Answer:
3.6*10³
Step-by-step explanation:
Jack cannot add the powers of 10 because they are in addition. We can apply the exponent rule only when they are in multiplication.
[tex]\sf 6 *10^2 + 3*10^3= 6*100 + 3*1000\\[/tex]
= 600 + 3000
= 3600
[tex]\sf = 3.6 * 10^3[/tex]
What is 1000 x 9.2 ?
A spherical balloon is inflated so that its volume is increasing at the rate of 12 cubicfeet per minute. How fast is the radius of the balloon increasing when the radius is 6feet?
Given:
The rate of change in volume = 12 cubic feet per minute.
We need to find the rate of change of radius at radius = 6 feet.
Consider the formula to find the volume of the sphere.
[tex]V=\frac{4}{3}\pi r^3[/tex]Differentiate with respect to t.
[tex]\frac{dV}{dt}=\frac{4}{3}\pi\times3r^2\times\frac{dr}{dt}[/tex][tex]\text{ Substitute }\frac{dV}{dt}=12\text{ and r=6 in the formula.}[/tex][tex]12=\frac{4}{3}\pi\times3(6)^2\times\frac{dr}{dt}[/tex][tex]12=144\pi\times\frac{dr}{dt}[/tex]Dividing both sides by 144pi, we get
[tex]\frac{12}{144\pi}=\frac{dr}{dt}[/tex][tex]\frac{dr}{dt}=\frac{1}{12\pi}[/tex][tex]\frac{dr}{dt}=\frac{1}{37.68}=0.0265\text{ feet per minute}[/tex]Hence the radius of the balloon increases by 0.03 feet per minute.
Find the value of angle A in the triangle below:
angle A =
A
B
95°
55
PLEASE HURRY
Please simplify this equation and find what y is
Answer: y=7
Step-by-step explanation:
We need to combine like factors in this term by adding up all the exponents and copying the base.
No exponent implies the value of 1.
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Answer:
y =7
Step-by-step explanation:
Help for trigonometry class please
The most appropriate choice for matrix and multiplicative inverse of matrix will be given by
B is the multiplicative inverse of A
What is a matrix and multiplicative inverse of matrix?
Matrix is a rectangular representation of numbers or symbols arranged in the form of rows and column. Matrix is a very important tool in mathematics.
To learn about multiplicative inverse, it is important to know about identity matrix
[tex]\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}[/tex] is a 2 x 2 identity matrix denoted by I.
Let A and B be two matrices
A is said to be a multiplicative inverse of B if AB = BA = I
Here,
A= [tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex] B = [tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]
AB =
[tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]
[tex]\begin{bmatrix} 2\times 1 + 1 \times -1& 2 \times -1 + 1\times 2\\1 \times 1+1\times-1 & 1 \times -1 + 1 \times 2\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]
BA =
[tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex]
[tex]\begin{bmatrix} 1\times 2 + -1 \times 1& 1 \times 1 + -1\times 1\\-1 \times 2+2\times 1 & -1 \times 1+ 2 \times 1\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]
AB = BA = [tex]\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]
So B is the multiplicative inverse of A
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Ava took a taxi from her house to the airport. The taxi company charged a pick-up fee
of $1.10 plus $3.75 per mile. The total fare was $19.85, not including the tip. Which
tape diagram could be used to represent the context if a represents the number of
miles in the taxi ride?
A
B
1.1
3.75
1.1
1.1X
3.75
19.85
1.1
19.85
3.75...
3-75
1.1
Using a linear function, it is found that her taxi ride was of 5 miles.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).For the cost function, we have that:
The slope is the cost per mile, hence m = 3.75.The intercept is the flat fee, hence b = 1.10.Thus the cost for a ride of x miles is of:
C(x) = 3.75x + 1.10.
Her total fee was of $19.85, hence the mileage is found as follows:
19.85 = 3.75x + 1.10
x = (19.85 - 1.10)/3.75
x = 5 miles.
Which was the length of her taxi ride.
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What is the missing height?
Answer:
h = 6.36619772 cm
Step-by-step explanation:
h = (3 * v) / (πr2)
Answer:
h = 20 cm
Step-by-step explanation:
the volume (V) of a cone is calculated as
V = [tex]\frac{1}{3}[/tex] πr²h ( where r is the radius )
given r = 9 and V = 540π , then
[tex]\frac{1}{3}[/tex] π × 9² × h = 540π
[tex]\frac{1}{3}[/tex] × π × 81h = 540π
27πh = 540π ( divide both sides by 27π )
h = [tex]\frac{540\pi }{27\pi }[/tex] = 20 cm
One factor of the function f(x) = x3 − 9x2 + 20x − 12 is (x − 6). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer.
For the given function f(x), x-intercepts are 1,2 and 6 and the y-intercept is -12
Given :
[tex]f(x) = x^{3} -9x^{2} +20x -12 \\[/tex]
One of the factors of f(x) is (x-6)
Dividing f(x) by (x-6), we get :
[tex]\frac{x^{3} -9x^{2} +20x -12 \\}{x-6} = x^{2} -3x +2[/tex]
Now expanding, [tex]x^{2} -3x +2[/tex]
[tex]x^{2} -3x +2 = x^{2} -2x -x +2 =x(x-2) -(x-2) = (x-2)(x-1)[/tex]
Hence, [tex]x^{3} -9x^{2} +20x -12 = (x-6)(x-1)(x-2)[/tex]
For x-intercept, f(x) = 0 . Then
(x-6)(x-1)(x-2) =0
x = 1,2 and 6
For y-intercept, x=0 in f(x)
f(0) = -12
Hence, the x-intercepts are 1,2, and 6 and the y-intercept is -12.
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what is the distributive property of 24+40
simplify:-
(-4)3
this is the chapter of exponents and power
Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?
2(25) + c
25c + 3
3(c) + 25
3(c + 25)
Answer:
3(c) + 25
Step-by-step explanation:
Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?
2(25) + c
25c + 3
3(c) + 25
3(c + 25)
Custard is heated to a temperature of 180°F. It is then allowed to cool in a refrigerator whose temperature is 30°F. The custard cools to 120°F in 30 minutes. Determine how long will it take for the custard to cool to 50°F.
Answer: About 65 minutes.
It changes an average of about 60 degrees Fahrenheit every half hour.
180 120 60 50
0 30 60 65
Now it is about ten degrees until it's fifty. Since it takes thirty minutes to go down sixty degrees, divide sixty by ten to get six. Then divide thirty by six to get five. So, it should take about 65 minutes to cool down to 50 degrees.
It will take approximately 35 minutes for the custard to cool from 120°F to 50°F.
To determine how long it will take for the custard to cool to 50°F, we need to consider the rate at which it cools. From the given information, we know that the custard cools from 180°F to 120°F in 30 minutes.
To find the rate of cooling, we can calculate the temperature change per minute.
The temperature decreases by 180°F - 120°F = 60°F over 30 minutes. So, the rate of cooling is 60°F / 30 minutes = 2°F per minute. Now, let's use this rate to calculate how long it will take for the custard to cool from 120°F to 50°F.
The temperature difference between 120°F and 50°F is 120°F - 50°F = 70°F. To cool from 120°F to 50°F at a rate of 2°F per minute, it will take 70°F / 2°F per minute = 35 minutes.
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What is the probability of
spinning a yellow?
[?]%
Answer:
12.5
Step-by-step explanation:
there are eight triangles and one yellow so 1/8=12.5%
Answer: 12.5%
Step-by-step explanation:
There are 8 sections and 1 of them is yellow so 1 divided by 8 is 0.125 or 12.5%
a function is said to have a horizontal asymptote if either the limit at infinity exists or the limit at negative infinity exists. show that each of the following functions has a horizontal asymptote by calculating the given limit.
A function can only have two horizontal asymptotes, hence the answer is no. By examining the degrees of the numerator and denominator, one can find the horizontal asymptote of a rational function.
If limxf(x)=L or limxf(x)=L, a function f(x) will have the horizontal asymptote y=L. Therefore, we simply calculate the function's limit as it approaches infinity and again as it approaches negative infinity to locate horizontal asymptotes. Based on the degree of the numerator, n, and the degree of the denominator, m, horizontal asymptotes adhere to three principles. The horizontal asymptote is y = 0 if n m. The horizontal asymptote is y = a/b if n = m. There is no horizontal asymptote if n > m. As x gets closer to 0, we say that f(xlimit )'s is infinite. A boundary or a limit is now a number.
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i have been working to become a major in math and i need some help with what this second word might be for this problem from last weeks exam
(20 points) i need help with this asap (the x is -20)
Answer:
119º and 61º
Step-by-step explanation:
2x-15 and 3x+5 are supplementary because the angles corresponding to 2x-15 is supplementary with 3x+5
2x-15+3x+5=180
5x-10=180
5x=190
x=38
fill in x
2(38)-15
=76-15
=61
angle is 61
fill in x for angle 2
3(38)+5
=114+5
=119
angle 2 is 119
A private university has a endowment fund that currently has 49 million dollars in it. if she invested in a one year cd that pays 5.12% interest compounded continuously, how much interest will it earn
If the university invest in a one year CD at 5.12% interest compounded continuously, the interest it will earn is determined by calculating as: Interest = Future value – Present value which would be $2.54 million
Continuously compounded interest means that a principal amount is constantly earning interest with infinite compounding periods for a certain time period. There are no increment compounding periods as with monthly or annually compounding.
The continuously compounding formula:
FV = PV* e^rt
Where FV is the future amount, PV is the initial amount, e is a mathematical constant (2.7183), r is the rate and t is the time period.
Hence,
FV = 49* 2.7183^(0.0512*1) =51.57
Interest earned= 51.57-49=2.54
Hence, the university will earn an interest of $2.54 million.
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Find the Properties to graph this Rational Expression. DO NOT GRAPH. If an answer is "none" type in "none" for the answer blank. Make sure to type in your Asymptotes correctly(x=y=)F(x)=-4x+8/x^2-x-2Need to answer:Hole:(___,___)Vertical asymptote:______X-intercept:(___,___)Y-intercept:(___,___)Horizontal asymptote:____
Given data:
The given expression is f(x)= (-4x+8)/(x^2 -x-2).
The hole of the graph is x=2.
The expression for the vertical asymptode is,
[tex]x=-1[/tex]The expression for the horizontal asymptode is,
[tex]y=0[/tex]There is no x-intercept, and y-intercept is,
[tex](0,\text{ -4)}[/tex]Thus, the
Mai is filling her fish tank. Water flows into the tank at a constant rate complete the table you answer the questions. 1. How many gallons of water will be in the fish tank after 3 minutes? Explain your reasoning. 2. How long will it take to fill the tank with 40 gallons of water. Explain your reasoning. 3. What is the constant of proportionality?
Table:
0.5 : 0.8
1 : ?
3 : ?
? : 40
1. Based on the proportional relationship table created, 4.8 gallons of water will be in the fish tank after 3 mins.
2. 25 minutes.
3. The Constant of proportionality is: 1.6.
How to Determine the Constant of Proportionality?In a proportional relationship between variables x and y, the Constant of proportionality, k, is determined using any pair of values from the table as:
k = y/x.
The relationship is modelled as y = kx.
Constant of proportionality = k = y/x = 0.8/0.5
Constant of proportionality = k = 1.6
The equation for the relationship would be: y = 1.6x. Use the equation to complete the table:
For x = 1:
y = 1.6(1) = 1
For x = 3:
y = 1.6(3) = 4.8
For y = 40:
40 = 1.6x
40/1.6 = x
x = 25
The complete table is:
x y
0.5 0.8
1 1.6
3 4.8
25 40
1. Using the proportional relationship table, we can conclude that, 4.8 gallons of water will be in the fish tank after 3 mins.
2. Using the proportional relationship table, the time it would take to fill the tank with 40 gallons of water is: 25 mins.
3. Constant of proportionality = k = 1.6.
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For a given recipe, 24 cups of flour are mixed with 12 cups of sugar. How many cups of sugar should be used if 8 cups of flour are used?
Answer:
First, 24 divided by 8 equals 3. this means you divide 12 by 3. you get 4. 4 cups of sugar will be used when 8 cups of flour are used.
#10 Eastern Mountain Sports is offering 20%
off of your entire purchase. You have an
online code that will give you an additional
10% off of the sale price(s). You decide to
buy a Kayak, a seat, and a paddle. How
much will you pay after receiving the
discount and using your online code?
EASTERN MOUNTAIN SPORTS
PELICAN Summit Kayak $299.99
BB Adjustable Paddle $191.96
YAK GEAR Kayak Seat $99.99
Answer: $426.20
Step-by-step explanation:
The subtotal is [tex]299.99+191.96+99.99=\$ 591.94[/tex].
[tex](591.94)(0.8)=\$473.552\\\\(473.552)(0.9) \approx \$426.20[/tex]
100%− 9/10 equals what
Answer: 100%-9/10= -0.8
Step-by-step explanation:
100%-9=-8
-8/10=-0.8
PLEASE HELP DUE IN 4 MINUTES, THANK YOU!!
Answer:
A 100% increase in a total means the final amount is 200% of the initial amount.
A 100% decrease in a total means the final amount is 0% of the initial amount.
Error means that you were a way off from the real value
Step-by-step explanation:
Is the expression −9×(−9)−9 equivalent to [−9×(−9)]−9? Explain.
Using BODMAS we can conclude, Yes, both will give same result.
The rule used to solve mathematical expressions is known as the BODMAS rule. The order of operations for mathematical formulas requiring several operations is known as BODMAS. B. Brackets, O. Order of powers, D. Division, M. Multiplication, A. Addition, and S. Subtraction make up the acronym.
−9×(−9)−9
⇒ - 9 × 81
⇒ -729
⇒ [−9×(−9)]−9
⇒ [81] -9
⇒ -729
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The cost of manufacturing a cake is directly proportional to the volume of the cake.
The baker makes a 70% profit when he sells a large rectangular cake.
The baker sells a large rectangular cake for £6.80 The baker decides to sell smaller rectangular cakes.
The length, width, and height of the smaller cakes are all half of those of the large rectangular cake.
He sells a pack of 6 of the smaller cakes for £6.50
How much profit does he make on the pack of smaller cakes?
Answer:
The baker makes £3.50 profit on smaller cakes================================
GivenLarge cake:
Price = £6.80,Profit = 70%Small cake:
Number = 6,Price = £6.50,Dimensions = each side is 1/2 of the large cakeSolutionThe profit is the difference of the cost and selling price.
Find the cost x of large cake:
x + 70% = 6.801.7x = 6.80x = 4Find the volume of the pack of smaller cakes, taking the volume of the large cake as a unit:
6*(1/2)³ = 6*1/8 = 3/4Cost of the pack of smaller cakes is proportional to the volume:
4*3/4 = 3Profit made on smaller cakes:
6.50 - 3 = 3.50
Assume that each circle shown below represents one unit. Express the shaded
amount as a single fraction and as a mixed number.
Shaded portion in single fraction is [tex]\frac{37}{10}[/tex] and mixed number is 3[tex]\frac{7}{10}[/tex] .
What is difference between fraction and mixed number?
Single fraction is represented as [tex]\frac{p}{q}[/tex] form where p is numerator and q is denominator and value of q can't be zero. Example [tex]\frac{5}{9}[/tex] .
Mixed number contains two part one is an integer and other is fractional part. It is represented as N [tex]\frac{p}{q}[/tex]. Example 5[tex]\frac{1}{2}[/tex] .
According to figure, one shaded circle is equal to one unit and one shaded circle contain 10 sector.
There are three shaded circle and a circle with 7 sector shaded.
So, Total shaded area in single fraction = 1 + 1 + 1+ [tex]\frac{7}{10}[/tex] = [tex]\frac{37}{10}[/tex]
and total shaded area in mixed number = 1 + 1 + 1 + [tex]\frac{7}{10}[/tex] = 3 + [tex]\frac{7}{10}[/tex] = 3[tex]\frac{7}{10}[/tex] .
Hence, shaded portion in single fraction is [tex]\frac{37}{10}[/tex] and mixed number is 3[tex]\frac{7}{10}[/tex] .
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3 Violet's Videos
clients. One week after launching the website, she had posted a total of 6 videos. At the end
Violet is a yoga instructor who regularly posts new exercise videos on a website for her
of week 2, she had a total of 10 videos. At the end of week 3, she had a total of 14 videos. At
the end of week 4, she had a total of 18 videos.
Find the Term Value
The completed table is:
Term Number 1 2 3 4 5 6
Term Value 6 10 14 18 22 26
What are the term values?In order to determine the term values, the rate of increase in the number of videos that Violet has at the end of each week has to be determined.
Rate of increase in the number of videos can be determined by dividing the change in the number of videos per week by the change in the number of weeks.
Rate of increase = change in the number of videos / change in the number of weeks
(10 - 6) / (2 - 1)
4 / 1 = 4 videos per week
Number of videos in week 5 = 18 + 4 = 22
Number of videos in week 6 = 22 + 4 = 26
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A driver travels 55km in 1 hour. He then drives at a speed of 35 km/h for 2 hours. Next, he drive 175km in 3 hours. What was his average speed
Answer:
108.333 km/hour
Step-by-step explanation:
See attached worksheet.
Graph the image of the figure using the transformation given.
Answer:
D
Step-by-step explanation:
Solve the equation.
-3x + 1 + 10x = x + 4
HN
0 x = -1/
5/6
0 x = 2/1/2
O x = 12
O x = 18
Value of x for equation -3x + 1 + 10x = x + 4 is 1÷2.
Given equation,
-3x + 1 + 10x = x + 4
Shifting the variables to the left-hand side and constant to the right-hand side,
-3x - x + 10x = 4 - 1
Simplifying the equation,
10x - 4x = 3
6x = 3
x = 1÷2
When x from the right side shifts to the left side, its sign changes, and similarly, when 1 from the left side shifts to the right side, its sign changes.
x = 0.5
Therefore, value of x = 1÷2 that is 0.5
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