If point N, with coordinates (1, 4) is translated to point N', with coordinates (-1,-1).
which translation did N undergo?
one unit left and three units down
two units left and three units down
two units left and five units down
one unit left and five units down

Answers

Answer 1
it should be 2 units left and 4 units up

Related Questions

Select the true statement.

Select the true statement.

Answers

The true answer is D.

1 1/2 yards = 54 inches.

Answer: D) 54 inches = 1 1/2 yards

explanation: 1 1/2 yards = 54 inches.

Traveling
All changes saved
8. Morgan is traveling from Dallas, Texas to San Francisco, California. She has the choice
of two airlines. She will check two bags, wants Wi-Fi access, and does not want a meal
on the plane. She does not mind a layover if it will get her a better deal. Which of the
following would be the best deal, and how much would she save?
> Lesson 82
> Lesson 83

Answers

Answer:

24

Step-by-step explanation:

i did it

This is 4th grade work what is the answer for my brother

 This is 4th grade work what is the answer for my brother

Answers

Answer:

1 unit is 2 inches 3 units are 6 inches

Answer:

12 inches

Step-by-step explanation:

width = 6 in.

length = 2 in.

6 x 2 = 12

Can i have brainliest plz i was the first one.

Is this correct or not?
If not please provide correct answer

Is this correct or not?If not please provide correct answer

Answers

Answer:

It is correct please I do not want yo sound rude can you give me brainliest answer.

Answer:

correct steps

Step-by-step explanation:

if asked to find angles in terms of the ratios, then don't forget to shift sin / cos / tan across the equal sign and change it to arc sin / cos / tan.

Please anyone that can help me

Please anyone that can help me

Answers

Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

Pre-Solving

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

Solving

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

A rectangular coil of wire with an area of 0.218 m2 is situated in a constant magnetic field whose magnitude is 0.450 T. Suppose the normal to the surface of the coil is parallel to the direction of the magnetic field (this means the magnetic field is also normal, or perpendicular, to the surface of the coil). What is the flux through the surface?
If the area of the coil is reduced to 0.150 m2 while keeping the orientation of the coil the same, what is the new flux through the surface?
Go back to a coil with an area of 0.218 m2, but instead rotate the coil such that the normal to the surface of the coil is perpendicular to the direction of the magnetic field (this means the magnetic field is parallel to the surface of the coil). What is the flux through the surface?

Answers

1) The flux through the surface is given by the product of the magnetic field and the surface area is 0.0981 Wb

2) If the area of the coil is reduced to 0.150 m2 while keeping the orientation of the coil the same, then the new flux through the surface is 0.0675 Wb

3) The flux through the surface is zero, and no magnetic field passes through the surface.

A magnetic field is a force field that surrounds a magnet or a current-carrying wire.

In the first scenario, we have a rectangular coil of wire with an area of 0.218 m2 situated in a constant magnetic field of 0.450 T.

Therefore, the flux through the surface is given by the product of the magnetic field and the surface area, which is:

Flux = magnetic field x surface area

= 0.450 T x 0.218 m2

= 0.0981 Wb

In the second scenario, the area of the coil is reduced to 0.150 m2 while keeping the orientation of the coil the same. The flux through the surface is given by:

Flux = magnetic field x surface area

= 0.450 T x 0.150 m2

= 0.0675 Wb

Therefore, by reducing the surface area, the flux through the surface also reduces.

In the third scenario, we go back to a coil with an area of 0.218 m2, but instead, we rotate the coil such that the normal to the surface of the coil is perpendicular to the direction of the magnetic field. In other words, the angle between the magnetic field and the surface is 90 degrees. In this case, the flux through the surface is given by:

Flux = magnetic field x surface area x cos(theta)

= 0.450 T x 0.218 m2 x cos(90)

= 0

Since the angle between the magnetic field and the surface is 90 degrees, the cosine of 90 degrees is zero.

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Find the quotient. 1 5 – 2. + 3 1 55+3= 2 (Type a whole number, fraction, or mixed number.)

