50. WATER HOSES A water hose can spray water at an
initial velocity of 40 feet per second. Use the formula
h(t) = vot – 16t², where h(t) is the height of the water
in feet, vo is the initial velocity in feet per second, and
t is the time in seconds.
-
a. How long will it take the water to hit the
nozzle on the way down?
b. Assuming the nozzle is 5 feet up, what is
the maximum height of the water?

Answer:

Step-by-step explanation:

rate of change

[tex]=\frac{f(b)-f(a)}{b-a} \\=\frac{f(9)-f(1)}{9-1} \\=\frac{28-20}{8} \\=\frac{8}{8} \\=1[/tex]

The solution of the geometric equation is x = 1/2 or x = 1

An equation is a mathematical expression that shows the relationship between variables.

A geometric series is the sum of a geometric sequence.

Since the equation 0 = ( 1 - X - X²-...) (2 - X - X²-...). To solve this, let the series x + x² + ... = p

So, 0 = ( 1 - X - X²-...) (2 - X - X²-...).

0 = (1 - [X + X²+...) (2 - [X + X²+...).

Substitute x + x² + ... = p. So,

0 = (1 - [X + X²+...) (2 - [X + X²+...).

0 = (1 - p)(2 - p).

So, (1 - p) = 0 or (2 - p) = 0

p = 1 or p = 2

Since x + x² + ... = p, the left side of the equation is the sum to infinity of a geometric series.

The sum to infinity of the geometric series is given by

S = a/(1 - r) where

For the given series,

So, S = a/(1 - r)

= x/(1 - x)

Since S = p, we have that

x/(1 - x) = 1 or x/(1 - x) = 2

So, x = 1 - x or x = 2 - x

x + x = 1 or x + x = 2

2x = 1 or 2x = 2

x = 1/2 or x = 2/2

x = 1/2 or x = 1

So, the solution is x = 1/2 or x = 1

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Answer:

$51,750

Step-by-step explanation: We are going to make x = 3 and we will use the  i=prt equation meaning

Step 1: (45,000)(0.05)(3)= 6750

Step 2: 45,000+ 6750= 51,750

Solution: $ 51,750

By using the formula for amount of money in a compound interest, it can be calculated that

Amount received after 7 years is $13675.08

What is a compound interest?

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, then the interest earned is called compound interest.

If p is the principal, r is the rate and n is the time in years, then

amount = [tex]p(1+\frac{r}{100})^n[/tex]

Difference between amount and principal gives the compound interest.

Principal = $8800

Rate = 6.5 %

Time = 7 years

Amount received = [tex]8800(1 + \frac{6.5}{100})^7[/tex]

                                 $13675.08

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Answer:

$26.33

Step-by-step explanation:

[tex](2a^7b^5\cdot 3ab^8)^2\implies \left( 2^2 a^{(7)(2)} b^{(5)(2)} \cdot 3^2 a^2 b^{(8)(2)}\right)\implies 4a^{14}b^{10}\cdot 9a^2b^{16} \\\\\\ (4)(9)a^{14}a^2b^{10} b^{16}\implies 36a^{14+2}b^{10+16}\implies 36a^{16}b^{26}[/tex]

The no. of truffles than can be included in the box is 135.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given, The dimensions of the box you decided to purchase are 15 inches by 12 inches by 1.5 inches.

∴ The volume of the box is,

= (15×12×1.5) inches³.

= 270 inches³.

Given each truffle has a volume of 2 iches³.

∴ No. of truffles than can be included in the box is,

= (270/2).

= 135.

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Answer:

[tex]( \frac{1}{2} )^5 = \frac{1}{32}[/tex]

Step-by-step explanation:

The probability of "not a tail" is 1/2.  The five tosses are independent, so the probability of "not a tail" 5 times in succession is

[tex]\left(\frac{1}{2}\right) \cdot \left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right)[/tex]

The probability that a 4 is drawn from from Urn A followed by a 2 from Urn B is  1/40 .

In the question ,

it is given that

the number of balls in Urn A is 8

which are  {1,2,3,4,5,6,7,8}

the probability of getting a 4 from Urn A is (P₁) = 1/8

the number of balls in Urn B is 5 .

which are {1,2,3,4,5}

the probability of getting 2 from Urn B is (P₂) = 1/5

So ,the required probability is = P₁ × P₂

On substituting the values of P₁ and P₂ ,
we get

= 1/8 × 1/5

= 1/40

Therefore , the  required probability is 1/40 .

The given question is incomplete , the complete question is

Find the probability.

Urn A has balls numbered 1 through 8. Urn B has balls numbered 1 through 5. What is the probability that a 4 is drawn from A followed by a 2 from B?

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Answer:

--------------------------

Cash 2300

Accumulated Depreciation  4940

Gain one of fixtures 240

Store fixtures  7000

From the question, we have

Bonham’s Bakery sold shelving units (store fixtures) that were 13 years old for $2,300 cash.

Accumulated Depreciation = (7000-1300)/15*13

=4940

Gain one of fixtures = 240

Store fixtures = 7000

Multiplication:

Mathematicians multiply the numbers in order to calculate the sum of two or more. A fundamental mathematical operation, it is applied frequently in daily life. In order to combine groups of similar sizes, we use multiplication. An illustration of the fundamental concept of repeated addition of the same number is multiplication. The product of two or more numbers refers to the result of the multiplication, and the factors are the amounts that are being multiplied. It is easier to add the same number repeatedly after it has been multiplied.

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The equation of line with a slope of 3/2 which passes through point (-4,-2) is y = (3/2)x + 4.

The equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Point (-4, -2 )

First, we determine the y-intercept 'b'.

Plug the point and slope slope into the equation of line formula and solve for b.

y = mx + b

-2 = (3/2)(-4) + b

-2 = (3)(-2) + b

-2 = -6 + b

b = -2 + 6

b = 4

Now, plug the slope and y-intercept into y = mx + b to determine the equation of the line.

y = mx + b

y = (3/2)x + 4

Therefore, the equation of the line is y = (3/2)x + 4.

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The slope of the line tangent to f(x) at x = 1 is -8

The instantaneous rate of change of f(x) at x = 1 is -8

The equation of line tangent to f(x) at x = 1 is y  = -8x + 9

The tangent line to a curve at a given point is the line which intersects the curve at the point and has the same instantaneous slope as the curve at the point.

so the slope of a line at that point is the slope of the curve at that point.

f(x) = -4[tex]x^{2}[/tex] + 5

To find the slope, we differentiate f(x) with respect to x

dy/dx  = d/dx( -4[tex]x^{2}[/tex]) + d/dx(5)

           = -8x + 0

dy/dx = -8x

The slope = -8x

at x = 1,

the slope becomes, -8(1) = -8

The instantaneous rate of change of f(x) at x = 1 is the same as the slope of the line tangent to f(x) = -8

The slope of the line is -8

to find the equation of the tangent line, we need to find the coordinates of the point the line touches the curve.

one of the coordinates x = 1, to find y, we substitute x into f(x)

f(x) = -4[tex](1)^{2}[/tex] + 5

f(x) = 1

so the point is (1, 1)

so equation of straight line

[tex]\frac{y - y_{1} }{x - x_{1} }[/tex] = m

y - 1/x - 1 = -8

by cross multiplying

y - 1 = -8(x - 1)

y - 1 = -8x +8

y = -8x + 9

In conclusion,

The slope o the line tangent to f(x) at x = 1 is -8

The instantaneous rate off change of f(x) at x = 1 is -8

The equation of line tangent to f(x) at x = 1 is y  = -8x + 9

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a ) The required measure of x = 90°

b ) The height of the right angled triangle = = [tex]\sqrt{244}[/tex]

Given is a triangle with measure 15, 20 and 25

a ) Since a perpendicular is dropped from above

the two angles of x are equal because the angle is bisected by an angle bisector

So to check whether the angle x is a right angled or not

we can use the pythagoras theorem and check if the LHS = RHS or not

LHS = 15² + 20² = 225 + 400 = 625

and RHS = 25² = 625

Since LHS = RHS thus the angle is 90 degrees

b ) The height of the right triangle ;

by using the Pythagoras theorem again

12.5² + h² = 20²  { side 25 is bisected = 12.5 }

h² = 400 - 156.25

h = [tex]\sqrt{244}[/tex]

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If the number of different account numbers are possible if repetitions of letters and digits are allowed is:45,697,600,000.

Let assume you have 26 choices for each of the first 4 slots and 10 choices for each of the last 5 slots.

Hence,

Total possibilities = (26× 26× 26×26) × (10×10×10×10×10)

Total possibilities = 26^4 × 10^5

Total possibilities = 456976×100000

Total possibilities = 45,697,600,000

Therefore we can assume that the total possibilities is : 45,697,600,000.

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Answer:

30 lb bag is cheaper by about $2.40

Step-by-step explanation:

to find per pound we divide

19.49/4= 4.8725

$4.87per pound

$73.99/30=2.46633

$2.47 per pound

30 lb bag is cheaper per pound

4.87-2.47=2.40

hopes this helps please mark brainliest

The correlation coefficient that is most likely to match a line of best fit of the form y = mx + b for this situation is of:

0.9.

The correlation coefficient is an index that measures correlation between two variables, assuming numeric values between -1 and 1.

If the correlation coefficient is positive, the relation is positive, that is, they are direct proportional. If the correlation coefficient is negative, they are inverse proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the two variables is classified as strong.

In the context of this problem, the variables are listed as follows:

The total price increases with the number of bananas bought, and there is a strong positive relationship between these two variables, hence the coefficient should be greater than 0.6 and the correct option is:

0.9.

The problem is given by the image shown at the end of the answer.

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When quadratic function is subtracted from cubic function, the resultant equation is cubic.

So, It is true.

Function is defined as, In any equation of two variable, we make change in one  accompanied by second.

For example, [tex]F(x)=2x+1[/tex] when we make changes in x , different values of y will obtain.

Quadratic function in which maximum power of variable is two. Similarly, the function which has maximum power on variable is three is called cubic function.

To solve the given problem, let suppose we have,

Quadratic function:[tex]f(x)=x^{2} +x+1[/tex]

Cubic function: [tex]g(x)= x^{3}+x^{2} +x+1[/tex]

According to question,

Subtract quadratic function from cubic function,we get

[tex]g(x)-f(x)=( x^{3}+x^{2}+x+1)-(x^{2} +x+1 )[/tex]

⇒ [tex]h(x)=x^{3} +1[/tex]

It is a cubic function.

Thus, given statement is True.

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2x+3  x-3 those are correct

Answer:

1. reflection

2.translation

3.rotation

4.translation

5.translation

6.reflection

7.rotation

8.reflection

Hope this helps

have a good day

God bless you!

Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.

According to the question,

We have the following information:

In 8 years, Estelle's bank account earned $1,270 simple interest at 2.5%.

Now, let's take the principal amount to be $x.

We know that the following formula is used to find simple interest:

Simple interest = (principal*rate*time)/100

(x*2.5*8)/100 = 1270

Using the cross multiplication method:

20x = 127000

x = 127000/20

x = $6350

Hence, Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.

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Answer:

Figure A was translated right 4 units and up 2 units

The required time that would it takes to reach the flames is 2.78 sec.

Given that,
A helicopter drops a bucket of water onto a forest fire from 38 meters above the blaze how long it takes the water to fall and reach the flames is to be determined.

Here,
According to the question,
The initial velocity of the water is u = 0, and s = 38
Speed gain by the water is due to the acceleration due to gravity g = 9.8.
The time for water to reach to the ground is given by the second equation of motion.
s = u²t + 1/2gt²
Substitute the values in the above equation,
38 = 1/2(9.8)t²
(9.8)t² = 76
t = √(76/9.8)
t = 2.78 sec.

Thus, the required time that would it takes to reach the flames is 2.78 sec.

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[tex]x=2.16*10^{11}u-7.2k[/tex].

Side note: This answer could be more precise if made usage of more significant figures. For practicality reasons, in this solution we reduced the amount of significant figures to use.

[tex]150u=0.694(x+7.2K)*10^-9[/tex]

[tex]150u=[(0.694*x)+(0.694*7.2K)]*10^-9\\\\150u=[0.694x+4.9968k]*10^-9\\ \\150u=10^-9*0.694x+10^-9*4.9968k[/tex]

[tex]150u-10^-9*0.694x=10^-9*0.694x-10^-9*0.694x+10^-9*4.9968k\\ \\150u-10^-9*0.694x=10^-9*4.9968k[/tex]

[tex]-150u+150u-10^-9*0.694x=10^-9*4.9968k-150u\\ \\-10^-9*0.694x=10^-9*4.9968k-150u[/tex]

5. Divide both sides by "-10^-9*0.694".

[tex]\frac{-10^-9*0.694x}{-10^-9*0.694} =\frac{10^-9*4.9968k-150u}{-10^-9*0.694} \\ \\\frac{-10^-9*0.694x}{-10^-9*0.694} =\frac{10^-9*4.9968k}{-10^-9*0.694}-\frac{150u}{-10^-9*0.694} \\ \\x=-7.2k-(-2.16*10^{11} u)\\ \\x=-7.2k+2.16*10^{11}u\\ \\x=2.16*10^{11}u-7.2k[/tex]

-------------------------------------------------------------------------------------------------------

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The correct statement about the model, using proportions, is given as follows:

The model shows that there are 4 pieces that are each 0.75 ft long.

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context of the problem.

The application of proportions in this problem is to find the length of each piece, which is obtained as the division of the total length of the model by the number of pieces, hence:

Length of each piece = Total length/number of pieces.

The measures are given as follows:

Hence the length per piece is given by:

3 ft / 4 = 0.75 ft.

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Answer:

answer is 3/4!!! hope this helped

The slope of the line x = 3 is undefined

How to describe the slope of the line

The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

Mathematically, the slope is the change in y divided by the change in x. That is:

Slope = y2-y1 / x2-x1

Let's pick any two convenient points on the line:

(3, 9) and (3, -9) = > x1 = 3, y1 = -9 and  x2 = 3, y2 = 9

Slope = 9-(-9) / 3-3  = 18/0

The denominator here is 0, if you evaluate this using a calculator you will a maths error. So we say the slope is undefined

Notice that: There is no change in x i.e. x1 = x2

Therefore, the slope of x = 3 is undefined because x = 3 is a vertical line

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The plane flies at a speed of 150mph

A plane can fly 300 miles in the same time as it takes a car to go 120 miles

Let the time taken be t

Let the speed of the plane be x

the car travels 90 mph slower than the plane,

Speed of the car is x - 90

Speed = distance / time

Time taken by plane = time taken by car

300/ x = 120/x - 90

300(x - 90) = 120x

300x - 27000 = 120x

300x - 120x = 27000

180x = 27000

x = 27000/180

x = 150

Therefore, the plane flies at a speed of 150mph

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a. The current ratio is 1.3125

b. The acid test is 1.09375.

c. The average day collection is 37 days.

d. The asset turnover is 1.28.

e. The profit margin on sales is 14.63%.

a. The current ratio will be:

= Current asset / Current liability

= 21000 / 16000

= 1.3125

b. Acid test quick ratio will be:

= (Current asset - Inventory) / Current liability

= (21000 - 3500) / 16000

= 1.09375

c. Average day collection will be:

= Account receivable / (Net sales / 360)

= 4200 / (41000 / 36)

= 4200 / 114

= 37 days.

d. Asset turnover will be:

= Net sales / Total asset

= 41000 / 28000

= 1.28

e. Profit margin will be:

= Net income / Net sales

= 6000 / 41000

= 14.63%

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