What details can you determine about the dive from the coordinates of the point (5, −8)?

Answer:

Probability of getting 4 hearts = 11/833

Step-by-step explanation:

Find:

Probability of getting 4 hearts

Computation:

Probability of getting 1st heart = 13 / 52

Probability of getting 2nd heart = 12 / 51

Probability of getting 3rd heart = 11 / 50

Probability of getting 4th heart = 10 / 49

Probability of getting 4 hearts = [(13 / 52)(12 / 51)(11 / 50)(10 / 49)]

Probability of getting 4 hearts = 11/833

Answer:

4

Step-by-step explanation:

y = mx+b where m is slope so the slope is 4

Answer:

slope is 4

Step-by-step explanation:

The equation y=mx+b is the linear equation and m represents slope. In this case m is 4

This question is incomplete

Complete Question

Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancies be filled

a) with any two of the nominees?

b) with any two of the women?

c) with one of the men and one of the women?

Answer:

a) 21 ways

b) 6 ways

c) 12 ways

Step-by-step explanation:

We solve this question using combination formula

C(n, r) = nCr = n!/r! (n - r)!

a) with any two of the nominees?

Probability (two of the nominees) = 7C2

= 7!/2! ×(7 - 2)!

= 7!/ 2! × 5!

= 7 × 6 × 5 × 4 × 3 × 2 × 1/2 × 1 ×(5 × 4 × 3 × 2 × 1)

= 21

b) with any two of the women?

We have a total of 4 women

Hence, the probability of any two of the four women, filling the vacancies =

P(any two of the women) = 4C2

= 4!/2! ×( 4 - 2)!

= 4!/ 2! × 2!

= 4 × 3 × 2 × 1/ 2 × 1 ×( 2 × 1)

= 6

c) with one of the men and one of the

Total number of men = 3

Total number of women = 4

= 3C1 × 4C1

= [3!/1! ×(3 - 1)! ] × [4!/1! ×(4 - 1)! ]

= [3!/1! × 2!] × [4!/1! ×3!]

= [3 × 2 × 1/ 1 × 2 × 1] × [4 × 3 × 2 × 1/ 1 × 3 × 2 × 1]

= 3 × [24/6]

= 3 × 4

= 12 ways

The probability for any two of the nominees is 21

The probability for two women is 6

This question is incomplete

Complete Question

Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancies be filled

a) with any two of the nominees?

b) with any two of the women?

We have given,

Total number of nominees for two vacancy =7

We solve this question using combination formula

What is the formula for combination?

[tex]C(n, r) = nCr = n!/r! (n - r)![/tex]

a) with any two of the nominees?

Total number of nominees(n)=7

We are selecting r nominees r=2

Probability  = 7C2

= [tex]\frac{7!}{2! (7 - 2)!}[/tex]

= 7!/ 2! × 5!

= 21

b) with any two of the women?

We have a total number of women=4

Out of 4 we have select 2 women

Hence, the probability of any two of the four women is

4C2

= 4!/2! ×( 4 - 2)!

= 4!/ 2! × 2!

= 6

Therefore,probability for two women is 6

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Answer:

12 feet

Step-by-step explanation:

For an inclined roof, the rise is the vertical distance from the roof rafter to the vertical top plate while the run is the distance from the edge of the wall to half of the center of the ridge.

The slope is the ratio of the rise to run. Given a rise to run ratio of 3 to 4. The house is 32 feet wide.

The run of the roof =  half of the width of the roof = 1/2 × 32 feet = 16 feet

Let the rise of the roof (height of the attic) be x, hence:

rise to run ratio = height of attic/ run of roof

3/4 = x/16

x = 3/4 × 16

x = 12 feet

The height of the attic is 12 feet

Answer:

1800

Step-by-step explanation:

The equation 600t is multiplication (600 x t). Since t represents hours, and they're asking you to solve for 3 hours, all you have to do is multiply 600 x 3, which will get you your answer of 1800.

