The lifetime of a certain type of battery is known to be normally distributed with standard deviation =σ17 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime for this type of battery.

The limit Lim x→1 (sinx - sin1)/(x - 1) = cos1

The limit of a function f(x) as x tends to a is the value of the function f(x) as x tends to a. It is written as [tex]\lim_{x \to a} f(x) = L[/tex]

GIven that we require the limit given as  [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1}[/tex]

So, substituting the value of x = 1 into the given equation, we have that

[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{sin1 - sin1}{1 - 1} \\= \frac{0}{0}[/tex]

Since 0/0 is one of the inderterminate forms, we use the L'hopital's rule to find the limit of the given function.

L'hopital's rule states that if [tex]\lim_{x \to a} f(x) = \lim_{x \to a} g(x) = 0[/tex] and f'(x) and g'(x) exist then [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]

Let the variables be

So, since we know that

[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{0}{0}[/tex],

So,  [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]

So, we differentiate both the numerator and denominator and find the limit.

So,

[tex]\lim_{x \to 1} \frac{f'(x)}{g'(x)} = \lim_{x \to 1} \frac{\frac{d(sinx - sin1)}{dx} }{\frac{d(x - 1)}{dx} } \\= \lim_{x \to 1} \frac{cosx - 0}{1 - 0} \\= \lim_{x \to 1}cosx \\= cos1[/tex]

So, [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = cos1[/tex]

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In order to get the total amount $91,000 at the end of the 7 year, the interest rate is 2.2% on compound interest basis.

Compound Interest:

The general form to calculate the compound interest is written as,

A = P(1 + r/n)ⁿˣ

where

A = Accrued amount (principal + interest)

P = Principal amount

r = Annual nominal interest rate as a decimal

n = number of compounding periods per unit of time

x = time in decimal years

Given,

Naomi is going to invest $78,000 and leave it in an account for 7 years. Assuming the interest is compounded daily.

Here we need to find the  nearest hundredth of a percent, would be required in order for Naomi to end up with $91,000.

Here we have to solve for rate r as a decimal

[tex]r = n[(A/P)^{1/nt} - 1][/tex]

r = 365 × [(91,000.00/78,000.00)1/(365)(7) - 1]

r = 0.022022202

Then convert r to R as a percentage

R = r * 100

R = 0.022022202 * 100

R = 2.202%/year

Therefore, the interest rate required to get a total amount of $91,000.00 from compound interest on a principal of $78,000.00 compounded 365 times per year over 7 years is 2.202% per year.

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Step-by-step explanation:

any particular result with 2 dice has a probability of

1/6 × 1/6 = 1/36

a 3 on one die or both simply means at least one 3.

so, if all the 36 different outcomes we are looking at

3 1

3 2

3 3

3 4

3 5

3 6

1 3

2 3

4 3

5 3

6 3

the 3 3 combination can be counted only once !

so, we have 11 desired outcomes out of the possible 36.

so, the probability of getting at least one 3 is

11/36

the sum of at least 10 means the corresponding cases

4 6

5 5

5 6

6 4

6 5

6 6

in this case we don't need to turn this around, because it would be exactly the same outcomes again, and we don't want to count them twice.

so, we have 6 desired outcomes of the 36.

the probability of that is

6/36 = 1/6

The average rate of change of the height as a function of time from 1 to 2 is 96

Rate of change

Rate of change defines the ratio that compares the change in values of the y variables to the change in values of the x variables.

Given,

The height (in feet) of a falling object with an initial velocity of 48 feet per second launched straight upward from the ground is given by h(t) = 16t² + 48t where is time (in seconds).

Here we need to find the average rate of change of the height as a function of time from 1 to 2.

In order to find the average rate of change we need to find the value for the time 1 and time 2.

For, that we have to apply the value on the function,

First, we have to apply the value of t as 1, then we get the value of the function as,

h(1) = 16(1)² + 48(1)

h(1) = 16 + 48

h(1) = 64

Now, we have to apply the value of t as 2, then we get,

h(2) = 16(2)² + 48(2)

h(2) = (16 x 4) + 96

h(2) = 64 + 96

h(2) = 160

Therefore, the average rate of change is,

=> rate of change = (160 -64) / 2 - 1

=> rate of change = 96

Therefore, the average rate of change from 1 to 2 is 96.

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Answer:

[tex]\frac{22}{5}[/tex]

Step-by-step explanation:

To write a mixed number as an improper fraction, you start by converting the "number part" into a fraction.

For example, in this problem 4 is the number part, and we want to rewrite 4 as fraction with a denominator of 5. To do this, we multiply four by 5, which is twenty and put this over 5: [tex]\frac{20}{5}[/tex]. This would be a fraction representing 4(you can check through division).

Next, we need to add [tex]\frac{2}{5}[/tex] to this. [tex]\frac{2}{5} +\frac{20}{5}[/tex] would just be [tex]\frac{22}{5}[/tex] because 20 + 2 = 22.

From the graph, the ordered pair that is included in the solution to the given system is (-6, -2). The correct option is the second option (−6, −2)

From the question, we are to determine the ordered pair that is included in the solution to the given system of inequalities

The given system of inequalities is

y ≥ 2/3(x) + 2

y < -1/3(x) + 1

To determine the ordered pair that is included in the solution, we will graph the given system of linear inequalities.

The graph of the system of linear inequalities is given below.

From the graph, we can observe that (-6, -2) is a solution to the given system of linear inequalities.

Hence, the ordered pair that is a solution is (-6, -2)

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Answer:

Option B: (-6, -2)

Step-by-step explanation:

i took the test xx

For the given passengers per month 6,000 paying $200 each with $1 increase in the ticket price with 100 lose passengers , then the number of passengers per month N as a function of the ticket price x :

N(x) = 26,000 - 100x where  x ≥ 200.

As given in the function,

Number of passengers carried by airlines per month = 6,000

Price of ticket of each passenger = $200

For each $1 increase in the ticket price lose of 100 passengers

Let N(x) be the function representing the number of passengers

And x represents the price of the ticket where  x ≥ 200.

Required function to represent the number of passengers is given by :

N(x) = 6,000 -100 ( x -200)

⇒ N(x) = 6,000 -100x + 20,000

⇒ N(x) = 26,000 -100x where  x ≥ 200

Therefore, for the given passengers per month 6,000 paying $200 each with $1 increase in the ticket price with 100 lose passengers , then the number of passengers per month N as a function of the ticket price x :

N(x) = 26,000 - 100x where  x ≥ 200.

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Option D is correct answer, The given model in the picture shows the division problem as: 0.78 ÷ 3 = 0.26.

What is division?

Along with addition, multiplication, and subtraction, division is one of the four basic mathematical operations. The act of separating anything into smaller groups so that each one has the same amount of items is known as division. It is a mathematical operation that is used to distribute and group things equally.

we can count that, there are 26 cubic blocks in each square in the picture,

10 each are vertically in two rows and 6 are horizontally present.

And there are total of 3 such squares present each with 26 cubic blocks.

So these all totals to 78 cubic blocks which is divided in 3 squares and in each squares there are 26 cubic blocks.

Therefore, the division problem representing this can be written as:

0.78 ÷ 3 = 0.26

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If Cassidy sells all of the popcorn, his profit would be equal to $208.00.

Mathematically, the slope-intercept form of a line can be modeled by using this linear function:

y = mx + b

Where:

In order to determine Cassidy’s profit, we would have to calculate the cost of the containers of popcorn by using this mathematical expression:

Note: the price tag for a container of popcorn is one dollar and fifty cents.

Cost of containers = revenue - total profit

Cost of containers = 1.50(15) - 5.50

Cost of containers = 22.5 - 5.50

Cost of containers = $17.00

Therefore, the linear function which models Cassidy’s profit is given by:

y = 1.50x - 17

If Cassidy sells all of the popcorn, his profit is given by:

Cassidy’s profit, y = 1.50x - 17

Cassidy’s profit, y = 1.50(150) - 17

Cassidy’s profit, y = 225 - 17

Cassidy’s profit, y = $208.00

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Complete Question:

Cassidy is selling popcorn for a fundraiser sale at the price shown.

A photo of a container of popcorn is shown. The price tag reads one dollar and fifty cents.

He purchases a total of 150 containers of popcorn to sell. After he sells 15 containers, he will make a total profit, after his upfront costs, of $5.50. Cassidy’s profit, after upfront costs, can be modeled by a linear function in the form y=mx+b.

What is Cassidy’s profit if he sells all of the popcorn?

HInt: Substitute 150 for x to find the profit if all the popcorn is sold.

The coordinates of pre-image point H is (c) (3, 2)

The graph represents the given parameter

On the graph, we have the coordinate of point H' (i.e. the image) to be

H' = (-3, -2)

The transformation rule is given as

Rotation 180° about the origin

Mathematically, this is represented as

(x, y) = (-x, -y)

This implies that:

H = (3, 2)

So, the coordinates are (3, 2)

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Answer:

-28 meters

Step-by-step explanation:

The speed of the submarine = (-3.5) per minute

Since it's descending, we know the answer will be negative.

The distance covered by the submarine is 8 minutes = (-3.5) x 8 = -28 meters.

Answer:

28

Step-by-step explanation:

-3.5*8

Answer:

No solutions

Step-by-step explanation:

-5y+7/2y=-5-3/2y-4

+3/2y.           +3/2y

-5y+3/2y+7/2y=-5-4

-5y+10/2y=-9

-5y+5y=-9

0=-9

No solutions

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

Let the trapezium be B.

Draw a line from the top of the trapezium to it's base and call the triangle formed B.

The base of is 2cm (8cm - 6cm

The area of the triangle = 40cm² ( 5cm x 4cm x 2cm)

Area of the trapezium =. ½ (base x height)

. = 18cm²

Add area of trapezium and triangle.

 = 40cm² + 18cm² = 58cm²

.

Answer:

A. TPR

B. NM

C. 6

Step-by-step explanation:

1. The triangle NKM matches up with TPR. We also already knew KMN= PRT. So, it was just a matter of aligning the order.

2.  If you flip PRT then TR will match with NM

3. 4x-3=21

4x-3+3=21+3

Simplify: 4x=24

4x/4=24/4

x=6

Answer:

Step-by-step explanation:

The equation that represent the given situation is y = 15x + 70

When she plants 3 stalks, each plant yields 115 ounces of beans

The first point = (3, 115)

When she plants 8 stalks, each plant yields 190 ounces of beans

The second point = (8, 190)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line m = (190-115) / (8-3)

= 75/5

= 15

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Choose one point and substitute the values in the equation

y - 115 = 15(x - 3)

y - 115 = 15x - 45

y = 15x - 45 + 115

y = 15x + 70

Hence, the equation that represent the given situation is y = 15x + 70

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Answer:

can you show me it so i can help

Step-by-step explanation:

Answer: 30 kids are in the math class

Step-by-step explanation: A simple way to solve this question is by knowing divisors. Since 24 is only 80% of X, then look for common divisors betweet 24 and 80% (4) If 6 is 20%, then 30 is 100%

The area between the curve y = x^2 - 3x for x between 1 and 8 is 1343 / 3 square units.

First, let us understand the area under the curve:

A definite integral between two points is used to calculate the area under a curve between them. Integrate y = f(x) between the limits of a and b to determine the area under the curve y = f(x) between x = a and x = b. This area can be estimated by integrating with specified limitations.

We are given:

y = x^2 - 3x

We need to find the area between the curve y = x^2 - 3x for x between 1 and 8.

Now,

Integrate the given function:

Integration y = Integration  x^2 - Integration 3x

y = [x^(2 + 1) / (2 + 1)] ^ 8 _1 - [3x^(1 + 1) / (1 + 1)] ^ 8 _1

y = [x^3 / 3] ^ 8 _1 - [3x^2 / 2] ^ 8 _1

y = [8^3 / 3 - 1^3 / 3] - [3 * 8^2 / 2 - 1 * 8^2 / 2]

y = [512 / 3 - 1 / 3] - [96 - 32]

y = 1535 / 3 - 64

y = 1535 - 192 / 3

y =  1343 / 3 square units.

So, the area is 1343 / 3 square units.

Thus, the area between the curve y = x^2 - 3x for x between 1 and 8 is 1343 / 3 square units.

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The area of the irregular shape is 288 sq. units

Given,

We have to estimate the area of the irregular shape;

Here,

The shape can be broken down into a trapezoid, a rectangle, and a triangle

The total area = 76.5 + 140 + 71.5 = 288 sq. units

Therefore,

The area of the irregular shape is 288 sq. units

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Answer:

×= -7½

Step-by-step explanation:

2x<15

2x<15=0

2x= -15

x= -15/2

x= -7½

The return received after 30 months on an investment of $6000 will be $1800.

According to the question,

We have the following information:

You invest $6000 in a restaurant. The investment has a return of 12% per year.

We know that the following formula is used to find the simple interest on the amount:

Simple interest = principal*rate*time/100

Now, we have the following values in this case which we will put in the formula:

Principal = $6000

Rate = 12%

Time = 2.5 years

Simple interest = (6000*12*2.5)/100

Simple interest = $1800

Hence, the amount received after 30 months on an investment of $6000 will be $1800.

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The expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.

According to the question,

We have the following information,

The given verbal phrase is one-half times a number m plus twenty-five.

Now, we will solve it step by step.

Now, we will first find one-half times a number m. We know that we will replace the word times with multiplication. So, we have the following expression:

m/2

Now, adding 25 to this term, we have the following final expression:

m/2+25

Hence, the expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.

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There are 420 arrangements for seven-digit numbers that can be formed with the digits of 2201213 by permutation.

The term permutation is simply the process of arrangement or selection of objects. It involves each of several possible ways in which a set or number of things can be ordered or arranged.

We can apply the formula for permutation;

[tex]p(n,r) = \frac{n!}{(n - r)!}[/tex]

where n = total number of object and r = number of objects selected.

Total number of digits = 7

number of the digit 2 = 3

number of the digit 1 = 2

number of the digit 0 = 1

number of the digit 3 = 1

so the permutation for the digits 2201213 is calculated as;

7!/(3! × 2! × 1! × 1!)

(7 × 6 × 5 × 4 × 3!)/(2 × 3!) {cancel out 3! with 3! and 4 with 2}

7 × 6 × 5 × 2

420 arrangements

Hence, by permutation, we can say that there are 420 arrangement for which seven-digit numbers can be formed with the digits of 2201213

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Answer:

$80

Step-by-step explanation:

hunter+ kid 1+kid 2+kid 3+kid 4= 60 dollars just for tickets

4 snacks= 20 dollars for snacks

$60+$20=$80

PLEASE MARK BRAINIEST

Sorry I don't have the answer but I can rule out 2.

Step-by-step explanation:

4,2 and 2,0 are not going to be correct because I got them wrong on a quiz I had 2 attempts to take.

So its either 1,-3 or -1,-5.

Hope this helps you.

Answer: $10,252.87

Step-by-step explanation:

Based on the linear model of data, the price of the car that is 10 year old is approximately 10,000.

Linear model.

Basically, the linear model describes the relationship between a dependent variable, y, and one or more independent variables, X. Where the dependent variable is also called the response variable. And the independent variables are also called explanatory or predictor variables.

Given,

Here we have the table of data that contains the fourteen cars were randomly chosen at a used car lot and the age of each car and its sale price.

Now, we have to find the sale price for the 10 year old car.

In order to find the price of the 10 year old car, we have to plot these given table on the graph.

Then we get the graph like the following.

By looking at the graph, the sales price of the 10 year old car is predicted as approximately 10,000,

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Answer:

[tex] \huge{ \boxed{y = - 3x - 12}}[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is given by

[tex]y = mx + c[/tex]

where

m is the slope

c is the y intercept

From the question

m = -3

In order to find c we substitute the point (−5,3) into the equation y = mx + c

We have

[tex]3 = - 3( - 5) + c \\ 3 = 15 + c \\ c =3 - 15 \\ c = - 12 [/tex]

We now substitute c and m into the main equation

We have the final answer as

[tex]y = - 3x - 12[/tex]

Hope this helps you

Answers in bold

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

Explanation:

Always start with what is given. The last statement is the thing we want to prove.

Complementary angles add to 90 degrees. They form a right angle.

When "definition of congruence" is mentioned, we go from two angles being congruent to having them be of the same measure. It's a slight change of notation.

Vertical angles form whenever we cross two lines to form an X shape. The vertical angles are opposite one another, and always congruent.

The substitution property is the idea of replacing one thing with something it is equivalent to. In other words, we plug in the item.

Notice on line 2, if we replace "angle 1" with "angle 4" (valid because the two angles are congruent), and then replace "angle 2" with "angle 3", then we get the result on line 7.

Answer:

1. Given.

2. Definition of complementary angles.

3. Given.

4. Definition of congruent angles.

5. Vertical Angles Theorem.

6. Definition of congruent angles.

7. Substitution Property of Equality.

8. Definition of complementary angles.

Step-by-step explanation:

Statement 1

∠1 and ∠2 are complementary.

Reason:  Given.

Statement 2

m∠1 + m∠2 = 90°

Reason:  Definition of complementary angles.

Complementary angles are two angles that sum to 90°.  Therefore, if ∠1 and ∠2 are complementary, then their measures must sum to 90°.

Statement 3

∠1 ≅ ∠4

Reason:  Given.

Statement 4

m∠1 = m∠4

Reason:  Definition of congruent angles.

Congruent angles are angles with exactly the same measure.  As angle 1 is congruent to angle 4, then their measures are equal.

Statement 5

∠2 ≅ ∠3

Reason:  Vertical Angles Theorem.

Vertical angles are always congruent.  

Statement 6

m∠2 = m∠3

Reason:  Definition of congruent angles.

Congruent angles are angles with exactly the same measure.  As angle 2 is congruent to angle 3, then their measures are equal.

Statement 7

m∠4 + m∠3 = 90°

Reason:  Substitution Property of Equality.

For all numbers a and b, if a=b, then a may be replaced by b in any equation or expression.

As m∠2 = m∠3 and m∠1 = m∠4, replacing them in m∠1 + m∠2 = 90° gives m∠4 + m∠3 = 90°.

Statement 1

∠3 and ∠4 are complementary.

Reason:  Definition of complementary angles.

Complementary angles are two angles whose sum is 90°.  Therefore, if the sum of m∠4 and m∠3 is 90°, this means that ∠4 and ∠3 must be complementary.

Answer:

[tex]y = x^2 - 2x -1[/tex]

Step-by-step explanation:

General Form of a parabola :

[tex]y = a (x - h)^2 + k[/tex]

Solving :

h and k refer to the point of the vertex. In this case, it's (1, -2), so :

[tex]y = a(x - 1)^2 - 2[/tex]

Plug in values for x and y. In this case, they're (0, -1), so :

[tex]-1 = a(0 - 1)^2 - 2\\-1 =a(1) - 2\\1 = a[/tex]

Plug in all values :

[tex]y = ( x - 1)^2 -2[/tex]

Further simplifying :

[tex]y = ( x - 1 )^2 - 2 \\y = (x^2-2x + 1) - 2\\y = x^2 - 2x -1[/tex]