9. the scenario in problem 14 generates an extraneous solution. neither solution makes a denominator equal zero. why can we not use both solutions?

This system of equations has been solved graphically and by using substitution: it has infinitely many solutions.

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x = 3y + 2     ......equation 1.

5x - 15y = 10     ......equation 2.

By substituting equation into equation 2, we have the following:

5(3y + 2) - 15y = 10

15y + 10 - 15y = 10

15y - 15y = 10 - 10 (infinitely many solutions)

Based on the graph (see attachment), we can logically deduce that the given system of equations has infinitely many solutions.

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Answer:

C

Step-by-step explanation:

It's the only graph that doesn't constantly have its y value increasing the same value each time.

(2 to 6 is +4, 6 to 10 is +4, but 10 to 16 is not +4)

Answer:

C

Step-by-step explanation:

Because you see from Point (-4, 2) to (0,6), the y increases by 4, and the x increase by 4. Same thing from (0,6) to (4,10). But from (4,10) to (8,16) the y increase by 6 so it is the wrong slope.

There are 504 multiple ways to go about doing something. the probability that perhaps a specific event (or group of events) would happen.

either as a range between 0 and 100% or even as a percentage on either a line plot between 0 (impossibility) to 1 (certainty).

THE PROCEDURE IS HERE.

The three airports will each receive a fleet of nine taxis.

Three people travel to airport A, five to airport B, and one to airport C.

There are several different methods that this can be done, including:

(9C3) (6C5) (1C1)

(84) (6) (1) (1)

= 504

The result is that this could be done in 504 different ways.

Based on the probability equation, the likelihood that a will take place is related to the ratio of favorable outcomes to all outcomes. Amount of favorable outcomes/Total Number of outcomes determines the probability that an event will occur, P(E).

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Answer: The number of pounds of sugar in 50% of syrup is 2.5 pounds.

Step-by-step explanation:

What is the percentage?

The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Anton wants to make 5 pounds of sugar syrup.

Let x be the number of pounds of sugar.

A) x/5 =50%

x=0.5×5

x=2.5 pounds

B) x/5 =5%

x/5 =0.05

x=0.25 pounds

C) x/5 =75%

x=0.75×5

x=3.75 pounds

D) x/5 =1.5%

x/5 =0.015

x=0.075 ponds

The volume of the solid with the semicircular base is equal to 2250π units³

In general term integral value means the value obtained after integrating or adding the terms of a function which is divided into an infinite number of terms .

Given here: A solid with a semi circular base with radius = 15 units

We know the the equation of the circle with its center at the origin is given by

x²+y²=15²

[tex]y=\sqrt{15^2-x^2}[/tex]

Thus constructing the integral we get

 [tex]\int\limits^{15}_{-15} \ \pi .\frac{1}{2}.( {15^2-x^2}} )\, dx[/tex]

=-πx.(x²-675) /6 +C |¹⁵₋ ₁₅

=2250π

Hence, The volume of the solid with the semicircular base is equal to 2250π units³

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The height of the cable from the road at a point 150 feet from the center of the bridge is 12.5 feet.

The equation for a parabolic cable is given by

y = ax^2 + bx + c

where x is the horizontal distance from the center of the bridge, y is the height of the cable from the road and a, b, and c are coefficients determined by the shape of the cable.

The height of the cable at the center of the bridge is 0

so, c = 0

The height of the cable at the towers is 80 feet

so, at x = ±300 feet, y = 80

Plugging in these two points into the parabolic equation, we can solve for a and b.

Using the formula

[tex]y = ax^2 + bx[/tex]

we have two equations:

[tex]80 = a * (300)^2 + b * 300 and 0 = a * (0)^2 + b * 0[/tex]

Solving for a and b, we find that

a = -0.000167 and b = 50

Finally, at x = 150 feet from the center,

the height of the cable from the road is

[tex]y = -0.000167 * (150)^2 + 50 * 150 = 50 - 0.000167 * 22500 = 50 - 37.5 = 12.5 feet.[/tex]

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The system of equations has no solution.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are x=4y-11 --------(I) and 3x-12y=-33 --------(II).

Substitute equation (I) in equation (II0, we get

3(4y-11)-12y=-33

12y-33-12y=-33

0=0

Equations has unique no solution.

Therefore, the system of equations has no solution.

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Because lines y and x are parallel, we can see that the angles that are congruent to ∠1 are:

∠5, ∠4, ∠6

We know that lines x and y are parllel lines.

So, the angles in the same quadrant of the two intersections will have the same measure, this means that:

∠1 = ∠5

∠2 = ∠6

and so on.

Also, remember that on an intersection the vertical angles have the same measure, that means that:

∠1 = ∠4

∠5 = ∠6

Then, the angles that are congruent to ∠1 are:

∠5, ∠4, ∠6

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There are 15 test scores that are 85 or greater out of a total of 30 test scores.

The third quartile, Q3, is the median of the upper half of the set of data. To determine the number of test scores that are 85 or greater, we must first find the median of the upper half of the data set. The formula to calculate the median is

Median = (n+1)/2

where n is the number of observations in the data set. In this case, n is 30. Plugging this into the formula we get

Median = (30+1)/2 = 15.5

Therefore, there are 15.5 test scores that are 85 or greater.

To calculate the number of test scores that are 85 or greater, we subtract 15.5 from 30. This gives us 14.5 test scores that are 85 or greater. Since 14.5 is not a whole number, we can round up to 15 test scores that are 85 or greater. Therefore, there are 15 test scores that are 85 or greater out of a total of 30 test scores.

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If we randomly select someone who was aboard the titanic, what is the probability that person is a man, given that he died is 1360/1517.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

Probability that person is a man, given that he died,

P(x) = Favorable outcome/Total

= 1360/ 1517.

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The number of gigabytes of data she can use while staying within her budget is 4.2.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 6 is an equation.

We have,

Cost of the flat per month = $51.50

Cost per gigabyte = $3

g = the number of gigabytes.

Now,

Maximum cost per month = $64.10

We can make an equation.

51.50 + 3g = 64.10

Solve for g.

51.50 + 3g = 64.10

Subtract 51.50 on both sides.

3g = 64.10 - 51.50

3g = 12.6

Divide 3 into both sides.

g = 12.6/3

g = 4.2

Thus,

The number of gigabytes she can use is 4.2.

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The value for question 5 is 15 and for the question 6 is 10.

This theorem says that if two chords intersect, the product of its segments will be equal.

The question gives two circles each one with two chords. For solving the exercise, you should apply the Chord Theorem.

        Segments of chord 1 = 23 and x

        Segments of chord 2 = 23 and 15

Applying the  Chord Theorem, you have:

23*x=23*15

23x=345

x=345/23

x=15

        Segments of chord 2= x+5 and 28

        Segments of chord 2 = 2x and 21

Applying the Chord Theorem, you have:

(x+5)*28=2x*21

28x+140=42x

-42x-28x=-140

-14x=-140

x=-140/-14

x=10

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The solution set of an equation is a collection of all the values called "solution set" or "root set" that make the equation true.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

The solution set of an equation is a collection of all the values that make the equation true. In mathematical terms, it's the set of all values that satisfy the equation.

The solution set can be represented graphically on a number line or coordinate plane, or it can be expressed as an ordered pair, a set of ordered pairs, or an interval. In some cases, the solution set may be empty, meaning there are no values that satisfy the equation. In other cases, it may contain a single solution, infinitely many solutions, or a range of solutions.

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The length of the sides of the triangle is, 11 cm.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

A median drawn on the side of an equilateral triangle divides its perimeter into 20 cm and 13 cm parts.

Here, The perimeter of an equilateral triangle = 20 + 13

                                                                       = 33 cm

Since, The triangle is an equilateral triangle.

Hence, All the sides are equal.

Let the side of an equilateral triangle = x

Hence, We get;

⇒ x + x + x = 33 cm

⇒ 3x = 33 cm

⇒ x = 11 cm

Thus, Each side of an equilateral triangle = 11 cm

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a. 4x + 8 b. 6x + 8x (???) c. 8x + 13 d. 6x + 6y × 6z

b doesnt make sense. is it x(6+8)?

Answer:

A=√16(16-14)(16-12)(16-6)

what is the height

Answer:use a plane and then you plot the points then count the spaces then u count to half the spaces and then look for the numbers on the places and then u have the central point.

Step-by-step explanation:

The slice was made perpendicular to the face BCEH.

The right rectangular prism has four rectangle-shaped lateral faces and two parallel end faces that are perpendicular to each of the bases. Parallelograms make up the faces of an oblique prism, a non-right rectangular prism. Another name for a right rectangular prism is a cuboid.

Given, The right rectangular prism in Figure has been sliced with a plane perpendicular to BCEH.

ZY = 6 inch

If we focus on ∠X of the slice, since it is a right angle, we know that WX must be perpendicular face to BCEH.  Wx lies in face of ABCD, which is perpendicular to both BCEH and ABCD, so WX is perpendicular to ABCD.

This means that WX must also be perpendicular to WZ.  A similar argument can be made for ∠Yof the slice, making all four angles of WXYZ right angles and making WXYZ a rectangle.

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The unit rate is equal to 3 dollars per book.

The unit rate can be determined by dividing the total amount of money raised by the number of books sold.

In the context of the situation, the point (6, 18) means 6 books were sold to raise a total amount of $18.

In Mathematics, the unit rate is sometimes referred to as unit price and it can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the unit price, we would use the following mathematical expression;

Unit price = Total raised/Number of books sold

Unit price = 6/2 = 12/4 = 18/6 24/8

Unit price = 3 dollars per book.

In conclusion, we can reasonably infer and logically deduce that the point (2, 6) means 2 books were sold at Garfield Elementary to raise a total amount of $6.

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13.50

40 - 26.50 = 13.50 because

50 + 50 is 100, so that's 1.00

26+13=39 + that 1.00 = 40

The difference between the experimental Ka and the actual value of Ka could be due to several factors:

It is important to control these sources of error in order to obtain more accurate results. Further investigation and repeat experiments may be necessary to confirm the experimental Ka value and minimize the error.

Complete question:

The actual value of  Ka is  1.78∗10^−5. What could be some reasons for the error between our experimental Ka = 2.19*10^-5 and actual values? CH3COOH⇋H++CH3COO−  To start, we mix the following ingredients in a beaker: 20 ml of 0.02M Acetic Acid 20 ml of 0.02M Sodium Acetate Methyl Red Bromocresol Green The ph was 4.66

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The probability of selecting exactly 2 white marbles out of 5 marbles from container b is approximately 0.144 or 14.4%.

To calculate the probability of selecting exactly 2 white marbles out of 5, we can use the binomial coefficient formula, which is given by:

P(X=k) = (n choose k) × [tex]p^{k}[/tex] × [tex]1-p^{n-k}[/tex]

where n is the total number of trials (in this case, 5), k is the number of successful outcomes (in this case, 2), p is the probability of success (in this case, the probability of selecting a white marble), and (n choose k) is the binomial coefficient.

First, let's find the probability of selecting a white marble from container B, which is given by:

p = (number of white marbles) / (total number of marbles) = (300 + 1) / (300 + 100 + 1) = 301 / 401

Next, we can use the formula to find the probability of selecting exactly 2 white marbles:

P(X=2) = (5 choose 2) × p² * (1-p)⁽⁵⁻²⁾ = (10) × (301/401)² × (100/401)³ = 0.144

So the probability of selecting exactly 2 white marbles out of 5 is approximately 0.144 or 14.4%.

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(p + 90)/6 is the expression equivalent to p/6+ ( 7+ 8)

An expression is combination of variables, numbers and operators.

The given expression is p/6+ ( 7+ 8)

p by six plus seven plus eight.

In the given expression Combine the like terms

p/6 + (7 + 8)

p/6 + 15

LCM 1, 6 is 6

(p + 90)/6

Hence, (p + 90)/6 is the expression equivalent to p/6+ ( 7+ 8)

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A “full house” (3 cards of one kind and 2 cards of another kind)

Since there are 13 sets of each type, we have to select any 2 kinds of it.

