)A math teacher graded 45 problems in of an hour. At that rate, how many problems
can she grade in 1 hour?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
problems
Subnt

Answer:

x-intercepts:  -4, -2, 1 and 3

y-intercept:  24

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x&-5&-3&0&2&4\\\cline{1-6}y&144&-24&24&-24&144\\\cline{1-6}\end{array}[/tex]

Step-by-step explanation:

Given polynomial:

[tex]y=(x+4)(x+2)(x-1)(x-3)[/tex]

The x-intercepts are the points at which the curve intersects the x-axis, so when the function equals zero.

Zero Product Property

If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Therefore, to find the x-intercepts, set each factor of the given polynomial equal to zero and solve for x:

Therefore:

[tex]\implies (x+4)=0 \implies x=-4[/tex]

[tex]\implies (x+2)=0 \implies x=-2[/tex]

[tex]\implies (x-1)=0 \implies x=1[/tex]

[tex]\implies (x-3)=0 \implies x=3[/tex]

Therefore, the x-intercepts are -4, -2, 1 and 3.

The y-intercept is the point at which the curve intersects the y-axis, so when x is zero.  

To find the the y-intercept, substitute x = 0 into the given polynomial:

[tex]\implies y=(0+4)(0+2)(0-1)(0-3)[/tex]

[tex]\implies y=(4)(2)(-1)(-3)[/tex]

[tex]\implies y=(8)(-1)(-3)[/tex]

[tex]\implies y=(-8)(-3)[/tex]

[tex]\implies y=24[/tex]

Therefore, the y-intercept is 24.

To find the other points on the graph, substitute each value of x into the polynomial and solve for y:

[tex]\begin{aligned}x=-5 \implies y&=(-5+4)(-5+2)(-5-1)(-5-3)\\&=(-1)(-3)(-6)(-8)\\&=(3)(-6)(-8)\\&=(-18)(-8)\\&=144\end{aligned}[/tex]

[tex]\begin{aligned}x=-3 \implies y&=(-3+4)(-3+2)(-3-1)(-3-3)\\&=(1)(-1)(-4)(-6)\\&=(-1)(-4)(-6)\\&=(4)(-6)\\&=-24\end{aligned}[/tex]

[tex]\begin{aligned}x=2 \implies y&=(2+4)(2+2)(2-1)(2-3)\\&=(6)(4)(1)(-1)\\&=(24)(1)(-1)\\&=(24)(-1)\\&=-24\end{aligned}[/tex]

[tex]\begin{aligned}x=4 \implies y&=(4+4)(4+2)(4-1)(4-3)\\&=(8)(6)(3)(1)\\&=(48)(3)(1)\\&=(144)(1)\\&=144\end{aligned}[/tex]

Therefore:

[tex]\large\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x&-5&-3&0&2&4\\\cline{1-6}y&144&-24&24&-24&144\\\cline{1-6}\end{array}[/tex]

Answer:

8505

Step-by-step explanation:

Step 1

Firstly, work out 5 × 243. The smaller figures in green are the tens figures carried over. Working from right to left:

5 × 3 = 15

Put the 5 in the appropriate column and carry the 1.

5 × 4 + 1(carried) = 21

Put the 1 in the appropriate column and carry the 2.

5 × 2 + 2(carried) = 12

Put the 2 in the appropriate column and carry the 1.

Step 2

Lastly, work out 30 × 243.

This can be written as 3 × 243 × 10.

Because we are multiplying by 10, we place 1 zero to the right and then work out 3 × 243.

3 × 3 = 9

3 × 4 = 12

Put the 2 in the appropriate column and carry the 1.

3 × 2 + 1(carried) = 7

Step 3

Finally, the 2 rows are added together starting at the right. The smaller figures in green are the tens figures carried over.

0 + 5 = 5

9 + 1 = 10

Put the 0 in the appropriate column and carry the 1.

2 + 2 + 1(carried) = 5

7 + 1 = 8

So: 243 × 35 = 8505

A hot-air balloon is at a height of 2,250 feet. It begins to descend at a rate of 150 feet per minute.

In context, after 6 minutes the balloon is at 1,350 ft, after 8 minutes the balloon is at 1,050 ft, and after 10 minutes the balloon is at 750 ft.

So for this, since the rate is linear we will be using the slope-intercept form, which is y = mx+b (m = slope/rate of change, b = y-intercept)

Since the rate of change "descends 150 ft per min", the m variable is -150.

The y-intercept is, in this case, the height of the balloon at 0 mins, or the starting height. Since the balloon "is at a height of 2250 ft", the b variable is 2250.

Putting our equation together, its y = -150x + 2250.

Since time is our independent variable, plug in 6, 8, and 10 mins into the x variable to solve for their heights:

y = -150(6)+2250

y = -900+2250

y = 1350

y = -150(8)+2250

y = -1200+2250

y = 1050

y = -150(10)+2250

y = -1500+2250

y = 750

Hence the answer, In context, after 6 minutes the balloon is at 1,350 ft, after 8 minutes the balloon is at 1,050 ft, and after 10 minutes the balloon is at 750 ft.

