esson Quiz
The ages, in years, of 6 volunteers at the local food pantry are listed below. If a 7th volunteer joins them, what would their age be so that the range of their ages will be 557
(56, 81, 54, 47, 45, 94)
O
S
8
18
10

We know that cos(45) = sin(45) = √2/2.

Substituting these values, we can simplify the expression as follows:

4cos(45) - 2sin(45)

= 4(√2/2) - 2(√2/2) (substituting cos(45) and sin(45) values)

= 2√2 - √2

= √2

Therefore, the answer is √2.

We can use trigonometric relations or Pythagorean's theorem, we will see that x = 8ft.

We can see that x is the hypotenuse of the triangle, and we know the length of one leg and the angle between them, then we can use the cosine trigonometric relation:

cos(60°) = 4ft/x

solving for x:

x = 4ft/cos(60°) = 8ft

Other way to find x is first find the other side and then use the pyhtagorean theorem, to get the other side y we need:

tan(60°) = y/4ft

y = 4ft*tan(60°)

Then using Pythagorean's theorem we get:

x = √( (4ft)² + (4ft*tan(60°))²)

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The pressure using Pete's model based on the information will be 2.79 N/cm³

A trapezium (often known as a trapezoid in some parts of the world) is a four-sided figure with at least one set of parallel lines. These two lines are often referred to as the bases, and the other sides as its legs.

Isosceles Trapezium is a type of trapezium has its legs of equal length, and its base angles possessing an equivalent measure..

Pete has an anvil used for metal working, he models the base as two trapeziums the anvil applied of 834 newton's

The pressure using Pete's model based on the information will be:

= 834 / 299.25

= 2.79 N/cm³

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Answer:

1.54

Step-by-step explanation:

Trapezium=

12+24=36

36 x (length) 15 = 540cm^2

Pressure= force/area

832/540 = 1.54N/cm^2

The matrix operation add -4(row 1) to row 3 is[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]

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

[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\4&-1&6&-8\end{array}\right][/tex]

From the question, we understand that

We are to add -4(row 1) to row 3

This means that

row 3 = row 3 - 4 * row 1

When these values are evaluated, we have

4: 4 - 4 * 1 = 0

-1: -1 - 4 * 2 = -9

6: 6 - 4 * 1 = 2

-8: -8 - 4 * -5 = 12

This means that we relace 4, -1, 6, and -8 in row 3 with 0, -9, 2 and 12

Using the above as a guide, we have the following:

[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]

Hence, the result of the matrix expression is [tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]

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Answer:

surface area=bh+2ls+lb

Step-by-step explanation:

If you think it is too long to remember, just find the area of each of the shapes on it and add them together.

Hope this helps :)

The cost of each chair and table is $2.5 and $8.75 respectively.

Given that the total cost to rent 3 chairs and 2 tables is $25 and total cost to rent 5 chairs and 6 tables is $65.

We need to find the cost of each chair and table,

Let the cost of each chair and table be x and y respectively,

3x+2y = 25.......(i)

5x+6y = 65.........(ii)

Multiply the equation (i) by 3 and subtract ii from i,

9x+6y = 75 - (5x+6y = 65)

4x = 10

x = 2.5

Put x = 2.5 in any equation to find the value of y,

3(2.5)+2y = 25

2y = 17.5

y = 8.75

Hence, the cost of each chair and table is $2.5 and $8.75 respectively.

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This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.

A polynomial f(x) of degree 5 with the given zeros can be represented in factored form as:

f(x) = [tex]A(x - 0)(x - 1)^2(x + 6)(x + 3)[/tex]

Since the leading coefficient is not specified, we can leave A as a constant factor. Simplifying the expression, we have:

f(x) = [tex]A(x)(x - 1)^2(x + 6)(x + 3)[/tex]

This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.

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Answer:

[tex]m = \dfrac{4}{\sqrt{3}} \text{ or, in rational form: } m = \dfrac{4\sqrt{3}}{3}[/tex]

[tex]n = \dfrac{2}{\sqrt{3}} \text{ or, in rational form: } n = \dfrac{2\sqrt{3}}{3}[/tex]

Not sure which form your teacher wants the answers, would suggest putting in both

Step-by-step explanation:

The missing angle of the triangle = 180 - (60 + 90) = 30°

We will use the law of sines to find m and n

The law of sines states that the ratio of each side to the sine of the opposite angle is the same for all sides and angles

Therefore since m is the side opposite 90° and 2 is the side opposite 60°,

[tex]\dfrac{m}{\sin 90} = \dfrac{2}{\sin 60}}\\\\[/tex]

sin 90 = 1

sin 60 = √3/2

So
[tex]\dfrac{m}{1} = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2 \cdot 2}{\sqrt{3}} \\\\m = \dfrac{4}{\sqrt{3}}\\\\[/tex]

We can rationalize the denominator by multiplying numerator and denominator by √3 to get
[tex]m = \dfrac{4\sqrt{3}}{3}[/tex]
(I am not sure what your teacher wants, you can put both expressions, they are the same)

To find n
Using the law of sines we get
[tex]\dfrac{n}{\sin 30} = \dfrac{m}{\sin 90}\\\\\dfrac{n}{\sin 30} = m\\\\\dfrac{n}{\sin 30} = \dfrac{4}{\sqrt{3}}\\\\[/tex]

sin 30 = 1/2 giving

[tex]\dfrac{n}{1/2} = \dfrac{4}{\sqrt{3}}\\\\n = \dfrac{1/2 \cdot 4}{\sqrt{3}} \\\\n = \dfrac{2}{\sqrt{3}}[/tex]

In rationalized form
[tex]n = \dfrac{2\sqrt{3}}{3}}[/tex]

Let's say there are $v$ varsity players and $j$ JV players.

The problem tells us that 2/3 of the varsity players are partnered with 3/5 of the JV players. So the number of varsity players partnered with a JV player is:

$\sf\implies\:(2/3)v$

And the number of JV players partnered with a varsity player is:

$\sf\implies\:(3/5)j$

Since these two numbers represent the same group of paired players, they must be equal:

$\sf\implies\:(2/3)v = (3/5)j$

To find the fraction of players who are partnered, we can divide the total number of paired players by the total number of players:

$\implies\:\frac{(2/3)v}{v} = \frac{2}{3}$ of the varsity players are paired

$\implies\:{\sf{\frac{(3/5)j}{j}} = \frac{3}{5}}$ of the JV players are paired

So the total fraction of players who are paired is:

$\sf\implies\:\frac{2}{3} + \frac{3}{5} - \frac{2}{15}$ (since some players will be counted in both fractions)

Simplifying:

$\sf\implies\:\frac{10}{15} + \frac{9}{15} - \frac{2}{15} = \frac{17}{15}$

Therefore, the fraction of players who are partnered for training is $\frac{17}{15}$, which is greater than 1. This means that the problem may have been set up incorrectly, or there may be additional information missing.

[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]

Answer:

Step-by-step explanation:

15.) [tex]\sqrt{12}[/tex]

      [tex]\sqrt{4}[/tex] * [tex]\sqrt{3}[/tex]

      Answer: 2[tex]\sqrt{3}[/tex]

17.) Distribute 3[tex]\sqrt{3}[/tex] into both sides of the parentheses

     3[tex]\sqrt{3}[/tex] * 4 = 12[tex]\sqrt{3}[/tex]

     3[tex]\sqrt{3}[/tex] * -3[tex]\sqrt{5}[/tex] = -9[tex]\sqrt{15}[/tex]

     Answer: 12[tex]\sqrt{3}[/tex] - 9[tex]\sqrt{15}[/tex]

19.) Distribute 4[tex]\sqrt{15}[/tex] into both sides of the parentheses

      4[tex]\sqrt{90}[/tex] + 4[tex]\sqrt{75}[/tex]

      4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex] + 4*[tex]\sqrt{25}[/tex]*[tex]\sqrt{3}[/tex]

      4*3*[tex]\sqrt{10}[/tex] + 4*5*[tex]\sqrt{3}[/tex]

      12[tex]\sqrt{10}[/tex] + 20[tex]\sqrt{3}[/tex]

21.) Distribute [tex]\sqrt{15}[/tex] into both sides of the parentheses

      2[tex]\sqrt{150}[/tex] - 4[tex]\sqrt{90}[/tex]

      2*[tex]\sqrt{25}[/tex]*[tex]\sqrt{6}[/tex] - 4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex]

      2*5*[tex]\sqrt{6}[/tex] - 4*3*[tex]\sqrt{10}[/tex]

      10[tex]\sqrt{6}[/tex] - 12[tex]\sqrt{10}[/tex]

In the given diagram, angle WAX and angle YAU are vertical angles

From the question, we are to determine if angles WAX and YAU are vertical angles or not

Vertically opposite angles are pairs of angles that are opposite each other and formed by the intersection of two straight lines.

When two straight lines intersect, they form four angles at the point of intersection. Vertically opposite angles are the angles that are opposite each other, that is, they are located on opposite sides of the intersection point and are formed by the pair of opposite rays.

Vertically opposite angles are congruent, which means that they have the same angle measure. This property holds true for any pair of vertically opposite angles, regardless of the angle size or the orientation of the lines.

Hence, angle WAX and angle YAU are vertical angles

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Answer:

Step-by-step explanation:

To find the equation of a circle given three non-collinear points, we can use the following steps:

Find the equations of the perpendicular bisectors of the line segments connecting the pairs of points.

Find the intersection point of the two perpendicular bisectors. This point is the center of the circle.

Find the distance between the center and any one of the three points. This distance is the radius of the circle.

Let's apply these steps to the given points:

Find the midpoint and slope of the line segments connecting the pairs of points:

Midpoint of (-18, -5) and (-7, -16): ((-18+(-7))/2, (-5+(-16))/2) = (-12.5, -10.5)

Slope of (-18, -5) and (-7, -16): (-16 - (-5))/(-7 - (-18)) = -11/11 = -1

Midpoint of (-18, -5) and (4, -5): ((-18+4)/2, (-5+(-5))/2) = (-7, -5)

Slope of (-18, -5) and (4, -5): (-5 - (-5))/(4 - (-18)) = 0

Midpoint of (-7, -16) and (4, -5): ((-7+4)/2, (-16+(-5))/2) = (-1.5, -10.5)

Slope of (-7, -16) and (4, -5): (-5 - (-16))/(4 - (-7)) = 11/11 = 1

The equations of the perpendicular bisectors passing through the midpoints are:

x + 12.5 = -1(y + 10.5) or x + y + 23 = 0

y + 5 = 0

Find the intersection point of the two perpendicular bisectors:

Solving the system of equations:

x + y + 23 = 0

y + 5 = 0

yields: x = -18, y = -5

So, the center of the circle is (-18, -5).

Find the distance between the center and any one of the three points:

Using the distance formula:

Distance between (-18, -5) and (-18, -5): sqrt(((-18)-(-18))^2 + ((-5)-(-5))^2) = 0

Distance between (-18, -5) and (-7, -16): sqrt(((-18)-(-7))^2 + ((-5)-(-16))^2) = sqrt(221)

Distance between (-18, -5) and (4, -5): sqrt(((-18)-4)^2 + ((-5)-(-5))^2) = 22

The radius of the circle is sqrt(221).

Therefore, the equation of the circle in standard form is:

(x + 18)^2 + (y + 5)^2 = 221

The standard equation of a circle with the points (-18;-5), (-7;-16) and (4;-5) is:

(x + 13)² + (y + 1)² = 41

From the question, we are to determine the standard equation of a circle with the given points

The given points are:

(-18;-5), (-7;-16) and (4;-5)

The standard equation of a circle is given by:

(x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle

and r is the radius.

Using the given points (-18, -5), (-7, -16), and (4, -5), we can find the equation of the circle as follows:

Find the midpoint of the line segments connecting the pairs of points:

Midpoint of (-18, -5) and (-7, -16): ((-18 + -7)/2, (-5 + -16)/2) = (-12.5, -10.5)

Midpoint of (-7, -16) and (4, -5): ((-7 + 4)/2, (-16 + -5)/2) = (-1.5, -10.5)

Midpoint of (-18, -5) and (4, -5): ((-18 + 4)/2, (-5 + -5)/2) = (-7, -5)

Find the equations of the perpendicular bisectors of the line segments:

Perpendicular bisector of the line connecting (-18, -5) and (-7, -16):

Slope of the line: (−16 + 5)/(-7 + 18) = -11/5

Slope of the perpendicular bisector: 5/11

Midpoint: (-12.5, -10.5)

Equation: y + 10.5 = (5/11)(x + 12.5)

Perpendicular bisector of the line connecting (-7, -16) and (4, -5):

Slope of the line: (-5 + 16)/(4 + 7) = 11/7

Slope of the perpendicular bisector: -7/11

Midpoint: (-1.5, -10.5)

Equation: y + 10.5 = (-7/11)(x + 1.5)

Perpendicular bisector of the line connecting (-18, -5) and (4, -5):

Slope of the line: 0

Slope of the perpendicular bisector: undefined (perpendicular bisector is a vertical line)

Midpoint: (-7, -5)

Equation: x + 7 = 0

Find the point of intersection of any two perpendicular bisectors:

Intersection of perpendicular bisectors 1 and 2:

y + 10.5 = (5/11)(x + 12.5)

y + 10.5 = (-7/11)(x + 1.5)

Solving for x and y, we get:

x = -13

y = -1

Thus,

The center of the circle is (-13, -1).

Find the radius of the circle:

Using the center (-13, -1) and one of the given points, say (-18, -5):

r² = (-18 - (-13))² + (-5 - (-1))²

r² = 25 + 16

r² = 41

Hence, the equation of the circle is:

(x + 13)² + (y + 1)² = 41.

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Answer:

Step-by-step explanation:

To show that the triangle ABC is a right-angled triangle, we need to prove that one of the angles of the triangle is a right angle, which means it measures 90 degrees.

We can use the Pythagorean theorem to check if the sides of the triangle satisfy the condition for a right-angled triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's find the length of each side of the triangle:

AB = √[(5-2)² + (2-(-3))²] = √(3²+5²) = √34

BC = √[(2-(-8))² + (-3-3)²] = √(10²+6²) = √136

CA = √[(5-(-8))² + (2-3)²] = √(13²+1²) = √170

Now, let's check if the Pythagorean theorem is satisfied:

AC² = AB² + BC²

170 = 34 + 136

Since the Pythagorean theorem is satisfied, we can conclude that the triangle ABC is a right-angled triangle, with the right angle at vertex B.

We know that,

the distance between two points=√(x2-x1)²+(y2-y1)²

∴ The distance between points A and B, AB=√(2-5)²+(-3-2)²

                                                                         =√(9+25)

                                                                         = √(34)

∴ The length of side AB = √(34)

Again,

The distance between points B and C, BC= √[(-8-2)²+{3-(-3)}²]

                                                                      = √(100+36)

                                                                      = √136

∴ The length of side BC =√136

Also,

The distance between points A and D, AC= √(-8-5)²+(3-2)²

                                                                      = √(169+1)

                                                                      = √170

∴ The length of side AC=√170

Now, we get three sides of the triangle as AB = √(34), BC = √136, and AC=√170

Since AC is the longest side, we take it as hypotenuse, and the other sides as base and height in the Pythagoras theorem,

AC²=170

BC²=136

AB²=34

Clearly, 170=136+34

or, AC²=AB²+BC²

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Answer:

To find the coordinates of the point of intersection of the given equations, we need to solve the system of equations simultaneously. We can use the elimination method to do this:

11x - 6y = 2 (multiply both sides by 5)

-8x + 5y = 3 (multiply both sides by 11)

55x - 30y = 10

-88x + 55y = 33

Adding the two equations, we get:

-33x + 25y = 43

Solving for y, we get:

y = (33x + 43)/25

Substituting this expression for y into either of the original equations and simplifying, we get:

x = -1/7

Substituting this value of x into the equation for y, we get:

y = 1/35

Therefore, the coordinates of the point of intersection are (-1/7, 1/35).

The four angles, one in each quadrant, with a common reference angle of with 285° are: 15°, 165°, 195°, 345°

A common reference angle is an angle that is shared by multiple angles in different quadrants when measured from the x-axis. The reference angle for an angle measured in degrees can be found by subtracting the nearest multiple of 90 degrees that is less than the angle.

For the angle 285°, the nearest multiple of 90 degrees that is less than it is 270°. Therefore, the reference angle for 285° is 285° - 270° = 15°.

Using this reference angle, we can find an angle in each quadrant with a common reference angle with 285° as follows:

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Based on the given function conditions of f(x) , the value of f(7) is equal to -6

To find f(7), we need to determine which function definition to use based on the value of x.

Since x = 7 is greater than 5, we know that we'll be using the third definition of the function: f(x) = -x + 1 for 2 < x ≤ 5.

Therefore, we can substitute x = 7 into the third definition of the function:

f(7) = -7 + 1 = -6

So, f(7) = -6.

In summary, to find f(7), we identified which function definition to use based on the value of x. Since x = 7 is greater than 5, we used the third definition of the function, f(x) = -x + 1 for 2 < x ≤ 5, and found that f(7) = -6.

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The answer

4.16666667 yards

Probability that event A or B takes place is, P(A or B) = 16/21.

Here from the Venn diagram we can obtain that,

Probability of occurring event A = 2/21 + 4/21 = (2 + 4)/21 = 6/21

Probability of occurring event B = 10/21 + 4/21 = (10 + 4)/21 = 14/21

Probability of occurring event A and event B both = 4/21

So, P(A) = 6/21

P(B) = 14/21

P(A and B) = 4/21

We know that the union of events formula,  

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 6/21 + 14/21 - 4/21

P(A or B) = (6 + 14 - 4)/21

P(A or B) = 16/21

Hence the value of P(A or B) = 16/21.

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From the interior angle theorem:

The Interior Angle Theorem states that if two secants or chords intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.

Considering the given circles:

m∠AED = ¹/₂(45 + 109)

m∠AED = 77°

m∠AEB = 180 - 77

m∠AEB = 103°

m∠LK = (2 * 62) - 74)

m∠LK = 50°

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Answer:

14

Step-by-step explanation:

28/2 is equivalent to 14. This is because when you divide a number by 2, you are essentially cutting it in half. So, 28/2 is the same as cutting 28 into two equal parts, which is 14.

Answer:

28

2

looks like a fraction but it is actually the whole number 14.

There is an infinity number of equivalent fractions to 28

2

.

To find an equivalent fraction to 28

2

, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:

By dividing the original fraction by 2, we get:

28 ÷ 2

2 ÷ 2

= 14

1

By multiplying the original fraction by 2, we get:

28 × 2

2 × 2

= 56

4

Here is the full list of equivalent fractions to 28

2

.

14

1

, 28

2

, 42

3

, 56

4

, 70

5

, 84

6

, 98

7

, 112

8

, 126

9

, 140

10

, 154

11

, 168

12

, 182

13

, 196

14

, 210

15

, 224

16

, 238

17

, 252

18

, 266

19

, 280

20

...

Answer:

x = 67

Step-by-step explanation:

The two triangles are identail.

Answer:

x = 67

because 67 and x the same

The unit rate that relates the two quantities of distance and volume of gas is:

U = 30 miles per gallon.

To do so, we can find the unit rate.

This would say how many gallons are consumed to drive a unit of distance, or which distance can you drive with one gallon.

Here we have the values:

10 gallons and 300 miles.

Then the unit rate is the quotient between these:

300miles/10 gallons = 30 miles per gallon

This says that with one gallon of gas you can travel 30 miles.

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The total cost of the several items that originally cost $128.25 with a coupon for 35% off and sales tax of 4% is C. $86.70.

The original cost is discounted by 35% using a discount factor of 0.65 and increased by a sales tax factor of 1.04.

After the multiplications, the product shows the total cost that Mary incurred for buying the items.

Original cost of several items Mary is buying = $128.25

Coupon discount = 35%

Discount factor = 0.65 (100 - 35)

Sales tax rate = 4%

Sales tax factor = 1.04 (100 + 4)

The total cost of the items = $86.70($128.25 x 0.65 x 1.04)

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Answer:

Step-by-step explanation:

no

The result of engaging in the row multiplication operation in a matrix would be [ 1 /2   0 | 3 / 4 ]

[ -1   5 | 4 ].

First, you should multiply the first row by the value given of 1 / 4 to be:

( 1 / 4 ) x 2 = 1 / 2

( 1 / 4 ) x 0 = 0

( 1 / 4 ) x 3 = 3 / 4

Then you can replace the values found by the values in the matrix to be :

[ 1 / 2   0 | 3 / 4 ]

[   - 1     5 | 4      ]

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The exponential value decay equation is solved and the value of the vehicle after 11 years is A = $ 13,413

Given data ,

Let the initial cost of the vehicle be = $ 29,800

Now , the rate of depreciation be r = 7 %

Let the number of years be n = 11 years

And , the exponential decay is given by the equation ,

x ( t ) = x₀ × ( 1 + r )ⁿ

On simplifying , we get

x ( 11 ) = 29800 ( 1 - 0.07 )¹¹

x ( 11 ) = 29800 ( 0.93 )¹¹

x ( 11 ) = 13,413.085

Hence , the cost of the vehicle after 11 years is A = $ 13,413

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The percentage increase in the number of water bottles the company manufactured from February to April is 19%.

In March, the company manufactured 7% more water bottles than in February:

Number of water bottles in March = 4,100 + 7% of 4,100

Number of water bottles in March = 4,387

In April, the company manufactured 500 more water bottles than in March:

Number of water bottles in April = 4,387 + 500

Number of water bottles in April = 4,887

To find the percent increase from February to April, we can use the following formula:

percent increase = (new value - old value) / old value x 100%

percent increase = (4,887 - 4,100) / 4,100 * 100%

percent increase = 787 / 4,100 x 100%

percent increase = 19%

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Based on the information given, it is not possible to determine whether the sample may be biased or not.

However, there is a possibility that the sample may be biased if the company's computer database does not accurately represent its entire customer base. For example, if the database contains only a specific type of customers, such as those who frequently make large purchases, then the sample may not be representative of the company's entire customer base. In this case, the survey results may not accurately reflect the opinions of all the company's customers.

It is also important to consider other factors such as how the survey was conducted and how the questions were framed, as these can also affect the validity of the survey results

Answer:

3π

Step-by-step explanation:

Given

Radius=9

Angle=60°

Since PQ is an arc

Perimeter of an Arc =(θ/360)×2πr

60/360×2π(9)

1/6×18π

3π