if 5x^2 + 7x = 6, which statement is correct?
A) x = 2 or x = 3/5
x = -2 or x = 3/5
X=2 or X= -3/5
x=-2 or X =-3/5

i am pretty sure you add up all of them

The percent change in the numerator for the cash coverage ratio, considering the changes in EBIT and depreciation, is 12.5%. Meanwhile, the percent change in the denominator, based on the interest expense, is 33.33%.

The cash coverage ratio is a measure of a company's ability to pay off its obligations and is calculated by adding depreciation and EBIT and then dividing by the interest expense. For this question, we are looking at the percent change in the numerator, which is EBIT + depreciation, and the denominator, which is the interest expense. With EBIT going from $30m to $33m, depreciation going from $10m to $12m, and interest expense going from $6m to $8m we can calculate as follows.

The original numerator value was $40m (EBIT of $30m + depreciation of $10m) and the new numerator is $45m (EBIT of $33m + depreciation of $12m). So, the percent change in the numerator of the cash coverage ratio is ((45-40)/40)*100 = 12.5%. The original denominator was $6m and the new denominator is $8m. Thus, the percent change in the denominator of the cash coverage ratio is ((8-6)/6)*100 = 33.33%.

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Answer:

  D.  f(q) = 2q + 3

Step-by-step explanation:

Choices B and C are eliminated right away because there is no "q" in the definition, just "s". If the function is to be a function of "q", then "q" is expected to appear in the definition.

__

The two variables in the given equation are "s" and "q". If "q" is designated as the independent variable, then the dependent variable is "s". The equation must be solved for "s":

  6q = 3s - 9

We observe that the coefficient of "s" is 3, and that all numbers are multiples of 3, so we can divide by 3 to simplify this a bit:

  2q = s - 3

Since we want an expression for s alone, we can add 3 to get ...

  2q +3 = s

Now, we can write ...

  s = f(q) = 2q +3

Answer:D

Step-by-step explanation:

Answer:

The correct answer is option C.

Sin 45 degrees = square root of 2 divided by 2, cos 45 degrees = square root of 2 divided by 2, tan 45 degrees = 1

Step-by-step explanation:

The sin cos tan table used to calculate values of the ratios for different angles can be used for the values.

The table is easily available on the internet.

WE can use a a right-angles isosceles triangle to find the exact values for the angle 45.

The equal sides have length 1. So the thirs side using the pythagoras theorem will be √2.

So

Sin 45 = √2/2

Cos 45 = √2/2

and

Tan 45 = 1

So the correct option is C.

The sine, cosine, and tangent of 45 degrees can be found using the values of the adjacent side, opposite side, and hypotenuse of a right triangle. The sine of 45 degrees is (√2) / 2, the cosine is (√2) / 2, and the tangent is 1.

The sine, cosine, and tangent of 45 degrees can be found using the values of the adjacent side, opposite side, and hypotenuse of a right triangle. In this case, for a 45-degree angle, the adjacent side and opposite side are equal, so we can use the Pythagorean theorem to find the value of the hypotenuse. Let's denote the length of the adjacent and opposite sides as x.

Sine (sin) 45 degrees: sin 45 degrees = opposite side / hypotenuse = x / √2x = 1 / √2 = (√2) / 2

Cosine (cos) 45 degrees: cos 45 degrees = adjacent side / hypotenuse = x / √2x = 1 / √2 = (√2) / 2

Tangent (tan) 45 degrees: tan 45 degrees = opposite side / adjacent side = x / x = 1

The total ribbon is 7 whole 7/12 yards if the Traci bought 1 1/4 yards of yellow ribbon, 2 5/6 yards of pink ribbon, and 3 1/2 yards of purple ribbon.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

Traci bought 1 1/4 yards of yellow ribbon, 2 5/6 yards of pink ribbon, and 3 1/2 yards of purple ribbon.

The total ribbon:

[tex]= \rm 1\dfrac{1}{4} +2\dfrac{5}{6} +3\dfrac{1}{2} \\\\=\rm \dfrac{5}{4}+\dfrac{17}{6}+\dfrac{7}{2}\\\\=\dfrac{15+34+42}{12}\\=\dfrac{91}{12}\\\\=7\dfrac{7}{12} \ yards[/tex]

Thus, the total ribbon is 7 whole 7/12 yards if the Traci bought 1 1/4 yards of yellow ribbon, 2 5/6 yards of pink ribbon, and 3 1/2 yards of purple ribbon

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Answer:

14.7

Step-by-step explanation:

a^2+b^2=c^2

15^2+b^2=21^2

225+b^2=441

subtract 441-225=216

square root of 216 = 14.6969384567

= 14.7

Answer:

x = 6[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

x² + 15² = 21²

x² + 225 = 441 ( subtract 225 from both sides )

x² = 216 ( take the square root of both sides )

x = [tex]\sqrt{216}[/tex] = [tex]\sqrt{36(6)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{6}[/tex] = 6[tex]\sqrt{6}[/tex]

a.

[tex]z=-\dfrac{5\sqrt3}2+\dfrac52i=5\left(-\dfrac{\sqrt3}2+\dfrac12i\right)=5e^{i5\pi/6}[/tex]

[tex]w=1+\sqrt3\,i=2\left(\dfrac12+\dfrac{\sqrt3}2i\right)=2e^{i\pi/3}[/tex]

b. Not exactly sure how DeMoivre's theorem is relevant, since it has to do with taking powers of complex numbers... At any rate, multiplying [tex]z[/tex] and [tex]w[/tex] is as simple as multiplying the moduli and adding the arguments:

[tex]zw=5\cdot2e^{i(5\pi/6+\pi/3)}=10e^{i7\pi/6}[/tex]

c. Similar to (b), except now you divide the moduli and subtract the arguments:

[tex]\dfrac zw=\dfrac52e^{i(5\pi/6-\pi/3)}=\dfrac52e^{i\pi/2}[/tex]

Answer:

  the origin, (0, 0)

Step-by-step explanation:

The coordinates of A' are 1/2 those of A, meaning each has been multiplied by the scale factor 1/2. When the dilated points are all the original points multiplied by the scale factor, the center of dilation is the origin.

_____

For center of dilation Q, the image of a point A after dilation by a factor of k is ...

  A' = kA + (k-1)Q

Then for points A, A', and dilation factor k, the center of dilation can be found to be ...

  (A' -kA)/(k-1) = Q

Here, that is ...

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

  Q = (0, 0)

A bc the Y numbers increase by 17 every time X increases by 1

The common difference of the associated arithmetic sequence is:

          Option: A

                  17

We know that the sequence is said to be arithmetic if each of the sequence is differ by the preceding term by a fix constant which is known as a common difference.

i.e. d is called a common difference of the sequence if [tex]a_n\ and\ a_{n+1}[/tex]

are the nth and (n+1)th term of the sequence then,

[tex]a_{n+1}-a_n=d[/tex]

Here we have a  table of values as:

X     Y              d

1      4        

2    21        21-4=17

3    38       38-21=17  

4    55        55-38=17

5    72        72-55=17

Hence, we get that the common difference is: 17

Final answer:

To find the standard deviation for the number of defects per batch, use the formula for the standard deviation of a binomial distribution.

Explanation:

To find the standard deviation for the number of defects per batch, we need to use the formula for the standard deviation of a binomial distribution.

Given that the company manufactures televisions in batches of 25 and there is a 1% rate of defects, we can calculate the mean and variance of the number of defects per batch.

The mean (μ) of a binomial distribution is given by μ = np, where n is the number of trials (batch size) and p is the probability of success (defect rate). In this case, μ = 25 * 0.01 = 0.25. The variance (σ^2) of a binomial distribution is given by σ² = np(1-p). In this case, σ² = 25 * 0.01 * (1-0.01) = 0.2475.

The standard deviation (σ) is the square root of the variance, so σ ≈ √0.2475 ≈ 0.4975. Therefore, the standard deviation for the number of defects per batch is approximately 0.4975.

To calculate the standard deviation for the number of defects per batch with a 1% defect rate, use the formula for the standard deviation of a binomial distribution. The standard deviation is approximately 0.4975, indicating the variation in defects per batch.

The question you asked is about finding the standard deviation for the number of defects per batch in a manufacturing process where there is a 1% rate of defects.

To calculate the standard deviation for a binomial distribution, which is the case here since each television can be either defective or not, we use the formula: σ = √(np(1-p)), where σ is the standard deviation, n is the number of trials (or televisions), and p is the probability of success (or defect in this context).

Since each batch contains 25 televisions and the defect rate is 1% (0.01), we have:

n = 25
p = 0.01
1-p = 0.99

Plugging these values into the formula we get:

σ = √(25 * 0.01 * 0.99) = √(0.2475) ≈ 0.4975

Therefore, the standard deviation for the number of defects per batch is approximately 0.4975, which means – on average – you would expect the number of defects to vary around this value.

Answer:

Correct option is:

A. 486 units²

Step-by-step explanation:

We have to find the surface area of cube with side length 9 units

We know that surface area of cube is:

6s²

where s is the side of the cube

Here, s=9 units

Surface area=6×9×9

                    = 486 units²

Hence, Correct option is:

A. 486 units²

486 units²

Given:

s = 9 units

Let us find out the surface area of a cube.

The formula of the surface area of a cube is [tex]\boxed{ \ S = 6(s^2) \ }[/tex],

where s is the length of one of the sides.

[tex]\boxed{ \ S = 6(9^2) \ }[/tex]

[tex]\boxed{ \ S = 6(81) \ }[/tex]

[tex]\boxed{ \ S = 6 \times 81 \ }[/tex]

Thus, the surface area of the cube is 486 sq. units.

Notes:

From the formula for surface area, we make it s as a subject.

[tex]\boxed{ \ 6(s^2) = S \ }[/tex]

[tex]\boxed{ \ s^2 = \frac{S}{6} \ }[/tex]

[tex]\boxed{\boxed{ \ s = \sqrt{\frac{S}{6}} \ }}[/tex] ... Equation-1

The formula of the volume of a cube is [tex]\boxed{ \ V = s^3 \ }.[/tex]

Substitute Equation-1 into the volume formula.

[tex]\boxed{ \ V = \bigg( \sqrt{\frac{S}{6}} \bigg)^3 \ }.[/tex]

Thus, we have connected formulas of surface area with the volume of the cube.

Keywords: what is the surface area of the cube, the length of the cube, volume, 9 units,  486 units², 508 units², 729 units², 405 units², the formula

Answer:

V = 1152π in³

Step-by-step explanation:

The formula for the volume of a hemishere is

[tex] \frac{ \frac{4}{3}\pi {r}^{3} }{2} [/tex]

Next we need to substitute the values from the question in.

[tex] \frac{ \frac{4}{3}\pi {12}^{3} }{2} [/tex]

Then finally we need to simplify.

[tex] \frac{2304\pi}{2} = 1152\pi[/tex]

ANSWER

A. y√y

EXPLANATION

The given expression is:

[tex] \sqrt{ {y}^{3} } + \sqrt{16 {y}^{3} } - 4y \sqrt{y} [/tex]

We factor the perfect square in the first two terms to obtain;

[tex] \sqrt{ {y}^{2} \times y} + \sqrt{ {(4y)}^{2} \times y } - 4y \sqrt{y} [/tex]

This simplifies to:

[tex]y\sqrt{y } + 4y \sqrt{y } - 4y \sqrt{y} [/tex]

We simplify to get;

[tex]y\sqrt{y } + 0 = y \sqrt{y} [/tex]

The correct choice is A.

Answer:

3/8

Step-by-step explanation:

8-5=3

The value of the angle measure of the dessert that was left ​is equal to

3/8.

We have given that,

Jake cut a round gelatin dessert into 8 equal parts. five of the pieces were eaten.

We have to determine the angle measure of the dessert that was left ​

An angle measure can be defined as the measure of the angle formed by the two rays or arms at a common vertex. Angles are measured in degrees ( °), using a protractor.

Therefore

Jake cut a round gelatin dessert into 8 equal parts is given by,

[tex]\frac{360}{8}=45^0[/tex]

8-5=3

Therefore the  angle measure of the dessert that was left ​is,

[tex]3(45^0)=135^0[/tex]

Therefore the value of the angle measure of the dessert that was left ​is equal to 3/8.

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Answer:

D

Step-by-step explanation:

2·(14·7+7·7+7·14) =490

Answer: D. 490 units^2

Step-by-step explanation:

7x7=49

49x2=98 units^2

14x7=98

98x2=196 units^2

14x7=98

98x2=196 units^2

196+196+98= 490 units^2

Answer:

Final answer is [tex]P(A^c)=\frac{3}{7}[/tex]

Step-by-step explanation:

We have been given a table containing a list of few places that are either city or in North America.

Total number of places in that list = 7

That means sample space has 7 possible events.

Given that a place from this table is chosen at random. Let event A = The place is a city.

Now we need to find about what is [tex]P(A^c)[/tex].

That means find find the probability that chosen place is not a city.

there are 3 places in the list which are not city.

Hence favorable number of events = 3

Then required probability is given by favorable/total events.

[tex]P(A^c)=\frac{3}{7}[/tex]

Answer:

It's 3/7

Step-by-step explanation:

Answer:it’s B

Step-by-step explanation:

Answer:

D) [tex]x^5 + 3x^4 - 2x^3 - 3x^2 + 2[/tex]

Step-by-step explanation:

A polynomial in its standard form is when the terms are arranged in descending order of exponent. The highest exponent goes first and smallest goes to the end of the polynomial.

The only one of the polynomials in the options that meets the requirements is D. Because the term with exponent 5 is at the beginning, then the term with exponent 4, and so on until the independent term.

The answer is: D) [tex]x^5 + 3x^4 - 2x^3 - 3x^2 + 2[/tex]

Answer:

Step-by-step explanation:

Left Frame

Formula

Area of Hexagon = 3*sqrt(3)*a^2 / 2

Area of a Square = a^2

In both cases a is a side length

Givens

A = 384*sqrt(3)

Solution

384*sqrt(3) = 3*sqrt(3)*a^2 / 2     Divide by sqrt(3) on both sides.

384 = 3 * a^2 / 2                           Multiply by 2

768 = 3 * a^2                                Divide by 3

256 = a^2                                     Take the square root of both sides

a = 16

Each side of the square will be = a

The area of the square = a^2

a^2 = 16^2 = 256

Center Frame

I don't know how to expand the question so that I'm doing some sort of step-by-step explanation. The question just means what does a equal when t = 0

The answer is 15.

Right Frame

The tangents meet the circumference of the circle at a 90o angle when the radius is connected by the point of  contact. Call the central angle (LON) = x

The two tangents and the two radii form a kite which is a quadrilateral.

All quadrilaterals have 4 angles that add up to 360.

x + 90 + 90 + 60 = 360           Combine the like terms on the left

x + 240 = 360                           Subtract 240 from both sides

x = 360 - 240

x = 120

The length of the arc is given by (Central angle / 360) * Circumference

x is the central angle so the central angle = 120

Length = (120 / 360) * 96

Length = 1/3 * 96

Length = 32

Answer:  (26996, 42744)

Step-by-step explanation:

24% of 112,483 = 26,995.92  --> rounded to the nearest person is 26,996

38% of 112,483 = 42,743.54  --> rounded to the nearest person is 42,744

The number of people who want a new restaurant is somewhere between 26,996 and 42,744.

Answer:

26,996-42,744

Step-by-step explanation:

To calculate the spam of the people that who are likely to want this restaurant you just have to multiply the total number people in the city by the two points in the extremes of the intervals.

24% * 112,483=26996

and the other one would be:

38%* 112,483= 42744

And those are the extremes of the interval of people in the city who are likely to want this new restaurant.

Answer:

Lin needs to drink 27 ounces of water to reach her goal.

Step-by-step explanation:

1 cup = 8 fluid ounces.

8 cups = [tex]8\times8=64[/tex] ounces.

As of now Lin has drank 37 ounces of water. So, this means till now she has drank [tex]\frac{37}{8}= 4.625[/tex] cups of water.

In terms of ounces, she needs to drink 64-37=27 ounces of water to reach her goal.

Hence, the answer is 27 ounces or 8-4.625=3.375 cups.

The correct answer is A. 27 ounces. Lin needs to drink 27 more ounces of water to reach her goal of 8 cups (64 ounces) of water daily.

To determine how much more water Lin needs to drink to reach her goal, we need to follow these steps:

Thus, Lin needs to drink 27 ounces more water today to reach her goal.

Complete question:

Lin's goal is to drink 8 cups of water every day.She drank 37 ounces before lunch today.How much more water does Lin need to drink today to reach her goals? (8 fluid ounces = 1 cup)

A. 27 ounces

B. 29 ounces

C. 59 ounces

D. 91 ounces

Answer:

A

Step-by-step explanation:

xbar is the average of all the x-values in the table. To get the average, we need to add all the x-values and then divide by the number of values there are (there are 5 values).

THus

x bar = [tex]\frac{8+9+10+11+12}{5}=10[/tex]

correct answer is A

The distance between the center to the circumcenter is called a radius. The radius can not be a chord.

It is the distance between the two points in a circle that is known as a chord.

1  Diameter - If the chord length is longest then it is called the diameter. This can be a chord.

2  Radius - The distance between the center to the circumcenter is called a radius. This can not be a chord.

3  Secant - The line passing through the circle is known as a secant. This can be a chord.

4  Tangent - The line which touches the circle then line is called a tangent. This can be a chord.

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Answer:

[tex]V = 2622\ in ^ 3[/tex]

Step-by-step explanation:

We have a composite figure, therefore the volume of the figure will be the sum of the volume of both figures.

The volume of the rectangular prism is the product of its length by its width by its height

[tex]V_r = 7 * 12 * 19\\\\V_r = 1596\ in^3[/tex]

The volume of the triangular prism is

[tex]V_t = A_b * l[/tex]

Where [tex]A_b[/tex] is the area of the triangular base and l is the length

[tex]A_b = 0.5 * 9 * 12 = 54\ in^2[/tex]

[tex]V_t = 0.54 * 19 = 1026\ in^3[/tex]

Finally

[tex]V = 1596 + 1026[/tex]

[tex]V = 2622\ in ^ 3[/tex]

The answer is:

The total volume is equal to:  [tex]2622in^{3}[/tex]

To calculate the total volume of the composite figure, we need to calculate the volume of both of the figures that creates the composite figure.

So, calculating we have:

First figure:

The first figure has a triangular base (side for this case) and height, to find its volume, we just need to calculate the area of its base and then, multiply it by its height.

We are given that:

[tex]base_{height}=9in\\base_{base}=12in\\length=19in[/tex]

Calculating the area of the side/base, we have:

[tex]A=\frac{b*h}{2}[/tex]

[tex]A=\frac{12in*9in}{2}=54in^{2}[/tex]

Now, calculating the volume, we have:

[tex]Volume_{1}=Area*Length\\\\Volume_{1}=54in^{2}*19in=1026in^{3}[/tex]

Second figure:

The second figure is a rectangle, we can calculate its volume using the following formula:

[tex]Volume_2=base*height*width\\\\Volume_2=12in*7in*19in=1596in^{3}[/tex]

Hence, we can calculate the total volume by adding the first volumen and the second volume:

[tex]TotalVolume=Volume_1+Volume_2\\\\TotalVolume=1026in^{3} +1596in^{3}=2622in^{3}[/tex]

The total volume is equal to  [tex]2622in^{3}[/tex]

Have a nice day!

To find the angle ∠KL, knowing m∠KJL = 27°, it is essential to apply the properties of tangents and circles.

The angle ∠KJL can be determined using the properties of tangents and circles. Since JK is a tangent to circle C, we know that angle ∠KJL is equal to half of the intercepted arc KL. Therefore, if m∠KJL = 27°, then m∠KL = 2 × 27° = 54°.

i think the answer is true

The statement is False, with only 13 percent of jobs in STEM fields being math-related in 2005. This means that out of all the jobs in the areas of Science, Technology, Engineering, and Mathematics, only 13 percent were math-related.

The statement is False.

The US Bureau of Labor Statistics reported that in 2005, 13 percent of jobs in the STEM fields were math-related occupations, not the percentage of math-related occupations in the overall job market.

This means that out of all the jobs in the areas of Science, Technology, Engineering, and Mathematics, only 13 percent were math-related.

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Answer:

Your choice is correct.

Step-by-step explanation:

The amplitude (multiplier of sin( )) is half the diameter, so is 17.5. The midline (value added to the sine function) is the difference between the maximum (50) and the amplitude (17.5), so is 50-17.5 = 32.5. All choices have the correct frequency.

The function will look like ...

  f(t) = 17.5·sin(2πt/5) +32.5 . . . . . as you have marked

Answer:

C

Step-by-step explanation:

We can multiply each equation by a constant so they'll equal either 15 or -15 since that is the LCM.

Since the answer choices want us to make the top a negative 15, we'll do that.

[tex]2x-5y=-21 \\ \\ 3(2x-5y)=(-21)*3 \\ \\ 6x-15y=-63[/tex]

To make the y's cancel out, the second equation would have to have the y's coefficient equal 15.

Let's do that.

[tex]3x-3y=-18 \\ \\ -5(3x-3y)=(-18)*-5 \\ \\ -15x+15y=90[/tex]

So the resulting equations are answer choice C.

Answer:

10.92 m

Step-by-step explanation:

  To solve for the height, we first find the area of the triangle. Since the area of a triangle is 1/2 of the base times the height, we get the area to be 109.2. Dividing it by 20 and then multiplying by 2, we get 10.92 as the height.

Final answer:

To find the perimeter of the dilated rectangle A'B'C'D', we need to know the dimensions of the original rectangle ABCD and the scale factor of the dilation. The perimeter of A'B'C'D' is equal to the sum of the lengths of all the sides in the dilated rectangle. Since AB = A'B' and BD = B'D', the perimeter can be simplified to AB + BC + CD + BD.

Explanation:

To find the perimeter of the dilated rectangle A'B'C'D', we need to know the dimensions of the original rectangle ABCD and the scale factor of the dilation.

If the scale factor is 3, it means that each side of the original rectangle will be multiplied by 3 to get the corresponding side of the dilated rectangle.

Since the rectangle ABCD is dilated with a center of dilation at vertex D, the length of side AB remains the same in the dilated rectangle A'B'.

To find the perimeter of A'B'C'D', we need to compute the lengths of all the sides in the dilated rectangle and sum them up.

Perimeter of A'B'C'D' = A'B' + B'C' + C'D' + D'A'

Since AB = A'B' and BD = B'D', the perimeter can be simplified to:

Perimeter of A'B'C'D' = AB + BC + CD + BD

The perimeter of rectangle A'B'C'D', which is a dilation of rectangle ABCD by a scale factor of 3 with center D, is three times larger than the original perimeter of ABCD.

If rectangle ABCD is dilated by a scale factor of 3 with a center of dilation at vertex D, to find the perimeter of A'B'C'D', we must first understand that a dilation scales all dimensions by the given factor. If the original lengths of the sides of rectangle ABCD are 'a' and 'b', with CD and AD being adjacent to vertex D, then after the dilation, the lengths of the corresponding sides would be '3a' and '3b'.

Since the perimeter of a rectangle is calculated by adding together the lengths of all its sides, the formula for the perimeter 'P' before dilation is P = 2a + 2b. After dilation, the new perimeter 'P' of A'B'C'D' will be P = 2(3a) + 2(3b) = 6a + 6b, which is simply three times the original perimeter. Therefore, the perimeter of rectangle A'B'C'D' after dilation is three times larger than the perimeter of the original rectangle ABCD.

Answer:

[tex]y=\sin(x-\frac{3\pi}{2})[/tex] is the graph of  [tex]y=\sin x[/tex] shifted to the right by [tex]\frac{3\pi}{2}[/tex] units.

Step-by-step explanation:

The given function is

[tex]y=\sin(x-\frac{3\pi}{2})[/tex]

The base function of this trigonometric function is [tex]y=\sin x[/tex]

In general, the transformation [tex]y=\sin(x-k)[/tex] will shift the graph of the base function, [tex]y=\sin x[/tex], k units to the right.

Therefore, [tex]y=\sin(x-\frac{3\pi}{2})[/tex] is the graph of  [tex]y=\sin x[/tex] shifted to the right by [tex]\frac{3\pi}{2}[/tex] units.

Answer:

B. 3pi/2 units to the right

Step-by-step explanation:

edge2021

Eve should knit between 3 and 6 scarves per day in the next 2 days to meet her goal, with a minimum total of 15 and a maximum of 21 scarves for the week.

Eve has already knitted 9 scarves and wants to knit at least 15 scarves and at most 21 scarves by the end of the week. With 2 days left in her work week, we need to calculate how many more scarves she should knit each day to achieve her goal.

First, let's calculate the minimum number of scarves she needs to knit to meet her goal of 15 scarves. She needs to knit 15 - 9 = 6 more scarves. Dividing 6 scarves by 2 days, we find she needs to knit a minimum of 3 scarves per day.

Now, let's calculate the maximum number of scarves to meet her goal of 21 scarves. She needs to knit 21 - 9 = 12 more scarves. Dividing 12 scarves by 2 days, we find she needs to knit a maximum of 6 scarves per day.

Therefore, to meet her goal for the week, Eve should knit between 3 and 6 scarves per day for the remaining two days.

Eve should knit between 3 and 6 scarves per day in the next two days to meet her goal.

To determine the number of scarves Eve should knit each day, we need to find how many more scarves she needs to meet her goal and then spread that number evenly over the 2 remaining days. Eve has made 9 scarves already.

The maximum and minimum scarves can be calculated as below:

Minimum scarves needed [tex]= 15 - 9 = 6[/tex]

Maximum scarves needed [tex]= 21 - 9 = 12[/tex]

Now the remaining scarves need to be completed in 2 days. So, it find number of remaining scarves to be completed per day we divide the maximum and minimum value by 2 as follows:

Minimum scarves per day [tex]= \frac{6}{2} = 3[/tex]

Maximum scarves per day [tex]= \frac{12}{2} = 6[/tex]

Therefore, Eve should knit between 3 and 6 scarves per day in the next two days to meet her goal.