Three pizzas are being split amongst friends. Everyone will get 1/4 of a pizza. How many friends can eat pizza?

Answer: A: S = {1, 2, 3, 4, 5, 6, 7}

Step-by-step explanation:

"If a fair seven-sided die is rolled, the sample space, or S = {1, 2, 3, 4, 5, 6, 7} will be the numbers from 1 to 7.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.A sample space is a set of potential results from a random experiment. The letter ""S"" is used to denote the sample space.

Events are a subset of an experiment's potential outcomes.Hence if a fair seven-sided die is rolled, the sample space will be the numbers from 1 to 7 that is S = {1, 2, 3, 4, 5, 6, 7}.

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The definite integral for this problem has the result given as follows:

[tex]\int_1^5 x^2 + 2x - \tan{x} dx = 212 - \ln{|\sec{5}|} + \ln{|\sec{1}|}[/tex]

The definite integral for this problem is defined as follows:

[tex]\int_1^5 x^2 + 2x - \tan{x} dx[/tex]

We have an integral of the sum, hence we can integrate each term, and then add them.

For the first two terms, applying the power rule, the integrals are given as follows:

The integral of the tangent is given as follows:

ln|sec(x)|

Then the integral is given as follows:

I = x³/3 + x² - ln|sec(x)|, from x = 1 to x = 5.

Applying the Fundamental Theorem of Calculus, the result of the integral is obtained as follows:

I = 5³/3 + 5² - ln|sec(5)| - (1³/3 + 1² - ln|sec(1)|)

I = 625/3 - 1/3 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 208 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 212 - ln|sec(5)| + ln|sec(1)|.

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The area of the shaded regions is 4π - 8

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

We start by calculating the area of the triangle using

Area of triangle = 1/2absin(C)

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

Area of triangle = 1/2 * 4 * 4 * sin(90 degrees)

Evaluate

Area of triangle = 8

Next, we calculate the area of the semicircle using

Area = 0.125πd²

Where

d² = (4² + 4²) = 32

So, we have

Area semicircle = 0.125π * 32 = 4π

The area of the circle is

Area circle = 0.25πd²

This gives

Area circle = 0.25π * 32 = 8π

The area of the shaded regions is

Shaded region = circle - semicircle - triangle

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

Shaded region =  8π - 4π - 8

Evaluate

Shaded region =  4π - 8

Hence, the shaded region is 4π - 8

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Using the Newton law of cooling;

a) 78

b) 4.4 min

c) 8.2 min

We know that;

T(t) = T(s)  + (To - Ts)e^-kt

T(t) = Temperature at time t

T(s) = Temperature of the surroundings

k = Rate of cooling

t = time taken

108 = 65 + (207 - 65)e^-2k

108 - 65 = (207 - 65)e^-2k

43 = 142e^-2k

43/142 = e^-2k

-2k = ln(0.3)

k = ln(0.3)/-2

k = 0.6

Thus;

At t = 4

T(t) = 65 + (207 -65)e^-4 *0.6

T(t) = 78

For T(t) = 75℉

75 = 65 + (207 -65)e^-t *0.6

75 - 65 = 142e^-t *0.6

10/142 = e^-t *0.6

-t *0.6 = ln(0.07)

t =  ln(0.07)/-0.6

t = 4.4 min

For T(t) = 64℉

64 = 65 + (207 -65)e^-t *0.6

-1 = 142e^-t *0.6

-1/142 = e^-t *0.6

t = ln(-0.007)/-0.6

t = 8.2 min

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Answer:

y - 9 = 3(x - 4)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = 3 and (a, b ) = (4, 9 ) , then

y - 9 = 3(x - 4) ← equation of line

Answer: y - 9 = 3(x - 4)

Step-by-step explanation: The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = 3 and (a, b ) = (4, 9 ) , then

y - 9 = 3(x - 4) ← equation of line

The value of y for the inequality is y  >  0

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

The inequality 2 times the quantity y plus one third end quantity is greater than two thirds can be written as:

2(y + 1/3) > 2/3

To determine the value of y in the inequality, you need to solve for y. That is:

2(y + 1/3) > 2/3  

y + 1/3 > 1/3     (Divide both sides by 2)

y > 1/3 - 1/3     (Collect like terms)

y > 0

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Answer:

1 mile to 0.033333333333 repentant

Step-by-step explanation:

Find out your answer below:

"If a coin is tossed 7 times, what is the probability of getting 4 tails?"

Use the binomial distribution directly. Let us assume that the number of tails is represented by x  (where a result of tails is regarded as success) and in this case X = 4

Assuming that the coin is unbiased, you have a probability of success ‘p’(where p is considered as success) is 1/2 and the probability of failure ‘q’ is 1/2(where q is considered as failure). The number of trials is represented by the letter ’n’ and for this question n = 7.

Now just use the probability function for a binomial distribution:

P(X = x) = nCxpxqn-x

Using the information in the problem we get P(X = 4) = (7C5)(1/2)5(1/2)2

= 21 × 1/32 × 1/4

= 21/128

Hence, the probability of flipping a coin 7 times and getting tails 4 times is 21/128.

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Answer:

Increasing: [tex](-\infty,-\frac{4}{3})\cup(\frac{4}{3},\infty)[/tex]

Decreasing: [tex](-\frac{4}{3},\frac{4}{3})[/tex]

Step-by-step explanation:

A continuous function increases where [tex]f'(x) > 0[/tex] and decreases where [tex]f'(x) < 0[/tex], so let's find our critical points:

[tex]f(x)=3x^3-16x+2\\f'(x)=9x^2-16\\[/tex]

[tex]9x^2-16=0\\\\9x^2=16\\\\x^2=\frac{16}{9}\\\\x=-\frac{4}{3},\frac{4}{3}[/tex]

We'll use [tex]x=-2, x=0, \text{and } x=2[/tex] as test points to see how the derivative's behavior is around the critical points:

[tex]f'(-2)=9(-2)^2-16=9(4)-16=36-16=20 > 0[/tex]

[tex]f'(0)=9(0)^2-16=-16 < 0[/tex]

[tex]f'(2)=9(2)^2-16=9(4)-16=36-16=20 > 0[/tex]

Hence, we can see that f(x) increases on the interval [tex](-\infty,-\frac{4}{3})\cup(\frac{4}{3},\infty)[/tex] and decreases on the interval [tex](-\frac{4}{3},\frac{4}{3})[/tex].

The function, f(x) is a one to one function.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = 2x – 3

When the independent variable and dependent variable in a given relationship are switched, a relationship known as an inverse function is created.

Simply swapping the x and y coordinates will reveal it.

So,  The statement that could be used in this problem to explain why f(x) = 2x - 3 has an inverse relation.

Hence, the function f(x) is a one to one function.

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The missing value in the proportion is C- 10

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that 2/5 = ?/25

Let x be the unknown number.

Here first we have the bottom half of type equation equal each other

5x=25 (2)

x= 25 (2) / 5

x = 5 (2)

x = 10

10 is the answer

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Answer:

w = 11

l = 42

Step-by-step explanation:

in word problems :

'more than' means +

'triple' means 3 times

'is' means =

perimeter means 2 times width plus 2 times the length

'length of a rectangle is nine more than triple the

width' means :

l = 9+3w

'perimeter is 106 inches' means

2l + 2w = 106

divide by 2

l + w = 53

substitute l with 9+3w to get the width

9+3w + w = 53

9 + 4w = 53

4w = 44

w = 11

go back to the perimeter equation

l + w = 53

put 11 for w

l + 11 = 53

l = 42

It is true the historical setting is important because due to this historical setting and the fact women were not allowed to vote politics were affected.

The historical setting refers to the conditions that affect a specific year, decade or historial moment. For example, in 1944 in you lived in Europe the most important factor of the historical setting was the Second War World.

It is true the historial settign greatly affected politics. Indeed historical conditions such as the fact women could not vote or were limited to do so affected not only those that were choosen as politicians but also the laws and policies created. For example, as there were not women in the government there were not laws to protect women.

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Anna moves 100 jellybeans from bottle a to bottle b, changing the number of red jellybeans in bottle a to 80% and the number of yellow jellybeans in bottle b to 40 percentage

Let x be the number of jellybeans Anna moves from bottle a to bottle b

Original:

Bottle a: 400 jellybeans, 75% red, 25% yellow

Bottle b: 300 jellybeans, 50% red, 50% yellow

After:

Bottle a: 400 jellybeans, 80% red, 20% yellow

Bottle b: 300 + x jellybeans, 40% yellow, 60% red

Equations:

75% of 400 = 300 red jellybeans in bottle a

50% of 300 = 150 red jellybeans in bottle b

80% of 400 = 320 red jellybeans in bottle a

60% of (300 + x) = 180 red jellybeans in bottle b

320 red jellybeans in bottle a - 300 red jellybeans in bottle b = 20 red jellybeans

180 red jellybeans in bottle b - 150 red jellybeans in bottle b = 30 red jellybeans

20 red jellybeans in bottle a = 30 red jellybeans in bottle b

x = 100 jellybeans

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Two-and-four-fifths is less than three-and-one-half.

The correct option is B.

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

For example, 5/10 is a fraction.

Here, 5 is a numerator and 10 is a denominator.

Comparing two-and-four-fifths and three-and-one-half.

two-and-four-fifths = [tex]2\frac{4}{5}[/tex]

three-and-one-half = [tex]3\frac{1}{2}[/tex]

Changing them from mixed fractions to improper fractions

[tex]2\frac{4}{5} = \frac{14}{5} \\\\3\frac{1}{2} = \frac{7}{2}[/tex]

We can deduce that [tex]\frac{14}{5}[/tex] < [tex]\frac{7}{2}[/tex]

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Answer:

x = 0, y = 1

Step-by-step explanation:

This is a system of simultaneous equations in two variables

One method of solving is to get the coefficients of one of the variables same, add or subtract to eliminate that variable and solve for the other variable.

We have

x + 3y = 3 ...............[1]
3x +5y = 5................[2]

If we multiply Equation [1] by 3 we can get the x coefficients the same

[1] x 3 :

3x + 9y = 9..............[3]

Subtract equation [2] from equation [3]

[3] - [2]

(3x + 9y) - (3x + 5y) = 9-5

3x - 3x + 9y - 5y = 4

4y = 4

y = 1

Substitute for y = 1 in equation [1] to get

x + 3(1) = 3

x + 3 = 3

x = 0

So answer is

x = 0, y = 1

Answer:

x=3-3y------eq_i

3x=5-5y

x=5-5y--------eq_ii

3

equating eq i and ii

x=x

3-3y=5-5y

3

3(3-3y)=5-5y

9-9y=5-5y

-9y+5y=5-9

-4y= -4

y=1

now, subsituting the value of y in eq i

x=3-3y

x=3-3×1

x=3-3

x=0

The value of x in the diagram is x = 5

The steps for this process are as follows

Step 1: Since MNP = AXYZ, we can set up an equation to solve for x.

Step 2: We can use the information from the diagram to form the equation.

Step 3: 3x + 4 = 6x - 11

Step 4: Subtract 3x from both sides of the equation.

Step 5: 4 = 3x - 11

Step 6: Add 11 to both sides of the equation.

Step 7: 15 = 3x

Step 8: Divide both sides of the equation by 3.

Step 9: 5 = x

The theory used in this question is algebra. Algebra is used to solve equations and determine values for variables. In this case, algebra was used to solve for the value of x.

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The number of people who receive a share of 2/5 from the given amount is 16 people.

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Given that the amount of share is GHc 40.00 and each individual person receives [tex]\frac{2}{5}[/tex] of the cedi.

The number of people who received the share can be calculated as:

[tex]n = 40 * \frac{2}{5}\\ \\n=16[/tex]

Hence, the number of people who receive a share of 2/5 from the given amount is 16 people.

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Answer:6.5

Step-by-step explanation:

it cant be 2 ft or 72 feet so it leaves us with the other two opsitions

When the ferris wheel rotates once every four minutes, your seat will be above 15 meters for 77.4 seconds of each revolution.

The spikes that go through the middle of a cycle's wheel from one end to the other are an illustration of diameter. Since the diameter is the line segment that begins at one end of a circle and finishes at the other end of the circle, passing through the center, we can compare this to the diameter of a circle. The diameter of a circle cuts through the center, whereas the radius circumscribes the circle from edge to edge. The size of a circle essentially divides it in two. the distance in a straight line going from one edge of a tumor or other item, through the middle, and out the other edge.

given

d = 20 m

r = 10 m

θ = θ1 + 90°

tan θ1 = 5 /10

θ1 = 26°

θ = 26° + 90°

= 116°

that wheel was rotated 116° for you to be at 15 m elevation .

wheel rotates 360° in 4 min

time taken for the wheel to rotate 116° will be

time taken = (116° / 360°) * 4 min

1.29 min = 77.4 sec

When the ferris wheel rotates once every four minutes, your seat will be above 15 meters for 77.4 seconds of each revolution.

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Answer: 1.15

Step-by-step explanation:

2/5+3/4=1.15

3 3/4cups,

2 1/2 cups of cranberry juice = 4 cups of club soda so we know that we would have to add 2 more cups of club soda which is equal to 1 1/4 of cranberry juice

4 = 2 1/2 and 2 = 1 1/4

2 1/2 + 1 1/4 = 3 3/4 cups

Therefore ,the solution to the given problem of equation comes out to be  y = 1/10 * x.

A formula for a mathematical equation combines two statements by using the equal sign (=) to denote equivalence. An equation in algebra is a statement proving the equality of two mathematical equations. For instance, the two numbers are connected by the relation 7x + 5 = 15. A numerical relationship is built between the sentences on either end of a letter. Usually, the symbol serves as the only variable and the only factor. For instance, 16x - 4 = 2.

Here,

Given : Every 30 minutes, an airplane makes

a 300-mile trip from Virginia to Nevada.

By taking all the information in concern,

We get,

x= time

and

y = distance

We get the equation as :

y = 1/10 * x

Therefore ,the solution to the given problem of equation comes out to be y = 1/10 * x.

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Step-by-step explanation:

2:6 = 1:3

1:3 = 1:3

5:15 = 1:3

only

7:22

cannot be reduced to 1:3.

odd one out = 7:22

The true statement about students enrolled in this course from

2018 to 2019 is B The absolute change is -253 students and the relative change indicates a decrease of 7%.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

Given that In the year 2018, the students enrolled were 700 and in the year 2019the students enrolled were 475.

Therefore, Initial value = 700 and Final value = 475.

The absolute change is -

Absolute change = Final value - Initial value =447 - 700 =- 253

The relative change is -

Relative change = Final value - Initial valueInitial value×100% =475-700/ 700×100% =-253

700×100% =-7%

Thus, the absolute change is -253 which indicates that there is a decrease of 7%.

The correct option is b.)

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The complete question is;

a.) The absolute change is –50 students and the relative change indicates a decrease of 11%.

b.) The absolute change is -253 students and the relative change indicates a decrease of 7 %.

c.) The absolute change is 50 students and the relative change indicates an increase of 11%.

d.) The absolute change is 50 students and the relative change indicates a decrease of 10%

The value of  y and x intercepts are 1 and -5/2

We should know that the x-intercept is the point where the x line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis respectively

The equation of the graph is give as follows

m=(y-y₁)/(x-x₊)

Taking the points (0,1) and (5,3)

We can use them to find the slope

3-1/5-0

m=2/5

Applying this to the equation of the line to get

2/5 = y-1/x-0

2/5=y-1/x

Cross and multiply to get

2x=5y-5

Rewrite the equation and make y the subject of the relation

y=2/5x+1

When y=0 2/5x=-1

This implies that x= -5/2

Also, when x=0

y=0+1 = 1

The y intercept is 1 and the x intercept is -5/2

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Answer: I am confused by this can you explain further

Step-by-step explanation:

Answer:

Step-by-step explanation:

All of the other answers except for PQY are lines. You can assume that the answer is PQY.

x+y≥9, 5x+10y≤70 and x≥0 and y ≥ 0 are the required system of linear inequalities that shows all possible combinations of the plants Emma could purchase.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Emma is buying new herbs for her garden

Basil plants cost $5 each and mint plants cost $10 each.

She wants to buy at least 9 plants but cannot spend more than $70.

Let x represents the number of Basil plants

y represents the number of mint plants

x+y≥9

5x+10y≤70

x≥0 and y ≥ 0

Now x=9-y

5x+10y≤70

5(9-y)+10y=70

45-5y+10y=70

45+5y=70

Subtract 45 on both sides

5y=70-45

5y=25

Divide both sides by 5

y=5

x+5=9

x=4

Hence, x+y≥9, 5x+10y≤70 and x≥0 and y ≥ 0 are the required system of linear inequalities that shows all possible combinations of the plants Emma could purchase.

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