You work at a hardware store earning $8. 50 per hour. You work no more than 40 hours each week. Your friend says that the function y = 8. 5x represents the amount of money you earn each week where the domain of x > 40 represents the number of possible hours you work. Is your friend correct? Explain

The class interval of a data set with 30 elements is 5.

The range of a data set is the difference between the largest and smallest values in the set. Once the range is calculated, the class interval can then be calculated by dividing the range by the number of elements in the set.

In the case of a data set with 30 elements, the class interval can be calculated by dividing the range of the data set by 30. This will tell us the size of the intervals that the data is divided into.

If the range of the data is 150, the class interval would be 150/30, which is equal to 5. Therefore, the class interval of the data set would be 5.

It is important to note that the class interval should be chosen so that it is not too small or too large. If the class interval is too small, the data may become too granular, making it difficult to interpret. If the class interval is too large, important details about the data may be lost

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375 different combinations of pizza Allie and his friends can create.

What is a combination?

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.

The vegetable toppings are mushrooms, broccoli, green peppers, olives, and onions.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

The meat toppings are pepperoni, salami, sausage, chicken, and ground beef.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

They can pick thick, hand-tossed, or deep-dish crust.

Here, n=3 r=1

So, C(n, r) = 3!/1!(3-1)!

= 3

They can also pick garlic, tomato, ranch, pesto, or barbecue sauce.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

Number of ways = 5×5×3×5

= 375

Hence, in 375 ways they can choose pizza.

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The value of 19 in Roman numerals is XIX

Roman numerals are defined as a numeral system which originated in ancient Rome and still remains the usual way of writing numbers throughout Europe into the Late Middle Ages.

Some examples of these numeral are;

We have to represent 19, we have;

X representing ten

IX representing nine

Put them together

19 is equal to XIX

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A probability mass function is a function that describes the probability of a discrete random variable taking on each possible value in its sample space.

A probability mass function (PMF) is a function that assigns a probability to each possible value of a discrete random variable. The PMF maps each value to the probability of that value occurring in the random variable's sample space. The probabilities assigned by the PMF must sum to 1, since the random variable must take on one of the possible values in its sample space.

The PMF is used to calculate the expected value, variance, and other statistical properties of the random variable. It is also used to create probability distributions and generate simulations of the random variable. Probability mass functions are commonly used in probability theory, statistics, and other fields that involve discrete random variables.

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[tex]\frac{1}{10}[/tex] of electricity is made up of other resources and it can be found by addition and subtraction of fractions.

Examine the fractions' denominators. Find the LCM of the denominators and rationalise them to make the denominators of the fractions the same. Add the fraction numerators while keeping the denominator constant. To get the final sum, simplify the fraction.

To subtract fractions, first calculate the denominator's LCM. Step 2: Multiply the numerator and denominator by the same number to get the LCM value. Step 3: When the denominator and numerator are equal, subtract the numerator. Step 4: If necessary, simplify the resulting fraction.

[tex]\frac{5}{10} + \frac{2}{10} + \frac{2}{10} + x = 1.\\\frac{9}{10} + x = 1.\\\frac{10x+ 9}{10} = 1\\10x + 9= 10\\x= \frac{1}{10}[/tex]

hence, 1/10 of the electricity is made up of other resources.

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Answer: i think the answer would be 75

Answer:

55 chairs.

Step-by-step explanation:

Note the way Liam arranges the chairs.

1) He arranges chairs in 8 rows of the same length, with 7 chairs left over.

8x + 7

2) He arranges chairs in 6 rows of the same length, with 19 chairs left over:

6x + 19

Set the two expressions equal to each other:

8x + 7 = 6x + 19

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 6x and 7 from both sides of the equation:

8x (-6x) + 7 (-7) = 6x (-6x) + 19 (-7)

8x - 6x = 19 - 7

2x = 12

Next, divide 2 from both sides of the equation:

(2x)/2 = (12)/2

x = 12/2

x = 6

Plug in 6 for x in both expressions. It should give the same answer:

8x + 7

8(6) + 7 = (8 * 6) + 7 = (48) + 7 = 55

6x + 19

6(6) + 19 = (6 * 6) + 19 = (36) + 19 = 55

~

Therefore, Liam has 55 chairs in all.

~

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The conversion of 5 million Yen to USD results in 37000 US Dollars .

We can convert the amount 5 million Japanese Yen to US Dollars by using the currency exchange rate .

The exchange rate can vary due to the fluctuations in the global financial markets , the current currency exchange rate from "Japanese Yen" to US Dollar is ;

⇒ 1 Yen is = 0.0074 US Dollar ;

The amount 5 million dollar can be numerically written as 5000000 ;

On multiplying the amount by 0.0074 , we get ;

⇒ 5000000 × 0.0074 = 37000 US Dollar .

Therefore , 5000000 Yen is equivalent to $37000 .

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Answer:

1% of $500 = $5

Total Saving from $500 to $ 860

[tex] = \frac{860}{5} = 172 \\ [/tex]

Now percentage of growth :-

[tex] \frac{172}{500} \times 100 \\ \\ \frac{17200}{500 } = 34.4[/tex]

Hence, the rate of change Sergio savings = 34.4%

Homogeneity of variance assumption assumes that the two populations have equal variances, so the correct answer is option c, "The two populations have equal variances.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The homogeneity of variance assumption assumes that the two populations have equal variances. Therefore, the correct answer is option c, "The two populations have equal variances."

This assumption is often made in statistical tests that compare the means of two groups, such as the t-test.

When the variances of the two populations are equal, it allows for more precise estimates of the standard error and can improve the accuracy of the test results.

However, if the variances are not equal, it can lead to biased and unreliable results.

In such cases, alternative methods, such as Welch's t-test or the Brown-Forsythe test, can be used to adjust for unequal variances.

Hence, homogeneity of variance assumption assumes that the two populations have equal variances, so the correct answer is option c, "The two populations have equal variances.

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The Longest Increasing Subsequence (LIS) problem is a classic problem in dynamic programming. Given a sequence of numbers, the problem is to find the longest subsequence in which the numbers are in increasing order. For example, given the sequence {3, 1, 5, 2, 4}, the longest increasing subsequence is {1, 2, 4}, which has length 3.

The LIS problem can be solved using dynamic programming by defining an array to store the length of the longest increasing subsequence that ends at each position in the sequence. The array is initialized to 1, and then for each position i in the sequence, the length of the longest increasing subsequence that ends at i is calculated by finding the maximum length of any subsequence that ends at a position j < i and has a smaller value than the value at i. The final solution is the maximum length of any subsequence in the array.

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The sides of the given right triangle are:

g = 33.80

h = 31.20

j = 13

What is a triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. Any three points in Euclidean geometry, when they are not collinear, produce a distinct triangle. A right triangle is a triangle with two perpendicular sides and one angle that is a right angle.

The given figure has a large right triangle with sides g,h and j and a small right triangle with sides 12, j and 5.

Using the small triangle, we can find the value of j.

By Pythagoras theorem,

j² = 12² + 5² = 144 + 25 = 169

j = 13

Now using trigonometric relation we can find the angle ∅  between j and 5.

sin ∅ = 12/13 = 0.923

∅ =  sin ⁻¹ (0.923) = 67.37°

This angle is common for both triangles.

So for large triangle,

tan 67.37 = h/j = h/13

2.4 = h/13

h = 31.2

By Pythagoras theorem,

g² = h² + j²  = 31.2²  + 13² = 1142.44

g = 33.8

Therefore the sides of the given right triangle are:

g = 33.80

h = 31.20

j = 13.

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The function representing the price for one dog to be trained in t years is option C: P(t) = [tex]2750(0.2)^t.[/tex]

In mathematics, a function is a relation between two sets of values, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). The output value of a function is determined by its input value and any relevant rules or formulas.

Formally, a function can be defined as follows: Let X and Y be two non-empty sets. A function f from X to Y is a rule or formula that assigns to each element x in X a unique element y in Y, denoted by f(x), such that for any two elements x1 and x2 in X, if x1 = x2, then f(x1) = f(x2). The set X is called the domain of the function, and the set Y is called the codomain or range of the function.

Functions can be represented graphically, algebraically, or in tabular form. The graph of a function shows how the output value of the function varies with the input value, and can be used to visualize the behavior of the function. The algebraic representation of a function can be given by a formula or equation that expresses the output value in terms of the input value. A tabular representation of a function shows the input-output pairs in a table.

Functions are used in many areas of mathematics, science, engineering, and economics to model and describe relationships between variables. They are also used in practical applications, such as in computer programming, where they are used to define algorithms and data structures.

The total income is earned from training 400 dogs, so the price for one dog to be trained is the total income divided by the number of dogs trained:

P(t) = M(t) / D(t)

Substituting D(t) and M(t), we get:

P(t) =[tex](1100000(0.02)^t) / (400(0.1)^t)[/tex]

P(t) = [tex]2750(0.2)^t[/tex]

Therefore, the function representing the price for one dog to be trained in t years is option C: P(t) = [tex]2750(0.2)^t.[/tex]

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Answer:

answer is in the graph

Step-by-step explanation:

label your y axis miles (horizontal axis) with intervals of 10

label your x axis hours (right to left axis) with intervals of 1

for every 1 hour (x axis) your graph increases by 10 miles (y axis)

so your points are

(1, 10) and (2, 20) and (3, 30) and so on

your equation for the line is  y=10x

see attached graph

Answer:

1/2 ton

Step-by-step explanation:

1/2 ton is 1102 pounds

The  value which we convert from 118 kilograms to pounds is equal to ( 260.15 ) pounds ( round upto two decimals ).

Convert 118 kilograms to pounds using standard relation  :

1 kilograms is equivalent to  2.20462 pounds

To covert 118 kilograms to pounds we have :

⇒ 118 kilograms = ( 118 × 2.20462  ) pounds

⇒ 118 kilograms =  ( 260.145 ) pounds

⇒ 118 kilograms =  ( 260.15 ) pounds ( round upto two decimals )

Therefore, converted relation between kilograms to pounds is given by :

118 kilograms =  ( 260.15 ) pounds ( round upto two decimals ).

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The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The manager of the shop gathered data from several donut shops in the city for the total cost, y, for different amounts of donuts, x.

Now, Let two point on the line are (3, 3) and (8, 7).

Hence, The value of slope is,

Slope = (7 - 3) / (8 - 3)

Slope = 4/5

Thus, We get;

The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80.

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Answer:

360 miles

Step-by-step explanation:

To calculate how far a freight train travels in 4.5 hours, you need to know the train's average speed. Once you know the average speed, you can use the following equation to calculate the distance traveled: Distance = Speed x Time. So, if the freight train is traveling at an average speed of 80 miles per hour, it will have traveled a total of 360 miles in 4.5 hours.

The value of the exponent 'x' in  5ˣ⁻⁵⁵ = 125⁵ is 70.

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, An equation in exponents 5ˣ⁻⁵⁵ = 125⁵.

5ˣ⁻⁵⁵ = 5³ˣ⁵.     (as 5³ is 125)

Therefore, x - 55 = 15.

x = 70.

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The most likely mean for the sample distribution is option c. negatively skewed.

Based on the given information, we know that the mean (M) is less than both the median and the mode. This suggests that the distribution is skewed to the left (negatively skewed), with a long tail on the left side of the distribution.

The mean of a sample distribution is the average value of all the observations or measurements in the sample. It is calculated by adding up all the values in the sample and dividing the sum by the total number of observations in the sample.

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The five-number summary calculator is a statistical method. It is used to find the third quartile, first quartile, median, minimum, and maximum value of the given data set.

A five-number summary calculator is a statistical test that includes five items. The items are Q₁ or first quartile, Q₃ or third quartile, the median, the maximum, and the minimum. This helps to give an idea about the data set. This also helps to calculate ascending order, descending order, and interquartile of the given data set.

In this method, we first input the list of numbers or data. Then, we arrange those numbers. From this, the minimum value and the maximum value will be found. Then, the median is calculated using the formula for odd and even numbers of terms. Then, the median of the lower half numbers gives the first quartile and the upper half number gives the third quartile.

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Answer: 56

Step-by-step explanation: Since we know both triangles are similar, we want to first find the scale factor between the two triangles, knowing side UP and side PQ are corresponding we can find that 84/60 or in simplified terms, 7/5 is the scale factor. Now we know that side VP and side PR are corresponding so 40 x 7/5 gives us 56 which is side PR. Hope this helped! :)

The politician should obtain a sample of at least 602 voters to estimate the proportion of voters supporting her position on forced busing with a 90% level of confidence and a 4% margin of error.

What is the proportion?

A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 5/10 equals 1/2.

To determine the sample size needed to estimate the proportion of voters supporting a certain position within a certain margin of error and level of confidence, we can use the following formula:

n = (Z² * p * (1 - p)) / E²

where:

n is the sample size

Z is the z-score corresponding to the desired level of confidence (in this case, 90%, which corresponds to a z-score of 1.645)

p is the estimated proportion of voters supporting the politician's position (we don't have an estimate, so we'll use 0.5, which maximizes the sample size and provides the most conservative estimate)

E is the desired margin of error (in this case, 4%, which is equivalent to 0.04)

Substituting the values given, we get:

n = (1.645² * 0.5 * (1 - 0.5)) / 0.04²

n = 601.5625

We need to round up to the nearest whole number since we can't have a fractional sample size, so the minimum sample size needed is 602 voters.

Therefore, the politician should obtain a sample of at least 602 voters to estimate the proportion of voters supporting her position on forced busing with a 90% level of confidence and a 4% margin of error.

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Answer: -25

Step-by-step explanation:

The measure of each angle if the measure of LQ is 26° less than the measure of R and, LQ and LR are complementary, is:

We can solve this problem by using the definition of complementary angles and setting up an equation.

Since LQ and LR are complementary, we know that the sum of their measures is 90°. So we can write the equation:

LQ + LR = 90°

Next, we are told that the measure of LQ is 26° less than the measure of LR. We can write this as:

LQ = LR - 26°

Now we can substitute the expression for LQ into the first equation and solve for LR:

LR - 26° + LR = 90°

2LR = 116°

LR = 58°

Now we can plug this value back into the equation for LQ to find the measure of LQ:

LQ = 58° - 26°

LQ = 32°

So the measure of LQ is 32° and the measure of LR is 58°. These are the measures of the complementary angles.

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The values in the composite functions are (u o w)(2) is 7 and (w o u)(2) is 3

A composite function is a function that results from the combination of two or more functions. To form a composite function, the output of one function is used as the input of another function. The composite function can be represented by a single formula or equation, which combines the individual functions.

Let's say we have two functions f(x) and g(x). The composite function f(g(x)) is formed by using the output of the function g(x) as the input of the function f(x). In other words, we first apply g(x) to x, and then we apply f(x) to the result. The resulting composite function is written as f(g(x)).

In the problem given;

u(x) = x² + 3

w(x) = √(x + 2)

a.

(u o w)(2) = 7

b.

(w o u)(2) = 3

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By using Taylor series, the limit does not exist, since the third term does not converge as x approaches 0.

To evaluate the limit using series, we can use the Taylor series expansion of each term in the limit as x approaches 0. A Taylor series is an infinite sum of terms that are expressed in terms of the derivatives of a function at a single point.

Starting with the first term:

lim x→0 (1/3) * x^3 = 0

Next, for the second term, we have:

lim x→0 ((x^3 - 1)/(2x^2)) = lim x→0 (x^3/2x^2) = lim x→0 (x/2) = 0

For the third term, we have:

lim x→0 (x - ln(1 + x))/x^4

= lim x→0 [(x - (x - x^2/2 + x^3/3 - ...))/x^4] (using the Taylor series expansion of ln(1+x))

= lim x→0 [x^2/2 - x^3/3 + ...]/x^4

= lim x→0 [1/2x^2 - 1/3x^3 + ...]

= ∞

Therefore, the limit does not exist, since the third term does not converge as x approaches 0.

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Answer:

59.8741928

Step-by-step explanation:

132lbs to kg is 59.8741928