a) Express the prime number 31 as the difference of two squares? 31 =​

Step-by-step explanation:

The perimeter of the rectangle is

[tex]P = 2(4x + 2x) = 12x[/tex]

The perimeter of the octagon is

[tex]P = 8(1.5x) = 12x[/tex]

So for x = 1, the perimeter of the rectangle, as well as the octagon, is 12 cm. For x = 2, its 24 cm. For x = 3, it's 36 and so on. So the pattern here is with each integer increase in x, the perimeter increases by 12 cm. Also that the perimeters of both shapes are equal.

Answer:

"a" is the answer because 3x+2 can not be equal to zero

Step-by-step explanation:

Hence, the probability that all four students select the same tire is [tex]\frac{1}{16}[/tex].

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Here given that,

Four students drive to school in the same car. The students claim they were late to school and missed a test because of a flat tire.

On the makeup test, the instructor asks the students to identify the tire that went flat; front driver's side, front passenger's side, rear driver's side, or rear passenger's side.

So, the probability of one person picking the tire is [tex]\frac{1}{4}[/tex].

Here four students so their probability is

[tex]\frac{1}{4(4)}=\frac{1}{16}[/tex]

Hence, the probability that all four students select the same tire is [tex]\frac{1}{16}[/tex].

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Answer:

1¼ cups

Step-by-step explanation:

2¼ ÷ 1/4/5 =

9/4 ÷ 9/5 =

9/4 x 5/9 =

5/4 = 1¼

Answer:

the answer to that is 10(N+14)=9N

Let the number = x

Set up an equation:

10(-150 + x ) = -110

Simplify:

-1500 + 10x = -110

Add 1500 to both sides

10x = 1390

Divide both sides by 10

X = 139

The number is 139

Answer:

The game's expected value is of -$1.5.

Step-by-step explanation:

Expected value:

Probability of each outcome multiplied by the outcome.

One out of 6 sides is 2:

1/6 probability of the player earning 45 - 9 = $36.

5/6 probability of the player losing $9. So

[tex]E = 36\frac{1}{6} - 9\frac{5}{6} = \frac{36 - 45}{6} = -\frac{9}{6} = -1.5[/tex]

The game's expected value is of -$1.5.

The maximum length of the seesaw is option c  4.00 meters.

A right-angled triangle is one in which one of the angles is equal to 90 degrees. A 90 degree angle is called a right angle, which is why a triangle made up of right angle is termed a right angled triangle.

A right-angled triangle has three sides- hypotenuse, base and height. Hypotenuse is the longest and also the opposite side of the right angle of the triangle, base and height of a right triangle are always the sides adjacent to the right angle.

The formula for measuring the hypotenuse is,

Height / Hypotenuse = Sinθ , where θ is the angle opposite to the height of the triangle.

In the given question, the seesaw should make an angle of 30° with the ground and the maximum height it should rise is 2 meters so the height here is 2 meters. So the seesaw will make a right angled triangle.

Height = 2 meters, θ = 30°,

Now using the formula,

2 / Hypotenuse = Sin30°

Rearranging we get,

Hypotenuse = 2 / Sin30°

The value of Sin30° is 1/2 and putting the value we get,

Hypotenuse = 2 / (1/2)

                     = 2 × 2

                     = 4 meters.

Therefore, the maximum length of the seesaw (that is the hypotenuse ) is 4 meters.

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Answer:

€36 = 30.62 pounds sterling

Answer:

$4,966.25

Step-by-step explanation:

3 x 15 = 45

After 15 years, Naomi would have earned a total of 45% interest rate.

3,425 x 1.45 = 4,966.25

Don't use .45 as the multiplier

3,425 x .45 = 1,541.25 <- incorrect

Answer:

M=$75

Step-by-step explanation:

I used M for money that Heather earned.

$20+M=$95

9514 1404 393

Answer:

  16.9

Step-by-step explanation:

The marked sides are the hypotenuse and the one opposite the angle. The relevant trig function is ...

  Sin = Opposite/Hypotenuse

Multiplying by the hypotenuse gives an equation for the opposite side.

  x = 22·sin(50°)

  x ≈ 16.9

Answer:

B, because it goes up by 8 until the last of because the jump from 24 to 30 is 6

Answer:

# of cases: 11

Additional units: 2

Step-by-step explanation:

If each case can hold 8 units, and we want to find the total # number of cases, we have to divide the # of units (8) for one case by the total # units (90).

As you can see, after dividing by 8, we have a total of 11 cases and a remainder of 2 units. The remainder will be the # of additional units because we cannot have another case filled with 8 units.

Answer:

A. <ECF and <BCF

Step-by-step explanation:

Complementary angles are angles that add up to give 90°

m<BCE = m<BCA = 90° (right angles)

m<ECF + m<BCF = m<BCA

m<ECF + m<BCF = 90° (Substitution)

Therefore, <ECF and <BCF are complementary angles.

9514 1404 393

Answer:

  b) 24 miles per gallon

Step-by-step explanation:

The usual metric measure of vehicle fuel efficiency is liters per 100 km. Greater efficiency is indicated by a lower value.

In the US, the measure is usually miles per gallon. Greater efficiency is indicated by a higher value. Since we want the efficiency expressed in miles per gallon, we need to divide distance by fuel consumption.

  (distance)/(fuel used) = (100 km)/(10 L)

  = (100 km)/(10 L) × (1 mi)/(1.6 km) × (3.8 L)/(1 gal) = (100×3.8)/(10×1.6) mi/gal

  = 23.75 mi/gal ≈ 24 mi/gal

Answer:

4999500

Step-by-step explanation:

first 5 = 5000000

second 5 = 500

difference = 5000000-500

By definition of average acceleration,

a (average) = (3.7 m/s - 14.3 m/s) / (2.0 s) = -5.3 m/s²

Answer:

2, 8

Step-by-step explanation:

-1/2x^2 + 5x = 8

-x^2 + 10x = 16 (Multiplying both sides of the equation by 2)

-x^2 + 10x  - 16 = 0

x^2 - 10x + 16 = 0 (changing the signs)

x^2 -2x -8x +16 = 0

x (x-2) -8 (x-2) = 0

(x-2) (x-8)

x-2 = 0

x = 2

or

x -8 = 0

x = 8

Answer from Gauthmath

The values of x are solutions to this equation that is 2, 8

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that the equation as;

-1/2x² + 5x = 8

-x² + 10x = 16

Now Multiplying both sides of the equation by 2;

-x² + 10x  - 16 = 0

Or

x² - 10x + 16 = 0

x² -2x -8x +16 = 0

x (x-2) -8 (x-2) = 0

(x-2) (x-8)

The solution are;

x-2 = 0

x = 2

or

x -8 = 0

x = 8

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The expression equivalent to x(y)^(2/9) is option D.  x [tex]\sqrt[9]{y^{2} }[/tex].

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is x(y)^(2/9).

We have to find the equivalent expressions of this.

We can write the exponent 2/9 as 2 × 1/9.

So, x(y)^(2/9) = x(y)^(2 × 1/9)

We have the power of a power rule,

(xᵃ)ᵇ = xᵃᵇ

Using this rule,

(y)^(2 × 1/9) = (y²)^(1/9)

So, x(y)^(2/9) = x (y²)^(1/9)

Also, we have,

[tex]\sqrt[n]{x}[/tex] = [tex](x)^{\frac{1}{n}}[/tex]

So, (y²)^(1/9) = [tex]\sqrt[9]{y^{2} }[/tex]

x(y)^(2/9) = x [tex]\sqrt[9]{y^{2} }[/tex]

Hence the equivalent expression is  x [tex]\sqrt[9]{y^{2} }[/tex].

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Your question is incomplete. The complete question is as follows.

Problem 4a

The instructions are incomplete. You set up the recursive formula, but didn't ask any question about said formula.

I'll assume that your teacher wants you to list out a few terms. I'll list out the first five terms.

The notation a_1 = 4 is the same as writing [tex]a_1 = 4[/tex] where the '1' is a subscript. It tells us that the first term is 4.

The nth term a_n or [tex]a_n[/tex] is defined as such

[tex]a_n = 2*(1/3 + a_{n-1})\\\\[/tex]

Notice how if we replaced n with 2, then we get

[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_2 = 2*(1/3 + a_{2-1})\\\\a_2 = 2*(1/3 + a_1)\\\\[/tex]

So the second term is directly tied to the first term, or it is dependent on it.

We'll replace a_1 with 4 to get the following

[tex]a_2 = 2*(1/3 + a_1)\\\\a_2 = 2*(1/3 + 4)\\\\a_2 = 2*(1/3 + 12/3)\\\\a_2 = 2*(13/3)\\\\a_2 = 26/3\\\\[/tex]

So the second term is 26/3.

As you can guess, the third term is going to be found in a similar fashion

[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_3 = 2*(1/3 + a_{3-1})\\\\a_3 = 2*(1/3 + a_2)\\\\a_3 = 2*(1/3 + 26/3)\\\\a_3 = 2*(27/3)\\\\a_3 = 2*(9)\\\\a_3 = 18\\\\[/tex]

So 18 is the third term.

We'll repeat for n = 4 to get the fourth term.

[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_4 = 2*(1/3 + a_{4-1})\\\\a_4 = 2*(1/3 + a_3)\\\\a_4 = 2*(1/3 + 18)\\\\a_4 = 2*(1/3 + 54/3)\\\\a_4 = 2*(55/3)\\\\a_4 = 110/3\\\\[/tex]

The fourth term is 110/3.

Lastly, we'll plug in n = 5

[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_5 = 2*(1/3 + a_{5-1})\\\\a_5 = 2*(1/3 + a_4)\\\\a_5 = 2*(1/3 + 110/3)\\\\a_5 = 2*(111/3)\\\\a_5 = 2*(37)\\\\a_5 = 74\\\\[/tex]

The fifth term is 74.

