f(x) = x2 - 4x - 21.
What will the function have at the y-intercept and where would the vertex be ?

Explanation

We are required to determine the inequality that satisfies the given graph.

This is achieved thus:

We can deduce from the graph that the curve drawn is not a broken line. Therefore, it cannot be strictly greater than or strictly less than.

We know that only "true" region is shaded. By testing the origin, we can deduce that the correct inequality is:

Hence, the answer is:

Option D

The situation described follows a geometric distribution because we are interested in the number of trials needed to achieve the first success (drawing a blue marble from the bag).

The situation described, where marbles are drawn from a bag with replacement until a specific event (getting a blue marble) occurs, follows a geometric distribution.

In a geometric distribution, we are interested in the number of trials needed to achieve the first success. In this case, the "success" is drawing a blue marble, and each trial consists of drawing a marble from the bag.

The key characteristics of a geometric distribution are:

1. The trials are independent, meaning that the outcome of one trial does not affect the outcome of subsequent trials.

2. The probability of success remains constant for each trial.

3. The trials are performed until the first success occurs.

In the given situation, the probability of drawing a blue marble remains constant at 6/15 (since there are 6 blue marbles out of a total of 15 marbles in the bag) for each trial. The trials are independent because we replace the marble after each draw. We continue drawing marbles until we obtain a blue marble, which is considered the first success.

Therefore, the situation described follows a geometric distribution because we are interested in the number of trials needed to achieve the first success (drawing a blue marble from the bag).

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Answer:

96

Step-by-step explanation:

The value of a and b are 11 and 14.

The equation on a graph shows the point where the equation intersects

on the x-axis and the y-axis.

We have,

The function as y = 2x² + ax + b

Where it intersects on the x-axis at the points (-7/2, 0) and (2, 0).

Now we can write it as:

At point (-7/2, 0).

0 = 2 (-7/2)² + a(-7/2) + b

0 = 49 / 2 - 7a/2 + b

7a/2 - b = 49/2 _____(1)

At point (2, 0)

0 = 2(2)² + 2a + b

0 = 8 + 2a + b

2a + b = -8 _____(2)

From (1) and (2) we can find a and b.

From (1)

7a/2 - 49/2 = b

b = (7a - 49) / 2 ______(3)

putting in (2)

2a + (7a - 49) / 2 = -8

4a + 7a - 49 = -16

3a - 49 = -16

3a = -16 + 49

3a = 33

a = 11

putting in (3)

b = (7x11 - 49) / 2

b = (77 - 49) / 2

b = 28 / 2 = 14

Thus the value of a and b are 11 and 14.

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The value of a and b for the given equation is 3 and -14 respectively.

The given equation is y=2x²+ax+b, (-7/2, 0) and (2, 0).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now put (-7/2, 0) and (2, 0) in the given equation and find a and b value.

That is, 0=2 (-7/2)²+a(-7/2)+b

⇒ 49/2 -7a/2+b=0 ----(I)

0=2(2)²+a(2)+b

⇒ 8+2a+b=0

⇒ b=-2a-8 -----(II)

Put b=-2a-8 in equation (I) and simplify.

That is, 49/2 - 7a/2 -2a-8=0

⇒ 49/2 - 11a/2 - 8 =0

⇒ 49 - 11a=16

⇒ 11a=33

⇒ a=3

Put a=3 in equation (II) and simplify.

That is, b=-2(3)-8=-14

Therefore, the value of a and b for the given equation is 3 and -14 respectively.

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The given problem is a 0-1 integer programming problem, which involves finding the maximum value of a linear objective function subject to a set of linear constraints, with the additional requirement that the decision variables must take binary values (0 or 1).

To solve this problem by implicit enumeration, we systematically evaluate all possible combinations of values for the decision variables and check if they satisfy the constraints. The objective function is then evaluated for each feasible solution, and the maximum value is determined.

In this case, there are three decision variables: x1, x2, and x3. Each variable can take a value of either 0 or 1. We need to evaluate the objective function 2x1 - x2 - x3 for each feasible solution that satisfies the given constraints.

By systematically evaluating all possible combinations, checking the feasibility of each solution, and calculating the objective function, we can determine the solution that maximizes the objective function value.

The explanation of the solution process, including the enumeration of feasible solutions and the calculation of the objective function, can be done using a table or a step-by-step analysis of each combination.

This process would involve substituting the values of the decision variables into the constraints and evaluating the objective function. The maximum value obtained from the feasible solutions will be the optimal solution to the problem.

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Answer:

you need 36cups of flour

Step-by-step explanation:

3 cups of flour = 8 ounces of water

x cups of flour = 96 ounces of water

96*3 =8x

288 =8x

288/8=36

x=36

Answer:

a = 80

b = 40

c = 58

d = 19

e = 34

f = 36

Pls mark brainliest. Thanks!

Answer:

a = 80

b=40

c=58

d=19

e=34

f=36

Step-by-step explanation:

The probability of selecting a human character randomly in the game is \(\frac{1}{3}\)

The probability that a human character will be chosen when the player selects a character randomly can be calculated by dividing the number of human characters by the total number of available characters.

There are 8 animal characters and 4 human characters, making a total of 12 characters to choose from. Therefore, the probability of selecting a human character randomly is:

P(Human) = Number of human characters / Total number of characters

P(Human) = 4 / 12

Simplifying this fraction, we find:

P(Human) = 1 / 3

Therefore, the probability of selecting a human character randomly is 1/3 or approximately 0.333.

In the given scenario, there are a total of 8 animal characters and 4 human characters, making a total of 12 characters to choose from. When a player selects a character randomly, each character has an equal chance of being chosen. Since there are 4 human characters, the probability of selecting one of them is determined by dividing the number of human characters (4) by the total number of characters (12).

When we simplify the fraction 4/12, we find that it is equal to 1/3.

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Answer:

I think your trying to ask what the answer is and it would be B.

Step-by-step explanation:

Put in the X column: 0 1 2

Put in the Y column: 0 5 10

If it asks for how you know, put that it’s basically multiplying by 5s.

The range of the data is R = 9

Given data ,

Let the range of the data be R

Now , the value of R is R = maximum value - minimum value

Let the data be A = { 5, 9.5, 3, 12, 6, 8, 4.5, 10, 6.5 }

The range of a set of data, we need to subtract the minimum value from the maximum value.

The minimum value in this set of data is 3 (which occurs in the third week), and the maximum value is 12 (which occurs in the fourth week).

Therefore, the range is:

range = maximum value - minimum value = 12 - 3 = 9

Hence , the value of the range for this set of data is 9

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Answer:

the answer is d

Step-by-step explanation:

if you take leg cb and leg fe, the leg cb is 2.5 times larger than leg fe.

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Answer: 27528 ft^3

Explanation:

24 x 31 x 37 = 27528

I hope this helped!

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Answer:

.70 cents

Step-by-step explanation:

Just divide $4.20 by 6. Hope this helps! God bless.

Answer:

Aaron will win the bet if they continue to increase their deliveries at the same rate.

Step-by-step explanation:

Isaac started out delivering twice as much as Aaron did on his fourth week. By week 4, Isaac had delivered a total of 250 pizzas, while Aaron had only delivered 45. However, Aaron's output is doubling each week, while Isaac is only delivering 7 more each week. During week 5, Aaron will deliver 48 pizzas, and Isaac will deliver 80. During week 6, Aaron will deliver 96 pizzas, and Isaac will deliver 87. During week 7, Aaron will deliver 192 pizzas, and Isaac will deliver 94.

Use the trigonometric identity is g(x, y + h) = g(x, y)cos(h) + xcos(y)sin(h) + hsin(x) when h is small.

(a) g(0, y) = 0 sin(y) + y sin(0) = 0 + 0 = 0

(b) g(x, y + h) = x sin(y + h) + (y + h) sin(x)

Using the trigonometric identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b), we can expand sin(y + h) as sin(y)cos(h) + cos(y)sin(h). Substituting this into the above equation, we get:

g(x, y + h) = x(sin(y)cos(h) + cos(y)sin(h)) + (y + h)sin(x)

g(x, y + h) = xsin(y)cos(h) + xcos(y)sin(h) + ysin(x) + hsin(x)

Therefore, g(x, y + h) = g(x, y)cos(h) + xcos(y)sin(h) + hsin(x) when h is small.

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Answer:

the answer is 6xy , hopefully that helped you

Answer:

2x^9 x

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x3"   was replaced by   "x^3".  

STEP  1 :

Multiplying exponential expressions :

1.1    x4 multiplied by x3 = x(4 + 3) = x7

The Equation at the end of step  1 :

 ((2x7 • x) • x) • y

STEP  2:  Final result :

 2x^9 y

Hope this helps!

Brain-List?

Answer:

y=-2x+5

Step-by-step explanation:

First, find the slope:

m=(y2-y1)/(x2-x1)  ==> slope formula where m is the slope

(–1, 7), (1, 3)  ==> (x1=-1, y1=7), (x2=1, y2=3)

m=(3 - 7)/(1 - (-1)) ==> plugin y2=3, y1=7, x2=1, and x1=-1 into the slope formula

m=(-4)/(1 + 1)  ==> simplify

m=(-4)/2

m=-2  ==> the slope is -2

y=mx+b  ==> slope-intercept equation

3=(-2)(1)+b  ==> plugin the slope(m=-2) and point B(1, 3)  ==> (x=1, y=3)

3=-2+b  ==> solve for b

3+2=-2+2+b  ==> add 2 on both sides to isolate b

b=5  ==> simplify

y=-2x+5  ==> plugin the slope and b=5 into the equation

Answer:

  a) 56.25 mph

  b) $1.59/lb

Step-by-step explanation:

The units of the "unit rate" tell you the math operation you need to perform.

Miles per hour (mi/h) is found by dividing miles by hours.

  (450 mi)/(8 h) = (450/8) mi/h = 56.25 mi/h

Dollars per pound ($/pound) is found by dividing dollars by pounds.

  ($7.95)/(5 pounds) = (7.95/5) $/pound = 1.59 $/pound

__

Additional comment

In the context of unit rates, "per" means "divided by."

What makes a rate a "unit rate" is the "1 unit" in the denominator. For miles per hour, the denominator is 1 hour. For dollars per pound, the denominator is 1 pound.

Answer:

you take 7.50 and divide it by 3 which equals $2.50

The constant of proportionality is 20 and y is equal to 8, x is equal to 2.5.

If y is inversely proportional to x, then we can write:

y = k/x

where k is the constant of proportionality.

To find the value of k, we can use the given information that y is equal to 10 when x is equal to 2.

Substituting these values, we get:

10 = k/2

Multiplying both sides by 2, we get:

k = 20

Therefore, the constant of proportionality is 20.

Now, we can use the equation y = k/x and the value of k to find the value of x when y is equal to 8.

Substituting y = 8 and k = 20, we get:

8 = 20/x

Multiplying both sides by x, we get:

8x = 20

Dividing both sides by 8, we get:

x = 2.5

Therefore, when y is equal to 8, x is equal to 2.5.

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Answer:

Direction of the police plane = N57.1E

Speed of the police airplane = 255 km/h

Step-by-step explanation:

The diagram of the situation described is presented in the attached image to this question.

Let the distance the police airplane has to travel to intercept the smuggler at 08:30 be x km

The police airplane moves at 06:30 and plans to intercept the smuggler at 08:30; thereby travelling for 2 hours.

By 08:30, the smuggler would have travelled for 2 hours 30 mins, that is, 2.5 hours, travelling at 200 km/h, that is a total distance of 500 km covered.

So, the paths form a triangle.

Using cosine rule, we can obtain the distance, x, that the police airplane has to travel to intercept the smuggler at 08:30.

x² = 150² + 500² - (2×150×500×cos 85°)

x² = 259,426.63858785

x = 509.34 km

We can obtain the direction, Φ, by finding the angle θ using some rule.

[(Sin 85°)/509.34] = [(Sin θ)/500]

Sin θ = (500 × sin 85°)/509.34 = 0.9779 = 77.94°

From the attached image,

Φ + θ = 90° + 45° = 135°

Φ = 135° - θ = 135° - 77.94° = 57.06° = 57.1°

Therefore,

Speed of police airplane = (distance)/(time) = (509.34/2) = 254.67 km/h = 255 km/h

Direction of the police plane = N57.1E

Hope this Helps!!!

1. The sample mean is 24 minutes. The population mean is 27 minutes. The estimated margin of error of the sample population is 3.5 minutes.

2. The difference in the means of the two groups is 7%. The difference in the means is not due to chance.

3. The point estimate for the percent who want to change the town's name is 0.82. The poll's margin of error is 0.04.

1a) The sample mean is calculated as follows:

(31 + 10 + 13 + 42 + 20 + 23 + 23 + 27 + 25 + 31 + 18 + 13) / 12 = 24 minutes

The population mean is calculated as follows:

(31 + 10 + 13 + 42 + 20 + 23 + 23 + 27 + 25 + 31 + 18 + 13) / 27 = 27 minutes

b) The estimated margin of error is calculated as follows:

z * s / sqrt(n) = 1.96 * 6.2 / sqrt(12) = 3.5 minutes

2. The difference in the means of the two groups is calculated as follows:

88% - 81% = 7%

The point estimate for the percent who want to change the town's name is calculated as follows:

(0.86 + 0.78) / 2 = 0.82

The poll's margin of error is calculated as follows:

(0.86 - 0.78) / 2 = 0.04

3. I think the town is most likely to change its name, because the point estimate is greater than 0.5 and the margin of error is small. This means that it is likely that the majority of adults in the town want to change the name.

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The first step you have to follow is to find k(1) by replacing each x in k(x) for 1:

Now, find g(k(1)), it means, g(-7):

(g°k)(1)=573.

Answer:

good for Mr. Sanchezbut thats a bit expensive ya know?????/

Step-by-step explanation:

Answer:

The slope is - 3 3/8

Step-by-step explanation:

Mathematically, we can calculate the slope m using the formula;

m = Δy/Δx

From the question;

Δy = 27 and Δx = -8

The slope will thus be;

m = 27/-8 = - 3 3/8

The probability of the horse winning the race is 0.95 when the odds of a horse winning a race are 20 to 1.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The three different categories of probabilities are axiomatic, experimental, and theoretical. Based on formulas and input quantities, the theoretical probability determines the likelihood. Based on the experimental values used in the computation, the experimental probability provides a realistic number. The results of theoretical and experimental probabilities frequently diverge. Additionally, the axiomatic probability is founded on the axioms that control probability notions.

Given,

The odds of a horse winning a race are 20 to 1.

The probability of the horse winning the race is:

20/21

0.95

The probability of the horse winning the race is 0.95 when the odds of a horse winning a race are 20 to 1.

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