A company needs to package 2400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box cost the company $0.50, while each cylindrical container $0.75

let's notice that this triangular pyramid has a triangular base, that triangle has a base of 14 and an altitude of 8.485, whilst the pyramid also has a height of 12.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} h=&12\\ B=&\frac{1}{2}(14)(8.485) \end{cases}\implies V=\cfrac{1}{3}\left[ \cfrac{1}{2}(14)(8.485) \right](12) \\\\\\ V=4\cdot (7\cdot 8.485)\implies V=237.58[/tex]

Answer: The answer is b, 2x=14

Step-by-step explanation:

You add the equations...

2x-14=0

Move -14 over...

2x=14

Answer:  The correct option is

(B) 2x = 14.

Step-by-step explanation:  We are given to solve the following system of equations by the method of Elimination :

[tex]x+y-6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y-8=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Also, to select the resulting equation when we eliminate y.

Adding equations (i) and (ii), we get

[tex](x+y-6)+(x-y-8)=0+0\\\\\Rightarrow 2x-14=0\\\\\Rightarrow 2x=14~~~~~~~~~~[\textup{this is the resulting equation}]\\\\\Rightarrow x=\dfrac{14}{2}\\\\\Rightarrow x=7.[/tex]

From equation (i), we get

[tex]7+y-8=0\\\\\Rightarrow y-1=0\\\\\Rightarrow y=1.[/tex]

Thus, the required solution is (x, y) = (-1, 7) and the resulting equation while eliminating y is 2x = 14.

Option (B) is CORRECT.

We know that because it forms a right angle, BOF is 90 degrees. We also know that FAO and AOB combine to make 90 degrees.

We already know the value of FOA, so subtract that from 90.

90-35=55.

The measure of AOB is C. 55.

Hope this helps!

Answer:

x² + x + 8 = 0

Step-by-step explanation:

Given

(x - 2)² + 5(x + 2) - 6 = 0 ← expand (x - 2)² and distribute parenthesis by 5

x² - 4x + 4 + 5x + 10 - 6 = 0 ← collect like terms on left side

x² + x + 8 = 0 ← equivalent quadratic equation

Answer:

x² + x + 8 = 0

Step-by-step explanation:

(x-2)^2 + 5(x+2) - 6=0                     { (a-b)² = a² -2ab + b²; here a = x & b = 2}

x²- 2*x*2 + 2² + 5 x + 10 -6 = 0

x² - 4x + 4 + 5x + 10 - 6 = 0

x² + x + 4 + 10 - 6 = 0

x² + x + 8 = 0

Answer: 11/156

Step-by-step explanation: There are 13 marbles at the beginning, and 12 at the end.

13 x 12 = 156

Since there are 2 marbles being picked from the 13, subtract 2 from 13.

13-2 = 11

The probability of choosing different colors is 11/156.

Answer:

C

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = 2x + 3 + x² - 8 ← collect like terms

               = x² + 2x - 5 ← in standard form → C

Using the properties of exponents the expression rewritten as

3 • b^5 • c^5

You can group the repeated factors (b and c) and use exponents to represent their multiplication.

The expression 3•b•b•b•b•b•c•c•c•c•c can be written as:

(3)•(b•b•b•b•b)•(c•c•c•c•c)

This can be further simplified by raising b and c to their respective exponents:

(3)•(b^5)•(c^5)

Therefore, the rewritten expression is 3•b^5•c^5.

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Answer:

y+7 = 4/3(x-9)

Step-by-step explanation:

Point slope form of an equation of a line is

y-y1 = m(x-x1) where (x1,y1) is the point and m is the slope

y--7 = 4/3(x-9)

y+7 = 4/3(x-9)

Answer:

SLOPE INTERCEPT FORM: y = 4/3x - 19

POINT SLOPE FORM: y - (-7) = 4/3(x - 9)

Step-by-step explanation:

Point slope formula is y - y1= m(x - x1)

Insert the information:

➡️y - (-7) = 4/3(x - 9)

(this is point slope form)^

distribute.

➡️y + 7 = 4/3x - 12

move constants on the left side to the right, to get y = mx + b.

➡️y = 4/3x - 19

I didn't know if you just wanted point slope form or to make it slope intercept form, so here's both.

Answer:

Proved,

P(A∪B)=0.72

Step-by-step explanation:

Sue travels by bus or walks when she visits the shops.

Probability( catch the bus to the shop ), P(A) = 0.4

Probability( catch the bus from the shop ), P(B) = 0.7

Both A and B are independent events.

