BOWLING A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y = 3.5x +4
represents the cost y of bowling games. Interpret the parameters of the function.
represents the price per game
$
represents the shoe rental charge.

Answer:  The last choice is correct \(\frac{9}{\sin\left(60\right)}\)

Step-by-step explanation: The information given in the diagram: AB is the hypotenuse of a right triangle, and the side opposite the 60° angle is 9 feet. you can use sine = 0pposite/Hypotenuse

You can find the sine of 60° which is the value of the ratio of the opposite side to the (unknown) hypotenuse.  sin 60° = 0.866

You can set up the equation on a scientific calculator as \(\frac{9}{\sin\left(60\right)}\)  but to see the logic use the value   0.866 = 9/h

reorganize to solve for h: divide both sides by 0.866 and multiply both by h to get  

h = 9/0.866   solving that you get the length of AB

h = 10.393, which, rounded, is a logical length for the brace on the gate:

 10.4 feet

the trigonometric ratios of angle C in right triangle ABC are: sin(C) = 8/17,  cos(C) = 15/17, tan(C) = 8/15, csc(C) = 17/8, sec(C) = 17/15 and cot(C) = 15/8

To determine the trigonometric ratios of angle C in right triangle ABC, we can use the values of the sides AC and BC. Here's how we can find the trigonometric ratios:

Given: AC = 17 units and BC = 8 units

Using the Pythagorean theorem, we can find the length of side AB:

AB² = AC² - BC²

AB² = 17² - 8²

AB² = 289 - 64

AB² = 225

AB = 15 units

Now we have the lengths of all three sides of the triangle:

AC = 17 units

BC = 8 units

AB = 15 units

Using these values, we can find the trigonometric ratios:

1. Sine (sin) of angle C:

sin(C) = BC/AC

sin(C) = 8/17

2. Cosine (cos) of angle C:

cos(C) = AB/AC

cos(C) = 15/17

3. Tangent (tan) of angle C:

tan(C) = BC/AB

tan(C) = 8/15

4. Cosecant (csc) of angle C:

csc(C) = 1/sin(C)

csc(C) = 1/(8/17)

csc(C) = 17/8

5. Secant (sec) of angle C:

sec(C) = 1/cos(C)

sec(C) = 1/(15/17)

sec(C) = 17/15

6. Cotangent (cot) of angle C:

cot(C) = 1/tan(C)

cot(C) = 1/(8/15)

cot(C) = 15/8

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Answer:

7 hrs

Step-by-step explanation:

formula :- speed=distance/time

speed= 96kph

distance= 672 km

time=?

S=D/T

96=672/T

(cross multiply)

96T = 672

T = 672/96

T = 7 hrs

It takes 7 hours to travel a distance of 672 km at a speed of 96 kph.

Time = Distance/speed

Time = 672 / 96

Time = 7

It takes 7 hours to travel a distance of 672 km at a speed of 96 kph.

Answer:

$1.75

Step-by-step explanation:

4.5-2.75=1.75

Answer:

1¾ dollars

Step-by-step explanation:

4.5 - 2.75 = 1.75

The value of X and y using substitution method for the quadratic equation given above would be = -3.6 and - 2.8 respectively.

The equations given are;

2x - 7y = 13. ----> equation 1

3x + y = 8 --------> equation 2

From equation 2 make y that subject of formula;

y = 8 - 3x

Substitute y = 8 - 3x into equation 1

2x - 7(8 - 3x) = 13

2x - 56 - 21x = 13

-19x = 13+56

-19x = 69

X = -69/19

X = - 3.6

Substitute X = -3.6 into equation 2

3(-3.6) + y = 8

y= 8 - 10.8

= - 2.8

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John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer:

48 years

Step-by-step explanation:

It is assumed the given figure is a parallelogram.

Use properties of a parallelogram:

Find the missing values:

The cat population in Catonsville in 2007 was 200. The answer is option B.

Population refers to the total number of people, animals, or objects in a particular group or area. It is the entire group or collection of individuals, things, or events that we are interested in studying or describing.

We can use the given equation to find the cat population at any given time in years since the beginning of 2010. However, to find the population in 2007, we need to make a conversion from years since the beginning of 2010 to years since the beginning of 2007.

From the beginning of 2007 to the beginning of 2010, there are 3 years, so if we subtract 3 from the number of years since the beginning of 2010, we will get the number of years since the beginning of 2007. Therefore, we need to substitute t = -3 into the given equation and solve for p:

\(p = 1600(2)^t\\p = 1600(2)^(-3)\\p = 1600(1/8)\\p = 200\)

Therefore, the cat population in Catonsville in 2007 was 200. The answer is option B.

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Prior to placing an order to buy ABCD stock at a lower price, the investment adviser must conduct thorough research and analysis, set a target price, and determine an appropriate entry point for the purchase.

