Answer: 350 gallon
Step-by-step explanation:
If 19.8% is 69.3gallons
1% is 69.3/19.8
100% used is 69.3/19.8 × 100/1
To obtain an average (arithmetic mean) of exactly 2/3, what fraction must be added to 1/6, 1/2, and 1/3?
A. 2/3
B. 1/1
C. 3/2
D. 5/3
Answer:
D. 5/3
Step-by-step explanation:
[tex]\frac{1/6+1/2+1/3+x}{4} =2/3[/tex]
[tex]1/6+1/2+1/3+x=8/3[/tex]
[tex]x=8/3-1/6-1/2-1/3[/tex]
[tex]x=8/3-1/6-3/6-2/6[/tex]
[tex]x=8/3-6/6[/tex]
[tex]x=16/6-6/6=10/6[/tex]
simplified
[tex]x=5/3[/tex]
Hope this helps
A(n)is used to uncover conditions and trends difficult to see by looking at individual amounts. It can be expressed as a percent, rate, or proportion.
A(n) ratio is used to uncover conditions and trends difficult to see by looking at individual amounts.
What is ratio?Ratio is used to show or express the number of times a number is in proportion to another number.
Ratio can be inform of the following:
Example of ratio is 1:2 or 1/2.
Therefore A(n) ratio is used to uncover conditions and trends difficult to see by looking at individual amounts.
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Peter set up the iron board to iron his shirt. 3 If m 3 is 65°, what is the measure of its vertical angle? OA. 155° OB. 65 OC. 25° OD. 115°
Answer:
the same 65 degrees
Step-by-step explanation:
The weights of 1500 bodybuilders are normally distributed with a mean of 190.6 pounds and a standard deviation of 5.8 pounds.
A. About how many bodybuilders are between 180 and 190 pounds?
B. What is the probability that a bodybuilder selected at random has a weight greater than 195 pounds?
Answer:
A. 637
B. 0.2240 (4 dp) = 22.4% (nearest tenth)
Step-by-step explanation:
Normal Distribution
[tex]\sf X \sim N(\mu, \sigma^2)[/tex]
Given:
[tex]\sf \mu = 190.6[/tex][tex]\sf \sigma=5.8[/tex][tex]\implies \sf X \sim N(190.6, 5.8^2)[/tex]
Part A[tex]\begin{aligned}\sf P(180 < X < 190) & = \sf P(X < 190)-P(X\leq 180)\\& = \sf 0.4588035995-0.03380583874\\& = \sf 0.4249977608\end{aligned}[/tex]
Total number of bodybuilders = 1500
Therefore, the number of bodybuilders between 180 and 190 pounds is:
[tex]\begin{aligned}\sf P(180 < X < 190) \cdot1500 & = \sf 0.4249977608 \cdot 1500\\& = \sf 637.4966412\\& = \sf 637\end{aligned}[/tex]
Part B[tex]\begin{aligned}\sf P(X > 195) & = \sf 1-P(X\leq 195)\\& = \sf 1-0.7759602537\\ & = \sf 0.2240397463\\ & = \sf 0.2240\:(4\:dp)\end{aligned}[/tex]
Sam buys a DVD player for $55. 95 and it is on sale for 40% off regular price. How much money will same save
Answer:
$ 22.38
Step-by-step explanation:
If the pre-sale price is $ 55.95
40 % of this would be .4 * 55.95 = $ 22.38
3/2+9/9= ???? Help me please...
Answer:
3/2+9/9=2.5
Step-By-Step Explanation
3/2=1.5
9/9=1
1.5+1=2.5
Drag the numbers to order them from greatest to least, with the greatest at the top.
Answer:
the order that they are in right now is right
Step-by-step explanation:
Please solve and show your work
SA=π(9)²+π9*19
* is how I do the multiplication symbol btw
Answer:
791.28
Step-by-step explanation:
1. 3.14*9²=254.34
2. 3.14*9*19=536.94
3. 536.94+254.34=791.28
If you can mow 90 lawns in 45 hours, how long will it take to mow 12?
Work Shown:
(90 lawns)/(45 hours) = (12 lawns)/(x hours)
90/45 = 12/x
2 = 12/x
2x = 12
x = 12/2
x = 6
It takes 6 hours to mow 12 lawns.
The function f(x) = 2* and g (x) = f(x) + k. If k = 2, what can be concluded about the graph of
g (x)?
Translations are transformations that change the position of the graph of a function. The general shape of the graph of a function is moved up, down, to the right or to the left. The translations are considered rigid transformations.
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
To graph y = f (x) -k, move the graph of k units down.
We have then:
f (x) = 2 ^ x
g (x) = f (x) + k
if k = 2
then,
the graph of g (x) is shifted vertically 2 units up
Answer:
the graph of g (x) is shifted vertically 2 units up
19. The ratio of blue to green marbles is
2:3. If there are only blue and green
marbles, what percent of the
marbles are blue?
Answer: 40%
Step-by-step explanation:
Mei runs the same distance 6 days each week. In 4 weeks, she runs 151.68 miles. How many miles does Mei run each day?
Answer: 6.32
Step-by-step explanation: 6 days a week in 4weeks Is 24days
Divide the total distance by 24
6834/17 please show your work
Answer:
6834 / 17 = 402
Step-by-step explanation:
• sorry i d k, I just got the ans on calculator
Please help!!
Find the value of x
A. 12
B. 6
C. 10
Answer:
x = 12
Step-by-step explanation:
Let's find the measure of major arc MNB:
360 - arc MB = major arc MNB
Now, let's plug in what we know:
360 - (80 + 60) = major arc MNB
Next, combine like terms, and replace "major arc MNB" with "x."
360 - 140 = x
220 = x
Now, we know that the measure of major arc MNB equals 220 degrees.
Angle MLB is going to be double the measure of major arc MNB, so let's set up an equation for this situation:
2(Angle MLB) = major arc MNB
Now, let's plug in what we know:
2(9x + 2) = 220
Finally, let's solve for x:
18x + 4 = 220
18x = 216
x = 12
Suav wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 19 ∘ ∘ angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest hundredth of an inch if necessary.
The height of the ramp rise from the ground at its highest end to the nearest hundredth is 8.79 inches.
The situation forms a right angle triangle.
What is a right angle triangle?A right angle triangle has one of its angles as 90 degrees. The sides can be found using trigonometric ratios.
Therefore, the hypotenuse of the right triangle formed is the length of the fiberboard.
The height of the ramp formed is the opposite side of the right triangle.
Hence,
sin 19° = opposite / hypotenuse
sin 19° = h / 27
cross multiply
h = 27 × sin 19°
h = 27 × 0.32556815445
h = 8.79034017034
h = 8.79 inches.
Therefore, the height of the ramp rise from the ground at its highest end to the nearest hundredth is 8.79 inches.
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Answer:
8.79 inches
Step-by-step explanation:
A circle has a central angle measuring startfraction 7 pi over 6 endfraction radians that intersects an arc of length 18 cm. what is the length of the radius of the circle? round your answer to the nearest tenth. use 3.14 for pi. 3.7 cm 4.9 cm 14.3 cm 15.4 cm
The length of the radius of the circle with a central angle measuring 7pi/6 is 4.9cm
How to calculate the length of aan arc?The formula for calculating the legnth of an arc is expressed as:
L = rtheta
r is the radius
Theta is the subtended angle
Given the following
18 = r(7pi/6)
7pi r = 18 * 6
7pi r = 108
r = 108/7pi
r = 4.9cm
Hence the length of the radius of the circle with a central angle measuring 7pi/6 is 4.9cm
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Answer:
B or 4.9cm
Step-by-step explanation:
Find the surface area and volume of a 1-inch cube and a 10-inch cube. What is the ratio of the surface areas? What is the ratio of the volumes?
[tex]\maltese \: \: \underline{\underline{\frak{Understanding~the~question :-}}} \\ \\[/tex]
For solving this question, we will take the help of the branch of mathematics that studies the sizes of different shapes may they be 2D or 3D, called mensuration.
⠀
There are two parts in the question, in the first part we have been asked to calculate the ratio of the total surface area of the two cubes, for that we will calculate their total surface areas and divide them in order to calculate the ratio. In the second part, we have been asked to calculate the ratio of the volume of the two cubes, and in order to calculate the ratio, at first we will calculate the volumes of the respective cubes and then divide them. And, thus, in this way, we will get our required answer.
⠀
[tex] \maltese \: \underline{ \underline{ \frak{Given :-}}} \\ \\ [/tex]
Two cubes in which the sides measure,
Cube 1 say A = 1 inchCube 2 say B = 10 inch⠀
[tex] \maltese \: \: \underline{ \underline{ \frak{Formula~Applied :-}}} \\ \\ [/tex]
[tex] \bigstar \begin{cases} \sf 1.~Volume_{cube} = {a} ^3\\ \\\sf 2.~T.S.A._{cube} = 6{a}^2\end{cases} \\ \\ [/tex]
[tex] \maltese \: \underline{ \underline{ \frak{Solution :-}}} \\ \\ [/tex]
Calculating the total surface areas,
⠀
[tex] \sf \longrightarrow TSA \: of \: A = 6( {1)}^{2} \: \: \: \\ \\ \\ \sf \longrightarrow TSA \: of \: A =6 \times 1 \: \: \: \\ \\ \\ \sf \longrightarrow TSA \: of \: A = {6 \: inch}^{2} \\ \\ [/tex]
[tex]\sf \longrightarrow TSA \: of \: B =6 {(10)}^{2} \: \: \: \: \: \: \\ \\ \\\sf \longrightarrow TSA \: of \: B =6 \times 100 \: \: \: \\ \\ \\ \sf \longrightarrow TSA \: of \: B = {600 \: inch}^{2} \\ \\ [/tex]
Thus, now we can calculate the ratio,
⠀
[tex]\sf \longrightarrow Ratio = \dfrac{TSA~of~A} {TSA~of~B} \\ \\ \\ \sf \longrightarrow Ratio = \dfrac{6}{600} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio = \cancel \dfrac{6}{600} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio = \dfrac{1}{100} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio =1 : 100 \: \: \: \: \: \: \\ \\ [/tex]
Thus, the ratio of the total surface area of the cubes is 1 : 100. Now, moving to the second part of the question, and calculating the volume of the cubes, we have,
⠀
[tex]\sf \longrightarrow Volume \: of \: A= {(a)}^{3 } \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: A= {(1)}^{3} \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: A= {1 \: inch}^{3} \\ \\ [/tex]
[tex]\sf \longrightarrow Volume \: of \: B = {(a)}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: B = {(10)}^{3} \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: B = {1000 \: inch}^{3} \\ \\ [/tex]
Now, calculating the ratio,
⠀
[tex]\sf \longrightarrow Ratio =\dfrac{Volume ~of~A} {Volume~of~B} \: \: \\ \\ \\ \sf \longrightarrow Ratio = \dfrac{ {1 \: inch}^{3} }{1000 \: {inch}^{3} } \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio = \cancel\dfrac{ {1 \: inch}^{3} }{ {1000 \: inch}^{3} } \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio =1 : 1000 \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Thus, the ratio of the volume of the cubes is 1 : 1000.