Answer:

Step-by-step explanation:

The quantity of food required for the two cats for one day is ...

  (3/4 can) + (1/2 can) = (3/4 +2/4) can = 5/4 can

Then the cost per day for cat food is ...

  $5/(3 cans) × (5/4 can/day) = $25/12 /day

We note that the cost for some number of days will be the product of this factor and the number of days, rounded up to the next higher $5.

1. The cost for 60 days is ...

  (60 days)($25/12 /day) = $25 × 60/12 = $125

A 60-day supply of cat food costs $125.

__

2. A 29-day supply costs ...

  (29 day) × $25/12 /day = $60 5/12, rounds up to $65 for 29 days

A 30-day supply costs ...

  (30 day) × ($25/12 /day) = $62.50, rounds up to $65 for 30 days

A 31-day supply costs ...

  (31 days) × ($25/12 /day) = $64 7/12, rounds up to $65 for 31 days.

These costs are all the same.

_____

3 cans last, on average, 2 2/5 days. That means some purchases of 3 cans will last for 2 days, and some will last for 3 days. It so happens that the purchase made to cover day 29 will also cover day 30 and day 31.

Answer:

2

Step-by-step explanation:

-r^2+5ry+4y^2

= -(-2)^2+5(-2)(3)+4(3)^2

= -(4)+5(-6)+4(9)

= -4-30+36

= 36-30-4

= 36-34

= 2

The question is incomplete. Here is the complete question.

(a) How many three-digit numbers can be formed from the digits 0,1,2,3,4,5 and 6, if each digit can be used only once?

(b) How many of these are odd numbers?

(c) How many are greater than 330?

Answer: (a) 180

              (b) 75

               (c) 105

Step-by-step explanation:

(a) In the group, there are 7 digits. A three-digit number can not start with zero, otherwise, it will be a 2-digit number. So:

For the hundreds position, there are 6 choices.

For the tens position, since the digit can be used only once, there are 6 choices.

For the unit position, there are 5 choices.

The total three-digit number formed is: 6*6*5 = 180

(b) To form an odd number, the unit position must be an odd digit, then:

unit position has 3 choices;

hundreds position has 5 choices;

tens position has 5 remaining choices.

The total three-digit odd number is: 3*5*5 = 75

(c) The number formed must be greater than 330, so:

If the number start with a 3, to be greater, there are 3 other choices (4, 5 and 6), so Tens position has 3 choices and Unit position has 5 choices.

Total number is: 3*5 = 15

Another possibility is the number starts with a digit bigger than 3 and so,  there are 3 choices.

Tens position has 6 choices;

Unit position has 5 choices;

Total possibilities are: 3*6*5 = 90

The total number of ways a three-digit number is greater than 330 is:

90 + 15 = 105

Answer:

-2y + 2

Step-by-step explanation:

Let's first remove the parentheses.  (x - y + 1) becomes x - y + 1 and -(x + y - 1) becomes -x -y + 1.   Combine like terms:

x - y + 1 - x - y + 1 = -2y + 2

Answer:

-2y + 2

Step-by-step explanation:

(x - y + 1) - (x + y - 1)

remove ( )

= x - y + 1 - x - y + 1

simplify

= -2y + 2

Answer: third one

Step-by-step explanation:

Answer:

alternate ext angles are <4 <5

Answer:

7.36

Step-by-step explanation:

7.3564 would round to 7.36

Answer:

7.36

Step-by-step explanation:

To round off a decimal to the hundredths or a number to the right you do this, if the number to the right of the hundredths is 4 or less you remove all the other digits including the hundredths, if the number is 5 or more you add one to the digit in the hundredths.

Answer:

34

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

(b - 2a)² + bc

Step 2: Define variables

a = 6

b = 5

c = 3

Step 3: Plug in

(5 - 2(6))² + 5(-3)

Step 4: Multiply

(5 - 12)² - 15

Step 5: Parenthesis

(-7)² - 15

Step 6: Exponents

49 - 15

Step 7: Subtract

34

Answer:

2x-3= x+1

or, 2x- x = 1+3

or, x = 4

so, x = 4

NOW,

6= 2y/3

or, 6×3 =2y

or, 18/2 = y

so, y = 9

X = 4 and Y = 9

ANS

The row of table reveals the x-intercept could be second ( -4, 0).

The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.

The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis where y is 0.

Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.

We have to find Which row of table reveals the x-intercept.

Thus, We can conclude that the second row shows the unit rate.

Hence, the row of table reveals the x-intercept could be second ( -4, 0).

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#SPJ5

Answer:

4 pints

Step-by-step explanation:

Because 16x4=64

Complete question :

Data of shoe sizes :

X:

8.5

9.0

9.0

9.5

10.0

10.0

10.5

10.5

11.0

11.0

11.0

12.0

12.0

12.5

Height (y) :

66.5

68.5

67.5

70.0

70.0

72.0

71.5

70.0

71.0

71.5

73.0

73.5

74.0

74.0

Answer:

Kindly check explanation

Step-by-step explanation:

Using the online regression calculator :

The regression model obtained in the form:

ŷ = mx + c is ;

ŷ = 1.792X + 52.176

Where ŷ is the predicted or dependent variable

m = 1.792 is the gradient or slope of the regression line

x = the independent variable

c = 52.176 = intercept, where the line of best fit intersects the y axis.

Given the following x values, predict ŷ

(a) x= 11.5

ŷ = 1.792(11.5) + 52.176 = 72.784

(b) x= 8.0

ŷ = 1.792(8.0) + 52.176 = 72.784 = 66.512

(c) x = 15.5

ŷ = 1.792(15.5) + 52.176 = 79.952

(d) x = 10.0

ŷ = 1.792(10.0) + 52.176 = 70.096

The predicted values are meaningful as they show are very close to the actual values of height (y). This could be attributed to the high correlation Coefficient of 0.9299 which exists between both variables

Answer:

4.472135955

Step-by-step explanation:

Answer:

He invested 3,000 at 7% and 4,000 at 9%.

Step-by-step explanation:

From the information given, you can write the following equations:

x+y=7,000 (1)

0.07x+0.09y=570 (2)

You can solve for x in (1)

x=7,000-y (3)

Now, you can replace (3) in (1) and solve for "y":

0.07(7,000-y)+0.09y=570

490-0.07y+0.09y=570

0.02y=80

y=80/0.02

y=4,000

Finally, you can replace the value of "y" in (3):

x=7,000-4,000

x=3,000

According to this, the answer is that he invested 3,000 at 7% and 4,000 at 9%.

Answer: 115

Step-by-step explanation: Supplementary angles add to 180, so 180-65 = 115

Answer:

115 degrees

Step-by-step explanation:

A supplementary angle is an angle that add up to 180 degrees

Because of the this we can create an equation that solves for x

65 + x = 180

x = Missing angle measure

All you have to do to solve for x is to subtract 65 from both sides, making x 115

(4). If we break down this piecewise function, we have 3 main expressions to deal with, 'h(x) = 5 if {x ≥ 4}' (represented by the green graph) 'h(x) = x if {0 ≤ x ≤ 4}' (represented by the blue graph) and 'h(x) = 1 / 2x + 2 if {x < 0}' (represented by the red graph).

Take a look at the attachment below for your graph of these 3 functions / expressions.

(5). For this part we want to determine the average rate of change of the function f(x) = 4x² - 5x - 8 over the interval [- 2,3]. Remember that to calculate average rate of change between the 2 points we use the following formula...

f(b) - f(a) / b - a,

f(3) = 4(3)² - 5(3) - 8 = 4(9) - 15 - 8 = 36 - 15 - 8 = 13,

f(- 2) = 4(- 2)² - 5(- 2) - 8 = 4(4) + 10 - 8 = 16 + 10 - 8 = 18

13 - 18 / 3 - (- 2) = - 5 / 5 = - 1

Therefore the average rate of change of the function f(x) = 4x² - 5x - 8 over the interval [- 2,3] will be - 1.

Answer:

A double integral can be written as:

[tex]\int\limits {f(x, y)} \, dx dy[/tex]

Now, to do this integral, we first can fix one of the variables, like in this case, we can fix x.

Now, with x fixed, this will be a function of only one variable, y, then we can do the integration over y.

Once the function is integrated over y, we can now do the integration over x.

Then the correct option will be:

" Varying the order variable y"

We keep x fixed, and integrate over the other variable.

Answer:

Both angles are right angles.

Step-by-step explanation:

Supplementary angles sum to 180°. Since we know that both angles are congruent, let's call them x and x. We can write the following equation:

x + x = 180

2x = 180

x = 90°

Therefore, we can conclude that both angles are right angles.

Answer:

Angles that are both congruent and supplementary each have a measurement that is equal to 90°.

Step-by-step explanation:

Answer:

13ft 10.2in

Step-by-step explanation:

First let's convert 3ft to in.

3 * 12 = 36 in

Now let's find the angle

We use tangent because we know the opposite and adjacent distances.

tan x = 36/13

tan x = 2.7692

On your calculator, input the value of your tangent. Then press "inv." This should give you the angle associated with that value. The angle associated with tan 2.7692 is 70.14 degrees.

Now that we know the angle we can find the height.

We use tangent again.

tan 70.14 = x / 5     We don't know the opposite but we know the adjacent length is 5ft.

2.77 * 5 = x

13.85 ft = x

To get it in ft and inches multiply .85 by 12

.85 * 12 = 10.2

13ft 10.2in

Answer:

x^2-6x+9  

Step-by-step explanation:

for f=x^2 subsititude x with g(x) = x-3 in which will give you (x-3)^2 using the perfect square formula ((a-b)^2=a^2-2ab+b^2)  in which a=x, b=3. you shall then get x^2 -2x · 3 + 3^2 to get x^2-6x+9  

Answer:

Option A.

Step-by-step explanation:

Note: Let as consider, we have to find the total amount after 9 years.

It is given that,

Principal amount = $1000

Rate of compound (yearly) interest = 15% = 0.15

Time = 9 year

The formula for total amount is

[tex]M=P(1+i)^n[/tex]

where, P is principal, i is rate of interest and n is number of years.

Substituting P=1000, i=0.15 and n=9, we get

[tex]M=1000(1+0.15)^9[/tex]

[tex]M=1000(1.15)^9[/tex]

[tex]M=1000(3.5178763)[/tex]

[tex]M=3517.8763[/tex]

[tex]M\approx 3517.88[/tex]

So, the total amount after 9 years is $3517.88.

Therefore, the correct option is A.

Answer:

241.3 feet

Step-by-step explanation:

From the above question, we solve for this using the law of cosines

Law of cosines

a² = b² + c² -2bc Cos A

a =  √b² + c² -2bc Cos A

a = The distance between the bases in Little League =  60 feet

b = ???

c = The distance from home plate to the fence in dead center at the Oak Lawn Little League field =  280 feet

A = It makes an angle of 45°

This is because the distance 60 feet and 280 feet are perpendicular to each other and they meet at a point that divides a right angle 90° into equal parts.

a = √280² + 60² - 2 × 280 × 60  × Cos 45

a = 241.33216 feet

Approximately = 241.3 feet

How far is it from the fence in dead center to third base? 241.3 feet

Answer:

The answer is D

Step-by-step explanation:

One this to remember when doing it is that all negatively skewed graphs or plots will always have the outlier that is on the left of the rest