Solve equation:
3 + 7(6 +2x) = 157

Answer:

63*

Step-by-step explanation:

Answer:

63

Step-by-step explanation:

The perimeter of a triangle with sides 4, 6, and 8 feet is 18 feet.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the perimeter of a triangle is the sum of it's all three sides.

In the case of an equilateral triangle, the perimeter is 3×side as all three sides have the same length.

∴ The perimeter of a triangle with sides 4, 6, and 8 feet is,

= (4 + 6 + 8) feet.

= 18 feet.

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The inequality to use to find the number of pounds for Earthen red clay and Porcelain white clay is:

0.75r + 1.1w ≥ 100

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

A ceramic artist orders two types of clay.

Earthen red clay

Porcelain white clay

Amount to spend = $100 or more

Earthen red clay costs = $0.75 per pound

Porcelain white clay costs = $1.10 per pound.

The inequality to use to find the number of pounds for Earthen red clay and Porcelain white clay.

= 0.75r + 1.1w ≥ 100

where r is the number of pounds of earthen red clay, and w is the number of pounds of porcelain white clay.

Thus,

The number of pounds for Earthen red clay and Porcelain white clay can be found using the inequality:

0.75r + 1.1w ≥ 100

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B would be the answer to this quadratic equation.

Answer:

B. x = 5 ± 10i

Step-by-step explanation:

ax² + bx + c = 0

quadratic formula = (-b ± [tex]\sqrt{b^{2}-4ac }[/tex])/2a

y = x² - 10x + 125

substitute the values:

(-(-10) ± [tex]\sqrt{(-10)^{2}-4(1)(125) }[/tex])/2(1)

= (10 ± [tex]\sqrt{100 - 500}[/tex])/2

= (10 ± [tex]\sqrt{-400}[/tex])/2

= (10 ± 20i)/2

= 5 ± 10i

The quadratic equations 5x² + 20x + 20 = 0 and x² + 6x + 9 = 0 are the only correct equations having only one solution.

Quadratic equations has it highest power to the degree of two and they have two solutions that makes them true. The solutions could be different or similar ( which implies there is only one solution). From the question we shall concentrate on the equations which have similar solution or rather only one solution.

For the equation 5x² + 20x + 20 = 0;

we divide through by 5 to get;

x² + 4x + 4 = 0

x² + 2x + 2x + 4 = 0 {we group the terms}

x(x - 2) +2(x + 2) = 0 {factorize}

(x + 2)(x + 2) = 0

either; x + 2 = 0 or x + 2 = 0

x = -2 or x = -2 {which are the same solutions}

For the equation x² + 6x + 9 = 0;

x² + 3x + 3x + 9 = 0 {we group the terms}

x(x + 3) + 3(x + 3) = 0 {factorize}

(x + 3)(x + 3) = 0

either; x + 2 = 0 or x + 2 = 0

x = -2 or x = -2 {which are the same solutions}

Therefore, the quadratic equations 5x² + 20x + 20 = 0 and x² + 6x + 9 = 0 each have only one solution which are -2 and -3 respectively.

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The Horton family subscribes to 3 premium channels. The total monthly subscription fee for the excel cable company is 48 dollars. The Horton family will save 24 dollars in one year by using the less expensive company.

(A) To find the number of premium channels for which the total monthly subscription fee for the excel and best cable companies will be the same, we set these two expressions equal to each other and solve for x:

32 + 8x = 26 + 10x

8x - 10x = 26 - 32

-2x = -6

x = 3

Therefore, the Horton family subscribes to 3 premium channels.

(B) The total monthly subscription fee for the excel cable company is 32 + 8 × 2 = 48 dollars if the Horton family subscribes to 2 premium channels. The total monthly subscription fee for the best cable company is 26 + 10 × 2 = 46 dollars if the Horton family subscribes to 2 premium channels.

Since the total monthly subscription fee for the best cable company is less than the total monthly subscription fee for the excel cable company, the Horton family should subscribe to the best cable company in order to spend less money.

(C) If the Horton family subscribes to the best cable company for one year, they will save 48 - 46 = 2 dollars per month. Over the course of one year, they will save 2 × 12 = 24 dollars.

Therefore, the Horton family will save 24 dollars in one year by using the less expensive company.

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Answer: (12,-6)

Step-by-step explanation:

Using a system of equations to solve the problem, the candy distributor must mix 190 Kilograms of the 20% chocolate and 10 Kilograms of the 60% chocolate to create 200 Kilograms of a 22% fat-content chocolate.

A system of equations means two or more equations solved simultaneously.

They are known as simultaneous equations and can be solved graphically, by elimination, by substitution, or matrix.

The fat-content of one of the chocolate blend = 20%

The fat-content of the second chocolate blend = 60%

The expected mixture will have a fat-content = 22%

The total kilograms of the end mixture = 200 kilograms

Let the 20% fat-content chocolate = x

Let the 60% fat-content chocolate = y

x + y = 200 ... Equation 1

Solving for x, x = 200 - y

0.2x + 0.6y = 0.22(200)  ... Equation 2

By substitution in Equation 2:

0.2(200 - y) + 0.6y = 44

40 - 0.2y + 0.6y = 44

40 + 0.4y = 44

0.4y = 4

y = 10

x = 200 - y

x = 190 (200 - 10)

Based on the system of equations, 190 kilograms of the 20%-fat-content chocolate must be mixed with 10 kilograms of the 60% fat-content chocolate.

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(a) According to the graph :  Local minimum point is : -3 , 4

(b) Local minimum values of g is: 1, -2

"Information available from the question"

In the question:

Here is a graph of the function g

Use the graph to find the following.

If there is more than one answer, separate them with commas.

(a) All values at which g has a local minimum:___

(b) All local minimum values of g :___

Now, According to the question:

If a function has a definite value at every neighborhood of a point and the value at that point is the minimum. The value of the function at that point is the local minimum.

(a)  All values at which g has a local minimum:

According to the graph :  Local minimum point is : -3 , 4

(b)  All local minimum values of g:

Local minimum values of g is: 1, -2

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In the exponent, the value of n when 5 is rounded to the nearest power of 10 will be 100000.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

The value of n when 5 is rounded to the nearest power of 10 will be:

= 10^5

= 100000

The value is 10000.

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By using the concept of control chart, it can be concluded that

A large number of plots are on or near the centerline.

Third option is correct.

What is control chart?

Control chart is used to show how a process changes over time.

There are three lines in a control chart.

They are the central line for the average, upper line for the Upper Control Limit (UCL) and a lower line for the Lower Control Limit (LCL)

It is known that the highest performance of a process is obtained when it is between the LCL and the UCL.

That means to get the best result, samples needs to be concentrated near the centerline.

So the third option is correct

A large number of plots are on or near the centerline.

Third option is correct.

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Complete Question

Quality control charts usually have a central line and upper and lower control limit lines. Which of the following is not a reason that the process being monitored with the chart should be investigated?

A sudden and sustained shift in the plots toward the upper or lower control limit

There is an upward trend in the plots

A large number of plots are on or near the central line

A single plot falls outside of the control limits

Answer:

8 beads per ring.

Step-by-step explanation:

50/6 = 8.333..

Since you cannot have less than half of a ring, the answer is 8.

Answer:

18.6 miles

Step-by-step explanation:

Subtract Distance traveled from total distance

Total distance: 24 miles

Distance Traveled: 5.4 miles

24 - 5.4 = 18.6

Answer:

Inequality Form:

x<−3

Interval Notation:

(−∞,−3)

Step-by-step explanation:

To sum it up

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Step-by-step explanation:

x < 2

I think is the answer when you subtract 7 from both sides you get 3x <6 and then you divide both sides by 3 getting x < 2 (not sure if that's how you solve this one but usually it would be solved like this. if wrong then I'm sorry)

Journalizing the entries to record the transactions is as follows:

Date      Account Titles and Explanation    Debit    Credit

Nov. 21 Notes Receivable                        $48,000

            Accounts Receivable                               $48,000

(To record the receipt of a 60-day 9% note dated November 21 from McKenna Outer Wear Co. on the past account.)

Dec. 31 Interest Receivable                         $480

            Interest Revenue                                           $480

(To accrue interest revenue on the note at year-end.)

Jan. 20 Cash                                          $48,720

             Notes Receivable                                  $48,000

             Interest Receivable                                     $480

             Interest Revenue                                        $240

(To record the full settlement of the note and interest.)

Journal entries are the first recording of business transactions in the company's day book.

With the journal entries, debit and credit accounts are identified, helping to organize the general ledger.

Nov. 21 Notes Receivable $48,000 Accounts Receivable $48,000

60-day 9% note dated November 21

Dec. 31 Interest Receivable $480 Interest Revenue $480 ($48,000 x 9% x 40/360)

Jan. 20 Cash $48,720 Notes Receivable $48,000 Interest Receivable $480 Interest Revenue $240 ($48,000 x 9% x 20/360)

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By studying the given situation, it can be concluded that

Heath is engaged in p- hacking.

What is p-hacking?

p-hacking is the misuse of statistical data to make a result statistically significant.

Heath analyzes his data using a bivariate correlation, as he previously planned; however, to his frustration, he quickly learns that his results are just short of being statistically significant.

Heath's main target is to make his result statistically significant.

He decides to try conducting a multiple-regression analysis instead and is pleased to see that with this method of data analysis, the results are statistically significant. Because the results were so similar, Heath doesn't bother reporting the bivariate correlation in his paper, as he thinks that clearly multiple regression was the correct test to run.

She Heath did not report the bivariate correlation in his paper, he is misusing the data to make his data statistically significant.

So Heath is engaged in p-hacking.

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Answer:

x=5

Step-by-step explanation:

or, 3x-9-4=2

or, 3x-13=2

Now, Adding 13 on both sides we get,

or, 3x-13+13=2+13

or, 3x=15

Now, Dividing both sides by 3 we get,

or, (3x)/3=15/3

Therefore, x=5

According to the geometric series 0.08 is the sum or state that the series diverges.

A geometric series is a series for which the ratio of each two consecutive terms is a constant function of the summation index . The more general case of the ratio a rational function of the summation index. produces a series called a hypergeometric series.

Given:

[tex]$$\sum_{n=2}^{\infty} \frac{3^n}{12^n}$$[/tex]

In the first term, it represents an unlimited geometric series.

b = 9/144

And the common ratio,

q = 3/12

By the ratio test ,it is convergent

Sum is

S = b/1-q

[tex]$=\frac{\frac{9}{144}}{1-\left(\frac{3}{12}\right)}$[/tex]

S = [tex]\frac{108}{1296}[/tex]

S = 0.08

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The complete question is-

Use the formula for the sum of a geometric series to find the sum or state that the series diverges (enter DIV for a divergent seris).

                                         [tex]$$\sum_{n=2}^{\infty} \frac{3^n}{12^n}$$[/tex]                                

Answer:

To solve the equation f(x) = 3, we can set the expression for f(x) equal to 3 and then solve for x. In other words, we want to find the values of x that make the equation 5 - \frac{x}{r^2} + 5 + 6 = 3 true.

We can start by simplifying the left side of the equation by combining like terms. This gives us

5 - \frac{x}{r^2} + 5 + 6 = 5 + 5 - \frac{x}{r^2} + 6 = 10 - \frac{x}{r^2} + 6

Next, we set this expression equal to 3 and solve for x:

10 - \frac{x}{r^2} + 6 = 3 \quad \Rightarrow \quad 10 - 6 = 3 - \frac{x}{r^2} \quad \Rightarrow \quad \frac{x}{r^2} = 7

To solve for x, we can multiply both sides of the equation by r^2:

x = 7r^2

Therefore, the solutions to the equation f(x) = 3 are $x = 7r^2$. Note that this is a general solution, and it may not give all the possible values of $x$ that make the equation true. It's also possible that there are no solutions, depending on the value of $r$.

Answer:

Step-by-step explanation: 0.2=1/5 0.002=1/500

1/5*1/500=1/2500 which equals 0.0004

[tex]2n=10[/tex]

Divide both sides by 2:

[tex]\dfrac{2n}{2} =\dfrac{10}{2}[/tex]

[tex]\fbox{n = 5}[/tex]

Answer:

The inequality represented in the given picture is:

[tex]x \le 5[/tex]

Note the inclusive less than sign since the graph has a filled-in dot.

This can be represented in interval notation as:

[tex](-\infty, 5][/tex]

Note the bracket on enclosing the 5, representing inclusiveness.

a) Using conditional probability, the likelihood that a driver purchases oil, given that he or she purchases gasoline is 5.62%.

b) Based on conditional probability, the chance that a driver purchases gasoline, given that he or she purchases oil is 71.43%.

Conditional probability is the likelihood or chance of an event or outcome occurring, based on a previous event or outcome that occurs.

Conditional probability considers two events occurring relatively.

The formula for conditional probability is intersection probability divided by base probability.

The percentage (proportion) of drivers who stop at a gas station to buy gasoline = 89%

The probability of buying both gasoline and oil = 5%

The percentage (probability) of purchasing oil = 7%

a) The probability that a driver purchases oil, given that he or she purchases gasoline = the probability of buying both gasoline and oil/the probability of stopping and buying gasoline.

= 5.62% (0.05/0.89).

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b) The probability that a driver purchases gasoline, given that he or she purchases oil = the probability of buying both gasoline and oil/the total probability of those who purchase oil.

= 71.43% (0.05/0.07 x 100).

Of the drivers who stop at a gas station, 89% purchase gasoline, and 5% purchase both gasoline and oil. A total of 7% purchase oil.

(a) What is the probability that a driver purchases oil, given that he or she purchases gasoline? Round your answer to the nearest hundredth.

b) What is the probability that a driver purchases gasoline, given that he or she purchases oil? Round your answer to the nearest hundredth.

In the broadest sense, inverse functions are those that "reverse" one another.

Any function can be solved for by substituting one variable for another to discover the inverse of that function.

Below is an example to help you understand.

Find the inverse of h (x) = (4x + 3)/(2x + 5)

Solution

H (x) should be changed to Y.

h (x) = (4x+3)/(2x+5) y = (4x + 3)/(2x + 5)

Change the order of x and y.

⟹ x = (4y + 3)/ (2y + 5).

The following formula should be used to solve for y in the equation above:

⟹ x = (4y + 3)/ (2y + 5)

Divide both sides by (2y + 5)

⟹ x (2y + 5) = 4y + 3

Distribute the x evenly.

⟹ 2xy + 5x = 4y + 3

isolate y.

⟹ 2xy – 4y = 3 – 5x

⟹ y (2x – 4) = 3 – 5x

Divide through by 2x - 4 to obtain;

⟹ y = (3 – 5x)/ (2x – 4) (2x – 4)

Finally, swap out y for h - 1. (x).

⟹ h – 1 (x) = (3 – 5x)/ (2x – 4) (2x – 4).

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