SOLUTION:
Step 1:
In this question, we are given that;
If a red and a blue fair six-sided die are rolled.
What is the probability the result is 8 or divisible by 3?
Step 2:
The table for the two dice rolled together is as shown below:
Green 1 2 3 4 5 6
Red
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
Step 3:
The probability that the result is 8 =
[tex]\begin{gathered} =\text{ }\frac{\nu mber\text{ of 8}}{\text{Total number }} \\ =\text{ }\frac{5}{36} \end{gathered}[/tex]Next,
The probability that the result is divisible by 3
=
[tex]\frac{12}{36}[/tex]Finally, the probability that the result is 8 or divisible by 3, we have that:
[tex]\frac{5}{36}+\frac{12}{36}\text{ =}\frac{17}{36}[/tex]
need help asap look at attachmen
The rectangle has a width of 7 yards and a length of 42 yards.
How to find the length and width?For a rectangle of length L and width W, the perimeter is:
P = 2*(L + W)
Here we know that:
L = 6*W
P = 98yd = 2*(L + W)
Then we have the system of equations:
L = 6*W
98yd = 2*(L + W)
If we substitute the first equation into the second one, we get:
98yd = 2*(6*W + W)
98yd = 14*W
98yd/14 = W = 7yd
So the width is 7 yards, and the length is 6 times that, so:
L = 6*7yd = 42yd
Learn more about rectangles:
https://brainly.com/question/17297081
#SPJ1
(Please show your work for question 18.)
It is given that AB = CB from this information we conclude that <A=<C by reason :angles opposite equal sides.
<A+<B+<C=180°(Sum of angles in a triangle)
[tex](4x - 13) + (5x - 2) + (4x - 13) = 180 \\ 4x + 5x + 4x - 13 - 2 - 13 = 180 \\ 13x - 28 = 180 \\ 13x = 180 + 28 \\ 13x = 208 \\ \frac{13x}{13} = \frac{208}{13} \\ x = 16[/tex]
x=6°
ATTACHED IS THE SOLUTION
GOODLUCK
The product 8 and the square of a number decreased by 5 is 67. Find the number.
Answer:
3 or -3
Explanation:
Let's call the unknown number x. The square of this number is x². The product of 8 and the square of this number is 8x². Finally, it is decreased by 5, so 8x² - 5 and it is equal to 67, then the equation that represents the statement is:
8x² - 5 = 67
Now, we can solve the equation for x. Add 5 to both sides
8x² - 5 + 5 = 67 + 5
8x² = 72
Divide both sides by 8
8x²/8 = 72/8
x² = 9
Find the square root of both sides
x = √9
x = 3 or x = -3
Therefore, the number is 3 or -3
Text-to-Speech 11. Diva wants to make a flower arrangement for her aunt's birthday. She wants 1/3 of the arrangement to be roses. She has 12 roses. How many other flowers does she need to finish the arrangement?
Domingo had 250 baseball cards, andJennifer had 82 baseball cards. At thefirst meeting of the Card Club and atevery meeting thereafter, Domingo sold12 cards to Jennifer. After which meetingdid the two have the same numberof cards?
Data:
Domingo: D
Jennifer: J
Initial number of cards:
D=250
J=82
After each meeting(m):
D=250-12m
J=82+12m
After the first meeting: m=1
[tex]D=250-12(1)=238[/tex][tex]J=82+12(1)=94[/tex]You increase in 1 the m after each meeting and get the next table:
Then, they have the same number of cards after 7th meetingexplain why there are two zeros in the product of 5 x 40
EXPLANATION
There are two zeros in the product of 5x40 because multiplying the number 40 5 times give us the number 200 wich is a hundred type number.
