1. Jack and Betty have 40 coins that are nickels and dimes. If the value of
the coins is $3.15, how many of each type of coin do they have?

Answer:

A f3(x)=f2(f1(x))=1.2x+2

Step-by-step explanation:

The "F1" key is to perform a 20% enlargement in both dimensions. So, first the function F1 increases the dimension x by 20%. That is, our new dimension x' is now the initial dimension plus the increase. The initial dimension is x and the increase is 20% of x = 0.2x. So, x' = x + 0.2x = 1.2x. So, F1(x) = x' = 1.2x

Then, the "F2" key is to increase the picture size by 2cm in both dimensions. So, the function F2 works on x' and add 2 cm to it. So, our new dimension is thus x" = x' + 2.

So F2(x') = x" = x' + 2 = F1(x) + 2

F2(F1(x)) = x' + 2 = 1.2x + 2

F3(x) = F2(F1(x)) = 1.2x + 2

F3(x) = 1.2x + 2.

So, the equivalent function for a picture x cm by x cm is F3(x) = F2(F1(x)) =  1.2x + 2.

The mathematical expression for the function that gives the center of mass is m=\(\(\int\limits \int\limits\)\(D_{p}\)(x, y)dA\)

The center of mass is a point specified relative to an object or set of things. It is the weighted average position of all the system's pieces. For simple stiff objects with homogenous density, the centroid is the location of the center of mass.

A lamina that occupies the region inside the circle x²+y²=14y

Outside the circle is x²+y²=49.m

x²+y²=\(\(\int\limits\)P(x, y)dA\)

Where

r²=14rsinθ

x²+y²=49r=7

Therefore, the center of mass is-x=\((i/m) \(\int\limits\)xp(x, y)dA\)

-x=\((1/m)\(\int\limits \int\limits\)(r cosθ)p(r, θ)r drdθ\)

-y=\((1/m)\(\int\limits \int\limits\)Dyp(x, y)dA\)

-y= \((1/m)\(\int\limits \int\limits\)D(rsinθ)p(r, θ)r drdθ\)

Therefore, the center of mass is

m=\(\(\int\limits \int\limits\)\(D_{p}\)(x, y)dA\)

The mathematical expression for the function that gives the center of mass is

m=\(\(\int\limits \int\limits\)\(D_{p}\)(x, y)dA\)

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The points (1,3) and (-1,-3) are on the line given by the given equation.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=6x+7. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=6 and b=7.

The question gives the equation y=3x from the standard form equation, you can identify that: m=3 and b=0.

For solving the question, you should check if the given coordinates comply with the equation y=3x.  See below.

         y=3*1

         y=3

Therefore, the coordinate (1,3) is on the line given by the equation y=3x.

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We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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Answer:

885.45

Step-by-step explanation:

Testuo monthly payments will be around 885$

It is a fee paid for borrowing money or other assets.

• the amount borrowed is called the principal.

•  the interest is expressed as a percentage rate of the principal

for a given time interval.

It is given that

Value of the car = $32000

Time period of loan repayment = 36 months

T = 3 years

Rate of Interest = 6.71%

10% down amount from 32000  =  3200 $

So the amount he is putting for finance = 32000 - (0.1 × 32000)

                                               = $28800

Rate of interest can be calculated from

I = P x R x T

I = Interest, P = Principle, R = Rate, T = Time

= (6.71 * 28800 * 3)/(100*12)

= $ 483.12

This is total interest for an year

In one month, rate of interest

= 483.12/12

 = $40.26

The principal amount that will be payable per month

= 28800/36

= $800

Total amount payable will be

= $ ( 800 + 40.26 )

= $840

Hence, we can conclude, Tetsuo needs to pay $840.26 as monthly installments, so in the options given it is 885$

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Answer:

2,-5

Step-by-step explanation:

The correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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The probability of a cash flow between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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By using the concept of supplementary angles and algebraic handling, the solution of the system formed by the two adjacent angles is equal to 41.

By geometry we know that a line crossed by another line non-parallel to it generates four pairs of supplementary angles. Two angles are supplementary whether they are adjacent to each other and the sum of their measures equals 180°. Then, we derive the following equation:

2 · x + 20 + 2 · x - 4 = 180

4 · x + 16 = 180

4 · x = 164

x = 164 / 4

x = 82 / 2

x = 41

By using the concept of supplementary angles and algebraic handling, the solution of the system formed by the two adjacent angles is equal to 41.

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The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

The if statement evaluates the test expression inside the parenthesis ().

If the test expression is evaluated to true, statements inside the body of if are executed.

If the test expression is evaluated to false, statements inside the body of if are not executed.

The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

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In conditional statements, the part of the statement following 'if' is called the antecedent.

The antecedent is the condition that needs to be true for the consequent to occur.

The consequent is the part of the statement that follows 'then.'

An antecedent is a noun or pronoun that denotes a specific being, place, object, or clause.

It's also referred to as a referent. Without an antecedent, a sentence may be insufficient or nonsensical since it is

required to establish what or to whom a pronoun in a sentence is referring.

In summary, a conditional statement is structured as "if (antecedent) then (consequent)."

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We can form an endless number of triangles when you are given two sides and no measurement of angle i.e a = 25 , b = 21

For Example -

We can chose the value of angle from 0-360 degrees with side length a = 25 and b =21, how many different triangles are possible to create?

Create one of the triangles with a protractor having the side lengths a = 25 m and b = 21 m and angle 12° and third side can be adjusted to your preferred length. You have built a triangle.

Similarly by changing the length of the third side and measure of the angle we will get an entirely new triangle.

It's important to notice that you choose the side lengths and angle. This suggests that you might make a different decision. By employing the same angles, you were able to make an infinite number of different triangles.

Therefore, with simply the measurements of one angle and a side length, we can create an endless number of triangles.

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Without specific information about the data set, it is not possible to determine which equation is the best fit.

To determine the linear function equation that best fits the data set, we need more information about the data set itself. Without the data points or any other details, we cannot accurately determine which linear function equation is the best fit.

However, I can provide a general explanation of the four options:

y = -2x + 5: This is a linear equation with a negative slope of -2. It represents a line that decreases as x increases. The y-intercept is 5.

y = 2x + 5: This is a linear equation with a positive slope of 2. It represents a line that increases as x increases. The y-intercept is 5.

y = -1/2x + 5: This is a linear equation with a negative slope of -1/2. It represents a line that decreases at a slower rate as x increases. The y-intercept is 5.

y = 1/2x - 5: This is a linear equation with a positive slope of 1/2. It represents a line that increases at a slower rate as x increases. The y-intercept is -5.

Without specific information about the data set, it is not possible to determine which equation is the best fit. The best fit would depend on how well the equation aligns with the actual data points.

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Answer:

y= -3x+5 for the graph one

Step-by-step explanation:

Answer:

f(x) = -3x + 5

Step-by-step explanation:

Answer:

non linear

Step-by-step explanation:

Answer:

Linear

Step-by-step explanation:

The area of the triangle is 59.6\(m^2\)

Now, According to the question:

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

In the question, Area unit is not mentioned.

But i take the unit in meter.

Now, We have the given data is:

In triangle HPK:

K = 8 m

P = 14.9 m

To find the area of triangle.

We know that :

Area of Triangle is  = 1/2 × b × h.

A  = 1/2 × 8 × 14.9

A = 59.6 \(m^2\)

Hence, The area of the triangle is 59.6

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Answer:

See below ~

Step-by-step explanation:

Question 12

Question 17

Part A

Part B

my answer is;

X = - 80/43

I'm numbering the right side for easy reference

A-3, B-4, C-1, D-2

9514 1404 393

Answer:

  24 cm^2

Step-by-step explanation:

The base of ∆Z is 4 cm, and its height is 12 cm. The area is given by the formula ...

  A = 1/2bh

  A = 1/2(4 cm)(12 cm) = 24 cm^2 . . . area of Z

Answer:

I think the answer is 2.) p^q

Step-by-step explanation:

hope this helps if it is wrong let me know have a blessed day

p → q represents “if p then q" represents "If x = 4, then y = −2”

Therefore, the correct representation is:

Thus Option 3 is correct. 3.) p → q

Given :Let p: x = 4 Let q: y = −2

To Find Which represents "If x = 4, then y = −2”?

we know that:

1. p ∧ q represents “p and q”

2.p ∨ q represents “p or q (or both)

3.p → q represents “if p then q”

4. p ↔ q represents “p if and only if q"

The statement "If x = 4, then y = -2" can be represented by the conditional statement "p → q" which reads "p implies q" or "if p, then q."

In the given representation:

p: x = 4

q: y = −2

The conditional statement "p → q" means that if x is equal to 4 (p is true), then y is equal to -2 (q is true).

So, we can see that p → q represents “if p then q" represents "If x = 4, then y = −2”

Therefore, the correct representation is:

Thus Option 3 is correct. 3.) p → q

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Answer:

sasuke

Step-by-step explanation:

B is The power W produced in an electrical circuit is directly proportional to the current I that flows through the circuit.  If a power of 750 watts is produced by a current of 9 amps, what power would be produced by a current of 6 amps?

Answer:

no mistakes

Step-by-step explanation:

4 * 3^x = 324

Divide each side by 4

4/4 * 3^x = 324/4

3^x = 81

Rewriting 81 as a power of 3

3^x = 3^4

Since the bases are the same, the powers are the same

x=4

Answer:There is not any mistakes.

Step-by-step explanation:

Solution:

Given;

The x-intercepts are;

CORRECT OPTION: D

Answer:

2

Step-by-step explanation:

It's up 20, right 10. 20 divided by 10 is 2. Therefore, the slope is 2

Answer:

Step-by-step explanation:

\(L.H.S = 1^2+Sin^2A+Cos^2A+2SinA+2CosA+2SinACosA\\ \{(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca\}\\ = 1 + (Sin^2A+Cos^2A) + 2SinA+2CosA+2SinACosA \\ \{Sin^2A+Cos^2A=1\}\\ = 1 + 1 + 2SinA+2CosA+2SinACosA \\ = 2(1 + SinA+CosA+SinACosA)\\ = 2(1^2 + (SinA+CosA).1+ SinACosA )\\ \{x^2+(a+b)x + ab = (x+a)(x+b)\} \quad here \quad x=1\\ = 2(1+SinA)(1+CosA).\\\)

The  probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.

Using the binomial probability formula, the probability of x successes in n independent trials with a probability of success p can be calculated as:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where "n choose x" represents the number of ways to choose x items from a set of n items, and is calculated as:

(n choose x) = n! / (x! * (n-x)!)

So, for the given parameters nequals=7, pequals=0.65, xequals=6, we have:

P(6) = (7 choose 6) * 0.65^6 * (1-0.65)^(7-6)
     = 7 * 0.65^6 * 0.35^1
     = 0.3052

Therefore, the probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.

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Answer:

5

Step-by-step explanation:

5 is the biggest number you can divide 5 by.

5/5=1

100/5=20

Answer: 5

Step-by-step explanation: The GCF, or greatest common denominator, is the highest factor of two or more numbers. Five divided by five is one, and one hundred divided by five is twenty.

Answer:

a. pick two between 2,5 or 11, they are all primes.

b. it's 11 since

\(11 {}^{2} = 121\)

c. that's

\(18 \times \frac{25}{100} = 4.5\)

(or think about it as half the half of 18, so half of 9)

d.

\( \sqrt{3} \)

Rest can be written as a fraction

Hello!

total = 3 + 1 = 4

1/4 = 1*9/4*9 = 9/36

3/4 = 3*9/4*9 = 27/36