how do i solve this question

Answer:

Angle VSR = 80 Degrees

Step-by-step explanation:

Straight lines have an equivalent degree of 180, which is half of 360.

Given that VSU's angle equals to 100 degrees, we may subtract 100 from 180 to get the remaining degree created by the other line.

180-100 = 80 Degrees

There are 40 Starbursts in the bag

From the question, we have the following parameters that can be used in our computation:

Pink = 12

30% of the bag are pink

This means that

30% * Bag = pink

Substitute the known values in the above equation, so, we have the following representation

Bag = 12/30%

Evaluate

So, we have the following representation

Bag = 40

HEnce, the amount is 40

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Answer:

$9,481.01

Step-by-step explanation:

The formula for compound amounts is

A = P(1 + r/n)^(nt), where n is the number of compounding periods per year, t is the number of years, P is the initial amount invested and r is the annual interest rate as a decimal fraction.

Here,

A = ($7,200)(1 + 0.023/4)^(12*4)

Evaluating this we get:

A = ($7,200)(1.00575)^48, or

A  = ($7,200)(`1.3168) = $9,481.01

Answer:

9,481.01

Step-by-step explanation:

According to the theory of rational functions, there are no vertical asymptotes at the rational function evaluated at x = 3.

Herein we know that the rational function is q(x) = (x² - 6 · x + 9) / (x² - 8 · x + 15), there are vertical asymptotes for values of x such that the denominator becomes zero. First, we factor both numerator and denominator of the equation to see evitable and non-evitable discontinuities:

q(x) = (x² - 6 · x + 9) / (x² - 8 · x + 15)

q(x) = [(x - 3)²] / [(x - 3) · (x - 5)]

q(x) = (x - 3) / (x - 5)

There are one evitable discontinuity and one non-evitable discontinuity. According to the theory of rational functions, there are no vertical asymptotes at the rational function evaluated at x = 3.

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Answer:

Yes it will

Step-by-step explanation:

A circular coin has circumference 32 pi millimeters. Will the coin fit through a slot that is 35 millimeters long? Explain.

The formula for the circumference of a circle = πD

Where D = Diameter which can also be referred to as the length of the circle

Circumference =32π mm

Hence:

32π = πD

Cancel out the π

D = 32 mm

The diameter of the coin = 32 mm

The length of the slot = 35 mm hence, the coin with a diameter of 32 mm can fit into the slot

Answer:

x = - 6, x = 6

Step-by-step explanation:

Given

x² + 7 = 43 ( subtract 7 from both sides )

x² = 36 ( take the square root of both sides )

x = ± \(\sqrt{36}\) = ± 6

Thus

x = - 6, x = 6

Answer:

x exponent 2=43-7

x^2=36

x=6

Step-by-step explanation:

Answer:(5)(10)

Step-by-step explanation:

Answer:

(5)(10)

Step-by-step explanation:

Answer:

steps below

Step-by-step explanation:

(a) first green: 8/23 AND 2nd green: 7/22

AND: multiplication.. 8/23 x 7/22 = 28/253 ≈ 0.11 (11%)

(b) 15/23 x 8/22

The standard form for the linear equation is y=6a+38.

An equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=5x+3. Where:

a= the slope.

b= the constant term that represents the y-intercept.

For the given example: a=5 and b=3.

The question gives:

- the value of the slope (a) = 6

- the coordinates of a point = (-3,20)

Thus, you can write from the question information :

y=ax+b

20=6*(-3)+b

20=-18+b

b=20+18=38

Therefore, the standard form for the linear equation is:

y=6a+38

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In the total amount of $261,000 received from contributors, a majority of $240,000 came from four contributors, with each contributing $60,000. The remaining $21,000 was obtained from smaller individual contributions.

This statement describes the breakdown of contributions received from different sources. Out of the total amount of $261,000, the majority, which is $240,000, came from four specific contributors. Each of these contributors donated $60,000, resulting in a combined contribution of $240,000. The remaining $21,000 represents the sum of smaller individual contributions from various sources.

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This cadence corresponds to three sets of 24 steps per set, totaling 72 steps per minute. Participants are required to step up and down on a 12-inch step platform for a duration of three minutes, following the 96 BPM rhythm.

The step cadence used during the YMCA 3-minute step test is a set of three stepping cycles per each 20-second period. This means that the participant takes a total of nine steps within each 20-second period. In other words, the participant steps up and down on the platform at a rate of approximately 24 steps per minute. It is important to maintain this consistent step cadence throughout the entire test in order to get an accurate measure of cardiovascular fitness. Overall, the YMCA 3-minute step test is a simple and effective way to assess an individual's aerobic fitness level.

The YMCA 3-minute step test utilizes a specific step cadence to measure an individual's cardiovascular fitness. The answer is that during the test, a cadence of 96 beats per minute (BPM) is used. This cadence corresponds to three sets of 24 steps per set, totaling 72 steps per minute. Participants are required to step up and down on a 12-inch step platform for a duration of three minutes, following the 96 BPM rhythm. Upon completion of the test, the participant's heart rate is measured for a minute to determine their fitness level. The test results can be compared to established norms to gauge overall cardiovascular health and endurance.

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Answer:

I didnt mean to answer

Step-by-step explanation: ignore this

The "critical-value" for a 98% "confidence-level" and a "sample-size" of 16 is approximately 2.602.

We see that the "sample-size" is "n = 16" is small, we use the t-distribution instead of the standard normal distribution.

The "critical-value" for a specific confidence-level and sample-size is determined by the degrees-of-freedom (df), which is equal to n - 1.

So, in this case, the degrees of freedom is 16 - 1 = 15.

We know that the "critical-value" for a 98% confidence level and 15 degrees of freedom. The critical value is approximately 2.602.

Therefore, the required critical-value is 2.602.

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The given question is incomplete, the complete question is

Find the critical value for confidence level "c = 0.98" and sample-size "n = 16". ​

(a) Equations for each of the given distances are as follows; P = (1,-2,3) ;P = (2,3,-4) ;P = (3,-3,5) ; P (x,y,z) with x, y, z > 0;P is distance 12 from P P is distance 9√3 from P P is distance 11 from P.

(b) The equations can be put in the form 2x + 4y - 6z = 130-1  -4x - 6y + 8z = 214-1  -6x + 6y - 10z = 78

(c) The point P is at (x, y, z) = (2.7151, 1.9345, 2.1167).

(d) The solution to the quadratic equation in r using MATLAB is:r = 3.3009 or r = 9.6036

Triangulation is a widely used method in surveying. Triangulation is a method used in surveying to establish the position of a point by forming triangles to it from known points whose positions have already been accurately determined, and then using the principles of plane trigonometry and spherical trigonometry to compute the angles and lengths that determine the position of the unknown point. This is done to locate a position in 3D if the distance to 3 fixed points is known. This is also how global position systems (GPS) work.

A GPS unit measures the time taken for a signal to travel to each of 3 satellites and back, and hence calculates the distance to 3 satellites in known positions.

Given, 3 points in a 3D space, P1 (1,-2,3), P2 (2,3,-4), P3 (3,-3,5) and a point P (x,y,z) with x, y, z > 0,

such that P is distance 12 from P1, distance 9√3 from P2, and distance 11 from P3.

(a) Equations for each of the given distances are as follows;

P = (1,-2,3) ;

P = (2,3,-4) ;

P = (3,-3,5) ;

P (x,y,z) with x, y, z > 0;

P is distance 12 from P P is distance 9√3 from P P is distance 11 from P

(b) The equations can be put in the form

2x + 4y - 6z = 130-1

 -4x - 6y + 8z = 214-1  

-6x + 6y - 10z = 78

To solve these equations using MATLAB, we can put all the equations in the matrix form as shown below:clc;clear all;

x=[ 2 4 -6;-4 -6 8;-6 6 -10];

y=[ 129; 213; 77];

r=x\y;

x=r(1);

y=r(2);

z=r

(c)The solution to the given system of linear equations using MATLAB is:

x = 2.7151

y = 1.9345

z = 2.1167

Therefore, the point P is at (x, y, z) = (2.7151, 1.9345, 2.1167).

(d) Substituting the values found for x, y, z into the equation r = 12 + y + z and solving the resulting quadratic equation in r using MATLAB:

x= 2.7151;

y= 1.9345;

z= 2.1167;

R=[1 -(12+y+z) y*z];

The solution to the quadratic equation in r using MATLAB is:r = 3.3009 or r = 9.6036

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Answer:

\( \frac{x + 4}{6x} = \frac{1}{x} \)

x(x + 4) = 6x

x^2 + 4x = 6x

x^2 = 2x

x = 0, 2

0 is an extraneous solution, so x = 2 is the only solution.

Answer:

they are all equivilent

Step-by-step explanation:

Answer:

B. 0.8, 0.80, 0.800

Step-by-step explanation:

The population size of mountain bighorn sheep after four years will be approximately 374 individuals.

The intrinsic growth rate of a population is the highest possible growth rate without any environmental or other constraints. Exponential growth is a growth pattern that arises when a population increases in size by a set percentage each year. Exponential growth is one method of modeling population growth and is defined by an accelerating growth rate over time.

The mountain bighorn sheep has an intrinsic growth rate of 0.2 per year, and the formula used to estimate the population size after a given number of years is P = P0ert. In this equation, P0 is the initial population size, P is the final population size, e is Euler's number, r is the intrinsic growth rate, and t is the time in years.

Therefore, to calculate the population size of mountain bighorn sheep after four years, we can use the equation as follows: P = P0ert. By substituting the values given in the problem into the equation, we obtain P = 170 x e^(0.2 x 4). Simplifying the equation yields P = 170 x e^0.8, and rounding this number yields P ≈ 373.96.

Hence, the population size of mountain bighorn sheep after four years will be approximately 374 individuals.

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The probability that m balls is P(m balls in first compartment) = (nCm) * ((n-1)^(n-m)) / (n^n).

The total number of possible arrangements of distributing n balls into n compartments is given by n^n. Each ball has n choices for which compartment to fall into, and since there are n balls, we multiply n by itself n times.

Now, let's consider the number of ways m balls can fall into the first compartment. We can choose m balls out of the n balls to go into the first compartment in nCm ways, which is the binomial coefficient.

The remaining (n-m) balls can go into any of the remaining (n-1) compartments in (n-1)^(n-m) ways. Therefore, the probability that m balls will fall into the first compartment is given by:

P(m balls in first compartment) = (nCm) * ((n-1)^(n-m)) / (n^n)

This formula calculates the ratio of favorable outcomes (m balls in the first compartment) to the total number of possible outcomes (all possible arrangements of distributing n balls into n compartments).

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9514 1404 393

Answer:

  (i) collinear

  (ii) not collinear

Step-by-step explanation:

See attached for a plot of the points and the connecting lines.

  (i) collinear

  (ii) not collinear

Answer: -9/2

Step-by-step explanation:

Answer:

x = -9/2

Step-by-step explanation:

Use the law of exponents

(a^p)^q = a^(pq)

here on the left-hand-side

a=3

p=3

q=2x+6

so

(a^p)^q = (3^3)^(2x+6) = 3^(3(2x+6)) = 3^(6x+18)

The right-hand-side = 3^(2x)

Equate exponents of both sides

6x+18 = 2x

6x-2x = -18

4x = -18

x = -9/2

Answer: The answer is 22

Step-by-step explanation: you divide the 36 and the 9 to get 4 then you add the 18 and the 4 to get 22

Answer:

22

Step-by-step explanation:

\(18+(\frac{36}{9})=?\\ 18+4=?\\22=?\)

The zeroes of the function f(x) = x² + 8x + 4 is calculated by shri dharachaya formula negative 0.54 and negative 7.46.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The function f(x) = x² + 8x + 4

The zeroes of the function will be given as

f(x) = 0

Then we have

x² + 8x + 4 = 0

a = 1, b = 8, c = 4

By the formula

\(\rm x = \dfrac{-b \pm \sqrt{b^2 - 4ac }}{2a}\)

Then

\(\rm x = \dfrac{-8 \pm \sqrt{8^2 - 4 * 1 *4}}{2*1}\\\\x = \dfrac{-8 \pm \sqrt{64 - 16}}{2}\\\\x = \dfrac{-8 \pm 4 \sqrt{3}}{2}\\\\x = -4 \pm 2\sqrt3\\\\x = -0.54, -7.46\)

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Answer:

x= -4 +/- 2 \(\sqrt{3}\)

Step-by-step explanation:

The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

We have a rectangular storage container without a lid.

The formula of volume of the box is

V = l × w × h

Where

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

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Container A:

diameter- 7 cm

height- 122 cm

radius- 3.5 cm

SA=2×π×r×r+2×π×r×h

SA=2(3.14)(3.5)(3.5)+2(3.14)(3.5)(122)

SA=76.93+2681.56

SA=2758.49 cm^2

diameter- 11 cm

height- 85 cm

radius- 5.5 cm

SA=2×π×r×r+2×π×r×h

SA=2(3.14)(5.5)(5.5)+2(3.14)(5.5)(85)

SA=189.97+2935.90

SA=3125.87 cm^2

The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.

The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.

Here, we will solve this system of equations using inverse of the matrix method as follows:

We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].

The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33]  where,

d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,

d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,

d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,

d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,

d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,

d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,

d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,

d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,

d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.

We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]

Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]

Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.

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Answer:12

Step-by-step explanation:

Answer:

it's the third one, x is greater than or equal to 25

The amount of money paid by each of the 4 persons will be $33.6.

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 a group of 4 people go to a restaurant and the bill without tax comes to $105.73. The tax is 6%. Remember to round to the nearest hundredth because this is money. After-tax is added, you want to leave a 20% tip on the new total.

Total cost = $105.73 x 1.06 x 120

Total cost = $134.48

Amount for each person,

A = $134.48 / 4

Amount = $33.62

Therefore, the amount of money paid by each of the 4 persons will be $33.6.

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The calculated value of the expression that is equivalent to √(x¹²qr²) is x⁶r√q

From the question, we have the following parameters that can be used in our computation:

√x12qr²

Express properly

So, we have

√(x¹²qr²)

Evaluating the expression in the brackets using the law of indices

So, we have

√(x¹²qr²) = x⁶r√(q)

Next, we open the brackets

This gives

√(x¹²qr²) = x⁶r√q

Hence, the expression that is equivalent to √(x¹²qr²) is x⁶r√q

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