For any real number √a²
a
- |al
lal.
-a

Answers

Answer 1

Answer:

|a|

Step-by-step explanation:

For any positive or negative a, when you square it, the answer is positive.

The square root symbol means the principal square root. For a positive number, the principal square root is positive. To make sure the square root is always non-negative, use absolute value.

Answer: |a|


Related Questions

An office manager buys 2 office chairs and 4 file cabinets for $380. Next year she buys 4 office chairs and 6 file cabinets for $660. What is the cost of each office chair, c? What is the cost of each file cabinet, f? Explain how you fond the cost of each chair and file cabinet.

Answers

Answer:

16.5

Step-by-step explanation:

Answer:

file cabinet = 50

chair = 90

Step-by-step explanation:

x = chair

y = file cabinet

1st year, solve for x

2x+4y = 380

2x = 380 - 4y

x = 190 - 2y

2nd year

Now substitute x = 190 - 2y in your 2nd year formula

4x+6y = 660

4(190-2y)+6y = 660

760 - 8y + 6y = 660

-2y = -100

y = 50

The cost of the filling cabinet is 50 each

Now use the value for y (50) in your first formula to get x

2x+4y=380

2x+4*50=380

2x=380-200

2x=180

x=90

The lifespan, in years, of a certain computer is exponentially distributed. The probability that its lifespan exceeds four years is 0.30. Let f(x) represent the density function of the computer's lifespan, in years, for x>0. Determine an expression for f(x).

Answers

Answer:

The correct answer is "[tex]0.300993e^{-0.300993x}[/tex]".

Step-by-step explanation:

According to the question,

⇒ [tex]P(x>4)=0.3[/tex]

We know that,

⇒ [tex]P(X > x) = e^{(-\lambda\times x)}[/tex]

⇒     [tex]e^{(-\lambda\times 4)} = 0.3[/tex]

∵ [tex]\lambda = 0.300993[/tex]

Now,

⇒ [tex]f(x) = \lambda e^{-\lambda x}[/tex]

By putting the value, we get

           [tex]=0.300993e^{-0.300993x}[/tex]

One of the lengths of a leg of a right angled triangle is 15 feet. The length of the hypotenuse is 17 feet. Find the length of the other leg.
4 feet
6 feet
8 feet
10 feet

Answers

the hypotenuse^2 = sum of the squares of the other two sides
so the other should be = squareroot of 17^2 - 15^2 = 8 feet. i guess

Answer:

8ft

Step-by-step explanation:

We need to find out the length of the other leg of the triangle . Since it is a right angled triangle, we can use Pythagoras Theorem here , as,

[tex]\sf\implies h^2 = p^2 + b^2 \\\\\sf\implies (17ft)^2= p^2 + (15ft)^2\\\\\sf\implies 289 ft^2 - 225ft^2 = b^2 \\\\\sf\implies b^2 = 64 ft^2\\\\\sf\implies \underline{\underline{ base = 8 \ ft }}[/tex]

Can someone help me with this question an also the rest of my school work?

Answers

Answer:

I think this one is B

Step-by-step explanation:

i need helpp pleaseee

Answers

To plot the point (3,-7) start at the origin (0,0) and move right three (3) units and then down seven (7) units.

A town recently dismissed 5 employees in order to meet their new budget reductions. The town had 4 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that no more than 1 employee was over 50

Answers

Answer:

0.7513 = 75.13% probability that no more than 1 employee was over 50

Step-by-step explanation:

The employees are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

4 + 16 = 20 employees, which means that [tex]N = 20[/tex]

4 over 50, which means that [tex]k = 4[/tex]

5 were dismissed, which means that [tex]n = 5[/tex]

What is the probability that no more than 1 employee was over 50?

Probability of at most one over 50, which is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,20,5,4) = \frac{C_{4,0}*C_{16,5}}{C_{20,5}} = 0.2817[/tex]

[tex]P(X = 1) = h(1,20,5,4) = \frac{C_{4,1}*C_{16,4}}{C_{20,5}} = 0.4696[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2817 + 0.4696 = 0.7513[/tex]

0.7513 = 75.13% probability that no more than 1 employee was over 50

Indicate the method you would use to prove the triangles congruent. If no
method applies, enter "none."
O SSS
k O SAS
O ASA
© None

Answers

Step-by-step explanation:

I suspect we don't see the full information for the problem here.

all listed 3 methods are typically used to prove that triangles are congruent (= when turned to have the same orientation, they would simply cover each other completely - no overhanging parts from either triangle).

I guess there is a diagram with 2 triangles and what is known about them.

and since we cannot see them, we cannot tell you which method would apply here.

just remember

SSS means all 3 sides of one triangle are exactly the same as the 3 sides of the other triangle. if you know the lengths of all 3 sides, there is only one triangle you can create. you can only orient it differently.

SAS means two sides and the enclosed angle are the same. again, only one triangle can be created with that information.

ASA means one side and the 2 angles at the end points of that side are known. again, only one triangle can be created with that information.

LMNP is a parallelogram.

On a coordinate plane, parallelogram L M N P is shown. Point L is at (negative 4, 1), point M is at (2, 4), point N is at (3, 2), and point P is at (negative 3, negative 1).

What additional information would prove that LMNP is a rectangle?

The length of LM is StartRoot 45 EndRoot and the length of MN is StartRoot 5 EndRoot.
The slope of LP and MN is –2.
LM ∥ PN
LP ⊥ PN

Answers

Answer:

LP ⊥ PN

Step-by-step explanation:

Given

[tex]L = (-4, 1)[/tex]

[tex]M = (2, 4)[/tex]

[tex]N = (3, 2)[/tex]

[tex]P = (-3, -1)[/tex]

See attachment

Required

What proves LMNP is a rectangle

The additional information needed is LP ⊥ PN

Because:

[tex](a)\ LM= \sqrt{45}; MN = \sqrt{5}[/tex]

This can be true for other shapes, such as trapezoid, etc.

[tex](b)\ m(LP) = m(MN) = -2[/tex]

The slopes of LP and MN will be the same because both sides are parallel; However, this is not peculiar to rectangles alone. Same as option (c)

(d) LP ⊥ PN

This must be true i.e. LP must be perpendicular to PN

Answer:

d

Step-by-step explanation:

According to the Venn Diagram below and given that P(A) = .4 as well as
P(B) = .3 what is P(AUB)?

Answers

Hello,

P(A)=0.4

P(B)=0.3

P(AUB)+P(A∩B)=P(A)+P(B)

P(AUB)=0.4+0.3-0.1=0.6

Answer C

The correct answer is option (C).

P(A ∪ B) = 0.6

Formula to find P(A ∪ B):

If A, B are two different events then P(A U B) = P(A) + P(B) - P(A ∩ B)

We have been given, P(A) = 0.4, P(B) = 0.3

From given Venn diagram,

P(A ∩ B) = 0.10

Now, P(A U B) = P(A) + P(B) - P(A ∩ B)

⇒ P(A U B) = 0.4 + 0.3 - 0.10

⇒ P(A ∪ B) = 0.6

Therefore, the correct answer is option (C) .6

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What is the sum of the first 7 terms of the geometric series:

Answers

Answer:

-15.875

Step-by-step explanation:

First, we can sum up the first 5 terms.

-8 + (-4) = -12

-12 + (-2) = -14

-14 + (-1) = -15

-15 + (-1/2) = -15.5

Next, we can find a pattern in the data. We can tell that the next number is one half of the current number. For example, -4 is one half of -8. To find the next number, we simply multiply our current number by one half. Thus, the sixth number is -1/4 and the seventh is -1/8. Adding these to our current total, we have

-15.5 - 1/4 = -15.75

-15.5 - 1/8 = -15.875 as our answer

Expand (2x - 4)2 using the square of a binomial formula.
(x)2 + 2(x)(4) + 42
O (2x)2 + 2(2x)(4) - 42
O(x2 - 2(x)(4) - 42
(2x)2 - 2(2x)(4) + 42

Answers

Step-by-step explanation:

We have to expand,

[tex]\longrightarrow [/tex] (2x 4)²

(a ― b)² = a² + b² ― 2ab

[tex]\longrightarrow [/tex] (2x)² + (4)² ― 2(2x × 4)

[tex]\longrightarrow [/tex] 4x² + 16 ― 2(8x)

[tex]\longrightarrow [/tex] 4x² + 16 ― 16x

[tex]\longrightarrow [/tex] 4x² ― 16x + 16

Hence, solved!

