Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.

CORRECT (SELECTED)
Josiah's distance from the starting line at a time when he is behind Chana.

Explanation: Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance.

Using the hypergeometric distribution, the probabilities are given as follows:

a) 0.0333 = 3.33%.

b) 0.5 = 50%.

c) 0.8333 = 83.33%.

d) 0.9667 = 96.67%.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

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

The parameters are:

The values of the parameters are:

N = 10, n = 3, k = 4.

Item a:

The probability is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,10,3,4) = \frac{C_{4,3}C_{6,0}}{C_{10,3}} = 0.0333[/tex]

Item b:

The probability is P(X = 1), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 1) = h(1,10,3,4) = \frac{C_{4,1}C_{6,2}}{C_{10,3}} = 0.5[/tex]

Item c:

The probability is:

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

In which:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,10,3,4) = \frac{C_{4,0}C_{6,3}}{C_{10,3}} = 0.1667[/tex]

Then:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1667 = 0.8333[/tex]

Item d:

The probability is:

[tex]P(X \leq 2) = 1 - P(X = 3)[/tex].

Considering item a:

[tex]P(X \leq 2) = 1 - P(X = 3) = 1 - 0.0333 = 0.9667[/tex]

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Let [tex]O[/tex] be the random variable for the number of bad oranges picked out. Then

[tex]P(O=o) = \dfrac{\dbinom6{3-o} \dbinom4o}{\dbinom{10}3}[/tex]

if [tex]o\in\{0,1,2,3\}[/tex] and zero otherwise, where

[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]

is the so-called binomial coefficient.

(a) Of the 6 good oranges, you pick 0. Of the 3 bad oranges, you pick 3. Of the 10 total oranges, you pick 3. So the probability of picking out all bad oranges is

[tex]P(O=3) = \dfrac{\dbinom60 \dbinom43}{\dbinom{10}3} = \boxed{\dfrac1{30}}[/tex]

(b) By similar reasoning, the probability of drawing exactly 1 bad orange is

[tex]P(O=1) = \dfrac{\dbinom62 \dbinom41}{\dbinom{10}3} = \boxed{\dfrac12}[/tex]

(c) "At least 1 bad orange" means you pick out 1, 2, or 3 bad oranges. These events are mutually exclusive, and we already know the probabilities of picking out exactly 1 or all 3 bad oranges. The remaining probability of drawing 2 bad oranges is

[tex]P(O=2) = \dfrac{\dbinom61 \dbinom42}{\dbinom{10}3} = \dfrac3{10}[/tex]

so the overall probability of drawing at least 1 bad orange is

[tex]P(O\ge1) = P(O=1)+P(O=2)+P(O=3) =\dfrac1{30} + \dfrac3{10} + \dfrac12 = \boxed{\dfrac56}[/tex]

(d) I assume you mean "at most 2 bad oranges," meaning you pick out 0, 1, or 2 bad oranges. Again, these events are mutually exclusive, and the probability of picking out no bad oranges is

[tex]P(O=0) = \dfrac{\dbinom63 \dbinom40}{\dbinom{10}3} = \dfrac16[/tex]

hence the probability of drawings at most 2 bad oranges is

[tex]P(O\le2) = P(O=0) + P(O=1) + P(O=2) = \dfrac16 + \dfrac12 + \dfrac3{10} = \boxed{\dfrac{29}{30}}[/tex]

Answer:

231,000

Step-by-step explanation:

In the ratio of 11:13, if you plug in 13, the corresponding value is 11.

Dividing 11 by 13 shows that if you also multiply 13 by 0.846 (Rounded) it also equals 11.

So multiplying 0.846 by the original price of 273,000, we get 231,000.

The new selling price of the car will be 231,000. Then the correct option is A.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The original selling price of a used automobile is N273,000. The price is dropped by the dealer by a ratio of 11:13.

The new selling price of the car will be given as,

Selling price = 273,000 x 11/13

Selling price = 21,000 x 11

Selling price = 231,000

Thus, the correct option is A.

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The number of spoons that can be purchased is 11, whereas the equation is given as 8x + 10 ≤ 100

An equation is an expression that shows the relationship between two or more variables and numbers.

The cost of each spoon is $8, hence A = 8. The cost of painting is 10, hence B = 10. Joshua can spend at most 100$, C = 100

8x + 10 ≤ 100

x ≤ 11.25

The number of spoons that can be purchased is 11, whereas the equation is given as 8x + 10 ≤ 100

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Answer:

92 spoons can be purchased.