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The simplified expression for (0.2a²b³)(-5a³b)² is given as follows:

5a^8b^5.

The expression for this problem is given as follows:

(0.2a²b³)(-5a³b)²

First we apply the power of power simplification, in which the square of each term inside the parenthesis is calculated as follows:

Now the expression is:

(0.2a²b³)(25a^6b²).

Then:

Hence the simplified expression is:

5a^8b^5.

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The radius of the cone if the volume of a right cone is 448 π cube units and if its height is 21 units is 8 units.

First, let us understand the cone:

It is a solid or hollow item with a round or approximately circular base that tapers to a point.

The volume of the cone is given by;

Volume = 1/3 π r^2 h

where r = radius of the base of the cone

and h = height of the cone

We are given;

The volume of a right cone is 448 π cube units.

Height is 21 units.

Put the values in the volume formula;

448 π = 1/3 π r^2 * 21

448 π = 7 π r^2

r^2 = 448 π / 7 π

r^2 = 64

r = 8 units

So, the radius of the base is 8 units.

Thus, the radius of the cone if the volume of a right cone is 448 π cube units and if its height is 21 units is 8 units.

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Answer:

8

Step-by-step explanation:

don't know how to explain it but I had he same problem and I got 8 and it was right.

Total triangles on all the quilt are 672.

What is quilt?

Quilts are often made of two or more layers of cloth or fibre and are multi-layered textiles. Three layers and a filler substance are frequently employed. These layers are often made up of a woven top, a batting or wadding layer, and a woven back that are all connected using quilting techniques.

Main Body:

Number of triangles on 1 quilt = 32

Total number of quilt = 21

So total triangles can be calculated by simply multiplying the two values,

Total triangles = 32*21

                        = 672 quilts

Hence total number of triangles = 672

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Answer:

Step-by-step explanation:

black wombat in the dessert jungle

i know its wrong but its right

trust it

the process

The correct conclusion is:

"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."

Given,

At a huge institution, a doctor is determining the typical height of the male students.

Inches are used to measure the heights of a sample of 40 male baseball team players.

The doctor computes the 95% confidence interval using this information (63.5, 74.4).

The following conclusions is valid:

"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."

We can guarantee that the target variable will be within the confidence interval for a given confidence level since we know the confidence interval reflects an interval.

The true mean of heights for male students at the college where the doctor measured heights is represented by the provided case's confidence level of 95% and confidence interval of (63.5, 74.4).

The doctor is therefore 95% certain that the range of the mean height of male students at the college is valid (63.5, 74.4).

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For n as 5,7,8 and 9 the relation will become function

A relation is a function if it has only One y-value for each x-value.

The given relation is two comma eight comma six comma zero comma four comma two comma two times of n comma n.

{(2,8), (6,0), (4,2), (2n,n)}

We need to make it  function for which n should not be 2,6, or 4.

When n is 1, it is not function

n is 3, it is not function

n is 5, it is function

n is 7, it is  function

n is 8, it is function

n is 9, it is function

Hence for n as 5,7,8 and 9 the relation will become function

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The expression that represents the perimeter is 8.6b  and the expression that represents the area of the exercise mat is  3.3b²  .

In the question ,

it is given that ,

the exercise mat is is 3.3 times as long as it is wide .

let the width of the exercise mat be = "b" .

So , the length of the exercise mat will be = 3.3b

The Perimeter of the exercise mat = 2( length + width)

= 2(3.3b + b)

= 2(4.3b)

= 8.6b

the perimeter is = 8.6b

The Area of the exercise mat = length × width

= 3.3b × b

= 3.3b²

the area is = 3.3b²

Therefore , The expression that represents the perimeter is 8.6b  and the expression that represents the area of the exercise mat is  3.3b²  .

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The miles that Jude needs to run on Thursday is 1 3/5 miles.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Total fraction = 7 3/15

Monday race = 2 3/15

Tuesday race = 1 1/15

Wednesday race = 2 1/3

The miles remaining will be:

= 7 3/15 - (2 3/15 + 1 1/15 + 2 1/3)

= 7 3/15 - 5 9/15

= 1 9/15

= 1 3/5 miles

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The value of the discriminant is -71. The roots of the equation are imaginary and two in number.

We are given a quadratic equation. The equation is given below.

2x² + 10x + 9 = 9x

We will simplify this equation.

2x² + x + 9 = 0

We need to find the discriminant of the equation. If the general quadratic equation is represented by ax² + bx + c = 0, then the discriminant is given below.

D = b² - 4*a*c

D = 1² - 4(2)(9)

D = 1 - 72

D = -71

The discriminant is negative, so no real roots exist for the given quadratic equation. Thus, there exist two imaginary roots for the given quadratic equation.

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The solution is

The distance between the point A and C is greater than the distance between the points B and C

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the first point be = A

The value of A = A ( 5 , 6 )

Let the second point be = B

The value of B = B ( 5 , 3 )

Let the reference point be C = C ( -3 , 2 )

Now , the distance between the points A and C = P

The distance between the points B and C = Q

Now , the value of P is calculated from the distance formula

Distance Q = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Substituting the values in the equation , we get

P = √ ( 5 - ( - 3 ) )² - ( 6 - 2 )²

P = √ ( 8 )² + ( 4 )²

P = √ ( 64 + 16 )

P = √80 units

Now , the value of Q is calculated from the distance formula

Substituting the values in the equation , we get

Distance Q = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Q = √ ( 8 )² + ( 1 )²

Q = √ ( 64 + 1 )

Q = √65 units

So , the value of Q is less than value of P

Therefore , the distance of point B to C is lesser than point A to C

Hence , The point B ( 5 ,3 ) is closer to the point C ( -3 , 2 )

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Jennifer had 25 percent increase in number of hours worked

Percentage increase describes the eventual increase in the quantity in percent form. The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time. Mathematically, this formula is represented as the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.

Data;

Percentage Increase = [(15 - 12) / 12] * 100

Percentage Increase = 3/12 * 100

Percentage Increase = 0.25 * 100

Percentage Increase = 25%

The increase is 25%

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Answer:

Step-by-step explanation:

there would be 18 muffins.

if you multiply each number by 3 then add them it will end up at 48.

6x3=18

10x3=30

30+18=48

30:18

Answer:a

Step-by-step explanation

let me know if this helps

Answer: 500 W (watt)

Step-by-step explanation:

Power = P = Work / time = W/t

W = Fd = Force x distance = 400N x 5m = 2000J

P = 2000J/4s = 500 W

Answer:

I belive c

Step-by-step explanation:

Answer:

$64.00

Step-by-step explanation:

4(9) + 2(6.5) + 4(3.75)

36 + 13 + 15

64

The solutions of the quadratic equation are:

A general quadratic equation:

a*x^2 + b*x + c = 0

Has solutions of the form:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4a} }{2a}[/tex]

In this case, the quadratic is:

2*x^2 + x + 2 = 0

a = 2

b = 1

c = 2

Then using above formula we get the two solutions:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*2*2} }{2*2} \\\\x = \frac{-1 \pm \sqrt{-8} }{4}[/tex]

So the solutions are:

x = (-1 +√8*i)/4

x = (-1 -√8*i)/4

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Answer:

Step-by-step explanation:

the numerical coefficient of x2 here is 3.

The student's having a sister is 0.4827 likely. And a random student is chosen who has a brother. Therefore, the probability that this student has a sister is 0.3636.

The fundamental assumption that something will almost certainly occur is known as probability. the percentage of positive occurrences to all occurrences.

Next, the probability is given as

P = (a favorable event) / (Total event)

The letters £ stand for the 29 students in the class, B for those who have brothers, and S for those who have sisters.

Next, the equation will be presented.

7 + 4 + 2x + x + 3 = 29

3x = 29 - 14

3x = 15

x = 5

2x will then have the value

2x = 2(5)

2x = 10

After that, x + 3 will have the value.

x + 3 = 5 + 3 = 8

The probability of the student having a sister is

P = (10 + 4) / 29

P = 14 / 29

P = 0.4827

If a student with a brother is randomly selected, the probability that this student also has a sister will be

P = 4/11

P = 0.3636

As a result, the probability that the student has a sister is 0.4827. And at random, one of the students with a brother is chosen. The likelihood that this student has a sister is then 0.3636.

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Answer:

x = 84

Hope this helped! If you need to know the steps, just let me know and I'll add it :)

Answer:

Step 1: Simplify both sides of the equation.

x/4−10=11

1/4x+−10=11

1/4x−10=11

Step 2: Add 10 to both sides.

1/4x−10+10=11+10

1/4x=21

Step 3: Multiply both sides by 4.

4*(1/4x)=(4)*(21)

x=84

Answer:

x=84

The occupations that fits her plan is Private detective

How would you define statistics?

Statistics is the study of data gathering, analysis, presentation, and interpretation. Early government demands for census data and knowledge of various economic operations were a major source of inspiration for the study of statistics.

What three sorts of statistics are there?

They are (i) the mean, (ii) the median, and (iii) the mode. The study of statistics involves gathering, analyzing, interpreting, presenting, and organizing data in a particular way.

According to the table, the private detective and mathematical activities are the professions that have an average pay over $ 33,500, desired by Jasmine. She must attend college, which she does not want to do, in order to become a math teacher. She can therefore choose to work as a private investigator.

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Answer:

b is the answer

Step-by-step explanation:

hi hope it helps