Write as a single logarithm: a) 3log₂a + 2log₂ blog2 c b) In x + 3 ln y c) 2 log3 a + log3 (a-3) - log3 (a²-9) Review condensing logarithmic expressions here.

Answer:

7/6 or 1 1/6

Step-by-step explanation:

Here's how you add them!

5 /6  + 2/6  

Step 1

Since our denominators match, we can add the numerators.

5 + 2 = 7

Answer:

7 /6

Step 2

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

Nope. Try the next prime number, 3...

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

No good. 7 is larger than 6. So we're done reducing.

Congratulations! Here's your final answer to 5/6 + 2/6

Answer:

\(\frac{5}{18}\)

Step-by-step explanation:

To calculate the amount of acres planted in strawberries, all you need to do is  simple multiplication.

\(\frac{5}{6}\) × \(\frac{1}{3}\)

multiply the numerators by each other

\(5\) × \(1\) \(= 5\)

the numerator of the new fraction is 5

multiply the denominators by each other

\(6\) × \(3=18\)

the new denominator is 18

the new fraction is \(\frac{5}{18}\)

Answer:

2000kkkkkkkkkkklllllk

We know that the initial temperature is -3 then it rises to 8 and drops by 6 degrees then you just need to subtract six from 8                                                         \(\displaystyle\ 8-6=2^\circ \\\\Answer: the\ secondary\ temperature \ will \ be equal \ to \ 2^\circ\)

Answer:

Explanation:

Here, we want to get the amount of horsepower produced by the engine at 2300 rpm

From the question, we have :

60 hp produced at 2000 rpm

At 2,300 rpm, there would be 15% increase in hp

Thus, at 2300 rpm, the hp would be:

Thus, this means that the engine produces 69 hp at 2300 rpm

Answer:

Approximatley 5.8 units.

Step-by-step explanation:

We are given two angles, ∠S and ∠T, and the side opposite to ∠T. We need to find the unknown side opposite to ∠S. Therefore, we can use the Law of Sines. The Law of Sines states that:

\(\frac{\sin(A)}{a}=\frac{\sin(B)}{b} =\frac{\sin(C)}{c}\)

Replacing them with the respective variables, we have:

\(\frac{\sin(S)}{s} =\frac{\sin(T)}{t} =\frac{\sin(R)}{r}\)

Plug in what we know. 20° for ∠S, 17° for ∠T, and 5 for t. Ignore the third term:

\(\frac{\sin(20)}{s}=\frac{\\sin(17)}{5}\)

Solve for s, the unknown side. Cross multiply:

\(\frac{\sin(20)}{s}=\frac{\sin(17)}{5}\\5\sin(20)=s\sin(17)\\s=\frac{5\sin(20)}{\sin(17)} \\s\approx5.8491\approx5.8\)

Answer:

The Answer is $0.17

Step-by-step explanation:

1) Divide the amount of money always first

so divide 4.99 to 30

2)you would get 0.166333333333

3) Now Round $0.17

4) That means its B.) $0.17 ounces  

Awnser:

c.) $6.01

Step-by-step explanation:

30 divided by 4.99 is 6.0120240481 but we need to round because money does not go that far. So we end up with 6.01

Answer: C

Step-by-step explanation:

Slope is the number right in front of x, which in this case would be -2. So C is the answer.

Creating a table is hard, so I'll try my best. Just pretend the vertical line is connected.

x|y

0|5

1|3

2|1

3|-1

4|-3

Answer:

andre has more money

Step-by-step explanation:

Answer:

You need to write an equation for each.

For Andre, he has 100 dollars, and every week gets 5 dollars more. You add the 5 dollars, and Since you don't know how many weeks it has been, use a variable.

100 + 5w

For Elena, she has 10 dollars, and gets 20 each week.

10 + 20w

Now that you know that it has been 4 weeks, you can plug in 4 for the variable for weeks.

Andrew:

100 + 5(4) =120

Elena

10 + 20(4) ==90

Andrew has more money in this time.

To find when they have the same amount, equal their expressions to each other. This means that they will have the same amount (because they are equalled) and you can solve to find the variable, which means the weeks that they are equal at.

Bring the like terms to each side by canceling them out. Since you have positive 10, then subtract 10 to each side. You have 5w, so subtract 5w to each side.

90+5w=20w

90=15w

90÷15=6

6=w

The answer will simplify down to 6 weeks.

Answer: 213.75

Step-by-step explanation:

Add a zero to the hundredths place of 345.5 making it 345.50, then subtract as you would normally.

The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

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In the novel "Brave New World," when Lenina states, "Never put off until tomorrow the fun you can have today," Bernard replies, "Two hundred repetitions, twice a week from fourteen to sixteen and a half"

This comment means that he is promoting individuality. Bernard is the most noticeable of all the characters who consider the worth of individuality. He is small and awkward, and he is unhappy with the system's blind devotion to conformity and pleasure.

His rejection of this way of life is most visible in his reluctance to indulge in promiscuous sex and drugs, which are fundamental components of the citizens' happy lives.A major theme in Brave New World is the rejection of individuality in exchange for happiness.

The residents of the World State are only concerned with their personal comfort and pleasure, which they gain through mind-numbing activities like sex and drugs.

Bernard, on the other hand, rejects these activities and prefers solitude and his own thoughts. He thinks that individuality is essential, and he refuses to give in to the conditioning that the other citizens accept.

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. The quadratic approximation of the function f(x) = (1 + x)^k at x = 0 using Taylor's formula with n = 2 is Q(x) = 1 + kx + (k(k-1)/2)\(x^{2}\)

To find the quadratic approximation, we need to use Taylor's formula with n = 2. The formula for the quadratic approximation Q(x) is given by:

Q(x) = f(0) + f'(0)x + (1/2)f''(0)\(x^{2}\)

Since f(x) =\((1 + x)^{k}\), we first find the derivatives of f(x) up to the second order. Taking the derivatives, we have:

f'(x) = k\((1 + x)^{k-1}\)

f''(x) = k(k-1)\((1 + x)^{k-2}\)

Now, we substitute these derivatives into the quadratic approximation formula:

Q(x) = f(0) + f'(0)x + (1/2)f''(0)\(x^{2}\)

At x = 0, we have:

Q(0) = f(0) + f'(0)(0) + (1/2)×0

= f(0)

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Variation can be direct, joint, inverse and combined.

The constant of variation is (a) -10

The inverse variation is given as:

\(xy = k\)

Rewrite the equation of the inverse variation as:

\(k = xy\)

When x = -2, and y = 5, the variation equation becomes

\(k = -2 \times 5\)

Multiply 2 and 5

\(k = -10\)

Hence, the constant of variation is (a) -10

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Answer:

A

Step-by-step explanation:

took the test

The value of x from the expression is,

⇒ x = 1/4 (Y - 3)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ Y = 4x + 3

Now, We can solve the expression for the value of x as;

⇒ Y = 4x + 3

Subtract 3, we get;

⇒ Y - 3 = 4x + 3 - 3

⇒ Y - 3 = 4x

Divide by 4;

⇒ (Y - 3) / 4= 4x/4

⇒ (Y - 3)/4 = x

⇒ x = 1/4 (Y - 3)

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Answer:

The area of the dilated flower garden is:

A' = (1/2)bh = (1/2)(2)(1.5) = 1.5 sq ft

Answer:

Step-by-step explanation:

You want Lisa's and Myra's ages if the sum of their ages is 40 and in 10 years, Lisa will be 3 times as old as Myra.

The current sum of their ages is 40. In 10 years, 10 will be added to each of their ages, so the sum will be 60.

At that time Lisa's age is 3 times Myra's age, so will be 3/(3+1) = 3/4 of the total.

  Lisa's age in 10 years = (3/4)(60) = 45

Lisa is 35 now, and Myra is 5 now.

__

Additional comment

We could write some equations, but we find a mental solution based on ratios to be quick and easy. Here is a solution using equations:

  L + M = 40

  (L +10) = 3(M +10) . . . . . . age relation in 10 years

  (40 -M) +10 = 3M +30 . . . . substitute for L

  20 = 4M . . . . . . . . . add M-30

  M = 5; L = 40-M = 35

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Answer:

the solution is (3,4). x = 3, y=4

Step-by-step explanation:

First, we refer to y = mx + b, where m is the gradient and b is the y-intercept. You can plug in any values of x to find values of y and plot them.

For the solution, you can equate the two equations. y1=y2 ; -x + 7 = x + 1, work from there to find the x which is 3 in this case. Then, substitute x=3 into one of the equations to get y = 4. That's the point where the two equations intersect with each other.

Answer:

b) y = 3x + 1

y = x+1

Step-by-step explanation:

Select all the systems of equations that have exactly one solution.

a)

y = 3x + 1

y = 3x + 7

y - 3x = 1.... Equation 1

y - 3x = 7...... Equation 2

We solve using Elimination

We Subtract Equation 2 from 1

(y - y ) - (3x - 3x) = 7 - 1

0 = 6

b) y = 3x + 1...... Equation 1

y = x +1...... Equation 2

x = y - 1

We substitute y - 1 for x in Equation 1

y= 3(y - 1) + 1

y = 3y - 3 + 1

y - 3y = -3 + 1

-2y = -2

y = -2/-2

y = 1

Solving for x

x = y - 1

x = 1 - 1

x = 0

x = 0, y = 1,

The Equations in b) have only one solution

c) x+y=10

x = 10 - y

2x+2y=20

We substitute

2(10 - y) + 2y = 20

20 - 2y + 2y= 20

-2y + 2y = 20 - 20

0 = 0

It has no solution

d) x+y=10.... Equation 1

x+y=12..... Equation 2

We solve using Elimination

We Subtract Equation 2 from 1

x - x + y - y = 12 - 10

0 = 2

When a ticket is drawn at random from the box and then replaced, it means that each time a ticket is drawn, the probability of drawing any particular ticket remains the same. This is because the number of tickets in the box stays constant and the drawing is done randomly.

Now, let's consider the situation where a ticket is drawn for the first time. Since there are n tickets in the box, the probability of drawing any specific ticket is 1/n.

After the first ticket is drawn and replaced in the box, the total number of tickets remains the same, n. So, when the second ticket is drawn at random, the probability of drawing any particular ticket is still 1/n.

To find the probability of drawing two specific tickets in succession, we multiply the probabilities of drawing each ticket individually. Therefore, the probability of drawing the first ticket and then the second ticket is (1/n) * (1/n) = 1/n^2.

In summary, if a ticket is drawn at random from a box marked 1 to n, replaced, and then a second ticket is drawn at random, the probability of drawing any specific pair of tickets is 1/n^2.

I hope this helps! If you have any more questions, feel free to ask.

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Answer:

Wow!

It is 10

Step-by-step explanation:

Answer:5+5=10

Step-by-step explanation:

For this all you would do is add 5 units to another 5 units you would have 10 units. Or we could use your hands for example you should have 5 fingers on each hand and you should also have 2 hands so if you look at your hands you should see 5 fingers on each hand or ten fingers in total.

To find the price at which the designer will sell the maximum number of shirts, we need to determine the vertex of the quadratic function representing the number of shirts sold.

The equation for the number of shirts sold is given by:

S = -4x^2 + 80x - 76

This is a quadratic function in the form of:

S = ax^2 + bx + c

To find the price at which the maximum number of shirts is sold, we need to locate the vertex of the quadratic function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

In this case, a = -4 and b = 80. Plugging in these values, we can calculate the x-coordinate:

x = -80 / (2*(-4))

x = -80 / (-8)

x = 10

Therefore, the designer will sell the maximum number of shirts at a price of $10. Hence, the correct option is c) $10.

Answer:

x <19.5

Step-by-step explanation:

X-3.3< 16.2

Add 3.3 to each side

X-3.3+3.3< 16.2+3.3

x <19.5

Answer:

\(y=\frac{5}{2}x-13\)

Step-by-step explanation:

Given the equation

\(y=-\frac{2}{5}x-1\)

comparing the equation with the slope-intercept form\(y=mx+b\)

Here,

so the slope of the line is m = -2/5

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line,

so  the slope of the perpendicular line will be: 5/2

Therefore, the point-slope form of the equation of the perpendicular line that goes through (2,-8) is:

\(y-y_1=m\left(x-x_1\right)\)

\(y-\left(-8\right)=\frac{5}{2}\left(x-2\right)\)

\(y+8=\frac{5}{2}\left(x-2\right)\)

subtract 8 from both sides

\(y+8-8=\frac{5}{2}\left(x-2\right)-8\)

\(y=\frac{5}{2}x-13\)

To use differentials to estimate the value of 1.2√4, we need to first find a suitable function and a point close to the one we want to estimate. Since we are dealing with square roots, we can use the function f(x) = √x. The point closest to 4.2 (1.2 added to 4) that we know the exact value for is 4, as √4 = 2.

1. Find the derivative of f(x) = √x:
f'(x) = (1/2)x^(-1/2)

2. Evaluate the derivative at the known point, x = 4:
f'(4) = (1/2)(4)^(-1/2) = (1/2)(2)^(-1) = 1/4

3. Compute the differential, using Δx = 0.2 (the difference between 4.2 and 4):
Δy = f'(4)Δx = (1/4)(0.2) = 0.05

4. Estimate the value of 1.2√4 by adding Δy to the exact value at x = 4:
1.2√4 ≈ 2 + 0.05 = 2.05

Now, let's compare this to the exact value of 1.2√4:
Exact value: 1.2√4 = 1.2(√4.2) ≈ 1.2(2.0494) ≈ 2.0593

The estimated value using differentials is 2.05, while the exact value is approximately 2.0593. The two values are relatively close, demonstrating the effectiveness of using differentials for estimation.

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Answer:

Each individual lost 6 pieces

Step-by-step explanation:

Initially, there were 32 pieces

After a while, 20 was left

The number of pieces lost will be 32-20 = 12 pieces

We are told that equal number of pieces were lost

So the number of pieces lost per individual will be:

12/2 = 6 pieces

Answer:

c

a

Step-by-step explanation:

Answer:

5. is C which is 9.

6. is B which is 37.

Step-by-step explanation:

The first on is C. 9 because to find the interquartile range you need to subtract the upper quartile range by the lower quartile range. The upper is 16 and the lower is 7 so you do 16-7 which is 9.

The last question is B. 37 because the lower quartile range is first line in the box plot which is 37.