Please help me answer this question please

The sphere's radius is 5, and its center is at (0, 3, -4).

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions.

In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.

The radius of the sphere is denoted by the letter r, and the given point is its center.

List a few typical sphere examples from everyday life.

In everyday objects, sphere shapes can be found in the form of marbles, balls, oranges, yarn, and bubbles.

So, the center and radius of the sphere will be:

We have the sphere's equation, which is given by and has a radius of r.

(x - h)² + (y - k)² + (z - l)² = r² ...(1)

We must convert the following equation in order to determine the center and radius of the provided sphere.

x² + y² + z² - 6y + 8z = 0

By combining the x, y, and z terms and filling in the square, we obtain

x² + (y² - 6y + 9) +(z² + 8z + 16) = 9 + 16

(x - 0)² + (y - 3)² + (z + 4)² = 52

So, the sphere's center is at (0, 3, -4) and its radius is 5.

Therefore, the sphere's radius is 5, and its center is at (0, 3, -4).

Know more about the sphere here:

https://brainly.com/question/22807400

#SPJ4

Complete question:

Find the center and radius of the sphere x2 + y2 + z2 - 6y + 8z = 0.

Answer:

£0.50

Step-by-step explanation:

t = one cup of tea

c = one piece of cake

t + c = £1.10

2t + c = £1.70

the cost increases by £0.60 (£1.70 - £1.10) when you order one more cup of tea which means that one cup of tea costs £0.60

substitute £0.60 into t + c = £1.10

£0.60 + c = £1.10

rearrange to get c = £1.10 - £0.60 = £0.50

so one piece of cake costs £0.50

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

For more such questions on profit function

https://brainly.com/question/16866047

#SPJ8

the sum of the series is 8/3. The series consists of reciprocals of positive integers whose only prime factors are 2s and 3s.

In other words, each term of the series can be expressed as a fraction of the form 1/n, where n is a positive integer that can be factored into only 2s and 3s. For example, the first term of the series is 1/1, the second term is 1/2, and the fourth term is 1/4.

To find the sum of the series, we can first list out the terms and their corresponding values:

1/1 = 1

1/2 = 0.5

1/3 = 0.333...

1/4 = 0.25

1/6 = 0.166...

1/8 = 0.125

1/9 = 0.111...

1/12 = 0.083...

and so on.

We can see that the terms of the series decrease in value as n increases, so we can use this fact to estimate the sum of the series. For example, we can take the sum of the first few terms to get an idea of how large the sum might be:

1 + 0.5 + 0.333... + 0.25 = 2.083...

We can see that the sum is greater than 2, but less than 3. To get a more accurate estimate, we can add a few more terms:

2.083... + 0.166... + 0.125 + 0.111... = 2.486...

We can continue adding terms in this way to get a more and more accurate estimate of the sum. However, it is not easy to find a closed-form expression for the sum of the series.

Alternatively, we can use a formula for the sum of a geometric series to find the sum of the series. A geometric series is a series of the form a + ar + ar^2 + ... + ar^n, where a is the first term and r is the common ratio between terms. In our series, the first term is 1 and the common ratio is 1/2 or 1/3, depending on whether n is even or odd. Therefore, we can split the series into two separate geometric series:

1 + 1/2 + 1/8 + 1/32 + ... = 1/(1 - 1/2) = 2

1/3 + 1/12 + 1/48 + 1/192 + ... = (1/3)/(1 - 1/2) = 2/3

The sum of the two geometric series is the sum of the original series:

2 + 2/3 = 8/3

Therefore, the sum of the series is 8/3.

To know more about geometric series click here:

brainly.com/question/21087466

#SPJ4

Answer: 1.24 is the answer

Answer:

3.33 hours

Step-by-step explanation:

you have a total of 60mg, it is asked how much hours it takes to remove half the caffeine which is 30mg

1 hour removes 15%, 15% of 60 is 9g

(15/100×60) = 9

now it removes only 9g in an hour, we have to find out how long (hours) it'll take to remove 30g

30÷9= 3.33 hours

Answer:

The GCF=8 The Sum=88

Answer:

The answers are:

1. 2(x2 + 6x + 9) = 3 + 18

2. 2(x2 + 6x) = 3

Let's take a look at the first choice:

2(x² + 6x + 9) = 3 + 18

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x + 2·9 = 3 + 18

2x² + 12x + 18 = 3 + 18

2x² + 12x - 3 = 18 - 18

2x² + 12x - 3 = 0

Let's take a look at the second choice:

2(x² + 6x) = 3

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x = 3

2x² + 12x = 3

2x² + 12x - 3 = 0 Man that was so hard MARK ME Brainilest Thanks Peace

Step-by-step explanation:

Answer:

65 degrees

Step-by-step explanation:

The angles will sum up to 360, just do 360 - all known angles

360 - 90 - 128 - 77 = 65

Answer:

Step-by-step explanation:

Sum of all angles is 360 degrees

Let the measure of angle M equal x.

x+90+77+128=360

x=65

Measure of angle M is 65 degrees

Answer:

well 5% of 600 is 30. so if you make 600 phone calls and an average of 5% of those calls are people signing up, then that would be 30.

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.

To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.

Given:

Length of the cylindrical steel pipe (hollow part) = 21 cm

Radius of the solid cylinder = 0.4 cm

Radius of the hollow cylinder = 0.1 cm

First, let's calculate the volume of the solid cylinder (hollow part):

V1 = π × \(r1^2\) × h

V1 = π × \((0.4 cm)^2\) × 21 cm

Next, let's calculate the volume of the hollow cylinder:

V2 = π × \(r2^2\) × h

V2 = π × \((0.1 cm)^2\) × 21 cm

Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:

Volume of liquid = V1 - V2

Let's calculate these values:

V1 = π ×\((0.4 cm)^2\) × 21 cm ≈ 10.572 cm³

V2 = π × \((0.1 cm)^2\) × 21 cm ≈ 0.693 cm³

Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³

To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:

Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.

Therefore, none of the options A, B, C, or D provided is the correct answer.

for such more question on volume

https://brainly.com/question/6204273

#SPJ8

Parenthesis

Exponent

Multiplication

Division

Addition

Subtraction

(left to right)

4²-(3.1+6.4)+4.5

According to PEMDAS, we will do what is inside the parenthesis.

3.1+6.4 = 9.5

4²-9.5+4.5

Then we do figure out the exponent.

4² =  (4)(4) = 16

16-9.5+4.5

Then we do subtraction then addition because PEMDAS also tells us we should do adding and subtracting from left to right. In this expression, subtracting is on the left side so we should do that first.

16-9.5 = 6.5

6.5 + 4.5 = 11

11 is your answer :)

Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’. Option D is correct .

What is a trapezoid simple definition?

A trapezoid, also referred to as a trapezium, is an open, flat object with 4 straight sides and 1 set of parallel sides.

                         A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively.

1) We have and isosceles trapezoid DEFG and and another trapezoid D'E'F'G' dilated.

2) E'F'G'H' is not congruent to EFGH (due to its legs) Besides that, E'F'G'H has undergone not to rigid motions. Rigid motions are better known as translations and rotations and they preserve length and angles. That was not the case.

3) So it's d, the only correct choice:

d) Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’.

Learn more about trapezoid

brainly.com/question/8643562

#SPJ1

The complete question is -

The coordinates of the vertices of trapezoid EFGH are E(-8, 8), F(-4, 12), G(-4, 0), and H(-8, 4).  The coordinates of the vertices of trapezoid E’F’G’H’ are E’(-8, 6), F’(-5, 9), G’(5, 0), and H’(-8, 3).   Which statement correctly describes the relationship between trapezoid EFGH and trapezoid E’F’G’H’?   a)     Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by reflecting it across the x-axis and then translating it up 14 units, which is a sequence of rigid motions. b)     Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by translating it down 2 units and then reflecting it over the y-axis, which is a sequence of rigid motions c)     Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by dilating it by a factor of 34 and then translating it 2 units left, which is a sequence of rigid motions d) Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’.

Answer:

Mean = 53.

Step-by-step explanation:

The median is the middle value so the 3 cards are

36, 46, x       where x is to be found.

The range is 41, so:

x - 36 = 41

x = 41 + 36

x = 77.

