What is the range of the given set of ordered pairs?
(9,-2) (4,3) ( 8, 10) (-4, 8)

Answer:

Take a look of the image below, we can think on this problem as a problem of two triangle rectangles.

We can see that both triangles share the adjacent cathetus, then the height of the flagpole is just the difference between the opposite cathetus.

Remember the relation:

Tan(a) = (opposite cathetus)/(adjacent cathetus)

So, if we define H as the height of the cliff

X as the distance between the observer and the cliff

and h as the height of the flagopole

we can write:

tan(40°) = H/X

tan(45°) = (H + h)/X

Notice that we have two equations and 3 variables (we should have the same number of equations than variables) then here is missing information, and we can't get an exact solution for the height of the flagpole.

But we can write it in terms of the height of the cliff H, or in terms of the distance between the observer and the cliff.

We want to find the value of h.

If we take the quotient between both equations, we get:

Tan(45°)/Tan(40°) = (H + h)/H

1.192 = (H + h)/H

1.192*H = H + h

1.192*H - H = h

0.192*H = h

So the height of the flagpole is 0.192 times the height of the cliff.

Answer:

Jose has 5.2 meters of fabric left.

Step-by-step explanation:

5.6 - 0.4 = 5.2

Answer:

0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean per capita consumption of milk per year is 131 liters with a variance of 841.

This means that [tex]\mu = 131, \sigma = \sqrt{841} = 29[/tex]

Sample of 132 people

This means that [tex]n = 132, s = \frac{29}{\sqrt{132}}[/tex]

What is the probability that the sample mean would be less than 133.5 liters?

This is the p-value of Z when X = 133.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{133.5 - 131}{\frac{29}{\sqrt{132}}}[/tex]

[tex]Z = 0.99[/tex]

[tex]Z = 0.99[/tex] has a p-value of 0.8389

0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.

Answer:

a) The probability of a pregnancy lasting X days or longer is given by 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

b) We have to find X when Z has a p-value of [tex]\frac{a}{100}[/tex], and X is given by: [tex]X = \mu - Z\sigma[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]

a. Find the probability of a pregnancy lasting X days or longer.

The probability of a pregnancy lasting X days or longer is given by 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

b. If the length of pregnancy is in the lowest a​%, then the baby is premature. Find the length that separates premature babies from those who are not premature.

We have to find X when Z has a p-value of [tex]\frac{a}{100}[/tex], and X is given by: [tex]X = \mu - Z\sigma[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

9514 1404 393

Answer:

Step-by-step explanation:

One way to write the relationship between time, speed, and distance is ...

  time = distance/speed

For the first part of the trip, the time is ...

  t1 = 240/r

For the second part of the trip, the time is ...

  t2 = 72/(r+10)

The total time is 6 hours, so we have ...

  t1 +t2 = 6

  240/r +72/(r+10) = 6

We can simplify this a bit by multiplying by (r)(r+10)/6 to get ...

   40(r+10) +12(r) = r(r+10)

  r² -42r -400 = 0 . . . . . . . . subtract the left side and collect terms

  (r -50)(r +8) = 0 . . . . . . . . factor

  r = 50 . . . . . the positive solution of interest.

The two average speeds were 50 mph and 60 mph.

Step-by-step explanation:

each point should be at a 2. the center is 0,0

Answer:

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex] --- set builder

[tex][-21,\infty)[/tex] --- interval notation

Step-by-step explanation:

Given

[tex]-3a - 15 \le -2a + 6[/tex]

Required

Solve

Collect like terms

[tex]-3a + 2a \le 15 + 6[/tex]

[tex]-a \le 21[/tex]

Divide by -1

[tex]a \ge - 21[/tex]

Rewrite as:

[tex]-21 \le a[/tex]

Using set builder

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex]

Using interval notation, we have:

[tex][-21,\infty)[/tex]

Answer:

8x +15

Step-by-step explanation:

f(x) = 10 + 2x and g(x) = 6x + 5

(f+ g)(x) =  10 + 2x + 6x + 5

Combine like terms

              = 8x +15

Answer:

8x+15

Step-by-step explanation:

(f+g)(x) = f(x)+g(x)

= (10+2x) + (6x+5)

= 8x+15

hope it helped, please mark me brainliest.

Step-by-step explanation:

21.

22.

23.

hope it helps

Answer:

21. (x+7)(x+3)

22. (x-7)(x+3)

23. 12

Step-by-step explanation:

X^2+10x+21

(X+7)(x+3)

(We know that 7*3 is equal to 21 and that 7+3= 10)

Now try the same thing for 22.

(X-7)(X+5)

(-7*5= -35 . and -7+5=-2)

23. Use SPOE to get like terms to one side:

-7x=-84

Then use DPOE to find the value of X

x=12

Answer:

In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared. The comparison is expressed as a ratio and is a unitless number.

