2. Convert the following into a single log statement from the many log statements to 1.

2 Log w + log 7 - 3 log x - 8 log y

NOTE: You must show this in at least two steps.

1st line should be to convert the 2 the 3 and the 8 only.

2nd line can be the final answer.

Answer:

( 4t + 15 ) / 20

Step-by-step explanation:

Let me show you the formula for this type of question,

[tex] \frac{a}{c} + \frac{b}{d} = \frac{ad + bc}{cd} [/tex]

So here for you,

[tex] \frac{t}{5} + \frac{3}{4} = \frac{ 4t+15 }{20} [/tex]

The intersection points are approximately (2.6, 1.29) and (2.6, -1.29).

The region where radio signals can be heard from both masts is the intersection of the two circles. We can find the intersection points by solving the system of equations:

(x - 1)² + y² = 1.5²

(x - 5)² + y² = 2²

Expanding the equations and subtracting them, we get:

10x - 26 = 0

So, x = 2.6. Substituting into either equation, we get:

y = ±✓(1.5² - (2.6 - 1)²) = ±1.29

The intersection points are approximately (2.6, 1.29) and (2.6, -1.29).

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Answer:

c.-5.81

Step-by-step explanation:

=-13/4 -2.56

=-581/100

=-5.81

Answer:

12 ft

Step-by-step explanation:

See image

The value of y at the value of x = 13 is,

⇒ y = 78

We have to given that;

The value of y varies directly with x.

And, at y = 102 then x = 17

Since, The value of y varies directly with x.

Hence, We get;

⇒ y = kx

at y = 102 then x = 17;

⇒ 102 = k × 17

⇒ k = 102 / 17

⇒ k = 6

Hence, Equation is,

⇒ y = 6x

Plug x = 13;

⇒ y = 6 × 13

⇒ y = 78

Thus, The value of y at the value of x = 13 is,

⇒ y = 78

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Among the given options, the measure that cannot be the length of the third side of the triangle is 12 cm. The correct option is C 12 cm.

Determining the length that cannot not be the measure of the third side of the triangle

From the question, we are to determine the length that cannot be the measure of the third side of the triangle

From the given information, Two sides of the triangle are 7 cm and 4 cm From one of the properties of a triangle, we know that the length of a side of triangle is greater than the difference of the two other sides and it is less than the sum of the two other sides.

Let the length of the third side of the triangle be x.

Therefore,

x < 7 cm + 4 cm

x < 11 cm and

x > 7 cm - 4 cm

x > 3 cm

Hence, the measure that cannot be the length of the third side is 12 cm.

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The amount of allowance Claire would have on the 14th day is given by the geometric progression and a₁₄ = $ 409.60

Given data ,

The pattern in which the allowance is increasing is a geometric sequence with first term $0.05$ and common ratio $r=2$ since each term is twice the previous term.

The given GP has a common ratio of 2. We can find the 14th term using the formula:

aₙ = arⁿ⁻¹

Here, a1 = 0.05 and r = 2. Therefore,

a₁₄  = 0.05 * 2^(14-1)

a₁₄ = 0.05 * 2^13

a₁₄ = 0.05 * 8192

a₁₄ = 409.6

Hence , the 14th term of the given GP is $ 409.60

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The measure of angle ZKLJ is approximately is 24.62°. Option C is right choice.

To find the measure of angle ZKLJ in the given rectangle:

Since a rectangle has opposite sides equal in length, we can divide the perimeter of 34 units by 4 to find the length of each side:

34 units / 4 = 8.5 units

Now, consider triangle ZKL. We know that ZK = 8.5 units and KL = 5 units.

Using the Pythagorean theorem, we can calculate the length of ZL:

[tex]ZL^2[/tex] = [tex]ZK^2 + KL^2[/tex]

[tex]ZL^2[/tex] = [tex](8.5 \:units)^2 + (5 \:units)^2[/tex]

[tex]ZL^2[/tex] = 72.25 + 25

[tex]ZL^2[/tex] = 97.25

ZL ≈ 9.86 units

Now, let's calculate the tangent of angle ZKL:

tan(ZKL) = KL / ZL

tan(ZKL) = 5 units / 9.86 units

tan(ZKL) ≈ 0.507

Using the inverse tangent (arctan) function, we can find the measure of angle ZKLJ:

ZKLJ ≈ arctan(0.507)

ZKLJ ≈ 27.46°

Therefore, rounding to the nearest hundredth, the measure of angle ZKLJ is approximately 27.46°.

The closest option to this answer is option C: 24.62°.

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Question-

Given that the rectangle above has a perimeter of 34 units, find mZKLJ. Round the answer to the nearest hundredth.

A. 8.46°

B. 22.62⁰

C. 24.62°

D. 65.38°

Answer: To solve this problem, we can use the formula for continuous compound interest:

A = Pe^(rt)

Step-by-step explanation:

A = Pe^(rt)

where A is the amount of money in the account after t years, P is the principal amount (initial investment), e is the mathematical constant (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years.

For Sally's investment:

P = $45,000

r = 0.119 (11.9% as a decimal)

a) After 10 years:

t = 10

A = 45000e^(0.119 x 10) = $158,086.34

Therefore, after 10 years, Sally would have approximately $158,086.34 in the account.

b) After 25 years:

t = 25

A = 45000e^(0.119 x 25) = $989,988.27

Therefore, after 25 years, Sally would have approximately $989,988.27 in the account.

c) To find how long it takes to double in value:

We can use the formula:

2P = Pe^(rt)

Simplifying this equation:

2 = e^(rt)

ln(2) = rt

t = ln(2)/r

Using the values of P and r from above:

t = ln(2)/0.119 = 5.81 years (rounded to two decimal places)

Therefore, it would take approximately 5.81 years for Sally's investment to double in value.

Answer:

4 and -4

Step-by-step explanation:

4²=16

-4²=1

The two values that f could be if f² is 16 are +4 and -4 because both the positive and negative square roots are considered in solving the equation f² = 16.

The solution to the equation f² = 16 is found by taking the square root of both sides. However, when we take the square root in solving an equation, we need to consider both the positive and negative roots. The square root of 16 is +4 and -4. These are the two possible solutions for f in the equation f² = 16.

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Answer:

B circle graph

Step-by-step explanation:

circle graph or pie chart is the best representation since bar chart is not present

The values of x in the absolute value function 5 - 9|4 - 8x| = -103 are (b) {-1, 2}

From the question, we have the following parameters that can be used in our computation:

5 - 9|4 - 8x| = -103

Subtract 5 from both sides of the equation

so, we have the following representation

- 9|4 - 8x| = -108

Divide both sides by -9

|4 - 8x| = 12

Remove the absolute bracket

Thisgives

4 - 8x = 12 or 4 - 8x = -12

So, we have

-8x = 8 or -8x = -16

Divide

x = -1 or x = 2

Hence, the values of x are (b) {-1, 2}

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Answer:

Natural numbers are a set of positive integers (whole numbers greater than zero) that are used for counting and ordering things. They are denoted by the symbol "N" and the set of natural numbers includes 1, 2, 3, 4, 5, 6, 7, 8, 9, and so on.

(Hi there, do you like stories? if so, go into my profile for my questions. Read the excerpt and give me feedback if you can)

Answer:

5 shipments had at least 10 broken tiles but less than 20 broken tiles.

Step-by-step explanation:

it says "college" in the headline of this question.

are you serious ?

this is an upper elementary or beginning of middle school problem.

if you have a problem with such a question in college, you really have a problem and would need intensive tutoring (you need to recover everything from the beginning of math).

in such problems, to find your way, always try to find the amount represented by 1 unit.

everything else can be then calculated in relation to that one unit.

3 cars cost $2.46

1 car costs therefore 1/3 of that :

2.46/3 = $0.82

and 25 cars cost then 25 times that of a single car :

0.82 × 25 = $20.50

in short, the direct approach is

$2.46 × 25/3 = $20.50

It is given that Hoku is paying the shirt company $880 for shirt design and the first 50 Shirts. So, the fixed price will be $880 for 50 shirts.

Now, for over & above 50 shirts the cost is $12 per shirt.

Now, adding both the amounts to get the total cost of uniform shirts for company. So, the equation for total cost for buying more than 50 uniform shirts becomes y = 12(x-50)+880.

Comparing the above equation with the given equation, the value of p comes out to be 880.

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the number of 5p = 2x

and the number of 20p = x

the total value = y

(2x)*(.05) + (x)*(.20)= y .......eqa1

if all 5p became 20p

20p = 2x

5p = x

(x)*(.05) + (2x)*(.20)= y+6 ..... eqa2

subtract the equations

eq2 - eq 1

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

0.05x + 0.4x =y+6

-

0.1x + 0.2x = y

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

0.45x= y+6

-

0.3x =y

= 0.15x = 6

x = 40

so number of 5p = 80 coins

and number of 20p = 40 coins

The correct statement when writing a proof, how do you construct the first statement is,

⇒ By copying the “given” statement(s) from the original problem.

Since, We know that;

Evidence or argument establishing or helping to establish a fact or the truth of a statement.

Now, We just start any proof or derivation

By copying the “given” statement(s) from the original problem.

Thus, The correct statement when writing a proof, how do you construct the first statement is,

⇒ By copying the “given” statement(s) from the original problem.

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Answer:

250.75

Step-by-step explanation:

Peak time cost = 0.85 × 45 = 38.25

Off peak time cost = 0.75 × 150 = 112.5

Monthly payment = R100

Total monthly bill = 100+112.5+38.25 = R 250.75

The value of the probability of the different events are,

The value of the probability P (3) is,

⇒ 1 / 5

And, The value of the probability P (blue & green) is,

⇒ 8/45

We have to given that;

A box contains 2 red marbles, 5 green marbles and 8 blue marbles.

