a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages.

Answer:

a. 0.06

b. 0.2

Step-by-step explanation:

a. P(B given A) = P(A and B) / P(A)

0.1 = P(A and B) / 0.6

P(A and B) = 0.06

b. P(A given B) = P(A and B) / P(B)

P(A given B) = 0.06 / 0.3

P(A given B) = 0.2

Answer: Continuous

If X is the random variable denoting the weights of employees,  X is a continuous random variable.

Step-by-step explanation:

Given: An entertainment company specifies that its employees must weigh between 40 kgs - 50 kgs.

here weights of the employees vary.

Also, weight is measured not counted , that means weight is a continuous variable.

If X is the random variable denoting the weights of employees,  X is a continuous random variable.

The weights of employees, X, is a: continuous random variable.

Therefore, the weights of employees, X, is a: continuous random variable.

Learn more about continuous random variable on:

https://brainly.com/question/15238425

Answer:

Perimeter= 40 units

Step-by-step explanation:

Ok

We are asked to look for the perimeter.

We have some clue given.

All at right angle and some sides are given it's full length.

We have the bae to be 11 unit

The height to be 7 unit.

What this mean is that taking either the base or the height should sum up to either 11 or 7 respectively.

Let's go for the other side of the height.

Let's take all the vertical height and sum it up to 7 because the right side is equal to 7.

So we have 7+7+11

But it's not complete yet.

We are given a dimension 2.

And the 2 is in two places so it's total 2*2= 4

The two is for a small base .

The base is actually an extra to the 11 of the other base.

So summing up

We have 2*11 + 2*7 + 2*2

Perimeter= 22+14+4

Perimeter= 40 units

Answer:

Step-by-step explanation:

Total money/ number of people

63.90/3 = 21.30

If you divide by 3 then the 3 friends will get the equal amount of money.

Answer:

Step-by-step explanation:

The total amount of money is $63.90. Also, there are 3 friends.

In order to pay equally, divide $63.90 and 3 friends, so the answer would be dollars per friend

$63.90/3 friends = $21.3/friend

So the items you would drag would be:

2 $10 bills

1 $1 bill

3 $0.10 dimes

Answer:

Step-by-step explanation:

Confidence interval for the population mean is expressed by the formula;

CI = xbar ± Z(S/√n) where;

xbar is the sample mean = 12.5

Z is the z score at 99% confidence = 2.576

S is the standard deviation = √variance

S = √2.4 = 1.5492

n is the sample size = 25

Substituting the given values into the formula given above,

CI = 12.5 ± 2.576(1.5492/√25)

CI = 12.5 ± 2.576(0.30984)

CI = 12.5 ± 0.7981

CI = (12.5-0.7981, 12.5+0.7981)

CI = (11.2019, 12.7981)

Hence the 99% confidence interval for the population mean is 11.2≤[tex]\mu[/tex]12.8 (to 1 decimal place)

A 99% confidence interval for the population mean will be "11.2 [tex]\leq[/tex] 12.8".

According to the question,

Sample mean, [tex]\bar x[/tex] = 12.5

Z score at 99%, Z = 2.576

Standard deviation, S = √Variance

                                    = √2.4

                                    = 1.5492

Sample size, n = 25

We know the formula,

Confidence interval, CI = [tex]\bar x \ \pm[/tex] Z ([tex]\frac{S}{\sqrt{n} }[/tex])

By substituting the given values, we get

                                        = 12.5 [tex]\pm[/tex] 2.576 ([tex]\frac{1.5492}{\sqrt{25} }[/tex])

                                        = 12.5 [tex]\pm[/tex] 2.576 (0.30984)

                                        = 12.5 [tex]\pm[/tex] 0.7981

Now,

                                   Cl = (12.5 - 0.7981, 12.5 + 0.7981)

                                        = (11.2019, 12.7981) or,

                                        = (11.2, 12.8)

Thus the above answer is appropriate.        

Find out more information about mean here:

https://brainly.com/question/7597734

Answer:

See picture attached

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%.

Step-by-step explanation:

In this case we need to test whether the popular charity has expenses that are higher than other similar charities.

The hypothesis for the test can be defined as follows:

H₀: The popular charity has expenses that are higher than other similar charities, i.e. μ > 0.31.

Hₐ: The popular charity has expenses that are less than other similar charities, i.e. μ < 0.31.

As the population standard deviation is not known we will use a t-test for single mean.

Compute the sample mean and standard deviation as follows:

[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{10}\cdot[0.26+0.12+...+0.26]=0.238\\\\s= \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 0.0674 }{ 10 - 1} } =0.08654\approx 0.087[/tex]

Compute the test statistic value as follows:

[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{0.238-0.31}{0.087/\sqrt{10}}=-2.62[/tex]

Thus, the test statistic value is -2.62.

Compute the p-value of the test as follows:

 [tex]p-value=P(t_{\alpha, (n-1)}<-2.62}[/tex]

                [tex]=P(t_{0.05,9}<-2.62)\\=0.014[/tex]

*Use a t-table.

Thus, the p-value of the test is 0.014.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.014 < α = 0.05

The null hypothesis will be rejected at 5% level of significance.

Thus, concluding that there is sufficient evidence to conclude that the mean is less than 31%.

Answer:

[tex]\boxed{V=lwh}[/tex]

Step-by-step explanation:

The formula for volume of a cuboid is:

[tex]V=lwh[/tex]

[tex]volume = length \times width \times height[/tex]

Answer:

V = l w h

Step-by-step explanation:

Volume of a Cuboid = Length × Width × Height

Where l = length, w = width and h = height

Answer:

0.02906

Step-by-step explanation:

number of questions =30

getting exactly right : 12

30C12 the number of possibilities

probability to get it right (1/4)^12

probability of failure =1-1/4=(3/4)^18     ( 18 = 30 questions -12 right )

P(12)=30C12*(1/4)^12*(3/4)^18=0.02906

hope it helps

Answer:

52 5/8

Step-by-step explanation:

To add fractions, you have to make sure both fractions have a common denominator.

As you can see, the fractions have different denominators, so to make both denominators 8, we have to multiply 1/4 by two, which gives us 2/8.

Then, we just add like normal!

49 2/8+ 3 3/8 = 52 5/8!

Hope this helped! :)

Answer:

Its D

Step-by-step explanation:

x=11 and x=18

Answer:

Last option is correct.

Step-by-step explanation:

[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]

Multiply the terms with the same base by adding their exponents

[tex] - 2 {x}^{3 + 2} {y}^{4 + 3} [/tex]

Add the numbers

[tex] - 2 {x}^{5} {y}^{7} [/tex]

Hope this helps..

Best regards!

[tex] - 2 {x}^{5} {y}^{7} [/tex]

Solution:

[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]

[tex] = 2 {x}^{(3 + 2)} {y}^{(4 + 3)} [/tex]

[tex] = - 2 {x}^{5} {y}^{7} [/tex]

[tex]{\boxed{\blue{\textsf{Some Important Laws of Indices}}}}[/tex]

[tex]{a}^{n}.{a}^{m}={a}^{(n + m)} [/tex]

[tex]{a}^{-1}=\dfrac{1}{a}[/tex]

[tex]\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}[/tex]

[tex]{({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}[/tex]

[tex] {a}^{\frac{1}{x}}=\sqrt[x]{a}[/tex]

[tex]a^0 = 1[/tex]

[tex][\text{Where all variables are real and greater than 0}][/tex]

Answer:

Step-by-step explanation:

The null hypothesis is described as the default hypothesis while the alternative hypothesis us always tested against this null ie the opposite of the null hypothesis.

In this case study, Let the proportion of houses that have home security be p

Thus, the null hypothesis is proportion of houses that have home security is 45% : p = 45%

The alternative hypothesis is proportion of houses that have home security is different than 45%: p =/ 45%

Answer:

45°

Step-by-step explanation:

This is a special 6 - 6 - 6√2 right triangle with angle measures 45° - 45° - 90°

Answer:  m∠R = 45°

Step-by-step explanation:

[tex]6^{2}\ +\ 6^{2} = 72[/tex]

[tex]\frac{\left(6\right)}{\sqrt{72}}=0.7071067812[/tex]

[tex]\sin^{-1}\left(\frac{\left(6\right)}{\sqrt{72}}\right)= 45[/tex]

Answer:

86 degrees farenheit

Step-by-step explanation:

First, we plug 30 in for C.

Next, solve for F

Multiplying both sides by 9/5 gives us 54=F-32

Add 32 to both sides    86=F

Answer:    2⁹5³ = 64,000

Step-by-step explanation:

There are 9 questions with 2 options (true or false) = 2⁹

There are 3 multiple questions with 5 options = 5³

true/false questions AND multiple choice questions

                  2⁹               x                5³                            = 2⁹5³

Answer:44

Step-by-step explanation:the two triangles are congruent , so we deduce from that the angle B=angle E =48

So, x+4=48 , x=44 degree

Answer:

The answer is below

Step-by-step explanation:

Given that:

mean (μ) = 138 lb, standard deviation (σ) = 34.9 lb

z score is used in statistic to determine by how many standard deviations the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

a) For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.

For 150 lb:

[tex]z=\frac{x-\mu}{\sigma}=\frac{150-138}{34.9}=0.34[/tex]

For 201 lb:

[tex]z=\frac{x-\mu}{\sigma}=\frac{201-138}{34.9}=1.81[/tex]

From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(0.34 < z < 1.81) = P(z < 1.81) - P(z < 0.34) = 0.9649 - 0.6331 = 0.3318 = 33.18%

b) If 39 different pilots are randomly selected i.e. n = 39. For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.

For 150 lb:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{150-138}{34.9/\sqrt{39} }=2.15[/tex]

For 201 lb:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{201-138}{34.9/\sqrt{39} }=11.3[/tex]

From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(2.15 < z < 11.3) = P(z < 11.3) - P(z < 2.15) = 1 - 0.9842 = 0.0158 = 1.58%

c) The probability from part C is more important

Answer:

The  p-value is  [tex]p-value = 0.013167[/tex]

Step-by-step explanation:

From the question we are told that

     The  population mean is [tex]\mu[/tex] =  200 milligrams

     The sample size is [tex]n = 70[/tex]

     The sample  mean is  [tex]\= x = 205.7[/tex]

      The  sample standard deviation is  [tex]\sigma = 21 \ milligram[/tex]

Generally the Null hypothesis is  mathematically represented as

      [tex]H_o : \mu = 200[/tex]

The Alternative  hypothesis is  

     [tex]H_a : \mu < 200[/tex]

The test statistics is mathematically represented as

       [tex]t_s = \frac{\= x - \mu }{\frac{\sigma}{\sqrt{n} } }[/tex]

substituting values  

     [tex]t_s = \frac{ 205.7 - 200 }{\frac{21}{\sqrt{70} } }[/tex]

     [tex]t_s = 2.270[/tex]

Now the p-value is mathematically represented as

      [tex]p-value = P(Z \le t_s )[/tex]

substituting values  

      [tex]p-value = P(Z \le 2.270 )[/tex]

Using the Excel function[=NORMDIST(2.270)] to calculate the p-value we obtain that

       [tex]p-value = 0.013167[/tex]

Answer:

A) 0.012

From CollegeBoard

Answer:

the value of the series;

[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]

C) 59

Step-by-step explanation:

Recall that;

[tex]\sum_{1}^{n}a_n = a_1+a_2+...+a_n\\[/tex]

Therefore, we can evaluate the series;

[tex]\sum_{k=1}^{6}(25-k^2)[/tex]

by summing the values of the series within that interval.

the values of the series are evaluated by substituting the corresponding values of k into the equation.

[tex]\sum_{k=1}^{6}(25-k^2) =(25-1^2)+(25-2^2)+(25-3^2)+(25-4^2)+(25-5^2)+(25-6^2)\\\sum_{k=1}^{6}(25-k^2) =(25-1)+(25-4)+(25-9)+(25-16)+(25-25)+(25-36)\\\sum_{k=1}^{6}(25-k^2) =24+21+16+9+0+(-11)\\\sum_{k=1}^{6}(25-k^2) = 59\\[/tex]

So, the value of the series;

[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]

Answer:

b. (10,10,0)

Step-by-step explanation:

r+v can be evaluated if the vectors/matrices have the same dimensions.

These do. They are both 1 by 3 vectors.

Just add first to first in each.

Just add second to second in each.

Just add third to third in each.

Example:

(5,-5,6)+(1,2,3)

=(5+1,-5+2,6+3)

=(6,-3,9)

Done!

In general, (a,b,c)+(r,s,t)=(a+r,b+s,c+t).

r+v

=(7,3,9)+(3,7,-9)

=(7+3,3+7,9+-9)

=(10,10,0)

Done!

It's 1000 charges and not 1.000 charges

Answer:

A)Null Hypothesis;H0: μ = 1000

Alternative Hypothesis;Ha: μ ≠ 1000

B) t-statistic = 1.4286

C) p-value = 0.15628

D) We conclude that we will fail to reject the manufacturers claim that its rechargeable batteries are good for an average of more than 1000 charges

Step-by-step explanation:

We are given;

x = 1002 charges

s = 14

μ = 1000 charges

n = 100

degree of freedom = n - 1 = 100 - 1 = 99

A) The hypotheses are;

Null Hypothesis;H0: μ = 1000

Alternative Hypothesis;Ha: μ ≠ 1000

B) t-statistic = (x - μ)/(s/√n)

(1002 - 1000)/(14/√100) = 1.4286

C) From the t-score calculator results attached, the p-value is approximately 0.15628

D) The P-value of 0.15628 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we conclude that the result is statistically nonsignificant.

Here is the correct format for the question

At 2:00 PM a car's speedometer reads 30 mi/h. At 2:15 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:15 the acceleration is exactly 80 mi/h².Let v(f) be the velocity of the car t hours after 2:00 PM.Then [tex]\dfrac{v(1/4)-v(0)}{1/4 -0} = \Box[/tex]. By the Mean Value Theorem, there is a number c such that 0 < c < [tex]\Box[/tex]  with v'(c) = [tex]\Box[/tex]. Since v'(t)  is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly 80 mi/h^2.

Answer:

Step-by-step explanation:

From the information given :

At  2:00 PM ;

a car's speedometer v(0) = 30 mi/h

At 2:15 PM;

a car's speedometer v(1/4) = 50 mi/h

Given that:

v(f) should be the velocity of the car t hours after 2:00 PM

Then [tex]\dfrac{v(1/4)-v(0)}{1/4 -0} = \Box[/tex] will be:

[tex]= \dfrac{50-30}{1/4 -0}[/tex]

[tex]= \dfrac{20}{1/4 }[/tex]

= 20 × 4/1

= 80 mi/h²

By the Mean value theorem; there is a number c such that :

[tex]\mathbf{0 < c< \dfrac{1}{4}}[/tex]     with [tex]\mathbf{v'(c) = \dfrac{v(1/4)-v(0)}{1/4 -0}} \mathbf{ = 80 \ mi/h^2}[/tex]

By the mean value, theorem a number [tex]C[/tex] is [tex]0 < C < \frac{1}{4}[/tex].

The velocity of the car is [tex]80 \ mi/h^{2}[/tex].

Speed is defined as The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

Given that,

at 2:00 pm [tex]v(0)=30 \ mi/h[/tex]

at 2:15 pm [tex]v(1/4)=50 \ mi/h[/tex]

Then,

[tex]=\frac{v(1/4)-v(0)}{1/4-0} \\=\frac{50-30}{1/4} \\=20\times4\\=80 \ mi/h^{2}[/tex]

By the mean value theorem a number [tex]C[/tex] such that express as,

[tex]0 < C < \frac{1}{4}[/tex].

Now with,

[tex]{v}'(c)=\frac{v\left ( \frac{1}{4} \right )-v\left ( 0 \right )}{\frac{1}{4}-0} \\ =80 \ mi/h^{2}[/tex]

Learn more about the topic Speed: https://brainly.com/question/26417650

Answer:

A

Step-by-step explanation:

For an inequality to have a shaded area above the graph, the variable has to be on the left side of a greater than sign, or a greater than or equal to sign.

A is the only option with one of these signs, so it is the correct answer.

Answer:

The beryllium atom; 1.99 times larger.

Step-by-step explanation:

The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.

(1.12 * 10^-10) / (5.6 * 10^-11)

= (1.112 / 5.6) * (10^-10 + 11)

= 0.1985714286 * 10

= 1.985714286 * 10^0

So, the beryllium atom is about 1.99 times larger than the other.

Hope this helps!

Answer:

The answer is below

Step-by-step explanation:

a) y=3x-1

The standard equation of a line is given by:

y = mx + c

Where m is the slope of the line and c is the intercept on the y axis.

Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:

3 × d = -1

d = -1/3

To find the equation of the perpendicular line passing through (0,0), we use:

[tex]y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x[/tex]

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

[tex]y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12[/tex]

b) y=1/4 x+2

Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:

1/4 × f = -1

f = -4

To find the equation of the perpendicular line passing through (0,0), we use:

[tex]y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x[/tex]

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

[tex]y=-4}x\\ 4=-4x\\x=-1[/tex]

a) Simply do 0.135(13.5%)*550 to get that his rent increases by $74.25.

b) Simply do 550+74.25 to get that his new rent is $624.25.

c) 624.25/550 = 1.135, or 100%+13.5%, the amount his rent increased.

Hope it helps <3

Answer:

A. $74.25

B. $624.25

C. 1.135, and this is a connection to part a because it's what we multiplied 550 by to get our new rent.

Step-by-step explanation:

If Shawn pays $550 per month for rent, and he has a 13.5% increase, we can multiply 550 by [tex]1+\frac{13.5}{100}[/tex] to get our new number.

[tex]1+0.135=1.135[/tex]

[tex]550\cdot1.135=624.25[/tex]

This is the new monthly rent, part B. To find Part A, let's subtract 550 from thi number.

[tex]624.25-550=74.25[/tex]

Now, for part C, let's divide 624.25 by 550.

[tex]624.25\div550 = 1.135[/tex]

If you notice, 1.135 is the same number we multiplied 550 by to get our new cost, and as a percent, 1.135 is 113.5%.

Hope this helped!

Answer:

2 /3 +5 = 3

5.666667≠3

False

Step-by-step explanation:

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

              Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Lets do this step by step.

~~~~~~~~~~~~~~~~~~~~

Multiply both sides of the equation by [tex]\frac{3}{2}[/tex] .

[tex]\frac{3}{2} . \frac{2}{3} . x = \frac{3}{2} . 5[/tex]

Simplify both sides of the equation.

~~~~

Simplify [tex]\frac{3}{2} . \frac{2}{3} . x .[/tex]

[tex]x = \frac{3}{2} . 5[/tex]

Multiply [tex]\frac{3}{2} . 5[/tex]

[tex]x = \frac{15}{2}[/tex]

The result can be shown in multiple forms.

Exact Form: [tex]x = \frac{15}{2}[/tex]

Decimal Form: [tex]x = 7.5[/tex]

Mixed Number Form: [tex]x = 7\frac{1}{5}[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

0.8413

Step-by-step explanation:

Find the z score.

z = (x − μ) / σ

z = (992 − 999) / 7

z = -1

Use a chart or calculator to find the probability.

P(Z > -1)

= 1 − P(Z < -1)

= 1 − 0.1587

= 0.8413

The required probability that a bottle has a volume greater than 992 mL is 0.84134. Option C is correct

Given that,
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and a standard deviation of 7 ml. The fill volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL, is to be determined

Probability can be defined as the ratio of favorable outcomes to the total number of events.

We use Z-statistic to find out the probability,

z = (x − μ) / σ

x = raw score = 992 mL
μ = population mean = 999 mL
σ = standard deviation
z = [992 − 999]/7
z = -1

P-value from Z-Table:

P(x<992) = 0.15866

P(x>992) = 1 - P(x<992) = 0.84134

Thus, the required probability that a bottle has a volume greater than 992 mL is 0.84134

Learn more about probability here:

brainly.com/question/14290572

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