Use the recursive formula to find the first five terms in the arithmetic sequence.

The 45th term of the arithmetic sequence is 178. Option C

Given the arithmetic sequence formula as;

an = 2 + 4(n − 1)

we have n = 45

Let's substitute the value of 'n' into the formula;

a = 2 + 4( 45 - 1)

expand the bracket

a = 2 + 4(44)

a = 2 + 176

a = 178

The 45th term is 178

Thus, the 45th term of the arithmetic sequence is 178. Option C

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the expression equivalent to 2x + 8 is (x+4) + (x+4)

using the commutative property we can say that

2x +8 = x + x + 8

also 2x + 8 = x + 4 + x + 4

hence 2x + 8 = (x+4) + (x+4)

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Answer:

1) 0.10

2) 0.15

3) 0.100

4) No

The rectangular pyramid rises 7 feet in height.

Pyramids are three-dimensional objects with triangle-shaped faces and an all-encompassing polygonal base. It is referred to as a rectangular pyramid if the base of the structure is rectangular. Although all pyramids have a rectangular foundation, they all have triangular edges.

How is the height of the rectangular pyramid determined?

First, we understand that a rectangular pyramid's volume is determined by:

                         [tex]V=B * H / 3[/tex]

The height H is determined by the base B.

When we know the volume is 56 [tex]ft^{3}[/tex] and the base is 24 [tex]ft^{2}[/tex], we can then swap out those two numbers in the volume calculation to get:

                          [tex]56 f t^{3}=24 f t^{2} * H / 3[/tex]

When we solve it for H, we get:

                          [tex]H=3 *\left(56 f t^{\circ} / 24 f t^{2}\right)=7 f t[/tex]

The rectangular pyramid rises 7 feet in height.

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The factored form of a - b is [tex]\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)[/tex].

A monomial is an expression that is the product of constant and non-negative integer powers of x, like [tex]3x^{2}[/tex]..

A monomial is expressed as a product of two or more other monomials when it is factored.

Here,

a = 125

[tex]$b=27 p^{12}$[/tex]

To find: a - b

a - b = 125 - [tex]27 p^{12}$[/tex]

a - b =  [tex]5^{3}-\left(3 p^{4}\right)^{3}$[/tex]

We know that,

[tex]$x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$[/tex]

Finding the factored form of a - b using this method:

[tex]$a - b=\left(5-3 p^{4}\right)\left(5^{2}+5\left(3 p^{4}\right)+\left(3 p^{4}\right)^{2}\right)$[/tex]

[tex]$a-b=\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex]

So, factored form of a - b is [tex]$\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex].

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Answer:

A.

Sample 1 mean: 6.375

Sample 2 mean: 6.375

Sample 3 mean: 6.625

B.

Range of sample means: 0.25

C.

The first and last boxes should be checked, as they are true.

Step-by-step explanation:

To calculate the mean you must add all of the numbers together and then divide the sum by the quantity of numbers. Ex: 3+7+8+3+7+9+6+8 = 51.

51/8 = 6.375.

Answer:

$6.07/hr. if I understand the question properly.  See below.

Step-by-step explanation:

I don't see the question, but will assume we want to find Larisa's base pay.  The $7/hr given is the average for the work sequence noted in the problem.  If this is incorrect, ignore the answer.

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

Let x be Larisa's base salary.  We are told, I think, that in one stretch of time Larisa earned an average of $7/hour.  That was composed of:

Hours  Rate($/hr)

  40           x

    3        1.5x

    6         2x

  49

Her total income over this period would be:

40x +3(1.5x) + 6(2x)  [The hours worked times the pay rate for each period]

Her average income per hour would be:

(40x +3(1.5x) + 6(2x))/49

which we are told is $7/hr.

(40x +3(1.5x) + 6(2x))/49 = 7

40x + 4.5x + 12x = 343

56.5x = 343

x = $6.07/hr

Answer:

x = 5

Step-by-step explanation:

Ashley and Adam spent a total of 31 hours on their projects so: 3x+2+4x-6 = 31

3x+2+4x-6 = 31

7x-4 = 31

7x = 35

x = 5

The total length of school installs fencing around a hexagon-shaped area for an outside concert, is 36 yards.

To find the fencing used by the school:

The distance formula can be given as: [tex]d=\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1})^{2} }[/tex]

First, we must calculate the length of the hexagon using the distance formula.

The hexagon's coordinates, according to the graph, are:

(-5, 4), (0, 6), (5, 4), (6, -2), (0, -4), and (-6, -2)

The distance between (-5, 4), (0, 6): [tex]d=\sqrt{(5)^{2} +(6-4)^{2} }[/tex]

Similarly, the distance between (-5, 4) and (6, -2):

And the distance between (6, -2) and (0, -4):

Amount of fencing required = 2(√29+√37+√40):

Therefore, the total length of school installs fencing around a hexagon-shaped area for an outside concert, is 36 yards.

