. In the cafeteria
3 out of every 5
students prefer
pizza. If there are
200 students in the
cafeteria how many
students prefer
pizza?

The angles associated to the trigonometric equation 2 · tan² θ - 7 · sec θ + 8 = 0 are θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°, θ₂₁ ≈ 120° and θ₂₂ ≈ 240°.

In this question we find a trigonometric equation, that is, an equation involving trigonometric functions, that must be solved for the interval between angles of 0° and 360°. This can be done by algebra properties and trigonometric formulas.

First, write the complete expression:

2 · tan² θ - 7 · sec θ + 8 = 0

Second, use trigonometric formulas and algebra properties to reduce the number of trigonometric functions within the equation:

2 · sin² θ / cos² θ - 7 / cos θ + 8 = 0

2 · sin² θ - 7 · cos θ + 8 · cos² θ = 0

2 - 2 · cos² θ - 7 · cos θ + 8 · cos² θ = 0

6 · cos² θ - 7 · cos θ + 2 = 0

Third, use algebraic subtitution and quadratic formula to determine the roots of the quadratic-like equation:

6 · u² - 7 · u + 2 = 0

u = - 7 / (2 · 6) ± [1 / (2 · 6)] · √[(- 7)² - 4 · 6 · 2]

u = - 7 / 12 ± (1 / 12) · 1

u = - 7 / 12 ± 1 / 12

There are two possibilities:

u₁ = - 2 / 3, u₂ = - 1 / 2

Fourth, find the angles associated to roots by inverse trigonometric functions:

u₁ = - 2 / 3

θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°

u₂ = - 1 / 2

θ₂₁ ≈ 120°, θ₂₂ ≈ 240°

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The correct option is D. 1 − 0. 125 is NOT  the correct way to find the value of fraction 5/8.

Consider the given options;

A. 5÷8

5÷8 = 5/8 (correct)

B. 5⋅0. 125

5*0.125 = 0.625

5*0.125 = 5/8 (correct)

C. 0. 5+0. 125

5+0. 125 = 0.625

5+0. 125 = 5/8 (correct)

D. 1−0. 125

1−0. 125 = 0.785

1−0. 125 = 7/8 (not correct)

Thus, option D is not the correct way to solve the equation.

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The correct question is attached.

Lines running horizontally and vertically are parallel. So, angles A, B, and C are right angles by definition of perpendicular lines. All right angles are equal. Therefore, △ABC ~ △DEF by the SAS similarity theorem.

Given that startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half

Step 1: Multiply both sides of the equation by de:

a/b * de = bc/ef * de

Step 2: Simplify the left side of the equation:

ade = bcde

Step 3: Divide both sides of the equation by ad:

a/d = b/e

Step 4: Multiply both sides of the equation by be:

ab/d = be/e

Step 5: Simplify the left side of the equation:

ab = be

Step 6: Divide both sides of the equation by be:

a/b = 1/e

Step 7: Multiply both sides of the equation by ef:

a/b * ef = 1/e * ef

Step 8: Simplify the left side of the equation:

aef = ef

Step 9: Divide both sides of the equation by ef:

a/b = 1/e

Conclusion: startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half

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Answer:

perpendicular

b and e

congruent

In the given diagram beside a coffee, the value of x is 38.

A diagram is a visual, symbolic representation of data. Diagrams have been used on cave walls since prehistoric times, but they became more common during the Enlightenment. The method occasionally employs the projection of a three-dimensional visualisation onto a two-dimensional surface. Sometimes the word "graph" is used in place of the word "diagram."

We know that all angles here add up to 360°

And with the vertical angles theorem we get the equation

2(36°) + 2(78 - x)° + 2(3x - 10) = 360°

2(36 + 78 - x + 3x - 10) = 360°

2(104 + 2x) = 360°

208 + 4x = 360°

4x = 360 - 208

4x = 152

x = 152/4

x = 38

Thus, In the given diagram beside a coffee, the value of x is 38.

