Answer:
21 miles
Step-by-step explanation:
Jeff drove [tex]=\dfrac{1}{2}[/tex] of the trip
Jason Joe drove [tex]=\dfrac{1}{4}[/tex] of the trip
Together Jeff and Jason Joe drove [tex]=\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{2}{4}+\dfrac{1}{4}=\dfrac{3}{4}[/tex] of the trip
All trip [tex]=1[/tex]
Remaining trip [tex]=1-\dfrac{3}{4}=\dfrac{4}{4}-\dfrac{3}{4}=\dfrac{1}{4}[/tex]
Susan and Sharon divided the rest of the drive equally, so
Susan drove = Sharon drove [tex]=\dfrac{1}{4}:2=\dfrac{1}{4}\cdot \dfrac{1}{2}=\dfrac{1}{8}[/tex] of the trip.
The entire trip was 168 miles, then
Sharon drove [tex]=\dfrac{1}{8}\cdot 168=21\ miles[/tex]
5. Which statement is NOT true?
If x = 1, then x2 = 1.
If x2 = 1, then x = 1.
If x= -1, then x2 = 1.
x2 = 1 if and only if x = 1 or x = -1.
Answer:
[tex]x^{2} =1, then\ x=1[/tex] is NOT true.
Step-by-step explanation:
1.
[tex]If\ x=1, then\ x^{2} =1[/tex] ......True
( 1 )² = 1
2.
If [tex]x^{2} =1, then\ x=1[/tex] ........ NOT True
∴ x =± 1 .........this is correct
3.
[tex]If\ x=-1, then\ x^{2} =1[/tex] ......True
( -1 )² = 1
4.
x2 = 1 if and only if x = 1 or x = -1. .........True
( 1 )² = 1
( -1 )² = 1
what is 3² in xpoient
Answer:
9
Step-by-step explanation:
It saying 3 times to the power of 2
or
3 squared
so basically it's saying
3^3=9
What’s the answer ?
Answer:
C. Parallel
D. Segment
F. Ray
Explaination:
Answers A, E, & G (line, point, & plane) are undefined terms.
The number 123,456 is divisible by...
Answer:
2
Step-by-step explanation:
Because the # ends in a even number, it can be divisible by 2
On five different tests Jake got: 75, 80, 81, 96, and 100. Would the mean of these numbers be greater than the median of these numbers?
Answer:
Yes the mean is greater than the median
Step-by-step explanation:
To find the mean of numbers, you add all of them and divide them by how many there are in total.
75+80+81+96+100= 432
There are five numbers so divide the total by 5.
432÷5= 86.4
That is your mean.
The median is the one in the middle. There are five numbers, so the one in the middle is 81.
The mean is 86.4 and the median is 81.
Answer:
the mean is greater
Step-by-step explanation:
well mean is average so lets do that first
to find the mean, you add all of the percentages up and divide it by the amount of percentage
75 + 80 + 81 + 96 + 100 = 155 + 177 + 100 = 432
and now you divide 432 by 5 to get 86.4
so the mean is 86.4
and the median is the middle:
75 80 81 96 100
↑
81 is the median since its in the middle
86.4 > 81
so the mean is greater than the median
Lashonda bought a desk on sale for $159.60. This price was 62% less than the original price. What was the original price?
p - 62%p = %=$159.60
p - 62p/100 = $159.60
100p - 62p = $15960
38p = $15960
p = $15960/38
p = $420
Fill in the missing term in the equation x/x^2-4x+4 - x/x^2-3x+2= ?/(x-2)^2(x-1)
Answer:3
Step-by-step explanation:
How do I graph and find slope intercept for for x+y=0
Answer:
y = -x + 0
slope intercept: 0
Step-by-step explanation:
You would start at the origin, since your slope intercept is 0. The slope, -1 (since -x is the same as -1x), is telling us the line will be negative, so the line you are graphing will be heading up one space at a time towards the left, up 1 and sideways 1. Rise over Run.
write the numerical expression as a power. (4 x4 x 4 = )
Answer:
[tex] {4}^{3} [/tex]
Step-by-step explanation:
your are taking 4 and multiplying it by itself three times hence 4 to the third power
Answer:
4³
Step-by-step explanation:
You take out $50,000 for loans during your college career. You must pay it back with 7% APR for 20 years, making monthly payments. Calculate the minimum monthly payment needed to do this.
Answer:
The monthly payment for the loan amount for 20 years is $806.167
Step-by-step explanation:
The principal loan amount= $ 50,000
The rate of interest = 7 %
the time period of loan = 20 years = 20 × 12 = 240 months
let the amount after 20 years = $ A
From Compounded method
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm Time}[/tex]
or, A = 50,000 × [tex](1+\dfrac{\textrm 7}{100})^{\textrm 20}[/tex]
or, A = 50,000 × [tex](1.07)^{20}[/tex]
Or, A = 50,000 × 3.8696
∴ Amount = $ 193,480
So, The amount after 20 years = $ 193,480
The monthly payment amount = $ [tex]\frac{193480}{240}[/tex] = $ 806.167
Hence The monthly payment for the loan amount for 20 years is $806.167 Answer
A company plans on selling MP3 players for $120. To make the MP3 players, a cost estimator determined it costs the company $1500 per week for overhead and $45 for each MP3 player made. How much profit would the company make if it sold 100 players in one week? Explain.
Answer:
6000
Step-by-step explanation:
Each mp3 sells at $120 per mp3 player multiply that by 100 its $12000
It cost them $45 per mp3 to be made multiply that by 100 its $4500 then add the $1500 for the week and its $6000
$12000-$6000=$6000
They make a profit of $6000 in a week
The company would make a profit of $6,000 from selling 100 MP3 players in one week after subtracting the total costs of $6,000 from a total revenue of $12,000.
The company's profit when selling 100 MP3 players in one week can be calculated by subtracting the total costs from the total revenue. First, we calculate the total revenue by multiplying the selling price of $120 per MP3 player by the number of players sold, which is 100. This results in a total revenue of $12,000 (120 x 100).
Next, we calculate the total costs, which include a fixed overhead of $1,500 per week and a variable cost of $45 per MP3 player. For 100 players, the variable cost sums up to $4,500 (45 x 100). Therefore, the total costs amount to $6,000 ($1,500 + $4,500).
To find the profit, we subtract the total costs from the total revenue:
Total Revenue = 100 x $120 = $12,000
Total Costs = $1,500 (fixed) + 100 x $45 (variable) = $6,000
Profit = Total Revenue - Total Costs = $12,000 - $6,000 = $6,000
Therefore, the company would make a profit of $6,000 if it sold 100 MP3 players in one week.
The number of students who attended the winter school dance was 20% less than the number of students attending the following if 220 students attend the Fall dance how many fewer students attended the winter day
Answer:
44
Step-by-step explanation:
20 percent less than 220
Answer:
The answer to this question is S=44
Step-by-step explanation:
Write an equation In slope intercept form for the line that is parallel to the given line and that passes through the given point
5x - 2y=10 (3 -5)
The equation of the parallel line in slope-intercept form is;
y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]
Step-by-step explanation:
Let us revise some facts about parallel lines
The equations of two parallel lines have:
Same slopesDifferent y-interceptThe slope-intercept form of the equation of a line is y = m x + b, where m is the slope of the line and b is the y-intercept
The given line has equation 5x - 2y = 10
Put it in the form of y = m x + b to find its slope
∵ 5x - 2y = 10
- Subtract 5x from both sides
∴ -2y = 10 - 5x
- Divide to sides by -2
∴ y = -5 + [tex]\frac{5}{2}[/tex] x
∴ y = [tex]\frac{5}{2}[/tex] x - 5
- The value of m is the coefficient of x
∴ m = [tex]\frac{5}{2}[/tex]
∴ The slope of the given line is [tex]\frac{5}{2}[/tex]
∵ Parallel lines have same slopes
∴ The slope of the parallel line is m = [tex]\frac{5}{2}[/tex]
- Substitute the value of m in the form of the equation
∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x + b
To find b substitute x and y in the equation by the coordinates of any point lies on the line
∵ The parallel line passes through point (3 , -5)
- Substitute x and y by the coordinates of the point (3 , -5)
∵ x = 3 and y = -5
∴ -5 = [tex]\frac{5}{2}[/tex] (3) + b
∴ -5 = [tex]\frac{15}{2}[/tex] + b
- Subtract [tex]\frac{15}{2}[/tex] from both sides
∴ b = [tex]\frac{-25}{2}[/tex]
∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{-25}{2}[/tex]
∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]
The equation of the parallel line in slope-intercept form is;
y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]
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Help answer this question
Answer:
a = 108° and b = 144°
Step-by-step explanation:
The opposite angles of a rhombus are the same and the sum of all the angles of the rhombus is 360°.
So, from the given diagram of the rhombus we can write
2b + 2× 36 = 360
⇒ 2b = 360 - 72 = 288
⇒ b = 144° (Answer)
Again, the each angles of a pentagon is given to be a.
Hence, we can write 3a + 36 = 360
⇒ 3a = 324
⇒ a = 108° (Answer)
- 18 = x-6
solve for x.
Answer:
x=-12
Step-by-step explanation:
-18=x-6
-18+6=x--6+6
-12=x
What is the area of a regular pentagon with a side of 10in?
Area of a regular pentagon with a side of 10in is 172
Step-by-step explanation:
Given:
Side of the regular pentagon = 10in
To Find:
Area of the regular pentagon=?
Solution:
We know that ,
[tex]Area of Pentagon = 5\times\text{ Area of triangle}[/tex]................(1)
Step 1: Finding the Area of the triangle
we know that in a right angle triangle, there are base, height and hypotenuse [tex]tan(\frac{\pi}{5}) =\frac{ height}{hypotenuse }[/tex]
So, from the above equation,
[tex]height=\frac{(base/2)}{tan(36^{\circ})}[/tex]
[tex]height=\frac{5}{tan(36)}=6.88[/tex]
area of right angle triangle
=> [tex]\frac{1}{2}\times base \times height[/tex]
=> [tex]=\frac{1}{2} \times 5\times 6.88[/tex]
=> 17.20
Area of the triangle =2 x area of right angle triangle
Area of the triangle =2 x 17.20
Area of the triangle= 34.40
Step 2: Finding the Area of the pentagon
Substituting the values in (1)
[tex]Area of Pentagon = 5\times 34.40 [/tex]
Area of Pentagon= 172
Find the zeros of the function
f(x)=x^2+5x+6
Answer:
x= -3 and x= -2
Step-by-step explanation:
(x+3)(x+2)
Hence, the zeroes are:
-3 and -2
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What is X +7 equals 14
Answer:
x = 7
Step-by-step explanation:
x + 7 = 14
Subtract 7 from both sides
x = 14 - 7 = 7
Answer: the answer is 7
Step-by-step explanation:
A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel?
Answer: 12.69 miles approx
Step-by-step explanation:
let x represent the number of miles traveled
1.75 + 0.65x = 10
0.65x = 8.25
x = 12.69 miles approx
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Ryaan goes skydiving and falls at a constant rate toward the ground. The equation y = -32x + 14,000 represents the situation where y is the height of Ryaan in feet above the ground and x is the seconds since she jumped.
Which statement describes the situation?
a. From a starting position of 14,000 feet above the ground, she is ascending at 32 feet per second.
b. From a starting position of 32 feet above the ground, she is ascending at 14,000 feet per second.
c. From a starting position of 14,000 feet above the ground, she is descending at 32 feet per second.
d. From a starting position of 32 feet above the ground, she is descending at 14,000 feet per second.
