Explanation
[tex]Volume=\frac{1}{3}\pi r^2h[/tex]Step 1
multiply each side by 3
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ V\cdot3=\frac{1}{3}\pi r^2h\cdot3 \\ 3V=\pi r^2h \end{gathered}[/tex]Step 2
divide both sides by
[tex]\pi r^2[/tex][tex]\begin{gathered} 3V=\pi r^2h \\ \frac{3V}{\pi r^2}=\frac{\pi r^2\text{ h}}{\pi r^2} \\ h=\frac{3V}{\pi r^2} \end{gathered}[/tex]let f(x)=3x+5 and g(x) =3x^2 -x-10. find (f/g)(x) and state it’s domain
(f/g)(x) = f(x)/f(g)
[tex]\begin{gathered} =\text{ }\frac{3x+5}{3x^2-x-10} \\ =\text{ }\frac{3x+5}{(3x+5)(x-2)} \\ =\frac{1}{(X-2)} \end{gathered}[/tex]Domain: x cannot equal 2
Ari took their partner out for dinner and got a check for $60.67. Ari wants to leave a 20% tip. How much is the tip? How much is the total cost for the meal? SHOW ALL OF YOUR WORK.
Given the following question:
Check = $60.67
Ari wants to leave a 20% tip
To find the answer we have to find 20% of $60.67
[tex]\frac{20\times60.67}{100}=20\times60.67=1213.4\div100=12.134[/tex][tex]\begin{gathered} 12.134 \\ 4\text{ < 5} \\ 12.13 \end{gathered}[/tex]The tip is $12.13
The total cost = tip + check
[tex]12.13\text{ + 60.67=}72.8[/tex]The total costs = $72.8
Graph the line. I am only able to use 2 points on this graph.
In order to graph line first we need to calculate the equation of the line
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1,y1) is a line where the line passing throught
in our case
m=3/4
(x1,y1)=(-4,5)
[tex]y-5=\frac{3}{4}(x+4)[/tex]Then we isolate the y
[tex]y=\frac{3}{4}x+3+5[/tex][tex]y=\frac{3}{4}x+8[/tex]We can calculate another point to obtain the graph in this case the y-intercept (0,8)
The points are
(-4,5) and (0,8)
the graph is
What would be the correct way to solve this?[tex] {x}^{2} - 5x - 84[/tex]
Answer:
(x + 7 ) ( x - 12 )
Explanation:
We know that if we multiply any two expressions x + a and x + b then we have
[tex](x+a)(x+b)=x^2+(a+b)x+ab[/tex]Now similarly,
[tex]x^2+(a+b)x+ab=x^2-5x-84[/tex]meaning
[tex]\begin{gathered} a+b=-5 \\ ab=-84 \end{gathered}[/tex]In other words, what are the two numbers that if I add them together I get -5 and If I multiply them I get -84. The answer comes from educated guesses. We guess that if we add 7 and -12 we get 5 and if we multiply then we get -84; therefore,
[tex]\begin{gathered} a=7 \\ b=-12 \end{gathered}[/tex]Hence, the expression can be factored as
[tex]=x^2-5x-84=(x-12)(x+7)[/tex]which is our answer!
Explain when 'p or q' is true. Select all that apply.A. 'p or q' is true when both p and q are false.B. 'p or q' is true when p is true and q is false.C. 'p or q' is true when p is false and q is true.D. 'p or q' is true when both p and q are true.
SOLUTION
From the truth-table of logic, (p or q) is true either if:
- p is true and q is false
- q is true and p is false
- both p is true and q is true.
Hence these 3 statements must p satisfied for (p or q) to be true.
So, looking at the options, B, C and D are correct
Hence the answer is B, C and D
A school band performed a concert on four different days. The band soldtickets and snacks each day of the concert for a fundraiser. The first tableshows the numbers of tickets sold and the amounts of money collected fromticket sales. The second table shows the numbers of snacks sold and theamounts of money collected from snack sales.
Part A:
To determine the price per snack, just multiply any value of the column Amount collected, by its corresponding value in the column of Number of snakcs sold:
53.75/43 = 1.25
Hence, the price per snack is 1.25 dollars
Part B:
The equation is a linear equation. The general formula for a linear equation is:
y - yo = m(x - xo)
where m is the slope and (xo,yo) is a pair of values of the table.
m is calculate as follow:
m = (y2 - y1)/(x2 - x1)
m =
The line with a slope of -1 and that contains the point (1, 3).Find the equation of the line in standard form.
