Find measure of angle MNO

Answer:160

formula:y=kx

16=(16)(10)

=160

Step-by-step explanation:

Answer: c=60

Step-by-step explanation: Based on the given conditions, formulate::

15/c= 6/24

By setting up and solving a proportion that represents the ratio of blue counters to total counters in two different scenarios, we find that an estimate for the total number of counters in the bag is 60.

We can set up a proportion to solve this problem. In this case, the counters represent the total numbers in different situations. Initially, there are 15 blue counters out of an unknown total 'x'. Meanwhile, Hussain picked 6 blue counters out of 24. As these are similar situations (picking blue counters out of a total), we can express this as a proportion as follows: 15/x = 6/24 .

To solve this proportion, simply cross multiply and solve for x: 15*24 = 6*x. Simplify this to 360 = 6x. Diving both sides by 6 gives the value of x as 60.

So an estimate for the total number of counters in the bag, or 'x', is 60.

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The solution of missing sides and angle  is:  A = 60°, B = 34.8°, C = 85.2°  a = 4, b = 5, c = √21

Trigonometric functions are used to obtain unknown angles and distances from known or measured angles in geometric drawings.

Basics of Trigonometry deals with measuring angles and problems related to angles. There are six basic trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent. All  important trigonometric concepts  are based on these trigonometric relationships or functions.

Solving a triangle means determining all  its angles and sides. In this case, we are given angle A and sides a and b, and we want to find the remaining angles and sides.

First, we can use the law of cosines c to find the third side:

c² = a²+ b² - 2ab cos(A)

c² = 4² + 5² – 2(4)(5) cos(60)

c² = 16 + 25 - 40 cos (60)

c² = 41-20

c² = 21

c = √21

Now that we have all three sides, we can use the law of cosines to find the remaining angles:

cos(B) = (a²+ c² – b²) / (2ac)

cos(B) = (4²  +(√21)² – 5²) / (2(4) (√21))

cos(B) = (16 + 21 - 25) / (8√21)

cos(B) = 12 / (8√21)

B = cos⁻¹ (12 / (8√21))

cos(C) = (a²+ b² – c²) / (2ab)

cos(C) = (4² + 5² – (√21)²) / (2(4)(5))

cos(C) = (16 + 25 - 21) / 40

cos(C) = 20/40

C = cos⁻¹ (20/40)

Simplifying  trigonometric functions:

B ≈ 34.8°

C = 85.2°

Therefore, the solution is:

A = 60°, B = 34.8°, C = 85.2°

a = 4, b = 5, c = √21

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The right Riemann sum of [tex]\int_1^5f(x).dx[/tex] with 4 rectangles of the function f(x) is 6 square units.

we have to find the area of the function from 1 to 5.

we have to use 4 rectangles.

So, the width of the each rectangle is = (5 - 1)/4 = 4/4 = 1 unit

The figure will be

The right Riemann sum with 4 rectangles will be given by

= [1*5 + 1*4 + 1*0 + 1*(-3)] square units

= (5 + 4 + 0 - 3) square units

= 6 square units.

Hence, the required right Riemann sum is 6 square units.

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The question is incomplete. The complete question will be -

"Given the graph of the function f(x) below, use a right Riemann sum with 4 rectangles to approximate the integral [tex]\int_1^5f(x).dx[/tex]."

Answer:

If the zeroes of a quadratic function are -1 and 6, then its factored form is:

(x + 1)(x - 6) = 0

Expanding the left side:

x^2 - 5x - 6 = 0

So the quadratic function in standard form is:

f(x) = x^2 - 5x - 6

Answer:

f(x) = x^2 - 5x - 6

Step-by-step explanation:

To create a quadratic function with zeroes -1 and 6, we can start by using the zero product property to write out the factors of the equation:

(x + 1)(x - 6) = 0

Expanding the factors, we get:

x^2 - 5x - 6 = 0

This quadratic equation is in standard form with a leading coefficient of 1. Therefore, the quadratic function with zeroes -1 and 6 is:

f(x) = x^2 - 5x - 6

This function can also be graphed on the coordinate plane as a parabola with a vertex at (2.5, -10.25) and its axis of symmetry at x = 2.5. The graph would intersect the x-axis at -1 and 6, confirming that these are the zeroes of the function.

