What is the unit rate per student?
12 students ate 4.5 pizzas

The value of i, the interest rate per period(monthly here)  that should be used in the considered formula is given by: Option B: 0.71

If we're given that:

Then, we get:

[tex]P = P_v\left(\dfrac{i}{1-(1+i)^{-n}}\right)[/tex]

For this case, we're provided that:

i = interest rate per period

And we have:

Interest rate compounding monthly = 8.5%

The interest rates are usually given for annual basis. Since i represents the rate per period, which is monthly here, thus, we will convert the rate 8.5% from annually to monthly.

Since 1 year = 12 months,

so 8.5% per year compounding monthly = (8.5/12)% per month compounding monthly

Thus, i = interest per period = interest per month = 8.5/12≈ 0.71 (in percentage)

Thus, the value of i, the interest rate per period(monthly here)  that should be used in the considered formula is given by: Option B: 0.71

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Answer:

Its D :)

Step-by-step explanation:

Answer:

Part a: A square and a rhombus both have sides of equal length.

Let's calculate the length of each side.

[tex]\overline{PL}: \sqrt{(0-5)^2+(3-3)^2}=\sqrt{25+0}=5\\\overline{LA}\sqrt{(5-2)^2+(3-(-1))^2}=\sqrt{3^2+4^2}=5\\\overline{AN}:\sqrt{(2-(-3))^2+(-1-(-1))^2}=\sqrt{25+0}=5\\\overline{NP}:\sqrt{(-3-0)^2+(-1-3)^2}=\sqrt{3^2+4^2}=5[/tex]

All sides measure 5. So it's at least a rhombus (think of a square as a rhombus with extra restrictions).

Part b: A square has extra restriction, more important all angles being 90° and diagonals having the same length. If you discussed about slopes it's easy to see that two sides are horizontal but the other two are NOT vertical. Which might be proof enough.

But the exercise looks about lengths on the plane, so let's measure diagonals.

[tex]\overline{PA}=\sqrt{(0-2)^2+(3-(-1))^2}= \sqrt{2^2+4^2}=\sqrt{20}\\\overline{LN}=\sqrt{(5-(-3))^2+(3-(-1))^2}= \sqrt{8^2+4^2}=\sqrt{80}[/tex]

The two diagonals have different lengths, so the figure cannot be a square.

The value for the diamonds which would make the game of pick a diamond from a deck of 52 cards fair is 6.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

From a card at random from an ordinary deck of 52 cards is picked.If the card is a diamond, you get some points. There are total 13 diamonds in a deck of cards.

Thus, the probability of picking a diamond from 52 cards is,

[tex]P=\dfrac{13}{52}\\P=\dfrac{1}{4}[/tex]

The probability of not picking a diamond from 52 cards is,

[tex]P'=1-\dfrac{1}{4}\\P'=\dfrac{3}{4}[/tex]

If the picked card is not a diamond, then the 2 points are lost. Let X is the score in the game. If the game is fair then the expected value for this should be 0. Thus,

[tex]0=x\times \dfrac{1}{4}+2\times\dfrac{(-3)}{4}\\x=6[/tex]

Hence, the value for the diamonds which would make the game of pick a diamond from a deck of 52 cards fair is 6.

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Answer:

6

Step-by-step explanation:

The answer above is correct.

Answer:

24 weeks

Step-by-step explanation:

I'm not sure exactly what you're asking but if he's making $50 a week it would take him 24 weeks to have enough money for the car. Here is an inequality for the amount he needs: 50x+1800≥3000

Answer:

C-One ball

Step-by-step explanation:

Side x- 4

Side Y- 6

Ball equals 2

4+2=6

6=6

Answer:

88145 doctors

Step-by-step explanation:

Percentage of male doctors=64/100×53100=

35046%.

Therefore 53100+35046=

88145 doctors

Answer:

x=1 and y=−1

Step-by-step explanation:

Use substitution in order to solve this.

Answer:

Option A

Step-by-step explanation:
To find the answer we need to graph the following equations to see which equation is parallel to the given equation 2x + y = -2x. Your answer is option A or "y = -2x + 3." One of the biggest rules when trying to find out if the two lines are parallel to each other is seeing if the two lines intercept. In this case if you graph all the following options, the only line that does not intercept the first line 2x + y = -2 is the option A, which means it's your answer.

Hope this helps.

Answer:

FBC=DBG

Step-by-step explanation:

Edge 2020

Based on the congruent supplements theorem which says that two angles are that are supplements of the same angle are congruent, therefore:  ∠FBC ≅ ∠DBG.

The congruent supplements theorem states that when two angles are congruent or supplements of the same angle, therefore, the two angles can be proven to be congruent angles.

Therefore, from the information given, we can conclude based on the congruent supplements theorem that:  ∠FBC ≅ ∠DBG.

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Answer:

Step-by-step explanation:

area of parking lot=(100-x)(100+x)=100²-x²=(10000-x²)ft²

original area=100²=10000 ft²

x²>0

so new area is decreased.

Check the picture below.

Answer:

36 ft

Step-by-step explanation:

I hope this helps!

Answer:

x = 25°

Step-by-step explanation:

The angles are equal and opposite. This means that if the top angle is 150°, then the angle at the bottom must be 150° too. However, it is currently 2x° + 100°, which turns it into an equation. So far we have 100° as a known angle, so we subtract that from 150° to get the value of 2x.

2x° = 50

Now we divide 50 by 2, and that gives us 25°.

x = 25°

- Educationist

Answer:

[tex]\displaystyle 0,1922986515...\pi = \theta \\ 35° \approx \theta[/tex]

Step-by-step explanation:

[tex]\displaystyle sec^{-1}\:1\frac{177}{823} = \theta; 0,1922986515...\pi\:[or\:34,613757274...°] \\ \\ \boxed{0,1922986515...\pi = \theta\:[35° \approx \theta]}[/tex]

OR

[tex]\displaystyle cos^{-1}\:\frac{823}{1000} = \theta; 0,1922986515...\pi\:[or\:34,613757274...°] \\ \\ \boxed{0,1922986515...\pi = \theta\:[35° \approx \theta]}[/tex]

I am joyous to assist you at any time.

Answer:

21+48.10=69.10

Step-by-step explanation:

21

+

48.10

=

69.10

Answer:

Here is the steps. 67.5 cm^3

Step-by-step explanation:

4.5 * 6 = 27

27 * 2.5 = 67.5

Answer:

67.5 cm

Step-by-step explanation:

[tex]4\frac{1}{2}[/tex] × [tex]6[/tex] ×[tex]2\frac{1}{2}[/tex] = [tex]67\frac{1}{2}[/tex] or [tex]67.5[/tex]

4. The measure of angle m is 110°

- since the two angles are vertical, they are congruent.

:)

Answer:

y < -3

Step-by-step explanation:

Answer: y<-3

Step-by-step explanation:

1) 3y<-9 divide both sides of the inequality by 3

2) 3y÷3< -9÷3

3)any expression divided by itself equals 1

y<-9÷3

4) calculate the quotient y<-3

The equation 4x+8 = -2-2+5x has only one solution x=12.

Given equation is:

4x+8 = -2-2+5x

An equation is an operator (denoted by =) that equates the two expressions.

On bringing variables to the left side and constants on the right side

4x-5x = -2-2-8

-x = -12

x =12

Therefore, the equation 4x+8 = -2-2+5x has only one solution x=12.

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Answer:

A. 75.6 in³

Step-by-step explanation:

The volume of a rectangular prism is V = Bh, where B = area of the base and h = height. We're given the dimensions of the base as 4.2 and 3, and the height as 6.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

A. 75.6 in³

Step-by-step explanation:

Given :-

Base area = 4.2 in x 3 in

Height = 6 in

To find :-

Volume

Formula required :-

Volume = length x breadth x height

Volume = base area x height

Solving :-

V = 4.2 x 3 x 6

V = 12.6 x 6

V = 75.6 in³

Solution :-

A. 75.6 in³

Answer:

the answer I got is:

a= 11√3b/b

b= 363/a^2

Answer:

It would be true

Answer:

10

Step-by-step explanation:

Let x represent the third side

This is a right triangle

In right triangle the sum of square value of both legs is equal to square value of hypotenuse(the third side in this case)

Let x represent the third side

5^2 + 5[tex]\sqrt{3}[/tex]^2 = x^2

25 + 75 = x^2

100 = x^2 find the root for both sides

10 = x

9514 1404 393

Answer:

Step-by-step explanation:

A) Any positive integer is all of real, natural, integer, and rational. A couple of examples of positive integers are 2, and 3.

Any non-complex number is real: -98.6, +29.7π.

Natural numbers are positive integers: 89, 10103.

Integers are any positive or negative number that has no fractional part. Zero is also an integer. A couple are -3, 0.

A rational number is one that can be expressed as the ratio of two integers. Any finite decimal number and any repeating decimal number are rational numbers. A couple of these are 22/7 and -0.0037285.

An irrational number is a number that cannot be expressed as the ratio of two integers. A cube root of a number that is not a perfect cube will be irrational, for example, The same is true of other roots. √2, ∛-5 are irrational. Pi (π) is a famous irrational number, along with 'e', the base of natural logarithms.

__

B) The terms inside parentheses are unlike, so cannot be combined. The only way this expression can be simplified is by removing the parentheses using the distributive property.

  -5(2x -3y +6z -10) = (-5)(2x) +(-5)(-3y) +(-5)(6z) +(-5)(-10)

  = -10x +15y -30z +50

Answer:

Step-by-step explanation:

For exact divisions such as 10 ÷ 5 = 2, we have an integer as a quotient, and for divisions such as 12 ÷ 5 = 2.4, the quotient is a decimal.

Answer:

The slope of the line is  [tex]-\frac{1}{7}[/tex]

Step-by-step explanation:

The rule of the slope of a line which passes through points

(x1, y1) and (x2, y2) is

∵ The line passes through points (19, 8) and (-2, 11)

∴ x1 = 19 and x2 = -2

∴ y1 = 8 and y2 = 11

→ Use the rule above to find the slope of the line

∵ [tex]m=\frac{11-8}{-2-19}=\frac{3}{-21}[/tex]

→ Simplify the fraction by divide up and down by 3

∴ [tex]m=-\frac{1}{7}[/tex]

∴ The slope of the line is  [tex]-\frac{1}{7}[/tex]