Answer:
Step-by-step explanation:
interval notation is (-∞,∞)
set-builder notation is {x|x ∈ R}
The points (3, – 1) and (2,s) fall on a line with a slope of – 9. What is the value of s?
giving free brainlist!
Answer:
8
Step-by-step explanation:
[tex]\sqrt{3(\sqrt{3}-1)^2 }[/tex]
Answer:
3-[tex]\sqrt{3}[/tex] is the exact form
I have one fair 6-sided die and one unfair 6-sided die. On the unfair die, the probabilities of rolling numbers 2,…,6 are equal and the probability of rolling a 1 has a different value. I roll each die once.
If the probability of rolling one 3 and one 4 is 1/24, what is the probability of rolling two 1’s?
Answer:
[tex]\dfrac{1}{16}[/tex]
Step-by-step explanation:
Probability Distribution Table for X
Where X is the score on a fair, six-sided dice:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} x & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(X=x) \phantom{\dfrac11}&\frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} \\\cline{1-7}\end{array}[/tex]
Probability Distribution Table for Y
Where Y is the score on an unfair, six-sided dice, and the probabilities of rolling numbers 2, 3, 4, 5 and 6 are equal, and the probability of rolling a 1 has a different value:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} y & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(Y=y) \phantom{\dfrac11}&1-5k&k&k&k&k&k\\\cline{1-7}\end{array}[/tex]
Note: The probabilities of all the possible values that a discrete random variable can take add up to 1.
The outcomes of rolling one 3 and one 4 are:
Rolling a 3 with the first die and a 4 with the second die, ORRolling a 4 with the first die and a 3 with the second die.Given the probability of rolling one 3 and one 4 is ¹/₂₄:
[tex]\implies \text{P}(X=3)\; \text{and} \; \text{P}(Y=4) \; \text{or} \; \; \text{P}(X=4) \; \; \text{and} \; \; \text{P}(Y=3)=\dfrac{1}{24}[/tex]
[tex]\implies \dfrac{1}{6} \times k +\dfrac{1}{6} \times k=\dfrac{1}{24}[/tex]
[tex]\implies \dfrac{k}{6} + \dfrac{k}{6}=\dfrac{1}{24}[/tex]
[tex]\implies \dfrac{2k}{6}=\dfrac{1}{24}[/tex]
[tex]\implies 24(2k)=6[/tex]
[tex]\implies 48k=6[/tex]
[tex]\implies k=\dfrac{1}{8}[/tex]
Therefore:
[tex]\implies 1-5k=1-\dfrac{5}{8}=\dfrac{3}{8}[/tex]
Hence, the probability distribution table for the unfair 6-sided dice is:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} y & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(Y=y) \phantom{\dfrac11}&\frac{3}{8} & \frac{1}{8} & \frac{1}{8}& \frac{1}{8} & \frac{1}{8}& \frac{1}{8} \\\cline{1-7}\end{array}[/tex]
There is only one possible outcome of rolling two 1's, so the probability of rolling two 1's is:
[tex]\implies \text{P$(X=1)$ and P$(Y=1)$}=\dfrac{1}{6}\times\dfrac{3}{8}=\dfrac{3}{48}=\dfrac{1}{16}[/tex]
Note: Please see attachment for the sample-space diagram showing the possible outcomes of rolling two dice. The possible outcomes of rolling one 3 and one 4 are highlighted in yellow. The possible outcome of rolling two 1's is highlighted in blue.
will give brainliest
write a word problem that could be represented by this number line.
Answer:
John had 8 apples. He gave away 4. How many apples does he have left?
Step-by-step explanation: First, an arrow added 8 on the number line. Then, another arrow took away 4.
Aaron Rodgers' yearly salary is 2.2 x 10' dollars. The yearly salary of one of his backup
quarterback's is 6.3x105 dollars. How many times greater is Aaron Rodgers' salary than his
backup's salary?
Aaron Rodgers salary is 2.19×[tex]10^1^1[/tex] greater than his backups.
To find how many times a quantity x is greater than y we do subtraction. That is we do [tex]x-y[/tex].
So, here Aaron's salary is given to be $ 2.2× [tex]10^1^0[/tex]
And his quarterback's salary is $ 6.3×[tex]10^5[/tex].
Thus the difference between salaries= 2.2×[tex]10^1^0[/tex] - 6.3 × [tex]10^5[/tex]
= 2.19×[tex]10^1^1[/tex]
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When x²+x-3 is subtracted from 3x² - 5, the result is
A. -2x² + x + 2
B. 2x² - x - 2
C. 2x² - x + 2
D. 4x²+x-8
Answer:
B 2x² - x - 2
Step-by-step explanation:
When x²+x-3 is subtracted from 3x² - 5
We get (3x² - 5) - (x² + x - 3)
==> step 1 remove parenthesis and change signs
3x² - 5 - x² - x + 3
==> step 2 combine like terms
2x² - x - 2
Remember like terms are terms with the same variable and degree.
For example 3a² and 5a² would be like terms because both terms have a variable of "a" and a degree of 2
Classify the quadrilateral whose vertices are: A(3,2); B(0,5); C(-3,2); D(0,-1)x Select all that apply
Solution
- We can plot the coordinates given using a graphing calculator as shown below:
- From the above, we can see that the sides are equal and the looks like a diamond
- Thus, the quadrilateral is a Rhombus
- Since all the angles are 90 degrees, it is also a square only that it was rotated.
- A square is a special type of rectangle, thus, the shape is also a rectangle
- A parallelogram as its opposite sides parallel and opposite angles equal. This is the same with our figure. Thus, it is also a parallelogram
An airplane left an airport flying at 180 mi/h. A jet that flies at 330 mi/h left one hour later. The jet follows the same route as the airplane at a different altitude. How many hours will it take the jet to catch up with the airplane? How many miles will the jet have flown?
Using the distance formula, Jet will take 2.2 hours to catch up with the airplane.
We will find the solution using distance formula.
distance formula is a formula that is used to find the distance between two points. These points can be in any dimension.
d=rt where
d is distance r is rate or speed and t is time
"distance airplane traveled" = "distance jet traveled"
Let x = hours "airplane" was flying
x-1 = hours "jet" was flying
.
180x = 330(x-1)
180x = 330x - 330
180x + 330 = 330x
330 = 150x
330/150 = x
2.2 hours = x
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7x2 – 5x + 10x – 8x2
Answer:
-1(x - 5)x
Step-by-step explanation:
7x2 - 5x + 10x -8x2
7x2 + 5x -8x2
7x2 + 5x - 8x2
-1x2 + 5x
-1x2 + 5x
-x2 + 5x
7x2 - 5x + 10x - 8x2
-1 (x2 - 5x)
-1 (x2 - 5x)
-1(x - 5)x
-1(x - 5)x
Abdul runs 8 miles in 60 minutes
How many miles does he run per minute
Answer:
2/15 mile per minute
Step-by-step explanation:
8 miles in 60 minutes is equivalent to 8/60 miles per minute
= 2/15 mile per minute
Answer:
Step-by-step explanation:
60/8=7.5
Calculate the value of 1 3/5 x 2/5
As a fraction in its simplest form
Answer:
16/25
Step-by-step explanation:
1 3/5 = 8/5
8/5 x 2/5 = 16/25
6 kg rice is enough for 20 people. How much rice is required for 100 people
Answer:
30.
Step-by-step explanation:
Apologies if I am late, but I believe this is the answer!
Using the given sample data, calculate the following measures of dispersion, to one decimal place.
Range = 15
Variance = 24.5Explanations
Standard deviation = 5.0
The formula for calculating the range is expressed as:
Range = Highest value - Lowest value
Range = 24 - 9
Range = 15
Calculate the variance
The formula for calculating the variance is expressed as:
[tex]Variance=\frac{\sum(x-\overline{x})^2}{n-1}[/tex]Find the mean
[tex]\begin{gathered} mean=\frac{9+13+15+18+19+20+24}{7} \\ mean\text{ }\overline{x}=\frac{118}{7}=16.9 \end{gathered}[/tex]Determine the variance
[tex]\begin{gathered} S^2=\frac{(9-16.9)^2+(13-16.9)^2+(15-16.9)^2+(18-16.9)^2+(19-16.9)^2+(20-16.9)^2+(24-16.9)^2}{7-1} \\ S^2=\frac{146.9}{6} \\ S^2\approx24.5 \end{gathered}[/tex]Determine the standard deviation
[tex]\begin{gathered} S=\sqrt{variance} \\ S=\sqrt{24.5} \\ S\approx5.0 \end{gathered}[/tex]andrea and lauren are 20 kilometers apart. they bike toward one another with andrea traveling three times as fast as lauren, and the distance between them decreasing at a rate of 1 kilometer per minute. after 5 minutes, andrea stops biking because of a flat tire and waits for lauren. after how many minutes from the time they started to bike does lauren reach andrea?
Lauren will reach Andrea after 65 minutes of biking.
What do we mean by mathematical operations?A mathematical function called an operation, also known as an "operand" or "argument," transforms zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The operations that are most frequently studied are unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, and binary operations (i.e., operations of arity 2), such as addition and multiplication.So, because Lauren is traveling at a speed that is one kilometer per minute slower than Andrea's and vice versa, Andrea's speed is 3/4 km/min and Lauren's is 1/4 km/min.
Thus, Andrea will have biked 3/4 × 5 = 15/4 km in 5 minutes.Lauren will have to bike the following kilometers in total:
20 - 15/4 = 80/4 - 15/4 = 65/4 kmHer speed being 1/4 km/min, the amount of time passed will be:
(65/4)/(1/4) = 65Therefore, Lauren will reach Andrea after 65 minutes of biking.
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In general, the air temperature decreases 12°F for every
4,000 feet increase in altitude. If a hiker climbs 3,000 feet, by how
much can she expect the temperature to decrease?
Answer: 9
Step-by-step explanation:
SOMEONE HELP! I NEED THIS QUICKLY! WILLING TO GIVE 45 POINTS!!! At 1 P.M., the total snowfall is 2 centimeters. At 4 P.M., the total snowfall is 7 centimeters. What is the mean hourly snowfall? Write your answer in simplest form as a fraction or mixed number.
The mean hourly snowfall is (5/3) centimeters per hour, which means that each hour there are 5/3 centimeters more of snow.
What is the mean hourly snowfall?The mean hourly snowfall is given by the quotient between difference between the total snowfall at the two given times and the total time.
Here we have:
Initial snowfall = 2cm
Final snowfall = 7cm
Difference = 7cm - 2cm = 5cm
And that happens between 1 P.M. and 4 P.M., so we have 3 hours.
Then the mean hourly snowfall is:
M = 5cm/3h = (5/3) centimeters per hour.
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Factor the expression using the GCF 6y + 3
[tex]3(2y+1)[/tex] I believe is the solution you seek.
You factor 3 out of 6y + 3, leaving you with the solution.
Hope this helps!
A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $40 million after 4 years, while profits increased $30 million per year. Select the linear function in slope-intercept form that models this situation (in millions).
Group of answer choices
y = 160x + 30
y = 40x + 4
y = 30x - 40
y = 30x - 80
How many non-identical triangles can be made using these side lengths:
5 cm, 7 cm, and 10 cm
By applying the Triangle Inequality Theorem, the number of non-identical triangles that can be made using the given side lengths is one.
What is the Triangle Inequality Theorem?In Mathematics, the Triangle Inequality Theorem can be defined as a type of theorem which states that the sum of any two (2) side lengths of a triangle must be greater than the measure of the third (2) side.
This ultimately implies that, the sum of the lengths of any two (2) sides of a triangle cannot be less than the length of the third (3) side of the triangle in accordance with the Triangle Inequality Theorem, as represented by this mathematical expression:
b - c < a < b + c
Where:
a, b, and c represent the side lengths of this triangle.
By applying the Triangle Inequality Theorem to the side lengths of this triangle, the number of non-identical triangles is given by:
5 + 7 > 10
12 > 10 (True).
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SOMEONE PLEASE HELPPPP!!! LOOK AT THE PICTURE!
Answer:
x+2=3
collect like terms
x=3-2
x=1
x-12=x+30
collect like terms
x-x=30-12
=18
2(x+6)=2x+12
open bracket
2x+12=2x-12
collect like terms
2x-2x=-12+12
=0
3(x-2)=3x-2
open bracket
3x-6=3x-2
collect like terms
3x-3x=-2+6
=4
Help pls math is not my thing
Answer: 2.25 x 10^18
Step-by-step explanation:
When dividing with exponents you subtract
56-38= 18
10 cancels out
(9 x 10^18) / 4
= 2.25 x 10^18
The sum of three consecutive numbers is thirty-three. What is the middle number
Answer:
The first number is 10
The middle number is 11
The last number is 12
please help and explain thank you
Answer:
x = 23 degrees
Step-by-step explanation:
Angle on a straight line = 180 degrees
therefore 180 - 75 = 105 degrees
105 + 52 = 157 degrees
Angle in a triangle is 180 degrees
therefore 180 - 157 = 23 degrees
Consider the relation R = {(4,7), (5,3), (6,2), (7, 7)}. What is the inverse of R? Enter your answer as a set of ordered pairs.
Check the picture below.
You are given that x = 5^m and y = 5^n
Write 5^m+n/2 in terms of x and y.
Answer:
X + e^(Y-5)/2
Step-by-step explanation:
X = 5^m
Y = 5^n
e^Y = n*e^5
n = e^(Y-5)
5.) Claire deposited $32 each week for 8 weeks. How much money did she deposit after 8
weeks?
O $256
O-$256
O-$40
O $40
Please SIMPILFY these
Answer:
a) 81
b) 16807
c) 100
d) 78125
PLEASE GIVE ME A BRAIN
what is the answer to Abdul drinks 1 1/2 pints of milk a day. How much is this in cups?
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
3 us cups
Step-by-step explanation:
multiply by 2
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Using the arithmetic operations, the total change in her monthly electric bill over 5 months is +$10.58
For the past 5 months,
The change in her July electric bill = +$18.02
The change in her August electric bill = +$1.03
The change in her September electric bill = -$0.44
The change in her October electric bill = -$6.84
The change in her November electric bill = -$1.19
The total change in her monthly electric bill over 5 months = Sum of all changes in her electric bill over 5 months
= +18.02+1.03-0.44-6.84-1.19
= +$10.58
Hence, the total change in her monthly electric bill over 5 months is +$10.58
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Samuel was absent for the last biology test. For those who took the test, the mean was 84.6, the median was 82, and the mode was 88. When Samuel took the test, the class mean went down to exactly 84. His score was different from every other students’ score. What effect, if any, did Samuel’s score have on the class mode?
A: None; the mode stayed the same.
B: It decreased the mode by exactly 1 point.
C: It increased the mode by exactly 1 point.
D: It increased the mode by greater than 1 point.
E: The effect of Samuel’s score on the mode cannot be determined from the given information.
The correct option is A: None; the mode stayed the same.
What is Mode?Mode of a data set is the value that occur most frequently in a data set.
There may be no mode, one mode or more than one mode for a data depending on the number of times values are repeating.
Given that before Samuel taking a test,
Mean = 84.6
Median = 82
Mode = 88
After Samuel took the test,
Mean = 84
Also given that, his score was different from every other students’ score.
This means that from the data of scores, Samuel's score is not repeating.
Mode is the most repeating element.
So Samuel's score does not effect the mode and thus stayed the same.
Hence the mode stayed the same.
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