Answers

we have

\(5\frac{1}{2}\colon3\)

Convert mixed number to an improper fraction

5 1/2=5+1/2=11/2

substitute

(11/2):3=11/(3*2)=11/6

convert to mixed number

11/6=6/6+5/6=1+5/6=1 5/6

answer is

11/6 or 1 5/6

Calculate each compound event probability: a. X ≤ 15, n = 20, π = .70 (Round your answer to 4 decimal places.) b. X > 8, n = 11, π = .65 (Round your answer to 4 decimal places.) c. X ≤ 1, n = 13, π = .40 (Round your answer to 4 decimal places.)

Answers

For X ≤ 15, n = 20, π = .70 ; compound event probability is approximately 0.0008 .

For X > 8, n = 11, π = .65 ; compound event probability is  approximately 0.9198.

For X ≤ 1, n = 13, π = .40 ; compound event probability is  approximately 0.6646 .

a. To calculate the probability of the event X ≤ 15, n = 20, π = .70, we will use the binomial distribution formula:

P(X ≤ 15)

=  ∑_(k=0)¹⁵〖(20Ck)(0.70)^k (0.30)^(20-k) 〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.0008 (rounded to 4 decimal places).

b. To calculate the probability of the event X > 8, n = 11, π = .65, we will first find the probability of X ≤ 8, and then subtract this value from 1 to find the complement probability:

P(X > 8) = 1 - P(X ≤ 8)

= 1 - ∑_(k=0)⁸〖(11Ck)(0.65)^k (0.35)^(11-k)〗

Using a binomial distribution calculator, we can find the probability of X ≤ 8 to be approximately 0.0802.

Therefore, the probability of X > 8 is approximately 0.9198 (rounded to 4 decimal places).

c. To calculate the probability of the event X ≤ 1, n = 13, π = .40, we will use the binomial distribution formula:

P(X ≤ 1)

= ∑_(k=0)¹〖(13Ck)(0.40)^k (0.60)^(13-k)〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.6646 (rounded to 4 decimal places).

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need help on my final, dealing with parent functions

need help on my final, dealing with parent functions

Answers

Answer:

x = 3 squared and it is the righr answer

Answer:

pretty hard to read. Sorry

Step-by-step explanation:

Use the following function to complete this question:
f(x)=(x-1)^3+5

Graph the function and fill in the blanks.
If the transformation listed is not applicable write none.
Fill in the blanks in the form:
4 left
5 up
Write infinity in the form: inf
Horizontal shift:
Vertical shift:
Vertical stretch factor:
Vertical compression factor:
Axis of reflection:
Domain:
Range:
Inflection Point:
Pic is attached below​

Use the following function to complete this question:f(x)=(x-1)^3+5 Graph the function and fill in the

Answers

The following is deduced from the equation f(x)=(x - 1)^3 + 5

Horizontal shift: 1 left

Vertical shift: 5 down

Vertical stretch factor: 1

Vertical compression factor: 1

Axis of reflection: -x + 6

Domain: all real numbers

Range: all real numbers

Inflection Point: (1, 5)

What is vertical stretch factor?

The vertical stretch factor is a term used in mathematics to describe the transformation that changes the height of a graph while leaving the horizontal axis unchanged. In other words, it's a factor by which the y-values of a function are multiplied to produce a new, stretched or compressed version of the original graph.

The stretch factor is usually represented by the symbol "k". For example, if the equation of a function is y = f(x), then the equation of its vertically stretched image would be y = k * f(x). A positive value of k stretches the graph upward, while a negative value of k compresses the graph downward. If k > 1, the graph is stretched vertically; if 0 < k < 1, the graph is compressed vertically; if k = 1, the graph remains unchanged.

