Which expression is equivalent to log Subscript 8 Baseline 4 a (StartFraction b minus 4 Over c Superscript 4 Baseline EndFraction)?

Answer:

So the correct option for this case would be:

0.48

Answer:

5/48

Step-by-step explanation:

(5/8 - 1/2) x 5/6

(5/8 - 4/8) x 5/6

1/8 x 5/6

5/48

Answer:

\(\dfrac{5}{48}\)

Step-by-step explanation:

\(\left(\dfrac{5}{8} - \dfrac{1}{2}\right) \times \dfrac{5}{6}\)

First, represent 1/2 as 4/8.

\(\dfrac{1}{2} \times \dfrac{4}{4} = \dfrac{4}{8}\)

\(\left(\dfrac{5}{8} - \dfrac{4}{8}\right) \times \dfrac{5}{6}\)

Then, simplify the subtraction.

\(\dfrac{1}{8} \times \dfrac{5}{6}\)

Finally, multiply the numerators and denominators of the resulting fractions.

\(\dfrac{1 \times 5}{8 \times 6}\)

\(\dfrac{5}{48}\)

Answer:

Q'(0, -1)

R'(2, 5)

S'(-1, 0)

T'(-2, 9)

Step-by-step explanation:

Rule defined by \(T_{(-1,2)}.R_{\text{x-axis}}\)

Step 1). Reflection of the figure about x-axis

(x, y) → (x, -y)

Step 2). Followed by the translation of 1 unit to the left and 2 units up  

(x, y) → (x - 1, y + 2)

Transformation of QRST by this rule,

Step 1.

Q(1, 3) → Q"(1, -3)

R(3, -3) → R"(3, 3)

S(0, 2) → S"(0, -2)

T(-2, 1) → T"(-2, -1)

Step 2.

Q"(1, -3) → Q'(0, -1)

R"(3, 3) → R'(2, 5)

S"(0, -2) → S'(-1, 0)

T"(-1, -1) → T'(-2, 9)

Answer:

$1000

Step-by-step explanation:

Check answers

1000x .03= 30

1000 - 30 = 970

We are given the following information:

110 oz of 60% acid solution

We need to find the amount of water needed to dilute it to 45%.

To answer this, let's set up the equation first.

We know that 60% of the 110 oz. is acid. This amount of acid must then be the same amount of acid that makes up 45% of the new solution. So our equation would be:

Solving for N, we get:

Now we know that the total amount must be 146.67 oz. We already have 110 oz. So we only need 146.67 - 110 = 36.67 oz of water to dilute the solution.

Answer:

Step-by-step explanation:

$16,250 is the down payment amount

Rewrite the percentage as a decimal by moving the decimal 2 places to the left.

25 % becomes 0.25

Now multiply the price of the house by 0.25:

65,000 x 0.25 = 16,250

The amount required is: $16,250

The value of the equation (1 - x)/2x² + x²/(2x - 2) is 0 if x² + x - 1 = 0

From the question, the equation is given as

x² + x - 1 = 0

Make x² the subject of the above equation

So, we have the following equation

x²  = 1 - x

The equation to calculate is given as

(1 - x)/2x² + x²/(2x - 2) = ?

Substitute x²  = 1 - x

(1 - x)/2x² + x²/(2x - 2) = x²/2x² + x²/(2x - 2)

Evaluate the quotient

So, we have the following equation

(1 - x)/2x² + x²/(2x - 2) = 1/2 + x²/(2x - 2)

Factor out -2

(1 - x)/2x² + x²/(2x - 2) = 1/2 - x²/2(1 - x)

Substitute x²  = 1 - x

Factor out -2

(1 - x)/2x² + x²/(2x - 2) = 1/2 - x²/2x²

Evaluate the quotient

(1 - x)/2x² + x²/(2x - 2) = 1/2 - 1/2

Evaluate the difference

(1 - x)/2x² + x²/(2x - 2) = 0

Hence, the solution to the equation is 0

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Answer:

9

Step-by-step explanation:

The \(n\)term is \(2n+1\).

\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + \(n^2\) = 99

\(n^2\) + 2n - 99 = 0

Split the terms

\(n^2\) - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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Answer: A = 3

Step-by-step explanation:

4x-2=10

4x=12

x =12/4

x=3

Answer: Just a question what was the present age of Zin Zin three years ago will really help?? Thank You

Step-by-step explanation:

Mean - this is the average. Add up the numbers and divide by the count of the numbers in the data set.

11+13+14+16+17+18+20+20+21+24+25+29 = 228

There are 12 numbers, so divide by 12.

228/12 = 19. The mean is 19.

Median - - - this is the MIDDLE number. Your data is already in numerical order (hooray!) so there are 12 numbers. Since it's even, we'll take the average of the 2 middle numbers. The 6th number is 18 and the 7th number is 20. The average of these is 19. So the median is 19.

(Side note: yes, median and mean can be the same.)

Mode - - - this is repeat/most common numbers! 20 repeats. 20 is the mode.

Range - - - biggest number is 29, littlest is 11. The range is 29-11 = 18.

Answer:

60

Step-by-step explanation:

21/.35 = 60; set up this equation and solve for x:

.35(x) = 21

Answer:

60

Step-by-step explanation:

Answer:

40800

Step-by-step explanation:

4 weeks = 1 month

So we use,

850 * 4 = 3400 (monthly)

12 months = 1 year

So we use,

3400 * 12 = 40800 (annually)

Each number should be dragged to a box to complete the table as follows;

Kilometers     Meters

1                        1,000

2                       2,000

3                       3,000

5                       5,000

8                       8,000

In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;

Conversion:

1 kilometer = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 kilometer = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 kilometer = 8,000 meters

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

a. \(Probability = 0.2496\)

b. No, it won't change

Step-by-step explanation:

Represent \(the\ head\) with H and \(Tail\ with\) T

Such that:

\(P(H) = 48\%\)

Solving (a): First head in second trial

First, we determine P(T) i.e. the probability of obtaining a tail

\(P(H)+P(T) = 100\%\)

\(P(T) = 100\% -P(H)\)

Substitute 48% for P(H)

\(P(T) = 100\% -48\%\)

\(P(T) = 52\%\)

If the first head is obtained in the second trial, the probability is:

\(Probability = P(T\ and\ H)\)

\(Probability = P(T)\ and\ P(H)\)

\(Probability = P(T)\ *\ P(H)\)

\(Probability = 48\%* 52\%\)

\(Probability = 0.2496\)

Solving (b): Will it change if tossed three or four times?

Irrespective of the number of times the coin is tossed, the probability of obtaining a head in the second toss will always be the same because the coin has to be tossed twice before the third and the fourth time.

Answer:

7.7

Step-by-step explanation:

I did it on edu!

You can use the fact that area of a rectangle is its length times its width.

The length of the given rectangle is 28 feet.

Area of a rectangle is its length times its width.

If a rectangle has length x units and width y units, then we have:

\(Area = x \times y \: \rm unit^2\)

Most of the times, you will get some other facts or information by which the unknown values of those items can be known. For simple daily life cases, we can use variables, which are nothing but just placeholders for those unknown values. We can then operate on those variables assuming them to be actual values, thus, getting near to their original values.

Let the length of the given rectangle be x units, and let its width be y

Then as it is given that

Length of the rectangle = 2 times width of the rectangle

or

\(x = 2 \times y\)

We have area= 392 square feet

Since area = length times width, thus, we have

\(Area = x \times y\\392 = 2 \times y \times y\\\\\dfrac{392}{2} = y^2\\\\y^2 = 186\\\\\text{\:(Taking positive root on both the sides since y is width, a non negative quantity)}\\\\y = \sqrt{196} = 14\)

Thus, the width of the rectangle is 14 feet

And thus, the length of the rectangle = double of width = 28 feet.

Thus,

The length of the given rectangle is 28 feet.

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Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

The null and alternative hypotheses can be stated as follows:

c. H0: µ = 12, Ha: µ ≠ 12

The null hypothesis (H0) assumes that the population mean content of the bottles is 12 ounces, indicating perfect adjustment of the filling machine. The alternative hypothesis (Ha) states that the population mean content is not equal to 12 ounces, suggesting that the machine is not in perfect adjustment.

The rejection region for α = 0.01 can be specified as:

c. |t| > 2.68

This means that we would reject the null hypothesis if the absolute value of the calculated t-statistic is greater than 2.68.

To calculate the p-value, we need the t-statistic corresponding to the sample mean and standard deviation. With a sample mean of 11.88 ounces, a standard deviation of 0.35 ounces, and a sample size of 49, we can calculate the t-statistic. The p-value represents the probability of observing a sample mean as extreme as the one obtained, assuming the null hypothesis is true.

The p-value cannot be determined without the t-statistic value or the corresponding degrees of freedom.

Without the p-value, we cannot draw a definitive conclusion. To make a conclusion, we would compare the calculated t-statistic to the critical t-value based on the chosen significance level (α = 0.01). If the calculated t-statistic falls within the rejection region (|t| > 2.68), we would reject the null hypothesis. If the calculated t-statistic falls outside the rejection region, we would fail to reject the null hypothesis.

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The pattern for the sequence 1.3, 8.3, 27.3, 64.3,… is f(n) = (n)³.3

The pattern in the question is given as

1.3, 8.3, 27.3, 64.3,…

In the above expressions and pattern, we can see that

From the above, we have the following

Current term = (n)³.3

Note that the decimal does not represent product

And also the pattern is a geometric sequence

Hence, the pattern for the sequence is f(n) = (n)³.3

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Answer:

45

Step-by-step explanation:

Put in '5' where 'x' is

2 (5)^2 - 5 = 45

What is the equation: \(2x^2-5\)

What do we want to find: f(5)

To find f(5), we must plug the value '5'

     ⇒ into the 'x' position

        ⇒ f(x)

So: \(f(5) = 2(5^2)-5 = 2 * 25 - 5 = 50 -5 = 45\)

Thus f(5) = 45

Hope that helps!

Answer:

The rental of each chair is $2.75

The rental of each table is $8.5

Step-by-step explanation:

Let's name the unknowns "c" for the cost of each chair rental, and "t" for the cost of each table rental.

Now we can create the equations that represent the statements:

a) "The total cost to rent 2 chairs and 3 tables is $31."

2 c + 3 t = 31

b) "The total cost to rent 6 chairs and 5 tables is $59."

6 c + 5 t = 59

now we have a system of two equations and two unknowns that we proceed to solve via the elimination method by multiplying the first equation we got by "-3" so by adding it term by term to the second equation, we eliminate the variable "c" and solve for "t":

(-3) 2 c + (-3) 3 t = (-3)  31

-6 c - 9 t = -93

6 c + 5 t = 59

both these equations added give:

0 - 4 t = -34

t = 34/4 = 8.5

So each table rental is $8.5

now we find the rental price of a chair by using any of the equations:

2 c + 3 t = 31

2 c + 3 (8.5) = 31

2 c + 25.5 = 31

2 c = 5.5

c = 5.5/2

c = $2.75

Answer:

a is the right anser

Step-by-step explanation:

The average rate of change from day 2 to day 10 is given by the slope of the line m =

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The number of houses sold on day 2 is P

The number of houses sold on day 10 is Q

Let the first point be P ( 2 , 8 )

Let the second point be Q ( 10 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2 - 8 ) / ( 10 - 2 )

Slope m = -6/8

m = -3/4

Therefore , the number of houses sold between day 2 and 10 is -3/4 houses per day

Hence , the slope is m = -3/4 houses per day

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The complete question is attached below :

The graph below shows the number of houses sold over x days. What is the average rate of change from day 2 to day 10

Length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

The area of Rectangle is length times of width

Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.

Here, the dimensions of the rectangles are the same.

The width of the two rectangles is W=2W+2W=4W

The length of the two rectangles is L=L+L+L=3L

Because the adjacent side has a common length.

3L+4W=200

3L=200-4W

Divide both sides by 3

L=(200-4W)/3

Let us form an equation using the area of rectangle formula:

A=2LW

=2(200-4W)/3.W

A=400-8W²/3

Let us differentiate to get the area to be maximized dA/dW=0

1/3×(400-8W²)=0

1/3(400-16W)=0

400-16W=0

400=16W

Divide both sides by 16

W=25

The width is 25 feet.

Substitute W value in equation to get L value:

L=200-4×25/3

=200-100/3

=100/3

=33.33

The length is 33.33 feet.

Now let us find the maximum area

A=2LW

=2×33.33×25

=1666.66

Hence, length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

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Answer:

Option 3

Step-by-step explanation:

Given data set is,

{(1.5, 1), (2.5, 3), (3, 3), (3, 5), (3.5, 5), (4.5, 7), (5, 7), (5, 9), (5.5, 9), (6.5, 11), (7.5, 13)}

By using linear regression calculator,

Equation of the linear function will be,

y = 2x - 2

Therefore, Option 3 will be the correct option.

Answer:

Depends on how many spoonfuls they use per sundae. If they use one spoonful they made 32 sundaes, if they use 2 spoonfuls they made 16 sundaes.

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Answer: The boat 1 moves with a speed of 40mi/h, and boat 2 moves with a speed of 20mi/h.

Step-by-step explanation:

First, we know the relation:

Distance = Speed*Time.

We can define the average rate of the boats as the average speed of the boats.

Now, we know that two boats travel in the same direction, let's define:

S₁ = speed of boat 1.

S₂ = speed of boat 2.

We know that one travels twice as fast as the other, then we can write:

S₁ = 2*S₂

We also know that after 3 hours of travel, they are 60mi apart, then if the slower one travelled a distance D in 3 hours, then:

S₂*3h = D

And the faster one will travel D + 60mi

S₁*3h = (D + 60mi)

Then we have the equations:

S₂*3h = D

S₁*3h = (D + 60mi)

We can replace S₁ by 2*S₂ to get:

S₂*3h = D

(2*S₂)*3h = (D + 60mi)

Now we have isolated D in the above equation, we can just replace it in the second equation to get:

(2*S₂)*3h = (S₂*3h + 60mi)

Now we can solve this for S₂

S₂*6h = S₂*3h + 60mi

S₂*6h - S₂*3h = 60mi

S₂*3h = 60mi

S₂ = 60mi/3h = 20mi/h

The speed of boat 2 is 20mi/h

And we knew that:

S₁ = 2*S₂

then:

S₁ = 2*(20mi/h) = 40mi/h

Answer:

154.44

Step-by-step explanation:

What is 13% of 396?

Y is 13% of 396

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 13% * 396

Converting percent to decimal:

p = 13%/100 = 0.13

Y = 0.13 * 396  

Y = 51.48

Now multiply by 3 (amount of continuous years)

51.48 * 3

=154.44

Hope it helps!

Step-by-step explanation:

If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote. If the polynomial in the numerator is a higher degree than the denominator, there is no horizontal asymptote.