There are 4 Board of Directors positions open. 2 will be for men, 2 will be for women.
Out of 20 candidates, 11 are men, 9 are women. How many total outcomes are
possible?

Answer:

First one is (x+2.4)

Second one is 4(x+2.4)=14.8

Step-by-step explanation:

Answer:

What expression would represent how far Bijan runs everyday?

✔ (x + 2.4)

What is the equation that represents his total distance after 4 days?

✔ 4(x + 2.4) = 14.8

Step-by-step explanation: I TOOK THE TEST

Answer:

(190-5a)°

Step-by-step explanation:

Sum of internal angles of a triangle equals to 180°

If the third angle is x, then we have:

The third angle is: (190-5a)°

Answer:

60 ounces

Step-by-step explanation:

İf she can make 10 brownies with 12 ounce mix then

For 50 she would need 5 × 12 = 60 ounces

Answer:

60 oz

Step-by-step explanation:

because 12 times 5 is 60    and 10 time 5 = 50 that's why you times 5 with 12    and because 12 oz makes 10 brownies and if you want to make 50 brownies just times 12 by 5

Answer:

a) 21.58% probability that exactly 3 people are repeat offenders

b) 97.91% probability that at least one person is a repeat offender

c) 3.69

d) 1.83

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders

This means that [tex]p = 0.09[/tex]

41 people arrested for DUI in Illinois are selected at random.

This means that [tex]n = 41[/tex]

a. What is the probability that exactly 3 people are repeat offenders?

This is P(X = 3).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158[/tex]

21.58% probability that exactly 3 people are repeat offenders

b. What is the probability that at least one person is a repeat offender?

Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So

[tex]P(X = 0) + P(X \geq 1) = 1[/tex]

We want [tex]P(X \geq 1)[/tex].

Then

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791[/tex]

97.91% probability that at least one person is a repeat offender

c. What is the mean number of repeat offenders?

[tex]E(X) = np = 41*0.09 = 3.69[/tex]

d. What is the standard deviation of the number of repeat offenders?

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83[/tex]

Answer: P(t) = 1.25.sin([tex]\frac{\pi}{3}[/tex].t) + 5.65

Step-by-step explanation: A motion repeating itself in a fixed time period is a periodic motion and can be modeled by the functions:

y = A.sin(B.t - C) + D or y = Acos(B.t - C) + D

where:

A is amplitude A=|A|

B is related to the period by: T = [tex]\frac{2.\pi}{B}[/tex]

C is the phase shift or horizontal shift: [tex]\frac{C}{B}[/tex]

D is the vertical shift

In this question, the motion of Pluto is modeled by a sine function and doesn't have phase shift, C = 0.

Amplitude:

a = [tex]\frac{largest - smallest}{2}[/tex]

At t=0, Pluto is the farthest from the sun, a distance 6.9 billions km away. At t=66, it is closest to the star, P(66) = 4.4 billions km. Then:

a = [tex]\frac{6.9-4.4}{2}[/tex]

a = 1.25

b

A time period for Pluto is T=66 years:

66 = [tex]\frac{2.\pi}{b}[/tex]

b = [tex]\frac{\pi}{33}[/tex]

Vertical Shift

It can be calculated as:

d = [tex]\frac{largest+smallest}{2}[/tex]

d = [tex]\frac{6.9+4.4}{2}[/tex]

d = 5.65

Knowing a, b and d, substitute in the equivalent positions and find P(t).

P(t) = a.sin(b.t) + d

P(t) = 1.25.sin([tex]\frac{\pi}{3}[/tex].t) + 5.65

The Pluto's distance from the sun as a function of time is

P(t) = 1.25.sin([tex]\frac{\pi}{3}[/tex].t) + 5.65

Answer:

P(t) = 1.25.sin(.t) + 5.65

Step-by-step explanation:

Answer:

Remote interior angle

Step-by-step explanation:

<Y is a remote (non-adjacent) interior angle for <w.

━━━━━━━☆☆━━━━━━━

▹ Answer

Remote Interior Angle

▹ Step-by-Step Explanation

∠Y is a non-adjacent interior angle for ∠W.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

7). y = 140

8). x = 9

Step-by-step explanation:

Question (7).

All-right pencil factory will produce the graphite pencils, table formed will represent a linear graph.

Three points on the graph are (12, 42) and (18, 63), (40, y)

Slope of the line passing through these points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{63-42}{18-12}[/tex] = [tex]\frac{y-42}{40-12}[/tex]

[tex]\frac{21}{6}[/tex] = [tex]\frac{y-42}{40-12}[/tex]

3.5 = [tex]\frac{y-42}{40-12}[/tex]

98 = y - 42

y = 140

Question (8),

If a bicyclist rides at a constant rate, table formed will represent a linear graph.

Slope of a line passing through three points (2, 25), (5, 62.5) and (x, 112.5) given in the table,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{62.5-25}{5-2}=\frac{112.5-62.5}{x-5}[/tex]

[tex]\frac{37.5}{3}=\frac{50}{x-5}[/tex]

37.5x - 187.5 = 150

37.5x = 337.5

x = 9

Answer:

b 150

Step-by-step explanation:

Answer:

0.65

Step-by-step explanation:

There are 65 student that do sports as 20+20+25=65. In total there are 100 student and you find this by adding up all the values. Now all you do is divide 65/100 and get 0.65 and that is the probability a random student plays sports.

Answer:

940.8 N

1254.4 N

Step-by-step explanation:

I would think the questions would be to calculate the forces at the top of the cube and at the sides. Thus:

On the top:

F = pressure * area

P = density * gravity * height

the height would be:

1m - 0.4m = 0.6m

replacing:

P = 1000 * 9.8 * 0.6 = 5880

A = (0.4) ^ 2 = 0.16

F = 5880 * 0.16

F = 940.8 N

On the sides:

dF = d * g * h * dA

dA = 0.4 * dh replacing

dF = 1000 * 9.8 * h * 0.4 * dh

dF = 3920 * h * dh

We integrate both sides and we have:

F = 3920 * (h ^ 2/2), h = 0.6 up to h = 1

F = (3920/2) * (1 ^ 2 - 0.6 ^ 2)

F = 1254.4 N

Answer:

Option (3)

Step-by-step explanation:

Given question is incomplete; here is the complete question.

The function f(x) = –x2 – 4x + 5 is shown on the graph. Which statement about the function is true?

The domain of the function is all real numbers less than or equal to −2.

The domain of the function is all real numbers less than or equal to 9.

The range of the function is all real numbers less than or equal to −2.

The range of the function is all real numbers less than or equal to 9

By using a graph tool we get a parabola opening downwards.

Since domain of a function is represented by x-values and range by y-values.

Domain of the given function will be (-∞, ∞)

Range of the function will be (-∞, 9] Or a set of all real numbers less thn equal to 9.

Therefore, Option (3) will be the answer.

Answer:

Domain : (-∞, ∞)

Range : (-∞, ∞)

Step-by-step explanation:

Parent function (y = [tex]\sqrt[3]{x}[/tex] ) of the given function y = -[tex]\sqrt[3]{x}[/tex] has been shown as the dotted line on the graph.

Solid curve represents the function,

y = [tex]-\sqrt[3]{x}[/tex]

Therefore, Domain of this function will be (-∞, ∞) Or x ∈ set of all real numbers.

And Range of the function will be (-∞, ∞) Or y ∈ set of all real numbers

Answer:

c = 6.25

Step-by-step explanation:

We are given the following piecewise function:

[tex]\left \{ {{cx^{2} + 2x, x < 3} \atop {3x^{3} - cx, x \geq 3}} \right[/tex]

Continuous function:

A function f(x) is continuous, at a point a, if:

[tex]\lim_{x \to a} f(x)[/tex] exists and [tex]\lim_{x \to a} f(x) = f(a)[/tex]

In this question:

Piece-wise function, so we have to verify if the limit exists.

The function changes at x = 3. So we verify at a = 3.

It will exist if:

[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)[/tex]

To the left:

Less than 3.

[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{-}} cx^{2} + 2x = c*(3)^{2} + 2*3 = 9c + 6[/tex]

To the right:

Greater than 3.

[tex]\lim_{x \to 3^{+}} f(x) = \lim_{x \to 3^{+}} 3x^{3} - cx = 3*3^{3} - 3c = 81 - 3c[/tex]

f continuous:

They have to be equal:

[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)[/tex]

[tex]9c + 6 = 81 - 3c[/tex]

[tex]12c = 75[/tex]

[tex]c = \frac{75}{12}[/tex]

[tex]c = 6.25[/tex]

Step-by-step explanation:

here,

31 cup of milk require 41 cup of water.

