what expression is equivalent to -3(6x+7)+4(7x+2)

Answer:

1.2 minutes

Step-by-step explanation:

5 laps >> 360 ( 6×60)

1 lap >> x

cross multiplication

5x = 360

x = 360/5

x= 72 second

x = 72/60 = 1.2 minute

Answer:

year, subtract that amount from the 230,000 gallons of seasonal water use. 230,000 gallons – 150,000 gallons = 80,000 gallons use for irrigation per year .

Step-by-step explanation:

I took the test

Solution

Using BODMAS to solve the fraction

Therefore the answer = -3/4

Answer:

13 calories

Step-by-step explanation:

39 calories =3 servings

1 serving = 13

39÷3 =13

Step-by-step explanation:

I assume this actually is

revenue : R(x) = 12x

cost : C(x) = 5x + 20

profit : P(x) = R(x) - C(x) = 12x - 5x - 20 = 7x - 20

The polynomial function in expanded form is f(x) = x² - 3x² + 4x - 2.

A polynomial function with rational coefficients that has the given numbers as zeros, considering their conjugates . Since 1+i is a zero, its conjugate 1-i must also be a zero.

Using the zero-product property,  that if a polynomial has a zero at a given number, then the polynomial must have a factor of (x - zero). Therefore, the polynomial function with the given zeros can be written as:

f(x) = (x - (1+i))(x - (1-i))(x - 1)

Expanding this expression,

f(x) = ((x - 1) - i)((x - 1) + i)(x - 1)

= ((x - 1)² - i²)(x - 1)

= ((x - 1)² + 1)(x - 1)

= (x² - 2x + 1 + 1)(x - 1)

= (x² - 2x + 2)(x - 1)

= x² - 2x² + 2x - x² + 2x - 2

= x² - 3x²+ 4x - 2

.

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Answer:

B-The flare signal was set off at a height of 3 feet.

The function whose graph is given by: y = sin x-3 because sin starts at 0 and goes up. Therefore, the correct option is D.

Function is a type of relation, or rule, that maps one input to specific single output.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For the example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

If we know that function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

The function whose graph is given by: y = sin x-3 because sin starts at 0 and goes up.

Therefore, the correct option is D.

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Answer:

B

Step-by-step explanation:

(6\(x^{5}\)z)^3

6^3 is 226

*(x^2)^3=  x^6        (5*3= 15)

*when there are exponents being raised to a power, the exponents are multiplied

**(z^1)^3= z^3     (3*1= 3)

** all numbers are raised to the 1st power (unless otherwise noted x^2, 5^4 2^2, etc)

So the top would end up being 226x^6z^3

Now, since this number is over 4x^4z^2,  you need to divide 226x^15z^3 by 4x^4z^2

**divide like terms**

226/4= 54

***x^15/ x^4= x^x^11

*** when you divide exponents, you subtract the bottom number from the top, in this case:

15-4

that equalls 11

So x^11

you do the same for z:

z^3/z^2= z^1 or z      (3-2=1 )

You put it all together and you end up with

54x^11z

******** If there are any mistakes I'm really sorry!!******

Answer:

3x + y = 7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Standard Form: Ax + By = C

Step-by-step explanation:

Step 1: Define

y = -3x + 7

Step 2: Rewrite

Find Standard Form.

Answer: this are the answers and your formula is (x+2, y-5)

k' (-1,-3)

i' (3,-1)

m' (1,-5)

n' (-3,-7)

............................

Given the information on the problem, we can draw the following right triangle:

we can find how high the ladder reach using the pythagorean theorem:

therefore, the ladder reaches 21 ft high up on the wall

To bisect a segment, Jessica should place the compass on one endpoint, open it to a width larger than half of the segment, draw two intersecting arcs with the compass, and draw a straight line through the intersection points to bisect the segment.

To bisect a segment, Jessica should first place the compass on one endpoint of the segment and open it to a width larger than half of the segment. She should then draw an arc that intersects the segment at two points. Next, she should place the compass on the other endpoint of the segment and draw a similar arc that intersects the first arc she drew.

Finally, she should draw a straight line through the two points where the arcs intersect to bisect the segment into two equal parts. This method is based on the concept of congruent triangles, as the two arcs create two congruent triangles with the segment as their base.

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The probability that the Yankees would score fewer than 5 runs when they win the game is 0.32.

