please help in maths

They should quote 150 hours so that they can get 98% of the batteries to meet the guarantee.

Given mean of 140 hours and standard deviation of 4 hours with confidence level=98%.

We have to find the lifespan which they should quote to get 98% confident that their batteries meet the guarantee.

We have to use z test for this .

μ=140 hours and σ=4 hours

Z=X-μ/σ

When p value is 0.98 then from z table z value will be 2.58.

Z=X-140/4

2.58=X-140/4

2.58*4=X-140

10.32=X-140

X=150.32

after rounding off we will get 150 hours.

Hence they should quote 150 hours of lifetime on batteries.

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Answer:

132

Step-by-step explanation:

The area of the rectangle is 240 square inches

The dimensions are given as:

Length = 15 inches

Width = 4/3 feet

Start by converting feet to inches

Width = 4/3 * 12 inches

Width = 16 inches

The area is then calculated as:

Area = Length * Width

This gives

Area = 15 * 16

Evaluate

Area = 240

Hence, the area of the rectangle is 240 square inches

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Answer:

see explanation

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - ( [tex]\frac{5}{2}[/tex] a² + [tex]\frac{3}{2}[/tex] a³ + [tex]\frac{a}{3}[/tex] - [tex]\frac{6}{5}[/tex] ) ← distribute parenthesis by - 1

= [tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - [tex]\frac{5}{2}[/tex] a² - [tex]\frac{3}{2}[/tex] a³ - [tex]\frac{a}{3}[/tex] + [tex]\frac{6}{5}[/tex] ← collect like terms

= ([tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{2}[/tex] a³ ) + (-[tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{5}{2}[/tex] + [tex]\frac{6}{5}[/tex] ) ← change to common denominators

=   ([tex]\frac{2}{6}[/tex] a³ - [tex]\frac{9}{6}[/tex] a³ ) + (- [tex]\frac{3}{4}[/tex] a² - [tex]\frac{10}{4}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{25}{10}[/tex] + [tex]\frac{12}{10}[/tex] ) ← simplify

= - [tex]\frac{7}{6}[/tex] a³ - [tex]\frac{13}{4}[/tex] a² - [tex]\frac{1}{3}[/tex] a - [tex]\frac{13}{10}[/tex]

Answer:

Step-by-step explanation:

[tex]\sf \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\left[\dfrac{5}{2}a^2+\dfrac{3}{2}a^3+\dfrac{a}{3}-\dfrac{6}{5}\right]=[/tex]

               [tex]\sf = \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\dfrac{5}{2}a^2-\dfrac{3}{2}a^3-\dfrac{a}{3}+\dfrac{6}{5}\\\\\\( Combine \ like \ terms)\\\\= \dfrac{1}{3}a^3 -\dfrac{3}{2}a^3 -\dfrac{3}{4}a^2-\dfrac{5}{2}a^2-\dfrac{a}{3}-\dfrac{5}{2}+\dfrac{6}{5}\\\\=\left[\dfrac{1*2}{3*2}-\dfrac{3*3}{2*3}\right]a^3 + \left[-\dfrac{3}{4}-\dfrac{5*2}{2*2}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{5*5}{2*5}+\dfrac{6*2}{5*2}\right]\\\\\\[/tex]

               [tex]\sf ==\left[\dfrac{2}{6}-\dfrac{9}{6}\right]a^3+\left[-\dfrac{3}{4}-\dfrac{10}{4}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{25}{10}+\dfrac{12}{10}\right]\\\\=\dfrac{2-9}{6}a^3+\dfrac{(-3-10)}{4}a^2-\dfrac{a}{3}+\dfrac{(-25+12)}{15}\\\\[/tex]

               [tex]\sf = \dfrac{-7}{6}a^3+ \dfrac{(-13)}{4}a^2-\dfrac{a}{3}+\dfrac{(-13)}{15}\\\\=-\dfrac{7}{6}a^3-\dfrac{13}{4}a^2-\dfrac{a}{3}-\dfrac{13}{15}[/tex]

Answer:

A, C, and D

Step-by-step explanation:

A) (4x + 3) (2x + 6) is equal to 8x² + 30x + 18 because when you multiply two binomials, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, (4x + 3) (2x + 6) can be rewritten as (4x)(2x) + (4x)(6) + (3)(2x) + (3)(6). This can further be simplified to 8x² + 24x + 18.

C) 2(4x² + 15x + 9) is equal to 8x² + 30x + 18 because when you multiply a number by a binomial, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, 2(4x² + 15x + 9) can be rewritten as 2(4x²) + 2(15x) + 2(9). This can further be simplified to 8x² + 30x + 18.

D) 4(2x² + 7x + 4) is equal to 8x² + 30x + 18 because when you multiply a number by a binomial, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, 4(2x² + 7x + 4) can be rewritten as 4(2x²) + 4(7x) + 4(4). This can further be simplified to 8x² + 28x + 16.

Answer:

[tex] < 25 = 56. < { \times 4 \div hwh3 \times }^{?} [/tex]

Answer:

Attached

Step-by-step explanation:

See attached image

Step-by-step explanation:

Exponential can't be odd, because any exponential function has a range that isn't defined for all reals

We can calculated each one out :

7 1/5 x 49 7/5 = 36/5 x 252 / 5 = 9072 / 25
49 2/10 x 7 1/5 = 980 / 10 x 36/5 = 35280 / 50 = 3528 / 5

or a much simpler way is that because both multiplication has 7 1/5 so we only have to compare the other terms, and since 49 7/5 is not equal to 49 2/10 these are not equal. and i didnt notice that till now.

The confidence interval or the mean noise level is (108.17,150.23) and sample standard deviation is 12.52.

Given noise levels:108,133,140,129,136. and confidence level 98%.

We have to find the confidence level and the sample standard deviation of the given data.

Confidence level=98%.

n=5

Sample standard deviation=[tex]\sqrt{(x-x bar)^{2} /n-1}[/tex]

=[tex]\sqrt{626.8/4}[/tex]

=[tex]\sqrt{156.7}[/tex]

=12.52

critical t value at 98% confidence level with degree of freedom(5-1) is 3.747

Standard error= critical t*s/[tex]\sqrt{n}[/tex]

Standard error is the difference between the real values and calculated values.

=3.747*12.52/[tex]\sqrt{5}[/tex]

=46.91/2.23

=21.03

Upper confidence interval=Mean +standard error

=129.2+21.03

=150.23

Lower confidence interval=Mean - standard error

=129.2-21.03

=108.17

Hence the confidence interval is (108.17,150.23) ,sample standard deviation is 12.52 and critical t value is 3.747.

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6. The system of equations has no solution.

7. B. Tables - 15 lbs, chairs - 3.5 lbs.

The values of x and y that makes two equations equal is the solution of a system of equations.

6. 3x + 4y = 12 --> eqn. 1

y = 3 - 3/4x --> eqn. 2

Substitute y = (3 - 3/4x) into eqn. 1 to find x:

3x + 4(3 - 3/4x) = 12

3x + 12 - 3x = 12

12 = 12 [unable to solve further for x]

This means that the system of equations has no solution.

7. t = tables

c = chairs

3t + 5c = 62.5 --> eqn. 1

3t + 2c = 52 --> eqn. 2

Subtract

3c = 10.5

c = 3.5 [chairs]

Substitute c = 3.5 into eqn. 2

3t + 2(3.5) = 52

3t + 7 = 52

3t = 52 - 7

3t = 45

t = 15 [table]

Therefore, the answer is: B. Tables - 15 lbs, chairs - 3.5 lbs.

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Answer:

NO

Step-by-step explanation:

Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.

Given that, ABCD is a quadrilateral, segment AB is congruent to segment CD, ∠1 is congruent to ∠2.

We need to prove that ABCD is a parallelogram.

If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram.

From the given quadrilateral ABCD:

AB=CD (Given)

∠1=∠2 (Given)

AC=AC (Diagonal)

From ASA congruency ΔABC and ΔADC are congruent.

By CPCT, AD=BC and ∠ABC=∠ADC.

Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.

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Binomial distribution will be used to know the probability that the total weight of the samples will exceed 530 pounds.

It is given that the rocket that will return the rock and soil samples to Earth cannot lift off if the total weight of the samples from the rovers exceeds 530 pounds.

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.

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The height of the tree which is the opposite side of the right triangle is 145 meters.

The angle of elevation is 36 degrees.

The situation forms a right angle triangle.

Therefore,

base of the triangle = 200 m

Hence, using trigonometric ratios,

tan 36 = opposite / adjacent

tan 36 = x / 200

x = 200 tan 36

x = 200 × 0.726542528

x = 145.308505601

x = 145.31 m

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Answer:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Step-by-step explanation:

1. The number to the right of 0 is 16.

2. The number that is the least is -15.

3. -15 is smaller than 0 than -9 is.

The proper sequence of steps in implementing the model in Excel presented in the textbook is option b which is organize the data, represent the decision variables, represent the objective function, represent the constraints and represent the bounds on the decision variables.

Given process of implementing the model in Excel and we have to choose the correct process.

The process of implementing the model in Excel is as under:

1) Organize the data: In excel, to organize the data we have to put similar items in the same column. We have to design the data so that all rows have similar items in the same column. We have to keep a range of data separate and leave at least one blank column and one blank row between a related data range.

2) Represent the decision variables: Now we have to represent the decision variables according to which logical function performs tasks.

3)Represent the objective function: It is important because on the basis of this all the logical function perform tasks.

4) Represent the constraints: In excel when we are using solver we have to now represent the constraints of the objective function.

5) Represents the bounds on the decision variables.

Hence the proper sequence of steps in implementing the model in excel is Organize the data, represent the decision variables, represent the objective function, represent the constraints, and represent the bounds on the decision variables.

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The color that has the greatest difference between the theoretical and experimental probability is yellow.

Theoretical probability of each color = number of color in each section / total number of sections

1/5 = 0.2

Experimental probability is based on the result of an experiment that has been carried out multiples times

Experimental probability

Experimental probability of choosing orange = 118 / 625 = 0.19

Difference = 0.2 - 0.19 = 0.01

Experimental probability of choosing purple = 137 / 625 = 0.22

Difference 0.22 - 0.2 = 0.02

Experimental probability of choosing brown = 122 / 625 = 0.20

0.2 - 0.2 = 0

Experimental probability of choosing yellow = 106 / 625 = 0.17

0.20 - 0.1696 = 0.0304

Experimental probability of choosing green = 142 / 625 = 0.23

0.2272 - 0.20 = 0.0272

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The inequality is explained below.

Inequality is a statement of an order relationship between two numbers or algebraic expressions

In this vase, with a number line with two points opposite from each other on a number line, the middle of it is always going to be 0.  

Therefore, both points are the same distance away from 0 just in opposite directions.

That means point Q is always going to equal the negative of point P. An example of this is if point p equals 5, point p equals -5.

This method only works when it is specifically stated that the two points are opposite from each other.

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Answer:

A

Step-by-step explanation:

because for black diamond its 10x+25

and for bunny hill its 5x+50

Answer: a monomial has one term, binomial has 2 terms, and trinomial has 3.

Step-by-step explanation:

using a bit of greek and latin roots, we can observe that all 3 terms have the same suffix of nomial in them. From this, we know that mono means one, bino means two, and tri means 3. Fun fact, there's also polynomial (if you did or didn't know), which is multiple terms more than 3.

The average number of points will be 15 points.

It should be noted that average or mean simply means the total added values fall the data in a set which is then divided by the number of data.

Let the assumed points be 10, 12, 24, 15, 23, and 6.

In this case, the average number of points will be:

= (10 + 12 + 24 + 15 + 23 + 6)/6

= 90/6

= 15 points

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Answer:

So, the correct answer is that as x gets bigger, f(x) moves towards positive infinity.

The measure of angle of ∠BAM (θ) will be 9°. Then the correct option is D.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

ABCD is a rectangle with AB = 3BC.

And M is the mid-point of BC.

2BM = BC

Then the tangent of angle of ∠BAM (θ) will be

tan θ = (BM) / (AB)

tan θ = (BM) / (3BC)

tan θ = (BM) / (3 × 2BC)

tan θ = 1/6

     θ = tan⁻¹ (1/6)

     θ = 9.46°

     θ ≅ 9°

Then the correct option is D.

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The new coordinates will be ( 7,5) and (11,9) , Option A is the correct answer.

The reciprocal function is the inverse of the function, such that 1/ f(x) is the reciprocal of f(x).

The given linear function has pairs of points

(5,7) and (9,11)

The reciprocal of this will be

interchanging of the coordinates

Therefore the new coordinates will be

( 7,5) and (11,9)

Option A is the correct answer.

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Answer:

3/1

Step-by-step explanation:

left one and three up

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of the given letters

J = 0.5 × 8 ft × 6 ft = 24 ft²

K = 8ft × 9ft = 72 ft²

L = 6ft  × 9ft = 54 ft²

M = 10ft × 9ft = 90ft²

N = 0.5 × 8 ft × 6 ft = 24 ft²

U = 0.5 × 16 yd × 15 yd = 120 yds²

V = 0.5 × 16 yd × 15 yd = 120 yds²

W = 16 yd × 16 yd = 256 yds²

V = 0.5 × 16 yd × 15 yd = 120 yds²

X = 0.5 × 16 yd × 15 yd = 120 yds²

A = 5 in × 10 in = 50 in²

B = 10 in × 12 in = 120 in²

C = 5 in × 12 in = 60 in²

D = 5 in × 10 in = 50 in²

E = 5 in × 12 in = 60 in²

F = 10 in × 12 in = 120 in²

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Answer:

[a] 11 feet

[b] 7 feet

[c] 10 feet

Step-by-step explanation:

     See attached. We will pull different details from the graph and information given to solve the different problems,

Answer:

See below

Step-by-step explanation:

Using the equation (instead of the graph....my answer got deleted for using the graph instead of the equation)

When the ball leaves fingers x = 0 :

a)  -1/25 ( 0-10)^2 + 11 =   7 ft

b)    max height will be at - b/2a

        -1/25 ( x^2 -20x +100 ) + 11       <====expand

         -1/25 x^2 + 4/5x +7        a = -1/25       b= 4/5

                then - b/2a =  -  4/5 / (2* -1/25) = 10=x

                     sub in this value of x into the equation to find max height = 11ft

c)  when x = 15

         -1/25 ( 15-10)^2 + 11 =   10 ft

Answer:

The answer is B. Tyrone's unit rate is 1 more mile per hour then John’s unit rate.

Step-by-step explanation:

First of all at the bottom is what the graph and the answer options are.

Hope this helped! :D