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if you could help that would be greatly appreciated

if you could help that would be greatly appreciated

Answers

Answer: search

Step-by-step explanation: look up the question on your browser and the answer will pop up

A manufacturer of floor wax has developed two new brands, A and B, which she wishes to subject to homeowners' evaluation to determine which of the two is superior. Both waxes, A and B, are applied to floor surfaces in each of 15 homes. Assume that there is actually no difference in the quality of the brands.

Required:
What is the probability that ten or more homeowners would state a preference for either brand A or brand B?

Answers

Answer:

Probability that ten or more homeowners would state a preference for either brand A or brand B = 0.302

Step-by-step explanation:

Given - A manufacturer of floor wax has developed two new brands, A and B, which she wishes to subject to homeowners’ evaluation to determine which of the two is superior. Both waxes, A and B, are applied to floor surfaces in each of 15 homes. Assume that there is actually no difference in the quality of the brands.

To find - What is the probability that ten or more homeowners would state a preference for either brand A or brand B?

Proof -

Given that,

There is actually no difference in the quality of the brands.

⇒P(A) = \(\frac{1}{2}\) = 0.5

  P(B) = \(\frac{1}{2}\) = 0.5

Now,

We know that,

Binomial distribution is equals to

B(n, x) = ⁿCₓ (p)ˣ (1 - p)ⁿ⁻ˣ

Now,

P(X(A) ≥ 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

               = ¹⁵C₁₀ (0.5)¹⁰ (0.5)⁵ + ¹⁵C₁₁ (0.5)¹¹ (0.5)⁴ + ¹⁵C₁₂ (0.5)¹² (0.5)³ + ¹⁵C₁₃ (0.5)¹³ (0.5)² + ¹⁵C₁₄ (0.5)¹⁴ (0.5)¹ + ¹⁵C₁₅ (0.5)¹⁵ (0.5)⁰

                =  0.092 + 0.042 + 0.014 + 0.003 + 0.0005 + 0.00005

                = 0.151

⇒P(X(A) ≥ 10) = 0.151

As given Quality of both brands are same ,

So, the probability of both the brands are equal

⇒P(X(B) ≥ 10) = 0.151

Now,

Probability that ten or more homeowners would state a preference for either brand A or brand B = P(X(A) ≥ 10) + P(X(A) ≥ 10)

                                           = 0.151 + 0.151

                                           = 0.302

∴ we get

Probability that ten or more homeowners would state a preference for either brand A or brand B = 0.302

One line passes through points (2, 11) and (−1, 2);
another line passes through points (0, −4) and (−2, −10).

Answers

Answer:

attracted more to oxygen's nucleus. This makes the hydrogen ends of the

Step-by-step explanation:

Answer:

its parallel

Step-by-step explanation:

sorry the other person did not help you. but i do rsm and i got this question right.

Geometry Section 58C/School Year/
For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A
Part B, and Part C
Part A: How many triangles can be formed if the measurements of a triangle are a 27,6-15, A-557
Part B: Explain how to determine the answer to Part A
Part C: Find all possible solutions for this triangle.
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Geometry Section 58C/School Year/For the three-part question that follows, provide your answer to each

Answers

1. Triangle inequality theorem.

3. The missing lengths and angles are:

<B = 27.07, <C = 98 and c = 32.64.

1. According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. To determine the number of triangles that can be formed, we can use the given measurements and check if the triangle inequality theorem is satisfied.

3. We have,

a = 27, b = 15, and A = 55°,

Using the Law of Sines,

sin A/ a = sin B/ b

sin 55 /27 = sin B / 15

0.81915204428 / 27 = sin B /15

0.4550844690444 = sin B

<B = 27.07

Now, <C = 180 - <A - <B = 180 - 55 - 27.07 = 98

Now, Using the Law of Sines

sin A/ a = sin C/ C

0.81915204428 / 27 = sin 98 / c

0.030338964602963 = 0.99026807 /c

c = 32.64

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What is the length of line segment KJ?

What is the length of line segment KJ?

Answers

Answer:

\(3 \sqrt{3} \)

Calculate the mean and the standard deviation of the sampling distribution of possible sample proportions for each combination of sample size (n) and population proportion (p).

Answers

Here is the full question.

Calculate the mean and the standard deviation of the sampling distribution of possible sample proportions for each combination of sample size (n) and population proportion (p).

a.) n = 64, p = 0.8

b.) n = 256, p = 0.8

Answer:

a.) Mean = 0.8

   Standard deviation = 0.05

b.)  Mean = 0.8

     Standard deviation = 0.025

Step-by-step explanation:

From the given information:

a.)

The population parameter (p) is the mean of the sampling distribution for the sample proportion.

Thus; The  Mean = 0.8

The standard deviation of the  distribution can be calculated as follows:

Let's first represent the standard deviation with Sd(\(\hat p\))

Then:

\(sd(\hat p) = \sqrt{\dfrac{p*(1-p)}{n} }\)

where;

p = 0.8

n = 64

Then:

\(sd(\hat p) = \sqrt{\dfrac{0.8*(1-0.8)}{64} }\)

\(sd(\hat p) = \sqrt{\dfrac{0.8*(0.2)}{64} }\)

\(sd(\hat p) = \sqrt{\dfrac{0.16}{64} }\)

\(sd(\hat p) = \sqrt{0.0025}\)

\(\mathbf{sd(\hat p) =0.05}\)

b.)

The population parameter (p) is the mean of the sampling distribution for the sample proportion.

Thus; The  Mean = 0.8

The standard deviation of the  distribution can be calculated as follows:

Let's first represent the standard deviation with Sd(\(\hat p\))

Then:

\(sd(\hat p) = \sqrt{\dfrac{p*(1-p)}{n} }\)

where;

p = 0.8

n = 256

Then:

\(sd(\hat p) = \sqrt{\dfrac{0.8*(1-0.8)}{256} }\)

\(sd(\hat p) = \sqrt{\dfrac{0.8*(0.2)}{256} }\)

\(sd(\hat p) = \sqrt{\dfrac{0.16}{256} }\)

\(sd(\hat p) = \sqrt{6.25 \times 10^{-4}}\)

\(\mathbf{sd(\hat p) =0.025}\)

The table shows the age of a painting (x) in years, and its estimated dollar value (y).

A 4-column table with 6 rows. Column 1 is labeled x with entries 50, 54, 62, 65, 68, sigma-summation x = 299. Column 2 is labeled y with entries 1,200, 1,500, 2,400, 3,200, 4,100, sigma-summation y = 12,400. Column 3 is labeled x squared with entries 2,500, 2,916, 3,844, 4,225, 4,624, sigma-summation x squared = 18,109. Column 4 is labeled x y with entries 60,000, 81,000, 148,800, 208,000, 278,800, sigma-summation x y = 776,600.

Which regression equation correctly models the data?

y = 41.47x + 0.09
y = 41.47x + 1,279.93
y = 153.32x – 6,688.54
y = 153.32x – 6,325.76

Answers

Regression equation correctly models the data is: y = -43.98x + 1,279.93

To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.

Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.

The slope (m) can be calculated using the formula:

\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)

Plugging in the values from the table:

m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)

m = (776,600 - 3,708,800 / 6(18,109) - 89,401)

m = (-2,932,200 / 66,654)

m ≈ -43.98

The y-intercept (b) can be calculated using the formula:

b = (Σy - m(Σx)) / n

Plugging in the values from the table:

b = (12,400 - (-43.98)(299)) / 6

b ≈ 1,279.93

The correct regression equation that models the data is:

y = -43.98x + 1,279.93

Out of the given options, the correct regression equation is:

y = -43.98x + 1,279.93

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What percentage of growth is needed annually to reach 400,000 in 3 years if today I have 200,000

Answers

Answer:

approx 26%

Step-by-step explanation:

you try find the multiplier

200000 * 1. ???? ^3= 400000

rearrange equation

\(\sqrt[3]{\frac{400000}{200000} }\)       =   multiplier

1.25992105

subract one

0.25992105

multiply by 100 to get percentage

25.9%

rounded to whole number = 26%

A baby girl weighs 7.16 pounds at birth. By the time she is 1 year of age, her weight has tripled.
How much does she weigh at her 1 year checkup?