Therefore,

P(A∩B) = 0.4×0.7

           = 0.28

Probability Sue walks one way = 1 - P(A∩B)

                                                   = 1 - 0.28

                                                   = 0.72

Hence, the probability that Sue walks at one way is 0.72

The probability that Sue walks one way is 0.18, derived by subtracting the probability that Sue takes a bus one way (0.82) from 1.

The question refers to the probability involving Sue's mode of transport to and from the shops. To show the probability that Sue walks one way, we need to first determine the probability that she takes a bus either to or from the shops, since taking a bus one way implies she walked the other way.

The probability that Sue takes a bus to the shops OR from the shops, but not both, can be calculated using the formula: P(A U B) = P(A) + P(B) - P(A ∩ B). In this case, A represents the probability Sue takes a bus to the shop (0.4) and B represents the probability she takes a bus from the shop (0.7). P(A ∩ B) is the probability she takes a bus both ways, which is 0.4 * 0.7 = 0.28.

Therefore, the probability she takes the bus one way is P(A U B) = 0.4 + 0.7 - 0.28 = 0.82.

Since Sue either takes a bus or walks, the sum of these two probabilities should be 1. Therefore, the probability Sue walks one way is 1 - the probability she takes the bus one way = 1 - 0.82 = 0.18, not 0.72 as suggested in the question.

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Answer: option b.

Step-by-step explanation:

You need to remember that:

[tex]b^\frac{m}{n}=\sqrt[n]{b^m}\\\\\sqrt[n]{a^n}=a[/tex]

Then, you can rewrite [tex](-32)^\frac{3}{5}[/tex] as:

[tex]=\sqrt[5]{(-32)^3}[/tex]

Now you need to descompose 32 into its prime factors:

[tex]32=2*2*2*2*2=2^5[/tex]

Rewriting:

 [tex]=\sqrt[5]{(-2^5)^3}[/tex]

The power of a power property states that:

[tex](a^b)^c=a^{(bc)}[/tex]

Then:

[tex]=\sqrt[5]{(-2)^{15}}=(-2)^3=-8[/tex]

The given function F(x) = x^2-8x+7 has a minimum point of (4, -9). This is found by using the formula for the vertex of a quadratic function.

This question seems to be incomplete as only one function, F(x) = x^2-8x+7, is provided. However, I can still help you find the minimum of this function. A quadratic function, such as this one, has a minimum or maximum at its vertex. The x-coordinate of the vertex (h) can be found using the formula h = -b/2a.

In this function, a = 1 and b = -8, so h = 8/2 = 4. So the minimum point of the function is at x = 4. To find the corresponding y value, we substitute x = 4 in our function. F(4) = 4^2-8*4+7 = -9. So the minimum point of F(x) = x^2-8x+7 is (4, -9).

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Answer:

1q = 2p

Step-by-step explanation:

One quart of liquid is the equivalent of 2 pints... one of the rare easy measures in the American measure system.

So, the equation needs to have 1 quart on one side, and 2 pints on the other side.  It's an equation because both values are equal, just expressed in different units.

1 quart = 2 pints, then rewritten to match the variables given in the question:

1q = 2p

Use the formula V= πr²h

π = [tex]\frac{22}{7}[/tex]

r = 3 ft

h = 10 ft

^^^^Plug these numbers into their corresponding spot into the formula given above

V = [tex]\frac{22}{7}[/tex]×[tex]3^{2}[/tex]×10

To evaluate apply the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

Parentheses

There are none so go on to the next step

Exponent

[tex]3^{2}[/tex] = 9

so...

V = [tex]\frac{22}{7}[/tex]×9×10

Multiplication (multiply from left to right)

V = [tex]\frac{198}{7}[/tex]×10

V = [tex]\frac{1980}{7}[/tex]

V ≈ 282.857 ft³

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

D

Step-by-step explanation:

Answer:

5 (Answer B)

Step-by-step explanation:

As we move from A to B, x increases by 3 and y decreases by 4.  Apply the Pythagorean Theorem:

(length of AB) = √(3² + [-4]²) = 5 (Answer B)

Answer: Option C

all real numbers

Step-by-step explanation:

We have the following equation

[tex]-2(x + 3) =-2x - 6[/tex]

We must solve for the variable x

[tex]-2(x + 3) =-2x - 6[/tex]

Apply the distributive property of the left side of equality

[tex]-2*x -2*3 =-2x - 6[/tex]

[tex]-2x -6 =-2x - 6[/tex]

Add 6 on both sides of equality

[tex]-2x -6 +6=-2x - 6+6[/tex]

[tex]-2x=-2x[/tex]

Divide between -2x on both sides of the equation

[tex]\frac{-2x}{-2x}=\frac{-2x}{-2x}[/tex]

[tex]1=1[/tex]

The variable x is eliminated. This means that equality does not depend on the value of x. In other words, equality is satisfied for any value of x. Therefore the equation has infinite solutions

The answer is  all real numbers

Answer:

all real numbers

Step-by-step explanation:

trust me it will pay off

Answer:

[tex]D=13.8\ ft[/tex]

Step-by-step explanation:

we know that

If the tank half-filled with water is at 20 feet, then the height of the tank is 40 feet

The volume of the cylindrical tank is equal to

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

we have

[tex]h=40\ ft[/tex]

[tex]V=6,000\ ft^{3}[/tex]

assume

[tex]\pi =3.14[/tex]

substitute and solve for r

[tex]6,000=(3.14)r^{2}(40)[/tex]

[tex]r^{2}=6,000/[(3.14)(40)][/tex]

[tex]r=6.9\ ft[/tex]

Find the diameter

Remember that the diameter is two times the radius

[tex]D=6.9*2=13.8\ ft[/tex]

Answer:

3.55 as a percentage is around an 80%

Step-by-step explanation:

1. Divide the number by 20.

2. Subtract 1 from that number.

Answer:

Somewhere around 80%

Step-by-step explanation:

Substitution.

Here is an example.

Let x be equal to 3 and y equal to 3.

[tex]x=3, y=3[/tex]

From this we can conclude that the values of both x and y are equal to three therefore x and y have the same value and are equal.

[tex]x\wedge y=3\Longrightarrow x=y[/tex]

Here in your case we have:

[tex]

AB=1, BC=1 \\

AB\wedge BC=1\Longrightarrow AB=BC[/tex]

Hope this helps.

r3t40

Answer:

Shanna's family

Step-by-step explanation:

d/t = r (distance/time = rate)

Harlin: 363/6 = 60.5 mph

Kevin: 435/7 = 62.14 mph

Shanna: 500/8 = 62.5 mph

Hector: 215/5 = 43 mph

The question is asking about how long it will take 3 people to trim a hedge if we know that 4 people can do it in an hour. This is an example of an inverse proportion problem. It would take the three people 45 minutes to trim the hedge.

The question asked is about the concept of rate and inverse proportion in mathematics. The problem states that four people can trim a hedge in one hour. If three people were to do the task, they would collectively be less productive per hour, consequently, it would take them longer to trim the hedge. We can calculate the new time by setting up a proportion of 4 people / 1 hour = 3 people / x hours

Cross-multiplying gives: 4x = 3 which simplifies to x = 3/4 hours. Since there are 60 minutes in an hour, multiply the fraction by 60 to convert to minutes. Thus, it would take the three people 45 minutes to trim the hedge.

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Answer:

C. x = 5, y = 2

Step-by-step explanation:

Simply plug in each given term in the answer choices, evaluate, then find out which two will make the system of equations authentic, or genuine.

Answer:

Number One

Step-by-step explanation:

This is because a natural number is a positive integer so it can't be 2,3,or 4 so the only other option is 1!!

Answer:

the values of x, y and z are: x=8, y = -5 and z = -7

Step-by-step explanation:

2x+6y+4z=−42       eq(1)

4x+3y+8z=−39       eq(2)

4x+3y+2z=3          eq(3)

We would solve the above equations using elimination method.

Subtracting eq(3) from eq(2)

4x+3y+8z=−39      

4x+3y+2z=3

-   -     -       -

_____________

0+0+6z = -42

z = -42/6

z = -7

Multiplying eq(1) with 2 and subtracting with eq(2)

4x + 12y +8z = -84

4x +3y +8z = -39

-    -      -        +

_______________

0+9y+0=-45

9y = -45

y = -45/9

y = -5

Putting value of y and z in eq(1)

2x + 6y +4z = -42

2x + 6(-5) +4(-7) = -42

2x -30 -28 = -42

2x -58 = -42

2x = -42 +58

2x = 16

x = 16/2

x= 8

So, the values of x, y and z are: x=8, y = -5 and z = -7

ANSWER

Point if discontinuity:

[tex]{x}= \pm3[/tex]

Zero of the function is

[tex]x = 0[/tex]

EXPLANATION

The given rational function is:

[tex]f(x) = \frac{3x}{ {x}^{2} - 9} [/tex]

This function is not continous when

[tex] {x}^{2} - 9 = 0[/tex]

[tex] {x}= \pm \sqrt{9} [/tex]

[tex]{x}= \pm3[/tex]

The function is zero when,

[tex]3x = 0[/tex]

[tex]x = 0[/tex]

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have

A(0, 0), C(a, b)

[tex]AC=\sqrt{(a-0)^2+(b-0)^2=\sqrt{a^2+b^2}[/tex]

B(a, 0), D(0, b)

[tex]BD=\sqrt{(0-a)^2+(b-0)^2}=\sqrt{(-a)^2+b^2}=\sqrt{a^2+b^2}[/tex]

Therefore AC = BD.

Answer:

There are 720 ways to award the medals

Step-by-step explanation:

* Lets explain the difference between permutations and combinations

- Both permutations and combinations are collections of objects

- Permutations are for lists (order matters)  

- Combinations are for groups (order doesn't matter)  

- A permutation is an ordered combination.  

- Permutation is nPr, where n is the total number and r is the number  

 of choices

# Example: chose the first three students from the group of 10

  students, n = 10 and r = 3,then 10P3 is 720

- Combinations is nCr, where n is the total number and r is the number  

  of the choices

# Example: chose a group of three students from the group of 10

  students n = 10 and r = 3,then 10C3 is 120

* Lets solve the problem

- There are six runner

- There are 6 medals awarded for first place through sixth place

- Each medal is different

- The order is important because they arranged from 1st position to

  the 6th position

∴ We will use the permutation

∵ There are 6 medals for 6 runners

∵ 6P6 = 6 × 5 × 4 × 3 × 2 × 1 = 720

∴ There are 720 ways to award the medals

Answer:

Here's what I get.

Step-by-step explanation:

[tex]x = 7\frac{1}{2} \div \frac{3}{4}[/tex]

1. Convert the mixed number to an improper fraction

[tex]x = \dfrac{15}{2} \div \dfrac{3}{4}[/tex]

2. Invert the proper fraction and change division to multiplication

[tex]x = \dfrac{15}{2} \times \dfrac{4}{3}[/tex]

3. Multiply numerators and denominators

[tex]x = \dfrac{60}{6}[/tex]

4. Divide the numerator and the denominator

[tex]x = 10[/tex]

The quotient is what you get after you invert the denominator in Step 2 and then multiply the two fractions in Step 3.

Here I'm assuming 7 1/2 / 3/4 is  [tex]7\frac{1}{2} / \frac{3}{4}[/tex]

So let's solve, this first convert the mixed fraction into an improper fraction that is its ideal form to solve an equation

[tex]7\frac{1}{2} = \frac{15}{2}[/tex]

therefore,

= [tex]\frac{15}{2} /\frac{3}{4}[/tex]

= [tex]\frac{15}{2} * \frac{4}{3}[/tex]

= 5 * 2

= 10

A mixed fraction is a combination of a whole number and proper fraction.

Improper fractions and proper fractions are the types of fraction numbers (A fraction number which is written in the form of a/b i.e., " [tex]\frac{a}{b}[/tex] " in which a is called as numerator and b is denominator). A fraction is called improper fraction when its numerator is greater than its denominator and for proper fraction, it's vice versa.

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Answer:

A. supplementary

Step-by-step explanation:

Note the angle measurements of BOC. m∠BOC = 90°

Now note that line FC is a straight line, which makes it's measurement = 180°

Subtract 90 from 180: 180 - 90 = 90°

Both are 90°, which, when combined makes a supplementary angle.

Answer:

The measurement of the required angle = 116°

Step-by-step explanation:

Let the measure of its supplement = x

The measurement of the required angle = 2x - 12

x + 2x -12 = 180

3x - 12 = 180

3x = 180 + 12

3x = 192

x = 192/3

x = 64°

The measurement of the required angle = 2 * 64 - 12 = 128 - 12 = 116°

Answer:

5/6

Step-by-step explanation:

Dividing fractions:

Step 1: Rewrite the first fraction as it is.

Step 2: Replace the division sign with a multiplication sign.

Step 3: Flip the second fraction.

Step 4: Multiply the fractions and reduce the product if necessary.

Let's use the rule of dividing fractions on your problem.

Step 1: Rewrite the first fraction as it is.

[tex] \dfrac{5}{8} [/tex]

Step 2: Replace the division sign with a multiplication sign.

[tex] \dfrac{5}{8} \times [/tex]

Step 3: Flip the second fraction.

[tex] \dfrac{5}{8} \times \dfrac{4}{3} [/tex]

Step 4: Multiply the fractions and reduce the product if necessary.

To multiply fractions, multiply the numerators together, and multiply the denominators together.

[tex] \dfrac{5}{8} \times \dfrac{4}{3} = \dfrac{5 \times 4}{8 \times 3} = \dfrac{20}{24} [/tex]

We notice that the greatest common factor of 20 and 24 is 4, so we divide both the numerator and denominator by 4 to reduce the fraction.

[tex] = \dfrac{4 \times 5}{4 \times 6} = \dfrac{5}{6} [/tex]