Social Science predicts that the population of barre, Vermont will double every 54 years. If the population in 1974 was 56000, in what year should we expect the population to reach 71000

For each birdhouse built, the total cost increases by $3.50.

The number 3.5 multiplies b, so when b increases by 1, f(b) increases by 3.5. Making 1 more birdhouse increases the total cost by $3.50.

Answer: For each birdhouse built, the total cost increases by $3.50.

Step-by-step explanation:

Given: The total cost for Sophia to build b birdhouses is represented by the function [tex]f(b)=3.5b+24[/tex]

We can see in the function 3.5 is multiplied to b, so when b increases , f(b) increases by 3.5.

[tex]f(1)=3.5(1)+24=3.5+24=27.5[/tex]

[tex]f(2)=3.5(2)+24=7+24=31[/tex]

[tex]f(3)=3.5(3)+24=10.5+24=34.5[/tex]

and [tex]f(2)-f(1)=f(3)-f(2)=3.5[/tex]

Therefore, the value of 3.5 represents that for each birdhouse built, the total cost increases by $3.50.

Answer:

41

Step-by-step explanation:

If you work through a series of obscure calculations involving area and the radius of the incircle, they boil down to a simple fact:

... For MN║BC, perimeter ΔAMN = perimeter ΔABC - BC = AB+AC

.. = 17+24 = 41

_____

Wow! Thank you for an interesting question with a not-so-obvious answer.

_____

A little more detail

The point I that you have defined is the incenter—the center of an inscribed circle in the triangle. Its radius is the distance from I to any side, such as BC, for example.

If we use "Δ" to represent the area of the triangle and "s" to represent the semi-perimeter, (AB+BC+AC)/2, then the incircle has radius Δ/s. The area Δ can be computed from Heron's formula by ...

... Δ = √(s(s-a)(s-b)(s-c)) . . . . where a, b, c are the side lengths

For this triangle, the area is Δ = √38480 ≈ 196.1632 units². That turns out to be irrelevant.

The altitude to BC will be 2Δ/(BC), so the altitude of ΔAMN = (2Δ/(BC) -Δ/s). Dividing this by the altitude to BC gives the ratio of the perimeter of ΔAMN to the perimeter of ΔABC, which is 2s.

Putting these ratios and perimeters together, we get ...

... perimeter ΔAMN = (2Δ/(BC) -Δ/s)/(2Δ/(BC)) × 2s

... = (2/(BC) -1/s) × BC × s = 2s -BC

... perimeter ΔAMN = AB +AC

The perimeter of triangle AMN is found using the angle bisector theorem to determine the lengths of AM and AN, and recognizing that MN = BC due to the parallelism. After calculating, the approximate perimeter of triangle AMN is found to be 54.86.

In triangle ABC, the angle bisectors BD and CE intersect at I. A line through I parallel to BC intersects AB at M and AC at N. Perimeter of triangle AMN is found by adding lengths AM, MN, and NA. Since IM is parallel to BC and bisectors divide the angles proportionally, we have:

AM/AB = AI/AD, where D is the intersection of angle bisector BD with BC.

AN/AC = AI/AD, using similar logic.

MN is parallel to BC, so MN = BC due to the properties of parallelograms.

Using AB = 17, AC = 24, and BC = 33, find AM and AN using the proportional segments:

AM = (AI/AD) * AB

AN = (AI/AD) * AC

The perimeter of triangle AMN is AM + MN + AN.

To solve for AI/AD, we use the angle bisector theorem which gives us AI/AD = AB/BC = 17/33. Substituting this into the equations for AM and AN we get:

AM = (17/33) * 17

AN = (17/33) * 24

Computing these we find:

AM = 8.77 (approximately)

AN = 13.09 (approximately)

Lastly, we add AM, AN, and BC to find the perimeter:

Perimeter = AM + AN + MN

Perimeter = 8.77 + 13.09 + 33 = 54.86 (approximately)

This is the approximate perimeter of triangle AMN.

Answer: They are fed 4/9 of what the polar bears are fed.

Step-by-step explanation:

7/9*4/7=

1/9*4/1=4/9

The 7's get cancelled out.

The penguins at the zoo are fed 4/9 bucket of fish a day. This fraction has been calculated by multiplying the amount of food the polar bears get (7/9 bucket) by 4/7 as specified in the problem.

To find out how much the penguins are fed, we first understand the given units involving the polar bears and penguins. The polar bears are fed 7/9 bucket of fish a day, and the penguins are fed 4/7 that amount. Therefore, to calculate the amount the penguins are fed, we multiply the amount the polar bears are fed by 4/7.

We get this by performing the calculation (7/9) * (4/7). The sevens cancel out, leaving us 4/9, which is the fraction of the bucket of fish that the penguins are fed each day.

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The radius of a circular ring is 4 feet. What is the circumference?

Answer: D.) 25.12 feet

Step-by-step explanation:

We apply the formula to calculate the circumference knowing the radius. We consider π = 3.14

C = 2 x π x Radius = 2 x 3.14 x 4 feet = 25.12 feet

Answer : D.) 25.12 feet

[tex]\textit{\textbf{Spymore}}[/tex]

The circumference of the circle is  25.12 feet.

The radius of a circular ring is 4 feet.

We have to determine the circumference

We apply the formula to calculate the circumference by knowing the radius.

We consider π = 3.14

C = 2 x π x Radius

use the given values in the above formula so we get,

C= 2 x 3.14 x 4 feet

C= 25.12 feet

Therefore option D is correct.

The circumference of the circle is  25.12 feet.

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c. Both A and B

A function is a mapping that maps each element of its domain (student's name) to exactly one element of its co-domain (favorite ...). Assuming student names are unique and the notion of "favorite" is exclusive (can't have two or more "favorites" of the same type), then both A and B describe mappings that are functions.

Answer:

c. Both A and B

Step-by-step explanation:

A function means each input  goes to only one output.  As long as each student is only entered once,  and they only have one favorite color and one favorite math teacher, then A and B are functions.

Answer:

 b.) and Kyle traveled 185 miles

Step-by-step explanation:

x+240=425

 -240  -240

x=185

The question is about simple subtraction in mathematics. Given that Kyle and Tyler together traveled 425 miles and Kyle traveled 240 miles, we use subtraction to find out that Tyler traveled 185 miles.

This is a classic problem of simple subtraction in mathematics. Given, Kyle and Tyler together traveled 425 miles. Now, if Kyle traveled 240 miles, Tyler must have covered the remaining distance. So, to find out how far Tyler traveled, subtract the distance that Kyle traveled from the total distance. This is represented by the equation (option B) x + 240 = 425, where x represents the distance that Tyler traveled. Solving this equation for x will give you the answer.

Setup the equation: x + 240 = 425

Subtract 240 from both sides: x = 425 - 240

This results in x = 185, meaning Tyler traveled 185 miles.

Answer:

25

Step-by-step explanation:

You must divide 75/3. This is because for every 3 hours, there is a distace of 75 miles. You have to find out his average speed by finding his distance each hour. 75/3 is 25.

Answer:  The average speed of Rohit is 25 miles per hour.

Step-by-step explanation:  Given that Rohit drove around the city for 3 hours and he traveled a total distance of 75 miles.

We are to find Rohit's average speed.

We know that

[tex]speed =\dfrac{distance}{time}.[/tex]

For the given situation, we have

distance, d = 75 miles  and  time, t = 3 hours.

So, the average speed of Rohit is given by

[tex]S=\dfrac{d}{t}=\dfrac{75}{3}=25.[/tex]

Thus, the average speed of Rohit is 25 miles per hour.

Find the x and y for each dot:

5,35

10,70

15,105

etc.

Divide the Y by the X:

35 / 5 = 7

70 / 10 = 7

etc.

The answer would be C) y = 7x

Answer:

Option C is correct

[tex]y = 7x[/tex]

Step-by-step explanation:

Direct variation states that:

[tex]y \propto x[/tex]          ......[1]

then, the equation is in the form of:

[tex]y=kx[/tex], where k is the constant of variation

From the given graph we have points in the form of (x, y) i.e,

(0, 0), (5, 35), (10, 70), (15, 105), (20, 140), (25, 175) and (30, 210)

Substitute any points i.e (5, 35) in [1] we have;

[tex]35 = 5k[/tex]

Divide both sides by 5 we have;

7 = k

or

k = 7

then;

[tex]y = 7x[/tex]

Therefore, the constant of  proportionality for the graph is, 7 and its form is, [tex]y = 7x[/tex]

y = 21·0.7^x

The pair (0, 21) tells you the multiplier is 21. (The exponential factor is 1 for x=0.)

Any adjacent pair of y-values can tell you the common ratio, hence the base of the exponential term. For example, using the y-values associated with x=0 and x=1, we find the base to be ...

... 14.7/21 = 0.7

Then the equation is ...

... y = multiplier · base^x

... y = 21·0.7^x

5/2

The ratio of perimeters is the same as the ratio of corresponding sides:

... (140 cm)/(56 cm) = 5/2

Answer:

5:2

Step-by-step explanation:

We have been given that triangles △ABC and △DFG are similar. The lengths of the two corresponding sides are 1.4 m and 56 cm.

Since both triangles are similar, therefore all corresponding sides will have same proportion.

Let us find proportion of corresponding sides of both triangles.

1 meter = 100 centimeter

1.4 meter = 1.4* 100 centimeters = 140 centimeters.

[tex]\frac{\text{Side of triangle ABC}}{\text{Side of triangle DFG}}=\frac{140}{56}[/tex]

[tex]\frac{\text{Side of triangle ABC}}{\text{Side of triangle DFG}}=\frac{5}{2}[/tex]

The ratio of sides of △ABC to sides of△DFG is 5:2.

Since perimeter of a triangle is sum of lengths of three sides of the triangle and all sides of both triangle have the ratio 5:2, therefore, their perimeters will be in same ratio, that is 5:2.

Answer:

Null Hypothesis : The true mean height of children is more than 60 inches.

Step-by-step explanation: Null Hypothesis is defined as a hypothesis that there is no significant difference between the observed and sampled mean.

So, if alternative hypothesis is " the true mean height of children is less than 60 inches" which denotes there is significant difference between sampled and observed mean heights so null hypothesis is taken as " true mean height of children is more than 60 inches"

Answer:

1. x =8

2.  x=9

Step-by-step explanation:

Since these figures are parallelograms, the opposite sides are equal.

1.     6 = 2x-10

Add 10 to each side

   6+10 = 2x-10+10

   16 = 2x

Divide  each side by 2

16/2 = 2x/2

 8 =x

2.  x+14 =23

    Subtract 14 from each side

x+14-14 = 23-14

x = 9

Final answer:

To convert 8 3/4% to a fraction, you transform the mixed number into an improper fraction, which equals 875%. Then, scale it by dividing by 100 to get 8.75%, and express this as 8.75/100. Simplify by dividing numerator and denominator by 25 to finally get 7/16.

Explanation:

To express 8 3/4% as a fraction, we first convert the mixed number to an improper fraction. There are 4 quarters in a whole, so 8 3/4 is the same as 8 + 3/4, which equals 35/4. To convert this into a percent, we need to consider that 1 whole is the same as 100%, so 35/4 as a percent is 35/4 * 100%. Simplifying this, we multiply 35 by 25 (100% divided by 4), which gives us 875%. Since we want to express 8 3/4%, not 800 3/4%, we divide by 100 to get back to the correct scale. So, 875% divided by 100 is 8.75%, which is the same as 8 3/4%.

Now, to convert 8.75% to a fraction, we can write it as 8.75/100. To simplify this fraction, we recognize that both the numerator and the denominator are divisible by 25. Dividing both by 25, we get 7/4 divided by 1 which simplifies to 7/4 divided by 100/25. This simplifies to 7/4 * 25/100, which equals 7/16 when simplified.

Thus, 8 3/4% as a fraction is 7/16.

Answer: The correct answer would be D: Model J

Step-by-step explanation:

For there are 3 segments in each box and 3 boxes are shaded leaving only 2 unshaded :)

Answer:

D. Model J

Step-by-step explanation:

Answer:

Republican residents of County 1:  

10.1 %  

Democratic residents of County 1:  

16.5 %

Total Republican residents:  

58.9 %

Total Democratic residents:  

41.1 %

Step-by-step explanation:

Answer:

Question 1)

Republican residents of County 1: (10.1)

Question 2)

Democratic residents of County 1: (16.5)

Question 3)

Total Republican residents: (58.9)

Question 4)

Total Democratic residents: (41.1)

Answer:

The answer is 96 when X= 8

Step-by-step explanation:

We have given that :

AE= [tex]x^2-16[/tex]  and CE=[tex]6x[/tex]

where AE and CE are the diagonals of the paralleogram

The diagonals of parallelogram bisect each other therefore,

 [tex]x^2-16 = 6x[/tex]

⇒ [tex]x^2-6x-16=0[/tex]

factors are (x+2)(x-8)=0

setting to each factor 0 the value of x= -2 or x= 8

therefore, two values of AC is

X= -2  ,AC= 2([tex]x^2-16[/tex])=2(-12)=-24

X= 8 ,AC= 2([tex]x^2-16[/tex])=2(48)=96

The answer is 96 when X= 8

∠K = ∠N = 60°

∠L = ∠M = 120°

In the attached, we have renamed F to G so Brainly will let us talk about it more easily. We have also added altitude MX.

AG is also a midsegment of ΔKLM, so LM = 2×AG = 4. Then ...

... NX = AB - LM = 7 -4 = 3

and we have right ΔMXN with hypotenuse 6 and leg 3. This is recognizable as a 30°-60°-90° triangle, with the 60° angle at N.

The angle at M is supplementary to that at N (because LM ║ KN), so measures 120°

The trapezoid is isosceles, so angles K and L have the same measures as angles N and M.

[tex]\mathsf{We\;know\;that : \dfrac{a^m}{a^n} = a^m^-^n}[/tex]

[tex]\mathsf{Given : \dfrac{3^-^8}{3^-^4}}[/tex]

[tex]\mathsf{\implies 3^-^8^+^4}[/tex]

[tex]\mathsf{\implies 3^-^4}[/tex]

[tex]\mathsf{\implies \dfrac{1}{3^4}}[/tex]

[tex]\mathsf{So,\;The\;Given\;Expression\;can\;be\;written\;as : 3^-^4\;(or)\; \dfrac{1}{3^4}}[/tex]

Answer:

No it is not.

Step-by-step explanation:

Answer:

I got 4 hours and 16 minutes

Step-by-step explanation:

I divided the amount of money he has ($26) to the amount it takes to rent for one hour ($6.25). To make it more simple you could just say 4 hours worth of rent.

Answer:

Step-by-step explanation:

Since Kevin only has $26 and the bicycle rends for $6.25 per hours this means that:

6.25h ≤ 26

Where h represents hours $6.25 is the slope (rate) at which Kevin is being charged and $26 is the amount of money he has.

By solving for the inequality above we obtain:

[tex]6.25h\leq 26\\\\\fra{6.25h}{6.25}\leq \frac{26}{6.25}\\\\h\leq4.16[/tex]

This means that Kevin can ride the bike for less than or equal to 4.16 hours.  Now that means 4 hours and 16% of an hour, let's calculate what 16% of an hour is equal to.  Since we know that there are 60 minutes in an hour and 16% is 0.16 (since 16÷100=0.16) in decimals we obtain:

60×0.16=9.6 minutes

This means 9 minutes and 60% of a minute, so we will calculate how much is 60% of a minute:

60×.6=36 seconds

Therefore, Kevin can ride this bike for less than or equal to 4 hours 9 minutes and 36 seconds.

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3 11/15 cm

AE is the angle bisector of ∠A, so divides the sides of the triangle into a proportion:

... BE:CE = BA:CA = 7:8

Then ...

... BE:BC = 7 : (7+8) = 7:15

ΔDBE ~ ΔABC, so DE = 7/15 × AC

... DE = 7/15 × 8 cm = (56/15) cm

... DE = 3 11/15 cm

To find the side of the inscribed rhombus, we can use the Pythagorean theorem and the properties of inscribed rhombuses.

To find the side of the rhombus, we need to understand the properties of inscribed rhombuses. In an inscribed rhombus, the diagonals are perpendicular bisectors of each other.

Let's label the side of the rhombus as 's'.

Using the given information, we can see that AB and AC are the diagonals of the rhombus.

Since AB = 7 cm and AC = 8 cm, we know that the diagonals bisect each other and form right angles.

Therefore, we can use the Pythagorean theorem to find the side of the rhombus:
s^2 = (AB/2)^2 + (AC/2)^2
s^2 = (7/2)^2 + (8/2)^2
s^2 = (49/4) + (64/4)
s^2 = (113/4)
s = sqrt(113/4)

The range is [minimum y-value, maximum y-value), so the range expression tells you directly what those values are.

For the function described, with range [1, ∞), ...

... minimum y-value = 1

... maximum y-value = infinity

6 cm, 8 cm, 12 cm

The perimeter of the reference triangle is  ...

... (15 +20 +30) cm = 65 cm

Then the similar triangle has a scale factor of ...

... (26 cm)/(65 cm) = 2/5

Multiplying the side lengths of the reference triangle by 2/5, we get ...

... {15 cm, 20 cm, 30 cm) × 2/5 = {6 cm, 8 cm, 12 cm}

These are the side lengths of the smaller similar triangle. (Check: their sum is 26 cm.)

Answer:

1/92

Step-by-step explanation:

There are C(3, 2) = 3 ways to select 2 jelly-filled donuts from the 3 in the box. There are C(24, 2) = 276 ways to select 2 donuts from the box.

The probability that you will select 2 jelly-filled donuts is ...

... 3/276 = 1/92

_____

C(n, k) = n!/(k!(n-k)!)

C(3, 2) = (3·2)/2 = 3

C(24, 2) = (24·23)/2 = 276

To determine the number of ways to choose two students to go first and second in a group of 17 students, we use permutations, resulting in a total of 17 * 16 = 272 ways.

The question inquires about the number of ways two students can be chosen from a group of 17 to go first and second in a spelling bee, which can be solved using combinatorics.

To choose the first student, we have 17 options. After choosing the first student, we have 16 remaining students to choose from for the second student. Therefore, the total number of ways to choose students for these two positions is the product of these two numbers. This scenario calls for a permutation calculation since the order in which we select the students matters.

The formula is n!/(n-r)!, where n is the total number of items to pick from, and r is the number we are picking. For our case, n = 17 and r = 2.

Total number of ways (permutations) = 17 * 16 = 272 ways.

C. 4(x-3)-x

All of the given expressions are equivalent to 3x+12 except selection C. Using that in your equation makes it be ...

... 3(x +1) +9 = 4(x -3) -x

... 3x +12 = 3x -12

... 12 = -12 . . . . . false

There is no value of x that will make this true, hence NO SOLUTION.

_____

Comment on the other choices

3x+12 = 3x+12 has an infinite number of solutions, as any value of x will make this true.

c

BECAUSE I SAID SO HUH YOU GOTTA PROBLEMO??

[tex]9.36\cdot10^4=9.36\cdot10,000=93,600[/tex]

Answer: 45

Step-by-step explanation:

Divide 90 by 2 and you will the the answer of 45.