Please help!

Let triangle ABC be an isosceles triangle where angle ABC is congruent to angle BCA. Prove that the sides (AB and AC) opposite the congruent base angles of a triangle are congruent.

Answer:

Step-by-step explanation:

considering A). hemisphere diameter = 48 yd

volume of hemisphere = (2/3)*pi*(r)^3

the radius of hemisphere = diameter/2 = 48/2 = 24 yd

hence, the volume of hemisphere = (2/3)*pi*(24)^3  yd^3

taking pi = 3.14

volume = 28938.24 yd^3 approximately volume = 28940 yd^3

considering B). Circumference of a great circle = 26 m

circumference of sphere = 2*pi*r

therefore r = 4.14 m

volume of sphere = (4/3)*pi*(r)^3

volume of sphere = 297.077 m^3

Answer:

24. A. 28952.9 yd²

B. 297.2 m³

Step-by-step explanation:

24.

A.

diameter=48 yd

radius (r)=diameter/2=48/2=24yd

We have

Volume of Hemisphere= ⅔*πr³=⅔*π*r³

Substituting value

Volume of Hemisphere=⅔*π*24³=28952.9 yd³

B.

Circumference of great circle=2πr=26m

2πr=26

r=26/(2π)

r=4.14

Now

Volume of sphere = 4/3*πr³

Volume of sphere=4/3*π*4.14³=297.2 m³

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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Answer:

I don't get the question

Step-by-step explanation:

Answer:

The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.

Answer:

M=54

Step-by-step explanation:

If you are trying to find the value of M, you add 5 to both sides

M-5+5=49+5

this way the M is all by itself on the left side of the equal sign because -5+5=0

when we combine the like terms we get

M+0=54

therefore M=54

Also 54-5=49

To prepare the employer's September 30 journal entry to record the payroll taxes expense and related liabilities, we need to calculate the amounts for each tax and liability based on the given information.

Let's break it down step by step:

Calculate the FICA Social Security taxes:

The FICA Social Security tax rate is 6.2%, and it applies to the first $137,700 paid to the employee. Since we have one employee, we need to calculate 6.2% of the employee's gross pay. Let's assume the employee's gross pay is $X.

FICA Social Security taxes = 6.2% * $X

Calculate the FICA Medicare taxes:

The FICA Medicare tax rate is 1.45%, and it applies to the entire gross pay of the employee.

FICA Medicare taxes = 1.45% * $X

Calculate the FUTA taxes:

The FUTA tax rate is 0.6%, and it applies to the first $7,000 paid to the employee.

FUTA taxes = 0.6% * $7,000

Calculate the SUTA taxes:

The SUTA tax rate is 5.4%, and it applies to the first $7,000 paid to the employee.

SUTA taxes = 5.4% * $7,000

Thus, the journal entry: Date: September 30

Payroll Taxes Expense $X

FICA Social Security Taxes Payable $A

FICA Medicare Taxes Payable $B

FUTA Taxes Payable $C

SUTA Taxes Payable $D

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The measure of angle x to the nearest tenth of a degree is 51.8°

The figure in the image is a right triangle.

From the image;

To solve for the measure of angle x, we use one of the six (6) trigonometric ratio.

Sine = Opposite / Hypotenuse.

Plug in the given values and solve for angle x.

sin( x ) = 11 units / 14 units.

Take the sine inverse.

x = sin⁻¹( 11/14 )

x = 51.7867

x = 51.8 degrees.

Therefore, the value of x is 51.8 degrees.

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Answer: To find the probability of drawing 2 nickels with replacement from the box, we need to first calculate the total number of possible outcomes. Since we are replacing the coins after each draw, the total number of possible outcomes is simply the product of the number of coins for each type:

Total possible outcomes = (6 + 9 + 3) = 18

To find the number of ways to draw 2 nickels, we can use the combination formula:

Number of ways to draw 2 nickels = C(9,2) = 36

Where C(n,r) represents the number of ways to choose r items from a set of n items without replacement.

Therefore, the probability of drawing 2 nickels with replacement is:

P(2 nickels) = number of ways to draw 2 nickels / total possible outcomes

= 36 / 18 x 18

= 1/2

So the probability of drawing 2 nickels with replacement is 1/2.

Step-by-step explanation:

Using the normal distribution, we have that:

a) There is a 0.6915 = 69.15% chance of a pride of lions having a territory less than 74-square miles.

b) There is a 0.7888 = 78.88% chance of a pride of lions having a territory between 60 and 80 square miles.

c) X = 54.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation are given, respectively, by:

\(\mu = 70, \sigma = 8\)

The chance of a pride of lions having a territory less than 74-square miles is the p-value of Z when X = 74, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (74 - 70)/8

Z = 0.5.

Z = 0.5 has a p-value of 0.6915.

Hence:

There is a 0.6915 = 69.15% chance of a pride of lions having a territory less than 74-square miles.

The change of the territory being between 60 and 80 square miles is the p-value of Z when X = 80 subtracted by the p-value of Z when X = 60, hence:

X = 80:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (80 - 70)/8

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

X = 60:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (60 - 70)/8

Z = -1.25

Z = -1.25 has a p-value of 0.1056.

0.8944 - 0.1056 = 0.7888.

Hence:

There is a 0.7888 = 78.88% chance of a pride of lions having a territory between 60 and 80 square miles.

For item c, we have that X is found when Z = -2, hence:

\(Z = \frac{X - \mu}{\sigma}\)

-2 = (X - 70)/8

X - 70 = -2(8)

X = 54.

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The function g (x) is called an inner function and the function f (x) is called an outer function. Hence, we can also read f [g (x)] as “the function g is the inner function of the outer function f”.

Given that,

f(x) = 2x²+2  and

g(x)=x2-1

So find the (f- g)(x).

(f- g)(x) means,

Multiply x into f and g functions

Then, (f- g)(x) = f(x)-g(x)

Replace with f(x) and g(x) values in this equation

So,

(f- g)(x)= f(x)-g(x)

          = (2x²+2) - (x2-1)

Distribute the subtraction to all three of the last terms.          

          = 2x²+2-2x+1

          = 2x²-2x+2+1

Combine like terms

  (f- g)(x) = 2x²-2x+3

Therefore,

f(x) = 2x²+2 and

g(x)=x2-1,    

So,

       (f- g)(x) = 2x²-2x+3.

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Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.

To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.

So, let's assume that g(x1) = g(x2). Then, we have:

f(x1) = f(x2)

x1(x1-1) = x2(x2-1)

x1^2 - x1 = x2^2 - x2

x1^2 - x2^2 - x1 + x2 = 0

(x1 - x2)(x1 + x2 - 1) = 0

Since x1 and x2 are distinct, we must have x1 + x2 = 1.

But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.

To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.

So, let's solve the equation f(x) = y for x:

x(x-1) = y

x^2 - x - y = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 4y))/2

Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.

Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.

The equation that represents the situation is P = a(2.50) + 80.

And the table;

P     a

80   0

82.5   1

85      2

87.5    3

A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.

Given:

A salesperson who sells computers at an electronics store is Deepa.

$2.50 is a commission for every computer sold.

And the base pay for Deepa is $80.

Let the total pay is P and 'a' represents Deepa's total payments on a day on which she sells a computer.

So, the equation is,

P = a(2.50) + 80

The table;

P     a

80   0

82.5   1

85      2

87.5    3

Therefore, the equation is P = a(2.50) + 80.

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Answer:

Total distance = 5 miles

Step-by-step explanation:

Given:

Total time for drive = 10 min = 10 / 60 = 1/6 hour

Time for stop = 5 min

Speed = 30 miles pr hour

Find:

Total distance

Computation:

Total distance = Speed × time

Total distance = 30 × (1/6)

Total distance = 5 miles

Answer:

•  All non-zero digits in a number are significant.

Example: Numbers 0.0000216, 0.0216, 21.6 and 216 have the same number of significant figures namely three (2, 1, 6).

•  All zeros between two non-zero digits are significant, no matter where the decimal point is, if at all.

Example : In the numbers 0.0000206, 0.0206, 20.6 and 206, the zero lying between the digits 2 and 6 is only significant.

•  If the number is less than 1, the zeroes on the right of decimal point but to the left of the first non-zero digit are not significant.

Example : In 0.0000206, the four zeros after decimal and before the digit 2 has no significance. Similarly, in 0.0206, the zero after decimal and before the digit 2 has no significance. So the number of significant figures of these numbers are three (2, 0 and 6).

Hope this helps, have a nice day/night! :D

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer:

\(\huge\boxed{f(x)=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x}\)

Step-by-step explanation:

\(f(x)=a(x+3)(x-0)(x-7)=ax(x+3)(x-7)\\\\=ax\bigg((x)(x)+(x)(-7)+(3)(x)+(3)(-7)\bigg)\\\\=ax(x^2-7x+3x-21)=ax(x^2-4x-21)\\\\=(ax)(x^2)+(ax)(-4x)+(ax)(-21)\\\\=ax^3-4ax^2-21ax\qquad(*)\\\\f(-8)=-5\)

\(\text{substitute}\ x=-8\\\\f(-8)=(a)(-8)^3-(4a)(-8)^2-(21)(-8)a=-512a-(4a)(64)+168a\\\\=-512a-256a+168a=-600a\\\\f(-8)=-5\\\\\text{therefore}\\\\-600a=-5\qquad|\text{divide both sides by (-600)}\\\\a=\dfrac{-5}{-600}\\\\a=\dfrac{1}{120}\)

\(\text{Substitute to}\ (*):\\\\f(x)=\dfrac{1}{120}x^3-4\cdot\dfrac{1}{120}x^2-21\cdot\dfrac{1}{120}x=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x\)

The ounces of shaving cream will be 230 ounces.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue ,the shaving cream will be:

= 56 ÷ 7/15

= 56 × 15/7

= 120

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Answer:

direction

shape

scatter plots

shape and outliers

Step-by-step explanation:

Correlation is defined as the degree of correspondence between two variables.

When the values increase together, correlation is positive and when one value decreases as the other increases, correlation is negative .

Calculating a correlation can help describe a relation between two quantitative variables' direction and shape. However, it is not sufficient to use a correlation coefficient to describe two variables.  The addition of scatter plots can provide other helpful details such as shape and outliers

The expression can be written as \(90,000(3.71)^{\frac{t}{5} }\)

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.

Given that, we have to express the function \(f(t) = 90,000(1.3)^t\) in the form of \(f(t) = ab^{\frac{t}{5} }\)

Comparing both the functions,

\(b^\frac{t}{5} = (1.3)^t\)

We can write, \((1.3)^t\) as

\((1.3)^t = (1.3^5)^\frac{t}{5}\)

\(= 3.71^\frac{t}{5}\)

Therefore, the equation ca be written as,  \(90,000(3.71)^{\frac{t}{5} }\)

Hence, the expression can be written as \(90,000(3.71)^{\frac{t}{5} }\)

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a) The Reynolds number for a sphere moving in air is 83,333.33.

b) Yes, Based on the Reynolds number, the flow around the sphere is turbulent (Re > 4000).

c) The Reynolds number for a sphere moving in water is 150,000.

a) To calculate the Reynolds number for a sphere moving in air at 15 m/s with a diameter of 10cm, we can use the formula:

Re = (density * velocity * diameter) / viscosity

Where density of air is 1.2 kg/m³, viscosity of air is 1.78 x 10⁻⁵ Ns/m² and diameter is 0.1m.

Re = (1.2 * 15 * 0.1) / (1.78 x 10⁻⁵)

Re = 83333.33

b) Based on the Reynolds number, the flow around the sphere is turbulent (Re > 4000). So, the answer is yes.

c) To calculate the Reynolds number for a sphere moving in water at 15 m/s with a diameter of 10cm, we can use the formula:

Re = (density * velocity * diameter) / viscosity

Where density of water is 1000 kg/m³ and viscosity of water is 0.001 Ns/m².

Re = (1000 * 15 * 0.1) / (0.001)

Re = 150000

Based on the Reynolds number, the flow around the sphere is turbulent (Re > 4000).

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Answer:The symbolism of angel number 1119 is usually related to generosity. It means that you may be a very generous person, but there are people who are ready to abuse your generosity. Angel number 1119 is warning you to be careful because not all people around you have good intentions.

Step-by-step explanation:

Qualitative data is data that cannot be counted easily using numbers is not have the correct definitions.

Qualitative data is used to address the research questionnaire regarding whats and how many(s) or also for research procedures to quantify a problem. This data can be used to compare or count data on a numerical scale.

This type of research typically involves in-depth interviews, focus groups, or observations in order to collect data that is rich in detail and context. This data is used for Qualitative research which is very helpful when understanding social reality and the attributes, beliefs, and motivations of people.

The main importance of this kind of project come into the limelight when someone is trying to understand the reason behind one's beliefs or behaviors.

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Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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Answer:

8 9 16 7 hope this helps

Step-by-step explanation:

I'm not to good with math lol

Answer:

9

Step-by-step explanation:

I believe this is missing part of the equation. But if you are looking for the value of f(x)=3^2x+1 when x=1/2, this is the answer you are looking for.

You will have to substitute the given value into the function and evaluate.

The graph of the function f(x) = 4(2/3)^x is added as an attachment

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

f(x)=4⋅(

2

3

​)

x

Express the equation properly

So, we have

f(x) = 4(2/3)^x

The above expression is a an equation of a exponential function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the equation in a graphing tool and attach the display

See attachment for the graph of the function

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Answer:

no.

Step-by-step explanation:

let's assume that fair means 1/5 effort you should give anything less or more seems like not fair. and 2/5>1/5

Answer:

No.

Step-by-step explanation:

You with your four friends makes five people

if you do 2/5 of the work and rest all does 1/5 of the work then 1 person doesn't have to do the work.

Answer:

4:5

Step-by-step explanation:

The ratio of the perimeter of the two similar shapes is equal to the scale factor of the two similar shapes.