Answer:
[tex]8m^2n[/tex]Step-by-step explanation:
To find the GCF (greatest common factor), we have to find the prime factors of each number. Then, we have to find similar factors.
In this exercise, we have:
24m⁴n = 2 * 2 * 2 * 3 * m * m * m * m * n
16m²n = 2 * 2 * 2 * 2 * m * m * n
The GCF will be 2 * 2 * 2 * m * m * n
So, The GCF is 8m²n.
10. A glass jar contains 8 red, 6 green, 12 blue, and 10 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a(a) red marble? (b) green marble? (c) blue marble?
Let:
• A ,be the event of getting a red marble
,• B ,be the event of getting a green marble
,• C ,be the event of getting a blue marble
We'll have that:
[tex]\begin{gathered} P(A)=\frac{8}{36} \\ \\ P(B)=\frac{6}{36} \\ \\ P(C)=\frac{12}{36} \end{gathered}[/tex]1. Select all values of x that are solutions to the equation: -2(x + 4)(3x - 18) = 0A) -6B) -4C) -2D) OE) 2F) 4G) 6
x = -4 OR x = 6
The correct options are B and G
Donna run 7 miles in 60 minutes. At the same rate, how many miles would she run in 24 minutes?
We know how many miles she runs in 60 mins, we can make a rule of three to find the miles in 24 mins
So if she runs 7 miles in 60 mins
how many x miles in 24mins
x = (24mins*7miles)/60mins = (24*7miles)/60 = 2.8 miles
So, Donna runs 2.8 miles in 24mins.
what is the range of this exponential function?1) all real numbers 2) { y | y > 0 }3) { y | y ≥ 0 }4) { y | y ≤ 0 }5) { y | y < 0 }
Remember that
The range is the data set of all possible values of y
In this function
y>0
the range is the interval (0, infinite)
therefore
answer is the second option
Graph the equation-6x + 2y = 10 2. Compare and Contrast this graph to the graph from the previous problem. pleas be SPECIFIC:)
we have the equation
6x + 2y = 10
To graph the line we need at least two points
Find out the first point
For x=0
6(0)+2y=10
2y=10
y=5
The first point is (0,5)
Find out the second point
For x=3
6(3)+2y=10
2y=10-18
2y=-8
y=-4
the second point is (3,-4)
Plot the points and join them to graph the line
using a graphing tool
v-7/3 = 0...........
Answer
Explanation
The question to be solved is
What is the range of the function?Type the answer using interval notation example : (#,#]
To analyze the range we need to look at the Y values. In this case the lowest Y value is 0 and the highest Y value it can go all the way up to positive infinity. So the range would be [0, +∞)
When multiplying or dividingpolynomials using the Tabular Method, write the number of terms for the polynomial ax^2+bx+c
Explanation
Answer
The number of terms for the polynomial is 3
Carol is depositing $1500 into an account earning 3% compounded semiannually. How much money will be in the account after 25 years?
ANSWER
$3157.86
EXPLANATION
We have that Carol is depositing $1500 into an account earning 3% that is compounded semiannually.
The formula for amount for a compound interest is:
[tex]A\text{ = }P(1\text{ + }\frac{r}{n})^{n\cdot t}[/tex]where P = principal (amount deposited)
r = interest rate
t = number of years
n = number of times interest is compounded
Since the interest is compounded twice a year (semiannually), n = 2.
From the question:
P = $1500
r = 3% = 0.03
t = 25 years
So, the amount of money that will be there after 25 years is:
[tex]\begin{gathered} A\text{ = 1500(1 + }\frac{0.03}{2})^{2\cdot25} \\ A=1500(1+0.015)^{50} \\ \text{A = 1500(1.015)}^{50} \\ A\text{ = \$3157.86} \end{gathered}[/tex]last Friday Adam had $22.33 over the weekend, she received some money for cleaning the attic period. He now had 32 dollars period, how much money did he receive.
Word Problem Leading to Simple Equation.
Last Friday Adam had $22.33 : 22.33
He received some money for cleaning: Let the amount of money he received be x, so that she now has:
[tex]22.33+x[/tex]He is left with $32, meaning his total money is now $32 :
Mathematically, we write:
[tex]\begin{gathered} 22.33+x=32 \\ \text{Collecting like terms, we get,} \\ x=32-22.33 \\ x=\text{ \$9.67} \end{gathered}[/tex]Hence, the correct answer is $9.67
Find the value of y at which the maximum occurs
Given
Z = 2x + y
Find
Find the value of y at which the maximum occurs
Explanation
objective function is maximum at point (12 , 0)
so , here value of x = 12
and value of y = 0
therefore ,
value of y at which the maximum occurs = 0
Final Answer
hence , x = 12 and y = 0
1. Which of the below is a binomial factor of thepolynomial shown?
The given polynomial is
[tex]\begin{gathered} 3x^2+11x+10^{} \\ \text{ By factoring completely, we obtain two paired factors 6 and 5,} \\ \text{ whose sum is 11 (the coefficient of x), and product 30 found from } \\ \text{ the product of the constant 10 and 3 (the coefficient of x}^2) \end{gathered}[/tex][tex]\begin{gathered} 3x^2+11x+10^{} \\ 3x^2+6x+5x+10 \\ 3x(x+2)+5(x+2) \\ (3x+5)(x+2) \end{gathered}[/tex]Therefore, a binomial factor of the polynomial is (x + 2) [Option A]
Determine the radius of the circle with center at (7,-4) and a point on the circle (-2, 5). Show organized work to support your answer. Round your answer to the nearest tenth.
The radius of the circle with center at (7,-4) and a point on the circle (-2, 5). is 9√2
Radius is the line segment extending from the center of a circle or sphere to the circumference or bounding surface, it is the distance betwee the center of the circle to a point on the circumference
the circle with center at (7,-4) and a point on the circle (-2, 5).
We can find the radius by using the distance formula
r = √((x₂ - x₁)² + (y₂ - y₁)²)
r = √((-2 -7)² + 5 - (-4)²)
r = √(9² + 9²)
r = 9√2
Therefore, the radius of the circle with center at (7,-4) and a point on the circle (-2, 5). is 9√2
To learn more about distance refer here
https://brainly.com/question/7243416
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A population of beetles are growing according to a linear growth model. The initial population (week 0) is Po = 9, and the population after 4 weeks is P4 = 25. Find an explicit formula for the beetle population after n weeks. Pn = After how many weeks will the beetle population reach 113?
Pn = 4n + 9
it will take 26 weeks
Explanation:Po = 9
P4 = 25
the linear model will be in the form of linear equation:
y = mx + c
where c = Po
x = 4
y = P4 = 25
we insert to get the m = slope or rate of change
25 = m(4) + 9
25 = 4m + 9
25 - 9 = 4m
16 = 4m
m = 16/4
m = 4
Inserting the m and c into the equation of line:
y = 4x + 9
We are told represent the number of weeks with n. Hence, we replace our x with n.
Also, y = Pn
Pn = 4n + 9
when Pn = 113, n = ?
Pn = 4n + 9
113 = 4n + 9
113 - 9 = 4n
104 = 4n
104/4 = n
n = 26
Therefore, it will take 26 weeks for the beetle population to reach 113
For Items 9-11, determine the length of each segmentwith the given endpoints.9. C(1, 4) and D(11, 28)10. Y(-2, 6) and Z(5, -8)11. P(-7,-7) and Q(9,5)
Use the following formula:
d = √((x2-x1)² + (y2-y1)²)
9.
C(1,4) = (x1,y1)
D(11,28) = (x2,y2)
d = √((11-1)² + (28-4)²) = √((10)²+(24)²) = 29.73213749
10.
