Solve for x : log(3x) + log(x + 4) = log(15).

Please explain it to me.​

Answer:

the answer is B

Step-by-step explanation:

are you a make a wish kid

Because i would love for you to bounce that

Answer:

17.1

Step-by-step explanation:

Exponential Functions:

y=ab^x

a=starting value = 310

r=rate = 6.4%=0.064

Exponential Decay:

b=1−r=1−0.064=0.936

Write Exponential Function:

y=310(0.936)^x

Put it all together

Plug in y-value:

100=310(0.936)^x

100/310 = 310(0.936)^x/310

​

Divide both sides by 310

0.322581=0.936^x

\log 0.322581=\log 0.936^x

Take the log of both sides

log0.322581=xlog0.936

Use power rule to bring x to the front

log0.322581/log0.936 = xlog0.936/log0.936

​

Divide both sides by log(0.936)

17.106221=x

x≈17.1

17.12 will it take until there are 100 grams of the element remaining

Two or more expressions with an Equal sign is called as Equation.

Given that  element with a mass of 310 grams decays by 6.4% per minute.

we need to find the time will it be until there are 100 grams of the element remaining

y=abˣ

a=starting value = 310

r=rate = 6.4%=0.064

Exponential Decay:

b=1−r

=1−0.064

=0.936

Plug in these values in the formula

y=310(0.936)ˣ

100=310(0.936)ˣ

Divide both sides by 310

100/310 = (0.936)ˣ

0.322581=0.936ˣ

Apply log on both sides

log 0.322581=xlog0.936

Divide both sides by log0.936

log0.322581/log0.936 = xlog0.936/log0.936

17.106221=x

Hence, 17.12 will it take until there are 100 grams of the element remaining

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Answer:

How to write numbers in standard form:

Write the first number 8.

Add a decimal point after it: 8.

Now count the number of digits after 8. There are 13 digits.

So, in standard form: 81 900 000 000 000 is 8.19 × 10¹³

Step-by-step explanation:

please mark this answer as brainliest

Answer:

3.15576 * 10 to the power of 7 will get you 31557600.

The values οf the basic trigοnοmetric functiοns fοr an angle in standard pοsitiοn passing thrοugh (6,8) are:

\(\sin \theta &= 0.8\\\) \(\cos \theta &= 0.6\), etc.

Trigοnοmetry is a branch οf mathematics that deals with the study οf triangles and the relatiοnships between their sides and angles.

We can begin by finding the length οf the hypοtenuse οf the right triangle fοrmed by the given pοint and the οrigin. This will give us the value οf the trigοnοmetric functiοns sine, cοsine, and tangent.

The hypotenuse can be found using the Pythagorean theorem:

\(c^2 &= a^2 + b^2\)

\(&= 6^2 + 8^2\)

\(&= 36 + 64\)

\(&= 100\)

\(c &= \sqrt{100}\)

\(c &= 10\)

Therefore, the point (6,8) is 10 units away from the origin.

The sine of the angle can be found by dividing the opposite side (8) by the hypotenuse (10):

\(\sin \theta &= \frac{8}{10}\)

\(&= 0.8\)

The cosine of the angle can be found by dividing the adjacent side (6) by the hypotenuse (10):

\(\cos \theta &= \frac{6}{10}\)

\(&= 0.6\)

The tangent of the angle can be found by dividing the opposite side (8) by the adjacent side (6):

\(\tan \theta &= \frac{8}{6}\)

\(&= \frac{4}{3}\)

Therefore, the values of the basic trigonometric functions for an angle in standard position passing through (6,8) are:

\(\sin \theta &= 0.8\)

\(\cos \theta &= 0.6\)

\(\tan \theta &= \frac{4}{3}\)

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Answer:the answer is app u welcome text me back if i got it wrong armstrongtamarion

Step-by-step explanation:

Answer:

15, 18, 21

Step-by-step explanation:

Statistical guidance should perform well in situations such as clinical trials and market research where rigorous data analysis and inference are necessary. Statistical methods provide a systematic approach to control biases, handle variability, and draw reliable conclusions, ensuring accurate decision-making and predictions based on the data.

