The following table shows Jace's earnings based on the number of hours that he works.

Number of hours 111 222 333

Jace's Earnings \$20$20dollar sign, 20 \$30$30dollar sign, 30 \$40$40dollar sign, 40

Are Jace's earnings proportional to the number of hours that he works?

Choose 1 answer:

Choose 1 answer:


(Choice A)

A

Yes


(Choice B)

B

No

1. Multiply both sides by 2. 4 + 3x = 5 * 2
2. Simplify. 4 + 3x = 10
3. Subtract 4 from both sides to single out x. 3x = 10 - 4
4. Simplify. 3x = 6
5. Divide by 3. x = 6/3
6. Simplify. x = 2

Input 2 into the original equation to check this answer and you will get 5 = 5 which means that x = 2 is your final answer.

Answer: x = 2

Step-by-step explanation:

    To solve for x, we will isolate the variable (x).

Given:

    [tex]\displaystyle \frac{4+3x}{2}=5[/tex]

Multiply both sides of the equation by 2:

    4 + 3x = 10

Subtract 4 from both sides of the equation:

    3x = 6

Divide both sides of the equation by 3:

    x = 2

Answer:

Hm

Step-by-step explanation:

The bacteria population is observed to double after five days, which means that its growth rate is 100% over a period of five days. This corresponds to a daily growth rate of r = 100%/5 = 20%.

If the initial population is 10,000, then the bacteria population after d days can be modeled by the exponential function:

f(d) = 10,000 * (1 + r/100)^d

Substituting r = 20% and simplifying, we get:

f(d) = 10,000 * (1.2)^d

Therefore, the correct option is:

D. f(d) = 10,000 * (1.2)^d

Thus, the given quadratic equation has two real roots x = 3 and x = -2.

A function or mathematical statement of degree two is a quadratic function. This indicates that two is the function's highest power. The roots of all quadratic functions are two.

Given equation:

x² - x - 6 = 0

Using the quadratic formula:

x = [-b ± √(b² - 4ac) ] / 2a

a = 1 , b = -1 and c = -6

x = [1 ± √((-1)² - 4*1*(-6) ] / 2*1

x = [1 ± √(1 + 24) ] / 2

x = [1 ± 5 ] / 2

Now,

x = (1 + 5)/2 = 3

x = (1 - 5)/ 2 = -2

Thus, the given quadratic equation has two real roots x = 3 and x = -2.

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complete question:

Check whether the given equation has, one solution, two solution ,many solution or no real solution.

x² - x - 6 = 0

The area of a circle is given by the formula:

A = πr^2

where r is the radius of the circle.

Substituting the value of the radius as r = 10 cm, we get:

A = π(10)^2

A = 100π

Therefore, the area of the circle with radius 10 cm is 100π square centimeters.

~~~Harsha~~~

Answer

Number 14: 7 faces, 15 edges, and 10 vertices.

Number 15: 10 faces, 24 edges, and 16 vertices.

Number 16: 7 faces, 12 edges, and 7 vertices.

:D

Step-by-step explanation:

If we consider a mountain number with its middle digit is larger than any other digit, then there are possible three-digit mountain numbers are equals the 240.

A number is called a 'mountain' if its decimal digits insitiate with 1, i.e. 'base camp', increase continuously to one largest digit, then decrease continuously back to one i.e. back to base camp. We have a number is called a mountain number. Now, there are 100 to 999 total 3-digit numbers. Now, with 2 in the middle, we have = 2 numbers[1 x 2] - 120 = 121

So, we have a total of Total Number = 2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 = 240 "mountain numbers". Hence, the required number , value is 240.

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A) The expected value of the sampling distribution is 0.40.

B) The standard error is 0.05.

C) The sampling distribution will be centered around the population proportion of 0.40, with a spread given by the standard error of 0.05.

D) By examining the sampling distribution, we can see how likely it is to obtain a certain sample proportion by chance alone, and therefore make conclusions about the population based on the sample.

A) The expected value (also called the mean) of a sampling distribution is equal to the population parameter being estimated. In this case, the population parameter is the proportion, p, which is 0.40.

B) The standard error is the standard deviation of the sampling distribution. For a proportion, the formula for the standard error is √((p(1-p))/n), where p is the population proportion and n is the sample size. Plugging in the values given, we get √((0.40(1-0.40))/100) = 0.049.

C) The sampling distribution of a proportion is approximately normal if both np and n(1-p) are greater than or equal to 10. In this case, np = 1000.40 = 40 and n(1-p) = 100*0.60 = 60, so the conditions for normality are met.

D) The sampling distribution of a proportion shows the distribution of all possible sample proportions of a given size that could be drawn from a population with a known proportion.

The sampling distribution allows us to make inferences about the population proportion, such as constructing confidence intervals or conducting hypothesis tests.

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Complete Question:

A random sample of size 100 is selected from a population with p =0 .40.

A. What is the expected value (to 2 decimals)?

B. What is the standard error (to 2 decimals)?

C. Show the sampling distribution (to 2 decimals).

D. What does the sampling distribution of show?

The amount of money less per hour which Melanie earn than Olivia is equal to $268.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about Melanie's earnings, we have the following:

y = 22.2x

When x = 40 hours, the y-value is given by;

y = 22.2(40)

y = $888.

Difference in earnings can be calculated as follows;

Difference = $1156 - $888

Difference = $268.

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The answers are:

a) 2 cakes cost £5

b) 1 cake costs £2.5.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

To find the cost of 1 cupcake, we need to subtract the cost of the tea from the total cost of 3 cupcakes:

3 cupcakes + 1 tea = £9

3 cupcakes = £9 - 1 tea = £9 - £1.5 (assuming the cost of 1 tea is the same in both cases) = £7.5

1 cupcake = £7.5 ÷ 3 = £2.5

So 2 cupcakes would cost:

2 cupcakes = 2 × £2.5 = £5

Therefore, the answers are:

a) 2 cakes cost £5

b) 1 cake costs £2.5.

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Based on the given pattern:

2 x 4 + 1 = 3 x 3

3 x 5 + 1 = 4 x 4

4 x 6 + 1 = __ + __

__ x 7 + 1 = __ x __

__ x __ + __ = __ + __

The general pattern is that the first term is multiplied by one more than itself, and then 1 is added to the result, which is equal to the second term squared.

When the first term is 25, the equation would look like:

25 x 26 + 1 = __ + __

The first blank would be filled with 26, and the second blank would be filled with 676 (which is 26 squared). So the complete equation would be:

25 x 26 + 1 = 26 + 676

The area of space with no carpet is 268.25 sq ft.

In order to calculate the area of square room we have to subtract the section that is not carpeted from the total area of the room.

The given dimensions of the room is 16 1/2‘ x 16 1/2‘ square room

therefore,

16.5 x 16.5 = 272.25 sq ft

now if we consider that the entertainment system is 2 feet in measurement then,

2 x 2 = 4 sq ft

hence, the space with no carpet is

271.25 - 4

= 268.25 sq feet

The area of space with no carpet is 268.25 sq ft.

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Let's label the 8 questions as Q1, Q2, Q3, Q4, Q5, Q6, Q7, and Q8.

Let's label the 8 students as A, B, C, D, E, F, G, and H.

Since each problem has been correctly solved by exactly 5 students, we can say that the following is true:

Q1: A, B, C, D, E

Q2

Answer: The least common denominator is 3x(x+10)

The equation will have 2 valid solutions

Step-by-step explanation: sorry if wrong

Answer:

square, quadrilateral, rhombus, parallelogram, rectangle



Answer:

Quadrilateral, rectangle, parallelogram, rhombus, square

Step-by-step explanation:

It is a quadrilateral bc it has four sides.

It is a rectangle bc it has four right angles.

It is a parallelogram bc it has two pairs of parallel sides.

It is a rhombus bc all four sides are congruent.

It is a square bc it is both a rectangle and a rhombus.

From a "standard-deck" of "playing-cards", the number of ways which are required to form a "5-card" hand with "2-pairs" is 123,552 ways.

A "Standard-Deck" of playing cards generally consists of 52 cards, divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 ranks: Ace, 2 through 10, and three face cards.

To form a 5-card hand with 2 pairs from a standard deck of playing cards, we break it down into two steps:

Step(1) : Select the values for the two pairs.

There are 13-ranks in a standard deck of playing cards, ranging from 2 to 10, and then Jack, Queen, King, and Ace, for a total of 13 possible values.

We need to select 2 of these values to form the two pairs. The number of ways to do this is "C(13, 2)" which is : 78,

So, there are 78 ways to select the values for the two pairs.

Step(2) : Select the specific-cards for each pair and the fifth card.

For each pair, we need to select 2 cards of that value from the 4 cards of each rank in the deck.

The number of ways to do this is "C(4, 2)" which is : 6,

So, there are 6 ways to select the specific cards for each pair.

Finally, for the fifth-card, we can choose any of the remaining "44-cards" in the deck (after selecting the 8 cards for the two pairs).

So, total number of ways to form a "5-card" hand with "2-pairs" from a standard deck of playing cards is,

⇒ 78 × 6 × 6 × 44 = 123,552 ways,

Therefore, the required number of ways are 123,552 ways.

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The given question is incomplete, the complete question is

Using a standard deck of playing cards, how many ways are to form a 5-card hand with 2 pairs?

The expression that is the difference of two squares is [tex]9a^2 - 4b^6[/tex]

The difference of two squares is an algebraic expression of the form a² - b², which can be factored as (a + b)(a - b).

Using this rule, we can determine which of the given expressions is the difference of two squares.

[tex]9a^2 - 4b^6[/tex] is the difference of two squares because [tex]9a^2[/tex] is a perfect square [tex](3a)^2[/tex]and [tex]4b^6[/tex] is a perfect square[tex](2b^3)^2[/tex]. Therefore, we can write:

[tex]9a^2 - 4b^6 = (3a + 2b^3)(3a - 2b^3)[/tex]

So, the expressions that are the difference of two squares is [tex]9a^2 - 4b^6[/tex]

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1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students. 2) The correct circle graph is option 2. 3) Option 4: Paddleboarding.

The frequency or relative frequency of the data points falling within each interval is depicted by the height of the bars in a histogram, which is a graphical representation of the distribution of continuous data. Histograms are frequently used in data analysis to show how a single variable is distributed and to spot any patterns or trends. Additionally, they can be used to compare the distributions of two or more variables or to spot anomalies or outliers in the data.

1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students.

2) Given the type of transportation we have he total number of visitors as:

(120+24+45+30+81=300)

Now, for walk we have:

120/300 = 40/100 = 40%

For Bicycle we have:

24/300 = 8%

Thus, the correct circle graph is option 2: circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent

3) For the central angle to be 54 the number of campers needs to correspond to this number. The activity that corresponds to 54 degrees is Paddleboarding.

4) For the number of principals in conference we set up a proportionality with total people as follows:

We know that, 52 principals out of 70 people thus:

52/70 = x/750

Now,

x = (52/70) * 750

x = 557.14

Hence, we can predict that there were about 557 principals in attendance at the conference.

5) Given that, out of 225 students 27 prefer cookies thus,

27/225 = 0.12

That is 12% students like cookies.

Now, for the total number of students we have:

0.12 * 4000 = 480

Thus, option A: The college will have about 480 students who prefer cookies.

6) For the given description of the line plot the median is:

For Bus 47 = 16

For Bus 18 = 13

The faster bus is Bus 47, with a median of 16.

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The 95% confidence interval for the standard deviation of the height of students at UH is (1.918, 5.732), which corresponds to option b.

To construct a 95% confidence interval for the standard deviation of the height of students at UH, we will use the Chi-square distribution. Given the sample standard deviation (s) of 3.2 feet, a sample size (n) of 19 students, and assuming normality for the data, we can find the confidence interval as follows:
1. Determine the degrees of freedom: df = n - 1 = 19 - 1 = 18
2. Identify the Chi-square values for the confidence level (95%): χ²_lower = 7.632, χ²_upper = 32.852 (using a Chi-square table or calculator)
3. Calculate the lower and upper bounds of the confidence interval:
Lower bound = sqrt((n - 1) * s² / χ²_upper) = sqrt(18 * (3.2)² / 32.852) ≈ 1.918
Upper bound = sqrt((n - 1) * s² / χ²_lower) = sqrt(18 * (3.2)² / 7.632) ≈ 5.732

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The 95% confidence interval for the standard deviation of the height of students at UH is approximately (1.918, 5.732), Option B.

Construct a 95% confidence interval for the standard deviation of the height of students at UH, we'll use the given data and the Chi-Square distribution.

Here's a step-by-step explanation:
SRS (simple random sample) of 19 students, which means the degrees of freedom (df) = n - 1 = 19 - 1 = 18.
The sample standard deviation (s) is given as 3.2 feet.
Assume normality for the data.
A 95% confidence interval, we'll use the Chi-Square distribution table to find the critical values.

The two tail probabilities are 0.025 and 0.975, so we'll look up the Chi-Square values for 18 degrees of freedom and these probabilities:
[tex]- X^2_{0.025} = 30.191 (upper limit)[/tex]
[tex]- X^2_{0.975} = 8.231 (lower limit)[/tex]
Calculate the confidence interval for the population standard deviation (σ):
[tex][tex](\sqrt((n - 1) \times s^2 / X^2_{upper}), \sqrt((n - 1) \times s^2 / X^2_{lower}))[/tex][/tex]
Plug in the values:
[tex]- n = 19[/tex]
[tex]- s = 3.2[/tex]
[tex]- df = 18[/tex]
[tex][tex]- X^{2} _{upper} = 30.191[/tex][/tex]
[tex][tex]- X^2_{lower} = 8.231[/tex][/tex]
Calculate the confidence interval:
[tex](√((18 \times 3.2^2) / 30.191), \sqrt((18 \times 3.2^2) / 8.231)) \approx (1.918, 5.732)[/tex]

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Answer:

a 1053

b 250

multiply 650 by 1.62 for part a.

for part b divide by 1.62 since pound is less than dollar

hope this helps :)

The probability that the total shown on the two dice after they are rolled is greater than or equal to 8 is 1/9.

If the amount of £15837.77 is to be increased by 18.5%, then the resulting amount after the increase is £18764.75.

A percentage is a number or ratio expressed as a fraction of 100. It represents a portion of something relative to the whole, and is commonly used to express changes or comparisons between two values

To increase a number by a percentage, you can use the following formula

New value = Original value + (Percentage increase / 100) × Original value

Using this formula, we can find the new value of £15837.77 after an 18.5% increase

New value = 15837.77 + (18.5 / 100) × 15837.77

= 15837.77 + 2926.98

= 18764.75

Therefore, an 18.5% increase on £15837.77 is £18764.75, rounded to 2 decimal places.

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Answer:

B) 3p/9

D)1/3p

Step-by-step explanation:

The equation of the circle is x² + y² - 4x - 6y - 60 = 0

The equation of a circle is generally given by the formula:

=> (x - a)²+ (y - b)² = r²

Where (a, b) is the center of the circle, and r is its radius. The equation describes all the points (x, y) in the xy-plane that are a fixed distance r from the center point (a, b).

Here we have

A circle with centre O(2, 3) contains the point A(5, 11).  

Since point A(5, 11) is located on the circle with center O(2, 3), use the distance formula to determine whether A is actually on the circle.

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

=> d = √(x₂ - x₁)² + (y₂ - y₁)²)

Using this formula, the distance between O(2, 3) and A(5, 11) is:

d = √(5 - 2)² + (11 - 3)²)

= √(3² + 8²)

= √(9 + 64)

=√(73)

This distance is the radius of the circle with center O.

Therefore, the equation of the circle is:

(x - 2)² + (y - 3)² = (√(73))²

x² - 4x + 4 + y² - 6y + 9 = 73

x² + y² - 4x - 6y - 60 = 0

Therefore,

The equation of the circle is x² + y² - 4x - 6y - 60 = 0

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The GCF of 48 and 60 is 12

To find the greatest common factor (GCF) of 48 and 60, we can start by finding the prime factorization of each number

48 = 2^4 × 3

60 = 2^2 × 3 × 5

Next, we can identify the common factors of both numbers by looking at their prime factorization

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The common factors of 48 and 60 are: 1, 2, 3, 4, 6, and 12.

The greatest common factor is the largest number that both 48 and 60 can be divided evenly by. In this case, that number is 12. Therefore, the GCF is 12.

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The given question is incomplete, the complete question is:

Find the GCF of 48 and 60.

The statements that are true are:

→ Line Segment KL ≅ Line Segment JM

→ Quadrilateral JKLM is a trapezoid.

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs.

In the quadrilateral JKLM

Using the distance formula, we can find the lengths of the line segments:

JK = √[(7-3)² + (8-5)²] = √58

KL = √[(13-7)² + (5-8)²] = √58

LM = √[(13-13)² + (0-5)²] = 5

JM = √[(13-3)² + (0-5)²] = √109

From this, we can analyze each statement:

a.) Line Segment KL ║ Line Segment JM

We can see from the sketch that the two line segments are not parallel. Therefore, statement a is false.

b.) Line Segment KL ≅ Line Segment JM

We found that the length of KL is equal to the length of JM. Therefore, statement b is true.

c.) Line Segment JK ≅ Line Segment LM

We can see from the sketch that the two line segments are not congruent. Therefore, statement c is false.

d.) Line Segment JK ║ Line Segment LM

We can see from the sketch that the two line segments are perpendicular. Therefore, statement d is false.

e.) Quadrilateral JKLM is a trapezoid.

A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. We can see from the sketch that line segments KL and JM are not parallel, but line segments JK and LM are parallel. Therefore, statement e is true.

f.) Quadrilateral JKLM is an isosceles trapezoid.

An isosceles trapezoid is defined as a trapezoid with congruent base angles and congruent non-parallel sides. We can see from the sketch that neither the base angles nor the non-parallel sides are congruent. Therefore, statement f is false.

Therefore, the statements that are true are b and e.

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Answer:

A) KL⎯⎯⎯⎯⎯∥JM⎯⎯⎯⎯⎯

C) JK⎯⎯⎯⎯⎯≅LM⎯⎯⎯⎯⎯⎯

E) Quadrilateral JKLM is a trapezoid.

F) Quadrilateral JKLM is an isosceles trapezoid.

Step-by-step explanation:

These where the correct answer I got when taking the assignment with that question

Answer:

189

Step-by-step explanation:

27,006 / 42

= [tex]\frac{27}{6/42}[/tex]

= [tex]\frac{27}{\frac{1}{7} }[/tex]

= 27 x 7

= 189

So, the answer is 189

This means that if the average weight of the men in the elevator is more than 180 lbs, the elevator would be overloaded.

To determine the average weight beyond which the elevator would be considered overloaded, we can follow these steps:
Find the total weight limit for 33 occupants: 5940 lbs.

Divide the total weight limit by the number of occupants to find the average weight per person: 5940 / 33 = 180 lbs.
Now, we need to find the difference between the average weight per person (180 lbs) and the mean weight of the population (166 lbs): 180 - 166 = 14 lbs.
Since we have the difference and the standard deviation (26 lbs), we can now calculate the Z-score:

Z = (difference) / (standard deviation) = 14 / 26 ≈ 0.54.
The average weight beyond which the elevator would be considered overloaded is 180 lbs.

The corresponding Z-score for this weight is approximately 0.54.

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Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.

Plugging in these values, we get:

average rate of change = (f(65) - f(9)) / (65 - 9)

average rate of change = (3√64 + 2 - 3√8 - 2) / 56

average rate of change = (3(4) + 2 - 3(2) - 2) / 56

average rate of change = (12 - 4) / 56

average rate of change = 8 / 56

average rate of change = 1 / 7

Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.

Plugging in these values, we get:

average rate of change = (f(65) - f(9)) / (65 - 9)

average rate of change = (3√64 + 2 - 3√8 - 2) / 56

average rate of change = (3(4) + 2 - 3(2) - 2) / 56

average rate of change = (12 - 4) / 56

average rate of change = 8 / 56

average rate of change = 1 / 7

Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.