on Practice Describe each of the following events as impossible, unlikely, as likely as not, likely, or certain.
a. Gavin rolls an even number on a number cube.
​

Applying the midpoint formula, the coordinates of B are: (-5, -8).

The midpoint formula is:

M(x, y) = [(x1 + x2)/2, (y1 + y2)/2].

Given the following:

M(x, y) = (-2, -6)

A(x1, y1) = (1,−4)

B(x2, y2) = (?, ?)

Plug in the values

M(-2, -6) = [(1 + x2)/2, (-4 + y2)/2]

Isolate each coordinate

-2 = (1 + x2)/2

(-2)(2) = 1 + x2

-4 = 1 + x2

-4 - 1 = x2

-5 = x2

x2 = -5

-6 = (-4 + y2)/2

(-6)(2) = -4 + y2

-12 = -4 + y2

-12 + 4 = y2

-8 = y2

y2 = -8

Therefore, applying the midpoint formula, the coordinates of B are: (-5, -8).

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Answer:

 2 touchdowns, 3 field goals

Step-by-step explanation:

The number of touchdowns cannot be more than 3, so it is relatively easy to find the solution by trial and error.

 23 is not divisible by 3, so 0 touchdowns is not a solution

 23 -7 = 16 is not divisible by 3, so 1 touchdown is not a solution

 23 -14 = 9 is divisible by 3, so 2 touchdowns and 3 field goals is a solution

 21 -21 = 2 is not divisible by 3, so there is only one solution.

Answer:

1 touchdown and 3 field goals

Step-by-step explanation:

To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.

The roots of f(x)=5x^2-80x+69, f(x)=-9x^2+81x+6 is mathematically given as

This is further explained below.

Generally,  the equation for the function is  mathematically given as

f(x)=5x^2-80x+69

Therefore

Set5 x^2-80 x+69 equal to 0 .

5 x^2-80 x+69=0

Solve for x.

Use the quadratic formula to find the solutions.

[tex]\frac{-b+\sqrt{b^2-4(a c)}}{2 a}[/tex]

Substitute the values a=5, b=-80, and c=69 into the quadratic formula and solve for x.

[tex]\frac{80 \pm \sqrt{(-80)^2-4 \cdot(5 \cdot 69)}}{2 \cdot 5}[/tex]

[tex]x=\frac{40 \pm \sqrt{1255}}{5}[/tex]

The final answer is the combination of both solutions.

[tex]x=\frac{40+\sqrt{1255}}{5}, \frac{40-\sqrt{1255}}{5}[/tex]

In conclusion, we implore the same format to solve for

f(x)=-9x^2+81x+6

Roots

x=9.07347, -0.07347

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Answer:

Yes

Step-by-step explanation:

Perpendicular lines form 90-degree angles

we can rewrite:

|x - 1| if x >1

as

(x - 1)   with x > 1.

Remember how the absolute value function works:

In this case, we have the function:

|x - 1| if x >1

Then the minimum value (not included) that this can take is:

|1 - 1| = 0

So it is only 0 or positive, then we can use the first bullet point only, then we can rewrite:

|x - 1| if x >1

as

(x - 1)   with x > 1.

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The length of AB of the given triangle ABC is 23.41cm.

So, Pythagoras's Theorem is used: a²+b² = c²

If we swap the values,

Then,

Therefore, the length of AB of the given triangle ABC is 23.41cm.

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Answer: The answer would be for "B" that it's 6 units to the left and 0 units down and for "C" It would 1 to the left and -5 units down!

Step-by-step explanation: I used a graph to help me determine these coordinates :D

Using permutations and combinations, The number of different ways this can be done is 316250 ways.

A permutation is an orderly arrangement of the items or numbers. Combinations are a means to choose items or numbers from a collection or set of items without regard for the items' chronological sequence.

We will solve it using permutations and combinations

a. The number is ²⁵P₄=  25! / (25 - 4)!

25! / 21! = 25 × 24 × 23 × 22 = 303600 ways.

b. The number is ²⁵C₄= 25! / 4! . (25 - 4)!

= 25! / 4! . 21! = 25 × 24 × 23 × 22 / 4 × 3 × 2

= 12650 ways

Total number of ways to select persons are =

303600 + 12650

= 316250

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Using integrals and probabilities, it is found that:

a) The value of a is of a = 8.

b) The reliability of the refrigerator for the first year is of 93.75%.

c) There is a 0.0004 = 0.04% probability that a refrigerator will fail during the first month.

The distribution is given as follows:

f(t) = t/a, 0≤t≤4.

The cumulative distribution function(cdf) is of 1, hence:

[tex]\int_{0}^{4} f(t) dt = 1[/tex]

[tex]\int_{0}^{4} \frac{t}{a} dt = 1[/tex]

[tex]\left(\frac{t^2}{2a}\right)_{t = 0}^{t = 4} = 1[/tex]

Applying the Fundamental Theorem of Calculus:

8/a = 1

a = 8.

Hence:

The value of a is of a = 8.

The probability that the refrigerator lasts more than one year is:

[tex]P(t > 1) = \int_{1}^{4} \frac{t}{8} dt[/tex]

[tex]P(t > 1) = \left(\frac{t^2}{16}\right)_{t = 1}^{t = 4}[/tex]

P(t > 1) = 1 - 1/16

P(t > 1) = 15/16

P(t > 1) = 0.9375 = 93.75%.

The reliability of the refrigerator for the first year is of 93.75%.

For item c, the probability that a refrigerator will fail during the first month is:

[tex]P\left(t < \frac{1}{12}\right) = \int_{0}^{\frac{1}{12}} \frac{t}{8} dt[/tex]

[tex]P\left(t < \frac{1}{12}\right) = \left(\frac{t^2}{16}\right)_{t = 0}^{t = \frac{1}{12}}[/tex]

Hence:

P(t < 1/12) = 1/(144 x 16) = 0.0004.

There is a 0.0004 = 0.04% probability that a refrigerator will fail during the first month.

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The vertical distance of the jump is 4.8 feet.

We know that the equation that relates the vertical distance of the jump and the time is:

t = √d/2

In this case, we know that the time is t = 1.09 seconds, replacing that in the equation we get:

1.09 = √d/2

Now we can solve that equation for d.

1.09*2 =  √d

Now we apply an exponent of 2 in both sides to remove the square root:

2.18^2 = d = 4.8 ft

The vertical distance of the jump is 4.8 feet.

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If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.

Time = Distance/speed

Time taken to row upstream:

(30/2) /(9 - x)

15/(9-x)

Time taken to row downstream:

15/(9 + x)

Total time spent is 6 hours hence,

15/(9- x) + 15/(9 + x) = 6

Cross multiplying

15(9 + x) + 15(9 - x) = 6(9+ x)(9 - x)

= 135 + 15x + 135- 15x =6(81 -9x + 9x - x²)

=270 = 6(81 - x²)

270/6 = 81- x²

45 = 81- x²

x² = 81- 45

x²= 36

x =√36

x = 6

Therefore If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.

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Answer: 32 i think

Step-by-step explanation:

assuming there was one original bacteria, then multiplying it by two, or splitting it in two five times means 32

The solution to the above question is -147

-3[(w-6) ^2+x] ^2 where the value of w = 5 and x amounts to 6

Using algebraic identity: (a-b) ^2 = (a^2 -2ab+b^2)

= -3 [(w^2 -2w*6 +6^2) + x] ^2

= -3 [(w^2 -12w+36) + x] ^2

now substitute the value of w = 5

= -3 [(5^2 -12*5+36) + x] ^2

= -3 [(25 -60+36) + x] ^2

= -3 [1+ x] ^2

Using algebraic identity: (a+ b) ^2 = a^2 +2ab + b^2

= -3 [1^2+2x*1+ x^2]

= -3 [1+2x+ x^2]

now substitute the value of x = 6

= -3 [1+2*6+ 6^2]

= -3 [1+12+ 36]

= -3 [49]

= -147

The above answer can be derived through direct substitution also. Both the methods will any way give the same answer.

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The absolute value inequality that represents the range of monthly car payments that you can afford is 52 < | x | ≤ 60.

An absolute value inequality is an inequality that has an absolute value sign with a variable inside.

Example:  | x + 2 | > 4

We have,

Financing a car for 5 years.

Monthly payment = $225

Since 5 years = 5 x 12 months = 60 months.

The cost of the car:

= 60 x $225

= $13500

Absolute deviation = $35

This means monthly payments can be increased maximum up to $35.

So if the monthly payment is increased maximum we have the monthly payment as:

= $225 + $35

= $260

If $260 is the monthly payment then,

The number of months the car finance can be done is:

= $13500 / $260

= 51.9 months

The absolute value inequality for the range of months is:

52 < | x | ≤ 60

Where x is the number of months to finance the car.

Thus the absolute value inequality that represents the range of monthly car payments that you can afford is 52 < | x | ≤ 60.

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=======================================================

Explanation:

The domain is the set of allowed x inputs.

The left-most part of the graph is at x = -9. There is no right-most part since it goes on forever in that direction due to the arrow.

So we can say [tex]x \ge -9[/tex] or [tex]-9 \le x[/tex] or [tex]-9 \le x < \infty[/tex]

That third inequality mentioned then turns into the interval notation [tex]\big[-9, \infty\big)[/tex]

Use a square bracket to include -9 as part of the domain. It's included because of the closed filled in circle, in contrast to a open hole.

We always will use a curved parenthesis for either infinity since we cannot actually reach it (it's not a number to reach).

---------------------

Now onto the range. This is the set of possible y outputs.

The graph stretches forever downward, so there is no lower bound. The upper bound, or highest part, is when y = 3

The range as a compound inequality is [tex]-\infty < y \le 3[/tex] which condenses to the interval notation of [tex]\big( -\infty , 3 \big][/tex]

Once again, use a square bracket to include the endpoint 3.

----------------------

The absolute max is the highest point of the graph. It's the peak of the mountain. In this case, the absolute max is y = 3. This is the relative max also. The relative max is the maximum within a certain specified interval.

There is no absolute min since the graph goes downward forever. There is no lowest point. This also rules out a relative min as well.

----------------------

The function is increasing when it goes uphill as you move to the right.

The graph shows the function increases on the interval -9 < x < -3 which condenses to the interval notation (-9, -3). This is NOT ordered pair notation which unfortunately looks identical to interval notation when using curved parenthesis for both endpoints.

In contrast, the function decreases when it goes downhill (when moving to the right). This occurs when [tex]4 < x < \infty[/tex] which shortens down to the interval notation of [tex](4, \infty)[/tex]

The graph is flat or constant when it's neither increasing nor decreasing. The graph is constant when -3 < x < 4 which translates to the interval notation of (-3, 4)

----------------------

Now onto the x and y intercepts

The x intercepts are where the graph crosses the horizontal x axis.

We have the two locations of x = -6 and x = 6 as the x intercepts

The y intercept is at y = 3, which is where it crosses the y axis. This also happens to be the max value mentioned earlier, though the y intercept won't always be the max.

-----------------------

Lastly, let's compute f(8)

Locate 8 on the x axis. Then draw a vertical line through this. The vertical line crosses the curve at (8, -3). Then move to the left until hitting y = -3 on the y axis

So x = 8 plugged in leads to y = -3 as the output.

Therefore, f(8) = -3

Answer: 1: $27.92

Step-by-step explanation: Multiply the amount of goodie bags (8) by how much they cost individually ($3.49) and you should come out with the answer $27.92.

Answer: 2 : $37.5

Step-by-step explanation: This would be considered not using long division but this should be the only practical answer. Using long division you would come up with 37 with a remainder of 2, which doesn't seem to be correct.

Answer: 3 : $177.92

Step-by-step explanation: Adding the cost of both the goodie bags and the 4 hours worth of the bounce house the total should have came out to be, $177.92

The ratio of their perimeters = 11/6

The ratio of their areas = 121/36

Similar figures are defined as two or more figures that have different sizes but the same shape. By implication, they have the same interior angle measures but different corresponding side lengths that are proportional to each other.

Thus, the ratios of their side lengths are all the same or congruent.

To find the perimeter of two similar figures, A and B, the following ratio is used:

Side length of figure A/Side length of figure B = Perimeter of figure A/Perimeter of figure B

To find the perimeter of two similar figures, A and B, the following ratio is used:

(Side length of figure A)²/(Side length of figure B)² = Area of figure A/Area of figure B.

Given:

Side length of the red figure = 11

Side length of the blue figure = 6

Therefore:

11/6 = Perimeter of red figure/Perimeter of blue figure

Perimeter of red figure/Perimeter of blue figure = 11/6

(11)²/(6)² = Area of red figure/Area of blue figure.

Area of red figure/Area of blue figure = 121/36

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Answer:

Fill in the blanks to declare sum equal to a + b (int _ = a __b)Which of the following is not a valid variable name in python?What shape represents the start and end of a flowchart?Which of the following is not a valid variable name in python?An integer data type can hold decimal values.Which of the following is not a valid variable name in python?An integer data type can hold decimal values.Which of the following is not a valid variable name in python?Fill in the blanks to declare sum equal to a + b (int _ = a __b)Variables must be defined with a name and a data type before they

can be usedAn integer data type can hold decimal values.Which of the following is not a valid variable name in python?Fill in the blanks to declare sum equal to a + b (int _ = a __b)Variables must be defined with a name and a data type before th

The most appropriate choice of percentage will be given by-

16.67 % of carton is cracked

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Here,

Number of eggs cracked = 2

Total number of eggs = 12

Percentage of carton cracked = [tex]\frac{2}{12} * 100[/tex]

                                                  = 16.67 %

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The total weight of 4 packets will be equal to 5 and 1 / 2 pounds.

We are given that:

The total number of packages = 4

Weight of each of the package is given as 1 and 3 / 8 pounds

Weight of 1 package = 1 and 3 / 8 pounds.

Weight of 1 package = 11 / 3 pounds

Now, we need to calculate the total weight of 4 packets.

We will do this my multiplying 4 with the weight of each packet.

So, we get that:

Total weight of 4 packets = 4 × 11 / 8 pounds.

Total weight of 4 packets = 11 / 2 pounds

Total weight of 4 packets = 5 and 1 / 2 pounds.

Therefore, the total weight of 4 packets will be equal to 5 and 1 / 2 pounds.

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The equation representing when the two planes would be at the same altitude is 9x=486

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

From (a) we get that: Altitude of Plane A = 990-18x

Altitude of Plane B = 1476-27x

make 890 - 18x = 1476-27x

-18x+27 x = 1476-890

9x=486

X= 54

so pass 54 seconds will the two plane at the same altitude.

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The ratio of Trout to Goldfish to Perch in the pond by using ratio and proportion theorem in its simplest form is 5:2:13

As per the question statement, we are supposed to find out the ratio of Trout to Goldfish to Perch in the given pond in its simplest form.

It is given that 25% of the fish in a pond are Trout, 10% are Goldfish and the rest 65% are Perch in the given pond.

Let's suppose there are 100 fishes in the pond so

Number of Trout = 25% of 100 = 25

Number of Goldfish = 10% of 100 = 10

Number of Perch = 65% of 100 = 65

Using ratio and proportion theorem,

Trout : Goldfish : Perch = 25:10:65

Trout : Goldfish : Perch = 5 : 2 : 13

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The amount invested at 15% was $900 whereas the $300 was invested in the 11% account

How do we represent the amounts invested in each account?

The fact that $900 more was invested in 15% account means that if the amount invested in the 11% is x, then amount in the other would be x+900

interest on 15% account=15%*(x+900)

interest on 15% account=0.15x+135

interest on 11% account=11%*x=0.11x

total interest=0.15x+135+0.11x

total interest on both accounts=0.26x+135

total interest earned=$213

213=0.26x+135

213-135=0.26x

78=0.26x

x=78/0.26

x=$300(amount invested in the 11% account)

amount invested in the 15% account=$300+$900

amount invested in the 15% account=$1200

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Step-by-step explanation:

0 steps to reach floor 0.

a.

floor 0 to floor 1 = floor 0 + 14 = 0 + 14 = 14

floor 1 to floor 2 = floor 1 + 14 = 14 + 14 = 28

floor 2 to floor 3 = floor 2 + 14 = 28 + 14 = 42

floor 3 to floor 4 = floor 3 + 14 = 42 + 14 = 56

floor 4 to floor 5 = floor 4 + 14 = 56 + 14 = 70

b.

when we look at the calculation for the stairs to floor 1, then we see

floor 1 = floor 0 + 14 = 0 + 14 = 14

and for floor 2

floor 2 = floor 1 + 14 = floor 0 + 14 + 14 = 0 + 14 + 14 = 28

and for floor 3

floor 3 = floor 2 + 14 = floor 0 + 14 + 14 + 14 = 42

and so on.

we see

floor n = s(n) = s(0) + 14×n = 0 + 14×n = 14n

s(n) = 14n

A. The function for the amount Kyle has after (w) weeks is f(w) = 450 + 75w.

B. We can assume a reasonable domain for the situation as [1, 2, 3, ... 6).

C. A reasonable range for the situation is {375}.

A domain refers to the set of all possible inputs (independent variables) for the function, including real numbers except zero.

The range refers to the difference between the largest and smallest output values (dependent variables) of a function.

Note that the range depends on the domain.

Initial deposit = $450

Weekly deposits = $75

For (w) weeks, the total deposits = 450 + 75w

Function for the amount Kyle has after (w) weeks is f(w) = 450 + 75w.

A reasonable domain (input value for w) = 6 (six weeks).

A reasonable range (output value for 6 weeks) is 375 (900 - 525).

Thus, the function for the amount Kyle has after (w) weeks is f(w) = 450 + 75w.

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Considering the definition of an inequality, the interval of hours parked for which Garage A is cheaper than Garage B is 6 hours.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "t" the time parked, in hours. If you want to determinate the interval of hours parked for which Garage A is cheaper than Garage B,  the inequality that expresses the previous relationship is

5 + 3t < 11 + 2t

Solving:

3t - 2t < 11 -5

t < 6

Finally, the interval of hours parked for which Garage A is cheaper than Garage B is 6 hours.

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Using proportions, it is found that the car uses gas at a rate of 31.25 miles per gallon.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The gas consumption of the car is given by the proportion of number of miles divided by the number of gallons, hence:

(5/8)/(1/50).

To divide two fractions, we multiply the numerator by the inverse of the denominator, hence:

5/8 x 50 = 31.25.

The car uses gas at a rate of 31.25 miles per gallon.

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