River boat ( ) a river boat leaves silver town and travels upstream to gold town at an average speed of 6 kilometers per hour. it returns by the same route at an average speed of 9 kilometers per hour. what is the average speed for the round-trip in kilometers per hour?

a.7.0

b.7.1

c.7.2

d.7.5

e.8.0

Answer:

[tex](x-9)^{2}+(y+4)^{2}=81[/tex]

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

(h,k) is the center

r is the radius

In this problem we have

[tex](h,k)=(9,-4)[/tex]

[tex]r=9\ units[/tex]

substitute

[tex](x-9)^{2}+(y+4)^{2}=9^{2}[/tex]

[tex](x-9)^{2}+(y+4)^{2}=81[/tex] ----> equation of the circle in standard form

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:

first 25%

Step-by-step explanation:

A quartile is a quarter, so the first 25% falls between the minimum and lower quartile

Answer:

A. 25%

Step-by-step explanation:

Because it asks you where one section to another section (on a box plot there are four areas containing 25% within each one.)

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

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:

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 and B: {4, 6}

A or B: {2, 3, 4, 5, 6, 8}

Complement of B: {1, 2, 7, 8}

Step-by-step explanation:

A and B refer to the elements that are in both A and B at the same time

The even numbers from 1 to 8 are {2, 4, 6, 8}

The numbers from 3 to 6 are {3, 4, 5, 6}

Look for the common elements between both sets.

A and B: {4, 6}

A or B is the union of the two sets

Join the elements of both sets

A or B: {2, 3, 4, 5, 6, 8}

The complement of B are all the elements that are not in B.

Write all the elements of the sample space except those of event B

Complement of B: {1, 2, 7, 8}

Event A: 2, 4, 6, 8; Event B: 3, 4, 5, 6.

In probability theory, events are outcomes or sets of outcomes from a random experiment. They are subsets of the sample space, representing possible results. Simple events consist of a single outcome, while compound events involve more than one outcome. Probability measures the likelihood of events occurring.

Event A consists of the even numbers 2, 4, 6, and 8.

Event B consists of the numbers 3, 4, 5, and 6.

The outcomes for Event A are 2, 4, 6, and 8.

The outcomes for Event B are 3, 4, 5, and 6.

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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:

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:

8 hours

Step-by-step explanation:

Joe spends 18.75% of his working day washing cars.

Joe spends 1.5 hours washing car.

Therefore 18.75% is equal to 1.5 hour.

18.75% = 1.5 hour

1% = 1.5 ÷ 18.75 = 0.08 hour

100% = 0.08 x 100 = 8 hours

Answer:

C

Step-by-step explanation:

Finding the z-score:

z = (x - μ) / σ

z = (66 - 57) / 9

z = 1

Using a z-score table or calculator:

P(z < 1) = 0.8413

84.13% of 4000 is:

0.8413 (4000) = 3365.2

Rounding up to the nearest whole number, approximately 3366 students will score less than 66.  Answer C.

Using the normal distribution, it is found that approximately 3366 students will score less than 66 on the test.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are given as follows:

[tex]\mu = 57, \sigma = 9[/tex]

The proportion of students that scored less than 66 is the p-value of Z when X = 66, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{66 - 57}{9}[/tex]

Z = 1

Z = 1 has a p-value of 0.8413.

Out of 4000 students:

0.8413 x 4000 = 3366, which means that option C is correct.

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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!

Answer:

82%

Step-by-step explanation:

We let the random variable X denote the number of defective units in the production run. Therefore, X is normally distributed with a mean of 21 defective units and a standard deviation of 3 defective units.

We are required to find the probability, P(17 < X < 25), that the number of defective units in the production run is between 17 and 25.

This can be carried out easily in stat-crunch;

In stat crunch, click Stat then Calculators and select Normal

In the pop-up window that appears click Between

Input the value of the mean as 21 and that of the standard deviation as 3

Then input the values 17 and 25

click compute

Stat-Crunch returns a probability of approximately 82%

Find the attachment below.

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.

More about the chord of a circle link is given below.

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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:

  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:

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:   {9, 21, 33}

Step-by-step explanation:

Ken worked 2, 8 and 14 hours on 3 separate days.

For working 2 hours, his earnings were f(2) = 2(2) + 5, or 9;

For working 8 hours, his earnings were f(28) = 2(8) + 5, or 21; and

For working 14 hours, his earnings were f(14) = 2(14) + 5, or 33

Thus, the range of this function for the days given is {9, 21, 33} (Answer D)

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:

[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

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:

  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)

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:

The answer should be 28.36

Step-by-step explanation:

You add them together

Hope this helps!

Answer:

28.36

Step-by-step explanation:

3.6 + 24.7 = 28.36

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:

Domain:  (-∞, ∞); range:  (-∞, ∞).

Step-by-step explanation:

In the given function, f(x)= -2x + |3sinx|, the range of the |3sinx| term is [0, 3].  That of the -2x term is (-∞, ∞).  

The range of f(x)= -2x+|3sinx| is thus  (-∞, ∞); the |3sinx| term has no effect on this.

There are no restrictions on the input to f(x)= -2x+|3sinx|.  The domain is thus (-∞, ∞).

Answer: Savings account - Apex

Answer:

Option D is the correct answer.

Step-by-step explanation:

The saving bonds are a good way to earn money but they work at fixed rate of interest over a set time period.

Money market accounts give a limited access to account and not more than three checks are written in a month. Its a type of short term savings.

The certificate of deposit or CD's have higher interest rate than savings account. But one cannot withdraw the money before the term maturity otherwise penalty is to be paid.

Savings account are deposit accounts that can be accessed whenever needed. These yield less interest as compared to money market accounts or CD's.

Therefore, the best option for Lionel to choose will be Savings account

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.

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°.

Answer:

  A.  Multiply 4 by 3. Then multiply 2 by 4. Add the two products.

Step-by-step explanation:

As with many rate problems, ...

  quantity = rate · time

The total quantity will be the sum of quantities associated with different rates or time periods:

  total quantity = quantity1 + quantity2

  = (rate 1)(time 1) + (rate 2)(time 2)

  = (4 books/week)(3 weeks) + (2 books/week)(4 weeks)

  = 4·3 books + 2·4 books . . . . . . units of (weeks/weeks) cancel

  = (4·3 + 2·4) books . . . . . . formula matches selection A