One cubic foot holds 7.48 gallons of​ water, and 1 gallon of water weighs 8.33 pounds. How much does 2.2 cubic feet of water weigh in​ pounds?
In​ tons?

If the equation be [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex] then the value is 1.22222

The term "numerical evidence" describes information that is expressed in a numerical manner, such as numbers, quantities, or statistical data. It is thought to be objective and quantifiable, and it is used to support a claim or argument.

The quantity of sales made during a specific business quarter is an example of numerical data. Simply put, if the response includes a number, the data is quantitative (numerical).

Let the equation be [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex]

Simplifying the above equation, we get

[tex]$\frac{x^2-x-30}{x^2-3 x-18}= \frac{x+5}{x+3}$[/tex]

[tex]$=\lim _{x \rightarrow 6}\left(\frac{x+5}{x+3}\right)$$[/tex]

Plug in the value x = 6

= (6 + 5)/(6 + 3)

= 11/9 = 1.22222

Therefore, the equation of [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex] be 1.22222.

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The value of x found using the assumption, ΔABC is an isosceles triangle and the measure using the fact that ∠ABC > ∠ACB are;

a) x = 4.5

The assumption made is that the triangle is an isosceles triangle

b) {x ∈ Z| -6 ≤ x ≤ 8}

An isosceles triangle is a triangle that has a pair of congruent sides.

Let ΔABC be an isosceles triangle, we get;

∠ABC is congruent to ∠ACB, (∠ABC ≅ ∠ACB), therefore, by the definition of congruence triangles, we get;

m∠ABC = m∠ACB

The question indicates that the measure of the angles are;

∠ABC  = 100 - 12·x

∠ACB = 8·x + 10

Which indicates, by the substitution property, that we get;

100 - 12·x = 8·x + 10

100 - 10 = 8·x + 12·x = 20·x

100 - 10 = 90 = 20·x

20·x = 90

x = 90/20 = 4.5

The assumption made is that the triangle ΔABC is an isosceles triangle

b) ∠ABC > ∠ACB, therefore;

100 - 12·x > 8·x + 10

100 - 10 > 8·x + 12·x = 20·x

100 - 10 = 90 > 20·x

20·x < 90

x <  90/20 = 4.5

x < 4.5

The possible integer values of x can be found as follows;

100 - 12·x ≥ 0

100 ≥ 12·x

x ≤ 100/12 = 8.[tex]\overline{3}[/tex]

x ≤ 8.[tex]\overline{3}[/tex]

100 - 12·x ≤ 180

100 - 180 ≤ 12·x

12·x ≥ -80

x ≥ -80/12 = -6.[tex]\overline{6}[/tex]

x ≥ -6.[tex]\overline{6}[/tex]

Similarly, we get;

8·x + 10 ≥ 0

x ≥ -10/8 = -1.25x

x ≥ -1.25

8·x + 10 ≤ 180

x ≤ (180 - 10)/8 = 21.25

x ≤ 21.25

The possible integer value of x, using the interval, x ≥ -6.[tex]\overline{6}[/tex], x ≤ 8.[tex]\overline{3}[/tex] are therefore; -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, which can be expressed as; {x ∈ Z| -6 ≤ x ≤ 8}

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A pie has 360 degrees, so a pie cut into 5 equal pieces produces 5 slices that each measure 360 / 5 = 72 degrees.

A small slice measures 27 degrees fewer than a large slice, so it measures 72 - 27 = 45 degrees.

To find the number of pieces a pie should be cut into so that each piece is a small slice, we need to determine how many degrees each slice measures. To do this, we divide 360 by the number of pieces:

360 / n = 45

Solving for n, we get:

n = 360 / 45 = 8

So, the Tasty as Pi Bakery should cut a whole pie into 8 equal pieces so that each piece is a small slice.

The option that was not an impact of the crusades is B. End of the Roman Empire.

The Crusades were a series of religious wars fought between Christians and Muslims in the Middle East during the medieval period. The Crusades had a significant impact on European society and culture, including:

Monarchs grew more powerful: The Crusades helped to strengthen the power of monarchs in Europe, as they became more involved in financing and organizing the Crusades.

However, the Crusades did not bring about the end of the Roman Empire. The Roman Empire had already collapsed centuries earlier, in the 5th century AD, and the Crusades took place in the 11th-13th centuries AD, during the medieval period.

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Answer:

Answer is in the attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note the perimeter of the rectangle is:

2 x Length + 2 x Width.

Answer:

2 x Length + 2 x Width.

Step-by-step explanation:

The height of the object at a time of 2 seconds is given as follows:

1106 feet.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

h(t) = -16t² + 1170.

At a time of 2 seconds, the height is found replacing the lone instance of t by two, hence:

h(2) = -16(2)² + 1170

h(2) = 1106 feet.

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Answer:     [tex]p(z > \frac{0.27-0.22}{\sqrt{\frac{(0.22)(0.78)}{300} } } )[/tex]

Step-by-step explanation:

[tex]P=\frac{22}{100} =0.22, n=300[/tex]     [tex]q=1-p=0.78[/tex]

[tex]p' = \frac{27}{100}=0.27[/tex]

[tex]p(z > \frac{p'-p}{\sqrt{\frac{p*q}{n} } } )[/tex]

 [tex]p(z > \frac{0.27-0.22}{\sqrt{\frac{(0.22)(0.78)}{300}} }[/tex]

The solution to the equation 4x² = 16 is x = 2.

Given the equation in the question;

4x² = 16

x = ?

To solve for x, first divide both terms by 4.

4x² = 16

4x²/4  = 16/4

x² = 4

Take the square roots of both sides

√x² = ±√4

x = ±2

x = -2 or 2.

Therefore, the value of x is 2.

Option D)2 is the correct answer.

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Answer:

D.2

Step-by-step explanation:

[tex]4 {x}^{2} = 16 \\ \frac{4 {x}^{2} }{4} = \frac{16}{4} \\ {x}^{2} = 4 \\ \sqrt{ {x}^{2} } = \sqrt{4} \\ x = \sqrt{4} \\ x = 2[/tex]

A situation in which a quadratic equation cannot be solved using the quadratic formula include the following: A. The right-hand side of the equation is 1.

Generally speaking, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

In this context, we can reasonably infer and logically deduce that a quadratic function cannot be solved by using the quadratic formula when the coefficient of the x²-term is equal to zero (0) or when right-hand side of the equation is equal to one (1).

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By subtraction we get that, Isabel has to pour 35.25 grams of salt into the container.

The operation or process of finding the difference between two numbers or quantities is known as subtraction. To subtract a number from another number is also referred to as 'taking away one number from another'.

According to the information in question:

Total salt = 90.45 grams

Amount of salt poured = 55.2 grams

Thus, the total amount of salt left with her which has to be poured will be calculated by subtraction:

Amount of salt left = 90.45 - 55.2

                               = 35.25 grams

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The value of 10p - 3p/4- 2 +5 for p=10 is 95.5.

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

We have 10p - 3p/4- 2 +5.

Now put the value of p =10 we get

= 10p - 3p/4- 2 +5

= 10(10) - 3(10)/4- 2 +5

= 100 - 30/4 -2 + 5

= 100 -7.5 -2 +5

= 95.5

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Each worker would take home a net pay of $586.71.

What is the net pay?

The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.

To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.

To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.

For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:

Gross Pay for 40 hours = $15.90/hour x 40 hours = $636

For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:

Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88

Therefore, their total gross pay would be:

Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88

Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:

Total Deductions = 28% x $814.88 = $228.17

Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:

Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71

Therefore, each worker would take home a net pay of $586.71.

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The rational function with the given characteristics is:

f(x) = -6(x + 4)*(x + 1)/[(x - 2)*(x + 3)]

We want to write a rational function with the given characteristics, first we want to have vertical asymptotes at x = -2 and x = 3, then the denominator must be:

(x - 2)*(x + 3)

We also want to have x-intercepts at (-4,0) and (-1,0), this means that the numerator must be:

a*(x + 4)*(x + 1)

Where a is a real number, then the rational function is:

f(x) = a*(x + 4)*(x + 1)/[(x - 2)*(x + 3)]

Now we want to have an y-intercept at (0, 4)

Then we must have:

f(0) = 4 = a*(0 + 4)*(0 + 1)/[(0 - 2)*(0+ 3)]

4 = a*4/-6

(-6/4)*4 = a

-6 = a

The rational function is:

f(x) = -6(x + 4)*(x + 1)/[(x - 2)*(x + 3)]

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Based on the information given, the estimated mean word length of the book is 4.9 letters and the estimated standard deviation of the sampling distribution is 0.15 letters.

The reading specialist is trying to estimate the population mean word length of an elementary school history textbook, but it is not practical or possible to measure the word length of every single word in the book. So, instead, the specialist takes repeated random samples of 100 words from the book and calculates the mean word length of each sample. Based on these repeated samples, the specialist estimates that the mean word length of the book is 4.9 letters. This means that, on average, the words in the book are about 4.9 letters long. The specialist also calculated the standard deviation of the sampling distribution, which is a measure of the variability of the sample means. In this case, the standard deviation of the sampling distribution is estimated to be 0.15 letters. This means that the mean word length of each random sample is expected to vary by about 0.15 letters from the population mean. It is important to note that these estimates are based on a specific set of samples and are subject to sampling variability. If the specialist were to take different random samples, the estimates may be slightly different. However, based on the information given, the estimated mean word length of the book is 4.9 letters and the estimated standard deviation of the sampling distribution is 0.15 letters.

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The discount on each orange is 81.3%

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

A sales discount is a reduced price offered by a business on a product or service.

The total price for the oranges is;

0.75 × 7 = $5.25

She paid $ 4.30 for the oranges, this means that the discount = 5.25-4.30 = $0.95

Therefore the percentage discount on all the oranges = 0.95/5.25 × 100

= 18.1%

by discount each orange = 4.30/7 =$ 0.61

Therefore the discount on each orange = 0.61/0.75 ×100 = 81.3 %

Therefore the discount on each orange is 81.3%

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The solution set to the given inequality is (−∞, 2.5].

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is 8(2x-3) ≤ 20-4.

Here, 8(2x-3) ≤ 16

Divide 8 on both the sides of an inequality, we get

2x-3≤2

Add 3 on both the sides of an inequality, we get

2x≤5

Divide 2 on both the sides of an inequality, we get

x≤2.5

Convert the inequality to interval notation.

(−∞, 2.5]

Therefore, the solution set is (−∞, 2.5].

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Answer:

x = 50 tablets

Step-by-step explanation:

Ket's call the number of tablets taken in a week "x".

A typical dose for a 100-pound person is 22 mg every six hours, so in 24 hours, they would take 22 mg * 24 hours / 6 hours = 88 mg.

In one week, they would take 88 mg * 7 days = 616 mg.

And since each tablet is 12.3 mg, they would take 616 mg / 12.3 mg/tablet = 50 tablets in a week.

So the answer is x = 50 tablets.

The interest for the first quarter would be $ 15

The value of the CD when it matures is $ 2, 030. 11

The interest is said to compound quarterly which means that the periodic interest rate per quarter is:

= 3 % / 4

= 0. 75 % per quarter

The interest in the first quarter :

= 0. 75 % x 2, 000

= $ 15

The value of the CD at maturity is:

= 2, 000 x ( 1 + 0. 75% ) ²

= $ 2, 030. 11

Note : 2 periods because 6 months is 2 quarters.

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Answer:

y = ( x - 4 )² - 4

Step-by-step explanation:

a² ± 2ab + b² = ( a ± b )²

~~~~~~~~~~~~

y = x² - 8x + 12

y = ( x² - 2(4)(x) + 4² ) - 4² + 12 = ( x - 4 )² - 4

y = ( x - 4 )² - 4

Answer:

3,291 pints used

Step-by-step explanation:

There are 8 pints in a gallon

Started with 412 gallons, multiply that by 8 to get 3,296 pints

At the end of day, he only had 5

So we can subtract 5 from the 3,296 that he started the day with, and we get the answer of 3,291 used throughout the day.

The correct answers are given below:

(a) 1 to 55

(b) 40%

Since Mansour scores 55% of his kicks, we'd want exactly 55% of the simulated numbers to denote Mansour scoring a penalty, thus, 1 to 5 is a possible range.

To find the percentage of trials where Mansour scored exactly one penalty, we have to count the trials where one of the simulated numbers is in the range of 1 to 5 (denoting Mansour scoring the penalty) and the other is in the range of 56 to 100 (denoting Mansour missing the penalty)

Trails 1, 3, and 4, 6 are such trials. Thus, Mansour scored exactly one penalty kick in 40% of the trials.

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Answer: 9/4

Step-by-step explanation:

A scale factor is the number by which all components of an object are multiplied in order to create a proportional enlargement or reduction.

The probability distribution does not add up to 1.0, in other words.

The complete question is:

A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?

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Answer:

It is not accurate

Step-by-step explanation:

If the complete question is:

A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?

THEN:

To determine whether the probability distribution is accurate, we need to check two conditions:

The sum of the probabilities should be equal to 1.

All probabilities should be between 0 and 1.

Let's check these conditions:

Sum of probabilities:

p(0) + p(1) + p(2) + p(3) + p(4 or more) = 0.22 + 0.30 + 0.16 + 0.12 + 0.25 = 1.05

The sum of the probabilities is greater than 1, which violates the first condition. Therefore, this is not a valid probability distribution.

All probabilities should be between 0 and 1:

The probability of making 0, 1, 2, or 3 mistakes are all between 0 and 1, so they satisfy this condition.

However, the probability of making 4 or more mistakes is 0.25, which is a valid probability, but it implies that the probability of making 0, 1, 2, or 3 mistakes is negative, which is impossible. Therefore, this distribution does not satisfy this condition.

Since this probability distribution violates both conditions for a valid probability distribution, it is not accurate, and the researcher should revise their data.

Answer:

12

Step-by-step explanation:

First find the missing angle S

Three angles of a triangle add up to 180°

So m∠S + 81 + 42 = 180

m∠S + 123 = 180

m∠S = 180 - 123 = 57°

Using the law of sines which states that the ratio of each side to the opposite angle is the same for both sides we get

[tex]\dfrac{r}{\sin 42} = \dfrac{q}{\sin81} = \dfrac{15}{\sin 57}\\\\\sin 57 = 0.83867\\\\ \dfrac{15}{\sin 57}= \dfrac{15}{0.83867}\\\\= 17.88545\\\\[/tex]

Hence
[tex]\dfrac{r}{\sin 42} = 17.88545\\\\r = 17.88545 \times \sin 42\\\\r = 17.88545 \times 0.66913\\\\r = 11.9677\\\\r = 12 \textrm{ rounded to the nearest tenth}[/tex]

Answer:

It will turn on again, just charge it. All phones come with a charger.

The average velocity, to the nearest hundredth, of a ceiling tile that fell 43 feet is 344 feet per second

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.

Given that the formula for the speed of a falling object is v= √64d,

where v is the speed of the object in feet per second and d is the distance the object has fallen, in feet.

And also given that d = 43 feet.

Substituting the value to the formula,

v = √64 (43)

v = 8 x 43

v = 344

Therefore, 344 feet per second is the velocity.

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Mortgage B requires $27,336.60 more interest than mortgage A. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

There are four fundamental mathematical operations that can be used to express any real number; these are referred to as "arithmetic operations." The four operations are multiplication, division, addition, and subtraction.

We are given the principal amount as $80,000.

So, interest on Mortgage A = Total amount payable - principal amount

Interest = $110,158.20 - $80,000

Interest = $30,158.20

Similarly, interest on Mortgage B = Total amount payable - principal amount

So,

Interest = $137,494.80 - $80,000

Interest = $57,494.80

So, difference in interest = $57,494.80 - $30,158.20 = $27,336.60

Hence, mortgage B requires $27,336.60 more interest than mortgage A.

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Answer:

Step-by-step explanation:

A) In a geometric sequence, t_(1)=625 and the common ratio is r=(1)/(5). For what value of n is t_(n)=(1)/(25)?

Step 1: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 2: Substitute the given values into the formula

t_n = 625 * (1/5)^(n-1)

Step 3: Solve for n when t_n = (1/25)

(1/25) = 625 * (1/5)^(n-1)

(1/25) / 625 = (1/5)^(n-1)

(1/5)^(n-1) = (1/25) / 625

(n-1) = log base (1/5) of ((1/25) / 625)

Step 4: Solve for n

n = 1 + log base (1/5) of ((1/25) / 625)

The value of n is the number of terms that have passed when t_n = (1/25).

B) (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

Step 1: Determine the type of sequence

A sequence is an arithmetic sequence if the difference between any two consecutive terms is constant. Since this sequence does not have a constant difference, it is not an arithmetic sequence.

A sequence is a geometric sequence if the ratio between any two consecutive terms is constant. We can see that the ratio between any two consecutive terms is constant, so this sequence is a geometric sequence.

Step 2: Find the common ratio

To find the common ratio, we can divide any two consecutive terms. For example, the common ratio is (3/6) / (2/5) = (3/2) / (6/5) = 5/6.

Step 3: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 4: Substitute the given values into the formula

To use this formula, we need to know the value of t_1. We are given t_1 = (2/5), so:

t_n = (2/5) * (5/6)^(n-1)

This is the formula for the nth term of the sequence (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

Answer:

the scale factor that Samir used in his drawing is 5/1.

Step-by-step explanation:

Here's a step by step explanation of how to find the scale factor of a drawing:

Identify the scale used in the drawing. In this case, the scale used in Samir's drawing is 5 inches = 1 yard.

Express the scale as a ratio between the two sizes. In this case, the ratio is 5 inches : 1 yard.

Simplify the ratio, if possible. In this case, the ratio 5 inches : 1 yard can be simplified to 5/1.

The simplified ratio, 5/1, is the scale factor of the drawing. This means that for every 5 inches on the drawing, the actual length in the real world is 1 yard.

So, the scale factor that Samir used in his drawing is 5/1.

Answer:

50 + 5x^2 + 4x.

Step-by-step explanation:

To find the sum of the expressions, we need to simplify each expression first and then add them up.

10 + 3x represents the first expression.

25 - 4x + 2x^2 represents the second expression. By simplifying this expression, we get 25 + 2x^2 - 4x.

3x^2 - 5x represents the third expression.

-x^2 + 2x + 15 represents the fourth expression.

Adding all four expressions gives us:

10 + 3x + 25 + 2x^2 - 4x + 3x^2 - 5x - x^2 + 2x + 15

By combining like terms, we get:

10 + 5x^2 + 4x + 25 + 15

The final simplified sum is:

50 + 5x^2 + 4x.