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exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph and if the log term involved in the given function then it is a logarithmic

How do you identify an exponential function from a graph?

Given a graph of a line, we can write a linear function in the form y=mx+b by identifying the slope (m) and y-intercept (b) in the graph. GIven a graph of an exponential curve, we can write an exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph

and if the log term involved in the given function then it is a logarithmic

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Starting out with the fraction of 5/9, Jess would be thinking of the fraction 144/125 at the end of the game if the ten coin flips turn out to be {THTTHTHTTT}.

Since both outcomes are equally likely, the probability of getting heads is 0.5 and the probability of getting tails is also 0.5. Alternatively, the probability of getting H or T in a coin flip is 1.

Probability is an important method for comprehending and making judgments regarding uncertain occurrences in many disciplines, including statistics, finance, and science. It aids in quantifying and forecasting the probability of specific events, enabling us to make better educated choices and comprehend the degree of risk involved with various activities. In summary, probability is a key idea in decision-making and risk management because it is a potent instrument for comprehending and managing uncertainty.

Taking the sequence of coin flips in ten tires, i.e THTTHTHTTT , and starting from the fraction 5/9, the fraction that jess would be thinking at the end of the game can be calculated as,

5/9 * (6/5)^7 *(5/6)^3 , since there are 7 Tails and 3 Heads during the whole game. Which is equal to the fraction 144/125.

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The X-intercept is the point where the line crosses the x-axis. This happens where the Y is equals to zero.

The point slope form of a line is an equation of the line that takes on the form y - y1 = m(x - x1). In this equation, m is the slope of the line, and (x1, y1) is a point on the line. The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. This always happens at the point where y is equal to 0. Therefore, we find the x-intercept of a line in point-slope form by plugging y = 0 into the equation and then solving for x. The point-slope formula is composed of a specific point of coordinates and a slope indicating a type of change over a given variable, such as distance over time. It is said to be as the x-coordinate of a point where a line, curve, or surface intersects the x-axis.

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Line segment theorem states that if a line segment is bisected by another line, then the two parts of the line segment are equal.

This theorem is also known as the Midpoint Theorem. The formula for the Line Segment Theorem is A/B = C/D, where A and C are the two halves of the line segment, and B and D are the distances from the midpoint to the two endpoints of the line segment.

For example, consider a line segment AB with endpoints at A(-3, 2) and B(3, 2). The midpoint of the line segment is at (0,2). To calculate the length of each half of the line segment, we would use the distance formula and plug in the coordinates of the two endpoints and the midpoint.

For half A, the distance is d(A, M) = sqrt[(-3 - 0)^2 + (2 -2)^2] = 3.

For half C, the distance is d(M, B) = sqrt[(3 - 0)^2 + (2 -2)^2] = 3.

Therefore, A/B = 3/3 = 1 and C/D = 3/3 = 1. This confirms that the two halves of the line segment are equal in length.

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The total distance traveled from 0 ≤ t ≤ 7, considering the position function x(t) = t³ - 6t² - 29, is given as follows:

288.75 units.

The position function for this problem is defined as follows:

x(t) = t³ - 6t² - 29.

The total distance traveled over an interval [a,b] is given by the definite integral of the function x(t) over the interval from x = a to x = b.

The definite integral in this problem is calculated as follows:

I = 0.25t^4 - 2t³ - 29t, from t = 0 to t = 7.

Applying the Fundamental Theorem of Calculus, the total distance is calculated as follows:

I = 0.25(7)^4 - 2(7)³ - 29(7) - (0.25(0)^4 - 2(0)³ - 29(0))

I = 288.75 units.

(which is the absolute value of the result of the definite integral).

