Khan Academy Question

Probability has to do with the possibility that an event may or may not happen.

The term probability has to do with the possibility that an event may or may not happen. The value of probability always ranges from zero to one.

Now;

Total number of fishes = 32 + 14 + 10 + 3 = 59

a) probability of catching a bass and then a carp = 32/59 * 10/59 = 320/3481

b) probability of catching two consecutive bull sharks= 3/59 * 3/59 = 9/3481

c) probability of catching  a fluke and then any different type of fish 14/59 * (32/59 + 10/59 + 3/59) = 14/59 * 45/59 = 630/3481

d) probability of catching  a bass, another bass, and a bull shark =  32/59 * 32/59 * 3/59 = 3072/205379

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Answer:

Step-by-step explanation:

d

Separate the variables.

[tex](x^2+1) \dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x^2+11} \, dx[/tex]

Integrate both sides. On the right, substitute [tex]u=x^2+11[/tex] and [tex]du=2x\,dx[/tex].

[tex]\displaystyle \int \frac{dy}y = \int \frac x{x^2+11}\,dx = \frac12 \int \frac{du}u[/tex]

[tex]\ln|y| = \frac12 \ln|u| + C[/tex]

[tex]\ln|y| = \ln\left(\sqrt{x^2+11}\right) + C[/tex]

[tex]e^{\ln|y|} = e^{\ln\left(\sqrt{x^2+11}\right)+C}[/tex]

[tex]\boxed{y = C\sqrt{x^2+11}}[/tex]

Using separation of variables, the solution to the differential equation is:

y = ksqrt(x² + 11)

In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.

In this problem, the differential equation is:

(x² + 11)y' = xy

Applying separation of variables, we have that:

y'/y = x/(x² + 11)

[tex]\int \frac{y^{\prime}}{y} = \int \frac{x}{x^2 + 11}[/tex]

[tex]\ln{y} = \frac{\ln{x^2 + 11}}{2} + K[/tex]

[tex]\ln{y} = \ln{(x^2 + 11}^{\frac{1}{2}}) + K[/tex]

[tex]\ln{y} = \ln{\sqrt{x^2 + 11}} + K[/tex]

Hence the solution is:

y = ksqrt(x² + 11)

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By testing the hypothesis we can conclude that the bag does not contain 11 kg of food.

Given mean of 10.6 kg, population standard deviation of 0.6 and sample size of 25.

We are required to find whether the company is right in saying that their bags contain 11 kg of food.

First we have to make hypothesis.

[tex]H_{0}[/tex]:μ≠11

[tex]H_{1}[/tex]:μ=11

We have to use t statistic because the sample size is less than 30.

t=(X-μ)/s/[tex]\sqrt{n}[/tex]

We will use s/[tex]\sqrt{n}[/tex]=0.6 because we have already given population standard deviation of weights.

t=(11-10.6)/0.6

=0.4/0.6

=0.667

Degree of freedom=n-1

=25-1

=24

T critical at 0.05 with degree of freedom 24=2.0639

T critical at 0.05 with degree of freedom is greater than calculated t so we will accept the null hypothesis.It concludes that the bags donot contain 11 kg of food.

Hence by testing the hypothesis we can conclude that the bag does not contain 11 kg of food.

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The effect of  Edible a portion Price on your profit margin , if we only use the as purchased price to determine our cost and selling price is that it will maximize the profit because it will account for every part of the production.

The portion cost can be calculated by multiplying the cost of a usable kg  with the  portion size.

This can be represented as : portion cost = (portion size x cost of usable kg)

It should be noted that Edible portion (EP)  serves as the  portion of food  which will be given top the   customer after  the preparation.

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Answer:

Step-by-step explanation:

❄ Hi there,

the first step in solving this inequality is

[tex]\sf{\dfrac{4}{7}x\times7=21\times7}[/tex]. Look what happens on the left side!

[tex]\sf{4x=147}[/tex]

Multiplying both sides of an equation, or inequality, by the fraction's denominator, is a nice little trick when you need to get rid of fractions to solve in terms of a variable.

Finish solving for x by dividing both sides by 4 –

[tex]\sf{x=\dfrac{147}{4}}[/tex]

❄

The percentage when Potiphar woke up late is 14.4%.

From the information, it was stated that Potiphar takes a horse and buggy to work everyday. In order to come on time, he must wake up promptly at 6.30am and then hop on the buggy and that anytime he wakes up late or the horse was in traffic, he will be late.

It was further illustrated based on the information given in the question that he was late 24.4% of the time and the horse was in traffic for 10% of the time.

Therefore, the percentage when he woke up late will be gotten by simply subtracting the percentages that we have above. This will be illustrated below:

= 24.4% - 10%

= 14.4%

Therefore, the percentage when Potiphar woke up late is 14.4%.

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The expression that represents the area of the new room is (c) 3.5s^2 + 5.25s

The given parameters are:

Wall =Square

Length = s

When the wall of the square room is torn down and rebuilt, the area of the new room is represented by 1.75s(2s + 3).

This means that

Area= 1.75s(2s + 3)

Expand the expression

Area= 1.75s * 2s + 1.75s * 3

Evaluate the products

Area= 3.5s^2 + 5.25s

This means that the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s

Hence, the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s

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Answer: 148 degrees

Step-by-step explanation:

The total measure of all exterior angles of a convex pentagon is 360 degrees.

If four of them equal 53 degrees then all those together is 212 degrees

53 times 4 = 212

Then you would just subtract 212 from 360 to see the measure of the last exterior angle. Which is 148 degrees!

Hope this helps :)

The odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76.

An odds ratio is a measure of the strength of an association with the exposure and outcome.

The odds ratio can be calculated by dividing the odds of the first group (exposure) by the odds of the second group (outcome).

                             Flies      Does not fly     Total

Long beak               11               7                     19

Not a long beak      3              13                     15

Total                       14             20                    34

Probability of long beaks flying = 0.79 (1/14)

Probability of not having long beaks flying = 0.21 (3/14)

Odds ratio = 3.76 (0.79/0.21)

Thus, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76, showing greater odds of association.

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Complete question

Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly? Round your answer to two decimal places.

Long beakNot a long beakTotalFlies11719Does not fly31315Total142034

The volume of the cone illustrated will be 117.2 unit³.

From the information illustrated, the glass inform of a the frustrum of a cone has the dimensions: radius 4cm and a height of 7cm.

It should be noted that the volume of a cone is calculated as:

= 1/3 πr²h.

where,

π = 3.142

r = radius = 4cm

h = height = 7cm

In this case, since we know the values of the dimensions, then we can calculate the volume. This will be:

= 1/3πr²h

= 1/3 × 3.14 × 4² × 7

= 117.2 unit³

Therefore, the volume of the shape is 117.2 unit³.

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Complete question:

A glass inform of a the frustrum of a cone has the following dimensions: radius 4cm and a height of 7cm. Calculate the volume of the shape.

Two or more triangles are congruent if on comparison, they have equal lengths of sides, and measure of angles.

Therefore, the required proofs for each question are shown below:

Problem 1:

Congruent triangles are triangles with equal lengths of corresponding sides and measures of internal angles.

Thus,

                     STATEMENT                          REASON

1. <NMQ ≅ <NPQ                            Any point on a perpendicular bisector      

                                                        makes equal measure of angle with the

                                                        two ends of the line segment.

2. NQ ⊥ MP                                     Definition of a line.

3. MQ ≅ PQ                                     Equal segments of a bisected line.

4. MN ≅ PN                                     Any point on a perpendicular bisector    

                                                        is at the same distance to the

                                                        two ends of the line segment.

5. <MNQ ≅ <PNQ                           Equal measure of the bisected angle.

Problem 2:

A line segment is the shortest distance between two points.

            STATEMENTS                    REASONS

1. m<PSR  ≅ m<PSQ                A perpendicular bisector is always at a right  

                                                  angle to the bisected line segment.

2. m<RPS ≅ m<QPS                 Equal measure of the bisected angle.

3. RS ≅ QS                                Property of a bisected line segment.

4. PR ≅ PQ                                Any point on a perpendicular bisector    

                                                  is at the same distance to the two ends of  

                                                 the line segment.

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Answer: 10204 millimeters

Step-by-step explanation: A gallon = 3875 mm. A quart is 946. 946x 3 = 2838. A pint is around 473 mm which, when multiplied by 7, is 3311. Finally, there are 6 ounces which are approximately 30 mm. 6x30 = 180. We add all of this up : 3875 + 2838+ 3311 + 180 = 10204.

The amount of the loss exists 1350.

Amount of Loss means an amount equivalent to the outstanding balance of the principal amount, less any amounts recognized by perfecting rights under a security agreement, together with such interest as the executive director shall permit, to a maximum of such interest as may be permitted by rule.

Given: Mr. Black purchased a television set for $450.00. He subsequently sold the television set at a defeat of 30%.

From the given information, we get

[tex]$4500\cdot \frac{30}{100}[/tex]

simplifying, we get

[tex]$4500\cdot \frac{30}{100}[/tex]

= 1350

Therefore, the amount of the loss exists 1350.

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P11 equals  769.417 and general formula is 19*(1.4)^(n)

Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself

The growth rate is .4 per time period.

the exponential growth model is f = p * (1 + .4) ^ n

f is the future value.

p is the present value.

r is the growth rate per time period.

n is the number of time periods.

in p0, n = 0

in p11, n = 11

you are given that p0 = 19

in the formula, that becomes f = 19 * (1 + .4) ^ 0 = 19 * (1.4) ^ 0 = 19.

the formula for p1 becomes f = 19 * (1 + .4) ^ 1 = 19 * (1.4) ^ 1 = 26.6

the formula for p11 becomes f = 19 * (1 + .4) ^ 11 = 19 * (1.4) ^ 11 = 769.417

the formula for pn becomes = 19*(1.4)^(n)

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Answer:

five-hundredths

Step-by-step explanation:

The focal length of the given ellipse is given as (±6, 0)

An ellipse is defined as a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant or when a cone is cut by an oblique plane which does not intersect the base.

The standard equation of an ellipse is expressed as;

x^2/a^2 + y^2/b^2 = 1

The formula for calculating the focus of the ellipse is given as:

c^2 = b^2 - a^2

Given the equation of an ellipse

(x-7)^2/64 + (y-5)^2/100 = 1

This can also be expressed as:

(x-7)^2/8^2 + (y-5)^2/10^2 = 1

Comparing with the general equation

a = 8 and b = 10

Substitute

c^2 = 10^2 - 8^2

c^2 = 100 - 64

c^2 = 36

c = 6

Hence the focal length of the given ellipse is given as (±6, 0)

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Answer:

y = 20x + 200

Step-by-step explanation:

The 200 is the constant.  It is only added once, but the monthly deposits are added at 20 every month.  

After 1 month:

y = 20x + 200

y = 20(1) + 200

y = 20 + 200

y =220       money deposited.

After 2 months:

y = 20x + 200

y = 20(2) + 200

y = 40 + 200

y =240 money deposited.

After 3 months:

y = 20x + 200

y = 20(3) + 200

y = 60 + 200

y = 260  money deposited

And so on, and so on, and so on...

Answer:

2 Inches or ~1.43 Inches

Step-by-step explanation:

2 Inches if it's not including the spacing before the first "E" and after the "S", ~1.43 Inches if it's including the spacing.

You would get 2 Inches since if each letter is 10 inches (total 6 letters), that would be 60 inches. There are 5 total spaces in between all the letters. 70 Inches(Banner size) - 60 Inches (total letter size) = 10 Inches, divided equally within the 5 spaces. That would equal 2 :)

You also get ~1.43 Inches by doing the same process as the one shown above^ (that is if you're including the spacing before and after the word)

:)

Using the normal distribution, the probability is given as follows:

P(x≤81) = 0.0158.

Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

For this problem, the proportion and the sample size are given by:

p = 0.000412, n = 250178

Hence the mean and the standard deviation for the approximation are given by:

The probability that x is of 81 or less than the p-value of Z when X = 81.5, accounting for continuity correction, hence:

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

[tex]Z = \frac{81.5 - 103.1}{10.15}[/tex]

Z = -2.13

Z = -2.13 has a p-value of 0.0158.

Hence:

P(x≤81) = 0.0158.

Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.

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Answer:

76 sodas

Step-by-step explanation:

152 divided by 2

Answer: 76 sodas

Step-by-step explanation:

To find the sodas, use the data you see. Bottles of water are twice the sodas. So divided water by 2 to get the sodas.
152 ÷ 2 = 76 ( sodas ) . Hope it helps !

Answer:

120 students don't have social media accounts

Step-by-step explanation:

Whether the sample is representative:

Estimate: [tex]\frac{3}{75} (3000)=\frac{9000}{75} =120[/tex]

Hope this helps

Answer:

a) (1,6 x 150)/100 = 2,4 dollars

b) (11,3 x 950)/100 = 107,35 dollars

c) (0,29 x 2000)/100 = 5,8 dollars

The future value interest earned semiannually at a  compound rate of 4% is $7598.89.

To calculate the future value in interest earned, we use the of compound interest

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Formula:

Where:

From the question,

Given:

Substitute the values above into equation 1

Hence, the future value interest earned is $7598.89.

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Answer:

Step-by-step explanation:

add both the equations then you will get

3x^3-x^2+2

but in the standard form there should be an x^1 term or x term since there is no term like that we write it as 0x

so the equation will be

3x^3-x^2+0x+2

Answer:

The linear function for the given pts. will be

[tex]y = \frac{ - 22}{3}x + 15[/tex]

Step-by-step explanation:

Hello!

[tex]first \: find \: the \: slope \: for \: the \: two \: pts. \\ m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{(15 - ( - 7))}{(0 - 3)} where \: y2 = 15 \\ y1 = - 7 \\ x2 = 0 \\ x1 = 3 \\ m = \frac{ - 22}{3} \\ thus \: y = mx + b \: \: solve \: for \: b \: using \: one \: of \: the \: two \: points \\ lets \: take \: the \: second \: point \\ y = mx + b \\ 15 = \frac{ - 22}{3} (0) + b \\ b = 15 \\ therefore \: substitute \: this \: value \: to \: get \: the \: \\ y = \frac{ - 22}{3} x + 15[/tex]

Answer:

Step-by-step explanation:

<E = <T                                Given

M is the midpoint of TE      Given

TM = ME                               Definition of a  midpoint

<TMI = <RME                        Property of Vertically Opposite Angles

ΔTMI = ΔRME                       ASA = ASA

MI = ME                                 Corresponding parts of Congruent triangles                                    are Congruent

answer:                              reasoning:

<E = <T                                given

M is the midpoint of TE      given

TM = ME                               definition of a  midpoint

<TMI = <RME                        property of Vertically Opposite Angles

ΔTMI = ΔRME                       ASA = ASA

MI = ME                                 corresponding parts of congruent triangles                                    are Congruent

hope this helps!