In ΔNOP, p = 70 inches, n = 97 inches and ∠O=163°. Find ∠N, to the nearest degree.

Our calculated t-value of \(4.22\) is greater than the critical t-value of 1.684, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean starting salary for college graduates who major in Statistics has increased.

We can use a one-sample t-test to test the claim that the mean starting salary for college graduates who major in Statistics has increased.

The null hypothesis is that the mean starting salary is still $\(54000\), while the alternative hypothesis is that the mean starting salary is greater than $\(54000\).

We can calculate the t-statistic as:

t = (sample mean - null hypothesis value) / (standard error of the mean)

= \((63500-54000)/(10540/\sqrt{40}\)

= \(4.22\)

where \(\sqrt{40}\) is the sample size.

The degrees of freedom for the t-test is \((n-1) = 39\), where n is the sample size.

Using a t-table or calculator with \(39\) degrees of freedom, a one-tailed test, and a significance level of \(0.05\), we find the critical t-value to be \(1.684\)

Since our calculated t-value of \(4.22\) is greater than the critical t-value of \(1.684\), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean starting salary for college graduates who major in Statistics has increased.

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Answer:

2z-4

Step-by-step explanation:

By using distributive property, 2/3 * 3z =  2z and 2/3 * -6 = -4

This means the answer is 2z-4

\(Answer: \large\boxed{2z-4}\)

Step-by-step explanation:

To solve:

\(\frac{2}{3} (3z-6)\)

We must use the distributive property and distribute 2/3 to the 3z and -6

...

\(\frac{2}{3} (3z-6)\)

\(=\frac{2}{3} (3z) + \frac{2}{3} (-6)\)

\(=\frac{6z}{3} + -\frac{12}{3}\)

\(=2z-4\)

Hello!

We will have three possible functions, according to the value of x, look:

f(x) = -2

f(x) = -x +1

f(x) = x² -1

Knowing it, let's analyze each statement:

f(-1) = -x +1

f(-1) = -(-1) +1

f(-1) = 1+1

f(-1) = 2

TRUE

f(-2) = -x +1

f(-2) = -(-2) +1

f(-2) = 2 +1

f(-2) = 3

FALSE

f(4) = x² +1

f(4) = 4² +1

f(4) = 16 +1

f(4) = 17

FALSE

f(1) = x² +1

f(1) = 1² +1

f(1) = 1 +1

f(1) = 2

FALSE

Given:

1 Van and 4 buses filled with 195 students.

1 Van and 5 buses filled with 241 students.

Let x and y be the number of students in Van and number of students in bus.

Subtract equation (1) from equation (2)

Substitute y=46 in equation (1)

Number of students that van can carry is 11.

Number of students that bus can carry is 46

Answer:

76

Step-by-step explanation:

6+13=19

19/2=9.5

9.5x8=76

In 5 pounds we will get  2.27 kilograms.

What is Kilogram and Pound?

Converting into required form, we get,

1 pound = 0.45359237 kg

Then 5 pound = 0.45359237  X 5

5 pound = 2.27 kilograms

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Step-by-step explanation:

\(-2(-9x + 6y)\) is factored, use the Distributive Property to un factor this expression.

Work:

\(-2(-9x + 6y) \\=-2(-9x)+-2(6y)\\=18x-12y\)

The acceleration of the car is 8 m/s^2.

The figure shown in the question is the distance-time graph of a muscle car accelerating from a standstill. The table lists the coordinates of points on the graph.The following observations can be made from the graph and the table: The car is at rest at time t=0 and at distance x=0. It then starts accelerating, and its speed increases uniformly with time. The slope of the distance-time graph is the velocity of the car.

Since the velocity is increasing uniformly, the slope of the graph is a straight line with a positive slope. The area under the graph between two points gives the displacement of the car during that time interval. The displacement can be calculated as the product of the average velocity and the time interval. Using the coordinates in the table, we can calculate the average velocities for each time interval and the displacement during that interval.

(a) The average velocity of the car between t=0 and t=2 is equal to the slope of the graph between the two points (0,0) and (2,32). This can be calculated as the difference in distance divided by the difference in time:Average velocity = (32 - 0) / (2 - 0) = 16 m/sThe displacement during this time interval is given by the area under the graph between the two points:Displacement = (1/2) x 32 x 2 = 32 m

(b) The acceleration of the car is given by the slope of the velocity-time graph. Since the velocity is increasing uniformly with time, the velocity-time graph is also a straight line with a positive slope. The slope of the velocity-time graph is equal to the acceleration. We can calculate the slope of the velocity-time graph between two points using the coordinates in the table. For example, the slope between t=0 and t=2 is given by the difference in velocity divided by the difference in time:Slope = (16 - 0) / (2 - 0) = 8 m/s^2

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Answer:

\(Range: \{2,4, 3, -9\}\)

Step-by-step explanation:

Given

The ordered pairs

Required

The range of the function

The range of a function is represented as:

\(Range = \{y_1,y_2,y_3,,,y_n\}\)

i.e. we only write out the y values.

So, the given ordered pairs can be represented as

\((x,y) = \{(1,2), (-3,4), (3, 3), (0, -9)\}\)

So, we have:

\(Range= \{2,4, 3, -9\}\)

Answer:

Is there any answer choices so I have some opions

Step-by-step explanation:

Answer:

52x < $211

Step-by-step explanation:

If Roland uses $289 to purchase the laptop from the $500 that was given to him then he would be left with

500 - 289 = $211

With this he can purchase video games. Since each video game costs the same price of $52 then we can use the variable x to represent the number of games he can buy with the following inequality...

52x < $211

Answer:

2

Step-by-step explanation:

13+7x=27

-13 -13

7x=14

÷7

x=2

Answer:

x = 2

Step-by-step explanation:

Given

#1) Subtract 13 from each side.

#2) Divide 7 from each side.

Answer:

98º

Step-by-step explanation:

Answer:

The Area of the composite figure would be 76.26 in^2

Step-by-step explanation:

According to the Figure Given:

Total Horizontal Distance = 14 in

Length = 6 in

To Find :

The Area of the composite figure

Solution:

Firstly we need to find the area of Rectangular part.

So We know that,

\(\boxed{ \rm \: Area \: of \: Rectangle = Length×Breadth}\)

Here, Length is 6 in but the breadth is unknown.

To Find out the breadth, we’ll use this formula:

\( \boxed{\rm \: Breadth = total \: distance - Radius}\)

According to the Figure, we can see one side of a rectangle and radius of the circle are common, hence,

\( \longrightarrow\rm \: Length \: of \: the \: circle = Radius\)

\(\longrightarrow \rm \: 6 \: in = radius\)

Hence Radius is 6 in.

So Substitute the value of Total distance and Radius:

\( \longrightarrow\rm \: Breadth = 14-6\)

\( \longrightarrow\rm \: Breadth = 8 \: in\)

Hence, the Breadth is 8 in.

Then, Substitute the values of Length and Breadth in the formula of Rectangle :

\( \longrightarrow\rm \: Area \: of \: Rectangle = 6 \times 8\)

\(\longrightarrow \rm \: Area \: of \: Rectangle = 48 \: in {}^{2} \)

Then, We need to find the area of Quarter circle :

We know that,

\(\boxed{\rm Area_{(Quarter \; Circle) } = \cfrac{\pi{r} {}^{2} }{4}} \)

Now Substitute their values:

\(\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 6 {}^{2} }{4} \)

Solve it.

\(\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 36}{4} \)

\(\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times \cancel{{36} } \: ^{9} }{ \cancel4} \)

\(\longrightarrow\rm Area_{(Quarter \; Circle)} =3.14 \times 9\)

\(\longrightarrow\rm Area_{(Quarter \; Circle) } = 28.26 \: {in}^{2} \)

Now we can Find out the total Area of composite figure:

We know that,

\(\boxed{ \rm \: Area_{(Composite Figure)} =Area_{(rectangle)}+ Area_{ (Quarter Circle)}}\)

So Substitute their values:

\(\longrightarrow \rm \: Area_{(Composite Figure)} =48 + 28 .26\)

Solve it.

\(\longrightarrow \rm \: Area_{(Composite Figure)} =\boxed{\tt 76.26 \:\rm in {}^{2}} \)

Hence, the area of the composite figure would be 76.26 in² or 76.26 sq. in.

\( \rule{225pt}{2pt}\)

I hope this helps!

Answer:

\(Rate = 0.13\)

Step-by-step explanation:

Given

\(y = \sqrt[3] x\)

Required

Determine the average rate of change over [2,7]

This is calculated as:

\(Rate = \frac{f(b) - f(a)}{b - a}\)

In this case:

\(b = 7\) and \(a = 2\)

So, we have:

\(Rate = \frac{f(7) - f(2)}{7-2}\)

\(Rate = \frac{f(7) - f(2)}{5}\)

From the table:

f(7) = 1.91

f(2) = 1.26

\(Rate = \frac{1.91 - 1.26}{5}\)

\(Rate = \frac{0.65}{5}\)

\(Rate = 0.13\)

The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form

The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.

The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.

The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.

Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.

Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.

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Jane has 6 - 14 - 12 = -20 boxes of beads left.

Jane initially had 6 boxes of beads.

She used 14 of those boxes to make face mask holders and gave 12 boxes to her sister.

To find out how many boxes of beads she has left, we need to subtract the boxes used and given away from the initial number.

First, let's calculate the total number of boxes used and given away:

Total boxes used and given away = Boxes used for face mask holders + Boxes given to sister

Total boxes used and given away = 14 + 12

Total boxes used and given away = 26

Next, we can subtract the total boxes used and given away from the initial number of boxes Jane had:

Boxes left = Initial number of boxes - Total boxes used and given away

Boxes left = 6 - 26

Boxes left = -20

The result is -20, which implies that Jane has a deficit of 20 boxes of beads.

This means she doesn't have any boxes of beads left; she has a shortage of 20 boxes based on the activities she performed.

It's important to note that having a negative value indicates that Jane doesn't have enough boxes to fulfill her activities.

If the result were positive, it would represent the number of boxes remaining.

However, in this case, Jane has used and given away more boxes than she initially had, resulting in a negative value.

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Answer:

Value of x = 11 ° , ∠B = 108° ,∠C = 36° ,∠D = 36°

Step-by-step explanation:

Given :

In ΔBCD , BC = BD And ∠B= (13x-35)° , ∠C= (5x-19)° ,∠D=(2x+14)°

To Find :

value of x and ∠D , ∠B and ∠C

Solution:

∵ BC=BD , So ∠C = ∠D

Therefore 5x-19 = 2x+14

3x = 33 , ∴ x=11°

So, ∠B = (13×11) - 35 = 108°

∠C = (5×11)-19 = 36°

∠D= (2×11) +14 =36°

The distance between the two towns on the map was found to be 30.67 centimeters by setting up and solving a proportion between the distances on the map and the actual distances.

The problem provides us with a scale on the map of 3 cm to 45 km, which means that every 3 centimeters on the map represents 45 kilometers in the actual world. Let x be the distance between the two towns on the map in centimeters. Using the proportion, we can set up the relationship between the distances on the map and the actual distances as follows:

3 cm / 45 km = x cm / 460 km

Here, we set up a ratio between the distance on the map and the actual distance, where the distance on the map is x centimeters and the actual distance between the towns is 460 kilometers. We can then cross-multiply to solve for x:

45 km * x cm = 3 cm * 460 km

This gives us:

45x = 1380

x = 1380 / 45

x = 30.67 cm

Therefore, the distance between the two towns on the map is 30.67 centimeters.

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Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16

The linear inequality depicted by the graph is: \(y \leq \frac{2}{3}x + \frac{1}{5}\)

A linear function is modeled by:

y = mx + b

In which:

For this line, when x = 0, y = 0.2, hence the y-intercept is of b = 0.2. When x = 3, y = 2.2, hence the slope is given as follows:

\(m = \frac{2.2 - 0.2}{3 - 0} = \frac{2}{3}\)

Hence the equation of the line is:

\(y = \frac{2}{3}x + 0.2\)

\(y = \frac{2}{3}x + \frac{1}{5}\)

The inequality is the values below(less) than the line, also including it, as it is not dashed, hence:

\(y \leq \frac{2}{3}x + \frac{1}{5}\)

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Answer:

∠ Y = 60° , WY = 7 in

Step-by-step explanation:

the sides WX and YX are congruent then the triangle is isosceles with base angles congruent, that is

∠ Y = ∠ W = (180 - 60)° ÷ 2 = 120° ÷ 2 = 60°

Since all 3 angles in the triangle are congruent , all 60° then the triangle is equilateral with 3 congruent sides, then

WY = 7 in

The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24

Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.

Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9

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The volume of the triangular prism will be 400 cubic feet.

Given that:

Width, W = 15 feet

Height, h = 8 feet

Base length, b = 6²/₃ feet

Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.

The volume of the triangular prism is calculated as,

V = 1/2 · b · h · W

V = 0.5 · 6²/₃ · 8 · 15

V = 400 cubic feet

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Answer:

The correct answer is B) The author repeats words with positive connotations to help emphasize her point. In the passage from A Vindication  of the Rights of Woman the author uses words like "perfection",  "reason", "virtue", "knowledge" and "happiness" which have positive connotation to emphasize her point that woman deserve equal rights.

Step-by-step explanation:

zero

Step-by-step explanation:

Since the given depths are negative when measured against the ground level, then that means that the ground level is represented by zero.

The relative frequency of the first class is 0.25.

Relative frequency is a term used to describe the proportion of times an event occurs in a set of data, compared to the total number of events. In other words, it's the ratio of the frequency of the event to the total frequency of all events.

To determine the relative frequency of the first class, we need to first find the frequency of the first class. The frequency is the number of times the event occurs in the data set. Let's say the frequency of the first class is "f". Then, the relative frequency can be found by dividing the frequency of the first class by the total number of events (let's say it's "n").

Relative frequency = f / n

We round our answer to three decimal places to make it easier to understand and compare to other data.

If there are 100 total events and the frequency of the first class is 25, then the relative frequency would be:

Relative frequency = 25 / 100 = 0.25

Complete Question:

Determine the relative frequency of the first class. round your answer to three decimal places when 100 total events and the frequency of the first class is 25

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The degree of the polynomial is even.

Algebraic expressions called polynomials include indeterminates and constants. Polynomials can be considered a particular type of mathematics. In practically all areas of mathematics, including calculus, they are used to express numbers. They are also regarded as being crucial in several areas of mathematics. Examples of polynomials include 2x + 9 and \(x^{2}\) + 3x + 11. The "=" sign is absent from all of these samples, as you may have observed.

The polynomial's degree is even since the final behavior is the same in both directions (for -x and for +x, y→∞).

The y-intercept is the fixed term. Since it is not an integer, evenness and oddness cannot be determined.

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