Use Conditional Probability Notation to Describe Events Question Let M be the event that a randomly chosen student passes a math test. Let S be the event that a randomly chosen student studies every day. Identify the answer which expresses the following with correct notation: The probability that a randomly chosen student studies every day, given that the student passes a math test Select the correct answer below: O P(MS) OPM AND S) O P(S) AND P(M) O P(SM)

The value of x is 0. This means that [tex]8/10 = 16/20 = 4x+6/4x+11[/tex], so the corresponding sides of triangles abc and def have the same ratio.

The similarity of two triangles can be determined by the ratio of their corresponding sides. In the case of triangles abc and def, the ratio of corresponding sides is [tex]8/10 = 16/20 = 4x+6/4x+11[/tex].

To calculate the value of x, we can use the first two ratios and cross-multiply. With 8/10 = 16/20, we get 8*20=16*10, which simplifies to 160=160. Therefore, the first two ratios are equal.

To calculate the value of x using the third ratio, we can use the same method. With 4x+6/4x+11, we get ([tex]4x+6)*(4x+11)=4x^2+44x+66[/tex]. This simplifies to [tex]4x^2+44x+66=4x^2+44x+66[/tex], so the third ratio is also equal.

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Complete question:

What is the value of x in the ratio 8/10 = 16/20 = 4x+6/4x+11?

According to the graph, the true statement is the population will increase more each year than the previous year. The Option B is correct.

in geography context, a population growth means the increase in the number of humans on Earth. In human history, the population size was relatively stable. But with innovation and industrialization, energy, food, water, and medical care became more available and reliable.

On this graph, we can observed how the population increases from 80,000 to 100,000, 120,000, 140,000, 160,000, 180,000, 200,000,  220,000. 240,000, 260,000 and 280,000 on the Y-Axis. Therefore, the statement that population will increase more each year than the previous year is true.

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The exponential function passing through the points (1960, 179323175) and (2010, 308745538) is given as follows:

y = 0.1(1.01092581)^x.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which the coefficients a and b are explained as follows:

The points for this problem are given as follows:

(1960, 179323175) and (2010, 308745538).

Considering that between 1960 and 2010 there is an increase of 50 in the input, the parameter b is obtained as follows:

b^50 = 308745538/179323175

b = (308745538/179323175)^(1/50)

b = 1.01092581.

Hence:

y = a(1.01092581)^x.

When x = 1960, y = 179323175, hence the parameter a is obtained as follows:

a = 179323175/[(1.01092581)^1960]

a = 0.1.

Hence the function is:

y = 0.1(1.01092581)^x.

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Answer:

3/4

Step-by-step explanation:

Hope this helps! Pls give brainliest!

From the given data of Nicole's wedding organization, 18 tables at the venue is sufficient for the total 145 arriving guest.

To determine whether there are enough tables for the guests, we need to calculate the total circumference required for all the guests and compare it to the total circumference of the available tables. The circumference of a circle is given by the formula C = πd, where C is the circumference, d is the diameter, and π is the constant pi, approximately equal to 3.14.

For the circular table with a diameter of 180cm, the circumference is:

C = πd

= π x 180cm                              

= 565.2cm

Each guest needs 7cm around the circumference of the table, so the total circumference required for one guest is 7cm.

For 145 guests, the total circumference required is:

Total circumference required

= 145 guests x 7cm per guest

= 1015cm

Now, we can calculate the total circumference of all the tables available:

Total circumference of all tables

= 18 tables x 565.2cm per table

= 10,174.4cm

Since the total circumference required for the guests (1015cm) is less than the total circumference of all the available tables (10,174.4cm), we can conclude that there are enough tables for the guests. Therefore, there are enough tables at the venue for the 145 guests.

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The probability of drawing an odd number or a multiple of 3 is 1/5.

Probability is simply the chance that something will happen.

Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome.

Analyzing events according to their probabilities is called statistics.

So, the given data set is:

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

Odd multiples of 3 are 3 and 9.

Then, the probability would be:

P(E) = 2/10

P(E) = 1/5

Therefore, the probability of drawing an odd number or a multiple of 3 is 1/5.

