[ 0] [ 1] [-1]
[ 0] [-1] [ 0]
Let v1 = [-1], v2 = [ 0], and v3 = [ 1]. [ 1] [ 0] [ 0]
Does not {v1, v2, v3} span R^4? Why or why not?

In this situation, the teacher could use a hypothesis test for a population means to determine if the computer-based instruction led to a statistically significant improvement in the student's test scores. The population in this case would be the entire class of students, and the mean would represent the average difference in test scores between the pretest and posttest.

The teacher can use a hypothesis test for a population means in the following situation:

1. Determine the population: The teacher's population consists of all the students who participated in the experiment.

2. Calculate the mean pretest score: The teacher will compute the average score of all the students' pretest results.

3. Implement computer-based instruction: The teacher teaches a lesson using a computer program.

4. Conduct a posttest: After the lesson, the teacher administers a posttest to each student.

5. Calculate the mean post-test score: The teacher will compute the average score of all the students' post-test results.

6. Formulate a null hypothesis: The null hypothesis states that there is no significant difference between the pretest and posttest mean scores. In other words, computer-based instruction did not have a significant impact on the students' performance.

7. Conduct a hypothesis test for a population mean: The teacher will use a statistical test, such as a t-test, to compare the pretest and posttest mean scores. This test will determine whether there is a significant difference between the two means that suggests the computer-based instruction had a positive effect on the student's performance.

8. Interpret the results: If the hypothesis test shows a significant difference between the pretest and posttest mean scores, the teacher can conclude that the computer-based instruction likely had a positive impact on the students' learning. Otherwise, the null hypothesis cannot be rejected, and the teacher may need to explore other instructional methods or factors that could have influenced the results.

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Answer:

8

Step-by-step explanation:

We can set this up in a ratio. In the picture shown, there is a large triangle and a small triangle inside it.

The ratio for the large triangle would be 21/28.

I got the '21' from '21/28' from doing 15+6.

Now the ratio for the small triangle is 6/x. As x is the unknown value.

To find x, we have to cross multiply and to do that we would do:

21x = 28x6

Simply and you get

21x=168

x=8

Hope this helps! :)

Answer:

First day, N(1) = 4

Second day, N(2) = 4 + 3 = 7

Third day, N(3) = 4 + 6 = 10

Fourth day, N(4) = 4 + 9 = 13

Fifth day, N(5) = 4 + 12 = 16

Step-by-step explanation:

She spent 5 days on her vacation.

She collected 50 seashells in those days. Each day she collected 3 more than the previous day.

We can represent this with an arithmetic progression:

N(n) = x + 3(n - 1)

Where x is the amount of sea shells collected on the first day.

n = the particular day

So, for the five days day:

N(1) = x + 3(1 - 1) = x + 3(0) = x

N(2) = x + 3(2 - 1) = x + 3(1) = x + 3

N(3) = x + 3(3 - 1) = x + 3(2) = x + 6

N(4) = x + 3(4 - 1) = x + 3(3) = x + 9

N(5) = x + 3(5 - 1) = x + 3(4) = x + 12

The sum of all the sea shells is 50:

N(1) + N(2) + N(3) + N(4) + N(5) = 50

=> x + x + 3 + x + 6 + x + 9 + x + 12 = 50

5x + 30 = 50

5x = 50 - 30 = 20

x = 20 / 5

x = 4

Therefore:

First day, N(1) = 4

Second day, N(2) = 4 + 3 = 7

Third day, N(3) = 4 + 6 = 10

Fourth day, N(4) = 4 + 9 = 13

Fifth day, N(5) = 4 + 12 = 16

To express the integrand as a rational function, we can make the substitution u = 1 + x^2. Then, du/dx = 2x, so dx = du/(2x).

You are asked to evaluate the integral of a function that can be expressed as a rational function using substitution. The given integrand is:

∫((Tc-4)^(-1/3) dTc)

Step 1: Make a substitution to express the integrand as a rational function
Let's perform a substitution:
u = Tc - 4

Then, differentiate both sides with respect to Tc:
du/dTc = d(Tc - 4)/dTc = 1

Now, solve for dTc:
dTc = du

Now, substitute the expressions for u and dTc into the original integrand:
∫(u^(-1/3) du)

Step 2: Evaluate the integral
Now, integrate the new expression:
∫(u^(-1/3) du) = (3/2)u^(2/3) + C

Step 3: Substitute back to the original variable, Tc
Now, substitute back the original variable, Tc, using u = Tc - 4:
(3/2)(Tc - 4)^(2/3) + C

Therefore, the integral of the given expression is:
(3/2)(Tc - 4)^(2/3) + C

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Answer:

a) 2 * 8 = 16

b) (-2.5)(-2.5) = 6.25 = \(\frac{625}{1000} = \frac{5}{8}\)

Step-by-step explanation:

The integral in terms of x is ∫x/(x² - 18x + 56) dx.

We must first complete the square in the denominator.

The expression x² - 18x + 56 can be rewritten as (x - 9)² - 1.

Therefore, the integral can be written as follows:

∫x/[(x - 9)² - 1] dx

This problem requires integration by substitution since we have an expression of the form x / (ax2 + bx + c).

Let's make the substitution u = x - 9 and solve for x in terms of u:

u = x - 9, then x = u + 9.

Substituting for x, we get:

∫(u + 9)/[(u² - 1)] disintegrating by partial fractions, we get:

∫[(1/2)/(u - 1)] - [(1/2)/(u + 1)] + (9/2) [(1)/(u² - 1)] du

After that, the indefinite integral in terms of x becomes:

∫x/(x² - 18x + 56) dx

= (1/2) ln(x - 9 - 1) - (1/2)

= ln(x - 9 + 1) + (9/2)

= ln(x - 9 + √55) - (9/2)

= ln(x - 9 - √55) + C

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Answer:

D) 5.9

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

We are to find:

Weight represents the top 10% of the zucchinis

Top 10% = 90th percentile

Z score for 90th percentile = 1.282

Hence

1.282 = x - 5 / 0.7

1.282 × 0.7 = x - 5

0.8974 = x - 5

x = 5 + 0.8974

x = 5.8974

Approximately = 5.9 ounces

The weight that represents the top 10% of the zucchinis is 5.9 ounces

Answer:

it's D: 5.9 ounces on Edge

Step-by-step explanation:

If it's wrong for you, you're on the wrong question. Check your questions before leaving a bad rating.

Answer:

15x^2 + 14x - 8.

Step-by-step explanation:

(3x + 4)(5x - 2)

= 3x(5x - 2) + 4(5x - 2)

= 3x*5x + 3x*-2 + 4*5x + 4*-2

= 15x^2 - 6x + 20x - 8

= 15x^2 + 14x - 8.

Answer:

C and D are same options

(D)\( f(x) = x^2 \)

Step-by-step explanation:

\(f(x) = {x}^{2} \\ plug \: x = - x \\ f( - x) = {( - x)}^{2} = {x}^{2} \\ f( - x) = f(x)\)

Answer:

Ross isn't right.

Step-by-step explanation:

Skateboard $125.95 at 40% off is $75.57

How I got the number:

125.95/100 = 1.2595

1.2595 x 40 = 50.38

125.95 - 50.38 = 75.57

Skateboard $169.95 at 60% off is $67.98

169.95/100 = 1.6995

1.6995 x 60 = 101.97

169.95 - 101.97 = 67.98

Therefore the skateboard that is 60% off is cheaper.

The inequality of the graph from the boundary line is y ≤ x - 3

From the question, we have the following parameters that can be used in our computation:

Boundary line: y = x  - 3

This means that

The inequality can be any of the following

y > x - 3

y < x - 3

y ≥ x - 3

y ≤ x - 3

In this case, we make use of y ≤ x - 3

So, we plot the graph

See attachment for the graph of the inequality expression y ≤ x - 3

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The negative integer -4°F  represents the change in temperature for every thousand feet a person climbs.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

here,
As a person climbs a mountain, the temperature drops 4°F for every thousand feet climbed.

