Which expression is equivalent to 15x – 2(3x + 6)?

The first of three consecutive terms after 55, which sum up to 738, is found to be 245 by setting up an equation and solving for n.

The student's question involves finding a variable, n, which represents the first of three consecutive terms, given that the sum of the three terms is 738 and that the sequence starts with a term after 55.

Let's denote the three consecutive terms as n, n+1, and n+2, where n is the first term that comes after 55. Since the sum of the terms is given as 738, we can formulate the following equation:

\(n + (n+1) + (n+2) = 738\)

Combining like terms, we get:

\(3n + 3 = 738\)

To find n, we'll subtract 3 from both sides of the equation and then divide by 3:

\(3n = 738 - 3\)

\(3n = 735\)

\(n = 245\)

Therefore, the first of the three consecutive terms is 245.

Answer:

5 ounce for $1.49 is you're answer.

Step-by-step explanation:

1.49/6 = 0.248 per oz

3.59/13 = 0.276 per oz

Answer: 17.28

Step-by-step explanation:

18*12 =216*.02=4.32

18*12=216*.10=21.6

21.6-4.32=17.28

In a year, by opting for online e-checks at a rate of $.02 per check instead of paper checks at $.10 per check for an average of 18 checks per month, your savings amount to $17.28.

The subject of your question is a practical application of mathematics, specifically an area often referred to as personal finance. To find out how much you've saved over a year by sending e-checks online instead of writing paper checks, we first need to calculate the cost of each method and then compare the two.

First, let's calculate how much it would cost for the e-checks. The bank charges you $0.02 for each e-check you send. If you send an average of 18 checks per month over a year (12 months), that's 18 checks/month x 12 months/year = 216 checks/year. At $0.02 a check, that comes out to 216 checks/year x $0.02/check = $4.32/year.

Now let's calculate the cost if you were writing paper checks. The bank charges $0.10 for each paper check you write, so that would have been 216 checks/year x $0.10/check = $21.60/year.

So, by choosing to send e-checks online instead of writing paper checks, you've saved $21.60/year - $4.32/year = $17.28/year.

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Answer:

9 square units

Step-by-step explanation:

Draw a rectangle around the triangle.  The rectangle is 4 units tall by 6 units wide.  The area of the triangle equals the area of the rectangle minus the triangles in the corners.

A = (4)(6) − ½(2)(4) − ½(1)(4) − ½(3)(6)

A = 24 − 4 − 2 − 9

A = 9

Answer:

  inconsistent

Step-by-step explanation:

The sum of the first and last equations is ...

  (2x +3y -z) +(x +3y +z) = (-1) +(12)

  3x +6y = 11

Three times the second equation is ...

  3(x +2y) = 3(5)

  3x +6y = 15

There are no values of x, y, or z that can make both of these equations true. They are inconsistent.

Answer:

Step-by-step explanation:

* The Null hypothesis was rejected.

* The confidence interval for the true difference in proportions between the first and second survey are:

0.008238357 and 0.003176164 respectively in 95% situations.

Please kindly go through the attached files for a step by step explanation of how these answer are gotten.

Answer:

A. 0.09

Step-by-step explanation:

Answer:

[tex]6147\:Tickets[/tex]

Step-by-step explanation:

Area of the first level [tex]=75 X 75=5625 \:ft^2[/tex]

Area of the second level [tex]=130 X 60=7800 \:ft^2[/tex]

Total Area of Standing Room [tex]=5625+7800=13425 \:ft^2[/tex]

Since each person will occupy 2.25 square feet.

Number of Persons that will occupy the standing room

[tex]= 13425 \div 2.25\\=5966.7 \approx 5767\:persons[/tex]

Therefore the number of Tickets that should be sold

=Number of seats + Number for standing Room

=180+5967

[tex]\approx 6147\:tickets[/tex]

Therefore, the concert venue should sell 6,147 tickets.

By calculating the total square footage available in the venue, and then dividing by the space each person occupies, it's determined that the venue can sell roughly 6046 tickets per show.

The main task is to calculate the total available space, in square feet, in the concert venue. For the standing room areas, we first calculate the total square footage of each level by multiplying the dimensions of each space. For the first level, the area of a square is calculated by squaring the side length, so 75' x 75' = 5625 sq. ft. For the second level, the area of a rectangle is calculated by multiplying the length by the width, so 130' x 60' = 7800 sq. ft. The seated area already specifies the number of people it can accommodate, so no calculation for square footage is needed. Altogether, the venue has 5625 + 7800 + 180 = 13605 sq ft. available.

The next step is to divide the total square footage by the space taken up by each person to find out how many people can be accommodated. We divide 13605 by 2.25, obtaining 6046.67, but since we can't sell a fraction of a ticket, we should round down to the nearest whole number. Therefore, the venue can sell roughly 6046 tickets per show.

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Answer:

3/2

Step-by-step explanation:

StartFraction 2 m + 4 Over 8 EndFraction divided by StartFraction m + 2 Over 6 EndFraction

I think you mean:

(2m + 4) / 8   divided by (m + 2)/6

=

(2m + 4)/8    times  (6 / (m + 2) )

= (m + 2)/4  times  6/(m + 2)

= 6/4 = 3/2

The quotient of the given (2m + 4)/8 divided by (m +2)/6 will be 3/2.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, the fraction is the division of the two numbers but the division is not wholly complete.

In another word, if we divide two numbers by each other then the upper word is called the numerator, and a lower word is called the denominator.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

Given that

(2m + 4)/8  ÷ (m +2)/6

⇒ (2m + 4)/8 × 6/(m +2)

⇒ 2 ×6 ÷8

⇒3/2 hence it will be the correct answer.

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Answer:

You don't need "models and equations"; if the denominator is the

same, just subtract the numerators.

Step-by-step explanation:

Answer:

she has 5

Step-by-step explanation:

16 vegetables subtracted by 6 = 10 carrots

10 carrots subtracted by 5 that she gives away = 5 that she has left

Answer:

x=500

Step-by-step explanation:

7/10=350/x

cross-multiply by multiplying 350 to 10 and multiply 7 to x.

example:

7•x

350•10

7x=3500

divide both sides by 7

-------------

x=500

-------------

Answer:

a. 84 < n + (n + 2) + (n + 4) < 96

b. 26 < n < 30

step-by-step explanation:

using 'n' to represent the smallest even number, the next even number would be 'n + 2' and the next even number would be 'n + 4'. so, the expression to represent three consecutive even numbers is: n + (n + 2) + (n + 4).

since the sum of the these numbers needs to be between 84 and 96, we can set up the following inequality:

84 < n + (n + 2) + (n + 4) < 96

in order to solve for 'n', we must first combine like terms:

84 < 3n + 6 < 96

subtract 6 from all sides: 84 - 6 < 3n + 6 - 6 < 96 - 6 or 78 < 3n < 90

divide 3 by all sides: 78/3 < 3n/3 < 90/3 or 26 < n < 30.

3m-2n=19

5m+7n=11

21m-14n=133

10m+14n=22

Now add equations

31m=155

m=5

Now let's find n

3×5-2n=19

-2n=4

n=-2

Answer: (5; -2)

The question is about solving a system of two linear equations with two variables, m and n, using substitution method. First, solve one of the equations for one variable and substitute this into the other equation. Solve the resulting equation to find the value of one variable and substitute this value into the first equation to find the value of the second variable.

The question represents a system of linear equations. Such system contains two equations with two variables, namely m and n. To solve such a system, we can use various methods, such as substitution, elimination, or matrix methods. Let's use the substitution method in this case.

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Answer:

The value of test statistic is -2.736.

The type of alternate hypothesis is Left- tailed.

Step-by-step explanation:

We are given that Historical data indicated that among the consumers who buy this detergent, the proportion who purchased it because they had seen it advertised on TV is 0.80. In a random sample of 400 consumers who bought this detergent, 296 indicated that they bought it because they saw it advertised on TV.

We have to test the hypothesis to determine if there is sufficient evidence to conclude that the population proportion is less than 0.80.

Let p = population proportion of people who purchased the detergent because they had seen it advertised on TV.

SO, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 0.80  {means that the population proportion of people who purchased the detergent because they had seen it advertised on TV is greater than or equal to 0.80}

Alternate Hypothesis, [tex]H_a[/tex] : p < 0.80  {means that the population proportion of people who purchased the detergent because they had seen it advertised on TV is less than 0.80}

The test statistics that will be used here is One-sample z-proportion test;

                      T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = proportion of people who bought detergent because they saw it advertised on TV in a sample of 400 customers = [tex]\frac{296}{400}[/tex] = 0.74

           n = sample of customers = 400

SO, test statistics = [tex]\frac{0.74-0.80}{\sqrt{\frac{0.74(1-0.74)}{400} } }[/tex]

                               = -2.736

Therefore, the value of the test statistic for the test described above is -2.736.

And the type of alternative hypothesis is left-tailed because we have to determine whether the population proportion of people who purchased the detergent because they had seen it advertised on TV is less than 0.80.

Final answer:

To test if the population proportion is less than 0.80, a hypothesis test can be conducted using the sample data. The test statistic can be calculated using the formula (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size). Using the given information, the test statistic is approximately -5.00.

Explanation:

To test whether there is sufficient evidence to conclude that the population proportion of consumers who purchased the detergent because of TV advertisements is less than 0.80, we can conduct a hypothesis test using the sample data.

Null Hypothesis:

The proportion of consumers who bought the detergent because of TV advertisements is 0.80 or higher.

Alternative Hypothesis:

The proportion of consumers who bought the detergent because of TV advertisements is less than 0.80.

We can calculate the test statistic, which is also known as the z-score, using the formula:

test statistic = (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size)

Using the given information, the sample proportion is 296/400 = 0.74. The hypothesized proportion is 0.80, and the sample size is 400.

Plugging these values into the formula, we get:

test statistic = (0.74 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 400)

Calculating this expression, we find that the test statistic is approximately -5.00.

Answer:

B. t<2 hours

Step-by-step explanation:

If Tim has to mow his lawn in under two hours.

It means:

Tim must finish mowing the lawn before two hours, therefore t<2 is the correct option.

To express that Tim must mow his lawn in under two hours, the correct inequality is t < 2. This indicates that the time, t, must be less than two hours to complete the task. Option B.

To express the condition that Tim has to mow his lawn in under two hours as an inequality, we represent the time it takes to mow the lawn with the variable t. The inequality that represents the situation is t < 2, meaning the time must be less than two hours. This is conveyed using the less than symbol (<).

In the context of other example inequalities, such as t=0, which represents a starting time, and t=t+1, which indicates an increment of time, these are used to express discrete points or changes in time. However, to represent a range of time under a specific amount, we use an inequality like t < 2 to denote that the time taken should not exceed two hours, option B.

The probability that an alkaline battery will fail before 185 days is approximately 0.457, or 45.7%. The probability that an alkaline battery will last beyond 2 years is approximately 0.228, or 22.8%.

To answer part (a), we need to find the probability that an alkaline battery will fail before 185 days. Since the length of life of an alkaline battery follows an exponential distribution with an average life of 340 days, we can use the formula for the exponential distribution to calculate the probability. The formula is:

P(X < t) = 1 - e^(-t/μ)

Where X is the random variable representing the length of life of the battery, t is the time (in days) we are interested in, and μ is the average life of the battery. Plugging in the values, we have:

P(X < 185) = 1 - e^(-185/340)

Solving this equation gives us a probability of approximately 0.457, or 45.7%.

For part (b), we want to find the probability that an alkaline battery will last beyond 2 years. Since there are 365 days in a year, 2 years is equal to 730 days. Using the same formula as before, we have:

P(X > 730) = 1 - P(X < 730) = 1 - (1 - e^(-730/340))

Solving this equation gives us a probability of approximately 0.228, or 22.8%.

Answer:

boardgamegeek.com/boardgame/245655/kings-dilemma

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(x - h)² + (y - k)² = r²

x² + y² = r²

(-3)² + (-5)² = r²

r² = 34

x² + y² = 34

Answer:

The number at tenth place is 6. Therefore, I guess there's 6 tens.

Step-by-step explanation:

There are 6 tens in the number 49,869.

To find the number of tens, we look at the digit in the tens place, which is the second digit from the right.

4 is in ten thousand place.

9 is in thousand place.

8 is in hundred place.

6 is in ten place.

As the digit in the tens place is 6.

The digit 6 represents six groups of ten in the number.

So, in the number 49,869, there are 6 tens.

Therefore, the correct answer is that there are 6 tens in the number 49,869.

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Answer:

$1,136 per ounce.

Step-by-step explanation:

To find the new value of gold, you have to find what 60% of 710 is. You do this by converting 60% into a decimal and multiplying it by 710. This results in 0.6*710. 60% of 710 is 426. 426 + the original price of 710 is equal to 1,136.

You can also solve this problem in a condensed manner by multiplying 710 by 1.6: the 1.0 stands for the original price (710) so you don't have to add it later. The 0.6 stands for the 60% more. Multiplying 710 by 1.6 gets you 1,136, which is the new value of gold/ounce.

The probability of rolling a factor of 8 with a six-sided die is 0.5 or 50%, as there are 3 favorable outcomes (1, 2, 4) out of 6 possible outcomes when rolling the die.

To find the probability of rolling factors of 8 with a fair, six-sided die, we first need to identify the factors of 8, which are 1, 2, 4, and 8. Of these, only 1, 2, and 4 are possible outcomes on a six-sided die. There are six possible outcomes when rolling a die (1, 2, 3, 4, 5, 6), so the probability of rolling a factor of 8 is the number of favorable outcomes (where the result is a factor of 8) divided by the total number of possible outcomes.

The favorable outcomes for this probability event are {1, 2, 4}, hence there are 3 favorable outcomes. Thus, the probability of rolling a factor of 8 is:

P(rolling a factor of 8) = Number of favorable outcomes / Total number of possible outcomes

P(rolling a factor of 8) = 3 / 6

P(rolling a factor of 8) = 0.5

Therefore, the probability of rolling a factor of 8 is 0.5 or 50%.

Answer:

(x-10) (x+1) =0

x=10                     x=-1

Step-by-step explanation:

x^2 -9x-10 =0

Factor

What two numbers multiply to -10 and add to -9

-10*1 = -10

-10+1=-9

(x-10) (x+1) =0

Using the zero product property

x-10 = 0             x+1=0

x-10+10=0+10       x+1-1=0-1

x=10                     x=-1

These are the x intercepts

Answer:

Just divide the sun-pluto distance by the milky way radius and you get the following ratio:

6.6 x 10^7 : 1

Answer:

(52,20)

Step-by-step explanation:

Answer: B

(52, 20)

Step-by-step explanation:

Answer:

Step-by-step explanation:

FIND THE SOLUTION BELOW

Answer:

  $41

Step-by-step explanation:

Fill in the values of the variables and do the arithmetic.

  3r +2.5p = 3(7) +2.5(8) = 21 +20 = 41

7 roses and 8 petunias cost $41.

Answer: 5/3

Step-by-step explanation:

This is a trigonometry ratio. Tangent of a right angle triangle

Tan0° = opposite

------------

adjacent.

Now from the question

Tan0° = 3/4 meaning that the opposite side is 3 while the adjacent side is 4. Going by the triple coordinate, when two of the sides of a right angle triangle are, 3 and 4, the third side should be 5, in other words you could as well use the Pythagoras theorem to find the other side which I believed you should be familiar with. Since the third side is known, the cosec could be calculated.

Cosec of an angle =

1/sine. From the question now,

Sine0° = opposite side

-----------------

Hypothesis

= 3/5

Therefore

Cosec0° = 1/3/5

= 1

---

3/5

= 5/3