Let the events be A: Yankees win a game

B: Yankees score 5 or more runs

C: Yankees lose a game

D: Yankees score fewer than 5 runs

We are given the following probabilities:

P(A) = 0.56 (probability of winning)

P(B) = 0.46 (probability of scoring 5 or more runs)

P(C and D) = 0.32 (probability of losing and scoring fewer than 5 runs)

We want to find the probability of scoring fewer than 5 runs when they win the game, which is P(D|A).

We can use Bayes' theorem to find this probability:

P(D|A) = P(A and D) / P(A)

Using the definition of conditional probability:

P(D|A) = P(D and A) / P(A)

We know that P(D and C) = P(C and D), as both events represent the same outcome.

Using the fact that the sum of the probabilities of mutually exclusive events is equal to 1:

P(D and C) + P(B and C) = 1

Rearranging the equation:

P(D and C) = 1 - P(B and C)

Now, let's find P(D and A):

P(D and A) = P(D and A and C) + P(D and A and not C)

P(D and A) = P(D and A and C) + 0

P(D and A) = P(C and D and A)

Substituting the probabilities we have:

P(D|A) = P(C and D) / P(A)

P(D|A) = P(C and D) / P(C and D) + P(B and C)

P(D|A) = 0.32 / (0.32 + P(B and C))

We need to find P(B and C), which we can calculate using the given probabilities:

P(B and C) = P(C and B)

P(B and C) = P(C) - P(C and D)

P(B and C) = 1 - P(C and D)

P(B and C) = 1 - 0.32

P(B and C) = 0.68

Now we can substitute this value into the equation:

P(D|A) = 0.32 / (0.32 + 0.68)

P(D|A) = 0.32 / 1

P(D|A) = 0.32

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The 99% confidence interval for the population proportion is approximately (0.439, 0.561).

To construct a 99% confidence interval for the population proportion, we will use the following formula:

CI = p-hat ± Z × √[(p-hat × (1 - p-hat)) / n]

where CI represents the confidence interval, p-hat is the sample proportion, Z is the critical value for the desired confidence level, and n is the sample size.

Given the information, x = 125 and n = 250.

1. Calculate p-hat (sample proportion):
p-hat = x / n = 125 / 250 = 0.5

2. Determine the Z-value for a 99% confidence interval (use a Z-table or calculator):
Z = 2.576

3. Plug the values into the formula and calculate the confidence interval:

CI = 0.5 ± 2.576 × √[(0.5 × (1 - 0.5)) / 250]
CI = 0.5 ± 2.576 × √(0.5 × 0.5 / 250)
CI = 0.5 ± 2.576 × √(0.001)

Now, calculate the lower and upper bounds:

Lower bound = 0.5 - 2.576 × √(0.001) ≈ 0.439
Upper bound = 0.5 + 2.576 × √(0.001) ≈ 0.561

Therefore, the 99% confidence interval for the population proportion is approximately (0.439, 0.561).

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The probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

To find the probability that a senior takes the bus to school every day given that he or she has a driver's license, we can use conditional probability.

Let's denote the event that a senior has a driver's license as A and the event that a senior takes the bus to school every day as B. We want to find the probability of event B given event A, denoted as P(B|A).

We are given the following information:

The conditional probability formula states that P(B|A) = P(A ∩ B) / P(A).

Substituting the given values, we have:

P(B|A) = P(A ∩ B) / P(A) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

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The probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

To find the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, we need to use the concept of conditional probability. Conditional probability is the probability of one event happening given that another event has already occurred. In this case, we want to find the probability of taking the bus to school every day, given that the student has a driver’s license.

We can use the formula:

P(A|B) = P(A and B) / P(B)

where P(A|B) is the probability of event A happening given that event B has happened, P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.

In the given problem, 84% of the seniors have driver’s licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver’s licenses and take the bus to school every day. We want to find the probability of taking the bus every day, given that the student has a driver’s license.

Plugging in the values into the formula:

P(Taking the bus every day | Having a driver’s license) = P(Taking the bus every day and Having a driver’s license) / P(Having a driver’s license)

P(Taking the bus every day | Having a driver’s license) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

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Answer:

the point ( 5, 7) lies in the first quadrant.

Step-by-step explanation:

X coordinate is positive and the Y coordinate is positive in the first quadrant.

Answer:

Quadrant I

Step-by-step explanation:

Quadrant I : (x, y)

Quadrant II : (-x, y)

Quadrant II : (-x, -y)

Quadrant IV : (x, -y)

Therefore, as the x and y values of (5, 7) are both positive, the point is located in Quadrant I

The two sided confidence interval on mean is 3.56 and 4.80.