Answer:

D is the correct answer (2x)2 – 2(2x)(4) + 42

Step-by-step explanation:

Choose the correct answers for (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save money at the monthly rate to buy the item for its cash price.
A bunk bed with a cash price of $1,998, at $143 per month for 15 months

Answers

Answer:

$2,145 ; $147 ; 14 months

Step-by-step explanation:

Given that :

The cash price, that is, the amount that would be paid if customer is to pay the entire amount item is worth at once = $1998

Monthly payment = $143

Period = 15 months

The total installment price ; total amount paid on a monthly pay for 15 months :

(monthly payment * period)

($143 * 15)

= $2,145

The carrying charge :

Installment pay - Cash amount

$(2,145 - 1,998)

= $147

The number of month needed to save at Monthly rate to buy item at it's cash price :

Cash price / monthly payment

$1998 / $143

= 13.97

= 14 months

Find the measure of of RA.

Answers

Answer:

RA = 24

Step-by-step explanation:

Since the triangle is isosceles ( 2 equal sides ) , then LU is a perpendicular bisector , so

AU = RU , that is

4r = 18 - 2r ( add 2r to both sides )

6r = 18 ( divide both sides by 6 )

r = 3

Then

RA = 18 - 2r + 4r = 18 + 2r = 18 + 2(3) = 18 + 6 = 24

Find the sum of the complex numbers (3+3i)+(8+7i)

Answers

Answer:

11 + 10i

Step-by-step explanation:

Just treat i like any other variable, and combine like terms. Hope that helps!

-3xy^2+5xy^2
Operations with polynomials

Answers

9514 1404 393

Answer:

  2xy^2

Step-by-step explanation:

The terms are "like" so can be combined. It might be helpful to think of this as an application of the distributive property.

  -3xy^2 +5xy^2 = (-3 +5)xy^2 = 2xy^2

-5(8a+1)+6=281
Does anyone know the answer

Answers

Step 1: Distribute

-40a - 5 + 6 = 281

Step 2: Combine Like Terms

-40a + 1 = 281

Step 3: Move Variables and Constants to Different Sides

-40a = 280

Step 4: Divide

a = -7

Hope this helps!

a = -7

Step-by-step explanation;

-5 ( 8a + 1 ) + 6 = 281

Step 1 :- Distribute -5 through parantheses.

-5 × 8a + 5 × 1 + 6 = 281-40a - 5 + 6 = 281

Step 2 :- Combine like terms.

-40a + 1 = 281

Step 3 :- Move constant to right-hand side and change their sign.

-40a = 281 - 1

Step 4 :- Subtract the numbers.

-40a = 280

Step 5 :- Divie both side by -40 .

-40a / -40 = 280 / -40a = -7

√(9+ √32)

Please simplify

Answers

Answer:

3.82

Step-by-step explanation:

[tex]\sqrt{(9+\sqrt{32}) }[/tex] Do not confirm the answer unless your equation looks like that?

[tex]\sqrt{(9+\sqrt{32}) }[/tex] Start by the [tex]\sqrt{32}[/tex]

[tex]\sqrt{(9+5.65) }[/tex] Now add (9 + 5.65)

[tex]\sqrt{14.65}[/tex]         Finally Simplify

[tex]3.82[/tex]              Final answer



√9


√32


3


5.6569
≈ 0.5303

On Friday Evelyn sold 9 dresses and 20 pairs of pants. On Saturday she sold twice as many dresses and 10 more pants than Friday. How many dresses did Evelyn sell on Friday and Saturday?

Answers

Answer: 27 Dresses and 50 Pants

Step-by-step explanation:

If she sold 9 pairs of pants and

9 x 2 = 18

18 + 9 = 27

20 + 10 = 30

30 + 20 = 50

Evelyn sold 9 dresses and 20 pairs of pants on Friday, and on Saturday, she sold 18 dresses and 30 pairs of pants.

Evelyn's sales of dresses and pants over two days, Friday and Saturday. We'll use some mathematical expressions and reasoning to find out how many dresses Evelyn sold on each day.

Let's start by assigning some variables to represent the number of dresses and pants Evelyn sold on Friday and Saturday. We'll use "F" for Friday and "S" for Saturday. So, let [tex]D_F[/tex] be the number of dresses sold on Friday, [tex]D_S[/tex] be the number of dresses sold on Saturday, [tex]P_F[/tex] be the number of pants sold on Friday, and [tex]P_S[/tex] be the number of pants sold on Saturday.

