Suppose that 60% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 50% end up investing in bonds, and 44% end up investing in both stocks and bonds. What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?

Answer:

Yes because it is a scalene triangle

Step-by-step explanation:

The overall average of the weights is 16.

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.

Given that the average of the first 4 weights is 5.

Avg = Total Sum / Total number of weights

Substituting the value of Avg = 5 and Total number of weights= 4 we have:

5 = Sum(4) / 4

Sum(4) = 20

The average of the next 11 weights was 20 pounds.

Substituting the values, we have:

20 = Sum(11) / 11

Sum(11) = 220

The total sum of the 4 weights and the 11 weights is:

Sum = Sum(4) + Sum(11)

= 20 + 220

= 240

The total number of weights are: 4 + 11 = 15

The overall average weight is:

Avg = Sum/ total number of weights

Avg = 240/ 15

Avg = 16

Hence, the overall average of the weights is 16.

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Answer:

After 5 minutes, Gordon and Erik will each have run 10 laps

Step-by-step explanation:

Let L =lap, M=minute, G=gordon, E=Eric

G=(1L*M)+5

E=(2L*M)+5

Answer:

After 5 minutes, Gordon and Erik will each have run 10 laps

Step-by-step explanation:

Gordon already completed 5 laps and each lap is completed in 1 minute

5 + 5 = 10

Eric completes a lap in 2 minutes

2 x 5 = 10

So after 5 minutes, Gordon and Erik will each have run 10 laps

Hope you get this right :)

8x

Step-by-step explanation:

2x x 2x x 2x

Answer: 24y+46

Step-by-step explanation:

6(4y+8)-2

=24y+48-2

=24y+46

= 2(12y+23)

Answer: 24y+46

Step-by-step explanation:

multiply 6 by 4y = 24y

multiply 6 by 8 = 48

you have left 24y + 48 - 2
subtract 2 from 48 and get 46

Answer:

x = -3, y = -5

Step-by-step explanation:

-6x - y = 23 ----------------(1)

y = 4x + 7 -------------------(2)

Put Eq. (2) in (1)

-6x - (4x + 7) = 23

-6x - 4x - 7 = 23

-10x - 7 = 23

-10x = 23 + 7

-10x = 30

Put x = -3 in Eq. (2)

y = 4(-3) + 7

y = -12 + 7

[tex]\rule[225]{225}{2}[/tex]

According to the unitary method, after 2.05 hours value of stock will be equal.

Here we have given that the following value are given in the question they are listed as follows:

Stock 1 has price of stock at 9 A.M is $16.12 and the Rate of increase is $0.12 per hour

Similarly, Stock 2 has price of stock at 12 P.M is $16.87 with the Rate of decrease is $0.07 per hour.

Here first we have to calculate price of stock at 12 P.M, then we get the value as,

=> 16.12 + (0.12 x 3) = 16.48

Now, let us consider that x hours after 12 P.M their price will be same

Then the First consider case of stock 1 as,

=> Price of Stock 1 after x hours from 12 P.M

=> 16.48 + 0.12x

For stock 2, the value is calculated as,

=> Price of Stock 2 x hours after 12 P.M

=> 16.87 - 0.07x  

Then we have to equate the price of stock x hours after 12 P.M:

=> 16.48 + 0.12x = 16.87 - 0.07x  

When we simplify this one then we get,

=> 0.19x = 0.39

=> x = 2.05

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Yes, 84 is divisible by 3. This can be demonstrated using the modulus operator.

The modulus operator returns the remainder of a division problem. In this case, we can divide 84 by 3 and see what the remainder is.

Calculation

84 ÷ 3 = 28

Remainder

84 % 3 = 0

Since the remainder is 0, this means that 84 is evenly divisible by 3. This can be shown mathematically as 84 = 3 × 28. In other words, 84 is a multiple of 3, meaning it is divisible by 3.

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A real function, usually referred to as a real-valued function, is one whose domain is the real numbers.  A function from complex numbers to complex numbers is referred to as a complex function.

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A periodic up-and-down motion should be imparted to the nozzle of a garden hose such that the resultant stream of water approximates a sine curve.

A sine curve is a mathematical function that oscillates between a maximum and minimum value in a repeating pattern. To approximate this with a stream of water from a garden hose, the nozzle of the hose should be moved in a periodic up-and-down motion. This motion will cause the water stream to oscillate between a higher and lower height, creating the repeating pattern characteristic of a sine curve. The speed at which the nozzle is moved, as well as the amplitude of the motion, can be adjusted to create a more accurate representation of a sine curve.

Also, the nozzle can be turned to make the water flow in a spiral, which looks even more like a sine curve.

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f^-1(x) is the inverse of f(x) as the composite functions f(f^-1(x)) and f^-1(f(x)) are both equal to x.

