What is 1 + 2? I think it's four, but I'm not sure.

A. P(E) = 1/5

B. P(F) = 1/5

C. P(G) = 1/5

D.  The probability of selecting either "Eben" or "Frank" is 2/5.

A: To find the probability of selecting the name "Eben," we need to determine the fraction of the total possible outcomes that result in selecting "Eben." Since there are a total of five names to choose from, the probability of selecting "Eben" can be expressed as:

P(E) = (Number of favorable outcomes) / (Total number of possible outcomes)

In this case, there is only one favorable outcome (selecting "Eben"), and there are five possible outcomes (choosing any of the five names). Therefore:

P(E) = 1/5

B: Similarly, to find the probability of selecting the name "Frank," we can apply the same approach. The probability of selecting "Frank" can be expressed as:

P(F) = (Number of favorable outcomes) / (Total number of possible outcomes)

Again, there is only one favorable outcome (selecting "Frank"), and there are five possible outcomes (choosing any of the five names). Thus:

P(F) = 1/5

C: To find the probability of selecting the name "Evelyn," we follow the same method as above. The probability of selecting "Evelyn" is:

P(G) = (Number of favorable outcomes) / (Total number of possible outcomes)

Once again, there is only one favorable outcome (selecting "Evelyn"), and there are five possible outcomes (choosing any of the five names). Therefore:

P(G) = 1/5

D: To find the probability of selecting either event E or event F (P(E U F)), we can add their individual probabilities and subtract the probability of their intersection (P(E ∩ F)). The probability of the union can be calculated as follows:

P(E U F) = P(E) + P(F) - P(E ∩ F)

Since event E and event F are independent, the probability of their intersection is zero (no name can be both "Eben" and "Frank" simultaneously). Therefore:

P(E U F) = P(E) + P(F) - 0

= P(E) + P(F)

= 1/5 + 1/5

= 2/5

Thus, the probability of selecting either "Eben" or "Frank" is 2/5.

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From the attached image, it can be seen that triangle PQR is an isosceles triangle and therefore option (A), option (B), option (C)  and option (D) are all correct.

An isosceles triangle has 2 sides equal meaning 2 opposite angles are also equal.

Let us assume the following:

PR = 1cm

QR = 1cm

PQ = 2cm

cos P = adj/hyp

         = PR/PQ = 1/2

cos Q = adj/hyp

          = QR/PQ = 1/2

Therefore cos P and cos Q are equal.

sin P = opp/hyp

        = QR/PQ = 1/2

sin Q = opp/hyp

         = PR/PQ = 1/2

Also sin P and sin Q are equal.

From this analogy, we can deduce the following:

sin P = sin Q = 1/2

cos P = cos Q = 1/2

sin P = cos Q = 1/2

cos P = sin Q = 1/2

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Hello !

-5 = 9 - 7y

-5 + 7y = 9

7y = 9 + 5

7y = 14

y = 14/7

y = 2

so no for all except for y = 2

Answer:

x = - 3, x = 1

Step-by-step explanation:

x² + 2x - 3 = 0

consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (+ 2)

the factors are + 3 and - 1 , since

3 × - 1 = - 3 and + 3 - 1 = + 2 , then

(x + 3)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

x - 1 = 0 ( add 1 to both sides )

x = 1

solutions are x = - 3 , x = 1

The number of hamburger is 375 and the number of cheeseburger is 311.

Here,

It should be noted that an expression is simply used to show the relationship between the variables.

In this case, the local hamburger shop sold a combined total of 686 hamburgers and cheeseburgers on Saturday and there were 64 fewer cheeseburgers sold than hamburgers.

Let Cheeseburger = x

Hamburger = x + 64

This will be:

x + x + 64 = 686

2x + 64 = 686

2x = 686 - 64

2x = 622

x = 622/2

x = 311

Cheeseburger = 311

Hamburger = x + 64 = 311 + 64 = 375

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Each radio requires 2 batteries, and each flashlight requires 6 batteries.

To solve this problem using the substitution method, we need to determine how many batteries each radio and flashlight need. Let's assume the number of batteries needed for a flashlight is represented by 'f', and the number of batteries needed for a radio is represented by 'r'.

From the given information, we can create two equations:

Equation 1: 12f + 6r = 84 (Karen's usage of batteries)

Equation 2: 5f + 10r = 50 (Jin's usage of batteries)

To solve the system of equations, we can use the substitution method. First, we'll solve Equation 1 for 'f' in terms of 'r':

12f = 84 - 6r

f = (84 - 6r)/12

f = 7 - (r/2)

Now, we substitute this expression for 'f' into Equation 2:

5(7 - (r/2)) + 10r = 50

35 - 5(r/2) + 10r = 50

35 - (5r/2) + 10r = 50

35 + (20r - 5r)/2 = 50

35 + 15r/2 = 50

15r/2 = 15

15r = 30

r = 2

Now that we have the value of 'r' as 2, we can substitute it back into Equation 1 to find the value of 'f':

12f + 6(2) = 84

12f + 12 = 84

12f = 72

f = 6

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Answer:

π√2 : 4

Step-by-step explanation:

if area of square is 9, each side = 3.

radius of circle = √[(3/2)² + (3/2)²]

= (3√2)/2.

Diameter = 2 X radius = 3√2.

Circumference = π X D

= 3π√2

perimeter of square = 3 + 3 + 3 + 3 =12.

ratio of circumference to perimeter is

3π√2 : 12

= π√2 : 4

To determine the area of the figure accurately, we need more information or a description of the figure. The measurements provided (4 cm, -3 cm, 8 cm, 6 cm) do not provide enough details to calculate the area. Please provide additional information or a description of the figure so that I can assist you in finding the closest measurement to its area.

The difference between the selling price and the cost price is the profit he earned.

Profit = Selling Price - Cost Price

Profit = $216 - $180

Profit = $36

To find the percentage profit, we need to calculate what proportion of the cost price the profit represents, and express that as a percentage :

Percentage Profit = (Profit : Cost Price) * 100%

Percentage Profit = ($36 : $180) * 100%

Percentage Profit = 0.2 * 100%

Percentage Profit = 20%

Therefore, his percentage profit is 20%.

The volume of the solid object is 69.30 in².

We have,

The volume of the triangular prism with a rectangular base is given by the formula V = (lw)h,

where s is the side of the base and h is the height of the prism.

Now,

h = 18.8 in

s² = 19.2² =  368.64 in²

Now,

The volume of the solid object.

= 368.64 x 18.8

= 69.30 in²

Thus,

The volume of the solid object is 69.30 in².

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The points in standard form  are 7 + 3i and  6 - 6i, distance between two complex numbers is  √82,  complex conjugate of z₂ = 6 + 6i and the value of z₂ - z₁ is -1 - 9i

Given that the points z₁ and z₂ are (7, 3) and (6, -6)

To represent the points z₁  and z₂ in standard form, we write them as complex numbers in the form a + bi, where a represents the real part and b represents the imaginary part.

For z₁ : (7, 3) = 7 + 3i

For z₂: (6, -6) = 6 - 6i

The distance between two complex numbers, we can use the distance formula:

Applying this formula to z₁  and z₂:

Distance = √[(6 - 7)² + (-6 - 3)²]

= √[(-1)² + (-9)²]

= √[1 + 81]

= √82

The complex conjugate of z₂ = 6 - 6i is denoted as z₂' and can be found by changing the sign of -6i:

z₂ = 6 + 6i

To find z₂ - z₁  geometrically, we can represent z₁  and z₂ as vectors and then subtract them.

First, let's plot the complex numbers z₁  and z₂ on the complex plane:

z₁  (7, 3) is represented by the vector from the origin to the point (7, 3).

z₂ (6, -6) is represented by the vector from the origin to the point (6, -6).

To find z₂ - z₁ , we subtract the vector representing z₁ from the vector representing z₂.

The resulting vector represents z₂ - z₁.

Using the geometric method, we subtract the vector representing z₁  (7 + 3i) from the vector representing z₂ (6 - 6i):

(6 - 6i) - (7 + 3i)

By performing the subtraction:

(6 - 7) + (-6 - 3)i

-1 - 9i

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The correct answer is (j - k)(x) = 10 + x.

