What is the length of the midsegment of the trapezoid made by the vertices A(0, 5), B(3, 3), C(5, -2) and D(-1, 2). Show equations and all work that leads to your answer.
Answers
Answer:
[tex]\frac{3\sqrt{13} }{2}[/tex]
Step-by-step explanation:
First we have to identify the parallel sides of the trapezium.
We know that the slopes are equal for parallel lines.
Slope of (x₁,y₁) and (x₂,y₂) is given by
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Slope of AB:
[tex]m_{AB} = \frac{3-5}{3-0}=-\frac{2}{3}[/tex]
Slope of BC:
[tex]m_{BC} = \frac{-2-3}{5-3}=-\frac{5}{2}[/tex]
Slope of CD:
[tex]m_{CD} = \frac{2+2}{-1-5}=-\frac{4}{6}=-\frac{2}{3}[/tex]
Slope of DA:
[tex]m_{DA} = \frac{2-5}{-1-0}=3[/tex]
We see that the slopes of AB and CD are equal, so, AB and CD are the parallel sides.
The length of the midsegment = (1/2)*(length of base1 + length of base2 )
Length of the bases can be calculated using distance formula,
[tex]d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
AB = [tex]\sqrt{(3-0)^{2}+(3-5)^{2}}= \sqrt{9+4} =\sqrt{13}[/tex]
CD = [tex]\sqrt{(-1-5)^{2}+(2+2)^{2}}= \sqrt{36+16} =\sqrt{52}=2 \sqrt{13}[/tex]
Length of the midsegment = (1/2) (√13 + 2√13) =3√13/2
Related Questions
9/10? of alien races think invading Earth is a bad idea. What percent of alien races think invading Earth is a bad idea?
Answers
Answer:
90%
Step-by-step explanation:
We are told that 9/10 of alien races think invading Earth is a bad idea.
To find the percent of alien races that think invading Earth is a bad idea we will have to find 9 is what percent of 10.
[tex]\text{The percentage of alien races that think invading Earth is a bad idea}=\frac{9}{10}\times 100[/tex]
[tex]\text{The percentage of alien races that think invading Earth is a bad idea}=9\times 10[/tex]
[tex]\text{The percentage of alien races that think invading Earth is a bad idea}=90[/tex]
Therefore, 90% of alien races think invading Earth is a bad idea.
90%
Step-by-step explanation:
mark me branilest
Identify the values of the variables. Give your answers in simplest radical form. HELP PLEASE!!!
Answers
Answer: [tex]\bold{(A): g=\dfrac{\sqrt{15}}{2},\quad h=\dfrac{\sqrt{5}}{2}}[/tex]
Step-by-step explanation:
This is a special triangle because the side lengths have the following relationship:
30° ⇄ side length "a" represented as "h" in your picture
60° ⇄ side length "a√3" represented as "g" in your picture
90° ⇄ side length "2a" represented as "√5" in your picture
Step 1: solve for "a" hypotenuse (2a) is given as √5
[tex]2a=\sqrt{5}[/tex]
[tex]a=\dfrac{\sqrt{5}}{2}[/tex]
According to your picture, a = h, so [tex]h=\dfrac{\sqrt{5}}{2}[/tex]
Step 2: use the a-value from Step 1 to solve for the remaining side
[tex]g=a\sqrt{3}[/tex]
[tex]=\bigg( \dfrac{\sqrt{5}}{2}\bigg)\sqrt{3}[/tex]
[tex]=\dfrac{\sqrt{15}}{2}[/tex]
Sal recorded the number of crackers in each snack-sized package he opened. Which statement must be true according to the box plot? The data is symmetric, and the lowest number of crackers in a package was 7. The data is symmetric, and the lowest number of crackers in a package was 8. The data is skewed, and the lowest number of crackers in a package was 7. The data is skewed, and the lowest number of crackers in a package was 8.
Answers
Answer:
The data is skewed, and the lowest number of crackers in a package was 7
Step-by-step explanation:
Hi,
First of all, since the question was incomplete due to the missing capture of the range shown on the box plot. I attached it for you so I could answer your question as well.
Taking into consideration the attached image's information, symmetric would be right down the middle, but it is not.
The image shows that it is positively skewed with the lowest number being 7.
Answer:
c
Step-by-step explanation:
did it on edge
Pants $80 buy one at regular pric. Get a second one for half price. (How much for 2 pair?)
