Suppose that an Internal Revenue Service (IRS) representative claims that the average tax deduction for medical care is $1,250, and assume that this variable is normally distributed. A taxpayer who believes that the deduction might be less than $1,250 decides to randomly sample 12 families who have an average deduction of $934 with a standard deviation of $616. a. What are the null and alternative hypotheses? b. What is the value of the test statistic, i.e. t-stat, in this example? Show your work. c. What is the p-value associated with this test statistic? (HINT: you have less than 30 observations so you will need to use t-table to obtain critical values.) d. What can you conclude at the 10-percent level of significance? What can you conclude at the 5-percent level of significance? Explain. (HINT: you have less than 30 observations so you will need to use t-table to obtain critical values.)

Using the distance formula, the length of segment PQ is:

C. √68 units

The distance formula is given as:

d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Segment PQ has the following endpoints:

P(-2, 3)

Q(6, 1)

To find the length of segment PQ using the distance formula, we can apply the formula, where:

\((x_1, y_1)\)are the coordinates of point P

\((x_2, y_2)\) are the coordinates of point Q.

Given:

P(-2, 3) = \((x_1, y_1)\)

Q(6, 1) = \((x_2, y_2)\)

Let's substitute the values into the formula:

PQ = √[(6 - (-2))² + (1 - 3)²]

PQ = √[(8)² + (-2)²)

PQ = √(64 + 4)

length of segment PQ = √68 units

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An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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The two z values are -1.96 and +1.96 this means that option A is the correct choice.

From the given information we know that P(-z<Z or Z>z) = 5% = 0.05.

Then the table (area under the normal curve) the probability of values smaller than a certain z-score of the standard normal distribution.

Now the standard normal distribution is symmetric about 0.

P(-z<Z)=P(-z<Z or Z>z)/2

P(-z<Z)=0.05/2

P(-z<Z)=0.025

Here we have to determine the corresponding z-score in area under the normal curve table.

The corresponding z-score z is then given in row/column title of area under the normal curve table which corresponding to a probability of 0.025 or the probability closest.

-z = -1.96

Two z -values , positive and negative that are equidistance from the mean so that the area in two tailed total 5% are,

= ±1.967 = ±1.96

z=-1.96,+1.96

Therefore, the correct option is A.

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Answer:

1.222

Step-by-step explanation:

The solution is given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Remember that the Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

According to this, the correct answer is: given below.

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Answer:

Brand A

Step-by-step explanation:

Brand A has a box of 25 forks for 1.99

Take the price per fork

1.99 /25 = .0796

              .08 per fork

Brand B has a box of 42 totals for 3.89

3.89 / 42

.092319048

.09 per fork

Answer:

Step-by-step explanation:

18 * 10 - 8 * 4    (remember pemdas)

180 - 32 =

148 cm²

The diameter of the circle when the circumference is  11 π ft will be 11 feet.

A circle's circumference is defined as the linear distance around its boundary, or if a circle is opened to form a straight line.

The formula for the circumference of a circle is:

C = πd

where C is the circumference and d is the diameter.

We are given that the circumference of the circle is 11π ft, so we can set up an equation:

11π = πd

Simplifying by dividing both sides by π:

11 = d

Therefore, the diameter of the circle is 11 feet.

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Answer:

I think AC is 6.

Step-by-step explanation:

This looks like an equilateral triangle so that means because there is a 3 on  one side of the line it should be the same on the other side of the line so 3 x 2 = 6.

Step-by-step explanation:

\(triangle \: abd \\ using \: pythagoras \: theorem \\ {hyp}^{2} = {adj}^{2} + {opp}^{2} \\ {12}^{2} = {3}^{2} + {opp}^{2} \\ 144 = 9 + {x}^{2} \\ 144 - 9 = {x}^{2} \\ 135 = {x}^{2} \\ take \: the \: square \: of \: both \: sides \\x = 11.62\)

using the opposite side of triangle and

\(using \: pythagoras \: theorem \\ {16}^{2} = {11.62}^{2} + {x}^{2} \\ 256 = 135.02 + {x}^{2} \\ 256 - 135.02 = {x}^{2} \\ 120.198 = {x}^{2} \\ take \: the \: roots \: of \: both \: sides \\ x = 10.96\)

therefore the length of line AC

\( = 3 + 10.96 \\ = 13.96\)

hope this helps

Answer: 9

Step-by-step explanation: To divide we need to flip the second fraction we are dividing by. For example:

10/1 divided by 1/4 = 10/1 times 4/1. So in this case, the answer is 40.

Now lets try it with 1/9.

X divided by 1/9 = X times 9/1.

So dividing by 1/9 is equal to multiplying by 9.

If each of X, Y, and N are positive integers, then the value of X+Y+N is 212.1

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

WE are given that A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses.

X = 7

Y = 10

If there are N packages (N ≥ 2) and the total value of them is $2021

X + Y = One packages

N packages = N(X + Y ) = 10 N

if each of X, Y, and N are positive integers, then;

10 N = 2021

N = 2021/10

N = 202.1

Therefore, X+Y+N = 10 + 202.1 = 212.1

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Answer:

its 0,6

Step-by-step explanation:

you just move however much it asks

Answer:

(0,6)

Step-by-step explanation:

your basically imagining that your moving that point following the directions in the word problem. go left 3 times, go up 2 times.

Answer:

There are two real solutions if the radicand is

✔ positive.

There is one real solution if the radicand is

✔ zero.

There are no real solutions if the radicand is

✔ negative.

Step-by-step explanation:

ON MY DOG KIDS DIS RIGHT

Answer:

1.Postieve

2.Zero

3.Negative.

Step-by-step explanation

i did it on ed and got it right.

V is a vector space with the operations of addition and scalar multiplication.

Since f(t) and g(t) are real numbers, you're utilizing the fact that the real numbers themselves are commutative in that step, which truly confused me when I first learned about it and after.

Let V denote the set of all differentiable real-valued functions defined on the real line.

You only need to mention that real-number addition is commutative. Since f is not a number until you evaluate, you couldn't do it before you did.

On a different note, you cannot say that

f+g=f(t)+g(t)

but you can say that (f+g)(t)=f(t)+g(t)

So  V is a vector space with the operations of addition and scalar multiplication.

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Answer:

Yes they are a 0 pair

Step-by-step explanation:

5+(-5)=0

5-5=0

Kris currently has $190 and wants to have at least $1,625 by the end of the summer. To find out how much money she needs to earn each weekend we need to subtract the money she already has from the money she wants to have and divide that by the number of weekends.

$1,625 - $190 = $1,435

$1,435 ÷ 8 = $179.38

So, Kris needs to earn at least $179.38 each weekend to reach her goal.

Answer choice C. Kris needs to earn at least $179.38 each weekend to meet her goal. is the best interpretation of the solution in the context of the problem.

An equation that describes the graph include the following: C. y = |x – 1| + 2.

In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the numerical value on the x-coordinate of the pre-image while the translation of a graph upward simply means adding a digit to the numerical value on the y-coordinate (y-axis) of the pre-image.

Since the parent function is f(x) = |x|, g(x) or y would be created by translating f(x) one (1) unit to the right and two units upward as follows;

f(x) = |x|

g(x) = f(x - 1) + 2

y = |x – 1| + 2

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Missing information:

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

Using translation concepts, the functions that have a maximum and are transformed to the left and down of the parent function are given by:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

For the translations, we have that:

The functions that respect these conditions are:

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Step-by-step explanation:

100%-> 940.00

100%-15%=85%

85%->940.00 ÷ 100 x 85

=799. 00

Usando la distribución hipergeométrica,  la probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es: 0.2 = 20%.

La fórmula es:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

Los parámetros son:

Los valores de los parámetros son:

N = 6, k = 3, n = 2.

La probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es P(X = 2), por eso:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,6,2,3) = \frac{C_{3,2}C_{3,0}}{C_{6,2}} = 0.2\)

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The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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According to given data collection, the answers are as follows: 17 cars had faulty light, 34 cars had only one fault, 11 cars had at least two faults and 41 cars had a fault in brake or light but not steering.

What is data collection?

Data collection is the process of gathering and measuring information or data on variables of interest, in an established systematic fashion that enables one to answer queries, stated research questions, test hypotheses, and evaluate outcomes.

i. To find the number of cars that had faulty light, we need to add up the number of cars that failed with faults in light: brake and light, steering and light only, and brakes, steering, and light. So, 10 + 3 + 4 = 17 cars had faulty light.

ii. To find the number of cars that had only one fault, we need to add up the number of cars that failed with only brake, only steering, or only light faults. So, 14 + 3 + 17 = 34 cars had only one fault.

iii. To find the number of cars that had at least two faults, we need to add up the number of cars that failed with 2 or 3 faults. So, 7 + 4 = 11 cars had at least two faults.

iv. To find the number of cars that had a fault in brake or light but not steering, we need to add up the number of cars that failed with only brake or light faults. So, 14 + 10 + 17 = 41 cars had a fault in brake or light but not steering.

Therefore, according to given data collection, the answers are as follows: 17 cars had faulty light, 34 cars had only one fault, 11 cars had at least two faults and 41 cars had a fault in brake or light but not steering.

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Answer:

5 seconds per foot

Step-by-step explanation:

Answer:A

Step-by-step explanation:

The equation of the line in slope-point form,  slope-intercept form, and  standard form are y = -100x + 1250, y - 1250 = -100(x-0) and 100x + y = 1250 respectively

The equation of a line in point-slope form is given as y − y 1 = m ( x − x 1),

where ( x 1, y1 ) is the point given and m is the slope

m = y2-y1 / x2-x1,   where x1 = 0, y1 = 1,250 and x2 = 5, y2 = 750

m = 750-1250 / 5-0

m = -500/5 = -100

Thus, the slope-point form:

y − y 1 = m ( x − x 1 )

y - 1250 = -100(x-0)

The equation of a line in slope-intercept form is given as y = mx+c,

where (x, y) is the point given, m is the slope and c is the y-intercept

where x1 = 0, y1 = 1,250 and m = -100

y = mx + c

1250 = -100(0) + c

c = 1250

Thus, the equation in slope-intercept form is:

y = -100x + 1250

The equation of a line in standard form is given as  ax + by = c, where a, b, c are real numbers

Rewrite y = -100x + 1250.  Thus, the equation in standard form is:

100x + y = 1250

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Answer:

2x^7

Step-by-step explanation:

add the exponents because they both are x

2x^4*x^3=2x^7

Answer:

Quantity that will maximize profit=1000

Step-by-step explanation:

Assume quantity=x

Revenue=price*quantity

=(4200-6x)x

=4200x-6x^2

Marginal revenue(MR) =4200-12x

Cost(x)= 16000 + 600x − 1.8x2 + 0.004x3

Marginal cost(MC) =600-3.6x+0.012x^2

Marginal cost=Marginal revenue

600-3.6x+0.012x^2=4200-12x

600-3.6x+0.012x^2-4200+12x=0

0.012x^2-8.4x-3600=0

Solve the quadratic equation using

x= -b +or- √b^2-4ac/2a

a=0.012

b=-8.4

c=-3600

x=-(-8.4) +or- √(-8.4)^2- (4)(0.012)(-3600) / (2)(0.012)

= 8.4 +or- √70.56-(-172.8) / 0.024

= 8.4 +or- √70.56+172.8 / 0.024

= 8.4 +or- √243.36 / 0.024

= 8.4 +or- 15.6/0.024

= 8.4/0.024 +15.6/0.024

= 350+650

x=1000

OR

= 8.4/0.024 -15.6/0.024

= 350 - 650

= -300

x=1000 or -300

Quantity that maximises profits can not be negative

So, quantity that maximises profits=1000

Answer:

Second answer:

"The product of two irrational numbers can be rational or irrational"

Step-by-step explanation:

notice from the first product

\(\sqrt{2} \,* \,\sqrt{2} = \sqrt{4} = 2\)

that the product of two irrational numbers can give us a rational one.

from the other three examples, the answer for the products always contains a square root that cannot be reduced, so they all result in an irrational number.

Then, depending on the type of irrationals used, the product can be either rational or irrational.

Given the function

Notice that

Then, integrate D(t) from t=0 to t=3, as shown below

Then,

As for the remaining integral, set x=2t+1; then dx=2dt. Solving using that substitution,

as for the integration limits, when t=3, x=7, and when t=0, x=1.

Therefore,

Rounding to three decimal places,

Thus, the answer is 6.081

Answer:

(8,-43)

(4,-22)

Step-by-step explanation:

In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.

For example:

(4,-22)

x=4 ; y=-22

Plug y into the inequality

y≤0

-22≤0

Since the statement is true, I know that (4,-22) must be a solution to the inequality.

Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.

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Have a GREAT day!!!

Answer:

Step-by-step explanation:

To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.

Let's check each ordered pair:

(8, -43):

The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(4, -22):

The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(-3, 25):

The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

(-7, 45):

The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

So, the solutions to the inequality y ≤ 0 are:

(8, -43) and (4, -22).