What is the factored form of the expressions 4x2 - 25?

To find the partial sum S₁7 for the arithmetic sequence with a first term (a) of 3 and a common difference (d) of 2, we can use the formula for the sum of an arithmetic sequence. Therefore, the partial sum S₁7 for the arithmetic sequence with a first term of 3 and a common difference of 2 is 323.

The formula for the sum of an arithmetic sequence is given by:

Sn = (n/2)(2a + (n-1)d)

In this case, we want to find the partial sum S₁7, which means we need to substitute n = 17 into the formula.

Plugging in the values, we have:

S₁7 = (17/2)(2(3) + (17-1)(2))

Simplifying the equation inside the parentheses, we get:

S₁7 = (17/2)(6 + 16(2))

Simplifying further:

S₁7 = (17/2)(6 + 32)

S₁7 = (17/2)(38)

Finally, evaluating the expression, we have:

S₁7 = 17(19)

S₁7 = 323

Therefore, the partial sum S₁7 for the arithmetic sequence with a first term of 3 and a common difference of 2 is 323.

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For the sequence of functions fr : [0,1] → R defined recursively by fo(x) = 1, fn(x) = Vxfn-1(x), n > 1, the sequence converges on [0, 1] and the convergence is uniform.

First, we need to show that the sequence is pointwise convergent. To do that, we take an arbitrary x ∈ [0,1] and use induction on n to prove that fn(x) is convergent.

Let A = sup{f1(x), 1}

Since f1(x) = √x ≤ 1, there exists a decreasing sequence (an) such that f1(x) ≤ an ≤ 1 for all n.

Noting that an → √A (since an is decreasing and bounded below), we have:

fn(x) = √x*fn-1(x) ≤ √A * fn-1(x)

Now, by induction, we have:

f2(x) ≤ √A * f1(x) ≤ √A * a1 ≤ √Afn(x) ≤ √A * fn-1(x) ≤ √A * an-1 ≤ A for all n.

So, by the squeeze theorem, fn(x) is convergent and since this holds for all x, the sequence is pointwise convergent.

We need to show that the sequence is uniformly convergent on [0,1].

Let ε > 0 be arbitrary and let N be such that |an - A| < ε/2 for all n > N.

Let M be such that 1/M < ε/2.

We want to show that |fn(x) - A| < ε for all x ∈ [0,1] and all n > N.

If n ≤ N, then we can write:

|fn(x) - A| ≤ |f

n(x) - an| + |an - A| < ε for all x ∈ [0,1].

So, assume n > N. Then we have:

|fn(x) - A| = |fn(x) - an + an - A| ≤ |fn(x) - an| + |an - A| < ε/2 + ε/2 = ε for all x ∈ [0,1] by the definition of N and M.

Therefore, the sequence is uniformly convergent on [0,1].

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Answer:

26 , 10 , 3

Step-by-step explanation:

Any number larger than 2 will work.

The joint PMF, marginal PMFs, and conditional PMF can be determined for the maximum and minimum outcomes when flipping a biased coin twice. The joint PMF describes the probabilities of different combinations of maximum and minimum outcomes, while the marginal PMFs represent the probabilities of individual outcomes.

The conditional PMF shows the probability of one outcome given another. Detailed calculations and explanations are required to provide a complete answer.
(a) To find the joint PMF px,y(x,y), we need to consider all possible outcomes of flipping the coin twice. Since X represents the maximum outcome and Y represents the minimum outcome, we can determine the probabilities for each combination of X and Y. For example, if X = 1 and Y = 0, it means that the first flip was a tail and the second flip was a head. The joint PMF will assign probabilities to all possible combinations of X and Y.
(b) The marginal PMFs px(x) and py(y) represent the probabilities of individual outcomes for X and Y, respectively. To find px(x), we sum up the probabilities of all combinations where X takes the value x. Similarly, to find py(y), we sum up the probabilities of all combinations where Y takes the value y.
(c) The conditional PMF Pxy(x|y) provides the probability of X taking a certain value given that Y has a specific value. It can be obtained by dividing the joint PMF px,y(x,y) by the marginal PMF py(y) for each y value.
To provide a more detailed answer with calculations and sketches, specific values for p, the probability of a head, are needed.

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Answer: 6773.27

Step-by-step explanation: volume formula for the cone is pie(radius)^2(height/3) just plug in your information into the formula and viola

The t-statistic of the slope coefficient is -19 is the answer.

Suppose a regression was run between y and one x variable.

The coefficient of the x variable (slope coefficient) was -0.76.

The associated standard error of the slope coefficient was 0.04, and p value of the slope coefficient was 0.

The t stat of the slope coefficient is -19.

To find the t-statistic value, divide the slope coefficient by the standard error.

This is given as t = slope / SE.

We have the values of the slope and the SE in the problem.

Substitute these values to get the t-statistic.t = -0.76 / 0.04 = -19

From this calculation, we can see that the t-statistic of the slope coefficient is -19.

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Answer:

4x - 2y can be simplified as 2(2x - y)

Answer: $45

Step-by-step explanation:

Let the original price be x.

Since there was a discount of 20%, it means the person bought the frying pan at (100% - 20%) = 80% of the original price. This can then be formed into an equation as:

80% × x = $36

0.8 × x = $36

0.8x = $36

x = $36/0.8

x = $45

The original price was $45

0%

Where rolling a pair of die, a pair is two so there is two die. Now we have to look at the sample space for the two dice.

1 2 3 4 5 6

1 l 2l 3l 4l 5l 6l 7l

2l 3l 4l 5l 6l 7l 8l

3l 4l 5l 6l 7l 8l 9l

4l 5l 6l 7l 8l 9l 10l

5l 6l 7l 8l 9l 10l 11l

6l 7l 8l 9l 10l 11l 12l

there is 36 outcomes in the sample space none of them include getting 15.

Answer:

Prism B has a larger base area

Step-by-step explanation:

Given

Base dimensions:

Prism A:

Lengths: 6cm, 8cm and 10cm

Prism B:

Lengths: 5cm and 5cm

Required [Missing from the question]

Which prism has a larger base area

For prism A

First, we check if the base dimension form a right-angled triangle using Pythagoras theorem.

The longest side is the hypotenuse; So:

[tex]10^2 = 8^2 + 6^2[/tex]

[tex]100 = 64 + 36[/tex]

[tex]100 = 100[/tex]

The above shows that the base dimension forms a right-angled triangle.

The base area is then calculated by;

Area = 0.5 * Products of two sides (other than the hypotenuse)

[tex]Area = 0.5 * 8cm * 6cm[/tex]

[tex]Area = 24cm^2[/tex]

For Prism B

[tex]Lengths = 5cm\ and\ 5cm[/tex]

So, the area is:

[tex]Area = 5cm * 5cm[/tex]

[tex]Area = 25cm^2[/tex]

By comparison, prism B has a larger base area because [tex]25cm^2 > 24cm^2[/tex]

Answer:

graph is shown

Step-by-step explanation:

slope: -1/3

y intercept: (0,-17/3)

Answer:

2

Step-by-step explanation:

The Intial value, also know as the y-intercept, is where the line crosses line y.

Therefore, looking at the graph, your initial value is 2.

Answer:

|-2| = 2

Step-by-step explanation:

Answer:

y=2x+4

Step-by-step explanation:

y=2x+4

Answer:

y = 2x + 4

Step-by-step explanation:

The formula for the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is where the line passes through the y-axis, which would be (0,4), which is positive. To find the slope, find where the line passes through a point, and then count how many units there are till the next point. For this example, you could start from the y-intercept, (0, 4) and to get to the next point, you will go up 2 units, and the right 1 unit. This means that the slope is 2/1 (because it's rise over run) which is the same as 2. So just plug it into the equation, and you get y = 2x + 4.

I hope this helped! :)

Temperature is an average measure of the kinetic energy of particles of matter.

Temperature can be in negative degrees.

The temperature at the end of the day is -3°F.

Temperature is an average measure of the kinetic energy of particles of matter.

The Celsius scale is generally used for measuring most temperatures.

The Fahrenheit (°F) temperature scale is also used.

We have,

The temperature at the beginning of the day = 6°F

The temperature drop by the end of the day = 9°F

Temperature can also be in negative degrees.

The temperature at the end of the day:

= 6°F - 9°F
= -3°F

Thus the temperature at the end of the day is -3°F.

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Answer:

Write abt a poem you like or something

Step-by-step explanation:

Answer:

1: x = 6

2: There is no solution. Sorry. (because the ending equation will be 0 = 7)

3: I can't see the other part of the equation, I need to see what the fraction is in order to solve it. If you can retake the picture, I can edit my response :)

Step-by-step explanation:

#1: 3(x-1) is pretty much just 3x-3. Simple.

Now, your equation becomes 3x-3 = 2x+9.

Arrange them so that the like terms are together.

Since you will be taking the 2x from 2x+9 over to the other side, it becomes 3x-2x-3 = 9.

Now, bring the 3 over to the side with the 9.

x = 6.

#2: Same as before, -2(x+1) is (-2x) - 2.

So, -2x-2 = -2x+5.

As I said before, you need to group the like terms together.

-2x and -2x go together, and -2 and 5 go together.

-2x+2x=5+2

0=7.

There is no solution.

#3: Like the other two, 4(x-1) is 4x-4. As for the other part, I cannot see the fraction before (x-8).

Answer:

Step-by-step explanation:

3

Answer:

>

Step-by-step explanation:

sqrt{17} > sqrt{11}

Answer: >

Step-by-step explanation: the square root of 17 is going to be larger than the square root of 11. since you add 3 to both equations, that is all you have to worry about.

Answer:

17x

Step-by-step explanation:

so first 2x is 2 x x = 2x

then +10 =12x then 5 + x = 5x so 5x + 12x = 17x

Answer:

----------------------

DC is the radius and its length is:

DC is the perpendicular bisector of EF.  Hence the half of the segment EF is the leg of a right triangle with the hypotenuse of EC = DC = 70 and other leg of 50 units.

Using the Pythagorean theorem, find the length of EF:

Answer: hello your question is incomplete below is the missing part

Based on your simulation, what is the average amount of error you expect to see in the sample proportions in this situation?

answer : 0.0458

Step-by-step explanation:

In 2005 - 2007 : 30% of all current smokers started smoking before the age of 16

n ( sample size ) = 100 smokers

The average amount of error expected can be calculated as

[tex]\sqrt{pq/n}[/tex]  = [tex]\sqrt{0.3*0.7/100}[/tex] = 0.0458

where : p = 0.3

             q = 0.7

              n = 100

Using a Normal distribution table , the value of the given probability is 0.0359

Find the row corresponding to the tenths digit of -1.8, which is -1.8 rounded to -1.9.

Find the column corresponding to the hundredths digit of -1.8, which is -1.8 rounded to -1.80.

The value in the intersection of the row and column is the probability of Z being less than -1.8.

Therefore, we find that the probability is approximately 0.03593

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Given: What should be done to both sides of the equation in order to solve y - 4.5 = 12.2?

To Find: What should be done on both side of equation.

Solution:

Step1 : Add 4.5 both sides so that +4.5 gets eliminated from LHS ,

=> y-4.5+4.5=12.2+4.5

=> y = 16.7

Hence the value of y is 16.7.

To need to solve the equation we need to add 4.5 on both sides and the value of y will be 16.7.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In other words, the equation must be constrained with some constraints.

As per the given equation,

y - 4.5 = 12.2

Add 4.5 on both sides of the equation,

y - 4.5 + 4.5 = 12.2 + 4.5

y = 16.7

Hence "To need to solve the equation we need to add 4.5 on both sides and the value of y will be 16.7".

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Answer:

For two fractions to be proportional, they must be equivalent. 32=1.5 and 188=2.25 , so these fractions are not proportional.

Step-by-step explanation:

Answer:

I think the correct answer is....... The measure of center for table 1 is 61, 62, 58, and 57 inches. The most kids had the same number of inches in this category.

I'm not 100% sure so try at your own risk

Have a great day!

The center of measures of table 1 height (task1) are Mean of heights of siblings are 58.29. Median of the height of 24 siblings are 61.5. Mode of the height 24 siblings 57,58,61,62 are the heights in inches.

Measures of center of data set is also "a way of describing data set. The two most widely used measures of the center is mean and median".

Mean is the process of "adding all values and then divided by total number of values".

Median is the "process of arranging data value in ascending or descending order and then divided data set into two if 'n' is odd then middle  point is the median or if 'n' is even then sum of two mid value and then divided by two".

Mode can be one, "two or more in the given data set. The number or data point which have more frequency is taken as mode".

According to the question,

Measures of center is the most appropriate for the data in Table 1 (Height) in Task 1.

Heights in inches                       Frequency

         55                                             1

          57                                              3

          58                                             3

          59                                              2

          60                                              1

          61                                               3

          62                                              3

          63                                              2

          64                                              2

          65                                              2

          66                                              1

           67                                              1

Total number of frequency = N = 1+3++3+2+1+3+3+2+2+2+1+1 =24. Number of siblings n =12

Mean = ∑(Height of inches × Frequency of height)/Total number of frequency.

= [tex]\frac{(55*1+57*3+58*3+59*2+60*1+61*3+62*3+63*2+64*2+65*1+66*1+67*1)}{24}[/tex]

= [tex]\frac{1399}{24}[/tex]

= 58.29.

Mean of heights of siblings are 58.29

Median of the height of 24 siblings are sum of 61 and 62 divided by 2.

= [tex]\frac{61+62}{2}[/tex]                           [since 'n' is odd]

=61.5.  

Median of the height of 24 siblings are 61.5.

Mode of the height 24 siblings 57,58,61,62 are the heights in inches.

Hence, the center of measures of table 1 height (task1) are Mean of heights of siblings are 58.29. Median of the height of 24 siblings are 61.5. Mode of the height 24 siblings 57,58,61,62 are the heights in inches.

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Answer: i don’t know what that is

Step-by-step explanation:

Answer:

15 pizzas.

Step-by-step explanation:

The rate is 3 pizzas for every 7 people. If there are 35 people at the party (7 times 5), the amount of pizzas you should buy is 15 pizzas (3 times 5). Hope I  explained that well (^^'')