2^x = 1/2

A:-1
B:-1/2
C:1

Answer:

fah)',55%9+*_)64•%π\¥)--_f

Answer:

2w+2(w+5)=1200

Step-by-step explanation:

Answer:

the answer is 329

I really hope it helps<3

Answer:

The answer is $131.60 not $329

Step-by-step explanation:

well, i canot be 329, considering there is only 658 and there are 4 girls so crossing 329 would be a good option. Since madeline is one of the four friends all you have to do is divide $658 by 5. really simple, you should get 131.6 and that would be $131.60.

The probability that the point lies in the shaded region is the ratio of the area of the shaded region to the total area of the figure.

To find the area of the shaded region, we need to subtract the area of the unshaded region from the total area of the figure. Let's assume that the total area of the figure is A and the area of the unshaded region is B. Then the area of the shaded region would be A - B.

To find the probability, we divide the area of the shaded region by the total area of the figure. So, the probability would be (A - B)/A or 1 - (B/A).

Without knowing the specific figure and the area of the shaded and unshaded regions, it's difficult to provide a numerical answer to this question. However, the general approach to finding the probability of a point lying in a shaded region is to use the formula mentioned in the main answer.

For example, let's say we have a circle with a radius of 5 units and a shaded sector that covers 90 degrees of the circle. To find the area of the shaded region, we would first find the area of the whole circle using the formula A = πr², where r is the radius of the circle. So, the total area of the circle would be A = π(5)² = 25π.

Next, we would find the area of the shaded sector by using the formula for the area of a sector, which is A = (θ/360)πr², where θ is the central angle of the sector. In this case, the central angle is 90 degrees, so θ = 90. Substituting the values, we get A = (90/360)π(5)²= 6.25π.

To find the area of the unshaded region, we would subtract the area of the shaded sector from the area of the circle. So, B = 25π - 6.25π = 18.75π.

Finally, we can use the formula mentioned in the answer to find the probability of a point lying in the shaded region. The probability would be (A - B)/A or 1 - (B/A). Substituting the values, we get the probability as (25π - 18.75π)/25π or 1 - (18.75π/25π) = 0.25 or 25%.

To know more about probability visit:

brainly.com/question/30034780

#SPJ11

Answer:

1. see the attached image

2. y < (6/2)x + 5/2, see the attached image for a graph

Step-by-step explanation:

1. see the attached image

2. 6x > 2y - 5

Add 5 to both sides:

6x + 5 > 2y

Divide by 2:

(6/2)x + 5/2 > y

Rearrange so that y is on the left:

y < (6/2)x + 5/2

Finally, shade below the line since the sign is less than.

See the attached image for the graph.

Answer:

x² + 2x + 9 - \(\frac{7}{x+3}\)

Step-by-step explanation:

Using Synthetic division

- 3 |   1    5     15   20

       ↓  - 3   - 6    - 27

     ----------------------------

       1     2      9     - 7 ← remainder r(x)

Quotient Q(x) = x² + 2x + 9

Thus

x³ + 5x² + 5x + 20 = x² + 2x +9 - \(\frac{7}{x+3}\)

The value of the triple integral ∫∫∫ e(-(x² + y² + z²))(3/2) dz dy dx, where the limits are x: -2 to 2, y: -(4-x²) to 4-x², and z: 0 to 4-x²-y², is approximately (2/3)π²e(-8).

To evaluate this triple integral, we can convert it to spherical coordinates. In spherical coordinates, the transformation equations are:

x = ρsin(φ)cos(θ)

y = ρsin(φ)sin(θ)

z = ρcos(φ)

The Jacobian determinant of the transformation is ρ²sin(φ). The integral becomes:

∫∫∫ e(-(ρ²sin²(φ)cos²(θ) + ρ²sin²(φ)sin²(θ) + ρ²cos²(φ)))(3/2) ρ²sin(φ) dρ dθ dφ

Simplifying the exponent, we have e(-ρ²sin²(φ))(3/2), which simplifies to e(-ρ³sin³(φ)).

The limits of integration in spherical coordinates are as follows:

ρ: 0 to 2

θ: 0 to 2π

φ: 0 to π/2

To continue the calculation, let's substitute the limits of integration in spherical coordinates:

∫∫∫ e(-ρ³sin³(φ)) ρ²sin(φ) dρ dθ dφ

Integrating with respect to ρ first:

∫∫ e(-ρ³sin³(φ)) ρ²sin(φ) dρ dθ

Integrating ∫ ρ²sin(φ) dρ gives (1/3)ρ³sin(φ). The integral becomes:

(1/3) ∫ e(-ρ³sin³(φ)) ρ³sin(φ) dθ

Integrating ∫ e(-ρ³sin³(φ)) ρ³sin(φ) dθ gives -e^(-ρ³sin³(φ)) ρ³sin(φ).

The integral becomes:

(1/3) (-e(-ρ³sin³(φ)) ρ³sin(φ)) ∫ dθ

The integral ∫ dθ with respect to θ is simply θ. Therefore, the expression becomes:

(1/3) (-e(-ρ³sin³(φ)) ρ³sin(φ)) θ

Now, we can integrate with respect to θ:

(1/3) (-e-ρ³sin³(φ)) ρ³sin(φ)) θ

Integrating ∫ θ dθ gives (1/2)θ². The expression becomes:

(1/3) (-e(-ρ³sin³(φ)) ρ³sin(φ)) (1/2)θ²

Now, we need to evaluate this expression with the limits of integration:

θ: 0 to 2π

ρ: 0 to 2

φ: 0 to π/2

Substituting these limits, the final result is:

(1/3) (-e(-8sin³(π/2))) (1/2)(2π)² - (1/3) (-e^(-0sin³(0))) (1/2)(0)²

Simplifying further, we have:

(1/3) (-e(-8)) (1/2)(4π²) - (1/3) (1/2)(0)

Finally, the simplified result of the triple integral is:

(2/3)π²e(-8)

Learn more about Spherical coordinates here:

https://brainly.com/question/30896060

#SPJ11

the complete question is:

Evaluate the triple integral in spherical coordinates:

∫∫∫ e(-(x² + y² + z²))(3/2) dz dy dx

where the limits of integration are:

x: -2 to 2

y: -(4-x²) to 4-x²

z: 0 to 4-x²-y²

Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

The prime factorization of the number 21 is:

21 = 3*7

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

Learn more about prime factorizations:

https://brainly.com/question/1081523

#SPJ1

Answer:

you would use tangent

AC = 6.5

Step-by-step explanation:

tan = \(\frac{opposite}{adjacent}\)

⇒ tan 30 = \(\frac{x}{11.2}\)

tan of 30 is 0.577

⇒ 0.577 =  \(\frac{x}{11.2}\)

multiply both sides by 11.2

⇒ 0.577 x 11.2 = \(\frac{x}{11.2}\) x 11.2

⇒ 6.4624

round to the nearest tenth:

⇒6.4624 = 6.5

The standard normal distribution has a mean of 0 and a standard deviation of 1. M ≈ 30.935. The median of the distribution is also 25.

(a) To find M, we first need to convert the given values of mean and standard deviation to the standard normal distribution. This can be done by using the formula Z = (X - μ) / σ, where Z is the Z-score, X is the value of interest, μ is the mean, and σ is the standard deviation. In this case, we have X ~ N(25, 9). Substituting the values into the formula, we get Z = (X - 25) / 3. Now we need to find the Z-score that corresponds to the desired probability of 0.95. Using a standard normal distribution table or a calculator, we find that the Z-score corresponding to a cumulative probability of 0.95 is approximately 1.645. Setting Z equal to 1.645, we can solve for X: (X - 25) / 3 = 1.645. Solving for X, we get X ≈ 30.935. Therefore, M ≈ 30.935.

(b) The median is the value that divides the distribution into two equal halves. In a normal distribution, the median is equal to the mean. In this case, the mean is given as 25. Therefore, the median of the distribution is also 25.

Learn more about Z-score here: brainly.com/question/30557336

#SPJ11

After using the test statistic z, P(3.6<X<53.5) = 0.967.

In the given question, suppose X is a normal random variable with mean 35 and sdev 10.

We have to find P(3.6<X<53.5).

Fro the given question,

Mean x = 35

sdev s = 10

Z = X - mu / sd

P(3.6<X<53.5) = P ( 3.6-35/10 < Z < 53.5-35/10 )

P(3.6<X<53.5) = P ( -31.4/10 < Z < 18.5/10 )

P(3.6<X<53.5) = P ( -3.14 < Z < 1.85 )

P(3.6<X<53.5) = P ( Z < 1.85) - P ( Z < -3.14)

left tail of both

P(3.6<X<53.5) = 0.9678 - 0.0008

P(3.6<X<53.5) = 0.967

To learn more about test statistic z link is here

brainly.com/question/3006526

#SPJ4

The right answer is:

Suppose X is a normal random variable with mean 35 and sdev 10. Find P(3.6<X<53.5)

The equation of the line that passes through the point (5, 4) and is perpendicular to the line whose equation 2x + y = 3 is y = 1/2x + 3/2

The given equation of the line is

2x + y = 3

y = 3 - 2x

y = -2x + 3

The slope of the line is -2

The slope of the original line will be negative inverse of -2

= - 1/-2

= 1/2

The line is passing through the point (5, 4)

The slope intercept form is

y = mx + b

Substitute the values in the equation

4 = 1/2(5) + b

4 = 5/2 + b

b = 4 - (5/2)

b = 3/2

Therefore, the equation of the line is y = 1/2x + 3/2

Learn more about slope intercept form here

brainly.com/question/29146348

#SPJ4

Answer:

a) 0.32 = 32/100 = 8/25

b) 3.003 = 3 + 3/1000 = 3000/1000 + 3/1000 = 3003/1000

c) 13.134 = 13 + 134/1000 = 13000/1000 + 134/1000 = 13134/1000

d) 5.2303 = 5 + 2303/10000

The solution of equation is x=-3

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given

The equation;√x+3=-6

Now,

√x=-6-3

√x=-9

x=-3

Therefore the answer of the given equation will be -3

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ1

Answer (assuming it can be in slope-intercept form):

\(y = -\frac{5}{4} x-7\)  

Step-by-step explanation:

1) First, find the slope of the line by using the slope formula, \(m = \frac{y_2-y_1}{x_2-x_1}\). Substitute the x and y values of the given points into the formula and solve:

\(m = \frac{(3)-(-7)}{(-8)-(0)}\\m = \frac{3+7}{-8-0} \\m = \frac{10}{-8} \\m = -\frac{5}{4}\)

So, the slope is \(-\frac{5}{4}\).

2) Now, use the point-slope formula \(y-y_1 = m (x-x_1)\) to write the equation of the line in point-slope form. Substitute real values for the \(m\), \(x_1\), and \(y_1\) in the formula.

Since \(m\) represents the slope, substitute \(-\frac{5}{4}\) in its place. Since \(x_1\) and \(y_1\) represent the x and y values of one point the line intersects, choose any one of the given points (either one is fine, it will equal the same thing at the end) and substitute its x and y values into the formula as well. (I chose (0, -7), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the following answer:

\(y-(-7) = -\frac{5}{4} (x-(0))\\y + 7 = -\frac{5}{4} x\\y = -\frac{5}{4} x-7\)

The total height of the iceberg is 38 meters and the total depth of the iceberg is 15 meters.

Height is a mathematical term that refers to the vertical distance between an object's top and base. Sometimes, it has the designation altitude. The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.

The depth of an object is the separation between its closest and farthest ends. Jane, for instance, measures a box. Jane estimates the depth of the box by calculating the distance between the end of the box that is closest to her and the end that is farthest away.

Given, the height of an iceberg above the water is 23 meters.

And also given that the bottom of the iceberg is 15 meters below sea level.

Total height = above the water + below the water

Total height=23+15=38 meters

Depth= total height - iceberg above the water

Depth=38-23=15 meters

The total height of the iceberg is 38 meters.

The total depth of the iceberg is 15 meters.

To know more about height and depth, visit:

https://brainly.com/question/9627917

#SPJ1

The mean of the given sequence is 7, the median is 8 and the mode is 10.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = [1, 2, 2, 3, 3, 3,..., 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]/ 55

Mean = 385 / 55

Mean = 7

Median represents the middle value of the given data when arranged in a particular order so,

Here the median is 8.

Mode is that number that appears most frequently in the given set of data which is 10.

Learn more about mean and median;

https://brainly.com/question/17060266

#SPJ2

According to the question 1.) False - 3 × 5 matrix columns can be linearly independent. 2.) True , 3.) True , 4.) True , 5.) True , 6.) True - 3 × 2 matrix transformation not one-to-one.

1.) True. If the set of columns of a 3 × 5 matrix is linearly dependent, it means that there exists a nontrivial linear combination of the columns that equals the zero vector.

2.) False. The effect of a linear transformation on the columns of the n × n identity matrix only determines the image of the standard basis vectors. It does not completely determine the entire transformation.

3.) False. If each row of matrix A has a pivot, it means that the rows of A are linearly independent, not linearly dependent.

4.) True. If A has a pivot in each row, it means that the rows of A are linearly independent, and the linear transformation T : Rn → Rm represented by A is one-to-one.

5.) True. Similar to statement 1, if the set of columns of a 5 × 3 matrix is linearly dependent, it means that there exists a nontrivial linear combination of the columns that equals the zero vector.

6.) True. If A is a 3 × 2 matrix, it means that the transformation x → Ax maps from R2 to R3. Since the dimensions of the domain and codomain are different, the transformation cannot be one-to-one.

To know more about nontrivial visit -

brainly.com/question/32541357

#SPJ11

Answer:

B

Step-by-step explanation:

I think its B but dont trust my math lol xd

Answer:

B

Step-by-step explanation:

5 and one-third units

At the end of the fifth day, a bricklayer has laid 324 bricks on the job.

Multiplication is a mathematical arithmetic operation.

It is also a process of adding the same types of expression to some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given, a bricklayer lays 4 bricks on the first day on the job.

On each day thereafter, he lays three times the number of bricks he laid on the previous day.

And he continued his pattern.

Let x be the number of bricks he laid in the previous day.

Then according to the question,

The number of bricks in total is = 3x

For the second day, x =4

Number of the bricks he laid on the second day = 12

Now the x =12 for the third day.

Number of the bricks he laid on the third day = 36

Now x = 36 for the fourth day.

Number of the bricks he laid on the fourth day = 108

Now the x = 108 for the fifth day.

Number of the bricks he laid on the fifth day = 324

Therefore, 324 bricks he has laid at the end of the fifth day.

To learn more about the multiplication;

https://brainly.com/question/19634536

#SPJ1

a) The probability of randomly selecting 4 males out of 7 spectators, given that 70% of the spectators are males, can be calculated using the binomial probability formula.

b) To find the probability that at most 5 of the randomly selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females from the total number of selected spectators.

a) To calculate the probability of selecting 4 males out of 7 spectators, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

- n is the total number of trials (number of people selected)

- k is the number of successful trials (number of males selected)

- p is the probability of success in a single trial (probability of selecting a male)

- C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)

In this case, n = 7, k = 4, and p = 0.70 (probability of selecting a male). Therefore, the probability of selecting 4 males out of 7 spectators is:

P(X = 4) = C(7, 4) * (0.70)^4 * (1 - 0.70)^(7 - 4)

b) To find the probability that at most 5 of the selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females. This can be done by summing the individual probabilities for each case.

P(X ≤ 5 females) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

To calculate each individual probability, we use the same binomial probability formula as in part a), with p = 0.30 (probability of selecting a female).

Finally, we sum up the probabilities for each case to find the probability that at most 5 of the selected spectators are females.

To learn more about probability  Click Here:  brainly.com/question/31828911

#SPJ11

The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

Learn more about demand here

https://brainly.com/question/14274996

#SPJ11

Answer:

4 minus 12 x

Trust me it is correct

Good Luck :)

Answer:-6(-4/6+2x)

Step-by-step explanation: Hope this helps

The value of x is 5°.

Given:

∠1 and ∠2 are vertical angles, m∠1 = 40° and m∠2 = (7x + 5)°.

Vertical angles are angles that are opposite to each other and by definition these angles are congruent or equal.

That is m∠1 and m∠2 are equal.

m∠1 = m∠2

40 = (7x + 5)

7x = 40 - 5

7x = 35

divide by 7 on both sides we get

7x/7 = 35/7

x = 35/7

x = 5°.

Therefore the value of x is 5°.

Learn more about the value and vertical angles here:

https://brainly.com/question/23087234

#SPJ1

The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

To learn more about inequatity refer to :

brainly.com/question/2456006

#SPJ1

Given that "Jane wrote all the natural numbers from 5 to k. Including 1 and k"

So Jane wrote k numbers.

lets take an example

if k = 10 , then natural numbers between 1 and 10 are 10 numbers that are 1 , 2 , 3 ,4 ,5 ,6 , 7 , 8 ,9 and 10.

Hence she write k numbers.

Jane wrote k - 4 natural numbers for the given condition.

Natural numbers are defined as which range from 1 to infinity and are the most fundamental sort of numbers. Commonly known as positive numbers or counting numbers, these numbers. Natural Numbers are represented by the symbol N.

Jane wrote all the natural numbers from 5 to k, including 5 and k.

So, she wrote the numbers as 5, 6, 7, 8, 9, ..., k.

To find out how many numbers Jane wrote, we have to subtract 4 from each of these numbers because 4 numbers (1, 2, 3, 4) come before 5.

1, 2, 3, 4, 5, ..., k-1

So, there are k-1 - 4 + 1 = k - 4 natural numbers between 5 and k, inclusive.

Therefore, she wrote k - 4 natural numbers.

Learn more about natural numbers here :

brainly.com/question/17429689

#SPJ2

Answer:

c. Might not be congruent

There is No congruence between ABC and DEF.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

From the figure we have given that

<A = <D

<B = <E

<C = <F

As, all the angles are equal but there is no Criteria which have AAA congruence rule.

Thus, there is no Congruence.

Learn more about Congruence here:

https://brainly.com/question/7888063

#SPJ7

To prove that triangle ABC is an isosceles right triangle, we need to show that two sides of the triangle are equal in length and one angle is a right angle.

Distance Formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the distance formula, we can calculate the lengths of the three sides of the triangle:

Side AB: d₁ = √[(6 - (-2))² + (2 - 4)²] = √[8² + (-2)²] = √(64 + 4) = √68

Side BC: d₂ = √[(1 - 6)² + (-1 - 2)²] = √[(-5)² + (-3)²] = √(25 + 9) = √34

Side AC: d₃ = √[(-2 - 1)² + (4 - (-1))²] = √[(-3)² + 5²] = √(9 + 25) = √34

Slope Formula:

The slope between two points (x₁, y₁) and (x₂, y₂) is given by the slope formula: m = (y₂ - y₁) / (x₂ - x₁)

Using the slope formula, we can calculate the slopes of the three sides of the triangle:

Slope AB:

m₁ = (2 - 4) / (6 - (-2)) = (-2) / 8 = -1/4

Slope BC:

m₂ = (-1 - 2) / (1 - 6) = (-3) / (-5) = 3/5

Slope AC:

m₃ = (4 - (-1)) / (-2 - 1) = 5 / (-3) = -5/3

From the distances calculated and the slopes of the sides, we can see that side AB is equal in length to side BC (both √34), indicating that two sides are equal. Additionally, the slope of side AC (m₃ = -5/3) is the negative reciprocal of the slope of side AB (m₁ = -1/4), indicating that the two sides are perpendicular, and hence, one angle is a right angle.

Therefore, triangle ABC is an isosceles right triangle.

Learn more about isosceles here

https://brainly.com/question/29793403

#SPJ11