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

Problem 4b

Again, the instructions are missing. I'll assume the same thing as problem 4a.

[tex]a_1 = 6[/tex] is the first term

Plug n = 2 into the first equation to get

[tex]a_n = \frac{n}{a_{n-1}}\\\\a_2 = \frac{2}{a_{2-1}}\\\\a_2 = \frac{2}{a_{1}}\\\\a_2 = \frac{2}{6}\\\\a_2 = \frac{1}{3}\\\\[/tex]

The second term is 1/3.

Repeat for n = 3

[tex]a_n = \frac{n}{a_{n-1}}\\\\a_3 = \frac{3}{a_{3-1}}\\\\a_3 = \frac{3}{a_{2}}\\\\a_3 = \frac{3}{1/3}\\\\a_3 = 3\div\frac{1}{3}\\\\a_3 = 3\times\frac{3}{1}\\\\a_3 = 9\\\\[/tex]

The third term is 9

Repeat for n = 4.

[tex]a_n = \frac{n}{a_{n-1}}\\\\a_4 = \frac{4}{a_{4-1}}\\\\a_4 = \frac{4}{a_{3}}\\\\a_4 = \frac{4}{9}\\\\[/tex]

The fourth term is 4/9

Repeat for n = 5

[tex]a_n = \frac{n}{a_{n-1}}\\\\a_5 = \frac{5}{a_{5-1}}\\\\a_5 = \frac{5}{a_{4}}\\\\a_5 = 5 \div a_{4}\\\\a_5 = 5 \div \frac{4}{9}\\\\a_5 = 5 \times \frac{9}{4}\\\\a_5 = \frac{5}{1} \times \frac{9}{4}\\\\a_5 = \frac{5*9}{1*4}\\\\a_5 = \frac{45}{4}\\\\[/tex]

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

Problem 4c

I'm not much help here for this problem. Not only are the instructions missing, but it's not clear how this sequence is set up. If I had to guess, it's somehow recursively defined. How exactly, I'm not sure. I would ask your teacher for any clarification.

Answer:

Step-by-step explanation:

A) 26*26*26 =17576

B)26*25*24=15600

C)26*26=676

D) 26

Answer:

x=15, y=5

Step-by-step explanation:

x+y=20

x-y=10

Adding both equations;

(x+x) + (y-y) = 20+10

2x = 30

x = 30/2 = 15

Substitute x=15 into x+y=20

y= 20-x = 20-15= 5

Answer:

Z = 1

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 normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Mean (mu) that equals 100 with a standard deviation (sigma) of 18

[tex]\mu = 100, \sigma = 18[/tex]

Sample of 9:

This means that [tex]n = 9, s = \frac{18}{\sqrt{9}} = 6[/tex]

What will be the computed z-score with a sample mean (x-bar) of 106?

This is Z when X = 106. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{106 - 100}{6}[/tex]

[tex]Z = 1[/tex]

So Z = 1 is the answer.

Answer:

12/55

Step-by-step explanation:

Probability is the ratio of the number of possible outcomes to the number of total outcomes.

Given that the bag contains 8 red balls and 3 white balls, the probability of picking a red ball

p(r) = 8/(8+3) = 8/11

Probability of picking a white ball

= 3/11

when a red ball is picked first, the total number of balls reduces to 10 hence the probability that the second ball is white, given that the first ball is red

=8/11 * 3/10

= 24/110

= 12/55

Answer:

0.6

0.308

0.26

0.193

Step-by-step explanation:

0.6

0.308

0.26

0.193

Answer:

graphs 1, 2, 3, and 4, can represent a function

graphs 5 and 6 can not represent a function.

Step-by-step explanation:

If for a given graph of a relationship you can draw a vertical line that intersects the graph in more than one point, then we can conclude that the graph does not represent a function.

Now, if we look at the first four graphs, we can see that no vertical line intersects more than one point, so the first four can represent functions.

The special case here is graph number 2, where we can see a white dot right below a colored dot, and if we draw a vertical line there, the line will touch both points. But, a white dot means that the exact point does not belong to the graph, so if the line passes through there, it will not intersect the graph.

For the last two, this is not the case, in graph 5 and graph 6 we could draw vertical lines that intersect the graphs twice

(any line like x = n, with n < 0, intersects two points in graph 5, while the line x = 0 intersects twice the graph number 6)

So graph 5 and graph 6 can't represent functions.

Answer:

-7

Step-by-step explanation:

x = y - 6

2x = 5y - 9

Use the internet for full steps

x = -7

y = -1

By observing the points you can learn a lot about a function. Concretely [tex]f(x)[/tex] passes through [tex](1,1)[/tex] but [tex]g(x)[/tex] passes through [tex](1,-\frac{1}{2})[/tex] that should give you a hint that [tex]g(x)=-\frac{1}{2}x^2[/tex].

Hope this helps :)