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Answer:

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Given:

Find the discount:

Find the discount %:

Surface area implies the external surface that bounds a given shape. The surface area of the shape is 384 sq in.

The surface area of a shape is the external side of the shape that can be seen. Sometimes, a given shape may have different shapes that forms its surface area.

From the given question,

i. The area of triangular surface = 1/2 * base* height

                          = 1/2*12*8

                          = 48

Area of the triangular surface = 48 sq in.

ii. The area of its rectangular sides = length * width

                                  = 9* 10

                                  = 90

Area of its rectangular sides = 90 sq in.

iii. The area of its base = length * width

                             = 9 * 12

                             = 108

Area of its base = 108 sq in.

Therefore,

the surface area of the shape = (2*48) + (2*90) + 108

                            = 96 + 180 + 108

                            = 384 sq in.

The surface area of the given shape is 384 square inches.

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The probability that the proportion surviving for at least five years will exceed 80% is 0.00084.

It is given to us that -

65% of the total dialysis patients can survive for at least 5 years

A simple random sample consists of 100 new dialysis patients

We have to find out the probability that the proportion surviving for at least five years will exceed 80%.

From the given information, we have -

Probability, p = 65% = 0.65

=> Population mean, μ = 0.65

Number of patients in the sample, n = 100

The raw data, x = 80% = 0.80

Now, we know the standard deviation of a given sample can be calculated as -

σ = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

=> σ = [tex]\sqrt{\frac{0.65(1-0.65)}{100} }[/tex]

=> σ = [tex]\sqrt{\frac{0.2275}{100} }[/tex]

=> σ = 0.04770 ----- (1)

We also know that the z-score can be calculated by the formula -

z = (x-μ)/σ

Substituting all the values in the above formula for z-score, we have -

z = (x-μ)/σ

=> z = (0.80-0.65)/0.04770

=> z = 3.14

From the normal distribution table, we can find out the corresponding area for the value of z = 3.14 which is equal to 0.99916.

For a value of the raw data, x to be more than 80%, the area to the right of normal distribution table for z = 3.14 is required.

=> P(x>80%) = 1-0.99916

=> P(x>80%) = 0.00084

Therefore, the probability that the proportion surviving for at least five years will exceed 80% is 0.00084.

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Answer:

60

Step-by-step explanation:

To find the least common multiple of 15 and 12, we can list the multiples of 15 and 12 and find the smallest number that appears in both lists:

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...

The least common multiple of 15 and 12 is 60, so Cameron and Brooks will go to the grocery store on the same day every 60 days.

A group of nine people can now be seated in a row in 40320 different ways.

The two people who insist on sitting next to one other can be situated in one of two ways. The remaining seven people can be seated in seven different ways.

As a result, the total number of ways in which the nine persons can be seated in a row is 1 x 7! = 40320.

In this situation, the two people who dislike each other can be seated in

(7-1)! different ways.

The remaining seven people can be seated in seven different ways.

As a result, the total number of possible combinations for seating 9 individuals in a row is (7-1)! x 7! = 40320.

A combination is a mathematical technique for determining the number of potential arrangements in a set of objects where the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken.

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Answer:

To determine the percentage decrease in W when x is decreased by 9.75%, we need to first determine the relationship between w and x. Since w is proportional to the square root of x, we can write an equation to represent this relationship as follows:

w = k * √x

where k is the proportionality constant.

If the value of x is decreased by 9.75%, we can write the new value of x as follows:

x' = x * (1 - 0.0975) = x * 0.9025

Substituting this expression for x' into the equation above, we get:

w' = k * √(x * 0.9025)

To determine the percentage decrease in w, we can divide the new value of w by the original value of w and multiply by 100% to get the percentage change, or:

percentage decrease in w = (w' / w) * 100%

Substituting the expressions for w' and w into this equation, we get:

percentage decrease in w = [(k * √(x * 0.9025)) / (k * √x)] * 100%

Simplifying this expression, we get:

percentage decrease in w = (√(0.9025)) * 100%

Since the square root of 0.9025 is approximately 0.95, we can say that the percentage decrease in w is approximately 5%. This means that the value of w decreases by approximately 5% when the value of x decreases by 9.75%.

The intervals in which both functions f(x) and g(x) are increasing are given as follows:

(-∞, -3) U (-1, ∞).

The behavior of a function is classified as either increasing, decreasing or constant, as follows:

From these bullet points and the functions given at the end of the answer, we have that the behavior of each function is given as follows:

Thus, both functions are increasing on the interval, (-∞, -3) U (-1, ∞), which is the first option.

