Answer:
Option c.
Step-by-step explanation:
If we have a vector of N components (or variables), and we have K linear independent restrictions for these N components (such that K < N, we can't have more restrictions than components.)
The dimension of the vector will be given by N - K.
Here we know that we have a vector of 5 components, that can be written as:
[tex]v = \left[\begin{array}{ccc}v_1\\v_2\\v_3\\v_4\\v_5\end{array}\right][/tex]
And we have two restrictions, so we can expect that the dimension of the vector is:
5 - 2 = 3
But let's see it, the restrictions are:
"the first row is equal to the second row"
Then we can rewrite our vector as:
[tex]v = \left[\begin{array}{ccc}v_1\\v_1\\v_3\\v_4\\v_5\end{array}\right][/tex]
Notice that now we have only 4 variables, v₁, v₃, v₄, and v₅
We also know that the sum of the rows is equal to zero, thus:
v₁ + v₂ + v₃ + v₄ + v₅ = 0
we know that v₂ = v₁, so we can replace that to get:
2*v₁ + v₃ + v₄ + v₅ = 0
Now we can isolate one of the variables, to write it in term of the others, for example, let's isolate v₅:
v₅ = -2*v₁ - v₃ - v₄
Now if we replace that in our vector, we have:
[tex]v = \left[\begin{array}{ccc}v_1\\v_1\\v_3\\v_4\\-2*v_1 - v_3 - v_4\end{array}\right][/tex]
Notice that our vector depends on only 3 variables, v₁, v₃, and v₄, so we can define our vector in a 3-dimensional space.
Then the correct option is c, the dimension of the vector space is 3.
I NEED HELP PLEASE!!!
Use the substitution methed to solve the system of equations. Choose the correct ordered pair.
2y+5x=13
2y+3x=5
Solve both equations for 2y :
2y + 5x = 13 ==> 2y = 13 - 5x
2y + 3x = 5 ==> 2y = 5 - 3x
Solve for x :
13 - 5x = 5 - 3x
8 = 2x
x = 4
Solve for y :
2y = 13 - 5×4
2y = -7
y = -7/2
As an ordered pair, the solution is then the point (x, y) = (4, -7/2).
f(x)=8x−4x+4 , then f(x−1)=
Answer: [tex]4x[/tex]
Step-by-step explanation:
[tex]f(x)=8x-4x+4\\f(x-1)=8(x-1)-4(x-1)+4\\f(x-1)=8x-8-4x+4+4\\f(x-1)=4x-8+4+4\\f(x-1)=4x[/tex]
work for 12 hours and earn $140 find the unit rate
Answer:
11.60
Step-by-step explanation:
To find unit rate, you need to use the formula:
(amount of money) ÷ (amount of hours)
Since we have both, we can plug in
140 ÷ 12 will give you approximately 11.6
So, you receive $11.60 every hour.
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
Write the piecewise defined function for the total cost of parking in the garage. That is, state the function C(x), where x is the number of hours a car is parked in the garage.
Answer:
[tex]C(x) = \left[\begin{array}{ccc}4x &0 \le x \le 2& \\4 +2x &2 < x \le 6& \\16 &6<x\le 8& \end{array}\right[/tex]
Step-by-step explanation:
Given
See attachment for question
Required
The piece-wise function
From the attachment, we have:
(1) $4/hr for first 2 hours
This is represented as:
[tex]C(x) = 4x[/tex]
The domain is: [tex]0 \le x \le 2[/tex]
(2) $2/hr for next 4 hours
Here, we have:
[tex]Rate = 2[/tex]
The total cost in the first 2 hours is:
[tex]C(x) = 4x[/tex]
[tex]C(2) = 4*2 = 8[/tex]
So, this function is represented as:
[tex]C(x) = C(2) + Rate * (Time - 2)[/tex] ----- 2 represents the first 2 hours
So, we have:
[tex]C(x) = C(2) + Rate * (Time - 2)[/tex]
[tex]C(x) =8 + 2(x - 2)[/tex]
Open brackets
[tex]C(x) =8 + 2x - 4[/tex]
Collect like terms
[tex]C(x) =8 - 4+ 2x[/tex]
[tex]C(x) =4+ 2x[/tex]
The domain is:
[tex]2 < x \le 2 + 4[/tex]
[tex]2 <x \le 6[/tex]
(3) 0 charges for the last 2 hours
The maximum charge from (2) is:
[tex]C(x) =4+ 2x[/tex]
[tex]C(6) = 4 + 2*6[/tex]
[tex]C(6) = 4 + 12[/tex]
[tex]C(6) = 16[/tex]
Since there will be no additional charges, then:
[tex]C(x) = 16[/tex]
And the domain is:
[tex]6 < x \le 8[/tex] --- 8 represents the limit
So, we have:
[tex]C(x) = \left[\begin{array}{ccc}4x &0 \le x \le 2& \\4 +2x &2 < x \le 6& \\16 &6<x\le 8& \end{array}\right[/tex]
Ray’s weight increased by 11% in the last two years. If he gained 16.5 pounds, what was his weight two years ago?
Answer:
Ray weighed 150 pounds two years ago.
Step-by-step explanation:
11/100 = 16.5/x
11x = 16.5(100)
11x = 1,650
(11x)/11 = (1,650)/11
x = 150
About time that he should start going to the gym!
Select all correct answers
What are the solution to this equation
-7+(x^2-19)^3/4=20
Correct options are -10 and 10
-7 + (-10² - 19)³/⁴ = 20
-7 + (100 - 19)^3/4 = 20
-7 + (81)^3/4 = 20
-7 + 27 = 20
20 = 20
RHS = LHS
-7 + (10² - 19)^3/4 = 20
-7 + (100 - 19)^3/4 = 20
-7 + (81)^3/4 = 20
-7 + 27 = 20
20 = 20
RHS = LHS
Rest options are incorrect
Answered by Gauthmath must click thanks and mark brainliest
Answer:
B and C, so 10 and -10
Step-by-step explanation:
A well-known brokerage firm executive claimed that 60% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is larger than 60% at the 0.01 significance level.
The null and alternative hypothesis would be:________
a. H0:μ=0.6H0:μ=0.6
H1:μ≠0.6H1:μ≠0.6
b. H0:μ=0.6H0:μ=0.6
H1:μ<0.6H1:μ<0.6
c. H0:μ=0.6H0:μ=0.6
H1:μ>0.6H1:μ>0.6
d. H0:p=0.6H0:p=0.6
H1:p≠0.6H1:p≠0.6
e. H0:p=0.6H0:p=0.6
H1:p>0.6H1:p>0.6
f. H0:p=0.6H0:p=0.6
H1:p<0.6H1:p<0.6
The test is:________
a. two-tailed
b. left-tailed
c. right-tailed
The test statistic is:_______ (to 3 decimals)
The p-value is:_______ (to 4 decimals)
Based on this we:________
a. Fail to reject the null hypothesis
b. Reject the null hypothesis
We are testing a hypothesis. So, first we identify the null and the alternative hypothesis, then we find the test statistic, and with the test statistic, the p-value is found.
Null and alternative hypothesis:
Claim the the proportion is of 60%, thus, the null hypothesis is:
[tex]H_0: p = 0.6[/tex]
Test if the proportion is greater than 60%, thus, the alternative hypothesis is:
[tex]H_1: p > 0.6[/tex]
And the answer to the first question is given by option c.
Classification:
We are testing if the proportion is greater than a value, so it is a right-tailed test.
Test statistic:
[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.
0.6 is tested at the null hypothesis:
This means that [tex]\mu = 0.6, \sigma = \sqrt{0.4*0.6}[/tex]
Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals.
This means that [tex]n = 100, X = 0.69[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.69 - 0.6}{\frac{\sqrt{0.4*0.6}}{\sqrt{100}}}[/tex]
[tex]z = 1.837[/tex]
The test statistic is z = 1.837.
p-value:
The p-value of the test is the probability of finding a sample proportion above 0.69, which is 1 subtracted by the p-value of z = 1.837.
Looking at the z-table, z = 1.837 has a p-value of 0.9669.
1 - 0.9669 = 0.0331
The p-value is 0.0331.
Decision:
The p-value of the test is 0.0331 > 0.01, and thus:
a. Fail to reject the null hypothesis
For another example of a problem of a test of hypothesis, you can take a look at:
https://brainly.com/question/24166849
If Jan can weed the garden in 2 hours and her husband can weed it in 1 hour and 30 minutes, find how long it takes them to weed the garden together.
Answer:
3 hours 30 minutes
Step-by-step explanation:
Jan :2 hours
her husband : 1 hour 30 minutes
2hr + 1 ½ hrs = 3 ½ hrs...that is 3 hours 30 minutes....?
Answer pleaseeeeeeeeee
Answer:
[tex]y=-\frac{8}{7}x+4[/tex]
Step-by-step explanation:
A line is perpendicular to another if its slope is the negative reciprocal of the other.
