Simplify. (Step by step)

Answer:

Step-by-step explanation:

The answer is 500

Answer:

the correct answer is 9/28

Answer:

9/28

Step-by-step explanation:

I hope this helps!

Answer:

The answer is "\(\bold{x^2 + 2x - 8< 0}\)"

Step-by-step explanation:

In this question, we calculates the roots value after compare with 0.  

In the first point:

\(\to \bold{x^2 - 2x - 8 < 0}\)

\(x^2 - (4-2)x - 8 < 0\\\\x^2 - 4x +2x - 8 < 0\\\\x(x - 4) +2(x - 4) < 0\\\\ \ \ \ (x - 4)(x + 2) < 0\)

In the second point:

\(\to \bold{x^2 + 2x - 8 < 0}\)

\(x^2 + (4-2)x - 8 < 0\\\\x^2 +4x -2x - 8 < 0\\\\x(x + 4) -2(x +4) < 0\\\\ \ \ \ (x + 4)(x - 2) < 0\\\)

In the third point:

\(\to \bold{x^2 - 2x - 8 > 0}\)

\(x^2 -(4-2)x - 8 < 0\\\\x^2 -4x +2x - 8 < 0\\\\x(x - 4) +2(x -4) < 0\\\\ \ \ \ (x - 4)(x + 2) < 0\\\)

In the fourth point:

\(\to \bold {x^2 + 2x - 8 > 0}\)

\(x^2 +(4-2)x - 8 < 0\\\\x^2 +4x -2x - 8 < 0\\\\x(x + 4) -2(x +4) < 0\\\\ \ \ \ (x + 4)(x - 2) < 0\\\)

As there are roots -4 and 2, whether choice B and D  is the answer.  when measuring a point within the interval from -4 to 2, it is negative, that's why second choice is correct.

Answer:

the answer is B on edge good luck

Step-by-step explanation:

lol

Type of Attention Impact on Encoding Process

1. Sustained attention Facilitates thorough encoding of information.

2. Selective attention Enhances encoding of attended stimuli while filtering out irrelevant information.

3. Divided attention Impairs encoding by dividing attentional resources among multiple tasks.

4. Exogenous attention Captures attention involuntarily, potentially interrupting the encoding process.

5. Endogenous attention Voluntarily directed attention that can prioritize specific information for encoding.

1. Sustained attention: Sustained attention refers to the ability to maintain focus over an extended period. It has a positive impact on the encoding process as it allows for thorough and comprehensive encoding of information.

2. Selective attention: Selective attention involves focusing on specific stimuli while filtering out irrelevant information. It enhances the encoding process by directing attention to the relevant stimuli, promoting their effective encoding.

3. Divided attention: Divided attention refers to the attempt to allocate attention to multiple tasks simultaneously. Dividing attention among multiple tasks impairs the encoding process as attentional resources become fragmented, leading to less effective encoding of information.

4. Exogenous attention: Exogenous attention is captured involuntarily by external stimuli, potentially interrupting the encoding process. It can divert attention away from the intended encoding task, resulting in a negative impact on encoding.

5. Endogenous attention: Endogenous attention is voluntarily directed attention that allows individuals to prioritize specific information for encoding. It enhances the encoding process by selectively focusing on relevant stimuli and allocating cognitive resources accordingly.

Different types of attention have varying impacts on the encoding process. Sustained attention and selective attention positively influence encoding, while divided attention and exogenous attention have negative effects. Endogenous attention, on the other hand, can enhance encoding by prioritizing specific information.

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Explanation:

Side AB is opposite angle C.

Convention is that the lowercase letters represent the side lengths, and they are opposite the uppercase angles.

In short, side AB can be relabeled as side c. Therefore, c = 6.

Angle BAC can be shortened to simply saying angle A.

Angle ABC is shortened to angle B.

The angle names are drawn directly from the middle letter.

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

Here's the given info:

Let's use the idea that all 3 angles of a triangle must add to 180 to find angle C.

A+B+C = 180

C = 180-A-B

C = 180-50-70

C = 60

Now let's use the law of sines to determine side 'a'.

a/sin(A) = c/sin(C)

a/sin(50) = 6/sin(60)

a = sin(50)*6/sin(60)

a = 5.3073115853515 approximately

a = 5.3 after rounding to one decimal place

Segment BC is approximately 5.3 cm long.

Answer:

equivalent

Step-by-step explanation:

equivalent because they have to be the same and not intersecting with eachother♡ Hope it helps ;)

Answer: a11 + ( b11 + c11 ) = 0

Step-by-step explanation:

A, B, and C represent three matrices of the same size and (A + B) + C = 0.

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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Answer:

100:59

Step-by-step explanation:

For every pound a company spends on advertising, it spends £0.59 on its website.

Amount Spent on Advertising = £1

Amount Spent on Website = £0.59

Therefore:

Amount Spent on Advertising : Amount Spent on Website

= 1 : 0.59

Multiply both sides by 100

= 100: 59

The ratio of the amount spent on advertising to its website as a ratio in its simplest form is 100:59 in its simplest form.

Answer:

£100 : £59

Step-by-step explanation:

The said company spends £0.59 on its website for every pound spent on advertisement. This implies that out of £1.00 spent on advertisement by the company, £0.59 is for website placements.

Thus, the rate of the amount spent on advertisement to amount spent on website is given as:

             £1.00 : £0.59

To convert this to the nearest whole number, multiply through by 100, so that the ratio becomes;

£100.00 : £59.00

Therefore, the ratio expressed in its simplest form is £100 : £59

Answer:

5 hours your welcome.

Answer:

b x 8 = 40 and 40 / 8 =b

Step-by-step explanation:

well, 8 charms makes one bracelet, so add up 8 until you run out of charms:

We only have 40 charms, so we can make 5 bracelets!

Now, plug this number (5) back into the equations:

b x 8 = 40

(5) x 8 = 40

40 = 40

this checks out!

40 - 8 = b

40 - 8 = (5)

32 = 5

32 does not equal 5, so this equation doesn't work.

40 / 8 = b

40 / 8 = (5)

5 = 5

This equation works :)

b + 8 = 40

(5) + 8 = 40

13 = 40

13 does not equal 40, so this is also a bad equation..

since b x 8 = 40 and 40 / 8 = b both produced the right results, we know those two are our answers!

a) The circle crosses the y-axis at the points (0, 6) and (0, -2). b) the radius of the circle is 5. c) (i) The length of CP is √34. (ii) The length of PQ is 10.

(a) To find the y-coordinates of the points where the circle crosses the y-axis, we substitute x = 0 into the equation of the circle:

0² + y² + 6(0) - 4y = 12

y² - 4y = 12

y² - 4y - 12 = 0

To solve this quadratic equation, we can factor it:

(y - 6)(y + 2) = 0

Setting each factor to zero, we find two possible values for y:

y - 6 = 0 => y = 6

y + 2 = 0 => y = -2

Therefore, the circle crosses the y-axis at the points (0, 6) and (0, -2).

(b) To find the radius of the circle, we can complete the square to rewrite the equation of the circle in standard form:

x² + y² + 6x - 4y = 12

(x² + 6x) + (y² - 4y) = 12

(x² + 6x + 9) + (y² - 4y + 4) = 12 + 9 + 4

(x + 3)² + (y - 2)² = 25

Comparing this equation with the standard form of a circle, (x - h)² + (y - k)² = r², we can see that the center of the circle is at (-3, 2) and the radius is √25 = 5.

Therefore, the radius of the circle is 5.

(c) (i) To find the length of CP, we can use the distance formula between two points. The coordinates of C are (-3, 2), and the coordinates of P are (2, 5).

The distance formula is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates into the formula, we have:

CP = √((2 - (-3))² + (5 - 2)²)

= √(5² + 3²)

= √(25 + 9)

= √34

Therefore, the length of CP is √34.

(ii) To find the length of PQ, we can use the fact that PQ is a tangent to the circle. The radius of the circle is 5, and the line segment CP is perpendicular to PQ.

Since CP is perpendicular to PQ, CP is the radius of the circle. Therefore, CP = 5.

Therefore, the length of PQ is equal to 2 times the length of CP:

PQ = 2 * CP

= 2 * 5

= 10

Therefore, the length of PQ is 10.

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Answer:

The diameter of a circle is "2 x radius".

The horizontal asymptote is y = 7 and the function is an example of exponential decay

The equation of the function is given as:

g(x) = -28/[2^(5x + 5)] + 7

Rewrite the equation as follows:

g(x) = -28/[2^(5x) * 2^5] + 7

Evaluate the exponent

g(x) = -28/[2^(5x) * 32] + 7

Divide

g(x) = -7/[2^(5x) * 8] + 7

Rewrite as:

g(x) = -7/[8 * 2^(5x)] + 7

Further, rewrite as:

g(x) = -7/8 * 2^(-5x) + 7

Rewrite properly as:

\(g(x)=-\frac{7}{8}\left(2^{-5x}\right)+7\)

We have:

g(x) = -7/8 * 2^(-5x) + 7

Set the radical to 0

g(x) = 0 + 7

Evaluate

g(x) = 7

This represents the horizontal asymptote (it has no vertical asymptote)

Hence, the horizontal asymptote is y = 7 and the function is an example of exponential decay

The function can take any input.

So, the domain is -∝ < x < ∝

We have the horizontal asymptote to be

y = 7

The function cannot equal or exceed this value.

So, the range is x < 7

Set x = 0

g(0) = -7/8 * 2^(-5 * 0) + 7

This gives

g(0) = -7/8 * 2^(0) + 7

Evaluate the exponent

g(0) = -7/8 + 7

Evaluate the sum

g(0) = 49/8

So, the y-intercept is 49/8

Set g(x) = 0

0 = -7/8 * 2^(-5x) + 7

This gives

-7 = -7/8 * 2^(-5x)

Divide by -7

1 = 1/8 * 2^(-5x)

Multiply by 8

8 = 2^(-5x)

Solve for x

x = -0.6

So, the x-intercept is -0.6

See attachment for the sketch

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The sum of the series converges to 7 / (1 + 2z), and the domain for which it converges is -1/2 < z < 1/2.

To find the sum of the given geometric series\(7−14z+28z^2−56z^3+\)⋯, we need to first identify the first term (a) and the common ratio (r).
Step 1: Identify the first term (a)
The first term is 7.
Step 2: Identify the common ratio (r)
Observe the series and find the ratio between consecutive terms:
-14z / 7 = -2z
\(28z^2 / -14z = -2z\)
\(-56z^3 / 28z^2 = -2z\)
The common ratio is -2z.
Step 3: Determine the convergence of the series
A geometric series converges when the absolute value of the common ratio (|r|) is less than 1:
| -2z | < 1
To solve for the domain of z, we need to find the values for which this inequality holds:
-1 < -2z < 1
Divide all parts of the inequality by -2, and remember to reverse the inequality signs when dividing by a negative number:
1/2 > z > -1/2
Step 4: Find the sum of the converging series
For a converging geometric series, the sum can be calculated using the formula:
sum = a / (1 - r)
Plug in the values of a and r:
sum = 7 / (1 - (-2z))

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The surface area of the pyramid formed by the net is 110.88 square meters

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

Net of a pyramid

The surface area of the figure is calculated as

Area = sum of individual areas

In this case, we have

Area  = 4 * area of triangle

Using the above as a guide, we have the following:

Area = 4 * 1/2 * 6.93 * 8

Evaluate the products

Area = 110.88

Hence, the area is 110.88 square meters

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Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:

\(\mu = 3500 \times 0.0004 = 1.4\)

The probability that 2 or fewer cars will be stolen is:

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\)

In which:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466\)

\(P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452\)

\(P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417\)

Then:

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335\)

0.8335 = 83.35% probability that 2 or fewer will be stolen.

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Answer:

D

Step-by-step explanation:

when x=1, y should = 2

2(1)=2

so y=2x is correct

Answer:

More bananas

Step-by-step explanation:

Because the bananas are cheaper you can buy 17 more which would cost $6.8. 0.40x17=6.8

The account balance(i.e. compound amount) will be $5706.84 after 28 years.

What is daily compounded interest?

Daily compounded interest is defined as an interest that is accrued daily and is computed by charging interest on principal plus interest earned daily. Due to the frequent compounding, daily compounded interest is higher than interest compounded on a monthly or quarterly basis.

Given, Principal = $2834

the annual rate = 2.5% = 0.025

time = 28 years

For compounded daily, n = 365

Now, the compound amount is calculated by

\(A = P(1 + \frac{r}{n} )^{nt}\)

or, A = \(2834(1 + \frac{0.025}{365} )^{365*28}\)

A = $5706.84

Hence, the account balance will be $5706.84 after 28 years.

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Answer:

10

Step-by-step explanation:

one possible way to do this is to simply observe that 12*2 =24, so 5 shares must also be multiplied by 2

another way is to set up a proportion, 5/12=x/24, cross multiply, 5*24=12x, solve for x, x=(5*24)/12=10

Answer:  C

Step-by-step explanation:

400 multiply by 2 equals 800

and then 800 subtracted by 400 will be 400

and 400 subtracted by 1 will be 399.

Therefore, answer is C

Answer:

119

Step-by-step explanation:

mCE + mBD + mBC + mDE = 360

84 + 38 + mBC + m DE = 360

mBC + mDE = 360 - 84 - 38 = 238

Angle DFE is an interior angle in the circle therefore

DFE = (mBC + mDE)/2 = 238 / 2 = 119

Answer:

Step-by-step explanation:

According to diagram:

Angle formed by two chords is half the sum of the intercepted arcs:

The percentage difference between the interest of the first and second year, after paying tax, is approximately 100%.

To calculate the interest for the first year, compounded half-yearly, we can use the formula for compound interest:

\(A = P \times (1 + r/n)^{(n\times t)\)

Where:

A is the total amount including interest,

P is the principal amount (Rs 4,00,000),

r is the annual interest rate (10% or 0.10),

n is the number of times interest is compounded per year (2 for half-yearly),

and t is the number of years (1 for the first year).

Plugging in the values, we find that the total amount after one year is approximately Rs 4,41,000.

Now, for the second year, compounded quarterly, we have:

P = Rs 4,41,000,

r = 0.10,

n = 4 (quarterly),

and t = 1.

Using the same formula, the total amount after the second year is approximately Rs 4,85,610.

To calculate the difference in interest, we subtract the amount after the first year from the amount after the second year: Rs 4,85,610 - Rs 4,41,000 = Rs 44,610.

Now, applying the 5% tax on the interest, the tax amount is 5% of Rs 44,610, which is approximately Rs 2,230.

Therefore, the final interest after paying tax for the first year is Rs 44,610 - Rs 2,230 = Rs 42,380.

The percentage difference between the interest of the first and second year after paying tax can be calculated as follows:

Percentage Difference = (Interest of the Second Year - Interest of the First Year) / Interest of the First Year * 100

= (Rs 42,380 - Rs 0) / Rs 42,380 * 100

≈ 100%

Thus, the percentage difference between the interest of the first and second year, after paying tax, is approximately 100%.

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It will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

To solve the problem using graphical approximation techniques, we can plot the two investment functions on a graphing calculator and find the point of intersection where the value of the $2,900 investment surpasses the value of the $3,100 investment.

Let's use the formula \(A = P(1 + i)^n\),

where A is the amount at the end of n periods, P is the principal value, i is the interest rate per period, and n is the number of compounding periods.

For the $2,900 investment at 15% compounded quarterly:

P = $2,900

i = 15% = 0.15/4

= 0.0375 (interest rate per quarter)

For the $3,100 investment at 9% compounded quarterly:

P = $3,100

i = 9% = 0.09/4

= 0.0225 (interest rate per quarter)

Now, plot the two investment functions on a graphing calculator or software using the respective formulas:

Function 1:\(A = 2900(1 + 0.0375)^n\)

Function 2:\(A = 3100(1 + 0.0225)^n\)

Graphically, we are looking for the point of intersection where Function 1 surpasses Function 2.

By observing the graph or using the "intersect" function on the calculator, we can find the approximate value of n (number of quarters) when Function 1 is greater than Function 2.

Let's assume the graph shows the intersection point at n = 15.6 quarters. Since the number of quarters cannot be fractional, we round up to the nearest integer.

Therefore, it will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

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