Find the solution of the exponential equation
5^-x/16=5
in terms of logarithms, or correct to four decimal places.

x= ------------


here is the picture if you need it.

Answer:

15

Step-by-step explanation:

I'm going to be very honest with you; one of my kids had this problem recently and I remember the answer is 15.

99=15+14+13+12+11+10+9+8+7

So the largest number is 15.

The way we solved it:

Call the 1st number x. Each number after x is x+(a number) all the way up to x+8 (the 9th number in the series of 9 consecutive whole numbers):

  x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6, x + 7 and x + 8

Add up those consecutive numbers (I know, it's kind of messy):

             x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 + x + 7 + x + 8

Combine the like terms:

           9x + 36 = 99

Subtract 36 from both sides:

            9x = 63

Divide by 9 on both sides:

            x = 7

So the largest number will be: x + 8

            7+8 = 15

And then check that it works:

99=15+14+13+12+11+10+9+8+7

The value of inverse of function is,

⇒ f ⁻¹ (x) = x² / 36

We have to given that;

Function is,

⇒ f (x) = 6√x

Now, We can find the inverse of the function is,

⇒ f (x) = 6√x

⇒ y = 6√x

Solve for x;

⇒ y/6 = √x

⇒ (y/6)² = x

⇒ x = y² / 36

⇒ f ⁻¹ (x) = x² / 36

Thus, The value of inverse of function is,

⇒ f ⁻¹ (x) = x² / 36

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18 will be the result of the given problem.

Applying the order of operations (PEMDAS), we first calculate the value inside the parentheses, which is 3 + 6 = 9.

Then we multiply 4 by 9, which gives 36.

Finally, we divide 36 by 2, which gives the final answer of 18. Therefore:

4 x (3 + 6) ÷ 2 = 18

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Answer:

Set your calculator to Degree mode.

10² = 6.78² + 4² - 2(6.78)(4)(cos x)

100 = 61.9684 - 54.24(cos x)

38.0316 = -54.24(cos x)

cos x = -.701173

[tex]x = {cos}^{ - 1} ( - .701173)[/tex]

x = 134.52°

Part A: The equation of the circle in standard form is x² + (y - 7)² = 2².

Part B: Center: (h, k) = (0, 7), Radius: 2

Part C: Please check the attachment.

In this problem we find the definition of the equation of a circle in general form, whose standard form must be found:

(x - h)² + (y - k)² = r²

Where:

This can be done by completing the square. First, write the equation of the circle:

x² + y² = 14 · y - 45

Second, complete the square by algebra properties:

x² + y² - 14 · y + 45 = 0

x² + (y² - 14 · y + 49) = 4

x² + (y - 7)² = 2² (PART A)

Third, write the coordinates of the center and the radius of the circle:

Center: (h, k) = (0, 7), Radius: 2 (PART B)

Finally, we proceed to graph the resulting expression.

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The Surface area of the composite figure is calculated as approximately: 234 sq. cm

Here, we have,

to Find the Surface Area of a Composite Figure:

The surface area of the composite figure is the area surrounding the faces of the solid as a whole. Therefore, we have:

Surface area (SA) = Surface area of the square prism + surface area of the square pyramid - 2(area of base)

Area of base = area of square = 6 * 6 = 36 sq. cm.

Surface area of the square prism = 2a² + 4ah

a = 6 cm

h = 4 cm

Plug in the values:

Surface area of the square prism = 2(6²) + 4*6*4

= 72 + 96

= 168 sq. cm.

Surface area of the square pyramid = 2bs + b²

b = side length = 6 cm

s = slant height = √(8² + 3²) = 8.5 cm

Plug in the values:

Surface area of the square pyramid = 2 * 6 * 8.5 + 6² = 138 sq. cm.

Surface area of the composite figure = 168 + 138 - 2(36) = 234 sq. cm

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complete question:

Find the surface area of each composite figure. Use 3.14 for π. Round to the nearest tenth. 12m. 6cm. 6cm. 4cm.​

The graph of the polynomial function with a positive leading coefficient and zeros at x = 4, 2, and -1 (multiplicity 2) is given by the image presented at the end of the answer.

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the zeros of the function, the linear factors are given as follows:

Considering the leading coefficient of a = 1, the function is defined as follows:

f(x) = (x - 4)(x - 2)(x + 1)²

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Answer:

A = 36π units²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

here r = 6 , then

A = π × 6² = 36π units²

Cameron and Rebecca are organizing a lunch for their friends. Within the dishes to be served, they will prepare a tomato, carrot and broccoli salad. The number of tomatoes and carrots are 10-partners and the total amount of vegetables is 12. If we increase the number of broccoli by three and decrease the number of tomatoes by two, the amount of tomatoes and broccoli will also be 10-partners. What is the number of tomatoes, carrots and broccoli bought by Cameron and Rebecca?

Cameron and Rebecca purchased 7 tomatoes, 3 carrots and 2 broccoli.

Number of tomatoes = x

Number of carrots = 10 - x

Number of broccoli = y

System of Equations:

x + 10 - x + y = 12

y = 12 - 10

y = 2

x - 2 + y + 3 = 10 (If we increase the number of broccoli by three and decrease the number of tomatoes by two, the amount of tomatoes and broccoli will also be 10-partners)

x + 1 + y = 10

x + y = 9

y = 9 - x

Substitution of y:

x + 10 - x + y = 12

x + 10 - x + 9 - x = 12

-x + 19 = 12

-x = 12 - 19

x = 7 ⇒ 10 - x = 3

Cameron and Rebecca purchased 7 tomatoes, 3 carrots and 2 broccoli.

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Answer:

The expression -7x^0 cannot be a part of a rational expression because any non-zero number raised to the power of 0 is equal to 1. Therefore, -7x^0 is equal to -7(1) = -7, which is a constant and not a variable expression. In a rational expression, the numerator and denominator should be polynomial expressions with variables.

The other options 4, 3x^2-4rootx, and 3x^2-4x+5 can be part of a rational expression as they are polynomial expressions with variables.

For the 4-hour infusion, 1500ml of the 20% acetylcysteine solution must be made up and combined with 500ml of glucose.

To calculate the volume of acetylcysteine that needs to be added to the glucose, we can use the following formula:

The volume of acetylcysteine (in ml) = (Total amount of acetylcysteine needed in mg / Concentration of acetylcysteine in mg/ml) x 100

We have been asked to add 3000mg of acetylcysteine to 500 ml of glucose. If the concentration of the ampoule containing acetylcysteine is 20%, this means that there are 20g of acetylcysteine in 100 ml of solution, or 200mg/ml.

Using the formula above, we can calculate the volume of acetylcysteine that needs to be added as follows:

Volume of acetylcysteine = (3000mg / 200mg/ml) x 100 = 1500ml

Therefore, 1500ml of the 20% acetylcysteine solution needs to be drawn up and added to the 500ml of glucose to make the 4-hour infusion.

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The probability of randomly choosing two boys is 0.174

If the selection is done at random, then the probability of choosing a boy is equal to the quotient between the number of boys and the total number of people.

There are 12 boys and 16 + 12 = 28 students in total, then the probability is:

P = 12/28

Now, for the second selection the probability is computed in the same way, but now there are 11 boys and 27 students (one was already choosen), then:

P = 11/27

the joint probability (for the two selections) is given by the product between the individual probabilities, we will get:

P = (12/28)*(11/27)

P = 0.174

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The inequality 2|x - 3| + 6 > 10 has the solution set:

x < 1 or x > 5

To solve the inequality 2|x - 3| + 6 > 10, we need to isolate the absolute value expression |x - 3|.

We can do this by subtracting 6 from both sides of the inequality:

2|x - 3| > 4

Then we can divide both sides by 2:

|x - 3| > 2

Now we need to consider two cases, one where x - 3 is positive, and another where it is negative:

When x - 3 is positive, the inequality |x - 3| > 2 becomes:

x - 3 > 2

Solving for x gives:

x > 5

When x - 3 is negative, the inequality |x - 3| > 2 becomes:

-(x - 3) > 2

Solving for x gives:

x < 1

Therefore, the solution set for the inequality 2|x - 3| + 6 > 10 is:

x < 1 or x > 5

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The complete question:

Match each absolute value inequality on the left side with its solution set on the right

2|x - 3| + 6 > 10 - 2

The function of the graph is f(x) = x²-3x -10

A quadratic function is a function in which the highest power of it's variable is 2. quadratic equation is given in the form f(x) = ax²+ bx +c

To form the quadratic function from a graph, we need to find the roots of the function from the graph. The root is the point where the curve intercept the x axis.

Therefore the roots are -2 and 5.

f(x) = x² -( z+y)x +zy

where z and y are the roots

z+y = -2 +5 = 3

zy = -2 × 5 = -10

f(x) = x²-3x -10

therefore the function of the graph is f(x) = x²-3x -10

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Answer:

a. The probability that all 5 selected transistors are defective is 0.0024 or 0.24%.

To calculate this probability, we use the formula for the probability of the intersection of independent events:

P(all 5 defective) = P(defective) x P(defective) x P(defective) x P(defective) x P(defective)

where P(defective) = 5/12 for each transistor.

Plugging in the values, we get:

P(all 5 defective) = (5/12) x (5/12) x (5/12) x (5/12) x (5/12) = 0.0024

b. The probability that none of the selected transistors are defective is 0.163 or 16.3%.

To calculate this probability, we use the complement rule:

P(none defective) = 1 - P(at least one defective)

To calculate P(at least one defective), we can use the complement rule again:

P(at least one defective) = 1 - P(none defective)

So, we need to find P(none defective) first:

P(none defective) = P(not defective) x P(not defective) x P(not defective) x P(not defective) x P(not defective)

where P(not defective) = 7/12 for each transistor.

Plugging in the values, we get:

P(none defective) = (7/12) x (7/12) x (7/12) x (7/12) x (7/12) = 0.163

Then, we can find P(at least one defective):

P(at least one defective) = 1 - P(none defective) = 1 - 0.163 = 0.837

Finally, we can find P(none are defective) using the complement rule:

P(none defective) = 1 - P(at least one defective) = 1 - 0.837 = 0.163.

We can simplify the square roots:

√2 = √(2 × 1) = √2 × √1

√18 = √(9 × 2) = √9 × √2 = 3√2

√50 = √(25 × 2) = √25 × √2 = 5√2

Now we can find the mean:

(mean) = (sum of numbers) / (number of numbers)

(mean) = (√2 + 3√2 + 5√2) / 3

(mean) = (9√2) / 3

(mean) = 3√2

Therefore, the mean of the numbers √2, √18, and √50 is 3√2.

This shaded region represents the solution to the system of inequalities.

We have,

The inequalities:

y ≤ -1 and x ≥ 1

To graph y ≤ -1, we first draw the horizontal line y = -1.

Since we want y to be less than or equal to -1, we shade the area below the line.

To graph x ≥ 1, we draw the vertical line x = 1.

Since we want x to be greater than or equal to 1, we shade the area to the right of the line.

The shaded regions of both inequalities overlap in the area to the right of x = 1 and below y = -1.

Thus,

This shaded region represents the solution to the system of inequalities.

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The simplified expression of [tex]\sqrt[4]{567(x^9)(y^{11})}[/tex] is [tex]3x^2y^2\sqrt[4]{7xy^3}[/tex].

Given expression:

[tex]\sqrt[4]{567(x^9)(y^{11})}[/tex].

We can simplify the expression using the property that says for any non-negative numbers a and b, and any integer n ≠ 0,

[tex](a\times b)^{n} = a^n \times {b^n}[/tex]

Using this property, we can simplify the expression as follows:

[tex](567x^9y^{11})^{1/4} = (567)^{1/4} \times (x^9)^{1/4} \times (y^{11})^{1/4}[/tex]

Now we need to simplify,

[tex](81\times 7)^{1/4}x^{9/4}y^{11/4}\\=(81)^{1/4}(7)^{1/4}(x^{\frac{8}{4}+\frac{1}{4})(y^{\frac{8}{4}+\frac{3}{4})[/tex]

Also,

[tex]{3^4}^{1/4}(7)^{1/4}(x^{2+\frac{1}{4}})(y^{2+\frac{3}{4}})\\=3^1 7^{1/4}x^2x^{1/4}y^2y^{1/4}\\=3x^2y^2(7^{1/4}x^{1/4}y^{3/4})\\=3x^2y^2(7xy^3)^{1/4}\\=3x^2y^2\sqrt[4]{7xy^3}[/tex]

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Answer:6

Step-by-step explanation:

Please upload an image or give a question.

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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The value of given expression is 57.

We are given that;

|—15u| + |3v| + 3

u=3, v = 3

Now,

To evaluate the expression, you need to substitute the values of u and v and simplify. The absolute value of a number is the distance from zero on the number line, so it is always positive or zero. You can write your solution as:

|—15u| + |3v| + 3 = |—15(3)| + |3(3)| + 3 = |—45| + |9| + 3 = 45 + 9 + 3 = 57

Therefore, by the given expression the answer will be 57.

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Answer:

-2x^2 - 2x + 5

Step-by-step explanation:

Combine like terms (same variable and degree) to simplify

3x^2-5x^2+5x-7x+3+2

-2x^2-2x+5

Answer:

Combining like terms, we get:

-2x² - 2x + 6

[tex]x=\textit{lbs of aluminum at 30\%}\\\\ ~~~~~~ 30\%~of~x\implies \cfrac{30}{100}(x)\implies 0.3 (x) \\\\\\ y=\textit{lbs of aluminum at 54\%}\\\\ ~~~~~~ 54\%~of~y\implies \cfrac{54}{100}(y)\implies 0.54 (y) \\\\\\ \textit{48 lbs of aluminum at 52\%}\\\\ ~~~~~~ 52\%~of~48\implies \cfrac{52}{100}(48)\implies 0.52 (48)\implies 24.96 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{lcccl} &\stackrel{lbs}{quantity}&\stackrel{\textit{\% of lbs that is}}{\textit{AL only}}&\stackrel{\textit{lbs of}}{\textit{AL only}}\\ \cline{2-4}&\\ \textit{1st alloy}&x&0.3&0.3x\\ \textit{2nd alloy}&y&0.54&0.54y\\ \cline{2-4}&\\ mixture&48&0.52&24.96 \end{array}~\hfill \begin{cases} x + y = 48\\\\ 0.3x+0.54y=24.96 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=48\implies y=48-x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation from above}}{0.3x~~ + ~~0.54(48-x)~~ = ~~24.96}\implies 0.3x+25.92-0.54x=24.96 \\\\\\ 0.30x-0.54x=-0.96\implies -0.24x=-0.96\implies x=\cfrac{-0.96}{-0.24} \\\\\\ \boxed{x=4}\hspace{9em}y=48-x\implies \boxed{y=44}[/tex]

The correct answer is: The median is the best measure of center, and it equals 19.

A box plot, also known as a box-and-whisker plot, is a graph that displays the distribution of a dataset.

The box represents the middle 50% of the data, with the bottom of the box being the first quartile (Q1) and the top of the box being the third quartile (Q3). The line inside the box represents the median.

The "whiskers" extend from the box to the dataset's minimum and maximum values or, in the case of outliers, a specific distance from the box (often 1.5 times the interquartile range).

The box plot in this instance reveals that the median number of tickets sold was 19, with the middle 50% of the data falling between 17 and 21 tickets sold.

A minimum of 10 and a maximum of 27 tickets may be sold before the whiskers are removed.

The median is the most suitable measure of the center for this dataset since it is the measure of the center that represents the middle of the dataset.

In light of this, the answer is "The median is the best measure of center, and it equals 19."

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We can use the exchange rate of 1 Euro = R18.32. Therefore,400 € = 400 x R18.32 = R7,328.

1.1.1 According to the table, the weakest currency is the yen with 14 yen being equivalent to only R0.14.1.1.2 R292 318 460 in words is Two hundred and ninety-two million, three hundred and eighteen thousand, four hundred and sixty Rand. 1.1.3

To determine the amount in rand that needs to be spent on ventilators in Spain, we need to find out the total amount of money raised, then use the ratio provided (1:2:4) to determine the amount to be spent on ventilators.

The ratio indicates that for every 1 unit of money, 2 units are to be spent on staff payment and 4 units on purchasing ventilators.

Therefore, if the total amount of money raised is €14 million, which is equivalent to R292 313 460, then the amount to be spent on ventilators is:4/(1+2+4) × 292 313 460 = R175 388 076.1.1.4 To find out how much 400€ would be in rand,

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