1 [tex]\frac{3}{4}[/tex] gallons per gour
divide number of gallons used by running time
4 [tex]\frac{3}{8}[/tex]÷ 2 [tex]\frac{1}{2}[/tex]
change mixed numbers to improper fractions
[tex]\frac{35}{8}[/tex] ÷ [tex]\frac{5}{2}[/tex]
leave the first fraction, change division to multiplication, turn the second fraction upside down
= [tex]\frac{35}{8}[/tex] × [tex]\frac{2}{5}[/tex]
= ( 35 × 2 ) / (8 × 5 ) = [tex]\frac{7}{4}[/tex] = 1 [tex]\frac{3}{4}[/tex]
Compare 9.36 to 9.359
9.36 is 0.001 more than 9.359
Both numbers round to the same value.
9.359 has greater precision.
The quotient of 5 times a number and 7 is equal to 10. What is the number?
A. 12
B. 13
C. 14
D. 15
The number when the quotient of 5 times a number and 7 is equal to 10 will be 15. The correct option is D.
What is a quotient?A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.
It is given that the quotient of 5 times a number and 7 is equal to 10. The number will be calculated as below:-
15 divided by 5 is 3 and 3+7 is equal to 10.
Therefore, the number when the quotient of 5 times a number and 7 is equal to 10 will be 15. The correct option is D.
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Suzy puts 2 slices of cheese on each sandwich. she makes 4 cheese sandwich. how many slices of cheese does Suzy use in all
If she puts 2 slices in 4 sandwiches, the answer would be 8.
(4 x 2)= 8.
Hope this helps & good luck. :)
if she has 4 sandwhiches and 2 slices of chesse on each you can multiply
4*2=8
PICK MORE THAN ONE ANSWER:
Eva earned the following test scores in science:
82, 100, 96, 90, 91
Ms. Wade entered the next score as 0 because Eva was absent on test day and hadn’t had a chance to make up the test. Which statements are true based on the data? Check all that apply.
After adding the 0 test score, the mean would be the most appropriate measure of center to describe the data.
After adding the 0 test score, the mean would be affected.
After adding the 0 test score, the median would be the most appropriate measure of center to describe the data.
Before the missed test, Eva’s median score was 96.
Before the missed test, Eva’s median score was 91.
Before the missed test, Eva’s mean score was 91.8.
Answer:
The correct answers are "After adding the 0 test score, the mean would be affected.", ad "Before the missed test, Eva’s median score was 91".
Step-by-step explanation:
We know that the mean and median scores would not be helpful in determining Eva's abilities since the 0 is not a representation of how much she knows. However, it will affect the average as adding a 0 to the numerator and a 1 to the denominator will lower the average.
Finally, we can tell the median is 91 before added as when we line up the scores in ascending order, the middle number is 91.
82, 90, 91, 96, 100
Answer:
Statements that are true based on the data:
-After adding the 0 test score, the mean would be affected.
-After adding the 0 test score, the median would be the most appropriate measure of center to describe the data.
-Before the missed test, Eva’s median score was 91.
-Before the missed test, Eva’s mean score was 91.8.
Step-by-step explanation:
-After adding the 0 test score, the mean would be the most appropriate measure of center to describe the data: NO, it won't because the data now has an extreme value that shifts the mean value significantly.
-After adding the 0 test score, the mean would be affected: YES, The mean value would be greatly impacted by adding the 0, (mean=76.5 with the 0; 91.8 without the 0),
-After adding the 0 test score, the median would be the most appropriate measure of center to describe the data: YES, because the median won't be affected as much as the mean by the extreme value.
-Before the missed test, Eva’s median score was 96: NO, the median score was 91 at that point.
-Before the missed test, Eva’s median score was 91: YES, the median score was 91, the median is defined as the value where 50% of sorted values are below and 50% are above
-Before the missed test, Eva’s mean score was 91.8: YES, the mean is defined as the sum of all values divided by the total number of values
The formula for calculating the median is:
-odd number of values: [tex]$ x_m = x_\frac{n+1}{2}[/tex]
-even number of values: [tex]$ x_m = \frac{x_\frac{n}{2}+x_\frac{n+2}{2}}{2}[/tex]
MEDIAN BEFORE ADDING THE 0: 82,90,91,96,100
[tex]$ x_m = x_\frac{5+1}{2}[/tex]=3 (third value)
MEDIAN AFTER ADDING THE 0: 0,82,90,91,96,100,
[tex]$ x_m = \frac{x_\frac{6}{2}+x_\frac{6+2}{2}}{2}[/tex]=average between the 3 and 4 values
[tex]$ x_m = \frac{90+91}{2}[/tex]=90.5
The formula for calculating the mean is: [tex]mean ={\frac{1}{n} \sum_{i=1}^n (x_i) $[/tex]
MEAN BEFORE ADDING THE 0
[tex]mean ={\frac{1}{5} \sum_{i=1}^5 (x_i) $[/tex]=[tex]\frac{459}{5}[/tex]=91.8
MEAN AFTER ADDING THE 0
[tex]mean ={\frac{1}{6} \sum_{i=1}^6 (x_i) $[/tex]=[tex]\frac{459}{6}[/tex]=76.5
Jeff found that 13 bag of popcorn weighed 14 pounds. How many pounds will one full bag of popcorn weigh? Express your answer in simplest form. a 112 lb b 17 lb c 37 lb d 34 lb
Let f(x) = cos(x). Find the x-intercepts of f(x) on [0, 2π).
the x-intercepts of cosx are
[tex]\frac{\pi }{2}[/tex] and [tex]\frac{3\pi }{2}[/tex] on [0, 2π )
The x-intercepts of the function f(x) = cos(x) on [0, 2π) are π/2 and 3π/2.
Explanation:The x-intercepts of the function f(x) = cos(x) on the interval [0, 2π) can be found by setting f(x) equal to zero and solving for x.
cos(x) = 0
To find the values of x for which cos(x) equals zero, we need to determine when the cosine function equals zero on the given interval. The cosine function equals zero at every multiple of π/2. Therefore, the x-intercepts of f(x) are π/2 and 3π/2.
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A window frame has a length of (5x + 3) inches and a width of (x + 6) inches. The area of the glass in the window is (4x² + 26x + 15) square inches.
What is the area of the trim around the glass in the window?
A. (x²+3x+7) square inches
B. (9x²+33x+59) square inches
C. (x²+7x+3) square inches
D. (9x²+59x+33) square inches
C
the area (A ) of the trim is the area of the window frame subtract the area of glass
area of window frame = (5x + 3)(x + 6) = 5x² + 33x + 18
A = 5x² + 33x + 18 - (4x² + 26x + 15)
= 5x^2 + 33x + 18 - 4x² - 26x - 15 = x² +7x + 3 inches²
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4. Work out the value of k.
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.
Gradient is the slope
So the slope of the line joining the points A(3,-5) and B(6,k) is 4
Slope of line joining two points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
A(3,-5) and B(6,k) are (x1,y1) and (x2,y2)
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
slope = [tex]\frac{k-(-5)}{6-3}=\frac{k+5)}{3}[/tex]
We know slope =4
[tex]\frac{k+5)}{3}=4[/tex]
Cross multiply and solve for k
k + 5 = 12
k = 7
The value of k = 7
My friend needed help with this and I found the height through the theorem but can't figure out how to get the base of the overall triangle
You found CD from the Pythagorean theorem to be ...
... CD = √(5² -2²) = √21
Since triangle ADC ~ triangle ACB, the ratios of corresponding sides are the same:
... AC/AD = AB/AC
... AB = AC²/AD
... AB = 5²/2 = 12.5 . . . . . . . the base of the overall triangle
_____
Then the area (A) is ...
... A = (1/2)bh
... A = (1/2)(12.5)(√21) ≈ 28.64 square units
_____
As you see here, the altitude of a right triangle divides it into three similar triangles. From smallest to largest, they are ...
