A battery producer claimed that the mean lifetime of a battery produced by his factory was 30 hours. A competitor thought that the figure was too high and took 8 batteries at random and the lifetime of each is as follows:
a) Can the claim by the battery producer be accepted at the 5% significant level? b) Can the claim by the battery producer be accepted at the 20% significant level?​

find the area of the rectangle;

w x l = 8 x 10 = 80ft^2

circle;

pi(r)^2

r = 4

pi(4)^2

pi(16) = 50.24

80 + 50.24 = 130.24

The probability density function as calculated from the given data is       fₙ (u)=−ln(u).

​

Y1 and Y2 are independent random variables and both have uniform distribution over the interval (0,1)(0,1).

We need to find out the density function of  U = Y1Y2 using the method of transformations.

Density function of Y1

= 0 or 1

Density function of Y2

= 0 or 1

Therefore joint density function is,

( 0 , 1)   where, 0≤y 1 ≤1,0≤y 2 ≤1

There are 3 steps to find joint density function of Y and U using methods of transformations

Hence, the required probability density function is :

fₙ (u)=−ln(u)

An independent random variable is one that has no effect on the other random variables in your experiment. In other words, it has no bearing on the likelihood of another occurrence occurring.

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The functions that have a vertex at x = 0 are (a) f(x) = |x| and (d) f(x) = |x| - 6

From the question, we have the following parameters that can be used in our computation:

The absolute functions in the options

As a general rule;

A absolute functions can be represented as

f(x) = a|x - h| + k

Where

Vertex = (h, k)

A vertex that has x value of 0 means

(h, k) = (0, k)

So, we have

f(x) = a|x - 0| + k

Evaluate

f(x) = a|x| + k

Looking at the options, we have

f(x) = |x| and f(x) = |x| - 6

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The monthly salary of an employee that has worked for 48 months at the bank is $1226.04. So the option d is correct.

The given table is:

                          Df          SS                     MS                F

Regression          1          555,420          555,420          7.64

Residual              27       1,962,873         72,699

Total                    28        2,518,293

                    Coefficients         Standard Error         t-stat        p-value

Intercept          784.92                322.25                    2.44           0.02

Service             9.19                     3.20                      2.87           0.01

We have to find the monthly salary of an employee that has worked for 48 months at the bank.

Salary = β(0)+ β(1) Service

y = β(0)+ β(1)x

where, Service = x(in months)

Service = y(in $)

From the table

y = 784.92+9.19x

If x=48 months

Then, y = 784.92+9.19(48)

y = 784.92+441.12

y = 1226.04

Hence, the monthly salary of an employee that has worked for 48 months at the bank is $1226.04. So the option d is correct.

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Answer:

C

Step-by-step explanation:

Answer:

B: It translates the graph 9 units to the right.

Step-by-step explanation:

The value 9 has the effect of translating the graph of function f(x) = |x| 9 units to the right. This is because the transformation g(x) = |x - 9| is obtained from f(x) = |x| by subtracting 9 from the argument of the absolute value function. This has the effect of shifting the graph of f(x) to the right by 9 units.

Therefore, the correct answer is B: It translates the graph 9 units to the right.

The meaning of slope of the line in the context of the problem is a student's test score goes up 9 points every time they complete 1 homework assignment.

Slope of line is shows how much a line is inclined with respect to the X axis. In other words, it can also be defined as the change in y coordinates with respect to the change in x coordinates.

Slope of the line can be calculated if two points (x₁, y₁) and (x₂, y₂) are given as,

Slope = (y₂ - y₁) / (x₂ - x₁)

From the graph, take any two points on the line.

For instance, we take initial point (1, 20) and final point (10, 100).

Slope = (100 - 20) / (10 - 1)

          = 80/9

          ≈ 9

From the definition of slope, slope equals 9 means y values goes 9 points up with respect to one unit up in the x values.

Hence we got that a student's test score goes up 9 points every time they complete 1 homework assignment.

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Answer: 3 of the squares should go down then 8 to the right.

Step-by-step explanation:

it just wants you to say how it was translated so take the corresponding points like p and p’ then count of many tiles it move to the right and then down to get from p to p’ you’ll see that it’s 8 right and 3 down.

hope this helps!

The correct answer is $34900.

X : Average amount of loan of student debt by state .

X = N ( μ = $28500 , σ² = ( 3200 )² )

To find : What is the cutoff point that would place a state in top 2.5%

Let it be X

P( X > x ) = 0.025

P(X-μ/σ > X - 28500/3200) = 0.025

P(z >Z ) = 0.025

1 - P(z<Z ) = 0.025

P(z<Z ) = 0.975

φ(z) = 0.975

Z = φ⁻¹(0.975)

X - 28500/3200 = 1.96

X = 34772

i.e; P(X > 34772) = 0.025

Since, it is nearly equal to $34900 option b is correct.

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By observing the figure we can make the pairs as

∠1 ≅ ∠3 ---------(Opposite angles)
∠2 ≅ ∠4 ---------(Opposite angles)
∠5 ≅ ∠7 ---------(Opposite angles)
∠6 ≅ ∠8 ---------(Opposite angles)
∠4 ≅ ∠6 ---------(Alternate angles)
∠3 ≅ ∠5 ---------(Alternate angles)

What are opposite angles and Alternate angles?

Opposite angles are angles that are located opposite each other, with respect to a straight line or a transversal. They are also called vertically opposite angles.

Alternate angles are angles that are located on opposite sides of the transversal and on the same side of the straight line or the transversal. They are also called corresponding angles.

In the given figure,

By observing the opposite angles and alternate angles we can fill the blocks,

∠1 ≅ ∠3 ---------(Opposite angles)

∠2 ≅ ∠4 ---------(Opposite angles)
∠5 ≅ ∠7 ---------(Opposite angles)
∠6 ≅ ∠8 ---------(Opposite angles)

∠4 ≅ ∠6 ---------(Alternate angles)

∠3 ≅ ∠5 ---------(Alternate angles)

Hence, we have found the opposite angles and alternate angles from the figure.

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Answer:

27.29 honestly this is a wild guess

Step-by-step explanation:

7.35% of 147.25 = 10.82

147.25-10.82=136.43

20% of 136.43 = 27.286(27.29)

Answer:

D (-8, -16)

Step-by-step explanation:

(4+x)/2 = -2

4+ x = -2 · 2

4 + x = -4

x = -4 - 4

x = -8

(4 + y)/2 = -6

4 + y = -6 · 2

4 + y = -12

y = -12 - 4

y = -16

The inverse of the equation is y = (5/x) + 1

From the question, we have the following parameters that can be used in our computation:

y = 5/(x - 1)

Start by swaping the positions of x an dy

So, we have the following representation

x = 5/(y - 1)

So, we have

x(y - 1) = 5

Divide both sides by x

y - 1 = 5/x

Add 1 to both sides

y = (5/x) + 1

Hence, the inverse is y = (5/x) + 1

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Answer i just need points

Step-by-step explanation: maybe 90

Answer:

a = 1

h = 4

k = -4

Step-by-step explanation:

Answer:

m∠2 = 110°

m∠4 = 110°

Step-by-step explanation:

Corresponding Angles Postulate

When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Transitive Property of Equality

If any angles are congruent to the same angle, then they are congruent to each other.

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

As line p is parallel to line q, according to the Corresponding Angles Postulate:

⇒ m∠2 = m∠10

According to the Vertical Angles Theorem:

⇒ m∠10 = m∠13

According to the Transitive Property of Equality:

⇒ m∠2 = m∠13

Therefore:

⇒ 8x + 14 = 10x - 10

⇒ 8x + 14 - 8x = 10x - 10 - 8x

⇒ 14 = 2x - 10

⇒ 14 + 10 = 2x - 10 + 10

⇒ 24 = 2x

⇒ 2x = 24

⇒ 2x ÷ 2 = 24 ÷ 2

⇒ x = 12

Substitute the found value of x into the expression for the measure of angle 2:

⇒ m∠2 = 8(12) + 14

⇒ m∠2 = 96 + 14

⇒ m∠2 = 110°

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

As line p is parallel to line q, according to the Corresponding Angles Postulate:

⇒ m∠12 = m∠4

⇒ 15y + 5 = 13y + 19

⇒ 15y + 5 - 13y = 13y + 19 - 13y

⇒ 2y + 5 = 19

⇒ 2y + 5 - 5 = 19 - 5

⇒ 2y = 14

⇒ 2y ÷ 2 = 14 ÷ 2

⇒ y = 7

Substitute the found value of y into the expression for the measure of angle 4:

⇒ m∠4 = 13(7) + 19

⇒ m∠4 = 91 + 19

⇒ m∠4 = 110°

The fixed cost of the plumber is £30 and the hourly rate for the plumber is  £25.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Let the fixed cost of a plumber is y.

Let the number of hours of work done be x.

As per the first condition, that one piece of work takes the plumber 5 hours and costs £155.

Then, the equation according to the statement will be,

y + 5x = £155      (i)

In the second condition, another piece of work takes the plumber 8 hours and costs £230.

Then, the equation according to the statement will be,

y + 8x = £230     (ii)

Now, subtract equation (ii) from the equation for the value of x,

y + 5x = £155

y + 8x = £230

-3x = -75

x = £25

Put x = £25 in equation (i)

y + 5x = £155

y + 5(25) = 155

y = 155 - 125

y = £30.

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(a) The balance be at the end of the year is $502.53.

(b) The Effective annual interest rate is 0.5%.

(c) The Effective annual interest rate must be less than 6%.

What is effective annual interest rate?

The percentage of interest on a loan or financial product that would apply if compound interest built up over a year without any payments would be called the effective interest rate, also known as the effective annual interest rate, annual equivalent rate, or simply effective rate.

Given:

P = $500,  n = 12,  r = 0.5% = 0.005, t = 1

So, the balance be at the end of year is,

[tex]A = P(1+\frac{r}{n})^n^t \\A = 500(1+\frac{0.005}{12})^1^2^*^1 \\A = 500(1.00042)^1^2\\A = 502.53[/tex]

Now to find the effective annual interest rate,

Effective annual interest rate = [tex]= (1+\frac{r}{n})^n-1 = (1+\frac{0.005}{12})^1^2 - 1= 0.005[/tex]

Effective annual interest rate = 0.5%

So, the Effective annual interest rate must be less than 6%.

Hence,

(a) The balance be at the end of the year is $502.53.

(b) The Effective annual interest rate is 0.5%.

(c) The Effective annual interest rate must be less than 6%.

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Answer: It's B

Step-by-step explanation:

It shows that Angle B is congruent to angle g but it actually isnt

Answer:

B.  ∠b ≅ ∠g

Step-by-step explanation:

Supplementary angles

Two angles whose measures sum to 180°.

Linear Pair

Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).

Same-side Interior Angles Theorem

When two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary (sum to 180°).

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

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

Statement A

∠f and ∠h are vertical angles.  Therefore, according to the Vertical Angle Theorem, ∠f ≅ ∠h.

Statement C

As ∠d and ∠h are the interior angles on the same side of the transversal [tex]\ell[/tex], according to the Same-side Interior Angles Theorem, ∠d and ∠h are supplementary.

Statement D

∠a and ∠b are a linear pair, therefore ∠a and ∠b are supplementary.

Therefore, Statement B cannot be supported by the evidence shown.

Ans (A)   P(CB/M) is  0.07

Ans (B)   P(CB ∩ M) is 0.0343

Ans (C)   P(CB) is 0.03634

Ans (D)   P(M/CB) is 0.94386

Let the population be 100.

Therefore,

No. of males (M) = 49

No. of females (F) = 51

No. of colourblind males =

[tex]\frac{7}{100} * 49 = \frac{343}{100} = 3.43[/tex]

No. of colourblind females =

[tex]\frac{0.4}{51} * 100 = 0.204[/tex]

Total colourblind people (CB) = 3.43 + 0.204 = 3.634

Ans (A)

P(CB/M) = P(CB ∩ M)/P(M) = 3.43/49 = 0.07

Ans (B)

P (CB ∩ M) = 3.43/100 = 0.0343

Ans (C)

P(CB) = 3.634/100 = 0.03634

Ans (D)

P (M/CB) = P(M ∩ CB)/P(CB) = 3.43/3.634 = 0.94386

These are the answers.

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The data item that corresponds to the z-score of 2.5 is 450.

What is Standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.

A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance. Although less robust in practice, it is algebraically easier than the average absolute deviation. The fact that the standard deviation is expressed in the same unit as the data, as opposed to the variance, makes it a valuable statistic.

As, x = z×s + u, where z=2.5, s=60, u=300

⇒ x = 2.5×60 + 300

⇒ x = 150 + 300

⇒ x = 450

The data item that corresponds to the given z-score is 450.

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Answer:

Below

Step-by-step explanation:

The first set of graphs is the correct one....it shows Y = constant 18

and shows Z as starting  at 10 (deposit) THEN INCREASING 2 per hour....

  where they cross is 4 hours and charges are the same

The missing angle in the parallel lines is as follows;

When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.

Therefore, let find angle m∠STW .

VX and SU are parallel lines. RY is the transversal line.

Hence,

m∠VWY = 125 degrees

m∠VWY =  m∠STW (corresponding angles)

Corresponding angles are congruent to each other.

Therefore.

m∠STW  = 125 degrees

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The table that represents a linear equation is the first one, and the line is:

y = 5x + 5

To check which table represents a linear function, you need to identify the increases in x, and check that al the increases/decreases in y are constant.

For example, if you look at the last table:

x = 0, 1, 2, 3

y = 1, 2, 4, 8

First x goes from 0 to 1, so 1 unit increase.

y goes from 1 to 2, 1 unit increase.

Then x goes from 1 to 2, 1 unit increase.

y goes from 2 to 4, 2 units increase.

The increase is not constant, thus it is not a linear equation.

The tables 2 and 3 can be discarded because have both increases/decreases.

Table 1 is the one that represents a linear equation:

x: 0, 1, 2, 3

y: 5, 10, 15, 20

Where the increases in y are always of 5 units, and the linear equation is:

y = 5*x + 5

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Answer:

what we cookin ma boi

Step-by-step explanation:

The coordinates of B after the rotation of 90 degrees about the origin is (c) (-5, 1)

The figure of the pentagon missing in the question is added at the end of this solution as an attachment

From the question, we have the following parameters that can be used in our computation:

Coordinate of point B = (1, 5)

Also, from the question, we have the transformation to be

Rotation of 90 degrees about the origin

Mathematically, the rotation of 90 degrees about the origin can be represented as

(x, y) → (-y, x)

Substitute the known values in the above equation, so, we have the following representation

Coordinate of point B after rotation = (-5, 1)

Hence, the coordinate of point B after the rotation is (c) (-5, 1)

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Answer:

The answer is going to be y because you can see that it hits 2 on the y-intercept and -3 on the x-intercept

Step-by-step explanation:

Here is the one that you need

To find the slope of the curve, first differentiate the equation of the curve and substitute the value of x in the result

The slope of the curve is the change in y coordinates with respect to the change in x coordinates of the line

To find the slope of the curve at a given point

First differentiate the given equation of the curve with respect to x

That is dy / dx.

The derivative of the equation of the curve  is the slope of the curve.

In next step substitute the value of x in the slope of the curve

The result will be the slope of the curve at a given point

Therefore, these are the steps to find the slope of the curve

I have answered the question in general, as the given question is incomplete

The complete question is:

How to find the slope of a curve at a given point?

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Answer:   C) 4.123 x 106

Step-by-step explanation: