Use the change of base formula to evaluate the expression then convert it to a logarithm in base eight round to the nearest thousandth

SOLUTION

Let the smaller number be x

Let the larger number be y

Since the larger number is 31 more than 5 times the smaller number, it folllows:

The sum of the two integers is 463, it follows

Substitute y=5x+31 into the equation

Solve for x

Substitute x=72 into y=5x+31

Therefore the two integers are 72 and 391

To get the required combining pairs : B, C , D, E , F

B (1, 10) = Pattern A - 1 and pattern B = 10

C (3, 6) = pattern a = 3 and pattern b = 6

D (5, 4)= pattern A = 5 and pattern B = 4

E (5, 6) = Pattern A = 5 and pattern B = 6

F (7, 4) = Pattern A = 7 and pattern B = 4

Given ; Pattern A : 1, 3, 5, 7, 9

Pattern B: 10, 8, 6, 4, 2

To get ;  A (1, 3) B (1, 10) C (3, 6) D (5, 4) E (5, 6) F (7, 4)

Thus to get the required pair we have to match it the following way

A ( 1, 3 ) = Pattern A - 1 and pattern B - ? thus not correct

B (1, 10) = Pattern A - 1 and pattern B = 10

C (3, 6) = pattern a = 3 and pattern b = 6

D (5, 4)= pattern A = 5 and pattern B = 4

E (5, 6) = Pattern A = 5 and pattern B = 6

F (7, 4) = Pattern A = 7 and pattern B = 4

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area = side x side = 20 x 30 =600 ft

we want to double the area, this is 1200 ft, therefore:

but, We don't measure in negative numbers, so we disregard this answer. and the other

therefore, the patio is now 30ft x 40ft

Answer:

wind speed 35 miles per hour

plane speed 210 miles per hour

Explanation:

Let us call p the place speed and w the wind speed.

We know that

p + w = 1225/5 = 245

p - w = 1225/7 = 175

adding the two equations above gives

2p = 245 + 175

2p = 420

dividing both sides by 2 gives

p = 210 miles per hour.

putting in the value of p in p + w = 245 gives

210 + w = 245

w = 245 - 210

w = 35 miles per hour

Given:

The sum of two numbers is 21, and their difference is 9.

Let x and y be the two numbers.

Equation 1: The sum of two numbers is 21.

Equation 2: Their difference is 9.

Answer

11 gallons of the 25% alcohol is required for the mixture.

4 gallons of the 10% alcohol is required for the mixture.

Explanation

Let the number of gallons of 25% alcohol required be x

Let the number of gallons of 10% alcohol required be y

The total amount of gallons required is 15 gallons. In mathematical terms,

x + y = 15

The alcohol content of the 15 gallons is to be 21%.

21% of 15 gallons = 3.15 gallons

From the first statements,

Let the number of gallons of 25% alcohol required be x

Let the number of gallons of 10% alcohol required be y

25% of x gallons = 0.25x gallons

10% of y gallons = 0.10y gallons

0.25x + 0.10y = 3.15

We can then bring these two equations together to solve simultaneously

x + y = 15

0.25x + 0.10y = 3.15

Solving this simultaneously with the calculator, we obtain

x = 11 gallons

y = 4 gallons

Hope this Helps!!!

Problem

Solution

For this case we we can find the area on this way:

And solving we got:

The area for this case is 88 unit^2

Let's use the variable L to represent the length and W to represent the width.

If the perimeter is 600 ft, we have:

The width is half the length, so we have:

Now, if each fence segment is 5 ft, we number of segments needed is:

In mathematics, a combination is a selection of items from a set that has distinct members

Formula

Where

n = 20

r =3

The final answer

1140 unique groups of volunteers are possible

To solve this question, we need to use integers to express different altitudes. We can sketch each situation as follows:

To find the depth at which each person rested, we need to algebraically sum all these altitudes.

Jim:

-8 -18 + 5 - 9 = -30. He rested at 30 feet below the surface.

Carla:

-16 + 5 - 18 = -29. She rested at 29 feet below the surface.

Therefore, Jim rested at a greater depth (30 feet below the surface).

x = 44

Note that:

Opposite angles of a cyclic quadrilateral are supplementary

m

mm

(3x + 10) + 38 = 180

3x + 10 + 38 = 180

3x + 48 = 180

3x = 180 - 48

3x = 132

x = 132/3

x = 44

The two graphs that reserve congruence are in the option A and option D

Congruent refers to something that is "absolutely equal" in terms of size and shape.

The shapes hold true regardless of how we rotate, flip, or turn them.

Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another. We will see that they will superimpose, or be positioned entirely on top of, one another. This demonstrates the congruence of the two circles.

The images on the graphs in the options A and options D both maintains congruence, The sizes are identical and has a rigid transformation

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The value of k for which the inequality has the given solution set is:

k = 8.5.

The inequality is presented as follows:

0.5 < -4x + k ≤ 12 - k.

Two inequalities compounded, hence the and operation is applied, which means that the solution set is composed by the elements that respect both conditions.

The solution set of the inequality is:

1.25 ≤ x < 2.

The lower bound of the solution is of 1.25, hence:

-4x + k ≤ 12 - k.

-4x + 2k ≤ 12

4x ≥ 2k - 12

x ≥ 0.5k - 3

Hence:

0.5k - 3 = 1.25

0.5k = 4.25

k = 4.25/0.5

k = 8.5.

The upper bound of the solution is of 2, hence:

-4x + k > 0.5

-4x > 0.5 - k

x < -0.125 + 0.25k

Hence:

-0.125 + 0.25k = 2

k = 2.125/0.25

k = 8.5. -> Which confirms the solution.

The problem is given by the image shown at the end of the answer.

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To evaluate the expression:

We can use PEMDAS. We can start from the parenthesis, then, since we have divisions and multiplications, and they have the same precedence, we can start doing the evaluation from the left to the right. Then, we have:

The answer is 54 (option D).

8x^2 + 19 = 54 + 3x^2

Solving for x:

8x^2 - 3x^2 = 54 - 19

5x^2 = 35

x^2 = 35/5 = 7

x^2 = 7

x = sqrt(7) = 2.6458

x = -sqrt(7) = -2.6458

Answer:

It has two solutions:

x = 2.6458 and x = -2.6458

apply the distributive property

apply the substraction property

Radius r:

r = 8 miles

Area of a circle:

A = π * r²

The area of a 180° arc is the half of the area of the entire circle:

A_arc = (π * r²)/2

Solving:

A_arc = 32π square miles

Answer:

Step-by-step explanation:

1260+11200=12460

so its, 1.246 x 10^4

In the picture we see that between 10 and 20 years old there are two rectangles . One goes to the 11% aproximately

the other rectangle reach 10% in the Y axis .

So then finally we have to add both percentages to obtain

10% + 11%= 21 %

21 percent are between ages 10 and 20 years old

The vertical line test consists in tracing various vertical lines throughout the function and checking wheter this lines will touch the function more than once.

As we can see none of the lines touch the graph more than once, therefore this graph is a function.

C(x) = 3x³ − 9x² − 243x + 1229

500 = 3x³ − 9x² − 243x + 1229

Subtract 500 on each side, as follows:

0 = 3x³ − 9x² − 243x + 729

(3x³ − 9x²) - (243x - 729) = 0

3x² (x - 3) - 243 (x - 3) = 0

(x - 3)(3x² - 243) = 0

x = 3, x = 9, x = -9; in the context of this problem, where x is the number

of units produced, negative values of x must be omitted, so x = 3 and x = 9

So we can say that if either 3 units or 9 units are produced the total cost

for the product will be at least $50000

[0, 3] U [9,∞)

Using the law of sines:

Using the heron formula:

Since the arc BAE is a semicircle, it measures 180°, and the angle that inscribes it, that is, angle ∠BCE, has half the measure, so ∠BCE = 90°.

The angle ∠ACE inscribes the arc AE, so the arc AE has double the measure of the angle ∠ACE, so AE = 56°.

Calculating the measure of the arc AB, we have:

So the first option is correct.

For the second option, these two angles inscribes the same arc (arc AE), so they have the same measure of half the measure of the arc. Therefore, they are congruent, so the second option is correct.

For the third option, there is nothing that proves that these angles are congruent, so the third option is false.

For the fourth option, there is nothing that proves that AC is a diameter, so the fourth option is false.

For the fifth option, the angle ∠BDE inscribes an arc of 180° (semicircle), so it has half the measure of the arc, therefore ∠BDE = 90°. So the fifth option is correct.

Explanation

The salary with regular pay rate is calculated as:

S is the salary, R is the regular pay rate and h is the number of hours worked.

The salary with over time is:

Because it pays double after 40 hours.

So the first 40 hours worked you'll get

The amount of overtime hours is 15 (55-40 = 15), so the overtime salary is:

The total Salary is the sum of the regular and the overtime salaries:

If the total salary was $840, then the regular pay rate R is:

Answer

Your regular pay rate is $12 / hour

From the question,

The two triangles that are congruent are :

Triangle CDM = Triangle ABM --------- Option C

The given graph represents a function, also notice that it is a one to one function because using the vertical line theorem we have that for all vertical lines it only intercepts the graph in just one point.

In a parallelogram, opposite sides are equal.

ON = LM

OL = NM

OL = y-6

NM= 1/3 x

ON= 5x-8

LM= 9x-26

First, solve for x

ON = LM

5x - 8 = 9x - 26

-8 + 26 = 9x - 5x

18 = 4x

18/4 = x

x = 4.5

Replace x=4.5 on NM, and solve for y:

OL = NM

y-6= 1/3x

y-6 = 1/3 (4.5)

y-6= 1.5

y= 1.5 + 6

y= 7.5 = 15/2

The lateral surface area is the total surface area minus the area of the two triangular faces at the top and bottom of the prism. t

Given that Billy used four colours to divide 4.20 by 4

To Determine: The model that shows this division

Solution:

It can be observed that 1 represents 100 small boxes

Dividing 4.20 by 4 would give

1.05 would be represented by small boxes

If we used colours, then each of the colours would have 105 boxes

From the above explanation, the model that shows 4.20/4 is OPTION D

Given

mean = 3 days

standard deviation = 1.7 days

Find

a. What is the distribution of X?

b. What is the median recovery time?

c. What is the Z-score for a patient that took 4.1 days to recover?

d. What is the probability of spending more than 2.4 days in recovery?

e. What is the probability of spending between 2.7 and 3.4 days in recovery?

f. The 80th percentile for recovery times

Explanation

a) Distribution of X is given by X ~ N( 3 , 1.7)

b) for the normal distibution ,the median is the same as the mean .

so , the median recovery time is 3 days

c) z - score for the patient that took 4.1 days to recover is

d) probability of spending more than 2.4 days in recovery

e) probability of spending between 2.7 and 3.4 days in recovery

Hence , the above are the required answers.