Waymon's weekly earnings for working 40 hours plus 3 hours of working overtime was
S479.27. If $48.47 of that paycheck was overtime pay, what was his hourly rate for the first
40 hours of work?

We can verify that a ⨯ (a ⨯ b) is orthogonal to a. We can solve it in the following way.

To find the cross product a ⨯ b, we can use the formula:

a ⨯ b = |a| |b| sinθ n

where |a| and |b| are the magnitudes of vectors a and b, θ is the angle between a and b, and n is a unit vector perpendicular to both a and b, determined by the right-hand rule.

Using the given vectors a and b, we have:

|a| = √(4² + 5² + 0²) = √41

|b| = √(1² + 0² + 3²) = √10

To find the angle between a and b, we can use the dot product:

a · b = |a| |b| cosθ

4(1) + 5(0) + 0(3) = √41 √10 cosθ

Simplifying:

4 = √410 cosθ

cosθ = 4/√410

θ ≈ 77.09°

Now we can find the cross product using the formula:

a ⨯ b = |a| |b| sinθ n

a ⨯ b = √41 √10 sin(77.09°) n

Using the right-hand rule, we can determine that the unit vector n points in the negative z-direction, so n = -k, where k is the unit vector in the positive z-direction.

Thus, we have:

a ⨯ b = -√410 sin(77.09°) k

Evaluating this expression, we get:

a ⨯ b ≈ -0.667i + 1.777j - 3.617k

To verify that this vector is orthogonal to both a and b, we can take the dot product of a ⨯ b with a and b separately. If the dot product is zero, then the vectors are orthogonal.

a ⨯ b · a = (-0.667)(4) + (1.777)(5) + (-3.617)(0) = 0

a ⨯ b · b = (-0.667)(1) + (1.777)(0) + (-3.617)(3) = 0

Since both dot products are zero, we can conclude that the vector a ⨯ b is orthogonal to both a and b.

Note: The dot product of a vector and its own cross product is always zero, which can be used to verify that a ⨯ (a ⨯ b) is orthogonal to a. In this case, we have:

a ⨯ (a ⨯ b) = (4, 5, 0) ⨯ (-0.667, 1.777, -3.617)

= -17.07i - 6.248j - 12.005k

(a ⨯ (a ⨯ b)) · a = (-17.07)(4) + (-6.248)(5) + (-12.005)(0) = 0

Thus, we have verified that a ⨯ (a ⨯ b) is orthogonal to a.

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I need more info for your problem :

Maybe this could help you :Assume a sector having a radius

Assume a sector having a radius r and a central angle of a degrees.The sector's area will be [tex]A^{2}[/tex] = (a / 360 °)* [tex]\pi[/tex]*[tex]r^{2}[/tex]

The area of an equilateral triangle having a side lenght a is A =( [tex]\sqrt{3}[/tex]/4) * [tex]a^{2}[/tex]

Babby has a 3/4 probability of obtaining the same number of heads as Abby.

Simply put, probability measures how probable something is to occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

The probability of an event happening is determined by probability: P(A) = f / N.

Probability and odds are related, but probability determines what the odds are.

So, the formula for probability is:

P(E) = Favourable events/Total events

Now, insert values:

Babby can get:
TT, HH, HT, TH

Abby will only get: H or T

Then,

P(E) = Favourable events/Total events

P(E) = 3/4

Therefore, Babby has a 3/4 probability of obtaining the same number of heads as Abby.

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Answer: Amount Saved = $23 (answer). In other words, a 50% discount for a item with original price of $46 is equal to $23 (Amount Saved).

Step-by-step explanation:

Answer:

Hope this helps

Step-by-step explanation:

Sum of series is donated by the for formula below

[tex] \sf \: Sn = \frac{n}{2} [2a + (n - 1)d][/tex]

Example 3,6,9,12,...

Let's say we're finding the sum of the 20 series

n = 20, a = 3, d = 6-3 = 3

Where,

n means number of terms

a means the first term

d means the constant value between terms

S20 = 20/2[2(3) + (20-1)d]

S20 = 10[6+19(3)]

S20 = 60 + 570

S20 = 630

Voila!!

Answer:

the answer is A. true

Step-by-step explanation:

I had this question before

Answer:

To graph the image of T(10, -2) after a reflection over the x-axis, you simply need to flip the point vertically so that it lies on the opposite side of the x-axis.

The x-coordinate of the point will stay the same, and the y-coordinate will change sign.

Starting with the point T(10, -2), reflect it over the x-axis to obtain the image point T'(10, 2), which is 10 units to the right of the y-axis and 2 units above the x-axis.

So the graph of T(10, -2) after a reflection over the x-axis is the point T'(10, 2), as shown in the following diagram:

     |

     |

     |

     |

     |

------T'(10, 2)

     |

     |

------x-axis------

     |

     |

     |

     |

     |

     |

     |

Note that the x-axis is the line that runs horizontally through the middle of the diagram, while the y-axis is the line that runs vertically through the middle of the diagram. I hope this helps.

Answer:

After making biscuits, Gene would have 144.15 ounces of flour left

Answer:

D. 16

Step-by-step explanation:

[tex]-\frac{1}{2} n=-8[/tex]

multiply by -2/1 on both sides

[tex](-2)-\frac{1}{2} n=-8(-2)[/tex]

simplify

[tex]n=16[/tex]

Answer:

Step-by-step explanation:

2x + 14 + 3x +3

17 + 5x

x=3.4

Answer:

The maximal area of the rectangle with the perimeter of 20 feet is 5*5 = 25 square feet.

So, the area can not be 26 square feet.

Step-by-step explanation:

Answer:

b = 136°

Step-by-step explanation:

b + 44 = 180°

180° - 44° = 136°

Answer:

see below

Step-by-step explanation:

I am not able to draw graphs or diagrams. However, I can provide a description of how to graph Aaron's data on a set of axes.

Note.The horizontal axis could be marked with a scale of every hour, while the vertical axis could be marked in increments of 2°F to fit all the data.

Surface area of the cylinder in terms of pi, given a diameter of 3.4 inches and a height of 3 inches, is [tex]28.36\pi[/tex] square inches.

To find the surface area of a cylinder in terms of pi, you need to add the areas of the top and bottom circles (which are identical) and the area of the curved lateral surface.

The formula for the area of a circle is [tex]A = \pi r^2[/tex], where r is the radius of the circle. Since the diameter of the circle is given as 3.4 inches, we can find the radius by dividing the diameter by 2:

r = 3.4 / 2 = 1.7 inches

Using this radius, the area of one circle is:

A = [tex]\pi (1.7)^2[/tex] = [tex]9.08\pi[/tex] square inches

Since the cylinder has two identical circles, the total area of both circles is:

2A = 2([tex]9.08\pi[/tex]) = [tex]18.16\pi[/tex] square inches

The lateral surface area of a cylinder can be found by multiplying the circumference of the base circle by the height of the cylinder. The formula for the circumference of a circle is C = 2πr, so the circumference of our circle is:

C =[tex]2\pi (1.7)[/tex]= [tex]3.4\pi[/tex] inches

The height of the cylinder is given as 3 inches, so the lateral surface area is:

A = Ch = ([tex]3.4\pi[/tex])(3) = [tex]10.2\pi[/tex] square inches

To find the total surface area of the cylinder, we add the areas of the two circles and the lateral surface:

Total surface area = 2A + A = [tex]18.16\pi + 10.2\pi[/tex] = [tex]28.36\pi[/tex] square inches

Therefore, the surface area of the cylinder in terms of pi, given a diameter of 3.4 inches and a height of 3 inches, is [tex]28.36\pi[/tex] square inches.

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The two digits are 3 and 2.

A number is a numerical unit of measurement and labeling in mathematics.

The natural numbers 1, 2, 3, 4, and so on are the first examples.

Number words are a linguistic way to express numbers.

Most commonly, specific numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five.

Basic numerals are frequently grouped in a numeral system, which is an ordered manner to represent any number, because only a small number of symbols can be learned.

The most widely used number system is the Hindu-Arabic number system, which enables the depiction of any number using a combination of 10 basic numerical symbols, or "digits."

According to our question-

3+2

=5

Hence, The two digits are 3 and 2.

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Answer:

Step-by-step explanation:

I hope this helps

Answer:

-8/5f - 15

or

-1.6f - 15

Step-by-step explanation:

-2.3f + 0.7f - 12 - 3 =

-8/5f - 15

or

-1.6f - 15

Answer:

[tex] \sf \: -1.6f - 15 [/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ -2.3f + 0.7f - 12 - 3

Let's simplify the expression,

→ -2.3f + 0.7f - 12 - 3

→ (-2.3f + 0.7f) - 12 - 3

→ (-1.6f) + (-12 - 3)

→ -1.6f + (-15)

→ -1.6f - 15

Hence, the answer is -1.6f - 15.

Answer:

99

Step-by-step explanation:

Take the whole shape apart, now, multiply every part on it using the formulas for each.
The area of the two triangle parts is 7.5+7.5=15

the side on the left would be found by doing 5*6=30

the middle side would be 6*6=36

and the right side would be 6*3=18

Add it all up to get 15+30+36+18=
15+66+18=

81+18=

99

As angle Z is bigger than angle Y and angle C must be greater than angle S, we also cannot say that mzC >mZS. The accurate disparity is: mZS >mZC .

An angle is just a geometric shape made up of two rays or splines that meet at a point in the middle known as the vertex. The angle's sides or legs are the rays or dotted lines that make up the angle. T

he standard unit of measurement for angles is the degree, with 360 degrees being one entire circle. Acute angles are those that are less than 90 °, right angles are those that are exactly 90 degrees, obtuse angles are those that are higher than 90 degrees but much less than 180 degrees, & straight angles are those that are exactly 180 degrees.

given

The right response is "mZC > mZS".

The right side of the figure is longer than the left side if RT is bigger than BA. Angle X is greater than angle W, and angle Z is greater than angle Y as a result.

Angles C and S will have the same measure if the triangles are identical because they are matching angles (they are in the same place in each triangle). We are unsure, nevertheless, whether the triangles are comparable.

We cannot therefore assert that mzC = mZS.

As angle Z is bigger than angle Y and angle C must be greater than angle S, we also cannot say that mzC >mZS. The accurate disparity is: mZS >mZC .

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Answer:

a. $76.00

b. y = 23x - 76

Step-by-step explanation:

a. If Anton earned $23 every week for twelve weeks, his total revenue would be 23 (12) = 276 dollars. He only had $200 after paying his parents back, though, so that means if you take away the $200 leftover money he got (after paying his parents back) from the $276 he earned over the 12 weeks, you'll get 276 - 200 = he borrowed $76.00 from his parents.

b. Anton is earning $23 every week, so the money, y, that he'll have after x weeks is y = 23x. But since he borrowed $76 from his parents, that much money should be subtracted from his money-making equation, leaving us with y = 23x - 76. Hope this was helpful!

Answer:

96 ÷ 32 = 3 packs of crayons.

Step-by-step explanation:

The answers for the following questions and fill uos are given below respectively.

Study of correlations between triangles' sides and angles is the focus of the mathematical field of trigonometry.

It solves mathematical problems, especially those involving geometric shapes and motion, by using the properties of triangle angles and sides.

We can use the given side lengths of the right triangle KJL to determine the trigonometric ratios:

sin K = opposite/hypotenuse = KJ/LK = 9/10

cos L = adjacent/hypotenuse = KJ/LK = 9/10

To express these trig ratios as fractions in simplest terms, we can simplify each fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case. Therefore:

sin K = 9/10

cos L = 9/10

Since sin K is the ratio of the opposite side (KJ) to the hypotenuse (LK), it corresponds to angle K. Similarly, cos L is the ratio of the adjacent side (KJ) to the hypotenuse (LK), it corresponds to angle L.

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The ratio of the opposing side (KJ) to the hypotenuse is called sin K, which is equivalent to angle K. (LK). Cos L is the ratio of the neighboring side (KJ) to the hypotenuse and is related to angle L. (LK).

The area of mathematics known as trigonometry focuses on the analysis of relationships between shapes' sides and angles.

It uses the characteristics of triangle angles and sides to answer mathematical problems, particularly those involving geometric shapes and motion.

The trigonometric ratios can be calculated using the side lengths of the right triangle KJL as given:

sin K = opposite/hypotenuse = KJ/LK = 9/10

cos L = adjacent/hypotenuse = KJ/LK = 9/10

We can simplify each fraction by dividing the numerator as well as the denominator by their greatest common factor, which is 1 in this instance, to express these trig ratios as fractions in the simplest possible terms.

sin K = 9/10

cos L = 9/10

Sin K correlates to angle K because it is the ratio of the opposite side (KJ) to the hypotenuse (LK). Similar to cos L, which correlates to angle L, cos L is the ratio of the adjacent side (KJ) to the hypotenuse (LK).

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The radius of the circle is approximately 16 units.

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

Here, ∠PQO = 45° So, ∠QPO = 45°   (because OP = OQ radius)

So, central angle is 90°

The formula of arc length of a circle is :

arc length = [tex]\frac{central angle}{360} * (2\pi r)[/tex]  ; here, the radius of the circle is r

Substituting the values we get:

27 = (90/360) x (2πr)

r = 54/π

Therefore, the radius of the circle is approximately 17.1 units.

by using radius we can find any area in circle.

So, nearby option D. is correct 16 units.

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The probability that at least one game will be rained out during the week is 0.3439

To calculate the probability of at least one rainout, we need to calculate the probability that all four games will be played and then subtract it from 1.

The probability that a game will not be rained out is 1 - 0.1 = 0.9.

Therefore, the probability that all four games will be played is

= 0.9 x 0.9 x 0.9 x 0.9

Multiply the numbers

= 0.6561

So the probability that at least one game will be rained out is

= 1 - 0.6561

Subtract the numbers

= 0.3439

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Answer: 75

Step-by-step explanation:

7+5=75

An equation which is made true by the opposite angles theorem include the following: D. 3y − 15 = 85 + y.

In Mathematics, a parallelogram simply refers to a four-sided geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that is composed of two (2) equal and parallel opposite sides.

According to the opposite angles theorem, the opposite angles of a parallelogram are always congruent or equal and as such, we have the following:

(3y − 15)° = (85 + y)°

Next, we would determine the value of y as follows;

(3y − 15)° = (85 + y)°

3y - y = 85 + 15

2y = 100

y = 100/2

y = 50.

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Answer:

Step-by-step explanation:

the answer is [3y-15=85+y]

The sequence for the number of miles that Amanda will run in the first 10 weeks of her training is

2, 1, 5, 0, 8, 3, 11, 5, 14, 7

What is a sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).

To find the sequence for the number of miles that Amanda will run in the first 10 weeks of her training, we need to first identify the pattern of increasing and decreasing miles she will run each week.

According to the given information, Amanda will start by running 2 miles in the first week.

In the second week, she will run one fewer mile, so she will run 2 - 1 = 1 mile. In the third week, she will run three more miles than she did in the first week, so she will run 2+3=5 miles.

In the fourth week, she will run two fewer miles than she did in the second week, so she will run 1 - 2 = -1 mile.

However, it doesn't make sense for Amanda to run a negative number of miles, so we can assume that she will take a rest week during the fourth week and not run any miles.

Then, she will resume her pattern of increasing and decreasing miles in the following weeks.

Therefore, we can write the sequence for the number of miles that Amanda will run in the first 10 weeks of her training as follows:

2, 1, 5, 0, 8, 3, 11, 5, 14, 7

To obtain this sequence, we applied the given pattern of running one fewer mile in the second week, followed by three more miles in the third week, and then repeating this pattern. We also accounted for the rest week during the fourth week by inserting a 0 in the sequence.

Hence, the sequence for the number of miles that Amanda will run in the first 10 weeks of her training is

2, 1, 5, 0, 8, 3, 11, 5, 14, 7

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