Answer:
c. 3 1/3
Step-by-step explanation:
8x-2-5x=8
3x=10
x=10/3=3 1/3
Answer:
x=[tex]3\frac{1}{3}[/tex]
Step-by-step explanation:
Hi there!
We want to find the value of x in this expression:
8x-2-5x=8
Our goal is to isolate x on one side
Combine like terms on the left side (add the terms with x together)
3x-2=8
Add 2 to both sides (-2+2=0)
3x-2=8
+2 +2
__________
3x=10
Divide both sides by 3
x=[tex]\frac{10}{3}[/tex]
Simplify the improper fraction
x=[tex]3\frac{1}{3}[/tex]
Hope this helps!
At a local company, 15% of the employees are women. every day, 9% of them bring their lunch to work, while only 3% of the men bring lunch. Find the probability that a randomly selected employee
a. is a woman goven that the person brings their lunch to work.
b. brings their lunch to work given that person is a woman.
c. is a woman given that the person brings their lunch to work.
Answer:
a) 0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.
b) 0.09 = 9% probability that a randomly selected employee brings their lunch to work given that person is a woman.
c) 0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Questions a/c:
Questions a and c are the same, so:
Event A: Brings lunch to work.
Event B: Is a woman.
Probability of a person bringing lunch to work:
9% of 15%(woman)
3% of 100 - 15 = 85%(man). So
[tex]P(A) = 0.09*0.15 + 0.03*0.85 = 0.039[/tex]
Probability of a person bringing lunch to work and being a woman:
9% of 15%, so:
[tex]P(A \cap B) = 0.09*0.15[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09*0.15}{0.039} = 0.3462[/tex]
0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.
Question b:
Event A: Woman
Event B: Brings lunch
15% of the employees are women.
This means that [tex]P(A) = 0.15[/tex]
Probability of a person bringing lunch to work and being a woman:
9% of 15%, so:
[tex]P(A \cap B) = 0.09*0.15[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09*0.15}{0.15} = 0.09[/tex]
0.09 = 9% probability that a randomly selected employee brings their lunch to work given that person is a woman.
In one year the population of
Zebras in the park was 3400. In
the following year the population
reduced by 25%. What was the
size of the population after
reduction?
Which expression is the best estimate of the product of 7/8and 8 1/10?
Answer:
7 7/80 or 7.0875
Step-by-step explanation:
product is the result of multiplication
7/8 * 81/10 = 567/80 = 7 7/80 or 7.0875
If one ruler and three pencils cost N120 and two
rulers and one pencil cost N140. Find the cost of
one ruler and one pencil
Answer:
N80
Step-by-step explanation:
One ruler is N60 and one pencil is N20.
A survey of 30-year-old males provided data on the number of auto accidents in the previous 5 years. The sample mean is 1.3 accidents per male. Test the hypothesis that the number of accidents follows a Poisson distribution at the 5% level of significance.
No. of accident No. of males
0 39
1 22
2 14
3 11
>=4 4
Required:
a. What's the Expected probability of finding males with 0 accidents?
b. What's the Expected probability of finding males with 4 or more accidents?
Answer:
0.2725
0.0431
Step-by-step explanation:
The distribution here is a poisson distribution :
λ = 1.3
The poisson distribution :
p(x) = [(e^-λ * λ^x)] ÷ x!
Expected probability of finding male with 0 accident ; x = 0
p(0) = [(e^-1.3 * 1.3^0)] ÷ 0!
p(0) = [0.2725317 * 1] ÷ 1
p(0) = 0.2725317
= 0.2725
2.)
P(x ≥ 4) = 1 - P(x < 4)
P(x < 4) = p(x = 0) + p(x. = 1) + p(x = 2) + p(x = 3)
p(x = 0) = p(0) = [(e^-1.3 * 1.3^0)] ÷ 0! = 0.2725
p(x = 1) = p(1) = [(e^-1.3 * 1.3^1)] ÷ 1! = 0.35429
p(x = 2) = p(2) = [(e^-1.3 * 1.3^2)] ÷ 2! = 0.23029 p(x = 3) = p(3) = [(e^-1.3 * 1.3^3)] ÷ 0! = 0.09979
P(x < 4) = 0.2725 + 0.35429 + 0.23029 + 0.09979 = 0.95687
P(x ≥ 4) = 1 - 0.95687 = 0.0431
Determine the value of X. Please explain the answer
We have two lines from the same point.
These two lines are also tangents to same circle which implies that they are of the same length.
That is 2x - 1 = 9
2x = 9 +1 = 10
x =10/2
x = 5
2.WHICH OF THE FOLLOWING IS A NON- NUMERIC DATA ? Required to answer. Single choice.
(1) 1,2,3,4,5,6
(2) 2,8,4,5,8
(3) A,B,AB,O
(4) NONE OF THE ABOVE
Answer:
3.) A,B,AB,O
Step-by-step explanation:
Non-numeric data refers to categorical data, or data that is not expressed quantitatively. Answers (1) and (2) contain quantitative data, so they would be eliminated as potential answer choices and therefore (4) would also be eliminated. This leaves answer (3), which does not have quantitative data and is therefore non-numeric.
please help find the solution to the system of equations
Answer:
x = 2 y = 3
Step-by-step explanation:
-2x + 7 = 5x - 7
-7x + 7 = -7
-7x = -14
x = 2
y = -2(2) + 7
y = -4 + 7
y = 3
*20 points*
how do you get the weighted average from this table?
Answer:
it is
[(2+3+4+6)-2*4]:4=1.75
I THINK
Step-by-step explanation:
What is the solution of log(4-3) = log(17-41)?
O4
O 5
O 15
O 20
Explanation:
The rule is that if log(A) = log(B), then A = B
Using this idea, we can then say,
log(t - 3) = log(17 - 4t)
t - 3 = 17 - 4t
t+4t = 17+3
5t = 20
t = 20/5
t = 4
The solution to the logarithmic equation is t = 5
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
log ( t - 3 ) = log (17 - 3t ) be equation (1)
On simplifying , we get
The bases of the logarithm are equal
So , the values are equal and therefore
t - 3 = 17 - 3t
Adding 3t on both sides , we get
4t - 3 = 17
Adding 3 on both sides , we get
4t = 20
Divide by 4 on both sides , we get
t = 20 / 4
t = 5
Therefore , the value of t is 5
Hence , the logarithmic equation is solved
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If the white rod is 1/3, what color is the whole??
Answer:
brown
Step-by-step explanation:
it might be brown because it compelled
How much wrapping is needed to cover a cubed gift box that is 9 inches high? (Include the bow which takes 115 sq. inches.)
Answer:
601 in²
Step-by-step explanation:
To obtain the amount of wrapping needed to cover the cube shaped gift box, including the bow
Area of bow = 115 in²
Surface area of cube shaped box = 6a²
a = side length of cube = 9
Hence,
Surface area of gift box = 6 * 9²
Surface area = 6 * 81 = 486 in²
Total wrapping required = area of gift box + area of bow = (486 in² + 115 in²) = 601 in²
State and prove the Cantor Intersection Theorem.
Answer:
Cantor's intersection theorem refers to two closely related theorems in general topology and real analysis, named after Georg Cantor, about intersections of decreasing nested sequences of non-empty compact sets.
Which expression is equivalent to
-32 3/5
-8
-3/325
3/325
1/8
Answer:
[tex]-32^\frac{3}{5} = -8[/tex]
Step-by-step explanation:
Given
[tex]-32^\frac{3}{5}[/tex]
Required
The equivalent expression
We have:
[tex]-32^\frac{3}{5}[/tex]
Rewrite as:
[tex]-32^\frac{3}{5} = (-32)^\frac{3}{5}[/tex]
Expand
[tex]-32^\frac{3}{5} = (-2^5)^\frac{3}{5}[/tex]
Remove bracket
[tex]-32^\frac{3}{5} = -2^\frac{5*3}{5}[/tex]
[tex]-32^\frac{3}{5} = -2^3[/tex]
[tex]-32^\frac{3}{5} = -8[/tex]
if for men working for hours for 4 days complete for unit of work then how many unit of work will be completed by two men working for two hours per day?
The 2 men working for 2 hours per 2 days will complete 1/2 unit of work. This is calculated by using the proportions formula.
What is the formula for calculating equal proportions?The formula for the given proportions is,
a: b = c: d
⇒ a/b = c/d
⇒ ad = bc
In this way, the required variable is calculated.
Calculation:For the given question, the proportion we can write
M1 × H1 × D1: M2 × H2 × D2 = W1: W2
⇒ M1 × H1 × D1 × W2 = M2 × H2 × D2 × W1
Where M1 = 4; H1 = 4; D1 = 4; M2 = 2; H2 = 2; D2 = 2 and W1 = 4
We need to calculate W2 - required units of work
So, on substituting,
M1 × H1 × D1 × W2 = M2 × H2 × D2 × W1
⇒ 4 × 4 × 4 × W2 = 2 × 2 × 2 × 4
⇒ 64 × W2 = 32
⇒ W2 = 32/64
∴ W2 = 1/2
Thus, the required units of work are 1/2.
So, 2 men working for 2 hours for 2 days will complete 1/2 unit of work.
Learn more about proportions here:
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Disclaimer: The given question is incomplete. Here is the complete question.
Question: If 4 men working for 4 hours for 4 days complete 4 units of work then how many unit of work will be completed by two men working for two hours per 2 days?
4. find possible value for m if
X=-3 and (3m-x)2=81
Answer:
m = 12.5
Step-by-step explanation:
x = - 3
(3m - x) 2= 81
(3m - (-3)) 2= 81
(3m + 3) 2= 81
6m + 6 = 81
- 6 - 6
6m = 75
[tex]\frac{6m}{6}[/tex] = [tex]\frac{75}{6}[/tex]
m = 12.5
hope this helps! if you have an questions, pls let me know!
Need to know Anwser yes or no
Answer:
Reflective symmetry over the line y = 4 is No
Reflective symmetry over the line y = 1/7x + 3 is Yes
Help! I need help with these two questions (10 points each!)
Answer:
see image...
the (x-h) shifts the curve left right (east west)
and the +k at the end shifts it up/down (north/south)
Step-by-step explanation:
The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms. Statistical analysis of the output suggests that the resistances can be approximated by a normal distribution with known standard deviation of 0.005 ohms. We are interested in testing the hypothesis that the resistors conform to the specifications.
Requied:
a. Determine whether a random sample of 10 resistors yielding a sample mean of 0.152 ohms indicates that the resistors are conforming. Use alpha = 0.05.
b. Calculate a 95% confidence interval for the average resistance. How does this interval relate to your solution of part (a)?
Answer:
a) The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
b) The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.
Step-by-step explanation:
Question a:
The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms.
At the null hypothesis, we test if this is the average resistance, that is:
[tex]H_0: \mu = 0.15[/tex]
We are interested in testing the hypothesis that the resistors conform to the specifications.
At the alternative hypothesis, we test if it is not conforming, that is, the mean is different of 0.15, so:
[tex]H_1: \mu \neq 0.15[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.15 is tested at the null hypothesis:
This means that [tex]\mu = 0.15[/tex]
Sample mean of 0.152, sample of 10, population standard deviation of 0.005.
This means that [tex]X = 0.152, n = 10, \sigma = 0.005[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.152 - 0.15}{\frac{0.005}{\sqrt{10}}}[/tex]
[tex]z = 1.26[/tex]
P-value of the test and decision:
The p-value of the test is the probability of the sample mean differing from 0.15 by at least 0.152 - 0.15 = 0.002, which is P(|z| > 1.26), given by two multiplied by the p-value of z = -1.26.
Looking at the z-table, z = -1.26 has a p-value of 0.1038.
2*0.1038 = 0.2076
The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
Question b:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.005}{\sqrt{10}} = 0.003[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.15 - 0.003 = 0.147.
The upper end of the interval is the sample mean added to M. So it is 0.15 + 0.003 = 0.153.
The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.
PLEASE HELPPPPPPPPPP
Answer: SORRY NEED AN ACCOUNT ON - 10
Step-by-step explanation:
To resolve the proposed issue, an explanation is needed in which the subject is addressed
a. 15
b. 16
c. 9
d. 14
Answer:
15
Step-by-step explanation:
1-0 =1
3-1 =2
6-3=3
10-6=4
We are adding 1 more each time
10+5 = 15
The perimeter of a triangle is 83 centimeters. If two sides are equally long and the third side is 8 centimeters longer than the others, find the lengths of the three sides.
Answer:
25, 33
Step-by-step explanation:
let the length of the one with equal sides be x
third side = x+8
x+x+x+8 = 83
3x+8 = 83
3x = 75
x = 25
x+8 = 25+8 = 33
The population of City A in 2000 was 40 thousand people and the population increased by 13% each year. The function f determines the population of this city (in thousands of people) in terms of x . Write a function formula for f .
Answer:
f(x) = 40(1 + 0.13)^x
Step-by-step explanation:
The general formula for an exponential growth function is;
f(x) = a(1 + r)^x
Where;
a= initial population of the city
r= population growth rate
x = number of years
Given that;
a= 40,000
r= 0.13
The population of the city in thousands of people in terms of x is;
f(x) = 40(1 + 0.13)^x
A soccer team wants new uniforms. A jersey costs $42, shorts cost $26, socks cost $6, and shinguards cost $18. How much does one
uniform cost?
$62
$74
$83
$92
Answer:
$92
Step-by-step explanation:
42 + 26 + 6 + 18 = 92
bHhHshsbsnsnsnsnsnsbsbsbckclccllcxldkdldkdkdk HELP
Answer:
Step-by-step explanation:
The reasons for each statement are inside the parentheses
1. <1 and <2 are complementary (given)
2. m<1 + m<2 = 90° (definition of complementary angles)
3. m<2 = 74° (given)
4. m<1 + 74° = 90° (Substitution)
5. m<1 = 16° (Subtraction property of equality)
This is gotten by subtracting 74° from both sides as follows:
m<1 + 74° - 74° = 90° - 74°
m<1 = 16°
18. A triangle has side lengths of 6, 8, and 9. What type of triangle is it?
•
acute
•
obtuse
•
equiangular
•
right
Answer:
obtuse
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What is the height of spanning tree obtained from Wn by the breadth-first search, starting at the central vertex of Wn?
Answer:
The height of the spanning tree is one by the breadth-first search at the central vertex of Wn.
Step-by-step explanation:
The graph is connected and has a spanning tree where the tree can build using a depth-first search of the graph. Start with chosen vertex, the graph as the root, and root add vertices and edges such as each new edge is incident with vertex and vertices are not in path. If all vertices are included, it will do otherwise, move back to the next level vertex and start passing. It is for depth-first search. For breadth-first search, start with chosen vertex add all edges incident to a vertex. The new vertex is added and becomes the vertices at level 1 in the spanning tree, and each vertex at level 1 adds each edge incident to vertex and other vertex connected to the edge of the tree as long as it does not produce.
A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 83 months with a variance of 81. If the claim is true, what is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors? Round your answer to four decimal places.
Answer:
0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.
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 establishes 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.
The production manager claims they have a mean life of 83 months with a variance of 81.
This means that [tex]\mu = 83, \sigma = \sqrt{81} = 9[/tex]
Sample of 146:
This means that [tex]n = 146, s = \frac{9}{\sqrt{146}}[/tex]
What is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors?
This is 1 subtracted by the p-value of Z when X = 81.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{81.2 - 83}{\frac{9}{\sqrt{146}}}[/tex]
[tex]Z = -2.42[/tex]
[tex]Z = -2.42[/tex] has a p-value of 0.0078.
1 - 0.0078 = 0.9922.
0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.
A basic cellular package costs $30/month for 60 minutes of calling with an additional charge of $0.40/minute beyond that time. The cost function C (2) for using x minutes would be • If you used 60 minutes or less, i.e. if if x < 60, then C (x) = 30 (the base charge). If you used more than 60 minutes, i.e. (x – 60 minutes more than the plan came with, you would pay an additional $0.40 for each of those (x – 60 minutes. Your total bill would be C (x) = 30 + 0.40 (x – 60). If you want to keep your bill at $50 or lower for the month, what is the maximum number of calling minutes you can use? minutes. The maximum calling minutes you can use is ? Number
Answer:
The maximum number of minutes to keep the cost at $50 or less is 110 minutes
Step-by-step explanation:
Given
[tex]C(x) = 30[/tex] ---- [tex]x < 60[/tex]
[tex]C(x) = 30 + 0.40(x - 60)[/tex] --- [tex]x \ge 60[/tex]
Required
[tex]C(x) = 50[/tex] ---- find x
We have:
[tex]C(x) = 30 + 0.40(x - 60)[/tex]
Substitute 50 for C(x)
[tex]50 = 30 + 0.40(x - 60)[/tex]
Subtract 30 from both sides
[tex]20 = 0.40(x - 60)[/tex]
Divide both sides by 0.40
[tex]50 = x - 60[/tex]
Add 60 to both sides
[tex]110 = x[/tex]
[tex]x =110[/tex]
For this problem I thought the answer would be 1.3 for part C since it said to find the mean. However, I am wrong. Can someone help me with the problem please? Thank you for your help!
Answer:
Step-by-step explanation:
the mean is
{(12x1)+(13x1)+(14x2)+(15x2)+(17)+(18)+(19x2)+(20)+(21x2)+(22)+(24)}/11
mean=264/11
mean=24