Step-by-step explanation:

10x + 8 ≤ 100

10x + 8 ≤ 100

8 - 8 10x 100 - 8

10x ≤ 92

x = 1/5

10 x 1/5 = 92.

<---------------------------------------------------------------------------------------------------------->

 <----------------------------------------------------0---------------------------- 92

The statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have Ken's statements are shown in the table:

Angle AOC = Angle BOD (given)

Angle AOB + Angle BOC = Angle BOC + Angle COD   (angle addition postulate)

Angle AOB = ANgle COD (subtraction property of equality)

Ken wrote direct proof using deductive evidence.

As we can in betty's proof:

Betty wrote an indirect proof using contradiction.

Thus, the statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.

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Answer:

x + 3

Step-by-step explanation:

x = Anna's age

y = John's age

z = Tamara's age

y = x + 1

z = x - 2

the expression for the sum of Anna's and John's age minus Tamara's age is

x + y - z

and when we use the equations above to simplify that :

x + (x + 1) - (x - 2) = x + x + 1 - x + 2 = x + 3

Answer:

y = 6x+9

Step-by-step explanation:

Equations that are parallel have the same slope

y = 6x+7 is written in slope intercept form where the slope is 6 and the y intercept is 7

The lines will have a slope of 6

The point (0,9) is the y intercept because the x value is 0

We can write the equation in slope intercept form y = mx+b

y = 6x+9

Answer:

Hello! The answer is y = 6x + 9.

Step-by-step explanation:

When lines are parallel, they will have the same slope but a different y-intercept.

The y-intercept, in this case, would be (0, 9) since the x-coordinate equals 0. This leaves us with 9 as the y-intercept.

Our slope-intercept form equation will be written as:

y = 6x + 9

The topsoil will be 4.05 inches deep

From the question, we are to determine how many inches deep the topsoil will be

From the given information,

The volume of the topsoil = 1 cubic yard

Convert to cubic feet

1 cubic yard = 27 cubic feet

∴ The volume of the topsoil = 27 cubic feet

Then,

The depth of the topsoil will be = 27/(8 ×10)

Depth of topsoil = 27/80

Depth of topsoil = 0.3375 foot

Now, convert to inches

1 foot = 12 inches

∴ 0.3375 foot = 0.3375×12 inches

= 4.05 inches

Hence, the topsoil will be 4.05 inches deep

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Answer:

5621 years

Step-by-step explanation:

Plug everything in first.

[tex]N=N_0e^{-kt}\\\\\implies 0.57 = e^{-0.0001t}\\\\\implies\ln \left(0.57\right)=-0.0001t\\\\t=-\frac{\ln \left(0.57\right)}{0.0001}[/tex]

Round to closest amount of years = 5621 years

The statement that describes a key feature of function g if g(x) = f(x + 4) is C. horizontal asymptote of y = 0.

It should be noted that a function is an expression that shows the relationship between the variables.

In this case, the statement that describes a key feature of function g if g(x) = f(x + 4) is that the horizontal asymptote of y = 0.

The horizontal asymptote is vital for guiding the variables

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The coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)

From the question, we are to graph the given equations.

The graph of the equations is attached below.

In the graph, we can observe that the coordinates of the point of intersection of the is (2, 3)

Hence, the coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)

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The Income Statement for Nascar Motors in April and May 2017 under Throughput Costing is given as attached.

This refers a costing technique, also known as super-variable costing, which solely takes direct materials into account when calculating product costs.

The other expenses are all classed as period costs and are all deducted from income in the time period in which they are spent.

It is to be noted that Throughput costing has the lowest operating income in April while having the greatest operating income in May.

More so than either absorption or variable costing, throughput costing emphasizes sales as the source of operational income. See the attached.

It is to be noted that production that doesn't result in a commensurate sale in the same time period is penalized under throughput costing.

When compared to variable costing, costs that are variable with regard to production but are not direct materials are expensed in the period of incurrence.

In contrast to variable costing or absorption costing, throughput costing offers less of motivation to create inventory.

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Answer:

16

Step-by-step explanation:

The outlier in the given dataset is "16".

Given is a data set 69, 16, 79, 80, 82, we need to determine the outliners of the set,

To identify outliers in a dataset, we generally use a statistical method such as the z-score or the IQR (interquartile range).

Since, the provided dataset is small with only five values, we can manually identify the outliers by observing the data.

An outlier is a value that significantly deviates from the rest of the dataset.

Let's examine the given dataset:

69, 16, 79, 80, 82

To identify outliers, we can consider any data points that are notably different from the others.

In this case, it seems that the value "16" is considerably lower than the other values.

Let's label it as a potential outlier.

Therefore, the outlier in the given dataset is "16".

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Answer:

The Prime Factorization of 220 is 22 × 51 × 111.

Step-by-step explanation:

Factors of 220 are integers that can be divided evenly into 220. It has total 12 factors of which 220 is the biggest factor and the prime factors of 220 are 2, 5, 11. There for, the  Prime Factorization of 220 is 22 × 51 × 111.

Answer:where are the options ???

Step-by-step explanation:

Answer:

Product 1

Step-by-step explanation:

Got it

The expected value of your bet will be the negative $16.27 that mean loses.

Binomial distributions consist of n independent Bernoulli trials.

The expected value will be

E(X) = np

Suppose that you and a friend are playing cards and decide to make a bet.

If you draw two face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards replacing the first card, you win $50.

Otherwise, you pay your friend $20.

Then the probability of winning will be

p = (12 / 52)(12 / 52)

p = 9 / 169

Then the probability of loosing will be

q = 1 – p

q = 1 – 9/169

q = 160 / 169

Then the expected value will be

E(x) = (9/169) x 50 + (160/169) x (-20)

E(x) = -$16.27

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Using substitution, the result of the indefinite integral is:

[tex]3\ln{(1 + x^{\frac{1}{3}})} + C[/tex]

The integral is:

[tex]\int \frac{1}{x^{\frac{2}{3}}(1 + x^{\frac{1}{3}})} dx[/tex]

The substitution is:

[tex]u = 1 + x^{\frac{1}{3}}[/tex]

Then the derivative is:

[tex]du = \frac{1}{3}x^{-\frac{2}{3}} dx[/tex]

ttex]dx = 3dux^{-\frac{2}{3}}[/tex]

Hence the integral is:

[tex]\int \frac{1}{x^{\frac{2}{3}}(1 + x^{\frac{1}{3}})} dx[/tex]

[tex]\int \frac{1}{x^{\frac{2}{3}}u} \times 3dux^{-\frac{2}{3}}[/tex]

[tex]\int \frac{3du}{u}[/tex]

[tex]3\ln{u} + C[/tex]

Returning to x:

[tex]3\ln{(1 + x^{\frac{1}{3}})} + C[/tex]

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Step-by-step explanation:

x/7 ≥ -6

we rewrite it as :

x/7 = -6

by cross multiplication

x = -42

In order words:

x ≥ -42

Hope this helps

Good luck ✅

Probability the selected number is even is 7/15

Probability the selected number is a multiple of 4 is 1/5

Probability the selected number is prime = 2/5

Probability is the likelihood of an event happening or an event not happening.

When it is certain an event would happen the probability is 1.

Probability can be independent or mutually exclusive.

Analysis:

Required outcome

A = {2, 4, 6, 8, 10, 12, 14} (even numbers)

Total entry = 7

Total Sample = 15

P(even numbers) = 7/15

B (multiples of 4) = {4, 8, 12}

Total entry = 3

P(B) = 3/15 = 1/5

C(prime numbers) = {2, 3, 5, 7, 11, 13}

Total entry = 6

P(C) = 6/15

P(A and C) = 0.

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It can be concluded that ΔWXY is equivalent to ΔBCD by the SAS rule because the corresponding sides and corresponding angle are congruent. Option D

SAS congruency states that  two triangles are said to be congruent if any two sides or angle between the sides of one triangle are equal to the corresponding two sides and also the angle between the sides of the second triangle.

Thus, it can be concluded that ΔWXY is equivalent to ΔBCD by the SAS rule because the corresponding sides and corresponding angle are congruent. Option D

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Answer:

B. No, because the corresponding congruent angles listed are not the included angles.

Step-by-step explanation:

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{y = 4/11}[/tex]

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Given: [tex]\textsf{2y + 14 = 6(4y + 1)}[/tex]

Find:  [tex]\textsf{Solve for y}[/tex]

Solution:  In order to solve for y we need to distribute the ride side of the expression, simplify, subtract 14 from both sides, subtract 24y from both sides, and divide both sides by -22.

Distribute and simplify

Subtract 14 from both sides

Subtract 24y from both sides

Divide both sides by -22

Therefore, the expression simplifies down to y = 4/11.

The equivalent pair of the given expression is; [4.8] and [3.21]

Floor function states that the greatest integer that is less than or equal to x. It is represented by:  ⌊ x ⌋.

Ceiling function states that the least integer that is greater than or equal to x. It is represented by ⌈ x ⌉.

Kareem wrote the expressions;

[3.2] [2.7] [2.9] [4.8]

By definition above;

[3.2] = 4

[2.7] = 2

[2.9] = 3

[4.8] = 4

Thus, the equivalent pair is [4.8] and [3.2]

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Answer:

d.) 226.2 cubic inches

Step-by-step explanation:

The soup pot is in the shape of a cylindrical.

And

[tex]\sf Volume \ of \ cylinder= \pi (radius)^2 (height)[/tex]

Here given:

So,

[tex]\sf Volume \ of \ pot= \pi (3)^2 (8)[/tex]

[tex]\sf Volume \ of \ pot= 72\pi \ in^3[/tex]

[tex]\sf Volume \ of \ pot= 226.2 \ in^3[/tex]

Answer: Width = 15cm

              L = 31cm

Step-by-step explanation:

P = 92 cm

L = 1 + 2W

P = 2L + 2W

P = 2(1+2W) + 2W

P = 2+4W+2W

P = 2 + 6W

92cm = 2 + 6W

subtract 2 on both sides to cancel the 2 on the right side.

90cm = 6W

W = 90/6

Width = 15cm

L = 1+2W

L = 1 + 30cm

L = 31 cm

Verification:

P = 2L+2W

P = 2(31)+2(15)

P = 62+30

P = 92cm

Hope I Helped!

Answer:

P = 2(L + W) = 2L + 2W (first part)

L = 2W + 1 (second part)

Step-by-step explanation:

L = length of rectangle
W = width of rectangle
P = perimeter of rectangle = 2 * (L + W)
So P = 2(L + W) = 2L + 2W  (1)

It is also given that length is 2 * width + 1

So we get the equation

L = 2W + 1 for L in terms of W  (2)

This question does not ask you to compute L and W but if you wanted to do that use the following steps
Substitute for L from equation 2 to equation 1 giving
P = 2(2W+1) + 2W = 4W + 2 + 2W = 6W + 2

We know P = 92

So 6W + 2 = 92
Subtracting 2 from both sides we get 6W = 90
Dividing both sides by 6 gives us W = 15
and L = 2 * 15 + 1 = 31

We can check this by finding the perimeter from L and W
perimeter = 2(L+W) = 2(31 + 15) = 2 (46) = 92 which matches the data in the question

6.5 s  take the projectile to hit the ground.

A projectile is any object thrown into space upon which the only acting force is gravity.

Given:

speed = 25 m/s

h(t) = -5t² + 25t  + 70

height = 70 m

Time to reach maximum height

( u sin90)/2g

= 25/2*9.8

= 1.275s

Max height = u²Sin²[tex]\theta[/tex]/g

=25*25/9.8

=63.775

So, total height=63.775 + 70 = 133.775 m

Now, time to fall back to the ground

h = ut+(1/2)gt²

t² = (h- ut)2/g

u=0

H= 133.775 m

(133.775*2)/9.8= t²

t² = 27.3010

t= 5.225 s

Total time taken to hit ground

= 5.225 + 1.275

= 6.5 s

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Answer: [tex]g(x)=\left|\frac{x}{5} \right|[/tex]

Step-by-step explanation:

See atached image.

Answer:

A. 2 and-6

Step-by-step explanation:

Like terms are terms that contain the same variables raised to the same powers. In other words, they have the same variables with the same exponents.

So in option A, we have the terms 2 and -6. These terms are not like terms because they do not have the same variables.

[tex]3y \geqslant 13 - 9[/tex]

[tex]3y \geqslant 4[/tex]

[tex]y \geqslant \frac{4}{3} [/tex]

[tex]3y \leqslant 13 - 1[/tex]

[tex]3y \leqslant 12[/tex]

[tex]y \leqslant 4[/tex]

[tex] \frac{4}{3} \leqslant y \leqslant 4[/tex]

Answer:

:)\

Step-by-step explanation: