Answer:
15 degrees
Step-by-step explanation:
Answer:
The earth turns 15 degrees in one hour. Hope this helps!
Step-by-step explanation:
A water tank in the shape of an inverted circular cone has a base radius of 3 m and height of 7 m . If water is being pumped into the tank at a rate of 4.3 m^3 / min , find the rate at which the water level is rising when the water is 3.5 m deep. (Round your answer to three decimal places if required)
The water level increases by 0.608 meters per minute when the water is 3.5 m deep
How to determine the rate?The given parameters are:
Radius, r = 3Height, h = 7Rate in, V' = 4.3m^3/minThe relationship between the radius and height is:
r/h = 3/7
Make r the subject
r = 3h/7
The volume of a cone is;
[tex]V = \frac 13\pi r^2h[/tex]
This gives
[tex]V = \frac 13\pi (\frac{3h}{7})^2h[/tex]
Expand
[tex]V = \frac{3h^3}{49}\pi[/tex]
Differentiate
[tex]V' = \frac{9h^2}{49}\pi h'[/tex]
Make h' the subject
[tex]h' = \frac{49}{9\pi h^2}V'[/tex]
When the water level is 3.5.
We have:
[tex]h' = \frac{49}{9\pi * 3.5^2}V'[/tex]
Also, we have:
V' = 4.3
So, the equation becomes
[tex]h' = \frac{49}{9\pi * 3.5^2} * 4.3[/tex]
Evaluate the products
[tex]h' = \frac{210.7}{346.36}[/tex]
Evaluate the quotient
h' = 0.608
Hence, the water level increases by 0.608 meters per minute
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Please help, will give the brainliest!
(J) 80 • 125
(K) (80+65) • 125
(L) (65 • 80) + (80 • 60)
M (65•80)+(80•60)
N (65•80)+ 1/2 (125 • 100)
Answer:
option N is the correct option, apply Formula of area of rectangle and triangle by splitting figure into 2 parts
Find the equation of the line parallel to y = 2x - 4 that runs through the point (-2, 4).
y = 1/2x + 4
y = 2x + 8
y = 2x + 4
y = -1/2x + 8
Answer:
y = 2x + 8
Explanation:
Equation: y = 2x - 4
Comparing it with slope intercept form "y = mx + b" where 'm' is slope and 'b' is y-intercept. This function has slope: 2 and y intercept of -4
Parallel lines has same slope.
Passes through (-2, 4)
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf y - 4 = 2(x - (-2))[/tex]
[tex]\sf y - 4 = 2(x + 2)[/tex]
[tex]\sf y = 2x + 4 + 4[/tex]
[tex]\sf y = 2x + 8[/tex]
Answer: y = 2x + 8
Step-by-step explanation:
This is a fairly simple problem. I hope this helps!
So, to find a line parallel, it's simple, and it only requires that for the other line to have the same slope and a different y-intercept (or same "m" and different "b" in the equation y = mx + b).
To find a line parallel to a point is slightly harder, but don't worry, I'll teach you how.
To do this, we have to recognize the point. The point given is (-2, 4) where -2 is the x-value and 4 is the y-value. Remember, points always go by (x, y).
So, we set y to 4, and we set x to -2.
When testing out lines that are parallel to a point, you must always be careful that you end up with the same value. Such as 4 = 4 or 8 = 8, etcetera.
We get:
4 = 2 × (-2) + 8
Simplifying, we get:
4 = -4 + 8
Adding -4 to 8, we get 4:
4 = 4
Thus, y = 2x + 8 is parallel to the point (-2, 4)
At school B, 108 year 8 students study French.
This is 60% of the year group.
How many students do not study French in year 8 in school B?
Step-by-step explanation:
108 = 60%
1% = 60%/60 = 108/60 = 1.8
100% = 1%×100 = 1.8×100 = 180
how many do not study French ?
the remainder of the students. that is 40% (100% - 60%) or 72 students (40×1.8 or simply 180-108).
Answer:
72 students do not study French.
Step-by-step explanation:
60% = 108 students
1. 108 ÷ 60 = 1.8 ( this is to find 1% of the students)
2. 1.8(1%) × 40 = 72
To check the answer:
108 + 72 = 180
180 × 60% = 108
distribute 5x(3x+7)
help asap
Answer:
The Answer is 50 or 50x
Answer: 15x^2+35x ✅
Step-by-step explanation:
Hii, do you need to distribute [tex]\boldsymbol{5x(3x+7)}[/tex]? No problem! (:
How to Distribute?We can solve problems like this one by using what is known as the "distributive property". What it says is: If you have a term that comes before the parentheses, you multiply it times every single term in the parentheses. Let me show you what I mean...
[tex]\twoheadrightarrow\sf 5x(3x+7)[/tex]
[tex]\bullet[/tex] Multiply 5x tmes 3x and 7 - you will obtain
[tex]\twoheadrightarrow\sf 15x^2+35x[/tex] (if we multiply x times x we obtain x²)
Voila! There's our solution, cheers! (:
--
Hope that this helped! Best wishes.
[tex]\it Reach\quad far.\:Aim\quad high. \,Dream\quad big.[/tex]
[tex]\bigstar\underbrace[/tex]
--
How many square feet of tile is needed for a room of 24 foot x 24 foot
Answer:576
Step-by-step explanation:
24 squared is 576
Statement: "Three less than four times a number is greater
than or equal to 41."
Answer:
x≥11
Step-by-step explanation:
4x-3≥41
4x≥41+3 -44
x≥44/4 = 11
What negative Z-score (standard score) would the area under the curve be 0.8621
z* = _______
What is the slope of the line that passes through the points (6, 2) and (4, 10)? −4 −14 14 4
Answer:
-4
Step-by-step explanation:
The equation for slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
m: Slope
(6, 2) = [tex](x_1, y_1)[/tex]
(4, 10) = [tex](x_2, y_2)[/tex]
Substitute these values into the equation:
[tex]m=\frac{10-2}{4-6}=\frac{8}{-2}=-4[/tex]
Therefore the slope is -4.
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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the slope of the line that passes through the points? 2 points given
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
The formula used here, is [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{\dfrac{10-2}{4-6}}[/tex] | subtract
[tex]\bf{\dfrac{8}{-2}}[/tex] | evaluate
[tex]\bf{-4}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Slope\;-4}[/tex]
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
Transportation officials tell us that 60% of drivers wear seat belts while driving. Find the probability that more than 562 drivers in a sample of 900 drivers wear seat belts.
The probability that more than 562 drivers is 0.9328
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given: p = 0.60
n = 900
Let X denote the number of drivers that wear a seat belt,
P(X > 562)
[tex]\mu[/tex] = n*p = 900(0.60) = 540
[tex]\sigma^{2}[/tex]= n*p*(1-p)
=900*0.60*0.40
=216
P(X >562) = Pr( Z > 1.4976)
= 0.9328
Hence, the probability that more than 562 drivers is 0.9328
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If you could please answer this that would be awesome!
Please graph it!
The graph is attached with the answer, This is looking like a horizontal staircase
What is a Step Function ?A step function is a piece wise function whose all pieces are horizontal line or a point.
It is given in the question to graph the interval
-2 ≤x≤2
for f(x) = |x+3|
-2 1
-1 2
0 3
1 4
2 5
The graph is attached with the answer.
This is looking like a horizontal staircase
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The credit remaining on a phone card (in dollors) is a linear function of the total calling trime made with the card ( in minutes). The remaining credit after 22 minutes is $36.70, and the remaining credit after 52 mintues is $32.20. What is the remaining credit after 85 mintues of calls?
After 85 minutes of calls, there are $27.25 left on the card.
What is the remaining credit after 85 minutes of calls?
A linear equation in slope-intercept form is:
y = a*x + b
Where a is the slope.
If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we know that the line passes through the points (22, 36.7) and (52, 32,20)
(points of the form (time, dollars)).
So the slope is:
[tex]a = \frac{32.2 - 36.7}{52 -22} = -0.15[/tex]
The linear equation is then:
y = -0.15*x + b
To find the value of b, we use the point (22. 36.7)
36.7 = -0.15*22 + b
36.7 + 0.15*22 = b = 40
Then the linear equation is:
y = -0.15*x +40
The amount remaining in the credit card after 85 minutes is given by evaluating the above equation in x = 85.
y = -0.15*85 + 40 = 27.25
This means that after 85 minutes of calls, there are $27.25 left on the card.
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If you drive 72 miles and use 6 gallons of gas, what is your rate
Answer:
Well, it depends if you are asking the rate per gallon it would be 12 miles per gallon.
What are the rotations that will carry this equilateral triangle onto itself?
A
B
90° counterclockwise rotation about its center P
270° counterclockwise rotation about its center P
120° counterclockwise rotation about its center P
240° clockwise rotation about its center P
O225 clockwise rotation about its center P
O200 counterclockwise rotation about its center P
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The rotations that will carry the equilateral triangle in discuss onto itself are;
90° counterclockwise rotation about its center P.270° counterclockwise rotation about its center P.Which rotations will carry this equilateral triangle onto itself?It follows from the task content that the rotation which produces the desired output in which case, the rotation maps exactly unto the equilateral triangle is required.
On this note, when the rotation is 90° and 270° about the center P in which case, the rotation can be clockwise or anticlockwise, the desired result is obtained.
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Answer: 240 and 120
Step-by-step explanation:
What are the zeros of the quadratic function f(x)=6x^2+12x-7
Answer:
[tex]A) \ x=-1 \ ^ +_-\frac{\sqrt{13} }{\sqrt{6}}.[/tex]
Step-by-step explanation:
if to solve the given equation, then
D=6²+42=78;
[tex]\left[\begin{array}{ccc}x=\frac{-6-\sqrt{78}}{6} \\x=\frac{-6+\sqrt{78}}{6} \end{array} \ = > \ \left[\begin{array}{ccc}x=-1-\sqrt{\frac{13}{6} } \\x=-1+\sqrt{\frac{13}{6} } \end{array}[/tex]
Value of x or y so that the line through the points has the given slope:
(X,9) and (9,-3), slope is -6/7
Sorry if it’s not worded great.
If we want the slope to be -6/7, then the value of x must be -5.
How to find the value of x?Remember that if a linear equation passes through (x₁, y₁) and (x₂, y₂), then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we have the points (x, 9) and (9, -3), and the slope must be -6/7, so we need to solve:
[tex]\frac{- 3 - 9}{9 - x} = \frac{-6}{7} \\\\\frac{-12}{9 - x} = \frac{-12}{14}[/tex]
Where on the second line we multiplied and divided the right fraction by 2.
Comparing the fractions, we see that we must have:
9 -x = 14
9 - 14 = x
-5 = x
So the value of x must be -5.
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Find the domain and range of the function graphed below. Write your answers in interval notation.
Answer:
Domain: [tex][1, \infty)[/tex]Range: [tex](-\infty, -2][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Find the inverse of the function y = 3x + 5 Find the inverse of the function y=3x+5
Answer:
First Inverse function= f^-1(x)=x/3-5/3
Second Inverse function=f^-1(x)=x/3-5/3
Step-by-step explanation:
Find the area of the shaded portion of the
figure. All angles are right angles.
Dimensions are in inches.
3
8
5
======================================================
Explanation:
The white rectangle is 3 by 6 with area of 3*6 = 18 square inches.
The larger rectangle is 8 by 5 with area of 8*5 = 40 square inches.
The difference of these will get us the shaded area:
40 - 18 = 22 square inches
If I=$312.50 R=25% T=0.25 what is P
Step-by-step explanation:
please mark me as brainlest
How much of an alloy that is 30% copper should be mixed with 200 ounce of an alloy that is 70% copper in order to get an alloy that is 40% copper?
The alloy of copper will be 600 ounces.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Let us represent
Number of ounce of 30% copper = x
Hence, our Equation will be given below:-
x × 30% + 200 × 70% = (x + 200) × 40%
0.3x + 140 = (x + 200)0.4
0.3x + 140 = 0.4x + 80
Collect like terms
0.4x - 0.3x = 140 - 80
0.1x = 60
x = 60/0.1
x = 600 ounces
Therefore the alloy of copper will be 600 ounces.
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Simplify each expression and state whether each is a volume, an area, or neither.
a) n(4)2 x
b) lw+lw+wh+wh+lh+lh
c) 8y2(10y2)
a. 2n^4b, neither a volume nor an area
b. 2Iw + 2wh + 2Ih, It is an area
c. 80 y^4, neither a volume nor an area
How to simply the algebraic expressionsa. n(4) 2 x b
n * n * n* n* 2 * b
2n^4b
It is neither an area nor a volume
b. lw+lw+wh+wh+lh+lh
Collect like terms
2Iw + 2wh + 2Ih
It is an area
c. 8y2(10y2)
8y^2 * 10 * y^2
80 y^4
It is neither a volume nor an area
Thus, the expressions are simplified as a. 2n^4b, b. 2Iw + 2wh + 2Ih, c. 80 y^4
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A motorboat moves across a lake at a constant speed. When it begins, it is 64 km from the shore. After 17 minutes, it is 30 km from the shore. Which function describes the motorboat's distance from the shore?
A. y=-17x+30
B. y=2x+64
C. y=-17x+64
D. y=-2x+64
Please solve fast!
I am giving a lot of points!
Answer:
y = -2x + 64
Explanation:
The x represents the time in minutes and y represents distance in km.
Determine coordinates: (0, 64), (17, 30)
Find slope:
[tex]\sf slope : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) : \dfrac{30-64}{17-0} = -2[/tex]
Find equation:
[tex]\sf y- y_1 = m(x - x_1)[/tex]
[tex]\sf y - 64 = -2(x - 0)[/tex]
[tex]\sf y = -2x + 64[/tex]
The law of cosines is a² + b² - 2abcosC = c². Find the value of 2abcosC.
A. 20
B. 40
C. 37
D. -40
Answer:
C
Step-by-step explanation:
a = 4
b = 5
c = 2
C = arccos((a² + b² - c²) / 2ab)
C = arccos((16 + 25 - 4) / 2(4)(5))
C = arccos(37 / 40)
C = 22.33°
2abcosC
2(4)(5)cos(22.33)
40(0.925)
37
Option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We have from law of cosines that a² + b² - 2abcosC = c²
We have to find the value of 2abcosC.
Now let us find the value of C
C = arccos((a² + b² - c²) / 2ab)
C = arccos((16 + 25 - 4) / 2(4)(5))
C = arccos(37 / 40)
C = 22.33°
Now plug in the value of C in 2abcosC.
2abcosC
=2(4)(5)cos(22.33)
=40(0.925)
=37
Hence, option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.
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In the 30-60-90 triangle below, side s has a length of.
length of
30
90⁰
S
10
60"
A. 5.2: 5.2
B. 5,10,3
and side q has a
Answer: C, 5, 5√3
Step-by-step explanation:
The short leg of a 30-60-90 triangle equal half the hypotenuse, 10/2 = 5. The long leg equals √3 times the short leg, 5*√3 = 5√3.
Help me and i'll help you earn more points if the question is right
The slope of the line below is 0.8. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side. Coordinates (-2,-3)
The equation of the line is y = 0.8x - 1.4 if the slope of the line is 0.8 and line passes through coordinates (-2,-3)
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope m = 0.8
The line passing through coordinates (-2,-3)
y = mx + c
y = 0.8x + c
Plug the point in the equation.
-3 = 0.8(-2) + c
c = -1.4
y = 0.8x - 1.4
Thus, the equation of the line is y = 0.8x - 1.4 if the slope of the line is 0.8 and line passes through coordinates (-2,-3)
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The Rainbow Motor Motel is a 50-room facility with a restaurant to accommodate its guests. The motel is open 365 days a year, even on leap years; as Lurena Boucha, the proprietor, closes down the facility every February 29, her birthday, for an all day celebration of four years of successful operations. On the average, 98% of the rooms are available for sale. For the year just ended, the actual number of rooms sold totaled 15,000 and the number of guests for the year totaled 20,000. The projected occupancy rate for the next year is 82% of the available rooms based on past experience. The food information is as follows:
Sales $150,000, Beg Inventory 8,000, Purchases $70,000, Ending Inventory, $ 13,000 Consumption by employees (free of charge) $3,000, Number of checks 64,139. Cost of sales ?
From the information given, the cost of sales is $65,000. See the explanation below.
What is the definition of cost of sales?Add your initial inventory to the purchases made over the time period, remove that amount from your ending inventory, and that is your cost of sales.
Cost of Sales = (Bi + P) - Ei
Where Bi is Beginning Inventory
P is Purchases; and
Ei is Ending Inventory.
So the derivation of the solution above is?Beginning Inventory = 8,000
(add) Purchase = 70,000
Bi + P = 78,000
Ending Inventory = 13,000
Cost of sales = 78,000 - 13,000
= $65,000
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Use the property of real numbers to write the expression 2/5 x (-7)x 5/2
The simplified form of the expression 2/5 x (-7)x 5/2 would be -7.
How to solve the expression?When two fractions are multiplying each other, the numerator of both fractions multiplies each other, likewise the denominator of both fractions respectively.
Use the property of real numbers to write the expression
[tex]\dfrac{2}{5} \times (-7) \times \dfrac{ 5}{2}\\\\\dfrac{10}{10} \times (-7) \\\\-7 \times 1\\\\= -7[/tex]
Therefore, The simplified form of the expression would be -7.
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NO LINKS!! Please help me with this problem
Answer:
23.1 years (nearest tenth)
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
A = $1200P = $600r = 3% = 0.03n = 12 (as compounded monthly)t = yearsSubstitute the given values into the formula and solve for t:
[tex]\implies \sf 1200=600\left(1+\dfrac{0.03}{12}\right)^{12t}[/tex]
[tex]\implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]
[tex]\implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]
[tex]\implies \sf 2=\left(1.0025\right)^{12t}[/tex]
Take natural logs:
[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]
[tex]\implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]
[tex]\implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]
[tex]\implies t=23.13377513...[/tex]
[tex]\implies t=23.1\: \sf years \:\:(nearest\:tenth)[/tex]
The money will double in value in approximately [tex]\boxed{\sf 23.1}[/tex] years.
Used formula
[tex]\boxed{\sf A=P(1+\dfrac{r}{n})^{nt}}[/tex]
[tex]\\ \implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]
[tex]\\ \implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]
[tex]\\ \implies \sf 2=\left(1.0025\right)^{12t}[/tex]
Apply natural logarithm on both sides[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]
[tex]\\ \implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]
[tex]\\ \implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]
[tex]\\ \implies t=23.1years[/tex]
