(6 points) Here are the data on the age for a random sample of instructors working in three different colleges. College A 54 46 53 47 51 49 College B 35 33 39 33 34 35 College C 48 48 46 45 44 45 Use

The average time allowed the 15 selected students to be 3.06hours

What is Average?

In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.

With a sample size of 15 and a p value of 0.04

From binomial probability, (nCx)px(1p) is where the application of binomial probability originates from (n-x)

1 - p = 0.96

a) P(x=1) is the probability that precisely 1 received a special accommodation.

= 15C1 x (0.04)^1 x (0.96) ^14 = 0.3388

b) P(x >=1) = 1 - P(x = 0) is the likelihood that at least 1 person received a special accommodation.

= 1 - [ 15C0 x (0.04)^0 x (0.96)^15 = 0.4579

c) the likelihood that two people at least obtained special accommodations

= [P(x = 0) + P(x = 1)] - [P(x>=2) = P(x>=2)

= 1 - [ 15C0 x (0.04)^0 x (0.96)^15 + 15C1 x (0.04)^1 x (0.96)^14]

= 1 - [0.5420 + 0.3388] .3388]

= 0.1192

d) likelihood that the proportion of the 15 who received a special accommodation is within two standard deviations of the proportion you would anticipate receiving one;

= P( x<=1) = P( x= 0) = 0.5429

e) expected average time = 0.04 x 4.5 + 0.96 x 3 = 3.06hours

Hence, The average time allowed the 15 selected students to be 3.06hours

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Answer:

B

Step-by-step explanation:

(hx)(gx)

(2x+5)(3x+2)

6\(x^{2}\)+4x+15x+10

6\(x^{2}\)+19x+10

Answer B

g (x) = 4x² + 10 is the equation for g(x) in the simplest form.

A special relationship where each input has a single output is called a function.

Given that, f(x) = 4x² + 6, the quadratic function g(x) is f(x) translated 3 units up.

The translation of a function f (x) in the Cartesian coordinate domain can be done by following the given guidelines:

Translation guidelines ;

Horizontal shifts

Right :  f (x) → f (x - a)

Left :  f (x) → f (x + a)

Vertical shifts

Up :  f (x) → f (x) + b

Down :  f (x) → f (x) - b

General shift (Horizontal and Vertical shift) is;

f (x) → f (x ± a) ± b

We will use the guidelines for Vertical shifts, where in this case the magnitude of b = 4.

f (x) = 4x² + 6

g (x) = f (x) + 4

g (x) = 4x² + 6 + 4

g (x) = 4x² + 10

Hence, the equation for g(x) in the simplest form is  g (x) = 4x² + 10

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The measure of the angles in the parallelogram are 144 and 36 degrees.

What is a parallelogram?

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are of equal length and the opposite angles are also equal.

Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.

Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle.

Angles in a parallelogram

a + b + c + d = 360

Opposite angles are equal, so

2a + 2(0.25a) = 360

2a + 0.5 = 360

2.5a = 360

a = 360/ 2.5

a = 144

the other angle = 180 - 144 = 36 degrees

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Answer:

true

Step-by-step explanation:

Answer:

True

because 6(8x+1)=48x+6

Answer:

2a^4 +2a

Step-by-step explanation:

the like terms have to have the same variable and be raised to the same power so when you combine them you get 2 a^4's and 2 a's so the answer would be 2a^4 +2a.

i hope this helps :)

The statement "Quadrilaterals A and B are both squares" does not provide enough information to determine whether A and B are scale copies of one another.

To determine if two quadrilaterals are scale copies of each other, we need to compare their corresponding sides and angles. If the corresponding sides of two quadrilaterals are proportional and their corresponding angles are congruent, then they are scale copies of each other.

In this case, since both A and B are squares, we know that all of their angles are right angles (90 degrees). However, we do not have any information about the lengths of their sides. Without knowing the lengths of the sides of A and B, we cannot determine if they are scale copies of each other.

Therefore, the statement cannot be determined as true or false based on the given information.

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Answer:

  6

Step-by-step explanation:

You want to know the number of uphill integers divisible by 15, where an uphill integer is one that has its digits strictly increasing.

An integer will be divisible by 15 if and only if it is divisible by 3 and 5. An integer is divisible by 5 if it ends in 5 or 0. An uphill integer cannot end in 0, so must end in 5.

An integer is divisible by 3 if the sum of its digits is divisible by 3

An uphill integer will have differences between successive digits that are positive integers. In order for the final digit to be 5, the sum of these differences must be 5. Hence we can find uphill integers by considering the "integer partitions" of 5: the sets of positive integers whose total is 5. Those sets would be ...

  {5}, {4, 1}, {3, 1, 1}, {2, 2, 1}, {2, 1, 1, 1}, {1, 1, 1, 1, 1}

Uphill integers will also have digit differences that are some permutation of each of these sets. For example, the digit differences may be {4, 1} or {1, 4}, corresponding to the numbers 45 or 15.

The uphill integers that end in 5 are ...

  5, 45, 15, 35, 25, 345, 145, 125, 245, 235, 135, 2345, 1345, 1245, 1235, 12345

We already know each of these is divisible by 5. The ones that have a digit total that is a multiple of 3 are ...

  15, 45, 135, 345, 1245, 12345

There are 6 uphill integers divisible by 15.

The total number of red marbles in the vase are 10.

A ratio is described as a comparison between two amounts with the same unit to determine the amount of 1 quantity is contained in the other. Ratios are divided into two sorts.

The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groupings.

Now, according to the question;

Let 'x' be the red marbles in the vase.

Let 'y' be the orange marbles in the vase.

The total number of marbles in the vase are 60

x  + y = 60 (equation 1)

The ratio of red marbles to orange ones is 1:5.

Thus, x/y = 1/5

cross multiplying;

5x = y

or y = 5x

substitute the value of y in equation 1;

x  + y = 60 (equation 1)

x  + 5x = 60

6x = 60

x = 10  (red marbles)

Thus, the number of red marbles in the vase are 10.

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The surface area of this locker is 432 square centimeters .

The right rectangular prism shown in the figure has dimensions 8 cm (length) x 6 cm (width) x 12 cm (height).

1. The top and bottom faces are both rectangles with dimensions 8 cm (length) x 6 cm (width). The area of each face is:

A = length x width = 8 x 6 = 48 cm²

Since there are two of these faces, the total area is:

2 x 48 = 96 cm²

2. The front and back faces are also rectangles with dimensions 8 cm (length) x 12 cm (height). The area of each face is:

A = length x height = 8 x 12 = 96 cm²

the total area is:

2 x 96 = 192 cm²

3. The left and right faces are rectangles with dimensions 6 cm (width) x 12 cm (height). The area of each face is:

A = width x height = 6 x 12 = 72 cm²

the total area is:

2 x 72 = 144 cm²

4. Therefore, the total surface area of the locker is the sum of all the faces:

Total surface area = 96 + 192 + 144 = 432 cm²

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Answer:

rebates mean to deduct or return an amount from the payment

Answer:

rebate is a partial refund of the cost of an item.

Answer:

The difference between the area of the original triangle and the area of the new triangle is \(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\).

Step-by-step explanation:

The equation for the area of a triangle (\(A_{\bigtriangleup}\)) is:

\(A_{\bigtriangleup} = \frac{1}{2}\cdot b \cdot h\)

Where:

\(b\) - Base, dimensionless.

\(h\) - Height, dimensionless.

The expression for each triangle are described below:

First Triangle (\(b = 3\cdot x + 7\), \(h = 5\cdot x - 1\))

\(A_{\bigtriangleup,1} = \frac{1}{2}\cdot (3\cdot x+7)\cdot (5\cdot x -1)\)

Second Triangle (\(b = 3\cdot (3\cdot x+7)\), \(h = 2\cdot (5\cdot x -1)\))

\(A_{\bigtriangleup,2} = 3\cdot (3\cdot x+7)\cdot (5\cdot x -1)\)

The difference between the area of the original triangle and the area of the new triangle is:

\(\Delta A_{\bigtriangleup} = A_{\bigtriangleup,2}-A_{\bigtriangleup,1}\)

\(\Delta A_{\bigtriangleup} = 3\cdot (3\cdot x+7)\cdot (5\cdot x-1)-\frac{1}{2} \cdot (3\cdot x+7)\cdot (5\cdot x-1)\)

\(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\)

The difference between the area of the original triangle and the area of the new triangle is \(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\).

Answer:

The technical writer should expect his annual pay to decrease by $1,059

Step-by-step explanation:

52 weeks = $55,068

51 weeks =

Cross Multiply

51 weeks × $55,068/52 weeks

= $54009

The writer will be paid $54009 for 51 weeks

His pay reduced by:

$55,068 - $54,009

= $1,059

Standard deviation is the square root of variance .

So,

It is used in measuring any deviation or shift from the calculated mean.  

From a data set, the mean of the data can be determined with which the standard deviation can be measure.

Therefore, Standard deviation is use to measure variation that exist in an individual data set. There are different type of data set from which variation is measured.

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Answer: a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.

Step-by-step explanation: the y-intercept is where the line meets the y line which in this case is -3. I used slope formula to find the m of the equation ( slope ) take a look at the attached image to see how I solved it.

Answer:

a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.

Step-by-step explanation:

The probability of getting 2 tails is option (b) 37.5%

The event of "2 tails" can occur in three possible outcomes: {htt, tht, tth}, so the probability of getting 2 tails is the sum of the probabilities of these three outcomes.

Each toss of a fair coin is independent and has a 50% chance of landing tails. Therefore, the probability of each of these three outcomes is:

P(htt) = 1/2 × 1/2 × 1/2 = 1/8

P(tht) = 1/2 × 1/2 × 1/2 = 1/8

P(tth) = 1/2 × 1/2 × 1/2 = 1/8

So, the probability of getting 2 tails is:

P(2 tails) = P(htt) + P(tht) + P(tth) = 1/8 + 1/8 + 1/8 = 3/8

= 0.375

0.375 multiplied by 100% gives:

P(2 tails) = 37.5%

Therefore, the correct option is (b) 37.5%

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The domain of H is given by the set notation:

Domain: {3, 9, 0}

The domain of a relation represents all the possible input values or x-values in the relation. In the given relation H = {(3, q), (9, n), (0, 3), (9, p)}, we can determine the domain by extracting all the x-values from the ordered pairs.

Looking at the relation, we see that the x-values are 3, 9, and 0. These are the values assigned to the first element of each ordered pair. Thus, the domain of H can be expressed in set notation as {3, 9, 0}.

In set notation, the domain lists all the unique x-values or inputs that exist in the relation. Since each x-value appears only once in the given relation, there are no repetitions or duplicates in the domain set.

Therefore, the domain of H is {3, 9, 0}, indicating that these are the valid input values for the relation H.

It's important to note that the domain of a relation can vary depending on the specific context and constraints. In this case, the domain is determined solely by the values present in the relation H.

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Step-by-step explanation:

y varies inversely as x=

y= k/xz

-5= k(-5)/6

k= 6

y=6/xz

y=6/5×-8

y= -3/20

#9

#a

\(\\ \sf\longmapsto (y+2z)^3\)

\(\\ \sf\longmapsto y^3+2z^3+3y^2(2z)+3y(2z)^2\)

\(\\ \sf\longmapsto y^3+8z^3+6y^2z+12yz^2\)

#b

Refer to attachment

#10

Answer:

nope u dont need to buy more

Step-by-step explanation:

u have 1/2 cup after spilling but the recipe only needs 1/3 which is less

\( \Large{\boxed{\sf r = 10.2 \: m \: \: (Rounded \: to \: the \: nearest \: tenth.) }} \)