Help pleaseee

Answers

7.16 times 2 is 14.32 therefore it is 14.32

Which graph shows the new image of the rectangle after a translation of two units to the left?

Which graph shows the new image of the rectangle after a translation of two units to the left?
Which graph shows the new image of the rectangle after a translation of two units to the left?
Which graph shows the new image of the rectangle after a translation of two units to the left?
Which graph shows the new image of the rectangle after a translation of two units to the left?
Which graph shows the new image of the rectangle after a translation of two units to the left?

Answers

The new image of the rectangle after a translation of two units to the left is of option D

How to draw a shifted figure if the shifts are provided?

Suppose the graph is drawn on the coordinate plane.

Let the shifting be (x,y) → (x+a, y+b)

Then, add 'a' to all x coordinates of the graph's points. Add 'b' to all y coordinates of the graph's points.

The resultant set of new points will be plotted.

Given;

A rectangle area on graph with coordinates (1,0), (6,0),(6,2), (1,2)

Now after the shift of 2 unit left, the x coordinates will be affected;

=(1-2,0), (6-2,0),(6-2,2), (1-2,2)

=(-1,0), (4,0),(4,2), (-1,2)

Therefore, the coordinates of shifted graph will be (-1,0), (4,0),(4,2), (-1,2)

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Graph makes no sense to me​

Graph makes no sense to me

Answers

Answer:

(a) 0
(b) 0
(c) 1
The function is not continous at x = 9

Step-by-step explanation:

To the left and right of the point x = 9, the graph would seem to continue at  f(x) = 0, however on the exact point x = 9 there is a hole in the graph allowing it to be equal to 1. Due to the hole in the graph, it is not continuous

Apologies if this is wrong its been a bit since I did calculus

What is the range of function g if g(x)=-2f(x)+1

Answers

The range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

The range of function g depends on the range of the function f.

Let's start by assuming that we know the range of f.

If the range of f is Rf, then the range of -2f is the set {-2y | y ∈ Rf}, which is just the set of all numbers that can be obtained by multiplying an element of Rf by -2.

Finally, we add 1 to each of these values to get the range of g. Therefore, the range of g is:

Rg = {1 - 2y | y ∈ Rf}

In other words, the range of g is obtained by taking the range of f, multiplying each element by -2, and adding 1 to each result.

If we don't know the range of f, we can still say something about the range of g. Specifically, we know that g(x) can never be greater than 1 (since the largest value that -2f(x) can take is 0, and adding 1 to 0 gives us 1), and g(x) can never be less than 1 - 2M, where M is the largest possible value that f(x) can take on. In other words, the range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

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Let be independent random variables with the common distribution function F and suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N (b) Find P(M1} (d) Use (b) and (c) to rederive the probability you found in (a).

Answers

suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N is  nλe^(-nλx)

Given fx (x) = λe^λx

Fx (x) = 1 – e^-λx      x…0

To find distribution of Min (X1,….Xn)

By applying the equation

fx1 (x) = [n! / (n – j)! (j – 1)!][F(x)]^j-1[1-F(x)]^n-j f(x)

For minimum j = 1

[Min (X1,…Xn)] = [n!/(n-1)!0!][F(x)]^0[1-(1-e^-λx)]^n-1λe^-λx

= ne^[(n-1) λx] λe^(λx)

= nλe^(-λx[1+n-1])

= nλe^(-nλx)

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5. Determine the value of t4 in an arithmetic sequence given that t₁ = 11 and S9 = 243.

5. Determine the value of t4 in an arithmetic sequence given that t = 11 and S9 = 243.

Answers

The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).

We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.

From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:

243 = (9/2)(2(11) + (9-1)d)

243 = 9(22 + 8d)

243 = 198 + 72d

45 = 72d

d = 45/72 = 5/8

Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:

tₙ = a + (n-1)d

t₄ = 11 + (4-1)(5/8)

t₄ = 11 + 3(5/8)

t₄ = 11 + 15/8

t₄ = 88/8 + 15/8

t₄ = 103/8

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( 3/4 ÷ 3/100 −23 1/2 )÷1 1/2 · 2/3 +1 1/6
All of the (/) are fractions. Sorry if it's unclear.

Answers

Answer:

Simplify:  = −7333 4400 (Decimal: -1.666591)

Answer: −7333/  4400

Step-by-step explanation:

Steps below

1: 343100−2312112(2)3+116

2: 14100−2312112(2)3+116

3: 1400−2312112(2)3+116

4: −46199400112(2)3+116

Answers:

Simplify:  = −7333 4400 (Decimal: -1.666591)

Answer: −7333/  4400

Hope this helps.

Answer:

The answer is 11/6

determine all combinations of lengths that could be used to make a traingle 1,3,6,8

Answers

Answer:

3, 6, and 8 for a triangle

Step-by-step explanation:

So, let's start with what we know

The sum of the 2 lesser lengths of a triangle must be greater than the greatest length of a triangle. Otherwise, it cannot be a triangle

a + b > c

Note: variables a and b are the lesser lengths of a triangle, and c is the greatest length.

We are to list out the possible combinations of triangles here with lengths  1, 3, 6, and 8.

So, with the formula above, we will get the combination of

3,6,8

Any other combinations of triangle lengths will not work

If you have any questions, please let me know in the comments section of this answer! If you could mark this answer as the brainliest, I would greatly appreciate it! :D

Tate is paid $17.35 per hour with time and a half overtime. What will his gross pay period in which he worked 35 hours one week and 44 hours next week for a total 79 hours?

Answers

Answer:

The new rule has a higher salary level for exemption from overtime, at $684 a week. This means that lower-pay exempt employees may qualify for overtime.

Step-by-step explanation: this is your answer plz rate e the most brainlest

need help on This question I’ll give you brainliest

need help on This question Ill give you brainliest

Answers

The area swept by the blade in model 3 is 66932 square feet.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The word "area" refers to a free space. A shape's length and width are used to calculate its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc. But a shape's area is a two-dimensional measurement.

The blade length for model 3 is r = 146.

The area of the circle is given by:

A = pi(r)²

A= (3.14) (146)²

A = 66932

Hence, the area swept by the blade in model 3 is 66932 square feet.

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Find the volume of a cone with a radius of 4 ½ m. and a height of 10 m.

Answers

The volume of the cone is approximately 211.06 cubic meters.

Why is that?

Well, the formula for the volume of a cone is:

V = (1/3)πr^2h


where:

V is the volume of the coneπ is pi (approximately 3.14159)r is the radius of the base of the coneh is the height of the cone


Substituting the given values, we get:V = (1/3)π(4.5m)^2(10m)

V = (1/3)π(20.25m^2)(10m)

V = (1/3)π(202.5m^3)

V = 67.5π


Using a calculator, we get:

V ≈ 211.06 cubic meters


Therefore, the volume of the cone is approximately 211.06 cubic meters.

Gretta is saving for retirement. She deposits $125 each month at 6% annual interest for 35 years. According to her calculations, at the end of 35 years, she should have $178,088.79 in her account. How much of this did Gretta contribute and how much of this is interest?

Answers

Answer:

Gretta's Contribution = $52,500

Interest = $125,588.79

Step-by-step explanation:

Gretta contributes $125 each month, for 35 years. Therefore, to find the amount she contributed, we multiply those pieces together (12 months in each year).

125 x 12 x 35 = $52,500

Therefore, over the 35 years, Gretta contributed $52,500.

If there was $178,088.79 in her account, and she contributed $52,500, then the rest is interest.

$178,088.79 − $52,500 = $125,588.79

There was $125,588.79 in interest earned on Gretta's account.

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