Which factorization is equivalent to this expression?

30x + 70



Answer 10(3x+7)


Hopes this helps.

From the portion of a four-year amortization schedule the principal has been paid off after twenty-five payments, is $9543.97.

Loan amount is the amount or sum of money, which is borrowed by one at some rate of interest for a period of time.

Here, the principal has to be calculated after twenty-five payments. At 25 months, the balance of the loan is 10,356 dollars and 3 cents. It can be written as $10356.03.

As, the loan amount or principal is 19,900 dollars. This balance is the total amount of the loan. If we substrate the remaining loan amount from the total amount of loan, the result will be the paid loan amount.

Suppose the paid loan amount is P. Therefore,

\(P=19900-10356.03\\P=9543.97\)

Thus, from the portion of a four-year amortization schedule the principal has been paid off after twenty-five payments, is $9543.97.

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\(\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$2607\\ P=\textit{initial amount}\dotfill &6400\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\dotfill &22\\ \end{cases} \\\\\\ 2607=6400(1 - \frac{r}{100})^{22} \implies \cfrac{2607}{6400}=\left( \cfrac{100-r}{100} \right)^{22} \implies \sqrt[22]{\cfrac{2607}{6400}}=\cfrac{100-r}{100}\)

\(\cfrac{r-100}{100}=-\sqrt[22]{\cfrac{2607}{6400}}\implies r-100=-100\sqrt[22]{\cfrac{2607}{6400}} \\\\\\ r=100-100\sqrt[22]{\cfrac{2607}{6400}}\implies {\Large \begin{array}{llll} r\approx 4 \end{array}}\)

Answer:25 m

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

6.7 / .6

Multiply top and bottom by 10

67/6

66/6 = 11 so this is close to 11

Answer:

r = 2

Step-by-step explanation:

4(3r + 4) - 6(r + 1) =22

12r + 16 - 6r - 6 = 22

6r = 12

r = 2

Therefore, the equation in the form of y = mx + b that represents this linear function is: y = -3.2x + 0.1

To write an equation in the form of y = mx + b for a linear function, we need to find the slope (m) and the y-intercept (b).

We can use any two points from the given set of points to find the slope:

m = (y2 - y1) / (x2 - x1)

Let's use the first and second points:

m = (-5.5 - 2.5) / (1.75 - (-0.25))

m = -8 / 2.5

m = -3.2

Now, we can use the slope and one of the points to find the y-intercept:

y = mx + b

-5.5 = (-3.2)(1.75) + b

b = -5.5 + 5.6

b = 0.1

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B. Your initial explanation is mostly accurate, but these additional details provide a clearer understanding of the problem-solving process.

A. The process you described is commonly known as problem-solving or decision-making. Here's a breakdown of the steps involved: Identify the problem, Generate alternative solutions, Evaluate alternatives, Select the best solution, Implement the solution.

Identify the problem: The first step is to clearly identify and define the problem at hand. This involves understanding the nature of the problem, its causes, and its consequences or effects. Without a clear understanding of the problem, it would be difficult to find an appropriate solution.

Generate alternative solutions: Once the problem is identified, the next step is to brainstorm and generate multiple possible solutions or approaches to address the problem. This step encourages creativity and exploration of different options.

Evaluate alternatives: After generating alternative solutions, each option should be evaluated carefully. Factors such as feasibility, cost, time, resources required, and potential risks or benefits should be considered. This evaluation helps in narrowing down the options to those that are most viable.

Select the best solution: Based on the evaluation, one or more solutions may stand out as being the most effective or suitable for solving the problem. The best solution is selected based on its ability to address the problem efficiently and meet the desired objectives.

Implement the solution: Once the best solution is chosen, it is put into action. Implementation may involve planning, executing tasks, allocating resources, and managing the necessary steps to bring the solution to fruition.

It's important to note that the order of the steps may vary depending on the context and the complexity of the problem. While it's generally logical to evaluate and select the best solution before implementing it, sometimes it may be necessary to iterate through the steps, re-evaluate options, or make adjustments during the implementation phase.

Regarding the other options you mentioned:

A. This option suggests starting with identifying the best solution without understanding the nature of the problem or considering other possible solutions. As you correctly pointed out, this approach is flawed because it skips important steps in the problem-solving process.

C. This option implies evaluating and selecting the best solution before understanding the problem or considering other alternatives. Again, this is incorrect because a thorough understanding of the problem and exploration of multiple solutions should precede the evaluation and selection stage.

D. This option suggests implementing the solution before evaluating and selecting the best one. However, it's generally more effective to assess the potential effectiveness of different solutions before committing to their implementation.

