Shireen had a nap for 2 h. After her nap, she played badminton for 1/2h and swam for 1/5h.
(a) How long did Shireen exercise?

(b) How much more time did Shireen spend on her nap than on
her exercise?

Both triangles in the image are similar based on the AAA similarity theorem. The radius of the circle B is therefore calculated as: AB = 12.

Similar triangles are geometric figures that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are in proportion to each other.

Since AD serves as a common tangent, angle BAE is equal to 90 degrees, which is also equal to angle CDE due to being opposite angles.

By the Angle-Angle-Angle (AAA) similarity criterion, triangles ABE and DCE are similar.

Therefore:

AB/EA = DC/ED

Substitute:

AB/18 = 4/6

Cross multiply:

AB = 18 * 4/6

AB = 12

Therefore, the radius of the circle B is: 12.

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Answer:

y = 5

Step-by-step explanation:

[tex]14y-7y=35\\7y=35\\y=5[/tex]

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.

Uniform acceleration towards the positive direction:

In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.

Uniform acceleration towards the negative direction:

Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.

The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.

Uniform deceleration towards the positive direction:

In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.

The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.

Uniform deceleration towards the negative direction:

Here, the object's velocity decreases in the negative direction, opposing its initial direction.

The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.

In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.

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The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

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Answer:

B. 0.00467

Step-by-step explanation:

This is a binomial probability problem. The probability of fewer than three adults watching prime-time TV live is the sum of the probabilities of 0, 1, and 2 adults watching prime-time TV live.

Let X be the number of adults watching prime-time TV live. The probability mass function of X is given by:

P(X=k)=(kn​)p^k(1−p)^n−k

where n is the number of trials (7 in this case), k is the number of successes, and p is the probability of success on a single trial (0.8 in this case).

So, the probability that fewer than three of the selected adults watch prime-time TV live is:

P(X<3) = P(X=0) + P(X=1) + P(X=2)

=(7  0)(0.8)^0(0.2)^7 + (7  1​)(0.8)^1(0.2)^6 + (7  2​)(0.8)^2(0.2)^5

=1/78125 + 28/78125 + 336/78125

=73/15625

=0.004672

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:

b = total_number_of_pears / pears_per_bag

In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.

Given that Natalie has a total of 48 pears, we can substitute the value into the equation:

b = 48 / pears_per_bag

Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.

Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:

b = 48 / 4

Simplifying the equation gives:

b = 12

So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.

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The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192

The formula for hourly wage can be presented as follows;

Hourly wage  = Total earnings/Total hours worked

The question in the link is presented as follows;

Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid

The amount Jaxon gets paid per hour (his hourly wage) = $6

The number of hours he works each day = 8 hours

The number of days Jaxon works = Four days

The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days

Therefore we get;

Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192

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Answer:

7

Step-by-step explanation:

V looking shape has ends at 1 & 8

8 - 1 = 7

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The value of the quadratic function y = x² - 4x + 3 is determined by substituting the given value of x into the equation and performing the necessary calculations.

1. Start with the quadratic function: y = x² - 4x + 3.

2. Determine the value of x for which you want to find the value of y.

3. Substitute the given value of x into the equation.

4. Perform the necessary calculations to simplify the expression.

5. Evaluate the expression to find the value of y.

For example, let's find the value of y when x = 2:

1. Start with the quadratic function: y = x² - 4x + 3.

2. We want to find the value of y when x = 2.

3. Substitute x = 2 into the equation: y = (2)² - 4(2) + 3.

4. Simplify the expression: y = 4 - 8 + 3.

5. Perform the necessary calculations: y = -1.

6. Therefore, when x = 2, the value of the quadratic function y = x² - 4x + 3 is -1.

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Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

Answer:

A.

3.25x + 13.50 ≤ 40

Step-by-step explanation:

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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Answer:

1. 9 2/7 = (63+2)/7 = 65/7

2. 2 4/5 = (10+4)/5 = 14/5

3. 65/7 * 14/5 = 910/35 = 26

Answer:

1.255 seconds

Step-by-step explanation:

We can use the formula:

time = distance ÷ speed

to find the driver's time. Here, the distance is 200 miles and the speed is 159.5 miles per hour. Substituting these values into the formula, we get:

time = 200 miles ÷ 159.5 miles per hour

time = 1.255 seconds

The appropriate shape to model each section of the tower are the cone and the cylinder.

The approximate surface area of each shape would be =

For cone = 1,041.27m²

For cylinder = 3,543.72m².

The first shape is a cone and the formula for the surface area = A = πr(r+√h²+r²)

where;

Radius = 24/2 = 12

height = 10m

Area = 1,041.27m²

For cylinder:

A = 2πrh+2πr²

where:

r = 12m

h = 35m

A = 3,543.72m²

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a)  the value of the tractor after two years is $10,400.

b)  the value of the tractor after six years is $5,200.

To find the value of the tractor after a certain number of years, we can substitute the value of t into the equation v = -1,300t + 13,000.

a) After two years:

Substituting t = 2 into the equation, we get:

v = -1,300(2) + 13,000

v = -2,600 + 13,000

v = 10,400

Therefore, the value of the tractor after two years is $10,400.

b) After six years:

Substituting t = 6 into the equation, we get:

v = -1,300(6) + 13,000

v = -7,800 + 13,000

v = 5,200

Therefore, the value of the tractor after six years is $5,200.

To find when the tractor will have no value, we need to find the value of t when v = 0. We can set the equation v = -1,300t + 13,000 equal to 0 and solve for t:

-1,300t + 13,000 = 0

-1,300t = -13,000

t = -13,000 / -1,300

t = 10

Therefore, the tractor will have no value after 10 years.

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Answer:

250

Step-by-step explanation:

[tex]x+0.22x=305\\1.22x=305\\x=250[/tex]

Answer:

250

Step-by-step explanation:

so when you add 22% to 250 it equals 305

Answer:

tourist: 28%

non-tourist: 72%

Step-by-step explanation:

total: 50

tourists: 14

non-tourists:50 - 14 = 36

tourist percentage: 14/50 × 100% = 28%

non-tourist percentage: 36/50 × 100 = 72%

The domain for the time in this context is (0, 7.4)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let h represent the height of the ball after spending t seconds. A ball is thrown straight up from the top of a building that is 168 ft high with an initial velocity of 96 ft/s.

Given the equation:

h(t) = -16t² + 96t + 168

The reasonable domain restriction for t, is when  the height of the rocket is above the ground. Hence the domain for the time in this context is (0, 7.4)

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The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.

The sequence is defined by the following formula:
a1 = 1, a2 = 3,
and
an = (-1)nan - 1 + an - 2 for n ≥ 3.
To find the third term (a3), we substitute n = 3 into the formula:
a3 = (-1)(3)(a3 - 1) + a3 - 2.
Next, we simplify the equation:
a3 = -3(a2) + a1.
Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:
a3 = -3(3) + 1.
Simplifying further:
a3 = -9 + 1.
Therefore, the third term (a3) is equal to -8.
To find the fourth term (a4), we substitute n = 4 into the formula:
a4 = (-1)(4)(a4 - 1) + a4 - 2.
Simplifying the equation:
a4 = -4(a3) + a2.
Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:
a4 = -4(-8) + 3.
Simplifying further:
a4 = 32 + 3.
Therefore, the fourth term (a4) is equal to 35.
To find the fifth term (a5), we substitute n = 5 into the formula:
a5 = (-1)(5)(a5 - 1) + a5 - 2.

Simplifying the equation:
a5 = -5(a4) + a3.
Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:
a5 = -5(35) + (-8).
Simplifying further:
a5 = -175 - 8.
Therefore, the fifth term (a5) is equal to -183.
In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.

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The output value is feasible. The input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.

Jade decided to rent movies for a movie marathon over the weekend.

The function g(x) represents the amount of money spent in dollars, where x is the number of movies.

The given function is g(x) which represents the amount of money spent in dollars, where x is the number of movies.

The solution given is (6.5, $17.50).

We need to find whether the solution makes sense for the given function or not.

The input is given as 6.5 and the output is given as $17.50.

This means that Jade rented 6.5 movies and spent $17.50 on renting those movies.

To check whether the solution makes sense or not, we need to see if the input and output values are feasible or not.

The input value 6.5 is not a feasible value because it is not possible to rent half a movie.

Jade can rent 6 movies or 7 movies but not 6.5 movies.

Therefore, the input value is not feasible.

On the other hand, the output value $17.50 is a feasible value because it is possible for Jade to spend $17.50 on renting 6 movies.

The output value is feasible.

Since the input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.

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a) The fruit vendor sold 3/10 of the grapefruits on Saturday, b) The vendor had 100 grapefruits at first, and c) 40 grapefruits were sold on Friday.

a) On Saturday, the fruit vendor sold 1/2 of the remaining grapefruits. Since 2/5 of the grapefruits were sold on Friday, there are 3/5 of the original amount left. Therefore, on Saturday, the vendor sold (1/2) x (3/5) = 3/10 of the grapefruits.

b) To find the original number of grapefruits, we need to calculate the total amount remaining after Friday's sales. Since there were 60 grapefruits left after Saturday's sales and 3/5 of the original amount remained, we can set up the equation (3/5) [tex]\times[/tex]x = 60, where x represents the original number of grapefruits.

Solving for x, we have x = (60 x 5) / 3 = 100 grapefruits. Therefore, the fruit vendor had 100 grapefruits at first.

c) To find the number of grapefruits sold on Friday, we subtract the amount remaining after Friday's sales from the original number. 2/5 of the grapefruits were sold on Friday, so the number sold is (2/5) x 100 = 40 grapefruits.

In summary, a) the fruit vendor sold 3/10 of the grapefruits on Saturday, b) the vendor had 100 grapefruits at first, and c) 40 grapefruits were sold on Friday.

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The statement "1 is NOT in the domain" is true because for the function f(x), the expression x - 7 results in division by zero when x equals 1, which makes 1 not a valid input for the function.

To determine if a value is in the domain of a function, we need to consider any restrictions or limitations on the input values.

For the function f(x) = √(x - 7), the square root function is defined only for non-negative values.

Therefore, the expression (x - 7) inside the square root must be greater than or equal to zero. In other words, x - 7 ≥ 0.

Solving this inequality, we find x ≥ 7.

This means that any value of x that is greater than or equal to 7 is in the domain of f(x).

However, the statement is asking specifically about the value 1.

Since 1 is less than 7, it does not satisfy the inequality x ≥ 7 and is therefore not in the domain of f(x).

Similarly, for the function g(x) = 4x - 8, there are no restrictions on the domain.

Any real number can be substituted into the function, including the value 1.

Therefore, the statement "1 isn't in the domain of f(0) g" is not accurate.

It is true that 1 is not in the domain of f(x), but it is in the domain of g(x).

In summary, the correct statement is that "1 is not in the domain."

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The area of the parallelogram is  189 square units

First, we have the determine the length of the base and height.

The distance between the lines x = 9 and f(x) = 9 + 2x is the height

We have that the line parallel to f(x) passes through (4, 11)

The equation in point-slope form is;

y - 11 = 2(x - 4

y = 2x + 3

Substitute x = 9 in the equation,  y = 2x + 3.

y = 2(9) + 3 = 21

The  points are then (9, 21) and (9, 0).

The distance between the y-axis and the line x = 9 is the base.

Base = 9 units.

The formula for calculating area of a parallelogram is given by ;

= base × height

= 9 × 21

= 189 square units.

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The probability that a cell phone will fail within 2 years is 0.4866.

The average lifetime of the cell phone is 6 years, so the decay rate is 1 / 6 = 0.1667.

The probability that a phone will fail within 2 years is given by:

[tex]P(x < 2) = 1 - e^{-0.1667 * 2} = 1 - 0.5134 = 0.4866[/tex]

Rounded to four decimal places, the probability is 0.4866.

Therefore, the probability that a cell phone will fail within 2 years is 0.4866.

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