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4-6 = -2

x/7-6

Substitute

28/7-6

PEMDAS

28/7 = 4

4-6 = -2

(If you're looking for the expression, it's 4-6. But if straight answer, -2)

Answer:

[tex] \sf \: \frac{x}{7} - 6 = - 2[/tex]

Step-by-step explanation:

Given information,

[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]

[tex] \sf \rightarrow \: x = 28[/tex]

Now the value of expression is,

[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]

[tex] \sf \rightarrow \: \frac{28}{7} - 6[/tex]

[tex] \sf \rightarrow \: 4 - 6[/tex]

[tex] \sf \rightarrow \: - 2 = > final \: value[/tex]

Therefore, the answer is -2.

Shortest distance between start and end point is 55.9 miles

According to given statement,

Terry had to travel south 50 miles and then west 25 miles.

We are taking X as a start point and Z is end point.

In triangle XYZ, we are taking angle Y to be of 90 degrees, which qualifies the Triangle XYZ to qualify Pythagorean theorem [The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right angle triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.]

XY = 50 miles

YZ= 25 miles

XZ^2 = XY^2 + YZ ^2

XZ^2 = (50) ^2 + (25) ^2 = 3125

XZ = 55.9

Shortest distance between start and end point is 55.9 miles

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One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.

A mole is a unit of measurement in chemistry that expresses the amount of a substance. It is defined as the number of entities (such as atoms, ions, or molecules) in a sample of the substance. The number of entities in one mole of a substance is known as Avogadro's number.

Avogadro's number is a fundamental constant of physics and chemistry, defined as the number of atoms, ions or molecules in one mole of substance. It is approximately 6.022 x 10^23 and is used in many calculations in chemistry and physics, such as the number of atoms in a sample of an element, the number of ions in a salt, or the number of molecules in a gas sample. The constant is named after Amedeo Avogadro, an Italian scientist who first proposed the concept in 1811.

One mole of a substance is equal to Avogadro's number, which is approximately 6.022 x 10^23.

The mole of H2 (hydrogen gas) is the number of H2 molecules in a sample of hydrogen gas. One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.

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Graph of given system of equations is shown in figure with intersection point (2, 4).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equation is,

⇒ 2x + y = 8

⇒ - x + 2y = 6

By solving both equation , we get;

⇒ (x, y) = (2, 4)

Thus, The graph of system of equation intersect on point (2, 4).

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The gradient of the linear equation 2x + 3y + 6 is (3/2).

The gradient of a linear equation in the form of y = mx + c is m, which represents the slope of the line. The slope is defined as the ratio of the change in y to the change in x. It represents the steepness of the line.

The equation 2x + 3y + 6 is not in the form of y = mx + c. It is in the form of Ax + By + C = 0, which is the general form of a linear equation. To find the gradient of such an equation we need to divide -A/B. In this case, the gradient of the line is -2/3.

The gradient of a line gives us the direction of the line, it is the slope of the line. It tells us how steep the line is and if it is going up or down. A positive gradient means the line is going up and a negative gradient means the line is going down.

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A watch increased in price by 4/5 is priced at £126, then the original price of the watch was £100.

We know that the price of the watch increased by 4/5. To find the original price of the watch, we can use the following formula:

original price = new price / (1 + increase percentage)

In this case, the new price of the watch is £126 and the increase rate is 4/5. So we have:

original price(1 + 4/5) = 126

original price = 126 / (1 + 4/5)

original price = 126 / (1+ 0.8)

original price = 126/1.8

original price = 70

So, the original price of the watch was £70.

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Therefore , the solution to the given problem of linear equation comes out to be T= 64.

Any function that fulfills the algebraic equation y=mx+b is said to be linear. B is the slope, and m is the y-intercept. Since both x and y are factors, the previous sentence is commonly referred to as an equation system with two variables." Two-variable linear equations are referred to as bivariate equations. There are several applications for linear equations: x + z = 2, and 3z - y + z = 3 both have a zero solution. If an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept, it is referred to as linear. The equation is written as Y=mx+b, where m denotes the slope and b the y-intercept.

