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Answer:

(-(7 x + 272))/4

Step-by-step explanation:

Simplify the following:

x/2 - (2 + 1/4) x - 70 - ( - 2)

Hint: | Put the fractions in 2 + 1/4 over a common denominator.

Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:

x/2 - 9/4 x - 70 - ( - 2)

Hint: | Multiply 4 and 2 together.

4×2 = 8:

x/2 - (1/48 + 1/4) x - 70 - ( - 2)

Hint: | Add the fractions over a common denominator to a single fraction.

8/4 + 1/4 = (8 + 1)/4:

x/2 - 9/4 x - 70 - ( - 2)

Hint: | Evaluate 8 + 1.

8 + 1 = 9:

x/2 - 9 x/4 - 70 - ( - 2)

Hint: | Multiply -1 and -2 together.

-(-2) = 2:

x/2 - (9 x)/4 - 70 + 2

Hint: | Put the fractions in x/2 - (9 x)/4 - 70 + 2 over a common denominator.

Put each term in x/2 - (9 x)/4 - 70 + 2 over the common denominator 4: x/2 - (9 x)/4 - 70 + 2 = (2 x)/4 - (9 x)/4 - 280/4 + 8/4:

(2 x)/4 - (9 x)/4 - 280/4 + 8/4

Hint: | Combine (2 x)/4 - (9 x)/4 - 280/4 + 8/4 into a single fraction.

(2 x)/4 - (9 x)/4 - 280/4 + 8/4 = (2 x - 9 x - 280 + 8)/4:

(2 x - 9 x - 280 + 8)/4

Hint: | Group like terms in 2 x - 9 x - 280 + 8.

Grouping like terms, 2 x - 9 x - 280 + 8 = (2 x - 9 x) + (8 - 280):

((2 x - 9 x) + (8 - 280))/4

Hint: | Combine like terms in 2 x - 9 x.

2 x - 9 x = -7 x:

(-7 x + (8 - 280))/4

Hint: | Evaluate 8 - 280.

8 - 280 = -272:

(-272 - 7 x)/4

Hint: | Factor a minus sign out of -7 x - 272.

Factor -1 out of -7 x - 272:

Answer: (-(7 x + 272))/4

1/2 x + (-70) - 2 1/4 x - (-2) = (-(7 x + 272))/4 = True

Answer:

30 cents per week

Step-by-step explanation:

The average is the sum of the numbers divided by how many there are.

60 + 10 + 20 = 90

90/3 = 30

Answer:

-30 per cents week !

Step-by-step explanation:

Answer:

a) H,N,K and I.

b) The line p.

c) The line r.

d) The line q can be also named putting the symbol '' ↔ '' over the capital letters JL, JK or KL.

e) The point N.

Step-by-step explanation:

Let's study each item in order to answer the question :

a) Four collinear points :

We know that two or more points are called ''collinear points'' wherever they belong to the same line.

In the diagram, the only line that contains four points which have name is the line r. The four points are H,N,K and I.

b) A line that contains point M :

In this case, the only line that contains to the point M is the line p because the point M is situated over the line p.

c) A line that contains points H and K :

The only line that contains both points is the line r because the points H and K are situated over the line r.

d) Another name for line q :

Another way to name any line is putting the symbol ''↔'' over a pair of points that are situated over the line (Let's remember that we write the points with capital letters).

One possible name for the line q can be written putting ''↔'' over JL.

The other two names can be written putting ''↔'' over the capital letters JK or KL.

e) The intersection of lines p and r :

There are three cases of intersection between lines :

1 - The case in which the lines don't intersect at any point at all.

2 - The case in which the lines intersect at one point.

3 - The case in which the lines intersect at infinite points (for this case, the lines are parallel and there are superimposed).

In this case, the intersection of the lines p and r is the point N (which belongs to both lines).

Answer: 99

Step-by-step explanation:

factor of 99: 1, 3, 9, 11, 33, 99

This is 6 factors, and they are all odd number

Hope this helps!! :)

Please let me know if you have any question

Answer:

The joint probability distribution of X and Y is shown below.

Step-by-step explanation:

The distributions of X and of Y are described as follows:

    X :    0           1

P (X) : 0.23      0.77

     Y :    1            2          3

P (Y) : 0.40     0.22     0.38

It is provided that X and Y are independent.

That is:

P (X ∩ Y) = P (X) × P (Y)

Compute the joint probability distribution of X and Y as follows:

[tex]P(X=0,Y=1)=P(X=0)\times P(Y=1)=0.23\times 0.40=0.92\\\\P(X=0,Y=2)=P(X=0)\times P(Y=2)=0.23\times 0.22=0.0506\\\\P(X=0,Y=3)=P(X=0)\times P(Y=3)=0.23\times 0.38=0.0874\\\\P(X=1,Y=1)=P(X=1)\times P(Y=1)=0.77\times 0.40=0.308\\\\P(X=1,Y=2)=P(X=1)\times P(Y=2)=0.77\times 0.22=0.1694\\\\P(X=1,Y=3)=P(X=1)\times P(Y=3)=0.77\times 0.38=0.2926[/tex]

      X       0                  1

Y                                              

1           0.9200        0.3080

2          0.0506        0.1694

3          0.0874         0.2926

Answer:

She have 345$ in her account.

Step-by-step explanation:

Given that,

Ellen has $75 in her savings account she deposits 25 every week her father also deposit 35 into the account every time Ellen most salon

Suppose, her savings account balance can be shown with the following expression:

75 + 25w + 35m

If Ellen saves for 8 weeks and most the salon 2 times, how much will she have in her account.

We know that,

When the numbers appear with variables it called coefficients.

When the numbers appear without variables it called constant.

Alphabets in an expression are called variables.

According to question,

25 and 35 are the coefficients and the number 75 appear without variables.

We need to calculate the balance in her account

Using expression

[tex] 75 + 25w + 35m [/tex]

Put the value in the expression

[tex]75+25\times8+35\times2[/tex]

[tex]=345$[/tex]

Hence, She have 345$ in her account.

Answer:

Step-by-step explanation:

[tex]14n+21\\\mathrm{Rewrite\:}21\mathrm{\:as\:}7\times\:3\\\mathrm{Rewrite\:}14\mathrm{\:as\:}7\times\:2\\\\=7\times\:2n+7\times\:3\\\\\mathrm{Factor\:out\:common\:term\:}7\\=7\left(2n+3\right)[/tex]

Answer:

fluid ounces

hope it helps;)

The most likely unit to measure the capacity of a mug is fluid ounces (fl oz).

The maximum amount that something can contain or hold is referred to as its capacity. It is useful for determining the volume of a container, such as a mug or a bucket. Capacity measurement units vary, but common ones include millilitres, litres, fluid ounces, and gallons.

Capacity is a measurement of how much fluid or material a container can hold, and it is usually expressed in ounces, millilitres, litres, or gallons.

Because a mug is a container that holds liquids, the appropriate unit of measurement to use when determining how much liquid a mug can hold is capacity.

Thus, the answer is fluid ounces.

For more details regarding capacity, visit:

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Answer:

Option (4)

Step-by-step explanation:

D = {x| x is a whole number}

D = {1, 2, 3, 4..........}

E = {x | x is a perfect square between 1 and 9}

E = {4}

F = {x | x is an even number greater than 2 and less than 9}

F = {2, 4, 6, 8}

(E ∩ F) = Set of common numbers of E and F

           = {4}

D ∩ (E ∩ F} = Set of common numbers in the sets of D and (E ∩ F)

                   = {4}

Therefore, Option (4) will be the answer.

Answer:

l = 26, w = 10

Step-by-step explanation:

These types of word problems always want you to use variables to find the answer. Variables are always going to represent the numbers you don't know.

This question wants you to find the length and width of the wall of the barn, so let's just use l for length (let l = length of barn wall) and w for width (let w = width of barn wall); this is called defining your variables, so that you--or anyone who looks at your work--know what the letter variable represents.

Now we use the other information we have to find what values the variables actually equal.

We know that the length is 6 feet longer than twice the width. To express this in terms of numbers and variables: l = 6 + 2w. This makes sense, right?

length = 6 + (2 * width)

If the total area of the wall is 260 square feet and we need to find the length and width, we can use the A = lw formula, which you can use for any rectangle. Since 260 is the area (A), we can put that into the formula so that we have 260 = lw.

Next, use the expression we came up with earlier (l = 6 + 2w) to help find the answer.

We have two equations now (l = 6 + 2w and 260 = lw) and we just need to put them together.

This part is the same as solving any other linear equation.

The approach I'll use is substitution:

l = 6 + 2w

260 = lw

Substitute 6 + 2w in for l:

260 = (6 + 2w) w

Distribute:

260 = 6w + 2w²

Solve:

w² + 3w - 130 = 0

w = -13, w = 10

(The width of a rectangle cannot be negative, so it has to be 10 ft.)

We're almost there. The last thing to do is to find the length. Just plug in 10 for w in the l = 6 + 2w formula:

l = 6 + 2(10) = 6 + 20 = 26

To check your work, we can double the width and add 6 to get 26, and 26 * 10 is 260.

So, the length of the wall of the barn is 26 and the width of the wall of the barn is 10.

Answer:

5 pounds

Step-by-step explanation:

(.15(20))/(20+w)=.12

3/(20+w)=.12

20+w=25

w=5

So 5 pounds of water must be added to the solution.

Answer:

h = 2A/b

Step-by-step explanation:

Step 1: Write out triangle formula

A = 1/2bh

Step 2: Multiply 2 on both sides to get rid of fraction

2A = bh

Step 3: Divide both sides by b to isolate h

2A/b = h

Step 4: Rearrange

h = 2A/b

Answer:

The question is incomeplete, below is the completed question

The World Malaria Report (2008) has information on the number of reported malaria cases from 2005–2006 for the ten countries listed in West Africa. The data are presented in the table below:

1. The mean reported West African malaria cases in 2005 is a. less than 116,698. b. greater than 1,600,000. c. 100,000. d. greater than 200,000.

2. The median reported malaria cases in 2006 is a. around 1,000,000. b. less than 200,000. c. 100,000. d. 3,000,000.

3. If the number of reported malaria cases in Sierra Leone were mistyped and reported as 1,160,666, what would happen to the mean and median? a. Both would remain unchanged. b. The mean would change, but the median would stay the same. c. The mean and median would change. d. You cannot tell without doing the actual calculation.

Answer:

The correct answers are:

1. greater than 200,000.  (d)

2. around 1,000,000 (a)

3. The mean and median would change (c)

Step-by-step explanation:

using the data in the attachment to this answer:

1.)The mean is a measure of ecntral tendency, calculated by summing the total of the values and dividing the result by the number of terms. From the data in the 2005 column, only one value is 116,698 and that value is (116,681), the rest of the 9 other values are greater than 116,698 hence option a (less than 116,698) is wrong.

b)Same reason holds for option b (greater than 1,600,000), only one value falls in this category, hence the mean cannot be more than 1,600,000.

c) since the lowest data in the dataset is 116,698, the mean cannot be 100,000, which is less than the lowest data in the dataset

d) The mean is greater than 200,000 because 8 out of 10 (80%) of the values are more than 200,000, hence this is the correct answer.

2) for the median of the 2006 data, let us arrange the values in ascending order:

160,000 266,188 566,450 861,847 1,022,592 1,105,272 1,253,408 1,555,310 2,060,867 3,511,452

For distribution with an even number of terms, the median = (sum of the two middle terms) ÷ 2

Two middle terms are 1,022,592, 1,105,272

Median = (1,022,592 + 1,105,272) ÷ 2

Median = 2127864 ÷ 2

Median = 1, 063, 932

Therefore median is around 1, 000, 000 (a)

3) mistyping the value for Sierra Leone as 1,160,666 instead of 160,666 for 2006, will increase the value by 1,000,000. Both the mean and the median will change, because the value 1,000,000 is a large number compared to the others on the list to cause a change.

Answer:

Step-by-step explanation:

Area of a triangle is given by

[tex]A = \frac{1}{2} bh[/tex]

where

b is the base

h is the height

From the question

Area = 21 m²

The statement

The height of a triangle is 8 m more than the length of the base is written as

h = 8 + b

Make b the subject

That's

b = h - 8

Substitute the expression into the above formula and solve for the height

That's

[tex]21 = \frac{1}{2} (h - 8)h[/tex]

Multiply through by 2

h² - 8h = 48

h² - 8h - 48 = 0

(h + 4)(h - 12) = 0

h + 4 = 0 h - 12 = 0

h = - 4 h = 12

Since the height cannot be a negative number we have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Since the actual probability of having a boy child is 0.51, the probability of having a girl child will be (1 - 0.51) = 0.49

A couple plans to have 3 kids; 2 of whom are boys

(A) Using the binomial model, the probability that 2 of the 3 children will be boys is (2/3) × 0.51 = 0.34

(B) The possible orderings of the 3 children are given below:

B1 B2 G / B1 G B2

B2 B1 G / B2 G B1

G B1 B2 / G B2 B1

Where B1 is one male child and B2 is the other male child

(C)  If we wanted to calculate the probability that a couple who plans to have 8 kids will have 3 boys, briefly describe why the approach from part (b) would be more tedious than the approach from part (a)

If the probability of 2/3 is 0.34 then the probability of 3/8 will be 0.1912 when you cross multiply

Answer:

a

  Yes

b

 [tex]P(1 \& 5) = \frac{1}{36}[/tex]

c

 [tex]P(5 \& 1) = \frac{1}{36}[/tex]

d

 [tex]P(5 \& 1 | 1\& 5 ) = \frac{1}{18}[/tex]

Step-by-step explanation:

From the question we are told that

     Two fair dice, one green and one red were rolled

Generally the  outcomes on the dice independent because the outcome on the first dice is not affected by the second die

Generally the  probability of getting a 1  on a dice rolled is  [tex]P(1) = \frac{1}{6}[/tex]

the  probability of getting a 5 on a dice rolled is  [tex]P(5) = \frac{1}{6}[/tex]

Generally the probability of P(1 on green die and 5 on red die) is mathematically represented as

         [tex]P(1 \& 5) = \frac{1}{6} *\frac{1}{6}[/tex]

         [tex]P(1 \& 5) = \frac{1}{36}[/tex]

Generally the probability of P(5 on green die and 1 on red die) is mathematically represented as

          [tex]P(5 \& 1) = \frac{1}{6} *\frac{1}{6}[/tex]

         [tex]P(5 \& 1) = \frac{1}{36}[/tex]

Generally the probability of P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) is mathematically represented as

          [tex]P(5 \& 1 | 1\& 5 ) = \frac{1}{36} + \frac{1}{36}[/tex]

         [tex]P(5 \& 1 | 1\& 5 ) = \frac{1}{18}[/tex]

Answer:

45

Step-by-step explanation:

5x-4y=

Let x=5 and y = -5

5*5 - 4 * (-5)

25 + 20

45

Answer:

-5/4

Step-by-step explanation:

the slope is the variable in front of x

y = mx + b

m = slope

b = y-int

Answer:

-5/4

Step-by-step explanation:

using slope intercept form, the slope is -5/4

m= -5/4

I hope this helps you...

Answer:

Option (2)

Step-by-step explanation:

To solve this question we will use the property of tangents drawn to a circle.

"Tangents drawn from an external point to a circle are equal in length"

From the figure attached,

In ΔDEF,

DA = DC = 14 units [Equal tangents]

EA = EB = 13.7 units [Equal tangents]

FB = FC = 9 units [Equal tangents]

Therefore, DE = DA + AE = 14 + 13.7 = 27.7 units

EF = EB + BF = 13.7 + 9 = 22.7 units

DF = DC + FC = 14 + 9 = 23 units

Perimeter of ΔDEF = DE + EF + DF

                               = 27.7 + 22.7 + 23

                               = 73.4 units                            

Option (2) will be the answer.

Answer:73.4

Step-by-step explanation:

Answer:

10.2% chance

Step-by-step explanation:

There are 12 peaches and 8 bananas for a total of 20 pieces of fruit.

So we can write it:

[tex]\frac{12}{20} * \frac{11}{19} * \frac{10}{18} * \frac{9}{17}[/tex] =  [tex]\frac{11880}{116,280}[/tex] = .102 or 10.2% chance

For ease multiply all numerators (top numbers) together, then multiply the denominators (bottom numbers) together, and then divide.

12 * 11 * 10 * 9 = 11880

20 * 19 * 18 * 17 = 116,280

We start with 12 peaches and 20 total fruit, as we select a peach the number of peaches and total fruit goes down by one. We do this 4 times because you draw 4 fruits. If you select 1 fruit your chances of it being a peach are 12/20, each time you select a fruit the chances of it being a peach go down because you have 1 less total fruit, and 1 less peach. This is why you multiply each probability together.

Answer:

He will need 9 tiles

Step-by-step explanation:

Step one:

let us highlight the given parameters

Given data

the size of the kitchen floor is 110 ft^2

the size of the bathroom is 28 ft^2

he used 32.5 tiles for the kitchen

and used x tiles for the bathroom

Step two:

if he used 32 tiles for 110 ft^2 kitchen

he will use x tiles for 28 ft^2 bathroom

cross multiplying we have

x= (32*28)/110

x= 896/110

x= 8.145

Approximately he will need 9 tiles

Answer:

-12, 0, 13, [-14], [-16], 17

Step-by-step explanation:

Answer:

1440 combinations ways

Step-by-step explanation:

We know that the total arrangements will be

6!= 720 because its a 6letter word

So if we take MI to be a one letter word

Same for IM

which will Also be 6!= 720

SO TOTAL possible combination will be 720+720= 1440

Answer:

1440 ways

Step-by-step explanation:

First, we must consider how many letters are in the word "minutes"

7.

This means that the word "minutes" can be arranged in 7! ways, or simply put in 5040 ways.

But then, we're interested in how many ways it can be arranged with I and M besides each other.

In how many ways can the word be arranged with the letters "MI" together

We would have, "MI, N, U, T, E, S" which happens to be 6!, or say 720 ways.

In how many ways can the word be arranged with the letters "IM" together

We would have, "IM, N, U, T, E, S"

which happens to be 6! or again, 720 ways.

Then, the number of ways it can be arranged with "IM" or "MI" together is

720 + 720, and therefore 1440 ways

Answer:

1. The mean of the data summarized in the given frequency distribution is 51.81 degrees

2. Comparing the computed mean (51.81 degrees) to the actual mean(56.6) degrees, the computed mean is lesser than the actual mean.

Step-by-step explanation:

1) We are given a Frequency distribution.

Mean of a frequency distribution = Fx/F

Where

Fx = Frequency × midpoint

Low Temperature ​(◦​F) Frequency

40−44 2

45−49 7

50−54 9

55−59 6

60−64 2

F =Total Frequency

= 2 + 7 + 9 + 6 + 2

= 26

a)For low temperature 40 - 44

Frequency = 2

Midpoint (x) = 40 +44/2 = 42

Fx =42 × 2 = 84

b) For low temperature 45 - 49

Frequency = 2

Midpoint (x) = 45+49/2 = 47

Fx =47 × 7 = 329

For low temperature 50 - 54

Frequency = 2

Midpoint (x) = 50 + 54/2 = 52

Fx =52 × 9 = 468

For low temperature 55 - 59

Frequency = 6

Midpoint (x) = 55 + 59/2 = 57

Fx =57 × 6 = 342

For low temperature 60 - 64

Frequency = 2

Midpoint (x) = 60 +64/2 = 62

Fx =62 × 2 = 124

Total Fx =84 + 329 + 468 + 342 + 124

= 1347

Mean =Total Fx/ Total Frequency

= 1347/26

= 51.807692308

Approximately = 51.81 degrees

Therefore, mean of the data summarized in the given frequency distribution is 51.81 degrees

2. Comparing the computed mean (51.81 degrees) to the actual mean(56.6) degrees, the computed mean is lesser than the actual mean.

Answer:

39 meters

Step-by-step explanation:

We know the bottom distance  ( 20-13) = 7

And we know the height 15-0 =15

We can use the Pythagorean theorem to find the hypotenuse

a^2 + b^2 = c^2

7^2 + 15^2 = c^2

49+225 = c^2

274 = c^2

Taking the square root of each side

sqrt(274) = c

We want the perimeter

a+b+c

7+15+sqrt(274)

22+sqrt(274)

22+16.55294536

38.55294536

Rounding to the nearest meter

39 meters

Answer:

[tex]\huge \boxed{\mathrm{39 \ meters}}[/tex]

Step-by-step explanation:

The perimeter of the right triangle is required.

The base of the triangle is 7 units.

The height of the triangle is 15 units.

The hypotenuse can be found through Pythagorean theorem.

a² + b² = c²

7² + 15² = c²

49 + 225 = c²

274 = c²

c = [tex]\sqrt{274}[/tex]

Adding all the three sides of the right triangle to get the perimeter.

P = a + b + c

P = 7 + 15 + [tex]\sqrt{274}[/tex]

P = 38.552945...

The perimeter of the right triangle is 39 meters rounded to nearest meter.

Answer:

5 sandwiches.

Step-by-step explanation:

$15 for the water, $10 for the soda. So if you add 15 and 10 that's 20. 40-25 = 15 on sandwiches. If each sandwich is $3, then that's 5 sandwiches.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The number of sandwiches bought is 3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of a bottle = $1.50

Cost of a soda = $2

Cost of a sandwich = $3

Number of bottles bought = 10

Number of sodas bought = 5

Number of sandwiches bought = S

Total amount spend = $40

Now,

10 x 1.50 + 5 x 2 + 3S = 40

Simplify.

15 + 10 + 3S = 40

25 + 3S = 40

Subtract 25 on both sides.

3S = 40 - 25

3S = 15

Divide both sides by 3.

S = 15/3

S = 3

Thus,

The number of sandwiches bought is 3.

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Answer:

The tails on a normal distribution go on forever and never touch the​ x-axis

Step-by-step explanation:

The normal distribution is also known as Gaussian distribution or bell shaped curve. The normal distribution is divided into two equal parts by the mean hence it is symmetrical at the mean. For a normal distribution, the height of the curve is determined by the mean while the width is determined by the standard deviation.

The two tails at both ends of the normal curve goes on and never touches the horizontal axis.