A man has $215,000 invested in three properties. One earns 12%, one 10% and one 8%. His annual income from the properties is $20,600 and the amount invested at 8% is twice that invested at 12%.

Answer:

B. m2=50 and m3=50

Step-by-step explanation:

Angle m1 and angle m3 combined make a straight line, the angle of a straight line is 180°, so you can do 180-130=50 amd theres you m3. Looking at m1 and m2 its the same thing, we already know m1 is 130° so its the same equation, 180-130=50 and thats m2 angle.

Ps. My hand writing is bad but this is how I solved it.

It follows that continuity at infinity is provided by having the same limit while approaching it from either side, i.e., the limit towards + and, which makes sense based on your understanding.

When a function can be extended to P1, it is said to be "continuous at infinity" (R).

Calculus's idea of the limit describes how a function behaves as its input gets closer to a particular value. As long as the limit is present, the value that f(x) approaches as x moves closer to c is represented by the notation lim(x -> c) f(x), which stands for the limit of a function at the point x = c.

You must demonstrate that all three of the following conditions are true in order to prove that a function f is continuous on an interval:

Every point in the interval has f specified, and the interval has f's bound.

For each and every > 0, there is a corresponding > 0 such that |x - c| implies |f(x) - f(c)| for all x and all c in the interval.

F is considered to be continuous on the interval if these requirements are met.

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The angle of depression is 32°.

The angle of depression is the angle formed when the item being seen is below the observer's level between the horizontal line and the line of sight of the observer.

The angle of depression is the angle formed by the horizontal axis and the downward axis of a line of sight. As an example, if you were perched on top of a hill or other structure and looked down at an object, you might determine the angle of depression. To measure these angles, a theodolite or a clinometer can be used. The maximum depression angle is 90 degrees. It can't be possible because any rational spectator would turn around the instant the object passed beneath him.

Due to the fact that AB is perpendicular to B and AD is the horizontal line of sight, we can conclude that AD AB (given).

∴ ∠DAB = 90°.

We can express this as DAB = DAC + BAC.

alternatively, 90° = ∠DAC + 58°

alternatively, ∠DAC = 90° - 58° = 32°.

The angle of depression is 32°.

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The calculation would have three significant figures, since both original numbers have three significant figure.

The number of significant figures in a calculation is determined by the number of significant figures in the original numbers used in the calculation. For example, if we have the calculation 3.14 + 2.7 = 5.84, the answer will have three significant figures because the original numbers, 3.14 and 2.7, each have three significant figures.

In general, significant figures are determined by counting all non-zero digits, plus any zeros that come between non-zero digits, such as in the numbers 10.0 and 0.07. If a number is a decimal, the zeros after the decimal point are also significant, such as in the number 0.07. Zeros that come before the first non-zero digit are not significant, such as in the number 0.0007.

In the above example, the calculation would have three significant figures, since both original numbers have three significant figures.

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Complete quetion:

What is the number of significant figures in the calculation 3.14 + 2.7 = 5.84?

Answer:

[tex]65.1\text{cm}^2[/tex]

Step-by-step explanation:

Area of Rectangle

[tex]A=bh=(8\text{cm})(5\text{cm})=40\text{cm}^2[/tex]

Area of Semicircle

[tex]\displaystyle A=\frac{\pi r^2}{2}=\frac{\pi (4\text{ cm})^2}{2}=8\pi\text{ cm}^2[/tex]

Combined Area

[tex]A_{total}=A_{rectangle}+A_{semicircle}=40\text{cm}^2+8\pi\text{cm}^2\approx65.1\text{ cm}^2[/tex]

The probability of getting 15 or more heads is :

P (Z > -0.18) = 1 - 0.4289 =  0.5714

Now, According to the question:

Normal Approximation to Binomial:

The normal distribution is used to approximate for the binomial distribution. The condition when binomial distribution is approximated to normal is that n should be large and probability should be close to 0.5

"Information available from the question"

n = 30

Probability, p(heads) = 1/2

Since sample size is large, we check for normal approximation.

np = 30(1/2) = 15

and, n(1 - p) = 30(1 - (1/2)) = 15 both are greater than 5, we use normal approximation.

Mean, μ = np = 30(1/2) = 15

Standard deviation, σ = [tex]\sqrt{np(1-p)}[/tex]

Standard deviation, σ = [tex]\sqrt{30(1/2)(1-1/2)}[/tex]

Standard deviation, σ =2.739

We have to find P (X ≥ 15). Using continuity correction, we deduct 0.5

P(X ≥ 15) = P(X > 14.5)

The respective Z-score with X = 14.5 is

Z = (x - μ)/ σ

Z = (14.5 - 15)/2.739

Z = -0.18

Now, we use z-tables to find probability greater than -0.18

P (Z > -0.18) = 1 - 0.4289 =  0.5714

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Answer:

y = 8

Step-by-step explanation:

6y+2 = 8y-14

2 = 2y - 14

16 = 2y

y = 8

Domain : { x ∈ R : x ≥ 7 }

Range: { f ∈ R : f ≥ 9 }

Given function is:

f(x) =

Firstly find the domain of the given function.

Domain is set of all real x's values where given function is defined.

In other words, we exclude all the x's values from all real values where function is undefined.

In case of square root function, inside the square root given expression must be greater or equal to zero.

So,

x - 7 ≥ 0

Solve for x

x ≥ 7

So, domain is all real x when x ≥ 7.

Now find the Range of this function.

Range is set of all output values.

So, lowest value of out put is 9 when x is 7

and maximum value of the function is infinite.

So, Range is all real f's values when f ≥ 9.

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The correct answer is option A which is the ordered pair of point P’ will be (8.75, 5.25).

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

here, we have,

If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’

Multiply the coordinates of point P by the scale factor 7/4  to get the coordinates of P'.

Given : P(-5,3)

P' (x,y) = P (-5 x 7/4 , 3 x 7/4)

           = P(-8.75, 5.25)

Therefore the correct answer is option A which is the ordered pair of point P’ will be (-8.75, 5.25).

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Not all square matrices can be diagonalized. If there are just two eigenvectors (up to multiplication by a constant), then the matrix cannot be diagonalized.

A collection of integers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix, are the integers. In addition to several mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital uses as well.

Thus, Not all square matrices can be diagonalized. If there are just two eigenvectors (up to multiplication by a constant), then the matrix cannot be diagonalized.

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Answer: y = 3x + 0 OR y = 3x

Step-by-step explanation:

M = slope. rise/run. compare the points on the line by how much they rise and how much they run. In this case it is 3/1 (3). the B = the y-intercept. (the point where the line meets the y line, in this case the line meets at the origin which is 0.)

The solution to the exponential inequality in this problem is given as follows:

x < 1.72.

The exponential inequality for this problem is defined as follows:

3^(4x - 5) < 8.

The number 8 is not a base of 3, hence the way to isolate the variable x is applying the log of base 3 to both sides, as follows:

log3(3^(4x - 5)) = log3(8)

4x - 5 = log3(8)

The logarithm of base 3 of 8 can be obtained applying the change of base property, as follows:

log3(8) = log(8)/log(3)

log3(8) = 1.893.

Hence the inequality is solved as follows:

4x - 5 < 1.895

4x < 6.896

x < 6.896/4

x < 1.72.

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The second graph is correct

Answer:

second graph

Step-by-step explanation:

just wanted to help the first person who answered get brainlist

The double integral of (xy y^(-2)) over the region R is equal to 0.

What is double integral ?

The term integral in math is defined as a method of adding or summing up the parts to find the whole and it is basically used to find the volume, area and the central values of many things. Double integrals are a two-dimensional integration method.

The given expression is the integrand of a double integral over the region R defined by the constraints 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2. To calculate this double integral, we would evaluate the following expression:

∬(xy y^(-2)) dA = ∬(xy y^(-2)) dx dy over the region R

We can evaluate this double integral using a change of variables, such as polar coordinates, or using rectangular coordinates.

In rectangular coordinates, we can evaluate the double integral using the following steps:

Evaluate the bounds of integration:

x: 0 to 2

y: 0 to 2

Evaluate the integral with respect to y first, keeping x fixed:

∬(xy y^(-2)) dx dy = ∫(x ∫(y y^(-2)) dy) dx, from 0 to 2

Evaluate the inner integral with respect to y:

∫(y y^(-2)) dy = -y^(-1) = -ln(y) + C, where C is an arbitrary constant

Substitute the solution for the inner integral back into the outer integral:

∫(x (-ln(y) + C)) dx = x(-ln(y)) - xC + D, where D is another arbitrary constant

Evaluate the outer integral with respect to x:

∫(x(-ln(y)) - xC + D) dx = (-x^2/2)ln(y) - (x^2/2)C + xD + E, where E is yet another arbitrary constant

Evaluate the constants of integration C, D, and E using the boundaries of integration for x and y:

-ln(2) - 0C + 0D + E = 0

-2ln(2) - 2^2/2 C + 2D + E = 0

Solving the system of equations, we find C = 2ln(2), D = 0, and E = 0

Substitute the values of C, D, and E back into the solution:

(-x^2/2)ln(y) - (x^2/2)C + xD + E = (-x^2/2)ln(y) - x^2ln(2)

Finally, evaluate the integral over the region R by substituting the bounds of integration for x and y:

(-2^2/2)ln(2) - 2^2ln(2) = -4ln(2) + 4ln(2) = 0

So, The double integral of (xy y^(-2)) over the region R is equal to 0.

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X = 1 means that we roll exactly 6 in the 3 trials. This means that the probability of rolling a 6 in this situation is 3(0.4)(0.6)2.

The probability of rolling a 6 in any given trial is 0.6 since Mrs. Chauvet's cube is unfair. The probability of getting a 6 in two of the three trials is 3(0.4)(0.6)2, while the probability of rolling a 6 in all three trials is 1(0.6)3. This means that the chance of rolling a 6 in any combination among three trials is the sum of the probabilities of rolling a 6 in each trial (0.6 + 0.6 + 0.6 = 1.8).

The probability of rolling a 6 exactly once in three trials is 3(0.4)(0.6)2, which is the probability of getting a 6 in one of the three trials and not getting a 6 in the other two.

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Answer:

1.59375

Step-by-step explanation:

51 divided by 32 which is 1.59375

to check if you are right you do 1.59375 times 32 which equals to 51

Using the graph of the function f, the relative maxima of function is at x = 3 and is equal to 6.

The graph of the function f is given below:

A relative maximum occurs at an x-coordinated position when the function value is higher than it is compared to nearby places. At that time, the function value is at its relative maximum (y coordinate).

A relative minimum occurs at an x-coordinated location where the function value is the lowest in relation to its neighbors.

The Relative maximum is determined by y's maximum value.

In the graph we can see that;

The greatest value of the y value for x = 3 is 6.

As a result, the function's relative maximum is at x = 3 and is equal to 6.

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The complete question is:

The graph of a function f is given. Use the graph to find each of the following.

The​ numbers, if​ any, at which f has a relative maximum. What are these relative​ maxima?

The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -

f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.

Also, the mean for an exponential distribution is given by u = 1/θ .

In the question it is 22 seconds.

So, the value of θ is 1/22.

Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.

P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -

P(X<x)= F(X) = 1- e^(-θ x) , where x>0.

Putting θ = 1/22 and x= 30 in F(X) , we get -

F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.

So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

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The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -

f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.

Also, the mean for an exponential distribution is given by u = 1/θ.

In the question, it is 22 seconds.

So, the value of θ is 1/22.

Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.

P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -

P(X<x)= F(X) = 1- e^(-θ x) , where x>0.

Putting θ = 1/22 and x= 30 in F(X) , we get -

F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.

So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

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The fully factored form of the equation is 2x(x + 3) (2x - 1) that is option B.

Synthetic division and the rational root theorem can be used to demonstrate this. According to the rational root theorem, p must divide the constant term and q must divide the leading coefficient if p/q is a rational root of the polynomial f(x). The constant term in this example is -6, the leading coefficient is 4, and the potential rational roots are 1, 2, 3, and 6.

When we divide 4x3 + 10x2 - 6x by 2x - 1 using synthetic division, we arrive at the following result:

4x^3 + 10x^2 - 6x = (2x - 1) (2x^2 + 8x + 6)

We can then factor the remaining quadratic, 2x^2 + 8x + 6, as (x + 3)(2x + 2).

Thus, the completely factored form of 4x^3 + 10x^2 - 6x is:

4x^3 + 10x^2 - 6x = 2x(x + 3)(2x - 1)

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The expression to represent the total cost to have 'x' burritos delivered is y = 10x + 5

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

A linear expression can either have two variables or one variable. For example y = 2+3x is an example of linear expression with two variables where x and y are the variable.

Represent the total cost by y

A burritos cost $10 and with $5 delivery fee. This means that the delivery for one burrito will be for x' burrito

therefore y = 10x +5

therefore the equation for x burritos to be delivered is y = 10x+5

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(a) The value of k is 64.

(b) The value of k is 25.

(c) The value of k is 25/4.

What is a trinomial?

An algebraic expression with three terms is called a trinomial. One or more terms in an algebraic expression each have variables and constants. These expressions use separators like +, -, ÷, and × that are symbols or operations. This algebraic expression includes a trinomial, a monomial, a binomial, and a polynomial.

(a)

Given trinomial is x² - 16x+k.

The algebraic identity is (a-b)² = a² -2ab + b²

Now equate  a² -2ab + b² with x² - 16x + k.

x² - 16x + k = a² -2ab + b²

Compare both sides:

x² = a², 16x = 2ab, k = b².

16 = 2b

b = 8

Taking square on both sides:

b² = 64

(b)

Given trinomial is x² + 10x + k.

The algebraic identity is (a+b)² = a² +2ab + b²

Now equate  a² -2ab + b² with x² + 10x + kk.

x² + 10x + k = a² + 2ab + b²

Compare both sides:

x² = a², 10x = 2ab, k = b².

10 = 2b  [Since x = a]

b = 5

Taking square on both sides:

b² = 25

(c)

Given trinomial is x² - 5x + k.

The algebraic identity is (a-b)² = a² -2ab + b²

Now equate  a² -2ab + b² with x² - 5x + k.

x² - 5x + k = a² -2ab + b²

Compare both sides:

x² = a², 5x = 2ab, k = b².

5 = 2b [Since x = a]

b = 5/2

Taking square on both sides:

b² = 25/4

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Answer:

Step-by-step explanation:

Assuming the oatmeal raisin and sugar cookies have an equal probability, it is less likely that a chocolate chip cookie will be picked since the other two cookies have a 37.5% chance of being picked. Despite this, it is still both likely and unlikely since it is only a small difference.

To conclude, it depends on what your teacher or textbook think. If they think a 12.5% difference between the other two cookies means that chocolate chip is unlikely, then it's unlikely. In my opinion, it is not equally but near equally likely and unlikely.

The distance between the ice cream parlor from the movie theater is 5 km.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

            School      

       |                       \

       |                          \

       |                              \   13 km

     12 km                          \

       |                                     \

Ice cream parlor                    Movie theater

Using Pythagorean theorem.

The distance between the ice cream parlor from the movie theater = x

Now,

13² = 12² + x²

169 = 144 + x²

x² = 169 - 144

x² = 25

x = 5

Thus,

The ice cream parlor from the movie theater is 5 km away.

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Answer: The answer is 3.

Step-by-step explanation:

Answer:

Translation and dilation

Step-by-step explanation:

Translation because the points move spaces on the graph, and dilation because it gets bigger/smaller than the other.

The average CPI of the processor is 1.95, which means that on average, it takes 1.95 clock cycles to execute one instruction.

The average CPI such as cycles per instruction of a processor is a measure of its performance.

In a processor with 3 instruction classes, A, B, and C, with relative frequencies of 45%, 35%, and 20% respectively, and individual CPIs of 1, 2, and 4 respectively, the average CPI can be calculated as follows:

Average CPI = (relative frequency of class A * individual CPI of class A) + (relative frequency of class B * individual CPI of class B) + (relative frequency of class C * individual CPI of class C)

Average CPI = (45% * 1) + (35% * 2) + (20% * 4)

Average CPI = 0.45 + 0.70 + 0.80 = 1.95

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Answer: 7/2

Step-by-step explanation: An easy way to calculate slope with two given points is to count the rise (y) between the points (7). Then count the run (x) between the points (2). Then put the rise over the run. 7/2

An expression for the volume V of the rectangular prism in terms of its width w is V = ( 3W³ + 12W² ) Units³

Given data :

we know that

The volume of a rectangular prism is equal to

V = LWH ------> Equation A

where

L is the length

W is the width

H is the height

we know that

L = 3W ----> Equation B

H = W + 4 ------> Equation C

substitute equation B and equation C in equation A

V = ( 3W ) (W) ( W + 4 )

Apply distributive property

V = ( 3W³ + 12W² ) units³

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