Why do ratios change?

When x = -2, we use the second part of the function, so g(-2)=0.

Similarly, g(4) = -4.

The solution of x in the given expression [tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex] is 4. However, if it is [tex]\mathbf{\sqrt{(3x-8)+1} = \sqrt{(x+5)}}[/tex], it is 6.

The solution to the given algebra expression involving surds can be seen in the steps below.

Given that:

[tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex]

Remove the square roots, we have:

12x - 32 = 4x² - 48x + 144

Solving the quadratic equation at the RHS and equating it to LHS, we have:

x = 11, x = 4

Verifying the solutions by replacing the value of x with the given equation:

Therefore, we can conclude that the value of x = 4

NOTE:

Given that:

[tex]\mathbf{\sqrt{(3x-8+1)} = \sqrt{(x+5)}}[/tex]

Square both sides

3x - 7 = x +5

Solve for x

3x - x = 5 + 7

2x = 12

x = 6

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Using the normal distribution, it is found that the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot is of 3.7 minutes.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 4.5, \sigma = 1[/tex]

The cut-off time is the 100 - 75.8 = 24.2th percentile, which is X when Z = -0.7, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.7 = \frac{X - 4.5}{1}[/tex]

X - 4.5 = -0.7

X = 3.7.

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The logarithmic function expresses the output variable, y, as a function of the logarithm of the input variable, x, as a function of a base b. The true statements are therefore;

The given logarithmic equation is presented as follows;

[tex]y = log_{b}(x) [/tex]

Therefore, we have;

[tex]x = {b}^{y} [/tex]

Where b = 1, we have that x will always be 1, therefore;

[tex]b = \sqrt[y]{x} [/tex]

Therefore;

Which gives;

The statements that are true is therefore;

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The conclusion is P(pass l morning) = 0.56

P(pass l afternoon) = 0.72

Conclusion: a student taking the test in the afternoon has a greater probability of passing than a student taking the test in the morning.

Probability is the odds that a random event would happen. The odds that the event would happen lies between 0 and 1. The closer the probability is to one, the more likely it is for the event to happen.

P(pass l morning) = number of students who took the test in the morning and passed / total number of students that took the exam in the morning

28 / 50 =  0.56

P(pass l afternoon) = number of students who took the test in the afternoon and passed / total number of students that took the exam in the afternoon  = 36 / 50 = 0.72

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Answer:

C

Step-by-step explanation:

Just took the quiz

Answer:

Step-by-step explanation:

10yy'=x

[tex]10y\frac{dy}{dx} =x\\separating~the~variables\\10 ydy=xdx\\integrating\\\int 10ydy=\int xdx+c\\\frac{10y^2}{2} =\frac{x^2}{2} +c\\10y^2=x^2+2c\\when~x=10\\y=4\\10(4)^2=10^2+2c\\160=100+2c\\2c=160-100=60\\c=\frac{60}{2} =30\\10y^2=x^2+60\\10y^2-x^2=60[/tex]

The probability of picking a ticket that is green or has a number greater than four is 3/5

The given parameters are:

Yellow = 1 - 5

Green = 1 - 5

Total = 10

There are 2 cards whose numbers are greater than 4 i.e. Yellow 5 and Green 5

So, we have:

P(Number greater than 4) = 2/10

There are 5 green cards.

So, we have:

P(Green) = 5/10

Also, 1 green card is numbered greater than 4

So, we have:

P(Green greater than 4) = 1/10

The required probability is:

P = P(Green) + P(Number greater than 4) - P(Green greater than 4)

This gives

P = 5/10 + 2/10 - 1/10

Evaluate

P = 6/10

Simplify

P =3/5

Hence, the probability of picking a ticket that is green or has a number greater than four is 3/5

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Answer:

Did you know that the first person convicted of speeding was going eight mph.

Step-by-step explanation:

Answer:

The solution for the above fraction is

[tex] \frac{146}{167} [/tex]

Step-by-step explanation:

Greetings!

look at the attachment above for the explanation.

The two statements that are true for g(x ) are:

g(x) = [tex]4^{x}[/tex] - 1

g(x) is translated both vertically and horizontally.

A function is a relation showing the relationship between two or more variables.

A function produces a unique output when a unique input is given to it. The input is called the domain and the output is called the Range.

Analysis:

If we use the values of x as 0,1,2,3

for x = 0

g(0) = [tex]4^{0}[/tex] -1  = 1 -1 = 0

for x = 1

g(1) = [tex]4^{1}[/tex] -1  = 4 - 1 = 3

for x = 2

g(2) = [tex]4^{2}[/tex] - 1 = 16 - 1 = 15

for x = 3

g(3) = [tex]4^{3}[/tex] - 1 = 64 - 1 = 63

Therefore g(x) = [tex]4^{x}[/tex] - 1

Also since the values of g(x) changes along the y - axis and x-axis also changes, therefore, g(x) is translated along both axes.

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Answer:

2358.1

Step-by-step explanation:

2.3581 x 10^3

= 2.3581 x 10000

=2358.1

Answer:

a. 13/26 = 1/2

b. 3/13

c. 2/26 = 1/13

Step-by-step explanation:

A. 26 red cards and 13 of them are hearts so 13/26 which can be simplified to 1/2

B. 13 hearts but only jack, queen king are higher than 10 so 3/13

C. 26 red cards altogether and we have a total of 2 red jacks so 2/26 which can be simplified to 1/13

is this what you wanted?

Answer:

y= 4x -4

Step-by-step explanation:

Slope-intercept form is given by y= mx +c, where m is the slope and c is the y-intercept.

Given that the slope is 4, m= 4.

Substitute the value of the slope into the equation:

y= 4x +c

The value of c can be found by substituting any point in which the line passes through into the equation above.

When x= 4, y= 12,

12= 4(4) +c

12= 16 +c

Subtract 16 from both sides:

c= 12 -16

c= -4

Thus, the equation of the line is y= 4x -4.

Additional:

For more questions on slope-intercept form, do check out the following!

Work Shown:

m^2+9m=0

m(m+9)=0

m = 0 or m+9 = 0

m = 0 or m = -9

For more information, check out the topics about factoring and the zero product property.

Answer:Joey is 18 hope that helped you

Answer:

C) 100

Step-by-step explanation:

250+600-350-400

850-350-400

500-400=100

The terms that completes the sentence are zeros; vertical. Option A

The functions of a sign chart include;

From the mentioned functions, we can se that the terms that completes the sentence are zeros and vertical asymptotes.

Thus, the terms that completes the sentence are zeros; vertical. Option A

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The cubic function can be graphed using the function behavior and the points.

x   0    1     2        3      4

y   0  −4   −12   −18  −16

Put  x = 0.

Replace the variable x with 0 in the expression.

[tex]f(0)=(0)^3-5(0)^2[/tex]

Raising 0 to any positive power yields 0.

f(0) = 0 − 5⋅0

f(0) = 0

y = 0

Put x = 1.

Replace the variable x with 1 in the expression.

[tex]f(1)=(1)^3-5(1)^2[/tex]

f(1) = 1− 5⋅1

f(1) = −4

y = −4

Put x = 2.

Replace the variable x with 2 in the expression.

[tex]f(2)=(2)^3-5(2)^2[/tex]

[tex]f(2)=8-5(2)^2[/tex]

f(2) = 8 − 5⋅4

f(2) = −12

y = −12

Put x = 3.

Replace the variable x with 3 in the expression.

[tex]f(3)=(3)^3-5(3)^2[/tex]

f(3) = 27 − 45

f(3) = −18

y = −18

Put x = 4.

Replace the variable x with 4 in the expression.

[tex]f(4)=(4)^3-5(4)^2[/tex]

[tex]f(4)=64-5(4)^2[/tex]

f(4) = 64 − 5 ⋅16

f(4) = 64 − 80

f(4) = −16

y = −16

The cubic function can be graphed using the function behavior and the points.

x   0    1     2        3      4

y   0  −4   −12   −18  −16

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Answer:

6 x 2 x 2 x 1

Step-by-step explanation:

6 x 2 = 12

12 x 2 = 24

24 x 1 = 24

The two sets of parametric equations for the rectangular equation are;

It follows from the task content that the parametric equations can be determined as follows;

By substituting the x= t+6 into the rectangular equation; we have;

y = (t+6-6)²-7(t+6)

y = t²-7t-42.

By substituting the x= 7t into the rectangular equation; we have;

y = (7t-6)² -7(7t)

y = 49t² - 84t +36 - 49t

y = 49t² - 133t +36.

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The expected value of the outcome of the bid is $0.18

So let's start by counting how many bids are placed up to a total of 160.

100*160 = 16000.

What will be your arbitrary bid? As each bid has an equal chance of success, the average of all bids is used. (One cent plus 160 dollars) / 2 = 80 dollars (rounded)

Your odds of winning are 1/16000 (1 bid out of 16000).

If you win, your profit is 1920 ($2000 minus $80.00).

1920/16000 is $0.12

Your cost to enter the auction is $1, and your average winning offer is $0.12.

The result is $0.18 (0.12-1=-0.88).

Thus the expected value of the outcome of the bid is $0.18

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The previous tax rate was 20%

What is tax rate?

Tax rate is the percentage of the earnings tax payers would pay to the government from their earnings as taxes.

It should be borne in mind that the new tax rate is 25% which has increased by 25% compared to the previous tax rate, which is the unknown.

The mathematical relationship between the current and prior tax rates is as shown below:

Current tax rate=previous tax rate*(1+% increase in tax rate)

Current tax rate=25%

previous tax rate=X

% increase in tax rate=25%

25%=X*(1+25%)

25%=X*1.25

X=25%/1.25

X=previous tax rate=20%

Technically speaking, an increase of 25% in 20% is 5%(i.e. 20%*25%=5%), which when added to the original 20% would give a tax rate of 25%.That the shortcut to affirming that the new tax rate of 25% is correct

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By definition of vectors exist as quantities that contain magnitude (positive or negative) and direction.

A) The unit vector in the direction of [tex]$F = i + \frac{3j}{2} +2k.[/tex]

B) The distance between [tex]F_{1}[/tex] and [tex]F_{2}[/tex] exists 2.

C) i.) Required vector = −4j − 5k

ii.) Required vector = 5i − 6j − 8k

To estimate the unit vector in the direction of V = 2i+3j+4k

|V| [tex]$= \sqrt{2^2+3^2+4^2}[/tex]

[tex]$= \sqrt{29}[/tex]

A) Unit vector

[tex]$F= \frac{V}{ |V|}[/tex]

[tex]$F= \frac{2i+3j +4k}{2}[/tex]

[tex]$F = \frac{2i}{2} + \frac{3j}{2} +\frac{4k}{2}[/tex]

[tex]$F= i + \frac{3j}{2} +2k.[/tex]

Therefore, unit vector in the direction of [tex]$F = i + \frac{3j}{2} +2k.[/tex]

B) To estimate the distance between [tex]F_{1}[/tex] = 3i+2j+ 5k and [tex]F_{2}[/tex] = 3i +4j +5k

[tex]$d = \sqrt{(3-3)^{2}+(4-2)^{2}+(5-5)^{2}}[/tex]

= 2

Therefore, the distance between [tex]F_{1}[/tex] and [tex]F_{2}[/tex] exists 2.

C) i.) P, (3,2,2), P₂(3,-2,-3)

Required vector =|[tex]P_{1}[/tex]P₂|=(3−3)i + ((−2)-2)j ​+ ((-3)-2)k

= −4j − 5k

ii.) P₂ (2,-3,-6), [tex]P_{3}[/tex] (-3,3,2) ​

Required vector =|P₂[tex]P_{3}[/tex]|=(-3-2)i + (3-(-3))j ​+ (2-(-6))k

= 5i − 6j − 8k

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Answer:

An equilateral triangle with a length of 2

Step-by-step explanation:

A 2-by-2 square implies that the square has a length and width of 2. Since equilateral triangles have the same length for all sides, it tells you that if one side is a certain length, all the other sides must have the same length. The largest length we can fit into this square would be 2 because any larger, the sides of the triangles would not fit into the square. Under the assumption that the length needs to be a whole number, the answer would be 2.

Answer:

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

We know each interior angle of an equilateral triangle is 60°, since each of three angles are of same value.

The middle triangle with two interior angles 4x and y has the missing angle also y, since it is isosceles, because both adjacent angles are equal at vertex N.

First

Measure of any angle in an equilateral triangle is 60°

So

And

Apply angle sum property

[tex]a {}^{2} + ab - 2 {b}^{2} [/tex]

[tex] = (a - b) {}^{2} [/tex]

Answer: 4766125

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Answer:

Step-by-step explanation:

first you we need to times 350,000 4.75 and you got 1662500 then subtract 1662500 - 13 years you got 1662487.

The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

A non linear function is a function whose graph is not linear or can be represented by a straight line.

The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.

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Answer:

10

9

0

Step-by-step explanation:

you subtract the number of all your answers

a. central angle is ∠QPR

b. semicircle is QRS

c. major arc is arc QTS

d. m∠QPR = 130° [central angle theorem]

e. arc QTS = 180°

The central angle theorem states that the measure of the intercepted arc will always be equal to the central angle.

a. A central angle is ∠QPR

b. A semicircle is QRS

c. A major arc is arc QTS

d. Measure of arc QR = m∠QPR = 130° [central angle theorem]

e. arc QTS = semicircle = 180°

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