Answer:
[tex]\fbox{\begin{minipage}{8em}Not a solution\end{minipage}}[/tex]
Step-by-step explanation:
Step 1: Consider the assumption:
Generally, [tex](6, 7)[/tex]) is supposed to be the pair of 2 components, in which, the first component is x-component (domain), the second component is y-component (range).
Hence, [tex]x = 6, y = 7[/tex]
Step 2: Substitute [tex]x[/tex] and [tex]y[/tex] into the inequality
[tex]y > 2x - 5[/tex]
<=> [tex]7 > 2*6 - 5[/tex]
Step 3: Simplify
<=> [tex]7> 12 - 5[/tex]
<=> [tex]7 > 7[/tex]
Step 4: Evaluate
Invalid
Reason: [tex]7 = 7[/tex]
Step 5: Conclude
[tex](6, 7)[/tex] is not a solution to the inequality [tex]y > 2x - 5[/tex]
Hope this helps!
:)
Which of the following is true regarding the solution to the logarithmic equation below? log Subscript 2 Baseline (x + 11) = 4. x + 11 = 2 Superscript 4. x + 11 = 16. x = 5. x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 2 x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 4 x = 5 is a true solution because log Subscript 2 Baseline (16) = 4 x = 5 is a true solution because log Subscript 4 Baseline (16) = 2
Answer:
Option C.
Step-by-step explanation:
The given logarithmic equation is
[tex]\log_2(x+11)=4[/tex]
It can be written as
[tex](x+11)=2^4[/tex] [tex][\because log_ax=y\Leftrightarrow x=a^y][/tex]
[tex]x+11=16[/tex]
[tex]x=5[/tex]
Now, to check whether [tex]x=5[/tex] is a true solution or not. Substitute [tex]x=5[/tex] in the LHS of given equation.
[tex]LHS=\log_2(5+11)[/tex]
[tex]LHS=\log_2(16)[/tex]
[tex]LHS=\log_22^4[/tex]
[tex]LHS=4[/tex] [tex][\because log_aa^x=x][/tex]
[tex]LHS=RHS[/tex]
Hence, [tex]x=5[/tex] is a true solution because [tex]\log_2(16)=4[/tex].
Therefore, the correct option is C.
Answer:
C on edge2021
Step-by-step explanation:
Your friend believes that he has found a route to work that would make your commute faster than what it currently is under similar conditions. Suppose that data were collected for a random set of 7 days, where each difference is calculated by subtracting the time taken on the current route from the time taken on the new route. Assume that the populations are normally distributed. Your friend uses the alternative hypothesis Ha:μd<0. Suppose the test statistic t is computed as t≈−3.201, which has 6 degrees of freedom. What range contains the p-value?
Answer:
The range of p-values
0.01 < p < 0.025
Step-by-step explanation:
Explanation:-
Given random sample size 'n' = 7
Assume that the populations are normally distributed
Null Hypothesis :H₀:μd=0.
Alternative Hypothesis:H₁:μd<0.
Degrees of freedom
ν = n-1 =7-1 =6
given the test statistic t = - 3.201
we will use single tailed test in t-distribution table
The test statistic t= 3.201 is lies between the critical values is 0.01 and 0.025
The range of p-values
0.01 < p < 0.025 (check t- distribution table single tailed test)
Final answer:-
The range of p-values
0.01 < p < 0.025
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Answer:
y = [tex]\frac{1}{2}[/tex]x - 5
Step-by-step explanation:
Use rise over run to find the slope, which will get you 1/2 as the slope
The y-intercept is at (0, -5) so put -5 in the equation
Answer: y= 1/2x + -5
Step-by-step explanation: slope is 1/2 because the line is going up one and over 2 (rise over run), the y intercept is -5 because that is where the line hits on the y axis
Help asap giving branlist!!!
Answer:
Option 2
Step-by-step explanation:
Because the slope is -0.09 the answer is the second option. A negative slope means a decrease.
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 260.5-cm and a standard deviation of 1.6-cm. For shipment, 8 steel rods are bundled together.Find the probability that the average length of a randomly selected bundle of steel rods is greater than 260.2-cm.P(M > 260.2-cm) = Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Answer:
P(M > 260.2-cm) = 0.702
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 normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, 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.
In this question, we have that:
[tex]\mu = 260.5, \sigma = 1.6, n = 8, s = \frac{1.6}{\sqrt{8}} = 0.5657[/tex]
P(M > 260.2-cm)
This is 1 subtracted by the pvalue of Z when X = 260.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260.2 - 260.5}{0.5657}[/tex]
[tex]Z = -0.53[/tex]
[tex]Z = -0.53[/tex] has a pvalue of 0.298.
