A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 8%, and the tax in the second city was 5%. The total hotel tax paid for the two cities was $692.50. How much was the hotel charge in each city before tax?

[tex]\square[/tex] The function is continuous. [False]

Both pieces of the function are continuous, so the overall continuity of [tex]g(x)[/tex] depends on continuity at [tex]x=0[/tex].

We have

[tex]\displaystyle \lim_{x\to0^-} g(x) = \lim_{x\to0} \left(\frac1{2^x} + 3\right) = 1 + 3 = 4[/tex]

and

[tex]\displaystyle \lim_{x\to0^+} g(x) = \lim_{x\to0} (-x^2+2) = 2[/tex]

The one-sided limits do not match, so [tex]g[/tex] is not continuous at [tex]x=0[/tex].

[tex]\square[/tex] As [tex]x[/tex] approaches positive infinity, [tex]g(x)[/tex] approaches positive infinity. [False]

[tex]g(x)[/tex] is a large negative number when [tex]x[/tex] is very large, so [tex]g(x)[/tex] is approaching negative infinity.

[tex]\boxed{\checkmark}[/tex] The function is decreasing over its entire domain. [True]

This requires [tex]g'(x) \le 0[/tex] on the entire real line. Compute the derivative of [tex]g[/tex].

[tex]g'(x) = \begin{cases}-\ln(2)\left(\dfrac12\right)^x & x<0 \\\\ ? & x=0 \\\\ -2x & x>0 \end{cases}[/tex]

• [tex]\left(\frac12\right)^x > 0[/tex] for all real [tex]x[/tex], so [tex]g'(x)<0[/tex] whenever [tex]x<0[/tex].

• [tex]x^2\ge0[/tex] for all real [tex]x[/tex], so [tex]-x^2\le0[/tex] and [tex]-x^2+2\le2[/tex]. Equality occurs only for [tex]x=0[/tex], which does not belong to [tex]x>0[/tex].

Whether the derivative at [tex]x=0[/tex] exists or not is actually irrelevant. The point is that [tex]g(b) < g(a)[/tex] if [tex]b>a[/tex] for all real [tex]a,b[/tex].

[tex]\boxed{\checkmark}[/tex] The domain is all real numbers. [True]

There are no infinite/nonremovable discontinuities, so all good here.

[tex]\boxed{\checkmark}[/tex] The [tex]y[/tex]-intercept is 2. [True]

When [tex]x=0[/tex],

[tex]g(0) = -0^2 + 2 = 2[/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:

36

Step-by-step explanation:

81 x (4/9) =

36

Step-by-step explanation:

you need to use the ruler to measure the lengths of it, like place the ruler from A to B and look at the measurement of it

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 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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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?

Using the z-distribution, the p-value would be of:

b) 0.0086.

At the null hypothesis we test if the means are equal, equivalent to a subtraction of 0, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, we test if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

For each sample, they are given as follows:

For the distribution of differences, it is given by:

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

z = -2/0.76

z = -2.63.

Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.

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Answer: 4766125

//////////

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 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:

[tex]\huge\boxed{\sf \{-3, 1/2\}}[/tex]

Step-by-step explanation:

4x² + 10x = 6

Take 2 common

2(2x² + 5x) = 6

Divide 2 to both sides

2x² + 5x = 3

Subtract 3 to both sides

2x² + 5x - 3 = 0

Using mid-term break

2x² + 6x - x - 3 = 0

Take common

2x(x + 3) - 1(x + 3) = 0

Take (x + 3) common

(x + 3)(2x - 1) = 0

Either,

x + 3 = 0      OR     2x - 1 = 0

x = -3           OR       2x = 1

x = -3            OR     x = 1/2

[tex]\rule[225]{225}{2}[/tex]

Answer: x = 3 or (-1/2)

Step-by-step explanation:

Given equation

4x² + 10x = 6

Subtract 6 on both sides

4x² + 10x - 6 = 6 - 6

4x² + 10x - 6 = 0

Use cross-multiplication to factorize the quadratic

Starting with:

2x             -6

2x             1

This gives us:

(2x - 6) (2x + 1) = 0

Assume each value in the parenthesis to be 0

PART I:

2x - 6 = 0 ⇒ Given equation

2x - 6 + 6 = 0 + 6 ⇒ Add 6 on both sides

2x / 2 = 6 / 2 ⇒ Divide 2 on both sides

[tex]\boxed{x=3}[/tex]

PART II:

2x + 1 = 0 ⇒ Given equation

2x + 1 - 1 = 0 - 1 ⇒ Subtract 1 on both sides

2x / 2 = -1 / 2 ⇒ Divide 2 on both sides

[tex]\boxed{x=-\frac{1}{2} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

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:

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

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

Answer:

2358.1

Step-by-step explanation:

2.3581 x 10^3

= 2.3581 x 10000

=2358.1

Answer: The base graph vertically stretched by a factor of 6.

Step-by-step explanation:

See attached image.

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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Answer:

10

9

0

Step-by-step explanation:

you subtract the number of all your answers

The equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1

A line is the shortest distance between two points. The equation of a line in slope-intercept form is expressed as;

y = mx + b

m is the slope

b is the y-intercept

Given that m=1, b=-3, the required equation will be y = x - 3 or x - y = 3

For the parameter m=1, (-1,2)

y - 2 =1(x+1)

y - 2 = x+1

y =x + 3

Hence the equation of the line for the parameters m=1, (-1,2)  is y = x + 3

For the coordinates (-2,3),(-3,4)

Slope = 4-3/-3+2
Slope = -1

For the intercept;

4 =-1(-3) + b

b = 4 - 3

b = 1

Hence the equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1

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Answer:

$17.2

Step-by-step explanation:

120 + 16*100 = 120 + 1600 = 1720

The member pays $1720 annually for 100 classes and membership fee combined.

1720/100 = 17.2

The student pays $17.2 per class on average.

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]

Answer:

It is proportional.  When You graph it, it will go through the origin.  The slope is 5.  The y intercept is 0.

Step-by-step explanation:

When a linear function is proportional, the slope will be in the form of y/x.

So, say we put 2 in for x, then y would be 10.  2 is the x and 10 is the y.  What is 10/2? 5 (the slope)

If we put in 6 for x, then y would be 30.  5 is the x and 30 would be the y.  What is 30/5? 5 (the slope)

if we put in -3 for x, then y would be -15.  -3 is the x and -15 would be the y.  What is -15/-3? 5 (the slope).

We could not find the slope this way, if the line was not proportional.

For example, if the y intercept is not zero, like

y = 5x + 2.  If I put 3 in for the x, then the y would be 17.  Is 17/3 equal to 5?  No, because the line is not proportional.

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 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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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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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!

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

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

The graph that best corresponds to the situation is graph 4; option C

Number of pages read is on the y - axis

Time taken is on the x - axis

Therefore, graph 4 represent the situation

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Answer:Joey is 18 hope that helped you

Using proportions, the property tax on a house with an assessed value of $762,000 is of $8,890.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The tax rate, as a proportion, is:

7280/624000 = 0.011667.

Hence, the property tax on a house with an assessed value of $762,000 is of:

0.011667 x 762,000 = $8,890.

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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.