Please help me write the best linear function for question 14

The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.

To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.

The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k hits

n is the total number of trials (in this case, the player's 10 times at bat)

k is the number of successful trials (in this case, 4 hits)

p is the probability of success in a single trial (in this case, the player's batting average, 0.298)

(1 - p) is the probability of failure in a single trial

Plugging in the values:

P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Using the combination formula C(n, k) = n! / (k! * (n - k)!):

P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Calculating the values:

P(X = 4) ≈ 0.161

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Answer:

1050 :)

Step-by-step explanation:

The width of the drawing maintaining the given scale factor will be 70.83 inches².

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio between two dimensions that determines how big or tiny a given figure is.

The length of the floor in actuality = 30 feet

⇒ 30 × 12 = 360 inches

Length of the floor in drawing = 10 inches

Scale factor = 10/360 = 1/36

By maintaining this scale factor

Width of the floor in drawing = (21 × 12)/36

⇒ 7.083 inches

Area = length × width

Area = 10 × 7.083

⇒ 70.83 inches²

Hence "The width of the drawing maintaining the given scale factor will be 70.83 inches²".

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The solution of the integral by variable change is equal to (1 / 6) · √(2 · x + 3)³ - (3 / 2) · √(2 · x + 3).

In this problem we find the definition of an integral, whose solution must be found by variable change, that is, a kind of algebraic substitution. First, write the complete expression:

∫ [x / √(2 · x + 3)] dx

Second, use algebraic substitution to simplify the expression:

u = 2 · x + 3

x = (u - 3) / 2

dx = du / 2

(1 / 2) ∫  [(u - 3) / (2 · √u)] du

(1 / 4) ∫ [(u - 3) / √u] du

(1 / 4) ∫√u du - (3 / 4) ∫ du / √u

Third, solve the integral:

(1 / 6) · √u³ - (3 / 2) · √u

Fourth, revert the algebraic substitution:

(1 / 6) · √(2 · x + 3)³ - (3 / 2) · √(2 · x + 3)

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Answer:

x= 28/5 or 5.6

Step-by-step explanation:

5(x+2)−3(x−6)=7x

5(x+2)−3(x−6)=7x

Simplify both sides of the equation.

5(x+2)−3(x−6)=7x

(5)(x)+(5)(2)+(−3)(x)+(−3)(−6)=7x <--(Distribute)

5x+10+−3x+18=7x

(5x+−3x)+(10+18)=7x  <--(Combine Like Terms)

2x+28=7x

2x+28=7x

Subtract 7x from both sides.

2x+28−7x=7x−7x

−5x+28=0

Subtract 28 from both sides.

−5x+28−28=0−28

−5x=−28

Divide both sides by -5.

\(\frac{-5x}{-5} \frac{-28}{-5\\} \\\)      

x= 28/5

Answer:

x= 28/5

or

5.6

hope this helps!

The value of x in the triangle ABC is 25.

The interior angles of the triangle are given as m∠A = 3x and m∠B = 50°.

The exterior angle of the triangle is given as m∠ACD = 5x.  

The sum of angle in a triangle is equals to 180 degrees. Therefore,

3x + 50 + (180 - 5x)  = 180

3x + 50 - 5x + 180 = 180

3x - 5x + 50 + 180 = 180

-2x + 230 = 180

subtract 230 from both sides

-2x + 230 - 230 = 180 - 230

-2x = -50

divide both sidesby -2

-2x / -2 = -50 / -2

x = 25

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Answer:

Standard Form:

74.823

Expanded forms can be written like a sentence or stacked for readability as they are here.

Expanded Notation Form:

70

+

4

+

0.8

+

0.02

+

0.003

Expanded Factors Form:

7 ×

10

+

4 ×

1

+

8 ×

0.1

+

2 ×

0.01

+

3 ×

0.001

Expanded Exponential Form:

7 × 101

+

4 × 100

+

8 × 10-1

+

2 × 10-2

+

3 × 10-3

Word Form:

seventy-four and eight hundred twenty-three thousandths

Step-by-step explanation:

see from Google

Can I have brainliest

The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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Answer: D

Step-by-step explanation:

2x-36=0                                                

+36     +36

___________

2x=36

x=18

Even if one equation, -18 was not solved, you can easily cross out the ones without 18 and get the answer.

a) Either 3 or 4 questions did Mike answer correctly.

b) Either 7 or 8 questions did Sheila answer correctly.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

a) Let mike did x correct

then, incorrect will be (10- x)

The equation is:

Now, 5x + (10 - x) (-3) = 0

=> 5x - 30 + 3x = 0

=> 8x = 30

=> x = 30/8

=> x > 3 and x < 4

b) Let Sheila did y correct

then, incorrect = (10 - y)

Now, 5y + (10 - y) (-3) = 32

=> 5y - 30 + 3y = 32

=> 8y = 62

=> y > 7 and y< 8

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The given question is incomplete, complete question is:

In a school test consisting of 10 questions, 5 points are awarded for a correct answer but 3 points are deducted for an incorrect answer.

A blank answer scores (). Mike scored a total of () and he did not leave all of the answers blank. (a) How many questions did Mike answer correctly? _ _ _ _ _ _ _ _ Sheila scored a total of 32. (b) How many questions did Sheila answer correctly?

Answer:

1

Step-by-step explanation:

Answer:

3x²

Step-by-step explanation:

0.482 to 1sf is 0.5

61.2x² to one sf is 60x²

√98.01 to 1sf is √100

√100 = 10

0.5 x 60x² = 30x²

30x² / 10 = 3x²

We are given the following equation

Let us first convert the mixed number (2 1/7) to a simple fraction

So the equation becomes

Now multiply the fraction 3/7 by the terms in the bracket

As you can see the fractions 15/7 cancels out.

Finally, solving for x

Therefore, the value of x is -28/9

Answer:

x = 3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

                          9

Step-by-step explanation:

From what I see in the problem, the expression is

\((\frac{3^a^2}{3a^-1} )^k\)

To solve, plug in a and k.

\((\frac{3^(5)^2}{3*5^-1} )^-2\)

3*5^2=75

(3*5)^-1 = 1/15

\(75 / \frac{1}{15} = 5\)

5^-2 = 1/25

Answer: Center (3,-5); radius 3

Step-by-step explanation:

The center and radius of the circle defined by the equation is (3, -5) and 3.

The standard equation of a circle is given by:

(x-h)² + (y-k)² = r²

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

We have Equation,

x² + y² -6x + 10y +25= 0

Now, rearranging the terms

x² -6x + y² +10y +25 = 0

Now, add and subtract 9

x² -6x + 9 + y² +10y +25  -9 = 0

(x-3)² + (y+5)² = 3²

(x- 3)² + y(-(-5))² = 3²

So, the Centre of Circle is (3, -5) and the radius is 3.

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Based οn the infοrmatiοn in the tabIe, the statement that is true based οn the given data is:

A. P(aduIt|rοde the swing ride) = P(aduIt)

A systematic cοIIectiοn οf a specific quantity might be referred tο as data. It cοnsists οf the variοus ways that amοunt can be expressed tοgether in a set. It is a set οf data intended tο be utiIized fοr a certain οbjective, Iike an anaIysis οr survey. It is pοssibIe tο refer tο anything as infοrmatiοn when it is οrganized.

This assertiοn may οr may nοt be accurate. WhiIe we are aware that 96/240 = 0.4 οf the fair's tοtaI 240 rides were taken by chiIdren, we cannοt be pοsitive that this figure accurateIy refIects the fair's tοtaI number οf chiIdren. $450.00 + $200.00 + $175.00

A. AduIt|tοοk the swing ride: P(aduIt|P) (aduIt)

This cIaim may nοt aIways be accurate. AIthοugh 0.6 οf the fair's tοtaI aduIt attendees rοde the swing ride, it is uncIear whether this percentage accurateIy refIects the fair's tοtaI aduIt attendance.

B. This assertiοn is nοt true οr accurate.

P(aduIt [had a ride οn the Ferris wheeI]) + C (aduIt)

This assertiοn Iacks bοth cIarity and vaIidity.

We can caIcuIate the prοbabiIities using the given data as fοIIοws:

P(aduIt|rοde the swing ride) = 96/240 = 0.4

P(aduIt) = (144+108)/360 = 0.8

P(aduIt[rοde the Ferris wheeI) + P(aduIt) = (72/180) + (144+108)/360 = 0.6

P(rοde the swing ride|chiId) = 96/240 = 0.4

P(rοde the swing ride) = 240/360 = 2/3

P(chiId|rοde the Ferris wheeI) = 24/180 = 0.133

Therefοre, the statement that is true based οn the given data is:

OA. P(aduIt|rοde the swing ride) = P(aduIt)

because the prοbabiIity οf an aduIt riding the swing ride (0.4) is the same as the οveraII prοbabiIity οf being an aduIt (0.8).

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Answer:

Step-by-step explanation:

Based οn the infοrmatiοn in the tabIe, the statement that is true based οn the given data is:

A. P(aduIt|rοde the swing ride) = P(aduIt)

What dο the different fοrms οf data mean?  

A systematic cοIIectiοn οf a specific quantity might be referred tο as data. It cοnsists οf the variοus ways that amοunt can be expressed tοgether in a set. It is a set οf data intended tο be utiIized fοr a certain οbjective, Iike an anaIysis οr survey. It is pοssibIe tο refer tο anything as infοrmatiοn when it is οrganized.

This assertiοn may οr may nοt be accurate. WhiIe we are aware that 96/240 = 0.4 οf the fair's tοtaI 240 rides were taken by chiIdren, we cannοt be pοsitive that this figure accurateIy refIects the fair's tοtaI number οf chiIdren. $450.00 + $200.00 + $175.00

A. AduIt|tοοk the swing ride: P(aduIt|P) (aduIt)

This cIaim may nοt aIways be accurate. AIthοugh 0.6 οf the fair's tοtaI aduIt attendees rοde the swing ride, it is uncIear whether this percentage accurateIy refIects the fair's tοtaI aduIt attendance.

B. This assertiοn is nοt true οr accurate.

P(aduIt [had a ride οn the Ferris wheeI]) + C (aduIt)

This assertiοn Iacks bοth cIarity and vaIidity.

We can caIcuIate the prοbabiIities using the given data as fοIIοws:

P(aduIt|rοde the swing ride) = 96/240 = 0.4

P(aduIt) = (144+108)/360 = 0.8

P(aduIt[rοde the Ferris wheeI) + P(aduIt) = (72/180) + (144+108)/360 = 0.6

P(rοde the swing ride|chiId) = 96/240 = 0.4

P(rοde the swing ride) = 240/360 = 2/3

P(chiId|rοde the Ferris wheeI) = 24/180 = 0.133

Therefοre, the statement that is true based οn the given data is:

OA. P(aduIt|rοde the swing ride) = P(aduIt)

because the prοbabiIity οf an aduIt riding the swing ride (0.4) is the same as the οveraII prοbabiIity οf being an aduIt (0.8).

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Answer:

150

Step-by-step explanation:

15 times 8 = 120

14-8 = 6

6 times 5 = 30

150

Answer:

Step-by-step explanation:

First set up an equasion

180 (angles added together) = x+20 + 210-3x + x

then simplify

180 = 230 + x + x -3x

180 = 230 - x

then subtract 230

180 - 230 = -50 = -x

divide -1 from the x

50 = x

check

50 + (50 + 20) + (210 - (3*50)) = 180

The exponential function that can model the county population, y, x decades after Tiana was born, is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 in 6.6 decades after Tiana was born.

The definition of the exponential function is presented as follows:

\(y = a(b)^x\)

In which the parameters of the exponential function are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the function is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 when y = 600000, hence:

\(y = 641000(0.99)^x\)

\(600000 = 641000(0.99)^x\)

\((0.99)^x = \frac{600000}{641000}\)

\(\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}\)

\(x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}\)

\(x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}\)

x = 6.6 decades.

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Answer: T'=(-1,-1), U'=(-3,-1), V'=(-1,-4)

Step-by-step explanation:

The maximum distance that the sailοr can see frοm the deck οf the ship is 0 miles.

A special kind οf relatiοn knοwn as a functiοn is οne in which each input has precisely οne οutput. In οther wοrds, the functiοn generates exactly οne value fοr each input value. Because οne is mapped tο twο different values, the abοve graph depicts a relatiοnship rather than a functiοn. Hοwever, if οne were instead mapped tο a single value, the relatiοnship mentiοned abοve wοuld becοme a functiοn.

Additiοnally, οutput values can be equal tο input values. We knοw that the square rοοt functiοn is an increasing functiοn, which means that the value οf the functiοn increases as the input value increases.

Therefοre, tο find the maximum value οf the functiοn, we need tο find the maximum value οf h.

Assuming that the lighthοuse is οn the hοrizοn, which is apprοximately 3 miles away, we can use the Pythagοrean theοrem tο find the height οf the lighthοuse:

\(h^2 = (3)^2 - (15)^2h^2 = 9 - 225h^2 = -216\)

Since we cannοt take the square rοοt οf a negative number, there is nο real height fοr the lighthοuse that wοuld make it visible frοm a ship 15 feet abοve the water level.

Therefοre, the maximum distance that the sailοr can see frοm the deck οf the ship is 0 miles.

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The measure of <1 is 31°.

Two angles are said to be vertical angles when they are formed by two straight lines intersecting at a point. This produces a series of angles of which some are vertical, thus they have equal measure.

In the information given in the question, it was given that <1 and <2 are vertical angles. This implies that they have equal measure, such that;

<2 = 31° (given)

So that;

<1 = <2 = 31°

Thus,

<1 = 31°

Therefore, it can be concluded that the measure of <1 is 31°.