The probability becomes : 2× ¹³C2 × ⁴C3 × ⁴C2 : ^52C5

On simplification,

= 3744 / 2598960

= 0.00144

So the probability of a “full house” is 0.00144.

Probability is a measure of the probability that an event will occur in future. Probability is expressed between 0 to 1 or in percentage".

There are three important things in discussing probability, namely trials (experiment), result (outcome). and events.

For example, the activity of tossing coins will result in the appearance of images or numbers, the activity of buying and selling shares will result in buying or selling events.

So the outcome is all the possible events that will occur as a result of an experiment or activity.

Events show the results that occur from an event. In every experiment or activity there is only one possible outcome. In the activity of buying and selling shares, if you don't buy, it means selling. When prices change, inflation or deflation occurs.

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Ordered pairs for the image of ABCD after dilated by 3/2 with the center of dilation at the origin is A’(-3, 4.5), B’(-6,-6), C’(6, 0), D’(7.5, 6).

Dilation is defined as for the given geometrical shape when the size of the given shape get changed as per the given condition without changing its shape.

According to the question,

From the given figure ABCD

Ordered pair of A ( -2,3) , B(-4,-4) , C(4,0), D( 5,4)

Dilated  3/2by  with the center of dilation at the origin

New ordered pair after dilation we have,

A¹(-2(3/2)), 3(3/2) =A¹(-3,4.5)

B¹)-4(3/2), -4(3/2) = B¹(-3,4.5)

C¹ (4(32), 0(3/2) = C¹(6,0)

D¹(5(3/2), 4(3/2) = D¹(7.5,6)

Hence, ordered pairs for the image of ABCD after dilated by 3/2 with the center of dilation at the origin is A’(-3, 4.5), B’(-6,-6), C’(6, 0), D’(7.5, 6).

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The probability that all 3 cards are clubs will be 0.0129

To find the chance that all three cards are clubs,

We can use the following formula:

[tex]P(\text{all 3 are clubs}) = \frac{\text{number of favorable outcomes}}{\text{number of possible outcomes}}[/tex]

The number of favorable outcomes is the number of ways to choose 3 clubs from the 13 clubs in the deck, which is given by the given binomial coefficient [tex]{13 \choose 3} = 286[/tex]

The number of possible outcomes is the number of ways to choose 3 cards from the deck, which is given by the binomial coefficient [tex]{52 \choose 3} = 22,!100[/tex]

Therefore, the value of the probability that all 3 cards are clubs is:

[tex]P(\text{all 3 are clubs}) = \frac{\text{number of favorable outcomes}}{\text{number of possible outcomes}} \\= \frac{286}{22,!100} \\\approx 0.0129[/tex]

Rounding to 3 decimal places, the answer is 0.013.

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The complete questions should be:

A standard deck of cards has 52 cards. There are 4 suits clubs, diamonds, hearts, and spades each of which has 13 cards. Suppose you draw 3 cards without replacement. What is the chance that all three are clubs? Round your answer to 3 decimal places

Answer: 40.82

Step-by-step explanation:

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).

13 * 3.14 = 40.82

This may be wrong, but I found this on the internet

Answer: $0.69

Step-by-step explanation: Divide $3.45 by 5 :)

1) The new coordinate of the triangle is gotten by the transformation rule; 180° counterclockwise

2) The coordinates of the point T' are; T'(2, 8)

1) The coordinates of the triangle XYZ are;

X(1, 2), Y(3, 5), Z(-3, 4)

The coordinates of the transformed triangle X'Y'Z' are;

X'(-1, -2), Y'(-3, -5), Z'(3, -4)

The transformation rule here is; (x, y) → (-x, -y)

This is a rotation of 180 degrees counterclockwise about the origin

2) The coordinates of the line are given as;

S(6, -1) and T(2, -8)

A rotation of 210° clockwise gives the transformation rule:

(x, y) → (x, -y)

Thus, we have the new coordinate of T as; T'(2, 8)

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