2. Find the area of the trapezoid. Leave your answer in the simplest radical form.

Answer:

1.) 5

2.) -6

3.) -3

4.) -15

5.) 5

Answer:

tanx-(\sqrt(11))/(5)cosx>0

Step-by-step explanation:

Because to do this kind of trig you first have to know how to do basic trg

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h,k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² - 6x

y = x² + 2(- 3)x + 9 - 9 + 2 = (x - 3)² - 7 ← in vertex form

with vertex = (3, - 7)

To determine whether maximum or minimum consider the value of a

• If a > 0 then minimum

• If a < 0 then maximum

here a = 1 > 0 ⇒ minimum

Hence (3, - 7) is a minimum

Answer:

  f(x)

Step-by-step explanation:

f(x) apparently has an initial value of 15.

g(x) apparently will have an initial value of 6 or less, since g(1) = 6 and it has increasing slope.

h(0) = 4^0 +3 = 3

j(0) = 10·2^0 = 10

The largest initial value among the initial values {15, <6, 3, 10} is 15.

  f(x) has the largest y-intercept

_____

The graph shows two ways g(x) can be modeled. One is exponential with an initial value of 4; the other is quadratic with an initial value of 6.

Final answer:

Among the functions provided, j(x) = 10(2)^x has the highest y-intercept, which is 10, found by evaluating the function at x equals 0.

Explanation:

To determine which function has the highest y-intercept, we need to examine each function and look for the point where the graph crosses the y-axis (when x is 0). Unfortunately, the only function provided with enough information to determine the y-intercept directly is h(x) = 4^x + 3. Evaluating h at x equals 0 gives us h(0) = 4^0 + 3, which simplifies to 1 + 3, yielding a y-intercept of 4. The function j(x) = 10(2)^x would have a y-intercept of 10 when x is 0. However, without the specifics of f(x) and not enough points to determine a pattern in g(x), it is not possible to accurately determine their y-intercepts. Thus, between h(x) and j(x), j(x) has the highest y-intercept at 10.

The outlier is 100- it will raise the mean and shift the median

Final answer:

The outlier in the data set is $100, which substantially increases the mean, making it a less reliable measure of the central tendency than the median, which remains unaffected by the outlier.

Explanation:

To identify the outlier in the data set, we first arrange the pledge amounts in ascending order: $10, $15, $17, $20, $20, $32, $40, $100. The value $100 stands out as the outlier because it's significantly higher than the rest of the data.

The mean (or average) is calculated by adding all the numbers together and dividing by the total number of amounts, which is 8 in this case. The outlier can drastically increase the mean, making it less representative of the central tendency of the remaining data. The median, however, is the middle value of the ordered list. Since we have an even number of values, the median is the average of the two middle numbers. In the presence of an outlier, the median remains unaffected because it depends only on the middle values.

Therefore, the outlier has a greater effect on the mean than it does on the median, making the median a more reliable measure of central tendency in this scenario.

Answer:

68

Step-by-step explanation:

We let the random variable X denote the height of students of the college. Therefore, X is normally distributed with a mean of 175 cm and a standard deviation of 5 centimeters.

We are required to determine the percent of students who are between 170 centimeters and 180 centimeters in height.

This can be expressed as;

P(170<X<180)

This can be evaluated in Stat-Crunch using the following steps;

In stat crunch, click Stat then Calculators and select Normal

In the pop-up window that appears click Between

Input the value of the mean as 175 and that of the standard deviation as 5

Then input the values 170 and 180

click compute

Stat-Crunch returns a probability of approximately 68%

Final answer:

Using the empirical rule for a normal distribution, approximately 68% of the students' heights fall within one standard deviation (170 cm to 180 cm) from the mean of 175 cm.

Explanation:

The student's question involves applying the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data, which states that:

About 68% of the data falls within one standard deviation of the mean.

About 95% falls within two standard deviations.

About 99.7% falls within three standard deviations.

In this case, the mean height is 175 cm and the standard deviation is 5 cm. The student is interested in the percentage of students with heights between 170 cm and 180 cm, which corresponds to one standard deviation below and above the mean, respectively. Therefore, using the empirical rule, we can conclude that approximately 68 percent of the students' heights will lie in this range.