Change in temperature  = -4°F

Thus, the negative integer -4°F  represents the change in temperature for every thousand feet a person climbs.

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=====================================================

Explanation:

Draw a square that is tilted on one side (so it resembles a diamond shape). Each side of the square is 65.

Draw a vertical line through the top and bottom vertices of the square to connect home plate (bottom) to 2nd base (top). This forms 2 right triangles that are mirror clones of each other, aka they are congruent triangles.

Focus on one of those right triangles. The legs are a = 65 and b = 65. The hypotenuse is unknown which I'll call c.

Use the pythagorean theorem to find c.

\(a^2 + b^2 = c^2\\\\65^2 + 65^2 = c^2\\\\4225 + 4225 = c^2\\\\8450 = c^2\\\\c^2 = 8450\\\\c = \sqrt{8450}\\\\c \approx 91.92388\\\\c \approx 91.92\\\\\)

The distance from home to 2nd is roughly  91.92 yards  

Side note: 91.92 yards = 91.92*3 = 275.76 feet

Answer:

7

Step-by-step explanation:

the answer is 7 because it is a 1 to three ratio.

Answer:

x+y=5

Step-by-step explanation:

y=-x+5

add x to both sides

x+y=5

Answer:

x + y = 5

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = - x + 5 ( add x to both sides )

x + y = 5 ← in standard form

5/45 = 1/9 represents the probability of the best-case scenario. 40/45 = 8/9 represents the probability of the worst-case scenario.

When two socks from the same pair are missing, the likelihood of the best-case scenario increases. As a result, all four pairs of socks are present. Now, 10C2 = 45 gives the total number of possible methods to choose 2 socks from a total of 5 x 2 = 10 socks. The probability of choosing one pair of socks from five pairs is equal to the number of ways to choose two socks from a pool of ten socks, and this is provided by the formula 5C1 = 5.  given by 5 / 45 = 1 / 9. The worst case situation is when they are not from the same pair of socks. As a result, all three pairs of socks are present. Now, 10C2 = 45 gives the total number of possible methods to choose 2 socks from a total of 5 x 2 = 10 socks. 10C2 - 5C1 = 45 - 5 = 40 is the number of ways to choose two socks from a group of ten so that they are not from the same pair.  given that by 40 / 45 = 8 / 9

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Answer:

3.78%

Step-by-step explanation:

The formula for compound interest is given by:

A(t) = P(1 + r/n)^(nt), where

Thus, we can plug in 8500 for P, 11022 for A(t), 1 for n, and 7 for t to find r:

Step 1:  Plug in the values and simplify:

11022 = 8500 * ( 1 + r/1)^(7 * 1)

11022 = 8500 * (1 + r)^(7)

Step 2:  Divide both sides by 8500:

(11022 = 8500 * (1 + r)^(7)) / 8500

11022/8500 = (1 + r)^(7)

5511/4250 = (1 + r)^(7)

Step 3:  Raise both sides to the 1/7 power (this is the same as taking the 7th root of both sides):

(5511/4250 = (1 + r)^(7))^(1/7)

1.037815641 = 1 + r

Step 4:  Subtract 1 from both sides to find r:

(1.037815641 = 1 + r) - 1

0.0378154607 = r

Step 5:  Multiply 0.0378154607 by 100 to find the interest rate as a percentage:

0.0378154607 * 100

3.78156407 = %

Step 6:  Round to the nearest two decimal places:

3.78

Thus, the interest rate is about 3.78%

Answer:

Goal  = x

45000 = 9/10 * x

x = 45000 * 10/9  = 50000

Step-by-step explanation:

You may find something useful on my you tube channel "Sciency Sergei". You may also suggest a topic to discuss or problems to solve.

Looking at figure A, we have a prism with a triangular base that looks like a right triangle.

Since the prism has a right triangular base, the base shape is a right triangle (shape 5).

Looking at figure B, we have a prism with a pentagonal base.

Since the prism has a pentagonal base, the base shape is a pentagon (shape 1).

Looking at figure C, we have a prism with a triangular base that looks like an equilateral triangle.

Since the prism has an equilateral triangle base, the base shape is an equilateral triangle.(shape 4).

Looking at figure D, we have a prism with a triangular base that looks like an equilateral triangle.

Since the prism has an equilateral triangle base, the base shape is an equilateral triangle.(shape 4).

Answer:

the ratio of distance descended over time

Step-by-step explanation:

Answer:

1) 45%

2) 24%

Step-by-step explanation:

1) Total number of people surveyed = 26 + 84 + 72 + 34 = 216

    number of people who own a smartphone = 26 + 72 = 98

           ∴ relative frequency = \(\frac{98}{216}\)   ˣ   100 = 45%

2) Total number of elementary school students = 26 + 84 = 110

               ∴ relative frequency = \(\frac{26}{110}\)   ˣ   100 = 24%

Hope this helps!

Answer:

(a) Index finger

(b) Ring finger

(c) Index finger

Step-by-step explanation:

Taking thumb as standard for the question.

Thumb series 1 , 9 , 17 ,25, 33......

general term for this

a(n) = 1 + (n-1)8

      = 1 + 8n -8

       = 8n -7

(a) For 1 to 10

     8n -7 = 10

     8n = 16+1 (remainder)

so the thumb is for 9 and the next is index finger.

10th = index finger.

(b) for 1 to 100

    8n - 7 = 100

      8n= 107

     107 = 13x 8 + 3(remainder)

so the third finger from thumb is Ring finger

100th = Ring finger

(c) 8n - 7 = 1000

   8n = 1007      

 1007= 125x8 +7 (remainder)

so the 7th finger next to thumb is Index finger

1000th = index finger

Therefore, we are 98% confident that the true mean weight of the newborn girl lies between 29.3306 and 32.0694 hg.

The solution to the given problem is as follows; Given summary statistics are; N = 174x = 30.7 hgs = 7.7 hg

To construct the confidence interval estimate of the mean, we will use the following formula;` CI = x ± t_(α/2) * (s/√n)` Where,α = 1 - confidence level = 1 - 0.98 = 0.02 Degrees of freedom = n - 1 = 174 - 1 = 173 (as t-value depends on the degrees of freedom)distribution is normal (because sample size > 30)

Now, to get the t-value we use the t-table which gives the critical values of t for a given confidence level and degrees of freedom. The t-value for a 98% confidence interval with 173 degrees of freedom is found in the row of the table corresponding to 98% and the column corresponding to 173 degrees of freedom.

This gives us a t-value of 2.3449. Calculating the interval estimate of the mean weight of the newborn girl;` CI = 30.7 ± 2.3449 * (7.7 / √174)`CI = 30.7 ± 2.3449 * 0.5852CI = 30.7 ± 1.3694CI = (29.3306, 32.0694)

The 98% confidence interval is (29.3306, 32.0694).

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Answer:

C; B

Step-by-step explanation:

The direct/explicit formula for a geometric sequence is the following:

\(a_n=a(r)^{n-1}\)

Where aₙ represents the term n, a represents the initial value, and r represents the common ratio.

Therefore, to find the nth term, we just need to find the initial value and the common ratio.

1)

-8, 24, -72, 216...

The common ratio is the ratio between each consecutive term. Do two to confirm that they are indeed the same. Thus:

\(r=24/-8=-3\\r=-72/24\stackrel{\checkmark}{=}-3\)

So, the common ratio is -3. And the initial value is -8. Thus, putting them into our equation:

\(a_n=-8(-3)^{n-1}\)

Thus, the eighth term will be:

\(a_8=-8(-3)^{8-1}\\a_8=-8(-3)^7\\a_8=17496\)

C

2)

Again, find the common ratio.