⠀
[tex] \underline{ \rule{227pt}{2pt}} \\ \\ [/tex]
Use the long division method to find the result when 4x3 -2x2 – 15x + 6 is
divided by x-2
Answer:
[tex]4x^2+6x-3[/tex]
Step-by-step explanation:
"/" substitutes the normal division symbol
[tex]4x^2[/tex] [tex]+6x[/tex] [tex]-3[/tex]
______________
[tex]x-2/4x^3-2x^2-15x+6[/tex]
[tex]4x^3[/tex] [tex]-8x^2[/tex]
______________________
[tex]6x^2[/tex] [tex]-12x[/tex]
______________________
[tex]-3x+6[/tex]
x multiplied by what equals [tex]4x^3[/tex]? [tex]x(4x^2)=4x^3[/tex], so the first number that goes on top is [tex]4x^2[/tex]. Multiply x by [tex]4x^2[/tex] and put it below to the [tex]4x^3[/tex] on the first row. Multiply x-2 by [tex]4x^2[/tex] and put it below the [tex]-2x^2[/tex] . Subtract the first row from the second row.
x multiplied by what equals [tex]6x^2[/tex]? [tex]6x[/tex]. Repeat the same process as before except with [tex]6x^2[/tex]
Write an equation for the line that is parallel to the given line and that passes though the given point
y = 4x -21 (again cool name btw) :)
y=4x-3 has slope = to the coefficient of the x term = 4
all parallel lines have the same slope.
y=4x + b, where b can be any real number, so just plug in the point (4,-5) into the general equation
y=4x+b = -5 = 4(4) + b
-5 = 16 + b
-21 = b
b = -21 = the y intercept, so the equation is
y=4x -21
The price of a pack of kitchen rolls is reduced by
1/6
The new price is £1.20
Work out the original price.
Answer: 1.44
Step-by-step explanation: 1.20 Is the remaining 5/6 which is 83.3%
Calculate for 100% to get actual amount
If 83.3% = 1.20
1% = 1.20/83.3
100% = 1.20/83.3 ×100/1
The original price is equal to £7.2
What are the cost price and selling price?1. Cost price = Selling price − profit ( when selling price and profit are given )
2. Cost price = Selling price + loss ( when selling price and loss are given )
Given here: New price =£ 1.20
let the original price be x then we have
x/6 = 1.20
x=£7.2
Hence, The original price is £7.2
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Arlo researched the starting salaries at the different companies that he applied to. Here is the data he found:
$24,640
$26,740
$23,620
$25,520
$24,710
$25,180
$25,520
$24,750
$24,710
$23,860
Find the mean, median, and mode of the data set. Show your work. (10 points)
Step-by-step explanation:
median -> $24.710+$25.180=$49.89
$49.98÷2=$24.945
mode -> $25.520 and $24.710
mean -> $24.640+$26.740+$23.620+$25.520+$24.710+$25.180+$25.520+$24.750+$24.710+$23.860= $249.25
$249.25÷10=$24.925
mean (add all your numbers together and then divide them by how many they are, here there are 10 numbers)
median (the middle one, if there are 2 in the middle, then you'd add those two numbers together and then divide by two)
mode (the number you see the most, mode *most*)
I hope all this helped, this took time. Take care!
If you borrow $1000 for 5 years at an interest rate of 10%, the amount of interest you pay is?
Answer:
p=1000
t=5 years
r=10%
i=(ptr)/100
i=(1000×5×10)/100
i=50000/100
i=500
Solve this to sin , and pls explain .
I do have exams for tomorrow.
Answer:
sinΘ =1
Step-by-step explanation:
cosΘ × cosΘ/sinΘ+ sinΘ = sinΘ
cos^2 Θ/sinΘ +sinΘ =sinΘ
cos^2Θ+ sin^2Θ /sin Θ = sinΘ
1/sinΘ =sinΘ
A circle with center O is inscribed in a square with a
perimeter of 40, as shown below. What is the area of the
shaded region?
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Areas and Volumes.
Area of Shaded region = Area of Square - Area of inscribed Circle.
Radius if circle = 10/2 ==> 5 units
hence,
Area of circle = 25 π units
Area of square = (10)^2 ==> 100 units
hence the area of shaded region = 100 - 25π
==> Area of shaded region = 25 (4 - π)
Correct option is G.)
(982x5.47)-(598x78)+28=y
Answer:
4805.38
Step-by-step explanation:
982×5.47=5371.54
598×78=46,644
5371.54-46644=4805.10
4805.10+28=4805.38
Please Help i need to know this asap
Answer:
(0, - 6)
Step-by-step explanation:
Midpoint Formula
M = (x₁ + x₂ / 2, y₁ + y₂ / 2)Solving
M = (-3 + 3 / 2, -7 - 5 / 2)M = (0, -12/2)M = (0, - 6)Answer:
The midpoint is (0, -6)
Step-by-step explanation:
Step 1: Determine the midpoint
[tex]midpoint = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
[tex]midpoint = (\frac{-3 + 3}{2}, \frac{-7 + (-5)}{2})[/tex]
[tex]midpoint = (\frac{0}{2}, \frac{-7 -5}{2})[/tex]
[tex]midpoint = (0, \frac{-12}{2})[/tex]
[tex]midpoint = (0, -6)[/tex]
Answer: The midpoint is (0, -6)
From her
eye, which stands 1.68 meters above the ground, Hannah measures the
angle of elevation to the top of a prominent skyscraper to be 31°. If she is standing at
a horizontal distance of 194 meters from the base of the skyscraper, what is the height
of the skyscraper? Round your answer to the nearest hundredth of a meter if
necessary.
The tangent or tanθ function of trigonometry is the ratio of its perpendicular to its base in a right triangle. The total height of the sky scrapper is 118.25 meters.
What is Tangent (Tanθ)?The tangent or tanθ function of trigonometry is the ratio of its perpendicular to its base in a right triangle. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
Since the horizontal distance between Hannah's eyes and the sky scrapper is 194 meters while the angle between the eye and the top of the sky scrapper is 31°. Therefore, the vertical height of the sky scrapper from the height of Hannah's eye level, using the tangent function can be written as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\\\\\\tan(31^o) = \dfrac{\text{Height of sky scrapper from eye level}}{194\ meters}\\\\\\\text{Height of sky scrapper from eye level} = 116.567\ meters[/tex]
Since the height of the eye level is 1.68 meters from the ground, therefore, the total height of the sky scrapper can be written as,
[tex]\rm \text{Total height of sky scrapper from ground}\\\\=(\text{Height of sky scrapper from eye level}) + 1.68\ meters\\\\= 116.567 + 1.68\\\\= 118.25\ meters[/tex]
Hence, the total height of the sky scrapper is 118.25 meters.
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An appropriate statistical tool for accounting for sampling error in an estimate is A. A scatter chart B. A frequency distribution C. A confidence interval D. A standardized score E. All of the above F. None of the above
The statistical tool for accounting for sampling error in an estimate is confidence interval.
What is sampling?The term sampling has to do with the selection of a given number of participants from the population in susch a way that reflects the population of the entire population.
Sampling is usually prone to given degree of error. The statistical tool for accounting for sampling error in an estimate is confidence interval.
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PLEASE HELP FAST ITS ABOUT GEMONETRY D:
PLEASE HURRY
The number of points Darin scores in a basketball game can be found using the expression 3s + 2t + u, where s is the number of three-point field goals made, t is the number of two-point field goals made, and u is the number of free throws made.
How many points did Darin score in a game where he made 2 three-point field goals, 5 two-point field goals, and 3 free throws?
A. 16
B. 19
C. 22
D. 25
Answer:
Option B - Darin scores in a basketball game is 19 Points
Step-by-step explanation:
Darin scores in a basketball game = 3s + 2t + u
where s is the number of three-point field goals made,
t is the number of two-point field goals made,
u is the number of free throws made.
Darin scores in a basketball game = 3(2) + 2(5) + 3
= 6 + 10 + 3
= 19 Points
Hope this helps!