A, B, and C are collinear points C is the midpoint of AB AC = 5x - 6 CB = 2x Find AB

Answer:

Part a

For this case n = 4. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506[/tex]

Part b

For this case n = 365. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776[/tex]

Step-by-step explanation:

We can use the future vaue formula for compound interest given by:

[tex] A= P(1+ \frac{r}{n})^{nt}[/tex]

Where P represent the present value, r=0.0675 , n is the number of times that the interest is compounded in a year and t the number of years.

Part a

For this case n = 4. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506[/tex]

Part b

For this case n = 365. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776[/tex]

Answer:

1

Step-by-step explanation:

g(-4) means what is the y value when x is -4.

Find x=-4, and when x=-4. y=1

Answer:

1

Step-by-step explanation:

Answer:

Rate of speed = 480 feet per minutes

Step-by-step explanation:

Given:

Distance covered by bike = 960 feet

Time taken to covered distance = 2 minutes

Find:

Rate of speed = ?

Computation:

⇒ Speed = Distance / Time

⇒ Rate of speed = Distance covered by bike / Time taken to covered distance

⇒ Rate of speed = 960 / 2

⇒ Rate of speed = 480 feet per minutes

Answer:

E) 0.99

Step-by-step explanation:

100 recruits x 0.4 chance of retiring as police officer = 40 officers

probability of being married at time of retirement = (1 - 0.25) x 40 = 30 officers

each new recruit will result in either 0, 1 or 2 new pensions

mean = µ = E(Xi) = (0 x 0.6) + (1 x 0.1) + (2 x 0.3) = 0.7

σ²  = (0² x 0.6) + (1² x 0.1) + (2² x 0.3) - µ² = 0 + 0.1 + 1.2 - 0.49 = 0.81

in order for the total number of pensions (X) that the city has to provide:

the normal distribution of the pension funds = 100 new recruits x 0.7 = 70 pension funds

the standard deviation = σ = √100 x √σ² = √100 x √0.81 = 10 x 0.9 = 9

P(X ≤ 90) = P [(X - 70)/9] ≤ [(90 - 70)/9] =  P [(X - 70)/9] ≤ 2.22

z value for 2.22 = 0.9868 ≈ 0.99

Answer:

h = p - l - w

Step-by-step explanation:

p = 4l + 4w + 4h       Divide l, w, and h by 4

p = l + w + h              Set the equation equal to h

h = p - l - w

Answer:

A just did it on edge<3

Answer:

Number of people

6

5

5

6

3

1

Step-by-step explanation:

All you had to do was the count how much numbers there were on the list.

Like there were 6 0s.

Answer:

Hope this helps

Step-by-step explanation:

6 people did 0 sit ups

5 people did 1 sit ups

5 People did 2 sit ups

6 people did 3 sit ups

3 people did 4 sit ups

1 person did 5 sit ups

Answer:

The median value in this set is -4.5

Step-by-step explanation:

Reorder the numbers from least to greatest

-28,-17,-8,-1,24,32

Then, since there is 6 digits in this data set there is no defined median value. In the numbers 1 to 8 there are 8 different numbers, the middle of 1 to 8 is 4.5. Then since were using the numbers -8,-1 the middle is -4.5

Answer:

The approximate probability that more than six students were born on Christmas day is P=0.105.

Step-by-step explanation:

This can be modeled as a binomial variable, with n=1460 and p=1/365.

The sample size n is the total amount of students and the probability of success p is the probability of each individual of being born on Christmas day.

As the sample size is too large to compute it as a binomial random variable, we approximate it to the normal distribution with the following parameters:

[tex]\mu=n\cdot p=1460\cdot (1/365)=4\\\\\sigma=\sqrt{n\cdot p(1-p)}=\sqrt{1460\cdot(1/365)\cdot(364/365)}=\sqrt{3.989}=1.997[/tex]

We want to calculate the probability that more than 6 students were born on Christmas day. Ww apply the continuity factor and we write the probability as:

[tex]P(X>6.5)[/tex]

We calculate the z-score for X=6.5 and then calculate the probability:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{6.5-4}{1.997}=\dfrac{2.5}{1.997}=1.252\\\\\\P(X>6.5)=P(z>1.252)=0.105[/tex]

Answer:

16.

Step-by-step explanation:

since given the radius and the formula of the circumference of a circle is 2pie*r

Answer:

107 meters

Step-by-step explanation:

Central angle = 123°

In radians

123° = 123π/180

123° = 2.147 radians

Putting in formula

S = r∅

S = (50)(2.147)

S = 107 meters

Answer:

Step-by-step explanation:

For a rectangular prism, a plane intersecting this prism produces a two dimensional figure as its cross section and in this case the cross section is a rectangle.

For a triangular prism, a plane intersecting this prism produces a two dimensional figure as its cross section and in this case the cross section is a triangle.

Answer:

Step-by-step explanation:

The formula to calculate the forecast could be determine by using the exponential smoothing method :

[tex]Ft = F(t-1) + \alpha [A(t-1) - F(t-1)][/tex]

Where ,Ft is the Forecast for period t

F(t-1) is the Forecast for the period previous to t

A(t-1) is the Actual demand for the period previous to t

[tex]\alpha[/tex] = Smoothing constant

To get the forecast for may and june   the above formula with [tex]\alpha =0.5[/tex] and april forecast of 500 will be used

For march

[tex]=500+0.5(520-500)\\\\=500+0.5\times20\\\\=500+10\\\\=510[/tex]

For April

[tex]=510+0.5(535-510)\\\\=510+0.5\times25\\\\=510+12.5\\\\=522.5[/tex]

For May

[tex]=522.5+0.5(550-5225)\\\\=522.5+0.5\times27.5\\\\=522.5+13.75\\\\=536.25[/tex]

So forecast for May = 536.25

Answer:

C.

Step-by-step explanation:

Volume of cylinder = πr²h

= (3.14)(4)(0.75)

= 9.4

Since she'll fill it half so

Amount of water to be filled = 4.7

Answer:

Hello!

I believe your answer is:

4a(b+2c)

Step-by-step explanation:

I hope this worked for you!  Good luck!

Answer:

[tex]\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]

Step-by-step explanation:

Volume of water in the tank = 1000 L

Let y(t) denote the amount of salt in the tank at any time t.

Initially, the tank contains 60 kg of salt, therefore:

y(0)=60 kg

Rate In

A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.

[tex]R_{in}[/tex] =(concentration of salt in inflow)(input rate of solution)

[tex]=(0.03\frac{kg}{liter})( 9\frac{liter}{min})=0.27\frac{kg}{min}[/tex]

Rate Out

The solution is mixed and drains from the tank at the same rate.

Concentration, [tex]C(t)=\dfrac{Amount}{Volume} =\dfrac{y(t)}{1000}[/tex]

[tex]R_{out}[/tex] =(concentration of salt in outflow)(output rate of solution)

[tex]=\dfrac{y(t)}{1000}* 9\dfrac{liter}{min}=0.009y(t)\dfrac{kg}{min}[/tex]

Therefore, the differential equation for the amount of Salt in the Tank  at any time t:

[tex]\dfrac{dy}{dt}=R_{in}-R_{out}\\\\\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]

Answer:

A

Step-by-step explanation:

Answer:

The answer here is A.

A) A is congruent to D.

A=

Step-by-step explanation:

AP E

Answer:

6 PM

Step-by-step explanation:

125 mg --- 300 mL

500 mg --- x mL

x = 500*300/125 = 1200 mL solution contains 500 mg

rate = 100 mL/h

1200 mL* 1h/100 mL = 12 h

6AM + 12 h = 6 PM

You need to stop infusion  at 6 PM

It is found that You need to stop infusion at 6 PM.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication.

125 mg = 300 mL

500 mg = x mL

x = 500*300/125

x = 1200 mL

Here solution contains 500 mg

The rate = 100 mL/h

1200 mL* 1h/100 mL = 12 h

6AM + 12 h = 6 PM

Therefore, You need to stop infusion at 6 PM.

Learn more about the unitary method;

https://brainly.com/question/23423168

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Answer:

Mean of the binomial distribution  μ = 82.68

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 106 diamonds

The probability that the diamonds fail to qualify as "gemstone grade

p = 78% =0.78

We will use binomial distribution

Mean of the binomial distribution

                                       μ = n p

                                       μ = 106 × 0.78

                                       μ = 82.68

conclusion:-

Mean of the binomial distribution  μ = 82.68

Answer:

1/18

Step-by-step explanation:

First you would add 1/2 and 1/2 to get 1 then you would divide it by 18 to get 1/18

Answer:

1/18

Step-by-step explanation:

plz mark me brainliest.

Answer:

1, 3,5

Step-by-step explanation:

Answer:

1,3,5

Step-by-step explanation:

Answer:

B:

Step-by-step explanation:

Measure of ARC AFB is 180°

Why?

This is because AB is a diameter.

Answer:

[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]

And replacing we got:

[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=2, p=1-0.16=0.84)[/tex]

The probability mass function for the Binomial distribution is given as:

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

Where (nCx) means combinatory and it's given by this formula:

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

And we can find this probability:

[tex] P(X \geq 1)[/tex]

And we can solve this probability like this:

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

And if we use the probability mass function we got:

[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]

And replacing we got:

[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]

Answer:

Step-by-step explanation:

Hello!

The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.

Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.

p the probability that the psychic identified the symbol on the cards correctly

You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01

The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:

p' ± [tex]Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]

Where  [tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex] is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:

Every time the psychic has to identify a card he can make two choices:

"Success" he identifies the card correctly

"Failure" he does not identify the card correctly

If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25

Let's say, for example, that the card has the star symbol.

The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25

And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75

So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.

The value of Z will be [tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]

Now using the formula you have to clear the sample size:

[tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]

[tex]\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p')}{n} }[/tex]

[tex](\frac{d}{Z_{1-\alpha /2}})^2 =\frac{p'(1-p')}{n}[/tex]

[tex]n*(\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')[/tex]

[tex]n = p'(1-p')*(\frac{Z_{1-\alpha /2}}{d})^2[/tex]

[tex]n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203[/tex]

To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.

I hope this helps!

Answer:

The sample size should be 6157

Step-by-step explanation:

Given that the margin of error (e) = ± 0.01 and the confidence (C) = 95% = 0.95.

Let us assume that the guess p = 0.25 as the value of p.

α = 1 - C = 1 - 0.95 = 0.05

[tex]\frac{\alpha }{2} =\frac{0.05}{2}=0.025[/tex]

The Z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is 1.96. Therefore [tex]Z_\frac{\alpha }{2}=Z_{0.025}=1.96[/tex]

To determine the sample size n, we use the formula:

[tex]Z_{0.025}*\sqrt{\frac{p(1-p)}{n} }\leq e\\Substituting:\\1.96*\sqrt{\frac{0.2(1-0.2)}{n} } \leq 0.01\\\sqrt{\frac{0.2(0.8)}{n} }\leq \frac{1}{196}\\\sqrt{0.16} *196 \leq \sqrt{n}\\78.4\leq \sqrt{n}\\ 6146.56\leq n\\n=6157[/tex]

Answer:

11453

Step-by-step explanation:

The puzzle are: 21, 30, 15, 333.

Clock:

Clock time=9 o'clock+9 o'clock+3 o'clock

Clock time=21

Calculator:

Calculator 1=1+2+3+4=10

Calculator 2=1+2+3+4=10

Calculator 3=1+2+3+4=10

Calculator=10+10+10

Calculator=30

Bulb:

The 3 bulb has 5 light each which represent the brightness of the 3 bulb.

Bulb=15+(15-15)

Bulb =15+0

Bulb=15

Fourth puzzle

Clock+Calculator×Bulb

9 o'clock+(1+2+2+4)× [3 bulb(3 bulb×4 light)]

9+9×(3×12)

Apply BODMAS

9+9×36

9+324

=333

Inconclusion the puzzle are: 21, 30, 15, 333.

Learn more about puzzle here:https://brainly.com/question/16999211

Answer:

Top right option

Step-by-step explanation:

Answer:

10 people

Step-by-step explanation:

Count the x's for more than 1 scarf, which is 2 or 3 scarfs

2 = 9

3 =1

total = 10

Answer:

The peak inventory will be 2 sales days of hamburguers, which is equivalent to 7,000 lbs. As they are consumed in 2 days, the average inventory is 3,500 lbs.

Step-by-step explanation:

If the meat should be no more than two days old on average when used, the stock of hamburguer in the refrigerator has to be at most the equivalent to 2 day of sales.

The "2 days old" represents the inventory turnover.

If we use all the hamburguers in the refrigerator and refill inmediatly, the average inventory is:

[tex]\bar I=\dfrac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\\\\\\bar I=\dfrac{2*3,500+0}{2}=3,500[/tex]

The peak inventory will be 2 sales days of hamburguers, which is equivalent to 7,000 lbs. As they are consumed in 2 days, the average inventory is 3,500 lbs.

Answer:

The null hypothesis is that all the different teaching methods have the same average test scores.

H0: μ1 = μ2 = μ3 = μ4 = μ5

The alternative hypothesis is that at least one of the teaching methods have a different mean.

Ha: at least one mean is different. (μ1 ≠ μi)

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above, let μ represent the average test scores for the teaching methods:

The null hypothesis is that all the different teaching methods have the same average test scores.

H0: μ1 = μ2 = μ3 = μ4 = μ5

The alternative hypothesis is that at least one of the teaching methods have a different mean.

Ha: at least one mean is different. (μ1 ≠ μi)