2, -14, 98, -686...

\(-14/2=-7\\98/-14\stackrel{\checkmark}{=}-7\)

The common ratio is -7. The initial value is 2. Thus:

\(a_n=2(-7)^{n-1}\)

And the sixth term will be:

\(a_6=2(-7)^{6-1}\\a_6=2(-7)^5\\a_6=-33614\)

B

To find the probability that a participant selected at random found the products favorable, we can calculate the weighted average of the favorable responses from both the industry-sponsored and non-industry-funded studies.

For the industry-sponsored studies, 65% of participants found the products favorable, and for the non-industry-funded studies, 47% found the products favorable. Since there were 65 industry-sponsored studies and 35 non-industry-funded studies, the overall probability is:

(65/100) * 0.65 + (35/100) * 0.47 = 0.4225 + 0.1645 = 0.587 or 58.7%

If a randomly selected participant found the product favorable, we can use Bayes' theorem to calculate the probability that the study was sponsored by the food industry given this favorable response. The calculation is:

P(Industry-sponsored | Favorable) = (P(Favorable | Industry-sponsored) * P(Industry-sponsored)) / P(Favorable)

P(Favorable | Industry-sponsored) = 0.65

P(Industry-sponsored) = 65/100

P(Favorable) = 0.587

P(Industry-sponsored | Favorable) = (0.65 * (65/100)) / 0.587 ≈ 0.719 or 71.9%

Similarly, if a randomly selected participant found the product unfavorable, we can use Bayes' theorem to calculate the probability that the study had no industry funding given this unfavorable response. The calculation is:

P(No industry funding | Unfavorable) = (P(Unfavorable | No industry funding) * P(No industry funding)) / P(Unfavorable)

P(Unfavorable | No industry funding) = 0.36

P(No industry funding) = 35/100

P(Unfavorable) = 1 - P(Favorable) = 1 - 0.587 = 0.413

P(No industry funding | Unfavorable) = (0.36 * (35/100)) / 0.413 ≈ 0.305 or 30.5%

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Answer:

3/7

Step-by-step explanation:

the original amount of marbles in the bag was 15(5+7+3) take away 1 which is the purple marble there is 14 left 6 of those are purple so you have a 6/14 chance of getting a purple marble simplify it and you have 3/7

Answer:

just do pythagorean theorem  

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

This is a Pythagorean Problem

Formula

a^2 + b^2 = c^2

a = 5

b = ?

c = 9

Solution

5^2 + b^2 = 9^2             Expand the givens

25 + b^2 = 81                  Subtract 25 from both sides

25-25+b^2 = 81- 25

b^2 = 56

√b^2 = √56

b = √8*7

b = √2*2*2*7

b = 2 √2*7

b = 2 √14

For every 2 prime factor under the square root sign, 1 of them can be taken out from under the root and the other is thrown away.

The correct option is b. When taking the subgroup samples from product produced over a period of time rather than at an instant of time, maximum variation within a subgroup occurs.

Variation refers to a change that occurs in the production process of an item or a product. A process that is consistent is one where variation has been reduced to the lowest possible level.

Subgroups are smaller parts of a whole. They are important when taking samples for statistical analysis. A subgroup will make it easier to identify if a process is consistent or inconsistent.

Each subgroup can be studied to determine the variation and how the process is functioning. Variation within a subgroup is a measure of how the samples within the subgroup differ from each other.

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Answer:

Car A's speed is 75 miles per hour

Step-by-step explanation:

As the distance-time graph represents the straight line. Thus, the slope of any line would remain constant along the line.

We also know that in a distance-time graph, the slope of the line would be equal to the speed of the object.

Taking two points from the graph

Determining the slope

Slope = [y₂-y₁] / [x₂-x₁]

          = [100 - 25] / [1 - 0]

          = 75 / 1

           = 75 miles per hour

Therefore, Car A's speed is 75 miles per hour

Answer:

I got it right in Imagine Math

Step-by-step explanation: