A circle has a circumference of 3.143.143, point, 14 units.
What is the diameter of the circle?
Use 3.14 for \piπpi and enter your answer as a decimal.

Answer:

Step-by-step explanation:

It will be 115$

Answer:  the answer is $21.7391304348 or round to $21.74 is the cost for 50 gallons

Step-by-step explanation: I did the calculations and it costs $2.30  a gallon

It takes 35 years for the population of West Fremont to double. We have the following condition;

West Fremont is a tiny town with 50,000 residents. If West Fremont experiences 2% growth. To solve the given case to get how long it takes for the population of West Fremont to double.

Here, we use the rule of 70 case. The rule of 70: By dividing the number 70 by the growth rate of the variable, the rule of 70 may be used to calculate how many years it will take for a variable to double.

According to the yearly rate of return, the rule of 70 is typically used to calculate how long it would take for an investment to double.

Doubling time = 70 / Growth rate                

= 70 / 2                        

= 35 years

So, it takes 35 years for the population of West Fremont to double.

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Answer:

11/36 = 0,305556 = 30,5556%

Step-by-step explanation:

5/6 * 5/6 = 25/36

36/36 - 25/36 = 11/36

Answer:

no because 60+48+36 is 144

Step-by-step explanation:

please mark brainliest

The total number of people is 144. The data is not consistent.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that at a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three.

The total number of the people in the party,

60+48+36 is 144

But it is given in the question that there are 100 in the party.

Therefore, the total number of people is 144. The data is not consistent.

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Answer:

f(f(x)) = [tex]x^{4}[/tex] + 2x² + 2

Step-by-step explanation:

to evaluate f(f(x)), substitute x = f(x) into f(x)

f(f(x))

= f(x² + 1)

= (x² + 1)² + 1 ← expand factor using FOIL

= [tex]x^{4}[/tex] + 2x² + 1 + 1

= [tex]x^{4}[/tex] + 2x² + 2

Answer:

[tex]f[f(x)]=x^4+2x^2+2[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=x^2+1[/tex]

To find the composite function f[f(x)], substitute the function f(x) in place of the x in function f(x):

[tex]\begin{aligned}\implies f[f(x)]&=f(x^2+1)\\&=(x^2+1)^2+1\\&=(x^2+1)(x^2+1)+1\\&=x^4+x^2+x^2+1+1\\&=x^4+2x^2+2\end{aligned}[/tex]

The first step is to find the increase in quantity.

The percentage increase is 10%.

From the information, the original quality is 1,500 and the new quality is 1,650.

The first step is to find the increase in quality will be:

= New quantity - Old quantity

= 1650 - 1500

= 150

The percentage increase will be:

= Increase / Old Quantity × 100

= 150 / 1500 × 100

= 10%

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Measurement of ∠ ABC is 90°

A linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

Given that ∠ CBD and ∠ ABC are linear pairs,

Therefore, m∠ CBD + m∠ ABC = 180°

m∠ ABC = 180° - 90° = 90°

Hence, Measurement of ∠ ABC is 90°

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The measured interior angles of the triangle are 40°, 60°, and 80° in ascending order.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

The triangle has interior angles are:

(2x)°, (3x)° and (4x)°

As we know that the sum of interior angles is 180 degrees in the triangle.

According to the given figure,

(2x)° + (3x)° + (4x)° = 180°

Apply the addition operation in the above equation,

9x = 180

x = 180/9

x = 20°

Thus, The triangle has interior angles are:

(2x)° = 2 × 20° = 40°

(3x)° = 3 × 20° = 60°

(4x)° = 4 × 20° = 80°

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The number of years to double the investment is 8.824 years.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

P = $3,900

R = 8%

n = 2

A = 2P = 2 x 3,900 = $7,800

Now,

A = P [tex](1 + r/n)^{nt}[/tex]

7,800 = 3,900 [tex](1 + 0.04)^{2t}[/tex]

78/39 = [tex](1.04)^{2t}[/tex]

2 = [tex](1.04)^{2t}[/tex]

Taking logs on both sides.

log 2 = 2t log(1.04)

0.30 = 2t x 0.017

0.30/0.017 = 2t

17.65 = 2t

Divide both sides by 2.

t = 17.65 / 2

t = 8.824 years.

Thus,

The number of years to double the investment is 8.824 years.

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Answers:

1st box:  0

2nd box:  67

===============================================

Explanation:

The y intercept always occurs when x = 0. This is when the function curve either crosses or touches the vertical y axis. Therefore, the y intercept is when the student studies 0 hours

Plug x = 0 into the equation

y = 2.7x + 67

y = 2.7*0 + 67

y = 67

Or you can note that the equation is of the form y = mx+b

The y-intercept of 67 tells us that the person studying for 0 hours is estimated to get a score of 67

If the child's weight is 60 pounds , then the doctor will prescribe 12 milliliter of medicine .

In the question, '

it is given that

the for every 25 pounds of weight 5 milliliter of pain reliever is required .

we need to find the amount of medicine for the child weighing 60 pounds

So , for 25 pounds =  5 milliliter is needed

for 1 pound = 5/25 ml is needed

hence for 60 pound = 60*(5/25) ml will be prescribed .

on simplifying further ,

we get

= 60*(5/25)

= 60*(1/5)

= 12 ml

Therefore , the doctor will prescribe 12 ml of medicines .

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The lengths of the piece she should cut is = 3  2/3

acc to our question-

hence,The lengths of the piece she should cut is = 3  2/3

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Thus, the number of ways in which  to choose 4 letters, without replacement, from 17 distinct letters is 57,120.

Total distinct letters are 17.

There are 17 alternatives for the initial letter if there are 17 letters.

There are just 16 alternatives left once you remove the letter.

Each time you remove a letter, the bag contains one fewer letter.

Number of ways = 17 x 16 x 15 x 14

Number of ways =  57,120

Thus, if the sequence of the alternatives is irrelevant, there are 57,120 options.

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The equation of the absolute value function graph is: y = |x - 3| + 5.

The equation of the absolute value function can be written in the vertex form as y = a|x – h| + k, where:

From the given graph, we have the following:

(h, k) = (3, 5) [the vertex]

Substitute the values into the equation, y = a|x – h| + k:

y = a|x - 3| + 5

A point on the graph is (2, 6). To find the value of a, substitute (x, y) = (2, 6) into y = a|x - 3| + 5:

6 = a|2 - 3| + 5

6 = a|-1| + 5

6 = a + 5

6 - 5 = a

1 = a

a = 1

To write the equation of the graph, substitute a = 1 into y = a|x - 3| + 5:

y = 1|x - 3| + 5

y = |x - 3| + 5

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Step-by-step explanation:

remember, the circumference of a circle is

2×pi×r

and that is for the full 360° of a circle.

how long will the arc length of 1° be ?

well,

2×pi×r / 360

and how long will the arc length of 78° be ?

well,

78 × 1° = 2×pi×r × 78/360

you see ? that is the whole trick ...

now we only need to enter the value for r (radius).

and that is GH = 9 units.

so, the length of the arc GJ is

2×pi×9 × 78/360 = 2×pi × 78/40 = pi × 78/20 =

= 12.25221135... ≈ 12.25 units

Sheri should invest $2000 in mutual fund and $13,200 in bond.

Let the amount to be invested in mutual fund be x. So, the amount to be invested in bond will be (15,200 - x). Forming the equation now -

1%×x + 4%×(15,200 - x) = 548

x/100 + 60,800/100 - 4x/100 = 548

60,800 - 3x = 54800

3x = 60800 - 54800

3x = 6000

x = 6000 ÷ 3

x = 2000

Amount to be invested in mutual fund = $2000

Amount to be invested in bond = 15,200 - 2000

Amount to be invested in bond = $13,200

Sheri should invest $2000 and $13,200 in mutual fund and bond respectively.

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Answer:

2,156 A. 21.56

Step-by-step explanation:

Hours taken by Bob and Bill if they work together is 3 1/13.

Here it is given that Bob can do a job in 5 hours and Bill can do the job in 8 hours.

We have to find the time taken by both to do the work if done together.

Time ratio of Bob and Bill = 5: 8

Efficiency of Bob and Bill = 8: 5

Total amount of work done = 5× 8 = 8× 5 = 40

The total efficiency of Bob and Bill = 13

Hours took by both bob and bill to do the work if done together = 40/13

                                                                                                              = 3 [tex]\frac{1}{13}[/tex]

Therefore the work done together is 3 [tex]\frac{1}{13}[/tex] hours.

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Answer:

2.5√2 units

Step-by-step explanation:

The shortest distance between a point and a line is the length of the line segment perpendicular to the line and passes through the given point.

~~~~~~~~~~~~~~~~~~~~~    

y = - x + 5 , slope m = - 1

Slope of perpendicular line is opposite reciprocal. In our case is 1 .

G ( 6 , 4 )

y - 4 = 1 × ( x - 6 )

y = x - 2

x - 2 = - x + 5 , x = 3.5

y = 1.5  

Perpendicular line intersect the given line at the point O ( 3.5 , 1.5 )

OG = [tex]\sqrt{(6-3.5)^2 +(4-1.5)^2 }[/tex] = 2.5√2 units

A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat  lowest cost is at (x,y) is (3,2).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given,

Function:

C = x + 1.5y

Subjected to:

30x + 20y ≥ 13/10 ×100 ≥ 130

10x + 4y ≥ 1/5 × 100 ≥ 20

50x + 75y ≥ 3 × 100 ≥ 300

Feasible region:

(0, 13/2), (3,2) (6,0)

C = x + 1.5y

(0, 13/2) ⇒ C = 0+ (1.5)(13/2)

(0.13/2) ⇒ C = 9.75

(3,2) ⇒ C = 3+ (1.5)(2)

(3,2) ⇒ C = 6

(6,0) ⇒ C = 6 + 0

(6,0)⇒ C = 6

A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat  lowest cost is at (x,y) is (3,2).

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Answer:

hmmm say 5)13

Step-by-step explanation:

i can't explain it

The equation of the line is y = (-3/5)x + 16

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line is given by:

y = mx + c

The line passes through:

(-5, 19) and (5, 13)

So,

m = (13 - 19) / (5 + 5)

m = -6/10

m = -3/5

Now,

(5, 13) = (x, y)

13 = (-3/5) x 5 + c

13= -3 + c

13 + 3 = c

c = 16

Now,

y = mx + c

y = (-3/5)x + 16

Thus,

The equation of the line is y = (-3/5)x + 16

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The simplest radical form of  √(11/(x + 4)) when x is 16 is; ¹/₁₀√55

Surds are actually the expressions of the number, and often use radicals. Meanwhile, the radical is just the symbol used to express the square root.

We are given the expression of the surd as;

√(11/(x + 4))

We want to solve this for when x = 16. Thus, we plug in 16 for x in the surd to get;

√(11/(16 + 4))

= √(11/20)

Now, we can rewrite the fraction in the bracket to have the denominator as a perfect square by multiplying both numerator and denominator by 5 to get;

√(55/100)

Square root of 100 is 10 and as such we now have;

√(55/100) = ¹/₁₀√55

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Answer:

[tex]r = 2279.41[/tex]

There was 110%  percent increase in the number of visitors.

Percent:

Basically, percentage refers the number or ratio that can be expressed as a fraction of 100.

Given,

p x 3,700=4,070

There was a % percent increase in the number of visitors.

Here we need to find the increase in the percentage.

While we looking into the given question we have identified that,

The Old population = 3700

And the new population  = 4070

So, the value of P is calculated as,

=> p = 4070/3700

=> p = 1.1

When we convert this into percent then we get 110% as increase.

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The mean of the distribution is 24.444.

Given, that 87.3% of all homes have a large-screen tv. a sample of 28 homes is selected.

Now, we have to find the mean of the distribution

As, we know

E(x) = np

where, n is the sample and p is the probability of success

So, n = 28 and p = 87.3% = 0.873

Now, on using the formula we get,

E(x) = (28)(0.873)

E(x) = 24.444

So, the mean of the distribution is E(x) = 24.444

Hence, the mean of the distribution is 24.444.

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The probability of a foot of male being between 10 and 12. 5 inches is 59%.

The z score of the distribution is found as-

z = (x - μ)/σ

In which,

μ = mean = (11)

σ = standard distribution (1.5)

The likelihood that a male's foot measures between 10 and 12. 5 inches.

P(10 < x < 12.5)

For x = 10

z = (10 - 11) / 1.5

z = -0.67

check the p-value fro z score table.

p (z = -0.67) = 0.2514

For x = 12.5

z = (1.5 - 11)/1.5

z = 1

p (z = 1) = 0.8413

P(10 < x < 12.5)  = 0.8413 - 0.2514

P(10 < x < 12.5)  = 0.5899

P(10 < x < 12.5)  = 58.99%

P(10 < x < 12.5)  = 59%.

Thus, the likelihood of a male's foot being between 10 and 12. 5 inches is 59%.

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The complete question is attached in figure.

Answer:

2.5991  <  3.7  <  3.706  <  3.76

Step-by-step explanation:

Answer:

235

Step-by-step explanation:

When estimating the product of two decimals, first round the decimals to their nearest whole numbers.

Therefore,

So an estimate of the product of the two decimals is:

[tex]\implies 4.8 \times 47.1 \approx 5 \times 47[/tex]

Partition 47 into tens and units:

[tex]\implies 5 \times 47 = 5 \times (40 + 7)[/tex]

Apply the distributive property of multiplication over addition:

[tex]\begin{aligned}\implies 5 \times (40 + 7) &= (5 \times 40) + (5 \times 7)\\&=200+35\\&=235\end{aligned}[/tex]

Therefore:

[tex]\boxed{4.8 \times 47.1 \approx 235}[/tex]

Sarah can run = 100 metres.

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