Therefore, the mean is

(36+46+77) / 3

= 159/3

= 53.

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

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

The parameters for this problem are given as follows:

\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

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

By the Central Limit Theorem:

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

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

Given,

The coordinate pairs are

{(2, 4), (2,5), (3,6), (3, 7) }

Here the argument 2 returns to both 4 and 5 while 3 returns to both 6 and 7.

This violates the defination of function.

Thus the coordinate pairs doesnot represent a function.

The answer is No.

Answer:

y = 2/3 x + 1/3

Step-by-step explanation:

First find the slope of the given line by solving for "y":

3 x + 2 y = -7

2 y = - 3 x - 7

y = - 3/2 x - 7/2

which shows a slope of "- (3/2)"

Then, the slope of a line perpendicular to it must be "the opposite of the reciprocal" of this slope, that is: "2/3"

We use this info and the requested point (1, 1) to find the complete equation of the perpendicular line:

y = 2/3  x + b

1 = 2/3 (1) + b

1 - 2/3 = b

b = 1/3

Then the equation of the line is:

y = 2/3 x + 1/3

which agrees with the third answer shown in the list of options.

Answer:

a) The mean is $55 and the standard deviation is $0.6957

b) The shape of the sampling distribution of x is approximately normal.

c) 0.0749 = 7.49% probability that the average cell phone service paid by the sample of cell phone users will exceed $56.

Step-by-step explanation:

Normal probability distribution

When the distribution is normal, we use the z-score formula.

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

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

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

Central Limit Theorem

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

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

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

In this question:

Mean of the distribution: 55

Standard deviation of the distribution: 22

Sample of 1000.

This means that:

\(\mu = 55, \sigma = 22, n = 1000\)

Part A: What are the mean and standard deviation of the sample distribution of X?

By the Central Limit Theorem, the mean is 55 and the standard deviation is \(s = \frac{22}{\sqrt{1000}} = 0.6957\).

Part B: What is the shape of the sampling distribution of x?

By the Central Limit Theorem, the shape of the sampling distribution of x is approximately normal.

Part C: What is the probability that the average cell phone service paid by the sample of cell phone users will exceed $56?

This is 1 subtracted by the pvalue of Z when \(X = 56\). So:

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

By the Central Limit Theorem

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

\(Z = \frac{56 - 55}{0.6957}\)

\(Z = 1.44\)

\(Z = 1.44\) has a pvalue of 0.9251

1 - 0.9251 = 0.0749

0.0749 = 7.49% probability that the average cell phone service paid by the sample of cell phone users will exceed $56.

Solution:

Given:

Let x be the principal for the 8% simple interest per year

Let y be the principal for the 6% simple interest per year

Hence,

The formula for calculating simple interest is;

Solving the two equations simultaneously;

Therefore,

Lucy invested $4,000 principal for 8% simple interest.

Lucy invested $26,000 principal for 6% simple interest.

Answer:

$ 18,000 was invested at 7%, and $ 5,000 was invested at 6%.

Step-by-step explanation:

Given that I invested $ 23,000 in two accounts paying 6% and 7% annual interest, respectively, and the total interest earned for the year was $ 1,560, to determine how much was invested at each rate, the following calculation must be performed:

23,000 x 0.07 + 0 x 0.06 = 1,610

22,000 x 0.07 x 1,000 x 0.06 = 1,600

21,000 x 0.07 x 2,000 x 0.06 = 1,590

20,000 x 0.07 x 3,000 x 0.06 = 1,580

19,000 x 0.07 x 4,000 x 0.06 = 1,570

18,000 x 0.07 x 5,000 x 0.06 = 1,560

Thus, $ 18,000 was invested at 7%, and $ 5,000 was invested at 6%.

Answer:

x = 66.74715005725

Step-by-step explanation:

First you bring over the added variable. 0.194185, and subtract it from 66. Then you divide your difference by 0.985897. This gives you 66.74715005725

Answer:

use your instincts

Step-by-step explanation:

trust your gut that is what my idiot dad told me to do

Answer:

NO, they are not similar.