Answers
Answer:
$200 will be price of 2 pairs
Step-by-step explanation:
It is given that the price of one pant is $80
The second is given at half price which is $40
but in the case of pants buying or anything buying when we are given an off then after buying an item the same discount is given for all
so as he bought one pant then the other pant will be given at half price
now the third pant will also be given at half price i.e: $40
fourth price will also be given at $40
so four pants will become 2 pairs
price of 2 pairs = $80+$40+$40+$40
=$200
An insurance policy pays 80% of the first $20,000 of a patient's medical expenses, and 60% of the remainder. If the patient's total medical bill is $72,000, how much will the policy pay?
Answers
In the described insurance policy, 80% of the first $20,000 is covered, which is $16,000. The remaining amount from the total cost of $72,000 is $52,000, of which 60%, or $31,200, is covered. Therefore, the total amount paid by the insurance policy is $47,200.
Explanation:The subject is dealing with a situation of an insurance coverage. The insurance policy pays 80% from the first $20,000 and 60% from the remaining amount of the medical bill. If the total amount of the medical bill is $72,000, we have to find out how much would the policy pay.
First, calculate 80% of the first $20,000: (80/100) * 20,000 = $16,000. The remainder of the medical bill above $20,000 would be $72,000 - $20,000 = $52,000. Then, calculate 60% of this remaining $52,000: (60/100) * 52,000 = $31,200. Finallly, add the two amounts, $16,000 + $31,200 = $47,200.
So, the insurance policy will pay $47,200 towards a total medical bill cost of $72,000.
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Please help! Need answered! Please and thank you.
Answers
Answer:
1. lim x→0 7e^x =7
2. lim f(x) does not exist
f(3) = 5
3. 1/12
Step-by-step explanation:
f(x) = 7e^x
lim x→0 7e^x =7
AS we can see from the graph it is around 7
We know that e^0 =1 so 7*1 =7
2. The limit does not exists, because approaching the limit from the left f(3-) is 3. Approaching the limit from the right f(3+) is 5. f(3) = 5 since there is a closed circle at 3 with a value of 5.
3. f(x) = x^ 1/2
We take the derivative
f'(x) = 1/2 x^ (-1/2)
= 1/2 1/( x^.5)
To find it at x=36
= 1/2 * 1/( 36^.5)
= 1/2 * 1/6
= 1/12
Since they are not equal, the limit does not exist.
Which expression is equivalent to 5x - 5x + 3x - 3x?
A) -16x
B) -4x
C) 4x
D) 0
what the answer
Answers
the answer is 0
which is d
paris run 3 1/2 laps around the circular track in the school gym. The track has a diameter of 1/2 mile. About how far does paris run?
Answers
Answer:
5.497787144 miles
Step-by-step explanation:
Remember that circumference of a circle can be calculated with:
[tex]2\pi r[/tex]
r=radius
We also know that the radius is just a half of the diameter.
So, the radius of the track is (1/2)/2=1/4 miles
Now, use the circumference of a circle formula to find how much she runs in 1 lap.
[tex]2\pi (\frac{1}{4} )[/tex]
Simplify
[tex]\frac{\pi }{2}[/tex]
This is how much she runs in 1 lap.
Multiply by 3.5 for 3 and a half laps.
[tex]\frac{\pi }{2}*3.5[/tex]
The answer is around 5.497787144 miles.
Please answer this question too! :D
Answers
Answer:
A
Step-by-step explanation:
We can find the surface area of the object by adding the surface areas of each part. We have many rectangle faces to count and two triangular faces. Each has a formula for the area. We will find the area of each and then add them all together.
Triangle - 0.5 *b*h
Rectangle - b*h
Triangles
There are two triangles on either side. The height is 1.5. The base is 1.8.
0.5(1.5)(1.8)=1.35 meters squared
Since there are two, we will add 1.35+1.35 in our final calculation.
Rectangles
We will start by calculating the largest rectangle on the side. It has height of 4 and a base of 2.5 (shown above left).
4(2.5)=10
Since there are two (one we can see and one we can't), we will add 10+10 in our final calculation.
Next we calculate the top and bottom. The height is 3 and the base is 2.5 on top. But the bottom sticks out more and adds 1.8 to its base.