Here,

Given : 3+ T/2 = 35

thus,

=>  3+ T/2 = 35

=> T/2 = 35-3

=> T/2 = 32 *2

=> T= 64

Therefore , the solution to the given problem of linear equation comes out to be T= 64.

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If the coach buys the packs of Gummi Bears at $0.60 and resales them at $1 , then the percent markup for the candy is (d) 67% .

The price for which the Coach buys Gummi Bears is = $0.60 ;

the price at which the Coach resales them is = $1 ;

So , the Markup is the difference in the price of purchase and price of resale of the candy ,

that means ; the [tex]Markup = \$1 - \$0.60[/tex] ;

= $0.4

So , the Percent Markup is = [tex]\frac{0.4}{0.6} \times 100[/tex]

= 66.66666...

≈ 67% .

Therefore , the percent Markup for the Candy is 67% .

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Answer: HG = CD.

Step-by-step explanation: If you tilt the second triangle so it's flat like the first triangle, you can see that HG is equal to CD.

Han is wrong , we do not agree with him. The value of the 7 in 735,208 is not the 10 times the value of the 7 in 137,342.

The value of 7 here refers to the place value of 7 , in 735,208  7 is at lakhs place whereas in 137,342 , 7 is in thousandth place .

Therefore , Han is wrong as because if we will the 7 in 137,342. when multiplied by 10 will go to the ten thousandth place and not the lakh place.

The  place value is a measure which is used to represent the position of each digit in a number . Based on their position in the number, digits are assigned place values such as ones, tens, hundreds, thousands, ten-thousands, and so on. For example, 1 in 512400 has a place value of ten thousands, i.e. 10000.

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Answer: O x<12

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

5x+25<85

Step 2: Subtract 25 from both sides.

5x+25−25<85−25

5x<60

Step 3: Divide both sides by 5.

5x/5 < 60/5

x<12

The sum of the first 20 terms of the sequence is - 206.25

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence. For example, the series of natural numbers: 1, 2, 3, 4, 5, 6,… is an Arithmetic Progression, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1). Even in the case of odd numbers and even numbers, we can see the common difference between two successive terms will be equal to 2

a + 18d = - 5

a + 14d = -7 1/2

---------------------

4d = -5 + 15/2

8d = -10 + 15

8d = 5

d = 5/8

a + 18(5/8) = -5

8a + 90 = -40

8a = -40 - 90

8a = -130

a = -130/8

The sum of the first 20 will be;

Sum = (20/2) (2(-130/8) + (20-1)(5/8))

Sum = 10 (-260/8 + 95/8)

Sum = 10 (-165/8)

Sum = - 206.25

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Answer:

(-1) & 4/3

Step-by-step explanation:

           3x² - x - 4

Sum = -1

Product = 3*(-4) = -12

Factors = -4 and 3       { (-4)*3 = -12 & (-4) + 3 = -1}

3x² - x - 4 = 3x² + 3x - 4x -4 {Rewrite the middle term using the factors}

               = 3x(x + 1) -4(x + 1)

               =(x + 1)(3x - 4)

x + 1 = 0   ;  3x - 4 = 0

     x = -1  ;          3x = 4

                            x = 4/3

[tex]\sf Zeroes \ of \ the \ polynomial \ are \ (-1) \ and \ \dfrac{4}{3}[/tex]

Verification:

         [tex]\sf 3x^2 - x - 4 = 0\\\\Divide \ the \ entire \ equation \ by \ 3\\\\\\\dfrac{3x^2}{3}-\dfrac{x}{3}-\dfrac{4}{3}=0\\x^2 - \dfrac{x}{3}-\dfrac{4}{3}=0[/tex]

       Coefficient of x = sum of the zeroes

                                  [tex]\sf = -1 + \dfrac{4}{3}\\\\=\dfrac{-3}{3}+\dfrac{4}{3}\\\\=\dfrac{1}{3}\\\\[/tex]

Constant = product of the zeroes

               [tex]\sf = (-1)*\dfrac{4}{3}\\\\=\dfrac{-4}{3}[/tex]

Thus verified.

Answer:

A

Step-by-step explanation:

Se them equal to each other

3x = [tex]x^{2}[/tex] - 4

[tex]x^{2}[/tex] -3x -4 = 0

(x + 1) ( x -4)

x + 1 = 0

x = -1

y = 3x

y = 3(-1)

y = -3

(-1,-3)

x - 4 = 0

x = 4

y = 3x

y = 3(4)

y = 12

(4, 12)

The equation for the maximum number of yards per second that can be run is y = 5/3 s.

A direct variation measurement between distance covered and time taken can be composed as:

y=kx,

where,

This is because the athlete's distance travelled directly varies with the amount of time it takes.

Find k using the given values:

y=kx,

10 = k(6)

k = 10/6

k = 5/3

As a result, the equation for the maximum number of yards per second is y = 5/3 s.

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The slope intercept form of the equation is

y = -1/4x -11/4

One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.

Any location that is not on the line will not fulfill the coordinates.

This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.

The line passes through (1,-3)

slope = -1/4

The equation of the line

y = mx + c

here m is the slope and c is the intercept.

putting the point and slope in the equation

-3 = -1/4 *1 + c

⇒ c = -11/4

So the slope intercept form of the equation is

y = -1/4x -11/4

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The height of the cone is 24.6cm and the volume of the cone is 1/3 * pi * 4^2 * 24.6 = 268.08cm^3

We can start by using the formulas for the surface area of a sphere and the curved surface area of a cone. The surface area of a sphere is given by 4 * pi * r^2, where r is the radius of the sphere. The curved surface area of a cone is given by pi * r * l, where r is the radius of the base of the cone and l is the slant height of the cone.

Given that the surface area of the sphere is five times the area of the curved surface of the cone, we can write the following equation:

4 * pi * (5^2) = 5 * pi * r * l

We can then solve for the slant height l of the cone:

l = (4*5^2) / r

Given that the radius of the cone is 4 cm, we can substitute this into the equation and solve for l:

l = 100/4 = 25cm

The volume of the cone is 1/3 * pi * r^2 * h, where r is the radius of the base and h is the height of the cone.

As we know the slant height and radius of the cone, we can use the Pythagorean theorem to find the height of the cone:

h = sqrt(l^2 - r^2) = sqrt(25^2 - 4^2) = sqrt(625 - 16) = sqrt(609) = 24.6cm

Therefore, the height of the cone is 24.6cm and the volume of the cone is 1/3 * pi * 4^2 * 24.6 = 268.08cm^3

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The number of people who bought fewer than 30 items exists 204.

The frequency distribution of a few data points for one variable is represented graphically by a histogram. Heterogeneous "bins" or "range groups" are frequently used in histograms in order to categorize data and count the number of data points that are part of each bin.

Among graphing tools, the histogram is widely used. It is utilized to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.

As opposed to bar charts, which show categorical variables, histograms visualize quantitative or numerical data. Typically, a histogram's numerical data will be continuous (having infinite values).

Number of people who bought fewer than 30 items

= (0.14 + 0.12 + 0.24)400

= 0.51 x 400 = 204

Therefore, the correct answer is option B) 204.

The complete question is:

The histogram shows the number of items that customers bought during a trip to the grocery store one day. Four hundred customers took a trip to the grocery store that day. Which is the best estimate for the number who bought fewer than 30 items during their trip?

A) 278

B) 204

C) 148

D) 106

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The answer is 4cd/3b

hope it's correct

answer:

b+24

step-by-step explanation:

it’s just asking for the sum so add the two values. there are no other integers given other than 24 so the answer is in expression form. hope that helps!