In Duck Creek, a bicycle license plate consists of one letter followed by one digit; for example, $Q7$ or $J1$. How many different license plates are possible

Correct options are: A. Zeros: -2 and 1

E. x-Intercepts: (-2, 0) and (1, 0)

What are zeros & x-intercepts of quadratic function?

The zero of the function is where the y-value is zero.

The x-intercept is where the graph crosses the x-axis.

The zeros of a quadratic function are the values of x for which the function equals zero. In other words, they are the solutions to the equation f(x) = 0. For the given quadratic function, the zeros

are -2 and 1.

The x-intercepts of a function are the points at which the function crosses the x-axis. In other words, they are the solutions to the equation f(x) = 0 when y = 0. For the given function, the x-intercepts are (-2, 0) and (1, 0) which are the points on the x-axis where the function crosses it.

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Answer:

x + 5 = 10

Step-by-step explanation:

7 hours Serenity worked if she made a total of $262. 50.

How do you calculate total hours in a number?

To find the total hours, subtract the time the employee clocked in from when they clocked out.

We can start by using the following equation to find the total number of hours Serenity worked:

Total Earnings = (Hourly Wage) * (Number of Hours) + (Tips)

In this case, we know that Serenity's total earnings were $262.50, she earned $12.50 per hour and made $175 in tips on Saturday. So we can substitute these values into the equation:

$262.50 = ($12.50) * (Number of Hours) + $175

To find the number of hours, we can subtract the tips from the total earnings and divide by the hourly wage:

Number of Hours = ($262.50 - $175) / $12.50

= $87.50 / $12.50

= 7

So Serenity worked 7 hours on Saturday.

Hence, 7 hours Serenity worked if she made a total of $262. 50.

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Answer:

x = 5/3

Step-by-step explanation:

6x + 11 = 21

6x = 10

x = 10/6

x = 5/3

Let's check

6(5/3) + 11 = 21

30/3 + 11 = 21

10 + 11 = 21

21 = 21

So, x = 5/3 is correct!

Answer:

14t²+42t

Step-by-step explanation:

So you're basically going to use distributive property.

(2t+6)+7t is the same as, (2t)7t + 6(7t).

2t(7t)= 14t² and 6(7t)= 42t.

Combine the two answers and you get 14t²+42t.

14t²+42t is the simplest form you can get to.

Answer:

3.5

Step-by-step explanation:

In this problem, the line's constant of proportionality is the same as its slope.

Slope is defined as rise / run (also notated as change in y / change in x).

Using the given point, we can deduce that the line's rise (change in y) is 3.5, and its run (change in x) is 1. Putting these values into the slope formula:

3.5 / 1 = 3.5

So, the constant of proportionality of this line is 3.5.

There is very strong evidence to reject the null hypothesis, and to conclude that the machine gives radiation doses lower than the maximum on the label.

Hypothesis testing is a statistical method used to test a claim or a hypothesis about a population parameter, based on a sample of data. The goal of hypothesis testing is to determine whether there is enough evidence in the sample data to support or reject a claim about a population.

A t-test is a type of statistical hypothesis test that compares the mean of a sample to a known population mean. There are different types of t-tests, depending on the design of the study and the number of samples being compared.

To test the claim that the machine gives a radiation dose lower than the maximum on the label (5.00 milliroentgens), we can use a one-sample t-test. A one-sample t-test compares the mean of a sample to a known population mean (in this case, the maximum on the label). The null hypothesis for this test is that the mean radiation dose given by the machine is equal to or greater than the maximum on the label (5.00 milliroentgens). The alternative hypothesis is that the mean radiation dose given by the machine is less than the maximum on the label.

The test statistic for a one-sample t-test is:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values:

t = (4.23 - 5.00) / (1.91 / sqrt(46)) = -4.05

We can use a t-distribution table to find the p-value associated with this test statistic. With 45 degrees of freedom (sample size - 1), the p-value for t = -4.05 is extremely low, much less than 0.001, the significance level commonly used in hypothesis testing.

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Answer:

I used desmos to make the graph

Step-by-step explanation:

Hopefully this helps!

1)

a) The equation Y=3/4x+3 can be used to represent the growth of the trees over time.

b) The y-intercept in this equation represents the starting height of the trees, which is 3 feet.

c) In 3 years, the height of the trees will be 5.25 feet according to the equation.

2)

No, the equation 3x - 4y = -12 cannot be used to represent the same information in question #1. This equation is not in slope-intercept form, which is necessary to represent a linear relationship between two variables.

a) The 3 and the 4 in this equation are coefficients of the variables x and y, respectively. They do not represent any specific value or quantity in the context of the problem.

b) It is not possible to determine the height of the tree in 24 years using this equation because it is not in the correct form.

c) To find the x-intercept, we can set y to 0 and solve for x. This gives us x = -3. The x-intercept in this equation represents the number of years at which the height of the tree is 0 feet. This does not have any meaning in the context of the problem.

Noah needs 108 cubes which is 4 times more than Lin's 27 cubes.

Noah would need more cubes to fill the 1 1/2 inch cube because the cubes he is using have a smaller edge length than the cubes Lin is using. The larger the edge length of the cubes being used, the fewer number of cubes needed to fill a given space.

To see this, you can calculate the volume of the cube being filled by both Lin and Noah. The cube that Lin is filling has a volume of (1.5)^3 = 3.375 cubic inches. The cubes Lin is using have a volume of (0.5)^3 = 0.125 cubic inches. So, Lin needs 3.375/0.125 = 27 cubes to fill the 1.5 inch cube.

The cube that Noah is filling also has a volume of (1.5)^3 = 3.375 cubic inches. The cubes Noah is using have a volume of (0.25)^3 = 0.03125 cubic inches. So, Noah needs 3.375/0.03125 = 108 cubes to fill the 1.5 inch cube.

As we can see, Noah needs 108 cubes which is 4 times more than Lin's 27 cubes.

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The statement "it is not the case that p and q are both true" is made in the negation of p ^ q.

As a result, when p q is true, that is, when one or both of p and q are true, (p q) is true precisely. The sentence is only untrue when both p and q are true. The opposite of the given mathematical statement is the negation of a statement in mathematics. If "P" is a statement, then "~P" is the statement's negation.

The words "~" or "¬" are used to denote a statement's denial.

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There are basically 6 types of angles are there which are acute, obtuse, right, straight, reflex and complete angles.

If an angle is less than 90 degrees, it is known as an acute angle. If an angle is more than 90 degrees, then it is called an obtuse angle. If an angle is exactly 90 degrees, then it is called the right angle.

If an angle is precisely 180 degrees, then it is called a straight angle. If the angle is more than 180 degrees but less than 270 degrees, it is known as a reflex angle. A full 360-degree angle is called a complete angle.

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The number of different ways is 7560 ways

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

Chiefs = 1

Supporting chiefs = 2

Members = 10

Inferior officers = 2

There are 10 members.

So, the number of ways to select a chief is 10

Now, there are 9 members left

The number of ways to select a supporting chief is then represented as

Supporting chief = ⁹C₂

Now, there are 7 members left

The number of ways to select an inferior officer is then represented as

Inferior officers = ⁷C₂

So, the total number of ways is

Ways = 10 * ⁹C₂ * ⁷C₂

Evaluate

Ways = 7560

Hence, the number of ways is 7560

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Answer:

Step-by-step explanation: its 90

Answer:

y=90°

since,70°+(X+X)+(180°-110°)=180°

or,70°+2X+180°-110°=180°

or,2X-40°=0

or,2X=40°

:.X=20°

Also,

X+y+70°=180°

or,y+90°=180°

:.y=90°

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Therefore , the solution of the given problem of median comes out to be

a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.

Specify median.

The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.

Here,

Given : mean age is 36.

Standard deviation = 3.5

a) z - score = (34 - 28.3)/3.8 = 1.50

b) Interpretation:

An age of 34 is about 1.50 standard deviations above the mean.

c) Option B is correct.

Therefore , the solution of the given problem of median comes out to be

a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.

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Answer:

A. x>-6

Step-by-step explanation:

x-11<2x-11+1+5

x-2x<-11+1+5+11

-x<6 (Now multiply by - )

x>-6

1(t) = 12(t) (2,2,4) +t(2,4,6) and Ia(t) = 12(t) (2,2,4) +t(2,4,6) represents the same line, as they are both equivalent to 12(t)(2,2,4) + t(2,4,6). So Option A is correct.

The equation of a line in 3-dimensional space can be represented in the form "r(t) = a + tb" where "r(t)" is a vector that represents any point on the line, "a" is a vector that represents a point on the line, and "b" is a vector that represents the direction of the line.

The given equations are:

1(t) = 12(t) (2,2,4) +t(2,4,6)

Ia(t) = 12(t) (2,2,4) +t(2,4,6)

As we can see that both equations are identical to equation 12(t) (2,2,4) +t(2,4,6) thus these three equations represent the same line.

The other given options B, C, and D are not equivalent to each other or to the original equation, thus they do not represent the same line.

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Answer

x ≥ 40

Step-by-step explanation:

Since Josh only exercises more or equal to 40 min, this is how you would represent this problem.

0.94 cups of milk is required for 5 batches of the macaroni and cheese.

Given that the recipe for macaroni and cheese takes:

3 tablespoons of milk

and 2 tablespoons of butter

To find: the number of cups of milk required

Let m be the number of cups of milk is required to make 5 batches of the macaroni and cheese.

a batch of the macaroni and cheese require 3 tablespoons of milk .

So by unitary method for 5 batches of the macaroni and cheese,

(5 × 3) = 15 tablespoons of milk is required.

We know that 1 US Cup = 16 US tablespoons

So by unitary method,

m = 15/16 cups of milk

m = 0.94 cups of milk

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Answer:

No, the point isn't in the shaded area

Step-by-step explanation:

Albert has made mistake in double number line in step 3 and 4.

The best time to utilize a double number line diagram is when the quantities have various units. The existence of several, maybe indefinitely numerous pairs of numbers in the same ratio, including those with rational number elements, can be illustrated using double number line diagrams. Unit rates (R) appear in the pair, just like in tables (R, 1).

Numerous equivalent ratios can be discovered using a double number line diagram. For instance, "Mix 5 cups of cranberry juice with 2 cups of soda water," is how a recipe for fizzy juice is written. Cranberry juice and soda water are combined in a 5:2 ratio. Equivalent ratios are produced by multiplying each constituents by the same number.

Albert has made mistake in step 3 and step 4,

Firstly he has written wrong units for the respective number line,

If ratio of 2 parts of blue and 5 parts of red is used(2:5)

The equivalent ratio will be 10:25

We get the desired output by multiplying (2:5) by 5.

The Correct units will be 5 instead of 20

And the number corresponding to 25 will be 10.

The correct double number line is drawn below.

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The number you thought of is -1.

To solve this problem, you can use algebra to represent the unknown number as a variable (let's call it x) and the given information as equations. The first step is to determine what the problem is asking for. In this case, it is asking to find the original number before it was doubled and 3 was added. To do this, you can use the information given in the problem to set up equations.

The first equation is (2x+3)*4 = 52. You can then solve this equation for x. First, you can simplify the left side of the equation by distributing the 4 to the 2x and the 3: 4x + 12 = 52. Then, you can subtract 12 from both sides to get 4x = 40. Finally, you can divide both sides by 4 to get x = 10. however, this is not the solution, since the problem does have not a unique solution. x=-1 is also the solution.

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The first number is 11 and second number is 12.We can find by solving two consective numbers.

Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number. The difference between consecutive numbers is always fixed and it follows a pattern. For example 1, 2, 3 are the first three consecutive natural numbers.

An odd number of consecutive numbers has a whole number as an average. This average is always the middle number. So that means that the sum of the numbers will be Sum = average \times number of consecutive numbers.

Now we find

Let x be a first number and x+1 be a second number.So

x+x+1=23

2x+1=23

2x    =23-1

2x    =22

  x   = 11

x+1= 11+1=12

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Answer: In order to calculate the value of 3h(2) + 4g(1), we would need to know the specific functions h(x) and g(x) that you are referring to. Without more information, it is not possible to determine the value of the expression.

Typically, piecewise functions are defined by several different expressions, each defined over a different interval of the input variable x. To evaluate a piecewise function at a specific value of x, we must first determine which interval that value of x falls into, and then use the corresponding expression for that interval to find the output value.

Are you able to provide the piecewise functions, or are you just using them as an example?

Also, in case if you want to describe the functions in words, please let me know.

Step-by-step explanation:

Answer:

54 is the correct answer

Answer: An equation of a line that is parallel to another line has the same slope as the original line. The slope of a line can be found by rearranging the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).

To find the equation of a line that is parallel to the line x - 5y = 15 and passes through the point (-5,7), we can first rearrange the equation of the original line in slope-intercept form:

x - 5y = 15

y = (1/5)x - 3

The slope of this line is (1/5). To find an equation of a line that is parallel to this line and passes through the point (-5,7), we can use the point-slope form of a line:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

Substituting in the values given in the question, we get:

y - 7 = (1/5)(x - (-5))

y - 7 = (1/5)x + 1

y = (1/5)x + 1 + 7

y = (1/5)x + 8

Therefore, the equation of the line that is parallel to the line x - 5y = 15 and passes through the point (-5,7) is y = (1/5)x + 8.

Step-by-step explanation:

Answer:

2.

Step-by-step explanation:

There are more boxes towards the highest numbers which means that the medians for northbound cars are generally high while the medians for southbound cars are located more on the smaller numbers representing the speed.

The Constraints of the inequality are

x ≤ 2y + 500

22500  < √ 35x + 50y

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

The Company A (x) at most 500 more than twice then unit by B(y).

So, x ≤ 2y + 500

Now, the square of Company Profit will be equal to 35x + 50y

Then, the constraints will be

1. x ≤ 2y + 500

2. Company Profit² < 35x + 50y

Company Profit < √ 35x + 50y

22500  < √ 35x + 50y

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While two milkshakes are cheaper by $0.15 than a cheeseburger, a cheeseburger costs $1.55 and costs $.85.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. The three main types of linear equations are the slope-intercept form, standard form, and point-slope form. A straightforward equation shows the connection between two terms on either side of an equal sign. Additionally, simple equations incorporate one or more of the addition, subtraction, multiplication, and division arithmetic operations.

given

Let a = the cost in cents of a cheeseburger

Let b = the cost in cents of a shake

4a+2b=7 .90

2b=a+15

-a+2b=15

Subtract (2) from (1)

4a+2b=7 .90

a-2b=-15

5a=775

a=155

2b=a+15

b=170/2

b=85

While two milkshakes are cheaper by $0.15 than a cheeseburger, a cheeseburger costs $1.55 and costs $.85.

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