Given that a=14 and b=25, work out the height of the triangle

The average rate of change for the exponential function over the interval from x = 3 to x = 5 is 12.

The average rate of change for an exponential function can be found by dividing the change in y-values over the change in x-values for the given interval.

For the interval from x = 3 to x = 5, the change in x-values is 5 - 3 = 2.

The corresponding y-values for x = 3 and x = 5 are

y = 8 and y = 32, respectively.

Therefore, the change in y-values over the interval is 32 - 8 = 24.

The average rate of change for the exponential function over the interval from x = 3 to x = 5 is:

Average rate of change = Change in y-values / Change in x-values

Average rate of change = 24 / 2

Average rate of change = 12

Hence, the average rate of change for the exponential function over the interval is 12

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Answer: 8

Step-by-step explanation:

6 + 2 is a simple arithmetic operation, which results in 8. When adding 6 and 2, you are combining two numbers to find their total. In other words, you are asking "if I have 6 items and someone gives me 2 more, how many items do I have in total?" The answer is 8, because you would have a total of 8 items.

Answer:

8

Step-by-step explanation:

[tex]6+2[/tex]

We can find the value of this by counting up 2 from 6.

7, 8

So the answer is 8

Answer: The two triangles are congruent by axiom AAS as the opposite side of equal angles are also equal.

Answer: 0.75

Step-by-step explanation:

The total frequency of all the colors is 20+9+11+7+16=63.

The probability of landing on red or green or purple is the sum of the frequencies of these three colors divided by the total frequency:

P(red or green or purple) = (20+11+16)/63

P(red or green or purple) ≈ 0.75(rounded to the nearest hundredth)

Therefore, the probability of the next spin landing on red or green or purple is approximately 0.75.

Answer:

0.75

Step-by-step explanation:

The total spins was 63. The total amount of spins for red, green or purple is 47.

Dividing, we get 47/63 ≈ 0.75.

Hope this helps!

Answer:

[tex]y=-3,\:x=6[/tex]

Step-by-step explanation:

hope this helped :P

The product of two random variables that follows the normal distribution with mean 0 and variance 1 is expected 0.

To compute the product of two random variables that are normal distributed with a mean of 0 and a variance of 1, the following procedure can be employed:

Thus, we can write the probability density function of the normal distribution as:

f(x) = (1/√2π) * e^(-x^2/2)

E[X] = ∫x * f(x) dx, where the integral is taken over the entire range of X.

E[Y] = ∫y * f(y) dy, where the integral is taken over the entire range of Y.

E[XY] = E[X] * E[Y]

E[X] = ∫x * f(x) dx = ∫x * (1/√2π) * e^(-x^2/2) dx = 0

E[Y] = ∫y * f(y) dy = ∫y * (1/√2π) * e^(-y^2/2) dy = 0

E[XY] = E[X] * E[Y]

= 0 * 0 ⇒ 0

Therefore, the product of two random variables that follow a normal distribution with mean 0 and variance 1 has an expected value of 0.

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The measure of ∠J in ΔJKL is approximately 57.5 degrees.

The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.

The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.

tan(∠J) = JK/KL

tan(∠J) = 7.3/4.7

∠J = arctan(7.3/4.7)

∠J = 57.5 degrees (rounded to the nearest tenth of a degree)

Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.

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The product of any two invertible matrices is invertible that is (BC) = A⁻¹

Now, let's consider the product of two invertible matrices, say A and B. Since A and B are invertible, they both have an inverse, denoted by A⁻¹ and B⁻¹, respectively.

To show that the product AB is also invertible, we need to find a matrix that satisfies the definition of an inverse. Let's call this matrix C.

If C is the inverse of AB, then we should have:

(AB)C = C(AB) = I

where I is the identity matrix.

Now, we can use the associativity of matrix multiplication to expand the left-hand side of the equation:

(AB)C = A(BC)

Notice that B and C are both matrices, so their product BC is also a matrix. Thus, we can write:

A(BC) = I

Since A is invertible, we can multiply both sides by A⁻¹ to get:

A⁻¹A(BC) = A⁻¹I

The left-hand side simplifies to:

(BC) = A⁻¹

Now, we have found a matrix C that satisfies the definition of an inverse for AB, which means that AB is invertible.