1 cup of milk require 41/31 cup of water.

so, 41/31 cup of water is required for 1 cup of milk.

hope u get it..

Answer:

Domain is all real numbers or (negative infinity, positive infinity)

Step-by-step explanation:

Domain is all values of x (inputs) that will work with the function. Since a parabola has no limits for x, and all numbers work for x, then the domain can be any number. That leaves us with All Real Numbers as our answer.

Answer:

The common difference is 1/2

Step-by-step explanation:

Data obtained from the question include:

3rd term (a3) = 0

Common difference (d) =.?

From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:

a7 – 2a4 = 1

Recall:

a7 = a + 6d

a4 = a + 3d

a3 = a + 2d

Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.

But, a3 = 0

a3 = a + 2d

0 = a + 2d

Rearrange

a = – 2d

Now:

a7 – 2a4 = 1

Substituting the value of a7 and a4, we have

a + 6d – 2(a + 3d) = 1

Sustitute the value of 'a' i.e –2d into the above equation, we have:

–2d + 6d – 2(–2d + 3d) = 1

4d –2(d) = 1

4d –2d = 1

2d = 1

Divide both side by 2

d = 1/2

Therefore, the common difference is 1/2

***Check:

d = 1/2

a = –2d = –2 x 1/2 = –1

a3 = 0

a3 = a + 2d

0 = –1 + 2(1/2)

0 = –1 + 1

0 = 0

a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2

a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2

= (–2 + 3)/2 = 1/2

a7 – 2a4 = 1

2 – 2(1/2 = 1

2 – 1 = 1

1 = 1

Answer:

2049.

Step-by-step explanation:

2045 - 1983 = 62 years.

So the competition will take place in 1983 + 60 = 2043.

After 2045  the competition takes place in 2049.

Answer: C - 600cm^2

Step-by-step explanation:

Area of one triangle:

(12)(5) ÷ 2 = 30

Area of two triangles:

30 x 2 = 60

Area of top rectangle:

Step 1: Figure out side length of triangle by using pythagorean:

√a^2 + b^2 =  c

√(5)^2 + (12)^2 =  c

√25 + 144 = c

√ 169 = c

13 = c

Step 2: Find area of top rectangle:

(18) x (13)

234

Find area of bottom rectangle:

(18) x (12)

216

Find area of back rectangle:

(18) x (5)

90

Add all the underlined numbers:

Area of two triangles + Area of top rectangle + Area of bottom rectangle + Area of back rectangle

60 + 234 + 216 + 90 = 600cm^2

Answer:

Given,

X=2

y=-2

z=3

Now,

[tex]3x + y - z \\ = 3 \times 2 + ( - 2) - 3 \\ = 6 + ( - 2) - 3 \\ = 6 - 2 - 3 \\ = 4 - 3 \\ = 1[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

1

Step-by-step explanation:

3X+Y-Z

Where X = 2, Y = -2 amd Z = 3

=> 3(2)+(-2)-(3)

=> 6-2-3

=> 4-3

=> 1

Answer:

Let the number be x

The statement is written as

[tex] \frac{3}{7}x = \frac{29}{14} [/tex]

Multiply through by 14

That's

[tex] 14 \times \frac{3}{7} x = \frac{29}{14} \times 14[/tex]

We get

2 × 3x = 29

6x = 29

Divide both sides by 6

That's

[tex] \frac{6x}{6} = \frac{29}{6} [/tex]

[tex]x \: = \frac{29}{6} \: \: or \\ 4 \frac{5}{6} [/tex]

Hope this helps you

Answer:

L'(3, 2)

M'(0, 2)

N'(0, -2)

O'(3, -2)

Step-by-step explanation:

Vertices of a rectangle LMNO are L(-4, 6), M(-1, 6), N(-1, 2) and O(-4, 2).

If a point (x, y) is reflected across y-axis, rule to be followed,

(x, y) → (-x, y)

After reflection across y-axis new ordered pairs will be,

L(-4, 6)   → L"(4, 6)

M(-1, 6)   → M"(1, 6)

N(-1, 2)   → N"(1, 2)

O(-4, 2)  → O"(4, 2)

Then these points were translated 4 units down and 1 unit left,

Rule to be followed for the translation will be,

(x'', y'') → [(x' - 1), (y' - 4)]

By this rule vertices of the rectangle after translation will be,

L''(4, 6) → L'(3, 2)

M''(1, 6) → M'(0, 2)

N''(1, 2) → N'(0, -2)

O''(4, 2) → O'(3, -2)

Answer:

L'(3, 2)

M'(0, 2)

N'(0, -2)

O'(3, -2)

Step-by-step explanation:

Hey there! :)

Answer:

Last option. (-1, 0) and (0, 6).

Step-by-step explanation:

Solve this system by setting the two equations equal to each other:

6x + 6 = -x² + 5x + 6

Rearrange the equation:

x² + 6x + 6 - 5x - 6 = 0

Combine like terms:

x² + x = 0

Factor out x:

x(x + 1) = 0

Set each factor equal to 0:

x = 0

x + 1 = 0

x = -1

These are the x values of the solutions. Plug these into an equation to solve for y:

y = 6(0) + 6

y = 6

-------

y = 6(-1) + 6

y = -6 + 6

y = 0

Therefore, the solutions to the equation are (-1, 0) and (0, 6).

Answer:

B. -1.

Step-by-step explanation:

[tex]i^1[/tex] = i

[tex]i^2 = -1[/tex]

[tex]i^3 = -i[/tex]

[tex]i^4 = 1[/tex]

...And it keeps going in a pattern, from i to -1 to -i to 1. And so, we have four values.

34 / 4 = 8 with a remainder of 2. That means that the value of [tex]i^{34}[/tex] is the same thing as [tex]i^2\\[/tex], so it is B. -1.

Hope this helps!

Answer:

if you would travel 50km/h then the time will be 2.4hours

Step-by-step explanation:

speed=v1=60km/h

time=t1=2h

speed=v2=50km/h

time=t2=?

as we know that

v1×t1=v2×t2

evaluating the expression

(v1×t1)/v2=t2

putting values

[tex]\frac{60km/h*2h}{50km/h}=t2[/tex]

[tex]\frac{120km/h^2}{50km/h}=t2[/tex]

2.4hours=t2

i hope this will help you :)

Answer:

so

slope is calculated this way:

[tex] \frac{3 - 6}{2 - 1} = \frac{ - 3}{1} = - 3[/tex]

let's calculate y init by:

3 = -3×2 + b

b = 9

so equation is:

y=-3x+9

Answer:

3

Step-by-step explanation:

Given  

y

=

2

x

2

−

4

x

+

3

The y-intercept is the value of  

y

when  

x

=

0

XXX

y

=

2

(

0

)

2

−

4

(

0

)

+

3

=

3

For a quadratic in the general form:

XXX

y

=

a

x

2

+

b

x

+

c

the determinant  

Δ

=

b

2

−

4

a

c

indicates the number of zeros.

Δ

⎧

⎪

⎨

⎪

⎩

<

0

==⇒  

no solutions

=

0

==⇒  

one solution

>

0

==⇒  

two solutions

In this case

XXX

Δ

=

(

−

4

)

2

−

4

(

2

)

(

3

)

<

0

so there are no solutions (i.e. no values for which the expression is equal to zero).

This can also be seen from a graph of this equation:

graph{2x^2-4x+3 [-6.66, 13.34, -0.64, 9.36]}

Answer link

Vinícius Ferraz

Nov 13, 2015

(

0

,

3

)

Explanation:

x

=

0

⇒

y

=

0

−

0

+

3

y

=

0

⇒

x

=

−

b

±

√

b

2

−

4

a

c

2

a

a

=

2

,

b

=

−

4

,

c

=

3

But  

Δ

< 0, then there is no real root  

(

x

0

,

0

)

.

Answer:

it has 2

Step-by-step explanation:

I hope this helps!

Answer:

CI: {0.4085; 0.6647}

Step-by-step explanation:

The confidence interval for a proportion (p) is given by:

[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]

Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:

[tex]p=\frac{22}{41}=0.536585[/tex]

Thus the confidence interval is:

[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]

The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}

Answers:

A ' = (-2, -3)

B ' = (0, -3)

C ' = (-1, 1)

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

Explanation:

To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.

Algebraically, the reflection rule used can be written as [tex](x,y) \to (x,-y)[/tex]

Applying this rule to the three given points will mean....

The diagram is provided below.

Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.

Answer:

(-2,-3)...(0,-3)...(-1,1)

Step-by-step explanation:

Answer:

a

The Null hypothesis represented as

     [tex]H_0: \mu_1 - \mu_2 = 0[/tex]

The Alternative hypothesis represented as

     [tex]H_a: \mu_1 - \mu_2 < 0[/tex]

b

p-value =  P(Z <  -3.37  )  = 0.000376

c

There is insufficient evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students

Step-by-step explanation:

From the question we are told that

   The population size is  [tex]n= 650[/tex]

    The  sample size for graduates is  [tex]n_1 = 300[/tex]

     The sample  mean for graduates is [tex]\= x _1 = 148[/tex]

      The sample  standard deviation for graduates is [tex]\sigma_1 = 16[/tex]

    The  sample size for under-graduates is [tex]n _2 = 350[/tex]

         The sample  mean for under-graduates is [tex]\= x _2 = 153[/tex]

         The sample  standard deviation for graduates is [tex]\sigma_2 = 21[/tex]

The Null hypothesis represented as

     [tex]H_0: \mu_1 - \mu_2 = 0[/tex]

The Alternative hypothesis represented as

     [tex]H_a: \mu_1 - \mu_2 < 0[/tex]

Where [tex]\mu_1 \ and \ \mu_2[/tex] are the population mean

  Now the test statistic is mathematically represented as

          [tex]t = \frac{(\= x_1 - \= x_2 ) }{ \sqrt{ \frac{ (n_1 - 1 )\sigma_1 ^2 + (n_2 - 1)\sigma_2^2}{n_1 +n_2 -2} } * \sqrt{ \frac{1}{n_1} + \frac{1}{n_2} } }[/tex]

substituting values

       [tex]t = \frac{(148 - 153 ) }{ \sqrt{ \frac{ (300- 1 )16 ^2 + (350 - 1) 21^2}{300 +350 -2} } * \sqrt{ \frac{1}{300} + \frac{1}{350} } }[/tex]

      [tex]t = -3.37[/tex]

The p-values is mathematically evaluated as

     p-value =  P(Z <  -3.37  )  = 0.000376

The above answer is gotten using a p-value calculator  at (0.05) level of significance

     Looking the p-value we see that it is less than the level of significance (0.05)  so Null hypothesis is rejected

Hence there is insufficient evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students

Following are the two-Sample of the T-Test and CI:

[tex]\boxed{\boxed{\begin{matrix}Sample& N &Mean& StDev& SEMean\\ 1 &350 &153.0& 21.0 &1.1 \\ 2& 300& 148.0& 16.0& 0.92\end{matrix}}}[/tex]

Calculating the difference:

[tex]= \mu (1) - \mu (2)\\\\[/tex]

The estimated difference: [tex]5.00[/tex]

When the [tex]95\%[/tex] of CI so, the difference:[tex](2.09, 7.91)[/tex]

Therefore the T-Test difference value = 0

[tex]\to (vs \neq): T-Value = 3.37 \\\\\to P-Value = 0.001 \\\\\to DF = 648[/tex]

When the both use Pooled so, the StDev = 18.8583

Therefore, the final value of t is "3.37".

Learn more:

brainly.com/question/16380581

Answer:

he additive inverse of:

a)  [tex]-6x^2-x-2[/tex] is : [tex]6x^2+x+2[/tex]

b)  [tex]6x^2-x+2[/tex]  is :  [tex]-6x^2+x-2[/tex]

c)  [tex]6x^2+x-2[/tex]  is :  [tex]-6x^2-x+2[/tex]

d)  [tex]6x^2+x+2[/tex]  is :  [tex]-6x^2-x-2[/tex]

Step-by-step explanation:

You need to consider that the additive inverse of a polynomial is that polynomial that consists of the opposite of each term of the polynomial given.

Then, the additive inverse of:

a)  [tex]-6x^2-x-2[/tex] is :  [tex]6x^2+x+2[/tex]

b)  [tex]6x^2-x+2[/tex]  is :  [tex]-6x^2+x-2[/tex]

c)  [tex]6x^2+x-2[/tex]  is :  [tex]-6x^2-x+2[/tex]

d)  [tex]6x^2+x+2[/tex]  is :  [tex]-6x^2-x-2[/tex]