Which of the following is true?

Answer:

35 in total

Step-by-step explanation:

Answer:

7pi/8

Step-by-step explanation:

Well the arc is 21pi/8 cm. Our formula to find the length of arc is r × theta(angle). Let's take the angle as x.

R × x = 21pi/8

x = 21pi/8 ÷ R = 21pi/8 ÷ 3 = 7pi/8 rad

Answer:

235 can be split into 200+30+5. Each of these can be divided by 5: 200/5+30/5+5/5=40+6+1=47 to give us the quotient.

Another way is to double 235=2*200+2*30+2*5=400+60+10=470 and divide the result by 10 by simply removing the zero to give the quotient 47. This works because dividing by 5 is the same as doubling and dividing by 10: 2/10=1/5.

There were 90 runners to start a race.

If 1/3 dropped out, that means only 2/3 of them are left, so we have:

     Number remaining after the first round of dropout = \(\frac{2}{3} *90 = \frac{180}{3} =60\)

If 2/3 dropped out in the second half, only 1/3 of them are left, so we have

    Number remaining after the second round of dropout = \(\frac{1}{3} *60 = 20\)

Thus there are 20 runners remaining at the end.

Answer:

\(\mathrm{No\:Solution}\)

Step-by-step explanation:

\(\frac{x}{x}+2-\frac{4}{x}-2=1\)

Step 1: Subtract \(2\:-2\) from both sides

\(\frac{x}{x}+2-\frac{4}{x}-2-\left(2-2\right)=1-\left(2-2\right)\\\\\frac{x}{x}-\frac{4}{x}=1\)

x over x is 1

\(1-\frac{4}{x}=1\)

Step 2: Multiply both sides by \(x\)

\(1\cdot \:x-\frac{4}{x}x=1\cdot \:x\\\\x-4=x\)

And when you solve for \(x-4=x\), the answer is \(\mathrm{No\:Solution}\), NOT THERE IS NO SOLUTION.

Answer: D

Step-by-step explanation:

-7 isn't greater than -4

The false statements are:

c. 3. z <= 4

d. 4. y > (z-x)

Statement 3 (z <= 4) is false because z is given as 8, which is greater than 4. Therefore, z is not less than or equal to 4.

Statement 4 (y > (z-x)) is false because when we substitute the given values, we get 6 > (8-5), which simplifies to 6 > 3. This is not true since 6 is not greater than 3.

The remaining statements are true:

Statement 1 (x == 5) is true because x is given as 5.

Statement 2 (x < (y + 2)) is true because when we substitute the given values, we get 5 < (6 + 2), which simplifies to 5 < 8.

Statement 5 (z >= (y+x)) is true because when we substitute the given values, we get 8 >= (6+5), which simplifies to 8 >= 11.

Statement 6 (y <= 6) is true because y is given as 6.

Therefore, the false statements are c. 3 and d. 4.

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Therefore, the value of the triple integral is (16/15)π.

The given triple integral is:

∭e (x + y^2 + z^2) dV

where e is bounded by the paraboloid x=4y^2+4z^2 and the plane x=4.

To evaluate this integral, we can use cylindrical coordinates, which are better suited for problems involving circular symmetry. In cylindrical coordinates, the region e is defined by:

0 ≤ ρ ≤ 2

0 ≤ θ ≤ 2π

0 ≤ z ≤ √(1/4)(4-ρ^2/4)

Here, ρ is the distance from the z-axis, θ is the angle in the xy-plane measured counterclockwise from the positive x-axis, and z is the height above the xy-plane.

The integrand (x + y^2 + z^2) can be expressed in cylindrical coordinates as:

x + y^2 + z^2 = ρ^2cos^2θ + ρ^2sin^2θ + z^2 = ρ^2 + z^2

Therefore, the triple integral can be written as:

∭e (x + y^2 + z^2) dV = ∫0^2 ∫0^2π ∫0^√(1/4)(4-ρ^2/4) (ρ^2 + z^2) ρ dz dθ dρ

Integrating with respect to z first, we get:

∫0^√(1/4)(4-ρ^2/4) (ρ^2 + z^2) ρ dz = (1/2)ρ^2√(1/4)(4-ρ^2/4)^3

Substituting this into the double integral and integrating with respect to ρ and θ, we get:

∭e (x + y^2 + z^2) dV = ∫0^2π ∫0^2 (1/2)ρ^2√(1/4)(4-ρ^2/4)^3 dρ dθ

= (16/15)π

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Answer:

After doing the following equation, I've come to the answer of 0.

(9-8)^7-(12-11)^10

1^7 - 1^10

= 0

0 --> ?/?  (There are multiple answers to this question.)

0/1  = 0

0/2 = 0

0/3 = 0

0/4 = 0

Forgive me if the answer is incorrect. I checked the answer with a calculator and it was still 0.

Answer:

\(\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Step-by-step explanation:

\(\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

The solution to the given recurrence relation is (c): ak = (3^k + 1) + 2^k + 1

The solution of the given recurrence relation can be found by substitution. We can substitute the given formula for ak into the equation for a_(k+1) and see if the two are equal. If they are equal, then we have the solution.

Starting with the equation for ak:

a_k = 2a_(k-1) + 3^k

Substituting the formula for ak-1:

a_k = 2(2a_(k-2) + 3^{k-1}) + 3^k

Expanding the right side:

a_k = 4 a_(k-2) + 2 * 3^{k-1} + 3^k

Continuing this process, we can see that the solution is:

a_k = 2^(k) a₀ + (2^{k-1} + 2^{k-2} + ... + 2^1) * 3^{k-1} + 3^k

Since the series 2^k-1 + 2^{k-1} + ... + 2^1 = 2^k - 1, we have:

a_k = 2^(k) a₀ + (2^k - 1) * 3^{k-1} + 3^k

Substituting the initial value a₀ = 5:

a_k = 2^(k) * 5 + (2^k - 1) * 3^{k-1} + 3^k

Simplifying:

a_k = 2^{k} (5 + 3^{k -1}) - 3^{k-1}(1 + 3)

a_k =  2^{k} (5 + 3^{k -1}) - 4* 3^{k-1}

a_k = 5* 2^{k} + 3^{k -1}( 2^{k}  - 4)

So, the solution to the given recurrence relation is (c):

ak = (3^k + 1) + 2^k + 1

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In Fourier series, To show that cos(mx) and cos(nx) for m ≠ n are orthogonal in [-π, π], we need to prove that∫-ππ cos(mx)cos(nx)dx = 0 if m ≠ n

Firstly, let's use the identity cos(A)cos(B) = (1/2) [cos(A + B) + cos(A - B)]So the above equation can be written as∫-ππ (1/2) [cos(m + n)x + cos(m - n)x] dx = 0Now, the integral of cos(m + n)x and cos(m - n)x over [-π, π] is 0 because they are odd functions. So we are left with∫-ππ cos(mx)cos(nx) dx = 0 which is what we needed to prove.

So, the functions cos(mx) and cos(nx) for m ≠ n are orthogonal in [-π,π].2. To expand the function f(x) = { 0 π < x < 0 π- x 0 < x < π into Fourier series, we need to compute the Fourier coefficients which are given by the formula an = (2/π) ∫f(x)sin(nx)dx and bn = (2/π) ∫f(x)cos(nx)dx Note that a0 = (1/π) ∫f(x)dx= (1/π) [∫0π (π - x) dx] = π/2

Computing an, we have an = (2/π) ∫π0 (π - x) sin(nx) dx= 2 ∫π0 π sin(nx) dx - 2 ∫π0 x sin(nx) dx= 2 [(1/n) cos(nπ) - (1/n) cos(0)] - 2 [(1/n²) sin(nπ) - (1/n²) sin(0)]= 2 (-1)^n / n²So the Fourier series becomes f(x) = π/2 + ∑n=1∞ 2 (-1)^n / n² sin(nx)

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Answer:

C = 5Q

Step-by-step explanation:

C = Length of Cloth in Meters (C)

Q = Number of Quilts Made (Q)

C = 5Q

Change C for the numbers under (Length of Cloth in Meters (C))
Nad change Q for the numbers under (Number of Quilts Made (Q))

So the new equations would be:

0 = 5(0) --------->  0 = 0

5 = 5(1) ---------> 5 = 5

10 = 5(2) ---------> 10 = 10

15 = 5(3) ---------> 15 = 15

20 = 5(4) ---------> 20 = 20

25 = 5(5) ---------> 25 = 25

So the only option that amkes sense is (C = 5Q)

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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1 goes in the green space

70 goes in the gray space

==============================================

Explanation:

There are 5 gold and 350 total. That forms the fraction 5/350 which fully reduces to 1/70 after you divide both parts by the GCF = 5

A = 5, B = 350

The fraction 1/70 can be thought of like saying "There's 1 gold coins in 70 coins total" or "there's 1 gold coin for every 70 coins".

Then we could scale up like so

I see a fraction. Don't you. Here it is 17/20. Now, let's divide 17 by 20 to get a decimal number, which is 0.85. Next, we multiply 0.85 by 100 to get the percent because that is what the question desires for us to express our answer. As a result, we get 85%, and Antonio made 85% of his free throws. By the way, I hope my response helps you.  

Step-by-step explanation:

1 way is to do 17/ 20 using long division...

    0. 85

20⟌1700    ( I tried my best)

   - 160

      100

So the answer would be 85%

Another way to do it is by bringing the denominator to 100

Since 20 is 1/5 of 100, you would have to multiply the numerator and denominator by 5

17/ 20 = 17*5/ 20*5 = 85/ 100

And you get 85%

Hope this helps!!!

Step-by-step explanation:

in option c

rectangle have four right angled and two pair of parallel side

in option b

only one pair of parallel side

Answer:

-2 is the slope

Step-by-step explanation:

use the formula y2-y1/x2-x1

And then solve it.

y2 is -8

y1 is 6

x2 is 3

x1 is -4

now -8-6=-14

3+4=7

-14/7 is -2

So -2 is the slope

Answer:

-2

Step-by-step explanation:

= -8-6/3+4

= -14/7

= -2

To find out what percent 567 is of 448, we can use the following formula:

What does math mean by percent?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

percent = (part / whole) x 100

where "part" is the value we are trying to find the percentage of (in this case, 567), "whole" is the total value (in this case, 448), and "percent" is the final answer.

So, we can plug in the values and get:

percent = (567 / 448) x 100

To get the percentage we need to multiply the fraction by 100

percent = 126.58%

So 567 is 126.58% of 448.

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No, rectangle DABC is not the result of a dilation of rectangle HEFG with a center of dilation at the origin.

Dilation is a geometrical transformation that changes the size of a shape or figure. It is one of the four basic transformations of geometry alongside translation, rotation, and reflection. Dilation involves resizing a shape by a scale factor and keeping its overall shape intact. The scale factor is the ratio of the size of the image to the size of the original figure.

Dilation involves a scaling of a shape, where each point on the shape is moved away from or closer to the center of dilation, proportional to its distance from the center. In this case, the angles of rectangle DABC are different from the angles of rectangle HEFG, so it is not the result of a dilation. The angles of rectangle HEFG are ∠2, ∠33, ∠EDC, whereas the angles of rectangle DABC are ∠ADB, ∠BDC, and ∠CDB.

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The statistical method that would be best to use in this situation is b) Regression analysis.

Regression analysis is a statistical technique used to examine the relationship between a dependent variable (in this case, the number of students registering each semester) and one or more independent variables (such as time, semester, or any other relevant factors). By analyzing past data on the number of students registering each semester, regression analysis can help identify trends, patterns, and the average number of students registering.

Using regression analysis, the university can estimate the average number of students registering each semester based on historical data and use this information to plan how many classes to run in the upcoming semester. It allows for a quantitative analysis and prediction based on the relationship between variables, making it a suitable choice for estimating the average number of students in this scenario.

Hence the answer is Regression analysis.

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Answer:

4miles, because it would just be 12 divided by 3.

Step-by-step explanation:

The type of set that allows you to position rollers diagonally and set from multiple points of origin is an oblong set.

An oblong set is a type of parallel set consisting of two parallel rectangular bars or blocks, with rollers positioned diagonally between them. The oblong shape of the set allows for the rollers to be positioned at a diagonal angle, which can be useful when setting up workpieces that need to be adjusted at an angle or from multiple points of origin.

In contrast, a half oval set and a half circle set are both types of circular sets that consist of rollers positioned in a semi-circular shape. These types of sets are useful for supporting workpieces that have a curved or circular shape, but they do not provide the flexibility to position rollers at a diagonal angle or from multiple points of origin.

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1.The total cost would be:50 cash registers x 450 AED per cash register = 22,500 AED

2.the cost of one new cash register at the end of 8 years would be approximately 661.39 AED.

3. the value of one old cash register after 8 years would be approximately 222.19 AED.

4.It is not possible to determine whether the money from selling the old cash registers is enough to pay for the new ones without knowing the selling price of the old cash registers.

5.It would take approximately 19 years for the value of the cash registers to reach 95 AED.

1. The company needs to buy at least 50 cash registers, each costing 450 AED. Therefore, the total cost would be:

50 cash registers x 450 AED per cash register = 22,500 AED

 2. The continuous compounding formula is A = \(Pe^(^r^t^)\), where A is the resulting amount, P is the initial amount, e is Euler's number, r is the annual interest rate, and t is the time in years. We can apply this formula here by setting P = 450 AED, r = 6%, t = 8 years and solving for A:

A = 450*e^(0.06*8) = 661.39 AED (rounded to two decimal places)

 3. The value of each old cash register decreases at a rate of 7.5% per year. We can use the formula for exponential decay, P = , where P is the resulting amount, P is the initial amount, e is Euler's number, r is the rate of change, and t is the time in years. Setting P to 450 AED, r to -7.5%, and t to 8 years, we can solve for the resulting value:

P = 450*e^(-0.075*8) = 222.19 AED (rounded to two decimal places)

 4. If the selling price is greater than the value of the old cash registers after 8 years (i.e., 222.19 AED), then the company would make a profit on each old cash register sold to help pay for the new ones; if the selling price is less than 222.19 AED, then the company would incur a loss on each old cash register sold.

 5. To find when the value of the cash register will be approximately 95 AED, we can use the formula from part (3).

95 = 450*e^(-0.075t)

Dividing both sides by 450 and taking the natural logarithm of both sides, we get:

ln(95/450) = -0.075t

Solving for t, we get:

t = -(1/0.075) * ln(95/450) ≈ 19.01 years

With a lifespan of only 8 years, it is not a realistic scenario for the cash registers to depreciate to such a low value. Therefore, it is important for the company to properly maintain and replace the cash registers on a regular cycle to ensure that their value remains close to the original purchase price.

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Marko has made profit of 17 dollars.

Given that, Marko earns $15 for each lawn he mows, $10 for each yard he weeds, and $5 for each yard he rakes.

Total amount spent = $(3+36+14)

= $53

Total money earned = $(15×3+5×5)

= $(45+25)

= $70

Profit = Total money earned-Total amount spent

= 70-53

= $17

Therefore, Marko has made profit of 17 dollars.

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