MUTIPLE CHOICE ANSWER!!!1
Answer:
C, because
-32 x seconds since she jumped + 14000
because 14000 would be 14000 units above 0, and -32 represents the seconds she had jumped, which would basically be -32+14000, which is the same as saying 14000 - 32.
the sum of two numbers is 19 and there difference is 7 what are the two numbers
Answer:14 and 5
Step-by-step explanation:
F(x)=x^2-8x+12 find the roots by graphing
Answer:
x² - 8x + 12 = 0
(x - 6)(x - 2) = 0
x = 2, 6
f(4) = -4
Plot (0, 12), (2, 0), (4, -4), (6, 0), and (8, 12) on the graph. Then draw a smooth curve that goes through these points.
The population of Collin County, which follows the exponential growth model, increased from 491,675 in 2000 to 782,341 in 2010. Find the exponential growth rate, k.
Answer:
p=ak^t
p1=491272*k^0
p2=782341*k^10
782341/491272 = k^10
k=1.047629
growth rate is 4.7629%
2012: predicted population is 491272*1.047629^12=858,642 people
1245863=491272*1.047629^t
1.047629^k=2.5363599
ln both sides is k ln 1.0476=ln 2.5363
t=20.000 years.
Rule of 72 would say 72/4.76 or 15.12 years for doubling
14.90 years
2017 predicted is 491272*1.0476^17 or 1083552, or more than actual, so the rate of growth is slowing down.
The required exponential growth rate, k is 4.7629%
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
The exponential function will be as
p=a[tex]k^t[/tex]
p₁=491272*k⁰
p₂=782341*k¹⁰
782341/491272 = k¹⁰
k = 1.047629
So, the growth rate is 4.7629%
2012: the predicted population is 491272 × 1.047629¹² =858,642 people
1245863=491272 × [tex]1.047629^t[/tex]
[tex]1.047629^k[/tex] = 2.5363599
ln both sides is k ln 1.0476 = ln 2.5363
t = 20.000 years.
Rule of 72 would say 72/4.76 or 15.12 years for doubling
14.90 years
2017 predicted is 491272 × 1.0476¹⁷ or 1083552, or greater than the real rate of increase, hence the rate of growth is decreasing.
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Multiply. Type your answer in the box. Do not use any spaces.
(–27) x (+8) =
Answer:
-216
Step-by-step explanation:
Negative times positive is negative.
27 * 8 = 216
Answer is negative, so
-27 * 8 = -216
Answer:
-216
Step-by-step explanation:
Write the problem as a mathematical expression. ( − 27 ) ⋅ ( 8 )
multiply -27 by 8
The coordinates of the vertices of triangle 1 are A(6,6), B(12,9), C(9,6).
The coordinates of the vertices of triangle 2 are A′(2,2), B′(4,3), C′(3,2).
What transformation was performed on triangle 1 to create triangle 2?
Answer:
A
Step-by-step explanation:
The transformation performed on triangle 1 to create triangle 2 is a translation by the vector (-4, -4), which means each point was moved 4 units to the left and 4 units down.
Explanation:The transformation used can be determined by observing the differences between corresponding coordinates in the two triangles. If we subtract the coordinates of A′(2,2) from A(6,6), for instance, we get a change of -4 in the x-direction and -4 in the y-direction. Similarly, subtracting B′(4,3) from B(12,9) and C′(3,2) from C(9,6) results in changes of -8 and -6 in the x-direction and -6 and -4 in the y-direction, respectively.
This means that every point on triangle 1 was moved 4 units to the left and 4 units down to create triangle 2. Thus, the transformation that took place is called a translation by the vector (-4, -4).
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Solve the equation 4(0.2x – 5) = 12.
Simplifying
4(0.2x + -5) = 12
Reorder the terms:
4(-5 + 0.2x) = 12
(-5 * 4 + 0.2x * 4) = 12
(-20 + 0.8x) = 12
Solving
-20 + 0.8x = 12
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '20' to each side of the equation.
-20 + 20 + 0.8x = 12 + 20
Combine like terms: -20 + 20 = 0
0 + 0.8x = 12 + 20
0.8x = 12 + 20
Combine like terms: 12 + 20 = 32
0.8x = 32
Divide each side by '0.8'.
x = 40
Simplifying
x = 40
Describe the pattern 0.13, 0.65, 3.25, 16.25
Let n be the current term and n+1 be the next term
Then the pattern is: n+1 = n * 5
Step-by-step explanation:
Given series is:
0.13, 0.65, 3.25, 16.25
We can find the ratio between consecutive numbers to find the pattern
So,
[tex]Ratio = \frac{0.65}{0.13}\\=5[/tex]
We can see that multiplying the previous term with 5 gives us the next term
0.13 * 5 = 0.65
0.65 * 5 = 3.25
3.25 * 5 = 16.25
Let n be the current term and n+1 be the next term
Then the pattern is: n+1 = n * 5
Keywords: Pattern, Sequence
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what is 2x + 1 = 15 if x =8
Answer:
17
Step-by-step explanation:
17=15
so this is not equal
A radar beacon 40 feet above the ground picks up an airplane approaching at an angle of elevation
of 43 degrees and a distance of 6,390 feet. How high above the ground is the plane in whole feet?
5,998.7714 ft
Step-by-step explanation:
Well find x in the illustration;
First To find the opposite side of the right-angled triangle we'll using tangent of the given angle
Tangent Ф = Length of the opposite side / Length of the adjacent side
Tan 43 = h / 6390
h = Tan (43) * 6390
h = 5,958.7714 ft
Then we'll add the height of the beacon which is 40 ft above ground;
x = 5,958.7714 ft + 40 ft
x = 5,998.7714 ft
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You are comparing apples to oranges in a fruit bowl. Is the ratio 2:3 the same as the ratio 3:2?
Answer:
No, the two ratios are not the same.
Step-by-step explanation:
When we are saying "apples to oranges", mathematically it means:
[tex]\frac{Apples}{Oranges}[/tex],
Which could be 2:3 or 3:2, which in fractional from are written as [tex]\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex] respectively.
We see that
[tex]\frac{2}{3} \neq \frac{3}{20}.[/tex]
In words the ratio 2:3 says "for every two apples there are three oranges", and 3:2 says "for every three apples there are two oranges". Again we see that the two sentences are not saying the same thing, therefore the ratio 2:3 is not same as 3:2.
Final answer:
The ratio 2:3 is not the same as 3:2 because they represent different relationships between the quantities of apples and oranges in a comparative scenario or barter trade. These ratios suggest different terms of trade and would result in different exchange outcomes.
Explanation:
The question is whether the ratio 2:3 is the same as 3:2 when comparing apples to oranges. To understand this, we must recognize that a ratio represents a relationship between two quantities, expressing how many times one value contains the other or is contained within it. In the context of a fruit bowl, a ratio of 2:3 would mean for every 2 apples, there are 3 oranges, while the ratio 3:2 means for every 3 apples, there are 2 oranges. Therefore, these two ratios are not the same as they represent different relationships between the quantities of apples and oranges.
Considering ratio comparisons like in barter trading, the terms of trade are critical. If 2 bushels of apples can be traded for 3 bushels of oranges, that is a 2:3 apple-to-orange trade ratio. On the other hand, if we reverse the ratio to 3:2, it would mean something quite different for trade or value comparisons. Specifically, you'd need 3 bushels of apples to get 2 bushels of oranges.
It's essential to compare apples to apples; comparative statistics are only useful when the comparison is logical and applicable. The ratios 2:3 and 3:2 convey different terms and thus would yield different outcomes in any exchange or comparative scenario.