9 A book publishing company selected 30 out of 50 books submitted for publishing.
What decimal is equivalent to the fraction of books selected for publishing?

Answer:

28 : 37

Step-by-step explanation:

Find how many male teachers there are by subtracting 9 from 37:

37 - 9

= 28

Create a ratio with this to the total number of teachers:

28 : 37

So, the ratio of the number of male teachers to the total number of teachers is  28 : 37.

Answer:

Step-by-step explanation:

Let D be the distance between Chelsea's home and her school.

t is the time to travel by bus.  The total time for both the bus and walking is 1 hour, so the time to walk is (1-t)hr.

We know that Distance = Speed x Time, or D = S*T

Going by bus:

D = (.75)t

Walking:

D = (2.5)(1-t)

D is the same, so we can write:

(0.75)t = (2.5)(1-t)

0.75t = 2.5-2.5t

3.25t = 2.5

t = 0.769 hours

It takes Chelsea 0.769 hours, or 46.15 minutes to travel to school by bus.  This doesn't seem correct, since it means it only takes her 13.85 minutes to walk home.  So double check my numbers, but it is possible that the bus makes many stops, plus a bad traffic light, after Chelsea is picked up.  When she walks straight home it takes her less time than the bus.

Option a. The car is 115.47 feet from the building is correct for the given right triangle.

A trigonometric formula known as the rule of sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. In other words, if a triangle has angles A, B, and C opposing its sides and sides a, b, and c, then:

If a/sin(A) = b/sin(B) = c/sin(C), then

If some of the other sides and angles of a triangle are known, this formula can be used to solve for those unknown sides or angles. However, it is restricted to triangles and calls for the measurement of at least one angle and one side's length.

The situation can be depicted as a right triangle, with building 200 feet, the angle of depression is 30 degrees.

Now,

tan(30) = opposite/adjacent = 200/distance

distance = 200/tan(30) ≈ 115.47 feet

Hence, option a. The car is 115.47 feet from the building is correct for the given right triangle.

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Answer:

x=34

Step-by-step explanation:

Answer:

y = -5x-4

Step-by-step explanation:

start with slope-intercept form:

-9-11/1+3 = -20/4 = -5

your slope is -5

next, do point-slope form:

y+9 = -5(x-1)

y+9 = -5x+5

 -9         -9

y = -5x-4

Answer: True

Step-by-step explanation: Because Im A Top G

Answer:

3 ; 1 minute ;75%

Step-by-step explanation:

Given :

Service time = 15 seconds = 15/60 = 0.25 minute per customer

μ = number of customers per minute = 1/0.25 = 4

Arrival rate, λ= 3 persons per minute

L = λ ÷ (μ - λ)

L = 3 ÷ (4 - 3)

L = 3 ÷ 1

L = 3

b) How long would you expect it to take to get a cup of coffee?

L / arrival rate (λ)

3 / 3

= 1 minute

c) What percentage of time is the urn being used?

Utilization rate = λ/ μ

= 3 / 4

= 0.75 = 0.75 * 100% = 75%

Answer:

3x-y=5

3*2(X)=6-1(Y)=5

Step-by-step explanation:

x=2

y=1

The expression that is equal to E is C) Q − RW. When Q is divided by W, the quotient (R) is the result of the division, and the remainder (E) is the leftover value.

We have, When Q is divided by W, the quotient is R and the remainder is E.

From this, we can write the equation

Q = W × R + E

The given equation can also be written as

Q = RW + E

By solving for E, we get

E = Q - RW

Now let us check the given options

A) RW + Q

B) RW - Q

C) Q - RW

D) QW - RE) Q/RW

The correct option that is equal to E is Q - RW. Hence the correct answer is an option (C).

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The height of the building is 44 meters

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

Height of the tree = 22 m

From the question, we understand that

Scale of the diagram = 2

This means that

Height of the building = Height of the tree * Scale of the diagram

Substitute the known values in the above equation, so, we have the following representation

Height of the building = 22 m * 2

Evaluate

Height of the building = 44 m

Hence, the height is 44 m

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Answer:

Rr = 51 : 68

Step-by-step explanation:

Step-by-step explanation:

The line representing the equation 7x1 + 4x2 = 28 goes through the points (4,0) and (0,7).