To find the difference in the amount of money between Joel's and Kevin's accounts, we subtract the value of Kevin's account (k(x)) from Joel's account (j(x)).

(j - k)(x) = (25 + 3x) - (15 + 2x)

            = 25 - 15 + 3x - 2x

            = 10 + x

This expression represents how much more money is in Joel's account compared to Kevin's account after x weeks.

Therefore, the correct function is (j - k)(x) = 10 + x.

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Answer: About 28 miles.

Step-by-step explanation:

First, we will find the rate of miles per minute.

    85 miles / 60 minutes = 1.41666667 miles per minute

Next, we will multiply this rate by 20 minutes:

    20 minutes * 1.41666667 miles per minute ≈ 28 miles

Answer:

Step-by-step explanation:

To find out how many miles the car would go in 20 minutes, we need to determine the distance covered in one minute and then multiply it by 20.

Given that the car's speed exceeded 85 miles per hour, we can calculate the distance covered in one minute by dividing 85 by 60 (since there are 60 minutes in an hour).

85 miles/hour ÷ 60 minutes/hour = 1.4167 miles/minute

Therefore, the car would travel approximately 1.4167 miles in one minute.

To find the distance covered in 20 minutes, we multiply the distance covered in one minute by 20:

1.4167 miles/minute × 20 minutes = 28.3334 miles

Rounding to the nearest whole mile, the car would go approximately 28 miles in 20 minutes.

The sampling distribution of the difference between the two-sample means, X1 - X2, can be characterized by the following properties:

1. Expected value (mean):

  E(X1 - X2) = E(X1) - E(X2) = mu1 - mu2

  The expected value of the difference is equal to the difference of the means of the two populations.

2. Variance:

  V(X1 - X2) = V(X1) + V(X2)

  Since X1 and X2 are independent, the variance of their difference is equal to the sum of their individual variances.

(b) Given the information provided:

For X1:

Mean (mu1) = 29.8

Standard deviation (sigma1) = 4

For X2:

Mean (mu2) = 34.7

Standard deviation (sigma2) = 5

Sample size for X1 (n1) = 20

Sample size for X2 (n2) = 20

To find the sampling distribution of X1 - X2:

Expected value (mean):

E(X1 - X2) = mu1 - mu2 = 29.8 - 34.7 = -4.9

Variance:

V(X1 - X2) = V(X1) + V(X2) = (sigma1^2 / n1) + (sigma2^2 / n2)

          = (4^2 / 20) + (5^2 / 20)

          = 16/20 + 25/20

          = 41/20

          = 2.05

Therefore, the sampling distribution of X1 - X2 has an expected value (mean) of -4.9 and a variance of 2.05.

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Answer:

Step-by-step explanation:Homework Progress

22 / 77

P and Q are points on the line 3y - 4x = 12

a) Complete the coordinates of P and Q.

P (0,4

,0)

b) Plot points P and Q on the graph.

Use the tool to plot the coordinates.

c) Draw the line 3y - 4x = 12 for values

of x from -3 to 3.

Answer:

The answer is

-5.79×10²³,6.88×10‐²³,5.73×10²³,57.8×10²²,5.83×10²³

Step-by-step Explanation:

Because ∠DAC equals ∠BAD, we can conclude that triangles ΔABC and ΔACD are similar according to the Angle-Angle (AA) similarity criterion. Then the length of the CD is 8.3.

To find the length of the CD, we can use the similarity of triangles ΔABC and ΔACD. Since∠ DAC is equal to ∠ BAD, we can conclude that triangles ΔABC and ΔACD are similar by the Angle-Angle (AA) similarity criterion.

Using the given information:

AB = 5.7

AC = 5.1

BD = 3.6

Let's set up the proportion based on the similarity of triangles  ΔABC and ΔACD:

AB/AC = BC/CD

Substituting the given values:

5.7/5.1 = (5.7 + 3.6)/CD

Simplifying the equation:

1.1176 = 9.3/CD

Cross-multiplying:

CD = 9.3 / 1.1176

Calculating CD:

CD ≈ 8.3214

Therefore, Rounding the CD to one decimal place, the length of the CD is approximately 8.3.

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(a) A formula to calculate the amount after n months: 1,500(1 + nx0.0046)

(b)  the amount owed after 14 months = $1596.6

Given that,

Principal amount =  P  = $1,500

interest of grown = R = 5.5%

Now we can write is,

5.5% = 5.5/100

        =  0.055

We know that,

The simple interest formula,

A = P(1 + rt)

Where,

A represents Amount after T years

R represents rate of interest

T is time in year

Now,

Since 1 month = 1/12 years

                        = 0.084

Therefore amount after 1 month be

A = 1,500(1+0.055x0.084)

  = 1,500(1+0.0046)

  = 1506.93

Amount after 2 month be

A =  1,500(1+ 2 x 0.055x0.084)

  = 1,500(1+2x0.0046)

Amount after 3 month be

A =  1,500(1+ 2 x 0.055x0.084)

  = 1,500(1 + 3x0.0046)

Hence amount of  n months = 1,500(1 + nx0.0046)

Hence,

The amount after 14 months,

=  1,500(1 + 14x0.0046)

= $1596.6

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Answer:

  C.  4 cm²

Step-by-step explanation:

You want the maximum possible area of a quadrilateral inscribed in a semicircle.

The figure is symmetrical about a vertical line, so the area will be maximized when the area of half the quadrilateral is maximized. The area of the quadrilateral in the right half of the figure is the product of the x- and y-coordinates of the corner point on the circle.

For coordinates (x, y), the area is A=xy. The graph of this function is a hyperbola, symmetric about the line y=x. The larger the value of A, the farther the graph is from the origin.

The maximum possible value of A will be found where the graph of xy=A is tangent to the circle. That point of tangency will lie on the circle and on the line y = x.

The equation for the semicircle is ...

  x² +y² = 2²

When x=y, this is ...

  x² +x² = 4

  x² = 2

This is the area of the quadrilateral in the right half of the figure.

The entire quadrilateral has an area twice this, or 2·2 = 4 (square cm).

The maximum possible area of the quadrilateral is 4 cm².

__

Additional comment

You will notice the figure is half of a figure of a whole circle with a square inscribed. This is not a coincidence.

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The statement means that the Separation Axioms, a set of principles in mathematics,   are not sufficient on their own to build acomprehensive framework for  settheory that includes its typical operations and construction.

The Separation Axioms are a collection of axioms that define the basic properties of topological spaces.   They are not strong enough to develop set theory with its usual operationsand constructions.

One reason forthis is that the Separation Axioms do not allow us to distinguish between different points in a topological space. For example, in a T0 space, we can say   that two points are distinct if there is an open set that contains one point but notthe other.

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The values of angle Q,R, S are 90°, 53.1° and 36.9° respectively.

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

sin(θ) = opp/hyp

cos(θ) = adj/hyp

sin(θ) = opp/adj

Finding angle R;

sinR = 8/10

sinR = 0.8

R = 53.1°

Q is a right angle , therefore Q is 90°

therefore to find angle S

angle S = 90- 53.1

= 36.9°

Therefore the values of angle Q,R, S are 90°, 53.1° and 36.9° respectively.

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Answer:

you would still pay the normal amout of tax of other normal technology. The tax would change depending on e=what state your in tho

Step-by-step explanation:

a) The terminal point is 0.896 radius length.

b) The value returned is -0.896.

We have,

The circle's radius is 3 units long and the terminal point is located at (−2.69,−1.33)

a. Since the circle's radius is 3 units long, we divide the x-coordinate by 3:

x-coordinate of terminal point: -2.69

Number of radius lengths to the right: -2.69 / 3 ≈ -0.896

However, since the angle is measured from the 3-o'clock direction, we consider it to be in the clockwise direction.

Thus, the number of radius lengths to the right is

Number of radius lengths to the right: -(-0.896) = 0.896

Therefore, the terminal point is 0.896 radius length.

b. Using Trigonometry

cos(h) = x-coordinate of terminal point / radius length

cos(h) = -2.69 / 3 ≈ -0.896

c. As, θ = h. From the given information, we have:

θ ≈ -0.896 radians

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Answer:

4th option

Step-by-step explanation:

using the rule of exponents

• [tex]a^{m}[/tex] ×[tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

then

[tex]x^{9}[/tex] × x = [tex]x^{9}[/tex] × [tex]x^{1}[/tex] = [tex]x^{(9+1)}[/tex] = [tex]x^{10}[/tex]

Then

[tex]\sqrt[3]{x^{10} }[/tex] ≡ [tex]\sqrt[3]{x^9 . x}[/tex]

Answer:

Step-by-step explanation:

D is the answer. See attachment for reason.

log₂ 24 can be expressed as 3 + log₂ 3 in terms of prime factors, using the properties of logarithms.

To express log₂ 24 in terms of prime factors, we can use the properties of logarithms and the fact that any positive integer can be expressed as a product of prime factors.

First, let's find the prime factorization of 24.

24 can be divided by 2, so we have 24 = 2 × 12.

12 can be divided by 2, so we have 12 = 2 × 6.

6 can be divided by 2, so we have 6 = 2 × 3.

Therefore, the prime factorization of 24 is 2 × 2 × 2 × 3, or 2³ × 3.

Now, using the properties of logarithms, we can express log₂ 24 as the sum of logarithms of its prime factors.

log₂ 24 = log₂ (2³ × 3)

According to the properties of logarithms, we can separate the factors inside the logarithm as individual terms:

log₂ (2³ × 3) = log₂ 2³ + log₂ 3

Since log₂ 2³ is equal to 3, we can simplify the expression further:

log₂ (2³ × 3) = 3 + log₂ 3

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hello

the answer to the question is (10, - 2)

Answer:

Step-by-step explanation:

Midpoint Formula:  [tex](\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )[/tex]

Midpoint = [tex](\frac{8+12 }{2} , \frac{3+(-7)}{2} )[/tex]

Midpoint = [tex](\frac{20 }{2} , \frac{-4)}{2} )[/tex]

Midpoint = (10, -2)

A probability value equal to or smaller than 0.05 would indicate that Gaurav's null hypothesis should be rejected at the 5% significance level.

In hypothesis testing, the significance level, denoted as alpha (α), is the predetermined threshold used to determine whether to reject the null hypothesis.

Gaurav has specified a 5% significance level, which means he wants to control the probability of making a Type I error (rejecting the null hypothesis when it is true) at 5% or less.

If Gaurav were to conduct a test and calculate the p-value, he would compare it to the significance level of 0.05.

The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.

If the p-value is less than or equal to the significance level (p ≤ α), it indicates that the observed difference is unlikely to occur by chance alone under the assumption of the null hypothesis.

Gaurav would reject the null hypothesis and conclude that there is a significant difference between the average amount of medication his patients are taking and the national average.

Conversely, if the p-value is greater than the significance level (p > α), it suggests that the observed difference could reasonably occur by chance, and Gaurav would fail to reject the null hypothesis.

This would imply that there is no significant difference between the average medication amounts of Gaurav's patients and the national average.

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Answer: quotient: x+7 remainder: -5

After calculating the average of numbers here, the average of the four odd numbers from [tex]8 \ to \ 15[/tex] is greater than the average of the four even numbers.

The step-by-step solution to this is given below:

To determine which average is greater, let's calculate the averages of the even and odd numbers separately.

The four even numbers from [tex]8 \ to \ 15 \ are \ 8, 10, 12, and \ 14[/tex]. To find their average, we sum them up and divide by [tex]4[/tex]:

[tex]\[\text{Average of even numbers} = \frac{8 + 10 + 12 + 14}{4} = \frac{44}{4} = 11\][/tex]

The four odd numbers from [tex]8 \ to \ 15 \ are \ 9, 11, 13, and \ 15.[/tex] Similarly, we calculate their average:

[tex]\[\text{Average of odd numbers} = \frac{9 + 11 + 13 + 15}{4} = \frac{48}{4} = 12\][/tex]

Now, the next step will be comparing the two averages, we find that the average of the four odd numbers, [tex]12[/tex], is greater than the average of the four even numbers, [tex]11[/tex].

Therefore, the average of the four odd numbers from [tex]8 \ to \ 15[/tex] is greater than the average of the four even numbers.

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