Top - 3(2.5)=7.5
Bottom-3(2.5+1.8)=12.9
Finally, we will calculate the front side and back(not visible) as well as the slant up front. The back side has height 4 and base 3. The front side has base 3 and height 4-1.5=2.5. The slant has base 2.3 and height 3.
Back - 4(3)=12
Front- 3(2.5)=7.5
Slant - 3(2.3)=6.9
We add all together for the total surface area: 1.35+1.35+10+10+7.5+12.9+12+7.5+6.9=69.5 meters squared.
Kevin is riding his bike to work. He can bike 6 1/2 kilometers in 3/5 of an hour. How many kilometers can Kevin bike in one hour?
Answers
Answer:
If Kevin can ride 13/2 kilometers in 3/5 of an hour then he can ride 13/6 in 1/5 of an hour. If you multiply 1/5 of an hour by 5 you would get an hour which would also be 5x the distance as 13/6. Kevin can bike 65/6 or 10 and 5/6 kilometers in an hour.
Kris has a box of 8 crayons. Silvia, s box has 6 times of many crayons as Kris box . How many crayons are in sylvia box
Answers
2 Math Questions about coordinates
Answers
Answer:
y = -3
x = -2
Step-by-step explanation:
2x - y = 17
y = x - 10
Adding these 2 equations:-
2x + y - y = 17 + x - 10
2x = x + 7
x = 7
Now substitute for x in the first equation:-
2(7) - y = 17
14 - 17 = y
y = -3 (answer)
Last equation:-
x + 3y = 16
4x - 5y = -38
Now multiply first equation by 5 and the second by 3:-
5x + 15y = 80
12x - 15y = -114 Adding:-
17x = -34
x = -2 (answer)
15 points!!!!!!The median AM of triangle ∆ABC is half the length of the side towards which it is drawn, BC . Prove that triangle ∆ABC is a right triangle.
Answers
Points A, B, and C are equidistant from point M, so lie on a circle centered at M. That makes BC a diameter, and it means that inscribed angle BAC intercepts an arc of 180°.
The measure of the inscribed angle is half the measure of the arc, so ∠BAC is 90° and ΔABC is a right triangle.
Final answer:
Given that the median AM of triangle ∆ABC is half the length of BC, by showing that triangles ADM and BMC are congruent with the right angle at A, we prove that ∆ABC is a right triangle because the median to the hypotenuse is half its length.
Explanation:
Given that the median AM of triangle ∆ABC is half the length of side BC, to prove that triangle ∆ABC is a right triangle, we can use the properties of triangles and the definition of a median.
Let's denote the midpoint of BC as D such that AD is the median and AD = DB = DC since AM is half of BC and M coincides with D.
Now, consider triangles ADM and BMC. They are right triangles because AD and DM are perpendicular to BC (definition of a median from a vertex to the midpoint of the opposite side). In ∆ADM and ∆BMC, we have AD = DB and DM is common.
Hence, triangles ADM and BMC are congruent by the Side-Side-Side (SSS) criterion. This implies that AM = MB and angle AMD (or AMB) is a right angle.
Since AM is also the median, for it to be equal in length to MB (half of BC), the only way this is geometrically possible is for triangle ABC to be a right triangle with the right angle at A. This is because the median to the hypotenuse of a right triangle is always half the length of the hypotenuse, which in this case is side BC.
Therefore, triangle ∆ABC must be a right triangle.
Please help!!!!
Write the equation of the given line in slope-intercept form.
Answers
y = -3x +2
Step-by-step explanation:The y-intercept is at +2, so that is the value of the added constant (b).
The line goes down 3 units for each unit to the right, so the slope (m) is ...
... m = ∆y/∆x = -3/1 = -3
Then in the form ...
... y = mx + b
with m=-3 and b=2, your line's equation is ...
... y = -3x +2
Please answer this question! Thirty points and brainliest!
Answers
Answer:
choice A
Step-by-step explanation:
Closed circles on the end of the number line means we include it in our inequality (has an equals)
-3 <= x <= 1
Answer:
The answer is A.
Step-by-step explanation:
Can someone please help me on this asap
Answers
Answer: Third option
= (6w + 2)(6w - 2)
Step-by-step explanation:
36w^2 - 4
= (6w)^2 - 2^2
=(6w + 2)(6w - 2)
Which of the following mappings is not a function?
Answers
A function in mathematics is a mapping where each input has exactly one output. A mapping is not a function if any input in the mapping maps to multiple outputs.
Explanation:In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. So a mapping is not a function if any input maps to multiple outputs.
For instance, if we have a mapping {a -> 1, b -> 2, c -> 1}, it is a function because even if 'a' and 'c' have the same output '1', it's okay because each individual input ('a', 'b', 'c') relates to exactly one output. But if we have a mapping {a -> 1, a -> 2}, this is not a function because 'a' maps to two different outputs ('1' and '2').
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Which equation shows a line that is parallel to the line
Answers
Susan’s business makes handmade dresses. The business sells three different kinds of dresses: evening gowns, sundresses, and cocktail dresses. To make an evening gown, it takes 3 hours to cut the material, 2 hours to pin the pieces together, and 5 hours to sew the dress. To make a sundress, it takes 1 hour to cut the material, 1.5 hours to pin the pieces together, and 3 hours to sew the dress. To make a cocktail dress, it takes 2 hours to cut the material, 1 hour to pin the pieces together, and 2.5 hours to sew the dress. Susan’s employees spent a total of 54 hours cutting, 38.5 hours pinning, and 91 hours sewing in a particular week. How many of each type of dress did they produce? That week, the employees produced evening gowns, sundresses, and cocktail dresses.
Answers
Total number of evening dresses, sundresses, cocktail dresses are 9 , 7, 10 respectively.
What is an equation?An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.
How to find how many of each type of dress did they produce?Let the number of evening dresses produced be x , sundresses produced be y and cocktail dresses produced be z.
According to the problem,
To produce a evening dress 3 hours of cut is required.To produce a sundress 1 hour of cut is required.To produce a cocktail dress 2 hours of cut is required.Total tie spent in cutting is 54 hours∴ We can write 3x + y + 2z = 54........(1)
Again, according to the problem,
To produce a evening dress 2 hours of pin is required.To produce a sundress 1.5 hours of pin is required.To produce a cocktail dress 1 hour of pin is required.Total tie spent in pinning is 38.5 hours∴ We can write 2x + 1.5y + z = 38.5........(2)
Again,
To produce a evening dress 5 hours of sew is required.To produce a sundress 3 hours of sew is required.To produce a cocktail dress 2.5 hours of sew is required.Total tie spent in sewing is 91 hours∴ We can write, 5x + 3y + 2.5z = 91......(3)
We have to solve the three equations.
From equation (1) we can write , y = 54 - 3x - 2z
Putting the value of y in equation (2), we get,
2x + 1.5(54- 3x - 2z) + z = 38.5
⇒ 2x + 81 - 4.5x - 3z + z = 38.5
⇒ 2z + 2.5x = 42.5.....(4)
Again, putting the value of y from equation (1) in equation (3), we get,
5x + 3(54- 3x - 2z) + 2.5z = 91
⇒ 5x + 162 - 9x - 6z + 2.5z = 91
⇒ 4x +3.5z = 71
⇒ x = (71 - 3.5z)/4
Putting the value of x in equation (4)
2z + 2.5{(71 - 3.5z)/4} = 42.5
⇒ 8z + 177.5 - 8.75z = 170
⇒ -0.75z = -7.5
⇒ z= 10
Again putting the value of z in equation (4)
x = (71 - 35)/4 = 9
Putting the value of x and z in equation (1)
y = 54 - 27 - 20
⇒ y = 7
Number of evening dress = 9
Number of sundresses = 7
Number of cocktail dresses= 10
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In that week, the employees produced 7 evening gowns, 7 sundresses, and 9 cocktail dresses in total.
Given equations:
[tex]\[3x + y + 2z = 54\] (1)[/tex]
[tex]\[2x + 1.5y + z = 38.5\] (2)[/tex]
[tex]\[5x + 3y + 2.5z = 91\] (3)[/tex]
We'll use the method of elimination to solve this system of equations.
Step 1: Multiply equation (2) by 2 to eliminate [tex]\(z\):[/tex]
[tex]\[4x + 3y + 2z = 77\] (4)[/tex]
Step 2: Subtract equation (1) from equation (4) to eliminate [tex]\(x\):[/tex]
[tex]\[(4x + 3y + 2z) - (3x + y + 2z) = 77 - 54\][/tex]
[tex]\[x + 2y = 23\] (5)[/tex]
Step 3: Multiply equation (1) by 2 and subtract equation (2) from it to eliminate [tex]\(y\):[/tex]
[tex]\[6x + 2y + 4z - (2x + 1.5y + z) = 108 - 38.5\][/tex]
[tex]\[4x + 3z = 69.5\] (6)[/tex]
Step 4: Multiply equation (5) by 2 and subtract equation (6) from it to solve for [tex]\(x\):[/tex]
[tex]\[2(x + 2y) - (4x + 3z) = 46 - 69.5\][/tex]
[tex]\[2x + 4y - 4x - 3z = -23.5\][/tex]
[tex]\[4y - 3z = -23.5\] (7)[/tex]
Step 5: Now, let's multiply equation (7) by 3 and add it to equation (6) to solve for [tex]\(z\):[/tex]
[tex]\[3(4y - 3z) + 4x + 3z = -23.5\][/tex]
[tex]\[12y - 9z + 4x + 3z = -23.5\][/tex]
[tex]\[4x + 12y - 6z = -23.5\] (8)[/tex]
[tex]\[4x + 3z = 69.5\] (6)[/tex]
Now, add equations (8) and (6):
[tex]\[4x + 12y - 6z + 4x + 3z = -23.5 + 69.5\][/tex]
[tex]\[8x + 12y - 3z = 46\][/tex]
Step 6: Plug in the values of [tex]\(x\) and \(z\)[/tex] into equation (6) to solve for [tex]\(y\):[/tex]
[tex]\[8x + 12y - 3(69.5 - 4x) = 46\][/tex]
[tex]\[8x + 12y - 208.5 + 12x = 46\][/tex]
[tex]\[20x + 12y = 254.5\][/tex]
[tex]\[20x = 254.5 - 12y\][/tex]
[tex]\[x = \frac{254.5 - 12y}{20}\] (9)[/tex]
Step 7: Substitute the value of [tex]\(x\)[/tex] from equation (9) into equation (5) to solve for [tex]\(y\):[/tex]
[tex]\[\frac{254.5 - 12y}{20} + 2y = 23\][/tex]
[tex]\[254.5 - 12y + 40y = 460\][/tex]
[tex]\[28y = 205.5\][/tex]
[tex]\[y = \frac{205.5}{28}\][/tex]
y ≈ [tex]7.34[/tex]
Step 8: Substitute the values of[tex]\(x\) and \(y\)[/tex] into equation (1) to solve for [tex]\(z\):[/tex]
[tex]\[3x + y + 2z = 54\][/tex]
[tex]\[3(\frac{254.5 - 12y}{20}) + y + 2z = 54\][/tex]
[tex]\[3(\frac{254.5 - 12(7.34)}{20}) + 7.34 + 2z = 54\][/tex]
z ≈ 8.72
Since we can't produce a fraction of a dress, we'll round [tex]\(y\)[/tex] down to 7 and [tex]\(z\)[/tex]up to 9.
So, the employees produced approximately:
- 7 evening gowns
- 7 sundresses
- 9 cocktail dresses
Complete Question:
Maria studied the traffic trends in India. She found that the number of cars on the roads increases by 10% each year. If there were 80 million cars in year 1 of her study, how many more cars were on the road in year 3 compared to year 2? 8,000,000 8,800,000 88,000,000 96,800,000
Answers
(1.1)(80,000,000)=88,000,000
That is the total cars for year two. To find the increase you would do
(1.1)(88,000,000)=96,800,000
Then you would subtract year 2 from year three
96,800,000-88,000,00=8,800,000
That gives you ur answer.
Answer:
B) 8, 800, 000
Step-by-step explanation:
The number of cars in year 1= 80,000,000
She found that the number of cars on the roads increases by 10% each year.
Now let's find 10% of 80,000,000
= [tex]\frac{10}{100} *80,000,000 = 8,000,000[/tex]
So the number of cars in year 2= 80,000,000 + 8,000,000
= 88,000,000
Now let's find 10% of 88,000,000.
= [tex]\frac{10}{100} *88,000,000 = 8,800,000[/tex]
So the number of cars in year 3= 88,000,000 million+8,800,000= 96,800,000
Now we have to find difference in year 3 compared to in year 2.
The difference in the cars in year 3 compared to year 2= 96,800,000 - 88,000,000
= 8,800,000
Therefore, the answer is B) 8, 800, 000
A sign says that the price marked on all music equitment is 30% off the original price. You buy an electric guitar for the sale price of $315. What is the original price?
Answers
Answer:
$450 is the original price
Step-by-step explanation:
We can create a proportion to find the sale on the original price. A proportion is an equation where two ratios are set equal to each other. We create two fractions using the prices and percents. It is marked down by 30% so we pay 70% of the original. The sale price is $315.
[tex]\frac{70}{100} =\frac{315}{x}[/tex]
We begin solving by cross multiplying numerator to denominator of each fraction.
[tex]70(x)=100(315)\\70x=31500\\\frac{70x}{70}=\frac{31500}{70} \\450=x[/tex]
Ari thinks the perfect milkshake has 33 ounces of caramel for every 55 scoops of ice cream. Freeze Zone makes batches of milkshakes with 66 ounces of caramel and 88 scoops of ice cream. What will Ari think about Freeze Zone's milkshakes?
Answers
[tex] \frac{33}{55} \: = \: \frac{66}{88} k[/tex]
[tex] \frac{3}{5} \: = \: \frac{6}{8} k[/tex]
[tex] \frac{3}{5} \: = \: \frac{3}{4} k[/tex]
[tex]k \: = \: \frac{4}{5} [/tex]
Since, k ≠ 1,
Ari will think Freeze Zone's Milkshakes don't have the required quality.
Answer:
Too much caramel.
Step-by-step explanation:
A forest covers 43,000 acres. A survey finds that 0.2% of the forest is old-growth trees. How many acres of old-growth trees are there?
Answers
Answer:
8,600 acres are old-growth trees.
Step-by-step explanation:
You can find this by multiplying the percentage by the overall number of acres
20% * 43,000 = 8,600
Answer:
There are 86 acres of old-growth trees.
Step-by-step explanation:
In order to answer the question, we need to calculate the 0.2% of 43,000.
We can calculate this stating that exists a linear relationship between the percentage and the amount of acres. We also need to state that 43,000 acres are the 100% of the acres.
Therefore, we can write the following equation to calculate the percentage :
[tex]\frac{43,000}{100}=\frac{x}{0.2}[/tex]
If we solve the equation in terms of ''x'' :
[tex]x=(\frac{43,000}{100}).(0.2)=86[/tex]
[tex]x=86[/tex]
We find that if 43,000 acres are the 100% of the acres ⇒ The 0.2% of the acres are 86 acres (in which there are old-growth trees).
I NEED HELP
You are given the system of equations to solve by the elimination method, which is an INCORRECT step that will NOT produce a system with the same solution?
5x + 3y = 5
8x + 2y = 6
A) subtract 3 times the second equation from 2 times the first equation
B) add 4 times the first equation and −6 times the second equation
C) multiply the first equation by
2
3
and subtract the second equation
D) multiply 3y by
2
3
in the first equation and subtract the second equation
Answers
The population of a pack of wolves is 88. The population is expected to grow at a rate of 2.5% each year.
Which function equation represents the population of the pack of wolves after t years?
f(t)=88(0.025)^t
f(t)=88(1.025)^t
f(t)=88(1.25)^t
f(t)=88(2.5)^t
Answers
Answer:
Option B is correct.
[tex]f(t) = 88(1.025)^t[/tex] represents the population of the pack of wolves after t years
Step-by-step explanation:
The exponential growth function is given by;
[tex]f(t) = a(1+r)^t[/tex] ......[1]
where
a represented the initial value
r represents the rate(in decimal)
t represents the time in years
As per the given statement: The population of a pack of wolves is 88. Also, the population is expected to grow at a rate of 2.5% each year.
⇒ a = 88 and r =2.5% = 0.025.
Substituting these values in equation [1], we have;
[tex]f(t) = 88(1+0.025)^t[/tex]
or
[tex]f(t) = 88(1.025)^t[/tex]
Therefore, the population model of the pack of wolves after t years is given by: [tex]f(t) = 88(1.025)^t[/tex]
Final answer:
The correct function equation that represents the population of the pack of wolves after t years is f(t) =[tex]88(1.025)^t[/tex]
Explanation:
The population of a pack of wolves can be represented by an exponential function equation. In this case, the population is expected to grow at a rate of 2.5% each year.
The correct function equation that represents the population of the pack of wolves after t years is f(t) = [tex]88(1.025)^t[/tex]
This equation takes the initial population of 88 and multiplies it by 1.025 raised to the power of t, which represents the number of years.
Tyler baked 702 cookies. He sold them in boxes of 18. After selling all of the boxes of cookies for the same amount each, he earned $136.50. How many boxes of cookies did Tyler sell
Answers
Answer:
I'm not quite sure but I believe he sold 39 Boxes for $3.50 a box.
Step-by-step explanation:
-You would divide 702 by 18 Since he puts them in boxes of 18.
702/18= 39
-Then you would divide $136.50 by 39
136.5/39= 3.5
Which means each box was $3.50 a piece
Tyler sold 39 boxes of cookies, with the price of each box is $3.5
Further explanation
Given:
Tyler baked 702 cookies
He sold them in boxes of 18 cookies
Tyler earned $136.50
Question:
How many boxes of cookies did Tyler sell?
to find out how many boxes of cookies he sold we are going to divide the total cookies he made with the number of cookies in each box
[tex]\boxed {= \frac{702}{18} = 39 }[/tex]
so there were 39 boxes of cookies. He sold all of them and earned $136.50. Price per box would be:
[tex]\boxed {\frac{136.50}{39} = 3.5 }[/tex]
With total earned $136.50, Tyler sold 39 boxes of cookies at $3.5/box
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Keywords: mixed fraction, fraction, division, division big numbers, math word problem, multiplication
An individual borrowed ?$89000 at an APR of 6?%, which will be paid off with monthly payments of ?$638 for 20 years. The number of payments per year
Answers
Answer: Total payments = $153,120
Interest paid = $64,120
Step-by-step explanation:
$638 x 12 months x 20 years = $152,120
Paid: $152,120
Borrowed: $89,000
Difference: $64,120
Juan's cell phone company charges $35 a month for phone service plus $0.50 for each text message.How many text messages does Juan send in a month if his bill was $52?
Answers
First, you have to subtract 35 from 52. The answer you should get is 17. If you divide 17 by $.50 you should get 34. Hope this helped!
The number of text messages sent by Juan in a month is 34.
What is the process of division?Multiplication is the inverse of division. If three parties of 4 add up to 12, 12 split into three equal groups adds up to 4 in each collective in division. The main goal of separating is to determine how many equal categories form or how many people are in each collective when sharing fairly.For the given question;
Total bill charged to Juan's cell by phone company is $52.
phone service = $35.
text message charge = $0.50 each.
The total cost for message is 52 - 35 = $17.
The number of messages = total message cost/ charge of each message
The number of messages = 17 / 0.5
The number of messages = 34
Thus, the number of text messages sent by Juan in a month is 34.
To know more about the division, here
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For every pound a company spends on advertising, it spends ?0.37 on its website. Express the amount spent on advertising to its website as a ratio in its simplest form.
Answers
Answer:
[tex]100:37[/tex]
Step-by-step explanation:
For every pound a company spends on advertising it spends £0.37 on its website.
Ratio of the the total amount spent on advertising to the amount spent on its website is,
[tex]=\dfrac{1}{0.37}[/tex]
[tex]=\dfrac{1\times 100}{0.37\times 100}[/tex]
[tex]=\dfrac{100}{37}[/tex]
[tex]=100:37[/tex]
Therefore, the ratio of the the total amount spent on advertising to the amount spent on its website is [tex]100:37[/tex]
A stack of three hundred cards is placed next to a ruler, and the height of stack is measured to be 5/8 of an inch. How thick is one card?
Answers
To calculate the thickness of one card from a stack of three hundred cards with a total height of 5/8 inch, you divide the total height by the number of cards, resulting in roughly 0.0020833 inches per card.
To compute the thickness of one card from a stack of three hundred cards, we must first determine the total height of the stack, which we already know is 5/8 of an inch. Then, we simply divide this height by the number of cards, which is 300, to find the thickness of a single card.
Here is the calculation:
Total height of the stack = 5/8 inch
Number of cards in the stack = 300
Thickness of one card = Total height of the stack
Number of cards
Thickness of one card = (5/8 inch)
300
Thickness of one card = 5/8
300
Thickness of one card = 0.0020833... inches (approx.)
Therefore, each card is approximately 0.0020833 inches thick.