The center of the sphere x2 + y2 +2 +4x – 2y – 62= Dis: - 6z= - (4, -2,9) 4 (-4, 2, 6) (1,1) (0,0,0) (-2,-1,3) (-2,1,3) (-4, 2, 6) (2, 1, 3) ?

Answer:

(7×X)+5

Step-by-step explanation:

Answer:

(7×x) +5

Step-by-step explanation:

product of 7 and a number means 7x. increase by 5 means + 5

Money invested by a man = $10,500

No.of years for which he invested his money = 7

Rate of interest = 5.5%

We know that :

\( \tt \: Simple \: interest = \frac{Principal × Rate × Time}{100} \)

Principal = 10500

Rate = 5.5%

Time = 7 years

Simple interest the man payed :

\( = \tt\frac{10500 \times 55 \times 7}{10 \times 100} \)

\( = \tt \frac{4042500}{1000} \)

\( \color{plum}=\tt 4042.50\)

Therefore, the simple interest payed by the man = $4042.50

Money invested by the man (principal) = $10,500

The simple interest he payed = $4042.50

We know that :

\(\tt \: amount = principal + interest\)

The amount the man collected after a period of 7 years :

\( = \tt10500 + 4042.50\)

\( =\tt 14520.50\)

Thus, amount = $14520.50

Therefore the amount he collected after a period of 7 years = $14520.50

Answer:

8x+13

Step-by-step explanation:

It goes through all, trust me. Put the equation and the point in desmos, a graphing calculator

The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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Total volume =   (V_cylinder)+(V_cone)

                      =  827.64 + 305 .45                                

                      =1133.09 ft³

To calculate the volume of the storage bin with a cylindrical portion and a conical top, we need to find the volume of each part and add them together.
Given:
Radius (r) = 5.8 ft
Height of cylindrical portion (h) = 7.9 ft
Overall height (H) = 16.7 ft
First, find the height of the conical top by subtracting the height of the cylindrical portion from the overall height:
Height of conical top (h_cone) = H - h = 16.7 - 7.9 = 8.8 ft
Now, calculate the volume of each part:
1. Volume of cylindrical portion (V_cylinder) = π*r²h = π(5.8²)(7.9) ≈ 827.64 ft³
2. Volume of conical top.           (V_cone) = (1/3)π*r²h.                   (V_cone) = (1/3)π(5.8²)(8.8) ≈ 305.45 ft³
Finally, add the volumes of both parts to find the total volume of the storage bin:
Total volume = V_cylinder + V_cone = 827.64 + 305.45 ≈ 1133.09 ft³

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Answer:

when the square on the hypotenuse of a right-angled triangle is equal in to the sum of the squares on the other two sides

Step-by-step explanation:

let's say......

h = ?

o = 4

a = 4

a^2+o^2=32

square root 32

5.65685424949

that is the value for h

Answer:

A^2+B^2=C^2

you use it the find any length of a right angled triangle

It is not surprising that the sample proportion is always included in the confidence interval, as the sample proportion is considered as the estimate of the confidence interval.

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

The point estimate is the sample proportion for a confidence interval of proportions, hence it is not surprising that the sample proportion is always included in the confidence interval for population proportions.

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The following a probability model? what do we call the outcome No, the provided information is not sufficient to determine if it is a probability model. The outcome "red" is typically referred to as an event.

A probability model is a mathematical representation of a random experiment, where the sample space is defined, and probabilities are assigned to all possible outcomes. To determine if the given information is a probability model, we would need to know the complete list of possible outcomes, their corresponding probabilities, and ensure that the probabilities meet the necessary conditions (sum up to 1 and are non-negative).

Based on the limited information provided, we cannot determine if it is a probability model. The outcome "red" is called an event in the context of probability.

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Answer:

B, 16.1

Step-by-step explanation:

cos 36 = 13/x

cos 36 × x = 13

x = 13/cos 36

(Use Calculator)

x = 16.068883...

x ≈ 16.1

Answer:

3c - 5 is equivalent

Step-by-step explanation:

For the notes section

Step 1 group like terms

-c - 10 + 4c + 5 = -c + 4c - 10 + 5

Step 2 add similar elements

= 3c - 10 + 5

Step 3 add/subtract the numbers

= 3c - 5

The equations are x² = y + 16 & 4y - 1 = 7x and the solution is (5, 9)

From the question, we have the following parameters that can be used in our computation:

x = first number

y = second number

Given that

The square of the first number is 16 more than the second number

This means that

x² = y + 16

Also, we have the difference expression to be

4y - 1 = 7x

When these equations are solved graphicaly, we have

(x, y) = (5, 9)

Hence, the equations are x² = y + 16 & 4y - 1 = 7x and the solution is (5, 9)

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Answer:

Shirt : Pant = 2 : 3 ,  & Pant : Shirt = 3 : 2 , Linear model can be used.

Step-by-step explanation:

Ratio of ' Number of shirts sold : Number of items sold' = 2 : 5

Let the common ratio be = x

Then, number of shirts sold = 2x. And, number of total items sold = 5x.

So, number of pants sold = Number of items sold - number of shirts sold = 5x - 2x = 3x

So, shirt to pant ratio = 2x / 3x = 2 : 3 .And,  pant to shirt ratio = 3 : 2

This model can be shown in linear equation, as all are linear powered.

There are 8 possible samples of size 3 that can be drawn in succession with replacement from a population of size 2.

The population size is 2, and we want to draw a sample of size 3 with replacement. With replacement means that after each draw, the item is placed back into the population, so it can be drawn again in the next draw.

To calculate the number of possible samples, we need to consider the number of choices for each draw. Since we are drawing with replacement, we have 2 choices for each draw, which are the items in the population.

To find the total number of possible samples, we need to multiply the number of choices for each draw by itself for the number of draws. In this case, we have 2 choices for each of the 3 draws, so we calculate it as follows:

2 choices x 2 choices x 2 choices = 8 possible samples

Therefore, there are 8 possible samples of size 3 that can be drawn in succession with replacement from a population of size 2.

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Answer:

Hey there!

Discrete Data is the number of friends you invited to your last birthday party.

Hope this helps :)

Answer:

a) The number of friends you invited to your last party.

Step-by-step explanation:

Let’s take a step back what is discrete, and what continuous?

Discrete

This is the type of data with certain whole numbers not 2.36 only 2 or 3.

Continuous

This is the data being specific like 1.373.

So a)

The is discrete because you can only have like 5 friends not 7.49 friends.

b)

This is continuous because height can be 5.26 feet.

c)

Time is continuous because there can be 4.3739 minutes.

d)

Weight is also continuous it can be 6339.373 pounds.

The probability that she makes 6 of them is 0.242

The probability is the likelihood that something will happen, to put it simply. When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several. The study of events that fit into a probability distribution is known as statistics.

Given,

A basketball player has a probability = 0. 603

The player shoots 10 free throws.

Let x be a random variable that represents the number of free throws made by a basketball player.

x ≈ Binomial (n,p)

p = 0.603

n= 10

P(x=k) =  n\(C_{k} p^{k} (1-p)^{n-k}\)

P(6) = ₁₀\(C_{6} (0.603)^{6} (1-0.603)^{10-6}\)

      = \(210(0.048)(0.397)^{4}\)

      = 210 ( 0.048 ) ( 0.024)

      = 0.242    

Therefore, the probability that she makes 6 of them is 0.242

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The value of f(4) is 28.

it can be found using the fundamental theorem of calculus.

The fundamental theorem of calculus states that if a function f is continuous on an interval and its derivative f' exists on that interval, then the definite integral of f' over the interval is equal to the difference in the values of the original function at the endpoints of the interval.

In this case, we are given that f '(x) is continuous, and that the definite integral of f '(x) over the interval [3, 4] is equal to 18. Therefore, using the fundamental theorem of calculus, we have that f(4) - f(3) = 18, and since f(3) = 10, we can solve for f(4) to get f(4) = 10 + 18 = 28.

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Complete question:

If f(3) = 10, f ' is continuous, and   \(\int\limits^4_3\) f '(x) dx = 18, what is the value of f(4)?

Answers in bold:

S9 = 2

i = 20

R = -2

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

Explanation:

\(S_0 = 20\) is the initial term because your teacher mentioned \(A_0 = I\) as the initial term.

Then R = -2 is the common difference because we subtract 2 from each term to get the next term. In other words, we add -2 to each term to get the next term.

Here is the scratch work for computing terms S1 through S4.

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{1} = S_{1-1} - 2 & S_{2} = S_{2-1} - 2\\S_{1} = S_{0} - 2 & S_{2} = S_{1} - 2\\S_{1} = 20 - 2 & S_{2} = 18 - 2\\S_{1} = 18 & S_{2} = 16\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{3} = S_{3-1} - 2 & S_{4} = S_{4-1} - 2\\S_{3} = S_{2} - 2 & S_{4} = S_{3} - 2\\S_{3} = 16 - 2 & S_{4} = 14 - 2\\S_{3} = 14 & S_{4} = 12\\\cline{1-2}\end{array}\)

Then here is S5 though S8

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{5} = S_{5-1} - 2 & S_{6} = S_{6-1} - 2\\S_{5} = S_{4} - 2 & S_{6} = S_{5} - 2\\S_{5} = 12 - 2 & S_{6} = 10 - 2\\S_{5} = 10 & S_{6} = 8\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{7} = S_{7-1} - 2 & S_{8} = S_{8-1} - 2\\S_{7} = S_{6} - 2 & S_{8} = S_{7} - 2\\S_{7} = 8 - 2 & S_{8} = 6 - 2\\S_{7} = 6 & S_{8} = 4\\\cline{1-2}\end{array}\)

And finally we arrive at S9.

\(S_{n} = S_{n-1} - 2\\\\S_{9} = S_{9-1} - 2\\\\S_{9} = S_{8} - 2\\\\S_{9} = 4 - 2\\\\S_{9} = 2\\\\\)

--------------------

Because we have an arithmetic sequence, there is a shortcut.

\(a_n\) represents the nth term

S9 refers to the 10th term because we started at index 0. So we plug n = 10 into the arithmetic sequence formula below.

\(a_n = a_1 + d(n-1)\\\\a_n = 20 + (-2)(n-1)\\\\a_n = 20 - 2(n-1)\\\\a_{10} = 20 - 2(10-1)\\\\a_{10} = 20 - 2(9)\\\\a_{10} = 20 - 18\\\\a_{10} = 2\\\\\)

In other words, we start with 20 and subtract off 9 copies of 2 to arrive at 20-2*9 = 20-18 = 2, which helps see a faster way why \(S_9 = 2\)

Answer: your answer is correct because if you put that equation into y=mx+b form you get y=1/2x-1

so you start at -1 and go over 2 and up 1 and you woulld land on 2

so you would graph at (2,-1) i think

Bytaking the quotient between the probabilities we can see that Getting a 17 is three times more likely to get a 18.

If you toss 3 dices with 6 sides each, then the total number of combinations is:

6*6*6 = 216

Now, the outcomes that add up to 18 are:

dice 1, dice 2, dice 3, sum:

6            6         6       , 18

The outcomes that add up to 17 are:

dice 1, dice 2, dice 3, sum:

5           6         6       , 17

6            5         6       , 17

6            6         5       , 17

So the probabilities are:

P(18) = 1/216

P(17) = 3/16

The quotient gives:

P(17)/P(18) = 3

Getting a 17 is 3 times more likely to get a 18.

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Answer:

The solution of the system of equations are;

(-2, -6) and (4, 6)

Step-by-step explanation:

-2·x + y = -2...............(1)

\(y = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2\)........(2)

Equation (1) gives;

y = 2·x - 2

From which we have;

\(2 \cdot x - 2 = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2\)

\(0= -\dfrac{1}{2} \cdot x^2 + x + 4\)

x² -2·x -8 = 0

(x - 4)·(x + 2) = 0

x = 4 or x = -2

The y-coordinate values are;

y = 2×(-2) - 2 = -6 and y = 2×(4) - 2 = 6

The solution points are;

(-2, -6) and (4, 6).

The points where the equation, -2·x + y = -2 and the equation \(y = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2\) intersect are  (-2, -6) and (4, 6).

Answer: X equals 7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

First you want to simplify the equation

8x + (-5) = 23 + 4x

-5 + 8x = 23 + 4x

Then solve for x, but before we do that we !!!must!!! move all terms that have x  to the left. Everything else would go to the right.

So we add -4x to both sides ..

-5+ 8x + (-4x) = 23 + 4x + (-4x)

-5 + 4x = 23 + 4x + (-4x)

-5 + 4x = 23 +0

-5 + 4x  = 23

Then add 5 to both sides of the equation:

-5 + 5 + 4x = 23 + 5

0 + 4x = 23 + 5

4x = 23 + 5

4x = 28

Then divide each side by 4:

x = 7

And there you have it. The answer is 7. Hope this helps! :)

The answer is −0.09

It should be simple multiplication.

