Thirteen and eight tenths

Answer:

2

Step-by-step explanation:

Here, the given function is,

f(x) = The quantity of 4x plus 1, divided by 3

[tex]\implies f(x)=\frac{4x+1}{3}[/tex]

The steps that involve in finding the inverse of f(x) are as follows,

Step 1  : Replace f(x) by y,

[tex]y=\frac{4x+1}{3}[/tex]

Step 2 : Switch x and y,

[tex]x=\frac{4y+1}{3}[/tex]

Step 3 : Isolate y in the left side of the equation,

[tex]3x=4y+1[/tex]

[tex]-4y=1-3x[/tex]

[tex]y=\frac{1-3x}{-4}[/tex]

[tex]y=\frac{3x-1}{4}[/tex]

Step 4 : Replace y by [tex]f^{-1}(x)[/tex],

[tex]f^{-1}(x)=\frac{3x-1}{4}[/tex]

For x = 3,

[tex]f^{-1}(3)=\frac{3\times 3-1}{4}=\frac{9-1}{4}=\frac{8}{4}=2[/tex]

Hence, First option is correct.

1. The quantity of fuel left in the tank when the plane lands will be 3,375 gallons.

2. The total distance of the flight is 6,325 miles.

The quantities are computed using basic mathematical operations, including subtraction, division, addition, and multiplication.

Full tank of the airplane = 40,000 gallons

Average speed = 550 miles per hour

Number of hours on first flight = 8 hours

The quantity of fuel left = 14,000

The quantity of fuel consumed in 8 hours = 26,000 (40,000 - 14,000)

The quantity of fuel consumed per hour or per 550 miles = 3,250 miles (26,000 ÷ 8)

Additional hours on the final flight = 3.5 hours

The quantity of fuel consumed during the final flight = 11,375 gallons (3.5 x 3,250)

The total quantity of fuel consumed for the flight = 37,375 gallons (26,000 + 11,375)

The quantity of fuel left after the flight = 2,625 gallons (40,000 - 37,375)

The total hours for the flight = 11.5 hours (8 + 3.5)

The total distance of the flight = 6,325 miles (550 x 11.5)

Mathematically, after flying 11.5 hours or 6,325 miles, the airplane consumed 37,375 gallons of fuel, leaving only 2,625 gallons in its tank.

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Answer:

The answer would be 23

Step-by-step explanation:

I think this is a composite function, so it would be

f(g(1))

you must first replace all the "x" in f(x) with g(x)

f(g(x) = -4(g(x))+7

f(g(x)) = -4(2x-6)+7

f(g(x)) = -8x+24+7

f(g(x)) = -8x+31

If x=1

f(g(1)) = -8*1+31

f(g(1)) = -8+31

f(g(1)) = 23

To find a line parallel to a given line and passing through a certain point, determine the slope of the given line, rearrange it to slope-intercept form, then substitute the point's coordinates to find the y-intercept of the parallel line.

To find a line parallel to the given line, we need the same slope of 3. Start by rearranging the given equation 3x - 4y = 7 to slope-intercept form: y = (3/4)x - 7/4. Since the parallel line passes through (-4,-2), substitute these values into the slope-intercept form to find the y-intercept. The equation of the line parallel to 3x - 4y = 7 that passes through (-4,-2) is y = (3/4)x + 2.

The value of x to solve the given equation is 16.

The given equation is:

[tex]log_2x=4[/tex]

A logarithm function is a special style to write an exponential function.

For example, If [tex]a^x=b[/tex] then we write it as [tex]log_ab=x[/tex].

So, [tex]log_2x=4[/tex] can be written as:

[tex]2^4=x[/tex]

Or, [tex]x=2^4[/tex]

[tex]x=16[/tex]

So, the value of x =16.

Hence, the value of x to solve the given equation is 16.

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Answer:

The correct option is C) 7/3.

Step-by-step explanation:

Consider the provided numbers.

If the rational number can be written in the form of [tex]\frac{p}{2^n\times 5^m}[/tex] then the rational number will be a terminating decimal.