1 - 0.298 = 0.702
So
P(M > 260.2-cm) = 0.702
What is the part to part ratio for gender in a daycare of children in which 16 of them are male
Answer:
16:0
Step-by-step explanation:
I need help with this
Answer:
-8.5
Step-by-step explanation:
-4x+8=42
-4x=42-8
-4x=34
x=34/-4
x=-8.5
The sum of an infinite geometric sequence is seven times the value of its first term.
a) Find the common ratio of the sequence.
b) Find the least number of terms of the sequence that must be added in order for the sum to exceed half the value of
the infinite sum.
Answer:
a). r = [tex]\frac{6}{7}[/tex]
b). At least 5 terms should be added.
Step-by-step explanation:
Formula representing sum of infinite geometric sequence is,
[tex]S_{\inf}=\frac{a}{1-r}[/tex]
Where a = first term of the sequence
r = common ratio
a). If the sum is seven times the value of its first term.
[tex]7a=\frac{a}{1-r}[/tex]
[tex]7=\frac{1}{1-r}[/tex]
7(1 - r) = 1
7 - 7r = 1
7r = 7 - 1
7r = 6
r = [tex]\frac{6}{7}[/tex]
b). Since sum of n terms of the geometric sequence is given by,
[tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex]
If the sum of n terms of this sequence is more than half the value of the infinite sum.
[tex]\frac{a[1-(\frac{6}{7})^{n}]}{1-\frac{6}{7}}[/tex] > [tex]\frac{7a}{2}[/tex]
[tex]\frac{1-(\frac{6}{7})^{n}}{1-\frac{6}{7}}> \frac{7}{2}[/tex]
[tex]\frac{1-(\frac{6}{7})^{n}}{\frac{1}{7}}> \frac{7}{2}[/tex]
[tex]1-(\frac{6}{7})^{n}> \frac{7}{2}\times \frac{1}{7}[/tex]
[tex]1-(\frac{6}{7})^{n}> \frac{1}{2}[/tex]
[tex]-(\frac{6}{7})^{n}> -\frac{1}{2}[/tex]
[tex](\frac{6}{7})^{n}< \frac{1}{2}[/tex]
[tex](0.85714)^{n}< (0.5)[/tex]
n[log(0.85714)] < log(0.5)
-n(0.06695) < -0.30102
n > [tex]\frac{0.30102}{0.06695}[/tex]
n > 4.496
n > 4.5
Therefore, at least 5 terms of the sequence should be added.
Please show me how to solve 40% of X is 23?
NOT what is 40% of 23. But what number is 40% of to equal 23.
Thank you!!
Answer: The answers are in the steps hopes it helps.
Step-by-step explanation:
40% * x = 23 convert 40% to a decimal
0.4 * x = 23 multiply 0.4 is by x
0.4x = 23 divide both sides by 0.4
x= 57.5
Check:
57.5 * 40% = ?
57.5 * 0.4 = 23
Determine whether the numerical value in braces is a parameter or a statistic. Explain your reasoning. In a certain soccer league (43%) of the 14 teams had won more games than they had lost.
Choose the correct answer below.
a. Statistic, because the data set of a sample of teams in a league is a sample.
b. Statistic, because the data set of a sample of teams in a league is a population.
c. Parameter, because the data set of all 14 teams is a population.
d. Statistic, because the data set of all 14 teams is a sample.
e. Parameter, because the data set of all 14 teams is a sample.
f. Parameter, because the data set of a sample of teams in a league is a population.
g. Parameter, because the data set of a sample of teams in a league is a sample.
h. Statistic, because the data set of all 14 teams is a population.
Answer:
C. Parameter since the data set of all 14 teams is a population.
Explanation:
Find the attachment
Find w and y, will give brainliest for the correct answer
Answer: w=12, y=6√3
Step-by-step explanation:
Looking at the figure, we can split the triangle into 2 separate triangles. One on the left and one on the left. The triangle on the right is a 30-60-90 triangle. For this triangle, the hypotenuse is 2x in length. This is directly opposite of the right angle. The leg opposite to 30° is x in length. The leg opposite 60° is x√3 in length. Once you know the length of one side, you can plug in x to find the length of the other legs.
In this case, w and y are located on the same 30-60-90 triangle. Normally we would focus on that triangle to find our values, but in this instance, we don't have any values. We have to use the left triangle to find the leg that both triangles share.
