Answer:
The answer is 13
Step-by-step explanation:
Two positive and consecutive old numbers are x and x - 2.
=> x(x - 2) = 143
=> x^2 - 2x - 143 = 0
=> x^2 + 11x - 13x - 143 = 0
=> x(x + 11) - 13(x + 11) = 0
=> (x + 11)(x - 13) = 0
=> x = -11 (invalid)
or x = 13 (valid), the remaining number is 13 - 2 = 11
=> The two numbers are 11 and 13, and the greater number is 13.
Hope this helps!
:)
Answer:
top: 2
bottom: 13
Step-by-step explanation:
step
by
step
explanation
Use the area to find the radius. If you could include steps that’ll be very helpful :)
Answer:
Area = PI * radius^2
radius^2 = Area / PI
radius^2 = 169*PI/PI
radius^2 = 169
radius = 13
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.
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.
What is the m
10
50
90
180
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.
A campaign strategist wants to determine whether demographic shifts have caused a drop in allegiance to the Uniformian Party in Bowie County. Historically, around 62% of the county's registered voters have supported the Uniformians. In a survey of 196 registered voters, 57% indicated that they would vote for the Uniformians in the next election. Assuming a confidence level of 95% and conducting a one-sided hypothesis test, which of the following should the strategist do?
a. Accept the hypothesis that the proportion of Uniformian voters has not changed.
b. Accept the hypothesis that the proportion of Uniformian voters has decreased.
c. Conclude that the proportion of Uniformian voters is now between 56% and 62%.
d. There is not enough evidence to support the hypothesis that the proportion of Uniformian voters has decreased.
Answer:
d. There is not enough evidence to support the hypothesis that the proportion of Uniformian voters has decreased.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that there is a significant drop in allegiance to the Uniformian Party in Bowie County.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.62\\\\H_a:\pi<0.62[/tex]
The significance level is 0.05.
The sample has a size n=196.
The sample proportion is p=0.57.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.62*0.38}{196}}\\\\\\ \sigma_p=\sqrt{0.001202}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.57-0.62+0.5/196}{0.035}=\dfrac{-0.047}{0.035}=-1.369[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.369)=0.0855[/tex]
As the P-value (0.0855) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that there is a significant drop in allegiance to the Uniformian Party in Bowie County.
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.
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
nancy will arrive at the hotel on July 8, and will stay three nights. What date will Nancy check out of the hotel?
Answer:
july 11
Step-by-step explanation:
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
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
Can someone help me please
Answer:
the triangles are not similar.
A package of 10 batteries is checked to determine if there are any dead batteries. Four batteries are checked. If one or more are dead, the package is not sold. What is the probability that the package will not be sold if there are actually three dead batteries in the package
Answer:
There is a probability of 76% of not selling the package if there are actually three dead batteries in the package.
Step-by-step explanation:
With a 10-units package of batteries with 3 dead batteries, the sampling can be modeled as a binomial random variable with:
n=4 (the amount of batteries picked for the sample).p=3/10=0.3 (the proportion of dead batteries).k≥1 (the amount of dead batteries in the sample needed to not sell the package).The probability of having k dead batteries in the sample is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}[/tex]
Then, the probability of having one or more dead batteries in the sample (k≥1) is:
[tex]P(x\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{4}{0} p^{0}q^{4}=1*1*0.7^4=0.2401\\\\\\P(x\geq1)=1-0.2401=0.7599\approx0.76[/tex]
what are 80 percent of 500
Answer: 400
Step-by-step explanation:
500 x 0.80 = 400
Answer:
400
Step-by-step explanation:
Of means multiply
80% * 500
Change to fraction form
80/100 * 500
Rewriting to reduce
80 * 500/100
80 * 5
400
What is the value of
3/7x0.1/5/21
?
7
А.1/98
B.9/50
С.9/5
D.18/1
Answer:
B
Step-by-step explanation:
[tex]\dfrac{3}{7}\times 0.1 \div \dfrac{5}{21}= \\\\\\\dfrac{3}{7}\times \dfrac{1}{10}\times \dfrac{21}{5}= \\\\\\\dfrac{3\times 1 \times 21}{7 \times 10 \times 5}=\\\\\\\dfrac{63}{350}=\\\\\\\dfrac{9}{50}[/tex]
Therefore, the correct answer is choice B. Hope this helps!
Answer:
The answer to your question is 9/50
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:
Alex has a bag of stuffed animals containing nine bears, six lions, and three monkeys. The probability that Alex will randomly pull out a bear and then a lion is . Using this probability, determine if the event of pulling out a bear and the event of pulling out a lion was independent, dependent, both, or neither.
Answer:
P = 0.1764
The events are dependent
Step-by-step explanation:
We have a total of 9 + 6 + 3 = 18 stuffed animals.
The probability of the first animal pulled being a bear is:
P(bear) = N(bear) / N(total)
P(bear) = 9 / 18 = 0.5
Then, for the second animal, we now have only 17 stuffed animals in total.
So the probability of the second animal pulled being a lion, given the first animal was a bear, is:
P(lion | bear) = N(lion) / N(total)
P(lion | bear) = 6 / 17 = 0.3529
So the final probability is the product of these probabilities:
P = P(bear) * P(lion | bear) = 0.5 * 0.3529 = 0.1764
To find if the events are dependent or independent, let's find the probability of the first pick being a lion:
P(lion) = N(lion) / N(total)
P(lion) = 6 / 18 = 0.3333
The probability of picking a lion is different from the probability of picking a lion given we already picked a bear, so the events are dependent.
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
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)]
Want to donate to a better cause? Consider micro-lending. Micro-lending is a process where you lend directly to entrepreneurs in developing countries. You can start lending at $25. Kiva.org boasts a 99% repayment rate. The average loan to an entrepreneurs is $388.44 and the average loan amount is $261.14. With a total amount loaned of $283,697,150, how many people are lending money if the average number of loans per lender is 8?
Answer:
135,797
Step-by-step explanation:
If the total loan amount is $283,697,150 and the average loan amount is $261.14, then the number of loans is ...
$283,697,150/$261.14 = 1,086,379.5
If the average number of loans per lender is 8, then the number of lenders is ...
1086379.5/8 = 135,797 . . . . people lending money
Which letter has at least one line of symmetry?
W
Z
S
F
Answer:
Both F and Z have symmetry.
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
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 the median of the following set of data: 4, 7, 2, 1, 4, 6,
2,6
Answer:
(4+4)/2 = 4
Hope this helps
Answer:
4
Step-by-step explanation:
1,2,2,4,4,6,6,7
The median is the number in the middle however there are an even amount of numbers so you get the number between 4 and 4 which is just 4
k(x)=-2x^2+10x+5, Evaluate k(3)
Answer:
17
Step-by-step explanation:
k(x)=-2x^2+10x+5
k(3)=-2(3)^2+10(3)+5
k(3)=-2(9)+30+5
k(3)=-18+35
= 17
Answer:
71
Step-by-step explanation:
-2(3)^2+ 10(3)+5
So first you multiply the -2 by the 3
(-6)^2+10(3)+5
then you do the exponents
36+10(3)+5
then you multiply the 10 by 3
36+30+5
then you would add 36 and 30
66+5
then add the 5
71
Please answer this correctly
Answer: 3 people, 2 people, 4 people, 6 people, 2 people, 3 people, 3 people
Step-by-step explanation:
3 given numbers within 30-39
32, 35, 38
2 given numbers within 40-49
45, 48
4 given numbers within 50-59
51, 52, 54, 59
6 given numbers within 60-69
60, 61, 65, 65, 66, 69
2 given numbers within 70-79
77, 78
3 given numbers within 80-89
83, 83, 84
3 given numbers within 90-99
95, 96, 98
Answer: see Frequency below
Step-by-step explanation:
This is a frequency table. How many times does a number appear in the data set that falls within the given interval?
Interval Data Frequency
30-39: 35, 38, 32 3
40-49: 48, 45 2
50-59: 59, 51, 52, 54 4
60-69: 61, 60, 66, 65, 65, 69 6
70-79: 77, 78 2
80-89: 83, 84, 83 3
90-99: 98, 96, 95 3
Check the total to make sure you included each number from the data set.
Total numbers in the data set = 23, Total Frequency = 23 [tex]\checkmark[/tex]
Which shows one way the equation can be represented in words?
Z-6=1.4
Answer:
6 less than a number is equal to 1 and 4 tenths
Step-by-step explanation:
please very soon I offer the crown !!! + 10 points urgently !!!
Answer:
For 90:
9 10p coins
7 10p coins and 1 20p coin
5 10p coins and 2 20 p coins
3 10p coins and 3 20p coins
For 60:
6 10p coins
4 10p coins and 1 20p coin
2 10p coins and 2 20p coins
3 20p coins
Step-by-step explanation:
Answer:
For 90 is having each containing both the 20 and10 for 2 boxes then the rest each a 20&10
For 60 is two 20s and two10
Step-by-step explanation:
Hope it helps
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
Solve the system of equations.
3x + 3y + 6z = 6
3x + 2y + 4z = 5
7x + 3y + 32 = 7
a. (x = 2, y = -2, z = 0)
b. (x = 3, y=-3, z = 3)
c. (x = 1, y = - 1,2= 1)
d. (x = 0, y = 0, z = 2)
Answer:
The answer is option c
x = 1 y = - 1 z = 1
Hope this helps.