Step-by-step explanation:

Width of rectangle J = 6 ft

Length of rectangle J = 9 ft

Width of rectangle K = 9 ft

Length of rectangle K = 12 ft

Find the ratio of their corresponding dimensions:

Ratio of their width = 6/9 = 2/3

Ratio of the length = 9/12 = 3/4

Their ratio of their corresponding dimensions are not equal. That is, their corresponding dimensions are not proportional to each other. Therefore, they are not similar.

Answer:

y = csc(x) does not have any zero.

Step-by-step explanation:

If we have:

y = f(x)

a zero of that function would be a value x' such that:

y = f(x') = 0

Here we basically want to solve:

y = csc(x) = 0

First, remember that:

csc(x) = 1/sin(x)

now, the values of sin(x) range from -1 to 1.

So we want to solve:

1/sin(x) = 0

notice that a fraction:

a/b = 0

only if a = 0.

Then is easy to see that for our equation:

1/sin(x) = 0

The numerator is different than zero, then the equation never will be equal to zero.

Then:

y = csc(x) = 1/sin(x)

Does not have a zero.

Answer:

a

start at the (0,-4) and go up 3 and over one.  answer "A" fits this criteria

The number 2/5 is both a ratio and a fraction.

The number 2/5 is both a ratio and a fraction. Fractions are meant to signify the numerator and denominator in an expression. in the above expression, we have the denominator as 5 and the numerator as 2.

The expression is also a ratio because it indicates the quantitative relationship between the figures.

Learn more about ratios and fractions here:

https://brainly.com/question/2328454

#SPJ1

Answer:

pppppppppppppppppppppppppppppppppppppppppp

If a train traveled 300 miles. The time is, 6 hours, 4.29 hours, 300/x hours, 300/(x+10) hours,300/(x+5) hours.

Distance = Rate × Time

Time =Distance/Rate

1. 50 mph

Time = 300/50

Time = 6 hours

2. 70 mph

Time = 300/70

Time = 4.29 hours

3. x mph

Time = 300/x

Time = 300/x hours

4. (x+10)mph

300/(x+10) hours

5. (x-5)mph

300/(x-5) hours

Therefore the  time is, 6 hours, 4.29 hours, 300/x hours, 300/(x+10) hours,300/(x+5) hours.

Learn more about time here:https://brainly.com/question/26046491

#SPJ1

Answer:

  a. y = 3

  b. x = 1

  c. y = 5

  d. x = -2.5

  e. m = 2

  f. y = 2x +5

Step-by-step explanation:

Find the mark -1 on the horizontal axis. Follow the vertical line up until it meets the red line being graphed. Then follow the horizontal line over to the vertical y-axis. This tells you the value of y when x = -1. It is 3.

  y = 3 when x = -1.

__

Find the mark 7 on the vertical axis. (It is the one closest to the top.) Follow the horizontal line over to the red line being graphed. Then follow the vertical line down to the horizontal x-axis. The number there is 1. This is the value of x when y = 7.

  x = 1 when y = 7.

__

The number where the red line crosses the vertical axis is the y-intercept. It is 5.

  y-intercept = 5

__

The red line crosses the horizontal axis halfway between -2 and -3. The value there is -2.5. This is the x-intercept.

  x-intercept = -2.5

__

The slope of the line is the ratio of "rise" (vertical change) to "run" (horizontal change). There are several ways to find it.

You already know the line crosses the y-axis at y = 5, and you know that it has a value of y=7 when x=1. The latter point is 2 units up and 1 unit right of the y-intercept point, so the slope is ...

  m = rise/run = 2/1 = 2

The slope of the line is 2.

__

The equation in slope-intercept form is ...

  y = mx + b

where m represents the slope (2), and b represents the y-intercept (5). Putting these numbers in their places gives the equation ...

  y = 2x +5

Answer:

a. when x = -1      y = 3

b. when y = 7       x = 1

c. when x = 0 (y-intercept)   y = 5

d. when y = 0 (x-intercept) x = -2.5

e. slope = (y2 - y1) / (x2 - x1) = (5 - 0) / (0 - (-2.5)) = 2        

f. y = m x + b     equation  for straight line

   y = 2 x + 5         equation of line

Check: when x = 0    y = 5      the y-intercept

See b:   if y = 7 then 7 = 2 x + 5   or x = 1      OK