ANSWER
x + y = 4
EXPLANATION
The standard form of a linear equation is given as:
ax + by = c
To do this, we have to find the equation of the line using point-slope method:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through
m = slope
The given slope is -1 ad the point the line passes through is (1, 3).
Therefore, we have:
y - 3 = -1(x - 1)
y - 3 = -x + 1
=> x + y = 1 + 3
x + y = 4
That is the equation of the line in standard form.
A bank pays 3% per annum compound interest, calculate how much interest would you get if you invested £45 for 3 years
Answer:
405
Step-by-step explanation:
don't forget to follow rate like
The vertices of a figure are A(1, -1), B(5.-6), and C(1, - 6). Rotate the figure 90 counterclockwise about the origin. Find the coordinates of the image. Polygon Undo Redo x Reset 7A 6. 5 4 3 2. 1 --7-6-5--4 -3 -2 -1 1 1 2 a 4 - 2 -3 -5 -6 -7 The coordinates of the image are:
The vertices of the given figure are
A(1, -1), B(5.-6), and C(1, - 6).
For a 90 counterclockwise about the origin, a coordinate, (x, y) would be (- y, x)
This means that after the 90 degrees rotation,
coordinate A would be (- - 1, 1) = (1, 1)
Coordinate B would be (- - 6, 5) = (6, 5)
Coordinate C would be (- - 6, 1) = (6, 1)
Describe in words where cube root of 30 would be plotted on a number line.
Between 3 and 4, but closer to 3
Between 3 and 4, but closer to 4
Between 2 and 3, but closer to 2
Between 2 and 3, but closer to 3
Cube root of 30 is 3.107.
How to find cube root of a number?
Cube root is the number that needs to be multiplied three times to get the original number.
The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:
Step 1: Start with the prime factorization of the given number.
Step 2: Then, divide the factors obtained into groups containing three same factors.
Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number is not a perfect cube and we cannot find the cube root of that number.
We have to find the cube root of 30.
Prime factorization of 30 = 2*3*5.
Therefore the cube root of 30 = ∛(2*3*5)= ∛30 .
As ∛30 cannot be reduced further, then the result for the cube root of 30 is an irrational number as well.
So here we will use approximation method to find the cube root of 30 using Halley's approach:
Halley’s Cube Root Formula: ∛a = x[(x³ + 2a)/(2x³ + a)]
The letter “a” stands in for the required cube root computation.
Take the cube root of the nearest perfect cube, “x” to obtain the estimated value.
Here we have a = 30
and we will substitute x = 3 because 3³ = 27< 30 is the nearest perfect cube.
Substituting a and x in Halley's formula,
∛30 = 3[(3³ + 2*30)/(2*3³ + 30)]
= 3[(27+60)/(54+30)]
= 3(87/84)
= 3*1.0357
∛30 = 3.107.
Therefore the cube root of 30 is 3.107.
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Determine the slope of the line represented by the equation: -5x - 7y = -9DO NOT USE 1 AS THE DENOMINATOR!
ANSWER
[tex]-\frac{5}{7}[/tex]EXPLANATION
We want to find the slope of the given line:
[tex]-5x-7y=-9[/tex]First, put the line in the slope-intercept form:
[tex]y=mx+b[/tex]where m = slope; b = y-intercept
Therefore, we have that:
[tex]\begin{gathered} -7y=5x-9 \\ \Rightarrow y=-\frac{5}{7}x+\frac{9}{7} \end{gathered}[/tex]From the equation above, we see that the slope of the line is:
[tex]-\frac{5}{7}[/tex]For which function is f(-x) = f(x)? (A) f(x) = sqaure root x(B) f(x) = 2x (C) f(x) = x2 (D) f(x) = x2 (E) f(x) = 2^x
Options C and D satisfy the given condition
The function is defined as an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given condition f(-x) = f(x)
Now to find which option satisfies the condition
So we can go through from the options to simply this
If f(x) = root x
= -root x
If f(x) = 2x
= -2x
If f(x) = x2
= x2
If f(x ) = x2
= x2
If f(x ) 2x
= 2-x
Therefore options C and D satisfy the given condition
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Answer:= 2-x
Step-by-step explanation:
A transformation is a nonrigid transformation if it does not preserve what? Can you name anonrigid transformation? What is the rule for the nonrigid transformation?Nonrigid transformationRule (x,y) →
A transformation is nonrigid transformation if it does not preserve the structure of the original object.
An example of a nonrigid transformation is the dilation, and its general rule is:
[tex]D_k(x,y)=(kx,ky)[/tex]where 'k' is the scale factor
A batter averaged 11 hits in 30 times at bat during the first half of the baseball season. He averaged 5 hits in 7 times at bat for the second half of the season. What was his average batting rate for the season?
*Find the answer to the nearest thousandth.
*(Compare total hits to total times at bat; the average of the two halves gives a wrong answer.)
Average batting rate for the season is 0.432.
Given,
Number of hits in first half of the season =11
Number of hits in second half of the season = 5
Number of times at bat during first half of the season = 30
Number of times at bat during second half of the season = 7
then,
Total number of hits in the season = 11+5 = 16
Total number of times at bat during the season = 30+7 =37
To find average batting rate use formula,
[tex]Average batting rate of season =\frac{Total number of hits in season}{Total number of at bat during season} \\\\=\frac{16}{37}\\\\ =0.432[/tex]
Hence, the batter's average batting rate for the season is 0.432.
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solve 10 + 15x - 30 = 40
We have the next equation
[tex]10+15x-30=40[/tex]We sum similar terms
[tex]15x-20=40[/tex]then we clear x
[tex]\begin{gathered} 15x=40+20 \\ 15x=60 \\ x=\frac{60}{15} \\ x=4 \end{gathered}[/tex]the value of x=4
6. Solve by any method:3x - 2y = 6x + y = 2
we can take any equation and solve for any variable, for example y will solve x from the second equation
[tex]\begin{gathered} x+y=2 \\ x=2-y \end{gathered}[/tex]now replace the value of x on the first equation
[tex]\begin{gathered} 3x-2y=6 \\ 3(2-y)-2y=6 \\ \end{gathered}[/tex]simplify
[tex]\begin{gathered} 6-3y-2y=6 \\ 6-5y=6 \end{gathered}[/tex]and solve for y
[tex]\begin{gathered} -5y=6-6 \\ -5y=0 \\ y=\frac{0}{-5} \\ \\ y=0 \end{gathered}[/tex]Value of y is 0 now we can replace y=0 on any equation and solve for x
for example I will replace y=0 on the second equation to find x
[tex]\begin{gathered} x+y=2 \\ x+(0)=2 \\ x=2 \end{gathered}[/tex]Value of x is 2
If we want to represent the solution as a point, the solution is
[tex](2,0)[/tex]4)Erica and Megan each improved theiryards by planting daylilies and shrubs.They bought their supplies from thesame store. Erica spent $200 on 9daylilies and 10 shrubs. Megan spent$185 on 13 daylilies and 5 shrubs. Whatis the cost of one daylily and the cost ofone shrub?Type text here
One daylily $10 and 1 shrub $11
1) Gathering the data from the question
Erica spent $200 on 9 daylillies and 10 shrubs
Megan spent $185 on 13 daylilies and 5 shrubs
9d+10s=200
13d+5s=185
2) Let's solve this system of linear equations now
9d+10s=200
13d+5s=185 Multiply by (-2)
9d +10s=200
-26d-10=-370
----------------------
-17d =-170
17d=170
d=10
9(10) +10s=200
90+10s-90=200-90
10s=200-90
10s=110
s=11
So the cost of one daylily is$10 and 1 shrub is $11
Find the midpoint M of the line segment joining the points C=(8,7) and D= (4,-5)
Explanation
We are told to find the midpoint of the line segment. To do so, we will use the formula:
[tex]midpoint=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}[/tex]In our case
[tex]\begin{gathered} x_1=8,y_1=7 \\ x_2=4,y_2=-5 \end{gathered}[/tex]Substituting the values above
[tex]\begin{gathered} Midpoint=\frac{8+4}{2},\frac{7-5}{2} \\ \\ Midpoint=\frac{12}{2},\frac{2}{2} \\ \\ Midpoint=(6,1) \end{gathered}[/tex]Thus, the midpoint is (6,1)
Find the area of this trapezoid. Be sure to include the correct unit in your answer. Continue 13 cm 20 cm 8 cm 5 cm 0 0/0 08 cm cm² X cm³ Ś ? LUULIO AUnicht Decopied Terms of Use | Priva
Given:
• Upper Base of trapezoid = 8 cm
,• Lower base = 20 cm
,• Length of one leg (also height) = 5 cm
,• Length of other leg = 13 cm
Let's find the area of the trapezoid.
To find the area of the trapezoid, apply the formula:
[tex]A=\frac{a+b}{2}*h[/tex]Where:
A is the area
a is the length of upper base = 8 cm
b is the length of the lower base = 20 cm
h is the height = 5 cm
Plug in the values for a, b, and h to find the area, A:
[tex]\begin{gathered} A=\frac{8+20}{2}*5 \\ \\ A=\frac{28}{2}*5 \\ \\ A=14*5 \\ \\ A=70\text{ cm}^2 \end{gathered}[/tex]Therefore, the area of the trapezoid is 70 cm^2
Use Composition of FunctionsBOX OFFICE A movle theater charges $8.50 for each of the xtickets sold. The manager wants to determine how much the movietheater gets to keep of the ticket sales If they have to glve thestudlos 75% of the money earned on ticket sales t(x). If the amountthey keep of each ticket sale is k(x), which composition representsthe total amount of money the theater gets to keep?
Given: The amout charged per ticket is $8.50
If x tickets are sold
Then the total revenue (amount made) will be =>
[tex]8.5\text{ x }x\text{ = \$8.50x}[/tex]If t(x) represents how much the studio collects
and k(x) represents how much is kept
Given: t(x) = 75% then
k(x)= (100 -75)%= 25 %
So that
The total amount that will be kept will be
25% of $8.50x
=>
[tex]\frac{25}{100}\text{ x (\$8.50x) }[/tex][tex]\frac{25\text{ x \$8.50x}}{100}\text{ = }\frac{212.5x}{100}=\text{ \$2.125x}[/tex]The amount that will be kept will be
= > $2.125x
Where x is the number of tickets
if 5 guys are putting yogurt in a girl's mouth and each liter is 5 liters how much is the girl carrying in her mouth ️️
5 guys are putting yogurt in a girl's mouth
Each of the yogurt is 5 liters
The total yogurt the girl is carrying = 5 x 5
= 25
The answer is 25 liters of yogurt
How can i calculate the number of students that graduated from the university faculty of natural sciences in 2002? how can i determine the sector angle that will represent the number of graduates in each subject? how can i hence construct a pie chart of radius 4cm to represent the information given in the table?
A table showing the number of graduates by subject from a university's faculty of natural science in 2002.
1) To calculate the number of students that graduated, find the sum of the number of graduates from each subject.
[tex]9+15+19+12+5=60[/tex]The number of students that graduated is 60.
2) To determine the sector angle that will represent the number of graduates in each subject, divide the number of graduates in each subject by the total number of students and then multiply by 360º.
3) To construct a pie chart with radius, 4cm to represent the information, draw a circle of radius 4cm and partition it into sectors with central angles as calculated in (2) above.
Can you pls help me with number 6 my treacher said that it was d but I got b is me correct or my treacher
Given the algebraic expression below
[tex]6a+4y+a+2a[/tex]Collect like terms
[tex]6a+2a+a+4y[/tex]Add possible like terms using the distributive property of algebra
[tex]\begin{gathered} (6+2+1)a+4y \\ 9a+4y \end{gathered}[/tex]Hence, the final answer is 9a + 4y
Option D is correct
Can some one help me with 7 , 8 and 9 please?
7) The angle asked is ajacent to the leg given and we also have the hypotenuse. So we can use cossine:
[tex]\begin{gathered} \cos x=\frac{8}{18}=\frac{4}{9} \\ x=\arccos (\frac{4}{9})=64\degree \end{gathered}[/tex]8) Here we want the hypotenus given an angle an its opposite leg. So we can use sine:
[tex]\begin{gathered} \sin (65\degree)=\frac{10}{x} \\ x=\frac{10}{\sin (65\degree)}=11.0 \end{gathered}[/tex]9) We want the leg which is opposite of a given angle and we have the hypotenuse. So we can use sine again:
[tex]\begin{gathered} \sin (28\degree)=\frac{x}{15} \\ x=15\cdot\sin (28\degree)=7.0 \end{gathered}[/tex]In the figure, RS is 24 units long. What is the length of WV ?
using,
RS/ST = WV/VT
Where,
RS = 24
ST = 2x + 11
WV
Please help me with this problem I am not able to help my son to understand we keep getting it wrong please help.The function y=−16x^2+v0x models Lindy's height in feet above a trampoline x seconds after she jumps straight up. In the equation of the function, v0 is her initial velocity in feet per second. Lindy lands back on the trampoline 1 second after she jumps. What is the value of v0?Enter your answer in the box.v0= ft/s
EXPLANATION:
We are given the function which models Lindy's height x seconds after she jumps straight up a trampoline. The function is expressed as;
[tex]y=-16x^2+v_0[/tex]Where x is the time in seconds after she jumps, and v_0 is the initial velocity. The result of the function is her height after jumping with the given time x.
If she lands back on the trampoline one second after she jumps, then she is at a height of zero.
The function can now be re-written as follows;
[tex]\begin{gathered} \text{With;} \\ x=1\text{ (time)} \\ y=0\text{ (height)} \end{gathered}[/tex][tex]0=-16(1)^2+v_0[/tex]We can now simplify;
[tex]-16(1)^2+v_0=0[/tex]Add
[tex]-16(1)^2[/tex]to both sides;
[tex]\begin{gathered} v_0=16(1)^2 \\ v_0=16 \end{gathered}[/tex]Therefore;
ANSWER:
The value of v_0( her initial velocity) is;
[tex]v_0=16[/tex]12 times a number g
12 times a number g means that the coefficient 12 is multiplying the variable g, just as follow:
12g
the table shows the scores of 20 people who took the paramedics licensing test. Find the mean and the standard deviation of the data. the deviation answer needs to be rounded to three decimal places as needed.
a) Mean = 76
b) Standard deviation = 6.728
Explanation:The data set has frequency. So we will apply the formula:
[tex]\text{Mean = }\frac{\sum ^{}_{}fx}{\sum ^{}_{}f}[/tex][tex]\begin{gathered} \text{Mean = }\frac{(69\times7)\text{ + (70}\times1)+(75\times3)\text{ + (81}\times6)\text{ + (82}\times2)+\text{ (92}\times1)}{7\text{ + 1 + 3+6+2+1}} \\ \text{Mean = }\frac{483\text{ + 70}+225\text{ + 486 + 164}+\text{ 9}2}{7\text{ + 1 + 3+6+2+1}} \\ \text{Mean = }\frac{1520}{20} \\ \text{Mean = 76} \end{gathered}[/tex]To get the standard deviation, we will apply the formula:
[tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{\sum^{}_{}f(x_i-\mu)^2}{n\text{ - 1}}} \\ \text{where }\sigma\text{ = standard deviation} \\ \mu\text{ = mean, }x_i\text{ = values of x} \\ n\text{ = }\sum ^{}_{}f=20 \end{gathered}[/tex][tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{860}{20-1}} \\ \sigma\text{ = }\sqrt[]{\frac{860}{19}} \\ \sigma\text{ = }\sqrt[]{45.2632} \\ \sigma\text{ = 6.7}28 \\ \\ \text{Standard deviation = 6.7}28 \end{gathered}[/tex]1. Write an equation for a polynomial with the following properties: it has even degree, it has at least 2 terms, and, as the inputs getlarger and larger in either the negative or positive directions, the outputs get larger and larger in the negative direction.
the polynomial must be even, so we chose x²
it has at least 2 terms, then we add 1 to the previous item, we get: x² + 1
to get outputs larger and larger in the negative direction, we have to multiply the previous item by -1 to get: -x² - 1
This function has a graph like the next one:
Then, -x² - 1 satisfies all the features needed
What is the approximate probability thata point chosen inside the rectangle is inthe shaded region?
In order to determine the required probability, calculate the total area of the shaded regions frist:
Consider that there is a rectangle and a triangle with shaded area, then, you have:
A1 = (1 ft)(2 ft) = 2 ft² rectangle area
A2 = (2 ft)(2 ft)/2 = 2ft² triangle area
Then, the total shaded area is:
A = A1 + A2
A = 2 ft² + 2 ft²
A = 4 ft²
Next, calculate the total area of the given figure:
A' = (3 ft + 1 ft)(2 ft) = 8 ft²
Next, the probability is the quotient in between the area of th shaded regions over the area of the total figure:
p = A/A'
p = (2 ft²)/(4 ft²)
p = 0.50
Hence, the probability that a point chosen is inside a shaded region is 0.50