Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola:
16.44y = x²
The focus is
The directrix is
The focal diameter is
The vertex is
The axis of symmetry is

Answer:

sin( 3pi/4 ) = -√2/2

So, B.

Answer:

6 hours

Step-by-step explanation:

So therefore,

4 roofers= 1 hour

1 roofer= 9 * 4

= 36 hours

6 roofers= 36/6=6 hours

The inequality representing the dollar amount, n, that Zack must be paid for each room in order to make a profit of more than $300 is n > $107.50.

Option C is the correct answer.

We have,

Profit = Amount Paid - Cost of Supplies

Given that the cost of supplies for each room is $32.50, we can represent the profit for each room as:

Profit per room = Amount Paid per room - $32.50

Zack wants to make a profit of more than $300 for painting 4 identical rooms.

The total profit for the 4 rooms should be greater than $300.

We can write this inequality as:

4 x (Profit per room) > $300

Substituting the expression for profit per room, we have:

4 x (Amount Paid per room - $32.50) > $300

Now, let's solve the inequality to find the dollar amount that Zack must be paid for each room:

4 x (Amount Paid per room - $32.50) > $300

4 x Amount Paid per room - 4 x $32.50 > $300

4 x Amount Paid per room - $130 > $300

4 x Amount Paid per room > $300 + $130

4 x Amount Paid per room > $430

Amount Paid per room > $430 / 4

Amount Paid per room > $107.50

Therefore,

The inequality representing the dollar amount, n, that Zack must be paid for each room in order to make a profit of more than $300 is n > $107.50.

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Answer:

Step-by-step explanation:

The area of a square is given by the formula A = s^2, where A is the area and s is the length of a side of the square.

Let y be the length of the side of the small square.

Then, the area of the small square is y^2 cm^2.

According to the question, the area of the small square is 1/25 of the area of the large square.

Thus, the area of the large square is (25)(y^2) cm^2.

The length of a side of the large square is given by the formula s = √A.

Therefore, the length of a side of the large square is √(25y^2) = 5y cm.

Since the length of a side of a cube is equal to its height, width, and length, the dimensions of the cube are 5y cm x 5y cm x 5y cm = (5y)^3 cm^3.

Therefore, y = 40/5 = 8.

Thus, the dimensions of the cube are 40 cm x 40 cm x 40 cm.

When we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16.

To evaluate f(x)=(1/4)^-x for specific values of x, we can substitute the given values into the function expression and simplify the calculations.

Evaluating f(-2):

Substitute x = -2 into the function f(x):

f(-2) = (1/4)^-(-2) = (1/4)^2 = 1/16

Evaluating f(1):

Substitute x = 1 into the function f(x):

f(1) = (1/4)^-1 = 4^1 = 4

Evaluating f(2):

Substitute x = 2 into the function f(x):

f(2) = (1/4)^-2 = (1/4)^2 = 1/16

Therefore, the evaluations of f(-2), f(1), and f(2) are:

f(-2) = 1/16

f(1) = 4

f(2) = 1/16

In conclusion, when we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16. These values represent the corresponding outputs of the function for the given inputs.

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Probability that exactly 10 flights arrive on time is 53.33%.

Given that,

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation.

Recently, Southwest Air had the best rate with 80% of its flights arriving on time.

Total number flights in sample = 15

Probability that exactly 10 flights arrive on time is,

P = 10/15 × 80%

  = 0.5333

  = 53.33%

Hence the required probability is 53.33%.

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Answer:

Step-by-step explanation:

( 8n - 5 ) - ( -2n - 3 )

( 8n - 5 ) + ( 2n + 3 )

8n - 5 + 2n + 3

10n - 2

Answer:

[tex]( - 2, 0 )\; and \; ( 4, - 6)[/tex]

Step-by-step explanation:

To find the ordered pairs set the right side expressions equal to each other and solve for x, then use those values for x to evaluate f(x) values

We get

x² - 3x - 10 = -x - 2

Moving -x - 2 to the left side gives

x² -3x - 10 + x + 2   = 0
(moving an expression from one side to another changes the signs of the terms)

Grouping like terms:
x² - 3x + x -10 +2 = 0

x² -2x -8 = 0

Expression on the left can be factored as (x + 2)(x-4)

This results in
(x + 2)(x - 4) = 0 giving

(x + 2) = 0 ==> x = -2 as one solution for x

(x - 4) =0 ==> x = 4 as the second solution

Plug in x = -2 into the second expression -x - 2 to get

f(-2) = -(-2) -2 = 2 - 2 = 0

So one ordered pair is (-2, 0)

Plug in x = 4 into -x - 2 to get
f(4) = - 4 -2 = -6

So (4, -6) is another ordered pair

The rigid transformations that can take AEFD to CFEB are translation, rotation, and reflection.

To describe the rigid transformations that take polygon AEFD to CFEB, we need to identify the transformations that preserve the shape and size of the polygon. Here are some possibilities:

Translation: A translation involves moving the entire polygon without changing its orientation or shape. If we shift polygon AEFD to the right, it will align with polygon CFEB. Therefore, translation is one way to achieve this transformation.

Rotation: If we rotate polygon AEFD around a fixed point, such as the center of the polygon or a vertex, by a certain angle, it can align with polygon CFEB. A rotation preserves the shape and size of the polygon.

Reflection: A reflection involves flipping the polygon across a line, resulting in a mirror image. If we reflect polygon AEFD across a line of reflection, it can match polygon CFEB.

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1 Yes  the set of rational expressions is closed under subtraction

2. Yes  the set of rational expressions is closed under multiplication

3. No  the set of rational expressions is not closed under division

1. The subtraction of two rational expressions results in another rational expression.

=  p(x)/q(x) - r(x)/s(x)= ((p(x)s(x) - r(x)q(x))/(q(x)s(x)))

this is also a rational expression.

2. The multiplication of two rational expressions results in another rational expression.

=(p(x)/q(x)) * (r(x)/s(x)) = ((p(x)r(x))/(q(x)s(x)))

this is a rational expression.

3. Division of two rational expressions may result in an expression that is not a rational expression.

= (p(x)/q(x)) / (r(x)/s(x)))

= ((p(x)s(x)) / (q(x)r(x)))

this may not be a rational expression if q(x)r(x) equals zero at some point, causing division by zero

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Answer:

The measure of the central angle in radians is 5.6/8 = 0.7 radians.

The amplitude and the period of the function f(x) = 2cos[3(θ + 45)] + 2 are 2 and 2π/3

The Phase shift is 45 and the vertical shift is 2

From the question, we have the following parameters that can be used in our computation:

f(x) = 2cos[3(θ + 45)] + 2

A sinusoidal function is represented as

f(x) = Acos(B(x + C)) + D

Where

Amplitude = A

Period = 2π/B

Phase shift = C

vertical shift = D

Using the above as a guide, we have the following:

Amplitude = 2

Period = 2π/2

Next, we have

Phase shift = 45

vertical shift = 2

Hence, the amplitude is 2 and the period is 2π/3

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The simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

The given expression is 5x²+6x+4+x²+x

Simplifying the given expression

5x²+6x+4+x²+x

Firstly, put the similar terms together

5x²+x²+6x+x+4

Adding the similar terms

6x²+7x+4

∵ The expression cannot be solved further, 6x²+7x+4 is the final solution.

Therefore, the simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

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Answer:

Step-by-step explanation:

a. The surface area of the cube is reduced .

b . The new surface area of the new solid is 90 in²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

a. The surface area of the original cube is 96 in² and a cube of another 6 in² is removed from the old cube.

This means that the surface area of the cube is reduced.

The surface area of a cube is expressed as;

SA = 6l²

where l is the side length of the cube.

b. The surface area of the new solid = surface area of big cube - surface area of old cube = 96-6

= 90 in²

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The exponential growth model for the baseball player's earnings, in millions of dollars, t years after 2015 is[tex]y = 3 \times (1.04)^t,[/tex]  with a base of 1.04.

