=213\)

213 months

213/12= 17.8 years

\(700000=4000\frac{1-(1+.00425)^{-n}}{.00425}\\.25625=(1.00425)^{-n}\\log_{1.00425}.25625\\n=321\)

321 months

321/12=26.8 years

\(700000=3000\frac{1-(1+.00425)^{-n}}{.00425}\\.008333333=(1.0045)^{-n}\\log_{1.0045}.00833333=-n\\n=1128.9\)

1128.9 months

1128.9/12= 94.1 years

1066 months

1066/12= 88.8 years

Answer:

2.0 is the correct answer

Step-by-step explanation:

hope it helps you