the lifetime of a certain type of battery is normally dis- tributed with mean value 10 hours and standard deviation 1 hour. there are four batteries in a package. what life- time value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages?

Answer:

answers found in pdf

Step-by-step explanation:

mathaway will help check your answers that what I did.

The possible numbers of additional miles that Lamar can run are all the solutions of the inequality:

0 ≤ x ≤ 15

We know that Lamar will run at most 37 miles this week, and he already did run 22 miles, then the (maximum) distance left this week is:

D = 37mi - 22mi = 15mi

So he can run at most 15 miles, this means that he can run any distance between 0 miles and 15 miles by the end of the week.

So, if we define x as the distance that he will run on the week (in miles), then we can write the inequality:

0 ≤ x ≤ 15

so the possible numbers of additional miles he will run on this week are all the values of x that are a solution for the above inequality.

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El precio final, esto es, el precio con descuento, del bolso es igual a $ 36.000.

En este problema debemos determinar el precio final de un bolso (C') adquirido por un cliente con descuento, igual al precio original (C) menos el descuento, descrito en la siguiente fórmula:

C' = C · (1 + r / 100)

Donde r es la tasa de descuento. Nótese que existe descuento para 0 < r < 100.

Si sabemos que C = 40.000 y r = - 10, entonces el precio final del bolso es:

C' = 40.000 · (1 - 10 / 100)

C' = 36.000

El precio final del bolso es igual a $ 36.000.

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Answer:

145 degrees

Step-by-step explanation:

The side through L is at a 35 degree angle, and the side through N is at a 180 degree angle. Taking the difference, we get 145 degrees.

Answer:

Marcy got 16 wrong.

Step-by-step explanation:

You simply multiply 1 ( from the missed side of the ratio ) by 4 ( how many Marcy got wrong ) which equals 4. Then you do the same to the other side. 4 ( from the "correct" side of the ratio ) by 4 ( how many Marcy got wrong ). 4 x 4 is 16. So, Marcy got 16 wrong.

Answer:

16

Step-by-step explanation:

The ratio is 1:4 means for 1 wrong word, she got 4 words correct. If she has 4 words wrong, multiply that with 4 and you got 16.

Answer: hi

Step-by-step explanation:

Answer:

To find the rate of change in a table, the same process applies:

Step-by-step explanation:

1. Find the coordinates of the given points. It's optional to label them.

2. Find the difference between the output values.

3. Find the difference between the input values.

4. Calculate the ratio between the change in y to the change in x: ΔyΔx.

A wire is cut into two pieces, one piece bent into square and other piece will be bent into circle. Therefore, the minimum length of wire that can be used is 43 m.

The relationships between the radius of a circle and its circumference and area are :

                                           C = 2πr

                                            A = πr²

The relationships between the side length of a square and its perimeter and area are :

                                        P = 4s

                                        A = s²

So, the length of wire will be

                         W= C + P

                        W = 2πr + 4s

Subject to the constraint that the sum of areas is 144 m²:

                                 πr² + s² = 144

Using the method of Lagrange multipliers to find the extremes of wire length, we want to set the partial derivatives of the Lagrangian (L) to zero.

                       L = 2πr + 4s + λ(πr² +s² -144)

                   ∂L/∂r = 0 = 2π +2πλr      ------------------------------- (1)

                   ∂L/∂s = 0 = 4 +2λs           ------------------------------- (2)

                   ∂L/∂λ = 0 = πr² +s² -144    -------------------------------- (3)

Solving for λ, we find,

                   1 +λr = 0      ---------------------------- (4)

                ⇒  λ = -1/r      ----------------------------- (5)

Substituting into equation (2), we get,

                  4 + 2(-1/r)s = 4

               ⇒  s/r = 2  -------------------------------- (6)

This tells us the maximum wire length is that which makes the circle diameter equal to the side of the square.

Substituting the relation s=2r into the area constraint, we find,

                          πr² +(2r)² =144  

                      ⇒  r = √(144/(π+4))

                      ⇒  r= 12/√(π+4) ≈ 2.068965 . . . m

∴ The minimum wire length will be required when the entire area is enclosed by the circle. In that case,

                           πr² = 144

                        ⇒  r = √(144/π)

           and,           C = 2πr

                         = 2π√(144/π)

                         = 24√π ≈42.5388 . . m

rounding up the minimum value 42.5388... in 43.

∴ The minimum wire length will be required is 43 m

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Answer:

you will need to go 80 km per hr

Step-by-step explanation:

2/5 fraction as a decimal is 0.4.

Any number that is expressed as a fraction has two components, the numerator and the denominator. Typically, we divide the numerator by the denominator to convert a fractional number to decimal form. The formula p/q, where q=0, is used to denote fractions. While the decimal numbers, such as 7.575, are created by joining the entire number and fractional parts with a decimal point. 

There are two methods to convert fraction to decimal which are given below:

For 2/5

We will divide them as mentioned above,

2/5 = 0.4

Hence, 2/5 is equal to 0.4 in decimal form.

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neverminding the jumbled wording

how much is 20% of 40?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 40}}{\left( \cfrac{20}{100} \right)40}\implies 8[/tex]

Answer:

1) 1.96

2) 6

3) 4/3

Step-by-step explanation:

think of exponents as repeated multiplication. the exponent is how many times you're going to multiply the number itself by.

1) [tex]1.4^{2}[/tex] is really just 1.4 * 1.4, which you can solve by long multiplication or a calculator to get 1.96

2) for this one, you can rewrite the expression as a fraction. you'll also want to use PEMDAS, starting with the parentheses

[tex]\frac{300}{ 2(0.5+4.5)^{2}}\\\\\frac{300}{2*(5)^2}\\\\\frac{300}{2*25} \\\\\frac{300}{50} = 6[/tex]

3) [tex](\frac{1}{2})^{3} = \frac{1}{2} *\frac{1}{2} *\frac{1}{2} = \frac{1}{8} \\[/tex]

you can rewrite the division as a fraction again, only this time. you can change the subtraction to the reciprocal of the denominator

[tex]\frac{1}{3} / (2*\frac{1}{8} )= \frac{1}{3} / \frac{1}{4} = \frac{1}{3} * 4 = \frac{4}{3}[/tex]

hope this helped!

Answer:

y=4/3x +7

Step-by-step explanation:

4x - 3y = -21

Move 4x to the other side

-3y = -21 -4x

Next divide the other side by -3

y= 7 +4/3x

Move numbers around

y = 4/3x + 7

Systematic errors are consistently in the same direction

In contrast , random errors produce different values in random directions

Random error causes a slight difference of one measurement to from the next. It is quite unpredictable in it's variation during an experiment.

Systematic error always affects measurements by the same proportion, provided that a reading is taken the same way each time. It is predictable

An example that illustrates this difference are

Systematic errors are consistently in the same direction

for example they are always 50g , 1% or 99 mm too large or too small

In contrast , random errors produce different values in random directions

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The compound interest earned by Evelyn in one year is $9.

Evelyn has a bank account. She deposited $90 in her account. She earns 10% interest on her deposited money. The interest earned is compounded annually. We need to calculate the interest earned by her in one year, to the nearest cent.

We need to calculate the compound interest. The formula is given below.

B = p(1 + r)^t

The variables 'B', 'p', 't', and 'r' represent the final amount, the initial amount, the time duration, and the rate of interest, respectively.

B = $90(1 + 0.1)^1

B = $90*1.1

B = $99

The final amount in her bank account after one year is $99. The interest earned is the difference between the final and the initial amount. Let the variable 'I' represent the interest earned.

I = B - p

I = $99 - $90

I = $9

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Lower Limit = 24.52

Upper Limit = 36.28

Error Bound = 5.88

Lower Limit: - The Lower Limit for every class is the smallest value in that class. For example: 5 is a lower lower limit for the set S= { 5,8,42,34}

Upper Limit: - A value that is greater than or equal to every element of a set of data. For example: - { 3,5,11,20,22} is a upper bound of 22.

Given that,

Population Mean,μ = 33.2

sample Mean, χ (x bar) = 30.4

sample Size, n = 25

α (Alpha) = 0.05

Population standard deviation,σ = 15

95% confidence interval:

μ ± z critical σ / √n

Putting the values, we get,

z critical at α0.05 = ± 1.96

30.4 ±1.96( 15/√25) = 30.4 ± 5.88 = (24.52,36.28)

a) Lower Limit = 24.52

b) Upper Limit = 36.28

c) Error Bound =

Margin of Error = z critical × σ /√n

                         =  1.96 × 15/√25

                          = 1.96  × 15/5

                          = 5.88

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The slope of origin (0, 0) with (1, 31); (5, 155), and (9, 279) is 31

The slope of a line will indicate the direction and steepness. It is also defined as the change in the y-coordinate for a corresponding change in the x-coordinate.  

Slope of a line with given points (x₁, y₁) and (x₂, y₂) is  

Here we have

Points (1, 31) (5, 155) and (9, 279)

We need to find slopes between two points

As we know the formula for slope with given points is

Slope, m = (y₂ -y₁) /(x₂-x₁)

Here coordinates of the origin are (0, 0)

The slope between (0, 0) and (1, 31)

=> m =  (31 - 0) /(1 - 0)  = 31/1 = 31

The slope between (0, 0) and (5, 155)

=> m =  (155 - 0) /(5- 0)  = 155/5 = 31

The slope between (0, 0) and (9, 279)

=> m =  (279 - 0) /(9 - 0)  = 279/9 = 31        

Therefore,

The slope of origin (0, 0) with (1, 31); (5, 155), and (9, 279) is 31

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The transformation rule used to transform Triangle PQR to P'Q'R' is; (x, y) → (⁵/₂x, ⁵/₂y)

We are given from the question that the triangle P'Q'R' was transformed from the triangle PQR.

We see from the image that the coordinates of the original triangle PQR are;

P(-1, 1)

Q(2, 0)

R(-1, -2)

We also see that the coordinates of the transformed triangle P'Q'R' are;

P(-5/2, 5/2)

Q(5, 0)

R(-5/2, -5)

Thus, we can conclude that the transformation rule used here is;

(x, y) → (⁵/₂x, ⁵/₂y)

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The expression can be written without negative exponents as 64xy²

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as 6⁴. Here, 4 is the exponent and 6 is the base.

Simplifying exponents is a method of simplifying the algebraic expressions involving exponents into a less complex form in a way that they cannot further be reduced. There are methods in algebra for simplifying exponents with different and same bases that we can use.

Steps to solving basic problems like this are;

Step 1

remove parentheses by multiplying factors.

Step 2

use exponent rules to remove parentheses in terms with exponents.

Step 3

combine like terms by adding coefficients.

Step 4

combine the constants.

In this case, we have an expression;

8√x²y⁴ which can be rewritten without using the square.

8√x²y⁴ = 64xy²

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Answer:

2.5x

Step-by-step explanation:

Given information for width:

Model: 10 in.

Real: 25 in.

Solve: How much times wider is real than model?

To find this, lets divide 25in. by 10in to find the scale factor.

25/10 = 2.5

2.5

We can verify this by multiplying 10 by 2.5

10 x 2.5 = 25

The price range of the Chevrolet HHR retro will be $14,500.

The range of the data is defined as the difference between the maximum value of data and the minimum value of the data.

The given data as:

$8,500, $8,500, $8,500, $9,900, $10,800, 10,800, 11,000, 12,500, $12,500, $13,000, 13,000, $14,500, and $23,000

According to the given information, the required solution would be as:

The maximum value of data = $23,000

The minimum value of data = $8,500

The range of the data = The maximum value of data - The minimum value of data

Substitute the values in the above formula,

The range of the data = 23,000 - 8,500

Apply the subtraction operation to get the answer

The range of the data = 14,500

Therefore, the price range of the Chevrolet HHR retro will be $14,500.

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The question seems to be incomplete the correct question would be:

Mitzi looked up prices of thirteen used Chevrolet HHR retro" tracks in the classified ads and found these prices: 8,500, 8,500, 8,500, 9,900, $10,800, 10,800, 11,000, 12,500, $12,500, $13,000, 13,000, $14,500, and $23,000. Find the range of the data.

Caroline would have $36 more money in her account than Jaxon.

From the question, we have

Caroline amount,

A = P* e^rt

= 900*e^(71*8)/800

= 900*e^(71/100)

=$1830.59

Jaxon amount,

A = P* e^rt

= 900*e^(69*8)/800

= 900*e^(69/100)

=$1794.34

Difference = $1830.59 - $1794.34

= $36.25

= $36 ( to the nearest dollar)

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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Answer:

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

The smaller figure is added, considering the coordinates of the image follow the rule:

Smaller stage is in blue. See attached

Since each side is half the original, the perimeter of the image is half the larger one:

Using theories of Rhode island ,we got that when the British ship Gaspee ran a ground in Rhode island, the local population 1) burned it.

On June 9, Gaspee gave chase to the packet ship Hannah, but the Gaspee ran aground in shallow water on the northwestern side of  bay on what is now Gaspee Point. Her crew were unable to free her and the Dudingston decided to wait for the high tide, which would possibly set the vessel afloat. Before that could happen, however, the band of Providence men led by John Brown decided to act on a "opportunity offered of putting an end to the trouble and the vexation she daily caused."  They rowed out to the ship and boarded at the break of dawn on June 10.

Hence, when the british ship gaspee ran aground in rhode island, the local population 1) burned it.

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Answer:

6(2x - 1)

Step-by-step explanation:

Just look up the answer on the calculator

The product of f(x) and g(x) is -2x² +16x -24.

A function is a relation such that there is only one unique output for every input.

Given that, the functions, f(x) = x-6 and g(x) = -2x + 4.

The value of f(x) × g(x) is,

f(x) × g(x)

= (x-6)(-2x+4)

= -2x²+4x + 12x -24

= -2x² +16x -24

Hence, the product of f(x) and g(x) is -2x² +16x -24.

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The inequality results to f > -3.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

-2f-3.7 < 2.3

Now, solving the inequality

Add 3.7 both side

-2f-3.7 + 3.7 < 2.3 + 3.7

-2f< 6

Divide both side by 2.

-f< 3

f> -3

Hence, the inequality results to f > -3.

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Answer:

also called a tariff.

Step-by-step explanation:

Please give the brainliest.