A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100. What percent of exam scores are between 400 and 600?

__% of exam scores are between 400 and 600.

Answer:

3 and 1/2

Step-by-step explanation:

because if one can holds 10 liters of gas, three cans would hold 30 because 10 times 3 is 30 plus the extra 5 liters in the remaining can

Answer:

7/10

Step-by-step explanation:

We have  liters of gas, and we need to figure out how many cans we can fill.

Hint #22 / 4

We need to divide the 7 liters by the 10 liters that each can holds.

For this case we must factor the following expression:

[tex]m ^ 2-14m + 48[/tex]

We must look for two numbers that when multiplied give as a result "48", and when summed, give as a result "-12". These numbers are:

-6 and -8

[tex]-6 * -8 = 48\\-6-8 = -14[/tex]

So, we have:

[tex](m-6) (m-8)[/tex]

ANswer:

Option D

Answer:

Step-by-step explanation:

DDDDDDDDDDDDDDDDDD

Answer: The height of the container is 10 centimeters. If its diameter and height were both doubled, the container's capacity would be 8 times its original capacity.

Step-by-step explanation:

The volume of a cone can be calculated with this formula:

[tex]V=\frac{\pi r^2h}{3}[/tex]

Where "r" is the radius and "h" is the height.

We know that the radius is half the diameter. Then:

[tex]r=\frac{12cm}{2}=6cm[/tex]

We know the volume and the radius of the conical container, then we can find "h":

[tex]120\pi cm^3=\frac{\pi (6cm)^2h}{3}\\\\(3)(120\pi cm^3)=\pi (6cm)^2h\\\\h=\frac{3(120\pi cm^3)}{\pi (6cm)^2}\\\\h=10cm[/tex]

The diameter and height doubled are:

[tex]d=12cm*2=24cm\\h=10cm*2=20cm[/tex]

Now the radius is:

[tex]r=\frac{24cm}{2}=12cm[/tex]

And the container capacity is

[tex]V=\frac{\pi (12cm)^2(20cm)}{3}=960\pi cm^3[/tex]

Then, to compare the capacities, we can divide this new capacity by the original:

 [tex]\frac{960\pi cm^3}{120\pi cm^3}=8[/tex]

Therefore,  the container's capacity would be 8 times its original capacity.

Answer:

i can’t see others answers

Answer:

68 - C = m

If he completes 33 it means :

c = 33

Substituting this in the equation we have :

m > 68 - 33

m > 35

Answer:

I think the first one is 68-c=m and the 2nd one is 35

Step-by-step explanation:

Jeez i hope im right i had to think really hard for some reason. I havent done this is a while >.<

Answer:

slope m=0.5, y-intercept b=5, the price of a 0 page book starts off at 5 and increases 0.5 every 50 pages

Step-by-step explanation:

point slope formula

[tex]y = mx + b[/tex]

choose a point on the line, I chose (2.00,6.00)

and b is the y-intercept at (0,5)

then plug those numbers in

[tex]6.00 = m2.00 + 5.00[/tex]

simplify & isolate the variable

[tex]6.00 - 5.00 = m2.00 + 5.00 - 5.00 [/tex]

[tex]1 = m2[/tex]

[tex]1 \div 2 = m2 \div 2[/tex]

solve for m

[tex]0.1 = m[/tex]

the y intercept is were the line crosses the y axis.

the y axis represents cost in dollars, the x axis represents number of pages

Answer:

One point:  (2/3, 0)

Step-by-step explanation:

The fastest way to determine this is to find the discriminant, b^2-4ac:

discriminant = (-12)^2 - 4(9)(4) = 144 - 144 = 0

The rule here states that if the discriminant is 0, the function has two real, equal roots.  Those roots are

       -(-12) ± √0

x =   ---------------- = 12/18, or 2/3.

             2(9)

The graph touches the x-axis at x = 2/3, but does not cross it.  In other words, the graph intersects the x-axis at only one x value:  2/3.

x = ------------------

The graph of the function y = 9x² - 12x + 4 intersect the x-axis at [tex]x = \frac{2}{3}[/tex] only.

