The convex polygon below has 8 sides. Find the value of x ?

Yes, we would have reason to believe that the proportion of rats developing tumors when subjected to this diet has increased if the experiment were repeated and 16 of 48 rats developed tumors.

To determine whether there is an increase in the proportion of rats developing tumors when subjected to a coffee bean diet, we can conduct a hypothesis test using the 0.05 level of significance.

1. State the hypotheses:

  - Null hypothesis (H0): The proportion of rats developing tumors remains the same.

  - Alternative hypothesis (Ha): The proportion of rats developing tumors has increased.

2. Identify the test statistic:

  We will use a z-test to compare the observed proportion of rats developing tumors with the expected proportion.

3. Set the significance level:

  The significance level (α) is given as 0.05.

4. Collect data:

  In the original experiment, 25% of rats developed tumors. In the repeated experiment, 16 out of 48 rats developed tumors.

5. Compute the test statistic:

  The test statistic formula for comparing proportions is:

  z = (p - P) / sqrt(P(1-P)/n)

  where p is the observed proportion, P is the hypothesized proportion, and n is the sample size.

  Using the observed proportion (16/48 = 0.333), the hypothesized proportion (0.25), and the sample size (48), we can calculate the test statistic.

6. Determine the critical value:

  Since we are using a 0.05 level of significance and conducting a one-tailed test (Ha: >), we can find the critical value from the standard normal distribution table. The critical value for a 0.05 significance level is 1.645.

7. Make a decision:

  If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the proportion of rats developing tumors has increased.

8. Calculate the test statistic:

  Plugging in the values into the formula, we calculate the test statistic:

  z = (0.333 - 0.25) / sqrt(0.25 * 0.75 / 48) = 1.404

9. Compare the test statistic and critical value:

  The test statistic (1.404) is less than the critical value (1.645).

10. Make a decision:

   Since the test statistic is not greater than the critical value, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the proportion of rats developing tumors has increased when subjected to this diet.

In summary, based on the given data and conducting a hypothesis test, we do not have reason to believe that the proportion of rats developing tumors has increased if the experiment were repeated and 16 of 48 rats developed tumors.

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Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

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The number is 11. 63

Algebraic expressions are mathematical expressions comprised of constants and variables.

These expressions combines numbers, symbols, variables and mathematical operators such as addition, subtraction, multiplication, etc

From the information, let the number be x

2( x + (-6)) = x - 3/ 8

expand the bracket

2x - 12 =  8x - 3 /8

cross multiply

8 ( 2x - 12) = 8x - 3

expand the bracket

16x - 96 = 8x - 3

collect like terms

16x - 8x = -3 + 96

8x = 93

Make 'x' the subject

x = 93/ 8

x = 11. 63

The number is 11. 63

Thus, the number is 11. 63

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Answer: 4 inches

Step-by-step explanation:

you would take the 20 and minis the 16

Answer:

See below.

Step-by-step explanation:

(5a^2 + 4ab – 3b^2) – (–5ab + 4b^2 + 3a^2)

5a^2+4ab-3b^2+5ab-4b^2-3a^2

(5a^2-3a^2)+(4ab+5ab)+(-4b^2-3b^2)

2a^2+9ab-7b^2

-hope it helps

Answer:

You can answer this with modern calculators very easily.

Step-by-step explanation:

\( = 47.000\)

\( = 4,7 \times 10.000 \)

\( = 4,7 \times {10}^{1+1+1+1} \)

\( = 4,7 \times 10^4 \)

Answer:

156 cm³

Step-by-step explanation:

The solid is a prism with a trapezoid base.

volume = (area of base) × height

V = (8 cm + 5 cm)(1/2)(4 cm) × 6 cm

V = 156 cm³

Answer:

hold yo ablo espanol

Step-by-step explanation:

Answer:

\frac{-3 + 3(a + h)^{2}  + 3 - 3a^{2} }{h}

Step-by-step explanation:

All you have to do is take your values and plug them in and simplify!

\(\frac{-3 + 3(a + h)^{2} - (-3 + 3a^{2}) }{h}\)

\(\frac{-3 + 3(a + h)^{2} + 3 - 3a^{2} }{h}\)

Answer:

0.5 (any number between 0 and 1)

Step-by-step explanation:

34 * 0.5 = 17

34 > 17 > 0

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of depression increases.

the arc formed as the line of sight drops from the horizon. The angle of depression is the angle formed when an object is perceived below the observer's height between the horizon and the line of sight of the observer. The depression angle is the angle formed between the line of sight looking down at the object and the horizontal line of sight. If you are on a hill or a building and you are looking down at something, you can tell the slope. To measure these angles, a theodolite or an inclinometer might be employed.

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of the depression increases.

∠x = 65° ≤ ∠XYZ

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With a triangle, the sum of any two side lengths must be greater than the third side length. If this is not true, then the side lengths cannot make a triangle. Let's go through each set of side lengths and determine which would and wouldn't work.

a. 3, 4, 8 - will not make a triangle

3 + 4 = 7 > 8 = false

3 + 8 = 11 > 4 = true

4 + 8 = 12 > 3 = true

b. 7, 6, 12 - will make a triangle

7 + 6 = 13 > 12 = true

7 + 12 = 19 > 6 = true

6 + 12 = 18 > 7 = true

c. 5, 11, 13 - will make a triangle

5 + 11 = 16 > 13 = true

5 + 13 = 18 > 11 = true

11 + 13 = 24 > 5 = true

d. 4, 6, 12 - will not make a triangle

4 + 6 = 10 > 12 = false

4 + 12 = 16 > 6 = true

6 + 12 = 18 > 4 = true

e. 4, 6, 10 - will not make a triangle

4 + 6 = 10 > 10 = false

4 + 10 = 14 > 6 = true

6 + 10 = 16 > 4 = true

Hope this helps!

Answer:

-4

Step-by-step explanation:

Answer:

x = -4

Step-by-step explanation:

Isolate the variable x

x - 8 = -12

To isolate the variable, add 8 to both sides (this cancels the 8 out on the left side)

x - 8 + 8 = -12 + 8

x + 0 = -4

x = -4

Answer:

75/100 = 3/4

Step-by-step explanation:

75% in rate form is: 75/100, which can be also given in reduced fraction form by simplifying two factors "5" : 75/100 = 3/4

Answer:

(3,-1/2)

Step-by-step explanation:

The term "100 points" usually indicates a high level of achievement or success in a particular area.

The term "100 points" can refer to a number of different things depending on the context. For example, in sports, it could refer to a team scoring 100 points in a game.

In wine tasting, it could refer to a perfect score given to a wine by a critic or judge. In school, it could refer to receiving a perfect score on an exam or assignment worth 100 points.

It's important to note that while a perfect score of 100 points is often seen as the ultimate goal, it's not always necessary or even possible in some situations. In many cases, simply doing your best and striving for improvement is enough to be considered successful.

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The inequality that represents p, the number of people the theater can seat is p ≤ 25

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

A movie theater can seat a maximum of 25 people

This means that

Maximum =  25 people

In other words, the movie theatre can allow 25 or less people to attend a movie

In inequality, 25 or less means less than or equal to 25

When represented as an inequality expression, we have

≤ 25

Using the variable p, we have

p ≤ 25

Hence, the inequality is p ≤ 25

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The intervals on which the graph is increasing at (-∞, 0) U (3.5, ∞). On the other hand, the graph is decreasing at (0, 3.5)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Increased or decreased functions are two categories of functions. Consequently, a function increases when the y-values grow, while a function decreases when the y-values decrease.

The graph indicates the y-values increase in the x-intervals from -∞  to 0 and from 3.5 to ∞. You can express that a function is increasing in the following ways using interval notation:  (-∞, 0) U (3.5, ∞).

The graph, on the other hand, is decreasing: (0, 3.5)

Hence, the intervals on which the graph is increasing at (-∞, 0) U (3.5, ∞). On the other hand, the graph is decreasing at (0, 3.5)

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The solution to the algebraic problem is \(x^{2}\)

What is an Algebraic Equation?

An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

Solution:

(\(x^{3}\) – 1) = (x+2)

On dividing (\(x^{3} - 1\)) by (x+2)

The first term of the quotient will be x^2 by following the Long Division Method of Algebraic Division.

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Answer: 96, 192, and 384

Step-by-step explanation:

It keeps doubling 48 + 48, 96 + 96, 192 + 192

We have to apply the next formula:

A= P(1+r)^t

Where:

P= original population (284)

r = growing rate (in decmal form) (4/100=0.04)

t= years passed (2020-2013= 7)

A= number of students after t years

Replacing:

A = 284 (1+0.04)^7

A= 284(1.04)^7

A= 373 students

Answer:

A cylinder has parallel discs bases that are congruent in size.

Step-by-step explanation:

Answer:

A, C, D

Step-by-step explanation:

\(\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}\)

1 hour = 6 pages

So,

5 hours = 6×5

ㅤㅤㅤㅤ= 30 pages

therefore, She writes 30 pages in 5 hours.

Answer:

30 pages

Step-by-step explanation:

This can be written as an simple ratio (x/y), a ratio of 6/1

X= is the number of pages

Y= the hour(s)

He can write 6 pages in 1 hour, now we have to find how many pages he can write in 5 hours

This can be write this as an equation, we already have the first ratio and we know the Y value of the second ratio which is 5

6/1= x/5

To find X or how many pages he can write in 5 hours, you have to cross multiply and you will get

30=1x or x=30

So he can write 30 pages in 5 hours

Answer:

If a graph is an Euler Circuit that mean that it can be traversed and begins and has all even verticies.  This allows you to start and stop at the same verticie.

Step-by-step explanation:

Answer:

3×10^9

Step-by-step explanation:

0.03x=90,000,000

x=90000000/0.03

x=3×10^9

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The calculated value of the mode(s) of the data is (a) 1

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

1, 0, 2, 2, 3, 0, 1, 1, 4, and 5

By definition, the mode of a data is the data that has the highest frequency

Using the above as a guide, we have the following:

The data element 1 has the highest frequency of 3

Other data elements have lesser frequencies

Hence, the mode(s) of the data is (a) 1

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We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

We have,

To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:

S = ∫(a to b) 2πy√(1 + (f'(x))²) dx

In this case,

f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).

Let's calculate the surface area:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx

Simplifying the expression inside the integral:

S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx

Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

To find the surface area of revolution about the x-axis of the function

f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx

Let's calculate the integral:

S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx

To simplify the calculation, let's simplify the expression inside the integral first:

S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx

Next, we can distribute the square root and simplify further:

S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx

Thus,

We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

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