The problem is given by the image shown at the end of the answer.

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The probability that this person has an IQ greater than 95 =62.93%

The area of mathematics known as probability is concerned with the outcomes of random events. Probability refers to a chance or potential for something to happen. It explains the likelihood that a specific event will take place.

We frequently say things like, "It will probably rain today," "He will probably pass the test, "There is very little chance of getting a storm tonight," and "Most likely the price of onions will increase once more." We substitute the word probability for all of the words chance, doubt, maybe, likely, etc. in these sentences.

In essence, probability is the ability to forecast an outcome based on the variety and quantity of potential outcomes or the analysis of historical data.

Let X be the IQ

IQ is normally distributed with a mean of 100 and a standard deviation of 15.

a) the probability that this person has an IQ greater than 95

=62.93%

b) the probability that this person has an IQ less than 125

=4.75%

c) Sample size =500

No of people = 0.2486(500) =124.3

d)

No of persons = 0.0047(500) = 2.35

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Answer:

11

Step-by-step explanation:

x + 6 + 2y

x + 2y + 6

x + 2y = 5

5 + 6 = 11

The number of hours in a week a student played basketball is [tex]11\frac{3}{8}[/tex].

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, One week a student exercised 3 hours at school and another 1/4 of an hour at home.

Also given that 1/4 of the exercise of a student came from playing basketball.

Therefore, Time playing basketball is one-fourth of the total time exercised which is,

= (3 + 1/4)×(1/4).

= (13/4)×(1/4).

= (13/8).

Therefore, In a week the student played (13/8)×7.

= 91/8.

= [tex]11\frac{3}{8}[/tex].

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Answer:

try 5/15 or 1/15

Step-by-step explanation:

this is because it shows one shaded box we know it's a third out of just that one column

so you multiple a third by 5 and you get 15 what ever you do to the denominators you do to the numerator

The value does 50% of the data lie above is 50.5 and is called the median.

The median is the value that's exactly in the middle of a dataset when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values.

Given that, The box plot shows the times for sprinters on a track team. A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 44, 48, 50.5, 53, and 56 are all marked by the box plot.

Data we get from the graph is

Minimum (min) = 44

Lower 1 (Q1) = 48

Median (med) = 50.5

Upper 3 (Q3) = 53

Maximum (max) = 56

The median is considered the second quartile (Q2).

The median cuts the data set in half. Half of the answers lie below the median and half lie above the median.

Hence, The value does 50% of the data lie above is 50.5 and is called the median.

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The probability that the deal of a five-card hand provides a pair of aces is 0.0399

In this question, we have been given a deck of playing cards contains 52 cards, four of which are aces.

We need to find the probability that the deal of a five-card hand provides a pair of aces.

The sample space for given experiment is: choosing 52 cars choosing 5.

n(S) = 52C_5

We need to find the chance of getting a pair of aces, there are 4 aces in the pack on 2 of them.

So, n(A) = 4C_2

So that means there are 48 cards left which are not aces in the pack and want 2 of those.

So, the required probability is:

P(A) = (4C_2 * 48C_3) / 52C_5

P(A) = (6 * 17296) /2598960

P(A) = 103776 / 2598960

P(A) = 0.0399

Therefore, the required probability is 0.0399

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Answer:

2/3x + 17

Step-by-step explanation:

2/3x represents the 2/3, then add the additional 17 at the end

Answer:

y=5x

Step-by-step explanation:

If y is 25 and x is 5

25 = 5 (5)

25=25

Answer: 168

Step-by-step explanation: f(51)= 3(51)+15, 3(51)=153.  153+15=168

Answer:

x = 12

Step-by-step explanation:

given

f(x) = 51

f(x) = 3x + 15

51 = 3x + 15

3x = 51 - 15

3x = 36

x = 12

The required solutions are as follows,
1. Angle e = Angle a
2. Angle f = Angle c
3. Ange a, b, and c add up to 180°.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

here.
Angle e = Angle and as they are alternate angles,
Angle f = Angle c as they are alternate angles,

Ange a, b, and c add up to 180°. as they lie on a straight line.
Therefore angles e, f, and b also be added to  180°

Thus, the solution of the angles is shown above.

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Answer:

Correct Statement : The y- intercept of Function A is greater than the y- intercept of Function B

The document do you need to have on hand when preparing to file your tax return is W-2

A tax return is a form or forms filed with a tax authority that reports income, expenses, and other pertinent tax information.

To file your return, you'll need the following on hand: Your W-2: This form will come from your company and list not only your salary for the year, but the amount of taxes withheld along the way. You're required to file your W-2 along with your taxes, so if you're a salaried employee, this form is non-negotiable.

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Answer:

x= 2 and x= -(2/3)

Step-by-step explanation:

Step 1 :Multiply all terms by the same value to eliminate fraction denominators

x^2/ x+6 = 1/2

2(x+6)*(x^2/x+6) = 2(x+6) * 1/2

Step 2: Cancel multiplied terms that are in the denominator

2x^2= x+6

Step 3: Move terms to the left side

2x^2 - (x+ 6) = 0

Step 4: Distribute

2x^2 - x - 6 = 0

Step 5: Use the quadratic formula

x= ( - (-1) +- Squar((-1)^2-4*2(-6)) ) / 2*2

Step 6: Simplify

x= (1+- 7)/ 4

Step7: Separate the equations

x= (1+7)/ 4 and x= (1- 7)/ 4

Step 8: Solve that 2 small equation

x= 2 and x= -(3/2)

Answer:

x = - [tex]\frac{3}{2}[/tex] , x = 2

Step-by-step explanation:

x² : x + 6 = 1 : 2

express the ratio in fractional form

[tex]\frac{x^2}{x+6}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x² = x + 6 ( subtract x + 6 from both sides )

2x² - x - 6 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 6 = - 12 and sum = - 1

the factors are - 4 and + 3

use these factors to split the x- term

2x² - 4x + 3x - 6 = 0 ( factor the first/second and third/fourth terms )

2x(x - 2) + 3(x - 2) = 0 ← factor out (x - 2) from each term

(x - 2)(2x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]

The length of ladder leaning against the side of a house is 10.44 m .

As  shown in the figure below h is the length of the house so we have to find h .

the ladder form a right angled traingle where base of the ladder is 3 m.

and the height of wall to which ladder is leaning against is 10m. and the ladder is the longest side of the right angled traingle i.e Hypotenuse

so we wil use Pythagoras theorem to find the longest side of ladder + wall system

so for a right angled traingle Pythagoras theorem states that

[tex]h^2 = p^2 + b^2[/tex]

where h=Hypotenuse ,p=perpendicular , b=base.

so we have to find h given p= 10m ,b=3m

so putting the values of p and b in the above equation we get

[tex]h^2 = 10^2 +3^2 =109[/tex]

so

[tex]h=\sqrt{109} = 10.44 m[/tex]

so the length of ladder is 10.44 m

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The answer is d. plane ADE, plane CGH.

Answer:

22.5

Step-by-step explanation:

total bill =$150

tip percentage =15%

now,

tip money = 15% of $150

=150×15/100

=2250/100

=$22.5

Answer:

Step-by-step explanation:

3x - 19 = 2x + 1

x - 19 = 1

x = 20

2(20) + 1 + 5y + 19 = 180

40 + 1 + 5y + 19 = 180

41 + 5y + 19 = 180

5y + 19 + 41 = 180

5y + 60 = 180

5y = 120

y = 24

Answer:

6 centimeters is equal to 0.07 yards.

Step-by-step explanation:

To convert 6 centimeters into yards, we need to first convert the distance from centimeters to meters by dividing the distance in centimeters by 100:

Distance in meters = Distance in centimeters / 100

Distance in meters = 6 cm / 100

Distance in meters = 0.06 m

Next, we can convert the distance from meters to yards by dividing the distance in meters by 0.9144, which is the number of meters in a yard:

Distance in yards = Distance in meters / Meters per yard

Distance in yards = 0.06 m / 0.9144 m/yard

Distance in yards = 0.0654 yards

Rounded to the nearest hundredth, 6 centimeters is equal to 0.07 yards.

Answer:

Step-by-step explanation:

0.0656168

round to the nearest hundredth is:

0.07

She sold more cheese boxes on Tuesday.

Comparing numbers in maths is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.

Given that, Marietta is selling cheeses for the holiday fundraiser. On Monday, she sold seven-ninths of the boxes of cheeses. On Tuesday, she restocked her supply and sold 0.85 of the boxes of cheeses.

On Monday = 7/9 = 0.777

On Tuesday = 0.89

Since, 0.89 > 0.777

Hence, she sold more on Tuesday.

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Answer:

10.8 - 2.3  = 8.5ft2 amount of $153

Can i use proportion for this?

8.5/153 : 1/x

8.5x = 153

x = 18

Step-by-step explanation:

Answer: About 2.2

Step-by-step explanation: Since 13 divided by 6 is 2.16 repeating, you can use the 6 to round up the 1, making it about 2.2