Your lines are in slope intercept form here, y=mx+b, where m is the slope. We can see the given line has slope [tex]\frac{7}{8}[/tex]. The negative reciprocal of that is [tex]-\frac{8}{7}[/tex], which is the slope of the third answer choice.
how many itegers from 15 to 85, inclusive are multibles of 8
Answer:
9
Step-by-step explanation:
First multiple of 8 in that range is 8(2)=16.
The last multiple of 8 in that range is 8(10)=80.
So we just need to find how many numbers there are between 2 and 10. inclusive.
10-2+1=9
It's also not that long to write out and count.
1-2
2-3
3-4
4-5
5-6
6-7
7-8
8-9
9-10
9 numbers there are
Multiply those 9 numbers by i you will have all multiples of 8 btw 15 and 85.
8(2)=16
8(3)=24
8(4)=32
8(5)=40
8(6)=48
8(7)=56
8(8)=64
8(9)=72
8(10)=80
Find the smallest possible value of x+y so that x^2 − y^2 is divisible by 74, where x and y are positive integers.
Answer: 2
Step-by-step explanation:
We know by different of squares, (x-y)(x+y)=74. Since we need to find the smallest possible answer for x+y, we let x+y=2, where both x and y = 1.
In how many ways can a committee of 3 men and 2 women can be formed from 7 men and 5 women?
Answer:
in five (5) ways a committee can be formed from 7 men and 5 women
Given the data, identity the type of data for each variable. (For example, determine whether the variable Day is categorical or quantitative data). Which variable is most appropriate to summarize using ungrouped frequency distributions
Answer:
Kindly check explanation
Step-by-step explanation:
The variables in the heavenly chocolate dataset is attached below :
Variables are classed as either Categorical or Quantitative.
Categorical variables are used for non - numeric variables which are used to group values based on labels whole quantitative variables are those which are numeric.
Therefore, the variables ;
Customer = Quantitative (represented with number values)
Day = Categorical (Non-numeric)
Browser = Categorical (Non - numeric)
Time = Quantitative (contains numeric values)
Pages viewed = Quantitative (contains numeric values)
Amount spent = Quantitative (contains numeric values)
Quantitative variables are most appropriate to summarize using ungrouped frequency as the attributed of the data can be adequately ibtia Ed without have to seperates or place data into categories.
What is the value of…
–13
–12
12
13
Answer:
-12
Step-by-step explanation:
that is b
A researcher utilizes a t-test to compare the average amount of beta-lactamase produced by two different types of bacteria. The Levene's test for equality of variances has a p value of 0.01. You know this means:
Answer:
The answer is "T-test results must not be presented if the same variations are expected".
Step-by-step explanation:
A t-test is used by a scientist to compare the average beta-lactamase of two distinct strains of bacteria. The Levene equality test does have a p-value of 0.01. Researchers know that all this means that research should report t-test findings with a failed assumption of identical variances because the Log-rank equality test has a p-value of 0.01 of less than 0.05 that shows different twp population variance.
Find the missing segment in the image below
Answer:
Step-by-step explanation:
In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____. a. parabolic band of points b. band of points having a slope consistent with that of the regression equation c. horizontal band of points centered near 0 d. widening band of points
Answer:
In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____.
c. horizontal band of points centered near 0
Step-by-step explanation:
This residual graph or plot shows the residual values (or the difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line) on the vertical axis and displays the independent variable on the horizontal axis. A linear regression model becomes appropriate for a dataset when the points are randomly dispersed around the horizontal axis near 0; otherwise, a nonlinear model becomes more appropriate.
A researcher would like to investigate whether or not there is a difference in IQ between Psychology and History majors. She gathers 16 students (8 whose major is Psychology, and 8 whose major is history) and has them all take an IQ test to test this hypothesis using an alpha level of .01. Below are the data: Psych History
110 90 120 98 100 100 90110 124 100 102 120 110 110 123 120
a. What is the appropriate test?
b. State the null hypothesis:
c. State the alternative hypothesis:
d. Find the critical value:
e. Calculate the obtained statistic:
f. Make a decision:
g. What does your decision mean?
Answer:
Paired t test
H0 : μd = 0
H1 : μd > 0
Critical value = 3.499
Test statistic = 2.230
Reject H0 if test statistic > Critical value
Kindly check explanation.
Step-by-step explanation:
Given the data :
110 90 120 98 100 100 90 110
124 100 102 120 110 110 123 120
The hypothesis :
H0 : μd = 0
H1 : μd > 0
Tcritical value, df = n - 1 = 8 - 1 = 7
Tcritical(0.01, 7) = 3.499
The difference, d = (-14,-10,18,-22,-10,-10,-33,-10)
The test statistic :
Xdbar / Sd/√n
The mean difference, Xdbar = Σx / n = - 11.375
The standard deviation of difference, Sd = 14.431
The test statistic :
-11.375 / (14.431/√8) ;
-11.375 / 5.102
= 2.230
Decison :
Reject H0 if test statistic > Critical value
Since ; 2.230 <3.499 ;
We fail to reject the null
The answer to the picture please
the required ans is 3√b+b/3b
A Basketball team won 8 games and lost 7 games. What are the odds in favor of winning a basketball game
Answer:
0.47
Step-step explanation:
Add 8+7 which gives you 15. So 7/15. Then turn it into decimal form which is 0.47. Hope this helps!
The functions q and r are defined as follows
q(x)=-2x-2
r(x)=x^2+1
Find the value of r(q(4)).
plug-in
-2(4) - 2
-8 - 2
-10
-10^2 + 1
-100 + 1
Your answer: -99
Mrs. Hanson has 3 pies for a party. She calculates that if she splits the pies evenly among the guests, they will each receive
1/6
of a pie. How many guests are there?
Answer:
18 guests.
Step-by-step explanation:
To find the number of guests, we can simply divide 1/6 from 3. The result gives us 18.
Is this the correct answer?
Answer:
25.40
Step-by-step explanation:
tickets ( 2 at 10.95 each) = 2* 10.95 = 21.90
popcorn ( 1 at 7.50) = 7.50
Total cost before discount
21.90+7.50=29.40
subtract the discount
29.40-4.00 =25.40
Answer:
Yep! That's correct!
Step-by-step explanation:
We know that Marilyn and her sister are each getting a ticket that cost $10.95. They are also getting a $7.50 popcorn to share. Let's add those values up.
(10.95 * 2) + 7.50 {Multiply 10.95 by 2 to get 21.90.}
21.90 + 7.50 {Add 7.50 to 21.90 to get 29.40}
$29.40 (without the credit) in toal
A credit on a movie reward card functions as a discount, so what we need to do next is subtract 4 from 29.40. That will get us $25.40 as the total cost.
After doing the math, I can deduce that your answer is correct!
What percentages of participants in the study were American?
round 12.5478 to the nearest hundredths
Answer:
12.04
Step-by-step explanation:
Find the number in the hundredth place 4 and look one place to the right for the rounding digit 1 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .
solve for x : 2(x^2+9)-4=0
Answer:
no solution
Step-by-step explanation:
multiply 2 and get 2x^2+18-4=0
combine like terms
2x^2+14=0
subtract 14
2x^2=-14
there can't be a square root of a negative number so there's no solution
Answer:
x = ±i sqrt(7)
Step-by-step explanation:
2(x^2+9)-4=0
Add 4 to each side
2(x^2+9)-4+4=0+4
2(x^2+9)=4
Divide by 2
2(x^2+9)/2=4/2
(x^2+9)=2
Subtract 9 from each side
x^2 +9-9 = 2-9
x^2 = -7
Taking the square root of each side
sqrt(x^2) =sqrt(-7)
x = sqrt(-1 *7)
x = ±i sqrt(7)
Please solve the problem
Answer:
does this have to do with graphs
If f(x) is an exponential function where f(-1.5) 26 and
f(5.5) = 7, then find the value of f(10), to the nearest hundredth.
Answer:
[tex]f(10) = 1147.25[/tex]
Step-by-step explanation:
Given
[tex]f(-1.5) = 26[/tex]
[tex]f(5.5) = 7[/tex]
Required
f(10)
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
[tex]f(-1.5) = 26[/tex] impleies that:
[tex]26 = ab^{-1.5}[/tex] --- (1)
[tex]f(5.5) = 7[/tex] implies that
[tex]7 = ab^{5.5}[/tex] --- (2)
Divide (2) by (1)
[tex]26/7 = ab^{-1.5}/ab^{5.5}[/tex]
[tex]3.71429 = b^{-1.5+5.5}[/tex]
[tex]3.71429 = b^{4}[/tex]
Take 4th root
[tex]b = 1.39[/tex]
Substitute [tex]b = 1.39[/tex] in [tex]26 = ab^{-1.5}[/tex]
[tex]26 = a * 1.39^{-1.5}[/tex]
[tex]26 = a * 0.6102[/tex]
Solve for (a)
[tex]a = 26/0.6102[/tex]
[tex]a = 42.61[/tex]
f(10) is calculated as:
[tex]f(10) = ab^{10}[/tex]
[tex]f(10) = 42.61 * 1.39^{10}[/tex]
[tex]f(10) = 1147.25[/tex]
