The table shows the speeds s (in feet per second) of sound in water at various
temperatures t (in degrees Fahrenheit). Write a function that models the data. Use
the model to approximate the speed of sound when the water temperature is 100°F.
Temperature (°F), t: 32 50 90 120 180 212
Speed (ft/sec), s: 4603 4748 4960 5049 5095 5062

Given:

Required:

We need to find the value of x when P(x)=80.

Explanation:

Solve for x.

Divide both sides by 25.

Final answer:

See a horizontal line from point 80 on the y axis and mark the intersection point on the graph.

we have:

Out of all the 500 people, how many are Men, shopping at Home Depot?

See the cell crossing "Men" row and "Home Depot" column.

it is 37

Hence, probability of shopper being a men who shops at Home Depot is:

37/500

In decimal:

0.074

In percentage:

let the first no. is 'a'

second no. is 'b'

so from the statement, One half of a number increased by a second number equals 5.

and One half of the first number decreased by the second number equals 1.

add both the equations,

put a= 6 in first equation

so the answer is,

a = 6 & b = 2

Answer:

Yes, after 3 and a half months, they will both have 215$ in their account.

Step-by-step explanation:

if x is the number of months

Rodney's equation: y=40x+75

Morgan: y = 50x + 40

Equate them together:

50x+40 = 40x+75

10x=35

x=3.5

:]

Yes, after 3 and a half months, they will both have 215$ in their account.

Given:

A graph which has an odd degree and a negative leading coefficient.

To find:

The nature of the graph.

Explanation:

Since the has an odd degree and a negative leading coefficient.

So, the end behaviours are,

So, the nature of the graph would be, up left and down right

Final answer:

up left; down right.

The interest she pays over 4 weeks is #5000 and the interest she pays per week is #1250.

According to the question,

We have the following information:

A woman borrows #20 000 for 4 weeks.

She agrees to pay #25 000 back at the end of the 4 weeks.

Now, we will subtract the borrowed amount from the amount paid after 4 weeks to find the interest paid after 4 weeks.

(a) Interest paid over 4 weeks = #(25000-20000)

Interest paid over 4 weeks = #5000

(b) Now, we can easily find the interest paid per week by the interest paid over 4 weeks by the total number of weeks.

Interest paid per week = Interest paid in 4 weeks/4

Interest paid per week = 5000/4

Interest paid per week = #1250

Hence, the answers to part a is #5000 and the answer to part b is #1250.

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we have that

Part c)

the probability is equal to

P=0.14+0.27+0.58

because is the sum of

x=1, x=2 and x=3

Part D

the probability is

P=0.01+0.14+0.27

because is less than or equal 2

Answer:21

Step-by-step explanation:

The measure of angle 1 is 42° . Angles Central angles can be expressed as Central angle = (Arc length 360o)/(2r) degrees or Central angle = Arc length/r radians, where r is the radius of the circle.

∴  The measure of angle 1 is 42°

180 - 48 - 90 = 42

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Orthocenter

Let

A(2,0)

B(3,2)

C(6,0)

step 1

Find out the slope AB

m=(2-0)/(3-2)

m=2/1

m=2

Remember that

If two lines are perpendicular, then, their slopes are negative reciprocal

so

the slope of the altitude that passes through C is -1/2

Find out the equation of the altitude that passes through C

y=mx+b

we have

m=-1/2

point C(6,0)

substitute

0=-(1/2)(6)+b

solve for b

0=-3+b

b=3

equation is y=-(1/2)x+3 -------> equation 1

step 2

Find out the slope BC

m=(0-2)/(6-3)

m=-2/3

so

the slope of the altitude that passes through A is 3/2

Find out the equation of the altitude that passes through A

y=mx+b

we have

m=3/2

point A(2,0)

0=(3/2)(2)+b

solve for b

0=3+b

b=-3

y=(3/2)x-3 ------> equation 2

step 3

the intersection point equation 1 and equation 2 is the orthocenter

y=-(1/2)x+3 -----> equation 1

y=(3/2)x-3 ------> equation 2

solve the system

solve by graphing

using a graphing tool

the intersection point is (3,1.5)

that means

the orthocenter is (3,1.5)

see the attached figure to better understand the problem

Answer: Melissa sleeps for 8 hours and wakes up at 7 am.

Step-by-step explanation: For this i was able to do just eliminate some answer. "Melissa sleeps for 7 hours and wakes up at 8 am," in this case Melissa would drink coffee because she slept less than 8 hours. "Melissa sleeps for 9 hours and wakes up at 5:30 am," in this case Melissa would drink coffee since she had woke up at 5:30 am. "Melissa sleeps for 7 hours and wakes up at 6 am," in this case Melissa would drink coffee since she had less than 8 hours of sleep. In conclusion, The only time Melissa wouldn't had drank coffee is when she had slept for 8 hours and woke up at 7 am. That is because had slept more than 8 hours and had woke up after 7 am.

The probability of matching x successes on n further trials in an experiment with two possible outcomes. There is a 4.88% chance that no one is worried that their employers are listening to their phone calls.

Given that,

The probability of matching x successes on n further trials in an experiment with two possible outcomes is known as the binomial probability (commonly called a binomial experiment).

The following formula gives it:

[tex]P=C_{n,x}p^{n}.(1-p)^{n-x}[/tex]

Where is the number of distinct combinations of x items drawn from a set of n elements, as determined by the formula below.

[tex]C_{n,x}=\frac{n!}{x!(n-x)!}[/tex]

And p is the probability that anything will happen.

Being aware that employers are monitoring phone calls is a victory in this issue.

43% of adults fear that their employers are listening to their phone calls,

p=43%=0.43

We must locate Four persons were questioned, and none expressed concern about phone call monitoring by companies.

We count four adults, n=4.

Is there a probability of success of 0? If so, then x = 0.

[tex]P=C_{n,x}p^{n}.(1-p)^{n-x}[/tex]

[tex]P=C_{4,0}(0.43)^{0}.(0.57)^{4}[/tex]

P=0.0488

Therefore, There is a 4.88% chance that no one is worried that their employers are listening to their phone calls.

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Answer:

Explanation:

Here, we want to get the amount of money Eric earns per week

Let the amount earned be n

Now, to get the value earned, we have to subtract the value he had before from what he has now or simply add what he had before to what he earned now and equate to his total balance now

Mathematically, we have that as:

The area of a triangle is 1/2 x base x height.

The area of a triangle is 24.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices

The area of a triangle is given by:

Area = 1/2 x base x height

We have,

A triangle ABC.

Angle bisectors are AD, BE, and CF, which intersect at I as shown in the figure below.

DI = 3

DI = AI = 3

Height of the triangle = AD = AI + DI = 3 + 3 = 6

BD = 4 = BC

Base of the triangle = BC = BD + DC = 4 + 4 = 8

The area of a triangle:

= 1/2 x base x height

= 1/2 x 8 x 6

= 1 x 4 x 6

= 24

Thus,

The area of a triangle is 24.

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Is this a simple random sample: Yes, because each student and sample of 100 has the same chance of being selected.

A simple random sample can be defined as a subset of items that are selected from a larger data set or statistical population, with each member of the subset having an equal or the same probability (chance) of being selected.

This ultimately implies that, each member of the subset are selected by chance and randomly, and as such a simple random sample is an unbiased representation of a larger data set or a statistical population.

In this context, we can reasonably infer and logically deduce that the data set or statistical population described in this scenario is a simple random sample.

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Reason:

The discriminant is

d = b^2-4ac

which is the stuff under the square root in the quadratic formula.

We have these three cases

The graph shows we have 2 solutions. Each solution is an x intercept, aka "root". We go for the case in which d > 0. Therefore, the discriminant is positive.

The expression of the fraction 10¹/₅ - 2¹/₆ as a mixed fraction is;  8¹/₃₀

We want to subtract two fractions.

Now, fractions could be either proper fraction, improper fraction or mixed fraction.

Now, a proper fraction simply means the numerator is smaller than the denominator, a mixed fraction simply means a whole number and a proper fraction while an improper fraction simply means the numerator is bigger than the denominator

We are given the operation;

10¹/₅ - 2¹/₆

Converting to improper fraction gives;

51/5 - 13/6

Factorizing gives us;

1/30((51 * 6) - (13 * 5))

= 241/30

Converting to mixed fraction gives 8¹/₃₀

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Given:

Total cups of punch made = 619

The punch contains tw different types of juice

Given the figure FGHJ with coordinates

F(0, 5), G(-5, 1), H(5, -7) and J(6, 4)

When we rotate a figure of 90 degrees clockwise, each point of the given figure has to be changed from (x, y) to (y, -x) and graph the rotated figure.

Therefore, for clockwise rotation, the coordinates of the image of FGHJ becomes

Note that, the blue graph represents the pre-image FGHJ and the green graph represents the image F'G'H'J'

When we rotate a figure of 90 degrees anti-clockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure.

Therefore, the anti-clockwise rotation the coordinates of the image of FGHJ becomes

Note that, the blue graph represents the pre-image FGHJ and the green graph represents the image F'G'H'J'

Answer:

qwdqdqwdwqdqdwqdqwwqdd

haha lol

Step-by-step explanation:

When you locate the coordinates of A it is (-4, 1)

Locate the coordinates of A', it is : (4, 5)

This implies, 8 was added to the x coordinate and 4 was added to the y-coordinate

Hence, the transformation is;

(x + 8, y+4)

Question:

Simplify the expression

Step 1:Apply the fraction rule

Step 2:Apply the law of indices

Step 3: Apply the fractional exponent of indices

Hence,

The final answer = w¹⁰/3y⁴

We will write it as a fraction in ordet to solve, that is:

We then operate as follows:

We have this, since 1 integer will be equal as a numerator divided by a denominator with equal values. Examples 1 = 2/2, 1 = 45/45, ...

Answer:

Step-by-step explanation:

12-2=10

9+7-10=6

Only brother: 9-6=3

Only Sister: 7-6=1

Both:6

The given equation is,

So, from this equation , we have to find the value of x. The left hand side of the equation has x with 1/3 as coefficient, therefore, inorder to make it x, we have to,

as the thress get cancelled. If we do some operation on one side of the equal sign, it is to be applied on the other side also so as to maintain the equivalency.

So here we have to multiply by 3.

But in option, there is no as such given , but it is given that divide by 1/3.

which is equuivalent to multiplying by three.

So the option " Divide by 1/3" is correct.

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

The correct answers are:

CONCLUSION:

The final answers are:

OPTION B and OPTION D

Given that f(x) is defined as the function below:'

To determine the value of f(1), we substitute the x with 1. Therefore:

The value of f(1) is -9.