To summarize, the product of two invertible matrices is invertible, and the proof relies on the fact that the inverse of a matrix is unique and the associativity of matrix multiplication.

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The correlation coefficient may assume any value between -1 and 1. Correct answer option A.

This means that the coefficient might be negative, zero, or positive, with -1 being a perfect negative correlation, 0 representing no connection, and 1 representing a perfect positive correlation.

The correlation coefficient is a numerical measure of two variables' linear connection. It is a measure of the strength of the link between two variables. A correlation coefficient of 1 indicates that there is a perfect positive connection, a coefficient of -1 indicates that there is a perfect negative correlation, and a coefficient of 0 shows that there is no correlation between the two variables.

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Figure SPOT is translated unit(s) right and unit(s) up to the right move 8 and to the up move 9.

An effective method for beginning to make this idea clear for translating squares is to give them a slice-out shape to get across the page truly.

Afterward, kids need to figure out how to have the option to interpret a shape without this support.

while doing the above task, ideally, let's begin by putting the effective method for beginning making this idea clear for translating square is to give them a slice out shape to get across the page truly.

Afterward, kids need to figure out how to have the option to interpret a shape without this support.

while doing the above task, ideally, let's begin by putting the mark of your pencil on the upper left-hand corner of the shape and afterward dropping your pencil down 1 and right 2, then, at that point, plotting the primary place of your new shape with a dab.

You would then have to do likewise with the upper right-hand corner of the shape, the bottom left, and afterward the bottom right.

To respond to this, they would have to interpret the square and afterward give the directions of point An on the new shape, which would be (8, 9).  mark your pencil on the upper left-hand corner of the shape and afterward drop your pencil down 5 and right 6, then, at that point, plot the primary place of your new shape with a dab.

You would then have to do likewise with the upper right-hand corner of the shape, the bottom left, and afterward the bottom right.

To respond to this, they would have to interpret the square and afterward give the directions of point An on the new shape, which would be (5, 4), (6, 3), (5, 2), and (4, 3).

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The perimeter of the figure with dimensions (4cm, 5cm, 8cm, and 3cm) is 20 cm

What is the perimeter?

The entire length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by combining the lengths of all of its sides and edges. Its dimensions are expressed in linear measures like centimeters, meters, inches, and feet.

Why is a perimeter important?

They help you to quantify physical space and also provide a foundation for more advanced mathematics found in algebra, trigonometry, and calculus. Perimeter is a measurement of the distance around a shape and area gives us an idea of how much surface the shape covers.

What is the formula for the perimeter of a rectangle?

The formula for the perimeter of a rectangle is,

P = length + breadth + length + breadth.

Perimeter of given figure(4cm, 5cm, 8cm, and 3cm) = 4 + 5 + 8 + 3

                                                                                      = 20

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The probability that student A or B can solve a problem chosen at random is 0.95.

Probability is calculated by dividing the number of favourable outcomes by the number of possible outcomes.

Random: An event is referred to as random when it is not possible to predict it with certainty. The probability that either student A or B will be able to solve a problem chosen at random can be calculated as follows:

P(A or B) = P(A) + P(B) - P(A and B) where: P(A) = probability of A solving a problem = 0.75, P(B) = probability of B solving a problem = 0.7, P(A and B) = probability of both A and B solving a problem. Since A and B are independent, the probability of both solving the problem is:

P(A and B) = P(A) x P(B) = 0.75 x 0.7 = 0.525

Now, using the above formula: P(A or B) = P(A) + P(B) - P(A and B) = 0.75 + 0.7 - 0.525 = 0.925

Therefore, the probability that student A or B can solve a problem chosen at random is 0.95 (or 95%).

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3.25x + 59 = 205.25 is an equation which can be used to determine x, the cost of the labor per hour.

Let's assume that the cost of labor per hour is x dollars.

The technician worked on the computer for 3.25 hours, so the cost of labor is 3.25x dollars.

In addition, Zoey was charged $59 for parts.

The total cost, including labor and parts, was $205.25.

Therefore, we can write the equation:

3.25x + 59 = 205.25

To solve for x, we need to isolate x on one side of the equation.

We can do this by subtracting 59 from both sides:

3.25x = 146.25

Finally, we can solve for x by dividing both sides by 3.25:

x = 45

Therefore, the cost of labor per hour is $45.

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Answer:

We are given two similar triangles, triangle ABC and triangle DEF, and some measurements of triangle ABC. We are also given that DF, one of the sides of triangle DEF, is equal to 15 units. Using this information, we are asked to find the difference between the lengths of sides AB and EF.

To solve the problem, we can first use the angle-angle similarity theorem to determine that the corresponding angles of the two triangles are equal. Therefore, angle DEF is equal to angle BCA, and angle ABE is equal to angle DFE.

Next, we can use the law of sines to find the length of side AB. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides and angles in the triangle. Applying this to triangle ABC, we have:

AB/sin(73) = BC/sin(48)

Substituting the value of BC as 19 units, we can solve for AB to get:

AB = 22.78 units

Similarly, we can use the law of sines to find the length of side EF. Since angle DFE is equal to angle ABE, we can use the same ratio as above to get:

EF/sin(73) = DF/sin(48)

Substituting the value of DF as 15 units, we can solve for EF to get:

EF = 18.20 units

Finally, we can subtract EF from AB to get:

AB - EF = 22.78 - 18.20 = 4.58 units

Therefore, the difference between the lengths of sides AB and EF is 4.58 units.

Answer:

Using the banker's method, we can use the following formula to find the interest:

Interest = (Principal x Rate x Days) / 360

Where,

Principal = $16,400

Amount = $16,851

Days = 180

We know that the interest plus the principal equals the amount, so we can set up the following equation:

Interest + Principal = Amount

Substituting the values:

(16,400 x Rate x 180) / 360 + 16,400 = 16,851

Multiplying both sides by 360:

16,400 x Rate x 180 + 5,904,000 = 6,066,360

16,400 x Rate x 180 = 162,360

Rate = 162,360 / (16,400 x 180)

Rate = 0.055 or 5.5%

Therefore, the interest rate of the loan is 5.5%.

24% of the students bought their lunch on Monday. Therefore, the number of students in the 6th grade is 190

Step-by-step explanation:

The factorizations of these integers above represent their factorizations into their respective prime numbers.

(a) 756 = 2^2.3^3.7, (b) 819 = 3^2.7.11, (c) 9,075 = 3^2.5^2.7The unique factorization theorem refers to an essential theorem in standard algebraic theory that characterizes the unique factorization properties of integers. Standard factored form, on the other hand, refers to an expression in which an integer is factored into its standard, irreducible components.In view of this, the three provided integers, 756, 819, and 9,075 can be factored as follows:756 = 2^2.3^3.7 (in standard factored form)819 = 3^2.7.11 (in standard factored form)9,075 = 3^2.5^2.7 (in standard factored form)Note that the factorizations of these integers above represent their factorizations into their respective prime numbers.

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The equation for the area of a rectangle is A = lw, where l is the length and w is the width. We are given the area (2x² - 3x - 2) and the length (2x + 1). To solve for the width, we can rearrange the equation to w = A/l.

Therefore, the expression to represent the width of the desk is w = (2x² - 3x - 2)/(2x +1).

The percentage of the teenagers who purchased something with their parents' money can be calculated from the two-way frequency table. About 38.64% of the teenagers purchased something with their parents' money.

There were a total of 88 teenagers who were surveyed by Alexis. 38 of them completed the purchase, and out of these 38 teenagers, 34 of them used their parents' money. So, the percentage of teenagers who purchased something with their parents' money can be calculated as follows:

Percent of teenagers who purchased something with their [tex]parents' money = \frac{Frequency of completed purchase}{Total Number of teenagers surveyed} *100[/tex]

Percent of teenagers who purchased something with their parents' money = [tex]\frac{34}{88} * 100%[/tex]%

Therefore percent of teenagers who purchased something with their parents' money = 38.64%

Therefore, about 38.64% of the teenagers purchased something with their parents' money.

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Adam needs to show that the diagonals are perpendicular, congruent, and bisect each other.Therefore Option D is correct.

To prove that PQRS is a square, Adam needs to show that all four sides are congruent and that all four angles are right angles.

One way to do this is by showing that the diagonals of PQRS are perpendicular, congruent, and bisect each other.

If the diagonals are perpendicular, then opposite angles are congruent and the quadrilateral is a kite.

If the diagonals bisect each other, then opposite sides are congruent and the kite is a rhombus.

If the diagonals are also congruent, then all sides are congruent and the rhombus is a square.

Therefore, He needs to show that the diagonals of PQRS are perpendicular, congruent, and bisect each other to prove that PQRS is a square.

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To fill the wooden box with potting soil precisely up to two-thirds of its capacity, Benito requires a volume of 3,584 cubic inches.

The volume of soil that Benito needs to fill the box two-thirds full can be calculated by finding two-thirds of the total volume of the box.

The volume of the box can be calculated by multiplying the width, height, and length:

16 inches (width) x 12 inches (height) x 28 inches (length) = 5,376 cubic inches.

Two-thirds of this volume can be found by multiplying the total volume by 2/3:

5,376 cubic inches x 2/3 = 3,584 cubic inches.

Therefore, Benito needs 3,584 cubic inches of potting soil to fill the box exactly two-thirds full.

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Step-by-step explanation:

40 Years is the right answer

Answer:

son is 10 , father is 40

Step-by-step explanation:

let x be the sons age then father is x + 30

in 5 years

son is x + 5 and father is x + 30 + 5 = x + 35

at this time the father is three times as old as his son , then

x + 35 = 3(x + 5)

x + 35 = 3x + 15 ( subtract x from both sides )

35 = x + 15 ( subtract 15 from both sides )

20 = x

then sons age = x = 10 and fathers age = x + 30 = 10 + 30 = 40

The Fourier series for f(x) is f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...].

The square wave function can be defined as:

f(x) = {1 -π ≤ x < 0

-1 0 ≤ x < π

To find the Fourier series for this function, we first need to determine the coefficients a_n and b_n.

a_n = (1/π) ∫_0^π f(x) cos(nx) dx

= (1/π) ∫_0^π (-1) cos(nx) dx + (1/π) ∫_(-π)^0 cos(nx) dx

= (2/π) ∫_0^π cos(nx) dx

= (2/π) [sin(nπ) - sin(0)]

= 0

b_n = (1/π) ∫_0^π f(x) sin(nx) dx

= (1/π) ∫_0^π (-1) sin(nx) dx + (1/π) ∫_(-π)^0 sin(nx) dx

= -(2/π) ∫_0^π sin(nx) dx

= -(2/π) [cos(nπ) - cos(0)]

= (2/π) [1 - (-1)^n]

Therefore, the Fourier series for f(x) is:

f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...]

To find the first three Fourier approximations, we truncate this series at the third term.

F_1(x) = -(4/π) sin(x)

F_2(x) = (4/π) sin(x) + (4/3π) sin(3x)

F_3(x) = (4/π) sin(x) + (4/3π) sin(3x) - (4/5π) sin(5x)

These are the first three Fourier approximations of the square wave function f(x). The more terms we include in the Fourier series, the closer the approximations will be to the original function.

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The required value of EC is 5 units.

Since DE is parallel to BC, we can use the property of similar triangles to set up a proportion:

AD/DB = AE/EC

We know that AD + DB = AB = x + 5. Since D is a point on AB, we can express AD and DB in terms of x:

AD = x, DB = x + 5 - x = 5

We also know that AE = 3 and ED = x + 1. Using these values, we can express AD in terms of ED:

AD = ED - AE = (x + 1) - 3 = x - 2

Substituting these values into the proportion, we get:

(x - 2)/5 = 3/EC

Multiplying both sides by 5EC, we get:

x - 2 = 15/EC

Multiplying both sides by EC, we get:

EC(x - 2) = 15

Expanding the left side, we get:

ECx - 2EC = 15

Solving for EC, we get:

EC = 15/(x - 2)

We are given that EC = x, so we can set these expressions equal to each other:

x = 15/(x - 2)

Multiplying both sides by (x - 2), we get:

x(x - 2) = 15

Expanding the left side, we get:

x² - 2x = 15

Bringing all terms to one side, we get:

x² - 2x - 15 = 0

We can factor this quadratic equation:

(x - 5)(x + 3) = 0

Therefore, x = 5 or x = -3. We reject x = -3 since we are given that EC > 0. Thus, the length of EC is: EC = x = 5.

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The probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.

The given table represents the joint probability mass function of the random variables, pxyc (r, y, c). r, y, and c denote the temperature, shock sensor, and health status of the disk drive. The values of r, y, and c are binary.The joint probability mass function of three random variables r, y, and c can be represented as follows:pxyc (r, y, c)= P(r, y, c)Here,P(r=0, y=0, c=0)= 0.1, P(r=0, y=1, c=0)= 0.2, P(r=1, y=0, c=0)= 0.2,P(r=0, y=0, c=1)= 0, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0,P(r=0, y=0, c=0)= 0, P(r=0, y=1, c=0)= 0, P(r=1, y=1, c=0)= 0.05,P(r=0, y=0, c=1)= 0.25, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0.From the given table, the probability of the disk drive being in a normal state, C=0, is P(C=0)=P(r=0, y=0, c=0)+P(r=0, y=1, c=0)+P(r=1, y=0, c=0)=0.1+0.2+0.2=0.5Hence, the probability of the disk drive being in a failed state, C=1, is:P(C=1)=P(r=0, y=0, c=1)+P(r=0, y=1, c=1)+P(r=1, y=0, c=1)+P(r=1, y=1, c=0)=0.25+0+0+0.05=0.3Therefore, the probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.

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The probability that a randomly selected finishing time is greater than 87 seconds is 14.08%. This can be calculated using the empirical rule.

The empirical rule states that for any data that is normally distributed, about 68% of the data will fall within one standard deviation of the mean (in this case, within 69 ± 6 seconds). Approximately 95% of the data will fall within two standard deviations (in this case, within 69 ± 12 seconds), and about 99.7% of the data will fall within three standard deviations (in this case, within 69 ± 18 seconds).Given the mean and standard deviation given, we can calculate the probability that a randomly selected finishing time is greater than 87 seconds.

We can do this by subtracting the area under the curve from the mean to the value we are interested in (in this case, 87 seconds). Since the total area under the curve is 1, subtracting the area from the mean to 87 seconds will give us the desired probability.To calculate the area under the curve, we need to calculate the Z-score, which is the number of standard deviations away from the mean a particular value is. In this case, the Z-score is (87 - 69) / 6, which is 2.16. Using a Z-table, the probability of a Z-score of 2.16 or higher is 0.8592. Therefore, the probability that a randomly selected finishing time is greater than 87 seconds is 1 - 0.8592, which is 0.1408. Rounding to two decimal places, this is 14.08%.

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Answer:

the value of x is 3

Step-by-step explanation:

6/3-3=6/0

which is undefinied

Answer:

3

Step-by-step explanation:

The two triangles have to have two equal angles that's congruent and one set of corresponding sides who are congruent or adjacent to the angles in order to satisfy the AAS (Angle-Angle-Side) a triangle congruence theory.

A right triangle's hypotenuse is its longest side, its "opposite" side was the one that faces a specific angle, and its "adjacent" side is the one that faces the angle in question. To define the edges of right triangles, we use specific terminology.

A triangle represents a closed, three-sided object in two dimensions. The various kinds of circles go by various titles. Three different kinds of triangles—scalene, isosceles, and equilateral—are distinguished by the lengths of their sides.

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The probability that a randomly selected firm will earn less than 96 million dollars is 0.8907

The given data is that the mean income of firms in the industry for a year is 80 million dollars with a standard deviation of 13 million dollars. Now, it is required to find the probability that a randomly selected firm will earn less than 96 million dollars if incomes for the industry are distributed normally.

The probability is calculated by the Z-score formula which is given as below:

z = (x - μ) / σ

Where,μ = 80 (Mean),  x = 96 (Randomly selected firm income),  σ = 13 (Standard deviation)

Putting the values in the formula we have,

z = (96 - 80) / 13z = 1.23

Now we will use the Z-table to find the probability value. From the Z-table, we can say that the probability of Z-score = 1.23 is 0.8907.

Therefore, the probability that a randomly selected firm will earn less than 96 million dollars is 0.8907 (approx) when rounded off to four decimal places.

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