Determine whether each mapping represents a function. Explain your reasoning.

Answer:

m∠B = 70.0° (nearest tenth)

Step-by-step explanation:

Sine Rule for Angles

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Given:

Substituting the given values into the formula to find m∠C:

\(\implies \sf \dfrac{\sin 40^{\circ}}{13}=\dfrac{\sin C}{19}\)

\(\implies \sf \sin C=\dfrac{19\sin 40^{\circ}}{13}\)

\(\implies \sf C=\sin^{-1}\left(\dfrac{19\sin 40^{\circ}}{13}\right)\)

\(\implies \sf m \angle C=69.96086904^{\circ}\)

Interior angles of a triangle sum to 180°

\(\implies \sf m \angle A+ m \angle B+m \angle C=180^{\circ}\)

\(\implies \sf 40^{\circ} + m \angle B+69.960...^{\circ}=180^{\circ}\)

\(\implies \sf m \angle B=70.03913...^{\circ}\)

Therefore, m∠B = 70.0° (nearest tenth)

Answer:

D

Step-by-step explanation:

Undefined terms are words that are not formally defined.

Hope this helps!

As there is no variables, so the given expression 9 + 10 is the numerical expression.

An object can be counted, measured, or labelled using a number, which is a mathematical value. Arithmetic calculations are often done with numbers. Natural numbers, whole numbers, rational and irrational numbers, among other types of numbers, are examples. A null value is also represented by the integer zero, or 0.

Numerical expression is a combination of the words numerical, which refers to numbers, and expression, which denotes a statement. Consequently, it is a statement that uses numbers.

Mathematical operations like add, subtract, multiply, and divide can be used to mix integers with numbers to create a numerical expression.

Given Expression 9 + 10

As it contains only numbers and mathematical operators,

So, it is the numerical expression.

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Option (B) is correct. The first group will have a commuting time of 0-15 minutes, as it covers the desired range and includes the shortest commuting time of 5 minutes.

The first group will have a commuting time of 0-15 minutes. This range is selected because it covers the desired commuting time range of 5-120 minutes. Since the shortest commuting time is 5 minutes, a range starting from 0 minutes would include it. Additionally, the upper limit of 15 minutes ensures that employees with longer commuting times are not included in this group.

By placing employees with commuting times ranging from 0-15 minutes in the first group, the employment agency can create a statistical grouping that represents those who have relatively short commutes. This grouping allows for better analysis and understanding of the distribution of commuting times among the 125 employees and can aid in making informed decisions regarding job placements and other related factors.

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Answer:

I think you wrote something wrong.

Step-by-step explanation:

If Alaina has $7 in her bank account and Joel had $48 in his Joel already has more then Alaina but I will attempt to teach you how to solve these types of problems.

for this example I'm giving Alaina 79 dollars.

First we know were starting with 79 dollars and increasing 6 dollars each day so the equation for this is; y = 6x + 79 that is Alaina's equation.

For Joel our equation will be; y = 8x + 48.

Since they already have 79 and 48 dollars in their bank we put those as our B in the equation cause they are our y-intercepts. (Y = mx + b) Next we know their increasing by 6 and 8 dollars a day so we make those our m. Once we have these equations we can plot them and see where the lines meet. (thats our answer) I plotted them on desmos graphing calculator.

They crossed at (15.5, 172) Which means it will take 16 days for Joel to catch up they will both have 172 dollars in the bank account on the 16th day.

Hope this helps!

Answer:

b.) To estimate the mean number of classes that students take at his university, Samuel collects data from a  randomly selected proportionate number of students from each grade level.

c.) David wants to estimate the mean grade point average of students at his school. He collects data by recording the grade point average of every 25th student on the list of students after a randomly selected first student.

d.) Helen wants to estimate the male to female ratio of the residents of her city. She collects data by recording the sex  of every 50th resident after selecting a random starting point on a list of residents.

Why? Because a sample is only biased if some individuals of the population are more or less likely to be chosen than others.

The sample from choice B isn't biased because every student has the same opportunity of being selected. It's the same predicament with choice C; it's also non-biased because again, each student has a chance of being in it, there is no preference.

