How do I write -2/3 as a decimal number?

We get the following answers:

A) The least square regression line is:

yi = 88.73 - 2.827(xi)

B) The slope  is β₁ = -2.827 and The intercept is β₀ = 88.73.

C) e*₆ = -0.6964, final grade is below average grade.

E) It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

we have Xi = No of absences

Yi = Final grade

The regression model is

Yi = β₀ +  β₁Xi + i

β₀ = y -  β₁x

we have n = 10, x bar = 4.5 , y bar = 76.01

cov(x,y) = -23.325 and var(x) = 9.1667

therefore,  β₀ = 88.73 and  β₁ = -2.827

A) Least square regression line is given by:

yi =  β₀+ β₁Xi

yi = 88.73 - 2.827(xi)

B) The slope  β₁ = -2.827 which means when no of absence is increased by 1 duty then the final grade will decrease by 2.827

The intercept  β₀ = 88.73 when there are 0 days absence the average grade is 88.73

C) Predicted graph for student who misses five class periods is

x = 5

y*5 = 88.73 - 2.827(5) = 74.5964

Hence for corresponding residual is:

e*₆ = 73.9 - 74.5964

e*₆ = -0.6964, final grade is below average grade.

D) please see graph

E) when student miss 15 class periods the final grade will be

X = 5

y* = 88.73 - 2.827(15)

= 46

It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

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The area of each part of the figure is Triangle B = 10 square units and Triangle A = 17.5 square units. The area of the whole figure is 27.5 square units.

A two-dimensional surface, like the surface of a shape or object, can be measured in terms of area. Usually, it is expressed in square quantities like square metres (m2) or square feet (ft2). By multiplying the length and breadth of a rectangle, or by applying particular formulas for other forms, such as base times height divided by two for a triangle, one can determine the area of a shape.

From the given figure we observe that the base of the slanted figure has true base length of 5 units.

Thus, for triangle B the area is:

Triangle B = 1/2(b)(h)

Triangle B = 1/2(5)(4) = 10 square units.

For triangle A we have:

Triangle A = 1/2(5)(7) = 35/2 = 17.5 square units.

The area of the whole figure is:

A = 10 + 17.5 = 27.5 square units.

Hence, the area of each part of the figure is Triangle B = 10 square units and Triangle A = 17.5 square units. The area of the whole figure is 27.5 square units.

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Using the Empirical Rule, it is found that 99.7% of the data will be between 11.7 and 32.7 inches.

It states that, for a normally distributed random variable:

In this problem, considering the mean and the standard deviation of the data-set, the bounds between which 99.7% of the data-set are given by:

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Answer: 11.7 & 32.7

Step-by-step explanation:

Approximately  $99.7\%$ of the snowfall amounts are between 1$$ inches and 2$$ inches.

Correct answers:

1: 11.7 2: 32.7

The Empirical Rule states that approximately 99.7% of the data is within 3 standard deviations of the mean. In terms of the sample mean x¯ and sample standard deviation s, that is between x¯−3s and x¯+3s.

The value 3 standard deviations below the mean is

x¯−3s=22.2−3(3.5)=11.7.

The value 3 standard deviations above the mean is

x¯+3s=22.2+3(3.5)=32.7.

So by the Empirical Rule, we can say that approximately 99.7% of the snowfall amounts are between 11.7 and 32.7 inches.

Answer:

c. The period is 2π

Step-by-step explanation:

The period of a function is the smallest value of $p$ for which\( f(x+p) = f(x)\) for all x.

For the function f(x) = 2cos(x^2), we can see that f(x+2π) = f(x) for all x.

This is because the cosine function has a period of 2π. Therefore, the period of f(x) = 2cos(x^2) is \(\boxed{2\pi}\)

Answer:

8

Step-by-step explanation:

1) find the least common denominator

48/8=6

64/8=8

2) check

8 times 6 is 49

8 times 8 is 64

The tank having shape of a rectangular prism, the volume of tank will be

4,500 inches³.

What exactly is a prism?

A prism is a three-dimensional geometric object that has a pair of identical, parallel polygonal bases and flat, parallelogram-shaped sides connecting them. The most common type of prism is a rectangular prism, which has two rectangular bases and four rectangular sides.

Prisms are classified based on the shape of their bases. For example, if the bases of a prism are triangles, it is called a triangular prism, if the bases are pentagons, it is called a pentagonal prism, and so on.

Now,

To calculate the volume of water that the tank can hold, we need to use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

Plugging in the values given:

Volume = 25 inches x 12 inches x 15 inches

Volume = 4,500 cubic inches

Therefore,

              the tank can hold 4,500 inches³ of water.

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The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Answer:

√52

Step-by-step explanation:

\( \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } \)

\( \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} \)

Answer:

her car can travel for (24 * 4) miles

which is

96 miles

Answer:

96 miles

Step-by-step explanation:

As it's 24 miles each gallon so , therefore 4 x 24 = 94

Answer:

1 ft = 12 in

1 in = (1/12) ft

30 in = (30/12) ft

30 in = 5/6 ft

The area of the surface that Jared needs to paint is:

2(12*9 + 15*9) - 2(5*6 + (5/6)*6) = 416 ft^2

Step-by-step explanation:

Answer:

3 gallons of paint

Step-by-step explanation:

Steps you have to take,

Formula:

\((A = lw)(2) + (A = lw)(2) - (A = lw)(2) - (A = lw)(2)\)

\((wall 1)(2) + (wall 3)(2) - (window)(2) - (door)(2)\) ↑

door = 30in by 6ft

30in to feet =  2.5 feet

\((A = 12(9))2 + (A = 15(9))2 - (A = 6(5))2 - (A =2.5(6))2\)

\((A = 108)2 + (A = 135)2 - (A = 30)2 - (A = 15)2\)

\((A = 216) + (A = 270) - (A = 60) - (A = 30)\)

\(combine\\(A = 486) - (A= 90)\\(A = 396)\)

396(2) =

792sq ft

We know that one gallon covers 350sq ft

792/350 =

2.26 gallons

(can't have .26 of a gallon so we round up)

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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Answer:

x ≥ 1.5

Step-by-step explanation:

2x - 3 ≥ 0 ( add 3 to both sides )

2x ≥ 3 ( divide both sides by 2 )

x ≥ 1.5

Answer:

➨ f(-1) = 0

Step-by-step explanation:

➨ Look at the table and compare.

Notice that when x = -1, f(x) = 0

f(-1) is like substituting x = -1 and get the f(x) value at x = -1.

Thus, f(-1) = 0

The least common multiple of 598 and 45 is 26, 910

To find the least common multiple of 598 and 45, you can use the prime factorization method. This involves finding the prime factors of both 598 and 45 and then multiplying these prime factors when they are in their highest power.

This gives:

598 prime factorization :

2 x 13 x 23 = 598

45 prime factorization :

3 x 3 x 5 = 45

The least common multiple is;

= 2 x 13 x 23 x 3 x 3 x 5

= 26, 910

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The number of short sleeves that Maria sold is 819.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.

In this case, Maria’s clothing store sold 1547 shirts with the ratio of short sleeve to long sleeve shirt being 9:8.

The number of short sleeves will be:

= Ratio for short sleeve / Total ratio × Total number of clothes

= 9 / (8 + 9) × 1547

= 9/17 × 1547

= 819

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Answer:

Step-by-step explanation:

First question:

Second question:

Step-by-step explanation:

The required combinatorial circuit can be constructed as follows:

Firstly, we need to find the negation of p, q and r which can be achieved using inverters as shown below:

p q r

| | |

| | |

NOT NOT NOT

| | |

| | |

~p ~q ~r

Next, we can use OR gates to form the term (¬p ∨ ¬r) and (q ∨ r) as shown below:

~p ~r q r

| | | |

| | | |

OR OR | |

| | | |

| | | |

pORr rORp qORr rORq

Then, we can use AND gates to form the terms (¬p ∨ ¬r) ∧ ¬q and ¬p ∧ (q ∨ r) as shown below:

~p ~r q r

| | | |

| | | |

OR OR | |

| | | |

| | | |

pORr rORp qORr rORq

| | | |

| | | |

NOT NOT NOT |

| | | |

| | | |

~q ~pORr ~qORr qORr

| | | |

| | | |

AND OR AND |

| | | |

| | | |

(~pORr ~q) qORr qORr

| | |

| | |

OR AND |

| | |

| | |

(~pORr ∨ ~q) (~pORr ∧ qORr)

| | |

| | |

| OR |

| | |

| | |

((~pORr ∨ ~q) ∨ (~pORr ∧ qORr))

| | |

| | |

| | |

OUTPUT

((~pORr ∨ ~q) ∨ (~pORr ∧ qORr))

Answer:

A

Step-by-step explanation:

To find the perimeter you must add all four sides together. Since it's a rectangle, the top and bottom are the same size and the left and right sides are the same size. You add all four together to get the perimeter.