What is confidence interval?

The proportion of probability, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.

The given data is  3.7, 4.5, 4.1, 4.7, 3.9.  Here n = 5

=> σ = 1- 95% = 5% = 0.05

We know that the confidence interval is

=> CI = \(\overline x {\displaystyle \pm }\frac{z(\sigma)}{\sqrt n}\)

Here 95% confidence level so z= 1.96

Mean \(\overline x = \frac{3.7+4.5+4.1+3.9+4.7}{5} = 4.18\) and σ = 0.5

Here  n<30 so we can use t instead of z then t-value = 2.776.

Now confidence level CI = \(\ 4.18 {\displaystyle \pm }\frac{2.776\times0.5}{\sqrt 5}\)

=> CI = 4.18 \(\display \pm\) 0.62 = ( 3.56 , 4.80)

Hence the two sided confidence interval on mean is 3.56 and 4.80.

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Answer:there were 100 adults  and 350 children tickets sold .

Step-by-step explanation:

Step 1

let number of adult tickets sold be represented as  x

and that of children be  y

such that the total number of adult and children who attended the center will be expressed as

x+ y = 450------equation 1

 and the total cost of tickets sold can be expressed as

4x+ 1.50 y= 925,...equation 2

Step 2--Solving

x+ y = 450------eqn1

4x+ 1.50 y= 925,...eqn 2

 By elimination method , Multiply equation 1  by 4 and subtract equation 2 from  the new equation  formed

4x+ 4y= 1800 ----- eqn 3

-4x+ 1.50 y= 925 eqn 2

2.5y=875

y= 875/2.5

y=350

to fnd x

x+ y= 450

x= 450- 350

x= 100

Therefore there were 100 adults  and 350 children tickets sold .

There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

There are 12 elements of the group     \(U_{13}\)   , namely all the positive integers less than 13, as these are relatively prime to 13. Now, if there are primitive roots, there are     \(\phi (\phi (n))\)    of them. So we must compute     \(\phi (12) = \phi (4\times 3) = \phi (4) \phi (3) = 2\times 2 = 4\)   . There are 4 incongruent primitive roots.

To find them, take the powers each element in turn:

1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1  (2 has order 12, it is a primitive root)

Of course, the higher powers of 2 cannot be.

Proceeding this way, we get next get that 6, 7, and 11 are also primitive roots.

For example, the powers of 6 give: 6, 10, 8, 9, 2, 12, 7, 3, 5, 4, 11, 1. We see 6 has order 12 and it is a primitive root. So 2, 6, 7, 11.

Therefore, There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

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The ordered pair lie on the inverse of the function is (62,−3).

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -(x - 1)³ - 2

The inverse of f(x).

y = -(x - 1)³ - 2

interchange x and y and solve for y.

x = -(y - 1)3 - 2

(y - 1)³ = -2 - x

(y - 1)³ = -(2 + x)

Cuberoot on both sides.

y - 1 = ∛-(2 + x)

y = ∛-(2 + x) + 1

Now,

Substitute in the inverse of g(x).

(62, -3) = (x, y)

(−4, 123) = (x, y)

(3, 1) = (x, y)

(3,−6) = (x, y)

So,

y = ∛-(2 + x) + 1

y = ∛-(2 + 62) + 1

∛-1 = -1

y = -1∛64 + 1

y = -1 x 4 + 1

y = -4 + 1

y = -3

So,

(62, -3) ______(1)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 - 4) + 1

∛-1 = -1

y = ∛(-2 + 4) + 1

y = ∛2 + 1

y =  1.26 + 1

y = 2.26

So,

(-4, 2.26) _______(2)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) _______(3)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) ______(4)

Thus,

From (1), (2), (3), (4) we see that,

(62, -3) is the solution to the inverse of g(x).

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Answer:

which are the chocies???

Answer:

I don't know what the choices are but maybe y=25x+5

Step-by-step explanation:

Answer: 30 goldfish

Step-by-step explanation: Bruce has 18 goldfish. If Isabelle has 5 times as many goldfish as Bruce she will have 18*5=90 goldfish. If Arlene has 1/3 times as many goldfish as Isabelle she will have 90/3=30 goldfish.

Answer: 58 adults and 38 children went to the concert.

Step-by-step explanation:

Let x= adults , y= children

As per given ,

x+y = 96  (i)

3.75x+3.50y = 350.50     (ii)

Multiply 3.75 to (i) , we get

3.75 x + 3.75y  = 360  (iii)

Eliminate (ii) from (iii)

\(3.75 y-3.50y= 360-350.50\\\\\Rightarrow\ 0.25y= 9.5\\\\\Rightarrow\ y=\dfrac{9.5}{0.25}\\\\\Rightarrow\ y= 38\)

put this in (i) ,  x+38 = 96

x= 96-38 = 58

So, 58 adults and 38 children went to the concert.

Answer:

8.8 Minutes or 528 Second.

Step-by-step explanation:

↓[ Read Below ]↓

Important Info:

Leslie Ran 3 Mile Race.

2nd Mile = 10% longer than 1st and 3rd Miles took her 24s longer than 2nd Mile

Question to Answer:

Leslie’s total time for the race was 26 minutes how long did the second mile take her?

Explanation/Solution:

Let for first mile, she took x minutes . And second mile took her 10 percent longer, so second mile took

x+ 10/100x = 110/100x=1.1x

And the third mile took 24 seconds longer as compared to second mile .

So third mile took

1.1x+24/60 = (1.1x+0.4) Minutes

And the total time for the race was 26 minutes, that is

x+1.1x+1.1x+0.4=26

3.2x=26-0.4

3.2x=25.6

x= 25.6/3.2 = 8 Minutes

So the first mile took 8 minutes. And therefore second mile took

= 1.1 (8) = 8.8 Minutes

Also Equal to 528 Second.

[RevyBreeze]

Probability generating function (PGF) and Moment Generating Function (MGF) are two useful functions used to obtain moments.

The probability generating function is more useful for calculating moments of a discrete random variable whereas the moment generating function is more useful for calculating moments of a continuous random variable. Let us see how to calculate PGF and MGF.

Given a random variable X, the Probability Generating Function is defined as

Π(t)=E[t X], t ∈ R.

Similarly, the moment generating function of a random variable X is defined asM(t) = E(e^(tX)) where t is the real parameter. It is always possible to use either a probability generating function or a moment generating function to determine moments of a distribution. Solution:(a) m(t) is the MGF of X. Then

Π(t)=E(tX)=∑ P(X=k)tk=∑ P(X=k)e^(tk log(e))=∑ P(X=k)e^(t(log(e))^k)=m(log(t))(b) We need to find dt k
d k
Π(t)
​
∣
∣
​
t=1
​
=E[X (k)].Let P_k be the probability that

X = k.P_k = Pr(X=k).ThenΠ(t) = ∑ P_k t^k.

Now differentiate Π(t) w.r.t t, we getdΠ(t) / dt = ∑ P_k k t^(k-1).Differentiating w.r.t. t again givesd^2Π(t) / dt^2 = ∑ P_k k(k-1) t^(k-2).And so on,dkΠ(t) / dt^k = ∑ P_k k(k-1) ... (k - j + 1) t^(k-j), where the sum is taken over j = 0, 1, 2, ... , k-1.Substituting t=1,dkΠ(1) / dt^k = E(X(X-1) ... (X-k+1)).Hence, the desired result isdt k
d k
Π(t)
​
∣
∣
​
t=1
​
=E[X (k)
].

Therefore, if m(t) is the MGF of X, then Π(t)=m(log(t)). Also, if we differentiate the probability generating function Π(t) k times and then substitute t=1, we will get the kth moment of X.

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Answer:

27 is 30% of what number?

D. 90

Step-by-step explanation:

You're welcome.

610 students must be randomly selected to estimate the mean weekly earnings of students at one college.

We have to find our α level, that is the subtraction of 1 by the confidence interval divided by 2.

So: α = (1 - 0.95)/2

      α = 0.025

Now, we have to find z in the Z-table as such z has a p-value of 1 - α .

so, Z = 1.96

Now, find the margin of error M as such,

M = z(σ/√n)

In which  is the standard deviation of the population and n is the size of the sample.

The population standard deviation is known to be $63.

This means that σ = 63

ample mean within $5 of the population mean

This is n for which M = 5.

So, M = z(σ/√n)

5 = 1.96(63/√n)

2.55 = (63/√n)

√n = 24.70

n = 610.4

n ≈ 610

Therefore, 610 students must be randomly selected to estimate the mean weekly earnings of students at one college.

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50%

since 98/2 = 49

Thats it

Answer:

The percent of 18 out of 60 is 30%

Step-by-step explanation: If you multiply 18/60 x 100% the answer will equal to 30%.

Hope this helps :)