For a class project, Jina made a model of the Empire State Building that was 23.7 centimeters tall. Her friend Caleb made a moel that was 23 3/5 centimeters tall. Whose model was taller? How much tall was it?

Answer:

The line x = 8 is our vertical asymptote

The limit of [tex]\frac{1}{x-8}[/tex] as x approaches 8 from the left is negative infinity; -∞

Step-by-step explanation:

We have been given the following function;

[tex]\frac{1}{x-8}[/tex]

Considering that the function is rational, it will defined everywhere on the real line except where the expression in the denominator will be 0;

That is the function will not be defined where;

x - 8 = 0

solving for x yields;

x = 8

The function will be approaching the vertical line x = 8 asymptotically, meaning that the function will never touch or cross this line. We can therefore say that,

The line x = 8 is our vertical asymptote for the given function

The limit of [tex]\frac{1}{x-8}[/tex] as x approaches 8 from the left;

[tex]\lim_{x \to8^{-} }\frac{1}{x-8}[/tex]

For x approaching 8 from the left, [tex]x<8[/tex] which implies that [tex]x-8<0[/tex]

The denominator will be a negative quantity approaching 0 from the left, that is -∞.

Thus;

[tex]\lim_{x \to8^{-} }\frac{1}{x-8}[/tex] = -∞

Find the graph attached.

Answer:

it goe towards negative infinity

Step-by-step explanation:

1/6-8=-1/2

1/7-8=-1

1-7.999-8=-10000

therefore you can assume that it is going to a negative infinity direction

Answer: $965

Step-by-step explanation:

The used car is priced at $2,695.

If you borrow the money for the car, your payments will be $122 a month for 30 months. This means that the total amount of money that you would have paid at the end of 30 months at a rate of $122 per month is the amount paid per month multiplied by the total number of months. It becomes

Total payment = 122×30 = $3660

This means that you ended up paying higher than you would have paid if you paid cash.

Amount that you would have saved = amount paid over 30 months - cost of the car

Amount that you would have saved

= 3660 - 2695 = $965

By paying cash for the used car priced at $2,695, you will save $965. Option C is correct.

The total amount paid when financing the car can be found by multiplying the monthly payment by the number of months:

Total amount paid when financing = Monthly payment × Number of months

= $122 × 30

= $3,660

To find the savings, we subtract the total amount paid when financing from the total cost of the car when paying cash:

Savings = Total cost of the car when paying cash - Total amount paid when financing

= $2,695 - $3,660

= -$965

Since the result is negative, it means you would actually be paying more when financing the car compared to paying cash.

Absolute value of savings = |- $965|

= $965

Therefore, the correct answer is  $965.

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Answer:

4x*2x^2+4x*3+(-2)*2x^2+(-2)*3

Step-by-step explanation:

The expansion of the given (4x – 2)(2x 2 + 3) is

4x*2x^2+4x*3+(-2)*2x^2+(-2)*3.

We have given that the (4x – 2)(2x 2 + 3)

We have to determine the expansion of the(4x – 2)(2x 2 + 3)

the act of expanding or the state of being expanded · something expanded; an expanded surface or part · the degree, extent, or amount by which something expands.

Therefore the expansion is given by

[tex](4x -2)(2x^ 2 + 3)=4x*2x^2+4x*3+(-2)*2x^2+(-2)*3[/tex]

Therefore we get the expansion of the given (4x – 2)(2x 2 + 3) is

4x*2x^2+4x*3+(-2)*2x^2+(-2)*3.

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Answer: 171 green marbles

Step-by-step explanation: There are 7 total marbles so 100/7 equals 14.28

Then there is a 2 out of 7 total tries so  14.28 * 2 equals 28.57% chance to get a green marble.

600 * 0.2857 = 171.41 marbles but you cant get half a marble so 171 green marbles.

Answer:

14 ft³

Step-by-step explanation:

First, find the volume of a single cube: V = s³, where s = side length

V = s³; s = 1/5

V = (1/5)³

V = 0.008 ft³

**Note: (1/5)³ is equal to 1/125 as a fraction. I put it down in decimal form because it's easier for me to work with decimals.**

Now, to find the volume of the prism (which is completely filled with cubes), multiply the volume of one cube by the total number of cubes: 1750.

(1750)(0.008)

14 ft³

The volume of the prism is 14 ft³.

Hope this helps!

Final answer:

A baker would need to use 7 scoops of flour with a 1 1⁄2 cup measuring scoop to have at least 4 3⁄4 cups of flour.

Explanation:

The question at hand requires us to determine how many scoops of flour a baker would need to use to obtain at least 4 3⁄4 cups of flour with a scoop that holds 1 1⁄2 cups. To solve this, we will divide the total amount of flour needed by the capacity of the scoop:

Therefore, the baker must use 7 scoops to have at least 4 3⁄4 cups of flour.

The calculated area of the triangle is 18 square units

How to calculate the area of the triangle in square units?

From the question, we have the following parameters that can be used in our computation:

(–2, –1), (4, –1), (6, 5)

The area of the triangle in square units is calculated as

Area = 1/2 * |x₁y₂ - x₂y₁ + x₂y₃ - x₃y₂ + x₃y₁ - x₁y₃|

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * |-2 * -1 - 4 * -1 + 4 * 5 - 6 * -1 + 6 * -1 - 5 * -2|

Evaluate the sum and the difference of products

Area = 1/2 * 36

So, we have

Area = 18

Hence, the area is 18 square units

Answer A becaus descriminant =16-4*3*2=-8

ANSWER

A. There are two complex roots.

EXPLANATION

The given quadratic equation is

[tex]3x^2+4x+2=0[/tex]

when we compare this to

[tex]a {x}^{2} + bx + c = 0[/tex]

we have a=3,b=4 and c=2.

We use the discriminant to determine the nature of roots.

[tex]D= {b}^{2} -4ac [/tex]

[tex]D= {4}^{2} -4(3)(2) [/tex]

[tex]D= 16-24[/tex]

[tex]D= - 8[/tex]

Since the discriminant is less than zero, the equation will have 2 complex roots.

Answer:

660

Step-by-step explanation:

Because the ration is 1:5, then 132 chaperones times 5 is 660 students. Please like me and rate!!

Answer:

Step-by-step explanation:

In general, graphs that go from lower left to upper right have a positive slope (think of it as going up the stairs...positive), and graphs that go from upper left to lower right have a negative slope (think of it as going down the stairs...negative).  I don't see graphs here but use this general idea and you'll be fine.  Of course, this applies to graphs of lines of the form y = mx + b.

To find the sum of the x-coordinates of all possible positive integer solutions to the equation 1/x + 1/y = 1/7, we can rearrange the equation and use Simon's Favorite Factoring Trick to solve for x.

To find the sum of the x-coordinates of all possible positive integer solutions to the equation 1/x + 1/y = 1/7, we can rearrange the equation to 7x + 7y = xy. Simplifying further, we have xy - 7x - 7y = 0. Applying Simon's Favorite Factoring Trick, we add 49 to both sides of the equation: xy - 7x - 7y + 49 = 49. Factoring the left side gives us (x - 7)(y - 7) = 49. Since we are looking for positive integer solutions, we can set x - 7 and y - 7 to be divisors of 49 and solve for x.

The divisors of 49 are 1, 7, and 49. Setting x - 7 = 1, we get x = 8. Setting x - 7 = 7, we get x = 14. And setting x - 7 = 49, we get x = 56. So the sum of the x-coordinates is 8 + 14 + 56 = 78.

Answer:

Part 1) [tex]\angle\ C=50.3\°[/tex]

Part 2) [tex]\angle\ B=67.4\°[/tex]

Part 3) [tex]\angle\ A=62.3\°[/tex]

Step-by-step explanation:

step 1

Find the measure of angle C

Applying the law of cosines

[tex]c^{2} =a^{2} +b^{2} -2(a)(b)cos(C)[/tex]

substitute the given values and solve for cos(C)

[tex]20^{2} =23^{2} +24^{2} -2(23)(24)cos(C)[/tex]

[tex]2(23)(24)cos(C)=23^{2} +24^{2} -20^{2}[/tex]

[tex]1,104cos(C)=705[/tex]

[tex]cos(C)=705/1,104[/tex]

[tex]C=arccos(705/1,104)=50.3\°[/tex]

step 2

Find the measure of angle B

Applying the law of cosines

[tex]b^{2} =c^{2} +a^{2} -2(c)(a)cos(B)[/tex]

substitute the given values and solve for cos(B)

[tex]24^{2} =20^{2} +23^{2} -2(20)(23)cos(B)[/tex]

[tex]2(20)(23)cos(B)=20^{2} +23^{2} -24^{2}[/tex]

[tex]920cos(B)=353[/tex]

[tex]cos(B)=353/920[/tex]

[tex]B=arccos(353/920)=67.4\°[/tex]

step 3

Find the measure of angle A

Remember that the sum of the internal angles of triangle must be equal to 180 degrees

[tex]\angle\ A+\angle\ B+\angle\ C=180\°[/tex]

substitute the given values and solve for ∠A

[tex]\angle\ A+67.4\°+50.3\°=180\°[/tex]

[tex]\angle\ A=180\°-117.7\°[/tex]

[tex]\angle\ A=62.3\°[/tex]

Answer:

16

Step-by-step explanation:

128 stamps and 8 pages have the same amount to add up to 128

So 128 ÷ 8 I'll make it easier

8÷8=1

40÷8=5

80÷8=10

(128÷8)

10+5+1 = 16

There are 16 stamps per page.

Answer:

16 stamps.

Step-by-step explanation:

128 stamps divided by 8 stamps per page is 16 stamps.

Answer:

C. 3 in x 6 in

Step-by-step explanation:

Jammal cuts the block in a straight line parallel to one side... so the section revealed when he finishes his cut will be identical as the parallel side to which the cut is done.

We know the the left side of the prism on the image is 3 inches wide and 6 inches high... so that will also be the dimensions of the exposed cross section.

The answer is then 3 inches y 6 inches. The thickness of the block (5 inches) has no impact on the exposed area of the cross-section.

Answer:

the first one is .6826%

Answer:

Step-by-step explanation:

Given that the graph shows the normal distribution of the length of similar components produced by a company with a mean of 5 centimeters and a standard deviation of 0.02 centimeters.

A component is chosen at random, the probability that the length of this component is between 4.98 centimeters and 5.02

=P(|z|<1) (since 1 std dev on either side of the mean)

=2(0.3418)

=0.6826

=68.26%

The probability that the length of this component is between 5.02 centimeters and 5.04 centimeters is

=P(1<z<2) (since between 1 and 2 std dev from the mean)

=0.475-0.3418

=0.3332

=33.32%

Okay the scale for this equation is each inch equals 30 miles. SO to get how many miles 4.5 inches equals to, we have to multiply 30 by 4.5, and the answer we get is 135.

I hope this helps!

Answer:

The first choice is the one you want

Step-by-step explanation:

Solve the inequalities one at a time:

[tex]\frac{2}{3}x>8[/tex]

Multiply both sides by 3:

2x > 24 and

x > 12

For the next one:

[tex]\frac{2}{3}x <4[/tex]

Again, multiply both sides by 3:

2x < 12 and

x < 6

So the solution set is {x I x > 12 or x < 6}

(3√-3)(3√-5)  multiply 3 and 3, and multiply √-3 and √-5 together, the √ stays

9√15   Your answer is A

Answer:

The correct answer is option A.  9 √15

Step-by-step explanation:

It is given that, 3√-3 and 3 √-5

To find the product

we have, 3√-3 and 3 √-5

(3√-3) * (3 √-5) = 3√-3 * 3 √-5

 = (3 * 3) (√-3 * √-5)

 = 9 * √(-3 * -5)

 = 9* √15

 = 9√15

Therefore the correct answer is option A.  9√15

Answer:

2.78

Step-by-step explanation:

We are given the expression [tex]x^2-1.78x[/tex]

As we know that x=2.78, we can plug that value into the expression and simplify it

[tex](2.78)^2-1.78(2.78)\\\\7.7284-4.9484\\\\2.78[/tex]

ANSWER

There are 210 different permutations

EXPLANATION

The word 'ALFALFA' has 7 letters.

The letter 'A' repeats three times.

The letter 'F' repeats two times.

The letter 'L' also repeats two times.

The number of different permutation is

[tex] \frac{7!}{3!2!2!} = 210[/tex]

There are 210 different permutations.

Answer: There are 210 distinct permutations of the letter of that word.

Step-by-step explanation:

Since we have given that

ALFALFA

Here, 3 A,

2 F,

2 L

Number of letters in that word = 7

So, Number of distinct permutations of the letters of the word "ALFALFA":

[tex]\dfrac{7!}{3!\times 2!\times 2!}\\\\=210[/tex]

Hence, there are 210 distinct permutations of the letter of that word.

Answer:

[tex](-\frac{3}{8},2)[/tex]

Step-by-step explanation:

Point Z divides XY into a 5:3 ratio, so Z is 5/3 of the way from X to Y.  That ratio is k, found by writing the numerator of the ratio (5) over the sum of the numerator and the denominator (5 + 3 = 8).  Our k value is 5/8.  Now we will find the rise and run values which is the slope of this line segment:

[tex]m=\frac{2-2}{-6-9} =\frac{0}{-15}[/tex]

Coordinates are found in this formula:

[tex]Z(x,y)=(x_{1}+k(run),y_{1} +k(rise))[/tex]

Filling that in:

[tex]Z(x,y)=(9+\frac{5}{8}(-15),2+\frac{5}{8}(0))[/tex]

which simplifies to

[tex]Z(x,y)=(9-\frac{75}{8},2+0)[/tex]

which gives us the final coordinates of Z to be [tex]Z(x,y)=(-\frac{3}{8},2)[/tex]

They left the park at 3:05

Answer:

1/2

Step-by-step explanation:

see the picture.

Answer:

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

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1, then

cosx = [tex]\sqrt{1-sin^2x}[/tex]

note that ([tex]\frac{\sqrt{3} }{2}[/tex] )² = [tex]\frac{3}{4}[/tex]

cosΘ = [tex]\sqrt{1-\frac{3}{4} }[/tex] = [tex]\sqrt{\frac{1}{4} }[/tex] = [tex]\frac{1}{2}[/tex]

This is actually quite comical as I just had a DBA concerning equations of circles so, I'm pretty sure I'm qualified to help you.

Equation of a Circle: (x-h)²+(y-k)²=r² where (h, k) is the center and r is the radius.

So, all we need to do is plug in your info:

(x+3)²+(y+2)²=5²

And, there goes your answer.

The Equation of Circle with center (-3, -2) and radius 5 is (x+3)²+(y+2)²=25.

A circle is a round 2-dimensional shape. It is a closed shape with a distance from center to circumference termed as radius 'r' and distance from one point on the circumference to another point passing through center termed as diameter 'd'.

Here,

Equation of a Circle:

                               (x-h)²+(y-k)²=r²

where (h, k) is the center and r is the radius.

So, all we need to put the value of h, k and r in equation of circle:

                                (x+3)²+(y+2)²=5²

                                 (x+3)²+(y+2)²=25

Thus, the Equation of Circle with center (-3, -2) and radius 5 is (x+3)²+(y+2)²=25.

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radius=diameter/2

therefore r=3÷2 ie 1.5m

area=pi (r^2)m^2

=1.5^2 pi m^2

2.25 pi m^2 is required area

Ethan's car used 6 gallons of gasoline for his 180 miles trip, which at a cost of $4 per gallon, results in a total gasoline cost of $24.

To calculate the total cost of gasoline for Ethan's trip, you need to understand how many gallons were used and then multiply that figure by the cost per gallon. As Ethan's car can travel 30 miles per gallon, and Ethan drove 180 miles in total, Ethan's car used 6 gallons of gasoline (180 miles ÷ 30 miles/gallon). Given that gasoline costs $4 per gallon including tax, Ethan therefore spent a total of $24 on gasoline for his trip (6 gallons x $4/gallon).

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The cost per gallon is $24.

To calculate the total cost of the gasoline, we need to divide the distance driven by the car by the car's gas mileage to find the number of gallons used.

Then, we can multiply the number of gallons used by the cost per gallon to find the total cost. In this case,

Ethan drove 180 miles and his car can travel 30 miles per gallon, so he used 180/30 = 6 gallons of gasoline.

The cost per gallon is $4, so the total cost is 6 * $4 = $24.

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Answer:

x³ + 5x² + 16x - 3

Step-by-step explanation:

(f+g)(x) is just another way of writing f(x) + g(x).

f(x) + g(x)

8x² + 16x + 6 + x³ - 3x² - 9

x³ + 5x² + 16x - 3

Answer:

[tex]y=0.2x+3[/tex]

Step-by-step explanation:

Let

x ----> the number of stickers

y ----> the price of the boxes

we have the points

[tex]A(15,6),B(25,8)[/tex]

Find the slope

[tex]m=(8-6)/(25-15)[/tex]

[tex]m=2/10=0.20[/tex]

Find the equation of the line into point slope form

The equation is equal to

[tex]y-y1=m(x-x1)[/tex]

substitute the value of m and the point A

[tex]y-6=0.2(x-15)[/tex]

[tex]y=0.2x-3+6[/tex]

[tex]y=0.2x+3[/tex] ----> linear equation that represent the situation

Answer:

The height of the can is [tex]h=9\ in[/tex]

Step-by-step explanation:

we know that

The surface area of the cylinder (can of peas) is equl to

[tex]SA=2\pi r^{2}+2\pi rh[/tex]

we have

[tex]SA=180.64\ in^{2}[/tex]

[tex]r=5/2=2.5\ in[/tex] ----> the radius is half the diameter

assume

[tex]\pi=3.14[/tex]

substitute and solve for h

[tex]180.64=2(3.14)(2.5)^{2}+2(3.14)(2.5)h[/tex]

[tex]180.64=39.25+15.70h[/tex]

[tex]h=[180.64-39.25]/15.70[/tex]

[tex]h=9\ in[/tex]

The height of the can of peas is equal to 33.628 inches.

Given the following data:

[tex]Radius = \frac{5}{2} = 2.5\;centimeters.[/tex]

To calculate the height of the can of peas:

Note: A can of peas is cylindrical in nature.

Mathematically, the surface area (SA) of a cylinder is given by this formula:

[tex] SA = 2\pi rh + 2\pi r^2[/tex]

Where:

Making h the subject of formula, we have:

[tex]h= \frac{SA-2\pi r^2 }{2\pi r} [/tex]

Substituting the given parameters into the formula, we have;

[tex]h= \frac{180.64-(2\times 2.5^2) }{2\times 2.5} \\ \\ h= \frac{180.64-(2\times 6.25) }{5} [/tex]

Height, h = 33.628 inches.

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Answer the answer is c

Step-by-step explanation:

I also got C for this answer