Picture explains it all
Answer: .1$ so 10cents
Step-by-step explanation:
1. Input, X 9753 1 Output, y 1 2 2 3 4 Function - Yes or no
before we can dtermone whether it is a function, there must be a relationship between X and y i.e they must have a constannt of proportionality as shown:
From the table:
when x = 9, y = 1
when x = 7, y = 2
when x = 5, y = 2
when x = 3, y = 3
when x = 1, y = 4
let us determine the constant of proportionality from the given values as shown:
k = y2-y1/x2-x1
when x = 9, y = 1
when x = 7, y = 2
k = 2-1/7-9
k = 1/-2
k = -1/2
Also
when x = 5, y = 2
when x = 3, y = 3
k = 3-2/3-5
k = 1/-2
k = -1/2
Also;
when x = 5, y = 2
when x = 3, y = 3
k = 3-2/3-5
k = 1/-2
k = -1/2
Since all the constant of proportionality are the same;
Hence y = kx
y = -1/2 x
This shows that the tabke is a function and X is directly proportional to y. hence the answer is YES, it is function
The parent function y = |x| is reflected across the x-axis to obtain ________________.y = -|x|y = -|x + 1|y = |-x|y = -|x + 5|
The given function is:
[tex]y=|x|[/tex]It is reflected across the x-axis to obtain a new function. This transformation follows the rule:
[tex]g(x)=-f(x)\rightarrow reflection\text{ }across\text{ }x-axis[/tex]If we apply this rule, we obtain:
[tex]y=-|x|[/tex]The answer is y=-|x|
Which measurement is closest to the area of the triangle in square centimeters? A 63 cm2 B 42.75 cm2 С 35.5 cm2 D 31.5 cm2
The measurement shows that the base of the triangle is approximately 7 cm
while the height is approximately 9cm
The area of the triangle is given by
[tex]\text{Area = }\frac{1}{2}\text{ x base x height}[/tex][tex]\begin{gathered} \text{Area =}\frac{1}{2}\text{ x 7 x 9} \\ \text{Area = }\frac{63}{2}cm^2 \\ \\ \text{Area = 31.5cm}^2 \end{gathered}[/tex]Option D is the closest to the answer
determine the volume of each rectangular or triangular prism round to the nearest tenth if necessary
Determine the volume of each rectangular or triangular prism round to the nearest tenth if necessary
____________________
volume = base (B)* height (H)
_____________________
Base area
Triangle
B = b*h/2
Rectangle
B= L1*L2
__________________
volume = base (B)* height (H)
H= 15
Triangle case
B = 4.8 *9.6 /2
B = 46.08 / 2
B= 23.04
V= 23. 04* 15
V= 345.6 in ^3
2x -1/4y = 1 Solve the equation for y.
Given:
Given the equation
[tex]2x-\frac{1}{4}y=1[/tex]Required: Solve for y.
Explanation:
Subtract 2x on both sides.
[tex]\begin{gathered} 2x-\frac{1}{4}y-2x=1-2x \\ -\frac{1}{4}y=1-2x \end{gathered}[/tex]Multiply both sides by -4.
[tex]\begin{gathered} y=-4(1-2x) \\ =4(2x-1) \end{gathered}[/tex]Final Answer: y = 4(2x - 1)
Show your work Round to the nearest whole number if needed
Given:
Radius, r = 6
Let's find the chance of hitting the shaded area by finding the ratio.
Since the radius of the cirlce is 6, the length of one side of the square is the diameter:
s = 6 x 2 = 12
To find the ratio divide the area of the circle by area of the square. The area of the circle is the shaded area while the area of the square is the total possible area.
Thus,we have:
[tex]\text{ Area of circle = }\pi r^2=3.1416\ast6^2=3.1416\ast36=113.0976\text{ square units}[/tex][tex]\text{ Area of square = }s^2=12^2=12\ast12=144\text{ square units}[/tex][tex]\text{ Ratio=}\frac{shaded\text{ area}}{total\text{ possible area}}=\frac{area\text{ of circle}}{area\text{ of square}}=\frac{113.0976}{144}=0.7854\approx0.79[/tex][tex]\text{ Percentage ratio = 0.7854 }\ast\text{ 100=}78.54\text{ \%}[/tex]Therefore, the chance of hitting the shaded region is 78.54%
ANSWER:
78.54%
10. Determine if the following sequence is arithmetic or geometric. Then, find the 67th term. 36, 30, 24, 18, ... a. arithmetic, -360 b. arithmetic, 12 c. geometric, -360 d. geometric, 12
hello
to determine if the sequence is arthimetic or a geometric progression, we check if a common difference or common ratio exists between the two sequence
the sequence is 36, 30, 24, 18,......
from careful observation, this is an arthimetic progression because a common difference exists between them
d = 30 - 36 = -6
or
d = 24 - 30 = -6
to find the 67th term, let's apply the formula
[tex]\begin{gathered} T_n=a+(n-1)d \\ T_{67}=a+(67-1)d \\ a=\text{first term = 36} \\ d=common\text{ difference = }-6 \\ T_{67}=36+(67-1)\times-6 \\ T_{67}=36+66\times-6 \\ T_{67}=36-396 \\ T_{67}=-360 \end{gathered}[/tex]PLEASE HELP! *not a test, just a math practice that I don't understand.
