In this problem the expression that represente the paint in terms of time is:
[tex]p(t)=6t[/tex]and the area is represent as:
[tex]A(p)=\pi p^2[/tex]Part A: So to have the area in terms of p we can replace the first equation in the secon one so wi will get:
[tex]\begin{gathered} A(t)=\pi(6t)^2 \\ A(t)=36\pi t^2 \end{gathered}[/tex]Part B: now we can replace the 8 minutes in the equation so we get:
[tex]\begin{gathered} A(8)=36\cdot3.14\cdot8^2 \\ A(8)=7234.56 \end{gathered}[/tex]How do you divide the fractions 3/8 divided by 1/24?
How do you divide the fractions 3/8 divided by 1/24?
We will divide the problem as follows:
[tex]\frac{3}{8}\div\frac{1}{24}=\frac{3}{8}\times\frac{24}{1}=\frac{3\times24}{8}=3\times3=9[/tex]Note: the divide sign becomes multiplication sign, then write the reciprocal of the second fraction, then simplify.
2(4х + 6) = 22 - 3(18 - 3x.What is the value of x
2(4х + 6) = 22 - 3(18 - 3x)
Distributing the multiplication over the addition, we get:
2*4x + 2*6 = 22 - 3*18 + 3*3x
8x + 12 = 22 - 54 + 9x
8x + 12 = -32 + 9x
8x is adding on the left, so it will subtract on the right. 32 is subtracting on the right, then it will add on the left.
12 + 32 = 9x - 8x
44 = x
An object moves at a rate of 1400cm every 2 min what is this object rate in inches per sec
Given that the object moves at a rate of 1400 centimeters every 2 minutes, it is important to remember that:
[tex]\begin{gathered} 1\text{ }in=2.54\text{ }cm \\ 1\text{ }min=60\text{ }sec \end{gathered}[/tex]You can determine the rate in centimeters per minute by dividing 1400 centimeters by 2 minutes:
[tex]\frac{1400\text{ }cm}{2\text{ }min}=700\text{ }\frac{cm}{min}[/tex]Now you need to convert it to inches per second. Set up the following:
[tex](700\text{ }\frac{cm}{min})(\frac{1\text{ }in}{2.54\text{ }cm})(\frac{1\text{ }min}{60\text{ }sec})[/tex]Evaluating, you get:
[tex]=\frac{(700)(1)(1)}{(2.54)(60)}[/tex][tex]=\frac{700}{152.4}[/tex][tex]\approx4.59\text{ }\frac{in}{sec}[/tex]Hence, the answer is:
[tex]4.59\text{ }\frac{in}{sec}\text{ \lparen approximately\rparen}[/tex]Can someone help me with this geometry question? First box: cylinder or sphereSecond box: divide by 4, divide by 2, and multiply by 2
Explanation
The given figure (silo) is a composite figure. This means that it consists of more than one figure
In our case, we have the composite figure to be a silo that comprises half a sphere (which is also called a hemisphere) and a cylinder
Thus, the volume of the cylinder will be
[tex]Area\text{ of silo =volume of a hemisphere + volume of a cylinder}[/tex]The total height of the silo is 100 feet
If the height of the silo is 100 feet, the height of the hemisphere will be 15 feet
Also. the radius of both cylinder and hemisphere is 15 feet
This means that the height of the cylinder will be 100feet - 15 feet = 85 feet
The volume of a hemisphere is
[tex]V=\frac{2}{3}\pi r^3[/tex]Also, it is
[tex]Volume\text{ of hemisphere = }\frac{1}{2}\times volume\text{ of a sphere}[/tex]Then we can answer the question :
To find the volume of the silo, find the volume of a sphere with a radius of 15 feet and divide by 2 . Then add the volume of a cylinder with a radius of 15 feet and a height of 85 feet
Use the triangle to find the cos. Write answer as an unsimplified fraction and as a decimal roundedto 3 decimal places.a = 3.0'. b = 1.8' c=3.5'
Answer:
• The value of cos θ as an unsimplified fraction = 1.8/3.5
,• The value as a decimal rounded to 3 decimal places = 0.514.
Explanation:
Cosine is the ratio of the adjacent side to the hypotenuse.
In the right triangle:
• The side adjacent to θ b = 1.8
,• The hypotenuse, c = 3.5
Therefore:
[tex]\begin{gathered} \cos\theta=\frac{b}{c} \\ =\frac{1.8}{3.5} \\ \approx0.514 \end{gathered}[/tex]• The value of cos θ as aniunsimplified fraction = 1.8/3.5
,• The value as a decimal rounded to 3 decimal places = 0.514.
A basketball player scored 9 times during one game. She scored a total of 12 points, two for each two-point shot and one for each free throw. How many two-point shots did she make? How many free throws? She made two-point shots (Simplify your answer)
For the points scored during the game, let the two point shots be represented by a, and let the free throws be represented by b.
This means her total 12 points can be broken down into the following;
[tex]\begin{gathered} a+b=9---(1) \\ 2a+b=12---(2) \end{gathered}[/tex]Equation (1) means that all shots either two-pointers or free throws were a total of 9 (that is she scored 9 times). Equation (2) means that every two-pointer counted as 2, while every free throw counted as 1, and adding all points gave her 12 point in all. Therefore;
[tex]\begin{gathered} a+b=9 \\ 2a+b=12 \\ \text{Let a = 9-b in equation }(1) \\ \text{Substitute for the value of a into equation (2)} \\ 2(9-b)+b=12 \\ \text{Expand the parenthesis} \\ 18-2b+b=12 \\ \text{Collect like terms} \\ 18-12=2b-b \\ 6=b \\ \text{Substitute for the value of b into equation (1)} \\ a+6=9 \\ \text{Subtract 6 from both sides} \\ a=3 \end{gathered}[/tex]This means she scored 3 two point shots, and
She also scored 6 free throws
Which of the following lines are perpendicular to the line y=-3x+ 5? (you may choose more than one answer)a. 3x-y=2b. y= 3x c. 3x+y=5d. 1/3x-y=3e. 3x-y=6
Explanation
2 lines are perpendicular if the product ot their slopes equals 1
then,
Step 1
find the slope of the given line
[tex]\begin{gathered} y=-3x+5\Rightarrow y=mx+b \\ m\text{ is the slope} \end{gathered}[/tex]so
[tex]Slope_1_{}=-3[/tex]Step 2
Now, let slope2 represents the slope of the line we are looking for ( perpendicular)
[tex]\begin{gathered} \text{slope}_1\cdot slope_2=-1 \\ \text{replacing} \\ -3\cdot Slope_2=-1_{} \\ \text{divide both sides by -3} \\ \frac{-3\cdot Slope_2}{-3}=\frac{-1}{-3} \\ \text{Slope}_2=\frac{1}{3} \end{gathered}[/tex]now, check in the answer options the function that has 1/3 as the factor of x
[tex]\begin{gathered} y=mx+b \\ m=\frac{1}{3} \end{gathered}[/tex]then, the answer is
[tex]d\text{. }\frac{1}{3}x-y=3[/tex]how do I solve Cos-1(0.839) step by step?
Answer:
32.965°
Explanation:
To solve the expression we need to use the calculator, so:
[tex]\text{cos}^{-1}(0.839)=32.965[/tex]Therefore, the answer is 32.965°
An elevator began at an elevation of 85.5 feet and ascended at a rate of 2.75 feet per second. Which expression represents the height of the elevator after s seconds?
We know that an elevator began at an elevation of 85.5 feet, and ascended at a rate of 2.75 feet per second.
This means that at 0 seconds, the elevator is at an elevation of 85.5feet.
[tex]\begin{gathered} \text{At 1 second: }85.5+1\cdot2.75 \\ \text{At 2 seconds: }85.5+2\cdot2.75 \\ \text{At 3 seconds: }85.5+3\cdot2.75 \end{gathered}[/tex]and so on. This means that if s is the number of seconds, the height will have the expression:
[tex]\begin{gathered} h=85.5+s\cdot2.75 \\ =85.5+2.75s \end{gathered}[/tex]2. The baker packs 36 bran muffins in boxes of 4. Draw and label a tape diagram to find the number of boxes he packs.
We have
36 packs
4 boxes
Then, the diagram is:
So, The number of boxes baker packs is 36 ÷ 4 = 9 boxes
Therefore, the baker packs 9 boxes of muffins.
Answer: he packs 9 boxes of muffins
Look at the two sets of data below. Which set has the larger median? What is the value of that median? O: 25, 32, 26, 60, 71, 33, 37 P: 19, 19, 49, 81, 36, 26, 50 Oset P, 19 set 0, 26 O set 0, 33 O set P, 36
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
set O
set P
median = ?
Step 02:
P: 19, 19, 26, 36, 49, 50, 81
median = 36
O: 25, 26, 32, 33, 37, 60, 71
median = 33
The answer is:
Set P has the larger median, 36.
Consider the figure below and the following rolotion. Rectangle SIDE is fomed when you reflect PATH across the y-axis. What composition of transformations can you perform if you want to map SIDE back onto PATH without reflecting it back across the y-axis?
Given that a reflection of rectangle PATH across the y-axis forms rectangle SIDE. To map rectangle SIDE back to rectangle PATH without reflecting across the y-axis you'll have to reflect rectangle SIDE across the x-axis, then reflect across y-axis, and then reflect across the x-axis again.
Performing the 3 reflections above will map SIDE back onto PATH
ANSWER:
Reflection of SIDE across the x-axis, then another reflection across the y-axis, and another reflection across the x-axis
7. Place the numbers in order from greatest to least. -0.76, 3/4, (26)^1/2, 2.6, 20% and 2pi
hello
to determine the numbers in terms of highest to lowest, let's start identifying them one after the other
[tex]\begin{gathered} \text{the numbers are} \\ -0.76,\frac{3}{4},\sqrt{26},2.6,20\text{percent and 2}\Pi \end{gathered}[/tex]in descending order,
[tex]2\Pi>\text{ }\sqrt{26}>2.6>\text{ }\frac{3}{4}>\text{ 20\% > -0.76}[/tex][tex]\begin{gathered} \text{ note}\colon\text{ 2}\Pi\text{ }=\text{ 2}\times\text{ }\frac{22}{7}\text{ = 6.284} \\ 20\text{ percent = 0.2} \\ \frac{3}{4}\text{ = 0.75} \\ \sqrt{26}=\text{ 5.099} \end{gathered}[/tex]In the figure below, Triangle A has been rotated about the origin. Which triangle shows a 270 counterclockwise rotation? Answers ABCDO
Answer:
D
Step-by-step explanation:
270 counterclockwise rotation:
Points (x,y) becomes points (y,-x).
Triangle A has one vertex at (2,3).
So the rotated triangle should have a vertex at (3,-2). So the rotated triangle is given by D.
or the missing pieces. 7. A deposit earns $102 after 36 months at a simple interest rate of 5%
Parallelogram PQRS is rotated 270' counter clockwise about the origin to create parallelogram P'Q'R'S. Which tule describes this transformation? A-(x,y)—-> (-x,y) B-(x,y)—-> (y,x) C-(x,y)—-> (x,-y) D-(x,y)—-> (y,-x)
Answer
Option D is correct.
(x, y)—-> (y, -x)
Explanation
When a rotation of 270° counterclockwise about the origin is done on some coordinate, A (x, y), it transforms this coordinates into A' (y, -x). That is, we switch y and x, then add negative sign to x.
Hope this Helps!!!
Monty documented the amount of rain his farm received on a monthly basis, as shown in the table. Month, x Rainfall (in.), 4 2 2 3 4.5 8 5 5 3 Part 1 Is the relationship linear? Why or why not? Complete the explanation. The change between months is constant, but the change in the amount of rain is not constant. So, the relationship is not linear. Part 2 out of 2 Can an equation be entered to describe the amount of rain? Complete the explanation. An equation (select) be written to describe the amount of rain because there is (select) pattern in th (select) Che can can not Next
so the answer is
the change between months is constant, but the change in the amount of rain is not constant. So, the relationship is not linear.
An equation can not be written to describe the amount of rain because there is not a fixed or variable pattern in the rainfall
Find the value of x and list the sides of ABC in order from shortest to longest of the indicated measures. (Hint: Find the angle measures first, then decide which sic longest.)
To solve this problem, we have to remember the triangle sum theorem, that says that the sum of the interior angles of a triangle is 180°. To find x, sum the expressions for each angle and make it equal to 180, this way
[tex]\begin{gathered} \measuredangle A+\measuredangle B+\measuredangle C=180 \\ 9x+29+93-5x+10x+2=180 \\ 14x+124=180 \\ 14x=180-124 \\ 14x=56 \\ x=\frac{56}{14} \\ x=4 \end{gathered}[/tex]With this value, find the measure of each angle.
[tex]\begin{gathered} \measuredangle A=9x+29=9\cdot4+29=65 \\ \measuredangle B=93-5x=93-5\cdot4=73 \\ \measuredangle C=10x+2=10\cdot4+2=42 \end{gathered}[/tex]Finally, let's remember this: the wider the angle, the longer is its opposite side. It means, the ordered sides from shortest to longest are:
AB (opposite to angle C)
BC (opposite to angle A)
AC (opposite to angle B)
Convert the rectangular equation to a polar equation that expresses r in terms of θ.
x² + (y+5)² = 25 in polar coordinates is r = -10sinθ.
Step - by - Step Explanation
What to find?
The polar equation.
Given:
x² + (y+5)² = 25
To find the polar coordinates, substitute x = rcosθ and y=rsinθ into the above.
(rcosθ)² + (rsinθ + 5)² = 25
Open the parenthesis.
r²cos²θ + r²sin²θ + 10rsinθ + 25 = 25
Subtract 25 from both-side of the equation.
r²cos²θ + r²sin²θ + 10rsinθ + 25 - 25= 25 - 25
r²cos²θ + r²sin²θ + 10rsinθ =0
Factor r²
r²(cos²θ + sin²θ) + 10rsinθ =0
Know that cos²θ + sin²θ=1
r² + 10rsinθ =0
Factor out r
r(r + 10sinθ) = 0
Thus, r+10sinθ = 0
Subtract 10sinθ from both-side
r = -10sinθ
Therefore, x² + (y+5)² = 25 in polar coordinates is r = -10sinθ.
2/3 x 1/4 yo I need help
We have the next operation
[tex]\frac{2}{3}\times\frac{1}{4}=\frac{2\cdot1}{2\cdot4}=\frac{2}{12}=\frac{1}{6}[/tex]Convert 6 pints into cubic feet. Round your answer to the nearest hundredth
We know that 1 pint is half a liter, it means that there are 2 pints in one liter. Use this information to convert pints to liters:
[tex]6pints\cdot\frac{1L}{2pints}=3L[/tex]6 pints are 3 liters. Now, convert liters to cubic feet, remember that 1L=0.0353ft³.
[tex]3L\cdot\frac{0.0353ft^3}{1L}=0.10ft^3[/tex]The answer is 0.10ft³.
Rachel works at an electronics store in a shopping mall. Her base pay is$1000 a month. Rachel also receives a commission of 2% of her salestotal. The linear model that gives Rachel's total monthly pay, y, in terms ofsales total, x, is y = 0.02x + 1000. Use the model to find Rachel's monthlypay for sales totaling $25,000.
the total sale is 25000 $
the equation of pay is
y = 0.02x + 1000
here x = sales
put x = 25000
y = 0.02 * 25000 + 1000
y = 500 + 1000
y = 1500 $
so her total pay is 1500 $.
A number m is at least 7.
This problem is about numerical language.
To solve it, we need to transform the normally given language into an algebraic expression.
Now, the phrase "a number", refers to a variable, to an unknown value, which we are going to call m.
Then, we have the phrase "at least", which indicates a minimum value that can be expressed as "equal to or more than".
Having said that, the algebraic expression is[tex]m\ge7[/tex]
Each side on a sticky note measures 9 centimeters. What is the area of the sticky note?
The sticky note has the shape of a square. The formula for determining the area of a square is
Area = length^2
Given that the sticky note measures 9 centimeters, its area would be
Area = 9^2
Area = 81 cm^2
The cost for a pack of 16 pounds is $3.68 find the unit price in dollars per pen if necessary round your answer to the nearest cent
We know that the cost of 16 pens is $3.68 and we need to find the unit price in dollars per pen.
To find the unit price we must divide the cost of a pack by the number of pens that it has
[tex]\frac{\text{ \$}3.68}{16}=\text{ \$}0.23[/tex]Finally, the unit price in dollars per pen is $0.23
he has a ribbon that is 60 inches long she cuts 40% of the river for an art project while working on a project she decided she only needs 75% of the piece she cut off how many inches of ribbon does Kelly end up using for her project
Input data
Ribbon 60 inches
40% for an art project
While working she needs 75% of the piece she cut off
Procedure
First
R = 60 * 40% = 24 inches
Now, while working
R2 = 24 * 75% = 18 inches
She would need a total of 18 inches
Find sin 2x, cos 2x, and tan 2x if sin x =1/Square root10and x terminates in quadrant I.
We have to find sin(2x), cos(2x) and tan(2x).
We know that sin(x) = 1/√10 and x belongs to the first quadrant.
The last means that 2x belongs to the first or the second quadrant.
sin(2x) will then be positive but cos(2x) can be either positive or negative, depending on the quadrant.
We can use the following identiy for sin(2x):
[tex]\begin{gathered} \sin(2x)=2\sin(x)\cos(x) \\ \sin(2x)=2\sin(x)\sqrt{1-\sin^2(x)} \\ \sin(2x)=\frac{2}{\sqrt{10}}\sqrt{1-\frac{1}{10}} \\ \sin(2x)=\frac{2}{\sqrt{10}}\sqrt{\frac{9}{10}} \\ \sin(2x)=\frac{2}{\sqrt{10}}\cdot\frac{3}{\sqrt{10}} \\ \sin(2x)=\frac{6}{10} \\ \sin(2x)=\frac{3}{5} \end{gathered}[/tex]We can now calculate cos(2x) as:
[tex]\begin{gathered} \cos(2x)=1-2\sin^2(x) \\ \cos(2x)=1-\frac{2}{10} \\ \cos(2x)=\frac{8}{10} \\ \cos(2x)=\frac{4}{5} \end{gathered}[/tex]Finally, we can calculate tan(2x) as:
[tex]\begin{gathered} \tan(2x)=\frac{\sin(2x)}{\cos(2x)} \\ \tan(2x)=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4} \end{gathered}[/tex]Answer:
sin(2x) = 3/5
cos(2x) = 4/5
tan(2x) = 3/4
Ms. Smith sells makeup and perfume part time. She is paid a monthly commission. She receives 19% of her first $2600 in sales and 22% on the balance of her sales. Last month she sold $5,000 work of makeup and perfume. How much commission did she earn last month?
Given:
Total Sales- $5000
Commision on first sale = 19%
First sale - $2600
Commision on the balance - 22%
Required:
Amount of commision earned
Solution
Amount of commision earned = 19% of First Sale + 22% of Balance of the Sale
= 0,19 ( 2600 ) + 0.22 ( 5000-2600)
= $ 1022
Given the function: y = 4x - 1, find f-¹ (7)
Step 1
Given;
[tex]y=4x-1[/tex]Required; To find
[tex]f^{-1}(7)[/tex]Step 2
Find the inverse of f(x)
Set x =y and y =x
[tex]x=4y-1[/tex]solve for y
[tex]\begin{gathered} 4y=x+1 \\ y=\frac{x+1}{4} \\ f^{-1}(x)=\frac{x+1}{4} \end{gathered}[/tex][tex]\begin{gathered} Find\text{ f}^{-1}(7) \\ \text{ f}^{-1}(7)=\frac{7+1}{4}=\frac{8}{4}=2 \\ \text{ f}^{-1}(7)=2 \end{gathered}[/tex]Answer;
[tex]\text{ f}^{-1}(7)=2[/tex]A car traveling at a rate of 54 Kilometers per hour How many kilometers will the car travel in 10 minutes
EXPLANATION
If the speed of the car is 54 kph and the traveled time is 10 minutes, we first need to turn the 10 minutes into hours by applying the unitary method as shown as follows:
[tex]\text{?hours=10 minutes}\cdot\frac{1\text{ hour}}{60\text{ minutes}}=0.16[/tex]Now, we can get the mount of kilometers by multiplying the time with the speed (unitary method) as following:
[tex]\text{?kilometers }=\text{ }0.16\text{ hours }\cdot\text{ }\frac{54\text{ kilometers}}{1\text{ hours}}\approx9\text{ kilometers}[/tex]The distance traveled in 10 minutes was 9 kilometers.