\( \\ \)

To find the radius of the circle, we will use the given formula:

\( \Large{\sf r = \left( \dfrac{A}{4 \pi } \right)^{\dfrac{1}{2}} } \)

Where:

\( \\ \)

\( \Large{\boxed{\sf Given \text{:} } \begin{cases} \sf A &=\sf 1493 \: m^3 \\ \sf \pi &=\sf 3.14 \: (Approximately) \end{cases} } \)

\( \\ \)

Substitute these values into our formula:

\( \sf r = \left( \dfrac{1493 \: m^3}{4 \times 3.14} \right)^{\dfrac{1}{2} } = \sqrt{ \dfrac{1493 \: m^3 }{12.56} } \approx 10.90272 \: m \)

\( \\ \)

Rounding our answer to the nearest tenth, we get:

\( \boxed{\boxed{\sf r = 10.9 \: m }} \)

Answer:

She spent $38.7 on the remaining boxes.

Step-by-step explanation:

total number of boxes of pencil bought by Ms. Smith, = 30 boxes

cost of each box = $2.15

fraction of boxes of pencil used = 6 / 15

number of boxes of pencil used = \(\frac{6}{15} *30 \ boxes = 12 \ boxes\)

number of boxes of pencil remaining = 30 boxes - 12 boxes = 18 boxes

Cost of the 18 boxes remaining = 18 x $2.15

                                                    = $38.7

Therefore, she spent $38.7 on the remaining boxes.

Answer:

11 hours remains

Step-by-step explanation:

Answer:

11 hours remaining

Step-by-step explanation:

11 hours remaining

Answer:

the answer would be 81

Step-by-step explanation:

6 to the second power would be 36 then you would multiply 36x2 and it would equal 72. then you would do 2x6 which is 12. then 72+12-3= 81

The exponents are;

1) x^7/4

2) 2^1/12

3) 81y^8z^20

4) 200x^5y^18

Exponents, sometimes referred to as powers or indices, are a type of mathematical notation used to indicate the size of a number raised to a specific power or the repeated multiplication of a number by itself. They serve as a condensed form of repeated multiplication.

We can see that;

1) 4√x^3 . x

x^3/4 * x

= x^7/4

2) 3√2 ÷ 4√2

2^1/3 -2^1/4

2^1/12

3) (3y^2z^5)^4

81y^8z^20

4) (5xy^3)^2 . (2xy^4)^3

25x^2y^6 . 8x^3y^12

200x^5y^18

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Answer: -10 degrees

Step-by-step explanation:

    If it drops 6 degrees per hour, then we can use multiplication to see how much it will have dropped after 3 hours:

          6 degrees * 3 hours = 18 degrees

     If the temperature is 8 degrees, and it drops 18 degrees, we will subtract:

         8 degrees - 18 degrees = -10 degrees

Answer:

26 degrees.

Step-by-step explanation:

The temperature will increase by 6 degrees per hour for three hours, so the final temperature after three hours will be:

\(\sf:\implies{8 + 6 \times 3 = 8 + 18 = 26 }\)

Therefore, the temperature at the end of three hours is 26 degrees.

There can be  347 sunny days in the Valley of the Sun in a year

Assuming that there are 365 days in a year, and that the calendar's claim of 95% sunny days is accurate, we can calculate the number of sunny days in the Valley of the Sun as follows:

Number of sunny days = 0.95 x 365 = 346.75

Since we can't have a fractional day, we can round up to the nearest whole number, which gives us:

Number of sunny days = 347

Therefore, we can expect there to be approximately 347 days in the Valley of the Sun in a year, based on the given information.

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Answer:

10 ounces

Step-by-step explanation:

Convert the original container into ounces. (1 quart=32 ounces)

5 x 32 = 160 ounces

Then the milk is divided into two containers.

160 / 2 = 80

Each container is then divided into 8 glasses.

80 / 8 = 10

Each glass has 10 ounces of milk in it.

Answer:

A

Step-by-step explanation:

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