1) Let's analyze those statements according to the Parallelism Postulates/Theorems.
8) If m∠4 = 50º then m∠6 =50º
Angles ∠4 and ∠6 are Alternate Interior angles and Alternate Interior angles are always congruent
So m∠4 ≅ m∠6
9) If m∠4 = 50, then m∠8 =50º
Angles ∠4 and ∠8 are Corresponding angles and Corresponding angles are always congruent
10) If m∠4 = 50º, then m∠5 =130º
Angles ∠4 and ∠5 are Collateral angles and Collateral angles are always supplementary. So
≅
How do you determine a relation is function on a GRAPH?
To Determine: How to determine a relation is function on a GRAPH
In other to achieve this, we will use the vertical test
If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function
Check the image below for a better clarification
With the use of the vertical line test, the graph in OPTION C and OPTION D are functions and the graph in OPTION A and B are not functions
In summary, you determine a relation is a function on a graph by using a vertical line test
Explain how you know 437,160 is greater than 43,716.4 grade student
437,160 is read as four hundred thirty-seven thousand one hundred sixty and 43,716 is read as fourty-three thousand seven hundred sixteen.
The first number has hundreds of thousand and the second one only has tens of thousand. It means that the first number is greater than the second one.
Another way to know this is because of the number of figures before the decimal point. The first number has 6 figures before the decimal point and the second one only has 5.
That way, we know that 437,160 is greater than 43,716.
Compute the percent of profit or loss on shares of stock purchased at8.625 and sold at 10.75.
ANSWER:
24.63%
STEP-BY-STEP EXPLANATION:
The first thing is to mention that it is a profit because it was bought at a lower amount than it was sold, therefore
We take 100% as the lowest value, and thus we calculate the profit percentage
[tex]10.75\cdot\frac{100}{8.625}=124.63[/tex]Then the difference between both percentages is the profit percentage
[tex]124.63-100=24.63[/tex]Solve: 5|4x+5|−2≤33 Give your answer as an interval. If no solutions exists - enter No solutions.
The expression given is,
[tex]5|x-3|+3>7[/tex]Subtract 3 from both sides
[tex]\begin{gathered} 5|x-3|+3-3>7-3 \\ 5|x-3|>4 \end{gathered}[/tex]Divide both sides by 5
[tex]\begin{gathered} \frac{5|x-3|}{5}>\frac{4}{5} \\ |x-3|>\frac{4}{5} \end{gathered}[/tex]Apply absolute rule:
[tex]\begin{gathered} x-3<-\frac{4}{5}\text{ or x-3>}\frac{4}{5} \\ \end{gathered}[/tex]Add 3 to both sides
[tex]\begin{gathered} x-3+3<-\frac{4}{5}+3\text{ or x-3+3>}\frac{4}{5}+3 \\ x<\frac{11}{5}\text{ or x>}\frac{19}{5} \end{gathered}[/tex]Therefore, the answer has the form:
[tex](-\infty,A)\cup(B,\infty)[/tex]Hence, the solution using interval notation is
[tex](-\infty,\frac{11}{5})\cup(\frac{19}{5},\infty)[/tex]solving rational equations 1[tex] \frac{9x}{x - 2} = 6[/tex]2[tex] \frac{7}{x + 2} + \frac{5}{x - 2} = \frac{10x - 2}{x {}^2{ - 4} } [/tex]3[tex] \frac{ x - 1}{2x - 4} = \frac{2x - 2}{3x} [/tex]step by step instructions please thank you
the given expression is.,
[tex]\frac{9x}{x-2}=6[/tex][tex]\begin{gathered} 9x=6x-12 \\ 9x-6x=-12 \\ 3x=-12 \\ x=-\frac{12}{3} \\ x=-4 \end{gathered}[/tex]also, the given expression is,
[tex]\frac{7}{x+2}+\frac{5}{x-2}=\frac{10x-2}{x^2-4}[/tex][tex]\begin{gathered} \frac{7x-14+5x+10}{x^2-4}=\frac{10x-2}{x^2-4} \\ 12x-4=10x-2 \\ 12x-10x=4-2 \\ 2x=2 \\ x=\frac{2}{2}=1 \\ x=1 \end{gathered}[/tex]help meeeeeeeeee pleaseee !!!!!
The composite functions are evaluated and simplified as:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3x² + 15
How to Evaluate a Composite Function?To evaluate a composite function, the inner function is evaluated first using the given input. After then, the output of the inner function is used as the input to evaluate the outer function.
Given the following:
f(x) = x² + 5g(x) = 3xTherefore:
a. (f o g)(x) = f(g(x))
Substitute g(x) for x into f(x) = x² + 5
f(g(x)) = (3x)² + 5
Simplify the function
f(g(x)) = 9x² + 5
b. (g o f)(x) = g(f(x))
Substitute f(x) for x into g(x) = 3x:
g(f(x)) = 3(x² + 5)
Simplify the function
g(f(x)) = 3x² + 15
Learn more about composite functions on:
https://brainly.com/question/10687170
#SPJ1
Which points sre vertices of the pre-image, rectangle ABCD?Makes no sense
Given rectangle A'B'C'D', you know that it was obtained after translating rectangle ABCD using this rule:
[tex]T_{-4,3}(x,y)[/tex]That indicates that each point of rectangle ABCD was translating 4 units to the left and 3 units up, in order to obtain rectangle A'B'C'D'.
Notice that the coordinates of the vertices of rectangle A'B'C'D' are:
[tex]\begin{gathered} A^{\prime}(-5,4) \\ B^{\prime}(3,4) \\ C^{\prime}(3,1) \\ D^{\prime}(-5,1) \end{gathered}[/tex]Therefore, in order to find the coordinates of ABCD, you can add 4 units to the x-coordinate of each point and subtract 3 units to each y-coordinate of each point. You get:
[tex]\begin{gathered} A=(-5+4,4-3)=(-1,1) \\ B=^(3+4,4-3)=(7,1) \\ C=(3+4,1-3)=(7,-2) \\ D=(-5+4,1-3)=(-1,-2) \end{gathered}[/tex]Hence, the answers are:
- First option.
- Second option.
- Fourth option.
- Fifth option.
Consider 0.6 X 0.2.How many digits after the decimal point will the product have?Number of digits =
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]0.6\times0.2[/tex]STEP 2: Evaluate the expression
It can be seen that the result of the expression is 0.12
Hence, there are 2 digits after the decimal point for the product
Which expression is equivalent to (m−5n−3)−3?
m−15n−9
m15n9
m−8n−6
1 over the quantity m raised to the eighth power times n raised to the sixth power end quantity
The expression (m⁻⁵n⁻³)⁻³ has an equivaent of m⁻¹⁵n⁹
How to determine the equivalent expressionFrom the question, the expression is represented as
(m−5n−3)−3
Rewrite the expression properly
This is done as follows;
(m⁻⁵n⁻³)⁻³
Open the brackets
So, we have the following equation
(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³
Evaluate the products
So, we have the following equation
(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹
This gives
So, we have the following equation
(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹
Hence, the solution is (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹
Read more about equivalent expression at
https://brainly.com/question/15775046
#SPJ1
The given expression (m⁻⁵n⁻³)⁻³ has an equivalent to the m⁻¹⁵n⁹
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The expression is represented as (m−5n−3)−3
Rewrite the expression as follows;
(m⁻⁵n⁻³)⁻³
Open the brackets , we have
(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³
Evaluate the products, we have;
(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹
(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹
Hence, the solution will be; (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹
Read more about equivalent expression at;
brainly.com/question/15775046
#SPJ1
If A is the image of A(3, 4) after a dilation with scale factor 7 about the origin, what is the distance between A and A? Hint: Use the distance formula: d = √√(x₂ − x₂)² + (Y₂ − 3₂)² .
0 7 units
○28 units
O 30 units
O 35 units
Answer:
Step-by-step explanation:
you can view this,its similar just the numbers are switched.
https://brainly.com/question/21685072
Answer:
35
Step-by-step explanation:
sorry if im wrong sorry
2. The area of the arena is 2160 in.2 a) Will the arena fit on the rug? Show your work and explain your answer below. b) If the length of the arena is 60 inches, what is the width? c) If the arena fits, and is placed exactly in the middle of the rug, how much standing room on the rug could a drive have? Use your measurements from above to help you. ? 3. If 15 robots can fit on the arena floor at one time, how much space does each robot take up?
Answers:
2a. The arena will fit on the rug
b. Width = 36 in
c. Standing room: 4 in
3. 144 in²
Explanation:
2. Part a.
First, we need to convert the measures of the rug to inches, so taking into account that 1 ft = 12 in, we get
Length = 6 ft x 12 in/ 1ft = 72 in
Width = 4 ft x 12 in/ 1 ft = 48 in
Then, the area of the rug will be
Area = Length x Width
Area = 72 in x 48 in
Area = 3456 in²
Therefore, the area of the arena, which is 2160 in² is lower than the area of the rug. It means that the area will fit on the rug.
Part b.
The area of the arena is equal to
Area = Length x Width
To find the width of the area, we need to solve the equation for the width, so
Width = Area/Length
So, replacing Area = 2160 in² and Length = 60 in, we get
Width = 2160 in² / 60 in
Width = 36 in
Therefore, the width of the area is 36 in.
Part c.
The measures that we get from parts a and b can be represented as
Therefore, the missing length can be calculated as:
(48 in - 36 in)/2 = 12 in/ 2 = 6 in
Therefore, a drive will have 6 in of standing room.
3.
Finally, to know how much space each robot take up, we need to divide the area of the arena by 15, so
2160 in²/ 15 = 144 in²
Therefore, each robot take 144 in²
In a third day of randomly selected subjects, the mean age of the 36 respondents is 40 years and the standard deviation of ages is 10 years. Use the sample results to construct a 95% confidence interval estimate of the mean age of the population from which the sample was selected. Repeat the previous problem assuming that the population standard deviation is known to be six years.
a. Given that:
- The mean age of the 36 respondents is 40 years.
- The standard deviation of ages is 10 years.
You need to construct a 95% confidence interval estimate of the mean age of the population from which the sample was selected.
Then, you need to use this formula:
[tex]x\pm z\cdot\frac{\sigma}{\sqrt{n}}[/tex]Where "x" is the sample mean, "z" is the confidence level value, "n" is the sample size, and σ is the standard deviation.
In this case:
[tex]\begin{gathered} x=40 \\ \sigma=10 \\ n=36 \end{gathered}[/tex]Therefore, by substituting values into the formula:
[tex]40\pm\frac{10}{\sqrt{36}}[/tex]You get these two values:
[tex]40+\frac{10}{\sqrt{36}}\approx41.67\text{ }[/tex][tex]40-\frac{10}{\sqrt{36}}\approx38.33[/tex]b. If you assume that:
[tex]\sigma=6[/tex]You get the following values by substituting them into the formula:
[tex]40+\frac{6}{\sqrt{36}}=41[/tex][tex]40-\frac{6}{\sqrt{36}}=39[/tex]Hence, the answers are:
a.
[tex](38.33,41.67)[/tex]b.
[tex](39,41)[/tex]
Graph the set {x|x2-3} on the number line.Then, write the set using interval notation.
Given,
The expression is,
[tex]\lbrace x|x\ge-3\rbrace[/tex]Required:
The graph of the line.
The interval notation is [-3, infinity).
The line of the inequality is,
Hence, the graph of the line is obtained.
I have a practice problem in the calculus subject, I’m having trouble solving it properly
The limit of a function is the value that a function approaches as that function's inputs get closer and closer to some number.
The question asks us to estimate from the table:
[tex]\lim _{x\to-2}g(x)[/tex]To find the limit of g(x) as x tends to -2, we need to check the trend of the function as we head towards -2 from both negative and positive infinity.
From negative infinity, the closest value we can get to before -2 is -2.001 according to the values given in the table. The value of g(x) from the table is:
[tex]\lim _{x\to-2^+}g(x)=8.02[/tex]From positive infinity, the closest value we can get to before -2 is -1.999 according to the values given in the table. The value of g(x) from the table is:
[tex]\lim _{x\to-2^-}g(x)=8.03[/tex]From the options, the closest estimate for the limit is 8.03.
The correct option is the SECOND OPTION.
Which statements are true?Select all that apply.A.The slope of AC is equal to the slope of BC.B.The slope of AC is equal to the slope of BD.C.The slope of AC is equal to the slope of line t.D.ECThe slope of line t is equal toAEE.FBThe slope of line t is equal toFDF.The slope of line t is equal to AB
Line t, segments AC, BC and BD are colinear, that is, all of them are in the same line. Then, the true statements are
A, B, and C
