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If ∠A and ∠B are acute angles such that cos A = cos B we have proved that ∠A = ∠B since AC = BC and angles opposite to equal sides of a triangle are equal.

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An acute angle has a degree that is less than 90 degrees, i.e. less than a right angle. Acute angle degrees include 12°, 35°, 48°, 65°, 80°, and 89°. An acute angle triangle (also known as an acute-angled triangle) is a triangle with all of its internal angles being acute angles. Remember that an acute angle is one that is less than 90°. Because all three angles are less than 90°, ABC is an acute angle triangle or acute-angled triangle.

The sine function for the angle yields the ratio of the length of the opposing side to the length of the hypotenuse.

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Yes, BD is the bisector of ∠ABC.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

Given is that ABC is straight angle. BD is drawn so that two adjacent angles are created. It is given that  m ∠ABD = 22x - 9 and m∠ CBD = 4x + 7.

For BD to be the bisector of ∠ABC, ∠ABD and m∠ CBD should be equal. So  we can write -

22x - 9 = 4x + 7

22x - 4x = 16

18x = 16

x = 8/9

Now, we can write -

m ∠ABD = 22x - 9 = 22 x 8/9 - 9 = 10.55°

m ∠ABD = 10.55°                                                    ...... (1)

m ∠CBD = 4x + 7 = 4 x 8/9 + 7 = 10.55°

m ∠CBD = 10.55°                                                    ...... (2)    

m ∠ABD = m ∠CBD                                                

Yes, BD is the bisector of ∠ABC.

Therefore, yes, BD is the bisector of ∠ABC.

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The shape of the bases for the following polyhedron depend on the type of polyhedron. For example, a triangular prism would have triangular bases, a square pyramid would have square bases, a rectangular prism would have rectangular bases, and a cone would have circular bases.

The shape of the bases for a polyhedron depend on the type of polyhedron. Polyhedra can have a variety of shapes, such as triangular, square, rectangular, and circular. For example, a triangular prism would have triangular bases, a square pyramid would have square bases, a rectangular prism would have rectangular bases, and a cone would have circular bases.

The shape of the bases for the following polyhedron depend on the type of polyhedron. For example, a triangular prism would have triangular bases, a square pyramid would have square bases, a rectangular prism would have rectangular bases, and a cone would have circular bases.

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The critical points, sign chart and intervals of increase and decrease is plotted for the function f(x) = x³/4 - 3x.

Critical points - (−2,4) and (2,−4)

Interval of increase - (−∞,−2)∪(2,∞)

Interval of decrease - (-2,2)

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

A continuous function f with x in its domain has a critical point at that point xx if it satisfies either of the following conditions -

f'(x) = 0,

f'(x) is undefined

The given function is f(x) = x³/4 - 3x

So, f'(x) = 3x²/4 - 3

In the graph of the function, only two points are there on the graph where f'(x) = 0, which is -

(x,f(x))=(−2,4)

(x,f(x))=(2,−4)

A sign chart tells you when the value of a function f(x) is negative or positive, which is the same as when the graph of f(x) is below or above the x-axis, respectively.

Draw a solid line when the y-value of the function is greater than zero, which is when f(x)>0.

Draw a dashed line when the y-value of the function is less than zero, which is when f(x)<0.

In the graph it can be seen that the graph is below zero up to x = -3.464 and between x = 0 and x = 3.464. In these intervals the sign chart is dashed. The graph is above the x-axis between x = -3.464 and x = 0 and when x>3.464. In these areas the sign chart is solid.

In the graph it can be clearly seen that the graph is increasing from point -∞ up to -2 and from 2 to ∞.

Also in the graph it can be clearly seen that the graph is decreasing from point -2 up to 2 .

Therefore, the critical points, sign chart and intervals of increase and decrease is found.

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The function f(x) will be : f(x) = 4x and f(2) = 8.

Given is that f(x) is a direct variation function .

        {K} = y/x = constant

It is given that -

f(3) = 12

We can write the slope of f(x) as -

m = (12 - 0)/(3 - 0)

m = 12/3

m = 4

So, f(x) will be -

f(x) = 4x

and

f(2) will be -

f(2) = 8

Therefore, the function f(x) will be : f(x) = 4x and f(2) = 8.

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The results of the x-intercept and y-intercept results from above (39.5, 0) and (x1, y1) and (x2, y2) (0,26.333)

2x + 3y = 79

2x + 3(0) = 79

x1 = 39.5 y1 = 0

the y-intercept

Where the graph crosses the y-axis is known as the y-intercept. We first solve for y before setting x2=0 to determine the y-intercept.

2x + 3y = 79

2(0) + 3y = 79

y2 = 26.333

x2 = 0

To draw a straight line on a graph, you must get two graph points. The format for the plot coordinates is (x1,y1) and (x2,y2).

Thus, we can obtain the graph plots for 2x + 3y = 79 as follows using the results of the x-intercept and y-intercept results from above:

(39.5, 0) and (x1, y1) and (x2, y2) (0,26.333)

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The square centimeters of the cylinder did Mariah paint in terms of π will be 24π cm².

Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,

SA = 2πrh square units

Mariah made a cylinder out of clay that had a radius of 6 cm and a volume of 72π cm³. The height of the cylinder is calculated as,

V = πr²h

72π = π x 6² x h

72 / 36 = h

h = 2 cm

Then the surface area of the cylinder is given as,

SA = 2 x π x 6 x 2

SA = 24π square cm

The square centimeters of the cylinder did Mariah paint in terms of π will be 24π cm².

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The differential equation that represents the relationship is

     dT/dt = - k * ( T - T0 ) from the condtion - dT/dt ∝ ( T - T0 ).

Given:

The engine fluid temperature rate of change, dT/dt

- dT/dt ∝ ( T - T0 )   [proportional to the difference of the fluid's instantaneous temperature, T, and the fluid's original temperature, T0.]

The Differential Equation that represents the relationship.

The framework is already set, there is only one thing that changes the proportionality to an equation. And that is a proportionality constant.

Let's call it 'k'

Since this is a directly proportional set up, the constant 'k' will be multiplied to the term of ( T - T0 )

                            - dT/dt = k * ( T - T0 )

And to make this look like a typical equation, multiply both sides by a -1 to get:

                           ∴ dT/dt = - k * ( T - T0 )

As expected, this comes to represent the same thermodynamic effect you'd see in Newton's Law of Cooling; it is expected because most of all fluids exhibit this cooling effect when interacting with other fluids of differing temperatures.

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Answer:

-1/2

Step-by-step explanation:

use slope formula

it'd be:

\frac{5-7}{-1+5} =\frac{-2}{4} =\frac{x}{y} -1/2\\

The blanks in the equation are filled as below

5 1/8 = 4 + 1 + 1/8 = 4 + 1/8 8 + 1/8 = 5 1/8

To fill the blanks the equation is written completely in figures

5 1/8 = 4 + 1 + 1/8 = 4 +   8 + 1/8 =  

From the knowledge of equality to maintains a true equation the last blank should be equal to 5 1/8.

With this information, we use addition operation to solve for the first blank as follows.

let the first blank be x

4 +   8 + 1/8 = 5 1/8

4 + x * 8 + 1/8 = 5 1/8

4 + 8x + 1/8 = 5 1/8

collection like terms

8x = 5 1/8 - 4 - 1/8

8x = 1

divide both sides by 8

x = 1/8

the blanks are 1/8 and 5 1/8

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The true statement about the sampling distributions is: Both will be approximately normal, and the mean for size 50 will be closer to 26.8 than the mean for size 4.

Thus, option (C) is correct.

According to the Central Limit Theorem, for a large enough sample size, the sampling distribution of the sample mean tends to follow a normal distribution, regardless of the shape of the population distribution.

Therefore, both sampling distributions of size 4 and size 50 will be normal.

Moreover, the mean of the sampling distribution of the sample mean will be equal to the population mean.

Since the population mean is given as 26.8 years, the mean for both size 4 and size 50 will be 26.8 years.

Thus, option (C) is correct.

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The three true statements are:

The standard form of the equation is (x – 1)² + y² = 3.

The center of the circle lies on the x-axis.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

What is the center of the circle?

A circle is named by the point in the center. A radius is a line segment from the center of the circle to the edge. A diameter is a line segment that passes through the center of a circle.

The true statements are:

The standard form of the equation is (x – 1)² + y² = 3.