The chance that the event B will never appear during the process until event A occurs can be calculated P(B never occurs) = P(B does not occur in the first trial) * P(B does not occur in the second trial) * P(B does not occur in the third trial) * ...

To compute this probability, we need to consider the probabilities of events B not occurring in each trial. Since events A, B, C, and D form a partition of the sample space, we can write:

P(B never occurs) = P(B does not occur in the first trial | A does not occur) * P(B does not occur in the second trial | A does not occur and B does not occur in the first trial) * P(B does not occur in the third trial | A does not occur and B does not occur in the first two trials) * ...

The conditional probabilities can be determined based on the information provided in the problem. However, without specific information about the relationships between events A, B, C, and D, or the probabilities associated with each event, it is not possible to calculate the exact probability of B never occurring until A occurs.

The calculation of this probability would require more specific information about the experiment and the relationships between events A, B, C, and D. It is important to have information about the probabilities associated with each event and any dependencies or conditional probabilities involved. Without such information, we can only express the concept of calculating the probability of B never occurring until A occurs, but the numerical calculation cannot be performed.

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Answer:

$239.02 and $10177

Step-by-step explanation:

Ann:

2868.32/6= 478.05

478.05/2= 239.02

Ann's sister:

3562.28/7= 508.89

508.89/5= 101.77

dont know if i did this right to be completely honest. but i feel like it's right. sorry if it's not.

Answer:

Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet. ... If you are using a ruler with a centimeter (cm) scale, then your units are going to be in cm, and if you ... We have to do the same thing to volume like we did with the surface area.

:)

Answer:

Rectangular prism

I chose a box of cereal.

Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).

Length: 20 cm

Width: 8 cm

Height: 32 cm

Part 2).

 Describe the shape of the cross-section when the box is cut parallel to the base.

The shape of the cross-section would be a rectangle in dimensions.

20 cm x 8 cm

Part 3)

What is the surface area of the box? 

surface area=2*area of the base + perimeter of the base*height

area of the base=20*8=160 cm²

perimeter of the base=2*[20+8]-----> 56 cm

height=32 cm

surface area=2*160+56*32------> 2,112 cm²

the answer part 3) is

2,112 cm²

Part 4)

What is the surface area of the box if it is scaled up by a factor of 10?

we know that

surface area of the larger box =[scale factor]²*surface area original box

scale factor=10

surface area original box=2,112 cm²

so

surface area of the larger box=10²*2,112-----> 211,200 cm²

the answer part 4) is

211,200 cm²

Part 5) 

What is the volume of the box?

volume of the box = L*W*H 20*8*32-5,120 cm³

the answer Part 5) is

5,120 cm³

Part 6) 

What is the volume of the box if it is scaled down by a factor of 1/10?

we know that

the volume of the smaller box =[scale factor]³volume original box

scale factor=1/10

volume original box=5,120 cm³

so

volume of the smaller box =[1/10]³*5,120 5.12 cm³

the answer part 6) is

5.12 cm³

The length is 6 in., the width is 2 in., and the height is 16 in.

The probability of selecting a boy from the class is 15/25, or 3/5, since there are 15 boys in a class of 25 students.

When selecting two students randomly without replacement, the probability of selecting a boy on the first draw is 15/25, and the probability of selecting another boy on the second draw (assuming the first student selected was a boy) is 14/24, since there will be 14 boys left out of 24 students remaining.

So the probability of selecting two boys in a row is:

(15/25) * (14/24) = 7/20

Therefore, the probability that both students chosen for the presentation are boys is 7/20, or approximately 0.35.

Answer:

x=5

Step-by-step explanation:

6(5)= 30

The Probability that you selected one good and one bad card is =  3/6

According to our question-

Hence,The probability that you selected one good and one bad card is =  3/6

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Answer:

* Lucy spent £289.2 on tiles *

Step-by-step explanation:

We know that the tiles are present in a 13 to 2 ratio ( 13 : 2 ) so if there are 16 blue tiles that she buys, the number of red tiles bought should be represented the following -

\(\frac{13}{2}\) = \(\frac{x}{16}\) ... now this is only assuming that the 13 : 2 ratio is meant by white : blue tiles. Let's solve through cross - multiplication,

13 \(*\) 16 = 2\(x\),

208 = 2\(x\),

\(x\) = 104 white tiles

So if there are 104 white tiles, and 16 blue tiles, we can determine the total amount Lucy spent on tiles by associating the cost to the type of tile,

£2.80 \(*\) 16 = £44.8,

£2.35 \(*\) 104 = £244.4,

Total Amount Lucy Spent on Tiles = £44.8 + £244.4 = £289.2

Lucy spent £289.2 on tiles

\(\frac{13}{2} = \frac{x}{16}\\\\ 13\times 16 = 2x\\\\ 2 x = 208\)

x = 104 while tiles

Now the total amount should be

\( 2.80 \times 16 = 44.8\\ And, \\ 2.35 \times 104 = 244.4\)

So,

= 44.8 + 244.40

= 289.2

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On solving the provided question ,we can say that As a result, the pie chart's slice representing sleep has a 45 degree centre angle

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

We must first determine the percentage of the 24 hours that Burt slept in order to determine the size of the centre angle of the slice of the pie chart that represents sleep.

Burt slept for three hours out of a total of twenty-four, thus this is how much time he slept:

3/24 = 1/8

We need to multiply this ratio by 360 degrees (the total number of degrees in a circle) to determine the centre angle of the slice indicating sleep:

1/8 times 360 equals 45 degrees.

As a result, the pie chart's slice representing sleep has a 45 degree centre angle.

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The measure of the central angle, in degrees, of the slice of the pie chart representing sleep is 45 degrees.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities. It is a way of expressing a number as a quotient of two integers, where the top number is called the numerator, and the bottom number is called the denominator.

To calculate the measure of the central angle representing sleep in the pie chart, we need to determine what fraction of the 24 hours Burt spent sleeping.

Burt slept for 3 hours out of 24, so the fraction of time he spent sleeping is:

3 / 24 = 1 / 8

To convert this fraction into an angle, we use the formula:

angle = fraction * 360 degrees

So, the central angle representing sleep in the pie chart would be:

angle = (1 / 8) * 360 degrees = 45 degrees

Therefore, the measure of the central angle, in degrees, of the slice of the pie chart representing sleep is 45 degrees.

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2. Critical numbers of a function h(t) = t^(3/4) - 3t^(1/4) are (1/16 , -1/16).

A number is critical if it makes the derivative of the expression equal 0.

Critical numbers are values of a function where the function's tangent lines are either horizontal or vertical.

Given function is,

h(t) = t^(3/4) - 3t(1/4)

We have to find critical points.

For this we will take derivative and set it with 0

Therefore

h'(t) = (3/4)t^(-1/4) - 3(1/4)t^(-3/4) = 0

3/4[t^(1/4)] = 3/4[t^(3/4)]

4t^(3/4) = t^(1/4)

4 = 1/√t

t = 1/16 and t= -1/16.

Therefore critical points are (1/16 , -1/16).

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Let 'h' represent the number of hours that Charles will work. Since he wants to work for at least six hours, then we have the following inequality:

but he also must work fewer than 16 hours this week, then the next inequality is:

then, combining the inequalities, we have:

Answer:

7 minutes

Step-by-step explanation:

420/60 = 7 minutes

Answer:

7

Step-by-step explanation:

420/60 which equals 7 mim

Answer:

r equals -4

Step-by-step explanation:

there's your help

Answer:

x - 9

Step-by-step explanation:

That should be it, and let me know if I'm wrong. x is by itself and if you were to add 3 and 6 you'd get 9. So x - 9

Since the focus is at (-5, -2) and the directrix is the line y = 1, we know that the vertex of the parabola lies halfway between them, which is at (-5, -0.5).

Since the directrix is a horizontal line, the parabola opens downward. Let (x, y) be a point on the parabola, and let d be the distance from (x, y) to the directrix (which is y - 1). Then the distance from (x, y) to the focus is d + 0.5 (half the distance between the focus and directrix).

Using the distance formula, we have:

√[(x - (-5))² + (y - (1))²] = d + 0.5

Simplifying, we get:

(x + 5)² + (y - 1)² = (d + 0.5)²

Since the point (x, y) lies on the parabola, its distance to the directrix is equal to its distance to the focus:

d = |y - 1 - (-0.5)| = |y - 0.5|

Substituting this into the equation above, we get:

(x + 5)² + (y - 1)² = (|y - 0.5| + 0.5)²

Expanding and simplifying, we get:

x² + 10x + y² - 2y - 12|y - 0.5| - 12 = 0

To put this in standard form, we need to eliminate the absolute value. We consider two cases:

Case 1: y ≥ 0.5

In this case, |y - 0.5| = y - 0.5, so we have:

x² + 10x + y² - 2y - 12y + 6 - 12 = 0

Simplifying, we get:

x² + 10x + y² - 14y - 18 = 0

Completing the square, we get:

(x + 5)² + (y - 7/2)² = 99/4

This is the standard form of the equation of the parabola.

Case 2: y < 0.5

In this case, |y - 0.5| = -(y - 0.5) = 0.5 - y, so we have:

x² + 10x + y² - 2y - 6(0.5 - y) - 12 = 0

Simplifying, we get:

x² + 10x + y² - 2y + 3 = 0

Completing the square, we get:

(x + 5)² + (y - 1)² = 21

This is also the standard form of the equation of the parabola, but it corresponds to a different part of the curve than the previous equation (since it has a different sign for the y-term).

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a) The critical points of the equation are (-2, 66) and (2, -66).

b) The interval of increase is (-∞, -2) U (2, ∞), and the interval of decrease is (-2, 2).

c) The relative minimum is (-2, 66), and the relative maximum is (2, -66).

d) There are no inflection points in the equation.

e) The concave is upward for the entire graph.

The given equation is y = 3x⁴ - 24x³ + 32 - 24x + 54x + 4.

To determine its critical points, we find the values of x where the derivative of y equals zero.

By taking the derivative, we obtain 12x³ - 72x² - 24, which can be factored as 12(x - 2)(x + 2)(x - 1).

Thus, the critical points are (-2, 66) and (2, -66).

Analyzing the derivative further, we observe that it is positive in the intervals (-∞, -2) and (2, ∞), indicating an increasing function, and negative in the interval (-2, 2), suggesting a decreasing function.

The relative minimum occurs at (-2, 66), and the relative maximum at (2, -66).

There are no inflection points in the equation, and the concave is upward for the entire graph.

The critical points of a function are the points where the derivative is either zero or undefined.

In this case, we found the critical points by setting the derivative of the equation equal to zero. The interval of increase represents the x-values where the function is increasing, while the interval of decrease represents the x-values where the function is decreasing.

The relative minimum and maximum are the lowest and highest points on the graph, respectively, within a specific interval. Inflection points occur where the concavity of the graph changes, but in this equation, no such points exist. The concave being upward means that the graph curves in a U-shape.

Understanding these characteristics helps us analyze the behavior of the equation and its graphical representation.

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If Q and R have coordinates of (xQ, yQ) and (xR, yR), respectively, then Q' and R' have coordinates of : Q' = (xQ + a, yQ + b) and R' = (xR + a, yR + b)

Assuming that "triangle PQR is translated to trinagle PQR" is a typo, and the second triangle should be denoted as triangle P'Q'R', we can find the coordinates of Q' and R' after the translation.

Let's say that the translation vector is (a, b), where a and b are the horizontal and vertical shifts, respectively. Then, the coordinates of Q' and R' can be found by adding (a, b) to the coordinates of Q and R, respectively.

If we assume that the coordinates of Q and R are (xQ, yQ) and (xR, yR), respectively, then the coordinates of Q' and R' are:

Q' = (xQ + a, yQ + b)

R' = (xR + a, yR + b)

Note that the coordinates of point P do not change, as it is not part of the triangle being translated.

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Answer:

d

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

x=1/4