What is the exponential form of 10x10?

The function that can be used to find the number of rides Jay went on is, f(x) = 4.5x + 10 = 46.5. Hence, the first option is the right choice.

Also, on solving the function we get that, Jay went on 8 rides.

We assume the number of rides Jay spent to be x.

The cost of each ride is given to be $4.50.

Thus, the total amount Jay spent on rides = $4.50x.

The entrance fee to the park is given to be $10.50.

Thus, the total expenditure of Jay can be shown as $(4.5x + 10.5).

But, in the question we are given that Jay spend $46.50 altogether.

Thus, the function to find the number of rides Jay went on can be shown as:

f(x) = 4.5x + 10 = 46.5.

Hence, the first option is the right choice.

To find the number of rides he went, we can solve this function as:

4.5x + 10 = 46.5,

or, 4.5x = 46.5 - 10.5 = 36,

or, x = 36/4.5 = 8.

Thus, Jay went on 8 rides.

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Answer:

Step-by-step explanation:

hello :

A) X=In(125)

Answer:

Cos (3pi/4) =0.999154554

Sin (3pi/4)=0.041111762

Step-by-step explanation:

On your calculator there should be SIN and COS next to each other

#1 tap COS

#2 put your given numbers, in this case

COS(3pi/4) = 0.999154554

same goes for SIN

SIN (3pi/4)=0.041111762

The percent of the class who voted for Math also voted for Science is 38.8%

Therefore,

1 = p(m) + p(s) - p(m ∩ s)

Hence,

p(m)  = 45% = 0.45

p(s)  = ?

p(m ∩ s) = 35% = 0.35

Therefore,

1 = 0.45 + p(s) - 0.35

1 - 0.45 + 0.35 = p(s)

p(s) = 0.9

Therefore,

p(m | s) = 0.35 / 0.9 = 0.38888888888 = 38.8%

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Answer:

25%

Step-by-step explanation:

3/12 = 0.25 = 25%

Answer:

25%

Step-by-step explanation:

$3 pent out of the original $12.  We can ask what is the percentage of $12 that is equal to $3?  This can be written as:

X($12) = $3, where X is the percentage.

X = (3/12)

X = 0.25 or 25%

Answer: {y | −5 ≤ y ≤ −1}

Step-by-step explanation:

The extreme values are -5 and -1.

So, the answer is {y | −5 ≤ y ≤ −1}.

The interval in which 99.7% of the sample means fall within 3 standard deviations of the mean is 19,306 to 21,694.

According to the central limit theorem,

Sample mean = Population mean = μ

Sample standard deviation = (Population standard deviation)/√n = σ/√n

where n is at least 30.

It is given that,

The overall population mean = 20,500

Population standard deviation σ = 2180

Sample size n = 30

Since n = 30, the central limit theorem can be applied.

According to the Empirical rule(68-95-99), 99.7% of the sample means fall within the 3 standard deviations of the mean.

So, the interval is calculated by

Sample mean = Population mean = μ = 20500

Standard deviation(sample) = σ/√n

⇒ S = 2180/√30 =398.011 ≅ 398

Thus,

The lower bound  = 20500 - 3 × 398 = 19,306

The upper bound = 20500 + 3 × 398 = 21,694

Therefore, the required interval is from 19,306 to 21,694.

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Answer:

c) 58x2

Step-by-step explanation:

Twice the number 29 is 58

So, 29 is related to 58

Therefore 29*4 = 58*2

The values of b and c are -4 and 4 respectively

The function is given as:

f(x) = x^2 + bx + c

Differentiate f(x)

f'(x) = 2x + b

Set to 0

2x + b = 0

Solve for b

b = -2x

The minimum is (2, 0).

So, we have:

b = -2 * 2

b = -4

Substitute b = -4 in f(x) = x^2 + bx + c

f(x) = x^2 - 4x + c

Substitute (2, 0)

0 = (2)^2 - 4(2) + c

This gives

0 = 4 - 8 + c

Evaluate

c = 4

Hence, the values of b and c are -4 and 4 respectively

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If both faucets are used together, it time taken by them to fill the tub is 4.8 minutes.

Time and work share a fundamental idea in common with other arithmetic topics, namely the idea of proportionality.

When the amount of work is constant, efficiency is inversely proportional to the length of time required.

Important Time and Work Formula:

Calculation for the time taken by both faucet to fill the tub.

The unit should be tub per minute.

Then, do the reciprocal of the result to have minute per tub.

The hot water faucet can fill the tub in 12 minutes.

The cold water faucet can fill the tub in 8 minutes.

The filling rate for both faucets filling the tub at the same time is the sum of their rates.

Let 't' be the time taken by both faucets.

Then,

[tex]\frac{1}{12} +\frac{1}{8} =\frac{1}{t}[/tex]

[tex]\frac{8+12}{8*12} =\frac{1}{t}[/tex]

[tex]\frac{1}{t} =\frac{20}{96}[/tex]

[tex]\frac{t}{1} =\frac{96}{20}[/tex]

t = 4.8

Therefore, the time taken by both faucets to fill the tub is 4.8 minutes.

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The probability that at least one of them is a kindergartner; 0.643.

Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."

Probabilities are always expressed in mathematics as fractions, decimals, or percentages with values ranging from 0 to 1.

Calculation for the probability of the one of them is a kindergarden;

The total number of children is 8.

The total number of kindergarden are 3.

The total number of first graders are 5.

Let 'P' be the probability that at least one of them is kindergarden.

P(at least one kindergartner) = 1 - P(no kindergartner) = 1 - P(all first-graders)

The probability that all are first-graders = (5/8)×(4/7)

                                                                  = 5/14

Therefore, P(at least one kindergartner) = 1 - (5/14)

                                                                   = 9/14

                                                                   = 0.643

Therefore, if two children are ill then, the probability that at least one of them is a kindergartner is 0.643.

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The correct question is-

A carpool contains three kindergartners and five first-graders. if two children are ill, find the probability that at least one of them is a kindergartner.

Applying the angle of intersecting chords theorem, the value of x is: 40º.

According to the angle of intersecting chords theorem the following equation is true:

x = 1/2(a + b).

Given the following:

a = 35º

b = 45º

Plug in the values

x = 1/2(35 + 45)

x = 1/2(80)

x = 40º

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To test the value of the mean in a population when only sample mean and sample deviation are known to perform the test then it is appropriate to use z-test procedure.

What is a Z-test?

A statistical method of testing a hypothesis is the z-test where either:

Additional prerequisites for using the z-test include the following:

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Answer:

V≈113.1in³.

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Answer:

The second choice.

Step-by-step explanation:

Correspond sides are in the same ratio

12/4 =  x/8

.

If  function 'f' is defined by f(x)=2-x and 2f(p)=8 then the value of f(2p) is 6.

Given, f(x) = 2-x

Solve this problem by making a series of substitutions.

First, find the value of p.

Then use the definition of the function f to find the value of f(2p).

We are given

f(x) = 2 - x

Multiply both sides by 2, and simplify.

2f(x) = 2(-x +2)

2f(x) = -2x + 4

Let x = p.

2f(p) = -2(p) + 4

We are given that 2f(p) = 8.

Substitute 20 for 2f(p).

8 = -2p + 4

2p = -4

p = -2

Now we know that p = -2, so we can find f(2p).

f(x) = -x + 2

f(2p) = -2p + 2

Substitute -2 for p.

f(2p) = -2(-2) + 2

f(2p) = 4 +2

f(2p) = 6

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Answer:

C is correct

Step-by-step explanation:

I'm not sure what the substituting part has to do anything, but here is how I got the answer

4(x+x+7)-2x+8-4

4(2x+7)-2x+4

8x+28-2x+4

6x+32

Factor and you get

2(3x+16), which is answer choice C

You can check that the answer is right by plugging in x=1 and x=2 into the original equation and the answer choice, which may be what that is asking.

Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

[tex]\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }[/tex]

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

[tex]\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}[/tex]

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

[tex]\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }[/tex]

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

[tex]\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}[/tex]

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

Permutations and combinations have many practical applications in various fields such as statistics, Probability theory, and computer science.

Permutations and combinations are two concepts in mathematics that deal with counting and arranging elements in a set.

Permutations refer to the number of ways in which a set of objects can be arranged or ordered. In other words, permutations involve counting the number of possible ways in which a group of objects can be arranged in a particular order. For example, if we have three objects A, B, and C, the possible permutations would be ABC, ACB, BAC, BCA, CAB, and CBA. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects being arranged.

Combinations, on the other hand, refer to the number of ways in which a subset of objects can be selected from a larger set, without regard to the order in which they are selected. In other words, combinations involve counting the number of possible subsets that can be formed from a larger set. For example, if we have three objects A, B, and C, the possible combinations would be AB, AC, and BC. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects being selected.

The key difference between permutations and combinations is that permutations involve ordering objects, while combinations do not. Another important distinction is that in permutations, each arrangement is considered distinct, whereas in combinations, different arrangements that contain the same objects are considered identical.

Permutations and combinations have many practical applications in various fields such as statistics, probability theory, and computer science. For example, they are commonly used in solving problems related to probability, combinations of locks, and permutations of passwords. Understanding these concepts is essential in order to effectively analyze and solve problems in these fields.

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It can be proved that Circles X and Y are similar.

We were told that circle Y have a  radius of s

And X have the  Radius r

Going with the theorem that Similar shapes are proportional, we can find the scale factor from circle X to circle Y  by making a division on the  radii of both circles.

Then the scale factor is [tex]\frac{s}{r}[/tex] which implies that circle Y will gotten by dilation of circle Y.

Therefore, both circles are similar

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Answer:

Step-by-step explanation:

Similar Triangle:

Triangle ABC has angles of 53 and 62 degrees....the sum is 115 degrees.  The third angle must be 180 - 115 = 65 degrees.

A triangle with one angle = 61 degrees cannot be similar

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Answer: The triangles are not similar; no expression for x can be found.

The linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

Cubic equations are polynomials of third grade, whose standard and factor forms are shown below:

Standard form

y = a · x³ + b · x² + c · x + d

Factor form

y = (x - r₁) · (x - r₂) · (x - r₃)

Where r₁, r₂, r₃ are the zeros of the cubic equation.

There are several approaches to find the roots of the polynomial, in this question we decided to use the graphical approach, which offers sufficiency and quickness for analysis. The roots of the polynomials are the points that pass through the x-axis.

In accordance with the image attached below, the polynomial has three real roots: r₁ = - 20, r₂ = - 5, r₃ = 15. Then, the linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

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Answer:

0.40x = 320

Step-by-step explanation:

If 40% of the total houseplants watered = 320

0.40 times x (total houseplants) = 320

Answer:

[tex]\frac{x}{0.40} = 320 Plants[/tex]

Step-by-step explanation:

[tex]\frac{x}{0.40} = 320 Plants[/tex]

[tex]X = (0.40)(320)Plants[/tex]

[tex]X = 128Plants[/tex]

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the explanation ~

Zeros or roots of a function is the value of independent variable (usually x - coordinate or absicca) where the value of dependent variable (y - coordinate or ordinate) is 0.

That is :

The point where it cuts the x - axis, it has an x - coordinate = -6

Therefore, we can conclude that The zero of given function is -6

Answer:

x = -6.

Step-by-step explanation:

It is where the graph cuts the x-axis  (where the function is zero).

That is -6.

The numerical length of VX is undefined

The given parameters are

VX = 4x

VW = 3x

WX = 5x

Point W is on line segment VX

So, we have

VX = VW + WX

This gives

4x = 3x + 5x

Evaluate

4x= 8x

The above equation is false

Hence, the numerical length of VX is undefined

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Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit

From the question, we are to determine if the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks

In the graph, we have a scatterplot.

The line drawn is the line of best fit

Hence,

Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit.

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Answer:

x= 10 y=14 : 10 3 point, 14 5 point

Step-by-step explanation:

Write your equation down vertically,

3x + 5y = 100

 x + y   =  24

Next find multiply bottom equation by one number from the tops opposite,

3x + 5y = 100

(-3)x +(-3)y = (-3)24

3x + 5y = 100

-3x - 3y= -72

Add the two functions to isolate y

2y= 28 y=14

Plug y back into original and solve

3x +5(14) =100 --> 3x + 70 =100 --> 3x = 30 x=10

Answer:

d

Step-by-step explanation:

there is a common difference between consecutive terms in the series, that is

4 - 13 = - 5 - 4 = - 14 - (- 5) = - 23 - (- 14) = - 9

this indicates the series is arithmetic with sum to n terms

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 13 and d = - 9 , then

S₂₉ = [tex]\frac{29}{2}[/tex] [ (2 × 13) + (28 × - 9) ]

      = 14.4(26 + (- 252))

      = 14.5(26 - 252)

      = 14.5 × - 226

      = - 3,277

Using the domain concept, the only value of x that is not on the domain of [tex]f(x) = \frac{1}{3x + 5}[/tex] is given as follows:

[tex]x = -\frac{5}{3}[/tex]

The domain of a function is the set that contains all possible input values for the function. For a rational function, for example, the zeros of the denominator are excluded from the domain. Another example is an even root, where the inside term has to be positive.

The rational function for this problem is given by the function f(x) presented below:

[tex]f(x) = \frac{1}{3x + 5}[/tex]

The denominator is 3x + 5, hence the restriction in the domain of f(x) is given as follows:

3x + 5 = 0

3x = -5

[tex]x = -\frac{5}{3}[/tex]

The solution to the equation above is the only value of x that is not part of the domain of f(x).

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