The x-intercepts are the points where the graph intersects the x-axis. The vertex is the point that defines the minimum or maximum of a parabola.

We have,

y = 9x² - 12x + 4

Now,

So, to get the x-intercept,

Put y = 0,

i.e.

0 = 9x² - 12x + 4

Now,

Using the mid term splitting method,

0 = 9x² - 12x + 4

0 = 9x² - 6x - 6x + 4

0 = 3x(3x - 2) -23(x - 2)

i.e.

0 = (3x - 2) (3x - 2)

Now,

3x - 2 = 0

⇒ [tex]x = \frac{2}{3}[/tex]

And,

Now,

3x - 2 = 0

⇒ [tex]x = \frac{2}{3}[/tex] ,

So,

The x -intercept is only at one point, i.e. [tex]x = \frac{2}{3}[/tex].

Hence, we can say that the graph of the function y = 9x² - 12x + 4 intersect the x-axis at [tex]x = \frac{2}{3}[/tex] only.

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Answer:

The EOC is an exam that is more logical, what I can recommend is to study the packages the teacher gave you and also study at USATESTPREP that can help you a lot

To factor the expression 3x^4 - 3x^3 - 18x^2 completely, factor out the GCF 3x^2, then factor the quadratic expression inside the parentheses (x^2 - x - 6) into (x - 3)(x + 2).

To factor the expression 3x^4 - 3x^3 - 18x^2 completely, we can first factor out the greatest common factor (GCF), which in this case is 3x^2. This gives us 3x^2(x^2 - x - 6). To factor the quadratic expression inside the parentheses, we can use the quadratic formula or factor by grouping. The quadratic expression x^2 - x - 6 can be factored as (x - 3)(x + 2).

Therefore, the completely factored expression is 3x^2(x - 3)(x + 2).

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Answer:

Part 1) The system of equations is equal to

12x+y=66.75

3x+10y=82.50

Part 2) The cost of one drink is $5

Step-by-step explanation:

Part 1) Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn

Let

x----> the price of one drink

y ----> the price of one bag of popcorn

we know that

Jason

12x+y=66.75 -----> equation A

Henry

3x+10y=82.50 -----> equation B

Part 2) Using these equations, determine and state the price of a drink, to the nearest cent

12x+y=66.75 -----> equation A

3x+10y=82.50 -----> equation B

Solve the system of equations by elimination

Multiply the equation A by -10 both sides

-10*(12x+y)=66.75*(-10)

-120x-10y=-667.5 -----> equation C

Adds equation B and C and solve for x

3x+10y=82.50

-120x-10y=-667.5

-----------------------------

3x-120x=82.50-667.5

120x-3x=667.50-82.50

117x=585

x=5

therefore

The cost of one drink is $5

Answer:

The reflection is across the x-axis

Step-by-step explanation:

* Lets revise the reflection

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

∴ Its image is (-y , -x)

* Now lets solve the problem

∵ The endpoints of a line segment are (3 , 2) and (2 , -3)

∵ The image of the endpoints after the reflection are (3 , -2) and (2 , 3)

* Lets study the change

# The x-coordinates of the points are 3 and 2

# The x-coordinates of the images are 3 and 2

# The y-coordinates of the points are 2 and -3

# The y-coordinates of the images are -2 and 3

- The change is in the signs of the y-coordinates

∴ The reflection is across the x-axis

The range of the function f (x) = (x - 1)² when the domain is {-5,0,5} is,

⇒ {36, 1, 16}

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable

Given that;

The function is,

⇒ f (x) = (x - 1)²

And, domain is {-5,0,5}.

Now, We can find the value of range as;

Put x = - 5 in above function,

⇒ f (x) = (x - 1)²

⇒ f (x) = (- 5 - 1)²

⇒ f (x) = (- 6)²

⇒ f (x) = 36

Put x = 0 in above function,

⇒ f (x) = (x - 1)²

⇒ f (x) = (0 - 1)²

⇒ f (x) = (- 1)²

⇒ f (x) = 1

Put x =  5 in above function,

⇒ f (x) = (x - 1)²

⇒ f (x) = ( 5 - 1)²

⇒ f (x) = ( 4)²

⇒ f (x) = 16

Thus, The range of the function f (x) = (x - 1)² when the domain is {-5,0,5} is,

⇒ {36, 1, 16}

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Answer:

The best possible answer is A

Step-by-step explanation:

Answer:

Option A is correct that is Surface Area of the Cylinder is 1659 in.²

Step-by-step explanation:

Given:

Radius of the Cylinder , r = 11 in.

Height of the Cylinder , h = 13 in.

We have to find the Surface Area of Cylinder to the nearest Whole number.

We know that,

Surface Area of the Cylinder = 2πr(r+h)

                                                 = 2 × 22/7 × 11 ( 11 + 13 )

                                                 = 2 × 22/7 × 11 × 24

                                                 = 1659.42 in.²

                                                 = 1659 in.²  (nearest whole number)

Therefore, Option A is correct that is Surface Area of the Cylinder is 1659 in.²

Answer:

Step-by-step explanation:

[tex]30x^2-26x+4=0\\\\30x^2-20x-6x+4=0\\\\10x(3x-2)-2(3x-2)=0\\\\(3x-2)(10x-2)=0\iff3x-2=0\ \vee\ 10x-2=0\\\\3x-2=0\qquad\text{add 2 to both sides}\\\\3x=2\qquad\text{divide both sides by 3}\\\\x=\dfrac{2}{3}\\\\10x-2=0\qquad\text{add 2 to both sides}\\\\10x=2\qquad\text{divide both sides by 10}\\\\x=\dfrac{2:2}{10:2}\\\\x=\dfrac{1}{5}[/tex]

ANSWER

The explicit formula is :

[tex]a_n = 8+ 3(n - 1)[/tex]

EXPLANATION

The given sequence is

8,11,14,17,20,23,26,...

The first term is

[tex]a_1=8[/tex]

The common difference is

d=11-8

d=3

The explicit formula is given by:

[tex]a_n = a_1 + d(n - 1)[/tex]

We substitute the values to get,

[tex]a_n = 8+ 3(n - 1)[/tex]

Answer: Assuming a unit of apples is one pound, the answer is .69 cents

Step-by-step explanation:

3.45 / 5 = .69

Answer:3360

Step-by-step explanation:

Answer:

The equation of the line is y = 7x - 10

Step-by-step explanation:

* Lets revise the form of the equation

- The form of the equation of a line is y = mx + c , where m is the slope

  of the line and c is the y-intercept

- The y-intercept means the line intersect the y-axis at point (0 , c)

- The slope of the line which passes through points (x1 , y1) , (x2 , y2)

 is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

* Lets solve the problem

∵ The y-intercept is y = -10

∴ The line intersects the y-axis at point (0 , -10)

∵ The line passes through the points (2 , 4) and (0 , -10)

- Lets find the slope of the line using the rule of the slope above

∵ [tex]m=\frac{-10-4}{0-2}=\frac{-14}{-2}=7[/tex]

∴ The slope of the line is 7

∵ c is the y-intercept

∵ The y-intercept is y = -10

∴ c = -10

∵ y = mx + c

∴ y = 7x + -10

∴ y = 7x - 10

* The equation of the line is y = 7x - 10

Answer:

no solution

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

The 2 lines shown here are parallel and never intersect

Hence the system has no solution

Answer: flower vase

Step-by-step explanation:

A container that has a liquid volume of about 1 liter at home is typically a soda bottle. A liter is a metric unit of capacity and is equivalent to 1,000 cubic centimeters or milliliters, making it a convenient measure for everyday use.

An example of a container that you might find at home which, when filled, has a liquid volume of about 1 liter is a soda bottle. Liters and milliliters are metric units for measuring capacity. A liter is a convenient measure for everyday liquid volumes and is commonly used for beverages and other liquids in the home. Since a liter is equal to 1,000 milliliters, and taking into account that a juice box holds about 25 centiliters, which is 250 milliliters, a soda bottle's capacity is approximately four times that of a typical juice box. It's interesting to note that the liter can also be connected to cubic meters, as 1 liter is the same as 1,000 cubic centimeters (1,000 cm³), making these units interchangeable.

If you divide any number by 1, the answer is itself. The answer is 7 and 1/2.

Hope this helps!

Answer:

7 1/2

Step-by-step explanation:

Take it like the following scenario.

There are 7 1/2 M&M's left in a bag.

Neither of your friends want any so you get to have all of them.

So, the 7 1/2 M&M's divided by one person is 7 12 since all of the M&M's go to you.

[Rememember that any number you divide by 1, the answer is itself

Ex: 4 divided by 1 = 4]

I hope this helps!

Answer:

B.  17%.

Step-by-step explanation:

The General Probability Addition Rule is

P(A∪B) = P(A) + P(B) − P(A∩B)   where P(A∪B) = P(A) or P(B)  and P(A∩B) = P(A) and P(B).

So applying this to our problem we have:

0.57 = 0.43 + 0.31 - P( household has a cat and a dog)

so the answer is 0.43 + 0.31 - 0.57

= 0.17 or 17%.

The probability that the household own both a cat and a dog will be 17%.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The General Probability Addition Rule is

P(A∪B) = P(A) + P(B) − P(A∩B)   where P(A∪B) = P(A) or P(B)  and P(A∩B) = P(A) and P(B).

So applying this to our problem we have:

0.57 = 0.43 + 0.31 - P( household has a cat and a dog)

so the answer is 0.43 + 0.31 - 0.57

= 0.17 or 17%.

Hence the probability that the household own both a cat and a dog will be 17%.

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Answer: The line that passes through the points  (0,1) and  (-7,0). Observe the graph attached.

Step-by-step explanation:

By definition, a line intersects the y-axis when the value of "x" is zero ([tex]x=0[/tex]), then if the y-intercept  is 1, then the point where the line intersects the y-axis is:

(0,1)

By definition, a line intersects the x-axis when the value of "y" is zero ([tex]y=0[/tex]), then if the x-intercept  is -7, then the point where the line intersects the x-axis is:

(-7,0)

Therefore, now you know this, you can graph a line that passes through the points  (0,1) and  (-7,0). Observe the graph attached.

Answer:

Check the attached graph

Step-by-step explanation:

Given that y-intercept is 1.

That means graph passes through the point (0,1).

Given that x-intercept is -7.

That means graph passes through the point (-7,0).

Now we need to graph the line using above information. So begin by graphing both points .

Now draw a line joining both points to get the final graph.

Answer:

A. 2x^5y^8 and 12xy^7

Step-by-step explanation:

The question is on laws of indices

when we have x^a × x^b = x^(a+b)

Given in the question 24x^6y^15

24 could be 2×12............for the length and width

Then x^6 = x^1 × x^5 = x^(1+5) = x^6

And  y^15 = y^8 ×y^7 = y^(8+7) = y^(15)

Answer:

The correct answer is :[tex]l=2x^5y^8,w = 12xy^7[/tex]

Step-by-step explanation:

Let the dimension of the rectangle be l and w.

A = [tex]24x^6y^{15}[/tex]

[tex]24x^6y^{15}=l\times w[/tex]

A) If the dimension are :

[tex]l=2x^5y^8,w = 12xy^7[/tex]

Area of the rectangle

[tex]= 2x^5y^8\times 12xy^7=24x^6y^{15}=A[/tex]

B) If the dimension are :

[tex]l=6x^2y^3,w = 4x^3y^5[/tex]

Area of the rectangle

[tex]= 6x^2y^3\times 4x^3y^5=24x^5y^{8}\neq A[/tex]

C) If the dimension are :

[tex]l=10x^6y^{15},w = 14x^6y^{15}[/tex]

Area of the rectangle

[tex]= 10x^6y^{15}\times 14x^6y^{15}=140x^{12}y^{30}\neq A[/tex]

D) If the dimension are :

[tex]l=9x^4y^{11},w = 12x^2y^4[/tex]

Area of the rectangle

[tex]= 9x^4y^{11}\times 12x^2y^4=108x^6y^{15}\neq A[/tex]

Answer:

8-3r

Step-by-step explanation:

we know that

The conjugate is where we change the sign in the middle of two terms

In this problem

we have

8+3r

so

The conjugate is

8-3r

Answer:

8-3sqrt

Step-by-step explanation:

Answer:

Paul is taller

2 meters is 6.5 feet.

Answer:Paul is taller the answer will be 6.5.

Step-by-step explanation:You had to convert the meters into feet to see which one will be taller.

ANSWER

[tex]3 \frac{1}{4} [/tex]

EXPLANATION

We want to find the distance between

[tex] - 3 \frac{1}{4} [/tex]

and

[tex] - 6 \frac{1}{2} [/tex]

This numbers can be located on the number line.

The distance between them is the absolute value of the difference between the two numbers.

[tex] | - 6 \frac{1}{2} - - 3 \frac{1}{4} | [/tex]

[tex] | - \frac{13}{4} | [/tex]

[tex] = \frac{13}{4} [/tex]

[tex] = 3 \frac{1}{4} [/tex]

Answer:

y = 1/4 x - 12.5

Step-by-step explanation:

8x + 2y = -8 (rewrite in y = mx + b form)

2y = -8x -8 (divide both sides by 2)

y = -4x -2 for first line

Perpendicular line L has "opposite/inverse" slope

y = -4x + b becomes y = 1/4 x + b

What's b (the y-intercept)?

Plug the point (2, -12) into the equation y = 1/4 x  + b to solve for b

-12 = 1/4 (2) + b

-12 = 1/2 + b (subtract 1/2 from both sides)

-12.5 =b (rewrite equation)

y = 1/4 x - 12.5

Answer:

The radius = 18 cm

Step-by-step explanation:

* Lets take about the inscribed triangle in a circle

- If the three vertices of a triangle lie on the circumference of a circle,

 then this triangle is inscribed in the circle

- The vertices of the triangle are inscribed angles in the circle

- The inscribed angle opposite to a circle's diameter is always a

  right angle (its measure is 90°)

- Now lets solve the problem

∵ Δ ABC is a right triangle at C

∴ m∠C = 90°

∵ Δ ABC is inscribed in a circle

∴ A , B , C lie on the circumference of the circle

∴ ∠A , ∠B , ∠C are inscribed angles in the circle

∴ m∠C = 90°

∵ ∠C is opposite to the side AB

∴ AB is the diameter of the circle ⇒ from the bold note above

∵ m∠B = 30°

∵ AC = 18 cm

- Lets use the trigonometry function to find the length of AB

* In Δ ABC

∵ AC is opposite to angle B

∵ AB is the hypotenuse

∵ sin Ф = opposite/hypotenuse

∴ sin B = AC/AB

∴ sin (30)° = 18/AB ⇒ using cross multiplication

∴ AB sin (30)° = 18 ⇒ divide both sides by sin (30)°

∴ AB = 18/sin(30)°

∵ sin(30)° = 1/2

∴ AB = 18/(1/2) = 36 cm

∵ AB is the diameter of the circle

∵ The length of the radius of a circle = 1/2 the length of the diameter

∴ The radius = 1/2 × 36 = 18 cm

Answer:

5

Step-by-step explanation:

8 quizzes / 2 weeks = 20 quizzes / x weeks

Cross multiply:

8x = 40

Divide:

x = 5

Harold will have to attend 5 weeks.

Multiply the given dimensions by the scale factor of 4:

2 x 4 = 8

3 x 4 = 12

6 x 4 = 24

The volume of a pyramid is found by multiplying the Length x the width x the height and dividing by 3:

Volume = (8 x 12 x 24) / 3

Volume = 2304 / 3

Volume = 768 cubic units.

The answer is D.

The volume of the larger pyramid is 768 units³.

Scale factor is the ratio of the dimension of the given original object and the dimension of the new object from the original.

Given that,

A machine assembly requires two pyramid-shaped parts.

Volume of the pyramid = 1/3 × base area × height

If the larger pyramid has a scale factor of 4, each dimension is 4 times this pyramid.3

Base area of the larger pyramid = (4 × 3) × (4 × 2)

                                                     = 96 units²

Volume of the larger pyramid = 1/3 × 96 × (6 × 4)

                                                 = 768 units³

Hence the required volume is 768 units³.

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