Evaluate the indefinite integral: 1/( t^2 − 6t + 45) dt

Answer:

Option B is correct.

Three less than five times of a quantity of a number plus two.

Step-by-step explanation:

Given the expression: [tex]5(x+2)-3[/tex]

To describe the given algebraic expression.

Here, x be the number.

x+ 2 means "a number plus 2"

5(x+2) means "five times the quantity of a number plus two".

and

5(x+2)-3 means "Three less than five times of a quantity of a number plus two".

Therefore, the following which best describe the algebraic expression [tex]5(x+2)-3[/tex] is,  Three less than five times of a quantity of a number plus two.

The sample statistic for the proportion of teens who send text messages to friends is 0.76 or 76%. This result was obtained with a 98% confidence interval and a margin of error of 0.03.

The sample statistic in this scenario is the proportion of teens who said they send text messages to friends. In statistics, a sample proportion (also known as a sample percentage) is a way to express the count of observations in a category as a ratio or a fraction of the total sample size.

In your case, the sample statistic is 0.76, meaning that 76% of the teens in your sample said they send text messages to friends. This result was accompanied by a margin of error of 0.030 for your 98% confidence interval.

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

The margin of error represents the range in which we are confident that the true population proportion lies given our sample statistic. With a confidence level of 98%, we are sure that if we repeated our sample many times, 98% of those samples would produce a proportion between 76%- 3% and 76% + 3%.

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The graph of g(x) is the graph of f(x) shifted 8 units to the right.

Option D is correct.

A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.

According to the question

g(x) = f(x – 8)

If the function is shifted to the left it is going to plus(+).

If the function is shifted to the right it is going to minus(-).

Hence, The graph of g(x) is the graph of f(x) shifted 8 units to the right.

Option D is correct.

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Answer:

20cm

Step-by-step explanation:

The order from least to greatest of the given numbers 5x10^4, 7x10^-5, 3x10^-9, 8x10^4 is 3x10^-9, 7x10^-5, 5x10^4, and finally 8x10^4. This is determined by comparing the exponents and coefficients of the scientific notation.

To find the order of 5x10^4, 7x10^-5, 3x10^-9, and 8x10^4 from least to greatest, we have to compare their exponents as they determine the size of the numbers. The exponent indicates how many times the number 10 is used in a multiplication.

Here are these numbers in order from the smallest to the largest:

The smaller the exponent (more negative), the smaller the number. The first is the smallest because it has the most negative exponent (-9), and the last is the largest with the exponent of 4. When exponents are the same, we then compare the coefficients (the numbers before the 'x10'), in this case, 5 is less than 8, so 5x10^4 is smaller than 8x10^4.

Answer:

  $187,500

Step-by-step explanation:

There must be 15,000/3 = 5,000 seats in each section. Then the total revenue can be ...

  5000·$10.00 + 5000·12.50 + 5000·15.00 = 5000·($10 + 12.50 +15.00)

  = 5000·$37.50 = $187,500

Stadium revenue can be $187,500 if all seats are sold.

The total earnings from selling out the stadium with tickets priced at $10.00, $12.50, and $15.00, equally distributed, would amount to $637,500.

The total earnings from selling out the stadium would be $15 x 15,000 = $225,000 for tickets priced at $10.00.

For tickets priced at $12.50, the earnings would be $12.50 x 15,000 = $187,500.

Lastly, for tickets priced at $15.00, the earnings would be $15 x 15,000 = $225,000.

To find the total earnings, add the earnings from each section: $225,000 + $187,500 + $225,000 = $637,500.

 Desiree made 100 cookies this week.  She baked 4 more than three times the total she made last week.  How many cookies did she bake last week.

3x + 4 = 100                                      x = 32 cookies               

Answer:

1) 45%

2) [tex]\frac{16}{5}[/tex]

3) 2.335

   237.5%

4) 0.0001

   [tex]\frac{1}{1000}[/tex]

5) 120%

 [tex]\frac{6}{5}[/tex]

6) 533.3%

    5.333        

Step-by-step explanation:

1) Divide the numerator by the denominator and multiply by 100, then:

[tex]\frac{9}{20}=0.45*100=45\%[/tex]

2) Write 320 has the numerator and 100 has the denominator, then reduce the fraction:

[tex]\frac{320}{100}=\frac{32}{10}=\frac{16}{5}[/tex]

3) As a decimal:

Divide the numerator by the denominator and add it to the integer part:

[tex]2+0.375=2.375[/tex]

As a percent:

Multiply the decimal number obtained above by 100:

[tex]2.375*100=237.5\%[/tex]

4) As a decimal:

Divide it by 100:

[tex]\frac{0.1}{100}=0.0001[/tex]

As a fraction:

As you can see, the decimal point were moved three spaces to the left. Therefore, the integer 1 is divided by 1000. Write 1 as the numerator and 1000 has the denominator:

[tex]\frac{1}{1000}[/tex]

5) As a percent:

Multiply 1.2 by 100, then:

[tex]1.2*100=120\%[/tex]

As a fraction:

To make 1.2 an integer you must multiply by 10, therefore, 12 will be the numerator and 10 the denominator:

[tex]\frac{12}{10}[/tex]

Reduce it:

[tex]\frac{6}{5}[/tex]

6) As a decimal:

Divide the numerator by the denominator and add it to the integer part:

[tex]5+0.33=5.333[/tex]

Multiply the decimal number obtained above by 100:

[tex]5.33*100=533.3\%[/tex]

Answer:

9/20 as a percent- 45%

320% as a fraction- 16/5

2 3/8 as a decimal- 2.38

2 3/8 as a percent- 237.5%

.1% as a decimal- 0.001

.1% as a fraction- 1/100

1.2 as a percent- 120%

1.2 as a fraction- 6/5

5 1/3 as a percent- 533.3%

5 1/3 as a decimal- 5.33

Final answer:

To find an acute angle using a protractor, choose the angle less than 90°. The acute angle could be 75°.

Explanation:

To determine an acute angle using a protractor, we look for an angle that is less than 90 degrees, as acute angles are those that measure less than 90 degrees.

75° could be the measure of the angle as it falls within the range of acute angles.

Hence, in this case, the angle that could be the measure of the acute angle is 75°.

Answer:

  70.7 ft

Step-by-step explanation:

The triangle formed by home plate, first base, and second base is an isosceles right triangle with hypotenuse 100 ft. Then the side length (base-line distance between bases) is (100 ft)/√2 ≈ 70.7 ft.

___

For an isosceles right triangle with side lengths 1, the hypotenuse can be found from the Pythagorean theorem to be ...

  hypotenuse = √(side² + side²) = √(1²+1²) = √2

Then the diamond distances satisfy the proportion ...

  hypotenuse/side = 100 ft/(base distance) = √2/1

or ...

  base distance = (100 ft)/√2 ≈ 70.71068 ft

Answer: I got (y-8x)(y-7x) by factoring out the factors of 56, that have a sum of -1.

8 and 7 are factors of 56 when you multiply them and to get a sum of -1, 8 should change to negative. 7 + -8 = -1

Answer:

[tex]y=9000(1.048)^x[/tex]

Step-by-step explanation:

This will be an exponential growth problem.  This is because the amount of burgers is expected to change at the same rate every month.

These equations are of the form

[tex]y=a(1+r)^x[/tex],

where a is the original amount, r is the growth rate and x is the amount of time.

In this problem, the original amount, a, is 9000.

The rate of growth is 4.8%; 4.8% = 4.8/1000 = 0.048

This gives us

[tex]y=9000(1+0.048)^x\\\\y=9000(1.048)^x[/tex]

Answer:

The answer is 9000(1.048)^t  {limit from n = 1 to n = 12}.

Step-by-step explanation: