What is the area of the base of the prism?
1 square centimeters
what is the volume of the prism?
cubic centimeters

Using the arrangements formula, it is found that 907,200 arrangements can be formed using the letters in the word FORGETTING.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are repeating elements, with the number of times given by [tex]n_1, n_2, \cdots, n_n[/tex], the number of arrangements is given by:

[tex]A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

In this problem, the word FORGETTING has 10 letters, of which G and T repeat twice, hence the number of arrangements is given by:

[tex]A_{10}^{2,2} = \frac{10!}{2!2!} = 907,200[/tex]

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The equation of the parabola with its focus at (–7,6) and its directrix at y = 4 will be (x + 7)² + 5.

By drawing the graph, it's can be depicted that the equation in this scenario is x² + 14x + 54.

Complete the square on the expression. This will be done by adding 49. This will be:

= x² + 14x + 7² + 54 - 49

= (x + 7)² + 5

Therefore, the equation of the parabola with its focus at (–7,6) and its directrix at y = 4 will be (x + 7)² + 5.

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Answer:

140

Step-by-step explanation:

10/8 = 1.25

1.25 * 112 = 140

The shape of the barrier is a a circle with a diameter of 5 feet.

A circle is a bounded figure which points from its center to its circumference is equidistant. The diameter of a circle is a straight line that passes through the center of the circle and touches two points on the circumference of the circle.

If all points from the flower is 2.5 feet, it means that the barrier has the shape of a circle.

Diameter = radius x 2

2.5 x 2 = 5 feet

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Answer:

look above

Step-by-step explanation:

hope it hepls

The statement that describes why the Bar Graph is not properly drawn is  D. The width of the bar representing Regular Ice Cream is more than the width of the other bars.

A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths that are proportional to the values that they represent.

Here, the width of the bar representing Regular Ice Cream is more than the width of the other bars.

A bar graph plots data using rectangular bars or columns that represent the total amount of observations in the data for that category.

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Step-by-step explanation:

[tex] = 4 + ( - 3) - 2 ( - 6)[/tex]

here ( + ) × ( - ) = ( - )

[tex] = 4 - 3 + 12[/tex]

[tex] = 4 + 12 - 3[/tex]

[tex] = 16 - 3[/tex]

[tex] = 13[/tex]

The correct result of this simplification is 13

To solve this question, we'll just apply the rule of signs - and then we'll calculate the operations.

- In the sign rule - when both signs are equal, the result will be positive. If the signs are different, the result is negative.

4 + ( - 3 ) - 2 · ( - 6 )

4 - 3 - ( - 12 )

4 - 3 + 12

1 + 12

13

Therefore, the alternative value will be 13

Answer:

value + value = 8379.70

249.99x + 329.99*30-329.99x = 8379.70

-80x + 9899.70 = 8379.70

-80x = -1520.00

x = 19

30-x = 11

Step-by-step explanation:

The type of equation is (a) consistent equations

The attached figure completes the question

From the graph, we can see that the two lines are not parallel and they do not represent the same line

This means that the lines are consistent

Consistent lines produce consistent equations

Hence, the type of equation is (a) consistent equations

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Answer:

The first one

Step-by-step explanation:

Answer:

I think it is 3.750

Step-by-step explanation:

Let's see

[tex]\\ \rm\dashrightarrow \dfrac{9}{x}=\dfrac{24}{12}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{9}{x}=2[/tex]

[tex]\\ \rm\dashrightarrow x=\dfrac{9}{2}[/tex]

[tex]\\ \rm\dashrightarrow x=4.5[/tex]

Answer: 60( 1 - 72)

Step-by-step explanation: i think it might be right so heres a proof

Answer:

a) x value is -2, min is -3(if thats y)

b) x value is 3, max is 21(if thats y)

Step-by-step explanation:

yes you do quadratic formula and such :)

The Pythagorean theorem also known as the Pythagoras' theorem, is the basic relationship between the three sides of a right triangle. The length of the diagonal of the screen is 7.211 ft.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

Given the diagonal is 4 feet tall and 6 feet wide. Therefore, using the Pythagorean theorem, The length of the diagonal of the screen can be written as,

[tex]\text{Length of the diagonal} = \sqrt{4^2+6^2} = \sqrt{52} = 7.2111\rm\ ft[/tex]

Hence, the length of the diagonal of the screen is 7.211 ft.

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Answer:

Rounding to nearest tenth, the answer is 0.3.

Step-by-step explanation:

[tex]\sf 7e^{6x}=42\\\frac{7e^{6x}}{7}=\frac{42}{7}\\e^{6x}=6\\[/tex]

[tex]\sf 6x = \ln(6)\\\\isolate~"x"~and~re-arrange\\\\x=\frac{\ln(6)}{6}[/tex]

≈ [tex]0.3[/tex]

Answer:

44%

Step-by-step explanation:

Existing garden:  L*W, where L and W are the length and width (We'll assume meters, but it can be any other linear measurement, such as miles, cm, or feet, etc.).

Area, A1 = L*W

New Area, A2 = (1.2L)*(1.2W)

  A2 = (1.2)*(1.2)*(L*W)

Since L*W = A1, we can write A2 = 1.44*A1

New Area = 1.44 the original area, a 44% increase.

Answer:

A) 1.2

Step-by-step explanation:

R can never be greater than 1

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Answer:

a: 20

b : 15

Step-by-step explanation:

3*5 = 15

2*5 = 10

15-10 = 5

15+5 = 20

10+5 = 15

Answer:

Let:

[tex] \: [/tex]

5 years ago,

[tex] \: [/tex]

According to the question,

[tex] \quad [/tex][tex] \quad [/tex][tex] \quad [/tex][tex]{ \large{ \rm{ \frac{x}{x - 5} = \frac{3}{2} }}} [/tex]

[tex]{ \green{ \implies}}{ \sf{2x = 3(x - 5)}}[/tex]

[tex]{ \green{ \implies}}{ \sf{2x = 3x - 15}} [/tex]

[tex]{ \green{ \implies}}{ \sf{3x - 2x = 15}} [/tex]

[tex]{ \green{ \implies}}{ \sf{x = { \boxed{ \pink{15}}}}} [/tex]

[tex] \: [/tex]

Therefore,

Present age of B (x) = 15 years.

Present age of A (x + 5) = 20 years.

The distance of point a from translated b is 9.2 units and the distance of point b from translated b is 3.6 units

A line is the distance between two points.

Analysis:

point a( -3,1) point b(2, -6) point translated b(-1, -8)

Distance ab = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]

Distance ab = [tex]\sqrt{(-1--3)^{2} + (-8-1)^{2} }[/tex] = 9.21 units

Distance btb = [tex]\sqrt{(-1-2)^{2} + (-8- -6)^{2} }[/tex] = 3.6 units

In conclusion, the distance of b from a is 9.2 units and b from b is 3.6 units.

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Answer:

Negative one over 6

Step-by-step explanation:

you must download mathspapa

and write that number to solve it

Answer: - 4

Step-by-step explanation:

Since x is already given, which is -1, just substitute the value.

7 * -1 * -1 * -1 + 5 * -1 * -1 - 2

7 * -1 + 5 * 1 - 2

-7 + 5 - 2

-2 - 2 = - 4

Answer:

It is C.

Step-by-step explanation:

First thing you would do is go through all the information and read the options then what you would do is see the labels and its will try to throw you off at A. saying that its Prizes instead of students that has won the prizes so there for

C. Six prizes were won by 4, 5, 6, or 7 students.

is your answer

Answer:

my bet would be d)

Step-by-step explanation:

ur asking math students btw

Answer:

18/95

Step-by-step explanation:

What is probability?

Probability is simply the chances of something occuring.

As a formula, I like to say that formula = # of favorable outcomes / total # of outcomes

Where favorable outcomes is what we want to happen and total # of outcomes is the total number of possibilities.

In order to find the probability of the occurrence of something in a row, we multiply the individual probabilities of each action

Understanding the question

Here we are given that caleb has 7 black caps 4 yellow caps and 9 blue caps in his wardrobe and given this we want to find the probability of Caleb randomly selecting 2 blue caps without replacing it the first being drawn.

So here # of favorable outcomes = # of blue caps = 9

and

total number of outcomes = total # of caps = 7 + 4 + 9 = 20

Finding the probability

For first draw

First let's find the probability that caleb will select a blue cap the first time.

We know that probability = # of favorable outcomes / total # of outcomes

We also know that # of favorable outcomes = 9 and total # of outcomes = 20

Plugging this in, we get that the probability of Caleb randomly selecting a blue cap on the first draw is 9/20

For second draw

Because it says that caleb will not replace the cap when drawn it's important to subtract 1 from both the # of caps and # of blue caps

This results us in having # of favorable outcomes as 8 and total # of outcomes as 19

Plugging this in we get that the probability of Caleb drawing a blue cap the second time is 8/19

Finally to find the total probability of him selecting two blue caps in a row without replacing the first cap, we multiply the individual probabilities

From doing so we acquire 9/20 * 8/19 = 18/95

Answer:

18/95

Step-by-step explanation:

Probability Formula :

Probability (Event) = Number of outcomes with Event / Total outcomes

=============================================================

Given :

⇒ 7 black caps

⇒ 4 yellow caps

⇒ 9 blue caps

===========================================================

Solving :

P (1st cap is blue) :

⇒ Number of blue caps / Total caps

⇒ 9 / 7 + 4 + 9

⇒ 9/20

It mentions the cap is not replaced. Hence, when taking the probability of the 2nd cap, subtract a blue cap from the number of blue caps and the total.

P (2nd cap is blue) :

⇒ Number of blue caps - 1 / Total caps - 1

⇒ 9 - 1 / 20 - 1

⇒ 8/19

P (both caps are blue) :

⇒ P (1st cap blue) × P (2nd cap blue)

⇒ 9/20 × 8/19

⇒ 9/5 × 2/19

⇒ 18/95

Step-by-step explanation:

a is the interior angle of the 2 opposing arc angles. the interior angle is the mean value between the 2 arc angles.

a = (145 + 45)/2 = 190/2 = 95°

b is the simply the supplementary angle to a (meaning together they are 180°, because the sum of all angles around a single point on one side of a line is 180°).

b = 180 - 95 = 85°

The probability that the volume of a can chosen at random is ≥382 is 0.47725

Probability is the likelihood or chance that an event will occur. For the given question, we need to calculate the  z value as shown;

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

Given the following parameters

[tex]x=382mL\\\mu (mean)=372mL\\\sigma(S.D)=5mL[/tex]

Substitute

[tex]z=\dfrac{382-372}{5} \\z=\dfrac{10}{5}\\ z=2[/tex]

In order to calculate the probability that the volume of a can chosen at random is ≥382, we will look for (z≥2)

z≥2 according to probability table is equivalent to 0.47725

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Answer:

y=1

Step-by-step explanation:

Start by plugging in -3 for x in the equation 2x+5y=-1 then solve for y.

2(-3)+5y=-1

-6+5y=-1 (add 6 to both sides)

5y=5 (divide both sides by 5)

y=1