an economist wishes to estimate the average family income in a certain population. the population standard deviation is known to be $4,800, and the economist uses a random sample of 225 families. what is the probability that the sample mean will fall within $600 of the population mean?

The number in which the digit 3 has a value that is 10 times as great as the value of the digit 3 in 143,728 is 392,097.

The unit digit of a number refers to the rightmost digit of that number when it is written in a positional numeral system. In the decimal system, which is the most common positional numeral system used today, the unit digit is the digit in the ones place.

Let's consider the options one by one:

A. 137,982: This number does not have any digit equal to 3.

B. 142,398: This number does not have a digit 3 with a value as 30,000.

C. 292,389: This number has a digit 3 in the hundred thousands place, which has a value of 3 x 100,000 = 300,000. This is more than 10 times the value of the digit 3 in 143,728, so this option does not satisfy the condition.

D. 392,097: This number has a digit 3 in the ten thousands place, which has a value of 3 x 10,000 = 30,000. This satisfies the condition, so the answer is (D) 392,097.

Therefore, the number in which the digit 3 has a value that is 10 times as great as the value of the digit 3 in 143,728 is 392,097.

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Answer:There are two cases to consider: a hand that consists of all red cards and a hand that consists of all black cards.

Case 1: All red cards

There are 26 red cards in a standard deck of 52 cards. To form a 5-card hand consisting of all red cards, we need to choose 5 cards from the 26 red cards. The number of ways to do this is:

C(26, 5) = (26!)/(5!21!) = 65,780

Case 2: All black cards

Similar to the first case, there are 26 black cards in a standard deck of 52 cards. To form a 5-card hand consisting of all black cards, we need to choose 5 cards from the 26 black cards. The number of ways to do this is:

C(26, 5) = (26!)/(5!21!) = 65,780

Therefore, the total number of hands that include all red cards or all black cards is the sum of the two cases:

65,780 + 65,780 = 131,560

So there are 131,560 hands that consist of either all red cards or all black cards.

Step-by-step explanation:

Answer: If Sydney needs to make exactly 8 dozen items for a bake sale, that means she needs to make a total of 8 x 12 = 96 items

The length of the bow of the circle is 9π/ 2 = 4.5 *3.14 = 14.13.  

The  bow time of a circle can be determined with the compass

and significant point of view exercising the bow time frame strategy.

 ⇒ angle =   arc/ radius  

⇒ 135 ° =   bow/ 6

 ⇒  arc =  135 ° * 6  

⇒  bow =  135 ° * π/ 180 ° * 6  

⇒  bow =  9π/ 2  

⇒ 9π/ 2 = 4.5 *3.14   ⇒14.13

  In calculation, a bow is characterized as a piece of the limit of a circle or a bend. It can likewise be indicated as an open bend. The limit of a circle is the border or the distance around a circle,  else called the circuit.

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The measure of the angle obtained from the specified measure of the arc CD and the diameter of the circle CF are;

An arc of a circle is a part or portion of the circumference of the circle.

1. The angle at C, obtained from the measure of the arc CD is; (360 - (120 + 120))/2 = 60 (Angle at the center of a triangle theorem)

Therefore; m∠CAF = 90° - 60°/2 = 60°

m∠CAF = 90° - 60°/2 = 60°

2. m∠AFB = m∠FCB = 30°

3. m∠CEF = m∠CAF = 60°

4. m∠CFB = m∠CAF = 60° (Corresponding angles theorem)

5. m∠DCF = m∠BCF = 30° (Sum of angles at a point and angles formed by the diameter of a circle)

6. m∠BCD = m∠BCF + m∠DCF

Therefore; m∠BCD = 30° + 30° = 60°

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Answer:

0.9375

Step-by-step explanation:

In summary, 15/16 inches is the same as 0.9375 inches and 15/16 inches is also the same as 0.078125 feet.

Answer:

B

Step-by-step explanation:

Answer:

The value of a+b+c is -2

Step-by-step explanation:

rewrite equation: a+b+c

substitute: (-1) + (2) + (-3)

simplify: -1 + 2 - 3

PEMDAS: 1 - 3

Which equals: -2

The three students who are correct in their approach to solving the problem are Nico, Aditi, Sandra.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols to solve equations and solve problems. It involves using letters, symbols, and numbers to represent variables and unknowns in mathematical expressions, equations, and functions.

In algebra, variables represent quantities that can vary, such as the height of a building, the speed of a car, or the price of a product. Algebraic expressions and equations involve combining these variables, symbols, and numbers using operations such as addition, subtraction, multiplication, and division.

Algebra includes various topics such as linear algebra, quadratic equations, polynomials, matrices, and functions. It also includes the use of graphs and charts to represent mathematical relationships and solve problems.

The three students who are correct in their approach to solving the problem are:

Nico: Two-fifths (5 + x) = 8. (Five-halves)

Aditi: Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8

Sandra: Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8

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Answer:

The system is consistent.

Step-by-step explanation:

Answer:

  (b)  There is not enough information to know whether the system is consistent or inconsistent.

Step-by-step explanation:

Given a system of equations consists of two lines with the same slope, you want to know whether the system is consistent or inconsistent, whether the lines are perpendicular, or if there is enough information to tell.

Lines with the same slope are either parallel or coincident. If they are parallel, the system of equations is inconsistent. If they are coincident, the system of equations is consistent.

Parallel or coincident lines are not perpendicular. Perpendicular lines have opposite reciprocal slopes.

Since we cannot tell whether the lines are parallel or coincident from the given description, we have to say, "there is not enough information to know."

The three orderer pairs in the form (x,y) that could be produced by the function y=12x+3x​ are (0,0), (1,15) and (-2,-30).

what is orderer pair?

The given function is:

y = 12x + 3x

Simplifying, we get:

y = 15x

To find ordered pairs in the form (x,y) that could be produced by this function, we can choose different values of x and substitute them into the equation to find the corresponding value of y. Here are three examples:

1. When x = 0:

y = 15x = 15(0) = 0

Therefore, the ordered pair is (0,0).

2. When x = 1:

y = 15x = 15(1) = 15

Therefore, the ordered pair is (1,15).

3. When x = -2:

y = 15x = 15(-2) = -30

Therefore, the ordered pair is (-2,-30).

In general, we can choose any value of x and find the corresponding value of y using the given function to obtain an ordered pair in the form (x,y).

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Answer:

$110.2

Step-by-step explanation:

$76 × 45%

$34.2

$76 + $34.2

$110.2

The average adult have 02 liters of blood in the body.

The amount of blood circulating in a person depends on their height and weight, but the average adult has more than 5 liters. Blood volume is tightly regulated and linked to various organ systems. Additionally, it is closely related to sodium levels and hydration status. Maintenance of blood volume is essential for normal functioning as it is necessary for the continuous perfusion of body tissues.

According to the Question:

Given that:

The average adult has 1. 2 to 1. 5 gallons of blood in their body.

Now,

Based on the given conditions, formulate: 1.2 ×1.5

Calculate the product or quotient: 1.8

Round the number: 2 gallons.

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a) The amount deducted from Marika Perez's paycheck for social security taxes is $171.62

b) The amount deducted for Medicare taxes is $40.10.

To calculate the amount of social security taxes deducted from Marika Perez's biweekly pay, we need to multiply her gross pay by the social security tax rate of 6.2%. Similarly, to calculate the amount of Medicare taxes deducted, we need to multiply her gross pay by the Medicare tax rate of 1.45%.

The calculations are as follows

Social Security tax deduction = gross biweekly pay x social security tax rate

= $2,768 x 0.062

= $171.62

Medicare tax deduction = gross biweekly pay x Medicare tax rate

= $2,768 x 0.0145

= $40.10

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Answer:

∠1 + ∠2 = 135°

Step-by-step explanation:

From the text, it is given that the two unknows are adjacent angles.

∠2x + ∠2x + 7 = 135°

∠4x + 7 = 135°

∠4x = 128°

x = 32

Answer:

[tex]\angle 1 = 64[/tex]°

[tex]\angle 2 = 71[/tex]°

Step-by-step explanation:

If two adjacent angles form at a resulting angle, this means that both angles form the full resulting angle.

This means [tex]\angle1[/tex] and [tex]\angle2[/tex] have a sum of [tex]135[/tex]°. This can also be written as:

[tex]135 = 2x+2x+7[/tex] or [tex]135 = 4x+7[/tex]

This can be worked out using simple rearrangement:

[tex]135 = 4x+7\\=135-7 = 4x\\=128 = 4x\\\therefore x = 32[/tex]

Therefore we can simply substitute to get our angles:

[tex]\angle 1 = 2x = 32\times2 = 64\\\angle 2 = 2x+7 = 32\times2+7 = 71[/tex]

Hope this helps!!!

Euler's theorem lets us draw the conclusion that a polyhedron cannot contain [tex]6[/tex] vertices or [tex]7[/tex] edges.

Four or even more plane face (all polygons) that meet in pairs along an edge and at least three edges that meet at a vertex make up a solid figure. Full solution, step-by-step Polyhedron: A three-dimensional object with only polygonal faces. There must be a minimum of different faces on a polyhedron.

A two-dimensional shape composed of line segments is known as a polygon. Square, triangle, hexagonal, etc. are a few examples. A polyhedron, on the other hand, is a three-dimensional object formed of polygons. For instance, a cube, a tetrahedron, etc.

[tex]V - E + F = 2[/tex]

In the case of a polyhedron with [tex]6[/tex] vertices and [tex]7[/tex] edges, we can plug in the values [tex]V=6[/tex] and [tex]E=7[/tex] to obtain:

[tex]6 - 7 + F = 2[/tex]

Simplifying this equation, we get:

[tex]F = 3[/tex]

Therefore, we can conclude that it is not possible for a polyhedron to have [tex]6[/tex] vertices and [tex]7[/tex] edges, based on Euler's theorem.

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The volume of the fish tank is 2000 cubic centimeters, which is calculated by multiplying the length, width, and depth of the tank (25 x 10 x 8 = 2000).

The volume of a fish tank is an important piece of information to know when setting up a fish tank. To calculate the volume of a fish tank, you must multiply the length, width, and depth of the tank. In this example, the fish tank has a length of 25 centimeters, a width of 10 centimeters, and a depth of 8 centimeters. To calculate the volume of the fish tank, we would multiply these three measurements, 25 x 10 x 8 = 2000. This means that the fish tank has a volume of 2000 cubic centimeters. Knowing the volume of the fish tank is important for selecting the right type and size of filter, heater, and other equipment for the tank, as well as for selecting the right number and size of fish for the tank. Furthermore, it is necessary to know the volume of the tank when adding water and testing water parameters, such as pH and nitrate levels, as these readings are related to the size of the tank. Knowing the volume of a fish tank is essential for successful fish keeping.

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Compounded Principal Interest Rate per Compounding Period Number of Compounding Periods Final Amount

Annually $9,200 6% / year 1 $20,101.83

Semi-Annually $9,200 3% / 6 months 30 $20,480.73

Quarterly $9,200 1.5% / 3 months 60 $20,740.64

Monthly $9,200 0.5% / month 180 $21,027.54

Weekly $9,200 0.12% / week 780 $21,118.33

Daily $9,200 0.016% / day 5,475 $21,183.05

What is compound interest ?

Compound interest is a method of calculating interest where interest is added to the principal amount, and the interest is also calculated on the accumulated interest. This results in the growth of the principal amount over time. Compound interest is often used in investments, loans, and savings accounts. The formula for calculating compound interest is [tex]A = P (1 + r/n)^{nt}[/tex], where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

According to the question:
Compound Interest Formula: [tex]A = P(1 + r/n)^{nt}[/tex]

where A is the final amount, P is the principal invested, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the money is invested.

Compounded Principal Interest Rate per Compounding Period Number of Compounding Periods Final Amount

Annually $9,200 6% / year 1 $20,101.83

Semi-Annually $9,200 3% / 6 months 30 $20,480.73

Quarterly $9,200 1.5% / 3 months 60 $20,740.64

Monthly $9,200 0.5% / month 180 $21,027.54

Weekly $9,200 0.12% / week 780 $21,118.33

Daily $9,200 0.016% / day 5,475 $21,183.05

Note: The final amounts have been rounded to the nearest cent.

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The measure of the missing angle is 43 degrees.

What is triangle?

A triangle is a geometric shape with three sides and three angles. It is a closed, two-dimensional figure with straight sides. The sum of the angles in a triangle always adds up to 180 degrees.

To find the measure of the missing angles, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can find the measure of the missing angle by subtracting the sum of the other two angles from 180 degrees.

Let's call the missing angle x. Then we have:

105° + 32° + x = 180°

Simplifying, we get:

x = 180° - 105° - 32°

x = 43°

Therefore, the measure of the missing angle is 43 degrees.

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1. Battling the stereotypes architects face.

2. Arguing for good design over cheap construction.

3. Making time for hand sketching

4. Finding great materials to match great designs.

5. Bridging the generation gap (making a design appealing to different generations)

The nth term of the sequence 45, 40, 35, 30 is given by the formula a(n) = 50 - 5n.

To find the nth term of the sequence 45, 40, 35, 30, we need to first identify the pattern that governs the sequence. Here, we can see that each term is obtained by subtracting 5 from the previous term.

So, we can express the nth term of the sequence as:

a(n) = a(1) + (n-1)d

where a(1) is the first term of the sequence, d is the common difference between consecutive terms, and n is the index of the term we want to find.

In this case, a(1) = 45 and d = -5, since we are subtracting 5 from each term to get the next one. Substituting these values into the formula, we get:

a(n) = 45 + (n-1)(-5)

Simplifying, we have:

a(n) = 45 - 5(n-1)

Expanding the brackets, we get:

a(n) = 45 - 5n + 5

Simplifying further, we get:

a(n) = 50 - 5n

Therefore, the nth term of the sequence 45, 40, 35, 30 is given by the formula a(n) = 50 - 5n.

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Answer:

The equation for the relationship is [tex]y=\frac{7}{2} \times x[/tex].

Step-by-step explanation:

Given that point [tex](x,y)=(6,21)[/tex] is part of a direct relationship. That is:

[tex]y \ \infty \ x[/tex]

[tex]y=k\times x[/tex] (1)

Where [tex]k[/tex] is the proportionality constant.

If we know that [tex]x=6[/tex] and [tex]y=21[/tex], then the proportionality constant is:

[tex]k=\dfrac{y}{x}[/tex]

[tex]k=\dfrac{21}{6}[/tex]

[tex]k=\dfrac{7}{2}[/tex]

Lastly, the equation for the relationship is [tex]y=\frac{7}{2} \times x[/tex].

The subdivider has to get the deposit back to Max within 30 days.

A deposit is an amount of money paid to a vendor or a seller to secure goods or services. A deposit is a partial payment made to a business in advance of a larger purchase or delivery.

A subdivision is a housing development built on a portion of land that has been divided into multiple lots. The subdivider divides a large piece of land into smaller plots and sells each lot to individuals who are looking to build their own homes, thus creating a subdivision.

Max can get his deposit back within 30 days. This is because the subdivider has to refund the deposit within 30 days if the buyer cancels the reservation of the plot due to any reason, including the delay that the subdivider has experienced.

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Answer:

z = 66

y = 120

Step-by-step explanation:

First, we can solve for z because it is supplementary to 114°.

114° + z° = 180°

-114°         -114°

z° = 66°

z = 66

Now, we can solve for y using the fact that the interior angles of a quadrilateral add to 360° (think about a rectangle: 4 x 90°).

We have to use the z value that we solved for earlier.

81° + 93° + y° + z° = 360°

↓ substituting in z-value

81° + 93° + y° + 66° = 360°

↓ combining like terms

240° + y° = 360°

-240°         -240°

y° = 120°

y = 120

Answer:

e. y = sin(x) + π

Step-by-step explanation:

We can see that the graph of y = sin(x) has been shifted vertically. This means that the added π should be outside the trigonometric function.

Therefore, e. y = sin(x) + π is the correct answer.

See the attached image for how a, b, c, and d values change the graphs of sine and cosine.

Yes, because[tex]np0 > 10[/tex]and [tex]n(1-p0) > 10[/tex].

Thus, the sampling distribution of p-hat is approximately normal, given the conditions of [tex]np0 > 10 and n(1-p0) > 10.[/tex]

This is because the sampling distribution of p-hat follows the Central Limit Theorem, which states that when sample sizes are greater than 30,

the sampling distribution of the sample proportion will be approximately normal. The Central Limit Theorem is used in this example because the number of BYU students from Texas (n) is greater than 30, so the sample proportion (p-hat) is normally distributed.

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Step-by-step explanation:

c = 2,8    and   d = 6,5

Use the distance formula  ( kind of a modified Pythagorean theorem)

s^2 = (x1-x2)^2  + (y1-y2)^2             ( s = distance)

s^2 = ( 2-6)^2 + ( 8-5)^2

s^2 = 25

s = 5 units

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{\sqrt{21}}\\ a=\stackrel{adjacent}{YZ}\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ (\sqrt{21})^2= (YZ)^2 + (3)^2\implies 21=YZ^2+9 \\\\\\ 12=YZ^2 \implies \sqrt{12}=YZ \\\\[-0.35em] ~\dotfill[/tex]

[tex]\tan(Y )=\cfrac{\stackrel{opposite}{3}}{\underset{adjacent}{\sqrt{12}}}\implies \tan(Y )=\cfrac{3}{\sqrt{12}}\cdot \cfrac{\sqrt{12}}{\sqrt{12}}\implies \tan(Y )=\cfrac{3\sqrt{12}}{12} \\\\\\ \tan(Y )=\cfrac{3\sqrt{2^2\cdot 3}}{12}\implies \tan(Y )=\cfrac{6\sqrt{3}}{12}\implies \tan(Y )=\cfrac{\sqrt{3}}{2}[/tex]