20 boxes of apples have been delivered to a restaurant. The number of apples in each box is counted. Complete the table below and answer the following question. What is the mean number of apples in a box?

Answer:

[tex]\dfrac{x^{2}}{1210000 } - \dfrac{y^{2}}{5759600} = 1[/tex]

Step-by-step explanation:

A hyperbola is a curve for which the difference of the distances |d₂ - d₁| of any point P from the foci is constant.

The definition leads to the equation

[tex]\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1[/tex]

1. Calculate the value of a²

Assume the neighbours are at the foci A and B.

The explosion is farther from B than from A, so it occurred on the right branch of the hyperbola.

Then AB = 1 mi = 5280 ft

and the distance from the focus to the y-axis is

c = 2640

The vertices are (±a,0).

The speed of sound is 1100 ft/s, so B is 2200 ft further from the explosion.  

The distance from A to the vertex V₁ is c - a. Then

AB = 2200 + 2(c - a) = 2200 -2(2640 - 2a) = 2200 +5280- 2a = 5280

2a = 2200

a = 1100

a² = 1 210 000

2. Calculate the value of b²

[tex]\begin{array}{rcl}a^{2} + b^{2} & = & c^{2}\\1100^{2} + b^{2} & = & 2640^{2}\\b^{2} & = & 2640^{2} - 1100^{2}\\& = & 6969600 - 1210000\\& = & \mathbf{5759600}\\\end{array}[/tex]

3. Write the equation for the hyperbola

[tex]\mathbf{\dfrac{x^{2}}{1210000 } - \dfrac{y^{2}}{5759600}} = \mathbf{1}[/tex]

The equation of the hyperbola is [tex]\frac{x^2}{1210000} -\frac{y^2}{5759600^2} = 1[/tex]

The equation of an hyperbola is represented as:

[tex]\frac{x^2}{a^2} -\frac{y^2}{b^2} = 1[/tex]

The given parameters are given as:

AB = 1 mile

a = 1100 feet

Express the distance AB as feet

AB = 5280 ft

So, the distance AB from the foci is:

[tex]c = \frac{AB}2[/tex]

This gives

[tex]c = \frac{5280}2[/tex]

[tex]c = 2640[/tex]

The value of b is calculated as:

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

So, we have:

[tex]1100^2 + b^2 = 2640^2[/tex]

This gives

[tex]b^2 = 2640^2 -1100^2[/tex]

Evaluate

[tex]b^2 = 5759600[/tex]

Recall that:

[tex]\frac{x^2}{a^2} -\frac{y^2}{b^2} = 1[/tex]

So, we have:

[tex]\frac{x^2}{1100^2} -\frac{y^2}{5759600^2} = 1[/tex]

[tex]\frac{x^2}{1210000} -\frac{y^2}{5759600^2} = 1[/tex]

Hence, the equation of the hyperbola is [tex]\frac{x^2}{1210000} -\frac{y^2}{5759600^2} = 1[/tex]

Read more about hyperbola at:

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Answer:

Step-by-step explanation:

180 - 67 = 113

180 - 113 - 42 = 25

α = 25º

Answer:

Step-by-step explanation:

A number line is a line that can be used to show the position of directed numbers. It has the negative numbers to its left ( i.e before zero) and positive number to the right (i.e after zero).

Rational numbers are positive or negative integers, fractions or decimals.

The rational number -2[tex]\frac{3}{5}[/tex] = -[tex]\frac{13}{5}[/tex] = -2.6 can be shown on the number line as indicated in the image attached to this answer.

Answer:A

Step-by-step explanation: i did the assignment on edge

Answer:

As shown in table, the probability that a person selected at random is going to city B is:

P = number of responses to city B/total number of people answered survey

  = 36/100 = 0.36

Hope this helps!

:)

Answer:

Assuming that the person does not account for probability changes when counters are not replaced, the answer is 20 counters.

Step-by-step explanation:

Please refer to the picture above.

Disclaimer: Probability is not used to deduce the question. The knowledge of fraction is used instead to avoid excess complexity.

Assuming the number of dabbed counters follow the ratio of 1/4 as deduced from the number of dabbed counters in 200 counters, you would expect the number of dabbed counters in 80 counters to follow the same ratio of 1/4. Hence the answer is 20.

Answer:

2*2*7

Step-by-step explanation:

28 = 2*2*7

Answer:

2 x 2 x 7

Step-by-step explanation:

Answer:

The probablility of getting a cat is 1/4 or 25%

The probability of getting a dog is 2/5 or 40%

Step-by-step explanation:

1/4 = .25 = 25%

2/5 = .4 = 40%

Answer:

94°, 120°, 152°

Step-by-step explanation:

Answer:A.

Step-by-step explanation:

Because 3 + 2 is 5.

Answer:

B. 1.85%

Step-by-step explanation:

The APR is the annual interest rate that the bank charges. So, to calculate the monthly percentage rate, you have to divide the APR by 12 that is the number of months in a year:

APR= 22.2%

Monthly percentage rate= 22.2%/12= 1.85%

According to this, the answer is that the monthly percentage rate on the card is 1.85%.

Answer:

(This is for the pizza question)The area of the box is 900 cm, so subtract 900 cm from the area of the circle which is (3.14)[times radius which is 12(half of 24) squared] [144*3.14] So the area of the circle is 452.16 which you get from the area formula of pi times radius squared.

Step-by-step explanation:

Find the area of the box first, then subtract it by the area of the circle. (please thank me for it)

Answer:

8

please see the attached picture for full solution

hope it helps

Good luck on your assignment

The value of x in the given algebraic expression is 12

An algebraic expression is an expression that usually comprises integers, real numbers, variables, and arithmetic operations. The purpose of the given expression is to find the value of x.

Given that:

3(x - 1) - 2(x - 1) = 7

Open the brackets;

3x - 3 - 2x - 2 = 7

Collect like terms

3x - 2x - 3 - 2 = 7

x - 5 = 7

x = 7 + 5

x = 12

Therefore, the value of x in the given algebraic expression is 12

Learn more about algebraic expression here:

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Answer:

YES

Step-by-step explanation: I DID IT

Answer:

6 minutes

Step-by-step explanation:

First convert the hours into minutes to give you 60 minutes.

0.1 of 1 hour is also 0.1 multiplied by 1 hour, so you change the 0.1 into a fraction which is [tex]\frac{1}{10}[/tex] and multiply it with the 60 minutes

[tex]\frac{1}{10} * 60\\= 6mins[/tex]

Answer:

0.65 c

Step-by-step explanation:

You can multiply $0.65 by $95 to get $61.75

Answer: 7.2 months

Step-by-step explanation:

Hi, to answer this question we have to substitute f(x) =500 in the equation given:

f(x) = 100(1.25)^x

500= 100(1.25)^x

Solving for x (number of months)

500/100 = 1.25^x

5 = 1.25^x

log 5 =log 1.25^x

log 5 =x (log 1.25)

log 5 /log 1.25 =x

x = 7.2 months

Feel free to ask for more if needed or if you did not understand something.  

Answer:

-8u+2u+12u-19u-2u=15

-6u+12u-19u-2u=15

6u-19u-2u=15

-13u-2u=15

-15u^2=15

-15u^2÷ 15=15÷15

-u=1

u=-1

that's answer is u=-1

Answer:

$80

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

She gets 16.00 for every 4 quarts she sells

The dollar amount increases by 16.00 after 4 quarts

Answer:

u = fv/(v - f)

Step-by-step explanation:

1/f = 1/u + 1/v

1/u = 1/f - 1/v = v/fv - f/fv = (v-f)/fv

1/u = (v-f)/fv

u = fv/(v - f)

Answer:

4/6 of the cake is left

Steps down below

Step-by-step explanation:

How i got the answer:

As we know that the question is asking how much, so and we also know that Susan ate 1/5 of 5/6 so the and for the equation will be 1/6. So 5/6 - 1/6 will give you the correct answer for this question.

Steps:

1: Subtract the numbers so 5/6 subtract 1/6 =4/6

Answer: 4/6

Hope this helps.

Answer:

m = 9

c = -4

Step-by-step explanation:

The formula for a line is y = mx+c, where m is the gradient and c is the intercept.

here,

m = 9

c = -4

Hope this helps

good Luck

Answer:

Step-by-step explanation:

y = mx + c

y = 9x - 4

Slope m = 9

Y-intercept = -4

Answer:

C.$35

Step-by-step explanation:

Commission = 7% of 500

= 0.07 * 500 = $35

Answer:

6 students are taking all three

20 students are taking none.

Step-by-step explanation:

Please check image attached.

From the total of 33 that are taking Arabic, 14 only take Arabic and 13 take Arabic and Bulgarian (b + d), so the students that take only Arabic and Chinese together is:

a = 33 - 14 - 13 = 6

From the total of 39 that are taking Bulgarian, 19 only take Bulgarian and 13 take Arabic and Bulgarian, so the students that take only Bulgarian and Chinese together is:

c = 39 - 19 - 13 = 7

Now, from the total of 40 that are taking Chinese, 21 only take Chinese, 6 take only Arabic and Chinese and 7 take only Bulgarian and Chinese, so the number of students that take all three languages is:

d = 40 - 21 - 6 - 7 = 6 students

The number of students that take any language is 14 + 19 + 21 + 6 + 7 + 13 = 80 students, so 100 - 80 = 20 students take none of the three languages

Answer:    1.y=  -2  2. y=2

Step-by-step explanation:

Answer:

the answer is -10

Step-by-step explanation:

2 × -5 =-10

The procedure for representing products 2 and -5 is described as follows:

Draw the distance of the first negative number then Extend the distance by the magnitude of the second negative number.

Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever.

This refers to those as closed number lines. Number lines might be alternatively left empty or blank.

In the number line, negative numbers represent leftward distances. The product of a negative number and a positive number will be equal to the distance of the negative one by the number of times such distance is repeated.

The procedure is described as follows:

Draw the distance of the first negative number then Extend the distance by the magnitude of the second negative number.

And Draw the distance of the reflection of the result found in 2.

Learn more about number line here:

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Answer & Step-by-step explanation:

For this problem, we will be doing subtraction. First, we need to find the measurement of the angle beside the angle that measures 95°. We can do this by subtracting 95 from 180 because those angles are a linear pair meaning their measurements equal 180°.

180 - 95 = 85

So, the measurement of that angle is 85°. Now that we know this measurement, we can find the value of x. We can do this by adding 60 to 85 and then subtracting that sum from 180. All triangles have a total interior angle sum of 180°.

180 - (60 + 95)

180 - 155

25

So, the value of x is 25°

Answer:

35

Step-by-step explanation:

first, find the angle next to 95. subtract 95 from 180 since those two angles create a line. how you have 85. the total measure of all angles in a triangle is 180. so, 60+85+x=130. when solved, x=35 :)

Answer:

C 3/16

Step-by-step explanation:

C 3/16

Answer: D

Step-by-step explanation:

I don’t know how to explain this to you step by step but when it comes to questions like this try to think more “logically” (if that makes sense) especially if you’re not familiar with the topic, like me. Think about it, if it was the first one the line on the graph would be above the middle line (its addition plus its greater than y so that wouldn’t be correct). Now the second one is subtraction but its less than y and everything thats coloured goes up not down so it has to be greater than y. C is not the correct answer because its a regular equation and thats not what the question wants plus its the only question out of the the 4 answers which is completely the odd one out so you can just cancel that out. Mow we come to the last answer which is the correct answer because it follows all the right “points” I mentioned earlier. I hope this makes sense to you, sorry I couldn’t explain it better!

Answer:

D

Step-by-step explanation:

i did this one

Answer:

its C

i just took the test

AM = CN serves as additional proof that the triangles AMD and CNB are comparable according to the HL theorem.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given Two right-angle triangles whose hypotenuse is equal.

From the HL-Theorem:

According to the hypotenuse-leg (HL) theorem, a right triangle is congruent if each of its hypotenuses and legs is congruent with its corresponding hypotenuse and legs in another right triangle. The HL theorem proves that these triangles are congruent.

This will work with any two right triangles that have the hypotenuse and one of the legs in proportion, as our selections of right triangles and their legs were arbitrary. Thus, the HL Similarity Theorem has been demonstrated.

Therefore, The additional information to prove if Both triangle AMD and CNB are similar by the HL theorem is AM = CN.

Learn more about right-angle triangles here:

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Answer:

[tex]V=V_p-V_cV=27.712 cm^3 - 4.019 cm^3V=23.693 cm^3V=23.6 cm^3[/tex]

Step-by-step explanation:

Given that:

Diameter of the cylinder: d=1.6 cm

Apothem of the hexagon: a=2 cm

Assuming the thickness of the steel hex nut: t=2 cm

Volume of metal in the hex nut: V=?

[tex]V=V_p-V_c[/tex]

[tex]\texttt {Volume of the prism}: V_p\\\\\texttt {Volume of the cylinder}: V_c[/tex]

Prism:

[tex]V_p=Ab h[/tex]

Ab=n L a / 2

Number of the sides: n=6

Side of the hexagon: L

Height of the prism: h=t=2 cm

Central angle in the hexagon: A=360°/n

A=360°/6

A=60°

[tex]\tan \frac{A}{2} =\frac{L}{2} / a[/tex]

[tex]\tan \frac{60}{2} =\frac{L}{2} / 2cm[/tex]

[tex]\tan 30 =\frac{L}{2} / 2cm[/tex]

[tex]\frac{\sqrt{3} }{3} =\frac{\frac{L}{2} }{2}[/tex]

[tex]2\frac{\sqrt{3} }{3} =\frac{L}{2}[/tex]

[tex]L=4\frac{\sqrt{3} }{3}[/tex]

[tex]Ab=n *L *\frac{a}{2}[/tex]

[tex]Ab=6(4\frac{\sqrt{3} }{3} )(2cm)/2[/tex]

[tex]=24\frac{\sqrt{3} }{3} cm^2\\\\=8\sqrt{3} cm^2[/tex]

[tex]V_p=Ab h[/tex]

[tex]=(8\sqrt{3} )cm^2(2cm)\\\\=16\sqrt{3} cm^3\\\\=16(1.732)cm^3\\\\=27.712cm^3[/tex]

Cylinder:

[tex]V_c=\pi\frac{d^2}{4} L[/tex]

π=3.14

d=1.6 cm

Height of the cylinder: h=t=2 cm

[tex]V_c=3.14\times\frac{1.6^2}{4} \times2\\\\=3.14\times\frac{2.56}{4} \times 2\\\\=2.0096\times2\\\\=4.019cm^3[/tex]

[tex]V=V_p-V_cV=27.712 cm^3 - 4.019 cm^3V=23.693 cm^3V=23.6 cm^3[/tex]

Answer:

23.6

Step-by-step explanation:

Edge 2020