In summary, your initial explanation is mostly accurate, but these additional details provide a clearer understanding of the problem-solving process.

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Answer:

yea by using a resipe

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

you need eggs, butter, flour, sugar, salt, oil (i prefer olive oil) and baking powder.

fruit if you like them in your sweets.

this makes 12 muffins

2 cups flour

3 tsps baking powder

1/2 tsp salt

3/4 cup sugar

1 egg

1 cup milk

1/4 cup oil

preheat oven. i usually do 350 F, increase the temperature if youd like them to cook faster but keep in mind youll need to check on them often with increased heat.

stir together your dry ingridents and in a seperate bowl beat your egg with a fork. stir in the milk and oil with the egg.

pour into your dry ingriedeints until everything is well mixed.

bake until golden

if you like fruit id suggest blueberries, 1 cup

Answer:

55

Step-by-step explanation:

\(\sqrt[3]{\frac{n}{4} } +\frac{n}{10} \\\\\sqrt[3]{\frac{500}{4} } +\frac{500}{10}\\\\\sqrt[3]{125} +50\\5+50\\55\)

Wouldn't it still just be 84 with or without the distributive property? :0

2(5+5)+2(16+16)

Step-by-step explanation:

lol and ignorw this wifnsnsjwjs

Answer:

biased

Step-by-step explanation:

Deone's length was 19.5 inches at birth. Assuming his development proceeds normally, his length should be about 29.5 inches by his first birthday.

We know that According to the Centers for Disease Control and Prevention (CDC), the average length for a boy at birth is around 20 inches, and the average length for a boy at one year of age is around 30 inches.

To estimate Deone's length at one year of age, we use the average growth rate between birth and one year, which is approximately 10 inches.

So , we add 10 inches to Deone's length at birth of 19.5 inches to estimate his length at one year of age:

⇒ Estimated length at 1 year = 19.5 inches + 10 inches = 29.5 inches

Therefore, Deone's length should be about 29.5 inches by his first birthday, assuming that his development proceeds normally.

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Answer:

This is rational because it has two integers

Step-by-step explanation:

IRRATIONAL NUMBER cannot be expressed in the form of the ratio or two integers

Example

This is an irrational number

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

v = 132

Step-by-step explanation:

divide 792 by 6 to get v

Answer:

v = 132

Step-by-step explanation:

Just divide the terms by 6 and then simplify.

The number of notes of each kind is 800 notes of $100, 1,200 notes of $50, and 4,000 notes of $10. The ratio of A:B:C is 4:5:6.

11. If 4A + 5B = 6C, the ratio of A : B : C can be found by dividing the coefficients of A, B, and C by their greatest common divisor (GCD). In this case, the GCD of 4, 5, and 6 is 1, so the ratio is 4 : 5 : 6.

12. Let's assume the three parts are A, B, and C.

We have:

A = 5/4 * B

8 : C = 3 : 4

We can set up the following equations:

A + B + C = 430 (since the total is $430)

A = 5/4 * B

8/ C = 3/4

Using the third equation, we can rewrite it as:

C = (4/3) * 8 = 32/3

Substituting the values of A and C into the first equation, we get:

(5/4)B + B + (32/3) = 430

Multiplying through by 12 to get rid of fractions:

15B + 12B + 128 = 5160

27B = 5032

B = 5032/27 ≈ 186.37

Since the ratio of A to B is 5/4, we can calculate A:

A = (5/4) * B = (5/4) * 186.37 ≈ 232.96

To find C, we already have its value as 32/3.

Therefore, A ≈ 232.96, B ≈ 186.37, and C ≈ 32/3.

13. We have the ratio of the shares: A : B : C = 2 : 3 : 4, and A's share is $200, we can find the shares of B and C by multiplying their respective ratios:

A = 2x, B = 3x, C = 4x

Since A's share is $200, we have:

2x = $200

Solving for x:

x = $200/2 = $100

Substituting the value of x into B and C's shares:

B = 3x = 3 * $100 = $300

C = 4x = 4 * $100 = $400

Therefore, A's share is $200, B's share is $300, and C's share is $400.

14. To divide $940 among A, B, and C in the ratio 1/3 : 1/4 : 1/5, we need to find the values of A, B, and C.

We have:

Ratio of A : B : C = 1/3 : 1/4 : 1/5

To simplify the ratios, we can find the least common multiple (LCM) of the denominators:

LCM(3, 4, 5) = 60

Now we can rewrite the ratio with a common denominator:

A : B : C = 20/60 : 15/60 : 12/60

Simplifying the ratio:

A : B : C = 1/3 : 1/4 : 1/5

To divide $940 in this ratio, we multiply each share by the total amount:

A = (1/3) * $940 = $940/3 ≈ $313.33

B = (1/4) * $940 = $940/4 = $235

C = (1/5) * $940 = $940/5 = $188

Therefore, A receives approximately

$313.33, B receives $235, and C receives $188.

15. If the ratio of the number of male teachers to female teachers in a school is 3:4, and there are 16 female teachers, we can find the number of male teachers.

Let's assume the number of male teachers is M. The ratio of males to females is given as 3:4. We can set up the following equation:

M/F = 3/4

Since we know that there are 16 female teachers (F = 16), we can solve for the number of male teachers (M):

M/16 = 3/4

Cross-multiplying, we get:

4M = 16 * 3

4M = 48

M = 48/4 = 12

Therefore, there are 12 male teachers in the school.

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The Surface Area of Triangular Prism is 680 unit².

We have,

Sides as 10 unit each

b = 10 unit, l = 20 unit and h= 8 unit

Now, Surface Area of Triangular Prism

= ( sum of Sides of Triangular face) l + bh

= (10 + 10 + 10)20 + 10 x 8

= 30 x 20 + 80

= 600 + 80

= 680 unit²

Thus, the Surface Area of Triangular Prism is 680 unit².

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Answer:

225 books

Step-by-step explanation:

you do 15 x 8 and you get 120 then you do 15 x 7 and you get 105 then you add 120 and 105 together and your final answer is 225 books

Answer:

ANswer: 225

Step-by-step explanation:

multiply: 15 x 7 = 105 & 15 x 8 = 120

now add " 105 + 120" together

Total: (See answer above)

The two expressions equivalent to \((x^{\frac{1}{3} } )^{2}\) are \(x^{\frac{2}{3} }\) and \(\sqrt[3]{x^{2} }\)

An index, or power, is the small floating number that appears after a number or letter. The plural of index is indices. Indices show how many times a number or letter has been multiplied by itself.

\((x^{\frac{1}{3} } )^{2}\) means multiply the exponent 1/3 with the exponent 2, which makes the final exponent to be 2/3 and the number in index form is reduced to  \(x^{\frac{2}{3} }\)

In index law a fractional index can be rewritten such that the denominator is the square root and the numerator is the square of the base number. so that  \(x^{\frac{2}{3} }\)  means the cube root of x to the power of 2 which is \(\sqrt[3]{x^{2} }\).

In conclusion the to forms of writing  \((x^{\frac{1}{3} } )^{2}\)  are \(x^{\frac{2}{3} }\) and   \(\sqrt[3]{x^{2} }\)

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Answer:

I think he might need 100ml.

Step-by-step explanation:

Brandon needs to use 100 ml of water to make 250 ml of hand sanitizer.

The percentage is defined as a ratio expressed as a fraction of 100.

To save money, Brandon made his own hand sanitizer. Hand sanitizer needs 60% alcohol to be effective.

We have to determine the amount of water to manufacture 250ml of hand sanitizer.

To make 250ml of hand sanitizer with 60% alcohol, Brandon needs to use 250ml x 60% = 150ml of alcohol.

Since the total volume of the hand sanitizer is 250ml,

Brandon needs to use 250ml - 150ml = 100ml of water to make 250ml of hand sanitizer.

Therefore, he needs to use 100 ml of water to make 250 ml of hand sanitizer.

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Answer:

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = - 120\)

Step-by-step explanation:

By the rule of Integer multiplications,

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = [ (-1) \times (-2) ] \times [(-3) \times (-4)] \times (-5)\)

                                                      \(= [2] \times [12] \times (-5)\)

                                                      \(= -120\)

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The dependent variable in this research question is the birth rate in Phoenix, AZ.

This can be represented mathematically as B, where B represents the birth rate in Phoenix, AZ. We can calculate the birth rate by taking the total number of live births in Phoenix, AZ (L) and dividing it by the total population in Phoenix, AZ (P), and then multiplying by 1,000. B = (L/P) * 1000.

For example, if there were 10,000 live births in Phoenix, AZ in a given year, and the population of Phoenix, AZ in that same year was 2,500,000, then the birth rate in Phoenix, AZ would be dependent variable as follows: B = (10,000/2,500,000) * 1000 = 4. This would mean that the birth rate in Phoenix, AZ is 4 births per 1,000 individuals.

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Complete question:If the researcher's question is "What are the reasons for an increase in the birth rate in Phoenix, AZ?", then the dependent variable is the birth rate in Phoenix, AZ.

To determine the convergence or divergence of an alternating series, you can use the Alternating Series Test. This test states that if the terms of an alternating series decrease in absolute value and approach zero, then the series converges.

Additionally, if the terms do not approach zero, the series diverges.

To apply the Alternating Series Test, you need to check two conditions:

1. The terms of the series must alternate in sign.

2. The absolute value of the terms must decrease or approach zero.

If both conditions are satisfied, you can conclude that the alternating series converges. However, if either condition fails, the series diverges.

If you want to determine the convergence or divergence more precisely, you can use the Integral Test or the Comparison Test. The Integral Test allows you to compare the convergence or divergence of a series to the convergence or divergence of an improper integral. If the integral converges, the series converges, and if the integral diverges, the series diverges.

The Comparison Test is another method to determine the convergence or divergence of a series. It involves comparing the given series with a known series whose convergence or divergence is already known. If the known series converges and the terms of the given series are less than or equal to the corresponding terms of the known series, then the given series also converges. Conversely, if the known series diverges and the terms of the given series are greater than or equal to the corresponding terms of the known series, then the given series also diverges.

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The correct answer is option C: shape that is approximately Normal by the central limit theorem. When the number of classified ads appearing on Mondays has a mean of 320 and a standard deviation of 30, the random variable x has a shape that is approximately normal by the central limit theorem.

Central Limit Theorem is defined as a statistical theory that states that the mean of a sample of data taken from a large population will be approximately distributed in a normal distribution. If the population is non-normal or skewed, the sample size must be large enough to ensure a normal distribution of the sample mean.

In this case, the number of classified advertisements appearing on Mondays on a certain online community site has a mean of 320 and a standard deviation of 30. Since a simple random sample of 100 consecutive Mondays can be regarded as sufficiently large, the mean number of classified advertisements in the sample (x) can be regarded as approximately normally distributed by the central limit theorem.

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Answer:

The college will have about 480 students who prefer cookies.

Step-by-step explanation:

We Know

The table shows the preference of 225 students.

Ice Cream, Candy, Cake, Pie, Cookies

81              , 9         , 72    , 36,   27

Which statement is the best prediction about the number of cookies the college will need?

We Take

4000 / 225 ≈ 17.78

Then we take

27 x 17.78 = 480.06 cookies

So, The college will have about 480 students who prefer cookies.

Answer:

area = 84 in²

Step-by-step explanation:

area = (9x12) - (6x8x0.5) = 84 in²

Answer:

These angles are called angle pairs. ... Supplementary angles are two angles whose sum is equal to \begin{align*}180^\circ\end{align*}. In other words when you add the measure of one angle in the pair with the other angle in the pair, they equal 180 degrees.

Step-by-step explanation:

Hope this helps you <3

To determine the x-axis symmetry, y-axis symmetry, and origin symmetry of the equation y = x^9, we need to analyze the properties of the equation and understand the concepts of symmetry.

The x-axis symmetry occurs when replacing y with -y in the equation leaves the equation unchanged. The y-axis symmetry happens when replacing x with -x in the equation keeps the equation the same.             X-axis symmetry: To determine if the equation has x-axis symmetry, we replace y with -y in the equation. In this case, (-y) = (-x^9). Simplifying further, we get y = -x^9. Since the equation has changed, it does not exhibit x-axis symmetry.

Y-axis symmetry: To check for y-axis symmetry, we replace x with -x in the equation. (-x)^9 = x^9. Since the equation remains the same, the equation has y-axis symmetry.

Origin symmetry: To determine origin symmetry, we replace x with -x and y with -y in the equation. The resulting equation is (-y) = (-x)^9. This equation is equivalent to the original equation y = x^9. Hence, the equation has origin symmetry.

In summary, the equation y = x^9 does not have x-axis symmetry but possesses y-axis symmetry and origin symmetry.

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Answer: ( 1.26 x 10 ^ 5 ) / ( 2.8 x 10 ^ 4 )

= 4.5 times bigger

Answer:

4.5

Step-by-step explanation:

always remember the ^. This is scientific notation.

( 1.26 x 10 ^ 5 ) / ( 2.8 x 10 ^ 4 )

Answer:

5040

Step-by-step explanation:

Brianna has 7 choices for the first spot in her line up. Once she places that first block, she'll have 6 blocks left. So for spot two in the line up, there are 6 choices. And after she places that block, there will five blocks left to choose from for the next spot. Then four choices, then three, then two, then only one block left for the last spot in the line up.

Mathematically, we multiply together the number of choices for each spot in the line up.

7•6•5•4•3•2•1

This is 7! (the exclamation mark is an actual math symbol) read: "seven factorial"

7!

= 7•6•5•4•3•2•1

= 5040

Most scientific calculators and graphing calculators have a factorial (!) button.