If it takes 6 hours for Matt to wash the car, then he washes at a rate of 1/6 cars per hour:
[tex]\begin{gathered} \frac{1}{x}=6 \\ x=\frac{1}{6} \end{gathered}[/tex]Let y be the time in which Matt's dad washes the car and state an equation that describes the situation in which Matt and his dad wash the car together:
[tex]\begin{gathered} \frac{1}{6}+\frac{1}{y}=2 \\ \frac{1}{y}=2-\frac{1}{6} \\ \frac{1}{y}=\frac{11}{6} \\ y=\frac{6}{11} \end{gathered}[/tex]It means that he washes the car in 6/11 hours (approximately 0.54hours).
John saves 2/5 of his take-home pay. After
6 paychecks, he has saved $4,800. How much is John's paycheck?
A. $800
C. $2,000
B. $1,920
D. $3,500
John's paycheck is $2,000.
According to the question,
We have the following information:
John saves 2/5 of his take-home pay.
After 6 paychecks, he has saved $4,800.
Now, let's take John's paycheck to be $x.
Now, 2/5 of this paycheck will be $2x/5.
So, this is the amount saved from 1 paycheck of John.
Now, to find the amount saved in 6 paychecks will be:
6*(2x/5)
Now, we can equate this to the amount saved by John after 6 paychecks.
6*(2x/5) = $4,800
12x/5 = 4800
12x = (4800*5)
x = (4800*5)/12
Now, dividing 4800 by 12:
x = 400*5
x = $ 2000
Hence, the correct option is C ($2,000).
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is the reflection of a figure in the x axis equivalent to the rotation of that same figure 180° (clockwise) about the origin?
The reflection across x-axis has the following rule applied
[tex](x,y)\rightarrow(x,-y)[/tex]The rotation of 180° about the origin has the rule
[tex](x,y)\rightarrow(-x,-y)[/tex]In this case, the new image are not the same, that is to say
Therefore, they are not the same.
For the exponential function f, find f^-1 analytically and graph both f and f^-1.f(x)=6^x-8
First, replace f(x) by y. This is done to make the rest of the process easier.
[tex]y=6^x-8[/tex]Now, replace every x with y and a every y with an x:
[tex]x=6^y-8[/tex]Now, solve this equation for y. Then, we must move -8 to the left hand side as +8. It yields
[tex]x+8=6^y[/tex]Now, we can apply logarithms in both sides:
[tex]\log (x+8)=\log 6^y[/tex]For the properties of logarithms, we have
[tex]\log 6^y=y\log 6[/tex]then, we have
[tex]\log (x+8)=y\log 6[/tex]and we obtain
[tex]y=\frac{\log(x+8)}{\log6}[/tex]Finally, replace y with f^1. Then, the inverse funcion is
[tex]f^{-1}(x)=\frac{\log(x+8)}{\log6}[/tex]The graphs of the function and its inverse are:
What does the variable r represent?The population correlation coefficientThe sample correlation coefficientThe coefficient of determinationThe critical value for the correlation coefficient
Given:
Variable r
To determine the what variable r represents, we first note that it is a common way to indicate a correlation value. We also note that coefficient of determination, r^2, is simply the square of the sample correlation coefficient (i.e., r).
Therefore, variable r means:
The sample correlation coefficient
Please help I am so bad at geometry
Which symbol correctly compares these fractions? -13\15 and -5\6 a: = b: > c:
Answer:
B
Step-by-step explanation:
None
Given: I II m. Write a flowchart proof to show that ∠1 ≅ ∠3.
flowchart proof
1) Lines m and l are parallel ------> given
2) ∠1 ≅ ∠2 -----> by alternate interior angles
3) ∠3 ≅ ∠2 -----> by vertical angles
4) ∠1 ≅ ∠3 ----> by the transitive property
Explain the meaning of 5!
a. 1+2+3+4+5
b.5-4-3-1-0
c.0×1×2×3×4×5
d. 5•4•3•2•1
The number 5 in mathematics denotes a quantity or value of 5. Five is the entire number between four and six. Five is the name of the number. Sam the little shows off five fingers.
What does 5 represent?The distance between 5 and 0 is the absolute value of 5. Then you go 1, 2, 3, 4, and 5. To the immediate right of zero, 5 is located. As a result, 5 has an absolute value of 5.
It denotes the sum of all succeeding integers, inclusively from 1 to 5.
That ' s 5! = 5*4*3*2*1 =120.
Also known as five factorials.
What's the name of a five-digit number?Ten-thousands
Answer and justification A five-digit figure is one that is in the tens of thousands. This is due to the fact that 10,000 is the smallest positive whole number with five digits.
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The length of the long leg in a 30°-60°-90° triangle is 3√2 cm. What is thelength of the short leg?
Answer
x = √6
Explanation
We will first sketch this triangle.
Let the short leg of the triangle be x
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
So, after noting the three sides in a right triangle, we will then use trignometric ratios to solve for any of the unknown. If the non-right-angle angle given is θ, the trignometric ratios in short forms are written as
SOH, CAH and TOA
SOH means Sin θ = (Opp/Hyp)
CAH means Cos θ = (Adj/Hyp)
TOA means Tan θ = (Opp/Adj)
So, the one to be used depends on the sides of the triangle that are provided.
For this triangle, using the angle 60° as the non-right-angle angle
Hypotenuse = ?
Opposite = 3√2
Adjacent = x
Angle = 60°
TOA means Tan θ = (Opp/Adj)
Tan 60° = (3√2)/x
Tan 60° = √3
Tan 60° = (3√2)/x
√3 = (3√2)/x
Cross multiply
x = (3√2)/(√3)
x = (√3) (√2)
x = √6
Hope this Helps!!!
Answer:
x = √6
Step-by-step explanation:
Lisa specializes in baking lemon cupcakes. She bakes 3 dozen cupcakes every hour. The cost (in dollars) of making n cupcakes is given by the function C(n) = 60 + 0.45n.
Consequently, it costs $62.70 to make cupcakes for two hours.
By making use of functions, We have: n(h) = 3h, The cost in terms of hours h is given by C(3h) = 60+1.35h, and Lisa's cost for making cupcakes for 2 hours is $62.70
According to the question, Lisa makes 3 dozen cupcakes an hour. To calculate how many she makes in h hours, we will apply the equality postulate as stated.
3 dozens = 1 hour
Hour = n(h)
Cross Multiplying,
n(h) × 1 = 3×h
n(h) = 3h
Therefore, n(h) = 3h is the function that predicts the number of cupcakes Lisa produces in h hours.
We shall locate the composite function C(n(h)) to obtain the cost function in hours.
C(n(h)) = C(3h) (3h)
If C(n) = 60 + 0.45n, then
By replacing n with 3h in the function as indicated, C(3h) is obtained;
C(3h) = 60+0.45(3h) (3h)
C(3h) = 60+1.35h
Thus, 60+1.35h is the cost function expressed in hours.
We will change h = 2 into the calculation C(h) = 60+1.35h to obtain the cost of baking cupcakes for 2 hours.
C(2) = 60+1.35(2) (2)
C(2) = 60+2.70
C(2) = 62.70
Consequently, it costs $62.70 to make cupcakes for two hours.
Complete Question:
Lisa specializes in baking lemon cupcakes. She bakes 3 dozen cupcakes every hour. The cost (in dollars) of making n cupcakes is given by the function C(n) = 60 + 0.45n. The function that models the number of cupcakes Lisa makes in h hours is n(h)=___. The cost in terms of hours h is given by ___. Lisa's cost for making cupcakes for 2 hours is___
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Find the interest and future value of a deposit of $8,750 at 3% for twenty years.
Answer
Interest = $5,250
Future value = $14,000
Explanation
Given:
Principal, P = $8,750
Rate, R = 3%
Time, T = 20 years
What to find:
The interest and future value.
Step-by-step solution:
The Interest
The interest can be calculated using the simple interest formula below.
[tex]Interest=\frac{P\times R\times T}{100}=\frac{\$8,750\times3\times20}{100}=\$5,250[/tex]The interest of $8,750 at 3% for twenty years is $5,250
The future value
Future value = Amount = Principal + Interest
Future value = $8,750 + $5,250
Future value = $14,000
The measure of an angle and it’s complement differ by 22 degrees. Find the larger angle.
The measure of an angle and its complement differ by 22 degrees and the larger is 56°
What are Complementary Angles?The total of the two angles' measurements determines their complement and supplement. The pair of angles is said to be complimentary if the product of the two angles equals the measurement of a right angle.
1. If the total of two angles equals 90°, the angles are considered to be complements of one another.
2. Let x° and y° be the two angles. Since they complement one another, the two angles' sum will be 90 degrees.
= x + y = 90°. (Assume equation 1 is used.)
3. The two angles differ by 22 degrees, hence the equation will be,
= x - y = 22°. (Put equation 2 in.
4. To determine the values of x and y, solve equations 1 and 2.
Add equations 1 and 2 together.
= x + y + x - y = 90 + 22,
= 2x = 112°,
= x = 56°.
5. In equation 1, change the value of x.
= 56° + y = 90°,
= y = 90 -56,
= y = 34°.
So, the measure of the two angles is 56°, and 34°.
And the larger angle is 56°
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The number of yards Y is equal to the number of feet F divided by 3 find formula and graph it
Respuesta:
Si el número de yardas (Y) es igual al número de pies (F) dividido por 3, entonces podemos establecer la siguiente ecuación:
[tex]Y=\frac{F}{3}\text{.}[/tex]La gráfica de esta ecuación es una linea recta con pendiente 1/3 y que pasa por el origen, como sigue:
You earn $\$34.50$ selling items at a craft show. Newton earns $5$ times as much as you. Descartes earns $0.1$ times as much as Newton does. How much do the three of you earn in all?
All the three person earn $230.75 in all.
What is mean by Addition?
The process of combining two or more numbers is called the Addition.
Given that;
You earn in selling items = $35.50
Newton earn 5 times as much you.
Descartes earns 0.1 times as much as Newton does.
Now,
You earn in selling item = $35.50
Newton earn in selling = 5 x $35.50
= $177.5
Descartes earn in selling = 0.1 x $177.5
= $17.75
So, Total earn = $35.50 + $177.5 + $17.75
= $230.75
Therefore, All the three person earn $230.75 in all.
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The price of stock A at 9 am was $15.48 since then the price has been increasing at the rate of $0.11 each hour at noon the price of stock B was $16.23 it begins to decrease at the rate of $0.12 Each hour if the two rates continue in how many hours will the prices of two stocks be the same
Please help me I’ll mark u brainly
Answer:
A: (-3,0)
B:(-3,-5)
C:(-6,0)
Step-by-step explanation:
invert the signs on all numbers to flip it 180 degrees, then add 4 to each y point to translate up 4
enrique needs our help again. He has 310 dollars he can afford to put towards a new car each month. he wants to be done in 5 years.
a. if he were to be approved for loan at 8% apr compounded monthly, what would the size loan granted to him be? what is he were approved for 3% compounded monthly?
b. one of your values should be higher then the other. Explain why it makes sense that your higher loan value paired with the apr that produced it makes sense?
The monthly payment of $310 compounded monthly at 8% and 3% will have a principal of $15,288.71 and $17,252.23 respectively
Monthly PaymentThe monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.
In order to solve this question, we can use the formula of monthly payment we can use a simple formula for that
[tex]A = p \frac{r(1+r)^n}{(1+r)^n-1}[/tex]
A = monthly paymentr = rate n = number of times compoundedPrincipal on the loanIn the first scenario, we can find the monthly payment at 8%
Substituting the values into the equation and solve
The principal at 8% is $152888.71 and the principal at 3% is at $17252.23
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PLS HELP DUE TODAY THE IXL
Answer:
Step-by-step explanation:
Answer:
Recall that the volume of the a right circular cone with height h and radius …
Given:
The change in volume by time is, (dV/dt) = 10 cubic feet per minute.
The diameter and height of the right circular one are equal, 2r = h.
Height of the pile is, h = 21 ft.
The objective is to find the rate of increase in height of the pile.
Explanation:
The general formula of volume of cone is,
[tex]V=\frac{1}{3}\pi r^2h\text{ . . . . . (1)}[/tex]From the given data, radius of the cone can be calculated as,
[tex]\begin{gathered} 2r=h \\ r=\frac{h}{2} \end{gathered}[/tex]Substitute the value of r in equation (1).
[tex]\begin{gathered} V=\frac{1}{3}\pi(\frac{h}{2})^2h \\ V=\frac{1}{3}\pi(\frac{h^2}{4})^{}h \\ V=\frac{1}{12}\pi h^3\text{ . . . . . (2)} \end{gathered}[/tex]To find rate of increase in height of the pile:
Now, differentiate equation (2) with respect to time t.
[tex]\begin{gathered} \frac{dV}{dt}=\frac{\pi}{12}\times\frac{d}{dt}(h^3) \\ \frac{dV}{dt}=\frac{\pi}{12}\times3h^2\frac{dh}{dt} \\ \frac{dV}{dt}=\frac{\pi}{4}\times h^2\frac{dh}{dt}\text{ . . . . (3)} \end{gathered}[/tex]Substitute (dV/dt) and h in equation (3).
On plugging the obtained values in eqation (3),
[tex]\begin{gathered} 10=\frac{\pi}{4}\times(21)^2\frac{dh}{dt} \\ \frac{dh}{\mathrm{d}t}=\frac{10\times4}{21^2\times\pi} \\ \frac{dh}{dt}=0.02887164\ldots.\text{.} \\ \frac{dh}{dt}\approx0.029\ldots\text{ ft/min} \end{gathered}[/tex]Hence, the rate of increase in height of the pile is 0.029 ft/min.
Mr. Emmer gave a test in his Chemistry class. The scores were normally distributed with a mean of 82 and a standard deviation of 4. A student is randomly chosen. What is the probability that the student scores an 88 or below?
Answer:
93.32 %
Step-by-step explanation:
88 - 82 = 6 points
this is 6 /4 = z-score + 1.5
from z score table , this corresponds to .9332 or 93.32 %
A parachute speed during a free fall reaches 135 miles per hour. What is this speed in feet per second? At this speed, how many feet will the parachute fall during 5 seconds free fall? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answer.
The parachutes speed during free fall will be : 990 feet per second
Given: A parachute speed during a free fall = 135 miles per hour.
This means Unit rate = 135 miles per hour
= 135 × [tex]\frac{5280}{60X60}[/tex] feet per second
Because it is given that 1 mile = 5280 feet per second
= [tex]135 X \frac{5280}{3600}[/tex]
On dividing 5280 by 3600
we get:
= 135 × 1.46
= 198.00 feet per second
Thus in 5 seconds the parachutes speed during free fall will be :
990 feet per second.
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Which steps should be used to graph the equation y-4 = 1/3 (x + 2)?
We have the following equation:
y - 4 = 1/3 (x + 2)
We clear y in order to be more unterstandable:
y - 4 = 1/3 (x + 2)
y = 1/3 (x + 2) + 4
y = 1/3 x + 2/3 + 4
y = 1/3 x + 2/3 + 12/3
y = 1/3 x + 14/3
Step 1In order to find the answer we are going to determine x value when y = 4:
y = 1/3 x + 14/3
4 = 1/3 x + 14/3
4 - 14/3 = 1/3 x
12 - 14 = x
-2 = x
Then, it passes through the point (-2 , 4), so we can discard options A and B (because it doesn't pass through (2, 4))
Step 2We know a linear equation is given by:
y = mx + b, where m and b are numbers: m is the slope of the line and b the y-intercept.
In this case y = 1/3 x + 14/3, the slope is 1/3. We know m is given by
m = Δy/Δx
Since in this case
m = 1/3 = Δy/Δx
Then
Δx = 3 and Δy = 1
That means that if it changes 3 units on the x-axis, then it changes 1 unit on the y-axis
Find the mean of the following numbers:
8
0
3
3
1
7
4
1
4
4
Answer:
the answer is 3.5 i think
8+3+3+1+7+4+1+4+4= 35
35/10=3.5
Write the fraction as a percent. Round to the nearest tenth of a percent if necessary.1/6A) 60%B) 16.7%C) 1.7%D) 27.8%
SOLUTION:
[tex]\frac{1}{6}=(\frac{1}{6}\times\frac{100}{1})\%=\frac{100}{6}\%[/tex]This can be simplified to give;
[tex]16.7\%[/tex]in and perform the symmetry test on each of the folha (b) 9x - y = 9 (d) 25x - 36y? = 900 (1)-25x + 4y = 100 (h) -x + 4y = 16 endpoints of the conjugate axis fundament for each
therefore the center of the hyperbole is (0,0) and it's symmetry axis is the y-axis and the x-axis. The intercepts are (0,-1) and (0,1)
What is the image point of (-6, -8) after the transformation R90° ory--r?
R90° transformation results in an image point that is (6, -8).
Describe Quadrant.The plane is divided into four infinite areas known as quadrants, each of which is bounded by two half-axes, using two-dimensional Cartesian axes.
These are commonly numbered from 1 to 4, and are denoted by Roman numerals: the coordinates for I are I (+, +), II (-, +), III (-, -), and IV (+, -).
We are aware that there are four quadrants: I (x, y), II (-x, y), III (-x, -y), and IV (-x, -y) (x, -y)
We can infer that the points are in quadrant III from the supplied point, which is (-6, -8). (-x, -y).
Now, if we turn right 90 degrees and enter sector IV (x, -y), the supplied point will change to (6, -8)
hence, following the transformation of R90°, we have the image point is (6, -8).
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What is the value of x? O x = 21 O x = 28 x = 35 O x = 37
The value of the missing variable x is; x = 37
What is the value of the missing angle?Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
Now, from the given problem, we see that we have two parallel lines with a transversal crossing them Thus, we can say that the two given angles are corresponding angles and as such they are congruent. Thus;
3x + 4 = 115
3x = 115 - 4
3x = 111
x = 111/3
x = 37
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I am just all around confused with this. Well explanation needed!
Given:
m∠A = (4x - 2) degrees
m∠B = (11x + 17) degrees
Let's find the value of x if the angles A and B are complementary angles.
Complementary angles are angles that sum up to 90 degrees.
Hence, we have:
m∠A + m∠B = 90
(4x - 2) + (11x + 17) = 90
Let's solve for x.
• Remove the parentheses:
4x - 2 + 11x + 17 = 90
• Combine like terms:
4x + 11x - 2 + 17 = 90
15x + 15 = 90
• Subtract 15 from both sides:
15x + 15 - 15 = 90 - 15
15x = 75
• Divide both sides of the equation by 15:
[tex]\begin{gathered} \frac{15x}{15}=\frac{75}{15} \\ \\ x=5 \end{gathered}[/tex]Therefore, the value of x = 5
ANSWER:
x = 5
Fill in the blank to make the two fractions equivalent. 4 = $ U A 30 ?
Given:
[tex]\frac{x}{30}=\frac{4}{5}[/tex]To find: The value of x (box)
Explanation:
Multiplying 30 on both sides. We get,
[tex]\frac{x}{30}\times30=\frac{4}{5}\times30[/tex]Solving we get,
[tex]\begin{gathered} x=4\times6 \\ x=24 \end{gathered}[/tex]Thus, the value of x is 24.
Final answer: The missing value is 24.
How far will a train travel per hour if it travels 282 miles in 2 1/2 hour?
1) Gathering the data
282 miles
2 1/2 hour We can rewrite that as 2.5
2) Let's use a proportion, or rather a formula for that
282 miles ------- 2.5
x -------------------- 1
2.5x = 282
x=282 /2.5
x =112.8 miles per hour
In one 1 hour, this train is able to get 112.8 miles if this train maintains its velocity