Step-by-step explanation:

I hope it helps

Answer: The first number is 2, the second number is 3 and the third number is -2

Step-by-step explanation:

Let the first number be 'x', the second number be 'y' and the third number be 'z'

The equations according to the question becomes:

⇒ x + y + z = 3              ....(1)

⇒ x - y + z = -3              ....(2)

⇒ x - z = 1 + y              ....(3)

Rearranging equation 3:

⇒ x - y = 1 + z                .....(4)

Putting in equation 2:

⇒ 1 + z + z = -3

⇒ 1 + 2z = -3

⇒ z = -2

Putting this value in equation 4 and equation 1, we get:

⇒ x - y = -1

⇒ x + y = 5

Cancelling 'y' by eliminiation method and equation becomes:

⇒ 2x = 4

⇒ x = 2

Putting value of 'x' and 'z' in equation 1:

⇒ 2 + y - 2 = 3

⇒ y = 3

Hence, the first number is 2, the second number is 3 and the third number is -2

Answer:

x = 14/3

Step-by-step explanation:

9.

The given equation is:

(x-2)+(x-3)+(x-9)=0

After opening the brackets,

x-2+x-3+x-9=0

3x+(-2-3-9) = 0

3x-14=0

x = 14/3

So, the value of x is equal to 14/3.

It is the graph of y= x translated 7 units up.

+7 in the function means it crosses the y axis at +7

The statement correctly describes the graph of y= x + 7 is y= x translated 7 units up.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

We have a function y = x.

and, a translated function y= x + 7

Here, The plus 7 at the end will shift the graph 7 units up.

It also means the the function cut the y axis at +7.

Thus, It is the graph of y= x translated 7 units up.

Learn more about Transformation here:

https://brainly.com/question/17104932

#SPJ2

NUE is 30° LUN is 60° EUS is 30° LUE is 90° LUS is 120°

Step-by-step explanation:

NUE is given

LUN was from the 90° angle LUE but just minus 30°

EUS is honestly a guess :/

LUE is obviously 90° as we used it earlier

LUS was the 90° plus the EUS

The options are;

1) AB is bisected by CD

2) CD is bisected by AB

3) AE = 1/2 AB

4) EF = 1/2 ED

5) FD= EB

6) CE + EF = FD

Answer:

Options 1, 3 & 6 are correct

Step-by-step explanation:

We are told that Point E is the midpoint of AB. Thus, any line that passes through point E will bisect AB into two equal parts.

The only line passing through point E is line CD.

Thus, we can say that line AB is bisected by pine CD. - - - (1)

Also, since E is midpoint of Line AB, it means that;

AE = EB

Thus, AE = EB = ½AB - - - (2)

Also, we are told that F is the mid-point of CD.

Thus;

CF = FD

Point E lies between C and F.

Thus;

CE + EF = CF

Since CF =FD

Thus;

CE + EF = FD - - - (3)

Answer:

[tex]-\frac{77}{24}[/tex]

Step-by-step explanation:

1. rewrite the equation in standard form: [tex]4\cdot \frac{3}{2}\left(y-\left(-\frac{41}{24}\right)\right)=\left(x-\left(-\frac{3}{2}\right)\right)^2[/tex]

2. find (h,k), the vertex. the vertex is [tex]\left(h,\:k\right)=\left(-\frac{3}{2},\:-\frac{41}{24}\right)[/tex]

3. find the 'focal length' of the parabola - the focal length is the distance between the vertex and the focus. from the vertex we can see that the focal length, p, = 3/2

4. Parabola is symmetric around the y-axis and so the asymptote is a line parallel to the x-axis, a  distance p from the [tex]\left(-\frac{3}{2},\:-\frac{41}{24}\right)[/tex] y coordinate which is at  [tex]-\frac{41}{24}\right)[/tex]. Set up the equation:

[tex]y=-\frac{41}{24}-p[/tex]

5. substitute and solve:

[tex]y=-\frac{41}{24}-\frac{3}{2}[/tex]

[tex]y = -\frac{77}{24}[/tex]

hope this helps, ask me questions if you still don't understand.

Answer:

45°

Step-by-step explanation:

<lmk=90°

angles in a triangle add up to 180

45+90+<o=180

<o=180-135

<o=45

Answer:

∠ O = 45°

Step-by-step explanation:

The angle between the tangent and the radius at the point of contact is 90°

The sum of the 3 angles in Δ OML is 180° , then

∠ O = 180° - (90 + 45)° = 180° - 135° = 45°

Answer:

The angle between them is 60 degrees

Step-by-step explanation:

Given

[tex]a = 2i + j -3k[/tex]

[tex]b = 3i - 2j -k[/tex]

Required

The angle between them

The cosine of the angle between them is:

[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]

First, calculate a.b

[tex]a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)[/tex]

Multiply the coefficients of like terms

[tex]a \cdot b =2 * 3 - 1 * 2 - 3 * -1[/tex]

[tex]a \cdot b =7[/tex]

Next, calculate |a| and |b|

[tex]|a| = \sqrt{2^2 + 1^2 + (-3)^2[/tex]

[tex]|a| = \sqrt{14[/tex]

[tex]|b| = \sqrt{3^2 + (-2)^2 + (-1)^2}[/tex]

[tex]|b| = \sqrt{14}[/tex]

Recall that:

[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]

This gives:

[tex]\cos(\theta) = \frac{7}{\sqrt{14} * \sqrt{14}}[/tex]

[tex]\cos(\theta) = \frac{7}{14}[/tex]

[tex]\cos(\theta) = 0.5[/tex]

Take arccos of both sides

[tex]\theta =\cos^{-1}(0.5)[/tex]

[tex]\theta =60^o[/tex]

Answer:

1/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

probability that the ticket drawn has a number which is a multiple of 5 =

Number of tickets that are a multiple of 5 / total number of tickets

Multiple of 5 = 5, 10, 15, 20

there would be 4 tickets that would be a multiple of 5

= 4/20

To transform to the simplest form. divide both the numerator and the denominator by 4

= 1/5

Answer:

Yes, P(E1)=P(E2)

Step-by-step explanation:

We are given that

Number of dice=3

Total outcomes of 1 die=6

Therefore,

Total number of outcomes =[tex]6^3=216[/tex]

E1={{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}

E2={(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}

We have to show that E1 and E2 have the same probability P(E1) = P(E2).

Probability, [tex]P(E)=\frac{Favorable\;outcomes}{Total\;outcomes}[/tex]

Using the formula

[tex]P(E_1)=\frac{6}{216}[/tex]

[tex]P(E_1)=0.0278[/tex]

[tex]P(E_2)=\frac{6}{216}[/tex]

[tex]P(E_2)=0.0278[/tex]

Hence, P(E1)=P(E2)

9514 1404 393

Answer:

   C.  y = 1/2x +2

Step-by-step explanation:

The magnitude of the slope is the measure of "steepness." The slope is the coefficient of x in these equations. Here those values are ...

  4, 3/4, 1/2, 10

Of these, 1/2 is the smallest (least steep). 1/2 is the slope in the equation ...

  y = 1/2x +2

Given:

The graph that shows the ennoblement for college R between 1950 and 2000.

To find:

The two decades that has the greatest change in enrollment.

Solution:

From the given graph, it is clear that the change in the enrollment is:

From 1950 to 1960 is [tex]4-3.5=0.5[/tex] thousand.

From 1960 to 1970 is [tex]5-4.5=1.5[/tex] thousand.

From 1970 to 1980 is [tex]5.5-5=0.5[/tex] thousand.

From 1980 to 1990 is [tex]6.5-5.5=1[/tex] thousand.

From 1990 to 2000 is [tex]7-6.5=0.5[/tex] thousand.

The two decades 1960-1970 and 1980-1990 have the greatest change in enrollment.

Answer:1980 to 1990

Step-by-step explanation:

Answer:

3 hrs

Step-by-step explanation:

5 * 24 = 120 miles

64x = 120 + 24x

40x = 120

x = 3 hrs

Answer:

5,5,6,6,13

Step-by-step explanation:

Mode means most often.  The 5 numbers has 2 modes 5 and 6

This means that 4 of the numbers must be 5,5,6,6

Median means the middle number must be 6

5,5,6,6,x is the only way to to get the middle number to be 6

We need to average to 7

(5+5+6+6+x) /5 = 7

(5+5+6+6+x) /5  *5= 7*5

(5+5+6+6+x) =35

22+x = 35

x = 35-22

x = 13

The other number is 13

Answer:

Buy 2 lollipops for $2.

Step-by-step explanation:

If you divide the total price by total items purchased, you get the price per unit. 2/2=1 or around $1, while 40/30=4/3 or around $1.3. You are paying 1$ per lollipop for the 2 lollipop choice and paying 1.3 dollars per lollipop for the 30 lollipop choice.

You do X2 + 15 and that will be your answer.

By the way, the 2 is a power and is meant to be smaller on top of the X.

Answer:

B. There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.6.

Step-by-step explanation:

The proportion of male golfers is less than 0.6.

At the null hypothesis, we test if the proportion is of at least 0.6, that is:

[tex]H_0: p \geq 0.6[/tex]

At the alternative hypothesis, we test if the proportion is of less than 0.6, that is:

[tex]H_1: p < 0.6[/tex]

Fail to reject the null hypothesis.

This means that there is not sufficient evidence to conclude that the proportion is less than 0.6, and thus the correct answer is given by option B.

Answer:

2 1/8

Step-by-step explanation:

7/8 is the same as 0.875 and therefore you need 0.125 also known as 1/8 to make it a whole number. When you add it to the already existing whole 2 you get three. Subtract three from five to make two which is what you need to add on top to finally get 5.

Answer:

7sin

2

x+3cos

2

x=4

4sin

2

x+3sin

2

x+3cos

2

x=4

4sin

2

x+3=4

4sin

2

x=1

sin

2

x=

4

1

sinx=

2

1

or sinx=−

2

1

Step-by-step explanation:

TAKING THE POSITIVE ROOT x=

6

π

tan(

6

π

)=

3

1