To model the exponential growth of the baseball player's earnings, we can use the formula:

[tex]y = a \times (1 + r)^t[/tex]

where:

y represents the earning in millions of dollars

a represents the initial earning in millions of dollars (in this case, $3 million)

r represents the growth rate per year (4%, which can be expressed as 0.04)

t represents the number of years after 2015

In this case, we want to find the earning y (in millions of dollars) t years after 2015.

Since the initial earning in 2015 is $3 million, we can substitute a = 3.

Therefore, the exponential growth model for the player's earnings is:

[tex]y = 3 \times (1 + 0.04)^t[/tex]

Simplifying the expression further, we have:

[tex]y = 3 \times 1.04^t[/tex]

The base of the model is 1.04, which is the decimal representation of the growth rate (4%).

Using this model, we can calculate the player's earnings for any year after 2015 by plugging in the value of t.

For example, if we want to find the earnings 5 years after 2015, we substitute t = 5 into the equation:

[tex]y = 3 \times 1.04^5[/tex]

This will give us the projected earnings in millions of dollars for that particular year.

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The missing angles in the cyclic quadrilateral are as follows:

a = 101°

b = 67°

c = 84°

d = 80°

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.

Opposite angles of a cyclic quadrilateral is supplementary.

c = 180 - 96

c = 84 degrees

d = 180 - 100

d = 80 degrees

100 = 1 / 2 (a + 99)

100 = 0.5a + 49.5

0.5a = 50.5

divide both sides by 0.5

a = 50.5 / 0.5

a = 101 degrees

84 = 1 / 2 (101 + b)

84 = 50.5 + 0.5b

84  - 50.5 = 0.5b

0.5b = 33.5

b = 33.5 / 0.5

b = 67 degrees

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The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.

To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.

The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.

Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.

Using this information, we can proceed to plot the circle on a graph:

Plot the center point: (3, -3).

From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.

Up: (3, -3 + 6) = (3, 3)

Down: (3, -3 - 6) = (3, -9)

Left: (3 - 6, -3) = (-3, -3)

Right: (3 + 6, -3) = (9, -3)

Connect the plotted points to form a circle.

The resulting graph should look like this:

    |            • (3, 3)

    |  

    |    •

    |                     •

__|_____________________________

    |

    |

    |

    |  

    |    • (3, -3)

The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.

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Answer: C 1/6*√2n

Step-by-step explanation:

• Simplify √n/18 as (1/3)^2*n/2

• Multiply them under the radical so the squares 1/3 cancels out to 1/3*√n/2

• Multiply the √n/2 on both sides as √2*n/√2*√2 so it comes out to √2n/2

• Multiply √2n/2 with 1/3 to make √2n/6

√2n/6 is equal to 1/6*√2n

The radical expression √n/18 when simplified is 1/3√n/2

From the question, we have the following parameters that can be used in our computation:

√n/18

Express 18 as 9 * 2

So, we have the following representation

√n/18 = √n/(9 * 2)

Rewrite as

√n/18 = √n/(2 * 9)

Take the square root of 9

This gives

√n/18 = 1/3 * √n/2

Evaluate the products

√n/18 = 1/3√n/2

Hence, the expression when simplified is 1/3√n/2

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A weak correlation between the two variables is depicted by the scatter plot in the supplied image.

The trend line's points are widely dispersed, which suggests that there is little correlation between the variables.

In a scatter plot, the degree of connection between the two variables can be classified as strong or weak.

A weak correlation indicates that there is a lot of scatter around the trend whereas a high relationship indicates that there is very little scatter in comparison to the trend's movement.

Thus, the given association is weak correlation.

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Answer:

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

Given:

Convert the interest rate to a decimal:

Convert the time from months to years:

Now, we can calculate the simple interest using the formula:

Finally, add the interest to the principal to find the amount due:

Susan's amount due for the loan is $1047.50.

The simple interest amount of Susan for time of 8 months is A = $ 1047.50

Given data ,

To calculate the amount due, we need to consider the principal amount borrowed, the interest rate, and the time period.

Principal (P) = $1000

Time (t) = 8 months

Interest rate (r) = 7 1/8% per annum

First, we need to convert the interest rate from a percentage to a decimal. To do this, we divide the given rate by 100:

r = 7 1/8% = 7.125% = 7.125/100 = 0.07125 (decimal)

Next, we can calculate the simple interest using the formula:

Simple Interest (I) = Prt

I = $1000 x 0.07125 x (8/12)

I = $1000 x 0.07125 x (2/3)

I = $47.50

Finally, to find the amount due, we add the principal amount to the simple interest:

Amount Due = Principal + Simple Interest

Amount Due = $1000 + $47.50

Amount Due = $ 1047.50

Hence , the amount is A = $ 1047.50

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We can expect 258 blocks in the bag to be green.

We have to given that,

A bag has 6 blocks in it. Jerry picks a block out of the bag 60 times. He gets the green block 43 times.

Since, We know that Jerry picked a block out of the bag 60 times, and got the green block 43 times.

So the probability of picking a green block is:

P = 43/60

P = 0.7167

This means that out of every 60 blocks picked, there are 43 green.

Now, For this probability to estimate the number of green blocks in the bag.

since, Jerry picked 60 blocks 6 times

When, we assume that the bag contains a total of 360 blocks , we can multiply this total by the probability of getting a green block:

360 x 0.7167 = 258.012

Thus, We can expect 258 blocks in the bag to be green.

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a. The category that was chosen as approximately 1/4 will be Cat.

b. The percentage that choose other or cat will be 35%.

c. The percentage that choose dog is 16%

a. It should be noted that to determine the category chosen by approximately one-fourth of the community, we need to look for the corresponding section of the pie chart. This shows the cat.

b. The percentage that choose other or cat will be:

= 10% + 25%

= 35%.

c. The percentage that choose dog is:

= 32% / 2

= 16%

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Angles in each quadrant with common reference angle as 311° are :

First quadrant = 49°, second quadrant = 131°, third quadrant = 229° and fourth quadrant = 311°.

Given that,

Reference angle = 311°

We have to find an angle in each quadrant with this reference angle.

311° is in the fourth quadrant.

The equivalent angle on the first quadrant is,

360° - 311° = 49°

Equivalent angle on second quadrant is,

180° - 49° = 131°

Equivalent angle on third quadrant is,

360° - 131° = 229°

Hence the angles are found.

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Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

Answer:

891 cm³

Step-by-step explanation:

Since they are the same shape with only their sizes different, that means they have a proportionate ratio so:

2673 / 9 = V / 3

Now make V the formula of the subject:

V = 2673 / 9 TIMES 3 = 891.

2/5 of the frogs in that portion of the South American rainforest are not poisonous.

On the off chance that 3/5 of the frogs in a rainforest in South America are poisonous, at that point, the remaining division speaks to the frogs that are not poisonous.

To discover this division, we subtract the division of poisonous frogs from 1 (which speaks to the complete):

1 - 3/5 = 5/5 - 3/5 = 2/5

Hence, 2/5 of the frogs in that portion of the rainforest are not poisonous. This fraction represents the parcel of frogs that don't have poisonous characteristics.

It is important to note that this calculation expects that all frogs within the rainforest are either poisonous or notpoisonous, and there are no other conceivable outcomes or middle states.

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The value of the angle m<WXY is 69 degrees

We need to know that the shape given is a parallelogram.

The properties of a parallelogram are given as;

From the information given, we have that;

Angel WZY and Angle WXY are opposite angles of the parallelogram

Then,

m<WXY = 69 degrees

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Answer: It has ans an equal chance of 50-50

Step-by-step explanation: There are 10 of each type, leaving 20 total, half of the candy is Cherry, the other half is Strawberry.