The investment adviser's primary responsibility is to act in the best interest of their client and make informed investment decisions. In this case, where the adviser believes ABCD stock is appropriate only if the price falls to $35 per share, several steps need to be taken before placing an order.

Firstly, the adviser should conduct comprehensive research on ABCD stock to understand its historical performance, financial health, industry trends, and any relevant news or events that might impact its future prospects. This research will help validate the adviser's belief that the stock is worth considering at a lower price.

Secondly, the adviser should establish a target price of $35 per share based on their analysis and the client's investment objectives. This target price serves as a reference point and provides a clear criterion for initiating the purchase.

Lastly, the adviser needs to identify an appropriate entry point for the purchase. This involves monitoring the stock's price movements and market conditions closely. The adviser may choose to set a limit order at $35 per share or implement a strategy to take advantage of potential price declines, such as dollar-cost averaging.

By following these steps, the investment adviser ensures that they have thoroughly evaluated the investment opportunity and have a plan in place before placing an order to buy ABCD stock for the client's account.

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The value cosθ is 0.707.

The value angle z is -45⁰, and 45⁰.

The value of angle θ  is 45⁰ and 315⁰.

The value cosθ, and angle Z is calculated by applying trigonometry ratio as follows;

for question 6,

tan θ = opposite side/adjacent

tan θ = 5/5

tan θ = 1

θ = 45⁰ = z

cos θ = 0.707

for question 7;

tan z = opp/adjacent

tan z = -5/5

tan z = -1

z = arc tan (-1)

z = -45⁰ =

The value of θ is calculated as;

θ = 360 - 45

θ = 315

cos (315) = 0.707

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The answer is 10√2

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

see explanation

Step-by-step explanation:

(a)

area of rectangle = lb ( l = 12 , b = 6 )

area = 12 × 6 = 72 cm²

(b)

area Δ A = \(\frac{1}{2}\) bh ( b = 3 , h = 6 )

area = \(\frac{1}{2}\) × 3 × 6 = \(\frac{1}{2}\) × 18 = 9 cm²

(c)

area Δ B = \(\frac{1}{2}\) bh ( b = 3, h = 6 )

area = \(\frac{1}{2}\) × 3 × 6 = 9 cm²

(d)

area of parallelogram = area of rectangle - area Δ A - area Δ B

                                     = 72 - 9 - 9

                                     = 72 - 18

                                     = 54 cm²

Answer:

b. The science students

Step-by-step explanation:

If you count the dots, they are the same for both class (9 people) but the range of the science students' scores are higher than the range for the math students, which means that the sum of their scores will be larger than the math students' and since they have the same number of people, the number being divided for the average would be the same, so the science students' average would be greater than the math's.

I hope this helped! ;D

Answer:

-2x+15=7

     -15

-2x=7

    +15

-2x=22

then divide -2 by 22 and you get -11

Step-by-step explanation:

hopefully this is right

Answer:

h = 5.5

Step-by-step explanation:

2.3 + h = 7.8

-2.3         -2.3

  h = 5. 5

A plasmid used in both yeast and bacteria requires two different selection markers because the same selection may not work for both hosts and bacteria and yeast recognize different promoters.

When using a plasmid in both yeast and bacteria, it is important to have two different selection markers for several reasons. First, the same selection, such as the presence of an antibiotic, may not be effective in both hosts. Different organisms have varying sensitivities to antibiotics, so a marker that works in bacteria may not work in yeast or vice versa. Therefore, two different selection markers are needed to ensure successful selection in both hosts.

Additionally, bacteria and yeast recognize different promoters, which are DNA sequences that control the initiation of gene expression. Promoters are specific to each organism and play a crucial role in regulating gene expression. By incorporating two different selection markers into the plasmid, each marker can be driven by a promoter recognized specifically by the corresponding host. This ensures that the selection marker is effectively expressed in the appropriate host organism, enabling accurate selection and maintenance of the plasmid.

In summary, using two different selection markers in a plasmid intended for both yeast and bacteria is necessary because the same selection may not be effective in both hosts, and different promoters are recognized by bacteria and yeast. This approach allows for successful selection and maintenance of the plasmid in both organisms.

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Trapezoid's height is 8.5 inches using the formula of the square of a trapezoid.

let's first try to understand what is a trapezoid.

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

Trapezoids are defined differently by different people. A trapezoid can have one and only one pair of parallel sides, according to one school of mathematics, while another contends that a trapezoid can have multiple pairs of parallel sides. If we take into account the second definition, then a parallelogram is also a trapezoid by that definition. However, the first definition excludes parallelograms from the definition of a trapezoid. since it is one of the quadrilateral types that we have already mentioned.

We know the trapezoid area formula is

A = \((a+b)/2*h\)

Where a = base1 b = base2 and h = height

in Question, it is given that base1 = 10.5 inches long

base2 = 11.5 inches long area  = 93.5square inches.

93.5 = (10.5+11.5)/2 * h

93.5 = 22/2 *h

93.5 = 11*h

h = 93.5/11

h = 8.5 inches.

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The height of the school is 8.75 meters.

Trigonometry is the study of the connections between triangle angles, lengths, and heights. It contains ratios, functions, identities, and formulae for solving issues based on right-angled triangles.

The method of Geometry Yuuf is using to determine the height of his school building is through the property that similar triangles have a common ratio of corresponding their sides.

The given parameters for the triangle formed by Yuuf and the mirror are :

The distance from Yuuf's eyes to the ground = 1.35 meters

The horizontal distance between Yuuf and the mirror at X = 2.15 m

The parameters of the triangle formed by the height 'h' of the school building and the mirror at X are :

The horizontal distance between the school building and the mirror = 13.95 m

The height of the school building = h

Therefore, we have :

The distance from Yuuf's eye to the ground/The height of the school building = Yuuf's horizontal distance from the mirror/Horizontal distance from school to center X

1.35/h = 2.15/13.95

h = (1.35 × 13.95)/2.15

h = 8.75m

Hence, the height of the school building is around 8.75 meters.

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Answer:

- 12

Step-by-step explanation:

The signed number that represents the total score​ (above or below​ par) for the four rounds for the golfer is - 12.

Answer:

0.41, 0.42, 0.43, 0.44

Step-by-step explanation:

Convert the percent to a decimal:

0.4 < x > 0.45

Now, the variable x has to be any number between 0.4 and 0.45, which include:

0.41, 0.42, 0.43, 0.44

Answer:

5/10

Step-by-step explanation:

So you can split this into two inequalities, x > 0.4 and x > 45%. First you can change the second one to decimal form, so x > 0.45. Because 0.45 is already greater than 0.4, you can just ignore the second inequality. (If x is greater than 0.45 it will automatically be greater than 0.4 so it doesn't matter).

From the 4 options you gave, 5/10, or 0.5, is the only one that is greater than 0.45.

Answer:

2/5 = c/145

Step-by-step explanation:

2/5 = c/145

Cross multiply

5c = 290

c = 58 computers needed for 145 students

The input and the output of a function are key components in understanding how a function operates. The input refers to the value or values that are given to the function as an argument, while the output refers to the result or results that the function returns after processing the input.

In other words, the input is what you provide to the function, and the output is what you get in return. The input can be a single value or a set of values, depending on the requirements of the function. The output can also be a single value or a collection of values, again depending on the function's purpose.

It's important to note that the input and output of a function are not always the same. The function may perform calculations or transformations on the input, and the output may be different from the input. This transformation is what gives functions their ability to perform specific tasks and solve problems.

In summary, the input is what you give to a function, and the output is what you get in return after the function processes the input.

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Answer:

What Are Irrational Numbers?

Real, Rational, and Irrational Numbers. By definition, a real number is irrational if it is not rational. ...

Spotting Rational and Irrationals. One nice thing about real numbers is that they all have decimal expansions.

The probability of choosing a uni-color pair of socks from the bag is 199/799.

The probability of choosing a uni-color pair of socks from a large bag with 100 pairs of each of red, blue, black, and white socks is calculated as follows:

Step 1: Calculate the total number of socks in the bag.
There are 100 pairs of each color, and each pair consists of 2 socks, so there are 100 x 2 = 200 socks of each color.
The total number of socks in the bag is 200 x 4 = 800 socks.

Step 2: Calculate the probability of choosing a uni-color pair of socks.
The probability of choosing a red sock on the first draw is 200/800 = 1/4.
The probability of choosing another red sock on the second draw is 199/799.
The probability of choosing a red pair is (1/4) x (199/799) = 199/3196.

Similarly, the probability of choosing a blue pair, a black pair, or a white pair is also 199/3196.

The probability of choosing a uni-color pair is the sum of the probabilities of choosing a red pair, a blue pair, a black pair, and a white pair.

So the probability of choosing a uni-color pair is (199/3196) x 4 = 796/3196 = 199/799.

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Answer:

Below

Step-by-step explanation:

● (3/4)×(z+7) = y

Divide both sides by (3/4)

● (3/4)÷(3/4)×(z+7) = y÷(3/4)

● 1×(z+7) = y ÷(3/4)

● (z+7) = y ×(4/3)

● z+7 = 4y/3

Substract 7 from both sides

● z+7-7 = (4y/3)-7

● z = (4y/3)-7

This equation has infinite solutions. Every time you input a value you get a different solution.