Now consider the provided options:

Option A) 7/5 can be written as: [tex]\frac{7}{2^0\times 5^1}[/tex]

Thus it is a terminating decimal.

Option B) 7/4 can be written as: [tex]\frac{7}{2^2\times 5^0}[/tex]

Thus it is a terminating decimal.

Option C) 7/3 can be written as: [tex]\frac{7}{2^0\times 5^0\times 3^1}[/tex]

Thus it is not a terminating decimal.

Option D) 7/2 can be written as: [tex]\frac{7}{2^1\times 5^0}[/tex]

Thus it is a terminating decimal.

Hence the only fraction that must be represented by a non terminating decimal is 7/3.

The correct option is C) 7/3.

Factoring  x2-13x+40 

The first term is,  x2  its coefficient is  1 .
The middle term is,  -13x  its coefficient is  -13 .
The last term, "the constant", is  +40 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 40 = 40 

Step-2 : Find two factors of  40  whose sum equals the coefficient of the middle term, which is   -13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  -5 
                     x2 - 8x - 5x - 40

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-8)
              Add up the last 2 terms, pulling out common factors :
                    5 • (x-8)
Step-5 : Add up the four terms of step 4 :
                    (x-5)  •  (x-8)
             Which is the desired factorization

The half life of an element which decays 3.401% is 20 days.

The time required for a radioactive substance (or one-half of its atoms) to decay or change into a new substance is commonly characterised as its half-life. Ernest Rutherford discovered the idea for the first time in 1907. It is commonly denoted by the symbols Ug or t1/2.

To help you comprehend the notion, consider a radioactive element with a half-life of one hour. In this example, one half would decay in an hour and the other half would decay in another hour.

We are given;

y = a[tex]b^{(t)}[/tex]

Where t is the half life

y = a/2 is the amount of substance remaining after decay

So, b = 100% - 3.401%

b = 96.599%

b = 0.96599

Now, a/2 = a[tex](0.96599)^t[/tex]

and, 0.5=  [tex](0.96599)^t[/tex]

Now, taking log on both side we get

ln (0.5) = t(ln 0.96599)

t = ln(0.5)/ln(0.96589)

t = 20.032 days

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Answer:

it's true

Step-by-step explanation:

The triangles made by diagonal parallelograms will be congruent so we can prove statements so will be True.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram.

A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

As per the parallelogram drawn.

ΔABC ≅ ΔADC (By SAS postulute of congruency)

So we can make the statement that the two triangles made by the diagonal of a parallelogram will be congruent.

Hence "The triangles made by diagonal parallelograms will be congruent so we can prove statements so will be True".

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Final answer:

Ariane earned $50 for the first 100 kits at $0.50 per kit, and for the additional 35 kits at $0.75 per kit, she earned $26.25. Adding these amounts, her total earnings are $76.25.

Explanation:

To calculate Ariane's earnings for assembling 135 craft kits, we need to consider two different pay rates: one rate for the first 100 kits and a higher rate for each kit above 100.

For the first 100 kits, she earns $0.50 per kit, which is 100 kits × $0.50/kit = $50. For the remaining 35 kits (135 total - 100), she earns a higher rate of $0.75 per kit, which is 35 kits × $0.75/kit = $26.25.

Now, we add both amounts to find the total earnings:

$50 (first 100 kits) + $26.25 (kits over 100) = $76.25 total earnings

Thus, Ariane earned $76.25 for assembling 135 craft kits this week.

Final answer:

The total number of miles Trip and Lindsey travel to and from school each week is 68 miles, determined by using the greatest common factor of 12 and 56, which is 4, and the distributive property to group and multiply the sum of the unit contributions by 4.

Explanation:

To find the total number of miles Trip and Lindsey travel to and from school each week using the greatest common factor (GCF) and the distributive property, we first identify the GCF of the two numbers. The GCF of 12 and 56 is 4. We can then apply the distributive property to factor out the GCF and write the equation as follows:

(3 + 14) × 4 = total number of miles traveled to and from school each week.

