Christopher collected data from a random sample of 800 voters in his state asking whether or not they would vote to reelect the current governor. Based on the results, he reports that 54% of the voters in his city would vote to reelect the current governor. Why is this statistic misleading?

The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

For more such information on: angle

https://brainly.com/question/25716982

#SPJ8

Answer:

200 lbs.

Step-by-step explanation:

Divide mass value by 16 to convert oz to lbs.

3,200/16=200

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

For more questions on cross-product property:

https://brainly.com/question/14542172

#SPJ8

Answer:

great! what else?

It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

To multiply the square roots V7 and V2, we can combine the numbers inside the square roots and simplify the result.

V7 * V2 = V(7 * 2) = V14

Multiplying the numbers under the square roots, we get 7 * 2 = 14. Therefore, the product of V7 and V2 is V14.

This means that the square root of 14 is the result of multiplying V7 and V2. However, it is important to note that V14 cannot be further simplified because 14 does not have any perfect square factors.

In summary, the product of V7 and V2 is V14. It is worth mentioning that when multiplying square roots, we can multiply the numbers inside the square roots and keep the square root symbol intact, unless the numbers inside have perfect square factors that can be simplified further.

It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

for such more question on simplest form

https://brainly.com/question/4077992

#SPJ8

Answer:

The height of the triangle would be

5

√

15

c

m

or

19.36

c

m

Step-by-step explanation:

The maximum volume of the cylinder is approximately 1257 cubic centimeters.

The volume V of a right circular cylinder with radius r and height h is given by:

V = πr²h

Substituting the given expressions for the radius and height of the cylinder, we get:

V = πx²(800/πx - x)

Simplifying the expression, we get:

V = 800x - πx³

To find the maximum value of V, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

dV/dx = 800 - 3πx² = 0

3πx² = 800

x² = 800/3π

x ≈ 6.43

Substituting this value of x back into the expression for V, we get:

V ≈ 1257

Learn more about volume of cylinder here: https://brainly.com/question/9554871

#SPJ1

Answer:1,4,7

Step-by-step explanation:

To simplify

Now,

Again,

Then,

So, the simplified form is

Answer:

6a + 8

Step-by-step explanation:

The opposite sides of the rectangle are equal , then

perimeter (P ) is calculated as

P = 2(2a) + 2(a + 4)

   = 4a + 2a + 8

   = 6a + 8

Answer:

$66.11

Step-by-step explanation:

32.25 increase 105% =

32.25 × (1 + 105%) = 32.25 × (1 + 1.05) = 66.1125

Answer:

45

Step-by-step explanation:

Answer:

3 hours

Step-by-step explanation:

the speed of the river current is 80% less

80% of 60 is 48

so the speed is now 48 mph, because the river is pushing the boat back (duh)

144 miles/ 48 mph is 3 hours.

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

When you distribute the 7 to each set you get 14-21n and 14-21n

Step-by-step explanation:

Answer:

140% procent increase of your vase

Answer:7cm

Step-by-step explanation:

m^3=343

Take the cube root of both sides

m=7

Answer:

the correct answer is 15.2

Answer:

he pays 2991.5 dollars state income tax

Step-by-step explanation:

5% or 0.05

59830 * 0.05 = 2991.5

he pays 2991.5 dollars state income tax

Answer:

27

Step-by-step explanation:

The formula for the volume of a cube is given as \(V=s^{3}\). if s=3in, then V=27inches cubed.

The context that represents linear growth is "A music service has a fixed monthly cost and charges $0.35 for each downloaded song".

A linear growth function has a constant slope, increases by a consistent amount over time, and is represented graphically as a line.

In other words, when a quantity rises in proportion to another factor or variable in a connection it is said to be a linear growth.

Let's check the given option to check whether it is linear growth or not.

1. A music service has a fixed monthly cost and charges $0.35 for each downloaded song.

Here there is a fixed cost and the cost will increase when the number of songs is increased

Let's say the constant charge is 'y' and the number of songs is 'x' then the equation that can represent the situation is

=> f(x) = y + x(0.35)

Here there is a constant increase in cost

∴ The given situation can represent Linear growth.

2. An elevator descends at a rate of 32 feet per second.

Here descends indicated the elevator decreases in speed of the elevator at a point the elevator speed will be zero

∴ It doesn't show the linear growth

3. OA town's population shrinks at a rate of 9.4% every year.  

Here the town's population is shrinking means It doesn't show any growth

∴ It doesn't show the linear growth  

4. The amount of certain medication in a person's bloodstream decreases by 1/4 every day.  

Here, the person's bloodstream decreases by 1/4 every day.  

∴ It doesn't show the linear growth    

Therefore,

The context that represents linear growth is "A music service has a fixed monthly cost and charges $0.35 for each downloaded song".

Learn more about Linear Growth at

https://brainly.com/question/4146101

#SPJ1

Answer:

They ordered 432 bottles of water

Step-by-step explanation:

1 multipack = 6 bottles

3 multipacks = 1 box

24 boxes = 24 (3 multipacks)

24 boxes = 72 multipacks

72 multipacks = 72 (6 bottles)

72 multipacks = 432 Bottles

The given statement is FALSE.

Given statement;

When practicing statistics in real life, it is not very important to check the necessary assumptions of a statistical procedure to effectively carry out and use the results.

The above-mentioned statement is FALSE.

→ We are aware that checking assumptions is crucial when applying statistics in daily life because failing to do so will prevent us from receiving fair answers to our statistical queries or drawing valid inferences. To use the good process and appropriate statistical distributions while utilizing statistics in daily life, it is crucial to examine assumptions.

To learn more about statistics click here:

brainly.com/question/23091366

#SPJ4

The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

Learn more about amplitude click;

https://brainly.com/question/9525052

#SPJ1

Edwin needs to sell 44,625 jars of jam to break even.

To determine how many jars of jam Edwin needs to sell to break even, we'll calculate the breakeven point using the following formula:

Breakeven Point = Fixed Expenses / (Selling Price per Unit - Variable Cost per Unit)

Given information:

Selling Price per Unit (SP) = $1.90

Variable Cost per Unit (VC) = $1.10

Fixed Expenses = $35,700.00 per year

Plugging in the values into the formula:

Breakeven Point = $35,700 / ($1.90 - $1.10)

Breakeven Point = $35,700 / $0.80

Breakeven Point = 44,625 jars

Therefore, Edwin needs to sell 44,625 jars of jam to break even.

for such more question on breakeven point

https://brainly.com/question/30551452

#SPJ8

The complement of the set {2,4,11,14,17} is {3, 6, 9, 19}.

The complement of set A is defined as a set that contains the elements present in the universal set but not in set B.

In other words, the complement of a set is the difference between the universal set and the set itself.

Therefore,

U = universal set =  {2, 3, 4, 6, 9, 11, 14, 17, 19}

Therefore,

complement of {2,4,11,14,17} is the values that are not in the universal set.

Therefore,

complement of  {2,4,11,14,17}  = {3, 6, 9, 19}

learn more on sets here: brainly.com/question/29166083

#SPJ1

Answer:

\(f(x)-g(x)=2x^2(1-x)\)

Step-by-step explanation:

Given that,

\(f(x)=x^2\\\\g(x)=2x^3-x^2\)

We need to find the value of f(x)-g(x).

Put the values of f(x) and g(x). So,

\(f(x)-g(x)=x^2-(2x^3-x^2)\\\\=x^2-2x^3+x^2\\\\=2x^2-2x^3\\\\=2x^2(1-x)\)

So, the value of f(x)-g(x) is equal to \(2x^2(1-x)\).

Answer:

D

Step-by-step explanation:

72.25 in^2

The minimum possible area of each square cardboard piece that is used to produce circular drink coasters is 72.25 in².

The equation of the circle is the equation that is used to represent the circle in the algebraic equation form with the value of the center point in the coordinate plane and measure of radius.

The standard form of the equation of the circle can be given as,

\((x-h)^2+(y-k)^2=r^2\)

Here (h,k) is the center of the circle, and (r) is the radius of the circle.

A company produces circular drink coasters. the equation which represents the size of a coaster is,

\(x^2+y^2=18.06\)

The units are in inches. This equation can be written as,

\(x^2+y^2=(280/16)\)

\(x^2+y^2=(17/4)^2\)

Compare it with the equation of the circle, we get,

h=0

k=0

r=17/4 inch

The radius of the circular coaster is 17/4. Its diameter of it is,

\(d=2\times \frac{17}{4}\\ \\d=\frac{17}{2}\)

Now, each coaster is cut from a square piece of cardboard. The diameter of the circular coaster will be equal to the side of the square piece of cardboard.

a=d=17/2 inch

The area of the square is the square of its side. Thus, the area of a square piece of cardboard is,

A=a^2

A=(17/2)^2

A=75.25inch^2

Thus, the minimum possible area of each square cardboard piece that is used to produce circular drink coasters is 72.25 in².

Learn more about the equation of circle here;

brainly.com/question/1506955

#SPJ2

Answer:

he would have to pick 1,2,3 or 5...so that is 4/6 chance

if you need the percentage (im not sure if its right) it would be 76%