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a) We need to add 2.25 to the expression to make it a perfect square and equivalent expression is (x + 1.5)^2.

b) We need to add 0.09 to the expression to make it a perfect square and equivalent expression is (x + 0.3)^2.

a) To make the expression X^2 + 3x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 3 is 1.5, and 1.5 squared is 2.25.

X^2 + 3x + 2.25 = (x + 1.5)^2

The equivalent expression in factored form is (x + 1.5)^2, which represents a perfect square trinomial.

b) Similarly, to make the expression X^2 + 0.6x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 0.6 is 0.3, and 0.3 squared is 0.09. Therefore, we need to add 0.09 to the expression to make it a perfect square:

X^2 + 0.6x + 0.09 = (x + 0.3)^2

The equivalent expression in factored form is (x + 0.3)^2, which represents a perfect square trinomial.

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The approximate amount of time period of a pendulum with a length of 12 feet is 1.85 seconds.

Calculus is a branch οf mathematics that deals with the study οf change and hοw things change οver time.

We can use the given equatiοn fοr the periοd οf a pendulum:

T = 2π√(L/32)

Substituting L = 12, we get:

T = 2π√(12/32)

Simplifying:

T ≈ 1.85 seconds

Hence, the approximate amount of time of the period of a pendulum with a length of 12 feet is 1.85 seconds.

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Answer:

Mr Drake is right.

Step-by-step explanation:

Because you first decreased it by 10% of the ORIGINAL value.

You then increased it by 10% of the DECREASED value.

The percentages are the same percentages, but on different base amounts.

Simple example:

$100 decreased by 10% of $100 ($10) is $90.

$90 increased by 10% of $90 ($9) is $99.

Answer:

Mr Drake Is correct

Step-by-step explanation:

When you increase something by 10%, you multiply the original value by 1.1. When you decrease it by 10%, you multiply the increased value by 0.9. So the final amount is:

original value x 1.1 x 0.9 = 0.99 x original value

Therefore, the new amount will be slightly smaller than the original amount, and Mr. Drake is correct.

Given that there is only one digit left and the sum is more than 10, the third digit must be 7, which it is. and the pass code to open anything it is guarding is 5 5 7, which may be inputted.

To decode the code, we know that the number is more than 10 and has three digits: . Moreover, we are aware that the value of the ones digit is 10 times that of the tenths digit. The code is 5 5 7, as may be inferred from the provided hints.

Given that the code contains two 5s, the first digit must be 5. As the value of the ones digit is 10 times that of the tenths number, the second digit must likewise be 5, which is 5. The number is bigger than 10, hence the third digit must be 7, as it is the only one still present.

In order to open whatever it is guarding, the code, which is 5 5 7, may be input.

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Here is the probability table to be completed:   A B P(A∩B) P(A∣B) 0.54 0.47 0.38 0.70 0.46 0.32 0.30 x 0.28 0.27 0.42 0.20 0.15 0.35 0.45

42. Let P(A) = 0.70, P(B∣A) = 0.55, and P(B∣AC) = 0.10. The following probabilities are found: a. P(AC) = 0.30 b. P(A∩B) = P(B∣A) × P(A) = 0.55 × 0.70 = 0.385 P(AC∩B) = P(B∣AC) × P(AC) = 0.10 × 0.30 = 0.03 c. P(B) = P(B∣A) × P(A) + P(B∣AC) × P(AC) = 0.55 × 0.70 + 0.10 × 0.30 = 0.415 d. P(A∣B) = P(B∣A) × P(A) / P(B) = 0.55 × 0.70 / 0.415 = 0.9289 43. Here is the probability table to be completed:   A B P(A∩B) P(A∣B) 0.54 0.47 0.38 0.70 0.46 0.32 0.30 x 0.28 0.27 0.42 0.20 0.15 0.35 0.45

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By writting all the numbers as decimals we can see that the lake that lost the least amount of water is the last one.

The first lake lost a fraction of 5/6 of its total water.

The second lake lost the 85% of its water.

The last lake lost a fraction of 246/300 of its water.

We want to see which of these 3 numbers is the smaller one, we can write all of them as decimals ot get:

5/6 = 0.833

85% = 0.85

246/300 = 0.82

With this we conclude that the lake that lost the least amount of water is the last one.

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Answer:

8 months

Step-by-step explanation:

I got it right

The growth constant is 0.69 and the population will increase to 12900 after approximately 3.7 years.

We have, Sunset Lake is stocked with 2500 rainbow trout and after 1 year the population has grown to 7050. Assuming logistic growth with a carrying capacity of 25000,

The logistic growth model is given by the equation

dN/dt=rN[(K-N)/K]

where, dN/dt = rate of change of population with respect to time,

N = population size at time t,

r = intrinsic rate of natural increase (growth constant),

K = carrying capacity.

The population size, "N" after 1 year = 7050

The initial population, "N₀" = 2500

The carrying capacity, K = 25000

We can use the following formula to find the value of the growth constant,

r = 2.303/t{ln(N_t/N₀) }........... (1)

Where, t = time taken for the population to increase from N_0 to N_t= 1 year (given)

Substituting the given values in equation (1), we get

r = 2.303/1 ln(7050/2500) ⇒ 0.688 ≈ 0.69

The value of the growth constant is 0.69.

Now, we can use the logistic growth equation to find the time required for the population to reach 12900.

dN/dt=rN[(K-N)/K]

Given, N₀ = 2500 and K = 25000

Differentiating both sides with respect to t,

dN/dt = rN[(K-N)/K] + Ndr/dt

Substituting the values of N, r, and K in the above equation, we get,

dN/dt= 0.69N[(25000-N)/25000] + N{dN/dt}

Let the population N become 12900 at time t = t₁

Therefore, at time t = 0, the population N₀ = 2500

Also, at time t = 1, the population N₁ = 7050

Substituting these values in the above equation, we get,

dN/dt= 0.69N[(25000-N)/25000] + N₁

dN/dt= 0.69(2500)[(25000-2500)/25000] + N₁

Solving for N₁, we get, N₁ = 7825

Substituting N₁ = 7825 in the above equation,

dN/dt= 0.69(7825)[(25000-7825)/25000] + N₁

dN/dt= 3263.25/1.69 ⇒ 1930.4

Now, to find t1, we can use the following formula;

ln[(K-N₁)/(K-N₀)] = rt₁

Substituting the given values, we get,

ln[(25000-12900)/(25000-2500)] = 0.69t₁

On solving for t₁, we get;

t₁ = ln[(1575/22500)]/0.69 ≈ 3.7 years

Hence, the population will increase to 12900 after approximately 3.7 years.

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The statements that are true are:

(A) The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.

(D) The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.

(E) The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.

Using the function A(t) = -1.4t + 96, we can determine the amount of oil, A, used in gallons for a given average temperature, t, in degrees Fahrenheit.

A) The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.

Substituting t = 10 into the function A(t), we get:

A(10) = -1.4(10) + 96 = 80

Therefore, the statement is true.

B) The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 °F.

Substituting t = 15 into the function A(t), we get:

A(15) = -1.4(15) + 96 = 76.5

Therefore, the statement is false.

C) The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 °F.

Substituting t = 68.5 into the function A(t), we get:

A(68.5) = -1.4(68.5) + 96 = -2.9

Therefore, the statement is false.

D) The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.

Substituting t = 55 into the function A(t), we get:

A(55) = -1.4(55) + 96 = 18

Therefore, the statement is true.

E) The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.

Substituting t = 0 into the function A(t), we get:

A(0) = -1.4(0) + 96 = 96

Therefore, the statement is true.

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The given question is incomplete, the complete question is:

A homeowner collects data about the amount of oil , in gallons, used to heat the house per month for 5 months and the average monthly temperature , in degrees

Fahrenheit, for those months. The scatter plot shows the data. The function A(t) = -1.4t + 96,  best fits these data.

Graph- (25,60), (40,40),(45,40),(55,20),(60,10)

Use the function  to determine which of the following statements are true. Select all that apply.

A- The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.

B- The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 °F.

C- The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 °F.

D- The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.

E- The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.

x=(17,4)^2+(−340,−80)+58y= y^2−20y+68

y=y^2−20y+68

Answer:

A

because it is a negative number and because it is less than -1/2

Answer:

Step-by-step explanation:

the answer is -1 as negative integers become smaller as they go to the left.

no problem

The value of ∠2KJM for the rhombus is ∠JKM = 23 + (5a/2).

A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is sometimes referred to as a diamond or rhombus. Rhombi or rhombuses are the plural forms of rhombus.

Let us suppose the measure of angle = x.

For rhombus all the four angles are congruent, thus,

∠MLN = (9a + 11)°

∠KLM = (-4a + 66)°

∠JLN = x

∠KLJ = x

The sum of the angles of a quadrilateral is 360 degrees, so:

∠JKL + ∠KLM + ∠MLN + ∠NJL = 360

Since JKL and NJL are vertical angles, they are congruent:

∠JKL = ∠NJL = x

Substituting in the given angles, we get:

x + (-4a + 66) + (9a + 11) + x = 360

2x + 5a + 77 = 360

2x = 360 - 5a - 77

2x = 283 - 5a

x = (283 - 5a)/2

Now, ∠JKM = 180 - ∠JKL

∠JKM = 180 - x

∠JKM = 180 - (283 - 5a)/2

Simplifying, we get:

∠JKM = 23 + (5a/2)

Hence, the value of ∠2KJM for the rhombus is ∠JKM = 23 + (5a/2).

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Answer:

∠ ABC = 38°

Step-by-step explanation:

given AB = DB then Δ ABD is isosceles with base angles congruent, that is

∠ BDA = ∠ BAD = 71°

the sum of the 3 angles in Δ ABD = 180° , so

∠ ABC + 71° + 71° = 180°

∠ ABC + 142° = 180° ( subtract 142° from both sides )

∠ ABC = 38°

35 1 + 2 = 17. To remember the mathematical operations in the correct order, people frequently use the abbreviation PEMDAS.

You must follow the order of operations, often known as PEMDAS, to evaluate this equation. Parentheses, exponents, multiplication and division (left to right), addition, and subtraction are all referred to as PEMDAS (from left to right).

When using PEMDAS, you would first calculate the output of the parenthesized expression—which is 3 times 5—and then add 2.

Thus, 35 1+2 reduces to:

3*5 1 + 2 = (3*5) + 2 (first calculate within the parentheses) = 15 + 2 (conduct multiplication) = 17 (perform addition)

Hence, 35 1 + 2 = 17.

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Answer:

You need to first identify the dum it's always multiplication

hope this helps good luck

if Ivy received two Paychecks during the time period shown on the statement, each paycheck would be $1,784.34.

To find out how much each of Ivy's paychecks is, we need to subtract the amount she withdrew from her account from the overall increase in her account balance.

So, the calculation would be:

Overall increase in account balance - Total amount withdrawn = Total amount deposited

$1,692.45 - $1,876.23 = -$183.78

This means that Ivy actually spent more than she earned during the time period shown on the statement. Therefore, we cannot determine the amount of each of her paychecks with the given information.

However, if we assume that Ivy did not have any other income or expenses during the time period, we can use the following equation:

2x - $1,876.23 = $1,692.45

where x is the amount of each paycheck.

Simplifying the equation, we get:

2x = $3,568.68

x = $1,784.34

Therefore, if Ivy received two paychecks during the time period shown on the statement, each paycheck would be $1,784.34.

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Beth will need approximately 3365.76 [tex]cm^{2}[/tex] of plastic wrap to cover all 12 jars of jam.

What is a Circle?

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

So now, to calculate the surface area of each jar, we need to find the area of the circular top and the area of the rectangular side.

The area of the circular top can be calculated using the formula for the area of a circle:

[tex]A=\pi r^{2}[/tex], where r is the radius of the circle.

The diameter of the jar is given as 7 cm, so the radius is half of that:

r = [tex]\frac{7}{2}[/tex] cm = 3.5 cm

Therefore, the area of the circular top is:

A_top = [tex]\pi r^2[/tex] = π[tex](3.5)^{2}[/tex] = 38.48 [tex]cm^{2}[/tex]

The area of the rectangular side can be calculated using the formula for the area of a rectangle:

A_side = base x height

The base of the rectangle is the circumference of the circular top, which can be calculated using the formula:

C = 2πr

C = 2π(3.5) = 22 cm

So the base of the rectangle is 22 cm, and the height is 11 cm, since that is the height of the jar.

Therefore, the area of the rectangular side is:

A_side = base x height = 22 cm x 11 cm = 242 [tex]cm^{2}[/tex]

To find the total surface area of each jar, we can add the area of the circular top and the area of the rectangular side:

A_total = A_top + A_side = 38.48 [tex]cm^{2}[/tex]+ 242 [tex]cm^{2}[/tex] = 280.48 [tex]cm^{2}[/tex]

For 12 jars, the total surface area of plastic wrap needed would be:

Total area = 12 x A_total = 12 x 280.48 [tex]cm^{2}[/tex] = 3365.76 [tex]cm^{2}[/tex]

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Answer: p+3

Step-by-step explanation:

if p=12 and you need the answer to be 15, all you need to do is find 12+_= 15. Since 12+3=15 your answer would be p+3.

The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.

A fraction is a mathematical expression which represents a part of a whole. It is written as a ratio that compares two numbers, the numerator and denominator. The numerator indicates the number of parts, the denominator indicates the total number of parts that make up the whole. Fractions can be expressed as decimals, percentages, and other forms of representation.

To solve this problem, we must use the formula for area of a triangle. This formula states that the area of a triangle is equal to one-half the product of the base and the height. In this problem, the area of the triangle is given as 1/16 square centimeters. This means that the base times the height must equal 1/8.

To find the length of the base, we must isolate the base from the equation. To do this, we must divide both sides of the equation by the height. This will leave us with the equation base = 1/8/height. Since the height is unknown, we can solve for it by taking the reciprocal of the base. This will give us the equation height = 1/8/base.

Combining both equations, we can solve for the base by multiplying both sides of the equation by 1/8. This will give us the equation base = (1/8)(1/8) = 1/64. The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.

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The simplified fοrm οf the square rοοt οf 7 divided by 20 is:

(7 + 2√(35)) / (20 * (√(7) + 2√(5))).

Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.

Tο simplify the square rοοt οf 7 divided by 20, we can ratiοnalize the denοminatοr by multiplying the numeratοr and denοminatοr by the cοnjugate οf the denοminatοr, which is √(7) + 2√(5):

(√(7)) / 20 = (√(7) / 20) * (√(7) + 2√(5)) / (√(7) + 2√(5))

Expanding the numeratοr using the distributive prοperty gives:

(√(7) * √(7) + √(7) * 2√(5)) / (20 * (√(7) + 2√(5)))

Simplifying the numeratοr gives:

(7 + 2√(35)) / (20 * (√(7) + 2√(5)))

Therefοre, the simplified fοrm οf the square rοοt οf 7 divided by 20 is:

(7 + 2√(35)) / (20 * (√(7) + 2√(5))).

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Step-by-step explanation:

6x6x10 FT = 1 sq cube foot

For the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. Yet, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.

The distance formula for the coordinates is given as:

d(A, B) = |x1 - x2|

From the figure we observe that,

d(A, B) = |2 - 4|

d(A, B) = |-2|

d(A, B) = 2 units.

Hence, option A is correct.

Also, the length of A'B' is:

d(A', B') = |3 - 6| = |-3| = 3 units.

Hence, option B is correct.

The original shape is called the pre-image in a transformation (in this example, a dilation), and the transformed shape is called the image.

The third response is untrue since the picture is larger than the pre-image.

The scale factor of the images is:

2k = 3

k = 3/2.

Hence, option 4 is correct.

The last option is also false, as the scale factor is already determined.

Hence, for the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.

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The complete question is:

The correct statement regarding the number of solutions of the equation is given as follows:

The function has one solution.

The function for this problem is defined as follows:

[tex]x - 8 = -\sqrt{x^2 - 8}[tex]

We can remove the term with x from the square root squaring both sides of the equality, hence:

[tex](x - 8)^2 = (-\sqrt{x^2 - 8})^2[/tex]

x² - 8 = x² - 16x + 64

16x = 72

x = 72/16

x = 4.5.

Hence the equation presented in this problem has a root, which is a solution, and the number of solutions is of one.

The function is given as follows:

[tex]x - 8 = -\sqrt{x^2 - 8}[tex]

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