Determine if this equation is true or false:

By proportion formula and Pythagorean theorem, the length of line segment AB is equal to 8 units.

Herein we find a geometric system formed by two similar right triangles, then we can determine the length of side BD by following proportion formula:

BD / AD = CD / BD

BD² = AD · CD

BD = √(AD · CD)

And the length of the line segment AB can be determined by Pythagorean theorem:

AB = √(BD² + AD²)

If we know that AD = 4 and CD = 12, then the length of the line segment AB is:

BD = √(4 · 12)

BD = √48

BD = 4√3

AB = √[(4√3)² + 4²]

AB = 8

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Answer:

unfortunately tdudeyiutddj try Zurich etu

The correct symbol for the given equation in the blank is the sign of non-equal to that ≠.

Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

here, we have,

Let's solve the given equation,

3 (3+4) = 3³

3 (7) = 27

21 ≠ 27.

Therefore, it shows that LHS ≠ RHS.

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Answer:

The first thing you want to d is find out how many centimeters are in 1 foot, because if a flat bar cost 2 pesos per centimeter, and they want 1 foot, then you will multiply how many centimeters in 1 foot, by how much each centimeter cost: 2 pesos:

There are exactly 30.48 centimeters in 1 foot, so you will multiply that by 2:

2 * 30.48 = 60.96

It will cost 60.96, or rounded up to 61 pesos for a 1 foot flat bar.

Step-by-step explanation:

Hope it helps! =D

Answer:

25

Step-by-step explanation:

Let's assume the number of boys in the class is "x". Then, according to the problem, the number of girls in the class is 2.5 times the number of boys, which can be expressed as:

number of girls = 2.5 * number of boys

We also know that the total number of students in the class is 35. Therefore, we can write an equation in terms of "x" as follows:

x + 2.5x = 35

Simplifying the above equation, we get:

3.5x = 35

Dividing both sides by 3.5, we get:

x = 10

This means that there are 10 boys in the class. To find the number of girls, we can use the equation we derived earlier:

number of girls = 2.5 * number of boys

number of girls = 2.5 * 10 = 25

Therefore, there are 25 girls in the class.

The supplied statement states that the candle would reach a height of 14.85 cm after 24 hours.

The terms "altitude" and "elevation" refer to the vertical distance between something's top and bottom or its base and it's something above it. Height is used to describe everything that may be measured vertically, high or low.

Let Y = height.

let X equal time

Y = mX + b, where the slope of m & b is the y-intercept, denotes the linear relationship between height and time.

We can determine the slope using the information provided (13, 15.4) and (29, 6.5)

Slope = (y2 - y1) / (x2 - x1) = (6.5 - 15.4) / (29 - 13) = -8.9 / 16 = -0.55

This indicates that the candle is losing height at a rate of 0.55 cm each hour.

As the first grid cell of 24 hours comes 13 hours afterwards, (13, 15.4), the height will go down by 13 * (-0.55) = -7.15 cm in the 13 hours between hour 13 and hour 24.

Hence, the candle's height 24 hours later = 15.4 - 0.55 = 14.85 centimeters

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The solutions of the system of inequalities are:

(0, 3)

(6, 2)

Here we have the graph of a system of inequalities, the solutions are all the points on the area where the two shaded regions intercept (it would be on the purple area).

And we can see that one line is solid, the points on that line are solutions, the other line is dashed, the points on that line are not solutions.

Then the points that are solutions are:

(0, 3)

(6, 2)

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This expression gives the mean number of coupons you will need to collect before you have a complete set, given that each coupon obtained is equally likely to be any one of the c types.

In general, probability is a measure of the likelihood that a certain event or outcome will occur. It is a branch of mathematics concerned with analyzing and quantifying uncertainty. In formal terms, the probability of an event is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. Probabilities between 0 and 1 represent the degree of uncertainty associated with the event.

Here,

The probability that the first n coupons collected do not form a complete set can be found as follows:

Let S be the event that the first n coupons do not form a complete set, and let Ci be the event that the i-th coupon collected is a new type (i.e., a coupon of a type that has not been collected before).

Then, the event S can be expressed as the intersection of the events C1, C2, ..., Cn, where each Ci is independent of the others and has probability (c-i+1)/c of occurring. This is because there are c-i+1 types of coupons remaining after i-1 types have been collected, and each of these types is equally likely to be the next coupon collected.

So, the probability of S can be calculated as:

P(S) = P(C1 ∩ C2 ∩ ... ∩ Cn) = P(C1) × P(C2) × ... × P(Cn)

= (c-1)/c × (c-2)/c × ... × (c-n+1)/c

= Π(i=1 to n) (c-i+1)/c

To deduce an expression for the mean number of coupons you will need to collect before you have a complete set, let X be the random variable representing the number of coupons collected until a complete set is obtained. Then, the expected value of X can be calculated using the formula:

E(X) = Σ(k=1 to c) P(X ≥ k)

This formula sums the probabilities of all possible numbers of coupons collected until a complete set is obtained, weighted by their respective probabilities.

Note that P(X ≥ k) is the probability that a complete set has not been obtained after k-1 coupons have been collected, which is equal to the probability of the event S above. So, we can substitute the expression for P(S) into the formula for E(X) to get:

E(X) = Σ(k=1 to c) P(X ≥ k)

= Σ(k=1 to c) Π(i=1 to k-1) (c-i+1)/c

= Σ(k=1 to c) Π(i=0 to k-2) (c-i)/c

= Σ(k=0 to c-1) Π(i=0 to k-1) (c-i)/c (by changing the index of summation)

= Σ(k=0 to c-1) (c-k)/cˣ

= c Σ(k=0 to c-1) (1/c)ˣ - Σ(k=0 to c-1) (k/c)ˣ

= c (1 - (1/c)ˣ)/(1 - 1/c) - B(c, 1/c)

where B(c, 1/c) is the sum of the first c terms of the series (k/c)ˣ.

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The equation and solution to find the length of mis teak wood piece is x=3*8 and 24.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The length of oak wood=8inches

Teak wood= 3* oak wood

Now,

Let the length of teak wood be x

Then,

x=3*8

x=24

Therefore, by algebra the answer will be 24.

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A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.

Step-by-step explanation:

f(x)= x¹ - x² +9

g(x) = x³ + 3x² + 12

To find (f-g)(x):

The operations on functions are as easy as the operations on numbers or polynomials.

We have to subtract the functions to find the above mentioned operation.

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

         = (x¹ - x² +9)-(x³ + 3x² + 12)

The minus will change the signs of function g.

Answer:

3 students

Step-by-step explanation:

Now for RSM Olympiad are 8 math kangaroo are 7 studs that did both are 4

Total number of studs that participated are

(8-4) + 4 + (7-4)

4+4+3=11

those who didn't participate are

11-14-13

The value of standard matrix of T is,

⇒ [tex]\left[\begin{array}{ccc}1&-2&3\\- 4&9&- 8\\\end{array}\right][/tex]

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

Given that;

Define T : R³ to R² as;

⇒ T(e₁) = (1, 4), T(e₂) = (-2,9), T(e₃) = (3,-8),

where e₁, e₂, and e₃ are the columns of the 3x3 identity matrix.

Now, The value of the standard matrix of T is,

T = [ T(e₁)   T(e₂)   T(e₃)]

  =  [tex]\left[\begin{array}{ccc}1&-2&3\\- 4&9&- 8\\\end{array}\right][/tex]

Therefore, The value of standard matrix of T is,

⇒ [tex]\left[\begin{array}{ccc}1&-2&3\\- 4&9&- 8\\\end{array}\right][/tex]

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Answer:

1.15%

Step-by-step explanation:

Step-by-step explanation:

the answer is 2(l+b) and it is verified

Applying the secant-tangent theorem, the value of x is calculated as: x = 5.

The secant-tangent theorem states that if there is a point outside of a circle and we draw a tangent line and a secant line from that point to the circle, then the length of the tangent line squared is equal to the length of the secant line multiplied by the length of the part of the secant line that is outside the circle.

Therefore, applying the secant-tangent theorem:

4 * (x + 4) = 6²

4x + 16 = 36

4x = 36 - 16

4x = 20

4x/4 = 20/4

x = 5

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Answer:

x ∈ R or (-∞,∞)

Step-by-step explanation:

The equation |x - 5| > -2 results in true for all x-values. No matter which x-values you substitute in the absolute value; positive, negative real numbers or zero, you'll always end up with the positive value which is greater than negative

Therefore, |x - 5| > -2 is true for all real x-values.

The probability that the individual must stop at at least one light that is 0.45.

Probability is the mathematical tool or procedure of predicting how likely a given event is going to happen.

Given is that there are two traffic lights on the route used by a certain individual to go from home to work. Let {E} denote the event that the individual must stop at the first light, and define the event {F} in a similar manner for the second light. Suppose that -

We can write -

P{E ∪ F} = P{E} + P{F} - P{E ∩ F}

P{E ∪ F} = 0.4 + 0.2 - 0.15

P{E ∪ F} = 0.6 - 0.15

P{E ∪ F} = 0.45

Therefore, the probability that the individual must stop at at least one light that is 0.45.

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Answer:

Step-by-step explanation:

Finally, we got the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 28 are written as 2 × 2 × 7 or 22 x 7, where 2 and 7 are the prime numbers.

Answer:

Step-by-step explanation:

a. The average rate of change in DVD sales during this period can be calculated as:

average rate of change = (change in DVDs sold) / (change in years)

We are given that in 2011, 6.1 billion DVDs were sold, and in 2021, 1.2 billion DVDs were sold. The change in DVDs sold is:

change in DVDs sold = 1.2 billion - 6.1 billion = -4.9 billion

The change in years is:

change in years = 2021 - 2011 = 10

So the average rate of change in DVD sales during this period is:

average rate of change = (-4.9 billion) / 10 = -0.49 billion DVDs per year

Therefore, DVD sales declined by an average of 0.49 billion per year during this period.

b. Using the numbers in 2011 as an initial value, we can write a linear model that models the number of DVD sales worldwide as:

DVD sales = -0.49(t - 2011) + 6.1

where t is the year and DVD sales are measured in billions.

c. If the rate stays the same, we can predict the number of DVD sales in the year 2023 by substituting t = 2023 into the linear model and solving for DVD sales:

DVD sales = -0.49(2023 - 2011) + 6.1 ≈ 0.5 billion DVDs

Therefore, if the rate of decline in DVD sales stays the same, we can predict that there will be about 0.5 billion DVDs sold worldwide in 2023.

Finally, we can use the earlier equations to find the number of bass and bluegills in pond B:

2x + 6y = 300

2(15) + 6(45) = 300

30 + 270 = 300

Therefore, pond B has 30 bass and 270 bluegills.

In algebra, a statement of mathematics that proves the equality of two mathematical expressions is known as an equation. Consider the equation 3x + 5 = 14, where the word "equal" is used to denote the relationship between the terms 3x + 5 and 14.

Let's denote the number of bass in pond A as "x" and the number of bluegills in pond A as "y".

According to the problem, Gage stocks pond B with twice the amount of bass as pond A, so the number of bass in pond B is 2x. He also stocks pond B with six times the amount of bluegills as pond A, so the number of bluegills in pond B is 6y.

We know that Gage stocks pond A with a total of 60 fish, so:

x + y = 60

We also know that Gage stocks pond B with a total of 300 fish, so:

2x + 6y = 300

x + 3y = 150

Now we have two equations:

x + y = 60

x + 3y = 150

We can solve for x in the first equation:

x = 60 - y

Substitute this expression for x into the second equation:

(60 - y) + 3y = 150

2y = 90

y = 45

Now that we know that pond A has 45 bluegills, we can use the equation x + y = 60 to find that pond A has 15 bass (since 45 + 15 = 60).

2x + 6y = 300

2(15) + 6(45) = 300

30 + 270 = 300

Therefore, pond B has 30 bass and 270 bluegills.

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Answer:

30 cm²

Step-by-step explanation:

The formula to find the area of a parallelogram.

Area = Base × Height

Accordingly, let us find the area.

Area = Base × Height

Area = 10 cm × 3 cm

Area = 30 cm²

Answer:

14

Step-by-step explanation:

So, 49 divided by 7 is 7 so there are 7 groups of 7 strawberries. With each of those 7 groups there are 2 blueberries. So, you are then going to multiply 7 by 2 and that gives you 14 blueberries.

The area of the blue-shaded region is 19.95 m²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,

Using the Pythagoras theorem,

15.5² = 14²+w² [width]

w² = 240.25-196

w² = 44.25

w = 6.65

Therefore, the width of the rectangle is 6.65 m

That mean, the height of the parallelogram is 6.65 m,

The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,

Area of the remaining region = 14×6.65-11×6.65

= 6.65(14-11) = 6.65×3

= 19.95 m²

Hence, the area of the blue-shaded region is 19.95 m²

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Therefore , the solution of the given problem of  test statistic comes out to be  Using a t-table or calculator, with 66 degrees of freedom (df = n1 + n2 - 2), we find the p-value to be approximately 0.039.

The Z-statistic has been the test statistics for anything resembling a Z-test and it confirms that the ordinary standard neutral hypothesis is true. Consider doing two separate X-y tests with a 0.05 level of significance and getting a 2.5 R-t value from your data (also referred as a Z-value). The p-value associated with this Z-value is 0.0124.

Here,

The hypotheses are:

Null hypothesis: There is no significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.

Alternative hypothesis: There is a significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.

To test this claim, we can use a two-sample t-test since we are comparing the means of two independent samples.

The formula for the test statistic is:

t = (x1 - x2) / sqrt((s1² / n1) + (s2² / n2))

where:

x1 = sample mean of those who smiled

x2= sample mean of those who remained neutral

s1 = sample standard deviation of those who smiled

s2 = sample standard deviation of those who remained neutral

n1 = sample size of those who smiled

n2 = sample size of those who remained neutral

Substituting the given values, we get:

t = (4.9 - 4.1) / sqrt((1.7² / 34) + (1.5² / 34))

t ≈ 2.116

Using a t-table or calculator, with 66 degrees of freedom (df = n1 + n2 - 2), we find the p-value to be approximately 0.039.

Since the p-value (0.039) is less than the significance level (0.10), we reject the null hypothesis. Therefore, we have sufficient evidence to conclude that there is a significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.

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Answer: 2

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

[tex]\frac{1}{2} *\frac{10}{1} = \frac{10}{2} = 5[/tex]

As wetlands make up about 31% of the area of Florida, the expressions that represent this fraction is:

Florida wetlands generally include swamps, marshes, bayheads, bogs, cypress domes and strands, sloughs, wet prairies, riverine swamps and marshes, hydric seepage slopes, tidal marshes etc. According to the United States Environmental Protection Agency (EPA), wetlands cover approximately 31% of the total land area of the state of Florida.

Total land mass of Florida is: 170,312 Km². The landmass of Wetland areas is: 31% *  170,312 Km² = 52796.72Km²

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Answer:

Add 1 to both sides. Add 11 and 1 to get 12. Divide both sides by 4. Divide 12 by 4 to get 3.

Answer:

B 16

Step-by-step explanation:

It will take 8 days to eat one carton so 2 cartons will be 16 days.