Answer:
1. Their answers differ because of approximation
2. See Explanation Below
Step-by-step explanation:
Given
Allison
[tex]Morning: 2\frac{7}{8} miles[/tex]
[tex]Afternoon: 3\frac{3}{8} miles[/tex]
Total: About 6 miles
Jennifer
[tex]Morning: 3\frac{1}{10} miles[/tex]
[tex]Afternoon: 3\frac{3}{10} miles[/tex]
Total: [tex]6\frac{4}{10} miles[/tex]
Required
How their answers differWhy they are both correctHow their answers differ
To understand how their answers differ; first we need to calculate the actual miles they both ran.
Total = Distance covered in the morning + Distance covered in the evening
For Allison
Total Distance = [tex]2\frac{7}{8} + 3\frac{3}{8}[/tex]
Convert mixed fractions to improper fractions
Total Distance = [tex]\frac{23}{8} + \frac{27}{8}[/tex]
Take LCM and add
Total Distance = [tex]\frac{23 + 27}{8}[/tex]
Total Distance = [tex]\frac{50}{8}[/tex]
Total Distance = 6.25 miles
For Jennifer
Total Distance = [tex]3\frac{1}{10} + 3\frac{3}{10}[/tex]
Convert mixed fractions to improper fractions
Total Distance = [tex]\frac{31}{10} + \frac{33}{10}[/tex]
Take LCM and add
Total Distance = [tex]\frac{31 + 33}{10}[/tex]
Total Distance = [tex]\frac{64}{10}[/tex]
Convert to improper fraction
Total Distance = [tex]6\frac{4}{10} miles[/tex]
From the calculation above, the total distance ran by Allison is 6.25 miles and she said she ran about 6 miles; This means that she approximated the total distance she covered.
Also from the calculation above, the total distance ran by Jennifer is [tex]6\frac{4}{10} miles[/tex] and she said she ran [tex]6\frac{4}{10} miles[/tex]; This means that she gave the actual distance she ran.
Hence, their answers differ because of approximation
Why they are both correct?
As mentioned above, the difference in their answer is approximation.
Approximation is rightly allowed in measurements as long as one is giving the right approximated value.
For Allison; the approximation of 6.25 miles is 6 miles;
For Jennifer; she gave the actual distance she ran ([tex]6\frac{4}{10} miles[/tex])
Base on this, we can conclude that both are correct
Which rule describes the translation?
O (x, y) = (x–8, y-3)
* (x, y) = (x-3, y + 3)
O (x, y) + (x+8, y-3)
O (x, y) + (x + 3, 7 + 8)
Answer:
c
Step-by-step explanation:
on ed 2020
Answer:
C) (x, y) → (x + 8, y – 3)
Step-by-step explanation:
To own and operate a home printer, it costs $100 for the printer and an additional $0.05 per page for ink. To print out pages at an office store, it costs $0.25 per page. Let p represent number of pages.
(1) For the costs to be the same, how many pages do you need to print?
(2) How much does it cost to print that many pages?
Answer:
1.) 500 pages
2.) $125
Step-by-step explanation:
Given that the printer cost $100. To operate at home will cost
100 + 0.05P
To print out pages at an office store, it will cost 0.25P
1.) For the costs to be the same, then
100 + 0.05P = 0.25P
0.25P - 0.05P = 100
0.20P = 100
P = 100/0.2
P = 500 pages
500 pages need to be printed
2.) How much does it cost to print that many pages?
Cost = 0.25P
= 0.25 × 500
= 125 dollars
Answer: (1) You would need to print 500 pages
(2) To print 500 pages from home would cost $125
Step-by-step explanation: The cost of printing at home has been given as a fixed cost of 100 plus an additional variable cost of 0.05 per page for ink, that is, Cost = 100 + 0.05p. Also, to print at the office, the cost has been given as 0.25 per page, that is, Cost = 0.25p.
Therefore for the costs to be the same, we need to equate both cost functions (that is, C = C) as follows;
100 + 0.05p = 0.25p
Collect like terms and we now have,
100 = 0.25p - 0.05p
100 = 0.20p
Divide both sides of the equation by 0.2
500 = p
To print 500 pages at home therefore would cost,
C = 100 + 0.05p
C = 100 + 0.05(500)
C = 100 + 25
C = 125
Therefore to print 500 pages from home would cost $125
Help, I'm really stuck on this, has to be in by tomorrow! The question = Describe fully the single transformation that maps shape A onto shape B
Answer:
One thing for sure is that there is a reflection along the x-axis
Step-by-step explanation:
Answer:
reflection
Step-by-step explanation:
its a reflection across the X axis
reflection is to turn a shape across an axis
other transformations are:...
translation= to slide a shape up or down left or right when they give u the units
dilation= to make a shape bigger or smaller with they center of dilation that they give
rotation= turn a shape depending if its clockwise or counter clockwise and they will give u a degree
hope this helped
Answer with A B C D. Correct answer gets brainlest.
Answer:
B
Step-by-step explanation:
Answer: B
Step-by-step explanation:
how many ounces of a 12 alcohol solution must be mixed with 6 ounces of a 20% alcohol solution to make a 16% alcohol solution?
Answer:
6 ounces
Step-by-step explanation:
So set your equation up as
12(x)+20(6)=16(x+6)
You set it up this way because with the first number you know the percet but not the ounces so your ounces would be x. The second set you know percet and ounces (the percent will alway go outside the parenthesis). then the last number is waht it wil equal; again we know the percent but not the product. We put x+6 in the parenthesis because you are adding the ounces your don't know(x) wiht the ones you do (6).
To solve distribute
12x+120=16x+96
Now all you have to do is solve for x. Subtract the 96 over then subtract the 12x over, so it would look like this.
12x+120=16x+96
-96 -96
12x+24=16x
-12x -12x
24=4x Now simply divide by 4 and you get 6=x
There should be 6 ounces mixed in order to get the required solution.
Let the number of ounces be represented by x.
Based on the equation, the equation to use will be:
12(x) + 20(6) = 16(x + 6)
Expand the equation
12x + 120 = 16x + 96
Collect like terms
16x - 12x = 120 - 96
4x = 24
Divide both side by 4
4x/4 = 24/4
x = 6
Therefore, the number of ounces will be 6 ounces.
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At the grocery store, Terry weighed his apples on the scale. They weighed 4.3 pounds. When he went to the register, he was charged $8.56. How much did Terry pay per pound of apples?
Answer:
$1.99
Step-by-step explanation:
Cost per pound = Total cost / weight of the apples
[tex]=\frac{8.56}{4.3}\\\\=\frac{8.56*10}{4.3*10}\\\\=\frac{85.6}{43}\\\\=1.99[/tex]
Answer:
$1.99
Step-by-step explanation:
You have to divide $8.56 by 4.3 pounds. Once done, you should have gotten approximately $1.99. You can double check it by multiplying $1.99 by 4.3 and you should get $8.56.
Cole is studying employment trends.
He found that 20% of the social workers he surveyed, or 45 social workers,
work part time. How many social workers did Cole survey altogether?
Answer:
225
Step-by-step explanation:
So we know that 20% of the social workers he surveyed was 45 people. The easiest way to find all 100% of the social workers is to do 45 x 5 because 20% x 5 = 100%. So 45 x 5 = 225.
Hope this helped! :)
On a scale drawing with a scale of 1cm:4.5 m, the height of a tree is 2.4 cm. how tall is the actual tree?
Answer:
10.80
Step-by-step explanation:
1cm:4.5 meters
So if one cm is 4.5 meters, just multiply 2.4 by 4.5.
2.4*4.5=10.8
If the radius of a circle is 15 units and the center
of the circle is (−3, 2), what is the equation of
the circle?
A. (x − 2)2 + (y + 3)2 = 30
B. (x + 2)2 + (y − 3)2 = 225
C. (x + 3)2 + (y − 2)2 = 225
D. (x − 3)2 + (y + 2)2 = 15
HELP ME PLEASE
Answer:
(x+3)^2 + (y-2) ^2 = 225
Step-by-step explanation:
We can write the equation of a circle in the form
(x-h)^2 + (y-k)^2 = r^2
where (h,k) is the center and r is the radius
(x- -3)^2 + (y-2) ^2 = 15^2
(x+3)^2 + (y-2) ^2 = 225
if sin(x) = 0 and cos(x) = 1, what is cot(x)?
Answer:
undefined
Step-by-step explanation:
Sin(x) = 0 where x = 0
Cos(x) = 1 where x = 0
Cot(0) is undefined
Undefined.
Trigonometry:The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (cosec).Given -
[tex]sin(x)=0\\cos(x)=1[/tex]
So [tex]cot(x)=-[/tex].
Therefore, [tex]cot(x)[/tex] is undefined.
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The Monarch Butterfly is essential to the pollination process of many native and farmed North
American plants. These butterflies migrate thousands of miles over several months. A Florida
Department of Forestry outpost in Hawthorne, Florida has been tracking their population since
the 2005 migration cycle.
-Part B: Of the following choices, which equation is the best fit line for the data? *
(1 Point)
f(x)=34x-320
f(x)=-34x-320
f(x)=34x+320
f(x)=-34x+320
Answer:
f(x)=-34x+320
Step-by-step explanation:
In the picture attached, the graph of the problem is shown.
From the picture we know that the best fit line for the data must have:
positive y-interceptnegative slopeThese two features are only satisfied by the last option.
-9x-6y=12 what’s there slope and y intercept
Answer: slope = -3/2
Y intercept = -2
Step-by-step explanation:
The radius of a circle is 2.7 feet. Find the diameter
Answer:
5.4 ft.
Step-by-step explanation:
Radius is half of the diameter, so multiply 2.7 by 2 to get the full distance, and you get 5.4 ft.
Answer:5.4
Step-by-step explanation: 2.7x2= 5.4
Radius is just half of the diameter so when given radius X2 when given diameter divide by 2
A graph titled Arnie's Airplane has time (minutes) on the x-axis and distance (miles) on the y-axis. A line goes through points (0, 0) and (2, 10). A 2-column table with 3 rows titled Bernie's Biplane. Column 1 is labeled Time (minutes) x with entries 3, 5, 8. Column 2 is labeled Distance (miles) y with entries 21, 35, 56.
Find each slope from the graph and table to compare the constant speeds of the two airplanes.
What is the constant speed (slope) of Arnie’s airplane?
What is the constant speed (slope) of Bernie’s biplane?
Who flew faster?
Answer:
its 5 7 bernie
Step-by-step explanatioi just did it
Answer:
5, 7, bernie
Step-by-step explanation:
I got it right
HURRY TIME LIMIT
y + 2 = negative 2 (x minus 5)
What is the equation in slope-intercept form?
Answer:
[tex]y = -2x + 8[/tex]
Step-by-step explanation:
Step 1: Solve
[tex]y + 2 = -2(x - 5)[/tex]
[tex]y + 2 - 2 = -2x + 10 - 2[/tex]
[tex]y = -2x + 8[/tex]
Answer: [tex]y = -2x + 8[/tex]
Answer:
y= -2x + 12
Step-by-step explanation:
y +2 = -2 ( x - 5 )
y+2 = -2x + 10
-2 -2
y= -2x + 12
2/3 × 6 + 2/3 × n for n = 2
Answer:
16/3 or 5 1/3
Step-by-step explanation:
Plugging in 2 for n, you get(2/3*6)+(2/3*2)=4+4/3=16/3= 5 1/3. Hope this helps!
Which are examples of Pythagorean Triples
A) 6, 8, 10
B) 8, 10, 12
C) 10, 16, 16
D) 12, 16, 20
E) 14, 18, 20
F) 15, 20, 25
check all the above !!
Answer:
It should be
A
F
D
Step-by-step explanation:
Just do A^2+B^2=C^2 and plug in what the three given numbers are, if A^2+B^2=C^2 and it comes out as correct meaning the sum of A and B is equal to C than boom you have a triple
Answer would be option(A){6, 8, 10}, (D) {12, 16, 20} and (F) {15, 20, 25} are examples of Pythagorean Triples
What is Pythagoras theorem?
Pythagoras theorem states that, a right-angled triangle, the square of the one side is equal to the sum of the squares of the other two sides.
{6, 8, 10}, {12, 16, 20} and {15, 20, 25} is the three Pythagorean Triples where any 2 side the sum of the squares adds up to be equal the other side.
We can test this:
6²+ 8² = 10² ⇒ 100=100
12²+16²= 20² ⇒ 400=400
15²+ 20²= 25²⇒ 625=625
Hence, {6, 8, 10}, {12, 16, 20} and {15, 20, 25} is the three Pythagorean Triples
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Suppose h(t) = -0.2t? + 2t models the height, in feet, of a ball that is kicked into the air where t is
given as time, in seconds.
After how many seconds does the ball reach its maximum height?
seconds
What is the maximum height of the ball?
After how many seconds does the ball reach the ground?
seconds
Answer:
Below in BOLD.
Step-by-step explanation:
h(t) = -0.2t^2 + 2t
We can find the maximum height and the time by converting to vertex form:
h(t) = -0.2(t^2 - 2t)
= -0.2[(t - 1)^2 - 1)
= -0.2(t - 1)^2 + 0.2
The time to get to maximum height = 1 second and the maximum height is 0.2 m.
When the ball reaches the ground h = 0 so
-0.2(t - 1)^2 + 0.2 = 0
(t - 1)^2 = -0.2 / -0.2 = 1
t - 1 = 1
t = 2 seconds.
if p is 2% of k. What is 50% of k intems of P and k and if 10% of a number is 7. What is 80% of the number?
Answer:
a.p/100
b.56
Step-by-step explanation:
2% of p=k
2/100 ×p=k
2p/100=k
Cross multiply 2p=100k
P=100k/2
p=50k
Let's make k the subject of formula
k=p/50
So 50% of k in terms of p
50/100×k
And k=p/50
So let's substitute
50/100×p/50
P/100
Therefore 50%of k=p/100
Let the unknown number be x
10% of x is 7
10/100×x=7
10x/100=7
Cross multiply
10x=(100)(7)
10x=700
Divide both sides by 10
X=70
So 80% of 70
80/100×70
5600/100
=56
Therefore 80% of 70=56
If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? (Assume both planets are aligned with the sun and are on the same side of the sun.) in scientific notation.
Answer:
1.08 ⋅ 10 ^8 km
Step-by-step explanation:
find the measure of angle b
Answer:
36 degrees
Step-by-step explanation:
If g(x ) = 3x + 1, evaluate g(-14). -5 -10 -41
Answer:
-41
Step-by-step explanation:
g(x) = 3x + 1
g(-14) = 3*(-14) + 1
= -42 + 1
= -41
Sketch the graph of the inequality.
Answer: D. Check Desmos for confirmation. Its your best friend for Graphing.
Step-by-step explanation:
Which of the following is most likely the next step in the series?
Answer:
the answer is C
What is the probability of spinning the spinner and the arrow landing on the number ‘1’ and then spinning it a second time and it landing on ‘2’ the second time?
Answer:
There isn't a picture, but i'm guessing they are on opposite ends. If so, it would be 50-50.
Step-by-step explanation:
no picture;;
Answer:
50-50
Step-by-step explanation:
Can someone personally help me with geometry and area? Please I have more questions like that
Answer:
272
Step-by-step explanation:
Finding the area on this problem has only a couple steps. First I divided the picture into two parts a rectangle and a triangle. I first found the area of the rectangle. The formula to finding a rectangle is base times height. In this case the base has a length of 19 in and has a height of 8 in. So the area of the rectangle would be 19*8= 152. Now we find the area of the triangle. To find the area of a triangle you use the formula base*height*1/2. In this case you do 20 * 12 * 1/2 = 120. Now for the last step add the areas together in this case 152+120=272. If you need help with finding the lengths reach out to me.p.s. I’m not actually 61Answer:
The area of the shaded region is 272 in²
Step-by-step explanation:
Since it is an odd shape, the real height(20 inches according to the picture) will help us alot. But first you'll want to split the shapes. and find the areas seperately in a way. I see a rectangle on the top and triangle on the bottom. Lets find the area of the rectangle first.
To find the area, you have to multiply length and width.
A = L x W
19 x 8 = 152(the area)
So now we know the area of the rectangle, but what about the triangle? Since there is no exact base measurement for the triangle, we will add the length of the rectangle(19) and the 1 inch.
19 + 1 = 20
So the base for the triangle is 20.
To find the height of the triangle, subtract 8(the rectangle's width) from the overall height(20 inches).
20 - 8 = 12
A = [tex]h_{b}[/tex]b ÷ 2
A= 120(area)
That is not the overall area yet, we have to add the two areas now.
152 + 120 = 272
That is how you find the area for this, let me know if you need anymore help.
A number cube for a game has six sides numbered 1–6. Find the probability that the number cube will land on a multiple of 2.
Answer:
50%
Step-by-step explanation:
2, 4, and 6 are all multiples of 2. Those are 3 numbers out of 6.
3/6 = 1/2
1/2= 50/100
50/100= 50%
Answer:
The probability that it lands on a multiple of 2 is 1/2
Step-by-step explanation:
1 2 3 4 5 6
There is 6 numbers and 3 numbers which is half are multiples of 2.
This makes half of the numbers multiple of 2 and half not.
or look at as odd and even.
the multiples of 2 are even and the non-multiples of 2 are odd.
Hope this helps.
He ran 220 meters farther than she ran she ran 2.4 kilometers.how many kilometers did he run
Answer:
He ran 2.62 km
9.5g of sugar is needed for every cake made. How much sugar is needed for 6 cakes?
Answer: 57
Step-by-step explanation:
Since you need 9.5 grams of sugar for each cake, and you need enough for 6 cakes, you need to multiply 9.5 to 6. Your final answer should be 57.
Answer:
39.2
Step-by-step explanation:
4 times 9.5 equals 39.2
Simplify the expression below.
(6-3)(66)
Answer:
198
Step-by-step explanation:
(6-3) x 66 subtract
3x66 multiply
198