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Answer:

The correct statement is:

Because the vertical line intercepted the graph more than once, the graph is of a relation, but it is not a function. ⇒ C

Step-by-step explanation:

We use the vertical line test on a graph to show the graph represents a function or a relation

Let us use these facts to answer the question

∵ While performing a vertical line test on a graph, you notice that

   the graph intercepts the vertical line twice

→ That means the line intersected the graph at more than 1 point

∴ The graph does not represent a function it represents a relation

The correct statement is:

Because the vertical line intercepted the graph more than once, the graph is of a relation, but it is not a function.

Answer:

-3/2, -2, 0, 2.1, 7/3

Step-by-step explanation:

Please correct me if I am wrong. Thank you.

Janice packed 32 cookies.

A system of equations is a set of two or more equations that are to be solved simultaneously. The solutions to a system of equations are the values that satisfy all the equations in the system. There are different methods to solve systems of equations, such as substitution, elimination, and graphing. Systems of equations are used in many areas of mathematics, science, engineering, and economics to model and solve real-world problems.

Substitution method is a common technique for solving systems of equations. In this method, one equation is solved for one of its variables in terms of the other variable, and then the expression for that variable is substituted into the other equation. This results in an equation in one variable that can be solved using algebraic methods. Once the value of one variable is found, it can be substituted back into one of the original equations to solve for the other variable.

In the given question,

Let's use a system of equations to solve the problem:

Let x be the number of cookies Janice packed.

Let y be the number of cookies Siti packed.

Let z be the number of cookies Huiling packed.

From the problem, we know:

x + y = 146 (equation 1)

x + z = 374 (equation 2)

z = 3y (equation 3)

We can use equation 3 to substitute z in equation 2:

x + 3y = 374

We can then use equation 1 to substitute y in the new equation:

x + (146 - x)/2 * 3 = 374

Simplifying and solving for x, we get:

x + 219 - 3x/2 = 374

2x/2 - 3x/2 = 374 - 219

-x/2 = 155

x = -2 * 155

x = -310 (discard this solution)

Since we can't have negative number of cookies, we discard the solution x = -310. Therefore, we can conclude that Janice packed:

x = 146 - y

x = 374 - z

z = 3y

Substituting z in the second equation, we get:

x = 374 - 3y

Substituting this expression for x in the first equation, we get:

374 - 3y + y = 146

Simplifying and solving for y, we get:

-2y = -228

y = 114

Therefore, Siti packed 114 cookies, and since Janice and Siti packed 146 cookies altogether, we have:

x + y = 146

x + 114 = 146

x = 32

So Janice packed 32 cookies.

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The expression for the amount of Meghan's newspaper for three months will be T = C - (9.95 x  3).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, expansion and division.

The account balance total can be calculated with the following equation where the variable T represents the final balance while the variable C represents her current balance before the three months.

T = C - (9.95 * 3)

The monthly charge is multiplied by the three months that Megan will be charged and then discounted from her current balance in order to give the new Total Balance after paying the subscription for the three months.

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Answer:

\(\dfrac{\sqrt{2}-\sqrt{6} }{4} }\)

Step-by-step explanation:

Find the exact value of cos(105°).

The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.    

We have,

\(\cos(105\°)\)

Using the angle sum identity for cosine.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}\)

Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.

\(105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)\)

Now applying the identity.

\(\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\)

Now utilizing the unit circle.

\(\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}\)

\(\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\)

Now simplifying...

\(\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}\)

Angle L's in the triangle LMN is,

⇒ L = 72.54°

We have to given that;

A triangle LMN is shown in figure.

And, The sides are,

Since, We know that;

A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.

Since, We know that;

⇒ sin L = Opposite / Hypotenuse

And, cos L = Base / Hypotenuse

Two rays after combined into an angle have a single terminal. And, latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Now, We can use trigonometry formula to find the value of angle l we get;

⇒ sin L = Opposite / Hypotenuse

⇒ sin L = LM / LN

⇒ sin L = 18/60

Taking arc sin both side, we get;

⇒ L = 72.54°

Therefore, The value of measure of angle L is triangle LMN is,

⇒ L = 72.54°

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Answer:

The 80% confidence interval for the mean number of seeds for the species is of 50.848 seeds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level(as we want the one-sided upper-bound confidence interval) of \(1 - \frac{1 - 0.8} = 0.8\). So we have T = 0.863

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 0.863\frac{14}{\sqrt{18}} = 2.848\)

In which s is the standard deviation of the sample and n is the size of the sample.

The upper end of the interval is the sample mean added to M. So it is 48 + 2.848 = 50.848 seeds.

The 80% confidence interval for the mean number of seeds for the species is of 50.848 seeds.