Izzy goes on 13 boat rides over the summer.
Bill goes on 5 fewer boat rides than Izzy.
How many boat rides does Bill go on?

Answer:

B. 175.84 square inches

Step-by-step explanation:

3.14 x 64= 200.96

200.96 / 8 = 25.12

25.12 x 7 = 175.84

Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.

To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.

So, let's assume that g(x1) = g(x2). Then, we have:

f(x1) = f(x2)

x1(x1-1) = x2(x2-1)

x1^2 - x1 = x2^2 - x2

x1^2 - x2^2 - x1 + x2 = 0

(x1 - x2)(x1 + x2 - 1) = 0

Since x1 and x2 are distinct, we must have x1 + x2 = 1.

But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.

To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.

So, let's solve the equation f(x) = y for x:

x(x-1) = y

x^2 - x - y = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 4y))/2

Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.

Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.

Step-by-step explanation:

First let solve the inequality

\(5 {x}^{2} + 2x - 3 < 0\)

Factor by grouping

\(5 {x}^{2} + 5x - 3x - 3 < 0\)

\(5x(x + 1) - 3(x + 1)\)

So the factor are

\((5x - 3)(x + 1)\)

So the factor are

\(x = \frac{3}{5} \)

and

\(x = - 1\)

Solutions to a quadratic can be represented by a absolute value equation because remeber quadratics

creates 2 roots and/or double roots.

The inequality

\( |x - b| < c\)

works as

b is the midpoint between 2 roots. And c is the

\( |x + b| = c\)

We know that the midpoint between both roots is-1/5.

so

\( |x - ( - \frac{1}{5} )| < c\)

\( |x + \frac{1}{5} | < c\)

Let use roots 3/5

\( | \frac{3}{5} + \frac{1}{5} | = \frac{4}{5} \)

-1 works as well.

\( | - 1 + \frac{1}{5} | = | - \frac{4}{5} | = \frac{4}{5} \)

So the absolute value equation is

\( |x + \frac{1}{5} | < \frac{4}{5} \)

The value of piecewise function at x = -1 is f(-1) = 11, and the value of piecewise function at x = 9 is f(9) = 1.

what is piecewise function?

A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a specific interval of the domain it applies to. Instead of being a property of the function itself, piecewise definition is a way to express the function.

We have to evaluate the piecewise function for x = -1 and x = 9.

Let, function has value for x = -1 in the domain x ≤ 5 which is 11.

And function has value for x = 9  in the domain 6 < x which is 1.

⇒  f(-1) = 11 and f(9) = 1

Hence, the value of piecewise function at x = -1 is f(-1) = 11, and the value of piecewise function at x = 9 is f(9) = 1.

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Answer:

F(x)=-x+2

Step-by-step explanation:

equation

mx+b

m= slope

x

b = y-intercept

The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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Answer:

yes

Step-by-step explanation:

By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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Check the picture below.

The circumference of the given circle is approximately 47.3 inches.

Since the length of the arc KL and the measure of the central angle ∠KOL are known, we can use the formula for arc length to find the circumference of the circle:

arc length = (central angle / 360°) x circumference

Plugging in the known values, we have:

4.6 in = (35° / 360°) x circumference

Solving for the circumference, we get:

circumference = 4.6 in / (35° / 360°)

circumference = 4.6 in x (360° / 35°)

circumference ≈ 47.3 in (rounded to the nearest tenth)

Therefore, the circumference of the circle is approximately 47.3 inches.

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Answer:

its A

Step-by-step explanation:

just took the test

Answer:

The first graph on edge 2021

Answer:

you should check out Microsoft Math! It's a free app :)

Answer:

a. 12:10 pm

b. 40 mph

Step-by-step explanation:

Assuming you meant to type 1 ¹/₄ hours later.

a. First convert that to a improper fraction and then a decimal:

= 5/4

= 1.25 hours

1.25 hours in minutes is:

= 1.25 * 60

= 75 minutes

= 1 hour 15 minutes

The motorist left at 10:55.

= 1055 + 1 hour

= 11:55

Add 15 minutes:

= 12:10 pm

b. Speed = Distance / Time

= 50 / 1.25 hours

= 40 miles per hour

Answer:

168 gallons

Step-by-step explanation:

Correct question;

If 14 gallon of paint covers 1/12 of a wall, then how many quarts of paint are needed for the entire wall?

If 14 gallon of paint covers 112 of a wall, this can be expressed as;

14 gallons = 1/12 of the wall

x gallons = entire wall (1 wall)

Cross multiply

1/12 * x = 14

x/12 = 14

Multiply both sides by 12

x/12 * 12 = 14*12

x = 168 gallons

Hence 168galons of paints are needed for the entire wall

Applying the Trigonometric ratios, the length of DC is approximately 30 units.

To find the length of DC, we have to apply the Trigonometric ratios.

First of all, find BD.

Considering right triangle ADB, we have:

Reference angle (∅) = 54°

Length of Hypotenuse = 20

Length of opposite side = BD = ?

Apply the sine ratio:

sin 54 = opp/hyp

sin 54 = BD/20

BD = sin 54 × 20

BD ≈ 16

Use the tangent ratio to find DC:

Reference angle (∅) = 28°

Length of adjacent side = DC = ?

Length of opposite side = BD = 16

tan 28 = opp/adj

tan 28 = 16/DC

DC = 16/tan 28

DC ≈ 30

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The equation of a line in slope-intercept form is given by:

Where m is the slope and b is the y-intercept.

We know two points on the line: (10,8) and (-10,30).

The slope can be found by using the following formula:

Where (x1,y1) and (x2,y2) are the coordinates of two points on the line. By replacing the known coordinates we obtain:

The y-intercept can be found by replacing the slope and one of the points in the slope-intercept formula, and solving for b:

Thus, the equation of the line is:

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To calculate the equation of the line first find the slope

Slope of the line using points

(0 , 0) and (4 , -2) is

\(m = \frac{ - 2 - 0}{4 - 0} = \frac{ - 2}{4} = - \frac{1}{2} \)

Now use the formula

y - y1 = m(x - x1) to find the equation of the line using any of the points

Using point (0,0)

That's

\(y - 0 = - \frac{ 1}{2} (x - 0)\)

The final answer is

\(y = - \frac{1}{2} x\)

Hope this helps you

Answer:

F

Step-by-step explanation:

The number that does not belong with the other three is D. 10 x 9.2 ⁻¹³

With the first three numbers, the base of the exponential that is being multiplied by the first number is 10. These numbers are:

With the last number however, we see that the base of the exponential is 9. 2 and not 10 like the others. This is why 10 x 9 . 2 ⁻¹³ does not belong with the rest.

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Answer:

false

Step-by-step explanation:

because if one of the right side goes to two or more of the left its not a function

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Answer: i believe x = 4

Step-by-step explanation: 16 - |-4| which is adding two positives and that equals 20 so then its 5x = 20 divide 20 by 5 and you get 4

Finn would run 18 miles after 6 track practices.

We have,

Generally, A unit rate is a ratio of two measurements with a denominator of 1. To find the number of miles Finn would run after 6 track practices, we can use the unit rate of miles per practice to multiply by the number of practices.

Unit rate: 6 miles / 2 practices = 3 miles per practice

To find the total number of miles Finn would run after 6 practices, we can multiply the unit rate of 3 miles per practice by the number of practices, 6.

Total miles: 3 miles/practice * 6 practices = 18 miles

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Answer: 3.65

Step-by-step explanation:

This question is asking basically what is 50% or 1/2 of 7.3.

Let's expand the number 7.3

Then, we end up getting 7.30.

We have to find 1/2 of 7.30.

\(\frac{1}{2}\) of 7.30 = \(3.65\)

Hope this helps you!

Answer:

Step-by-step explanation:

Perimeter:  

     \(P=(x+y+z) \ cm\)

Semi-perimeter:

     \(SP=\frac{1}{2} (x+y+z) \ cm\)

Answer:

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = 0.5445

Step-by-step explanation:

Step(i):-

Given mean of the Population μ = 5.3 days

Given standard deviation of the population 'σ' = 2 days

Let 'X' be the random variable in normal distribution

Let    x₁ = 4

\(Z_{1} = \frac{x_{1}-mean }{S.D} = \frac{4-5.3}{2} = -0.65\)

Let    x₂ = 7

\(Z_{2} = \frac{x_{2}-mean }{S.D} = \frac{7-5.3}{2} = 0.85\)

Step(ii):-

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = P(-0.65≤Z≤0.85)

             =  P(Z≤0.85) - P(Z≤-0.65)

            = 0.5 + A( 0.85) - ( 0.5 - A(-0.65)

            = 0.5 + A( 0.85) -  0.5 +A(0.65)   ( ∵A(-0.65) = A(0.65)

           =   A(0.85) + A(0.65)

          = 0.3023 + 0.2422

         = 0.5445

Final answer:-

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = 0.5445

Answer:

Step-by-step explanation:

A

The probability that you select a Jack given that it is a Club P(Jack∣Club) is 1/13.

The probability that you select a Club given that it is a Jack is P(Club∣Jack) is 1/4.

The probability that you select a card that is NOT a Jack given that it is NOT a Club,P(NotJack∣NotClub) is 47/38

The probability that you select a card that is NOT a Club given that is it NOT a Jack is 38/47

The probability that you select a Jack given that it is a Club P(Jack|Club):

There are 4 Jacks in a deck (one for each suit), and since we are given that the selected card is a Club, we only need to consider the 13 cards in the Club suit.

So, the number of favorable outcomes is 1 (the Jack of Clubs), and the total number of possible outcomes is 13 (the number of cards in the Club suit)

P(Jack|Club) = 1 / 13

The probability that you select a Club given that it is a Jack

P(Club|Jack):

P(Club|Jack) = Number of favorable outcomes / Total number of possible outcomes

P(Club|Jack) = 1 / 4

The probability that you select a card that is not a Jack given that it is not a Club

P(NotJack|NotClub):

The number of cards that are not Jacks is 52 - 4 = 48 (since there are 4 Jacks in the deck), and the number of cards that are not Clubs is 52 - 13 = 39 (since there are 13 cards in the Club suit).

P(NotJack|NotClub) = Number of favorable outcomes / Total number of possible outcomes

P(NotJack|NotClub) = (48 - 1) / (39 - 1)

=47/38

P(NotClub|NotJack) = (39 - 1) / (48 - 1)

=38/47

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