Which of the following points is in the solution set of y < 2x²-3x - 12?


(0,-12) | (4,-4) (0,-15) (3,-3) | (-2,1) (-2,2)​

The ratios that can be used to illustrate how many heads of lettuce,X, he would need to head 275 guests would be = 37/100 = X/275. That is option A.

The number of heads of lettuce needed to feed 100 guest = 37

The number of heads of lettuce that will be needed for 275 guests = X.

Mathematically;

100 guests = 37

275 guests =X

That is,

X * 100 = 37 ×275

Which is the same as = 37/100 = X/275

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The probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

To find the probability that a random student will be taking both Algebra 2 and Chemistry, we need to use the concept of conditional probability.

Let's denote the event of taking Algebra 2 as A and the event of taking Chemistry as C. We are given that P(A) = 0.08 (8% probability of taking Algebra 2) and P(C|A) = 0.17 (17% probability of taking Chemistry given that the student is taking Algebra 2).

The probability of taking both Algebra 2 and Chemistry can be calculated using the formula for conditional probability:

P(A and C) = P(C|A) * P(A)

Substituting the given values:

P(A and C) = 0.17 * 0.08

P(A and C) = 0.0136

Therefore, the probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

It is important to note that the probability of taking both Algebra 2 and Chemistry is determined by the intersection of the two events, which means students who are taking both courses. In this case, the probability is relatively low, as it depends on the individual probabilities of each course and the conditional probability given that a student is taking Algebra 2.

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Answer:

The volume of the Pyramid is 318.3 cubic foot

Step-by-step explanation:

Here, we want to calculate the volume of the Pyramid

Mathematically, the volume of the pyramid is the area of the square base multiplied by the height of the Pyramid.

Since the perimeter is 15.8 and the formula for the perimeter is 4L

we can get the length of the side of the square

The length of the side will be 15.8/4 = 3.95

The area of the square base is thus equal to;

3.95^2 = 15.6025 square feet

Now we can multiply this by the height

Mathematically, that will be;

15.6025 * 20.4 = 318.291 which is approximately 318.3 cubic foot

Answer:

106.1 ft

Step-by-step explanation:

Answer & Step-by-step explanation:

(5√2 - 4√3)(5√2 - 4√3)

We can rewrite this equation into a more simpler form.

(5√2 - 4√3)²

Now, we multiply. When multiplying, its important we multiply each term instead of combining them together.

When you multiply a radical by itself, then the base number will be by itself as the product.

So......

(5)² = 25

(4)² = 16

(√2)² = 2

(√3)² = 3

So, now the equation looks like this..

(25 * 2) + (16 * 3)

Multiply the terms.

50 + 48

Add the numbers.

50 + 48 = 98

So, your answer will be answer choice D. The radical in choice D represents the radicals that are in the problem multiplied together.

Yes, even if you don't know how many handshakes there were overall, you can be sure that there were at least two guests who had the same number.

Assume that the gathering will have n visitors. With the exception of oneself, each person may shake hands with n-1 additional individuals. For each guest, this means that there could be 0, 1, 2,..., or n-1 handshakes.

There will be the following number of handshakes if each guest shakes hands with a distinct number of persons (i.e., no two guests will have the same number of handshakes):

0 + 1 + 2 + ... + (n-1) = n*(n-1) divide by 2

The well known formula for the sum of the first n natural numbers . The paradox arises if n*(n-1)/2 is not an integer since we know that the actual number of handshakes must be an integer. The identical number of handshakes must thus have been shared by at least two other visitors.

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Answer:

The line from point F to point C shows the diameter.

Step-by-step explanation:

The diameter of a circle is the measure from one side of it to the other, but it must run directly through the middle. The only line the runs directly through the middle of this circle is line FC, the line that goes from point F to point C.

I hope this helps!

The perpendicular line symbols in the diagram indicates that the true statements are;

Perpendicular lines are lines that form an angle of 90 degrees with each other.

The plane R and the plane S are both perpendicular to the lines m and n, therefore, the planes R and S will continue indefinitely, maintaining the same distance from each other and the plane R and S are parallel, therefore;

The lines m and n which are perpendicular to the same planes R and S, indicates that they are perpendicular to the line drawn on the planes, joining the lines. The lines m and n which firm the same corresponding angle to the line joining them indicates that the lines m and n are parallel, and will not eventually intersect.

The drawing indicates the line m is perpendicular to the lines p and q, therefore;

The planes R and S are parallel and the lines m and n are also parallel, therefore, the lines joining the lines m and n on both planes and the lengths AD and BC form a parallelogram, such that AB and BC are facing sides of the parallelogram, therefore, AB = BC

The point E is on the line n, and the point C is on the plane S, therefore, the distance \(\overline{EC}\) is the shortest distance from the point E to the plane S, therefore;

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Fatma's account needs to earn a rate of return of approximately 0.2957% per month to stretch her money out for 17 years.

To determine the required rate of return for Fatma's account, we can use the future value formula:

FV = PV * (1 + r)^n

Where:

FV = Future value (amount needed for 17 years of expenses)

PV = Present value (initial amount Fatma has)

r = Rate of return

n = Number of compounding periods (monthly withdrawals over 17 years)

Given:

PV = $182,000.00

Monthly expenses = $1,350.00

Number of years = 17

Number of compounding periods = 17 years * 12 months = 204 months

We can rearrange the formula to solve for the required rate of return (r):

r = (FV / PV)^(1/n) - 1

Substituting the given values:

FV = $1,350.00 * 204 = $275,400.00

r = ($275,400.00 / $182,000.00)^(1/204) - 1

Calculating this expression:

r ≈ 0.002957 (approximately 0.2957%)

Therefore, Fatma's account needs to earn a rate of return of approximately 0.2957% per month to stretch her money out for 17 years.

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Answer:

X'= (-3,6)

Y'=(7,8)

Z'=(11,2)

Step-by-step explanation:

when a point is reflected over the y axis, (x,y) becomes (-x,y). so the x value is just multiplied by -1

Answer:

X′(−3, 6), Y′(7, 8), Z′(11, 2)

Step-by-step explanation:

Imagine you are a spy who needs to infiltrate a secret base located at the origin of the coordinate plane. You have three accomplices, X, Y, and Z, who are waiting for you at different points on the plane. X is at (3, 6), Y is at (-7, 8), and Z is at (-11, 2). You have a device that can reflect any point over the y-axis, which you plan to use to confuse the enemy guards. You decide to reflect X, Y, and Z over the y-axis to create X', Y', and Z', respectively. What are the coordinates of these new points?

To find the coordinates of X', you simply change the sign of the x-coordinate of X. So, X' is at (-3, 6). Similarly, to find the coordinates of Y' and Z', you change the sign of the x-coordinates of Y and Z. So Y' is at (7, 8) and Z' is at (11, 2). Now you have three new points that are symmetric to the original ones over the y-axis.

But wait! There's a problem. The enemy guards have noticed that something is wrong. They see four points on their radar: one at the origin (you) and three on the right side of the y-axis (X', Y', and Z'). They realize that these points are reflections of some other points on the left side of the y-axis. They quickly deduce that there must be a spy among them. They start searching for you.

You need to act fast. You use your device again to reflect yourself over the y-axis. This creates a new point at (-0, 0), which is exactly the same as (0, 0). You have effectively disappeared from their radar. You sneak into the base while they are busy looking for you on the wrong side of the plane.

You have successfully completed your mission. Congratulations! You are a master of reflections.

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

Answer:

so shortcut method for finding slope in equation is simply slope = - coefficent of x/ coefficient of y

Answer:

5/6

Step-by-step explanation:

put the equation into slope-intercept form:  y = mx + b

5x - 6y = 30

-6y = -5x + 30

y = (-5/-6)x - (30/6)

y = 5/6x - 5

Therefore, slope = m = 5/6

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The arithmetic mean provides a single measure for a certain population, also called the average.

The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.

The ratio of the total number of observations divided by the sum of all the given observations is known as the arithmetic mean. For instance, if the data set contains 5 observations, it is possible to get the arithmetic mean by adding all 5 of the given observations and dividing by 5.

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Answer:

$7.34

Step-by-step explanation:

To compute sum of dollars that are not whole numbers. Using the sum of$5.89 and$1.45 as an illustration :

$5.89 + $1.45

Taking the whole numbers first:

$5 + $1 = $6

Take the sum of the decimals :

$0.89 + $0.45 = $1.34

Sum initial whole + whole of sum of decimal

$6 + $1 = $7

Remaining decimal : $1.34 - $1 = $0.34

$7 + $0.34 = $7.34

a) The first five terms of the sequence are 2, 12, 72, 432, 2592.
b) The first five terms of the sequence are -1, 2, -4, 8, -16.

c) The first five terms of the sequence are 2, -1, -3, -2, 1.

To find the first five terms of the sequence defined by each of these recurrence relations and initial conditions, we will use the given recurrence relation and initial conditions to find the next terms in the sequence.

a) an = 6an-1, a0 = 2

The first term is given as a0 = 2. We will use the recurrence relation to find the next terms.
a1 = 6a0 = 6(2) = 12
a2 = 6a1 = 6(12) = 72
a3 = 6a2 = 6(72) = 432
a4 = 6a3 = 6(432) = 2592

So, the first five terms of the sequence are 2, 12, 72, 432, 2592.

b) an = −2an-1, a0 = −1

The first term is given as a0 = -1. We will use the recurrence relation to find the next terms.
a1 = -2a0 = -2(-1) = 2
a2 = -2a1 = -2(2) = -4
a3 = -2a2 = -2(-4) = 8
a4 = -2a3 = -2(8) = -16

So, the first five terms of the sequence are -1, 2, -4, 8, -16.

c) an = an-1 – an-2, a0 = 2, a1 = −1

The first two terms are given as a0 = 2 and a1 = -1. We will use the recurrence relation to find the next terms.
a2 = a1 - a0 = -1 - 2 = -3
a3 = a2 - a1 = -3 - (-1) = -2
a4 = a3 - a2 = -2 - (-3) = 1

So, the first five terms of the sequence are 2, -1, -3, -2, 1.

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Answer:

1

Step-by-step explanation:

from the rule of exponents

• \(a^{0}\) = 1 , then

\((5x)^{0}\) = 1

The original price of the shoes was $108.85.

What is the original price?

The price that was established by the MSRP (manufacturer's suggested retail price) is known as the original pricing.

The original price was often always less expensive than the current price, though original and current prices occasionally coincide.

The cost price of an item is always used to determine the sales tax, which is then applied to the total of the bill.

Tim purchased a pair of running shoes = $79.20

sales tax =10%

shoes were on sale for 40% off the original price,

Let the original price of the running shoes be x.

Converting a given problem into an equation and solving for variable x.

(X-0.4X)+0.1X=79.20

X-0.4X+0.1X=79.2

7X=792

X=108.85

The original price of the shoes was $108.85.

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The value of the measure of angle ∠D of the triangle is m∠D = 34°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the first triangle be represented as ABE

Let the second triangle be represented as DEC

On simplifying the equation , we get

The measure of ∠A = 58

The measure of ∠B = 55

Now , for a triangle ∠A + ∠B + ∠C = 180°

The measure of m∠E = 180 - ( m∠A + m∠B )

The measure of m∠E = 180 - ( 58 + 55 )

On simplifying the equation , we get

The measure of m∠E = 67

And , measure of m∠E of ΔABE = measure of m∠E of ΔDEC ( vertically opposite angles )

The measure of m∠C = 79

Now , for a triangle ∠A + ∠B + ∠C = 180°

So , the measure of m∠D = 180 - ( 67 + 79 )

On simplifying the equation , we get

The measure of m∠D = 34

Hence , the measure of ∠D of the triangle is ∠D = 34

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Answer:

175.84 ft 2

Step-by-step explanation:

50.24 x 2 = 100.48

100.48 + 75.36 = 175.84

The surface area of the cylinder will be 175.84 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called as the surface area.

It is given that:-

Area of each base: 50.24 ft2

Area of lateral surface: 75.36 ft2

Total surface area = (Area of each base x 2 )+ Area of the lateral surface

Total surface area =( 50.24 x 2 )+ 75.36

Total surface area = 175.84 square feet

Hence the surface area of the cylinder will be 175.84 square feet.

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Answer:

2nd option is correct answer

Answer:

-56/8 = -7

Step-by-step explanation:

The experiment of drawing two cards without replacement from a deck consisting of only the ace through 10 of a single suit (e.g., only hearts) has a sample space consisting of all possible pairs of cards that can be drawn. There are a total of 45 possible outcomes in the sample space.



Ai = {(j,k) : j + k = i, where j and k are values of the cards in the suit}
For example, if i = 7, then the event A7 consists of the following outcomes:
A7 = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

Note that we have excluded the outcome (1,1) from this event, since we are assuming that an ace counts as 1 and not 11. If we wanted to include the possibility of an ace being worth 11, we would need to modify the definition of Ai to account for this. However, the problem statement specifies that we should treat the aces as having a value of 1, so we will stick with this convention.

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The procedure for revising probabilities based on additional information is referred to as Bayesian updating

The procedure for revising probabilities based on additional information is referred to as Bayesian updating. Bayesian updating is a fundamental concept in Bayesian statistics, which allows for the incorporation of new evidence or data to update and refine prior beliefs or probabilities.

In Bayesian updating, the process begins with an initial prior probability, which represents the initial belief or knowledge about an event or hypothesis before any evidence is observed. As new evidence or data becomes available, it is used to update the prior probability and generate a posterior probability. The posterior probability represents the revised belief or probability after incorporating the new information.

Bayesian updating follows the principles of Bayes' theorem, which mathematically describes the relationship between prior probabilities, likelihoods, and posterior probabilities. It involves combining the prior probability with the likelihood of observing the data given the hypothesis and then normalizing the result to obtain the posterior probability.

The beauty of Bayesian updating is that it allows for a flexible and iterative process of continuously updating beliefs and probabilities as new information emerges. It provides a framework for incorporating both subjective prior beliefs and objective data to make more informed decisions and predictions. Bayesian updating has applications in various fields, including machine learning, decision-making, and scientific research.

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In the given time interval [0,7]:

(a) the maximum speed is 1096.63 units at t = 7 and

(b) the minimum speed is 0.91 units at time t = ln2/4.

Parametric equations of the curve

x(t) = \(e^t + e^{-t}\)

y(t) = \(e^{-t}\)

so, dx/dt = \(e^t - e^{-t}\)

dy/dt = \(-e^{-t}\)

So, speed: v(t) = \(\sqrt{(dx/dt)^2 + (dy/dt)^2}\) = \(\sqrt{(e^t-e^{-t})^2 + (-e^{-t})^2}\)

When v(t) is maximized or minimized, evidently v² is also maximized or minimized because speed is a positive quantity.

or (speed)² = v² = \((e^t-e^{-t})^2 + (-e^{-t})^2\) = \((e^{2t} + 2e^{-2t} -2)\)

Now, to get the maxima or minima of a curve we have to derivate function

d/dt(v²) = 0 or d/dt\((e^{2t} + 2 e^{-2t} -2)\)

or \(2e^{2t} -4 e^{-2t} = 0\) or \(e^{2t} = 2 e^{-2t}\)

taking logs on both sides

4t lne = ln2 or 4t = ln2 or t = ln2/4

so, the only critical point is t = ln2/4 ∈ [0,7]

To calculate the maxima/minima of v, we will find functional values at the critical point and boundary values of the given interval [0,7].

At t = 0 : v(0) = \(\sqrt{e^0 + 2e^0 - 2} = \sqrt{1+2-2}\) = 1

At t = ln2/4: v(ln2/4) = \(\sqrt{e^{2ln2/4} + 2e^{-2ln2/4} - 2} = \sqrt{2\sqrt{2} -2 }\) = 0.91

At t = 7: v(7) = \(\sqrt{e^{14} + 2e^{-14} - 2}\) = 1096.63

Therefore, in the given time interval [0,7]: (a) the maximum speed is 1096.63 units at t = 7 and (b) the minimum speed is 0.91 units at time t = ln2/4.

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Answer:

the question is uncompltre

Step-by-step explanation:

Answer:

hope it is helpful to you

To create a validation rule in Salesforce that automatically selects grade A when the percentage is set to 90, you can use the ISPICKVAL function. This function allows you to check the selected value of a picklist field and perform actions based on the value. By using ISPICKVAL in the validation rule, you can ensure that the grade field is populated with A when the percentage field is set to 90.

To implement this validation rule, follow these steps:

Go to the Object Manager in Salesforce and open the Student object.

Navigate to the Validation Rules section and click on "New Rule" to create a new validation rule.

Provide a suitable Rule Name and optionally, a Description for the rule.

In the Error Condition Formula field, enter the following formula:

AND(ISPICKVAL(Percentage__c, "90"), NOT(ISPICKVAL(Grade__c, "A")))

This formula checks if the percentage field is selected as 90 and the grade field is not set to A.

In the Error Message field, specify an appropriate error message to be displayed when the validation rule fails. For example, "When percentage is 90, grade must be A."

Save the validation rule.

With this validation rule in place, whenever a user selects 90 in the percentage field, the grade field will automatically be populated with A. If the grade is not set to A when the percentage is 90, the validation rule will be triggered and display the specified error message.

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Answer:

The hundreds place

Step-by-step explanation:

143, first digit is , 1 is in the hundreds place

Answer:

3

Step-by-step explanation:

\(( \sqrt{3} + \sqrt{6) } \times ( \sqrt{6} - \sqrt{3} )\)

\(( \sqrt{6} + \sqrt{3} ) \times ( \sqrt{6} - \sqrt{3)} \)

\(6 - 3\)

\(3\)

Answer:

\( \sf \: x = 25\)

Step-by-step explanation:

Given equation,

→ (x - 7)2 = 36

Now the value of x will be,

→ 2(x - 7) = 36

→ (2 × x) - (2 × 7) = 36

→ 2x - 14 = 36

→ 2x = 36 + 14

→ 2x = 50

→ x = 50/2

→ [ x = 25 ]

Hence, the value of x is 25.

Answer:

x = 25

Step-by-step explanation:

(x-7)2 = 36

divide both sides by 2

x-7 = 18

add 7 to both sides

x = 25

Answer:

$79.7468

Step-by-step explanation: