At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 103 miles per hour (mph) and the standard deviation of the serve speeds was 11 mph.Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph?
A) approximately 16%
B) at most 34%
C) at most 2.5%
D) at most 13.5%

Answer:

22.5 cm

Triangle area is (L x W) / 2

7.5 x 6 = 45

45 / 2 = 22.5

Step-by-step explanation:

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Answer:

(Choice B) B It decreases.

Step-by-step explanation:

According to the situation, the solution of the value of the expression is as follows

Let us assume

r         80 -2r

5        80 - 10 = 70

4        80 - 8 = 72

3        80 - 6 = 74

2        80 - 4 = 76

1         80 - 2 = 78

As we can from the above calculation that expression value risen if r value decreased

Therefore the correct option is B.

Answer:

It increases

Step-by-step explanation:

Answer:

Dimensions of square shaped pit = 6m [tex]\times[/tex] 6m

Dimensions of rectangular pit = 1m [tex]\times[/tex] 36m or 2m [tex]\times[/tex] 18m or 3m [tex]\times[/tex] 12m or 4m [tex]\times[/tex] 9m

Step-by-step explanation:

Given:

Two pits in the school playground area (one square shaped and one rectangular shaped).

Each pit must have an area = 36 [tex]m^2[/tex]

To find:

Dimensions of each pit = ?

Solution:

First of all, let us have a look at the formula for area of a square and a rectangle:

[tex]Area_{square} = (Side)^2[/tex]

[tex]Area_{Rectangle} = Length\times Width[/tex]

Now, let us try to find out dimensions of square:

[tex]36 = Side^2\\\Rightarrow Side = 6\ m[/tex]

So, dimensions of Square will be 6m [tex]\times[/tex] 6m.

Now, let us try to find out dimensions of rectangle.

[tex]36 = Length\times Width[/tex]

We are not given any restrictions on the Length and Width of the rectangle.

So, let us explore all the possibilities by factorizing 36:

[tex]36 = 1 \times 36\\36 = 2 \times 18\\36 = 3 \times 12\\36 = 4 \times 9[/tex]

6 [tex]\times[/tex] 6 factors not considered because then it will become a square and which is not the required case.

Dimensions of rectangular pit = 1m [tex]\times[/tex] 36m or 2m [tex]\times[/tex] 18m or 3m [tex]\times[/tex] 12m or 4m [tex]\times[/tex] 9m

Answer:

5

Step-by-step explanation:

If Lisa has x quarters and Brenda has 3x quarters, we can write:

80% * 3x = 4 + (20% * 3x + x) -- We write 4 because 1 dollar =  4 quarters

0.8 * 3x = 4 + (0.2 * 3x + x)

2.4x = 4 + 1.6x

0.8x = 4

x = 5

Answer:

C

Step-by-step explanation:

Given

f(x) = 2x³ + 3x² - 3x - 2

Note that

f(1) = 2 + 3 - 3 - 2 = 0 , thus

(x - 1) is a factor

Dividing f(x) by (x - 1) gives

f(x) = (x - 1)(2x² + 5x + 2) = (x - 1)(x + 2)(2x + 1)

To find the roots equate f(x) to zero, that is

(x - 1)(x + 2)(2x + 1) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x + 2 = 0 ⇒ x = - 2

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]

The solution set is therefore

{ - 2, - [tex]\frac{1}{2}[/tex], 1 } → C

Answer:

(x + 3)² + (y + 1)² = 100

Step-by-step explanation:

Equation of a circle is:

(x − h)² + (y − k)² = r²

where (h, k) is the center of the circle and r is the radius.

