8. (10 points) Evaluate the following: a) log3 27 b) In 1 9. (5 points) Find the domain of f(x) = log3 (6-4x) and express in interval notation.

The statement that is true about whether A and B are independent events is D. A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25.

Let A be the event that the person rides the bus to school, then:

P(A) = 75/300

P(A) = 0.25

Let B be the event that the person has 3 or more siblings, then:

P(B) = 24/300 = 0.25

P(A/B)=9/24

P(A/B)=0.375

Since P(A/B)=0.375 is different from P(A)=0.25 the events are not independent.

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Answer:

Given: y = x2 + 4x – 5

Find the following

y-intercept

x-intercepts or the zeros of the functions or roots

graph of the function, given vertex is at (-2, -9)

Solve the system of linear equations      – x + 6y = 8        2x + 5y = 3

Write the names of curves, given their equations:  

x2/16 + y2/9 = 1

3y = 2x + 5

(x - 5)2 + (y + 6)2 = 25

x2/16 – y2/25 = 1

y = 2x2 + 10x + 25

Write down the first five terms of the arithmetic progression with the first term 8 and common difference 7, then find the 17th

Write down the first five terms of the geometric progression with the first term 3 and common ratio 2, then find the 17th

The expression to represent the total price of the hats before sales tax is 4.7x.

Given that, Brandon purchased 5 hats.

Calculating the sales tax applied to a purchase is a matter of simply multiplying the tax rate by the purchase price using the equation sales tax = purchase price × sales tax rate. Adding the sales tax to the original purchase price gives the total price paid with tax.

Let the cost of each hat be x.

Here, sales tax is 6%

So, the total price of the hats before sales tax is

5x- 6% of 5x

= 5x-0.06 ×5x

= 5x-0.3x

= 4.7x

Therefore, the expression to represent the total price of the hats before sales tax is 4.7x.

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"Your question is incomplete, probably the complete question/missing part is:"

Brandon purchased 5 hats. Each hat cost the same amount. The total price of the hats was dollars before the store added a 6% sales tax. Write a expression to represent the total cost of hats before sales tax.

The solution to the system is x = 2 and y = 6, represented as the ordered pair (2, 6). This corresponds to option (B) in the answer choices.

To solve the system using substitution, we'll substitute the value of one variable from one equation into the other equation and solve for the remaining variable.

Given the system:

x + y = 8

y = 3x

Substituting the value of y from the second equation into the first equation, we have:

x + (3x) = 8

4x = 8

x = 2

Now, substitute the value of x into the second equation to solve for y:

y = 3(2)

y = 6

Therefore, the solution to the system is (2, 6). Option (B) is the correct answer.

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An interest rate of 4.5%, you would accumulate approximately $27,364.81 in 18 years.

To calculate the total amount accumulated, we can divide the problem into two parts: the first 6 years and the subsequent 12 years.

During the initial 6 years, the account earns interest at a rate of 3%. Using the formula for compound interest, the amount accumulated after 6 years can be calculated as A = P\((1 + r/n)^{nt}\), where A is the final amount, P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values, we find that the amount after 6 years is approximately $4,334.25.

After 6 years, an additional $11,500 is deposited into the account, making the total balance $15,834.25. From this point onward, the interest rate becomes 4.5%. Using the same compound interest formula, we can calculate the amount accumulated after the next 12 years. Plugging in the values, we find that the amount after 12 years is approximately $27,364.81.

Therefore, in a total of 18 years, you would accumulate approximately $27,364.81 in the account.

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Answer:

1. AA = 4t + 12

2. BB = 5t + 6

3. Garage A would be cheaper to park for 10 hours.

Step-by-step explanation:

1. Garage A's situation is linear, meaning that there is a constant rate of change, or slope.

A linear function in slope-intercept form is: \(y = mx + b\), where m is the rate of change, and b is the y-intercept, or the initial value.

2. Garage B's situation is linear, meaning that there is a constant rate of change, or slope.

A linear function in slope-intercept form is: \(y = mx + b\), where m is the rate of change, and b is the y-intercept, or the initial value.

