A 3-gallon container of window cleaner costs $17.76. What is the price per quart?

A local minimum or a local maximum are both examples of local extremums.

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The sum of two interior angles other than the adjacent angle of extended length will be equal to the external angle of extended length thus m∠PQR will be 18°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus. The identical endpoint of the two rays known as the vertex is referenced as an angle's sides.

In any triangle, the sum of two interior angles other than the adjacent angle of extended length will be equal to the external angle of extended length.

In the given triangle,

m∠PQR = m∠OPQ + m∠POQ

4x - 10 = x + 9 + x - 5

4x - 10 = 2x + 4

2x = 14

x = 7

So,

m∠PQR = 4(7) - 10 = 18°

Hence the measure of m∠PQR will be 18° for the given triangle.

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Answer:

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

Simplify the equation by distribution, then substitute the value of d and solve for c:

The average daily balance on the June 5 bill is $1,037.32, including the finance charge.

The average daily balance is the total balance divided by the number of days in the billing cycle.

May has a 31-day billing cycle.

The average daily balance determines the finance charge, which is a product of the monthly interest rate (MPR) and the ending average daily balance.

                                                       Daily Balance

May 5 Credit card balance $939    $11,260 ($939 x 12)

May 17 Purchase                    216     $4,620 ($1,155 x 4)

May 20 Payment                  -100   $15,825 ($1,055 x 15)

Total daily balances                       $31,705

Average daily balance                   $1,023 ($31,705 ÷ 31)

Interest rate per month = 1.4%

Finance charge for the month = $14.32 ($1,023 x 1.4%)

June 5 balance = $1,037.32 ($1,023 + $14.32)

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Answer:

98.53

Step-by-step explanation:

[tex]100 \times 5 = 1500 \\ 1500 - 22 = 1478 \\ 1478 \div 15 = 98.53[/tex]

Answer:

[tex]6g=900[/tex]

Step-by-step explanation:

The number of calories in one bar multiplied by six is the number of calories in six bars. This is given to be equal to 900.

The solution for the given system of equation is (x,y,z) is = (0 , (3-4t) , t) .

In the question ,

it is given that the system of equations are ,

3x + 3y + 12z = 9

x + y + 4z = 3

2x + 5y + 20z = 15

-x + 2y + 8z = 6

we have to solve the equations for x, y , z.

writing the given equations in augmented matrix form ,

we get ,

[tex]\left[\begin{array}{ccc}3&3&12\\1&1&4\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}9\\3\\15\\6\end{array}\right][/tex]

Applying the operation , R₁/3 ⇒ R₁

[tex]\left[\begin{array}{ccc}1&1&4\\1&1&4\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}3\\3\\15\\6\end{array}\right][/tex]

Applying the row operation , R₂ - R₁ ⇒ R₂  .

[tex]\left[\begin{array}{ccc}1&1&4\\0&0&0\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}3\\0\\15\\6\end{array}\right][/tex]

After applying more row operations , in the above matrix ,

to make the lower triangle matrix 0 ,

we get ,

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&4\\0&0&0\\0&0&0\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}0\\3\\0\\0\end{array}\right][/tex]

The above result can be expressed as x = 0,

and y + 4z = 3 .

So , the system of equations have infinite solutions .

So , the solution x, y, and z expressed in terms of the parameter t is

(0 , (3-4t) , t)  .

Therefore , the solution is (x,y,z) is = (0 , (3-4t) , t) .

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Answer:

x-24 > 9

x >33

it should be greater than or equal sign

The Probability of carcking the six digit code is 0.00139

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Solution:

We need to use Permutation to find total number of outcomes

6P6 = 6! = 6*5*4*3*2*1 = 720 outcomes

But only one outcome is correct

Probability is 1/720

Probability = 0.0013899 = 0.00139 (approx)

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Answer:

24 / 16

Step-by-step explanation:

divide and do the thing

Using the t-distribution, the 99% confidence intervals for the given standard deviation are given as follows: (5053.39 , 4126.61)

Given that,

Number of college students = 23

A simple random sample with a mean = $4590

A simple random sample with a standard deviation = $860

The t distributions is wide (has thicker tailed) for smaller sample sizes, reflecting that s can be smaller than σ. The thick tails ensure that the 80%, 95%, 99% confidence intervals are wider than those of a standard normal distribution (so are better for capturing the population mean).

The confidence interval is:

= μ ± [tex]t\frac{s}{\sqrt{n} }[/tex]

In which:

μ is the sample mean.

t is the critical value.

n is the sample size.

s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 23 - 1 = 22 df,

Upon using a t -table or a calculator, we see that the critical t -value for this 99% confidence interval is t0.005=2.581

The parameters are:

μ = $4590

n = 23

Hence, with s = 860, the bounds of the interval are:

= μ ± [tex]t\frac{s}{\sqrt{n} }[/tex]

= 4590 ± 2.581 [tex]\frac{860}{\sqrt{23} }[/tex]

= 4590 ± 2.581 [tex]\frac{860}{4.79}[/tex]

= 4590 ± 2.581 (179.54)

= 4590 ± 463.39

Then,

= 4590 + 463.39   ,      4590 - 463.39

= 5053.39              ,       4126.61

Therefore,

Using the t-distribution, the 99% confidence intervals for the given standard deviation are given as follows: (5053.39 , 4126.61)

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Answer:

D)8.00

σ = √64

= 8

The error step in the problem of finding an inverse is Step 4.  

What is an inverse function?

In relation to the original function f, the inverse function is denoted by the symbol [tex]f^{-1}[/tex], and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively.

Given, based on the inverse function

Step 1: y = 6x - 11        (Given equation)

Step 2: x = 6y - 11       (Exchange of variables x and y with each other                 respectively)

Step 3: x + 11 = 6y      (Adding 11 on both sides)

Step 4: x/6 +11 = y      Error step ( because dividing both sides by 6 will give x/6 + 11/6 = y)

Hence, the error step in the problem of finding an inverse is Step 4.  

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The greatest common factor of 4, 8 and 12 is 4

The first number = 4

The second number = 8

The third number = 12

The GCF is stands for greatest common factor.

To find the greatest common factor use the prime factorization method

Prime factorization

Factorize the number 4 = 2 × 2

Factorize the number 8 = 2 × 2 × 2

Factorize the number 12 = 2 × 2 × 3

Here we have to take the common terms from the prime factorization

The greatest common factor = 2 × 2

Multiply the number

= 4

Therefore, the greatest common factor is 4

I have solved the question in general,  as the given question is incomplete

The complete question is:

What is the GCF of 4 and 8 and 12?

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The value of x for which the parallelogram and a triangle have the same area is 6 cm.

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 area of a triangle is (1/2)×base×height.

We also know the area of a parallelogram is base×hright.

∴  The values of 'x' for which the parallelogram and a triangle have the same area is,

x×(x + 4) = (1/2)×x×20.

x²  4x = 10x.

x² = 6x.

x = 6.

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The cost of the task, given the perimeter of the figure, and the cost of feets of fence, is $ 5.17

First, find the perimeter of the figure which is just the distance around the shape:

= 4 + 2 + 6 + 3

= 15 cm

The fence needs 5 % more :

= 15 x ( 1 + 5%)

= 15.75 cm

This distance in feet is :

= 15 . 75 / 30.48 cm per feet

= 0. 5167 feet

The cost of the task is therefore:

= 0. 5167 x 30 / 3 feet

= $ 5.17

In conclusion, the cost of the entire task after accounting for the various costs, is $ 5.17.

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We are given the following data set:

10, 12,20, 15,17,10, 28,35, 28, 19,27, 25,22, 33, 37,14,21,20

Standard deviation = 8.043

Confidence level = 1 - Significance Level = 1 - 99.74% = 4.56% = 0.0456

The fraction 2/5 added by 3/4 will be 1 3/20.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

The fraction will be illustrated thus:

=✓2/5 + 3/4

= 8/20 + 15/20

= 23/20

= 1 3/20

The value is 1 3/20.

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Answer: D) Two sides are congruent

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

the author compares the color of the water to the color of the sky. so that makes it figurative language.

hope this helps.

The population of the country in 2003 is, 368.3 million.

What is population?

The term "population" refers to all citizens who are either permanently residing in a nation or are only temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.

Given:

The exponential model a = 368.3e^0.002t describes the population,

'a' is the population of a country in millions,

t years after 2003.

We have to find the population of country in 2003.

At 2003, t = 0.

So plug t = 0 in above exponential model.

a = 368.3e^0.002(0)

a = 368.3e^0

a = 368.3

Hence, the population of the country in 2003 is, 368.3 million.

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The total shipment amount of $ 33,066 must be paid back in order to receive a cash reimbursement for the $20,040 in goods that were returned.

When describing a singular noun that CANNOT be measured, you should use the word amount. – When discussing a singular, plural, or countable noun, the word number should be used. – Any single or plural noun that can be counted or measured should be referred to as having a certain quantity.

1/10 n (unclear) indicates that the consumer settled their debts within 10 days and was entitled to a 1% sales discount.

Therefore, the consumer should receive a refund equal to what they paid, which is 1% less than the total amount.

Using that as a basis, the calculation is,

Amount owed * (1-discount rate)

= $ 33,400 * ( 1 - 0.01)

= $ 33,066

$ 33,066 is is the sum that must be reimbursed.

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After solving, the regular singular points are x=0, 5i, -5i.

We have to determine the singular points of the given differential equation. Classify each singular point as regular or irregular.

(x^3+25x)y"–5xy'+6y = 0

On comparing with the equation P(x)y''+Q(x)y'+R(x)y=0

P(x) = (x^3+25x)

P(x)=0

x^3+25x = 0

x=0, 5i, –5i be the singular point.

Now write equation 1 in the standard form

Divide by x^3+25x on both side, we get;

y"–5x/(x^3+25x) y'+6/(x^3+25x) y = 0

y"–5/(x^2+25) y'+6/x(x^2+25) y = 0

Comparing with the standard form of equation;

y''+P(x)y'+Q(x)y = 0

P(x) = –5/(x^2+25)      Q(x)=6/x(x^2+25)

We know that if [tex]\lim_{x \to x_{o}}(x-x_{o})p(x)\text{ and }\lim_{x \to x_{o}}(x-x_{o})^2q(x)[/tex] exist finite. Then the singular point [tex]x_{o}[/tex] is regular singular point else irregular singular point.

(a) At [tex]x_{o}[/tex]=0

[tex]\lim_{x \to 0}(x-0)p(x)=\lim_{x \to 0}\frac{-5x}{x^2+25}[/tex]

[tex]\lim_{x \to 0}(x-0)p(x)[/tex] = 0 (Finite)

[tex]\lim_{x \to 0}(x-0)^2p(x)=\lim_{x \to 0}\frac{6x^2}{x(x^2+25)}[/tex]

[tex]\lim_{x \to 0}(x-0)^2p(x)=\lim_{x \to 0}\frac{6x}{(x^2+25)}[/tex]

[tex]\lim_{x \to 0}(x-0)p(x)[/tex] = 0 (Finite)

So x=0 is a regular singular point.

(b) At [tex]x_{o}[/tex]=5i

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{-5(x-5i)}{(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{-5}{(x+5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)[/tex] = -1/i (Finite)

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{6(x-5i)^2}{x(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{6(x-5i)}{x(x+5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)[/tex] = 0 (Finite)

So x=5i is a regular singular point.

(c) At [tex]x_{o}[/tex]=-5i

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{-5(x+5i)}{(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{-5}{(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)[/tex] = 1/i (Finite)

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{6(x+5i)^2}{x(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{6(x+5i)}{x(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)[/tex] = 0 (Finite)

So x=-5i is a regular singular point.

Hence, the regular singular points are x=0, 5i, -5i.

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The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

As per the given graph of a function,

The time period is the time interval after curves repeat their behavior.

The given graph repeats after 1 + 1 + 1 + 1 = 4 thus period will be 4.

Hence "The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4".

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The correct option is (d) i.e; MD = 3 with s2 = 20 for the difference scores because it generates a repeated-measures study's population mean difference with the widest 90% confidence interval.

Given that,

Which of the following will result in the widest 90% confidence interval for the population mean difference for a repeated-measures research, provided the sample size is kept constant?

MD = 3 with s2 = 20 for the difference scores.

Therefore, the correct choice is MD = 3 with s2 = 20 for the difference scores because it produces the widest 90% confidence interval for the population mean difference for a repeated-measures study.

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To get 80% percentage you need to attempt 20 question

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.

For example, 45% (read as "forty-five per cent") is equal to the fraction

45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total.

now we need to find  80% of a 25 question test

80% of 25 can be written as 80% × 25

= 80/100 × 25

= 20

To get 80% you need to attempt 20 question

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The weight of clothing is the ratio of weight to dye is different from the other ratios is B. 42 pounds.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

It should be noted that from the information given, others have a ratio of 1:7. This is different for 42 pounds since the ratio is:

= 42/9

= 14:3

In conclusion, the correct option is B.

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Answer:

A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

A topic sentence is used to bring

to a paragraph.

Answer: She had 167.57 remaining in her account

Step-by-step explanation:

You add all her expenses and then subtract it from the beginning balance