Question:
A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling a number greater than 2.
If there is more than one element in the set, separate them with commas.
Answer:
[tex]S = \{1,2,3,4,5,6\}[/tex]
[tex]Greater2 = \{3,4,5,6\}[/tex]
Step-by-step explanation:
Given
A roll of a 6 sided number cube
Solving (a): The sample space
This implies that we list out all number on the number cube.
So:
[tex]S = \{1,2,3,4,5,6\}[/tex]
Solving (b): Outcomes greater than 2
This implies that we list out all number on the number cube greater than 2 i.e. 3 to 6.
So:
[tex]Greater2 = \{3,4,5,6\}[/tex]
Calculate the exact value of cos(a−b) given that sin a=12/13 with π/2
Answer:
Step-by-step explanation:
[tex]sin ~a=\frac{12}{13} ,\frac{\pi}{2} <a<\pi\\a ~is~in~2nd~quadrant.\\sin~b=\frac{3}{5} ,0<b<\frac{\pi}{2} \\b~is~in~1st~quadrant.\\cos~b=\sqrt{1-sin ^2b} \\=\sqrt{1-(\frac{3}{5} )^2} \\=\sqrt{\frac{25-9}{25} } \\=\sqrt{\frac{16}{25} } \\=\frac{4}{5} ,\\cos~a=-\sqrt{1-sin^2 a} \\=-\sqrt{1-(\frac{12}{13} )^2} \\=-\sqrt{\frac{169-144}{169} } \\=-\sqrt{\frac{25}{169} } \\=-\frac{5}{13} \\cos(a-b)=cos~acos~b+sin~a sin~b\\=\frac{-5}{13}* \frac{4}{5} +\frac{12}{13}* \frac{3}{5} \\=?[/tex]
HELP! ITS DUE RIGHT NOW HELP
Answer:
Step-by-step explanation:
D
Answer:
x > 2
Step-by-step explanation:2 and under
The histogram below shows the number of push-ups the students in Hayley's class can do.
Select all of the true statements about the data.
The majority of students can do more than 15 push-ups.
The data distribution is skewed to the right.
More students did 6-10 push-ups than 11-15 push-ups.
The students in Hayley's class can do between 1 and 25 push-ups.
The data distribution is skewed to the left.
find the missing variables pythagorean theorem
Answer:
y = 12 x = 12√2 z = 12√3
Step-by-step explanation:
The 45° triangle will also have a height of y so....
y² + y² = x² 2y² = x² y² = x²/2 y = √(x²/2)
The 30° triangle
y² + z² = 24² y² = 24² - z² y = √(24² - z²)
sin 30 = y/24 1/2 = y/24 y = 12
y² = x²/2
12² = x²/2²
2(144) = x² x = √(288) x = 12√2
y² + z² = 24²
z² = 24² - y²
z² = 24² - 12²
z² = 576 - 144
z² = 432
= √(16·9·3)
z = 4·3√3
z = 12√3
y² + z² = 24²
12² + (12√3)² = 24²
144 + 144·3 = 576
2y² = x²
2(12)² = x²
288 = (12√2) = 144·2 = 288
At a party, if 1/5 of one sheet
cake is uneaten and Tom eats
1/6 of the uneaten cake, what
fraction of the original cake
did Tom eat?
Answer:
Step-by-step explanation:
He eats 1/6 or 1/5 of the original cake.
All you need to do to get the answer is multiply the denominators.
1/5 * 1/6 = 1/30
If there was something in the numerators. you would multiply them too.
So suppose the two fractions were 3/5 and 2/7
The answer would be 3 * 2 / 5 * 7 = 6 / 35
General rule
When multiplying two fractions, multiply numerator * numerator / (denominator * denominator).
Please help me with this for 20 points !!!!
Answer:
A (the first answer)
Step-by-step explanation:
find the missing length
Answer:
PQ=36
Step-by-step explanation:
If the triangles are similar, then they must have a common ratio between them.
RQ corresponds with CB, so [tex]\frac{84}{18}=\frac{14}{3}[/tex]
If the ratio is [tex]\frac{14}{3}[/tex], then [tex]\frac{168}{\frac{14}{3}}=36[/tex], so PQ=36.
What is 1/2 plus 1/3 plus 5/6 ??
Answer:
10/6 or 5/3
Step-by-step explanation:
1/2 ---> 3/6
1/3 ---> 2/6
5/6 ---> 5/6
Add those new fractions together:
(3/6) + (2/6) + (5/6) = 10/6 or 5/3
Answer:
10/6 or 5/3
Step-by-step explanation:
Hope it help's :)
Josh cycled 8 laps on a bicycle path surrounding a lake. Each lap was the same length. If he cycled a total of 26.4mi, what was the length of each lap around the lake? Write your answer in feet. Use the table of conversion facts as necessary, and do not round your answer. ft
Answer:
The length of each lap around the lake was of 3.3 miles.
Step-by-step explanation:
Given that Josh cycled 8 laps on a bicycle path surrounding a lake, and each lap was the same length, to determine what was the length of each lap around the lake if he cycled a total of 26.4 miles, the following calculation must be performed:
26.4 / 8 = X
3.3 = X
Thus, the length of each lap around the lake was 3.3 miles.
DeVondrea stacked 2
quarters and a nickel on top
of each other. What is the
thickness of the stack of
coins?
Answer:
Step-by-step explanation:
Number of nickels = $1 * 1 nickel/$0.05 = 20 nickels
Thickness of 20 nickels = 20 nickels * 1.95 mm = 39 mm
Let's do the same for the quarters. Each quarter is worth $0.25.
Number of quarters = $1 * 1 quarter/$0.25 = 4 quarters
Thickness of 4 quarters = 4 quarters * 1.75 mm = 7 mm
Find the ratio of the two:
39 mm/7 mm = 5.57
let f(x)=ln(x^2) and g(x)=√e^3x. find fog(x) and its domian
Answer:
[tex](f\ o\ g)(x) = 3x[/tex]
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
Given
[tex]f(x) = ln(x^2)[/tex]
[tex]g(x)=\sqrt{e^{3x}}[/tex]
Solving (a): (f o g)(x)
This is calculated as:
[tex](f\ o\ g)(x) = f(g(x))[/tex]
We have:
[tex]f(x) = ln(x^2)[/tex]
[tex]f(g(x)) = \ln((g(x))^2)[/tex]
Substitute: [tex]g(x)=\sqrt{e^{3x}}[/tex]
[tex]f(g(x)) = \ln(\sqrt{e^{3x}})^2[/tex]
Evaluate the square
[tex]f(g(x)) = \ln(e^{3x})[/tex]
Using laws of natural logarithm:
[tex]\ln(e^{ax}) = ax[/tex]
So:
[tex]f(g(x)) = \ln(e^{3x})[/tex]
[tex]f(g(x)) = 3x[/tex]
Hence:
[tex](f\ o\ g)(x) = 3x[/tex]
Solving (b): The domain
We have:
[tex]f(g(x)) = 3x[/tex]
The above function has does not have any undefined points and domain constraints.
Hence, the domain is: [tex]-\infty < x < \infty[/tex]
Devon has $5,768 in his savings account, which is $2,709 more than Serena has in her savings account. How much money does Serena have in her savings account?
Find the range of values of k for which -7x^2+9x+k is always negative for all real values of x.
Answer:
-7x^2 +9x-ki
Step-by-step explanation:
A triangle has a 90° angle and two sides that measure 5 cm in length. Which statements are true about this triangle?
Answer:
what are the statements
Step-by-step explanation:
A punch bowl has 1/3 of a gallon of Rainbow sherbet, 1/2 of a gallon of Sprite, and 1/6 of a gallon of Sundrop. After the punch is split equally among two serving bowls how much of each ingredient is in one serving bowl. How much Rainbow Sherbet will be in the bowl if it is split equally between two bowls?
Answer:
1/6
Step-by-step explanation:
To solve this, multiply the denominator by 2, which would be 2x3 which would be 6.
H) Cole worked 20 hours and
earned $500. How many hours must Cole work in order to earn $700?
Please help me :)
Answer:
he would have to work 28 hours
Step-by-step explanation:
Answer:
Cole have to work 28 hours
What’s the missing side length? Round to the nearest tenth please :)))
Answer:
the answer is 4.6
Step-by-step explanation:
the explanation is shown in the following attachment below...
hope this helps...
300 is what percent less than 599
Answer:
59.8%
Step-by-step explanation:
599 - 300 = 299. Now we need to find the percentage 299 is of 500.
299 / 500 = 0.598
0.598 as a percent is 59.8%.
Answer: 59.8%
Hope this helps!
Plz give the answer for 8th and 9th question
Answer:
8. 8/9 is not the multiplicative inverse of –1⅛
9. 0.3 is the multiplicative inverse of 3⅓
Step-by-step explanation:
To answer the above questions, we must understand the meaning of multiplicative inverse. This is illustrated below:
Let y be the number.
The multiplicative inverse of y denoted by y¯¹ (or 1/y) when multiplied with y will give an identity of 1 i.e
y × y¯¹ = 1
Or
y × 1/y = 1
Now, let us answer the questions given above by calculating the multiplicative inverse.
8. The number (y) = –1⅛ = –9/8
Multiplicative inverse (y¯¹) =?
y × y¯¹ = 1
–9/8 × y¯¹ = 1
Divide both side by –9/8
y¯¹ = 1 ÷ –9/8
y¯¹ = 1 × –8/9
y¯¹ = –8/9
Thus, 8/9 is not the multiplicative inverse of –1⅛
9. The number (y) = 3⅓ = 10/3
Multiplicative inverse (y¯¹) =?
y × y¯¹ = 1
10/3 × y¯¹ = 1
Divide both side by 10/3
y¯¹ = 1 ÷ 10/3
y¯¹ = 1 × 3/10
y¯¹ = 3/10
y¯¹ = 0.3
Thus, 0.3 is the multiplicative inverse of 3⅓.
In 2011, 51% of cell phone owners in a country reported that their cell phone was a smartphone. The following year, the researchers wanted to test to see if the proportion of cell phone owners in that country who have a smartphone has increased over time at the a = 0.05 level. They surveyed a random sample of 934 cell phone owners in that country and found that 501 of them had a smartphone. They conducted a significance test and found the p-value to be 0.0532. Is there convincing evidence that the proportion of cell phone owners in that country who have a smartphone has increased over time?
Answer:
The calculated value Z = 1.5950 < 1.96 at 0.05 level of significance
The null hypothesis is accepted at a 0.05 level of significance
The proportion of cell phone owners in that country who have a smartphone has not increased over time
Step-by-step explanation:
Step(i):-
Given that the random sample size 'n' = 934
Given that the population proportion P = 0.51
Q= 1-P
Q = 1- 0.51 = 0.49
The sample proportion
[tex]p = \frac{x}{n} = \frac{501}{934} = 0.5364[/tex]
Level of significance = 0.05
Critical value Z₀.₀₅ = 1.96
Step(ii):-
Null hypothesis: P < 0.51
Alternative Hypothesis : P > 0.51
Test statistic
[tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.536-0.51}{\sqrt{\frac{0.51 x 0.49}{934} } }[/tex]
Z = 1.5950
Final answer:-
Given that P-value 0. 0532
P-value > 0.05
Rejected Alternative Hypothesis and accepted null hypothesis
( OR)
The calculated value Z = 1.5950 < 1.96 at 0.05 level of significance
The null hypothesis is accepted at a 0.05 level of significance
The proportion of cell phone owners in that country who have a smartphone has not increased over time
One number is five less than a second number. Five times the first is 2 more than 2 times the second. Find the numbers.
Help me please it’s due tonight!
Answer:
B.
[tex] \frac{5}{8} [/tex]
Give one word for the following.
To find the way, carefully and safely
GPS.....................GPS..............................................................................................
Name a pair of lines that are perpendicular
Answer:
Two distinct lines intersecting each other at 90° or a right angle are called perpendicular lines. Here, AB is perpendicular to XY because AB and XY intersect each other at 90°. The two lines are parallel and do not intersect each other. They can never be perpendicular to each other.
Step-by-step explanation:
hope it helps:)
Multiple Choice Question:
x2+2x-48=0 is a(n)
A.) Equation
B.) Expression
Answer:
This is an equation.
Step-by-step explanation:
An expression would mean that there is no equal sign, but since there is, that makes it an equation.
I need find the value of x
Answer:
x = 115
Step-by-step explanation:
The chord- chord angle x is half the sum of the arcs intercepted by the angle and its vertical angle, then
x = [tex]\frac{1}{2}[/tex] (145 + 85 ) = 0.5 × 230 = 115
Step-by-step explanation:
answer is 115 you should solve it also your answer will be same
According to the Labor Department, the average duration of unemployment for adults ages 20 to 24 was 34.6 weeks during a recent month. Assume that the standard deviation for this population is 10.2 weeks. A random sample of 36 adults in this age group was selected. What is the probability that the average duration of unemployment was between 30 and 37 weeks
Answer:
0.9173 = 91.73% probability that the average duration of unemployment was between 30 and 37 weeks.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 34.6, standard deviation of 10.2
This means that [tex]\mu = 34.6, \sigma = 10.2[/tex]
Sample of 36
This means that [tex]n = 36, s = \frac{10.2}{\sqrt{36}} = 1.7[/tex]
What is the probability that the average duration of unemployment was between 30 and 37 weeks?
This is the pvalue of Z when X = 37 subtracted by the pvalue of Z when X = 30.
X = 37
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{37 - 34.6}{1.7}[/tex]
[tex]Z = 1.41[/tex]
[tex]Z = 1.41[/tex] has a pvalue of 0.9207
X = 30
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{30 - 34.6}{1.7}[/tex]
[tex]Z = -2.71[/tex]
[tex]Z = -2.71[/tex] has a pvalue of 0.0034
0.9207 - 0.0034 = 0.9173
0.9173 = 91.73% probability that the average duration of unemployment was between 30 and 37 weeks.
a car is moving 70 miles per hour. how far does it travel in 16secs
HELP ME PLS ITS URGENT!!!!!!!!!!!!
Answer:
180
Step-by-step explanation:
Find the area of the figure below. Round to the nearest tenth.
Bob took out a 5 year loan for $4000 and paid 3% annual simple interest
Bill took out a 4 year loan for $4000 and paid 5% annual simple interest
What is the sum of amounts of interest bob and bill paid for their loans
