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Brut [27]
3 years ago
13

A dance studio requires each dancer to pay a registration fee plus an hourly rate for all lessons. If the total cost, y, of a da

ncer's lesson is modeled by the equation y = 25x + 50, how could the y-intercept be interpreted?
Mathematics
1 answer:
Marat540 [252]3 years ago
7 0

Answer:

(0,50)

Step-by-step explanation:

Given the total cost of a dancers lesson  modeled by the equation y = 25x + 50, the y intercept occurs at the point where x = 0.

Substitute x = 0 into the expression

y = 25x + 50

y = 25(0) + 50

y = 0+50

y = 50

Hence the y intercept is (0, 50). This shows that the total cost of the dancers lesson registration fee is 50

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Triangle P Q R is shown. Angle P Q R is a right angle. The length of hypotenuse P R is q, the length of P Q is r, and the length
mojhsa [17]

The cosine ratios which are correct for the ΔPQR are CosineP = r/q and CosineR = p/q.

We have,

Δ PQR,

Length of hypotenuse PR = q

The length of PQ = r,

And the length of QR = p

NOw,

We know that Trigonometric ratios of CosineΘ;

CosineΘ = Base/Hypotenuse

So,

CosineP = r/q

And,

CosineR = p/q

So, from the above find out values we can say that these values are given in option (a) and option (d).

Therefore, the cosine ratios which are correct for the ΔPQR are CosP = r/q and CosR = p/q.

Learn more about Trigonometric ratios here:

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8 0
2 years ago
A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Mater
Gala2k [10]
L = 2 W
B = L x W = 2 W²
Side Area = 2 W H + 2 L H = 2 H ( W + L ) = 6 H W
V = 2 W² H = 10
H = 5 / W²
Cost = 15 * 2 W² + 9 * 5/W
= 30 W² + 270/ W 
C ` = 60 W - 270 / W² 
= ( 60 W² - 270 ) / W² = 0
60 W² = 270
W ² = 270 : 60
W² = 4.5
W = √ 4.5 = 2.12
Cost (min) = 15 * 2 * 4.5 + 30 / 2.12 = 135 + 14.15 = $149.15
Answer: The cost of materials for the cheapest such container is $149.15. 
8 0
3 years ago
An equilateral triangle is inscribed in a circle of radius 2r. Express the area A within the circle but outside the triangle as
defon

Answer:

A=8\pi r^2-\dfrac{49\sqrt{3}x^2}{4}\ un^2.

Step-by-step explanation:

An equilateral triangle with the side 7x units is inscribed in a circle of radius 2r units.

1. The area of the circle is

A_{circle}=2\pi (2r)^2=2\pi \cdot 4r^2=8\pi r^2\ un^2.

2. The area of the equilateral triangle is

A_{\triangle }=\dfrac{(7x)^2\sqrt{3}}{4}=\dfrac{49\sqrt{3}x^2}{4}\ un^2.

3. The area A within the circle but outside the triangle is

A=A_{circle}-A_{\triangle}=8\pi r^2-\dfrac{49\sqrt{3}x^2}{4}\ un^2.

7 0
3 years ago
Since an instant replay system for tennis was introduced a a major tournament, men challenged 1390 referee calls, with the resul
alexandr402 [8]

Answer:

H0: μm − μw = 0

against the claim

Ha: μm − μw ≠ 0

Since the calculated value of z= 0.6177 does not lie in the critical region the null hypothesis is accepted that men and women have equal success in challenging calls.

Step-by-step explanation:

1) Let the null and alternate hypothesis be

H0: μm − μw = 0

against the claim

Ha: μm − μw ≠ 0

2) The significance level is set at 0.05

3) The critical region is z > + 1.96 and z< -1.96

4) The test statistic

Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]

Here p1= 411/ 1390= 0.2956     and    p2= 213/753=0.2829

pc = 411+ 213/1390+753

pc=624/2143

pc= 0.2912

qc= 1-pc= 1-0.2912=0.7088

5) Calculations

Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]

z= 0.2956-0.2829/√ 0.2912*0.7088( 1/1390+ 1/753)

z= 0.0127/ √0.2064 (0.00204)

z= 0.0127/0.02056

z= 0.6177

6) Conclusion

Since the calculated value of z= 0.6177 does not lie in the critical region the null hypothesis is accepted that men and women have equal success in challenging calls.

3 0
3 years ago
Answer this graph based Question I will provide you 50 points + make you brainliest.​
bearhunter [10]

Part a: The value of y is 11 for x = 2.

Part b: The graph for the function y = x² + 4x -1 is drawn.

Part c: Range; (-∞,-3.75]∪[-0.25,∞)

Part d: The function is  y =  -5 - (x + 2)².

Part e: The approximate value of √3  is 1.732.

<h3>What is defined as the term function?</h3>
  • A function is an expression, rule, or law in mathematics that defines a relationship between one dependent variable (a independent variable) and also one more variable (the dependent variable).
  • Functions are common in mathematics and are required for the formulation of actual relationships with in sciences.

For the given function;

y = x² + 4x -1, the values of y for the corresponding x is given in tables shown.

Part a: value of y when x = 2.

Put x = 2 in the function;

y = x² + 4x -1

y = 2² + 4×2 -1

y = 11

The value of y is 11 for x = 2.

Part b: The graph for the function y = x² + 4x -1 is drawn using the scale of 10 small divisions as 1 unit along x and y axis.

Part c: Range of value of x for which y ≥ -2.

Locate the point of x from the graph for which the value of y  y ≥ -2.

Range; (-∞,-3.75]∪[-0.25,∞)

Part d: The function in the form of y = k - (x - h)², where k and h are the vertex.

The vertex from the graph is found as (-2, -5) (h, k)

Putt in the equation;

y = k - (x - h)²

y = -5 - (x - (-2))²

y =  -5 - (x + 2)²

Part e: 2 - √3 is the root of the equation 0 = x² + 4x -1.

It  2 - √3 is the root of the equation, then by putting this value at x the equation becomes zero.

The approximate value of √3  is 1.732 which is found by long division method.

To know more about the function, here

brainly.com/question/22340031

#SPJ13

7 0
1 year ago
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