Step-by-step explanation:

Scatter plot is the correct answer

Answer:

D

Step-by-step explanation:

ANYTHING that's raised to the power of zero will always be one. In this case, letters a, b, c are all raised to the power of zero. So all of them equal 1.

1 x 1 x 1 = 1

Answer:

D.

Step-by-step explanation:

Answer is 1

a^0= 1

b^0= 1

c^0= 1

Answer:

Step-by-step explanation:

52 weeks in a year

Divide 52 by 2 = 26 weeks

26 weeks x 147 dollars = 3822 dollars

Thus the answer is 3822 dollars yearly

Answer:$3,528

Step-by-step explanation:

since there are 4 weeks in a month that would mean you would have to multiply 147 by two and that would = to $294.00/month so then you would have to multiply that by 12 so then that would = to $3,528.00 a year.

Answer:

the correct answer would be 1,800

Answer:

Nancy can cut 6 full circles

Step-by-step explanation:

Length of aluminium strip = \(7 \frac{1}{7} cm\)

Length of aluminium strip =\(\frac{50}{7} cm\)

Breadth of aluminium strip =\(1 \frac{3}{7} cm\)

Breadth of aluminium strip =\(\frac{10}{7} cm\)

Area of strip = \(Length \times Breadth = \frac{50}{7} \times \frac{10}{7} =\frac{500}{49}\)

Diameter of circle = \(1 \frac{3}{7} cm\)

Diameter of circle = \(\frac{10}{7} cm\)

Radius of circle =\(\frac{10}{ 7 \times 2}=\frac{10}{14} cm\)

Area of circle =\(\pi r^2 = \frac{22}{7} \times (\frac{10}{14})^2=\frac{550}{343} cm^2\)

No. of circles can be cut = \(\frac{\frac{500}{49}}{\frac{550}{343}}=6.3636\)

So,Nancy can cut 6 full circles

Answer:

The answer is 16 because

Step-by-step explanation:

3(6 - 8)² + 8÷2 = 3(-2)² + 8÷2

        = 3 * 4 + 8÷2

        = 3 * 4 + 4

        = 12 + 4

        = 16

The value of x after solving −0.28x − 8.4 = 8.26  is   x = −59.5 .

What is linear equation in one variable ?

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.

To solve linear equation in one variable:

Step 1: Simplify each side, if needed.

Step 2: Use Add./Sub. Properties to move the variable term to one side and all other terms to the other side.

Step 3: Use Mult./Div. Properties to remove any values that are in front of the variable.

Given :

-0.28x - 8.4 = 8.26

Adding 8.4 both the sides , we get

-0.28x + (-8.4 + 8.4) = 8.26 + 8.4

-0.28x = 16.66

x = - (16.66/0.28)

x = -59.5

Hence , the value of x after solving −0.28x − 8.4 = 8.26  is   x = −59.5 .

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Answer:

\(\frac{5}{16}\) hours or \(18\frac{3}{4}\) minutes

Step-by-step explanation:

\(\frac{1}{x} +\frac{1}{4x}= 4\\\\\frac{4}{4x}+\frac{1}{4x} =4\\\\\frac{5}{4x} =4\\\\5=16x\\\\x=\frac{5}{16}\)

Calculating into minutes.

\(60*\frac{5}{16}=\\\\\frac{300}{16} =\\\\18\frac{3}{4}\)

The Slope of a line that passes through the points (x₁,y₁) and (x₂,y₂) is given by the formula:

Notice from the graph that the blue line passes through points (0,2) and (3,0).

Substitute (x₁,y₁)=(0,2) and (x₂,y₂)=(3,0) into the slope formula:

Hence, the slope of the blue line is -2/3.

Notice from the graph that the green line passes through the points (1,-2) and (4,-4):

Substitute (x₁,y₁)=(1,-2) and (x₂,y₂)=(4,-4) into the slope formula:

Hence, the slope of the green line is -2/3.

The slope of both lines is -2/3.

The solution to the inequality expression is x ≥ - 5

What is inequality?

Inequality shows relation between two expression which are not equal to each others.

Inequality expressions

Inequality are expressions not separated by an equal sign. Given the inequality;

–4(x + 3) ≤ –2 – 2x

Expand

-4x - 12  ≤ -2 - 2x

Collect the like terms

-4x + 2x  ≤ -2 + 12

-2x  ≤  10

Divide both sides by -2

-2x/-2  ≤ 10/-2

x ≥ - 5

Hence, the solution to the inequality expression is x ≥ - 5

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