you choose a marble at random from a bag containing 15 red marbles, 7 yellow marbles, and 3 pink marble. you replace the marble and then choose again. find the probability of P(both red)

Answer:

Due to the higher Z-score, Norma should be offered the job

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

Whoever has the higher z-score should be offered the job.

Alissa:

[tex]X = 68.5, \mu = 60.4, \sigma = 9[/tex]

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{68.5 - 60.4}{9}[/tex]

[tex]Z = 0.9[/tex]

Morgan:

[tex]X = 252.5, \mu = 227, \sigma = 17[/tex]

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{252.5 - 227}{17}[/tex]

[tex]Z = 1.5[/tex]

Norma:

[tex]X = 7.96, \mu = 6.7, \sigma = 0.7[tex]

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{7.96 - 6.7}{0.7}[/tex]

[tex]Z = 1.8[/tex]

Due to the higher Z-score, Norma should be offered the job

[tex]the \: answer \: is \: 22.4 \: cm \\ please \: see \: the \: attached \: picture \\ for \: full \: solution \\ hope \: it \: helps[/tex]

The length of AE is 22.4cm rounded to one decimal place.

Answer:

72.1

Step-by-step explanation:

G(x) =19.60 + 1.75x

Let x = 30

G(30) =19.60 + 1.75*30

          =19.60 +52.5

            72.1

Answer:

The approximate percentage of cars that remain in service between 73 and 84 months

P( 73 < x < 84 ) = 0.02145 = 2.1 %

Step-by-step explanation:

Explanation:-

Given mean of the Population 'μ ' = 51 months

Standard deviation of the Population 'σ' = 11 months

Let 'X' be the random variable of Normal distribution

Let    'X'  = 73

[tex]Z = \frac{x-mean}{S.D} = \frac{73-51}{11} = 2[/tex]

Let  'X' = 84

[tex]Z = \frac{84-51}{11} = 3[/tex]

The approximate percentage of cars that remain in service between 73 and 84 months

P( 73 < x < 84 )      = P( 2 < Z < 3)

                              = P( Z<3) - P( Z <2)

                             =  0.5 + A(3) - ( 0.5 + A(2))

                            = A(3) - A( 2)

                            = 0.49865 - 0.4772     ( From Normal table)

                            = 0.02145

 P( 73 < x < 84 ) = 0.02145

The approximate percentage of cars that remain in service between 73 and 84 months

P( 73 < x < 84 ) = 0.02145 = 2.1 %

Answer:

286 degrees and 143 degrees

Step-by-step explanation:

When line intersect the two vertical angle adds up to 180 degrees

To find the other vertical angle:

180 -37=143 degrees

So for two vertical angles

we take (180*2)-(37*2)=286 degrees

Answer:

(C)72.4 in

Step-by-step explanation:

Given an acute triangle in which the longest side measures 30 inches; and the other two sides are congruent.

Consider the attached diagram

AB=BC=x

However to be able to solve for x, we form a right triangle with endpoints A and C.

Since the hypotenuse is always the longest side in a right triangle

Hypotenuse, AC=30 Inches

Using Pythagoras Theorem

[tex]30^2=x^2+x^2\\900=2x^2\\x^2=450\\x=\sqrt{450}\\x=21.21$ inches[/tex]

Therefore, the smallest possible perimeter of the triangle

Perimeter=2x+30

=2(21.21)+30

=42.42+30

=72.4 Inches (rounded to the nearest tenth)

Answer:

80

Step-by-step explanation:

46+15+19 which should give you a total answer of 80

Answer:

Step-by-step explanation:

5x - c = k

Add c  to each side

5x - c+c = k+c

5x = (k+c)

Divide each side by 5

5x/5 = (k+c)/5

x = (k+c)/5

Answer:

x=(k+c)/5

Step-by-step explanation:

5x-c=k (Original Equation)

5x-c+c=k+c (Addition Property of Equality)

5x=k+c (Simplify)

x=(k+c)/5 (Division Property of Equality)

Answer:

Dear user,

Answer to your query is provided below

The dimensions to maximise the printed area to 2160 is length = 100cm and width = 60cm

Step-by-step explanation:

Explanation for the answer is attached in the image

Answer:

The answer would be 50%

Step-by-step explanation:

You Would get this by dviding 36/72 which would give you .5 and then you convert that to a percentage

Answer:

50%

Step-by-step explanation:

Answer:

You want the curve to be decreasing from left to right since they are decreasing the amount spent so we can eliminate options 2 and 3. The initial amount (when x = 0) has to be 12 so the answer is the last option.

Answer:

(9x - 1)²

Step-by-step explanation:

If you can tell, the square root of 81 is 9. This should be a clue that the polynomial could be one binomial squared. If you tried factoring starting out with 9x in both parenthesis, you could see that you would get (9x - 1)² as your answer.

Answer:

(9x-1)²

Step-by-step explanation:

81x² - 18x + 1= (9x)²- 2*9x+1²= (9x-1)²

Answer:

Angle LOA = angle LMA

Step-by-step explanation:

I just took the test

From the diagram, the two triangles have an indication of a pair of

congruent angles.

Reasons:

The given parameters of ΔLOA and ΔLAM are;

The shared side of the triangles = Side LA

From the attached diagram, we have;

∠ALO = ∠ALM

Required:

The additional information needed to prove that the triangles are congruent using AAS

Solution:

The AAS congruency is an acronym for Angle Angle Side, which states

that, two triangles are similar if two angles and a non included side of one

triangle are equal to two angles and a non included side on another

triangle, then the two triangles are congruent.

The angle on ΔLOA that will make the side LA a non included side is ∠LOA.

Similarly;

The angle on ΔLAM that will make the side LA a non included side is ∠LMA.

Therefore, the additional information needed to prove that the triangle are congruent using the AAS congruency theorem is; ∠LOA ≅ ∠LMA

Learn more about Angle Angle Side, AAS, rule of congruency here:

https://brainly.com/question/17033697

Answer:87

Step-by-step explanation:

866

Answer:

the answer is 5

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

5x-10=15

5x=25

x=5

Answer:

30 different ways

Step-by-step explanation:

Hi

for the first topping she can choose 1 of 6 items

so she has 6 choices

and then the second topping she has 5 choices as each topping can only be chosen once

so it comes 6 * 5 = 30

Answer:

A

Step-by-step explanation:

RT=12

TU=5

RU=12+5=17

RS=17+7=24

SU=√(RS²-RU²)=√(24²-17²)=√(24-17)(24+17)=√(7×41)=√287

area=1/2×12×√287=6×√287≈101.6 unit²

Answer:

  A'(4, 3)

Step-by-step explanation:

When a point is reflected across the line y = x, the transformation is ...

  (x, y) ⇒ (y, x)

  A(3, 4) ⇒ A'(4, 3)

The reflected point is (4, 3).

Answer:

work is shown and pictured

Answer:

y= 3/2x -2

Step-by-step explanation:

make y be on one side by itself ( -2y = -3x + 4 )

divide by negative 2 in order to get y by itself ( -2y/-2 = -3/-2 + 4/-2 )

two negatives make a positive ( y = 3/2 + -2 )

Answer:

The Supreme Court.

Step-by-step explanation:

After the end of the Civil War and the enactment of the Thirteenth Amendment in 1865, slavery was officially abolished in the United States. Thus, the millions of African American slaves that inhabited the southern states of the country won their freedom and equality before the law against whites.

Now this situation began to dismember in 1877, when federal troops left the southern states and Reconstruction officially came to an end. From then on, Democratic governors and legislators began to sanction the Black Codes and Jim Crow Laws, aimed at curtailing the civil and political rights of African-Americans.

This situation was tested before the Supreme Court in 1896 in the case Plessy v. Ferguson. But in the ruling of said case, the Supreme Court established that racial segregation was constitutional and therefore neglected African Americans and their rights.

Answer:

7/13

Step-by-step explanation:

Answer:

a) $12,440.43

b) $8,000.00

c) $4,440.43

Step-by-step explanation:

the question is a bit ambiguous, I calculated from zero initial Deposit to $100 per quarter. If they deposited $100 initially and then $100 quarterly for 20 years then the numbers are as follows.

a) $12,671.05

b) $8,100

c) $4,571.05

a) $12,440.43

b) $8,000.00

c) $4,440.43

Step-by-step explanation:

the question is a bit ambiguous, I calculated from zero initial Deposit to $100 per quarter. If they deposited $100 initially and then $100 quarterly for 20 years then the numbers are as follows.

a) $12,671.05

b) $8,100

c) $4,571.05

Answer:

Step-by-step explanation:

These are mostly calculator problems. The only trick is the last one. Your calculator will have either a y^x button or ^ button. They both do the same thing.

So for the last one, you must do it as

64 y/x (1÷6)= and you will get 2. Perhaps all of them should be done that way.

If your calculator uses ^ then you would do it

64^(1÷6)= which is the same thing.

Answers

a 4

b 10

c 5

d 2

Answer:

Step-by-step explanation:

Hello!

The objective is to test the claim that less than 41% of the publisher's readers own a laptop.

To do so, a sample of 320 readers was taken and the proportion of readers that own a laptop resulted in 36%

Be X: number of readers that own a laptop.

X~Bi(n;p)

n=320

Sample proportion p'= 0.36

The hypotheses are:

H₀: p ≥ 0.41

H₁: p < 0.41

α: 0.05

[tex]Z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]≈N(0;1)

[tex]Z_{H_0}=\frac{0.36-0.41}{\sqrt{\frac{0.41(1-0.41)}{320} } }= -1.82[/tex]

This test is one-tailed to the left, meaning, that you'll reject the null hypothesis to small values of Z, there is only one critical value that defined the rejection region:

[tex]Z_{\alpha }= Z_{0.05}= -1.645[/tex]

The decision rule is:

If [tex]Z_{H_0}[/tex] ≤ -1.645, reject the null hypothesis.

If [tex]Z_{H_0}[/tex] > -1.645, do not reject the null hypothesis.

The calculated value is less than the critical value, then the decision is to reject the null hypothesis.

So at a 5% significance level, the test is significant. You can conclude that the population proportion of the publisher's readers that own a laptop is less than 41%.

I hope this helps!

Answer:

(a) [8, 14]

(b)  [tex]8 \leq x \leq 14[/tex]

(c)See attachment

Step-by-step explanation:

We want to choose a value of x within 3 units of 11.

(a)Now, 11-3=8 and 11+3=14

The possible values of x ranges is in the closed interval [8,14]

(b) Since x is within 3 units of 11., we have:

[tex]|11-x|\leq3[/tex]

Solving the absolute inequality

[tex]-3 \leq 11-x \leq 3\\$In $ -3 \leq 11-x\\ x \leq 11+3\\x \leq 14\\\\$In $ 11-x \leq 3\\ 11-3 \leq x\\8 \leq x\\$Therefore,an inequality that represents all values of x that meet this constraint is:$\\8 \leq x \leq 14[/tex]

(c)To draw the number line, we use a closed dot since we have the less than or equal to sign.

The solution of the inequality is [tex]8\leq x\leq14[/tex]

According to the question, we need to choose a value of x within 3 units of 11. This can be represented by the inequality

[tex]|11-x|\leq3[/tex]

The expression in modulus can be negative or positive:

For the positive inequality

[tex]11-x \leq3\\-x \leq3 -11\\x\geq8\\8\leq x[/tex]

For the negative inequality

[tex]-11+x \leq3\\x \leq3 +11\\x\leq14\\[/tex]

Combining the inequalities

[tex]8\leq x\leq14[/tex]

Hence the solution of the inequality is [tex]8\leq x\leq14[/tex]

Learn more here: https://brainly.com/question/15816805

Answer:

Step-by-step explanation:

A. x² = –100

This equation has no solution because x² is always positive.

B. 5x² = 1

then x² = 1/5

then x = 1/(√5) or x = -1/(√5)

C. 6x² + 17 = 11

then 6x² = 11 - 17 = -6

then x² = -6/6 = -1  

This equation has no solution because x² is always positive.

D. 7(x + 6) = 42

then x + 6 = 42/7 = 6

then x = 6 - 6 = 0

_____________________

:)

Answer:

m∠3 = 115°

Step-by-step explanation:

Since measure of angle 6 = (2x - 5)°

And measure of angle 8 = (x + 5)°

Since ∠6 and ∠8 are the supplementary angles,

m∠6 + m∠8 = 180°

(2x - 5)° + (x + 5)° = 180°

3x = 180°

x = 60°

Therefore, m∠6 = (2x - 5) = (120 - 5) = 115°

and m∠8 = (x + 5) = 65°

Since angle 6 and angle 3 are interior alternate angles,

Therefore, m∠6 = m∠3 = 115° will be the answer.