A ball is thrown in the air from a platform. The path of the ball can be modeled by the function h(t)=-16 t^{2}+32t+4 where h(t) is the height in feet and t is the time in seconds.How long does the ball take to reach its maximum height?

To multiply, we'll use all the terms in the 1st bracket and multiply all the terms in the 2nd bracket;

So, the required expression is 6x^2 - 7x -5

intial value = 30,000

final value = 31,590

30,00 ( 1 + x) = 31,590

Solve for x ( increase in decimal form)

30,000+ 30,000x = 31,590

30,000x = 31,590-30,000

30,000x =1,590

x= 1,590/30,000

x= 0.053

Multiply by 100

0.053 x 100= 5.3%

Given Data:

The central angle is, θ = 138.

The radius is, r = 12 cm.

The area of the sector can be calculated as,

Substituting the values, the area can be calculated as,

Answer: I believe 65%

Step-by-step explanation:

Add all the pages together from the books. Add all the pages they  read. Lastly divide the pages they read by the pages there is in total. You get a decimal. move the decimal two numbers over.

The total number of bills are 23.

The probability to get single = 8/23

The probability to get five = 10/23

The probability to get twenty = 2/23

The probability to get a hundred = 3/23

So, the fair price to play this game is calculated below:

Thus, the fair price to play this game is $17.30

To express the statement algebraically, we will break down the sentence into phrases or words we can interprete numerically:

the unknown number = w

one fourteenth = 1/14

one fourteenth of some number w:

10 more: it means we will be adding 10 to the algebraic expression after

10 more than one-fourteenth of some number w will be:

Solution

Step 1:

Write the equation:

Step 2

Step 3:

Step 4

Substitute t = 4.5 into the height equation.

find the slope of the line.



(-3,0), (2,2), (7,4), (12,6)​

To find the slope we need two points

so

we take

(-3,0), (2,2)

so

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

m=2/5

Verify with the other two points

(7,4), (12,6)​

m=(6-4)/(12-7)

m=2/5 ----> is ok

therefore

ANSWER

k = 1 or 21

STEP-BY-STEP EXPLANATION:

According to the question, we were given the below trigonometric function

Recall that, we have trigonometric identity which is written below

The next thing is to rewrite the equation

The next thing is to find the value of P by factorizing the above equation.

Recall that, the standard form of the quadratic function is given as

Let

a = 1

b = -22

c = 21

The next thing is to find the value of ac

Hence, the value of k is 1 or 21

3y+6÷ 2x​ = 1/ 2x ( 3y + 6 )

We are given a diagram showing a pole with a guy wire attached to the top of it and anchored into the ground.

From the base of the pole to the bottom end of the guy tower is given as a 20-feet distance. The pole itself is 24 feet tall. The guy wire from the top of the pole to the ground forms the hypotenuse of what we can describe as a right angled triangle.

We can now use the Pythagoras' theorem to solve for the missing side (hypotenuse).

The theorem states;

Where the variables are;

We can now substitute the values given;

Take the square root of both sides;

Rounded to the nearest tenth of a foot, the length of the guy wire is;

ANSWER:

Length = 31.2 ft

The second option is the correct answer.

Given the expression:

Let's simplify the expression by multiplying -3x to each of the terms inside the parenthesis.

We get,

Therefore, the simplified form of the given expression is -12x^2 - 36x.

Given:

Required:

We need to find the function h(k(x)) and k(h(x)).

Explanation:

We get

and

We know that

Final answer:

Because he wants to mantain a constant rate over the first hours, we can see that on the first hour he should travel 26 miles.

The total race is 150 miles, if we discount the last 20 miles (that Jackson will bike as fast as he can) we get:

150mi - 20mi = 130mi

We know that he travels these 130 miles at a constant rate over 5 hours, so the distance that he moves each hour (an particularly the first hour) is given by the quotient between the distance and the time.

R = 130mi/5h = 26mi/h

So he should travel 26 miles in the first hour.

Learn more about constant rates:

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• The proportional situation represents an Inverse Variation

• The constant of variation, k = 13750

• If all 100 students participate in the fundraiser, each will contribute $137.5

From the given information, we notice that the more students involved in the fundraiser, the less the amount each student needs to contribute.

This is an INVERSE VARIATION

Let s represent the number of students who participated in the fundraiser, and t represents the amount needed to be contributed by each student, we have:

To find k, we use the information that s = 50 when t = 275

So,

From the above, we have the formula:

If 100 students participate in the fundraiser, we have:

Each student needs to contribute $137.5

with the pythagorean theorem

using the formula of the quadratic equation

the length cannot be negative, therefore x=7

length of the shorter leg is: 7ft

length of the longer leg is: 3+3(7)= 24ft

length of the hypotenuse is: 4+3(7)= 25ft

here is the session with equation in question

We can find the inverse function writing f(x) as y in the original function and then changing x with y and isolating y again, so

Changing y with x we have

Now we must get y on one side of the equation again, then

The domain of the inverse function in the image of the original function f, the image of f is x ≥ -5, then the domain of the inverse of will be x ≥ -5, so our answer is

We can see than 300 is a constant, so mary has 300 stamps for sure.

Now, in that side of the equation, it is added 2x (variable). So that means she is collecting/adding 2stamps per week (where x is number of weeks).

Now, the other side is 10x, so that must be 10 stamps per week.

No constant means initial stamp is 0.