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The complete question is given below:

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

The school puts up fencing around an area in the shape of a hexagon for an outdoor concert. How much fencing does the school use? Round your answer to the nearest whole yard.

Answer:

36 yards of fencing

Step-by-step explanation:

the reason I know this is because I got it right.

Step-by-step explanation:

the mean value is the sum of all data points divided by the number of data points.

so, in our case we have after 9 pieces of work

(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) / 9 = 46

that means

(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) = 46×9 =

= 414

now we need to add a p10, so that

(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9 + p10) =

= 50 × 10 = 500

only then do we get

(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9 + p10)/10 =

= 50

so,

(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) + p10 = 500

414 + p10 = 500

p10 = 500 - 414 = 86%

the student must at least achieve 86% for the 10th piece of work.

Answer:

A

Step-by-step explanation:

First, we should put this equation in slope-intercept form by isolating y.

Thus, we have:

[tex]2x-\frac{4}{3}y=4\\ -\frac{4}{3}y=4-2x\\ y=\frac{3}{2}x-3[/tex]

The slope-intercept equation shows that the y-intercept is -3 and the slope is 3/2.

Only answer A meets these requirements.

Answer:

(x+1),(x+3),(x+5)

Step-by-step explanation:

may be this answer helps to solve the problems

72 grams tea is needed to prepare 288 fluid ounces of tea.

According to the statement

we have given that the yvette uses 6 grams of tea leaves to make 24 fluid ounces of tea.

And we have to find that the how much grams of tea uses to make 288 fluid ounces of tea.

So, For this purpose,

the given terms are:

6 grams tea = 24 fluid ounces of tea

Now, we use division method

1 gram of tea = 4 fluid ounces of tea

It means

4 fluid ounces of tea prepared by 1 gram of tea.

then

288 fluid tea prepared = ?

So,

288 fluid tea prepared by grams of tea = 288/4

288 fluid tea prepared by grams of tea = 72.

So, 72 grams tea is needed.

So, 72 grams tea is needed to prepare 288 fluid ounces of tea.

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Answer:

C

Step-by-step explanation:

You are dividing BOTH sides by 3.

"The division property of equality states that when we divide both sides of an equation by the same non-zero number, the two sides remain equal."

Answer:

C.  They most likely used an observational study asking students to keep track of their TV habits and weight.

A.  This is an experiment because a treatment was applied to a group.

Step-by-step explanation:

According to our question:

1. The study concluded that there is a relation between watching TV and the weight gain in college freshmen.

Now, this is possible when a group of college students were asked to participate to watch TV for more than 1 hour for a specific amount of time and have a record of their weights.

So, the study is an observational study where the habits and weights of college students were observed.

Hence, option C is correct.

2. The students were divided onto two groups where one group used the computer program and the other did not to check the improvement in the reading levels.

This means that the students were given a procedure to follow during the study in order to see the results..

So, the study is an experiment where a treatment is applied to the group of students.

Hence, option A is correct.

Answer: C

For the people who want only one answer and not 2 for the question if you can only submit one answer :)

Answer:

Step-by-step explanation:

part A:   when you graph both y=7x-9 and y=3x-1 the two lines will intersect this is how you solve the graphing part of the system of equations.

Both of these lines are in slope form (y=mx+b) where m is the slope which is 7 and 3 and b is the y-intercept which is -1 and -9.

part B

7x-9=3x-1

subtract 3x from both sides

4x-9=-1  

add 9 to both sides

4x=8  

divide both sides by 4

x=2,

making y=3x-1 become:

y=3(2)-1=6-1=5,  

the answer is (2,5)

The numbers are 14.42 and 3.6055.

It is the whole which is to be divided into different equal parts. For example, if 10 divided by 2 is 5, then 10 is the dividend here, which is divided into two equal parts whereas 2 is the divisor, the quotient is 5 and the remainder is 0.

We can write the system of equations

x*y=52   .......(1)

[tex]\frac{x}{y}[/tex]=4         ........(2)

We can use substitution to solve

From equation (2) we get,

x = 4y     .......(3)

now substitute in equation (1)

4y*y = 52

[tex]4y^{2} = 52[/tex]

[tex]y^{2} = \frac{52}{4}[/tex]

[tex]y = \sqrt{13}[/tex]

y = 3.605

We can solve for x = ?

from equation (3)

x = 4y

x = 4*3.605

x =   14.42  

Hence, The numbers are 14.42 and 3.6055.

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The z-score corresponding to a sample mean of m = 69 is -0.167

In this problem, we have been given :

population mean (μ) = 70, standard deviation (σ) = 12,  sample size (n) = 4, sample mean (m) = 69

We know that, the Z-score measures how many standard deviations the measure is from the mean.

Also, the formula when calculating the z-score of a sample with known population standard deviation is:

[tex]Z=\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

where z = standard score

μ = population mean

σ = population standard deviation

m = the sample mean

and [tex]\frac{\sigma}{\sqrt{n} }[/tex] is the Standard Error of the Mean for a Population

First we find the Standard Error of the Mean for a Population

σ /√n

= 12 / √4

= 12 / 2

= 6

So, the z-score would be,

⇒ [tex]Z=\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

⇒ [tex]Z=\frac{69-70}{6 }[/tex]

⇒ Z = -1/6

⇒ Z = -0.167

Therefore, the z-score corresponding to a sample mean of m = 69 is -0.167

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The general solution of the given higher-order differential equation. y''' − 9y'' 15y' 25y = 0 is Y= c1e^-x +c2e^5x + c3xe^5x

m^3 -9m^2+15m+25=0

Possible rational roots = 1,-1,5,-5,25

Now on putting these possible rational roots which have been found by the discriminant and hit and trial method,

we will check these roots.

m=-1 comes out to be a root of the equation.

m^2-10m+25=0

(m-5)(m+5)=0

(m-5)^2=0

m=5

So the general equation comes out to be

Y= c1e^-x +c2e^5x + c3xe^5x

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Answer:

0.213

Step-by-step explanation:

→ Convert into binomial information

x ~ B ( 12 , 0.4 )

→ Write down probability required

p ( x = 4 )

→ Evaluate

0.2128

Answer:

1/3.

Step-by-step explanation:

P(event a occurs) = 3/9 = 1/3

P(event b occurs) = 3/9 = 1/3

P(a) ∩ P(b) = 1/3 * 1/3 = 1/9

P(b|a) = P(a) ∩ P(b) / P(a)

          =  1/9 / 1/3

          =  1/3.

well, let's notice the denominators, hmmm so we can use as the LCD say the expression of "rpq", so, let's multiply both sides by the LCD of "rpq" to do away with the denominators.

[tex]\cfrac{2}{r}+\cfrac{1}{p}=\cfrac{1}{q}\implies \stackrel{\textit{multiplying both sides by } ~~ \stackrel{LCD}{rpq}}{rpq\left( \cfrac{2}{r}+\cfrac{1}{p} \right)=rpq\left( \cfrac{1}{q} \right)}\implies 2pq+1rq=1rp \\\\\\ 2pq+rq=rp\implies rq=rp-2pq\implies rq=\stackrel{\textit{common factoring}}{p(r-2q)}\implies \cfrac{rq}{r-2q}=p[/tex]

Angles in quadrilateral add to 360

108 +67 +10 =185

4x + 3x = 7x

185 + 7x = 360

- 185

7x. = 175

÷ 7

x = 25

Check:

4x25 = 100

100 + 67 + 108 = 275

275 + (3x25) = 350 + extra 10 is 360

Hope this helps!

The scatter plot to make reasonable prediction is scatter plot (a)

Before determining the best scatter plot that makes the most reasonable prediction, we need to highlight the following properties:

Using the properties stated above, we have the following highlights:

Scatter plots 3 and 4 cannot be considered because they do not obey the aforementioned properties

Scatter plot 2 do not have about equal points on each sides

Hence, the scatter plot to make reasonable prediction is scatter plot (a)

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Answer:

1.ABC is equilateral triangle because all sides are equal

3.because they are the joined figure of a triangle

Using the Pythagorean Theorem, it is found that the unknown side length of the triangle is of 7.9 cm.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Researching this problem on the internet, we have that:

Hence:

x² + 9² = 12²

x = sqrt(12² - 9²)

x = 7.9 cm.

The unknown side length of the triangle is of 7.9 cm.

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The next step she should take is to use her ruler to join the given point to the point where the arcs intersect.

From this, we can deduce that her next step is to use her ruler to join the given point to the point where the arcs intersect

Thus, the next step she should take is to use her ruler to join the given point to the point where the arcs intersect.

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Step-by-step explanation:

1 meter = 100 centimeter = 1000 millimeter

therefore, 1 cm = 10 mm

4.6 m = 4.6 × 1000 = 4600 mm

88 cm = 880 mm

and so, they cut off

880 mm + 1630 mm = 2510 mm

that means

4600 - 2510 = 2090 mm = 2.09 m

are left.

Answer:

4x+2y = 14  The original equation

2y = 14-4x  Subtract 4x from both sides

2y = -4x+14  Rearrange so x is first

y = -2x+7  Divide everything by 2

Explanation:

The steps above practically explain everything needed, so there's not much to add. The standard form is Ax+By = C while slope intercept form is y = mx+b

In the case of y = -2x+7, we have a slope of m = -2 and y intercept of b = 7. This means (0,7) is one point on the line. Use the slope to move down two and to the right one unit to arrive at (1, 5) as another point on this line.