write an equation for the function graphed.

Write An Equation For The Function Graphed.

Answers

Answer 1

The equation for the graphed quadratic function is:

y = -1*(x - 3)^2 + 2

How to write an equation for the function graphed?

Here we have the graph of a quadratic equation. Remember that if the leading coefficient is a and the vertex is (h, k) then we can write:

y = a*(x - h)^2 + k

Here the vertex is at (3, 2) then we can write:

y = a*(x - 3)^2 + 2

We can see that it also passes through the point (1, -2), replacing these values we will get:

-2 = a*(1 - 3)^2 + 2

-2 = a*4 + 2

-2 - 2 = a*4

-4/4 = a = -1

Then the quadratic equation is:

y = -1*(x - 3)^2 + 2

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Related Questions

Question 30
A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 4 digits
long, and that each digit could be a number between 0 and 4. Assume that the hacker makes random
guesses. What is the probability that the hacker guesses the password on his first try? Round to six decimal
places.
Probability:

Answers

The probability that the hacker guesses the password on his first try is, 0.001600.

What is probability?

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The probability of a hacker guessing the correct password on their first try would be 1 in 10,000, since there are a total of 5⁴ possible combinations of 4 digits, each between 0 and 4, inclusive.

The probability can be calculated as:

= 1 / 5⁴

= 1 / 625

= 0.0016

Rounded to six decimal places, the probability is: 0.0016 = 0.001600.

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A 10-ft board is cut into 2 pieces so that one piece of 6 feet longer than 3 times the shorter piece. If the shorter piece is x feet long find the lengths of both pieces

Answers

The lengths of the pieces are 1ft and 9ft

How to determine the length of sides

From the information given, we have that;

The shorter side = x

The longer side of the board = 6 +3x

The total length = 10

Substitute the values, we have;

x + 6 + 3x = 10

collect the like terms

x + 3x = 10 -6

Add or substract the like terms, we have;

4x = 4

Now, make 'x' the subject of formula by dividing by 4, we get;

4x/4 = 4/4

x = 1 ft

The longer side = 9ft

Hence, the values are 1 and 9

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Out of 1000 students who appeared for Cost accounting examinations,750 failed in maths,600 failed in accounts and 600 in costing,150 failed in both accounts and costing,450 failed in both maths and accounts,400 failed in both maths and costing.the students who failed all three subjects were 75.Prove that the above data is not correct​

Answers

Answer: This data can be proven to be incorrect using the Principle of Inclusion-Exclusion.

The Principle of Inclusion-Exclusion states that for two events A and B, the number of elements in the union of A and B is equal to the sum of the number of elements in A and the number of elements in B minus the number of elements in their intersection.

Let's denote the number of students who failed in Maths as M, Accounts as A, and Costing as C.

From the information given, we have the following relationships:

M = 750

A = 600

C = 600

A ∩ C = 150

M ∩ A = 450

M ∩ C = 400

M ∩ A ∩ C = 75

Applying the Principle of Inclusion-Exclusion, the number of students who failed in at least one subject is:

M + A + C - (A ∩ C) - (M ∩ A) - (M ∩ C) + (M ∩ A ∩ C) = 750 + 600 + 600 - 150 - 450 - 400 + 75 = 925

However, the number of students who appeared for the exams is 1000, which means that the number of students who passed in all subjects should be 1000 - 925 = 75.

But we have already determined that the number of students who failed in all subjects is 75, which means that there are 75 students who are counted twice. This leads to a contradiction, and therefore the data given cannot be correct.

Step-by-step explanation:

1) Find the 9th term of the sequence:
60, 30, 15, ...
*

Answers

Answer:

Step-by-step explanation:

Let me explain step by step:

Determine the common ratio: We see that each term is half the previous term, so the common ratio is 1/2.

Write the formula for the nth term: We can use the formula for an infinite geometric series to find the nth term:

a_n = a_1 * r^(n-1), where a_1 is the first term (60), r is the common ratio (1/2), and n is the term number.

Plug in the values: We want to find the 9th term, so we plug in the values into the formula:

a_9 = 60 * (1/2)^(9-1)

Calculate the expression: We can simplify the expression by using the exponent rule for powers of 1/2:

a_9 = 60 * (1/2)^8

Divide the result by 256: We can simplify the expression further by dividing both sides by 256:

a_9 = 60 * 1/256

a_9 = 60 / 256

Get the final answer: We divide 60 by 256 to get the final answer:

a_9 = 0.234375

So the 9th term of the sequence is approximately 0.234375.

the company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays except on Saturdays which is limited to the minimum of 4 water tankers a day. Calculate the total number of water loads that were supplied to the project on the constitution site by the water tanker in March 2022​

Answers

Note that in order to solve the above, we had to assume a start date for the construction. Hence, by March 2022​, a total number of liters supplied is 3,380,000 liters.

What is the rationale for the above response?

To solve the problem, we need to know how many weekdays are in March 2022. March 2022 has 23 weekdays (31 days - 4 Saturdays - 4 Sundays).

Since the company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays, we can assume an average of 14 water tankers per weekday. Therefore, the total number of water tankers to be supplied on weekdays in March 2022 would be:

14 water tankers/day x 23 weekdays = 322 water tankers

On Saturdays, the company has to supply a minimum of 4 water tankers. Since there are 4 Saturdays in March 2022, the total number of water tankers to be supplied on Saturdays in March 2022 would be:

4 water tankers/day x 4 Saturdays = 16 water tankers

Therefore, the total number of water tankers to be supplied in March 2022 would be:

322 water tankers (weekdays) + 16 water tankers (Saturdays) = 338 water tankers.

Assuming each water tanker carries a load of 10,000 liters, the total volume of water supplied to the construction site in March 2022 would be:

338 water tankers x 10,000 liters/tanker = 3,380,000 liters

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Full Question:

The company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays except on Saturdays which is limited to the minimum of 4 water tankers a day. Assuming the start month for the construction was February 2022, Calculate the total number of water loads that were supplied to the project on the constitution site by the water tanker in March 2022

j is the midpoint of HI and GH. complete the proof that GHJ ≅ GIJ

Answers

4. Reflexive property

5. SSS

Robert scored a 42 out of 48 on Quiz-1 and Julie scored a 43 out of 50 on Quiz-2.
Who received a higher percentage?

Answers

Answer:Robert

Step-by-step explanation: 42/48 = 0.875,
43/50 = 0.86

0.875 > 0.86

TO determine which side of a linear inequality to shade in for its graph, you
should pick a point on one side of the dashed or solid line and plug its
coordinates into the original inequality. If the coordinates satisfy the
inequality, you should shade in that half of the plane.
• A. True
• B. False

Answers

The given statement about inequality is true.

What is inequality?

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

The statement is true ''Pick a point on one side of the solid or dashed line and enter its coordinates into the original inequality to determine which side of a linear inequality to colour in for its graph. On that side of the plane, you should shade if the coordinates satisfy the inequality''.

The statement defines how to write an inequality the meaning of inequality is that one part of the inequality will be shaded by some colour indicating that the region is falling under the area of inequality.

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Will your battery capacity go down if you update your iphone?

Answers

Unfortunately, a lot of software apps tend to use up battery life even if you aren't currently using the phone. This leads to the phone feeling more sluggish over time. To help combat this, it's helpful to clear out any unused apps and clear up the cache.

Even if software was perfectly written the most efficiently, and apps weren't intrusive, the physical nature of the battery itself has limitations. The capacity of the battery will slowly decay each time you charge or use your phone. Even just sitting idle it slowly loses capacity. This loss is very small that it's hard to detect. But add it up over time and the losses will get more noticeable. This is why you cannot simply charge a battery an infinite number of times. As with all things in life, there's a limit.

Summary: Yes the capacity will go down but ever so slightly. It depends how often the updates are done and what software is being updated. Ideally the updated software should be more efficient with the battery life. However, life isn't perfect and there will likely be flaws.

Help quick!! Which of the following tables represents a relation that is a function?

Explained answer please

Answers

D because none of the inputs (x) are repeated. All the others have the same input with two or more different outputs.

ite the equations of the lines with the following properties Two points, (1, 3) and (9,8)​

Answers

The linear equation that passes through the two given points is:

y = (5/8)*x + 19/8

How to write the linear equation?

We want to find the equation of a line that passes through (1, 3) and (9, 8).

Remember that the slope of a line that passes through two points (x₁, y₁) and (x₂, y₂) is given by the equation:

slope = (y₂ - y₁)/(x₂ - x₁)

Here we know the two points (1, 3) and (9, 8).

Then the slope is:

slope = (8 - 3)/(9 - 1) = 5/8

We can write the line as:

y = (5/8)*x + b

To  find the value of b,we can evaluate in one of the given points, for example, if we use (1, 3) then we will get:

3 = (5/8)*1 + b

3 = 5/8 + b

3 - 5/8 = b

24/8 - 5/8 = b

19/8 = b

The linear equation is:

y = (5/8)*x + 19/8

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At a recent Algebra lover's convention, 4 times as many people attended on Sunday as on Thursday. If a total of 2,910 people attended the convention on the two days combined, how many people attended on Thursday? How many people attended on Sunday?
people attended on Thursday.
people attended on Sunday.

Answers

2,910 people attended the convention on the two days combined. Since 4 times as many people attended on Sunday as on Thursday, we can set up the equation:

4x = 2,910 - x

Solving for x gives us x = 1,455. This means that 1,455 people attended on Thursday and 4 × 1,455 = 5,820 people attended on Sunday.

hope this helps:)

I Given that x is an Intergen write down the three lowest values of x in each of the Following. al 10-3x > 8 62 5x-27 > 7x solution​

Answers

The lowest values of x are;

1. x = 1/2, x = 2/4, x = 3/6

2. x = 14, 15, 16

How to determine the values

From the information given, we have that;

10-3x > 8

collect the like terms, we get;

-3x > 8 - 10

subtract the values

-3x > -2

Make 'x' the subject

x > 2/3

5x-27 > 7x

collect the like terms

5x - 7x> 27

subtract the like terms

-2x> 27

Make 'x' the subject

x > -27/2

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guys i swar this is the last one just this one and thats it <3

Answers

Answer:

Choice B is the closest

Step-by-step explanation:

A-lateral = 2πrh

r = D/2 = 16.5/2 = 8.25

h = 14

A = 2π(8.25)(14) = 725.7 in²

Which is stronger? 3 scoops of coffee for 4 cups of water, or 4 scoops of coffee for 6 cups of water? Show Your Work.

Answers

The stronger one is 4 scoops of coffee for 6 cups of water.

How strong coffee is made?

Strong coffee is prepared by employing a greater coffee grounds-to-water ratio. Typically, 2 teaspoons of coffee grinds are used for every 6 ounces of water in a strong cup of coffee. To make a truly strong cup of coffee, use 3 teaspoons of ground coffee for every 6 ounces of water. If you use a French press, you need also increase the steeping time.

In the given question, it is stronger to use 4 scoops of coffee for 6 glasses of water. This is due to the fact that there are more coffee grounds in relation to the amount of water, resulting in a higher concentration of coffee in the combination.

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The value of a car deprecates by 35% each year.at the end of 2007 the value of the car was £5460. Work out the value of the car at the end of 2006

Answers

Answer:

£3549

Step-by-step explanation:

The value of the car depreciates by 35% each year, so we can calculate the depreciation for 2006 as follows:

Depreciation for 2006 = 0.35 * £5460 = £1911

The value of the car at the end of 2006 is:

£5460 - £1911 = £3549

Answer:

The depreciation rate:

Step-by-step explanation:

Step 1: Total depreciation = 35% x 2 years = 70%

Step 2: Find the value of the car at the end of 2006:

Value at the end of 2006 = 5460 x (100 - 70)/100 = 1638

Therefore, the value of the car at the end of 2006 was £1638.

A student's course grades and their corresponding weights are given in the table.

What is the minimum grade needed on the final exam to earn an overall grade of 83% in the class

Answers

Answer: 75%

Step-by-step explanation: To calculate,

(0.1 x 100) + (0.3 x 80) + (0.2 x 95) + (0.4 x 75) = 83%

2. The population of chickadees in a certain region is smaller by 30% than the population of
phoebes, and the population of blue jays is 30% of the population of phoebes.
The population of phoebes is 12,000.
Find the sizes of the chickadee and blue jay populations in the region.

Answers

The population of chickadees in the region is 8,400 and the population of blue jays is 3,600.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

First, we can find the population of chickadees by multiplying the population of phoebes by 0.7 (100% - 30%):

Population of chickadees = 0.7 x 12,000 = 8,400

Next, we can find the population of blue jays by multiplying the population of phoebes by 0.3:

Population of blue jays = 0.3 x 12,000 = 3,600

Therefore, the population of chickadees in the region is 8,400 and the population of blue jays is 3,600.

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A company that bottles mustard is allowed to advertise their bottle size as 21 ounces as long as the actual amount in the bottle is within 0.15 ounces of that amount. Which inequality shows all the possible actual bottle volumes (v) that the manufacturer would be able to advertise as 21 ounces?

Answers

Answer:

Step-by-step explanation:

the Answer is b

the preimter of a rectangel measures 78 centimterers the measure of the with is 15 cenimeters what is the area of the rectangel

Answers

Answer:

360 cm^2

Step-by-step explanation:

The length of the rectangle can be found using the formula for perimeter:

Perimeter = 2 * (length + width)

Rearranging the equation, we can solve for the length:

length = (Perimeter - 2 * width) / 2

Plugging in the given values:

length = (78 - 2 * 15) / 2 = (78 - 30) / 2 = 48 / 2 = 24 cm

Next, the area of the rectangle can be found using the formula:

Area = length * width

Plugging in the given values:

Area = 24 * 15 = 360 cm^2

A quadratic function is shown on the graph

What is the range of the function?

Answers

The range is the set of all y-values used by the graph.

This graph's lowest y-value is 3 at the point (0,3).

The graph almost reaches as y-value of 12, but doesn't actually get there because of the closed circle at (-3,12).

The range is [3, 12) or { y | 3 ≤ y < 12}, depending on the notation needed.

Complete the table.
q=p+7
Р
q
0
1
8
2
3
4
11

Answers

Given expression q=p+7

Expression can be defined as contains one or more variables and constants with one or more arithmetic operators.

Simply put the p values in the expression. solve it and get the q values.

q=p+7 in the place of p submit p=0

q=0+7

q=7

q=p+7  in the place of p submit p=2

q=2+7

q=9

q=p+7  in the place of p submit p=3

q=3+7

q=10

Therefore, The values of q are 7,9,10

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The missing numbers are:

7,9 and 10 when 0, 2, and 3 respectively.

What is an equation?

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

An equation,

q = p + 7.

Substituting the values of p:

When p = 0,

q = 0 + 7

q = 7.

When p = 2,

then q = 9.

And when p = 3,

q = 10

Therefore, all the required values are given above.

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Which is NOT a liability?

A. Debt owed by a business
B. Debt that must be paid within the current year
C. Debt that must be paid after the current year
D. Machines, vehicles, furniture and appliances

Answers

Answer:

D. Machines, vehicles, furniture, and appliances are not considered liabilities. Liabilities are obligations or debts that a business owes to others. They are usually in the form of loans or accounts payable and represent money that must be paid in the future.

Machines, vehicles, furniture, and appliances are assets, which are resources that a business owns and that have monetary value. Assets can be sold to generate cash or used to produce goods or provide services. While assets can be used to secure loans, they do not represent a debt or obligation that must be paid in the future like a liability

Answer:

D

Step-by-step explanation:

current liability is money owed to suppliers in the form of accounts payable . Current liabilities are typically settled using current assets, which are assets that are used up within one year.

A function has the following properties:

• It is increasing and linear when the value of x is between -5 and -3.

• It remains constant when the value of x is between -3 and 0.
• It is decreasing and linear when the value of x is between 0 and 3.

• It is increasing and nonlinear when the value of x is between 3 and 5.

Which graph best represents this function?

Answers

Answer:

c

Step-by-step explanation:

trust me

the sum of three consecutive odd integers is 19 less than twice the smallest of the three integers.​

Answers

-17, -15 and -13 are the three consecutive odd integers.

Word problem involving linear equation

Linear equation are equation that has a leading degree of 1

Let the smallest integer is '2x - 1'

The next two integers are 2x + 1 and 2x + 3

If the sum of three consecutive odd integers is 19 less than twice the smallest of the three integers, hence;

2x  - 1 + 2x + 1 + 2x + 3 = 2(2x-1) - 19

6x + 3 = 4x - 21

6x - 4x = -21 -3

3x = -24

x = -8

First number = 2(-8) - 1 = -17

Second number = 2(-8) + 1 = -15

Third number = 2(-8) + 3 = -13

Hence the 3 consecutive odd integers are -17, -15 and -13.

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Complete question

The sum of 3 consecutive odd integers is 19 less than twice the smallest of integers , what are the integers?

The weight of potato chips in a medium sized bag is stated to be 10 ounces. The amount that
the packaging machine puts in these bags is believed to be normally distributed with a mean of 10.2
ounces and a standard deviation of 0.12 ounces. Is it unusual for a bag to contain 9.8 ounces of
chips? Explain your answer.

Answers

No, it is not unusual for a bag to contain 9.8 ounces of chips. This is because the amount of chips in a bag follows a normal distribution, which means that the probability of any given value occurring is determined by its distance from the mean. In this case, 9.8 ounces is only 0.4 ounces away from the mean, which is relatively close and therefore not considered unusual. To put this into perspective, if we look at the probability of a bag containing 9.8 ounces of chips, it would be approximately 0.24 (calculated using the z-score formula). This means that there is a 24% chance of a bag containing 9.8 ounces of chips, which is not considered unusual or rare.

Hope this helps you :)

Step-by-step explanation:

a normal distribution with mean m and standard deviation d gives us a few regular pieces of information.

for example, we know that 68.2% of all events are within the interval

m ± d

and 95.4% of all events are in the interval

m ± 2d

and 99.7% of all events are in the interval

m ± 3d

that means only 0.3% of all events are outside the interval

m ± 3d = 10.2 ± 3×0.12 = 10.2 ± 0.36

now, when a bag is filled with 9.8 ounces, it is 0.4 off the mean (10.2).

that means it is outside the 10.2 ± 0.36 interval and inside the 0.3% "exception" range.

you have to see it also that way : 0.3% means 3 out of 1000 bags are in that range.

so, yes, it is considered unusual.

A total of tickets were sold for the school play. They were either adult tickets or student tickets. There were fewer student tickets sold than adult tickets. How many adult tickets were sold?

Answers

There were 375 adult tickets sold and 316 student tickets for the school play.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let the number of student tickets would be x and the number of adult tickets would be y

As per the question, we have a system of equations:

x + y = 691   ....(i)

x = y - 59     ....(ii)

Substitute the value of x = y - 59 in equation (i),

y - 59 + y = 691

2y = 691 + 59

2y = 750

y = 375

Substitute the value of y = 375 in equation (ii), and solve for x:

x = 375 - 59

x = 316

Thus, there were 375 adult tickets sold.

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The complete question would be as:

A total of 691 tickets were sold for the school play. There were 59 fewer student tickets sold than adult tickets. How many adult tickets were sold?

Solving right triangle

Answers

Answer:

[tex]BC= 2.23[/tex]

Step-by-step explanation:

We can solve this problem using the trigonometric identity of [tex]sin[/tex].

We know:

[tex]sin(\theta) = \frac{opposite}{hypotenuse}\\\\sin(50 \textdegree) = \frac{?}{3}\\[/tex]

If we solve for [tex]?[/tex] we get:

[tex]3sin(50 \textdegree) \approx 2.23[/tex]

PLEASE ANSWER QUICKLY!

For students majoring in Hospitality Management, it was determined that 5% have visited 1–10 states, 16% have visited 11–20 states, 45% have visited 21–30 states, 19% have visited 31–40 states, and 15% have visited 41–50 states. Suppose a Hospitality Management student is randomly selected. What is the probability that the student has visited 21 or more states?

A. 0.15
B. 0.21
C. 0.45
D. 0.79

Answers

The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.

What is probability?

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

here, we have,

from the given data we get,

The categories are mutually exclusive, so we have ...

P(≥21) = P(21-30) +P(31-40) +P(41-50)

           = 45% +19% +15%

 P(≥21) = 79%

           =0.79

The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.

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Statistics: Suppose the population variance for a given
population is 36. If we select all possible samples of a certain size from this population, then, on average, what will be the value of the sample variance?

Answers

If we select all possible samples of a certain size from this population, then, on average, the value of the sample variance is 36.

What is a population?

In Science, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.

What is a sample?

In Statistics and science, a sample can be defined as a set of data that is collected from a population based on a well-defined sampling procedure.

In this context, we can reasonably infer and logically deduce that the sample variance on average would be equal to 36 because all possible samples of a certain size are selected from a population of 36 members.

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a formal region is defined: conceptually - typically in terms of feelings, attitudes and images. in terms of its interdependent parts that are typically linked to a central node. in terms of the uniformity or homogeneity of certain characteristics. by the national geographic Need help really please What is the vapour pressure of water at 25 degree Celsius? ill give brainliest to whoever can answerRobert uses f(x) = 1000(1.06)^x to calculate the interest he earns each year for his savings account. What is the yearly interest rate as a percent? Suppose you obtain a $5,000 T-note with a 3% annual rate, paid semi-annually, with maturity in 5 years. How much interest will you earn? in a cross-country comparison of preschools in china, japan, and the united states, researchers found that parents in the three countries view the purpose of preschools very differently. japanese parents view them primarily as a way of: what is the best translation of the following sentence?Run.Corra.Correr.Corras.Corrs. NEED HELP DUE ON FRIDAY Use the image in the lesson to answer questions 2, 3, and 4.2. How does the distance between the focus and directrix affect the shape of the parabola?3. What seems to need to be true in order for the parabola to open downward (that is, to be shaped like a hill instead of a valley)?4. The vertex of the parabola is the lowest point on the curve if it opens upward, or the highest if it opens downward. Where is the vertex located in relationship to the focus and directrix? in a group of 8 students, 5 are first-year students, while 3 are second-year students.in how many unique ways can we form three groups comprising 3, 3, and 2 students? (within group order does not matter) According to Vygotsky, which of these is a key factor in a child's cognitive development?a. Balanced dietb. Social interactionsc. Genetic endowmentd. Successful resolution of psychosocial crises g a card game is made of 108 cards.25 each are red, yellow,blue and green and 8 are wild cards.each play- ers is dealt a seven card hand. a)what is the probability that hand will contain ex- actly 2 wild cards? b) what is the probability that hand contains seven yellow cards? Is Tom Clancy's Rainbow Six Siege Good An angular distance measured north or south of the equator from the center of earth is termedA) longitude. B) latitude. C) zenith. D) Greenwich distance. QuestionWhich one of the following statements with regard to embryonic development in humans is correct?ACleavage divisions bring about considerable increase in the mass of protoplasm.BIn the second cleavage division, one of the two blastomeres usually divides a little sooner than the second.CWith more cleavage divisions, the resultant blastomeres become larger and larger.DCleavage division results in a hollow ball of cells called morula.Hard Which equation has infinitely many solutions?1/3(6x - 12) = 2(x-2)1/2(4x+8)=2x+83(2x-7)= 6(x-4)-35 (2+1)= 3x + 2(x+1)+4 describe two environmental benefits of using algae for biofuel production, rather than corn, palm oil, or sugarcane. A small child and a teenager are at the top of a hill on skateboards. What could the child do to decrease his gravitational potential energy? Before an interview, you should perform a self-assessment to:OA. review your strengths, weaknesses, and career goals.OB. find out what careers are right for you.C. choose what you should study in college.OD. discover what you like to do.The answer is A. review your strengths, weaknesses, and career goals. what physical or chemical properties were the defining ones to identify the three unknowns? for example, was the odor the most obvious? the flammability? In what three ways did the Little Rock Nine change the United States?