Solve for x in the following equation.
9(5x +9)
=
9(9x + 2)

Answer:

x=\(\frac{2}{8}\)a

Step-by-step explanation:

8ax-5 = -3

Move the -5 to the right side ; -3 + 5 = 2

8ax=2

Get rid of 8a so you are left with x alone by dividing it out

\(\frac{8ax}{8a}\) = \(\frac{2}{8a}\)

You are left with

x= \(\frac{2}{8}\)a

The value of x is 1/4a

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S.

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15.

Given equation:

8ax−5=−3

8ax= -3+5

8ax= 2

x= 2/8a

x= 1/4a

Hence, the value of x is 1/4a

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\(\huge\red{\boxed{Answer}}\)

Given:

To find:

Solution:

⇛y - 2 = 6

⇛y = 6 +2

⇛y = 8

substitute 8 in place of y

⇛y + 4

⇛8 + 4

⇛12

12 is the answer

.

The present age of Earl is 12 years, Robin is 24 years and Adam is 4 years old.

Let us consider the present age of Earl to be x years.

According to the given question, the present age of Robin is twice that of Earl = 2x

And since it is given that Adam is 8 years younger than Earl, then his age

= x - 8

After 6 years, the age of Earl will be x + 6

Robin's age  will be = 2x + 6

Adam's age will be = x - 8 + 6 = x - 2

According to the given question, Robin's age will be thrice the age of Adam.

Hence, 2x + 6 = 3 (x - 2)

⇒ 2x + 6 = 3x - 6     ⇒ 6 + 6 = 3x - 2x     ⇒ 12 = x

Thus, the present age of Earl is 12 years,

Robin's age = 2x = 2 x 12 = 24 years

Adam's age = x - 8 = 12 - 8 = 4 years

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Answer:

3

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

A function is a relation where each input has its own output

In other words a function is a relation where each x value has its own y value.

If an x value repeats than the relation is not a function

It appears that the relation shown is a function as each x value has its own y value and none of the x values repeats, therefore the answer is yes

Answer:

Center ( 4 , -2) and r = 6

Step-by-step explanation:

x² - 8x + y² + 4y - 16 = 0

x² - 8x  + y² + 4 y = 16

x²- 2*4x + y² + 2 *2y = 16

(x² - 2*4x + 16 ) - 16 + (y² + 2*2y + 4) -4 = 16

(x - 4)² + (y + 2)² = 16 + 16 + 4

(x - 4)² + (y -[-2])² = 36

(x- 4)² + ( y - [-2] )² = 6²

Compare with (x - h)²+ (y - k)² = r²

Center ( 4 , -2) and r = 6

Answer:

votes

z is inversly proportional to r then z = k/r

zr = k

If z = 32 when r = 1.5

32(1.5) = k

48 = k

k = 48

If z = 8 then r = ?

8r = k

8r = 48

Divide to each side by 8.

r = 48/8

r = 6

Part A: The range of the function is (-∞, 0) ∪ (0, +∞).

Part B: There is a horizontal asymptote at y = 5 for x → 3^- and x → 3^+; there is a horizontal asymptote at y = 0 for x → +∞.

Part C: As x approaches negative infinity, f(x) approaches negative infinity, and as x approaches positive infinity, f(x) approaches 0.

Part A: To determine the range of the function, we need to examine the possible values that f(x) can take.

From the definition of the piecewise function, we have two cases:

For x ≤ 3, f(x) = 3^(x - 1) - 4.

In this case, the base of the exponential function is 3, which means that as x decreases, f(x) approaches negative infinity.

Additionally, since \(3^{(x - 1)\)  is an increasing function, f(x) will also increase as x increases. Therefore, the range of this part of the function is (-∞, +∞).

For x > 3, f(x) = 15/x.

Here, we can see that as x approaches infinity, f(x) approaches 0. Conversely, as x approaches 0, f(x) approaches positive infinity. Therefore, the range of this part of the function is (0, +∞).

Combining the two cases, we can conclude that the range of the function f(x) is (-∞, 0) ∪ (0, +∞), which means that f(x) can take any real value except for 0.

Part B: To determine the asymptotes of the function, we consider the behavior of f(x) as x approaches certain values.

As x approaches 3 from the left (x → 3^-), f(x) approaches 3^(3 - 1) - 4 = 3^2 - 4 = 5. Therefore, there is a horizontal asymptote at y = 5 for x → 3^-.

As x approaches 3 from the right (x → 3^+), f(x) approaches 15/3 = 5. Hence, there is a horizontal asymptote at y = 5 for x → 3^+.

As x approaches positive infinity (x → +∞), f(x) approaches 0. Therefore, there is a horizontal asymptote at y = 0 for x → +∞.

No vertical asymptotes are present in this function because there are no values of x for which f(x) becomes undefined.

Part C: The end behavior of f(x) can be described as follows:

As x approaches negative infinity (x → -∞), the function has no constraints on the range, and the behavior of f(x) is determined by the first part of the piecewise function.

Since \(3^{(x - 1)\) is an increasing function, f(x) will approach negative infinity as x decreases without bound.

As x approaches positive infinity (x → +∞), the function is determined by the second part of the piecewise function, which is 15/x.

As x becomes very large, f(x) will approach 0, indicating that the function gets closer and closer to the x-axis without actually crossing it.

Therefore, the end behavior of f(x) is that it approaches negative infinity as x approaches negative infinity and approaches 0 as x approaches positive infinity.

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Answer:

(\(GS\)) || (\(EA\))

Step-by-step explanation:

When two lines are parallel, all four angles formed by the intersection of the two lines are right angles, meaning their angle measures are (90°). This means that alternate interior angles are congruent because all alternate interior angles measures equal (90°). Therefore, by the alternate interior angles converse theorem, lines (\(GS\)) and (\(EA\)) are parallel.

The alternate interior angles converse theorem states if two angles are congruent and they have the relation of being a part of two lines intersected by a third line, then the two non-intersecting lines are parallel.

Answer:

5$

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

$161.50

Step-by-step explanation:

4.25% of $3800 is $161.50

When we use the word automobile to refer to a category of transport vehicles, we are using this word as a concept. The correct answers is concept

A concept is an abstract idea that takes form in your mind. This is known as the structures of thoughts and beliefs. They are important because it gives a clear explanation of a particular subject.

An automobile, byname auto, also called motorcar or car, a usually four-wheeled vehicle designed primarily for passenger transportation and commonly propelled by an internal-combustion engine using a volatile fuel, this term is generally used for an vehicle when refering to its category.

When we think of the word automobile, the first thing that comes to your mind is a category of transport. The mind connects the thoughts around the structures build. That’s a concept

Thus, when we use the word automobile to refer to a category of transport vehicles, we are using this word as a concept.

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Answer:

see explanation

Step-by-step explanation:

(a)

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 7 , then

sum = 180° × (7 - 2) = 180° × 5 = 900°

(b)

since the polygon is regular then the 7 interior angles are congruent

each interior angle = 900° ÷ 7 ≈ 128.6° ( to 1 decimal place )

(c)

the sum of the exterior angles of a polygon is 360°

since the polygon is regular then the 7 exterior angles are congruent

each exterior angle = 360° ÷ 7 ≈ 51.4° ( to 1 decimal place )

Answer:

a) 900°

b) ≈ 128,6°

c) ≈ 51,4°

Step-by-step explanation:

a) s = (n - 2) × 180°

n - the number of sides (in this case, it's 7)

s - the sum of interior angles

s = (7 - 2) × 180° = 5 × 180° = 900°

.

b) In order to find the size of each angle, we have to divide the sum by the number of sides:

900° / 7 ≈ 128,6°

.

c) Since the sum of exterior angles of a polygon is 360°, we can find the size of one exterior angle by dividing this sum by the number of sides:

360° / 7 ≈ 51,4°

Answer:

6

Step-by-step explanation:

150 goes into 25 evenly so it would not be a mixed number but a whole one

Also 2 multiplied by 25 is 50 so multiply 25 by 4 and you get 100 multiply it by 6 and you would get 150

Answer: Here’s the answer from Plato.

Step-by-step explanation:

I hope it right.

Answer:

Scale factor = \(\frac{1}{2}\)

Step-by-step explanation:

Perimeter of the actual flag = 22 in.

Perimeter of the scale drawing of the flag = 11 in.

Since, perimeter of a triangle = Sum of all three sides of the given triangle

Therefore, scale factor of the drawing

= \(\frac{\text{Measure of the side of drawing}}{\text{Measure of the side of actual}}\) = \(\frac{\text{Perimeter of drawing}}{\text{Perimeter of actual}}\)

= \(\frac{11}{22}\)

= \(\frac{1}{2}\)

Therefore, scale factor of the drawing will be \(\frac{1}{2}\).                                        

Each side of the scaled triangle will be half of the actual triangle.

Based on the given information, the compass will lag behind the airplane during a turn from the south. This means that the compass reading will be slower to update and indicate the correct heading compared to the actual direction of the airplane. Therefore, the first statement "The compass exaggerates the rate of turn" is false.

During a turn, the compass needle is affected by the magnetic field of the Earth, and it takes some time for the needle to align with the new heading. This lag in the compass reading is due to the inertia of the compass needle and the damping effect of the compass mechanism. As the airplane turns, the compass needle will gradually catch up and align with the new heading. Therefore, the second statement "The compass will lag behind the airplane" is true.

The third statement "The compass will match the exact heading" is false because, as mentioned earlier, the compass will lag behind the airplane during a turn. It will eventually align with the correct heading, but it will not match the exact heading instantaneously.

In summary, during a turn from the south, the compass will lag behind the airplane, but it will eventually align with the correct heading. It does not exaggerate the rate of turn, and it does not immediately match the exact heading.

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The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).

For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.

To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.

In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.

Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

Here's a sketch to visualize the calculation:

                  |

                  |

                  |

                  |       **

                  |      *  *

                  |     *    *

                  |    *      *

                  |   *        *

                  |  *          *

                  | *            *

-------------------|--------------------------

      18.9        |       20

The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.

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The answer are: a. Total outflows: $2,007,901, b. Total inflows: $827,080, c. Net present value: $824,179, d. Should the old issue be refunded with new debt? Yes

To determine whether the old bond issue should be refunded with new debt, we need to calculate the present value of total outflows, the present value of total inflows, and the net present value (NPV). Let's calculate each of these values step by step: Calculate the present value of total outflows. The total outflows consist of the call premium, underwriting cost on the old issue, and underwriting cost on the new issue. Since these costs are one-time payments, we can calculate their present value using the formula: PV = Cash Flow / (1 + r)^t, where PV is the present value, Cash Flow is the cash payment, r is the discount rate, and t is the time period.

Call premium on the old issue: PV_call = (7% of $22 million) / (1 + 0.1)^16, Underwriting cost on the old issue: PV_underwriting_old = $530,000 / (1 + 0.1)^16, Underwriting cost on the new issue: PV_underwriting_new = $680,000 / (1 + 0.1)^16. Total present value of outflows: PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. Calculate the present value of total inflows. The total inflows consist of the interest savings and the tax savings resulting from the interest expense deduction. Since these cash flows occur annually, we can calculate their present value using the formula: PV = CF * [1 - (1 + r)^(-t)] / r, where CF is the cash flow, r is the discount rate, and t is the time period.

Interest savings: CF_interest = (12% - 10%) * $22 million, Tax savings: CF_tax = (40% * interest expense * tax rate) * [1 - (1 + r)^(-t)] / r. Total present value of inflows: PV_inflows = CF_interest + CF_tax.  Calculate the net present value (NPV). NPV = PV_inflows - PV_outflows Determine whether the old issue should be refunded with new debt. If NPV is positive, it indicates that the present value of inflows exceeds the present value of outflows, meaning the company would benefit from refunding the old issue with new debt. If NPV is negative, it suggests that the company should not proceed with the refunding.

Now let's calculate these values: PV_call = (0.07 * $22,000,000) / (1 + 0.1)^16, PV_underwriting_old = $530,000 / (1 + 0.1)^16, PV_underwriting_new = $680,000 / (1 + 0.1)^16, PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. CF_interest = (0.12 - 0.1) * $22,000,000, CF_tax = (0.4 * interest expense * 0.4) * [1 - (1 + 0.1)^(-16)] / 0.1, PV_inflows = CF_interest + CF_tax. NPV = PV_inflows - PV_outflows.  If NPV is positive, the old issue should be refunded with new debt. If NPV is negative, it should not.

Performing the calculations (rounded to the nearest whole dollar): PV_call ≈ $1,708,085, PV_underwriting_old ≈ $130,892, PV_underwriting_new ≈ $168,924, PV_outflows ≈ $2,007,901,

CF_interest ≈ $440,000, CF_tax ≈ $387,080, PV_inflows ≈ $827,080.  NPV ≈ $824,179.  Since NPV is positive ($824,179), the net present value suggests that the old bond issue should be refunded with new debt.

Therefore, the answers are:

a. Total outflows: $2,007,901

b. Total inflows: $827,080

c. Net present value: $824,179

d. Should the old issue be refunded with new debt? Yes

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As per the BMI, the dependent variable is outcome

In this study, the researcher wants to compare the effectiveness of two different exercise programs in reducing BMI in individuals with diabetes. The participants will be randomly assigned to either the aerobic dancing group or the walking group, and their BMI will be measured before and after the six-month exercise program.

The changes in BMI between the two groups will be compared to determine which exercise program is more effective in reducing BMI in this population. The dependent variable in this study is the change in BMI, as it is the outcome that is being measured and compared between the two groups.

Overall, this study will provide valuable insights into the effectiveness of different exercise programs in reducing BMI in older adults with diabetes, which can have important implications for their overall health and wellbeing.

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Answer:

True

Step-by-step explanation:

Answer: True

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{1}{n} =\frac{9}{6} \\9n=6\\n=\frac{6}{9} =\frac{2}{3} \\1:n=1:\frac{2}{3}\)

Answer:

3:2

In fraction form :

Step-by-step explanation:

Pls mark as brainliest

Since the sum of the numbers selected must exceed 1, we know that n must be at least 1. Therefore, the expected value of X is finite and is equal to 2.

The expected value of the count of numbers that are selected can be found using the geometric distribution, since it models the number of trials until a success occurs.

Let X be the number of numbers that are selected until the sum of all numbers exceeds 1. Then X has a geometric distribution with parameter p, where p is the probability of success on each trial, i.e. the probability that the sum of all numbers selected does not exceed 1.

Since the numbers are selected uniformly over [0, 1], the probability of success on each trial is given by the area under the curve between 0 and 1 after the first number is selected.

On the first trial, the probability of success is 1. On the second trial, the probability of success is the area under the curve between 0 and (1 - the first number selected).

On the third trial, the probability of success is the area under the curve between 0 and (1 - the sum of the first two numbers selected), and so on.

The expected value of X can be found using the formula for the expected value of a geometric distribution:

E(X) = 1/p

Since the expected value of the sum of n independent and identically distributed uniform [0, 1] random variables is n/2, we can use this to find p:

E(X_1 + X_2 + ... + X_n) = n/2

where X_1, X_2, ..., X_n are the n numbers selected.

So, p = 1 / (1 + n/2).

Finally, we can substitute this into the formula for E(X) to find the expected value of X:

E(X) = 1 / (1 - n/2) = 2 / (2 - n)

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Answer:

18b - 45

Step-by-step explanation:

Like terms are terms that are similar.  Ex:  19t - 2t.  19t and -2t are similar because they both have t in common.

Another way to write 36b - 45 - 18b is to combine like terms.

36b - 18b = 18b

So, to rewrite, 18b - 45.

Answer:

\( \sf \: 18b - 45 \)

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 36b - 45 - 18b

Let's simplify the expression,

→ 36b - 45 - 18b

→ 36b - 18b - 45

→ (36 - 18)b - 45

→ (18)b - 45

→ 18b - 45

Hence, the answer is 18b - 45.

Answer:

available

Step-by-step explanation:

if its available if available comment

After 22 thousand cell phones have been sold, sales are increasing by 3 thousand phones per month. 0.180y (1-y/90) is the differential equation describing cell phone sales.

The Logistic model is given by,

dy/dt = ry (1-y/m)

where r is the rate constant.

M is the maximum capacity.

plugin M,

dy/dt = ry (1-y/90)

Now we need to find rate constant r,

put y = 22, y' = 3

3 = 22r (1- 22/90)

3 = 22r (1- 90-22/90)

3 = 22r (68/90)

3 = 11r (68/45)

748r = 135

r = 135/78

r = 0.180481283422.

rounding off to 3 decimals,

r = 0.180

Now the final differential equation becomes,

dy/dt = 0.180y (1-y/90).

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The effect of educational attainment on the time spent sleeping per week is examined using the simple regression model sleep = β0 + β1educ + u. The sample mean and standard deviation of sleep and educ can be calculated using the data in PS2 Q4.dta.

To find the sample mean of sleep and educ, sum up all the values of sleep and educ respectively and divide by the total number of observations.

The standard deviation can be calculated by taking the square root of the variance, where the variance is the average of the squared deviations from the mean.

These calculations provide measures of central tendency and dispersion for the variables sleep and educ.

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The value of the expression below when x=5x=5?

8x+9 is equal to \(7^{2}\) (or) 49.

Substitute \(\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)\)

The expression,

y = 8x + 9

If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:

So, we can substitute x = 5,

Then, y = 8 * 5 + 9

Calculate the product or quotient,

y = 40 + 9

Calculate the sum or difference,

y = 49

We can write alternative form,

y = \(7^{2}\)

Therefore,

Hence the value of the expressions if x = 5 is \(7^{2}\) (or) 49.

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Answer:

M

Step-by-step explanation:

The angle bisector is M