Find the first, fourth, and eighth terms of the sequence.

A(n) = −2 ∙ 5x − 1

Answer:

a)95%  confidence intervals for the population mean of light bulbs in this batch

(325.5 ,374.5)

b)

The calculated value Z = 4 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The manufacturer has not right to take the average life of the light bulbs is 400 hours.

Step-by-step explanation:

Given sample size n = 64

Given  mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

The tabulated value Z₀.₉₅ = 1.96

95%  confidence intervals for the population mean of light bulbs in this batch

[tex](x^{-} - Z_{\frac{\alpha }{2} } \frac{S.D}{\sqrt{n} } , x^{-} + Z_{\frac{\alpha }{2} }\frac{S.D}{\sqrt{n} } )[/tex]

[tex](350 - 1.96\frac{100}{\sqrt{64} } , 350 + 1.96\frac{100}{\sqrt{64} } )[/tex]

[tex](350 -24.5, 350 +24.5)[/tex]

(325.5 ,374.5)

b)

Explanation:-

Given mean of the Population μ = 400

Given sample size n = 64

Given  mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

Null hypothesis : H₀:The manufacturer has right to take the average life of the light bulbs is 400 hours.

μ = 400

Alternative Hypothesis: H₁: μ ≠400

The test statistic

[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z = \frac{350 -400}{\frac{100}{\sqrt{64} } }[/tex]

|Z| = |-4|

The tabulated value   Z₀.₉₅ = 1.96

The calculated value Z = 4 > 1.96 at 0.05 level of significance

Null hypothesis is rejected.

Conclusion:-

The manufacturer has not right to take the average life of the light bulbs is 400 hours.

23x^6=()+(3x^6)=

We move all terms to the left:

23x^6-(()+(3x^6))=0

The value of the unknown in the algebraic equation is 120.

Algebra is the branch of mathematics, that deals with the representation of numbers and values with alphabets and symbols.

An algebraic equation is an equation containing an algebraic term in it.

From the given question,

Let the blank  be represented by x,

23 * 6 = x + (3 *6)

Multiply the numbers on the left side of the equation.

138 = x + (3 *6)

Multiply the expression inside bracket.

138 = x + 18

Solve the equation for x.

x = 138 - 18

x = 120

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Answer:

  the correct choice is marked

Step-by-step explanation:

The zero-crossings at -3 and +3 tell you that one of the factors is the difference of squares:

  (x +3)(x -3) = x^2 -9

The zero crossing at -1 tells you that x+1 is a factor.

So, the polynomial factors as ...

  f(x) = (x^2 -9)(x +1)

Multiplying this out, we get ...

  f(x) = x^2(x +1) -9(x +1)

  f(x) = x^3 +x^2 -9x -9 . . . . . . matches the first choice

Answer:

[tex]A=2400ft[/tex]

Step-by-step explanation:

A rectangle is a closed planer quadrilateral with four  right angles and its opposite sides are the same length. The fence around it including the gates is 200 feet long, so basically they are providing the perimeter of the rectangle. The perimeter of a rectangle is equal to the sum of all its sides. Hence:

[tex]Perimeter=w+h+w+h=2w+2h\\\\Where:\\\\w=Width\\h=Height[/tex]

The ectangular playground is 40 feet wide, so:

[tex]w=40ft[/tex]

Therefore:

[tex]Perimeter=2w+2h\\\\200=2(40)+2h\\\\200=80+2h[/tex]

Solving for h:

[tex]2h=200-80\\\\2h=120\\\\h=\frac{120}{2} \\\\h=60ft[/tex]

The area of a rectangle is equal to the product of two of its contiguous sides, hence:

[tex]A=wh\\\\A=(40)(60)=2400ft[/tex]

I attached you a picture of the rectangle

Answer:

The answer is 10/36 or if you want to simplify, 5/18

Step-by-step explanation:

To solve the area of a rectangle, you need to multiply the sides with each other, so 5/12 x 2/3 is 10/36 (unsimplified) . You multiply the numerators and then the denominators and simplify.

Answer:

93.25% probability that they have taken this steroid

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Positive test

Event B: Taking the steroid.

Suppose the probability of an athlete taking a certain illegal steroid is 10%.

This means that [tex]P(B) = 0.1[/tex]

Given that the athlete has taken this steroid, the probability of a positive test result is 0.995.

This means that [tex]P(A|B) = 0.995[/tex]

Positive test:

99.5% of 10%(If the athlete has taken).

100-99.2 = 0.8% of 100-10 = 90%(Athlete has not taken)

Then

[tex]P(B) = 0.995*0.1 + 0.008*0.9 = 0.1067[/tex]

Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.1*0.995}{0.1067} = 0.9325[/tex]

93.25% probability that they have taken this steroid

Answer:

Part A:  8x + 24

Part B:  Expressions M and N are not equivalent for any value of x because if you do 8x + 24 = 8x + 10, the 8x will cancel out from both sides and you are left with 24 = 10, which is not true, and therefore has no solution.

Step-by-step explanation:

For Part A, to apply the Distributive Property, you multiple the 4 with both terms in the parentheses. So, you do 4(2x) + 4(6). This expression is equal to 8x + 24.

Hope this helped! :)

Answer: (x-1)² + (y-2)² = 6.25

Step-by-step explanation:

The standard equation of a circle is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius. The center of this circle is (1,2) and the radius is 2.5, so the equation of this circle would be (x-1)² + (y-2)² = 6.25

Answer:

(x-1)² + (y-2)² = 6.25

Step-by-step explanation:

Answer:

Parallel, since [tex]\vec u = 2\cdot \vec v[/tex].

Step-by-step explanation:

The relation between both vectors is determined by the use of the dot product, whose expression is:

[tex]\cos \theta = \frac{\vec u \bullet \vec v}{\|\vec u\| \|\vec v\|}[/tex]

Where:

[tex]\cos \theta = 1[/tex] if vectors are parallel to each other and [tex]\cos \theta = 0[/tex] if vectors are orthogonal. Then, norms and dot product are calculated hereafter:

[tex]\|\vec u\| = \sqrt{18^{2}+8^{2}}[/tex]

[tex]\|\vec u\| \approx 19.698[/tex]

[tex]\|\vec v \| = \sqrt{9^{2}+4^{2}}[/tex]

[tex]\|\vec v\| \approx 9.849[/tex]

[tex]\vec u \bullet \vec v = (18)\cdot (9) + (8)\cdot (4)[/tex]

[tex]\vec u \bullet \vec v = 194[/tex]

[tex]\cos \theta = \frac{194}{(19.698)\cdot (9.849)}[/tex]

[tex]\cos \theta = 1[/tex]

The two vectors are parallel to each other, which is also supported by the fact that one vector is multiply of the other one. That is,

[tex]18i + 8j = 2\cdot (9i + 4j)[/tex]

[tex]\vec u = 2\cdot \vec v[/tex]

Answer:

The first choice.

Step-by-step explanation:

6 * 10^8 /  1.5 * 10^-4

= (6/1.5)  * (10^(8 - (-4))

= 4 * 10^12.

Answer:

4 x 1012

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

hundreds  tens  ones

2                   9      9

We look at the tens

It is 5 or higher so we round up the hundreds place

2 becomes 3

300

Answer:

300

Step-by-step explanation:

its obv 300 because 299 is greater than 249 and if it is less than 249 it is rounded to 200.

Answer:

on what

Step-by-step explanation: normaly you have a button that you can have certain characters

Answer:

y = 3/2

Step-by-step explanation:

Answer:

x=4y-6  

Geometric figure: Straight Line

 Slope = 0.500/2.000 = 0.250

 x-intercept = -6/1 = -6.00000

 y-intercept = 6/4 = 3/2 = 1.50000

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    x-(4*y-6)=0  

Step by step solution :

Step  1  :

Equation of a Straight Line

1.1     Solve   x-4y+6  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  x-4y+6  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 3/2 so this line "cuts" the y axis at y= 1.50000

 y-intercept = 6/4 = 3/2  =  1.50000  

Calculate the X-Intercept :

When y = 0 the value of x is -6/1 Our line therefore "cuts" the x axis at x=-6.00000

 x-intercept = -6/1  = -6.00000  

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 1.500 and for x=2.000, the value of y is 2.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 2.000 - 1.500 = 0.500 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  0.500/2.000 =  0.250  

Geometric figure: Straight Line

 Slope = 0.500/2.000 = 0.250

 x-intercept = -6/1 = -6.00000

 y-intercept = 6/4 = 3/2 = 1.50000

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Firstly, [tex]x^{-y} = \frac{1}{x^y}[/tex], so in this case, you multiply [tex](6^{-8})^4[/tex], which equals [tex]6^{-32}[/tex]. Then, plug it into [tex]x^{-y} = \frac{1}{x^y}[/tex] and you get

[tex]6^{-32} = \frac{1}{6^{32}}[/tex], so it's [tex]\boxed{A.}[/tex]

Answer:

5 different ways

Step-by-step explanation:

for the 8

2 and 6

3 and 5

4 and 4

for then tens

5 and 5

4 and 6

Answer:

Step-by-step explanation:

The answer to the volume of a sphere/hemisphere should only be written a cubic unit, because volumes depends on three coordinates to be defined, width, lenght and height, where each coordinates is a length itselft, which multiplied give a cubic length unit, due to the power properties.

For example, imagine that you have all three dimensions in meters, then the product would be [tex]m \times m \times m=m^{3}[/tex].

Therefore, the answer that completes the statment is cubic unit. A volume should be always written in cubic units.

Answer:

The answer to the volume of a sphere/hemisphere should only be written as a function of the radius.

Step-by-step explanation:

An hemisphere is half of a sphere. Its volume can be determined by dividing the volume of a given sphere by 2. The volume is the maximum space or capacity that a 3 dimensional object occupies.

volume of a sphere = [tex]\frac{4}{3}[/tex] [tex]\pi[/tex] [tex]r^{3}[/tex]

volume of an hemisphere = [tex]\frac{2}{3}[/tex] [tex]\pi[/tex] [tex]r^{3}[/tex]

In both cases, the volume is dependent on the value of radius.

The answer to the volume of a sphere/hemisphere should only be written as a function of the radius. Volume is measured in cubic units.

Answer:

$19.24

Step-by-step explanation:

Take 14.25 times 1.35.

The markup rate will be 35% when the cost of the book is $14.25 and sells for $19.237.

The markup rate is computed by dividing a unit's gross profit (its sales price less its cost to create or buy for resale) by its cost.

Barnes and Noble buy a book for $14.25. They mark up the price of the book by 35%.

As per the question, we have

cost = $14.25

markup rate = 35% = 0.35

Let's x represent markup for the book,

markup rate = markup/sale price × 100%

35% = x / $14.25

0.35 = x / $14.25

x = $14.25 × 0.35

Apply the multiplication operation, and we get

x = 4.9875

So sale price = markup + cost

So sale price = $4.9875 + $14.25

So sale price = $19.237

Thus, the markup rate will be 35% when the cost of the book is $14.25 and sells for $19.237.

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Answer:  $0.16

Step-by-step explanation:

Hi, to answer this question we simply have to divide the variable cost ($1,972.50) by the number of miles driven (the variable; 12,000 miles)

Mathematically speaking:

1,972.50 /12000 = 0.16

The cost per mile for Omar to operate his vehicle last year was $0.16

Feel free to ask for more if needed or if you did not understand something.

Answer:1.A 2.C 3.A 4.B

Step-by-step explanation:

1. (answer) a- 257 grams.

2. (answer) c. 1.18 kilometers.

3. (answer) b. 56.

4. (answer) a. 14 7/8 pounds.

Answer:

8. -⅓ cos³x + C

9. sec x + eˣ + C

Step-by-step explanation:

8. ∫ sin x cos²x dx

If u = cos x, then du = -sin x dx.

∫ -u² du

-⅓ u³ + C

-⅓ cos³x + C

9. ∫ (sec x tan x + eˣ) dx

∫ sec x tan x dx + ∫ eˣ dx

These are both standard integrals:

sec x + eˣ + C

Question 8:

∫sinxcos²xdx

∫-u²du (let u = cos(x))

-∫u²du

-u(^2+1)/2+1

-cos^(2+1)(x)/2+1

-1/3cos³(x)

-1/3cos³(x) + C

Question 9:

∫(secxtanx + eˣ)dx

∫sec(x)tan(x)dx + ∫eˣdx (apply sum rule)

sec(x) + eˣ (sec(x)tan(x)dx = sec(x) and eˣdx = eˣ)

sec(x) + eˣ + C

Best of Luck!

Answer: 10,000 steps is 5 miles aka 2,000 feet

Step-by-step explanation:

Question:

1. How many full boxes of lemon bars can Shira fill?

2. How many delicious lemon bars will she be taking home?

Answer:

1. Number of filled box = 21

2. Number of take home = 2

Step-by-step explanation:

Given

Number of lemon bars = 170

Each bar contains 8 lemon bars

Required

(1) & (2)

To calculate the number of boxes Shira can fill, we simply divide the total number of bars by constituents of each bar .

i.e.

Number of filled box = 170/8

Number of filled box = 21.25

But here, we only need the quotient of the division because it represents the filled boxed.

So,

Number of filled box = 21

Calculating the number of take home.

We'll follow the same steps as (1) above but here, we only need the remainder of the division.

When 170 is divided by 8, the remainder is 2.

So, number of boxes she'll take home is 2.

See calculation below

Number of take home = 170 % 8

Number of take home = 2

Answer:

Brown house driveway; larger by 5 feet

Step-by-step explanation:

Lets convert yds to ft

We know 3 ft = 1yd

3*7 = 21

so 7yds = 21 ft

Add the 9 ft

7yds 9ft = 21+9 = 30 ft

The house with the 35 ft driveway is longer by (35-30)  or 5 ft

Answer:

a. Manua Loa

Step-by-step explanation:

brainliest really needed!!

Answer:

A is your answer

Step-by-step explanation:

Answer:

j= 13

just subtract 12 from 25

Start by isolating the j.

Subtract 12 from both sides.

On the left, the 12 and -12 cancel.

On the right, 25 - 12 is 13.

So we have j = 13.

Answer:34%

Step-by-step explanation:I think this is right but I don’t really understand

Answer:

After travelling 360 miles, 15 litres of petrol will be left.

Step-by-step explanation:

If a car can travel 480 miles with a full tank of 60 liters of petrol, it could be said that each liter of petrol allows to travel 8 miles (480/60 = 8). Therefore, since the driver has driven his car for 360 miles, his tank has spent 45 liters of petrol (360/8 = 45). In conclusion, given that the tank has a capacity of 60 liters and that it was full at the time of departure, having spent 45 liters, 15 liters remain in the tank.

Answer:

8u+9v

Step-by-step explanation:

Answer:

8u+9v

Step-by-step explanation:

Answer:

D. 26

Step-by-step explanation:

We have to round to whole numbers before adding.

When approximating to whole numbers, if the number after the decimal is less than 5, you round down to 0 but if it is greater or equal to 5, you round up to 1.

17.36 ≅ 17

8.7 ≅ 9

Therefore:

17 + 9 = 26

Answer: 4800

Step-by-step explanation: 80 x 60 = 4800