Answer:

John receives a pay of $3,500.00

Step-by-step explanation:

x = John's pay

x = 1/2x + 250 + 3/7x     [1/2 = 7/14 and 3/7 = 6/14]

x = 13/14x + 250

x - 13/14x = 13/14x - 13/14x + 250    [1x = 14/14]

1/14x = 250   [multiply both sides by 14]

x = 3500

Check:

3500 = 1/2(3500) + 250 + 3/7(3500)

3500 = 1750 + 250 + 1500

3500 = 3500

John's pay is -$3500. This means he owes money instead of receiving any pay.

In order to calculate John's pay, we need to follow the given steps:

Step 1: Let's assume John's pay as 'x'.

Step 2: John gives half of his pay to his family. Therefore, he has (1/2)x left.

Step 3: John gives $250 to his landlord. Therefore, he has (1/2)x - $250 left.

Step 4: John has exactly 3/7 of his pay left over. Therefore, we can write the equation (1/2)x - $250 = (3/7)x and solve for 'x'.

To solve the equation, we can start by multiplying both sides by 14 to get rid of the denominators: 7((1/2)x - $250) = 14((3/7)x)

Simplifying both sides, we have 7x/2 - $250*7 = 6x

Combining like terms, we get 7x/2 - $1750 = 6x

Subtracting 7x/2 from both sides, we have -x/2 - $1750 = 0

Multiplying both sides by 2, we have -x - $3500 = 0

Adding $3500 to both sides, we have -x = $3500

Finally, multiplying both sides by -1, we have x = $-3500

Therefore, John's pay is -$3500. This means he owes money instead of receiving any pay.

Answer:

A) Sample bias

Step-by-step explanation:

If a sample of 100 participants includes 20 men and 80 women, then the sample is biased. Women account for;

(80/100)*100 = 80% of the total participants while men only for 20%.

The sample does not represent the entire population in fair proportions hence the sample is biased

Answer:

Step-by-step explanation:

What sets a vector apart from a scalar is that the vector has both magnitude (length) and direction, whereas a scalar has only magnitude, no direction.

Answer:

Direction is correct

Step-by-step explanation:

A scalar quantity has magnitude but no direction while

a vector has both magnitude and direction

I Believe the Answer is 44 Units 2

Hope it helped, Not completely sure...

Answer:

The correct option is 4.

Step-by-step explanation:

It the given composite figure we have 3 triangles and 1 rectangle.

The area of a triangle is

[tex]A=\frac{1}{2}\times base\times height[/tex]

The area of first triangle is

[tex]A_1=\frac{1}{2}\times 4\times 3=6[/tex]

The area of second triangle is

[tex]A_2=\frac{1}{2}\times 4\times 3=6[/tex]

The area of third triangle is

[tex]A_3=\frac{1}{2}\times 8\times 2=8[/tex]

The area of a rectangle is

[tex]A=length \times width[/tex]

[tex]A_4=8 \times 3[/tex]

[tex]A_4=24[/tex]

The area of composite figure is

[tex]A=A_1+A_2+A_3+A_4[/tex]

[tex]A=6+6+8+24=44[/tex]

The area of composite figure is 44 units². Therefore the correct option is 4.

Answer:

Step-by-step explanation:

cosΘ=sin(90-Θ)

cos(48)=sin(90-48)

cos(48)=sin(42)

Answer:

cosine (48) = 0.66913

The arc sine of (.66913) = 42 degrees

Step-by-step explanation:

Answer:

"first number line shown in the diagram"

Step-by-step explanation:

Whenever we have inequality of the form

| x + a | > b

we can write

1.  x+a > b, and

2. -(x+a) > b

and solve both.

So we can write

1. 8x + 16 > 16

2. -(8x+16) > 16

Solving 1:

8x > 16 - 16

8x > 0

x > 0

Solving 2:

-(8x+16) > 16

-8x - 16 > 16

-16 -16 > 8x

-32 > 8x

-32/8 > x

-4 > x

Putting these together, we can say x is greater than 0 & x is less than -4

The first number line is right.

The answer is:

The first option.

[tex]-4>x>0[/tex]

To solve absolute values inequalities, we need to remember that absolute value functions have a positive and a negative solution.

For example, we have that:

[tex]|x|>1[/tex]

The solution will be

[tex]-1>x>1[/tex]

So, we are given the inequality:

[tex]|8x+16|>16[/tex]

Isolating "x", we have:

[tex]-16>8x+16>16[/tex]

[tex]-16-16>8x+16-16>16-16[/tex]

[tex]-32>8x>0[/tex]

[tex]\frac{-32}{8}>\frac{8x}{32}>\frac{0}{32}\\\\-4>x>0[/tex]

Hence, we have that the correct option is the first option.

The solution is:

[tex]-4>x>0[/tex]

or

(-∞,-4)U(0,∞)

Have a nice day!

ANSWER

Adjacent Angles

EXPLANATION

Angles that have a common vertex and side are called adjacent angles.

The vertex is the point of intersection of the arms of an angle.

A vertex can be formed by two more rays.

From the diagram, angle x and y and adjacent angles.

The common vertex is V.

The common side is VZ

Angles m and n are not adjacent angles because they do not have the same vertex.

This is an example of exponential growth. The population of this village triples every hundred years. Given the village was founded 400 years ago by 20 people, the current population would be 1620 people.

The given situation is an example of exponential growth, which can be found in various scenarios such as population growth. From the information provided, the population of the village triples every hundred years. Since the village was founded four hundred years ago and initially had 20 people, we can calculate the population today using the following steps:

So, the population of the village today would be 1620 people.

https://brainly.com/question/12490064

#SPJ12

The population of the village today is 720 people.

To find the population of the village today, we need to calculate the number of population doublings that have occurred over the four hundred year period.

Since the population triples every one hundred years, it doubles twice in that time frame.

Doubling a number is the same as multiplying it by 2.

So, the population at the start was 20, then it doubled to 40 after one hundred years, and doubled again to 80 after two hundred years.

Finally, it tripled to 240 after three hundred years, and tripled again to 720 after four hundred years.

Therefore, the population of the village today is 720 people.

https://brainly.com/question/18415071

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Answer:

The correct answer is A.

Step-by-step explanation:

Because it is 5 more than, that would mean you would +5. And obviously twice meaning 2. So 2x+5 is the correct answer.

The correct Answer is A

Answer:

50t/n minutes.

Step-by-step explanation:

The  equation of proportionality is  t = kn   where k is a constant.

So k = t/n.

So for 50 new message the time  = 50k = 50 * t/n

= 50t/n minutes.

Answer:

T'(4, -2)

Step-by-step explanation:

Rotation 180° about the origin (same as reflection across the origin) negates both coordinates:

T' = -T = -(-4, 2)

T' = (4, -2)

Answer:

105.25 g

Step-by-step explanation:

The average weight is the sum of the weights divided by the number of pies.

(105 + 105 + 106 + 108 + 108 + 103.5 +102 +104.5) / 8

= 105.25

Answer:

Here for anybody at k12 :)

Step-by-step explanation:

Took it and got it correct :)

Step-by-step answer:

We know that for a given circle of radius R, the longest chord is the diameter, which is at 0 distance from the centre.

As we move the chord away from the centre, the chord length diminishes, up to at a distance R from the centre, the chord length is zero.

Therefore, the chord at 3 inches from the centre is longer than that at 5, assuming the radius is 5 inches or more.

Answer:

one shirt = $4.75 , one pant = $36

Step-by-step explanation:

Create two equations.

3p + 3s = 93.75

4p + 2s = 134.50

Use elimination by making s values the opposite of each other.

(3p + 3s = 93.75) -2

(4p + 2s = 134.50) 3

-6p -6s = -187.5

12p + 6s = 403.5

6p = 216

p = 36

Plug the cost of one pant into an equation

3(36) + 3s = 93.75

108 + 3s =93.75

14.25 = 3s

s = 4.75

I will set up the equations.

Let s = shirts

Let p = pants

3s + 3p = 93.75

2s + 4p = 134.50

Use the substitution method to find p and s.

Take it from here.

Answer A, Answer C, Answer D

Hello there! The answers are:

Where is your favorite vacation spot?

What is the last book you read?

Let look at all the options:

What year did you graduate high school? - This is bad for 12 year olds since mot 12 year olds are 6-7th through 7th grade, and graduate when they are 17/18.

What color was your first car? - You can't get your drivers license until you are 16 (at least in the U) so a 12 year old would not own their own car.  

Where is your favorite vacation spot? - You can co on vacation  young as a baby, so this would be a suitable question.

What is the last book you read? - By 12 you should for sure be able to read, so this is a  correct choice.  

Should taxes be increased to fund a new park? - 12 year old are way to young to understand taxes so this is also incorrect.

I hope this helps and have a great rest of your day! :)

The ball hits the ground at 2.5sec

The answers aren’t all showing but neither of the top two showing are correct. Pick the answer that fits with the ball being in the air for 2.5sec.

Answer:

[tex]3,744.45\ m^{2}[/tex]

Step-by-step explanation:

we know that

The area of a sector is equal to

[tex]A=\frac{\theta}{360\°}\pi r^{2}[/tex]

where

[tex]\theta[/tex] ------> is the angle in degrees

r is the radius of the circle

In this problem we have

[tex]r=45\ m[/tex]

[tex]\theta=212\°[/tex]

assume

[tex]\pi =3.14[/tex]

substitute the values

[tex]A=\frac{212\°}{360\°}(3.14)(45)^{2}[/tex]

[tex]A=3,744.45\ m^{2}[/tex]

Answer:

A, B, D

Step-by-step explanation:

A is true.  From week 5 to week 11, the curve goes down.

B is true.  After week 11, the curve goes up.

C is false.  The curve passes $320 twice in the first ten weeks, not three times.

D is true.  The curve starts at about $110.

E is false.  As time increases, the graph goes up.  As time decreases, the graph goes down.

About $110 in commission were initially earned and The commission earned increased in the beginning of employment and after week 11.

A function is an expression used to show the relationship between two or more numbers and variables.

From the graph:

About $110 in commission were initially earned and The commission earned increased in the beginning of employment and after week 11.

Find out more on function at: https://brainly.com/question/25638609

Answer:

  D)  (-2, -3)(-4, -3)(-2, -9); because corresponding pairs of sides and corresponding pairs of angles are congruent

Step-by-step explanation:

For triangles to be congruent, it is not enough that corresponding angles are congruent. In addition, there must be at least one pair of corresponding sides that are congruent. (Then all pairs will be congruent.)

The points listed in choices B and D are points that form a right triangle with leg lengths 2 and 6. However, choice B only refers to the angle measures, and not the sides. Choice D is the correct one.

To determine which triangle is congruent with the original triangle, we'll need specific criteria to compare. Congruent triangles have all corresponding sides and angles that are congruent, which means they will have the same size and shape but may be in different positions or orientations.
Assuming that the original (unillustrated) triangle has been given to us, we would compare it with the triangles listed in the options. However, without the original triangle's information, I can't directly compare it with the options given, so I will offer a step-by-step guide on how you could establish the congruence between triangles if the original triangle's dimensions were known.
Step 1: Determine the lengths of the sides of each of the given triangles using the distance formula, which is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Step 2: Calculate the angles between each pair of sides using the dot product formula or by using the law of cosines. Remember that for angles, you might initially find the cosine of the angle with the dot product and then use the inverse cosine function to find the angle itself.
Step 3: Compare the lengths of sides and the measures of angles of the given triangles to those of the original triangle. If all sides and angles match, the triangles are congruent.
Step 4: Choose the correct answer based on which triangle has all three sides and angles that match the original triangle.
Let's briefly analyze the given triangles in the options:
Option A and Option C describe the same triangle: (-1, 1), (-2, 1), (-1, 4). In a congruence context, the reason for congruence would be the same whether it's because of corresponding pairs of angles or both sides and angles, but usually the congruence criteria involve both sides and angles (SSS, SAS, ASA, AAS).
Option B and Option D also describe the same triangle: (-2, -3), (-4, -3), (-2, -9). The reasoning provided once again does not fundamentally alter the congruence relationship since congruence should involve both sides and angles.
However, since we can't see the original triangle, I can't confirm which one is congruent. If you have the specific characteristics of the original triangle, you could use the steps outlined above to find out which triangle from these options is congruent with it. Remember, for two triangles to be congruent, they must have exactly the same three side lengths and the same three angles.

For this case we must find the product of the following expression:[tex]3 (x + 4) (x-5)[/tex]

We must apply distributive property to the terms of the first parenthesis:

[tex](3x + 12) (x-5) =[/tex]

Again we apply the distributive property:

[tex]3x ^ 2-15x + 12x-60 =\\3x ^ 2-3x-60[/tex]

ANswer:

[tex]3x ^ 2-3x-60[/tex]

Step 1: Distribute the 3 to x and 4

(3x + 12)(x - 5)

Step 2: FOIL (First, Outside, Inside, Last)

Multiply the first of the values in the parentheses together

(3x + 12) (x - 5)

[tex]3x^{2}[/tex]

Multiply the outside values in the parentheses together

(3x + 12)(x - 5)

-15x

Multiply the inside values of the parentheses together

(3x + 12)(x - 5)

12x

Multiply the last values of the parentheses together

(3x + 12)(x - 5)

-60

Step 3: Add all the FOIL values together

3[tex]x^{2}[/tex] + (-15x) + 12x + (-60)

Step 4: Combine like terms

3[tex]x^{2}[/tex] + (-15x) + 12x + (-60)

3[tex]x^{2}[/tex] - 3x - 60

Hope this helped!

Answer:

adults ticket sold= 60

student tickets =125

Step-by-step explanation:

So we need to make a system of equations. Lets say the variable a stands for adults tickets and the variable s stands for student tickets. Our first equation is going to be

s-a=65

that is because there are 65 more student tickets than adults.

the second equation is going to be

3s+5a=675

that is because the tickets will add up 675.

Now we have to make sure one of the variable cancels out when we add them together. So we have to multiply the first equation by 5.

5[s-a=65]

3s+5a=675

So then we end up with

5s-5a=325

3s-5a=675

We need to add them together and we end up with.

8s=1000

We need to divide by 8

s then equals 125.

So there are 125 students tickets.

We now plug 125 back into one of the equations. To make things easy lets to the first equation.

s-a=65

125-a=65

move the 125 over

-a=-60

multiply by a negative

a=60

So you have 60 adults tickets

Final answer:

By setting up and solving a system of equations, it's determined that 125 student tickets and 60 adult tickets were sold.

Explanation:

The task involves solving a system of equations to find out how many adult and student tickets were sold. Let the number of student tickets be s and the number of adult tickets be a. We have two pieces of information: First, the drama club sold 65 fewer adult tickets than student tickets, which translates to a = s - 65. Second, the total revenue from ticket sales was $675, with student tickets selling at $3 each and adult tickets at $5 each, giving us the equation 3s + 5a = 675.

To solve for s and a, we substitute the first equation into the second to get 3s + 5(s - 65) = 675. Simplifying this equation yields 8s - 325 = 675, so s = 125. Substituting s = 125 back into the first equation, a = 125 - 65, we find a = 60. Therefore, 125 student tickets and 60 adult tickets were sold.

The answers are:

1

[tex]x=2[/tex]

2

[tex]y=-4[/tex]

3

[tex]z=4[/tex]

4

[tex]x=-5[/tex]

Solving for each of the given equations and variable, we have:

[tex]-2x + 5 = 4x - 7[/tex]

Solving for "x", we have:

[tex]-2x + 5 = 4x - 7\\\\-2x-4x=-7-5\\\\-6x=-12\\\\x=\frac{-12}{-6}=2[/tex]

So, we have that:

[tex]x=2[/tex]

[tex]12y+4=8y-12[/tex]

Solving for "y", we have:

[tex]12y+4=8y-12\\\\12y-8y=-12-4\\\\4y=-16\\\\y=\frac{-16}{4}=-4[/tex]

So, we have that:

[tex]y=-4[/tex]

[tex]7z-18 =-2z+18[/tex]

Solving for "z", we have:

[tex]7z-18 =-2z+18\\\\7z+2z=18+18\\\\9z=36\\\\z=\frac{36}{9}=4[/tex]

So, we have that:

[tex]z=4[/tex]

[tex]10x+15 =5x-10[/tex]

Solving for "x", we have:

[tex]10x+15 =5x-10\\\\10x-5x=-10-15\\\\5x=-25\\\\x=\frac{-25}{5}=-5[/tex]

So, we have that:

[tex]x=-5[/tex]

Hence, the answers are:

1

[tex]x=2[/tex]

2

[tex]y=-4[/tex]

3

[tex]z=4[/tex]

4

[tex]x=-5[/tex]

Have a nice day!

Answer: the answer is b

Step-by-step explanation:

Answer:

the answer is letter b.

[tex]1 - 2x + {5x}^{4} [/tex]

Final answer:

To find the product (f × g)(x), simply multiply the functions f(x) = 3x + 8 and g(x) = x^2 together. The result is (f × g)(x) = 3x^3 + 8x^2.

Explanation:

To find the product (f × g)(x), you need to multiply the function f(x) by the function g(x). Given f(x) = 3x + 8 and g(x) = x^2, the product (also known as the composition of functions) is obtained by multiplying these two functions together.

The product is calculated as follows:

(f × g)(x) = f(x)×g(x) = (3x + 8)×(x^2).

Now, distribute the x^2 term across the terms inside the parentheses:

(f × g)(x) = 3x^3 + 8x^2.

This is the simplified form of the product of the two functions.