Trip contributes '3' units of the GCF and Lindsey contributes '14' units of the GCF. To find the total, we add 3 and 14 to get 17, and then multiply by the GCF:

17 × 4 = 68

Therefore, Trip and Lindsey travel a total of 68 miles to and from school each week.

The solution is : 4.75 as an improper fraction in simplest form is 19/4.

Here, we have,

given that,

4.75 as an improper fraction

we need to find the simplest form

we have,

4.75

= 4 75/100

= 475/100

= ( we can divide numerator and denominator by 25 )

=475/25 /100/ 25

= 19/4

[ in simplest form]

Answer:

4.75 as an improper fraction in simplest form is 19/4.

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The percent error in Mark's estimate to the nearest tenth of a percent is 6.9%.

Percentage is the ratio such that it can be expressed as a fraction of 100. Percentage is calculated by dividing the number with the whole and then multiplying by 100.

The symbol used to denote percentage is '%'.

Percent error is the absolute value calculated by finding the difference of the estimated value and the actual value and then dividing by the actual value followed by multiplication with 100.

Percent Error = [(Estimated value - Actual value) / Actual value] × 100

                      = [(15.5 - 14.5) / 14.5] × 100

                      = (1 / 14.5) × 100

                      = 6.897%

                      ≈ 6.9%

Hence, there is a 6.9% percent error in Mark's estimate if his estimated distance from his house to the school is 15.5 m and the actual distance is 14.5 m.

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The percent error in Mark's estimate is 6.9%.

To calculate the percent error, we use the formula:

[tex]\[ \text{Percent Error} = \left( \frac{\text{Estimated Value} - \text{Actual Value}}{\text{Actual Value}} \right) \times 100\% \][/tex]

Given the estimated distance is 15.5 mi and the actual distance is 14.5 mi, we can plug these values into the formula:

[tex]\[ \text{Percent Error} = \left( \frac{15.5 \text{ mi} - 14.5 \text{ mi}}{14.5 \text{ mi}} \right) \times 100\% \][/tex]

[tex]\[ \text{Percent Error} = \left( \frac{1 \text{ mi}}{14.5 \text{ mi}} \right) \times 100\% \][/tex]

[tex]\[ \text{Percent Error} \approx \left( \frac{1}{14.5} \right) \times 100\% \][/tex]

[tex]\[ \text{Percent Error} \approx 0.069 \times 100\% \][/tex]

[tex]\[ \text{Percent Error} \approx 6.9\% \][/tex]

Therefore, the percent error in Mark's estimate is approximately 6.9%.

D.) Quadrant lll or Quadrant IV

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Answer:

commutative property

Step-by-step explanation:

Given equation: [tex]\pi+10=10+\pi[/tex]

The property of real number used in this equation is Commutative property

Commutative property : A binary operation [tex]{\displaystyle *}[/tex] on a set   is commutative if  [tex]a {\displaystyle *}b= b{\displaystyle *}a[/tex]

Following this property  [tex]\pi+10=10+\pi[/tex]

Answer:

Szymborska's overall opinion of humanity in "A Contribution to Statistics" is overall positive

Step-by-step explanation:

Szymborska is a poet who likes to comment on society with irony and sarcasm.One example of this is when she splits people into categories in her poem “A Contribution to Statistics”. Here Szymborska’s overall opinion of humanity may seem negative due to her bluntness and dry humor. For example, she says in the tenth stanza, “cruel when forced by circumstances -better not to know even ballpark figures.” It’s implied in this line that most people (maybe even all)are cruel or can be. She also says, “taking only things from life -thirty”which comments how lots of people are selfish. However, this seemingly cynical poem takes a sweeter turn near the end with statistics like, “worthy of compassion - ninety-nine” and “mortal- a hundred out of a hundred.” These lines reveal that even though Szymborska believes that humanity is extremely flawed the mass majority of us deserve and are worthy of love. Plus the fact that we’re all mortal may seem dark but the fact remains that both the righteous and the sinners will all end up in the same place. The fact that no one can escape

death gives humans equality in a way. Szymborska’s overall opinion of humanity turned out to be more optimistic after all.