A carnival game has the possibility of scoring 50 points, 75 points, or 150 points per turn. The probability of scoring 50 points is 60%, 75 points is 30%, and 150 points is 10%. The game operator designed a simulation using a random number generator to predict how many points would be earned for a turn.
Integer Value Points Frequency
0 - 5 50 55
6 - 8 75 32
9 150 13
10. What is game’s expected value of points earned for a turn?
(SHOW WORK)
Answer:
The game’s expected value of points earned for a turn is 71.
Step-by-step explanation:
Here we know that:
Points Frequency
50 55
75 32
150 13
Here points earned is a random variable.
We need to find its expected value,
Finding Expected value:
Expected value of a random variable is its mean value. So we will first find the mean value of points earned per turn from the table we are given.
Total number of turns = sum of frequencies
= 55 + 32 + 14 = 100
Total points earned = 50(55) + 75(32) + 150(13)
= 7100
Expected value of points earned for a turn = Mean value of points
= Total points/no. of turns
= 7100/100
= 71
Which expression is a difference of cubes?
Answer:
Option 4 is correct.
Step-by-step explanation:
Given the following options
we have to choose the difference of cubes.
Option 1:
[tex]9w^{33}-y^{12}[/tex]
[tex]9(w^{11})^{3}-(y^4)^3[/tex]
which is not the difference of cubes
Option 2:
[tex]18p^{15}-q^{21}[/tex]
[tex]18(p^5)^3-(q^7)^3[/tex]
which is not the difference of cubes
Option 3:
[tex]36a^{22}-b^{16}[/tex]
[tex](6a^{11})^2-(b^8)^2[/tex]
which is the difference of square
Option 4:
[tex]64c^{15}-a^{27}[/tex]
[tex](4c^5)^3-(a^9)^3[/tex]
which is the difference of cubes.
What is the product of -3x5y2 and 9x3y8?
For this case we must find the product of the following expression:
[tex](-3x ^ 5y ^ 2) * (9x ^ 3y ^ 8)[/tex]
Then, by definition of powers of the same base we have to put the same base and add the exponents:
[tex](-3 * 9) x^{5 + 3} (1 * 1)y^{8 + 2} =[/tex]
[tex]-27x ^ 8*1y ^ {10}[/tex]
ANswer:
[tex]-27x ^ 8y ^ {10}[/tex]
Identify any extraneous solution. See above pic
Answer:
There are no extraneous solutions
Reasoning:
An extraneous solution is a solution that isn't valid, it might be imaginary like the square root of a negative number.
first we want to isolate z:
1+sqrt(z)=sqrt(z+5)
^2 all ^2 all
(1+sqrt(z))(1+sqrt(z))=z+5
expand
1+2sqrt(z)+z=z+5
-1 -z -z -1
2sqrt(z)=4
/2 /2
sqrt(z)=2
^2 all ^2 all
z=4
Since there is one solution and it is a real number, there are no extraneous solutions.
[tex]D:z\geq 0\wedge z+5\geq 0\\D:z\geq 0\wedge z\geq -5\\D:z\geq0\\\\1+\sqrt z=\sqrt{z+5}\\1+2\sqrt z+z=z+5\\2\sqrt z=4\\\sqrt z=2\\z=4[/tex]
[tex]4\in D[/tex] so there are no extraneous solutions.
1.
Evaluate u + xy , for u = 2, x = 9, and y = 6.
56
24
66
17
Answer:
Your answer is 56.
Step-by-step explanation:
To solve this problem, we simply need to plug in the given numbers into the expression.
If we do this, we get the following:
u + xy
2 + (9*6)
Using PEMDAS, we know that we have to perform the multiplication in this problem before the addition. Thus the first step in simplification is multiplying 9 and 6 together. If we do this, we get:
2 + 54
Next, we simply add together the two remaining terms.
54 + 2 = 56
Therefore, your answer is 56, the first option.
Hope this helps!
Solve 3 -x = 243 -5 1/5 5
Answer:
[tex]x=-243[/tex]
Step-by-step explanation:
The equation is
[tex]-3^{-5}=\frac{1}{x}[/tex]
Solve for x
we know that
[tex]-3^{-5}=-\frac{1}{3^{5}}=-\frac{1}{243}[/tex]
substitute
[tex]-\frac{1}{243}=\frac{1}{x}[/tex]
so
[tex]x=-243[/tex]
Answer:
-5
Step-by-step explanation:
Fine the value of k for which the pair of linear equation kx+3y=k+2 and 12x+ ky has no solution
Answer:
Step-by-step explanation:
it will have no sol. when a1/a2=b1/b2!=c1/c2
!= means not equal to
kx+3y=k+2
kx+3y-(k+2)=0 equation 1
12x+ky=0
taking a1/a2=c1/c2
k/12=3/k
k^2=36
k=6
when k= 6 it will have no sol
The endpoints of a diameter of a circle are A(2,1) and B(5,5). Find the area of the circle in terms of pi.
Answer:
The area of the circle is [tex]A=6.25\pi\ units^{2}[/tex]
Step-by-step explanation:
step 1
Find the diameter of circle
we know that
The diameter of the circle is equal to the distance AB
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]AB=\sqrt{(5-1)^{2}+(5-2)^{2}}[/tex]
[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]
[tex]AB=\sqrt{25}[/tex]
[tex]AB=5\ units[/tex]
therefore
the diameter of the circle is
[tex]D=5\ units[/tex]
step 2
Find the area of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
[tex]r=5/2=2.5\ units[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (2.5)^{2}[/tex]
[tex]A=6.25\pi\ units^{2}[/tex]
A restaurant owner needs to order at least 176 filet mignon steaks to be stocked for a busy Friday night. He only has room to store 321 steaks in his refrigerator. Model the number of steaks the restaurant owner can order, using a compound inequality.
x ≥ 176 and x ≤ 321
x ≤ 176 and x ≥ 321
x ≤ 176 and x ≤ 321
x ≥ 176 and x ≥ 321
Answer:
x ≥ 176 and x ≤ 321
Step-by-step explanation:
Let
x -----> the number of steaks the restaurant owner can order
we know that
[tex]x\geq 176[/tex] ----> inequality A
[tex]x\leq 321[/tex] ----> inequality B
so
the compounded inequality is equal to
[tex]176 \leq x \leq 321[/tex]
Explanation of modeling the number of steaks a restaurant owner can order using a compound inequality.
Explanation:To model the number of steaks the restaurant owner can order using a compound inequality, we represent the situation with x ≥ 176 and x ≤ 321. This means the owner can order any amount of steaks from 176 to 321. So, the correct compound inequality is x ≥ 176 and x ≤ 321.
Factor completely, then place the answer in the proper location on the grid. 49x 2 + 42xy + 9y 2
Answer:
(7x + 3y)(7x + 3y) or we could write it as (7x + 3y)^2.
Step-by-step explanation:
49x 2 + 42xy + 9y 2
The square root of 49xy^2 = 7x and the square root of 9y^2 = 3y.
Now 7x *3y = 21xy and 2 * 21xy = 42xy so the factors are:
(7x + 3y)(7x + 3y).
49x 2 + 42xy + 9y 2 is a perfect square trinomial.
Answer:
[tex](7x+3y)(7x+3y)[/tex]
Step-by-step explanation:
We are given that an expression
[tex]49x^2+42xy+9y^2[/tex]
We have to find the factor of given expression
[tex](7x)^2+2\times (7x)\times 3+(3y)^2[/tex]
Identity:[tex](a+b)^2=a^2+2ab+b^2[/tex]
Using the identity,then we get
[tex](7x+3y)^2[/tex]
[tex](7x+3y)(7x+3y)[/tex]
Hence, the factor of given expression is given by
[tex](7x+3y)(7x+3y)[/tex]
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
In thinking about what number each term may be multiplied by to eliminate the fractions, we can take one of two courses:
1) Find the lowest common multiple, ie. the lowest value that each of the fraction denominators have in common as a multiple.
Now a multiple is basically that number multiplied by an integer - for example, multiples of 2 are 2, 4, 6, 8, 10, etc.
So, let us write out the first few multiples for each of the denominator values:
4 (from 3/4): 4, 8, 12, 16, 20
3 (from 1/3): 3, 6, 9, 12, 15, 18
2 (from 1/2): 2, 4, 6, 8, 10, 12, 14, 16
Looking at the values above, we can see that the lowest value that occurs in all three sets of numbers is 12, thus 12 is the lowest common multiple.
Therefor, in order to eliminate the fractions before solving, each term must be multiplied by 12.
2) You could alternatively try multiplying the equation (or simply each fraction) by each of the possible answers and seeing if that will eliminate all of the fractions - this may seem quicker at first but it is always worthwhile understanding how to calculate this question without having possible answers, and as you complete more questions, the process of finding the lowest common multiple will become more natural and even quicker in the end. Nonetheless, let us try this method:
a) Multiplying each fraction by 2
(3/4)*2 = 3/2
This does not eliminate the fraction, therefor 2 is not the answer.
b) Multiplying each fraction by 3
(3/4)*3 = 9/4
This does not eliminate the fraction, thus 3 is not the answer.
c) Multiplying each fraction by 6
(3/4)*6 = 9/2
This does not eliminate the fraction, therefor 6 is not the answer.
d) Multiplying each fraction by 12
(3/4)*12 = 9 (this works so far)
(1/3)*12 = 4 (this also works so far)
(1/2)*12 = 6 (this also works)
Since multiplying each fraction by 12 will eliminate the fractions, 12 is the answer.
Answer:
D is the answer
Step-by-step explanation:
Find the area of an equilateral triangle with a side of 6 inches
Answer:
9√3in^2 hope this helps. found an answer...
Answer:
9 sqrt 3
Step-by-step explanation:
It was correct on my quiz
1/4 x 6 squared x sqrt 3
in a parallelogram one of the angles is 65 degrees, find the the sizes for all.
Answer: Another angle would be 65 and two other angles would be 115.
Step-by-step explanation: Attachment shown.
Erika has three pieces of ribbon. Each piece is 25 yards long. She needs to cut pieces that are 22 inches long. What is the greatest number of 22-inch pieces that she can cut from the three pieces of ribbon?
Annmarie can plow a field in 240 minutes. Gladys can plow a field 80 minutes faster. If they work together, how many minutes does it take them to plow the field?
A)96 min
B)160
C)400
D)480
Thanks for the help!
Answer:
Option A is the correct answer.
Step-by-step explanation:
Let the work plow a field be x.
Annmarie can plow a field in 240 minutes.
Rate at which Annmarie can plow[tex]=\frac{x}{240}[/tex]
Gladys can plow a field 80 minutes faster
Time taken by Gladys = 240 - 80 = 160 minutes.
Rate at which Gladys can plow[tex]=\frac{x}{160}[/tex]
If they combine time taken to plow [tex]=\frac{x}{\frac{x}{240}+\frac{x}{160}}=\frac{240\times 160}{240+160}=96\texttt{ minutes}[/tex]
Option A is the correct answer.
the time taken for Annmarie and Gladys to plow the field together is 96 minutes. The correct answer is A) 96 min.
Annmarie can plow a field in 240 minutes, and Gladys can do it in 160 minutes (since she is 80 minutes faster). To find out how long it would take for them to plow the field together, we can use the formula for combined work rates:
Let A be Annmarie's work rate and G be Gladys's work rate. Annmarie's work rate is 1 field per 240 minutes, or 1/240 fields per minute. Gladys's work rate is 1 field per (240 - 80) minutes, or 1/160 fields per minute.
Combined work rate of Annmarie and Gladys: A + G = 1/240 + 1/160.
Now, to find the time it would take them working together, we take the reciprocal of the combined work rate.
The combined work rate is:
1/240 + 1/160 = 1/240 + 1/160 = (1x160 + 1x240) / (240x160) = (160 + 240) / (240x160) = 400 / (240x160)
The time it takes for them to work together is the reciprocal of 400 / (240x160), which is (240x160) / 400.
Calculate: (240x160) / 400 = 38400 / 400 = 96
Therefore, the time taken for Annmarie and Gladys to plow the field together is 96 minutes. The correct answer is A) 96 min.
A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Select two options.
A - (–2, 0) and (2, 5)
B - (–4, 5) and (4, –5)
C - (–3, 4) and (2, 0)
D - (1, –1) and (6, –5)
E - (2, –1) and (10, 9)
Answer:
A and E
Step-by-step explanation:
A line has a slope of -4/5, then a perpendicular line has a slope 5/4, because
[tex]-\dfrac{4}{5}\cdot \dfrac{5}{4}=-1[/tex]
Find the slopes of the lines in all options:
A. True
[tex]\dfrac{5-0}{2-(-2)}=\dfrac{5}{4}[/tex]
B. False
[tex]\dfrac{-5-5}{4-(-4)}=-\dfrac{5}{4}[/tex]
C. False
[tex]\dfrac{0-4}{2-(-3)}=-\dfrac{4}{5}[/tex]
D. False
[tex]\dfrac{-5-(-1)}{6-1}=-\dfrac{4}{5}[/tex]
E. True
[tex]\dfrac{9-(-1)}{10-2}=\dfrac{5}{4}[/tex]
Answer:
C
Step-by-step explanation:
=(0-4)/(2+3)
=-4/5
What are the domain and range of f(x)=(1/5)^x ?
A.)The domain is all real numbers. The range is all real numbers.
B.)The domain is all real numbers. The range is all real numbers greater than zero. C.)The domain is all real numbers greater than zero. The range is all real numbers. D.)The domain is all real numbers greater than zero. The range is all real numbers greater than zero.
The domain is the input value for x, which can be any real number.
The range would be the output value, which in this equation would be any number greater than 0.
The answer is B.
Answer:
ITS B
Step-by-step explanation:
Hope this helps
Kevin bought seven tickets to the Haunted Graveyard at Lake Compounce for $209.93. How much does one ticket cost?
Answer:
$29.99
Step-by-step explanation:
This is a division problem.
$209.93/7 = $29.99
Answer: $29.99
Answer:
$29.99
Step-by-step explanation:
$209.93 divided by 7 is $29.99
Evaluate 4k2 + 3 when k = 5
Answer:
103
Step-by-step explanation:
Evaluate 4k2 + 3
To evaluate 4k² + 3, when k = 5, which means when you sees k, put 5 in replacement
4k² + 3 = 4(5)² + 3
4(5×5) + 3
4(25) + 3
open the bracket
4 × 25 = 100
∴ 100 + 3 = 103
Please mark me brainliest
[tex]\text{Hey there!}[/tex]
[tex]\text{If k = 5 the replace the 'k' value with 5}[/tex]
[tex]\text{4(5)}^2+3[/tex]
[tex]\text{(5)}^2=5\times5=25[/tex]
[tex]\text{4 (25)+ 3 = ?}[/tex]
[tex]\text{4 (25) = 25 + 25 + 25 + 25 = 100}[/tex]
[tex]\text{100 + 3 = 103}[/tex]
[tex]\boxed{\boxed{\bf{Your\ answer: 103}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
26 POINTSSSS PLEASEEE HELPPPP
Answer:
3. 32:4
4. three times
Step-by-step explanations:
20000000000000x 3065
Answer:
61300000000000000
Step-by-step explanation:
Multiplying 20,000,000,000,000 by 3,065 results in 61,300,000,000,000,000.
Write down the numbers in standard form:
2 x[tex]10^{13}[/tex] for 20,000,000,000,000 and
3.065 x 10³ for 3,065.
Multiply the two standard forms:
(2 x [tex]10^{13}[/tex]) * (3.065 x 10³).
Combine the powers of 10:
2 * 3.065 = 6.13 and
[tex]10^{13}[/tex] * 10³ = [tex]10^{16}[/tex]
The result is 6.13 x [tex]10^{16}[/tex]
In standard numerical form, this is 61,300,000,000,000,000.
So, 20,000,000,000,000 x 3,065 equals 61,300,000,000,000,000.
Complete Question:
Multiply 20000000000000 x 3065.
Which choice below is a boxplot for the following distribution?
66, 62,58,52, 48, 46, 44, 34, 33, 31, 31, 30, 27, 25, 24, 21, 19
Answer: b
Step-by-step explanation:
The boxplot of the distribution 66, 62, 58, 52, 48, 46, 44, 34, 33, 31, 31, 30, 27, 25, 24, 21, and 19 is given below.
The correct option is B.
The given distribution is as follows: 66, 62, 58, 52, 48, 46, 44, 34, 33, 31, 31, 30, 27, 25, 24, 21, 19.
To create a boxplot, we need to identify the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum values.
Arranging the data in ascending order, we have: 19, 21, 24, 25, 27, 30, 31, 31, 33, 34, 44, 46, 48, 52, 58, 62, 66.
The minimum value is 19, the maximum value is 66, and the median (Q2) is the middle value of the sorted data, which is 33.
To find the quartiles, we need to locate the positions that divide the data into quarters. The lower quartile (Q1) is the median of the lower half of the data, and the upper quartile (Q3) is the median of the upper half.
Counting from the minimum, we find that Q1 is 27, and counting from the maximum, we find that Q3 is 48.
With this information, the box plot is given in the attached image below.
Therefore, the correct option is B.
To learn more about the box-and-whisker plot ;
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i need help on this question, someone please help!!
show your work too!
i even looked up the answer to this, and it doesn't even match my choices.
thank you!:)
Answer:
y=−x−1/3x−8
Step-by-step explanation:
y=8x−1/3x+1
To find the inverse function, swap x and y, and solve the resulting equation for x.
If the initial function is not one-to-one, then there will be more than one inverse.
So, swap the variables: y=8x−1/3x+1 becomes x=8y−1/3y+1.
Now, solve the equation x=8y−1/3y+1 for y.
y=−x−1/3x−8
Sorry I was in a rush and couldn't do the fractions as formulae. Hope it helped anyways.
Can someone tell me the answers
The wall is 12 feet long. They are placing studs every 18 inches. If there are studs on each end of the wall, how many studs will they place?
Answer:
9
Step-by-step explanation:
1 feet is 12 inches, so 12 feet is 12 * 12 = 144 inches.
If studs are placed 18 inches apart, in 144 inches, there will be:
[tex]\frac{144}{18}=8[/tex]
But remember, there is a stud at the very beginning (at 0 feet).
So in total there are going to be 9 studs
To find the number of studs placed on the wall, subtract 2 from the total number of spaces between the studs, making total as 10 studs.
Explanation:To find the number of studs placed on the wall, we need to calculate the number of spaces between the studs.
Since there are studs on each end of the wall, we subtract 2 from the total number of spaces.
The wall is 12 feet long, which is equal to 12 * 12 = 144 inches.
Each stud is placed every 18 inches, so the number of spaces between the studs is 144 / 18 = 8.
Therefore, the total number of studs placed is 8 + 2 = 10 studs.
Learn more about Calculating the number of studs placed on a wall here:https://brainly.com/question/12865093
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how do you solve ¾ = 1/12 x + 2?
Answer:
x=-15
Step-by-step explanation:
Change 2 to a denominator of 4 2x4=8
1/12x+8/4=3/4 (take away 8/4)
1/12x=-5/4 ( 5multiply by 12)
x=-60/4 (divided by 3)
x=-15
Can someone please help me!!
Answer:
x = 6Step-by-step explanation:
Use Angle Bisector theorem (look at the picture).
We have the equation:
[tex]\dfrac{3}{x}=\dfrac{x-4}{4}[/tex] cross multiply
[tex]x(x-4)=(3)(4)[/tex] use the distributive property
[tex]x^2-4x=12[/tex] subtract 12 from both sides
[tex]x^2-4x-12=0\\\\x^2+2x-6x-12=0\\\\x(x+2)-6(x+2)=0\\\\(x+2)(x-6)=0\iff x+2=0\ \vee\ x-6=0[/tex]
[tex]x+2=0[/tex] subtract 2 from both sides
[tex]x=-2<0[/tex]
[tex]x-6=0[/tex] add 6 to both sides
[tex]x=6[/tex]
What is the range of f(x) = 3/4x – 4?
Answer:
(-∞, ∞).
Step-by-step explanation:
This function can have any real value.
Range = (-∞, ∞).
The range of f(x) = 3/4x – 4 is [tex]\( (-\infty, \infty) \)[/tex].
To find the range of the function [tex]\( f(x) = \frac{3}{4}x - 4 \)[/tex], we need to consider all possible output values of the function as x varies.
The function x is a linear function with a slope of [tex]\( \frac{3}{4} \)[/tex], which means it increases or decreases steadily as x increases or decreases, respectively. Since there are no restrictions on the domain of the function (i.e., x can take any real value), the range of the function is also unrestricted.
To find the range, we can examine the behavior of the function as x approaches positive infinity and negative infinity:
1. As x approaches positive infinity, [tex]\( f(x) \)[/tex] also approaches positive infinity.
2. As x approaches negative infinity, [tex]\( f(x) \)[/tex] also approaches negative infinity.
Therefore, the range of the function [tex]\( f(x) = \frac{3}{4}x - 4 \)[/tex] is all real numbers. In interval notation, we can represent the range as [tex]\( (-\infty, \infty) \)[/tex].
The perimeter of the rectangle below is 184 m .What is the value of y
Step-by-step explanation:
2x + 2y = 184 ---- eqn 1
y = 184 - 2x / 2
y = 92 - x ---- eqn 2
Can someone answer C. Please it’s my last try I got it wrong 2 times so please explain!
Answer:
5.
Step-by-step explanation:
What you require is the area of the rectangle whose base is between 210 and 215.
The number having levels between 210 and 214
= 20 * the relative frequency
= 20 * 0.25
= 5 (answer).