There are a total of 14 possible outcomes, one for each marble in the bag.

The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is selecting a marble from the bag.

There are 14 marbles in the bag in total.

When the first marble is selected, there will be 13 marbles remaining in the bag, then 12, then 11, and so on.

Therefore, the number of outcomes in the sample space is:

3 + 4 + 2 + 5 = 14

There are 14 possible outcomes, one for each marble in the bag.

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Answer:

B and D

Step-by-step explanation:

A and C are linear because they are going in a straight line. E is going downwards, so it is decreasing. That leaves B and D, which have exponential growth.

Answer: 6 units

Step-by-step explanation: To find the mass of the lamina, we need to integrate the density function fi(x,y,z) over the volume of the lamina. The lamina is a portion of the cone z=sqrt(x^2+y^2) between the planes z=1 and z=3. We can express this volume using cylindrical coordinates, where rho is the distance from the origin to the point (x,y,z), phi is the angle between the positive x-axis and the line connecting the origin to the point (x,y,z), and z is the height of the point (x,y,z) above the xy-plane.

We have:

1 <= z <= 3

0 <= rho <= 3sin(phi)

0 <= phi <= 2pi

The density function is given by fi(x,y,z) = x^2z. In cylindrical coordinates, we have x = rhocos(phi), y = rhosin(phi), and z = z. Therefore, we can express the density function as:

fi(rho, phi, z) = (rhocos(phi))^2 * z = rho^2cos^2(phi) * z

The mass of the lamina is given by the triple integral of the density function over the volume of the lamina:

M = ∭ fi(rho, phi, z) dV

= ∫∫∫ rho^2cos^2(phi) * z dz dA

= ∫∫[1,3] ∫[0,2pi] ∫[0,3sin(phi)] rho^2cos^2(phi) * z dz d(phi) drho

= ∫[0,2pi] ∫[0,3] ∫[0,rhosin(phi)] rho^2cos^2(phi) * z dz drho d(phi)

= ∫[0,2pi] ∫[0,3] (1/3)rho^3sin(phi)cos^2(phi) d(phi) drho

= ∫[0,2pi] (1/3)[9sin(phi)cos^2(phi)] d(phi)

= (1/3)[9(2/3)]

= 6

Therefore, the mass of the lamina is 6 units.

The equation of the line that passes through the points (4, 1) and (12, -3) is y = (-1/2)x + 3.

Explain the term equation

An equation is a mathematical statement that expresses the equality of two expressions or values. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to represent relationships between quantities and to solve problems in various fields, including mathematics, physics, and engineering.

According to the given information

We can use the point-slope form of the equation of a line to find the equation of the line that passes through the two given points.

The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

To find the slope of the line that passes through (4, 1) and (12, -3), we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (4, 1) and (x2, y2) = (12, -3)

m = (-3 - 1) / (12 - 4) = -4 / 8 = -1/2

Now that we have the slope of the line, we can use one of the two given points and the slope to find the equation of the line. Let's use the point (4, 1):

y - y1 = m(x - x1)

y - 1 = (-1/2)(x - 4)

Distributing the -1/2, we get:

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

Adding 1 to both sides, we get:

y = (-1/2)x + 3

Therefore, the equation of the line that passes through the points (4, 1) and (12, -3) is y = (-1/2)x + 3.

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Answer: 96 fifth grade students outside for exercise. 48 students playing soccer, 24 students playing basketball, 12 students jogging around the track, and 12 students tossing footballs.

Step-by-step explanation:

Let x be the total number of fifth grade students.

- 1/2x are on the soccer fields

- 1/4x are on the basketball courts

- 1/8x are jogging around the track

- 12 students are tossing footballs

x = 1/2x + 1/4x + 1/8x + 12

x = 4/8x + 2/8x + 1/8x + 12

x = 7/8x + 12

1/8x = 12

x = 12*8

x = 96

Therefore, there are 96 fifth grade students outside for exercise.

Soccer fields: 1/2x = 1/2 * 96 = 48 students

Basketball courts: 1/4x = 1/4 * 96 = 24 students

Jogging around the track: 1/8x = 1/8 * 96 = 12 students

Tossing footballs: 12 students (as given in the problem)

There are 48 students playing soccer, 24 students playing basketball, 12 students jogging around the track, and 12 students tossing footballs.

Answer:

96 students in general

Step-by-step explanation:

I drew an Euler circle to make it more clear. so we can see that 1/8 class = 12

so 1/4 class is 12×2=24

1/2 class is 12×4=48

12+12+24+48=96

I hope this helped

The function ω that gives the length per ruler for the line 3x + 15y = 12y - 45 is:

ω(x) = √(2)

rewrite the equation of the line as:

3x - 3y = -45

The line has a slope of:

m = 3/3 = 1

We choose two points on the line with integer coordinates:

Point 1: (0, 15)

Point 2: (15, 30)

d = √t((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of the two points, we get:

d = √((15 - 0)^2 + (30 - 15)^2)

d = √(225 + 225)

d = √t(450)

d = 15√(2)

Length per ruler = (distance between points) / (total length of line)

3x + 15((3/2)x + 15) = 12((3/2)x + 15) - 45

we simplify this equation, we get:

3x + (45/2)x + 225 = (18/2)x + 180 - 45

Combining like terms, we get:

(57/2)x = 0

Solving for x, we get:

x = 0

Substituting this value of x into the expression for the total length of the line, we get:

y = (3/2)x + 15

y = 15

Length per ruler = (15√(2)) / 15

Length per ruler = √(2)

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the area of the triangle shown is  14 square inches

It is important to note that the formula that is used for calculating the area of a triangle is expressed with the equation;

A = 1/2bh

Such that the given parameters of the equation are;

From the information given, we have that;

b = 3 + h = 3 + 4 = 7 inches

h = 4 inches

Now, substitute the values, we get;

Area = 1/2 (7)(4)

multiply the value and expand the bracket

Area = 1/2(28)

divide the values

Area = 14 square inches

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Answer:

266

Step-by-step explanation:

36 hours x 7 people.

Hope this helps...

Please mark me brainliest.

Answer: 266 hours

Step-by-step explanation:

38 x 7 = 266 hours. Each worker worked 38 hours, and there are 7 people. So, multiply worker by time.

The word problem shows that we only have enough food for 5 days, which means we need to make some tough decisions about who gets to continue to the South Pole and who needs to turn back.

The plan for the rest of the trip involves splitting the group into two parts: 3 members continuing to the South Pole with 2.5 days of food, and 2 members returning to base camp with 2.5 days of food.

28,000 calories / 5,600 calories per day = 5 days of food

So we only have enough food for 5 days, which means we need to make some tough decisions about who gets to continue to the South Pole and who needs to turn back.

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The supplied value 4 is a solution to the equation m + 2(m + 1) = 14.

To solve the equation m + 2(m + 1) = 14 for the supplied value of m = 4, we substitute the value of m into the equation and simplify both sides of the equation.

First, we replace every occurrence of m in the equation with 4:

m + 2(m + 1) = 14

Substitute m with 4

4 + 2(4 + 1) = 14

The parentheses around (4 + 1) indicate that we need to add 4 and 1 together first, before multiplying by 2. This gives us:

4 + 2(5) = 14

We simplify further by performing the multiplication:

4 + 10 = 14

14 = 14

Therefore, when we substitute m = 4 into the equation, we get a true statement. Therefore, 4 is a solution to the equation.

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The closest option among the given options is option B: 120 units².

What is cylinder?

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases.

The formula for the surface area of a right cylinder is:

SA = 2πr² + 2πrh

where r is the radius and h is the height.

Substituting the given values, we get:

SA = 2π(4)² + 2π(4)(11)

SA = 2π(16) + 2π(44)

SA = 32π + 88π

SA = 120π

Using the approximation π ≈ 3.14, we can calculate the surface area to be:

SA ≈ 120(3.14)

SA ≈ 376.8

Therefore, the closest option among the given options is option B: 120 units².

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The best type of graph for the data set below is a bar graph. So the correct option is A.

The pictorial representation of data which is generally grouped, in the form of vertical or horizontal rectangle-shaped bars is called a bar graph. In this type of graph, the length of bars is a representation of the measure of data. They are also called bar charts. In statistics, bar graphs are one of the ways of data handling.

Statistics is the collection, presentation, analysis, organization, and interpretation of data observations. There are various methods for the representation of this statistical data. These can be tables, bar graphs, pie charts, histograms, frequency polygons, etc.

There are three main characteristics of bar graphs. These are:

It helps in comparing the different sets of data among different groups.

The relationship using two axes is shown where the categories are on one axis and the values are on the other axis.

Major changes in data over time are shown.

Therefore the correct option is A.

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The complete question is:

a. The total quantity of employed women among the sample of 7 who are not married yet is the random variable X of interest in this situation. b) Probability = 0.2749.

The number of successes in a defined number of independent trials with two possible outcomes (success or failure) and a constant probability of success are described by a discrete probability distribution called a binomial distribution. The number of trials (n) and the likelihood that a trial will succeed (p) serve as the two parameters that define the binomial distribution.

a. The total quantity of employed women among the sample of 7 who are not married yet is the random variable X of interest in this situation.

b) The probability of 2 women who have never been married is:

P(X = 2) = (7 choose 2) * (0.2)² * (0.8)⁵

P(X = 2) = 21 * 0.04 * 0.32768

P(X = 2) = 0.2749

c) For 2 or fewer have never been married:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X ≤ 2) = (7 choose 0) * (0.2)⁰ * (0.8)⁷ + (7 choose 1) * (0.2)¹ * (0.8)⁶ + (7 choose 2) * (0.2)² * (0.8)⁵

P(X ≤ 2) = 0.0577 + 0.2013 + 0.2749

P(X ≤ 2) = 0.5339

d) The mean is given as:

μ = np

Substitute n = 7 and p = 0.2:

7 * 0.2 = 1.4

Now, the standard deviation is given as:

σ = √(np(1-p)) = √(7 * 0.2 * 0.8) = 1.0198

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Step-by-step explanation:

when we are supposed to find each degrees of a certain angle on an equilateral triangle all we have to know is that a triangle is equal to 180° there for each angle or each line is equal to 180° / 3

Answer:

Draw a picture of Angkor Wat

Answer:

The inequality v ≥ 3 can be satisfied by any number greater than or equal to 3, such as 4, 5, 6.7 etc. The smallest value that will make the inequality true is 3 itself. As long as the number chosen for v is greater than or equal to three then it will satisfy the given equation and make it true.

Step-by-step explanation:

The values that make the inequality v ≥ -3 make true are -3, -2.99, -2.9, and 0.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have the inequality v ≥ -3.

Here the inequality shows that the value is equal to greater than -3.

1. -11 < -3.

2. -8 < -3

3. -6 < -3

4. -4< -3

5. -3.1< 3

6. -3.01 < -3

7. -3.001 < -3

8. -3 = -3

9. -2.999 > -3

10. -2.99 > -3

11. -2.9 > -3

12. 0 > -3

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Answer:

Yes

Step-by-step explanation:

we all know there is 60 minutes in an hour. So in order to answer this question we need to know the percentage of 15 to 60 which is really really just 15/60=0.25 so Henry's answer is correct:
6.25 Hours are 6 hours and 15 minutes

and 0.25 really is just a quarter because 4 x 0.25 = 1 so in fraction it is 1/4 so Jenny is also correct on :

6 1/4 hours are 6 hours and 15 minutes

the correct answer is a reflection across the x-axis.

How to solve questions?

Based on the given image, the type of transformation shown is a reflection across the x-axis.

A reflection is a transformation that flips a figure over a line of reflection, in this case, the x-axis. The resulting image is a mirror image of the original figure, with corresponding points on either side of the line of reflection equidistant from it.

In the given image, polygon ABCD is the preimage, and polygon A'B'C'D' is the resulting image. We can see that the two polygons are mirror images of each other across the x-axis. For example, point A in the preimage is reflected across the x-axis to point A' in the resulting image, which is directly below point A. Similarly, point B in the preimage is reflected to point B', point C to C', and point D to D'.

A 90° clockwise rotation would result in a different orientation of the polygon, where point A would move to the position of point B, point B to C, point C to D, and point D to A. A horizontal or vertical translation would result in a shift of the polygon in the respective direction, which is not the case here.

Therefore, the correct answer is a reflection across the x-axis.

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The solution is, :

(See attachment below)

Here, we have,

we know ,

Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis.

The following information is derived from the graphic:

X-Intercepts: (-3,0), (1,0)

Y-Intercepts: (0,-3)

Vertex: (-1,-4)

Axis of symmetry of the function: x = -1

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Answer:

The length of AB is

[tex] \sqrt{ {5}^{2} + {5}^{2} + {5}^{2} } = \sqrt{75} = 3 \sqrt{5} [/tex]

3√5 cm is about 6.7 cm.

Answer:

  (I₁, I₂) = (1, 1)

Step-by-step explanation:

You want the matrix version of the given circuit equations, and the solution by matrix methods and by Cramer's rule.

The coefficients of the variables fill matrix A; the constants fill matrix (column vector) B:

  AI = B

  [tex]\left[\begin{array}{cc}15&5\\25&5\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}20\\30\end{array}\right][/tex]

The solution to this matrix equation can be found by left-multiplying both sides by the inverse of matrix A. The inverse of a 2×2 matrix is the transpose of the cofactor matrix, divided by its determinant. It can be written down, as the form is simple: diagonal elements are swapped; off-diagonal elements are negated.

  [tex]A^{-1}=\dfrac{1}{15(5)-25(5)}\left[\begin{array}{cc}5&-5\\-25&15\end{array}\right]=\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\\\\\textsf{Multiplying by $A^{-1}$, we have ...}\\\\\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\left[\begin{array}{cc}15&5\\25&5\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\left[\begin{array}{c}20\\30\end{array}\right][/tex]

  [tex]\left[\begin{array}{cc}1&0\\0&1\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}(-0.1)(20+(0.1)(30)\\(0.5)(20)+(-0.3)(30)\end{array}\right]\\\\\\\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}1\\1\end{array}\right][/tex]

Cramer's rule requires we find three determinants. We already found the determinant of the coefficient matrix, above. It is D = -50. The other two are ...

  [tex]D_1=\left|\begin{array}{cc}20&5\\30&5\end{array}\right|=(20)(5)-(30)(5)=-50\\\\\\D_2=\left|\begin{array}{cc}15&20\\25&30\end{array}\right|=(15)(30)-(25)(20)=-50\\\\\\I_1=\dfrac{D_1}{D}=\dfrac{-50}{-50}=1\qquad I_2=\dfrac{D_2}{D}=\dfrac{-50}{-50}=1\\\\\\\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}1\\1\end{array}\right][/tex]

The dimensions of each book are 3 inches by 8 by 9 inches.  The dimensions of the crate cannot be determined from the information provided.

A) The dimensions of the crate are 36 inches by 96 inches by 108 inches.

No. The dimensions of the crate cannot be determined from the information provided.

B) The total volume of the books is 2,592 cubic inches.

Yes. The volume of each book is 3 x 8 x 9 = 216 cubic inches. Therefore, the total volume of 12 books would be 12 x 216 = 2,592 cubic inches.

C) The crate could also hold 24 books that are each 3 inches by 8 inches by 9 inches.

Thus, The crate could not hold 24 books of the given dimensions because each book has a height of 9 inches, and the height of the crate is only 12 inches.

Therefore, the crate can only hold 12 books of the given dimensions.

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Answer:

y= -1/5x-5

Step-by-step explanation:

You can use the slope formula and the slope intercept form which is y=mx+b.