Statistical methods are crucial in determining sample sizes, designing the study, and analyzing the data to draw valid conclusions about the effectiveness and safety of the treatment.

In this situation, statistical guidance should do well because it provides a systematic framework to control for biases, random variability, and confounding factors, ensuring robust and reliable results that can be generalized to a larger population.

One example where statistical guidance should perform well is in clinical trials for new drugs or treatments.

Another example is in market research and opinion polling. Statistical techniques can be used to collect and analyze data from a representative sample of the target population, allowing for accurate estimation and prediction of consumer preferences, market trends, or election outcomes.

Statistical guidance should do well in this situation because it provides methods for random sampling, hypothesis testing, and confidence interval estimation, which help minimize sampling errors and increase the reliability of the findings.

Additionally, statistical models can capture complex relationships and make accurate predictions based on the observed data.

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The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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For part (a), we have to find the number of ways to distribute 3 medals among 52 athletes without any ties. This can be solved using the permutation formula, which is n!/(n-r)! where n is the total number of options and r is the number of options being selected.

For part (b), we are trying to find the number of possible 4-letter passwords using lowercase letters of the alphabet with no repetition. This can be solved using the permutation formula again, with n=26 and r=4.

(a) We apply the permutation formula to determine the total number of possible distributions for the three medals among the 52 competitors. We want to determine the number of permutations of 52 objects taken three at a time because the order in which the medals are awarded is significant:

P(52,3) = 52!/(52-3)! = 52!/49! = 52 × 51 × 50 = 132,600

Therefore, there are 132,600 possible ways to distribute the gold, silver, and bronze medals among 52 athletes.

(b) We use the permutation formula once more to determine the total number of 4-letter passwords that can be created using lowercase letters of the alphabet without repetition. We want to determine the number of permutations of 26 objects taken four at a time since there are 26 letters in the alphabet:

P(26,4) = 26!/(26-4)! = 26!/22! = 26 × 25 × 24 × 23 = 35,360

Therefore, there are 35,360 possible 4-letter passwords that can be made using lowercase letters of the alphabet with no repetition.

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Answer:

x = y

Step-by-step explanation:

x/3 + x/6 = 7/2

2x + x = 21

3x = 21

(divide 3 on both sides)

x = 7

a. The chart did not maintain consistent scaling

b. The graph is not the appropriate graph type to display such data

c.  The display had inaccurate or distorted visual representations

When the actual data may not support it, changing the scales on the axes might give the appearance of big changes or differences.

The visual effect of data can be exaggerated or minimized, for instance, by adopting a non-linear scale or deleting specific sections of the axis.

So it important to Choose appropriate graph type that best represents the data and the relationship you want to convey.

It also advisable to make use of  clear and accurate labeling with descriptive titles and units of measurement.

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Answer:

Choice 1) 181.5 mm

Step-by-step explanation:

41.5+55+85 = 181.5

There is a typo in the question. Where it reads 'state of' should read 'shaded'

Answer:

\(A=27.47\ mm^2\)

Step-by-step explanation:

Area of a Circle

Given a circle of radius r, its area can be calculated as follows:

\(A=\pi r^2\)

The area of the shaded region can be found by subtracting the area of the large circle minus the area of the small circle.

We already know the area of the large circle:

\(A_l=28.26\ mm^2\)

Now we calculate the area of the small circle of radius r=0.5 mm:

\(A_s=\pi\cdot 0.5^2\)

Calculating:

\(A_s=0.79\ mm^2\)

The area of the shaded region is:

\(A=A_l-A_s=28.26\ mm^2-0.79\ mm^2\)

\(\mathbf{A=27.47\ mm^2}\)

If Tina earns $60,000 a year and has adjustments of $1,000 and a standard deduction of $13,850 then Tina  pays $9,933 in income tax.

Tina's taxable income can be calculated by subtracting her adjustments and standard deduction from her gross income:

Taxable income = $60,000 - $1,000 - $13,850 = $45,150

Her income tax can be calculated by multiplying her taxable income by the tax rate:

Income tax = $45,150 × 0.22 = $9,933

Therefore, Tina pays $9,933 in income tax.

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A 90% confidence interval will use the same z-score as 95% of the data. 0.95 is exactly between the z-scores of 1.64 and 1.65, so estimate the z-score as 1.645. The z-score associated with a 90% confidence interval is 1.645.

To determine the value of a, we use the formula: a = z*(standard deviation/sqrt(n)). The value of a determines the size of the margin of error in our confidence interval.

The value of a is an important component in determining the 90% confidence interval. It is used to calculate the range of values that are likely to contain the true population mean with a certain level of confidence. In other words, it tells us how confident we are that the true population mean falls within a certain range of values. To determine the value of a, we use the formula: a = z*(standard deviation/sqrt(n)), where "z" is a critical value from a standard normal distribution table, "standard deviation" is the standard deviation of the sample, and "n" is the sample size. The critical value "z" is chosen based on the desired level of confidence. In this case, since we are aiming for a 90% confidence level, we would use a critical value of approximately 1.645.

A smaller value of a means a narrower interval, which in turn indicates a higher level of confidence in the interval containing the true population mean. Conversely, a larger value of a leads to a wider interval and a lower level of confidence.

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The statement describes that the survey of high school teenagers reporting that 96% of those sampled are interested in pursuing a college education to be descriptive statistics.

A given data collection, which may be a sample of a population or a representation of the complete population, can be summarised using descriptive statistics, which are concise informational coefficients. Measurements of variability and measures of central tendency make up descriptive statistics (spread). Data are summarised using descriptive statistics.

The statements made by descriptive statistics only apply to the data set from which they were derived; they never extend beyond the data you have. To characterise the fundamental characteristics of the data in a study, descriptive statistics are used. They offer concise summaries of the sample and the measurements. They serve as the foundation for almost all quantitative data analyses, along with straightforward graphical analysis.

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Answer:

prob of being a red=1/2

prob of being an ace=1/13

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The example of quantitative data among the given options is option A. North America is moving across Earth's surface several centimeters per year

Quantitative data refers to numerical or measurable information. In option A, the statement provides specific numerical measurements by stating that North America is moving across Earth's surface several centimeters per year. This information can be quantified and measured, making it an example of quantitative data.

Options B, C, D, and E do not provide numerical or measurable information. They describe qualitative characteristics or observations that cannot be easily quantified or measured.

B. The river has flooded a low-lying area describes a qualitative observation of a flood occurrence.

C. The volcano is releasing much steam describes a qualitative observation of steam release.

D. Volcanoes are dangerous makes a general statement without providing specific numerical information.

E. When held, one rock feels heavier than another rock is a subjective comparison and does not provide specific quantitative measurements.

Therefore, option A is the example of quantitative data as it provides numerical information that can be measured and quantified.

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Answer:

5

Step-by-step explanation:

24-8X=-16

24+16=8X

40=8X

X=5

Answer:

x=5

Step-by-step explanation:

24 - 8x = -16

=> 24 + 16 = 8x

=> 8x = 24 + 16

=> 8x = 40

=> x = 40/8

=> x = 5

By using the travel distance formula, we found out that it takes 1 hour for the car and the truck to meet if they leave at the same time and travel toward each other.

It is given to us that -

Two cities are 145 miles apart

Truck travels this distance in 2.5 hours

Car is 1.5 times as fast as the truck

We have to find out the time taken for the car and the truck to meet if they leave at the same time, and travel toward each other.

We know that -

\(Speed = \frac{Distance}{Time}\) ----- (1)

Let us say that the speed of the truck is given by \(S_{t}\) and the speed of the car is given by \(S_{c}\).

Now, from equation (1), we can say that the speed of the truck,

\(S_{t}=\frac{145}{2.5} \\= > S_{t}= 58 miles per hour\) ----- (2)

It is given to us that the car is 1.5 times as fast as the truck

=> \(S_{c}= 1.5 * 58\\= > S_{c}= 87 miles per hour\) ----- (3)

It is mentioned that the car and the truck leave at the same time to meet each other.

Let us say that the truck meets the car at a distance 'd'.

This implies that the distance travelled by the car to meet the truck at a given point = (145-d)  --- (4)

From equation (1), we can say that

\(Time = \frac{Distance}{Speed}\)

Also, we know that -

Time taken by truck to travel d miles = Time taken by car to travel (145-d) miles

\(\frac{d}{58}=\frac{145-d}{87} \\= > 87d = 8410-58d\\= > 145d=8410\\= > d = 58\)

Thus, the truck will travel 58 miles to meet car after they leave at the same time.

So, the time taken for the car and truck to meet =

\(\frac{58 miles}{58 miles per hour} = 1 hour\)

Therefore, according to the distance formula, it takes 1 hour for the car and the truck to meet if they leave at the same time and travel toward each other.

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Answer: S and T.

Step-by-step explanation:

I watched a video on how to do this just to answer, so it might not be right LOL. But since the angles are the same if you draw them from each other they both show the angles are equal which means the lines are parallel.

Mixture

5 gal 48% fruit juice contains

From brand B,

Therefore, pure juice from brand A is,

therefore percentage is,

To determine the maximal velocity from an acceleration vs. time graph, you need to follow these steps:

Identify the time interval during which the acceleration remains constant or nearly constant. This interval can be identified as a straight line on the graph.

Calculate the acceleration value during this interval by finding the slope of the line. The slope is the change in acceleration divided by the change in time.

Use the acceleration value and the time interval to calculate the change in velocity during this interval using the formula:

Δv = aΔt

Where Δv is the change in velocity, a is the acceleration, and Δt is the time interval.

Add the change in velocity to the initial velocity at the start of the time interval to obtain the maximal velocity. If the initial velocity was zero, then the maximal velocity will be equal to the change in velocity.

vmax = vi + Δv

Where vmax is the maximal velocity and vi is the initial velocity.

Note that this method assumes that the acceleration is constant or nearly constant during the time interval of interest. If the acceleration changes significantly during this time interval, you will need to break it down into smaller intervals and repeat the above steps for each interval to determine the maximal velocity.

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The domain of f(x)/g(x) is (-∞, 7)U(7, ∞).

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Option B. $9,255.75, Only option (b) includes a value close to $1,000, which is the present value of the infinite stream of

To find the present value of an infinite stream of cash flows, we can use the formula:

PV = CF / r

where PV is the present value, CF is the cash flow per period, and r is the interest rate per period.

In this case, CF = $100 (received at the end of each year forever) and r = 10%.

Plugging in the numbers, we get:

PV = $100 / 0.10 = $1,000

So the present value of the infinite stream of cash flows is $1,000.

However, we need to adjust for the fact that the cash flows are received at the end of each year, not at the beginning. To do this, we can use the formula:

PV = CF / (r - g)

where g is the growth rate of the cash flows, which in this case is 0 (since the cash flows are constant).

Plugging in the numbers, we get:

PV = $100 / (0.10 - 0) = $1,000

So the present value of the infinite stream of cash flows received at the end of each year is also $1,000.

Therefore, the answer must include the present value of an infinite stream of cash flows. Only option (b) includes a value close to $1,000, which is the present value of the infinite stream of cash flows.

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Step-by-step explanation: Begin with 2x+3 > -9.

(1) The first step is to subtract 3 from both sides. You are left with 2x > -12. Remember, when you do something to one side of the inequality you must do it to the other side.

(2) Next, divide BOTH sides of the equation by 2. We do this so we can isolate x and get rid of the 2 next to it.

(3) When you divide, you are left with x > -6.