... ADC ~ CDB ~ ACB
You can figure this using AAA similarity, since the smallest and largest triangles listed above share an acute angle vertex (∠A). That, together with the right angle, means all angles are congruent. After that, then you know ∠ACD ≅ ∠CBD, so you can show the middle sized triangle is similar to the other two.
chest volume is 8100 cubic inches the length is 30 inches and the width is 15 inches how tall will the chest be
The volume of a cuboid is given in terms of length, width, and height by ...
... V = LWH
Filling in the given numbers, we can solve for the height.
... 8100 in³ = (30 in)(15 in)H
Dividing by the coefficient of H, we have ...
... (8100 in³)/(450 in²) = H = 18 in
The chest will be 18 inches tall.
the function h(x)=g(x+2)-1, what is the value for h(2) and h(-2)
Put 2 where x is:
h(2) = g(2+2) -1 = g(4) -1
_____
Put -2 where x is:
h(-2) = g(-2+2) -1 = g(0) -1
$300 was deposited in a Certificate of Deposit (CD) yielding 6% interest compounded quarterly. how many years will it take the CD to reach a value of $876.34?
The future value (A) of a one-time investment of principal amount P at interest rate r compounded n times per year for t years is ...
... A = P(1 +r/n)^(nt)
Putting your given numbers into the formula, we have
... 876.34 = 300(1 +.06/4)^(4t)
Taking logarithms, this becomes the linear equation
... log(876.34) = log(300) + 4t·log(1.015)
Solving for t in the usual way, we get
... log(876.34) -log(300) = 4t·log(1.015) . . . . . . . subtract the constant term on the right
... (log(876.34) -log(300))/(4·log(1.015)) = t ≈ 18.00 . . . . divide by the coefficient of t
It will take 18 years for the $300 CD to reach a value of $876.34.
Find the angle complementary to the angle 80°.
The answer is 10 degrees since 90 - 80 = 10
the angle = 10°
Complementary angles sum to 90°
the complement of 80° is 90° - 80° = 10°
PLZ HELP GEOMETRY BELOW
c (16, 7 )
the transformation which maps KLMN to K'L'M'N' is a translation < 10, 3 >
Applying the same translation to STUV
T(6, 4 ) → T'(6 + 10, 4 + 3 ) = T'(16, 7 )
Which os larger 5.13 or 5.099? I think it's the 5.099?
5.13 is larger. Because it is closer to a whole number. That’s what I believe it is at least. Forgive me if I am wrong
PLZ HELP ME WITH GEOMETRY
You just need to use your test-taking skill to eliminate the wrong answers here.
There is no such thing as a "Congruent Angles Postulate," so the last two choices can be eliminated.
The AA Similarity Postulate refers to triangles, not angles, so the second choice can be eliminated.
That only leaves the (correct) first choice.
In 1970, a record 1.5 inches of rain fell in one minute at Brasse Terre, Guadalupe in the Caribbean. At this rate how much rain fell in 3 seconds or 0.05 of a minute? A 3 inches... B 0.075 inch... C 0.75 inch... D 30 inch. Pick one. Evan chose D as the correct answer. How did he get that answer?
Answer:
B. 0.075 in
Evan apparently divided by time. He might do that if he were not paying attention to units.
Step-by-step explanation:
The given rainfall rate is ...
... (1.5 in)/(60 s) = (1/40) in/s = 0.025 in/s
To find the rainfall in 3 s, you need to multiply rate by time:
... (0.025 in/s)×(3 s) = 0.075 in
If you keep the rate and time in terms of minutes, then you have:
... (1.5 in/min)×(0.05 min) = 0.075 in
_____
Evan apparently divided, instead. His number is not inches.
... (1.5 in/min)/(0.05 min) = 30 in/min² . . . . not the appropriate units for the problem
The correct amount of rain that fell in 3 seconds at Brasse Terre, Guadalupe, is 0.075 inches, as calculated by multiplying the rate of 1.5 inches per minute by 0.05 minutes. Evan made an error leading to answer D, which is incorrect.
In 1970, a record 1.5 inches of rain fell in one minute. To find out how much rain fell in 3 seconds, which is 0.05 of a minute, we need to multiply the rate of rainfall by the fraction of the minute we are interested in. The calculation is as follows:
1.5 inches/minute x 0.05 minute = 0.075 inches
Evan seems to have misunderstood the calculation, leading to answer D, but the correct amount of rain that fell in 3 seconds is 0.075 inches, which corresponds to option B.
Ben drank 2/5 of a pitcher of lemonade Tonya drank 1/4of the lemonade. What fraction of the lemonade did they drink together?
Hello there,
So you have two fractions 2/5 and 1/4, but none of them have the same denominator... However a LCD that you can get from both of these is 20, so if you multiplied 4 on the top and the bottom for 2/5, you would get 8/20, and for 1/4, multiply 5 on the top and the bottom, and soon you end up with 5/20. If you added these two fractions together, now knowing that they have the same denominator... you would end up with 13/20 which is the answer to your problem.
Hope this was helpful for you :)
Given: ∠A ≅∠D, ∠B ≅∠E m∠C = x, m∠F = 2x−30° Find: m∠C
This is 2 seperate triangles
ABC is one triangle and DEF is a different triangle
Answer:
[tex]m\angle c = 30^\circ[/tex]
Step-by-step explanation:
We are given the following information in the question:
ΔABC and ΔDEF
[tex]\angle A \cong \angle D\\\angle B \cong \angle E\\m\angle c = x \\m\angle F = 2x-30[/tex]
According to angle sum property of the triangle the sum of all angles of triangle is equal to 180 degrees.
Since two corresponding angles of the two triangle are equal, therefore the third angle is also equal.
[tex]x = 2x - 30\\\Rightarrow x = 30[/tex]
Thus,
[tex]m\angle c = 30^\circ[/tex]
The measure of the angle from the given information is m∠C = 2x - 30°
How to determine the measure of the angle?Given the information, we have two separate triangles: ABC and DEF.
In triangle ABC, we are given that ∠A ≅ ∠D and ∠B ≅ ∠E.
In triangle DEF, we are given that m∠C = x and m∠F = 2x - 30°.
To find m∠C, we need to find the value of x.
Since ∠A ≅ ∠D, and ∠B ≅ ∠E, we can conclude that triangle ABC is congruent to triangle DEF by the Angle-Angle (AA) congruence criterion.
Using this congruence, we can determine that m∠C = m∠F.
Therefore, we have:
m∠C = m∠F
Since we know that m∠F = 2x - 30°, we can substitute this value into the equation:
m∠C = 2x - 30°
This gives us the measure of angle C in terms of x.
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A line contains (34,12) and (32,48) what is the slope of the line in simplified form? HELP ASAPl
Answer:
[tex]m=-18[/tex]
Step-by-step explanation:
1. The line contains the points (34,12) and (32,48). Then, you need to use the slope formula, which is:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
2. When you substitute values into the formula, you obtain:
[tex]y_{2}=48\\y_{1}=12\\x_{2}=32\\x_{1}=34[/tex]
[tex]m=\frac{48-12}{32-34}\\m=\frac{36}{-2}\\m=-18[/tex]
Please see attached below. Please explain
Answer:
8 years
Step-by-step explanation:
The formula for the computation of simple interest is ...
... I = Prt
where I is the interest amount, P is the principal amount, r is the rate, and t is the number of years.
Fill in the given numbers and solve for t.
... 5704 = 15500×0.046×t
... 5704/713 = t = 8 . . . . . . divide by the coefficient of t
It takes 8 years to earn $5704 on that investment at 4.6% per year.
Someone please help, it will be so appreciated!
Keisha solved the following equation:
4x − 2x + 8 = 6(x + 4)
Which step has an incorrect justification? (Make sure to type only the number of the step into the blank: 1, 2, 3, 4 or 5)
Hello,
Question:
Keisha solved the following equation:
4x − 2x + 8 = 6(x + 4)
Which step has an incorrect justification? (Make sure to type only the number of the step into the blank: 1, 2, 3, 4 or 5)
Correct Solution:
x − 2x + 8 = 6(x + 4)
4x + −2x + 8 = (6) (x) + (6) (4) (Distribute)
4x + −2x + 8 = 6x + 24
(4x + −2x) + (8) = 6x + 24 (Combine Like Terms)
2x + 8 = 6x + 24
2x + 8 = 6x + 24
Subtract 6x from both sides.
2x + 8 − 6x = 6x + 24 − 6x
−4x + 8 = 24
Subtract 8 from both sides.
−4x + 8 − 8 = 24 − 8
−4x = 16
-4 x -4 = 16
x = -4
Answer:
Where keisha went wrong was forgeting to subtract 6x to both sides.
Incorrrect step is #3
The solution to the equation is correct.
on the line - 4x + 8 = 24 to the next line
- 4x = 16
4 should be Subtraction property of equality and not addition property of equality
6>2k+4 whats k hih9h9hhi
K=0
brainiest plz eeeeeeeeeeeeeeeeeee
What is the expanded equivalent of cos(a – b)?
cos(a-b) = cos(a)cos(b)+sin(a)sin(b)
The table shows a linear function.
Which equation represents the function?
x f(x)
10 −1
5 2
0 5
−5 8
A)f(x)=−53x+5
B)f(x)=−35x+5
C)f(x)=53x+5
D)f(x)=53x−1
Answer:
B) f(x) = -3/5x +5
Step-by-step explanation:
There are several ways you can write the equation of a line from a list of points. When you look through the list and see that one of them is the y-intercept, then the problem can be easier. When you look through the list of answers and see that the required answer is in slope-intercept form, then you know all you need to do is find the slope to go with the intercept you've located.
The point (x, f(x)) = (0, 5) tells you the y-intercept is 5.
The slope, the change in y divided by the change in x for two points, is ...
... (-1 -2)/(10 -5) = -3/5
This is the slope and the coefficient of x in the linear equation.
Now, we know the y-intercept (b=5) and the slope (m=-3/5), so we can fill in the slope-intercept form of the equation of a line:
... y = mx + b
... y = (-3/5)x + 5
PLZ HELP ME WITH GEOMETRY
B a counterclockwise rotation about the origin of 90°
under a counterclockwise rotation about the origin
a point ( x , y ) → (- y, x)
figure Q to figure Q'
( 4,2 ) → (- 2, 4 )
(7, 5 ) → (- 5, 7 )
(3, 7 ) → (- 7 , 3 )
(2, 4 ) → (- 4, 2 )
(5, 4 ) → (- 4, 5 )
the coordinates of the original points of the vertices of Q map to the corresponding points on the image Q'
Plz answer this ASAP! What is the x-coordinate of the solution for the system of equations? {y−x=910+2x=−2y Enter your answer in the box.
:) Here is your answer -7
Answer:
the answer is -7
Step-by-step explanation:
thxs person who answered before me :)
list the single-digit factors of 924
The prime factorization is ...
... 2²×3×7×11
Single-digit prime factors are ... 2, 3, 7
Single-digit divisors are ... 1, 2, 3, 4, 6, 7
What is the value of x?
3x−8=8x+4/2
Enter your answer in the box.
Answer:
x = -2
Step-by-step explanation:
3x -8 =8x +4/2
3x -8 =8x +2
3x -3x -8 = 8x -3x +2 (subtract 3x both sides )
-8 = 5x +2
-8-2 =5x+2 -2 (subtract 2 both sides )
-10 =5x
-10/5 = 5x/5 (divide 5 both sides)
-2 = x
Which of the following graphs represents the function f(x) = −x2 − x + 6?
(Correct Answer will receive 30 points and be marked as Brainliest)
The function f(x) describes a parabola that opens downward. The only graph with that shape is the 2nd one.
_____
The degree of 2 on the x² term means there will be only 1 turning point (1 less than the degree). The bottom two choices have more turning points than that.
The minus sign on the coefficient of x² means the graph opens downward—that it tends toward -∞ when x gets very large in magnitude, either positive or negative.