An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $22.4 for a random sample of 2128 people. Assume the population standard deviation is known to be $9.3. Construct the 98% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.

Step 1: Find the slope

Slope formula = (y2 - y1) / (x2 - x1)

---You can choose any two points when finding the slope!

Point 1 = (-2,-10)

Point 2 = (-1,-3)

Slope = (-3 - - 10) / (-1 - - 2)

Slope = 7 / 1

Slope = 7

Step 2: Find the y-intercept

Now that we have the slope, we'll plug that and one point into slope-intercept form. Then, we'll solve for b.

Slope-Intercept Form: y = mx + b

---m is the slope, b is the y-intercept

Point = (-1, -3)

Slope = 7

-3 = 7(-1) + b

-3 = -7 + b

b = 4

Step 3: Put it all together

Now that we know the slope and y-intercept, all that's left to do is plug them into slope-intercept form.

Slope-Intercept Form: y = mx + b

Slope = 7

Y-Intercept = 4

Line: y = 7x + 4

Correct Answer: A

Hope this helps!

Answer:

1 = C

2 = B

3 = B

4= C

Step-by-step explanation:

Im not 100% sure but.. i tried

Answer:sike i lied i must provide

Step-by-step explanation: its ez just do it

Answer:

Volume V = 18.735 m3

Step-by-step explanation:

hope this helps

The set of prime numbers greater than 11 with the cardinality of 5 is {13, 17, 19, 23, 29}

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

Set = prime numbers

Cardinality = 5

The cardinality implies that the number of elements in the set is 5

5 prime numbers greater than 11 are 13, 17, 19, 23, 29

Hence, the set is {13, 17, 19, 23, 29}

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Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.

The most common symbols used in inequalities are:

">" (greater than): indicates that the value on the left side is larger than the value on the right side.

"<" (less than): indicates that the value on the left side is smaller than the value on the right side.

"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.

"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.

"≠" (not equal to): indicates that the values on both sides are not equal.

Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

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Answer:

x = 30

Step-by-step explanation:

1/2(x+6) = 18

Expand brackets or use distributive law.

1/2(x) + 1/2(6) = 18

1/2x + 6/2 = 18

1/2x + 3 = 18

Subtract 3 on both sides.

1/2x + 3 - 3 = 18 - 3

1/2x = 15

Multiply both sides by 2.

(2)1/2x = (2)15

x = 30

Answer:

30

Step-by-step explanation:

The number of ways to put eight different books in five boxes can be calculated by using probability formula which is 6660 ways.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

No box is allowed to be empty.

So, we can put one book in each box in  mays.

Now remaining 3 books we can put in by  ways

Total number of ways will be

Now calculating the value,

(8!)/(8-5)!  - (5!)/(5-3)!

(8!)/(3!) - (5!)/(2!)

(8*7*6*5*4) - (5*4*3)

6720 - 60

6660

There can be 6660 ways to put eight different books in five boxes.

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(a) The rate of change of the brightness after t days is dB/dt = (2π/4.4) * 0.45 * cos(2πt/4.4).

(b) The rate of increase after one day is  0.22 radians/day.

For the given case the equation for the brightness of cepheid joe is  B(t)=4.2 +0.45sin(2pit/4.4). This equation tells us that the brightness of the star is determined by the sine of the time multiplied by a constant. Since the sine of a number is always changing, the brightness of the star is always changing too.

Therefore, the rate of change of the brightness is given by the derivative of the equation, which is   2π/4.4)*0.45*cos(2πt/4.4), when t is  1 day, we can plug this value into the equation to get the rate of increase after one day, which is dB/dt = (2π/4.4) * 0.45 * cos(2π/4.4) = 0.22 radians/day.

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Answer:

  y = {11, 3, -5, -13}

Step-by-step explanation:

You want the value of y for various values of x, given that y = -4x +3.

Put the value of x where x is in the function rule and do the arithmetic.

  y = -4x +3

  y = (-4)(-2) +3 = 8 +3 = 11 . . . . for x = -2

  y = (-4)(0) +3 = 0 +3 = 3 . . . . for x = 0

  y = (-4)(2) +3 = -8 +3 = -5 . . . . for x = 2

  y = (-4)(4) +3 = -16 +3 = -13 . . . . for x = 4

__

Additional comment

You will notice that the change in y is -4 times the change in x. This means each increase of 2 in the value of x will result in a decrease of 8 in the value of y. Realizing this, you only need to subtract 8 from the previous y-value to get the next one.

9514 1404 393

Answer:

  6.7

Step-by-step explanation:

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides.

  x^2 = 6^2 +3^2 = 45

  x = √45 ≈ 6.7

The missing side length is about 6.7 units.

Answer:

Step-by-step explanation:

hope it helps

To answer this question, we need to find the area of the rectangle with sides 14 cm and 9 cm, and, then, we need to subtract from this area, the area of the semicircle with radius = 7 cm (that is, 14 cm /2 = 7 cm).

Therefore, we have:

1. Find the area of the rectangle:

2. Find the area of the semicircle:

The area of a circle is given by:

Therefore, for a semicircle, we have:

Then, we need to subtract this value from the obtained in calculating the area of the rectangle:

From the question, the answer is option D, 49.07 cm squared.

Answer:

8x+4

Step-by-step explanation:

The sum of all two-digit numbers which are not divisible by 3 is 2240.

What is Arithmetic progression?

An arithmetic sequence or progression is defined as a sequence of numbers in which for every pair of consecutive terms, the second number is obtained by adding a fixed number to the first one.

The sum of two-digit number in AP is Sn = n/2[2a+(n-1)d]

First, sum of  two digit number 10, 11.....99 is

n = 90, a = 10 an= 99

Sn = n/2[2a+(n-1)d]

Sn = 90/2[2(10)+(90-1)1]

Sn = 45[20+89]

Sn= 4905

Now, the sum of two digit number divisible by 3 =

12, 15,...99

a = 12, n = 30, d = 3

Sn = n/2[2a+(n-1)d]

Sn=30/2[2(12)+(30-1)3]

Sn= 1665

Hence, sum of two digit number not divisible by 3 are 4905-1665

=2240

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Answer:

the answer for this question is

A(-3,0)

Answer:

  75% reduction

Step-by-step explanation:

The price dropped by $120. As a percentage of the original price, that is ...

  -$120/$160 × 100% = -75%

The price changed by -75%.

Answer:

75% decrease.

Step-by-step explanation:

The original price is $160 and we went to $40.

That means the price got reduced by $120 in the process.

$120/$160 = 0.75 = 75%.

So in other words, we lost 75% of the price ($120) and got left with 25% of the price ($40).

I hope this helps!

The formula for y in terms of x is y=160​/x^2.

We are given that;

y = 20 when t=4

And t = 8 when x = 2

Now,

To find the value of k by using the fact that y = 20 when t = 4:

20=k⋅4

k=5

Also, y=5t

Next, we use the fact that t is inversely proportional to the square of x. We can write:

t=x2k​

where k is a constant of proportionality. We can find the value of k by using the fact that t = 8 when x = 2:

8=22k​

k=32

Now we know that:

t=x232​

Substituting this into the equation for y:

y=5t=5⋅x232​=160​/x^2

Therefore, by proportions the answer will be y=160​/x^2.

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Answer: 4

Step-by-step explanation:

Answer:4

2+2=4 if I have two apples and pick up two more I now have 4 total

The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.

We have,

In set theory, a proper class is a class that is not a set.

A class is a collection of objects, and a set is a class that can be a member of other classes.

On the other hand, a proper class cannot be a member of another class.

The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.

This means that V cannot be an element of any other class or set within the context of the set theory being considered.

The concept of proper classes is used to prevent paradoxes and contradictions that can arise when unrestricted comprehension is allowed in set theory.

Thus,

The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.

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Answer:

1.2

Step-by-step explanation:

1.Arrange the numbers in order by size.

15,20,25,30,35,41

2.If there is an odd number of terms, the median is the center term.

with these numbers they are even (6 numbers total)

3.If there is an even number of terms, add the two middle terms and divide by 2.

30 ÷ 25=1.2

Answer:

40

Step-by-step explanation:

8 and 5 are factors of 40. (8 x 5 = 40)

Answer:

This a hard one. I think it is 8. XD

Step-by-step explanation:

The algebraic rule describes the translation of quadrilateral HIJK to quadrilateral H'I'J'K' is (x, y) => (x+1, y-8)

Translation is defined as the movement on a straight line

Given: quadrilateral HIJK to that translated H'I'J'K'

To determine the algebraic rule, we need to get the coordinates of  HIJK and H'I'J'K' and then subtract them to get the translation:

H => (x, y) = (4, 6)  |  H' => (x, y) = (5, -2)

I =>  (x, y) = (6, 4)   |  I' =>  (x, y) = (7, -4)

J => (x, y) = (4, 2)   |  J' => (x, y) = (5, -6)

K => (x, y) = (4, 2)  |   K' => (x, y) = (3, -6)

Using points H and H' (you can use any point):

The difference in x is 5-4 = +1 => x+1

The difference in y is -2-6 = -8 => y-8

Therefore, the algebraic rule describes the translation is (x, y) => (x+1, y-8). Option C is the answer

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Answer:

(x, y) => (x+1, y-8)

Step-by-step explanation:

F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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We observe that the

height of the cone is 8 in.

radius of the cone is 2 in.

Volume of a cone = 1/3 π r² h

where R = radius and h = height

Using the formula we get :

Volume = 1/3 π 2 × 2 × 8

= 32 / 3 π cm³

= 33.5 cm³ ( rounded to 10)

Answer:

V=12m

Step-by-step explanation:

V=l×w×h​

V=3×4×1

V=12m

Answer:

4m*3m*3m - 2m*2m*2m

Step-by-step explanation:

The all filled values according to the graph are: a = 4, f(a) = 3a - 5, f(4) = 7, f (4.5)  = 8.5

A linear equation, which is an equation that describes a straight line, is shown graphically on a graph called a linear graph. The relationship between two variables, typically depicted on the x and y axes, is proportional and follows a straight line in this type of graph. In science and mathematics, linear graphs are frequently utilized for data display, scenario modeling, and problem solving. Understanding the relationship between variables, predicting outcomes, and making decisions based on data analysis are all made easier with their assistance.

here, y = 3x - 5 and also x = a

So, x = 4,  then a = 4

f(a) = 3a - 5

f(4) = 3×4 - 5

f(4) = 7

f (4.5) = 3×4.5 - 5

f (4.5)  = 8.5

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The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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The expression can be simplified to obtain as 9 + 6t.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given algebraic expression is 9 + 12t – 6t.

It can be simplified as follows,

9 + 12t – 6t

Here 9 is a constant.

And, the terms 12t and 6t have the same variable t.

Which implies they are like terms.

Since the like terms in an expression can be added to subtracted, the given expression can be simplified as below,

9 + 12t – 6t

⇒ 9 + 6t

Hence, the simplification of the given expression results as 9 + 6t.

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