Which of the following expressions has a coefficient of 10 and a constant of 5?
10-5
102 + 5
10+5
10+52
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The probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively, in a drawing of 200 people in contest that no one win the prize is equals to 0.0000001269.

Total number of people present= 200

so, total possible outcomes= 200

We have to determine the probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively.

The number of favourable outcomes for winning first prize = 1

So, probability that abby win the first prize = \(\frac{1}{200} \)

The number of favourable outcomes for winning second prize = 1

So, probability that barry win the second prize = \(\frac{1}{199} \)

The number of favourable outcomes for winning third prize = 1

So, probability that sylvia win the third prize = \(\frac{1}{198} \)

Now, total probability that no one can win more than one prize = \(\frac{1}{200} × \frac{1}{199} × \frac{1}{198} \)

= 0.0000001269

Hence, required probability value is 0.0000001269.

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Complete question :

what is the probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively, in a drawing of 200 people enter the contest no one can win more than one prize.

Answer:

x=2

Step-by-step explanation:

5x+3)+(2x2-3x-7)

Answer:

y=2x+5

Step-by-step explanation:

Answer:

l= 234/r

Step-by-step explanation:

Given data

Surface area of cone=734.76 square meters.

The formula for the lateral surface area is

S.A=πrl

substitute the surface area

734.76 = 3.14*r*l

734.76/3.14=rl

234=rl

l= 234/r

Hence, with a value for r, the expression for the slant height l is given as

l= 234/r

On solving the provided question, we can say that equation that make the most sense to solve with the Zero Product Property is  4x² + 16x = 12

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

equation that make the most sense to solve with the Zero Product Property is

4x² + 16x = 12

as when putting x = 0 we get 12

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The values that represented the dimensions in centimeters of the rectangular prism are:

L = 6cm

B = 3cm and

H = 2cm.

A rectangular prism is a three-dimensional shape with six rectangular faces

Let the lenght, breadth and height be

x, y, and z.

xy = 12

xz = 18

yz = 6

(x,y) (xz) (yz) = 12 x 18 x 6

(xyz)² = 1296

xyz = 36

xyz/xy = 36/12

xyz/yz = 36/6

xyz/zx = 36/18

z = 3

x = 6, and

y = 2

Thus, Length = 6cm

Breadth = 3cm and

height = 2cm

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached

The answer is (a) Zimbardo did not use a control group.

The stanford prison experiment was a two week simulation of a prison environment that examined the effect of situational variables on participants reactions and behaviors.

The Stanford prison experiment, one of the most famous and compelling psychological studies of all time.

The major flaw in the research design of the Stanford prison experiment was that the Zimbardo did not use a control group.

A control group is used to establish a cause-and-effect relationship by isolating the effect of an independent variable. A control group was necessary to study a particular variable in prison. He had no alternative group to compare to measure the results of the experiment.

A control group in an experiment does not receive the treatment. Instead, it serves as a comparison group for the treatments.

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Answer:

5) AB = CB = 9√2

6) JK = 3√3          LK = 6√3

7) UV = 6√3         VW = 6

8) RQ = 5√10       PQ = 10√5

Step-by-step explanation:

SOH    CAH    TOA

5) tan 45° = 1 = \(\frac{CB}{AB}\)

CB = AB

Sin 45° = \(\frac{1}{\sqrt{2} } = \frac{CB}{18}\\CB = \frac{18}{\sqrt{2} } \\CB = 9\sqrt{2}\)

since CB = AB

∴ AB = 9√2

6) Tan 60° = \(\sqrt{3} = \frac{9}{JK}\\ JK = \frac{9}{\sqrt{3} } \\JK = 3\sqrt{3}\)

Sin 60 = \(\frac{\sqrt{3} }{2} = \frac{9}{LK}\\ LK = \frac{18}{\sqrt{3} } \\LK = 6\sqrt{3}\)

7) Sin 60 = \(\frac{\sqrt{3} }{2} = \frac{UV}{12}\\ UV = 6\sqrt{3}\)

Cos 60 = \(\frac{1}{2} = \frac{VW}{12}\\ VW = 6\)

8) Tan 45 = 1 = \(\frac{RQ}{5\sqrt{10} }\)

RQ = 5\(\sqrt{10\)

Sin 45 = \(\frac{1}{\sqrt{2}} = \frac{5\sqrt{10} }{PQ}\\ PQ = 10\sqrt{5}\)

Answer:

3 with an arrow pointing to the left

Step-by-step explanation:

\( \textsf{\qquad\qquad\huge\underline{{\sf Answer}}} \)

Volume of a rectangular prism is ~

\( \sf{Volume_{cuboid}= Length × Width × Height} \)

\(\qquad \sf  \dashrightarrow \: v = (4x + 2) \times (3x - 5) \times (7x + 4)\)

\(\qquad \sf  \dashrightarrow \: v = (12 {x}^{2} - 20x + 6x - 10) \times (7x + 4) \)

\(\qquad \sf  \dashrightarrow \: v = (12 {x}^{2} - 14x- 10) \times (7x + 4)\)

\(\qquad \sf  \dashrightarrow \: v = 84 {x}^{3} + 48 {x}^{2} - 98x {}^{2} - 56x - 70x - 40\)

\(\qquad \sf  \dashrightarrow \: v = 84 {x}^{3} - 50 {x}^{2} - 126x - 40\)

So, the correct choice is B

f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

Answer:

We can factor out a 4x from the numerator and a 2 from the denominator, which gives:

(4x(x+1)) / 2( x^2 - 1)

We can then factor the denominator further using the difference of squares formula, which gives:

(4x(x+1)) / 2(x+1)(x-1)

Simplifying this expression further, we can cancel out the (x+1) terms in the numerator and denominator, which gives:

2x / (x-1)

Therefore, 4x^2 + 4x / 2x^2 - 2 simplifies to 2x / (x-1).

Answer:

Step-by-step explanation:

-2

Answer:

(-3,-3)

Step-by-step explanation:

I think I think

I hope this helps!

-AxekickNebulite

a) The level in the filter is reduced at a rate of change of 0.509 inches per minute.

b) The level in the cofeepot is increased at a rate of change of 0.353 inches per minute.

In this question we find the case of coffee being drained and fallen into a coffeepot. The filter has a form of cone and the coffeepot has a form of a cylinder. The volume formulas for the cone and the cylinder are, respectively:

Cone

V = (π / 3) · r² · h

r / h = k

Cylinder

V = π · R² · h

Where:

a) The rate of change of the volume drained from the filter, in cubic inches per minute, is the same volume received by the coffeepot, the rate of change in the level of the filter is defined by first derivative:

V = (π / 3) · k² · h³

V' = π · k² · h² · h'

Where h' is the rate of change of the coffee level, in inches per minute.

If we know that k = 1 / 2, h = 5 and V' = - 10, then the rate of change is:

h' = V' / (π · k · h²)

h' = - 10 / [π · (1 / 2)² · 5²]

h' ≈ - 0.509 in / min

b) And the rate of change for the coffee level in the coffeepot is:

V' = π · R² · h'

h' = V' / (π · R²)

If we know that V' = 10 and R = 3, then the rate of change is:

h' = 10 / (π · 3²)

h' ≈ 0.353 in / min

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Answer:

C = 100 + 40n

The independent variable is n (number of months) and the dependent variable is C ( total cost)

Step-by-step explanation:

Let the total cost of the fitness center = C

Given fixed cost = $100

given cost per month = $40

let number of month = n

The total cost of the fitness center in a given 'n' month is calculated as;

C = 100 + 40n

From the above equation;

the independent variable is n (number of months) and

the dependent variable is C ( total cost)

C = 100 + 40n The independent variable is n (number of months) and the dependent variable is C ( total cost)

Answer:

\(\huge\boxed{11}\)

Step-by-step explanation:

\(\sf = y^2-x^2\\\\Put \ y = 6 \ and \ x = 5\\\\=(6)^2-(5)^2\\\\=36-25\\\\= 11\\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

3500=3.5

500=.5

1=.001

x is not shown on there.

Answer:

142 506

Step-by-step explanation:

here the order does not matter

Then

we the number of sets is equal to the number of combinations.

Using the formula :

the number of sets is 30C5

\(C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}\)

      \(=142506\)

There are 142506 ways in which 5 students can be selected out of 30 students.

The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.

By using the formula:

\(\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}\)

where;

\(\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}\)

\(\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}\)

\(\mathbf{^nC_r = 142506}\)

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Based on the significant difference between the relative frequencies of 0.21 and 0.79, along with the calculated sum of 1.0, the data supports the conclusion that there is likely an association between the categorical variables.

Based on the data, if the relative frequencies being compared are 0.21 and 0.79, we can draw some conclusions. Firstly, the sum of the relative frequencies is 1.0, indicating that they account for all the occurrences within the data set. However, the more crucial aspect is the comparison of the relative frequencies themselves.

Considering that the relative frequencies of 0.21 and 0.79 are significantly different, it suggests that there may be an association between the categorical variables. When there is a strong association, we would generally expect the relative frequencies to be similar or close in value. In this case, the disparity between the relative frequencies supports the notion of an association between the categorical variables.

Therefore, the conclusion most likely supported by the data is that there is likely an association between the categorical variables because the relative frequencies are not similar in value. The fact that the sum of the relative frequencies is 1.0 does not provide evidence for or against an association, but rather serves as a validation that they represent the complete set of occurrences within the data.

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Answer:

23

Step-by-step explanation:

To solve this question I have used some formula.

1. Formula to find the value of term

x + (term number - 1) × {(greater term number - smaller term number) ÷ (greater term containing value) - (smaller term containing value)}

2. Formula to find the value of x given in 1st formula

x = value containing by term - (term number - 1) × {(value containing by greater term - value containing smaller term) ÷ (6-4)}

Here greater term number means the value containing by the greater term. In this question greater term is 6 which contain a value in it that is 18. So, greater term number in this question is 18. So, smaller term number means the smaller term containing a value in it or the number containing by the greater term.

4th term = 8

To find the value of 7th term first we need to find the value of x.

              x = 8 - (4 - 1) × {(18 - 8) ÷ (6 - 4)}

              x = 8 - 3 × (10 ÷ 2)

              x = 8 - 3 × 5

              x = 8 - 15

              x = -7

Now, to check whether the value of x is -7, I have find the 4th term by replacing x with -7 in the 1st formula.

              = -7 + (4 - 1) × {(18 - 8)} ÷ (6 - 4)

              = -7 + 3 × (10 ÷ 2)

              = -7 + 3 × 5

              = -7 + 15

              = 8

Answer came 8 and its correct answer. So, the value of x is -7

I have also find the 6th term so you understand it more properly.

6th term = 18

              = -7 + (6 - 1) × [{(18 - 8)} ÷ (6 - 4)]

              = -7 + 5 × {(10 ÷ 2)}

              = -7 + 5 × 5

              = -7 + 25

              = 18

Answer of 6th term is also correct.

I think now you know how to find the 7th term.

7th term = -7 + (7 - 1) × {(18 - 8) ÷ (6 - 4)

              = -7 + 6 × (10 ÷ 2)

              = -7 + 6 × 5

              = -7 + 30

              = 23

If you think that I have made mistake anywhere or you did not understood my explanation than please ask me in comment or you can report this answer. But, before reporting please see carefully because, once any answer got reported you can't undo it.

Answer:

8 months

Step-by-step explanation:

12/3 = 4, 1/3 is 4 so 1/3 + 1/3 = 2/3 or 8

Answer:

r = 14,8

Step-by-step explanation:

Hope you can read my writing ;-)                                                                                

The length that can be found using the Law of Sine rule is

r= 14.80 units

Generally,

Generally, the equation for sin rule is  mathematically given as

\(\frac{p}{sinP} = \frac{q}{sinQ} = \frac{r}{sinR}\)

Where

p = 9.5 units

∠P = 27°

∠R = 135°

Therefore

\(\frac{9.5}{sin 27^0} = \frac{q}{sin Q} = \frac{r}{sin 135^0}\)

\(\frac{9.5}{sin 27^0} = \frac{r}{sin 135^0}\)

9.5 x 0.7071 = r x 0.4540

r = 14.80 units

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Answer: it will be 48 in 4 years.

Step-by-step explanation: If it’s triples every 6 months that mean times 3 so 2 times 3 is 6 and since there are 12 months you can also do times 6 so 2 times 6 is 12 . And it’s 4 years so 12 times 4 is 48

The area of the circle-shaped rug is 379.94 square inches

The formula for calculating the area of a circle is expressed as;

Area = πr^2

Where;

From the information given, we have the value of the circumference as 69.08 inches

We need to find the value of the radius.

The formula for calculating the circumference of a circle is mathematically expressed as;

Circumference = 2πr

Where: r is the radius of the circle and π takes the value 3. 14

Now, substitute the value into the formula for circumference of a circle, we have;

69.08= 2(3.14)r

Divide both sides by the coefficient of r

r = 69.08/6. 28

r = 11 inches

Then, area = 3.14 × (11)^2

Area = 3.14 × 121

Area = 379.94 square inches

Hence, the value is 379.94 square inches

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Complete question:

Marcy is making a hooked circle-shaped rug for her mother. The circumference of the circle-shaped rug is 69.08 inches. Find the area

Answer:

I think b because line was on x-e

The correlation coefficient for this data set is approximately 0.65.

The correlation coefficient (r) is the square root of the coefficient of determination (r²). In this case, the given value for r² is 0.4225.

To find the correlation coefficient (r), we take the square root of r²:

r = √0.4225

r ≈ 0.65

Therefore, the correlation coefficient for this data set is approximately 0.65.

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