So, this must be Nick's.

Since both sides are equal and we can solve for x, that means:

when will their collection be equal (in what number of weeks).

Looking at the choices, A seems to be correct.

The total GB is 1000

The available GB is 105 GB.

Each 256 GB and cost $10.

Let C be the number of memory cards, then we have,

Thus, option D is correct.

Given that ;

R=R¹+R² -------- make R² the subject of the formula as;

Take R¹ to the left side of the equation as;

R-R¹ = R²

So;

Answer:

R² = R - R¹

Step-by-step explanation:

R = R¹ + R²

To make R² as the subject subtract R¹ from both sides.

R - R¹ = R²

b) We have to calculate the probability that a group of 25 men exceeds the average allowed weight per passenger.

As the water taxi has a load limit of 3500 lb, the maximum average weight per passenger is 3500/25 = 140 lb.

Then, we can calculate the probability that the mean of a sample of size n = 25 is greater than 140 lb.

The population distribution from where the sample is taken has a mean of 189 lb and a standard deviation of 39 lb.

We can calculate the z-score for M = 140 lb for this sample as:z

Then, the probabilitty can be expressed as:

It is almost certain that the sample mean will be greater than 140 lb.

c) We now have to calculate the probability that a sample of size n = 20 has a mean that is greater than 175 lb, the new load limit per passenger.

We can repeat the procedure calculating the z-score with this new values (M = 175 and n = 20):

Then, we can look up the probability for the standard normal distribution when z = -1.6 and obtain:

We can express this as:

d) As the probabilty of exceeding the load limit per passenger is too high, we can consider that 20 passengers is still not safe enough.

Answer:

b) P(M > 140) = 1

c) P(M > 175) = 0.9452

d) Not safe

The number 5.73 10^6 is shown in scientific notation.

Its standard form is: 5,730,000 (five million 7 hundred thirty thousand)

The number 600 can be written in scientific notation by using the digit "6" followed by a product by 100: 6 * 100 and now writing the 100 in powers of ten:

100 = 10 * 10 = 10^2

then the scientific notation formof 600 is:

6 10^2 (6 times 10 to the power 2)

The number 0.24 is the same as the number 24 divided by 100 so notice that there is DIVISION by powers of ten now, and such division becomes a "negative" power of the base 10.

The way to quickly write 0.24 in scientific notation is:

1) count how many spaces you have to move the decimal point to the right in order to get to a number between 1 and something smaller than 10. In our case to get to 2.4.SO the decimal point has to move ONE space to the right. Now,that number of spaces you move to the right is going to becoma the exponent of the base 10:

2.4 10 ^(-1) (remember that since this is a division, the power is NEGATIVE.

The number 4.07369 is the same written in scientific notation and in standard form, because the number shown is in between 1 and something smaller than 10.

Your teacher may want tho to have yu write the exponent of 10 (you write it in this case as a zero):

4.07369 = 4.07369 10^0

Recall that 10^0 is 1, so there is no actual change to the number by multiplying by it.

Step 1. The information we have is.

The initial amount of the investment which is called the principal P is:

The interest rate is 7.05%, this will be r:

We will need to represent the interest rate as a decimal number, for that, we divide by 100:

As additional variables, we will have:

Step 2. Use the Continuous compounding formula:

where A is the amount including interest, P is the principal amount of the investment, r is the interest rate, and t in years.

Also, e is a constant which is equal to:

But we will only represent it as e.

Step 3. Substitute P and r into the continuous compounding formula:

That is the equation that models the situation.

Answer:

Given the expression:

You can simplify it as follows:

1. Multiply the signs applying the Sign Rules for Multiplication:

Then:

2. Notice that the signs of the numbers are different. Therefore, you have to subtract them. The result will have the same sign of the number with the greatest absolute value (in this case, it will be positive:

Hence, the answer is:

Step 1

Name all sides

Side facing given angle is the opposite = h

Side facing right angleis the hypotanuse

The other side is the adjacent = 875 feet

Hello! We can solve this exercise using proportionality.

Let's look at the triangles:

In the smallest, there are two sides with measurement which equals 16.

In the biggest, there are the same sides but with another measurement: 20.

Knowing that we know that the biggest triangle follows the same structure as the smallest, but a teeny bit bigger, right?

So, as we can say that they follow the same proportionality, let's equal them:

So, n = 30.

Another way:

we know that the same side before measured 16 and now measures 20, so we can write the proportion: 16/20.

If we simplify this fraction we will get 4/5, or in decimal, 0.8.

Now, we will divide the previous measure of the long side by this obtained proportion:

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.

In geometry, a secant is a line that intersects a curve at a minimum of two distinct points.

Answer:

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.

In geometry, a secant is a line that intersects a curve at a minimum of two distinct points.

Step-by-step explanation:

Solution

The given equation to get the accumulated amount is

Therefore, by substituting in these values, t will be given as

t approximately = 6.9 years to 1 decimal place.

x= adult passes

y= child passes

z=ride tickets

the first family:

the sencond family

third family

now we have the 3 equations, and we can solve x, y and z

for the equation of the second family we have:

reeplace the new equation(4) in (1), we have:

reeplace (4) in (3)

with 5 and 6, we have a 2x2 equation

that we can solve easier

solving 5 and 6, we have:

reeplace 7 in 6

now we find y, reeplace z in (7)

and finally we can find x, reeplacing y and z in (4)