According to the problem, on Friday, Evelyn sold 9 dresses, which can be expressed as:

[tex]D_F[/tex] = 9

She also sold 20 pairs of pants on Friday:

[tex]P_F[/tex] = 20

Now, let's move on to Saturday's sales. It says she sold twice as many dresses as Friday, which means the number of dresses on Saturday is double that of Friday's sales:

[tex]D_S = 2 * D_F[/tex]

Additionally, she sold 10 more pairs of pants on Saturday compared to Friday:

[tex]P_S = P_F + 10[/tex]

We already know that [tex]D_F = 9[/tex], so we can find the number of dresses sold on Saturday by substituting this value into the equation for [tex]D_S[/tex]:

[tex]D_S = 2 * 9 = 18[/tex]

Next, we'll calculate the number of pants sold on Saturday using the given information. Since [tex]P_F = 20[/tex], we can find [tex]P_S[/tex]:

[tex]P_S = 20 + 10 = 30[/tex]

So, to summarize, Evelyn sold 9 dresses and 20 pairs of pants on Friday, and on Saturday, she sold 18 dresses and 30 pairs of pants.

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A movie theater has a seating capacity of 283. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2060 on a sold out night, how many children, students, and adults attended

Answers

Answer: adults = 79

children = 158

student = 46

Step-by-step explanation:

Let a = adults

Let c = children

Let s = student

From the information given,

a + c + s = 283 ....... i

c/a = 2, c = 2a ....... ii

5c + 7s + 12a = 2060 ...... iii

Put the value of c = 2a into equation i

a + c + s = 283

a + 2a + s = 283

3a + s = 283

s = 283 - 3a

Note that c = 2a

From equation iii

5c + 7s + 12a = 2060

5(2a) + 7(283 - 3a) + 12a = 2060

10a + 1981 - 21a + 12a = 2060

10a + 12a - 21a = 2060 - 1981

a = 79

Note c = 2a

c = 2 × 79 = 158

Since a + c + s = 283

79 + 158 + s = 283

s = 283 - 237

s = 46

adults = 79

children = 158

student = 46

The graph of a line goes through the points (-4,3) and (6,8). What is the equation of the line in slope-intercept form?
Enter the correct answer in the box by replacing m and b with the appropriate values.
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a, sin cos tan sin costan!
μ ρ Φ
CSC seccot log log. In
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Σ
U (0)
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5
A
>
S
2
II
1
y = mx + b
I
Submit
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Type here to search
73°F Mostly cloudy
327 PM
7/3/2001

Answers

Answer:

[tex]y=\frac{1}{2}x+5[/tex]

Step-by-step explanation:

Hi there!

Slope intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that lie on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug the given points (-4,3) and (6,8) into the equation

[tex]m=\frac{8-3}{6-(-4)}\\m=\frac{8-3}{6+4}\\m=\frac{5}{10}\\m=\frac{1}{2}[/tex]

Therefore, the slope of the line is [tex]\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex] :

[tex]y=\frac{1}{2}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{1}{2}x+b[/tex]

Plug in one of the given points and solve for b

[tex]8=\frac{1}{2}(6)+b\\8=3+b[/tex]

Subtract 3 from both sides to isolate b

[tex]8-3=3+b-3\\5=b[/tex]

Therefore, the y-intercept is 5. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:

[tex]y=\frac{1}{2}x+5[/tex]

I hope this helps!


Andrew worked over 40 hours this week. He earns $12 an hour and gets paid time and a half for overtime. If x represents total hours worked, which equation will result in the
amount of money earned for the week?

Answers

Answer:

y = 480 + 1.5 (x-40)

Step-by-step explanation:

sometimes its better to answer the question and make the formula from that

40 x 12 = 480

1.5 for overtime

x

y = 480 + 1.5 (x-40)

I need help with these questions

Answers

Answer:

1) 6m+8n

4) 21x+14y

7) 14c+16d

10) d+3e

Step-by-step explanation:

Simplify -|-5 + 2|
someone help quick

Answers

Answer:

-3

Step-by-step explanation:

an interest expense of $125 has been incorrectly debited to utilities expense.

Answers

Answer:

125x=(62.50+(62.50)×0

Round 100.9052 to the nearest hundredths

Answers

To round 100.952 to the nearest tenth consider the hundredths’ value of 100.952, which is 5 and equal or more than 5. Therefore, the tenths value of 100.952 increases by 1 to 0.

100.952 rounded to the nearest tenth = 101.0

An amusement park offers 2 options on tickets into the park. People can either buy 5 admission tickets for $130 or buy 1 admission ticket for $30. How much money will a group of 5 people save by buying 5 admission tickets for $130?

Answers

Answer:

You could save $20

Step-by-step explanation:

For buying them separately for $30 each for 5 people it would be $150 but if you buy the first option you would get 5 admission tickets for only $130

Answer:

20 dollars

Step-by-step explanation:

for the first deal is 5 for $130

and the second is for $30

$30 times 5 (the number of people) = $150

$150-$130= is 20

answer: $20

TRUE or FALSE: The regression equation is always the best predictor of a y value for a given value of x. Defend your answer.

Answers

Answer:

FALSE

Step-by-step explanation:

The regression equation is a prediction model which is generated for a given independent, x and dependent, y variable. The regression model is usually ideal when both the dependent and independent variables are numerical. The regression equation cannot be generated if either the x or y value is non-numeric. In such situation, classification models may be better suited for such cases especially if there is no efficient method of converting the non-numeric column into a numeric variable.

PLEASE HELPPPP WILL GIVE BRAINLIESTTTT

Factor the following expressions completely. Show and check all work on your own paper.
9x2-18x+9

Answers

Hi there!

[tex]\large\boxed{9(x - 1)^{2}}[/tex]

9x² - 18x + 9

We can begin by factoring out a 9 from each term:

9(x² - 2x + 1)

Now, find two terms that add up to -2 and equal 1 when multiplied. We get:

9(x - 1)(x - 1)

Or:

9(x - 1)²

HELP ME WITH THIS TO EARN BRAINLIEST!!!!!!

Answers

Answer:

Step-by-step explanation:

answer C looks good  

Answer:

option c is answer

Step-by-step explanation:

as we can see r^2 =(d/2)^2

r^2=(6/2)^2

r^2=36/4=9

A=πr^2

A=9π

The following data set represents the ages of all 6 of Nancy's grandchildren.
11, 8, 5, 6, 3,9
To determine the "spread" of the data, would you employ calculations for the sample standard deviation, or population
standard deviation for this data set?

Answers

Answer:

Use calculation for the population  standard deviation

Step-by-step explanation:

We are given that the data data set represents the ages of all 6 of Nancy's grandchildren

11,8,5,6,3,9

We have to determine which standard deviation would used for calculation of  the given data set.

Sample standard deviation :If the data values represent the data collected from   subset of  population .Then the sample standard deviation should be used.

Population standard deviation:

If the data values represents the data collected from entire population, then population standard deviation should be used.

We can see that the given data collected from entire population.

Therefore, we would use  calculation for population standard deviation of given data set.

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For example, the exploration of the American West during the 19th century is a prime example of American exploration that led to the advancement of society. More land was found on the western frontier for settlement and new resources were discovered for use, leading to the nation's growth. Some have argued that many of the distinctive characteristics that make up American society, including inventiveness, inquisitiveness, and individualism, derived from the existence of a frontier. Although the western frontier closed around 1890, Americans later found a new frontier where that same curiosity translated to space exploration. Space as a new frontier has always been a driver of the U.S. space programs. As H. G. Wells said many years ago, "Human history becomes more and more a race between education and catastrophe." We are still in that race today, and surely an international cooperative venture into space strikes a blow against catastrophe and leads to a victory for civilization. Great things were achieved in the past in the name of competition, including the Apollo program, which would never have happened without Cold War competition. The Space Race between the Soviet Union and the U.S. led to the development of programs devoted to scientific research and inventions. Specifically, after the Soviet Union successfully launched Sputnik I, the world's first artificial satellite, America responded by developing and launching a satellite known as Explorer I. It now remains to be seen whether great things may be done in the name of international cooperation. If history has taught us anything, we must look to the future with the goal of preserving a culture that embraces endless possibilities in the spirit of both science and exploration. As we have seen in the past, exploration of the unknown leads to advancements and improvements that are beneficial to society. Select ALL the correct answers.Which two sentences from the passage are details and evidence used to support the author's claim?-More land was found on the western frontier for settlement and new resources were discovered for use, leading to the nation's growth.-We are still in that race today, and surely an international cooperative venture into space strikes a blow against catastrophe and leads to a victory for civilization.-Specifically, after the Soviet Union successfully launched Sputnik I, the world's first artificial satellite, America responded by developing and launching a satellite known as Explorer I.-Some have argued that many of the distinctive characteristics that make up American society, including inventiveness, inquisitiveness, and individualism, derived from the existence of a frontier.-Space as a new frontier has always been a driver of the U.S. space programs. 15< 4 + xO A. x>11O B. X> 19O C. x< 19O D. x< 11 Explain why it is not advisable for two sickle cell carriers to marry. show that pv=nrt has the same unit with energy Calculate the volume in liters of a 1.60 mol/L sodium nitrate solution that contains of sodium nitrate . Round your answer to significant digits.