Y(-2,6) = (x1,y1)
Z(5,-8) = (x2,y2)
d = √((5-(-2))² + (-8-6)²) = √((7)² + (-14)²) = 15.65247584
11.
P(-7,7) = (x1,y1)
Q(9,5) = (x2,y2)
d = √((9-(-7))² + (5-(-7))²) = √((16)²+(12)²) = 20
write 33_88 in simplest form
Answer
33 : 88 = 3 : 8
(33/88) = (3/8)
Explanation
33 : 88
THe best way is to do this is to divide both numbers by 11
(33/11) : (88/11)
= 3 : 8
Hope this Helps!!!
What is the location of the point (5, 0) translates 4 units to the down and reflected across the y-axis?
STEP-BY-STEP EXPLANATION:
Given information
The given ordered point = (5, 0)
Step 1: We need to translate the point 4 units down
To translate down means we will be subtracting a value from the y--axis
Hence, we have
[tex]\begin{gathered} (x,\text{ y) }\rightarrow\text{ (x, y-b)} \\ \text{where b = 4} \\ (5,\text{ 0) }\rightarrow\text{ (5, 0 - 4)} \\ (5,\text{ 0) }\rightarrow\text{ (5, -4)} \end{gathered}[/tex]When translated 4 units down, we got (5, -4)
Step 2: Reflect over the y-axis
The general rule for reflecting over the y-axis is (-x, y)
This means the value of x will be negated and the value of y will remain the same
[tex]\begin{gathered} \text{Over the y-ax}is \\ (x,\text{ y) }\rightarrow\text{ (-x, y)} \\ (5,\text{ -4) }\rightarrow\text{ (-5, -4)} \end{gathered}[/tex]Step 3: the graph the point
Determine the point (x, y) on the unit circle associated with the following real numbers. Write the exact answer as an ordered pair. Do not round.5xS-3
Given:
[tex]s=-\frac{5\pi}{3}[/tex]To find the point (x,y) on the unit circle:
The coordinate of the unit circle can be derived by,
[tex](\cos s,\sin s)[/tex]Substituting the value of s, we get
[tex]\begin{gathered} (\cos (-\frac{5\pi}{3}),\sin (-\frac{5\pi}{3}))=(\cos (2\pi-\frac{5\pi}{3}),\sin (2\pi-\frac{5\pi}{3})) \\ =(\cos (\frac{\pi}{3}),\sin (\frac{\pi}{3})) \\ =(\frac{1}{2},\frac{\sqrt[]{3}}{2}) \end{gathered}[/tex]Hence, the coordinate point on the unit circle is,
[tex](\frac{1}{2},\frac{\sqrt[]{3}}{2})[/tex]The mean score on a Statistics exam is 88 points, with a standard deviation of 6 points. Apply Chebychev's Theorem to the data using k=2. Interpret the results.
Step 1
Given;
Step 2
State Chebychev's theorem
Thus;
[tex]\begin{gathered} k=2 \\ 1-\frac{1}{2^2}=1-\frac{1}{4}=\frac{3}{4} \end{gathered}[/tex]The empirical formula that applies to this is about 2 standard deviations of the mean
[tex]\begin{gathered} (\mu+2\sigma)\text{ and \lparen}\mu-2\sigma) \\ (88+2(6))\text{ and \lparen88-2\lparen6\rparen\rparen} \\ 100\text{ and 76} \end{gathered}[/tex]Answer;
[tex]At\text{ least 75\% of the exam scores falls between 76 and 100}[/tex]Which expressions are equivalent to the one below? Check all that apply. 212 32
Given:
[tex]\frac{21^x}{3^x}[/tex]Aim:
We need to find the equivalent expression for the given expression.
Explanation:
[tex]Use\text{ }\frac{a^n}{b^n}=(\frac{a}{b})^n.\text{ Here a=21, b=3 and n=x.}[/tex][tex]\frac{21^x}{3^x}=(\frac{21}{3})^x[/tex][tex]Use\text{ 21=7}\times3\text{ in the given expression.}[/tex][tex]\frac{21^x}{3^x}=\frac{(7\times3)^x}{3^x}[/tex][tex]Use\text{ }(a\times b)^x=a^x\times b^x.\text{ Here a=7, b=3 and n=x.}[/tex][tex]\frac{21^x}{3^x}=\frac{7^x\times3^x}{3^x}[/tex]Cancel out common terms.
[tex]\frac{21^x}{3^x}=7^x[/tex]Final answer:
[tex]B.\frac{7^x\times3^x}{3^x}[/tex][tex]C.\text{ }7^x[/tex][tex]D.\text{ }(\frac{21}{3})^x[/tex]
Given that a function, g, has a domain of -1 ≤ x ≤ 4 and.a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, seleccould be true for g.OOg(3) = 18g(2)=4g(1) = -2g(5) = 12Submit
Answer:
[tex]g(3)\text{ = 18 is possible}[/tex]Explanation:
Here, we want to get the possible true value for the function
From the given range values, g(x) cannot be negative since the lowest number is 0
Thus, g(-1) = 2 is wrong
Looking at the domain also, we have values existing from -1 to 4
This means that g(5) does not exist
Now, we are left with g(3) = 18 and g(2) = 4
We already have g(2) = 8
g(2) cannot possess two values
Thus, the possible correct value is g(3) = 18
A book sold 37,900 copies in its first month of release. Suppose this represents 9.1% of the number of copies sold to date. How many copies have been sold to date? Round your answer to the nearest whole number.
We know that 9.1% of the total copies sold are 37,900.
If we call N to the total amount of copies sold and see that 9,1% correspond to a proportion of 9.1/100=0.091, we can calculate N as:
[tex]\begin{gathered} 0.091\cdot N=37,900 \\ N=\frac{37,900}{0.091} \\ N\approx416,484 \end{gathered}[/tex]Answer: the total number of copies sold is approximately 416,484.
I solved part A of the problem I just need help solving part B
Given:
The function given is,
[tex]g(x)=0.009x-17.66[/tex]x represents the years.
Required:
The predicted increase in the temperature in the year 2011.
Explanation:
The predicted increase in the temperature in the year 2011 is given by,
[tex]\begin{gathered} g(2011)=0.009\times(2011)-17.66 \\ \Rightarrow g(2011)=0.439 \\ \Rightarrow g(2011)=0.4\degree \end{gathered}[/tex]Final Answer:
[tex]0.4\degree C[/tex]What is the surface area of the cylinder with height of 6cm and radius of 7cm?Round your answer nearest thousanddth
The radius of cylinder is r=7 cm.
The heighht of cylinder is h= 6 cm
Determine the surface area of the cylinder.
[tex]\begin{gathered} SA=2\pi rh+2\pi(r)^2 \\ =2\pi\cdot7\cdot6+2\pi\cdot(7)^2 \\ =572 \end{gathered}[/tex]So answer is 572 centimeter square.
Find the equation of the line in standard form that passes through the following points. Eliminate anyfractions and simplify your answer.(4, -8) and (9, 11)
We want to find the equation of the line that passes through the points:
(4 , -8) and (9 , 11)
First, we're going to find the slope between these points using the fact that:
If we have two points that lie on a line:
[tex](x_1,y_1)\text{ and }(x_2,y_2)[/tex]The slope between them can be found using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]If we replace our values:
[tex]\begin{gathered} (x_1,y_1)=(4,-8) \\ (x_2,y_2)=(9,11) \\ x_1=4 \\ x_2=9 \\ y_1=-8 \\ y_2=11 \end{gathered}[/tex]The slope will be:
[tex]m=\frac{11-(-8)}{9-4}=\frac{11+8}{5}=\frac{19}{5}[/tex]Now, we could apply the point-slope equation. This equation tells us that we can find the equation of the line if we got a point (x1,y1) on the line, and the slope m:
[tex]y=y_1+m(x-x_1)[/tex]Replacing our values:
[tex]\begin{gathered} y=-8+\frac{19}{5}(x-4) \\ y=-8+\frac{19}{5}x-\frac{76}{5} \\ y=\frac{19}{5}x-\frac{116}{5} \end{gathered}[/tex]This, is the general form. We want to express the last equation as a standard form like this:
[tex]Ax+By=C[/tex]If we re-write:
[tex]\begin{gathered} y=\frac{19x-116}{5} \\ \\ 5y=19x-116 \\ 19x-5y=116 \end{gathered}[/tex]Therefore, the standard for the equation of the line that passes through (4 , -8) and (9, 11) is:
19x-5y=116
write 2.25% as fraction to the simplest form
2.25% can also be written as 0.0225 if we divide 2.25% by 100% and we eliminate the percentages:
To make the decimal 0.0225 a fraction, we have to multiply by a number in which the decimal will be an integer:
[tex]\frac{0.0225}{1}\times\frac{10000}{10000}=\frac{225}{10000}[/tex]Simplifying the fraction obtained:
[tex]\frac{225}{10000}=\frac{9}{400}[/tex]Answer:
[tex]\frac{9}{400}[/tex]In the picture provided, describe the three dimensional figure that will be produced if the rectangle is rotated about the vertical axis.A. a cylinder with radius of 5 cm and height of 3 cm B.a cylinder with height of 5 cm and radius of 3 cm C. a cylinder with diameter of 5 cm and height of 3 cm D. a cylinder with height of 5 cm and diameter of 3 cm
To answer this question, we need to do a drawing like this:
If we see the figure from above, we will see that the figure will have a radius of 5 cm, and, therefore, a diameter of 10 cm. The height will be always 3 cm.
Therefore, if the rectangle is rotated about the vertical axis, we will have a cylinder of radius equal to 5 cm and a height of 3 cm.
Hence, the answer is option A: a cylinder with a radius of 5 cm and a height of 3 cm.
how much does Taryn charge to mow a lawn she mowed ,9 lawns time spent mowing lawns in an hour 7.5 and money earned $112.50
step 1
Find the unit rate
Taryn
(9,112.50)
Divide 112.50 by 9
112.50/9=$12.50 per law
Alastair
Divide 122.50 by 7
122.50/7=$17.5 per law
Find out how much Taryn earn per hour
Divide 112.50 by 7.5
112.5/7.5=$15 per hour
Find out how much Alastair earn per hour
Divide 122.50 by 5
122.5/5=$24.5 per hour
therefore
Alastair earns more per hour
Which of the following expressions are equivalent to -19/8.(-50)?Choose all answers that apply.
To answer this question we notice the result of the original expression is positive; now, using the law of sign we notice that the negative sign in the fraction in option A will cancel out, leaving only the outer minus sign; after that if we make the product the result will be positve. This does not happens in option B, in this case the final result will be negative.
Therefore, the answer is A.
16For an arithmetic series a₁ = -10 and S6 = -285, find the common difference.A-35B-25C -15D -5
Given:
An arithmetic series a₁ = -10 and S6 = -285
We will find the common difference (d) using the formula of the sum.
[tex]S=\frac{n}{2}(2a+(n-1)d)[/tex]Substitute S= -285, a = -10, n = 6
[tex]\frac{6}{2}(2(-10)+(6-1)d)=-285[/tex]Solve the equation to find (d):
[tex]\begin{gathered} 3(-20+5d)=-285 \\ -20+5d=-\frac{285}{3} \\ \\ -20+5d=-95 \\ 5d=-95+20 \\ 5d=-75 \\ \\ d=-\frac{75}{5}=-15 \end{gathered}[/tex]So, the answer will be option C) -15