A function is composite when the co- domain of the first mapping is the domain of the second mapping.

We shall evaluate the functions f(f^-1(x)) and f^-1(f(x)) as follows:

f(f^-1(x)) = [(3x+5 / x+1) - 5] ÷ [3 - (3x+5 / x+1)]

changing division to multiplication;

f(f^-1(x)) = [3x + 5 - 5(x + 1)]/(x + 1) × (x + 1)/[3(x + 1) - (3x + 5)]

(x + 1) is common and will cancel out

f(f^-1(x)) = (3x + 5 - 5x - 5)/(3x + 3 - 3x - 5)

f(f^-1(x)) = -2x/-2

f(f^-1(x)) = x

f^-1(f(x)) = [3(x-5 / 3 -x) + 5] ÷ [(x-5 / 3 -x) + 1]

changing division to multiplication;

f^-1(f(x)) = [3(x - 5) + 5(3 - x)]/(3 - x) × (3 - x)/[x - 5 + (3 - x)]

(3 - x) is common and will cancel out

f^-1(f(x)) = (3x - 15 + 15 - 5x)/(x - 5 + 3 - x)

f^-1(f(x)) = -2x/-2

f^-1(f(x)) = x

Therefore, since composite functions; f(f^-1(x)) = x and f^-1(f(x)) = x, then f^-1(x) is the inverse of f(x).

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Bar, circle, and line graphs are the three most often utilized graph kinds. Each form of graph can be used to display a certain kind of data.

Therefore the correct answer is option B .

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Answer:

c = 50

Step-by-step explanation:

The given angles are alternate angles and their measures are equal.

We can write the following equation based on this information:

2c - 3 = 97

2c = 100

c = 50

The equation that best represents the relationship is y = ½x + 2

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

From the values of x and y, let's check if the graph of y against x is linear

taking points x( 2,4) y(3,4)

slope =( 4-3)/4-2

slope = 1/2

therefore the graph is linear and slope is 1/2

the equation of a straight line = y − y 1 = m ( x − x 1 )

= y-3 = m( x- 2)

= y = 1/2(x-2)+3

y = ½x -1+3

y = ½x +2

therefore the equation that best represents the relationship is y = ½x + 2

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Answer:

4

Step-by-step explanation:

speed = distance/time

time = distance/speed

time = 4/5 mile / 12 mph

time = 0.0666... hours × (60 minutes)/(1 hour)

time = 4 minutes

Answer: 6

Step-by-step explanation: Very simple, just do 17 - 11 and you'll get 6. I hope that's the correct answer

The solution to the system of equation is as follows:

x = 2 and y = 4

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Let's solve the system of equation using elimination method as follows:

11x - 5y = 2

x - 5y = -18

subtract equation(ii) from equation(i) to eliminate the variable y.

Therefore,

10x = 20

divide both sides by 10

x = 20 / 10

x = 2

Let's find y by substituting the value of x in equation(ii)

x - 5y = -18

2 - 5y = -18

-5y = -18 - 2

-5y = -20

divide both sides by -5

y = -20 / -5

y = 4

Therefore, x = 2 and y = 4.

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In general, if the rectangles are all the same width and if they are placed to the right of the curve, the Riemann sum will be an overestimate of the true area. On the other hand, if the rectangles are placed to the left of the curve, the Riemann sum will be an underestimate of the true.

Another method to determine if a Riemann sum is an overestimate or underestimate, we can compare it to the exact value of the definite integral. If the Riemann sum is larger than the definite integral, it is an overestimate. If the Riemann sum is smaller than the definite integral, it is an underestimate. Additionally, we can also check the sign of the function being integrated and the width of the rectangles. If the function is positive and the width of the rectangles is decreasing, then the Riemann sum will be "an overestimate". If the function is negative and the width of the rectangles is decreasing, then the Riemann sum will be "an underestimate".

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The following is an example of a quadratic inequality: x^2 + 2x - 8 > 0.

This is an example of a quadratic inequality because it is an inequality involving a quadratic function (x^2 + 2x - 8) which is of the form ax^2 + bx + c where a, b, and c are constants.

Quadratic inequalities can be solved by factoring the quadratic expression, using the Quadratic Formula, or graphing the inequality. In order to solve a quadratic inequality, it is important to understand the types of solutions that can be expected.

Solutions may include one solution, two solutions, or no solutions. Additionally, when graphing a quadratic inequality, the graph may be a line or a region. To determine which type of graph to use, the type of inequality must be identified (greater than or less than). If the inequality is a greater than or less than inequality, then the graph will be a region. If the inequality is an equal to inequality, then the graph will be a line.

Solving and graphing quadratic inequalities is an important skill in algebra as it allows us to visualize and solve complex problems.

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[tex](2x^5)^3\implies \left(2^3x^{5\cdot 3} \right)\implies 8x^{15}[/tex]

The truth values of the statements are:

The complete question is added as an attachment, where we have the following parameters:

Height, h = 2.5 feet

Diameter, d = 4

The base area is then calculated as

Area = п(r²)

So, we have

Area = п(2²)

The volume is then calculated as

Volume = Base area * Height

So, we have

Volume = п(2²) * 2.5

Evaluate

Volume = 31.4

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In order to determine the volume of the cuboid, we would need to know its length, width, and height in centimeters.

The volume of a cube is given by the formula:

V = s^3

Where V is the volume and s is the length of one side of the cube.

Since this cuboid is made up of centimeter cubes, it means that the length, width, and height are in centimeters.

It is not mentioned the dimension of the cuboid, so it is not possible to determine the volume of the cuboid.

In order to determine the volume of the cuboid, we would need to know its length, width, and height in centimeters.

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Therefore , the solution of the given problem of arithmetic mean comes out to be a5 = 3334.

The group's arithmetic average, often known as the mean, is calculated by multiplying the sum of all the entries in a list by the number of products in that list, then dividing that sum by both. This follows the same mathematical development. The number 3 is the median of the numbers 9, 11, and 7. For instance, the number 7 is obtained by dividing 21 (there are actually three numbers) by the equation 5 + 7 + 9.

Here,

It speaks about sequences where every other term is provided as a rule but needs on a number of the preceding terms, as opposed to implicit series where an expression.

The order is as follows: 

The order is as follows:

=> a1 = 6

=> an= -5a(n-1) + 4

To calculate the value of a5, follow these steps:

=>  a2= -5(6) + 4 = -26

=> a3= -5(26) + 4 = 134

=> a4= -5(134) + 4 = -666

=> a5= -5(-666) + 4 = 3334.

Therefore , the solution of the given problem of arithmetic mean comes out to be a5 = 3334.

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Answer:

19 rounds

Step-by-step explanation:

To find this, we take

990 / 54 = 18.33

It will not be 18 rounds because Olive needs 18.33 rounds to beat his old score, so we have to round up to 19 rounds.

Answer:

19 rounds

Step-by-step explanation:

990/54=18.33 round to 19

The coordinates of the vertices of the polygon, given the scale factor and the coordinates of the original image, would be:

To find the coordinates of the new image, when a dilation happens at the origin, use the coordinates of the image and multiply it by the scale factor.

The coordinates of the image, shown on the graph are:

J = (- 5, 3 )

K = ( 2, 3 )

M = ( -5, -3 )

L = ( 2, - 3 )

The coordinates of the new image is therefore:

J ' = ( -5 , 3 ) x 1 / 2

= ( - 2.5, 1 . 5)

K ' = ( 2, 3 ) x 1 / 2

= ( 1, 1 . 5)

M' = ( -5, -3 ) x 1 / 2

= ( - 2.5, - 1. 5 )

L ' = ( 2, - 3 ) x 1 / 2

= ( 1, - 1. 5 )

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A correlation value of -0.8 or lower denotes a significant negative link, whereas one of -0.3 or lower denotes a negligibly weak relationship.

How to interpret a correlation coefficient?

The statistical measure of how well changes in the value of one variable predict changes in the value of another is called a correlation coefficient. The value rises or falls in step with positively associated variables.

Why is correlation coefficient significant? What does it mean?

As a whole, correlation coefficients are used to evaluate the direction and strength of the linear correlations between two sets of variables. When both variables have a normal distribution, use Pearson's correlation coefficient; otherwise, use Spearman's correlation coefficient.

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The formula for enlargement = New length = original length × scale factor.

What is enlargement?

A shape's size can be changed by enlarging it. A shape can be made larger by multiplying all of its lengths by the scaling factor. We can calculate how much larger the shape will be by using the scaling factor. For instance, if a shape is scaled up by a factor of 2, all of the sides will lengthen by the same factor.

Here,

We have to determine the formula for enlargement.

We concluded that New length = original length × scale factor.

When we enlarge a shape by a scale factor, the area of the shape is multiplied by the square of the scale factor. When we enlarge a shape by a scale factor, the volume of the shape is multiplied by the cube of the scale factor.

Hence, the formula for enlargement = New length = original length × scale factor.

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The correct answer is option B: 60 ft.

To find the length of the model, you can use the formula:

Length of model = (Length of original object) x (Scale factor)

The scale factor in this case is 99 feet / 6 inches = 16.5 feet/inch

So the length of the model = (6 inches) x (16.5 feet/inch) = 60 ft

The solution to the expression 2x²-x will be 45.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 2x²-x. The solution of the expression at x= 5 will be calculated as,

E = 2x²-x

E = 2 x ( 5 )² - 5

E = 2 x 25 - 5

E = 50 - 5

E = 45

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