Ariel dropped a golf ball from her second story window. The ball starts from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. Find the average acceleration of the golf ball.

The number of hour (time) for which workout plan A would last is 0.75 hour. Also, the number of hour (time) for which workout plan B would last is 0.5 hour.

In order to solve this word problem, we would assign variables to the number of hours (time) each plan and then translate the word problem into algebraic equation as follows:

Translating the word problem into an algebraic equation, we have;

On Friday  ⇒     6x + 5y = 7    ....equation 1.

On Saturday  ⇒ 2x + 3y = 3     ....equation 2.

Next, we would solve the simultaneous equation by using elimination method:

3 × (2x + 3y = 3) = 6x + 9y = 9    ........equation 3.

Subtracting equation 1 from equation 3, we have:

6x + 9y = 9

6x + 5y = 7

4y = 2

y = 2/4

y = 1/2

y = 0.5 hour.

For the value of x, we have:

6x + 5y = 7

6x + 5(0.5) = 7

6x + 2.5 = 7

6x = 7 - 2.5

6x = 4.5

x = 4.5/6

x = 0.75 hour.

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Complete Question:

Charmaine the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 6 clients who did Plan A and 5 clients who did Plan B. On Saturday there were 2 clients who did Plan A and 3 who did Plan B Charmaine trained her Friday clients for a total of 7 hours and her Saturday clients for a total of 3 hours. How long does each of the workout plans last?

Answer:

Step-by-step explanation:

Answer:

(1,3)

Step-by-step explanation:

You can use the distance formula to help you solve the answer

Answer:

(1; 3)

Step-by-step explanation:

x = (-1 + 3)/2 = 1

y = (6 + 0)/2 = 3

Answer:

p=12.3

Step-by-step explanation:

-1.5-9p= -6p+35.4

36.9=3p

p=12.3

The most appropriate choice for surds will be given by-

[tex]-11\sqrt{3}[/tex] is the correct answer.

What are surds?

There are some natural numbers which are not perfect squares. Their square root are not natural numbers. Those numbers are called surds. The most important method for simplification of surds is prime factorization.

[tex]10\sqrt{3} - 4 \sqrt{48}-\sqrt{75}\\10\sqrt{3} - 4\sqrt{2\times2\times 2\times 2\times3}-\sqrt{3\times 5\times5}\\10\sqrt{3} - 4\times 2\times 2\sqrt{3} - 5\sqrt{3}\\10\sqrt{3} - 16\sqrt{3}-5\sqrt{3}\\-6\sqrt{3} - 5\sqrt{3}\\-11\sqrt{3}[/tex]

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Answer:

I agree with your answer.

Step-by-step explanation:

Remember that the slope-intercept equation of the line is:

where 'm' is the slope and b is the y-intercept.

In this case, we have the following:

therefore,, the slope is m = 2

Answer:

x=50

Step-by-step explanation:

5(2-x)-10=25-2(3x+40)

Distribute:

10-5x-10=25-6x-80

Combine like terms

-5x-10=-6x-55

Put x to one side

x-10=-55

Make x by itself

x=-55

Answer:  x=−55

Step-by-step explanation:

Solve the equation step-by-step:

5(2−x)−10=25−2(3x+40)

Simplify both sides:

5(2−x)−10=25−2(3x+40)

Distribute:

(5)(2)+(5)(−x)+−10=25+(−2)(3x)+(−2)(40)

10+−5x+−10=25+−6x+−80

Combine Like Terms:

(−5x)+(10+−10)=(−6x)+(25+−80)

−5x=−6x+−55

−5x=−6x−55

Add 6x to both sides.

−5x+6x=−6x−55+6x

x=−55

Which graph shows the circle whose equation is (x−1)2+(y+3)2=16?

circle formula:

[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]

Given:

[tex](x-1)^{2} +(y+3)^{2} =4^{2}[/tex]

put into circle formal format:

[tex](x-h)^{2} +(y-k)^{2} =r^{2}\\(x-1)^{2} +(y-(-3))^{2} =4^{2}[/tex]

The center of the circle is at point (h,k)

[tex](x-1)^{2} +(y+3)^{2} =4^{2}[/tex]

center should be at:  (1,-3)

Answer:

lower row, left grid.

Answer:

Lower left, bottm, circle

Step-by-step explanation:

See attached graph

Answer:

chad's other friend picked up 1 3/8 pounds of berries

Step-by-step explanation:

chad = 2 1/2 = 2 4/8

friend 1 = 1 3/8

2 4/8 + 1 3/8 = 3 7/8

5 1/4 = 5 2/8

5 2/8 - 3 7/8 = 1 3/8

[tex]4a^{2} -25=0\\(2a-5)(2a+5)=0\\2a-5=0 \\or 2a+5=0\\\\a=\frac{5}{2} \\\\or\\\\a=-\frac{5}{2}[/tex]

IF YOU CHECK CAREFULLY YOU WILL FIND THAT THIS EQAUTION IS MADE OF DIFFERENCE OF SQUARES.

GOODLUCK!!

The given expression is

First, we change 1/3 for its reciprocal to transform the division into a product.

Then, we multiply the fractions.

At last, we transform the fraction into a mixed fraction.

The probability of no loads occurring during that period is at most 0.3 exists 3.2 years.

Given: Mean time between occurrence = 0.4 year

A number of loads expected to occur during a 4 year period

Period = 4

Mean time = 0.4

Let the formula = Period/Mean Time

The number of loads expected to occur during a 4-year period

= 4/0.4 = 10 loads

B. Probability that more than 11 loads occur during 4 year period

The expected number of loads during 4-year period = 10 (from A above)

mean = 10

Using Poisson distribution,

P(k events in interval)= (λ^k * e^-k)/k!

where: k = 0, 1, 2,3,4, . . ., 11 and λ = 10.

P(k = 0) = (1[tex]0^0[/tex] × [tex]e^{-10[/tex])/0! = 0.000045

P(k = 1) = (1[tex]0^1[/tex] ×  [tex]e^{-10[/tex])/1! = 0.000454

P(k = 2) = (10² ×  [tex]e^{-10[/tex])/2! = 0.00227

P(k = 3) = (10³ ×  [tex]e^{-10[/tex])/3! = 0.007567

P(k = 4) = (1[tex]0^4[/tex] ×  [tex]e^{-10[/tex])/4! = 0.018917

P(k = 5) = (1[tex]0^5[/tex] ×  [tex]e^{-10[/tex])/5! = 0.037833

P(k = 6) = (1[tex]0^6[/tex] ×  [tex]e^{-10[/tex])/6! = 0.063055

P(k = 7) = (1[tex]0^7[/tex] ×  [tex]e^{-10[/tex])/7! = 0.090079

P(k = 8) = (1[tex]0^8[/tex] ×  [tex]e^{-10[/tex])/8! = 0.112599

P(k = 9) = (1[tex]0^9[/tex] ×  [tex]e^{-10[/tex])/9! = 0.12511

P(k = 10) = (1[tex]0^{10[/tex] ×  [tex]e^{-10[/tex])/10! = 0.12511

P(k = 11) = (1[tex]0^{11[/tex] ×  [tex]e^{-10[/tex])/11! = 0.113736

The probability that more than 11 loads occur during a 4-year period is then given by the following Express

1 - [P(k = 0) + P(k = 1) + P(k = 2) + . . . + P(k = 11)]

substitute the values in the above equation, we get

= 1 - [0.000045 + 0.000454 + 0.00227 + 0.007567 + 0.018917 + 0.037833 + 0.063055 + 0.090079 + 0.112599 + 0.12511+ 0.12511 + 0.113736]

simplifying the equation, we get

= 1 - 0.571665 = 0.428335

C. How long must a time period be so that the probability of no loads occurring during that period is at most 0.3

(λ^0 * e^-λ)/0! = 0.3

⇒ e^-λ/1 = 0.3

simplifying the above equation, we get

⇒ e^-λ = 0.3

⇒ -λ = ln 0.3

⇒ -λ = -1.204

⇒ λ = 1.204

The time period = 4 years / 1.204

Time period = 3.2 years

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Using a quadratic function, it is found that:

a) The coordinates of the second x-intercept are: (50,0).

b) The vertex shows the maximum flight of the projectile.

c) The coordinates of the vertex are (25, 62).

3) The graph of the equation y = -0.0992(x² - 50x) is given at the end of the answer.

A quadratic function has two x-intercepts, x' and x'', and is defined as follows:

y = a(x - x')(x - x'').

The intercepts are given as follows:

The vertex is found as follows:

Hence the coordinates are: (25, 62).

The equation can be defined as follows:

y = ax(x - 50)

y = a(x² - 50x).

When x = 25, y = 62, hence the leading coefficient is found as follows:

62 = a(25² - 50(25))

-625a = 62

a = -62/625

a = -0.0992.

Hence the equation is:

y = -0.0992(x² - 50x).

The domain of the function is between the roots, hence 0 ≤ x ≤ 50, and the graph is sketched at the end of the answer.

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since z=6, so z+15 is equal to 21

or a+k+z=21

Answer:

(2,-3)

Step-by-step explanation:

[tex]\frac{\left(y+3\right)^2}{9}-\frac{\left(x-2\right)^2}{2}=1\\\frac{\left(y-k\right)^2}{a^2}-\frac{\left(x-h\right)^2}{b^2}=1\:\mathrm{\:is\:the\:standard\:equation\:for\:an\:up-down\:facing\:hyperbola}\\\frac{\left(y-\left(-3\right)\right)^2}{3^2}-\frac{\left(x-2\right)^2}{\left(\sqrt{2}\right)^2} =1\\(2,-3)[/tex]

The total money spent on fruits is $7.03

While at  the fruit stand, Ramon bought the following fruits,

3 pounds of apples that cost $0.89 per pound

4 cantaloupes that each cost $1.09

So, the total amount he spent on the materials he bought without including taxes is,

Total money spent = 3 x ( 0.89 ) + 4 x ( 1.09 )

                                = 2.67 + 4.36

                                = 7.03

The total money spent on fruits is $7.03

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3 × 90 thus equals 280 degrees.

The figure moves onto the following quadrant of the graph with each 90 degree rotation. In order to shift Figure I to the location of Figure J, you must move the three figure quadrants in a clockwise direction. 3 × 90 thus equals 280 degrees. Only one transformation is needed.

Which transformation corresponds to turning a figure 90 degrees counterclockwise?

The coordinate transformation (x, y) (y, x) is equivalent to a rotation of the origin 90 degrees counterclockwise. The coordinate transformation (x, y) (x, y) is comparable to a 180 degree counterclockwise rotation of the origin.

Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x and y, making y negative.

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The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters so option (C) is correct.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities.

There could be only two terms, but there could be one hundred, a thousand, or a million.

Here are always an integer number of terms in a summation.

As per the given,

Length of the trench on the first day = 18/20 meters

Length of the trench on the second day = 9/20

Total length of the trench = 18/20 + 9/20

Take LCM as 20

⇒ (18 + 9)/20 = 27/20

⇒ 1.35 which is closest among the given option by 1 1/2 meters.

Hence "The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters".

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Answer: 65$

Step-by-step explanation:

1. 40% of 150 is 60 so 60$ off of 150 is 90

2. total amount off is 85$. 60 is the 40% off and additional 25 for the rebate

3. final price will be 65$. 90-25=65

Answer:

$754.92

Step-by-step explanation:

699.00 plus 8% of 699.00 is 754.92

Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]

Step-by-step explanation:

[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]

Answer:

p = 20

Step-by-step explanation:

7 + 3(p - 1) = 64 ( subtract 7 from both sides )

3(p - 1) = 57 ( divide both sides by 3 )

p - 1 = 19 ( add 1 to both sides )

p = 20

The value of f¹(x) = x/5

What is function?

A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.

We are given f(x) = 5x

and we are to find inverse of f(x).

Replace f(x) by y.

So,

y = 5x

Isolate x

x = y/5

Replace x by f'(y)

So,

f'(y) = y/5

Replace all occurrences of y by x.

So,

f'(x) = x/5

Therefore, the inverse of function f(x) = 5x is f'(x) = x/5

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In order to determine the value of the missing length b, use the Pithagorean theorem, given by:

h² = a² + b²

where:

h = 6.5 mm

a = 2.5 mm

solve the previous equation for b, as follow:

b = √(h² - a²)

b = √(6.5² - 2.5²)mm

b = √36 mm

b = 6 mm

Hence, the value of the missing length is 6 mm

The equation models this scenario regarding the hiker is x - 450 = 2300.

Elevation is simply used to illustrate the height above the sea level.

In this case, the hiker descended 450 feet down to an elevation of 2300 feet.

The equation that can model the scenario will be x - 450 = 2300

where x = Initial elevation

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Answer:

6 and 16

Step-by-step explanation:

→ Find the most recurring number in sequence A

6

→ Find the most recurring number in sequence B

16

Answer: 18 combinations

Step-by-step explanation: you want to multiply the amount of ice cream flavors by the amount of children to be able to find the amount of possible combinations. so, 6 children x 3 flavors of ice cream = 18 different combinations. 6 x 3 = 18

The given pair of lines are parallel lines.

So, graph the lines on the given equation:

(Refer to the graph attached below)

We can easily look at the graph and tell that the given lines of the equations are parallel to each other.

Therefore, the given pair of lines are parallel lines.

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The sum of  -1 (3/4) and 2 (1/2) is the same as the difference between 2 (1/2) and 1 (3/4).

Firstly, we will convert the mixed fractions into improper fractions.

-1 and 3/4 = -7/4

2 and 1/2 = 5/2

Addition of -1 (3/4) and 2 (1/2) = -7/4 + 5/2 = -7/4 + 10/4 = 3/4

Difference between  2 and 1/2 and 1 and 3/4 = 5/2 - 7/4 = 10/4 - 7/4 = 3/4

As both the values equal to 3/4 , we can say that the addition of  -1  and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.

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