The center of the circle lies on the x-axis.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Given an equation of x2 + y2 – 2x – 8 = 0, we can make the following observations:

We can complete the square to get the equation in standard form. (x – 1)² + y² = 3². This is true statement.

The center of the circle is (1,0) which is on the x-axis, this statement is true.

The radius is 3 units, which is the same as the radius of the circle x² + y² = 9 (3²). This statement is true.

The center of the circle does not lie on the y-axis as its x-coordinate is not 0.

Hence, The three true statements are:

The standard form of the equation is (x – 1)² + y² = 3.

The center of the circle lies on the x-axis.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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The normalized input admittances are the inverse of the normalized input impedances and can be found on the Smith Chart.

The Smith Chart is a graphical tool used to quickly calculate the reflection coefficient, impedance, admittance, and other characteristics of a transmission line. To find the normalized input admittances corresponding to the normalized input impedances, we first need to find the normalized reflection coefficient for the given normalized input impedances. This can be done by locating the given normalized impedance on the Smith Chart and then determining the normalized reflection coefficient from the radial and angular coordinates. Once the normalized reflection coefficient has been determined, the normalized input admittance can be found by using the formula Y = 1/Z. The normalized input admittance is then located on the Smith Chart in the same manner as the normalized input impedance, using the radial and angular coordinates.

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Answer:11/12

Step-by-step explanation:

The probability of a random variable X with a uniform distribution being greater than 0.49 can be calculated using the formula P(X > 0.49) = 1 - P(X ≤ 0.49).

Since X has a uniform distribution, it means that the probability of any number between 0 and 1 occurring is the same. Therefore, P(X ≤ 0.49) = 0.49.

The probability of X being greater than 0.49 can be calculated using the formula for uniform distributions, which is P(X>a) = 1 - P(X≤a). In this case, P(X>0.49) = 1 - P(X≤0.49). The probability of X being less than or equal to 0.49 can be calculated by multiplying the probability of each individual outcome (since they are all equally likely) by the number of outcomes that satisfy the condition .Substituting this into the formula to calculate P(X > 0.49), we get P(X > 0.49) = 1 - 0.49 = 0.51. Therefore, the probability of a random number generated being greater than 0.49 is 0.51.

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There were 50 single tickets sold and 40 couples tickets were sold.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that is equal.

Let's call the number of single tickets sold "x". Then the number of couple tickets sold would be "y".

We know the total number of attendees is 130, so we can write the equation:

x + 2y = 130

We also know that the total revenue from the ticket sales is $24,000, so we can write another equation using the cost of the tickets:

200x + 350y = 24,000

We now have a system of two equations that we can solve for x and y then we get the values are:

x = 50 and y = 40

So, 50 single tickets were sold and 40 couples tickets were sold.

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The probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal is 0.4608.

The probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal is 0.4608.

P(x < 9.65) = P(Z < (9.65 - 9.70) / 0.03)

= P(Z < -0.17)

= 0.4608

The first step is to calculate the Z-score for 9.65 ounces. To calculate the Z-score, you subtract the mean (9.70 ounces) from the value (9.65 ounces) and then divide by the standard deviation (0.03 ounces). The Z-score in this case is -0.17. The next step is to use a Z-table to find the probability of a Z-score less than -0.17. The probability is 0.4608. Therefore, the probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal is 0.4608.

The probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal is 0.4608.

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Answer: 3 players

Step-by-step explanation: Hello! You know that there are 31 players on the softball team, there are 8 cars in total for everyone to drive in, and there are 4 players in each car for the first 7 cars.  What you have to find out is how many players are traveling in the eighth car.  The first thing that you want to know is how many players are already in the cars.  You already know that 4 players are in each of the 7 cars.  To know how many players are in the 7 cars, multiply the 4 players by the 7 cars.  4 x 7 = 28.  28 players are in the first 7 cars.  You know that there are 31 players in total.  To find the number of players in the last car, subtract the number of players in the first 7 cars from the total amount of players.  31 - 28 = 3.  There are 3 players on the softball team in the eighth car.  Hope this helps!

Answer:

Step-by-step explanation:

The probability that ŕose will choose a science book first is 5/8 and the probability of the adventure book is 3/8

If you solve 3x - 2y = -5 for slope-intercept form, you'd have:

     y = 3/2 x + 5/2

If you solve 3x - 2y = 8 for slope-intercept form, you'd have:

     y = 3/2 x - 4

Since the slopes are the same, but the y-intercepts are different, these lines are parallel.

i. The tangent ratio for ΔRBK is 16/ 38.4

ii. The tangent ratio for ΔHMK is 8/ 19.2

Trigonometric functions are set of functions that are applicable when the side or angle of a triangle is to be determined. Some basic trigonometric functions are: Sine, Cosine, Tangent etc.

The tangent of an angle relates its opposite side to the reference angle with the adjacent side to the same angle.

So that;

Tan θ = opposite/ adjacent

In the given question,

1. From ΔRBK, the tangent ratio is given as;

tan θ = opposite/ adjacent

            = RB/ BK

but BK = BM + MK

           = 19.2 + 19.2

          = 38.4

So that;

tan θ = 16/ 38.4

2. From ΔRBK, the tangent ratio is given as;

tan θ = opposite/ adjacent

        = HM/ MK

tan θ = 8/ 19.2

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The PMF of the number of letters needed to draw to have seen both A and B is pmf(L=k) = $\frac{1}{26 \choose k-1}$ for k = 2, 3, ..., 26. Given that we have already drawn k many cards and neither A nor B have yet appeared, the probability that these two letters will be drawn consecutively is $\frac{2}{26-k}$.

(a) pmf(L=k) = $\frac{1}{26 \choose k-1}$ for k = 2, 3, ..., 26

(b) P(AB or BA | k cards already drawn) = $\frac{2}{26 - k}$

(a) Since the deck is shuffled randomly, we can assume that each of the 26 letters has an equal probability of being drawn. The probability of drawing A and B before any other letter is $\frac{1}{26 \choose k-1}$.

(b) The probability of drawing AB or BA is $\frac{2}{26-k}$, since there are two possible combinations and we have (26-k) cards left to draw.

The PMF of the number of letters needed to draw to have seen both A and B is pmf(L=k) = $\frac{1}{26 \choose k-1}$ for k = 2, 3, ..., 26. Given that we have already drawn k many cards and neither A nor B have yet appeared, the probability that these two letters will be drawn consecutively is $\frac{2}{26-k}$.

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Answer:  ≈ 174.01

Thus, The Sky Scraper  ≈  174.01

Step-by-step explanation:

From his eye, which stands 1.55 meters above the ground, Tyler measures the angle of elevation to the top of a prominent skyscraper to be 57∘

∘. If he is standing at a horizontal distance of 112 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.

1 - Draw Diagrams, Label Knowns:

Unknowns: X

2 - Identify: OPPOSITE, ADJACENT, HYPOTENUSE

3 -  WHAT FUNCTION USES THE OPPOSITE AND THE ADJACENT?

SOH - CAH - TOA

NOW SHOWING WORK:

tan 57 = opposite/adjacent =  x/112

tan 57 = x/112

tan 57/1  = x/112

112 tan 57 = x         ( Cross Multiply)

x = 172.464875    (Now, type into the calculator)

So, Now we ADD:

1.55, the distance from the ground to his eye.

172.464875  +   1.55  =  174.014875

≈ 174.01     (Round to The Nearest HUNDREDTH)

Thus, the Sky Scraper is ≈ 174.01 meters tall.

So, your answer would be :  

Sky Scraper  ≈  174.01

Hope I have explained it and helped you in your studies!

The height of the skyscraper is given by H = 174.01 m

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

We can start by drawing a right triangle, where the horizontal distance from Tyler to the base of the skyscraper is one leg, the height of the skyscraper is the other leg, and the line of sight from Tyler's eye to the top of the skyscraper is the hypotenuse.

Then we can use trigonometry to solve for the height of the skyscraper.

Let the height above the ground from his eye = 1.55 m

Now , the angle of elevation θ = 57°

The horizontal distance from the base of the skyscraper = 112 m

Now , from the trigonometric relations ,

tan θ = opposite / adjacent

So , tan 57° = x / 112

Multiply by 112 on both sides , we get

x = 172.46 m

Now , the total height of the skyscraper = 172.46m + 1.55 m

So , height H = 174.01 m

Hence , the skyscraper has a height of 174.01 m

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Expression that can be used to find -6.3 x -4.2 are

(1): -4.7 - 2.3x + 0.5 - 4x

(2):-5.3x-4.2-x

(3):-3.4-6.3x-0.8

Expression can be defined  as a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction and multiplication

By Collecting like terms and adding the answer I get -6.3x - 4.2

(1):-4.7-2.3x+0.5-4x

Collect like terms

-2.3x-4x-4.7+0.5

-6.3x-4.2

(2):-5.3x-4.2-x

Collect like terms

-5.3x-x-4.2

-6.3x-4.2

(3): -3.4-6.3x-0.8

Collect like terms

-6.3x-3.4-0.8

-6.3x-4.2

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The option are:

-4.7 - 2.3x + 0.5 - 4x

-5.3x - 4.2 - x

-3.4 - 6.3x - 0.8

-6.2x - 4.2

-4.2x - 6.3

-3.7 - 5.3x + 0.5

multiple choice

The sequence from least to greatest is d) √65 < |-7.82| < 7.2/3.

To calculate this, we first need to find the square root of 65, or √65. This can be done using the formula √a = b, where a is the number to be square rooted and b is the result of the square root. In this case, a = 65, so we calculate √65 = 8.062257748. Next, we need to find the absolute value of -7.82, which is |-7.82| = 7.82. . To calculate this, the absolute value formula is used, which is |x| = |x|. Finally, 7.2/3 is the greatest of the three numbers. To calculate this, first convert 7.2/3 to a decimal by dividing it by 3. Then divide 7.2 by the result to get the final answer.Finally, we find 7.2/3, which is equal to 2.4. Therefore, the sequence from least to greatest is √65 < |-7.82| < 7.2/3, or 8.062257748 < 7.82 < 2.4.

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Hong rode the scooter for 61 minutes.

What is the algebra?

Algebra is a branch of mathematics that deals with mathematical equations and their properties. It is a way to represent and solve problems using mathematical symbols, letters and numbers.

We can use algebra to solve for the number of minutes Hong rode the scooter. Let x be the number of minutes Hong rode the scooter.

We know that the total bill is the sum of the start fee and the per-minute fee.

So, we can set up the equation as:

Total bill = start fee + per-minute fee

In this case:

10.88 = 6 + (x * 0.08)

We can then solve for x by isolating it on one side of the equation:

10.88 = 6 + (x * 0.08)

10.88 - 6 = x * 0.08

4.88 = x * 0.08

x = 4.88 / 0.08

x = 61

So, Hong rode the scooter for 61 minutes.

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Answer: [tex]\triangle TUS \cong \triangle QRP[/tex]

Step-by-step explanation:

When naming congruent triangles, corresponding vertices must have the same positions in the names of the triangles.

Answer:

Step-by-step explanation:

When an employer asks for "how many years of basic math experience do you have" on an application, it is generally understood that they are asking for the amount of time you have spent working with basic math concepts in a professional setting. This would typically include time spent working in roles that required the use of basic math skills, such as data entry, accounting, or similar positions.

However, if you have no professional experience in a math-related field but you have studied math in school, you can mention that you have a certain number of years of education in math and that you are familiar with basic math concepts.

It's up to you how many years of math classes you want to include, but it's not necessary to include all the years you've studied math since primary school, it's better to just mention that you have a certain level of education in math, or give an estimate of the number of years that you have studied it in a higher level education like college or university.

It's important to be honest and transparent in your application, but also to highlight the skills and experience that make you a good fit for the role.

The weight gains of beef steers were measured over a 140 -day test period .then mean is 3.545 and median is 3.435

Given

3.89 3.51 3.97 3.31 3.21 3.36 3.67 3.24 3.27

mean = 3.89+3.51+3.97+3.31+3.21+3.36+3.67+3.24+3.27 /10

= 35.45/10

= 3.545

average is the sum of all terms present in the question divided by the number of terms that is the way of calculating average

Solving (a): The mean = 3.545

This is calculated as:

median = 10+1 /2 term

 = 11/2

=5.5 term

So, we have:

median = 3.435

The weight gains of beef steers were measured over a 140 -day test period .then mean is 3.545 and median is 3.435

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