3. To find how much it will cost Rahul to park in Garages A and B for 10 hours, substitute 10 into t, which is the number of hours. Then, determine which cost is lower.

answer:

4

explanation:

3x-6=19

3x=19-6

3x=13

3x÷3=13÷3

x=4

0.688 will be the probability of getting a nickel from the jar.

Given,

Probability;-

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The number of fortunate situations divided by the total number of coins would be the product between the probability of each occurrence and the likelihood of each event.

Therefore,

P(nickel) = 19/69

P(penny) = 17/68

That is,

P = 19/69 × 17/68

P = 323/4692

P = 0.0688

That is,

The probability of getting nickel from the jar is 0.06888

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Answer:

5 people - Tip  per person  = $0.90  

Total  per person =  $5.39

10 people - Tip  per person  = Tip  per person  $0.45

Total  per person =  $2.70

Answer: the answer is $4.49 because if your bill is 22.41 and you divide that by 20 its 4.482 so then you add the 2 to the 8 which is 9 so 4.49

An angle bisector is a line that is drawn between the angle, which divides the angle into two equal parts. For example, if we bisect an angle that is 70°, then it will be two angles of 35°

We can draw an angle bisector either by measuring the angle using a protractor or marking the half. But the commonly used method is by using a compass.

Step 1

Draw the angle with vertex a, b, and c

Step 2

Draw a circle with b as the Centre, that intersects with each side of the angle.

Step 3

Draw congruent circles or arcs, centered at each intersection point on the sides of the angle.

Step 4

Use a straight line to connect point b with the intersection of two overlapping circles or arcs.

The properties of angle bisectors are

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Answer:

1) 2002

2) 92

Step-by-step explanation:

1)

First, you need to find the area of the triangular base. The height of the triangle is 7, and the base is 26, meaning that the area is 7*26/2=91. Multiplying this by the length of the prism, you get 2002 cubic meters.

2)

First, you need to find the area of the trapezoidal base. The two bases of the trapezoid have lengths 12 and 11, while the height is 8, meaning that the area is 8*(12+11)/2=92 cubic centimeters.

Hope this helps!

The result of the expression as a mixed fraction is -1 5/12

Given the expression

\(1\frac{1}{2}+\frac{3}{4}\div (-\frac{1}{3} ) -\frac{2}{3}\)

Write as an improper fraction

\(\frac{3}{2}+\frac{3}{4}\div (-\frac{1}{3} ) -\frac{2}{3}\)

Using the PEDMAS rule;

\(=\frac{3}{2}+(\frac{3}{4}\div (-\frac{1}{3} )) -\frac{2}{3}\\=\frac{3}{2}+(\frac{3}{4}\times -3) -\frac{2}{3}\\=\frac{3}{2}-(\frac{9}{4}) -\frac{2}{3}\\\)

Find the LCM of the result

\(=\frac{18-27-8}{12}\\= \frac{-17}{12}\\= -1\frac{5}{12}\)

Hence the result of the expression as a mixed fraction is -1 5/12

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Answer:

\(\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \frac{20}{23}\:\\ \:\mathrm{Decimal:}&\:x\ge \:0.86956\dots \\ \:\mathrm{Interval\:Notation:}&\:[\frac{20}{23},\:\infty \:)\end{bmatrix}\)

Step-by-step explanation:

\(-\frac{2}{3}\left(2x-\frac{1}{2}\right)\le \frac{1}{5}x-1\)

Expand \(-\frac{2}{3}\left(2x-\frac{1}{2}\right)\le \frac{1}{5}x-1\) \(-\frac{4}{3}x+\frac{1}{3}\)

\(-\frac{4}{3}x+\frac{1}{3}\le \frac{1}{5}x-1\)

\(\mathrm{Subtract\:}\frac{1}{3}\mathrm{\:from\:both\:sides}\)

\(-\frac{4}{3}x+\frac{1}{3}-\frac{1}{3}\le \frac{1}{5}x-1-\frac{1}{3}\)

\(Simplify\)

\(-\frac{4}{3}x\le \:-\frac{4}{3}+\frac{1}{5}x\)

\(\mathrm{Subtract\:}\frac{1}{5}x\mathrm{\:from\:both\:sides}\)

\(-\frac{4}{3}x-\frac{1}{5}x\le \:-\frac{4}{3}+\frac{1}{5}x-\frac{1}{5}x\)

\(Simplify\)

\(-\frac{23}{15}x\le \:-\frac{4}{3}\)

\(\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\)

\(\left(-\frac{23}{15}x\right)\left(-1\right)\ge \left(-\frac{4}{3}\right)\left(-1\right)\)

\(\mathrm{Simplify}\)

\(\frac{23}{15}x\ge \frac{4}{3}\)

\(\mathrm{Multiply\:both\:sides\:by\:}15\)

\(15\cdot \frac{23}{15}x\ge \frac{4\cdot \:15}{3}\)

\(Simplify\)

\(23x\ge \:20\)

\(\mathrm{Divide\:both\:sides\:by\:}23\)

\(\frac{23x}{23}\ge \frac{20}{23}\)

\(\mathrm{Simplify}\)

Hence the final answer is \(\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \frac{20}{23}\:\\ \:\mathrm{Decimal:}&\:x\ge \:0.86956\dots \\ \:\mathrm{Interval\:Notation:}&\:[\frac{20}{23},\:\infty \:)\end{bmatrix}\)

Part (A)

We have n = 5 sides, so the measure of any exterior angle of a regular pentagon is E = 360/n = 360/5 = 72

Each interior angle is therefore 180-E = 180-72 = 108 degrees.

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

Alternatively, you could use the formula below with n = 5

i = interior angle

i = 180(n-2)/n

i = 180(5-2)/5

i = 180(3)/5

i = 540/5

i = 108

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

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

Part (B)

We're told that CDF is 70 degrees. From part (A) we know that angle CDE is 108 degrees, so this must mean that angle EDF is 108-70 = 38 degrees.

Similarly, angle FEA is 85 degrees, which subtracts from angle AED to get 108 - 85 = 23 degrees. This is the measure of angle DEF.

So far we found

angle EDF = 38

angle DEF = 23

Let's call these x and y for shorthand. Let z be the missing third angle of triangle DFE.

So,

x+y+z = 180

38+23+z = 180

61+z = 180

x = 180-61

x = 119

Interior angle DFE is 119 degrees.

Note how 90 < x < 180 showing we have an obtuse angle. It is not a reflex angle because the statement 180 < x < 360 is false.

So we subtract the value of x from 360

360-x = 360-119 = 241

This is the reflex angle DFE

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

A variable is any property, number, or quantity that can be measured or counted. Variables can also be referenced as data items.

Inference: Inference uses selected samples from a population to estimate the properties of unknown people.

A record (or record) is a collection of data. For tabular data, a record corresponds to one or more database tables, each table column represents a specific variable, and each row corresponds to a particular record in that data set.

Therefore:

All the data collected in particular is referred to as Data Set.

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Answer:

$1592.03

Look at image above...

Answer:

5.48

Step-by-step explanation:

Convert

√30 to a decimal.

5.47722557

Find the number in the hundredth place 7 and look one place to the right for the rounding digit 7. Round up if this number is greater than or equal to 5 and round down if it is less than 5.

The tangent ratio for g degree is 2

The right triangle ACB has the following characteristics:

The length of the leg directly across from the angle divided by the length of the leg directly next to the angle is known as the tangent ratio on an angle in a right triangle.

According to the question, we can write

Tangent of angle g, i.e., \(tan (g^{o})\) = x/y = 10/5 = 2

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Answer:

32cm

Step-by-step explanation:

Let x represent the width

if the width = x

therefore the length = x+8

The perimeter = 72cm

\(x + x + 8 = 72\)

\(x + x + 8 - 8 = 72 - 8\)

\(x + x = 64\)

\(x + x = 2x\)

\(2x = 64\)

\( \frac{2x}{2} = \frac{64}{2} \)

\(x = 32\)

Answer:

18cm

Step-by-step explanation:

wide = 8cm + length

perimeter = 2(L + B)

The average rate of change in f(x) between x=1 and x=5 is 10.

To calculate the average rate of change in f(x) between x=1 and x=5, we need to find the difference in the values of f(x) divided by the difference in the corresponding x-values.

The given values of the function f(x) for different x-values are:

x f(x)

-3 2

1 20

3 57

5 60

7 98

To find the average rate of change between x=1 and x=5, we need to consider the difference in f(x) and the corresponding x-values:

Difference in f(x) = f(5) - f(1) = 60 - 20 = 40

Difference in x = 5 - 1 = 4

Now, we can calculate the average rate of change by dividing the difference in f(x) by the difference in x:

Average Rate of Change = (Difference in f(x)) / (Difference in x) = 40 / 4 = 10

As a result, between x=1 and x=5, the average rate of change in f(x) is 10.

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Answer:

Can you please give us figure of following ?

Answer:

its the last one 212°

212°

212°

212°

212°

212°

Step-by-step explanation:

212°

Answer:

there were 8 dog ears in all.

Step-by-step explanation:

Since the statement says that they saw two teachers each walking with two dogs, you have to multiply the number of teachers for the number of dogs each one had to find the total number of dogs they had:

2*2=4

Now, as the statement indicates that each dog had two ears you have to multiply the number of dogs for the number of ears each one has:

4*2=8

According to this, the answer is that there were 8 dog ears in all.

Answer:

The index of x should  be 0 so that its value will be equal to 1.

The given curve is a smooth curve which is increasing and concave up.

The point (1, 0) and a parametrization $r(t) = \left\langle t^2 - 1, t^3 - t\right\rangle$. Let's find the arc length measured from the point (1, 0) in the direction of increasing t with respect to the arc length.Therefore, the unit tangent vector is given as:$\begin{align}\vec T(t) &= \frac{\vec v(t)}{\lVert \vec v(t) \rVert}\\ &= \frac{\left\langle 2t, 3t^2 - 1\right\rangle}{\sqrt{(2t)^2 + (3t^2 - 1)^2}}\\ &= \frac{\left\langle 2t, 3t^2 - 1\right\rangle}{\sqrt{13t^2 - 6t + 1}}\end{align}$Therefore, the distance measured from the point (1, 0) can be calculated as:$\begin{align}\int_{1}^{t} \left\lVert \vec T(u) \right\rVert \,du &= \int_{1}^{t} \frac{1}{\sqrt{13u^2 - 6u + 1}} \,du\\ &= \frac{1}{\sqrt{13}} \ln \left(\sqrt{13}t^2 - 3t + 1 + 2\sqrt{13}t - 2\sqrt{13}\right) - \frac{1}{\sqrt{13}} \ln(2\sqrt{13} - 2\sqrt{13})\\ &= \frac{1}{\sqrt{13}} \ln \left(\sqrt{13}t^2 - 3t + 1 + 2\sqrt{13}t - 2\sqrt{13}\right) + C\end{align}$So, the simplest form of reparametrization can be given as:$\begin{align}s(t) &= \frac{1}{\sqrt{13}} \ln \left(\sqrt{13}t^2 - 3t + 1 + 2\sqrt{13}t - 2\sqrt{13}\right)\\ &= \frac{1}{\sqrt{13}} \ln \left(\sqrt{13}t^2 + 2\sqrt{13}t - \sqrt{13}\right)\end{align}$Therefore, we can conclude that the given curve is a smooth curve which is increasing and concave up.

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Answer: look at the image for the answer and solution

Step-by-step explanation:

Answer:

the answer is 10.52547%

Step-by-step explanation:

Answer: 14,344

Step-by-step explanation: