A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean
lifetime, μ, of 12 years. To test the company's claim, a competitor has selected 35 of these batteries at random. The mean
lifetime of the sample is 12.5 years. Suppose the population standard deviation of these lifetimes is known to be 3.5 years.
Is there enough evidence to reject the claim that the mean lifetime of the newest model is 12 years? Perform a hypothesis
test, using the 0.10 level of significance.

The total cost of the bracelet after tax cost addition would be = $21.2

The initial cost of the bracelet = 20$

The percentage of tax = 6%

The cost of tax = 6/100 ×20/1 = $1.2

The total cost of the bracelet after the addition of tax would be = 20+1.2 = $21.2

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Using the inequality rule we know that 11 is greater than -11, (11 > -11).

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.

Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.

So, let's say the inequality equation looks like this: A

Right now, A is valued at

Let p be used to representing the initial number.

P equals 11, so

Let q be used to representing the second number.

Q has a value of -11.

-11 and 11 are both numbers that are greater than zero.

Then, 11 > -11 ... (1)

A has a value of 11 > -11.

Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).

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Correct question:
Is 11 greater than, equal to, or less than -11?

Applying the properties of a rhombus, we have:

AB = BD = CD = AC = 11

A rhombus is a type of quadrilateral, which is a four-sided polygon with four angles. A rhombus is a special type of parallelogram in which all four sides are equal in length.

Therefore, we would create an equation to find the value of  using the properties of rhombus:

2x - 3 = x + 4

2x - x = 3 + 4

x = 7

AB = 2x - 3 = 2(7) - 3 = 11

All sides are equal, therefore:

AB = BD = CD = AC = 11

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The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.

A this double shape's perimeter is the space encircling its outside edge. It is the length of the object's sides. As an illustration, the perimeter of a rectangle is equivalent to the total of its four sides' lengths.

given

Assume that the rectangular field has a width of "x" yards.

The problem states that the field's length is three times its breadth, or three times yards.

The lengths of all the sides make up the rectangle's perimeter, therefore we can write:

[tex]Perimeter = 2 (length + width).[/tex]

In place of the values we hold:

[tex]400 = 2(3x + x)\\400 = 2(4x) (4x)\\400 = 8x\\x = 50[/tex]

The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.

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Francine can type 38 words per minute at this rate.

To find out how many words Francine can type per minute, we need to convert the time she took to type the words into minutes. Since there are 60 minutes in 1 hour, 1 hour and 30 minutes is equivalent to 1 × 60 + 30 = 90 minutes.

Next, we can use the formula:

words per minute = total words / total minutes

where "total words" is the number of words Francine typed (3,420) and "total minutes" is the time she took in minutes (90).

Substituting these values into the formula, we get:

words per minute = 3,420 / 90 = 38

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By using the properties of logarithms, The logarithm "log₅(98)" can be written as log₅(2) + log₅(7) + log₅(7).

We use the "product' and "quotient" logarithmic identities to write log₅(98) in terms of log₅(2) and log₅(7):

⇒ logₐ(b × c) = logₐ(b) + logₐ(c)      ....(product rule)

⇒ logₐ(b/c) = logₐ(b) - logₐ(c)           ...(quotient rule)

First, we write the number "98" as the product of 2 and 7, which is :

⇒ log₅(98) = log₅(2 × 7 × 7),

Using the product rule, we can split this into three logarithms;

⇒ log₅(2 × 7 × 7) = log₅(2) + log₅(7) + log₅(7),

So, we have,

⇒ log₅(98) = log₅(2) + log₅(7) + log₅(7),

Therefore, log₅(98) is equal to log₅(2) + log₅(7) + log₅(7).

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The given question is incomplete, the complete question is

Use the properties of logarithms to write the logarithm in terms of log₅(2) and log₅(7).

The logarithm is log₅(98).

Answer:

25 + x + x = 90

2x = 65

x = 32.5°

The equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

We can observe from the table that the number of books collected increases by 10 for each week.

Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:

b = mw + c

where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).

The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):

10 = 10 * 1 + c

c = 0

Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

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the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).

Weeks (w) Books Collected (b)

1 10

2 20

3 30

4 40

Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?

Step-by-step explanation:

when we are supposed to find each degrees of a certain angle on an equilateral triangle all we have to know is that a triangle is equal to 180° there for each angle or each line is equal to 180° / 3

Suppose you are driving a car with the velocity function represented by the following equation: f(x)= 2x^3-3x^2-12x+1. The derivative would be: f'(x) = 6x^2 - 6x - 12

To find the acceleration of the car at a particular moment, we would need to calculate the derivative of the velocity function f(x). In this case, the derivative would be:

f'(x) = 6x^2 - 6x - 12

The result of this calculation would give us the instantaneous acceleration of the car at a given time x.

In terms of the car's motion, a positive value for f'(x) would indicate that the car is accelerating, while a negative value would indicate that the car is decelerating. The magnitude of the value would indicate the rate of change of the car's velocity, with larger values indicating a more rapid change.

Translated question "A derivative problem from everyday life using the following function: f(x)= 2x^3-3x^2-12x+1"

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Answer:

$23.30

Step-by-step explanation:

We Know

You paid $6.99

The shirt was 70% off

$6.99 = 30%

What was the original price of the shirt?

We Take

(6.99 ÷ 30) x 100 = $23.30

So, the original price is $23.30

Clara's and Stefan's pizzas did not have the same ratio of pepperoni pieces to ham pieces.

For Clara,

The number of pepperoni pieces = 4

The number of ham pieces = 6

The ratio = 4:6 = 2:3

For Stefan,

The number of pepperoni piece = 6

The number of ham piece = 10

The ratio = 6:10 = 3:5

Therefore the ratio of Clara's and Stefan's pizzas is not the same.

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The slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

The slope of the line of best fit on a scatter plot represents the rate of change between the two variables being plotted.

In the case of Keilantra's math teacher, the slope of the line of best fit between student grades on weekly quizzes and the number of hours they say they study represents the change in grades for every additional hour of studying.

For example, if the slope is positive (i.e., the line slopes upward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to increase as well.

On the other hand, if the slope is negative (i.e., the line slopes downward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to decrease.

Therefore, the slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.

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The height of the pole is approximately 10.2 yards tall.

Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (the longest side).

In this case, the pole is the vertical side of the right triangle, the ground is the horizontal side, and the rope is the hypotenuse. Let's call the height of the pole "h". Then we have:

h² + 11² = 15²

Simplifying:

h² + 121 = 225

Subtracting 121 from both sides:

h² = 104

Taking the square root of both sides:

h = √104

Simplifying:

h ≈ 10.2

Therefore, the pole is approximately 10.2 yards tall.

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Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.

Step-by-step explanation:

To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.

Answer:

the afternoon is the right one

second square

add up all the inches and youll see second had bigger number leading to the answer b

The hanger in the illustration will have the value x = 6, and it will remain balanced.

Mathematical expressions with two algebraic expressions on either side of the equals (=) sign are called equations. It demonstrates the equality of the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in each mathematical equation. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved.

Here's the query,

Considering the graph,

The hanger's equation is as follows:

4x= 24

There are 4 numbers here that represent the value of the hanger.

So, x+x+x+x will be 24.

The equation is thus:

4x = 24.

Now, by resolving the equation, we can determine the value of x that balances the hanger:

4x = 24.

When you divide 4 on both sides:

x = 24/4

x = 6.

As a result, the hanger will remain in equilibrium for x = 6.

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The two numbers given by the algebraic expressions are x = 5 and y = 2.

A system of equations is a set of two or more equations that are to be solved simultaneously. In other words, a system of equations represents multiple relationships between variables that need to be solved for at the same time. A system of equations can be solved using various methods, such as substitution or elimination. The goal of solving a system of equations is to find the values of the variables that satisfy all of the equations in the system. One common method for solving systems of linear equations is called Gaussian elimination, which involves manipulating the equations in the system to eliminate one variable at a time until a solution is found.

Let us suppose the numbers as x and y.

From the given statement the mathematical expression can be set as:

y = 2x - 8

x + y = 7

Now. substituting the value of y in equation we have:

x + (2x - 8) = 7

3x - 8 = 7

3x = 15

x = 5

Now, for x = 5 the value of y is:

y = 2(5) - 8

y = 2

Hence, the two numbers are x = 5 and y = 2.

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The complete question is:

The number y is 8 less than 2 times another number x, their sum is 7. Find the number.

The amount of space or volume inside the box but outside the basketball is 6589.44 cm³.

We have to find the volume of the box and volume of the basketball to determine the space outside it.

Box is in rectangular shape.

Volume of the box = 24 × 24 × 24

                                = 13824 cm³

Basketball is spherical in shape.

Volume of the sphere = 4/3 π r³

                                     = 4/3 π (12)³

                                     = 2304π

                                     = 7234.56 cm³

Amount of space inside the box but outside the basketball is,

13824 cm³ - 7234.56 cm³ = 6589.44 cm³

Hence the required space is 6589.44 cm³.

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With additive inverse and by grouping like terms the simplified form of the expression is 6a²-13ab-b².

The given expression is 3a²-5ab+b²-(-3a²+2b²+8ab).

Here,

3a²-5ab+b²+3a²-2b²-8ab

Group like terms, that is

(3a²+3a²)+(-5ab-8ab)+(b²-2b²)

= 6a²-13ab-b²

Therefore, with additive inverse and by grouping like terms the simplified form of the expression is 6a²-13ab-b².

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Answer:

The party opposed to expanding slavery in the United States was the Republican Party. It was actually formed to go against slavery.  

Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

Step-by-step explanation:

Look at the points  (0,-3)  and  ( 3,0)

slope,  m = rise / run =   3 / 3 =  1  

Answer:

1

Step-by-step explanation:

y=x+3

a. The total quantity of employed women among the sample of 7 who are not married yet is the random variable X of interest in this situation. b) Probability = 0.2749.

The number of successes in a defined number of independent trials with two possible outcomes (success or failure) and a constant probability of success are described by a discrete probability distribution called a binomial distribution. The number of trials (n) and the likelihood that a trial will succeed (p) serve as the two parameters that define the binomial distribution.

a. The total quantity of employed women among the sample of 7 who are not married yet is the random variable X of interest in this situation.

b) The probability of 2 women who have never been married is:

P(X = 2) = (7 choose 2) * (0.2)² * (0.8)⁵

P(X = 2) = 21 * 0.04 * 0.32768

P(X = 2) = 0.2749

c) For 2 or fewer have never been married:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X ≤ 2) = (7 choose 0) * (0.2)⁰ * (0.8)⁷ + (7 choose 1) * (0.2)¹ * (0.8)⁶ + (7 choose 2) * (0.2)² * (0.8)⁵

P(X ≤ 2) = 0.0577 + 0.2013 + 0.2749

P(X ≤ 2) = 0.5339

d) The mean is given as:

μ = np

Substitute n = 7 and p = 0.2:

7 * 0.2 = 1.4

Now, the standard deviation is given as:

σ = √(np(1-p)) = √(7 * 0.2 * 0.8) = 1.0198

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Answer: 195 adult tickets and 262 children tickets

Step-by-step explanation:

     Let a be adult tickets and c be children tickets.

We know there are 457 seats.

     a + c = 457

We also know the cost of the tickets and how much money was made.

     $54a + $17c = $14,984

Now, we have a system of equations we can use to solve.

     a + c = 457

     $54a + $17c = $14,984

Lastly, we will graph this system, see attached. The point of intersection, or where the lines intersect, is our answer.

     195 adult tickets and 262 children tickets.

Answer:

Chidden tickets were 262 and adult tickets were 195 tickets

Step-by-step explanation:

Let x = the number of children tickets

Let y = the number of adult tickets.

x + y = 457

17x + 54y = 14984

Use substitution

x + y = 457 Solve for y

y = 457 -x  Substitute 457 -x for y in the equation 17x + 54y = 14984

17x + 54y = 14984

17x + 54(457 -x) = 14984  Solve for x  Distributer the 54

17x + 24678 - 54x = 14984  Combine like terms

-37x = -9694   Divide both sides by -37

x = 262

The number of children tickets.

x + y = 457  Substitute 262 for x and solve for y

262 + y = 457  Subtract 262 from both sides

y = 195

The number of adult tickets.

Helping in the name of Jesus.

The values of b and c include the following:

c = 8

b = 4√3

In order to determine the length of b, we would apply the law of tangent because the given side lengths represent the adjacent side and opposite side of a right-angled triangle.

Tan(θ) = Opp/Adj

Where:

Therefore, we have the following tangent trigonometric function:

Tan(θ) = Opp/Adj

Tan(30°) = 4/b

√3/3 = 4/b.

b = 4√3

From Pythagorean Theorem, the length of c is given by;

c² = (4√3)² + 4²

c² = 48 + 16

c = √64

c = 8

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.