And finally, the sample from option D is non-biased, because every resident that is being selected has an equally fair chance of being selected at random.

Hope this helps ;)

Answer:

Step-by-step explanation:

To estimate the mean number of classes that students take at his university, Samuel collects data from a randomly selected proportionate number of students from each grade level.

David wants to estimate the mean grade point average of students at his school. He collects data by recording the grade point average of every 25th student on the list of students after a randomly selecting first student.

Helen wants to estimate the male to female ratio of the residents of her city. She collects data by recording the sex of every 50th resident after selecting a random starting point on a list of residents.

Answer:

(6t) + (3t) + (4t)

Simplified it would be 13t

The distance from the entrance which is located at (-3,7) to the garden at points (3,-2) is \(3\sqrt{13}\).

First, let us understand the distance formula:

The distance formula is the measurement of the distance between 2 points. It calculates the straight line distance between the given points.

The distance formula is given by:

Distance = \(\sqrt{(a-c)^2+(b-d)^2}\)

Where A(a, b) and B(c, d) are the coordinates.

We are given;

The park entrance is located at (-3, 7).

Another point at (3, -2).

We need to find the distance from the entrance to the garden at another given point.

Substitute the given values in the distance formula, we will get;

Distance = \(\sqrt{(a-c)^2+(b-d)^2}\)

Distance = \(\sqrt{(-3-3)^2+(7-(-2))^2}\)

Distance = \(\sqrt{(6)^2+(9)^2}\)

Distance = \(\sqrt{36+81}\)

Distance = \(\sqrt{117}\)

Distance = \(3\sqrt{13}\)

So, the distance between the given points is \(3\sqrt{13}\).

Thus, the distance from the entrance which is located at (-3,7) to the garden at points (3,-2) is \(3\sqrt{13}\).

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y = (5/3)^x

For x= 0 , y = 1

For x=1,. y= 5/3

For x=2. y = 25/9= 2 + 7/9

For x= 3. y= (25/9)•5/3 = 10/3 + 35/27

For x= 4. y= (10/3 + 35/27)•5/3= 50/9 + 175/81= 625/81

For x= 5 y = (625/81)•5/3= 3125/243

For x=6. y= 15625/243 = 64 + 73/243

For x=7. y=78125/729 = 107+ 122/729

For x=8. y= 390625/2187= 178+ 1339/2187

NOW Part 2 Drawing it

Answer:

  undefined

Step-by-step explanation:

The slope of a line is the ratio of the vertical change between two points to the horizontal change between those same two points. When the line is vertical, the horizontal change is zero. That means the slope is some (non-zero) value divided by zero. Division by 0 gives a result that is "undefined."

The slope of a vertical line is "undefined."

Answer:

\( \huge{ \boxed{ \boxed{ \sf{ \red{ \sf{x = 1}}}}}}\)

Step - by - step explanation :

\( \underline{ \underline{ \sf{Solution}}} : \)

USING ELIMINATION METHOD :

\( \sf{ - 3x - 9y = - 12}\) ••••••• equation ( i )

\( \sf{ - 3x + 7y = 4}\) ••••••• equation ( ii )

Subtracting equation ( ii ) from ( i )

Note that while subtracting equation ( ii ) from ( i ) , sign of each term of equation ( ii ) changes and hence becomes 3x - 7y = -4.

\( \sf{ \cancel{ - 3x} - 9y = - 12}\)

\( \sf{ \cancel{3x} - 7y = - 4}\)

_____________________

➺ \( \sf{ - 16y = - 16}\)

➺ \( \sf{ \frac{ - 16y}{ - 16} = \frac{ - 16}{ - 16}} \)

➺ \( \sf{y = 1}\)

The value of y is 1. Since , we are asked to find the value of x , substituting the value of y in equation ( i) , we get :

➺ \( \sf{ - 3x - 9 \times 1 = - 12}\)

➺ \( \sf{ - 3x - 9 = - 12}\)

➺ \( \sf{ - 3x = - 12 + 9}\)

➺ \( \sf{ - 3x = - 3}\)

➺ \( \sf{ \frac{ - 3x}{ - 3} = \frac{ - 3}{ - 3}} \)

➺ \( \sf{ x = \boxed{ \bold{ \red{ \sf{1}}}}}\)

Hence , the value of x is 1 .

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☞ \( \underline{ \sf{Extra \: Info}} : \)

There are many methods to solve such simultaneous equations. They are :

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✑ Learn more :

Solve system of equations using elimination method :

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Hope I helped ! ツ

Have a wonderful day / night ♡

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The 95% confidence interval for the true proportion of people who favor candidate is (0.419,0.481).

A random sample of 1000 people was condidered for testing.

Number of people in sample favoured candidate

= 450

So, sample proportion, p = 450/1000 = 0.45

Confidence level= 95% i.e, alpha = 1 - 0.95=0.05, From standard normal Z- table, the value of Z( 0.025) is equals to 1.96..

Confidence interval formula,

CL = p ± Z× √(p×(1-p)/n)

Lower bound of interval is ,

=0.45 - 1.96× √(0.45× (1-0.45)/1000)

= 0.45 - 1.96× √(0.45× 0.55/1000)

= 0.45 - 1.96× √(0.0002475)

=0.419165~ 0.419

So the Upper bound is

= p + Z×√(p×(1-p)/n)

= 0.45 + 1.96× √(0.45× (1-0.45)/1000)

= 0.45 + 1.96× √(0.0002475)

= 0.480835 ~0.481

Hence, the required confidence interval is (0.419,0.481).

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A cylinder is the solid shape that is created when square is rotated about a horizontal or vertical axis passing through its center. This solid does have a square for a base but does not have a square for a cross-section.

When a square is rotated about a horizontal or vertical axis passing through the center of the square, it creates a solid called a cylinder. A cylinder is characterized by its curved lateral surface and two circular bases at each end.

The base of the cylinder is formed by the square that was rotated. Hence, the base of the cylinder formed by rotating a square about a horizontal or vertical axis through its center is indeed a square.

However, when we consider a cross-section of the cylinder, it is not a square. The cross-section of a cylinder is a circle, regardless of the orientation of the axis of rotation.

As we move along the height of the cylinder, the cross-section remains consistent and is always circular. Therefore, the solid formed by rotating a square about a horizontal or vertical axis through its center has a square for a base but does not have a square for a cross-section.

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Based on the relationship between the number of orders served by Mary, Joe, and Deandre, the number of orders they each served was:

Assuming that the number of orders served by Mary was x, the formula for the total orders served would be:

Deandre's orders + Mary's orders + Joe's orders = 95
3x + x + (x - 10) = 95

Solving for Mary's orders gives:

3x + x + x - 10 = 95

5x - 10 = 95

5x = 95 + 10

x = 105 / 5

x = 21

Number of orders by Deandre:

= 21 x 3

= 63 orders

Orders by Joe:

= 21 - 10

= 11 orders

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Answer:

C

Step-by-step explanation:

Since the triangles are congruent then corresponding angles are congruent

x is the angle between line with 3 strokes and 2 strokes

The corresponding angle is therefore ∠ C

∠ C = 180° - (63 + 29)° = 180° - 92° = 88°

Then x = 88 → C

The relative risk of being alive at 5-years after diagnosis associated between white men and black men is 2.03.

In the US, among a representative group of 6,006 white men and 1,126 black men, ages 70-79 years at diagnosis of stage IV prostate cancer: 2,337 white men and 344 black men were alive after 5 years of follow-up.

In order to calculate the relative risk of being alive at 5-years after diagnosis associated between white men and black men, we can use the following formula:

Relative risk = [ (number of white men alive after 5 years) / (total number of white men) ] ÷ [ (number of black men alive after 5 years) / (total number of black men) ]

Therefore, substituting the values given in the formula we get;

[ (2,337) / (6,006) ] ÷ [ (344) / (1,126) ] = 0.63 ÷ 0.31 = 2.03

Therefore, the relative risk of being alive at 5-years after diagnosis associated between white men and black men is 2.03.

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ANSWER:

STEP-BY-STEP EXPLANATION:

Graphically the solution are points of intersection between both graphs, just like this:

We have the following system of equations:

We solve by means of equalization

Now, for y:

Therefore, the solutions are:

Answer:

The answer is ten. Perimeter is all the sides added together. Area is length times width.

Step-by-step explanation:

Where's my cookie?

Answer:

To find perimeter, all you need to do is length times width. In this case, that's 4 + 1

Your answer is 5 in.

Answer:

1/4

Step-by-step explanation:

So if 1= 4, 2=8, 4=16, 5=20.... it's going up by 4s so muffins per cup of flower is 1/4... I think.

Answer:

-11

Step-by-step explanation:

See the picture for your understanding.

Since a and b are oppoiste angles of 80° and 60° respectively

a = 80°

b = 60°

Since sum of three angles in a triangle is 180°

x + 51 + 60° + 80° = 180°

x = -11

The type of sampling used by the BLS (Bureau of Labor Statistics) for its National Compensation Survey, where employers are divided by size in the second stage of sampling, is known as stratified sampling.

Stratified sampling involves dividing the population into subgroups or strata based on certain characteristics or criteria. In this case, the BLS divides the employers into different size categories. Within each stratum, a sample is then randomly selected to represent that specific subgroup. This approach allows for a more precise estimation of employment costs within each size category. By using stratified sampling, the BLS ensures that the sample is representative of the different employer sizes and allows for more accurate and reliable estimates of employment costs at a national level.

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The ellipses centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1) is mathematically given as

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

Generally, the equation for three points is mathematically given as

a+2b+4c=1.....1  for the variable (1, 2)

4a+4b+4c=1.....2  for the variable (2, 2)

9a+3b+c=1.....3  for the variable (3, 1)

Step 1

Here we solve equations 1 and 2 simultaneously to find the value of b

Therefore

equ 2-equ1

3a+2b=0

b=-1.5a....4

Step 2

We solve equations 1 and 3 simultaneously to find the value of c

Where

9*equ1-equ3 gives

-15b-35c=-8

c=8-15b

subbing equ 4 we have

c=8+22.5a ....5

Step 3

Put values of b and c in equation 2, and we have

4a-6a+32+90a=1

a=-31/88

a=-0.3523

The value of b will be

b=-1.5*a

b=0.5284

The value of b will be

c=8-22.5*a

c=15.9268

Step 4

In conclusion, the equation is given as

By substituting the values of a b and c into the general formula we have

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

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Answer:

its a right angle!

Step-by-step explanation:

<ABC is a complementary angle.

In testing the equality of population proportions using chi-square, at least 3 categories or populations need to be able to perform this analysis

Now, According to the question:

A chi-square test for equality of two proportions is exactly the same thing as a z-test. The chi-squared distribution with one degree of freedom is just that of a normal deviate, squared. You're basically just repeating the chi-squared test on a subset of the contingency table.

The chi-square test is used to compare more than two independent populations. The test is pretty similar to that of two population proportions except for the fact that the contingency table involved in the study includes 2 rows and c number of columns indicating the number of populations.

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The formula for for Rn is given as Rn = Σ 18/n (1 - 12i/n + 36i²/n²).

We are given the function f(x) = 3x² on the interval [-1, 5] . This gives

Δx =6/n and xi= -1 + 6i/n.

Therefore,

Rn =  Σ f(xi) Δx

     = Σ 3 (-1 + 6i/n)² 6/n

     = Σ 18/n (1 - 12i/n + 36i²/n²)

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The concept of limit is specifically used in the various definitions of continuity. Roughly speaking, a function is continuous if all of its limits agree with the values of the function. The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

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To use Descartes's Rule of Signs, we need to look at the coefficients of the polynomial function in standard form, which are 3, -4, 1, and 2.

First, we count the number of sign changes in the coefficients of f(x). There are two sign changes: from positive to negative (between 3 and -4) and from negative to positive (between -4 and 1).

Therefore, f(x) has either 2 or 0 positive real zeros.

Next, we apply the rule to the coefficients of f(-x). We get the polynomial -3x - 4(-x)^2 - x + 2, which simplifies to -4x^2 - 4x + 2.

There are two sign changes: from negative to positive (between -4 and -4) and from positive to negative (between -4 and 2).

Therefore, f(x) has either 2 or 0 negative real zeros.

In summary, f(x) has 2 possible positive real zeros and 2 possible negative real zeros.

Given the function f(x) = 3x - 4x^2 + x + 2, we can rewrite it in descending order of exponents: f(x) = -4x^2 + 4x + 2.

To find the possible number of positive real zeros, count the sign changes in the polynomial:

-4x^2 (negative) to +4x (positive): 1 sign change.
+4x (positive) to +2 (positive): no sign change.

There is 1 sign change, so there is a possibility of 1 positive real zero.

Now, we need to find the possible number of negative real zeros. To do this, substitute -x for x in the polynomial:

f(-x) = -4(-x)^2 + 4(-x) + 2 = -4x^2 - 4x + 2.

Count the sign changes in this polynomial:

-4x^2 (negative) to -4x (negative): no sign change.
-4x (negative) to +2 (positive): 1 sign change.

There is 1 sign change, so there is a possibility of 1 negative real zero.

In conclusion, using Descartes's Rule of Signs, the given function f(x) = -4x^2 + 4x + 2 has a possible 1 positive real zero and 1 negative real zero.

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The derivative dy/dx is equal to -2 / (5x) in terms of x and y.

We are asked to find the derivative dy/dx of the implicitly defined function x² × \(y^5\) × \(e^y\) = 0. To find this, we'll use implicit differentiation.
Implicit differentiation means we differentiate both sides of the equation with respect to x, treating y as a function of x, and then solve for dy/dx. So, let's differentiate both sides:
d/dx (x² × \(y^5\) × \(e^y\)) = d/dx (0)
First, we'll differentiate the left side using the product rule and chain rule:
(2x × y^5 × e^y) + (x² × 5y^4 × e^y × dy/dx) = 0
Now, we'll isolate dy/dx by subtracting the first term from both sides and then dividing by the second term:
dy/dx = - (2x × \(y^5\) × \(e^y\)) / (x² × \(5y^4\) ×\(e^y\))
We can simplify this expression by canceling out some common factors:
dy/dx = - (2x) / (5x²)
Further simplification gives:
dy/dx = -2 / (5x)
Thus, the derivative dy/dx is equal to -2 / (5x) in terms of x and y.

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Answer:

99

Step-by-step explanation:

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51 ,53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99

Just go up 2 numbers 50 times

The x-intercept is (-0.67, 0), which means that when y = 0, x = -0.67. The y-intercept is (0, 2), which means that when x = 0, y = 2.

To find the x and y-intercepts of the graph on a calculator, follow the steps given below:

First, we need to graph the equation in the calculator to obtain its graph. Then, we can read off the x and y-intercepts from the graph. Here are the steps:

Step 1: Press the ‘Y=’ button on the calculator to enter the equation in the calculator. For example, if the equation is y = 3x + 2, type this equation in the calculator.

Step 2: Press the ‘Graph’ button on the calculator. This will show the graph of the equation on the screen. The graph will show the x and y-intercepts of the equation.

Step 3: To find the x-intercept, look for the point where the graph crosses the x-axis. The x-coordinate of this point is the x-intercept. To find the y-intercept, look for the point where the graph crosses the y-axis. The y-coordinate of this point is the y-intercept. For example, consider the equation y = 3x + 2. The graph of this equation looks like this: Graph of y = 3x + 2

The x-intercept is (-0.67, 0), which means that when y = 0, x = -0.67.

The y-intercept is (0, 2), which means that when x = 0, y = 2.

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Answer: 12 cups

Step-by-step explanation:

Answer:

12 cups

Step-by-step explanation:

1 pint = 2 cups

6 pints = 6 × 2 cups = 12 cups