Andy Foll is 6 times as old as Mel Kaas. Andy is 15 years older than Mel. What is Mel's age?

a) g(x) = 10 + 0.5x

b) 17 days

Let the number of days be represented by x

Let the intial height of the zucchini plant be g₀

g₀ = 10 cm

Size of growth per day = 0.5 cm

Let the growth after x days be represented by g(x)

a) The rule that represents the function is therefore:

g(x) = g₀ + 0.5x

g(x) = 10 + 0.5x

b) After how many days will the Zucchini pant be 0.185 meters tall

That is g(x) = 0.185 meters

since 1 meter = 100 cm

g(x) = 0.185 x 100 cm

g(x) = 18.5 cm

Thereofre substitute g(x) = 18.5 into the equation g(x) = 10 + 0.5x

18.5 = 10 + 0.5x

18.5 - 10 = 0.5x

0.5x = 8.5

x = 8.5 / 0.5

x = 17

The zucchini plant will be 0.185 meters tall after 17 days

The number which is decreased by 20% and result is 336 then number is 420

According to the question, given that

when a number is decreased by 20 % of itself, it became 336

then, the number is :

x - (x ×[tex]\frac{20}{100}[/tex] )= 336

x - [tex]\frac{x}{5}[/tex] = 336

[tex]\frac{5x - x}{5}[/tex] = 336

[tex]\frac{4x}{5}[/tex] = 336

x = [tex]\frac{336 *5}{4}[/tex]

x = 84 * 5

x = 420

Therefore, we get the number is 420

PERCENT INCREASE =(new amount−original amount)/original amount

Some people append 100% at the end of this calculation to stress that it should be stated as a percent since it represents an increase in percentage.

So, as an alternative, here is the formula:

PERCENT INCREASE = (new amount−original amount)/original amount*100%

PERCENT DECREASE=(original amount−new amount)original amount

OR

PERCENT DECREASE=(original amount−new amount)original amount*100%

Both formulas have the following pattern:

PERCENT INCREASE/DECREASE=change in amount /original amount

OR

PERCENT INCREASE/DECREASE=change in amount/ original amount*100%

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Solution

otal number of cCustomer = 11 + 9 + 11 + 5 + 5 + 1 + 3 = 45

Let A denotes the event that the Customer waited for at least 12 minutes

Let B denotes the event that the Customer waited between 8 and 15 minutes

We want to find

hus, the probability is 0.556

Option D

By using a trigonometric identity, we will see that the value of sin(x/2) is:sin(x/2) =  ±√39/√56 = ± 0.834

Here we need to use the identity: (sin(x/2))^2 = (1 - cos(x))/2

So, we know that:

cos(x) = -11/28

Then:

(1 - cos(x)) = 1 + 11/28 = 28/28 + 11/28 = 39/28

Replacing the identity that we get:

(sin(x/2))^2 = (1 - cos(x))/2 ]= (39/28)/2 = (39/56)

Now we can apply the square root in both sides, so we will get:

sin(x/2) = ±√(39/56)=  ±√39/√56 = ± 0.834

So, the value of sin(x/2) can be either 0.834 or -0.834.

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The mean and the average values are the same. They represent a dataset by calculating the central value.

The range can be understood as the variation of the data. The higher the range, the wider the variation.

From the table, we can see the average temperature of Rio de Janeiro is higher than in Caracas.

We can also see the variation of the temperature is higher in Caracas than in Rio de Janerio.

This corresponds to choice A.

The value of x in the given right triangle is 8√5.

Pythagoras theorem states the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

The length of side z of the triangle is calculated as follows;

z² = y² + 4²

The length of side x is calculated as follows;

x² + z² = (16 + 4)²

x² + z² =  20²

substitute the value of z² into the equation,

x²  + y² + 4² = 20²

x²  + y² = 20² - 4²

x²  + y² = 384

Considering the second triangle, with sides, 16, x and y, the value of side y is calculated as follows;

y² = x² - 16²

y² = x² - 256

x²  + y² = 384

x²  + x² - 256 = 384

2x² = 384 + 256

2x² = 640

x² = 640/2

x² = 320

x = √320

x = √(64 x 5)

x = √64 . √5

x = 8√5

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The given expression is :

To simplify the expression for x :

Add 5 on both side :

Divide the expression by 4 on both side :

Thus : x ≥ 3

The graph is :

Since x is greater than or equal to 3

So, it is closed on 3

Answer :

The graph has a closed circle on 3 and is shaded to the right of the origin

Answer:

P(B) = 0,35

Step-by-step explanation:

P(B) = P(A and B) divided by P(A)

Answer:

3y = 80v - x

Step-by-step explanation:

she need to change the operation. x should be –

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

frequency histogram

Step 02:

discrete math:

sum of two dice:

we must analyze the graph to find the solution.

most frequent outcome:

value of dice = 8

frequency = 20

least frequent outcome:

value of dice = 2

frequency ≅ 2

how many times (7):

15 times (frequency)

percentage of times (7):

percentage (7) = (15 / 100) * 100%

percentage (7) = 15%

shape of distribution:

non-symmetric, bimodal

That is the full solution.

[tex]S=4+64t-16t^2\implies \stackrel{\textit{at a height of 32}}{32=4+64t-16t^2}\implies 16t^2-64t-4+32=0 \\\\\\ 16t^2-64t+28=0\implies 4(4t^2-16t+7)=0\implies 4t^2-16t+7=0 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{4}t^2\stackrel{\stackrel{b}{\downarrow }}{-16}t\stackrel{\stackrel{c}{\downarrow }}{+7}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]

[tex]t= \cfrac{ - (-16) \pm \sqrt { (-16)^2 -4(4)(7)}}{2(4)} \implies t = \cfrac{ 16 \pm \sqrt { 256 -112}}{ 8 } \\\\\\ t= \cfrac{ 16 \pm \sqrt { 144 }}{ 8 }\implies t=\cfrac{16\pm 12}{8}\implies t= \begin{cases} \frac{1}{2}&\textit{on the way up}\\\\ \frac{7}{2}&\textit{on the way down} \end{cases}[/tex]

Answer: a. 291/2020 b. 77/465 c. 874/2020 d.145/376 e. 41/157 f. 41/157 g. 53/157 h. 433/465 I. 335/376

Step-by-step explanation:

A. 291- column of loyal customers for 10-14 years over total amount. Question about the overall group 2020.

B. 77- people in the east that have been loyal 10-14 years in the east over the east group that's given that they're apart of 465.

C. 874 - customers loyal for more than 10 years in the west over the total amount. Question about the overall group 2020.

D.145 (45+100) - customers loyal for over 10 years in the west over the west group 376.

E. 41 people that have been loyal less than 1 year in the west over the group that has been loyal for less than 1 year 157.

F. 53 people that have been loyal less than 1 year in the south over the group that has been loyal for less than 1 year 157.

G.433 (465-32) people that have been loyal more than a year in the east over the east group 465.

I.335 (376-41) people that have been loyal in the west over the west group 376.

Population of Planet Eenie is  1.4 × [tex]10^{3}[/tex] times greater than the population of Planet Meenie.

Two planets named Eenie and Meenie.

Population of  Planet Eenie = 72,980,001

Population of  Planet Meenie =  54,908

We need to find how many times greater is the population of Planet

Eenie than the population of Planet Meenie. So, we need to follow the steps written below:

( Population of  Planet Eenie / Population of  Planet Meenie )

= ( 72,980,001 / 54,908 )

= 1329.1323

= 1.33 × [tex]10^{3}[/tex]

This calculated value is near option 2 i.e., 1.4 × [tex]10^{3}[/tex]. So,  1.4 × [tex]10^{3}[/tex] is the correct option.

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Solution

The formula for calculating margin of error is given to be

n = 390 bacteria (nearest whole number)

For given details the function is f(t) = 2400 - 48t

a) the amount of air in the tank is a function of the number of minutes it contain the air.

b) Domain of the function: [0, 50] and  the domain is continuous one.

c) Graph of the function is attached below.

Function:

The function also know as expression, rule, or law that defines a relationship between one variable and another variable.

Given,

The amount of air in a scuba diving tank with a capacity of 2400 liters is decreasing at a constant rate of 48 liters per minute.

Here we need to find the following:

a) Whether the amount of air in the tank a function of the number of minutes?

b) Domain of the function

c) Graph of the function

Through the given question we know that,

The total amount of air in the tank = 2400 liters

Discharge unit per minute = 48 liters

Let us consider f(t) be the amount of air in a scuba diving tank.

where t represents the time in minutes.

Through the given information we get a function,

f(t) = 2400 - 48t

While using the given function, we can observe that the amount of air in the tank a function of the number of minutes.

Now, we need to find the domain of the function f(t)

Let us consider f(t) = 0

2400 - 48t = 0

2400 = 48t

t = 2400 / 48

t = 50

Therefore, t takes values in from the interval [0, 50]

We know that time is continuous to the function.

so, the domain is also continuous.

Now we have to plot the graph of the function..

Therefore, for given situation the function is f(t) = 2400 - 48t is attached below.

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The description of the motion of the ball, which is a projectile are as follows;

(a) The window coordinates are; (0, 138.49)

(b) The x–component is 7.22 m)s

The y–component is -3.22 m/s

(c) The equations for displacement are;

(d) 16.07 m from the base

(e) Height of the ball location before it was thrown is 138.49 meters

(f) Time to reach 10.0 m. is 1.14 s

Projectile motion is the motion of an object that is thrown or thrusted into the air such that the major force acting on an object is the force of gravity

(a) The parameters of the motion of the ball are;

Initial velocity of the ball = 7.8 m/s

Direction to which the ball is tossed = 24° below the horizontal

Time it takes the ball to strike the ground = 5.00 s

Location of the origin of the coordinates = The base of the building

[tex]h = v_{iy} \cdot t + 0.5 \cdot g \cdot t²[/tex]

Where;

h = The height of the window

[tex]u_{y}[/tex]

The initial vertical velocity = 7.8×sin(24°) ≈ 3.173 m/s

g = The acceleration due to gravity ≈ 9.81 m/s²

t = The time duration of the motion = 5.00 s

Therefore;

h = 3.173×5 + 0.5×9.81×5²≈ 138.49

The height of the window, h ≈ 138.49 meters

Given that the window shares the same x–coordinates with the base, which is 0, we have;

(b) The x and y–component of the initial velocity are therefore;

v = 7.9 m/s × (cos(24°)•i - sin(24°)•j)

v = 7.22•i - 3.21•j

The x and y component of the velocity are therefore

x–component [tex] v_{ix} [/tex] = 7.22•i

y–component, [tex] v_{y} [/tex] = -3.21•j

Therefore;

(c) The equation of the x–component of the position is found as follows;

x = 7.9×cos(24°) × t = 7.22 •t

y = 7.9×sin(24°) × t+ 0.5× 9.81×t²

(d) The distance from the base of the building where the ball lands is given by the equation

d ≈ 3.21 × 5 ≈ 16.07

(e) The height from which the ball was thrown, h, is given by the y–coordinate in option (a) therefore;

(f) When the distance traveled = 10 meters, we have;

[tex]h = v_{iy} \cdot t + 0.5 \cdot g \cdot t²[/tex]

Which gives;

10 = 3.21•t + 0.5×9.81×t²

Solving with a graphing calculator, gives;

t ≈ -1.79 or t = 1.14

The possible value for the time it takes to reach the point 10 meters is therefore;

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Area = l x w

convert to improper fraction and evaluate

Answer:

multiply length times width.

Step-by-step explanation:

The given expression xy = yx represents the cumulative property of multiplication.

If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics. Numerous binary operations share this essential characteristic, and numerous mathematical arguments rely on it.

The given expression is xy = yx.

The expression xy = yx is representing the cumulative property of multiplication. According to this property, the value of the expression will remain the same after the order is changed.

Let x = 5 and y = 10. Now verify the cumulative property of multiplication.

xy = yx

5 x 10 = 10 x 5

50 = 50

Therefore, the given expression xy = yx represents the cumulative property of multiplication.

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As the circle is centered in the origin , we only need to know the radius of the circle. The radius is the distance from (0,0) to (-2,0) and it is 2. So the equation is

Parent function:

Transformations:

a indicates a reflection acrross x-axis (if it is a<0) and/or a stretch or shrink

h indicates a horizontal translation

k indicates a vertical translation

As you have:

The tangent relation is given by the length of the opposite side to the angle over the length of the adjacent side to the angle.

So we have:

Therefore the correct option is C.

The amount that a $90,000 loan cost Lauren than Demarcus will be $8280.

From the information, Demarcus and Lauren each take out a $90,000 loan for a new condo and each has to repay the loan in 10 years. It should be noted that 10 years in months will be:

= 10 × 12 = 120 months

The difference in the amount paid as a result of the credit score will be:

= ($840 × 120) - ($771 × 120)

= $100800 - $92520

= $8280

Therefore, the amount is $8280.

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The perimeter is the sum of all the sides of a geometric figure, so

To resolve this inequality you can first subtract 8 from both sides

Then you divide by 4 on both sides of the inequality

Therefore, for the perimeter of the rectangle to be less than 120, its shortest side must measure less than 28.

The savings plan balance (future value) after 3 years with a 7% APR and monthly payments of $100 is $3,993.01.

The future value is the present value or cash flows compounded at an interest rate for a period.

The future value can be computed using an online finance calculator.

N (# of periods) = 36 months

I/Y (Interest per year) = 7%

PV (Present Value) = $0

PMT (Periodic Payment) = $100

Results:

FV = $3,993.01

Sum of all periodic payments = $3,600 ($100 x 36)

Total Interest = $393.01

Thus, at the end of 3 years, the saving plan balance grew to a future value of $3,993.01.

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Using the arithmetic progression, If a theatre has 30 rows of seats there are 22 seats in the first row,26 in the second row, 30 in the third row, then the total number of people that the theatre hold is 2400

The total number of rows = 30

Number of seats in the first row = 22

Number of seats in the second row = 26

Number of seats in the third row = 30

Common difference= Second term - first term

= 26-22

= 4

The given sequence is in arithmetic progression

Sum of n terms = [tex]\frac{n}{2}[2a+(n-1)d][/tex]

Substitute the values in the equation

= [tex]\frac{30}{2}[2(22)+(30-1)4][/tex]

= 15[44+29×4]

= 15[44+116]

= 15×160

= 2400

Hence, using the arithmetic progression, if a theatre has 30 rows of seats  and there are 22 seats in the first row,26 in the second row, 30 in the third row, then the total number of people that the theatre hold is 2400

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The perimeter of the hexagon ABCDEF is 36.01.

Given,

The hexagon ABCDEF

We have given the points:

A(-6, 2), B(1, 5), C(6, 5), D(6, -1), E(1, -3), F(-6, -3)

We have to find the perimeter of hexagon.

Perimeter of hexagon = AB + BC + CD + DE + EF + FA

Now,

Distance formula is as [tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

So,

A(-6, 2), B(1, 5) : x₁ = 1, x₂ = -6, y₁ = 2, y₂ = 5

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(1-(-6))^{2} +(5-2)^{2} }[/tex]

=[tex]\sqrt{7^{2} +3^{2} }[/tex]

= [tex]\sqrt{49+9}[/tex]

= √58

= 7.62

B(1, 5), C(6, 5) : x₁ = 1, x₂ = 6, y₁ = 5, y₂ = 5

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(6-1)^{2}+(5-5)^{2} }[/tex]

= √5²

= 5

C(6, 5), D(6, -1) : x₁ = 6, x₂ = 6, y₁ = 5, y₂ = -1

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(6-6)^{2}+(-1-5)^{2} }[/tex]

= √-6²

= 6

D(6, -1), E(1, -3) : x₁ = 6, x₂ = 1, y₁ = -1, y₂ = -3

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(1-6)^{2}+(-3-(- 1))^{2} }[/tex]

= [tex]\sqrt{(-5)^{2} +(-3+1)^{2} }[/tex]

= [tex]\sqrt{25 + 4}[/tex]

= √29

= 5.39

E(1, -3), F(-6, -3)  : x₁ = 1, x₂ = -6, y₁ = -3, y₂ = -3

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(-6-1)^{2}+(-3-(-3))^{2} }[/tex]

= √-7²

= 7

F(-6, -3), A(-6, 2)  : x₁ = -6, x₂ = -6, y₁ = -3, y₂ = 2

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(-6-(-6))^{2} +(-3-(2))^{2} }[/tex]

= √-5²

= 5

So, we have

AB = 7.62

BC = 5

CD = 6

DE = 5.39

EF = 7

FA = 5

Now,

Perimeter of hexagon = AB + BC + CD + DE + EF + FA

Perimeter of hexagon= 7.62 + 5 + 6 + 5.39 + 7 + 5

Perimeter of hexagon = 36.01

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After evaluting the  expression 8+ 9/4 (-2) we get 8 1/4.and result in decimals: 8.25

Given expression -

8+ 9/4 (-2) = ?

Combine the whole numbers and fractions together:

(8 – 2) + (9/4 - 0)

The whole numbers part is:

8 – 2 = 6

For the fractions part:

(9/4 - 0)

The Least Common Multiple (LCM) of 4 and 1 is 4. Multiply the numerator and denominator of each fraction by whatever value will result in the denominator of each fraction being equal to the LCM:

9/4 - 0 = 9/4 - 0/4

Now that the fractions have like denominators, subtract the numerators:

9 - 0/4 = 9/4

9 ÷ 4 = 2R1, therefore

9/4 = 2 1/4

Put the whole number and fraction together:

6 +2(1/4) 1

8 1/4.

Hence , the result of the expression 8+ 9/4 (-2) = 8 1/4.

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