The left triangle is a 45-45-90 triangle. For this triangle, the legs opposite of 45° is x in length. The hypotenuse is x√2. Since we know the hypotenuse, we can use it to find x.
x√2=8
x=8/√2
x=5.7 or 6 [Let's use 6 so that it is easier to work with a whole number]
Now that we know x, we can find w and y. Going back to the right triangle, we know the hypotenuse is 2x. We plug in 6 to find the length.
w=2x
w=2(6)
w=12
We know the leg opposite of 60° is x√3. We can plug in x.
y=6√3
Which letter has at least one line of symmetry?
W
Z
S
F
Answer:
Both F and Z have symmetry.
Find the area of the circles. Use 3.14 for . (Show work for full credit)
Answer:
Figure 1
The area of circle is 452.16 inches ².
Figure 2
The area of circle is 615.44km².
Figure 3
The area of circle is 132.665 km².
4) The radius of circle is 9 cm and diameter is 18cm.
According to the U.S. Census Bureau, the mean of the commute time to work for a resident of Boston, Massachusetts, is 27.3 minutes with a standard deviation of 8.1 minutes. What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean
Answer:
By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean
By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean
95% of commuters in Boston has a commute time within 2 standard deviations of the mean
Empirical ruleEmpirical rule states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean.
Hence, 95% of commuters in Boston has a commute time within 2 standard deviations of the mean
Find out more on Empirical rule at: https://brainly.com/question/10093236
The loaves of rye bread distributed to a local store by a certain bakery have an average length of 30 centimeters and a standard deviation of 2 centimeters. Assuming the lengths are normally distributed. What percentage of loaves are between 26.94 and 32.18 centimeters
Answer:
79.91% of loaves are between 26.94 and 32.18 centimeters
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 30, \sigma = 2[/tex]
What percentage of loaves are between 26.94 and 32.18 centimeters
This is the pvalue of Z when X = 32.18 subtracted by the pvalue of Z when X = 26.94.
X = 32.18:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32.18 - 30}{2}[/tex]
[tex]Z = 1.09[/tex]
[tex]Z = 1.09[/tex] has a pvalue of 0.8621
X = 26.94:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{26.94 - 30}{2}[/tex]
[tex]Z = -1.53[/tex]
[tex]Z = -1.53[/tex] has a pvalue of 0.0630
0.8621 - 0.0630 = 0.7991
79.91% of loaves are between 26.94 and 32.18 centimeters
13. Carla drew two acute non-overlapping
angles that share a ray and labeled them
ZJLK and Z KLM. The two angles have
different measures. Carla says
ZILM is
greater than a right angle.
An acute angle is open
less than a right angle.
Answer:
An acute angle is open
Step-by-step explanation:
An acute angle is an angle that is less than [tex]90^{0}[/tex]. Two or more acute angles are set to be complementary if their sum equals a right angle.
Clara's diagram involves two acute angles JLK and KLM with both sharing the side LK.
If the acute angles are complementary angles, then JLM would be a right angle.
If the acute angles are not complementary angles, then JLM would be less than a right angle.
So the appropriate choice to select is an acute angle is open. Which implies that JLM may be a right angle or not depending on the degrees of the acute angles involved.
Halley's birthday is on Friday. On Monday she receives 23 birthday cards. On Tuesday she receives 5 birthday cards. On Wednesday she receives 13 birthday cards. On Thursday she receives 17 birthday cards, and on Friday she receives 22 birthday cards. How many total birthday cards does Halley receive?
Answer:
80
Step-by-step explanation:
17+13=30
22+23+5=50
30+50=80
Answer:
80 cards
Step-by-step explanation:
23+5=28
13+17=30
28+30=58
58+22=80
What single decimal multiplier would you use to increase by 7% followed by a 4% decrease?
Answer: To increase an amount by 7%, you would want to use 1.07 as the multiplier. To decrease it, you would use 0.93
Step-by-step explanation:
Which data collection method would provide an unbiased sample?
Answer:
The best data collection method or sampling method to provide an unbiased sample is the random sampling method.
Step-by-step explanation:
There are 5 popular known sampling methods or data collection methods.
1) Random Sampling
In random sampling, each member of the population would have an equal chance of being surveyed. One of the best ways to use random sampling is to give all the members of the population numbers and then use computer to generate random numbers and pick the members of the population with those random numbers.
2) Systematic sampling is easier than random sampling. In systematic sampling, a particular number, n, is counted repeatedly and each of the nth member is picked to be sampled.
3) Convenience Sampling
This is the worst sampling technique. It is also the easiest. In Convenience sampling, the surveyor just picks the first set of members of the population that they find and surveys.