I hope this helps!

Answer:

out of

Step-by-step explanation:

Answer:

(1) divided by, (2) quotient of, (3) out of, (4) unit price, (5) ratio of.

Step-by-step explanation:

are signal words indicating division will be used

To make a decision for the hypothesis test, we need to analyze the ANOVA summary table for the test of significance of the overall regression model.

From the table, we can see that the regression sum of squares (SS) is given as 20, and the residual sum of squares (SS) is given as 400. We also know that the total sum of squares (SS) is the sum of the regression SS and the residual SS.

Since the degrees of freedom (df) for the regression model is equal to the number of predictor variables (k) minus 1 (k - 1), and the df for the residual is the total sample size (n) minus the number of predictor variables (k), we can calculate the df for the regression and the residual.

Given that the sample size (n) is 45 and the number of predictor variables (k) is 4, we can calculate:

df for regression = k - 1 = 4 - 1 = 3

df for residual = n - k = 45 - 4 = 41

Next, we need to calculate the mean square (MS) for the regression and the residual by dividing the SS by their respective degrees of freedom.

MS for regression = SS for regression / df for regression = 20 / 3

MS for residual = SS for residual / df for residual = 400 / 41

Finally, we can calculate the F-statistic by dividing the MS for regression by the MS for residual.

F = (MS for regression) / (MS for residual)

Now, we can compare the calculated F-statistic to the critical F-value at the given significance level (α = 0.05). If the calculated F-statistic is greater than the critical F-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Without the information of the critical F-value or the calculated F-statistic, we cannot make a definitive decision or final conclusion for the hypothesis test. Please provide the necessary values, and I will be able to help you with the decision and conclusion.

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Answer:

∠ A = 138° , ∠ C = 75°

Step-by-step explanation:

ABCD has parallel bases and is a trapezium

each lower base angle is supplementary to the upper base angle on the same side.

∠ A + 42° = 180° ( subtract 42° from both sides )

∠ A = 138°

∠ B + ∠ C = 180 , that is

12x - 3 + 9x - 6 = 180

21x - 9 = 180 ( add 9 to both sides )

21x = 189 ( divide both sides by 21 )

x = 9

Then

∠ C = 9x - 6 = 9(9) - 6 = 81 - 6 = 75°

Answer:

120 children and 388 adults bought tickets for the swimming pool

Explanation:

Create two simultanous equations:

Let c stand for the number of children that bought a ticket, and a stand for the number of adults that bought a ticket, you get your first equation, being

c

+

a

=

508

then, you now create a second equation for the prices of the tickets.

(price of childrens tickets)(number of children that swam)+(price of adults tickets)(number of adults that swam) = total money collected

so:

1.75

c

+

2.25

a

=

1083.00

now we still know, that

a

=

508

−

c

so we can substitute it into the second formula

1.75

c

+

2.25

(

508

−

c

)

=

1083

now its just simple algebra

1.75

c

+

1143

−

2.25

c

=

1083

60

=

0.5

c

so:

c

=

120

now we know, that 120 children went to the swimming pool.

and we still have the formula from before:

a

=

508

−

c

so

a

=

388

When receiving ammunition, unit personnel perform three tasks: ensuring items requested match item numbers on DA Form 3151-R, loading and securing the ammunition, and placarding the vehicle.

The first task performed by unit personnel when receiving ammunition is to ensure that the items requested match the item numbers on DA Form 3151-R. This form serves as a record of the types and quantities of ammunition being received. By comparing the requested items with the item numbers on the form, personnel ensure accuracy and prevent any discrepancies or errors in the delivery.

The second task involves the loading and securing of the ammunition. Unit personnel are responsible for safely and efficiently loading the ammunition onto the designated vehicle or storage area. This includes following proper handling procedures, using appropriate equipment, and adhering to safety protocols. The ammunition must be securely stored and arranged to prevent shifting or damage during transportation.

The final task is to placard the vehicle. Placarding involves visibly displaying the necessary warning signs or labels on the vehicle that indicate the presence of ammunition. This step is crucial for safety and compliance purposes, as it alerts other personnel and drivers to exercise caution when approaching or handling the vehicle. Clear and prominent placarding helps prevent accidents and ensures that everyone involved is aware of the potential hazards associated with transporting ammunition.

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