Hence, Total marbles = 2 + 5 + 8 = 15

So, The value of the probability P (3) is,

⇒ 3 / 15

⇒ 1 / 5

And, The value of the probability P (blue & green) is,

⇒ 8/15 x 5/15

⇒ 8/15 x 1/3

⇒ 8 / 45

Thus, The value of the probability P (3) is,

⇒ 1 / 5

And, The value of the probability P (blue & green) is,

⇒ 8/45

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The function is solved and f(x) represents the total number of hours; x represents the number of weeks he exercises this summer

Given data ,

Luke is keeping track of the total number of hours he exercises. He started the summer having already put in 15 hours, and he then exercises 7 hours each week.

So , the function is given by

The function to keep track of his exercise is f(x) = 7x + 15

On simplifying the equation , we get

f(x) represents the total number of hours; x represents the number of weeks he exercises this summer

Hence , the function is f(x) = 7x + 15

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Answer:

[tex] \frac{3}{5} \times \frac{4}{3} \times 3 = \frac{3}{5} \times 4 = \frac{12}{5} = 2 \frac{2}{5} [/tex]

The volume of this rectangular prism is

2 2/5 cm^3.

[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ c = \sqrt{7^2+8^2~-~2(7)(8)\cos(32^o)} \implies c = \sqrt{ 113 - 112 \cos(32^o) } \\\\\\ c \approx \sqrt{ 113 - (94.9814) } \implies c \approx \sqrt{ 18.0186 } \implies c \approx 4.2[/tex]

Make sure your calculator is in Degree mode.

The value of m∠Q as shown in the right-angled triangle is 54.718°.

The Formula used is:

m∠Q = cos⁻¹(s/r)........................ (1)

Where:

a = 8 m

b = 8√3 m

Now, Substitute these values into equation 1

m∠Q = cos⁻¹(8/8√3)

m∠Q = cos⁻¹(1/√3)

m∠Q = 54.718.

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The most common number of hours volunteered is 22.

Option B is the correct answer.

We have,

A.
The number of students who volunteered more than 30 hours is greater than the number of students who volunteered fewer than 30 hours.

This can not be determined from the given stem-and-leaf plot as it only shows the frequency distribution of hours volunteered without any specific count of students.

The plot only indicates that there are some students who volunteered between 31-36 hours (stem 3, leaves 33, and 36) and one student who volunteered for 44 hours (stem 4, leaf 4).

Therefore, option A is not supported by the given data.

B.

The most common number of hours volunteered is 22.

From the stem-and-leaf plot, we can see that the mode is 22 as it has the highest frequency (stem 2, leaves 2, 5, 7, 8).

Hence, option B is supported by the given data.

C.

The number of students who volunteered between 9 and 20 hours is greater than the number of students who volunteered more than 40 hours.

This statement cannot be confirmed by the given stem-and-leaf plot as there are no leaves in stem 1, which means there are no students who volunteered less than 10 hours. Also, there are no leaves in stem 4, except for one leaf with a value of 44.

Therefore, we can not determine how many students volunteered between 9-20 hours and more than 40 hours. Hence, option C is not supported by the given data.

D.

The most common number of hours volunteered is 41.

There are no leaves in stem 4 except for the value of 44, which means there is no student who volunteered for 41 hours.

Hence, option D is not supported by the given data.

Therefore,

The most common number of hours volunteered is 22.

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The correct option is c because the measure of the arc angle RE is 62° using the Angles of Intersecting Chords Theorem.

The Angles of Intersecting Chords Theorem states that the angle formed by the intersection of the chords is equal to half the sum of the intercepted arcs, and conversely, that the measure of an intercepted arc is half the sum of the two angles that intercept it.

66° = (RE + ST)/2

66° = (RE + 70)/2

RE + 70 = 2 × 66 {cross multiplication}

RE + 70 = 132

RE = 132 -70 {collect like terms}

RE = 62°

Therefore, the measures of the arc angle RE is 62° using the Angles of Intersecting Chords Theorem

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Answer:

(.47 + .36 + 1)/3 = 1.83/3 = .61 = 61%

A math ACT score of 19.55 or lower corresponds to the 30th percentile of scores at this college.

To do this, we can use a standard normal distribution table or a calculator with a normal distribution function. The standard normal distribution is a special case of the normal distribution with a mean of 0 and a standard deviation of 1.

By using a table or calculator, we can find the z-score that corresponds to the 30th percentile. The z-score represents the number of standard deviations away from the mean that a certain point is. Once we have the z-score, we can use it to find the actual math ACT score by using the formula:

actual score = mean + (z-score)(standard deviation)

If we use a standard normal distribution table, we can find that the z-score corresponding to the 30th percentile is -0.52. Therefore, the math ACT score that corresponds to the 30th percentile at this college is:

actual score = 21.8 + (-0.52)(4.9) = 19.55

In other words, 30% of the scores are below 19.55, and 70% of the scores are above 19.55.

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