4) Stratified Sampling
Stratified sampling divides the population into groups called strata. A sample is taken from each of these strata using either random, systematic, or convenience sampling.
5) Cluster sampling
Cluster Sampling divides the population into groups which are called clusters or blocks. The clusters are selected randomly, and some members or every element/member in the selected clusters is surveyed.
Hope this Helps!!!
20sin^4 x power reduction
Answer:
Step-by-step explanation:
20 sin^4x
=5(4sin^4 x)
=5(2sin²x)²
=5(1-cos 2x)²
=5(1-4cos2x+cos²(2x))
=5[1-4cos(2x)+{1+cos (4x)}/2]
=5/2[2-8cos(2x)+1+cos(4x)]
=5/2[3-8cos (2x)+cos (4x)]
Can someone help me please
Answer:
the triangles are not similar.
Choose the inequality that could be used to solve the following problem.
Three times a number is at most negative six.
Answer:
3x ≤ -6
Step-by-step explanation:
"At most" means "less than or equal to." If x represents the number, then you have ...
(three) times (a number) (is at most) negative 6 . . . . . English
3 · x ≤ -6 . . . . . . . . . . . . . . . . Math
__
3x ≤ -6
Answer:
3x ≤ -6
Step-by-step explanation:
Multiply or divide as indicated.
10x^5 divide 2x^2
Answer:
5x^3(to the power of 3)
Step-by-step explanation:
10x^5/2x^2
divide the 10/2 like normal to get 5
x^5/x^2 (subtract the powers 5-2 when dividing powers)
you would get 5x^3
For the following report about a statistical study, identify the items below.
To find the public’s views on pollution, researchers waited outside a car dealership they had randomly selected from a list of such establishments. They stopped every 10th person who came out of the dealership and asked whether he or she thought pollution was a serious problem.
A) The population...
B) The population parameter of interest..
C) The sampling frame...
D) The sample...
E) The sampling method, including whether or not randomization was employed...
F) Any potential sources of bias you can detect and any problems you see in generalizing to the population of interest...
Answer:
Check Explanation
Step-by-step explanation:
In finding the public's view on pollution, the researchers waited outside a car dealership they had randomly selected from a list of such establishments. They stopped every 10th person who came out of the dealership and asked whether he or she thought pollution was a serious problem.
A) The population
The population is the sum total of every member of the public whose opinions on pollution, the researchers are interested in.
B) The population parameter of interest
Since the researchers stopped every member of the sample to ask them whether they thought pollution was a serious problem or not, it follows that the population parameter of interest is the proportion of the population who think that pollution is a serious problem.
C) The sampling frame
The sampling frame is defined as the source material where the sample is drawn from. And for this question, the sampling frame is the population of people leaving car dealership establishments.
D) The sample
The sample is the set of people that were asked the question of whether population was a serious problem or not. The sample includes every 10th person that came out of the chosen car dealership establishments.
E) The sampling method
Note that
- In random sampling, each population member would have an equal chance of being surveyed.
- Stratified sampling divides the population into groups called strata. A sample is taken from some or all of these strata using either random, systematic, or convenience sampling.
- In systematic sampling, a particular number, n, is counted repeatedly and each of the nth member is picked to be sampled.
Hence, this stratified sampling method uses random sampling technique to pick the strata where the samples will be obtained from and systematic sampling is now used for the picking of the members of the sample.
F) Any potential sources of bias you can detect and any problems you see in generalizing to the population of interest.
This survey only limits the members of the sample to those who visit a car dealership, and this cuts out a large percentage of the total population of humans.
Mostly men visit car dealership establishments, Hence, women, children, old people are at a disadvantage as they do not all have an equal chance of being surveyed.
Infact, only a financial class of the population visits car dealership establishments, so, it would be very wrong with all of this bias to use the results of this surveyor generalize for the whole population of people.
Hope this Helps!!!
Which of the following statements are true?
A. The equation Ax = b is referred to as a vector equation.
B. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution.
C. The first entry in the product Ax is a sum of products.
D. The equation Ax = b is consistent if the augmented matrix [Ab] has a pivot position in every row.
E. If the columns of an m \times n matrix A span {\mathbb R}^m, then the equation Ax = b is consistent for each b in {\mathbb R}^m.
F. If A is an m \times n matrix whose columns do not span {\mathbb R}^m, then the equation Ax = b is inconsistent for some b in {\mathbb R}^m.
Answer:
B, C, E, & F
Step-by-step explanation:
Option A is incorrect because the equation Ax = b is referred to as a matrix equation, not a vector equation.
Option B is correct. If Ax = b has a solution, vector b will a linear combination of columns of matrix A.
Option C is correct. In a matrix equation, product Ax when defined, is a sum of products.
Option D is incorrect. If an augmented matrix [Ab] had a pivot position in every row, there could be a pivot in the last column which would make it inconsistent.
Option E is correct. If the columns of an m×n matrix A span[tex] R^m[/tex], then the equation Ax=b is consistent for each b in
Option F is correct. IfA is an m x n matrix whose columns do not span, then the equation Ax = b is inconsistent for some b in [tex] R^m[/tex]
Options B, C, E, and F are correct.
Vlad tried to solve an equation step by step.
-8p 14 = 42
-8p = 28 step 1
p= -3.5 step 2
Find Vlad's mistake.
Choose 1 answer:
A)Step 1
B)Step 2
C)Vlad did not make a mistake
Answer:
C
Step-by-step explanation:
-8 14 = 42 (He subtracted 14 from 42)
-8p = 28 (Which is how he got 28)
p = -3.5 (He took 28 divide by -8 which got him -3.5)
Answer:
C
Step-by-step explanation:
C
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Density = Mass / Volume
D = 3/0.2
D = 15 kg/m³
Answer:
density=mass/volume
d=3kg/0.2m3
=15kgm-3
Lydia is going to invest $210 and leave it in an account for 17 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Lydia to end up with $330?
Answer:
To the nearest hundredth of a percentage= 0.03
Step-by-step explanation:
Formula for compound interest
A= p(1+r/n)^nt
A= $330
P= $210
n = 356
t= 17
r = ?
330 = 210(1+r/356)^(356*17)
330 = 210(1+r/356)^(6052)
330/210 = (1+r/356)^6052
(6052√(330/210) - 1 )356 = r
(1.000074686-1)356= r
0.02658 = r
To the nearest hundredth of a percentage= 0.03
Answer:
2.66
Step-by-step explanation:
At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 519 ml. The filling process follows a normal distribution with a known process standard deviation of 6 ml.
1) The normal distribution should be used for the sample mean because:_____.
a) the sample population has a large mean.
b) the population distribution is known to be normal.
c) the population standard deviation is known.
d) the standard deviation is very small.
2) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance. The hypothesis for a two-tailed decision is:_______.
A. H0: mu not equal to 519, H1: mu = 519, reject if z < -1.96 or z > 1.96.
B. H0: mu not equal to 519, H1: mu = 519, reject if z > 1.96 or z < -1.96.
C. H0: mu = 519, mu not equal to 519, reject if z> 1.96 or z< -1.96.
D. H0: mu = 519, H_1: mu not equal to 519, reject if z > -1.96 or z< 1.96.
a. a.
b. b.
c. c.
d. d.
3) If a sample of 16 bottles shows a mean fill of 522 ml, does this contradict the hypothesis that the true mean is 519 ml?
A) Yes.
B) No
Answer:
1) The normal distribution should be used for the sample mean because the population distribution is known to be normal (answer b).
2) C. H0: mu = 519, H_1: mu not equal to 519, reject if z> 1.96 or z< -1.96.
3) Yes. There is enough evidence to support the claim that the true mean is not 519 ml.
Step-by-step explanation:
1) When the population follows a normal distribution, it is correct to assume a normal distribution for the sample mean.
2) As it is a two-tailed decision rule, we are interested in detecting a significant difference below and above the mean. This is why we use the unequal sign in the alternative hypothesis.
The null hypothesis state that there is not significant difference from 519.
The critical value for a significance level of 5% is z=1.96.
[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]
3) The claim is that the true mean is not 519 ml.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]
The significance level is 0.05.
The sample has a size n=16.
The sample mean is M=522.
The standard deviation of the population is known and has a value of σ=6.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{16}}=1.5[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{522-519}{1.5}=\dfrac{3}{1.5}=2[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z>2)=0.046[/tex]
As the P-value (0.046) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the true mean is not 519 ml.
A student's tuition was $1200. A loan was obtained for 5/6 of the tuition. How much was the loan?
Answer:
the loan was 1000
Step-by-step explanation:
Take the tuition and multiply by 5/6
1200 *5/6
1200/6 *5
200 *5
1000
Answer:
$1000
Step-by-step explanation:
In order to find 5/6 of the tuition, we just need to multiply the 2 values together.
5/6*1200
Note that 1200 = 1200/1
5/6*1200/1
When multiplying fractions, we can multiply the numerators together, and the denominators together.
5*1200/6*1
6000/6
Divide.
1000
Therefore, the loan was $1000.
