what's the answer to my problem

We can use the logarithmic identity log_a(b) + log_a(c) = log_a(bc) to simplify the left side of the equation:

log_2(x) + log_4(x+1) = log_2(x) + log_2((x+1)^(1/2))

Using the rule log_a(b^c) = c*log_a(b), we can simplify further:

log_2(x) + log_2((x+1)^(1/2)) = log_2(x(x+1)^(1/2))

Now we can rewrite the equation as:

log_2(x(x+1)^(1/2)) = 3

Using the rule log_a(b^c) = c*log_a(b), we can rewrite this as:

x(x+1)^(1/2) = 2^3

Squaring both sides, we get:

x^2 + x - 8 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -8. Plugging in these values, we get:

x = (-1 ± sqrt(1^2 - 4(1)(-8))) / 2(1)

x = (-1 ± sqrt(33)) / 2

x ≈ -2.54 or x ≈ 3.54

However, we must check our solutions to make sure they are valid. Plugging in x = -2.54 to the original equation results in an invalid logarithm, so this solution is extraneous. Plugging in x = 3.54 yields:

log_2(3.54) + log_4(4.54) = 3

0.847 + 0.847 = 3

So x = 3.54 is the valid solution to the equation.

The equation of the line that passes through the point (-3, 7) and has a slope of -5/3 is y - 7 = (-5/3)(x + 3).

We are given the point (-3, 7) and the slope of the line as -5/3.The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.

To obtain the equation of the line, we need to substitute the values of slope and point in the slope-intercept form and solve for b.(7) = (-5/3)(-3) + b 21/3 = b.

Now we have the value of b, and we can substitute the values of m and b in the slope-intercept form.y = (-5/3)x + 21/3 is the equation of the line in slope-intercept form.

To obtain the equation in the standard form Ax + By = C, we multiply each term by 3.3y = -5x + 7Add 5x to both sides5x + 3y = 7.

This is the equation of the line in standard form.

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The image's distance from the mirror is -1.87, by using the mirror equation.

Note:-  Although the question is missing, I believe the issue is asking where the image is located.

To find the solution to the problem, the mirror equation can be used:

Mirror equation =  \(\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }\)

Where,

f = mirror's focal length

\(d_{o}\) = object's distance from the mirror

\(d_{i}\) =  image's distance from the mirror

The focal length is assumed to be negative for a convex mirror in our problem.

f = -2.8 m

The object's distance (do) = 5.6m

By using the mirror equation, the image's distance from the mirror can be determined

\(\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }\)

i.e, \(\frac{1}{d_{i} } = \frac{1}{f} -\frac{1}{d_{o} }\)

= \(-\frac{1}{2.8} -\frac{1}{5.6}\) =  \(-\frac{3}{5.6}\)

= - 0.5357

\(d_{i} =\) \(-\frac{5.6}{3}\)

= -1.87 m

The virtual nature of the image is indicated by the negative sign (located behind the mirror)

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The three questions are illustrations of arithmetic operations and geometric progressions

(1) Acid concentration

The given parameters are:

pH of acid lemon juice = 2

pH of acid urine = 5.5

The difference between their pH is calculated as follows:

Difference = 5.5 - 2

Difference = 3.5

Multiply the difference by 10, to calculate the acidity

Acidity = 3.5 * 10

Acidity = 35

Hence, the acid like lemon juice is 35 times stronger than urine

(2) Depreciation

The depreciation is given as:

r = 18%

In 1998, the car's worth is $19995.

This is represented as:

a = 19995

2012 is 14 years from 1998.

This is represented as:

n = 14

So, the worth of the car in 2014 is calculated using:

\(\mathbf{Worth =a(1 -r)^n}\)

So, we have:

\(\mathbf{Worth =19995 \times (1 -18\%)^{14}}\)

Express percentage as decimal

\(\mathbf{Worth =19995 \times (1 -0.18)^{14}}\)

\(\mathbf{Worth =19995 \times 0.82^{14}}\)

Evaluate

\(\mathbf{Worth =1243}\)

Hence, the worth of the car in 2012 is $1243

(3) Spread of Gossip

The spread of the gossip is an illustration of geometric progression, where

a = 1 ---- the first term

r = 3 --- the common ratio

L =1200 --- the last term

So, we calculate the number of terms from 1 to 1200 using the following nth terms of geometric progression

\(\mathbf{L = ar^{n-1}}\)

This gives

\(\mathbf{1200 = 1 \times3^{n-1}}\)

\(\mathbf{1200 = 3^{n-1}}\)

Take logarithm of both sides

\(\mathbf{log(1200) = log(3^{n-1})}\)

Apply law of logarithm

\(\mathbf{log(1200) = (n-1)log(3)}\)

Divide both sides by log(3)

\(\mathbf{n - 1 = log(1200) \div log(3)}\)

\(\mathbf{n - 1 =6.45}\)

Add 1 to both sides

\(\mathbf{n =7.45}\)

Since the gossip spreads every two minutes.

The total time is:

\(\mathbf{Total =2minutes \times 7.45}\)

\(\mathbf{Total =14.9\ minutes}\)

Hence, it will take 14.9 minutes for the gossip to spread to 1200 students

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Answer:

The probability that more than 4 calls will be received during the noon hour, on some particular Thursday is 0.9113.

Step-by-step explanation:

The random variable X can be defined as the number of incoming phone calls during the noon hour on Thursdays.

The random variable X describes a finite number of occurrences of an event in a fixed time interval.

The random variable X follows a Poisson distribution with parameter λ = 8.2.

The probability mass function of X is:

\(P(X=x)=\frac{e^{-8.2}(8.2)^{x}}{x!};x=0,1,2,3...\)

Compute the probability of more than 4 calls as follows:    

\(P(X>4)=1-P(X\leq 4)\)

                \(=1-\sum\limits^{4}_{x=0}{\frac{e^{-8.2}(8.2)^{x}}{x!}}\\\\=1-[0.00027+0.00225+0.00923+0.02524+0.05174]\\\\=1-0.08873\\\\=0.91127\\\\\approx 0.9113\)

Thus, the probability that more than 4 calls will be received during the noon hour, on some particular Thursday is 0.9113.

Answer:

U GO TO DHS

Step-by-step explanation:

Answer:

∠ 53°

Step-by-step explanation:

\(Hope\\This\\Helps\)

Answer: The researcher has made a Type II error in this case.

A Type II error occurs when the null hypothesis is not rejected even though it is false, i.e., the researcher fails to detect a significant difference when one actually exists. In this case, the null hypothesis is that the mean weight of the spice packets is 50 g, and the researcher has failed to reject this null hypothesis based on the sample mean of 50 g.

However, the population mean is not actually 50 g, and the researcher has made an error in failing to detect this difference. The sample size of 60 boxes may not have been large enough to detect a significant difference, or there may have been other factors that affected the measurements.

Therefore, the researcher has made a Type II error in this case by failing to reject the null hypothesis when it is actually false.

Step-by-step explanation:

The angle θ is changing is 36.9 degrees per second.

The distance between the dog and its owner when the dog is 46 meters at the northernmost point of the track.

As per the question, the circumference of the circular track is

⇒ 2 × 3.14 × 14 = 87.92 meters.

Since the dog is running at a constant speed of 9 meters per second, it will take the dog 87.92 / 9 = 9.77 seconds to complete one lap of the track.

The angle θ is defined as the angle between the position of the dog and the position of the owner, measured from the center of the track.

Since the track is circular, the angle theta will change at a constant rate of 360 degrees per lap. Since it takes the dog 9.77 seconds to complete one lap, the rate at which the angle θ is changing is 360 / 9.77 = 36.9 degrees per second.

To answer the second question, we must first calculate the distance between the dog and its owner when the dog is at the northernmost point of the track.

The owner is standing a distance of 48 meters from the center of the track, and the radius of the track is 14 meters, the distance between the dog and its owner is given by the Pythagorean theorem: d = √(48² - 14²) = 46 meters.

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The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Yes , it is true that two pairs of adjacent sides of a kite are equal .

A quadrilateral with two pairs of adjacent sides equal in length is called a kite. Kites also have one pair of opposite angle equal as shown in the figure below.

Hence , the given statement is true .

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The expected value of the raffle ticket is $-7.17.

The expected value is the probability-weighted value.

It is computed by multiplying the sum of the values by the probability of winning.

In mathematics, the expected value describes the product of the probability of an event occurring and the value of the actual observed occurrence.

The cost per raffle ticket = $9

The number of tickets sold = 709

The winning value = $1,300

The probability of winning the raffle = 1/709

The expected value = $-7.17 [($1,300 x 1/709) - $9].

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Answer: The selection choice A. 30

Step-by-step explanation:

Do the PEMDAS method.

Parenthesis: 100 - 14 / 2 x (10)

Exponents: N/A 100 - 14 / 2 x (10)

Multiplication & Division: 100 - 70

(Left to Right)

Addition & Subtraction: (3)

(Left to Right)

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Given

To find

Let the purchase value be P,

ATQ,

P -3 x 0.1P = Rs 43,740

P-0.3P = Rs 43,740

0.7P = Rs 43,740

P = Rs 43,740/0.7

P = Rs 62,486 (approx)

Hence, the purchase value of the machine would be Rs 62,486

Answer:

∠ BCA = 25°

Step-by-step explanation:

the inscribed angle BCA is half the measure of the central angle BOA , so

∠ BCA = \(\frac{1}{2}\) × 50° = 25°

Answer:

The probability that​ his/her household has four or more cell phones in use is 0.122 or 12.2%.

Step-by-step explanation:

The complete question is: In a survey of consumers aged 12 and​ older, respondents were asked how many cell phones were in use by the household.​ (No two respondents were from the same​ household.) Among the​ respondents, 215 answered​ "none", 280 said​ "one", 362 said​ "two", 149 said​ "three," and 140 responded with four or more. A survey respondent is selected at random. Find the probability that​ his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in​ use? Consider an event to be unlikely if its probability is less than or equal to 0.05.

We are given that among the​ respondents, 215 answered​ "none", 280 said​ "one", 362 said​ "two", 149 said​ "three," and 140 responded with four or more.

A survey respondent is selected at random.

As we know that the probability of any event is calculated as;

                Probability = \(\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}\)

Here, we have to find the probability that​ his/her household has four or more cell phones in use;

Number of respondent having four or more cell phones in use = 140

Total number of respondents asked = 215 + 280 + 362 + 149 + 140 = 1146

So, the required probability = \(\frac{140}{1146}\)

                                              = 0.122 or 12.2%

No, it is not unlikely for a household to have four or more cell phones in​ use because the probability is not less than or equal to 0.05 but in actual it is greater than 0.05.

Evaluating [log2(3)].[log3(4)].[log4(5)]...[log63(64)] is 6

We can use the property that [log_a(b)]=[log_c(b)/log_c(a)] to simplify the expression. Applying this property repeatedly, we get:

[log2(3)].[log3(4)].[log4(5)]...[log63(64)]

= [log2(3)/log2(2)].[log3(4)/log3(3)].[log4(5)/log4(4)]...[log63(64)/log63(62)]

= [log2(3)/1].[log3(4)/1].[log4(5)/1]...[log63(64)/1]

= log2(3) log3(4) log4(5) ... log63(64)

Now, we can use the identity [log_a(b)log_b(c)log_c(d)...log_y(z)] = log_a(z) to combine the logarithms into a single logarithm with a base of 2:

log2(3) log3(4) log4(5) ... log63(64) = log2(64)

Since 2^6 = 64, we have:

log2(64) = 6

Therefore,  [log2(3)].[log3(4)].[log4(5)]...[log63(64)] evaluates to 6.

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Answer:

Step-by-step explanation:

We can start by using the fact that the chain fits tightly around both gears, which means that the length of the chain is equal to the sum of the circumferences of the two gears. Let r be the radius of the smaller gear. Then we have:

circumference of larger gear + circumference of smaller gear = length of chain

2π(19) + 2π(r) = 32π

Simplifying this equation, we get:

38π + 2π(r) = 32π

2π(r) = -6π

r = -3

\(\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\log(x)=2\hspace{5em}\log(y)=3\hspace{4em}\log(2)\approx 0.3\hspace{4em}\log(3)\approx 0.48 \\\\[-0.35em] ~\dotfill\\\\ \log\left(\sqrt[3]{x^4\cdot y^2} \right)\implies \log\left(\left( x^4\cdot y^2 \right)^{\frac{1}{3}} \right)\implies \cfrac{1}{3}\log(x^4 y^2) \\\\\\ \cfrac{1}{3}[\log(x^4)~~ + ~~\log(y^2)]\implies \cfrac{1}{3}[4\log(x)~~ + ~~2\log(y)]\implies \cfrac{1}{3}[4(2)~~ + ~~2(3)] \\\\\\ \cfrac{1}{3}[8~~ + ~~6]\implies {\Large \begin{array}{llll} \cfrac{14}{3} \end{array}}\)

Answer:

Step-by-step explanation:

187.5

Answer:   Choice C

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

Explanation:

An exponential function can be written in the form

y = a*b^x

where,

If 0 < b < 1, then we have decay. If b > 1, then we have growth.

For choice A, we need to rewrite that negative exponent to make it positive. So we have \(5(6)^{-x} = 5(1/6)^{x}\) to show we have decay going on since b = 1/6. If it helps, then 1/6 = 0.167 approximately.

Similarly, choices B and D also show decay because those b values are between 0 and 1 excluding each endpoint.

Choice C on the other hand has b = 4/3 = 1.333 approximately to fit the inequality b > 1. Therefore, choice C represents exponential growth and not decay.

You can use graphing tools like a TI83, geogebra, or desmos to visually confirm that graph C is an exponential growth function that goes up forever as you move to the right.

The others move closer and closer to the x axis (but never reach it due to it being an asymptote), which show that we have decay for graphs A, B and D.

The value of c in the polynomial is - 7.

The polynomial is given as follows:

p(x) = 2x³ - x² +  cx + 2 . The value of c if x - 2 is a factor of p(x) can be computed as follows:

Therefore,

p(x) = 2x³ - x² +  cx + 2

when x - 2 is a factor, p(x) = 0

Therefore,

0 = 2x³ - x² +  cx + 2

Hence,

2(2)³ - (2)² +  2c + 2 = 0

16 - 4 + 2c + 2 = 0

12 + 2 + 2c  = 0

2c = - 14

divide both sides by 2

c = - 14 / 2

c = - 7

Therefore,

c = -7

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Answer:

c) vertical stretch by a factor of 2

Step-by-step explanation:

Answer:

b.

Step-by-step explanation:

Horizontal stretch by a factor of 1/2.

We can also describe this as a horizontal compression by a factor 2

Answer:

35

Step-by-step explanation:

i did the sqrt of 1225 and got 35 so there should be 35 rows each with 25 plants

Answer:

x = -5

Step-by-step explanation:

Step-by-step explanation:

×First expand the expression on the left side

×Finally solve for x (ie.make x the subject)

using either the balancing or the transpose methods . Either way will work

Step-by-step explanation:

-26=3v+1

-1 on both sides

-27=3v

divide by 3 both sides

-9=v