What is the shape of the cross-section formed when a cylinder intersects a
plane as shown in the drawing?

Answer:

The probability of waking up early at least one day is 1.2

Step-by-step explanation:

We are given the tree diagram

We are supposed to find the probability of waking up early at least one day

So, we are supposed to find the probability of waking up early for 1 and more than 1 day

By studying the tree diagram

So the probability of waking up early for 1 and more than 1 day =[tex]\frac{2}{5}+\frac{2}{5}+\frac{2}{5}[/tex]

The probability of waking up early at least 1 day = [tex]\frac{2}{5}+\frac{2}{5}+\frac{2}{5}=1.2[/tex]

Hence the probability of waking up early at least one day is 1.2

Answer:

6 times 7 times 8

Step-by-step explanation:

Answer:

Marvin spent $5 on a value meal after he earned $0.50 a day for doing chores at home

Step-by-step explanation:

The relationship between two quantities could be additive (In this case, one quantity is a result of adding a value to the other quantity) or multiplicative (In this case, one quantity is the result of multiplying the other quantity by a value).

Multiplicative Relationship is a relationship that shows two quantities expressed as multiples of each other.

It can be written as: y = nx

where y and x are multiples of each other

n is equivalent to the ratio of y to x

Let's consider the options we have:

a) On her diet, Mrs. Jackson lost 5 pounds every month.

y = x -a (a= constant)

y = x-5

There is no multiplicative relationship of a unit rate of 0.5 in the statement.

b) Mila eats 12 cup of yogurt every day.

There is no multiplicative relationship of a unit rate of 0.5 in the statement.

c) Marvin spent $5 on a value meal after he earned $0.50 a day for doing chores at home.

y = nx

n = 0.5

y is the result of multiplication of 0.5 by x

y = 0.5x

d) Manuel has 5 pet turtles. He hopes to add a new turtle to his reptile habitat each month.

y = x+a (a = constant)

y = x +1

There is no multiplicative relationship of a unit rate of 0.5 in the statement.

Answer:

∠72°.

Step-by-step explanation:

If a circle has a circumference of 20 and an arc with a length of 4, we can simply set up a ratio to determine the angle of the arc in degrees:

[tex]\frac{4}{20} = \frac{x}{360}[/tex]

Cross multiply:

[tex]1440 = 20x\\[/tex]

Divide both sides by '20':

x = 72°.

Therefore, the measure of the central angle of the arc is ∠72°.

Answer:

1

Step-by-step explanation:

The Other Dimension:

2/3 divided by 1 1/2 = 2/3 x 3/2 = 1

Hope this helps

Ps. I have taken the dimension length to be  a mixed number, because they were farther apart. please let me know if wrong

Given:

The value of x = 2.

Solution:

F ( x ) = 2x⁴ - x³ + 5x - 9

=> 2 ( 2 )⁴ - ( 2 )³ + 5 × 2 - 9

=> 2 × 16 - 8 + 10 - 9

=> 32 - 8 + 10 - 9

=> 24 + 1

=> 25

A. 25

Answer:

Step-by-step explanation:

The worth of the card =$75

The value of the card decreases after each music purchase forming a sequence:

75,74.11,73.22,72.33...

Now,

We see that the sequence forms an arithmetic sequence:

Where the first term, a is 75

Common difference, d=-0.89

We want to write an equation to define A(n), the amount of money on the gift card after n song purchases.

For an arithmetic sequence,the nth term A(n)=a+(n-1)d

Therefore:

The amount of money on the gift card after n song purchases.

A(n)=75-0.89(n-1)

A(n)=75+0.89-0.89n

A(n)=75.89-0.89n

To find out how many songs can Josh purchase with this card only, we take our nth term A(n) of the sequence to be 0 and solve for n.

A(n)=75.89-0.89n

0=75.89-0.89n

0.89n=75.89

Divide both sides by 0.89

n=85.3

n=85

Therefore, Josh can purchase 85 songs with this card only

Answer:

105cm^2

Step-by-step explanation:

5 times 6 = 30

30 div 2 = 15

6 times 15 = 90

90 + 15 = 105

Answer:

90 miles per hour is the average speed.

Step-by-step explanation:

The formula for Average Speed can be given as follows:

[tex]\text{Average Speed}= \dfrac{\text{Total Distance Traveled}} {\text{Total Time Taken}}[/tex]

Here time taken is from 1 PM to 4 PM i.e.

Total Time taken = (4-1) hours = 3 hours

Also, it is given that the Total distance covered = 270 miles

As per the formula above:

[tex]\text{Average Speed} = \dfrac{270}{3}\\\Rightarrow \text{Average Speed} = 90\ miles/hour[/tex]

So, answer is: 270 miles/ hour is the average speed of the train from Philadelphia to Boston.

Answer: [tex]12\ mph[/tex]

Step-by-step explanation:

Given

First cyclist travels [tex]3\ miles[/tex] in [tex]15\ min[/tex]

Then, [tex]7\ miles[/tex] in [tex]35\ min[/tex]

Average speed is given by [tex]=\dfrac{\text{Distance}}{\text{time taken}}[/tex]

[tex]V_{avg}=\dfrac{3+7}{15+35}[/tex]

[tex]V_{avg}=\dfrac{10}{50}=\dfrac{1}{5}\ mile/min[/tex]

[tex]V_{avg}=\dfrac{1}{5}\times 60\ miles/hr[/tex]

[tex]V_{avg}=12\ mph[/tex]

Thus cyclist speed is [tex]12\ mph[/tex]

Answer:

y= x2+x-3

Step-by-step explanation: i think this is the answer

Answer:

7

Step-by-step explanation:

15 + 8(2 - 3)

15 + 16 - 24

15 - 8

= 7

Answer:

l = 626.4/bh

Step-by-step explanation:

A triangular prism have a base that is triangular in shape. The volume of a prism has the volume represented as follows.

volume = Al

where

A = Base area

l = width

Since the base is a triangle the base area will be the area of a triangle. Therefore,

volume of a triangular prism = 1/2bh l

where

b = base of triangle

h = height of triangle

volume = 313.2 ft³

313.2 = 1/2bh l

Make the width(l) subject of the formula

multiply both sides by 2

626.4 = bhl

divide both sides by bh

l = 626.4/bh

l = 626.4/bh

recall l = width

Answer: 5. The second box required more material to make.

6. A company saves about $84.94 by choosing to make fifty boxes of the smaller box in comparison to fifty boxes of the larger box.

Step-by-step explanation:

5.  To solve this problem you need to find the volume of the boxes.

Volume of the first box.

v= 8 * 6.25 * 10.5

v= 525  

Second box volume

9 * 5.5 * 11.75 = 581.625

Which means the second box required more material to make because it has the greatest volume.

6. To solve this you have to multiply the volume of small and large boxes by 50 the multiply it by 0.03.

525 * 50 = 26250 * 0.03 = 785.5

581.625 *50 = 29081.25 * 0.03= 872.4375

872.4375 - 785.5  = 84.9375 which is about $84.94.

Answer:

100

Step-by-step explanation:

6x6=36

adding 4 is equal to 10

10x10 = 100

Answer:

483,000

Step-by-step explanation:

10^5=100,000

4.83×100,000=483,000

Answer:

t15 is equal to 30-x so therefore t= 30-x/15

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

add the exponents

(7+(-6)

=7-6

=1

and let the same base =4^1 =4

Answer:

$32.55

Step-by-step explanation:

Before Tax Price: $30.00

Sale Tax: 8.50% or $2.55

After Tax Price: $32.55

Answer:

2,000,000,000.

Step-by-step explanation:

We know that when rounding, we take a look at the digit next to the digit we are rounding. So if I were to ask for you to round 122 to the nearest hundred, then the answer would be 100.

Remember that we round down if the digit next to it is 0-4. If the digit is 5-9, then we round up.

In this case, the digit next to the 2 is a 4. We know that we round down with a 4, so we go to the nearest whole billion, in this case 2 billion.

I hope this helps!

Answer:

(–1, 3), (–2, 2) and (–5, –1)

Step-by-step explanation:

On a coordinate plane, a line has points (-2, -4) and (4, 2). Its slope is:

m = [2 - (-4)]/[4 - (-2)] = 1

To be parallel, both lines have the same slope.

General equation of a line:

y = mx + b

Replacing with m = 1 and Point P (0, 4), we get:

4 = 1(0) + b

4 = b

Therefore, the equation of the line is:

y = x + 4

Replacing x = -4 into the equation:

y = -4 + 4 = 0

Replacing x = -1 into the equation:

y = -1 + 4 = 3     then (-1, 3) lies on the line

Replacing x = -2 into the equation:

y = -2 + 4 = 2     then (-2, 2) lies on the line

Replacing x = 4 into the equation:

y = 4 + 4 = 8

Replacing x = -5 into the equation:

y = -5 + 4 = -1     then (-5, 1) lies on the line

Answer:

[tex](-1,3), (-2,2), (-5,-1)[/tex]

Step-by-step explanation:

1) There's Need for the segment. Reminds me the centroid of a triangle which divides the triangle into two segments in a 2:3 ratio.

2.On a coordinate plane, a line has points (negative 2, negative 4) and (4, 2). Point P is at (0, 4). Which points lie on the line that passes through point P and is parallel to the given line? Select three options. (–4, 2) (–1, 3) (–2, 2) (4, 2) (–5, –1)

1) Let's find the slope of the line [tex]r[/tex] with points [tex]A(-2,-4) \:and\:B(4,2)[/tex]

[tex]m=\frac{2-(-4)}{4-(-2)}=\frac{6}{6}=1[/tex]

2) Now the linear coefficient,

[tex]y=mx+b\\0=1(-2)+b\\b=-2[/tex]

Then the first line [tex]r[/tex] whose points are [tex]A(-2,-4) \:and\:B(4,2)[/tex] is [tex]y=x-2[/tex]

3) From Analytical Geometry, a Parallel line must have the same slope, so that these lines may never intercept each other just like the graph below. So the slope, the angular coefficient must value the same amount.

[tex]m_1=m_{2} \therefore m_{1}=m_{2}=1[/tex]

So, the line [tex]s[/tex] is :

[tex]y=mx+b\\4=1*0+b\\\therefore b=4\\y=x+4[/tex]

4) Testing the points

[tex]2=-4+4 \:\\2\neq 0\\(-1,3)\\3=-1+4\\3=3\\(-2,2)\\2=-2+4\\2=2\\(4,2)\\2\neq 2+4\\(4,2)\\2\neq 4+2\\(-5,-1)\\-1=-5+4\\-1=-1[/tex]

Answer:

480.

Step-by-step explanation:

We would need to draw the line of best fit through these point.

An estimate would be about 480.

Answer:

C

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

114° is an external angle of the triangle , thus

y + y = 114°

2y = 114° ( divide both sides by 2 )

y = 57° → C

Option D 13 dollars per hour

Answer:

B. It is Decreasing

Step-by-step explanation:

When X = -1, Y = 7/3 putting a point at (-1, 7/3)

When X = 1, Y = -1/3 putting another point at (1, -1/3)

The Y value decreases from X = -1 to X = 1

Answer:

Step-by-step explanation:

The graph and the related function are decreasing at a steady rate on the interval (-1, 1).

Answer:

Step-by-step explanation:

We can solve the height of a square pyramid using the Pythagoras theorem, this is because the slant height the height and the section of the base form a right triangle

the slant height is equivalent to the hypotenuse

the height is equivalent to the opposite

while the base(half) is the adjacent

Given

the base of the pyramid= [tex]22.2 in[/tex]

the adjacent is = [tex]\frac{22.2}{2} = 11.1 in[/tex]

the slant height (hypotenuse)= [tex]88.2 in[/tex]

we know that Pythagoras theorem states that "The sum of the squares of the lengths of the legs of a right triangle ('a' and 'b' in the triangle) is equal to the square of the length of the hypotenuse ('c').

[tex]c^2=a^2 + b^2[/tex]

[tex]hyp^2=opp^2+adj^2[/tex]

substituting we have

[tex]88.2^2=opp^2+11.1^2\\opp^2= 88.2^2-11.1^2\\opp^2=7779.24-123.21\\opp^2=7656.03\\opp=\sqrt{7656.03} \\opp=87.498\\opp=87.50 in[/tex]

Answer:

To make it clearer, I just put every thing under the formal form

f(x) = [tex]\left \{ {{2x^2-1~~~~if~~~~ x\leq -1} \atop {3x+2~~~~~if~~~~~x>-1}} \right.[/tex]

Step-by-step explanation:

Now, you have 2 equations with 2 conditions. One is > -1, and one is < -1.

The question is about f (5). So, which equation you use to replace x = 5? The first one or the second one? and why?

Answering those questions help you understand how it works.

Answer:

0

Step-by-step explanation:

Smallest value of C would be when A = - 2 and B = - 2

[tex]\because C = (A - B) ^2 \\ \therefore C = \{ - 2- ( - 2) \}^2 \\ \therefore C = \{ - 2 + 2 \}^2 \\ \therefore C = \{ 0 \}^2 \\ \huge \red{ \boxed{\therefore C = 0}}[/tex]