A rectangular pool is 9 meters wide and 11 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.

Answer:

x=-1

Step-by-step explanation:

5x-2x-7=-10

3x-7=-10

3x-7+7=-10+7

3x=-3

x=-1

\(\text{Hey \: there!}\)

\(\text{5x - 7 - 2x = 10}\)

\(\bf{(5x - 2x) \: which \: gives \: us \: 3x}\)

\(\text{3x - 7 + 7 = 10 + 7}\)

\(\bf{ - 7 + 7 \: because \: it \: gives \: you \: 0}\)

\(\bf{10 + 7 = 17}\)

\( \frac{3x}{3} = \frac{17}{3} \)

\(\text{we \: cant \: divide \: 17 \: from \: 3 \: because \: itll \: give \: us \: a \: decimal}\)

\(\boxed{\bf{thus \: your \: answer \: is \: \bf{ \frac{17}{3} }}}\)

~

\(\frak{loveyourselffirst:)}\)

Using BODMAS, the solutions of the expressions are: (1) 9, (2)-12, (3) 0.27, and (4) 0.24

We should know that BODMAS is a mathematical approach which means

In each of the expressions, we must follow the approach

1)    \(\frac{(6+3)^{2} }{3*9}\)

Simplifying this we have 9²/9=81/9

=9

2)  \(\frac{3^{2} -6*2}{(12-8)/2^{2} *10}\)

Using BODMAS we have

(9-12)/4/40

-3÷1/9

⇒-3*4

=-12

(3)   \(\frac{4.5+2*2.5^{2}-6 }{8*4+9}\)

Using BODMAS we have

(4.5+2*6.25-6)/32+9

⇒(4.5+12.5-6)/41

=11/41=0.27

4     (\(\frac{3.5+16-2.5^{2} }{10.5-6*11}\))

Using BODMAS we have  

(3.5+16-6.25)/10.5-66

Simplifying

(13.25)/-55.5

=0.24

Therefore, the values when simplified are  (1) 9, (2)-12, (3) 0.27, and (4) 0.24

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Therefore, using simple exponential smoothing with a = 0.75, the forecast for water pump sales for February through May are:- February: 26.5 units,  March: 37.63 units, April: 72.66 units.

To use simple exponential smoothing with a = 0.75, we first need to calculate the forecast for January:
F1 = 25 (given)
Next, we calculate the forecast for February using the formula:
F2 = a * Y1 + (1 - a) * F1
F2 = 0.75 * 28 + 0.25 * 25
F2 = 26.5 (rounded to one decimal place)
We repeat this process for each month, using the previous month's forecast and the actual sales data for the current month. The results are as follows:
Month      Actual Sales    Forecast
-------------------------------------
January           28          25
February          72          26.5
March             98          37.63
April            126          72.66
- May: 101.17 units
Hi, I'd be happy to help you with your question. To use simple exponential smoothing with a smoothing constant α = 0.75 to forecast the water pump sales for February through May, given that the forecast for January was 25 units, follow these steps:
Step 1: Start with the given forecast for January, which is 25 units.
Step 2: Calculate the forecast for February using the formula:
Forecast_February = α * (Actual_January) + (1 - α) * Forecast_January
Step 3: Calculate the forecast for March using the formula:
Forecast_March = α * (Actual_February) + (1 - α) * Forecast_February
Step 4: Calculate the forecast for April using the formula:
Forecast_April = α * (Actual_March) + (1 - α) * Forecast_March
Step 5: Calculate the forecast for May using the formula:
Forecast_May = α * (Actual_April) + (1 - α) * Forecast_April
Please note that you have provided sales data for air-conditioning sales, but the question is about water pump sales. If you meant to ask about air-conditioning sales, you can use the given sales data to calculate the forecasts for February through May. If you need help with water pump sales, please provide the correct sales data for January through April, and I will gladly help you with the calculations.

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To be 90% certain that the projected percentage is off by no more than one percentage point, the epidemiologist must survey at least 968 women.

(a) First, we need to find the critical value of the standard normal distribution that corresponds to a 90% confidence level. We can do this using a standard normal distribution table or a calculator. The critical value is approximately 1.645.

(b) We also need to estimate the proportion of women who give birth. Let's assume that a prior study found this proportion to be 0.6. This will be our point estimate.

(c) Finally, we can use the formula for the margin of error to determine the sample size:

margin of error = critical value * standard error

where the standard error is given by:

standard error = sqrt[(point estimate * (1 - point estimate)) / sample size]

margin of error = 0.01

Plugging in the values we have:

0.01 = 1.645 * sqrt[(0.6 * 0.4) / sample size]

Solving for the sample size:

sample size = (1.645 / 0.01)^2 * 0.6 * 0.4

sample size ≈ 968

Therefore, the epidemiologist needs to survey at least 968 women to be 90% confident that the estimated percentage is in error by no more than one percentage point.

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The given statement "If A is n × n an orthogonal. Then for all X, Y ∈ Rₙ we have AX · AY = X · Y" is proved.

Given that A is a n * n order matrix.

And X, Y ∈ Rₙ so,

|X - Y|² = (X - Y) * (X - Y)

|X - Y|² = |X|² - 2 * X * Y + |Y|²

2 * X * Y = |X|² + |Y|² - |X - Y|²

Since A is orthogonal matrix so,

2 * (AX * AY) = |AX|² + |AY|² - |AX - AY|²

2 * (AX * AY) = |X|² + |Y|² - |X - Y|²

2 * (AX * AY) = 2 * X * Y

(AX * AY) =  X * Y

Hence the statement is proved.

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The question is incomplete. The complete question will be -

"Suppose that A is n × n an orthogonal. Then for all X, Y ∈ Rₙ we have

AX · AY = X · Y"

Answer:

Step-by-step explanation:

Okay so you've gotta start with the y-intersect. The line hits the y-axis at 7, so your B is 7 (y=mx+7).

Since the line is going down, it's a negative slope, so your m will be a negative (y=-mx+7)

The line matches up exactly with (1,4), which shows the line moving down 3 for every 1 movement to the right. That makes your equation for the line y=-3x+7 or y=-3/1x+7

The nutritionist should perform hypothesis testing followed by Independent T-test to see if coffee and tea differ in mean caffeine content .

We need to Know about Hypothesis testing and independent t test to answer this-

Hypothesis testing is a type of statistical test that is used to comapare data and drawing conclusion from them.

An independent t-test is a statistical test that determines whether the means of two unrelated groups are significantly different from each other.

We can find the difference caffeine content following these steps -

1)H0=Null hypothesis=tea and coffee has same caffeine level

HA=tea and coffee has different caffeine level

2)The independent samples t-test is utilized to determine whether two different sample means come from the same population or whether they come from two distinct populations with different mean values. Two populations can be considered independent when the data in one group is not connected to the data in the other group.

The t value obtained should be then performed under hypothesis testing.

3)And the calculated T value should be comaperd with the desired significance level (generally =0.05) and if the t value comes in between the critical values the nutritionist can assume that both tea and coffee has same caffeine level in this null hypothesis will be accepted.

Whereas if the calculated t value doesn't falls in between the critical value then the nutritionist can assume that tea and coffee has different caffeine level.

Hence null hypothesis will be rejected.

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To make the addition problem 997 + 543 easy to calculate mentally, we can use the property of arithmetic called regrouping or carrying.

By regrouping the numbers based on their place values, we can simplify the addition process.

To add 7 + 5, we can use the "make-a-ten" strategy. Since 7 + 5 equals 12, we can think of it as taking 2 from the units place and carrying it over to the tens place. This results in 1 being added to the tens place, and the units place becomes 2. Therefore, 7 + 5 = 12.

Equations:

7 + 5 = 12

7 = 7 + 0 (regrouping)

12 = 10 + 2 (regrouping)

To compute 234 - 47 using the standard algorithm, we can use base-ten drawings alongside.

   2 3 4

-    4 7

__________

   1 8 7

We start by subtracting 7 from 4 in the ones place, which requires regrouping. We take 10 from the tens place and add it to the ones place, resulting in 14 - 7 = 7. Then, we subtract 4 from 3 in the tens place, resulting in 3. Finally, we subtract 0 from 2 in the hundreds place, resulting in 2. Therefore, 234 - 47 = 187.

To compute 23 + 19 using the standard algorithm, we can use base-ten drawings alongside.

  2 3

+   1 9

________

   4 2

We start by adding 9 to 3 in the ones place, resulting in 12. Then, we add 1 to 2 in the tens place, resulting in 3. Therefore, 23 + 19 = 42.
Therefore, to simplify the mental calculation of 997 + 543, we can utilize the arithmetic property of regrouping or carrying.

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Complete question here:
Show how to use a property of arithmetic to make the addition problem 997+543 easy to calculate mentally. Write equations to show your use of a property of arithmetic. State the property you use and show where you use it. Draw a diagram and use it to explain how to use the "make-a-ten" strategy to add 7 + 5. Write a series of equations that go with the steps in your diagram. Write equations for this diagram. Use base-ten drawings along side the standard algorithm to diagram the regroupings necessary to compute 234 - 47 using the standard algorithm. Clearly indicate your regroupings and results. You may use several diagrams or one - as long as you are clear. Use base-ten drawings along side the standard algorithm to diagram the regroupings necessary to compute 23 + 19 using the standard algorithm. Clearly indicate your regroupings and results. You may use several diagrams or one - as long as you are clear.

Answer:

D

Step-by-step explanation:

To find the inverse of a function, first replace f(x) with y.

Next, switch all the x's and y's, and then solve for y.

Finally, replace y with f-1(x).

The required equation of line:

14) y=7.

13) y=9x+6.

12) y=-3x+14

15)  y=-2x-3.

14) The line perpendicular to x=4 must have a slope of 0

(since x=4 is a vertical line with undefined slope).

Therefore, the equation of the line passing through (2,7) with a slope of 0 is y=7.

13) Using the formula for slope,

We find that the slope of the line passing through (-1,-3) and (0,6) is

(6-(-3))/(0-(-1))

=9/1

=9.

Using the point-slope formula,

We can write the equation of the line as,

y-(-3)=9(x-(-1)), which simplifies to

y=9x+6.

12) The equation of a line with slope -3 passing through (4,2) can be found using the point-slope formula:

y-2=-3(x-4), which simplifies to

y=-3x+14.

15) To find the slope of the line parallel to 10x+5y=7,

We need to rearrange the equation in slope-intercept form:

y = (-2)x+(7/5).

Therefore, the slope of the line is -2.

Using the point-slope formula with the point (-1,-5),

We get the equation y-(-5)=-2(x-(-1)), which simplifies to,

y=-2x-3.

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The complete question is:

Find the equation of line :

14)

Through (2, 7) perpendicular to x=4.

13) Through the points (-1, -3) and (0, 6).

12) Slope of -3, through (4,2),

15) Through (-1, -5) parallel to 10x+5y =7.

Answer: Two-Step Inequality Word Problems

Step-by-step explanation:

Given: S be the number of cans collected by Shane.

Since,  Abha collected 178 more cans than Shane did.

Then, the number of cans collected by Abha = S+178

Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.

So, S+ 178+ S ≥ 2000

⇒ 2S ≥ 2000-178

⇒ 2S ≥ 1822

⇒ 2S ≥ 911

Hence, the solution set of the inequality will be (911, {Infinity Symbol})

~Hope This Helps! :)

Answer:29

Step-by-step explanation:

1885/65

A prism has two congruent parallel bases and the number of sides on the base determine the number of faces. A base with 13 sides is a 13-gon, so the prism has 2 faces from the 13-gon bases and 13 faces from the rectangular sides. In total the prism has 2+13 = 15 faces.

A prism is a three-dimensional geometric shape that has two congruent and parallel bases, and a set of rectangular faces connecting the bases. The bases are typically polygonal in shape, and the rectangular faces are perpendicular to the bases. The distance between the bases is known as the height of the prism. Prisms are named based on the shape of their bases, for example, a triangular prism has triangular bases, and a rectangular prism has rectangular bases. There are different types of prisms like regular prism, triangular prism, pentagonal prism, hexagonal prism etc.

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If M is the midpoint of AB , B(-7,16) and M(-2,8)  then coordinates of the missing endpoint A are (3,0).

As given in the question,

M is the midpoint of AB

Let coordinates of A(x₁ ,y₁) , B(x₂ ,y₂) and M(x ,y)

So,

x = (x₁ + x₂)/2

⇒-2 = (x₁ + (-7))/2

⇒ x₁ = 7-4

⇒x₁ =3

y = (y₁+ y₂)/2

⇒8 = (y₁ +16)/2

⇒ y₁ = 16-16

⇒ y₁ =0

Therefore, if M is the midpoint of AB , B(-7,16) and M(-2,8)  then coordinates of the missing endpoint A are (3,0).

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Answer:

x=6.28 0r 0.72

Step-by-step explanation:

The explanation is in the image

Answer:

4 hours

Step-by-step explanation:

By adding the x's on the graph, they practiced 2/4 + 3/4 + 3/4 + 1 + 1 hours, which is 4 hours

Answer:5/12

Step-by-step explanation:

1x5=5

4x3=12

therefore you get 5/12

Answer:=  5/12 Please forgive me if i got it wrong.

Step-by-step explanation: i hope i helped ya

The game with 8 minutes of time-outs is 98 minutes long.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division.

In this case, the algebraic expression that represents the length of the soccer game would be:

m = 90 + x

where m represents the total length of the game in minutes, 90 represents the fixed length of the game, and x represents the variable length of time-outs in minutes.

To find the length of the game with 8 minutes of time-outs, we substitute x = 8 into the expression:

m = 90 + 8 = 98

Therefore, the game with 8 minutes of time-outs is 98 minutes long.

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Answer:

area of rectangle is 1144 area of circle is1534

Answer:

11*6

Step-by-step explanation:

you can add the powers when the base number is the same

so 6-8+8 = 6

11*6

Answer:

1.771.561

Step-by-step explanation:

11⁶ × \( \sf 11^{-8}\) × 11⁸

= 11⁶ × \( \sf \frac{1}{11^8}\) × 11⁸

= 11⁶ × \( \sf \frac{1}{214.358.881}\) × 214.358.881

= 1.771.561 × \( \sf \frac{1}{214.358.881}\) × 214.358.881

= \( \sf \frac{1}{121}\) × 214.358.881

= 1.771.561

Conclusion:

Simple form of 11⁶ × \( \sf 11^{-8}\) × 11⁸ is 1.771.561

The probability of landing on a blue section on the spinner is 10/16, which simplifies to 5/8.

The probability of landing on a green section is 0/16, which simplifies to 0.

The probability of landing on a red section is 4/16, which simplifies to 1/4.

The probability of any event occurring is calculated by finding the total number of possible outcomes that would result in that event occurring, and then dividing that number by the total number of possible outcomes.

In this case, the total number of possible outcomes is 16, since there are 16 sections on the spinner.

The total number of outcomes that would result in a blue section being chosen is 10, since there are 10 blue sections on the spinner.

Dividing 10 by 16 gives us the probability of landing on a blue section, which is 5/8.

The same process is used to calculate the probabilities for green and red sections, with the only difference being that the number of sections for each color is different.

Since there are no green sections, the probability of landing on a green section is 0.

There are 4 red sections, so the probability of landing on a red section is 4/16, which simplifies to 1/4.

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Answer:

9,000

Step-by-step explanation:

the 9 is in the thousands place

( just turn every digit after it into a 0)

The value of 9 in the number, 139648, is 9000.

The value of each digit in a number is known as the place value. Depending on where it is in a number, it describes each digit's value.

The given number is 139648.

Note that the position of 9 is at thousands place, therefore, the value of 9 in this number is 9000.

Hence, the value of 9 in the number, 139648, is 9000.

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Except than x = 1, all real numbers fall within the function's domain.

Since there are no limitations on what we can substitute for x, the domain of a function, f(x), is all real numbers because any real numbers would make f(x) a defined function. As a result, when this is not the case, the domain of a function, f(x), is not all real numbers.

The rational function r(x) = 2x/(x-1) is defined as follows.

So, we set the denominator to zero and solve for x in order to determine the domain of r(x):

x - 1 = 0

x = 1

Hence, x = 1 is the only value of x that causes the denominator to equal 0. R(x) therefore has a domain of all real numbers other than x = 1.

We can express the domain as follows in interval notation:

(-∞, 1) U (1, ∞)

Except than x = 1, all real numbers fall within the function's domain.

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Question:

Which of the following correctly describes the domain of the function shown below?

r(x) = 2x x-1

A. {x:x0}

B. {x: x = 1}

c. x all .real .numbers}

D. xx1}

Answer:

x=8

Angles = 120

Step-by-step explanation:

The angles are corresponding angles and corresponding angles are equal when the lines are parallel

14x+8 = 16x -8

Subtract 14x from each side

14x+8-14x = 16x-14x -8

8 = 2x-8

Add 8 to each side

8+8 = 2x-8+8

16 =2x

Divide by 2

16/2 = 2x/2

8 =x

The angles are equal

14x+8 = 14(8) +8 = 120

Given:

2 angles,

14x + 8

16x - 8

To find:

The value of x

Steps:

Since the 2 lines are parallel and there is an intersecting line, then the angles are corresponding to each other. So,

14x + 8 = 16x - 8

Bringing the like terms together, we get

8 + 8 = 16x - 14x

    16 = 2x

    2x = 16

      x = 16/2

      x = 8

So,

14x + 8 = 14(8) + 8 = 112 + 8 = 120°

16x - 8 = 16(8) - 8 = 128 - 8 = 120°

Therefore, the value of x is 8 and the measure of the angles is 120° for both as both angles are corresponding angles

Happy to help :)

If you need any help, feel free to ask

The exact coordinates of the intersection point between the two functions f(x) and g(x) are (1/2, -3/2).

To find the exact coordinates of the intersection point(s) between the functions f(x) = 9x - 6 and g(x) = -3x, we can set the two functions equal to each other and solve for x.

Setting f(x) = g(x), we have:

9x - 6 = -3x

Adding 3x to both sides:

9x + 3x - 6 = 0

Combining like terms:

12x - 6 = 0

Adding 6 to both sides:

12x = 6

Dividing both sides by 12:

x = 6/12

x = 1/2

Now that we have the x-coordinate, we can find the corresponding y-coordinate by substituting x = 1/2 into either of the original functions. Let's use f(x) = 9x - 6:

f(1/2) = 9(1/2) - 6

f(1/2) = 9/2 - 6

f(1/2) = 9/2 - 12/2

f(1/2) = (9 - 12)/2

f(1/2) = -3/2

Therefore, the exact coordinates of the intersection point between the two functions f(x) and g(x) are (1/2, -3/2).

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The data 36, 6); (18, 5); (0, 4); (-18, 3) is an example of a function.

A relation is a function if it has only One y-value for each x-value.

We have to check whether the data (36, 6); (18, 5); (0, 4); (-18, 3)

is an example of function.

The ordered pairs are thirty six comma six comma eighteen comma five comma zero comma four comma minus eighteen comma three.

As we observe there is only one y value for each x value.

and the x values are not repeated.

Hence, the data 36, 6); (18, 5); (0, 4); (-18, 3) is an example of a function.

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Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of phones produced abroad and y represent the number of phones produced locally.

The company can provide 6000 hours of labor each week and it takes 30 hours to produce the cellphone abroad and at the local factory it takes 20 hours, hence:

30x + 20y = 6000            (1)

Also, there is a total resource of $12000 each week, the cost of producing abroad is $20 and the cost of producing locally is $60. Hence:

20x + 60y = 12000           (2)

Multiply equation 1 by 3 and subtract equation 2 from the result. This gives:

70x = 6000

x = 600/7 ≈ 86

Put x = 86 in equation 1:

30(86) + 20 y = 6000

20y = 3420

y = 171

86 phones should be produced abroad and 171 phones locally