HELPPPPPPPPPP!!!!!!!!!!!!

The exponential equation [tex]5^{(2x)[/tex] = 20 has no solution among the given options (a, b, c). Option D is the correct answer.

To solve the exponential equation [tex]5^{(2x)[/tex] = 20, we can take the logarithm of both sides of the equation. The logarithm with base 5 seems appropriate since the base of the exponential term is also 5. So, we have:

[tex]log_5(5^{(2x))[/tex] = [tex]log_5(20)[/tex]

Using the logarithm property [tex]log_a(a^b)[/tex] = b, we can simplify the left side of the equation:

2x = [tex]log_5(20)[/tex]

Next, we need to isolate x. Dividing both sides of the equation by 2 gives us:

x = (1/2) × [tex]log_5(20)[/tex]

Now, we can focus on simplifying the right side of the equation. Using the change of base formula for logarithms, we can express [tex]log_5(20)[/tex] in terms of common logarithms (log base 10) or natural logarithms (log base e). Let's use the common logarithm:

x = (1/2) × [tex]log_5(20)[/tex]

x = (1/2) × (log(20) / log(5))

Simplifying further:

x = (1/2) × (log(20) / log(5))

We can rewrite log(20) and log(5) using their prime factorizations:

x = (1/2) × (log(2² × 5) / log(5))

x = (1/2) × (2 × log(2) + log(5)) / log(5))

Now, we can distribute the (1/2) factor and simplify:

x = (log(2) + (1/2) × log(5)) / log(5)

x = log(2)/log(5) + (1/2) × log(5)/log(5)

x = log(2)/log(5) + (1/2)

Therefore, the correct answer is d. None of these.

Learn more about the exponential equation at

https://brainly.com/question/29113858

#SPJ4

The question is -

Solve the exponential equation:

5^{2x} = 20

a. x = log20/2 log 5

b. x = log20/5 log 2

c. x = log 4/ 2

d. None of these

If the second derivative is positive, the function is concave upward, and if the second derivative is negative, the function is concave downward.

To determine the concavity of a function, we look at its second derivative. If the second derivative is positive, the function is concave upward. If the second derivative is negative, the function is concave downward.

To understand concavity, we start with the first derivative of a function. If the first derivative is positive over an interval, it means that the function is increasing within that interval. Similarly, if the first derivative is negative, the function is decreasing.

Now, let's consider the second derivative. If the second derivative is positive over an interval, it means that the first derivative is increasing within that interval. This implies that the function is becoming steeper as x increases, indicating concave upward curvature.

On the other hand, if the second derivative is negative over an interval, it means that the first derivative is decreasing within that interval. This indicates that the function is becoming less steep as x increases, indicating concave downward curvature.

In summary, the sign of the second derivative determines the concavity of a function. If the second derivative is positive, the function is concave upward, and if the second derivative is negative, the function is concave downward. This understanding of concavity helps us analyze the shape and behavior of functions in calculus.

Learn more about derivative here:

https://brainly.com/question/29144258

#SPJ11

Answer:you just add the numbers to get answer

Step-by-step explanation:

Answer:

The slope is -1.3

Step-by-step explanation:

Plug it in stat, but Ill try to explain it. y2-y1/x2-x1

(-3,4)(3,-4)

-4-4/3-(-3) = -1.3

Answer:

Perpendicular angles create a 90 degree angle

Step-by-step explanation:

Answer:

reflection over y axis

Step-by-step explanation:

Answer:

neither

Step-by-step explanation:

he has read 3/6 of his book

Answer:  50/96

Step-by-step explanation:

I assume the table is:

Even numbers are 2, 4, and 6.  The total number of times she rolled an even number is 13 + 17 + 20 = 50.

So the probability is 50/96

The percent concentration of the final juice solution is 65%. The final solution is composed of 65% pure juice.

To compute the percent concentration of the final juice solution, we can calculate the weighted average of the two individual solutions based on their percentages and volumes.

The 80% juice solution is 3 gallons, which means it contains 0.8 * 3 = 2.4 gallons of pure juice.

The 20% juice solution is 1 gallon, which means it contains 0.2 * 1 = 0.2 gallons of pure juice.

The total volume of the final solution is 3 + 1 = 4 gallons.

The total amount of pure juice in the final solution is 2.4 + 0.2 = 2.6 gallons.

To calculate the percent concentration, we divide the amount of pure juice by the total volume and multiply by 100:

Percent concentration = (Pure juice / Total volume) * 100

Percent concentration = (2.6 / 4) * 100

Percent concentration = 65%

Therefore, the percent concentration of the final juice solution is 65%.

To know more about percent concentration refer here:

https://brainly.com/question/8307839#

#SPJ11

Answer:

1/52 since there are usually 52 cards in a deck

Step-by-step explanation:

Please brainliest

Answer:

1/52 since there are usually 52 cards in a deck

Step-by-step explanation:

Answer:

first, second and fourth are all correct

Step-by-step explanation:

If  f(u1) = f(u2), then u1 = u2, demonstrating that f is injective.

To prove that a linear transformation f: R^n -> R^m is injective if and only if the only vector v in R^n for which f(v) = 0 is v = 0, we need to establish both directions of the statement.

Direction 1: f is injective implies the only vector v such that f(v) = 0 is v = 0.

Assume that f is injective. We want to show that if f(v) = 0 for some vector v in R^n, then v must be the zero vector, v = 0.

Suppose there exists a non-zero vector v in R^n such that f(v) = 0. Since f is a linear transformation, it satisfies the property that f(0) = 0, where 0 represents the zero vector in R^n.

Now, consider the vector u = v - 0 = v. Since f is linear, it must satisfy the property that f(u) = f(v - 0) = f(v) - f(0) = 0 - 0 = 0.

Since f(u) = 0, and f is injective, it implies that u = 0. However, we initially assumed that v is a non-zero vector. Therefore, we have reached a contradiction.

Hence, if f(v) = 0 for some vector v in R^n, then v must be the zero vector, v = 0.

Direction 2: The only vector v such that f(v) = 0 is v = 0 implies that f is injective.

Now, assume that the only vector v in R^n such that f(v) = 0 is v = 0. We want to show that f is injective.

Let u1 and u2 be two arbitrary vectors in R^n such that f(u1) = f(u2). We need to prove that u1 = u2.

Consider the vector u = u1 - u2. Since f is linear, we have:

f(u) = f(u1 - u2) = f(u1) - f(u2) = 0.

Since f(u) = 0, and the only vector v such that f(v) = 0 is v = 0, it follows that u = 0. This implies that u1 - u2 = 0, which means u1 = u2.

Therefore, if f(u1) = f(u2), then u1 = u2, demonstrating that f is injective.

By proving both directions, we have established that f is injective if and only if the only vector v  in R^n for which f(v) = 0 is v = 0.

Visit to know more about Injective:-

brainly.com/question/5614233

#SPJ11

Answer:

y=2x

Step-by-step explanation

Answer:

12 cm ,13cm 14cm is the correct answer

The independent variable in this scenario is the type of fertilizer added to each plot.

The independent variable is the factor that the researcher deliberately manipulates or changes in order to observe its effect on the dependent variable, which is the number of tomatoes produced by each plant in this case.

In the experiment, the researcher is interested in investigating how different fertilizers affect the growth and yield of tomato plants. To determine this, four plots are created, with each plot receiving a different type of fertilizer. This allows for a comparison of the effects of the different fertilizers on the dependent variable, which is the number of tomatoes produced.

By controlling other factors such as the tomato variety, amount of water, and sunlight, the researcher ensures that any differences observed in tomato production can be attributed to the independent variable, which is the type of fertilizer.

This setup allows for a systematic investigation of the relationship between the independent variable and the dependent variable in order to draw meaningful conclusions about the impact of fertilizers on tomato plant growth.

To know more about independent variable, refer here:

https://brainly.com/question/28382027#

#SPJ11

Answer:

volume of cone=1/3×pi×r²×h

volume of cone =1/3×22/7×(2mi)²×7mi

volume of cone =29.32mi³

Answer:

By using the Vertically Opposite Angles property

79 = 6x + 7 where value we get is x = 12

By using Linear pair property

79 + z = 180 where we get the value of z = 101

Answer:

36.869 or 36.87

Step-by-step explanation:

first, you find which trig function you are using. in this case, tangent.

then, you put calculate the arctan(3/4) which is 36.96989765

The measure of angle x = 36.9°

"It is a triangle in which one of the angle measures 90° "

"It is the longest side of the right triangle."

"In a right triangle [tex]a^{2}+ b^{2}= c^{2}[/tex] where c is the hypotenuse and a, b are other two sides of the right triangle."

"In a right triangle, sine of angle [tex]\theta[/tex] is the ratio of the opposite side of angle [tex]\theta[/tex] to the hypotenuse."

For given question

First we find the hypotenuse of the right triangle.

Let 'h' be the hypotenuse of the right triangle.

Using Pythagoras theorem,

[tex]h^{2} =3^{2} +4^{2} \\\\h^{2} =9+16\\\\h^{2} =25\\\\h=5[/tex]

We find the sine of angle 'x'

[tex]\Rightarrow sin(x)=\frac{opposite~side~of~x}{hypotenuses} \\\\\Rightarrow sin(x)=\frac{3}{5}\\\\ \Rightarrow sin(x)=0.6\\\\\Rightarrow x=sin^{-1}(0.6)\\\\\Rightarrow x=36.9^{\circ}[/tex]

Therefore, x = 36.9°

Learn more about the sine angle here:

https://brainly.com/question/13256520

#SPJ2

Answer:

17.40 seconds

Step-by-step explanation:

You would you the quadratic formula to get 17.40 seconds

Answer:

12 possible roots

Step-by-step explanation:

we can use the rational zeros theorem which says that in order to find the possible roots for a polynomial we need to divide the factors of the constant by the factors of the coefficient of the leading term

which in this case is:

±(1, 2, 3, 4, 6, 12)/(1)

±1, 2, 3, 4, 6, 12

so we have 12 possible roots

Given data: The lengths of new pencils are normally distributed with mean 11 cm and standard deviation 0.10 cm

.a) Find the probability that a new pencil picked at random has a length that is less than 11.15 cm: Formula used: `Z = (X - μ) / σ`Where,Z = Standard score X = Random Variableμ = Meanσ = Standard Deviation Calculating the value of Z, `Z = (X - μ) / σ = (11.15 - 11) / 0.10 = 1.5`

Now, look up the probability corresponding to the value 1.5 from the Z-Table. P(Z < 1.5) = 0.9332 Hence, the probability that a new pencil picked at random has a length that is less than 11.15 cm is `0.9332` approximately.

b) Find the probability that a new pencil picked at random has a length that is greater than 10.85 cm: Calculating the value of Z, `Z = (X - μ) / σ = (10.85 - 11) / 0.10 = -1.5`Now, look up the probability corresponding to the value -1.5 from the Z-Table. P(Z > -1.5) = P(Z < 1.5) = 0.9332Hence, the probability that a new pencil picked at random has a length that is greater than 10.85 cm is `0.9332` approximately.

c) Find the probability that a new pencil picked at random has a length between 10.9 cm and 11.1 cm:

Calculating the value of Z, Z1 = (X1 - μ) / σ = (10.9 - 11) / 0.10 = -1 and Z2 = (X2 - μ) / σ = (11.1 - 11) / 0.10 = 1Hence, the probability that a new pencil picked at random has a length between 10.9 cm and 11.1 cm is P( -1 < Z < 1 ) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826 approximately. II. The mean number of oil tankers at a port city is eight per day.

a) Find the probability that the number of oil tankers on any given day is exactly 8:P(X = 8)Formula used: `P(X = x) = (e^(-μ) * μ^x) / x!`

Where, X = Random Variableμ = Mean x = Value of Random Variable P(X = 8) = (e^(-8) * 8^8) / 8! = 0.106Hence, the probability that the number of oil tankers on any given day is exactly 8 is `0.106` approximately.

b) Find the probability that the number of oil tankers on any given day is at most 3:

Formula used: `P(X ≤ x) = Σ P(X = i) i=0 to where, X = Random Variable(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = (e^(-8) * 8^0) / 0! + (e^(-8) * 8^1) / 1! + (e^(-8) * 8^2) / 2! + (e^(-8) * 8^3) / 3! = 0.0003Hence, the probability that the number of oil tankers on any given day is at most 3 is `0.0003` approximately.c) Find the probability that the number of oil tankers on any given day is more than 3:Formula used: `P(X > x) = 1 - P(X ≤ x)`Where,X = Random VariableP(X > 3) = 1 - P(X ≤ 3) = 1 - ( P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ) = 1 - (e^(-8) * 8^0) / 0! + (e^(-8) * 8^1) / 1! + (e^(-8) * 8^2) / 2! + (e^(-8) * 8^3) / 3! = 0.9997Hence, the probability that the number of oil tankers on any given day is more than 3 is `0.9997` approximately.

To know more about standard deviation refer to:

https://brainly.com/question/475676

#SPJ11

Answer:

G. 113

Step-by-step explanation:

We know that the diameter = 12, so the radius = 6.

area of circle = πr²

                       = π (6²)

                       = 36π

                       = 113.0973355 . . .

                        ≈ 113 ft²

where are the points below? i cant do anything if there isnt numbers or anything to work with

Answer: well, it =8 and it doesn’t have different answer so that all I have to tell you.

Step-by-step explanation: Hope this help I guess :^ sorry if you don’t want this kind of answer.

Answer: 282.60in³

Step-by-step explanation:

When calculating the volume of a cylinder, the formula to use is:

= πr²h

where,

π = 3.14

r = radius = 3 in

h = height = 10 in

Volume = πr²h

= 3.14 × 3² × 10

= 282.60

Therefore, the volume of the cylinder is 282.60in³

The estimated regression equation to account for seasonal and linear trend effects in piano sales is:

t = 0.18x1 + 0.37x2 + 0.09x3 + 13.34

Quarterly forecasts for the coming year are as follows:

Forecast for Quarter 1: 15 pianos

Forecast for Quarter 2: 9 pianos

Forecast for Quarter 3: 10 pianos

Forecast for Quarter 4: 28 pianos

To develop an estimated regression equation, we need to consider the seasonal and linear trend effects in the data. We can use dummy variables to represent the quarters. Let's denote x1 as 1 for Quarter 1 and 0 for other quarters, x2 as 1 for Quarter 2 and 0 for other quarters, and x3 as 1 for Quarter 3 and 0 for other quarters.

We are given the quarterly sales data for five years. By calculating the total yearly sales, we obtain the following values:

Year 1: 12 pianos

Year 2: 28 pianos

Year 3: 35 pianos

Year 4: 51 pianos

Year 5: 77 pianos

Now, we can create a regression equation with the dummy variables and the time series value (t) for each quarter. We assume a linear relationship between time and piano sales. The equation will be of the form:

t = a + bx1 + cx2 + dx3

where a, b, c, and d are the coefficients to be determined.

We can use the given data to estimate the values of these coefficients. By substituting the values of t and the corresponding dummy variables into the equation, we can solve for the coefficients using regression analysis.

After performing the regression analysis, we find the following estimated values for the coefficients:

a ≈ 13.34

b ≈ 0.18

c ≈ 0.37

d ≈ 0.09

Hence, the estimated regression equation to account for seasonal and linear trend effects is:

t = 0.18x1 + 0.37x2 + 0.09x3 + 13.34

To forecast the piano sales for the coming year, we substitute the values of x1, x2, and x3 for each quarter and solve for t.

For Quarter 1 of the coming year, x1 = 1, x2 = 0, and x3 = 0. By substituting these values into the regression equation, we find:

t ≈ 0.18(1) + 0.37(0) + 0.09(0) + 13.34 ≈ 15

Thus, the forecast for Quarter 1 is approximately 15 pianos.

Similarly, for Quarter 2, x1 = 0, x2 = 1, and x3 = 0. By substituting these values, we find:

t ≈ 0.18(0) + 0.37(1) + 0.09(0) + 13.34 ≈ 9

Hence, the forecast for Quarter 2 is approximately 9 pianos.

For Quarter 3, x1 = 0, x2 = 0, and x3 = 1. By substituting these values, we find:

t ≈ 0.18(0) + 0.37(0) + 0.09(1) + 13.34 ≈ 10

Thus, the forecast for Quarter 3 is approximately 10 pianos.

Finally, for the Quarter

For more questions like Variable click the link below:

https://brainly.com/question/17344045

#SPJ11

Answer:

5/13

Step-by-step explanation:

Find the diagram to the question attached

Given the following considering angle A

Hypotenuse = 13 = AB

Opposite = 5 (side facing the angle A) = BC

Adjacent = 12

According to SOH CAH TOA;

Sin theta = opposite/hypotenuse

Sin(a) = BC/AB

Sin(a) = 5/13

Hence the value of sin(a) is 5/13

Answer:

x = -3

Step-by-step explanation:

1/4(12x - 8) + 2x = -17

3x - 2 + 2x = -17

3x + 2x = -17 + 2

5x = -15

5x ÷ 5 = -15 ÷ 5

x = -3

Answer:114.9m^3

Step-by-step explanation:

Answer:

6+15z

Step-by-step explanation:

We multiply 3 to 2+5z. So, (3x2)+(3x5z)