The center is on the line x − 4y = 1, so:

h − 4k = 1

h = 1 + 4k

(x − 1 − 4k)² + (y − k)² = r²

Two points on the line are (3, 7) and (5, 5), so:

(3 − 1 − 4k)² + (7 − k)² = r²

(5 − 1 − 4k)² + (5 − k)² = r²

Set the equations equal:

(3 − 1 − 4k)² + (7 − k)² = (5 − 1 − 4k)² + (5 − k)²

(2 − 4k)² + (7 − k)² = (4 − 4k)² + (5 − k)²

4 − 16k + 16k² + 49 − 14k + k² = 16 − 32k + 16k² + 25 − 10k + k²

4 − 16k + 49 − 14k = 16 − 32k + 25 − 10k

53 − 30k = 41 − 42k

12k = -12

k = -1

h = 1 + 4k

h = -3

(3 − 1 − 4k)² + (7 − k)² = r²

(3 − 1 + 4)² + (7 + 1)² = r²

6² + 8² = r²

r = 10

Therefore, the equation of the circle is:

(x + 3)² + (y + 1)² = 10²

Answer:

x = -1.47, 1.14

Step-by-step explanation:

Quadratic Formula: [tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

We are given a = 3, b = 1, and c = -5. Simply plug it into the Quadratic Formula:

Step 1: Plug in variables

[tex]x=\frac{-1+/-\sqrt{1^2-4(3)(-5)} }{2(3)}[/tex]

Step 2: Solve

[tex]x=\frac{-1+/-\sqrt{1+60} }{6}[/tex]

[tex]x=\frac{-1+/-\sqrt{61} }{6}[/tex]

Step 3: Plug into calculator to evaluate into decimals

You should get x = -1.46837 and 1.13504

Answer:

1.13 and -1.46

Step-by-step explanation:

Our quadratic equation is:  3x²+x-5=0

The method we will use is te dicriminant method

let Δ be the discriminant:

Δ = b²-4*a*c

61 is a positive number so we have solutions x and x':

so the two solutions are :

-1.46 and 1.13

It seems like information is missing. If so, then please update.

When intersecting a plane and a line, there are two possibilities:

Answer:

Sum of interior angles of 12 sided object = 1800°

Step-by-step explanation:

Formula to calculate the sum of interior angles of a polygon is,

Sum of the interior angles of a polygon = (n - 2) × 180°

Where n = number of sides of the polygon.

If number of sides of a polygon are 12,

For n = 12,

Sum of interior angles = (12 - 2) × 180°

                                     = 10 × 180°

                                     = 1800°

Therefore, sum of interior angles of a 12 sided polygon will be 1800°.

Answer:

137.5 lbs.

Step-by-step explanation:

Arthur = 54 + x

Lily = x

Arthur + Lily = 6x - 280

(54 + x) + x = 6x - 280

54 + x + x = 6x - 280

54 + 2x = 6x - 280

54 = 4x - 280

334 = 4x

83.5 = x

Arthur = 54 + x

Arthur = 54 + 83.5

Arthur = 137.5

Answer:

The coordinates of point P are (-7/2, 5/4)

Step-by-step explanation:

Here, we want to give the coordinates of the point P that divide CD in the given ratio

To do this , we shall be making use of a mathematical formula;

Let’s say the ratio 1:3 represents a:b, our formula those becomes

{(bx1 + ax2)/(a + b) ,( by1+ay2)/a+b}

From the question, we can identify that

(x1,y1) = (-6,-1)

(x2,y2) = (4,8)

a = 1 and b = 3

Plugging these values into the formula we have

3(-6) + 1(4)/(1+3) , 3(-1) + 1(8)/(1+3)

= (-18 + 4)/4 , (-3+ 8)/4

=-14/4, 5/4

= (-7/2, 5/4)

Answer:

9.16

Step-by-step explanation:

We know that

Total expense = price of sugar * consumption

let price of sugar was 100

So total expense = 100*10=1000

But now new expense =1100 (I,e.10% more than 1000)

and new price =120(i,e. 20% more than 100)

So new consumption = new expense/ new price=

1100/120

=110/12

=9.16

HOPE IT HELPS :)

PLEASE MARK IT THE BRAINLIEST!

Answer:

16 2/3 %   or approx. 16.67%

Step-by-step explanation:

Original price = 100%

New price = 100+20% = 120%

To reduce back to 100%

we need to reduce 20% from 120 % = 20/120 = 1/6 = 16 2/3 % = 16.7% approx.

Answer:

1800cm^3

Step-by-step explanation:

l=10cm

w=10cm

h=18cm

V=l.w.h

V=10cmx10cmx18cm

V=100cm^2x18cm

V=1800cm^3

Hope this helps. ❤❤❤

Answer:

600 cm³

Step-by-step explanation:

Volume of a square-based pyramid = a² × h/3

a = 10

h = 18

10² × 18/3

100 × 6

= 600

Answer:

h=−6, k=−30

Step-by-step explanation:

did on edge

Considering the equation of the parabola, the coefficients of the vertex are:

h=−6, k=−30

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](h,k)[/tex]

In which:

[tex]h = -\frac{b}{2a}[/tex]

[tex]k = -\frac{b^2 - 4ac}{4a}[/tex]

In this problem, the equation is:

[tex]f(x) = x^2 + 12x + 6[/tex]

Hence the coefficients are a = 1, b = 12, c = 6, thus:

[tex]h = -\frac{12}{2} = -6[/tex]

[tex]k = -\frac{120}{4} = -30[/tex]

More can be learned about the equation of a parabola at https://brainly.com/question/24737967

Answer:

a. 0.6975

b. 0.25

c. The events are independent and inclusive

Step-by-step explanation:

a. The proportion of five-star football recruits in the nation that go to universities in the three most competitive athletic conferences = 75%

Therefore, the probability of a five-star football recruits chooses to go to a university in the three most competitive athletic conferences p(A) = 75% or 0.75

The proportion of the times five-star football recruits get full football scholarships = 93%

Therefore, the probability that a five-star football recruit get full football scholarships p(B) = 93% or 0.93

Therefore, the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship can be written as -the probability that a randomly selected five-star recruit who chooses one of the best three conferences and will be offered a full football scholarship is therefore;

p(A) ∩ p(B) = p(A) × p(B) = 0.75×0.93 = 0.6975

b. The probability that a randomly selected five star recruit will not select a university from one of the three best conferences = 1 - p(A) = 1 - 0.75 = 0.25

c. The events are independent as the given probability of occurrence of one event does not alter the probability of the other event

The events are inclusive events are exclusive events as P(A)and P(B) can take place simultaneously.

Answer:

The 90% confidence interval

(74.71, 82.63)

Step-by-step explanation:

Confidence Interval Formula is given as:

Confidence Interval = μ ± z (σ/√n)

Where

μ = mean score

z = z score

N = number of the population

σ = standard deviation

The mean is calculated as = The average of their scores

N = 6 students

(71.6 + 81.0 + 88.9 + 80.4 + 78.1 + 72.0 )/ 6

Mean score = 472/6

= 78.666666667

≈ 78.67

We are given a confidence interval of 90% therefore the

z score = 1.645

Standard Deviation for the scores =

s=(x -σ)²/ n - 1 =(71.6 - 78.67)²+(81.0 - 78.67)²+(88.9 - 78.67)² + (80.4 - 78.67)²+ (78.1 - 78.67)²+( 72.0 - 78.67)2/ 6 - 1

= 5.886047531

= 5.89

The confidence interval is calculated as

= μ ± z (σ/√N)

= 78.67 ± 1.645(5.89/√6)

= 78.67 ± 3.9555380987

The 90% confidence interval

is :

78.67 + 3.9555380987 = 82.625538099

78.67 - 3.9555380987 = 74.714619013

Therefore, the confidence interval is approximately between

(74.71, 82.63)

Answer:  [tex]\sum\limits_{i=1}^{n} n^2[/tex] , where n is a natural number.

Step-by-step explanation:

A series can be represented in a summation or sigma notation.

Greek capital letter, ∑ (sigma), is used to represent the sum.

For example: [tex]\sum\limits_{n=1}^{\infty} n=1+2+3+4+5+...[/tex], where n is a natural number.

The given series : 1,4,9,16 which can be written as [tex]1^2, 2^2, 3^2,...[/tex] .

So , we can write it as

[tex]\sum\limits_{n=1}^{\infty} n^2[/tex] , where n is a natural number.

Answer:

B=6

C=n^2

Just did the test

Step-by-step explanation:

Answer:

hello :

Step-by-step explanation:

x(x+3)(x+3)=0  means : x=0 or x+3=0 or x+3=0

x=0 or x=-3 or x=3

Answer:

This contradict of the chain rule.

Step-by-step explanation:

The given functions are

[tex]f(x)=x^2[/tex]

[tex]g(x)=|x|[/tex]

It is given that,

[tex](f\circ g)(x)=|x|^2=x^2[/tex]

[tex](g\circ f)(x)=|x^2|=x^2[/tex]

According to chin rule,

[tex](f\circ g)(c)=f(g(c))=f'(g(c)g'(c)[/tex]

It means, [tex](f\circ g)(c)[/tex] is differentiable if f(g(c)) and g(c) is differentiable at x=c.

Here g(x) is not differentiable at x=0 but both compositions are differentiable, which is a contradiction of the chain rule

Answer: B

Step-by-step explanation:

Answer:

The last option

Step-by-step explanation:

The centroid is the point that is equidistant from all the vertices, not the incenter. Furthermore, the incenter is formed by finding the point of concurrency (intersection) of the angle bisectors.

Answer:

B

Step-by-step explanation:

The inscribed angle's arc measures 36°, and central angle's arc measures 72°.

Answer:

the answer is B

Step-by-step explanation:

Answer:

7.3 mi

Step-by-step explanation:

*Make sure your calculator is in degree mode*

Do this with the SOHCAHTOA method using angle V. Since we are trying to find the side that is the opposite of angle V (WY) and since the hypotenuse is already given, you would use SOH (sinΘ=[tex]\frac{opposite}{hypotenuse}[/tex])

sin(27)=[tex]\frac{x}{16}[/tex]

Multiply by 16 on both sides to cancel out the fraction:

16sin(27)=x

7.3=x

Answer:

$17,028.06

Step-by-step explanation:

Given that :

Kaylee's down payment = $4500

monthly payment = $300

If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate).

the  maximum amount Kaylee can afford to spend on the car is being calculated as the present value for all the payments.

= [tex]=\$4,500 +\dfrac{\$300}{(1+\frac{0.07}{12})} + \dfrac{\$300}{(1+\frac{0.07}{12})^2} +\dfrac{\$300}{(1+\frac{0.07}{12})^3} + ....+ \dfrac{\$300}{(1+\frac{0.07}{12})^{46}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{47}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{48}}[/tex]

Using the online desmos calculator to determine the maximum amount Kaylee can afford to spend on the car; we have:

= $17,028.06

Answer:

a) 4.236 x 10^2

b) 7.194548 x 10^6

c) 5.0023 x 10^2

d) 7.123884 x 10^1

e) 5.62 x 10^-1

f) 3.48 x 10^-2

g) 1.23 x 10^-4

h)  5.603002 x 10^-1

Hopefully this helps :)

Answer:

a) 423.6=4.236*10^2

b) 7,194,548=7.194548*10^6

c) 500.23=5.0023*10^2

d) 71.23884=7.123884*10^1

e) 0.562=5.62*10^-1

f) 0.348=3.48*10^-1

g) 0.000123=1.23*10^-3

h) 0.5603002=5.603002*10^-1

Step-by-step explanation:

The numbers in which the point lies must be between 0 and 10

Hope this helps ;) ❤❤❤

Part A

Answer:  33.2 degrees F

Explanation: Adding on a negative is the same as subtracting. So 72.3 + (-39.1) = 72.3 - 39.1 = 33.2

================================================

Part B

Answer: 70 +  2   +  0.3    + (-30) + (-9) + (   -0.1   )

Explanation:

Think of 72 as 70+2. Furthermore, think of 72.3 as 70+2+0.3; we just break the number up into its corresponding digits (adding zeros when needed). The 7 is in the tens place, the 2 is in the units or ones place, and the 3 is in the tenths place.

Similarly, we have 39.1 break down into 30+9+0.1, in which all three terms are made negative to represent -39.1

================================================

Part C

Answer:   70 + (-30) + 2 + (-9) + 0.3 + ( -0.1  )  

Explanation: Arrange the tens place value items to be next to each other. Same goes for the units place value, and also the tenths place value.

================================================

Part D

Answer:  [70 + (-30)] +  [ 2 + (-9) ] + [ 0.3 + ( -0.1  ) ]

Explanation: Take the result of part C and surround each pair of terms in square brackets to show how the terms pair up.

Answer:

Both the relations are functions, the correct answer is a.

Step-by-step explanation:

In order to solve this problem we will first find the inverse relation as shown below:

[tex]y = 3x^2 + 5\\x = 3y^2 + 5\\3y^2 = x - 5\\y^2 = \frac{x - 5}{3}\\y = \sqrt{\frac{x - 5}{3}} = \frac{\sqrt{x - 5}}{\sqrt{3}}\\y = \frac{\sqrt{x - 5}\sqrt{3}}{\sqrt{3}\sqrt{3}} = \frac{\sqrt{3x - 15}}{3}[/tex]

Functions are relations between two groups of numbers, for which the input must generate only one output. Using this definition we can classify both the relation and its inverse as a function, therefore the correct answer is a.

Answer:Let PQRS to be the rhombus where PQ=12cm and RS = 16cm

step 1:let,PQ and RS intersect each other at O.Now, diagonals of rhombus bisect each other at right angles.

STEP 2:Since POQ is a right angled triangle, by pythagoras theoram.

STEP 3:After applying formula , PQ =10cm .length of each side of rhombus is 10cm.

Step-by-step explanation:

Answer:

10cm

Step-by-step explanation:

As you can see in the first image is a rhombus with its diagonals 12cm and 16cm

You can see that the diagonals divide the rhombus into four right triangles and that the hypotenuse of each triangle is one side of the rhombus.

In the second image I picked out one triangle from the rhombus and slashed the length of the diagonals of the rhombus in half to get the sides of the triangle.

Now all you have to do is use the Pythagorean theorem to find the hypotenuse of the triangle which will give you the length of side of rhombus

6² + 8² = hypotenuse²

36 + 64 = h²

100 = h²

h = √100

h = 10

All the side of the rhombus are equal so all the sides of the rhombus are 10cm

Step-by-step explanation:

[tex]a + b = 6[/tex]

[tex]ab = 1 \times 5 = 5[/tex]

[tex]a = 1 \: \: \: \: \: \: \: \: b = 5[/tex]

[tex]( {x}^{2} + x) + (5x + 5)[/tex]

[tex]x(x + 1) + 5(x + 1)[/tex]

[tex](x + 1)(x + 5)[/tex]

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

A) [tex]1<x<\infty[/tex]

Step-by-step explanation:

Given:

A graph of a function.

When we analyze the given graph, it is of a parabola.

To find:

The interval of values of [tex]x[/tex] where the function is increasing.

Solution:

First of all, let us learn about the meaning of increasing and decreasing functions.

1. A function [tex]y=f(x)[/tex] is known as increasing  in an interval [tex]a<x<b[/tex] when

Value of y keeps on increasing when we move from the value of x from a to b.

2. A function [tex]y=f(x)[/tex] is known as decreasing  in an interval [tex]a<x<b[/tex] when

Value of y keeps on decreasing when we move from the value of x from a to b.

On analyzing the given graph , we can see that the graph is decreasing on the interval: [tex]-\infty<x<1[/tex]

and is increasing on the interval: [tex]1<x<\infty[/tex]

When we choose from the options,

The correct answer is option A) [tex]1<x<\infty[/tex]