Explain how to solve the given equation for "x".

By answering the presented question, we may conclude that Therefore, Pythagorean the length of the third side of the triangle is [tex]2/\sqrt(5)[/tex]and the height is 4/5.

The Pythagorean theorem is a fundamental mathematical principle that describes the connection between the sides of a right triangle. It asserts that the sum of the squares of the other two sides' lengths equals the square of the hypotenuse's length (the side opposite the right angle). The mathematical theorem is as follows: c2 = a2 + b2 Where "c" denotes the hypotenuse length and "a" and "b" indicate the lengths of the other two sides, known as the legs.

Let's use the formula for the area of a triangle:

[tex]A = 1/2 * b * h2/5 = 1/2 * (6/5) * h\\h = 4/5\\a^2 = (6/5)^2 - (4/5)^2\\a^2 = 36/25 - 16/25\\a^2 = 20/25\\a^2 = 4/5\\[/tex]

[tex]a = \sqrt(4/5)\\a = 2/\sqrt(5)[/tex]

Therefore, the length of the third side of the triangle is [tex]2/\sqrt(5)[/tex]and the height is 4/5.

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Equation of line: y = -3/4 x + 3. Here , slope m = -3/4 and y intercept is 3.

We need to knowing the slope of the line and indeed the intercept where the line crosses the y-axis in order to use the slope-intercept formula. Suppose a straight line with y-intercept b and slope m. For one straight line with slope "m" and y-intercept "b," the slope intercept program is designed is: y = mx + b.

Given coordinates are:

(2,3) and (4,0).

Slope m = (y2 - y1)/(x2 - x1)

m = (0 - 3)/(4 - 0)

m = -3/4

Equation of line:

y - y1 = m(x - x1)

y - 0 = -3/4(x - 4)

y = -3/4 x + 3

Here , slope m = -3/4 and y intercept is 3.

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Complete question:

Find the slope intercept equation of line passing through (2,3) and (4,0).

The probability that the duration of rainfall at least 2 hours is 0.473,  at most 3 hours is 0.683, and between 2 and 3 hours is 0.156.

1. Find the rate parameter (λ):
λ = 1/2.725 ≈ 0.367
2. To find P(X ≥ 2):

P(X ≥ 2) = 1 - P(X < 2).

The (pdf) is:
P(X < x) = 1 - e^(-λx)
P(X < 2) = 1 - e^(-0.367 * 2) ≈ 0.527
P(X ≥ 2) = 1 - 0.527 ≈ 0.473
3. To find P(X ≤ 3):
P(X ≤ 3) = 1 - e^(-0.367 * 3) ≈ 0.683
4. To find P(2 ≤ X ≤ 3):
P(2 ≤ X ≤ 3) = P(X ≤ 3) - P(X ≤ 2) = 0.683 - 0.527 ≈ 0.156
The probability that  duration  at least 2 hours is 0.473,  at most 3 hours is 0.683, and between 2 and 3 hours is 0.156.

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The probability that Betty is first in line or Mary is last in line is (n^2 - n - 1)/n(n-1), as a function of n.

We can approach this problem by considering the probability of the complementary event, i.e., the probability that neither Betty is first in line nor Mary is last in line, and then subtracting this probability from 1 to get the probability we want.

The total number of ways the n kids can line up is n!, since there are n choices for the first person in line, n-1 choices for the second person, and so on down to 1 choice for the last person.

The number of ways in which neither Betty is first in line nor Mary is last in line is (n-2)!, since there are (n-2) choices for the first person in line (excluding Betty and Mary), (n-3) choices for the second person, and so on down to 1 choice for the second-to-last person.

Therefore, the probability that neither Betty is first in line nor Mary is last in line is

[(n-2)! / n!] = 1/n(n-1)

The probability we want is

1 - 1/n(n-1) = (n^2 - n - 1)/n(n-1)

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The given question is incomplete, the complete question is:

A class with n kids lines up for recess. The order in which the kids line up is random with each ordering being equally likely. There are two kids in the class named Betty and Mary. The use of the word “or” in the description of the events, should be interpreted as the inclusive or. That is “A or B” means that A is true, B is true, or both A and B are true.

What is the probability that Betty is first in line or Mary is last in line as a function of n? Simplify your final expression as much as possible and include an explanation of how you calculated this probability.

The experimental probability of choosing the name Maya is [tex]23/118[/tex].

and theoretical probability is of choosing name maya is [tex]1/5[/tex]

Probability is a measure of how likely an event is to occur. Many events are impossible to forecast with absolute accuracy. We can only anticipate the possibility of an event occurring, i.e. how probable they are to occur, using it. Probability can range from 0 to 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of all events in a sample space equals one.

According to the given information:

The experimental probability = [tex]\frac{Number of times an event occur}{ Total number of trials}[/tex]

Here total trials = 118,

The number of times the name maya has been chosen =23 times.

Therefore, experimental probability = [tex]\frac{23}{118}[/tex].

Theoretical probability = [tex]\frac{Number of favourable outcome}{Number of possible otucome}[/tex]

favourable outcome = 1 (Maya)

Possibleble outcome = 5 (Total no of Names in a hat)

And the theoretical possibility of the name maya has been chosen is [tex]1/5[/tex]

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If there are 30 students in the class, then the number of students who play soccer but do not play basket-ball are 13 students.

The total-students in the class is = 30 students,

The Number of students who play basketball is = (2/5) × 30 = 12,

The Number of students who play soccer is = (7/10) × 30 = 21,

⇒ Number of basketball players who also play soccer = (2/3) × 12 = 8,

So, out of the 21 students who play soccer, 8 also play basketball.

To find the number of students who play soccer but not basketball, we can subtract the number of students who play both from the total number of soccer players:

⇒ 21 - 8 = 13 students play soccer but not basketball.

Therefore, the required number of students are 13 students.

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The answer is 3/20. By calculating the probability of selecting a female who plays the clarinet out of the total number of sophomores, we can get an accurate representation of the selection of the current sophomore class.

It is calculated by dividing the number of possible outcomes by the total number of possible outcomes.

This can be calculated by taking the number of females who play the clarinet (18) and dividing it by the total number of sophomores (120).

This gives us 18/120= 3/20.

This is the correct answer because it shows the probability of selecting a female who plays the clarinet out of the total number of sophomores. Option 1, 31/120, would show the probability of selecting a female or a clarinet player out of the total number of sophomores.

Option 3, 3/11, would show the probability of selecting a female who plays the clarinet out of the total number of female sophomores.

Option 4, 18/31, would show the probability of selecting a female out of the total number of clarinet players.

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option (c) -No, 20 is NOT a reasonable solution because at x=-20,

an equation in which highest power of variable is always 1.

by solving the equation -6+2log(-5x)=-2 :

-6 + 2log(-5x) = -2

2log(-5x) = 4

log(-5x) = 2

-5x = 10^2

-5x = 100

x = -20

So, we found that x = -20 satisfies the equation. However, we need to check whether it is a reasonable solution or not.

Option C is correct: -20 is NOT a reasonable solution because at x = -20, the logarithm is not defined. The logarithm function is defined only for positive real numbers.

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Regenerate response

Step-by-step explanation:

a) from n = 1 to 4 this equals

      -4       -4 (2/3)      -4 (2/3)^2    - 4 (2/3)^3

=      -4       - 8/3          - 16/9          - 32/27

b) converges  ===  since  common ratio, r= (2/3) is less than 1

c ) sum =  -4 / ( 1-r) =   -4 / (1- 2/3 ) =  -12    

Step-by-step explanation:

Remember that in order to find the volume you need to multiply 6.3 x 2.4 x 8.   I don't know for sure but if that is true the answer should be 120.96.  If they ask you to round I think you know how to do that.  

Hope this helps.

The area of the triangles are:

Triangle 1: 144√3 unit²

Triangle 2: 64√3 unit²

The area of a triangle is given by the formula:

A = 1/2 * b * h

where b is the base and h is height of the triangle

1st triangle:

The vertical line divides the base into two right triangles.

Considering the right triangle to the right. Let L represent the length of the base. Thus, we can say:

tan 60° = (12√3)/L

√3 = (12√3)/L

(√3)L = 12√3

L = 12

Since b = 2* L

b = 24 units

A = 1/2 * 24 * 12√3

A = 144√3 unit²

2nd triangle:

cos 60° = L/16

0.5 = L/16

L = 0.5 * 16

L = 8 units

b = 2 * 8 = 16 units

h = √(16² - 8²)    (Pythagoras)

h = 8√3 units

A = 1/2 * 16 * 8√3

A = 64√3 unit²

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To make the larger sculpture with each linear dimension 75% greater, the artist needs to use 265.625% or 3.65625 times more clay than the original sculpture.

Let's assume that the original sculpture is a cube with side length x cm. Therefore, its volume would be x³ cm³.

To make the larger sculpture, each linear dimension needs to be increased by 75%, which means that each side length will become 1.75x cm. Thus, the new volume of the sculpture will be (1.75x)³ = 5.378125 x³ cm³.

To find the amount of clay required to make the larger sculpture, we need to find the ratio of the new volume to the original volume (5.378125 x³ cm³) / (x³ cm³) = 5.378125

This means that the artist needs to use 5.378125 times more clay than the original amount used to make the larger sculpture.

Therefore, to find the actual amount of clay needed, we multiply the original amount of clay by 5.378125: n cm³ x 5.378125 = 5.378125n cm³

So, the artist needs to use 3.65625 or 265.625% times more clay than the original sculpture to make the larger sculpture with each linear dimension 75% greater.

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1) You will Rewrite both side by combining like terms. Thus, option D is correct.

2) Yes, they have same solution x = 2.

Balancing an equation in math typically refers to solving an equation for a specific variable. The goal is to isolate the variable on one side of the equation and simplify the other side. The steps for balancing an equation in math can vary depending on the type of equation, but here are some general steps to follow:

1) Identify the variable you want to solve for.

You have given:

5x - 2 + x = x - 4

Also

5x - x = x - 4

Here, as you can see x - 4 is common in both equation, (option D) Rewrite one side (or both) by combining like terms i.e. x - 4:

5x - 2 + x = 5x - x = x - 4

4x - 2  = 4x  = x - 4

4x - 4x - 2  = x - 4

- 2 = x - 4

4 - 2 = x

x = 2

Thus, You will Rewrite both side by combining like terms. Thus, option D is correct.

2) Yes, they have same solution x = 2

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You can expect 95% of your customers to stay in your store between range of  39.7 minutes and 49.9 minutes.

To determine the range in which 95% of your customers would stay in your store, we will use the properties of a normally distributed data set with a mean of 44.8 minutes and a standard deviation of 2.6 minutes.
Identify the mean and standard deviation.
The mean is 44.8 minutes, and the standard deviation is 2.6 minutes.
Determine the z-score for a 95% confidence interval.
A 95% confidence interval corresponds to a z-score of 1.96. This means that 95% of the data lies within 1.96 standard deviations from the mean.
Calculate the range using the z-score, mean, and standard deviation.
To find the lower and upper limits of the range, we will multiply the standard deviation (2.6 minutes) by the z-score (1.96) and then subtract or add the result to the mean (44.8 minutes).
Lower limit: Mean - (Z-score × Standard deviation)
44.8 - (1.96 × 2.6) = 44.8 - 5.096 ≈ 39.7 minutes
Upper limit: Mean + (Z-score × Standard deviation)
44.8 + (1.96 × 2.6) = 44.8 + 5.096 ≈ 49.9 minutes
State the range in which 95% of customers would stay in the store.

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The probability that the sample contains two rotten apples is 0.0612.

The sample of three apples can be selected in 14C3 (14 choose 3) ways and the probability that we select a rotten apple will be 2/14 and the probability of selecting an apple that is not rotten is 12/14.

Now we can apply the binomial distribution formula, to calculate the probability as follows,

P = (3 choose 2) × (2/14)² × (12/14)

P = (3! / (2! × 1!)) × (2/14)² × (12/14)

P = 3 × (1/49) × (12/14)

P = 0.06122449

So, the probability of selecting a sample of three apples in which 2 are rotten and one is not rotten is 0.0612 or approximately 6.12%.

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Answer: 1280 in³

Step-by-step explanation:

Volume of 8 Soup Cans = Volume of box

V = l x b x h

V = 10 x 16 x 8

V = 1280

As a result, 2x + 10 is the expression that describes how long Malik will cook the sirloin for if the asparagus grills for x minutes.

So, 1+1 is a straightforward illustration of a statement. This expression has one action, two constant elements, and (addition). Another illustration is x3.

Let's start by using the given information to create expressions for each item:

Let's call the time it takes to grill the fish "f". Then, according to the problem, Malik grills the steak for "f + 10" minutes.

Grilling time for the seafood is double that of the vegetables. Thus, if it requires "x" minutes to grill asparagus, "2X" minutes are needed to grill salmon.

For "x + 1" minutes, and this is one minute more than he roasts the asparagus, Malik cooks the tomatoes that have been cut in half.

Using these expressions, we can create an equation for the time it takes to grill the steak:

Time to grill steak = Time to grill fish + 10

(f + 10) = 2x + 10

Therefore, if the asparagus cooks for x minutes, the phrase that denotes how long Malik will grill the sirloin is:

2x + 10

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Vertical angles are a pair of opposite angles formed by two intersecting lines. Vertical angles are congruent, meaning they have the same measure.

For example, if two lines intersect and form four angles, the two angles that are opposite each other  are vertical angles.

Adjacent angles are two angles that have a common vertex and a common side but do not overlap.

In other words, they share a ray or line segment, but they don't share any interior points.

Adjacent angles may or may not be congruent, depending on their measurement.

For example, if two angles are next to each other and share a vertex and a side, they are adjacent angles.

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Answer:

[D] No, it is not a polynomial

Step-by-step explanation:

Polynomial- (Have)

Polynomial -(Can't/Don't)

There are 3 different types of polynomials:

As we can see based on the given;

5x²y⁴ + x√3 isn't a polynomial.

As a result, the answer is [D] No, it is not a polynomial

RevyBreeze

Answer:

20

Step-by-step explanation:

c²=a²+b²

c²=16²+12²

c²=400

c=20

The parabola's equation is therefore for A: y  = 7x2 - 5$1.

As a result, the parabola's equation for B  is y = -1/2(x - 1)² + 4.

A parabola with vertex (h,k) has the basic equation y = a(x-h)² + k². In this instance, h=0 and k=-5 are equal because the vertex is at $(0,-5)$. Moreover, the parabola has a point at (-1 . 2). When we substitute these numbers in the general parabola equation, we obtain:

2 = a(-1-0)² -5

7 = a

The parabola's equation is therefore y = 7x2 - 5$1.

A cone and a plane perpendicular to its side cross to create a symmetrical open plane curve known as a parabola1. It is a U-shaped curve whose vertex and axis of symmetry characterise it. The line dividing the parabola into its two mirror counterparts is known as the axis of symmetry. The parabola's vertex is where the axis of symmetry intersects it.

A parabola's vertex is represented by the equation y = a(x - h)²+ k, where (h,k) represents the vertex. We may utilise the vertex version of the equation and substitute the values of h, k, and the x and y coordinates of the point to determine the equation of a parabola that passes through a particular point and has a certain vertex.

B.  Here, the vertex is (1, 4), and the point (5,-4). In the vertex form equation, we may therefore substitute h=1, k=4, x=5, and y=-4 to obtain:

-4 = a(5 - 1)²2 + 4 \s-8 = 16a

a = -1/2

As a result, the parabola's equation is y = -1/2(x - 1)² + 4.

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The calculated value of n in the cube with the given properties is 5

If we cut the original cube into smaller cubes of side length 1 unit, then the total number of smaller cubes is given by the formula:

Total number of smaller cubes = (number of cubes along each edge of the original cube)^3 = n^3

So, we have

n^3 = 125

Take the cube root of both sides

n = 5

Hence, the value of n is 5

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Answer:

  7. shifted right 8 units

  8. shifted left 4 and up 12 units

  9. shifted up 8 units

Step-by-step explanation:

You want to compare the given functions with p(x) = a(x -h)² +k and tell the value and effect of a, h, and k on the vertex.

In the equation for p(x) above, the value 'a' represents a vertical scale factor. It expands the graph vertically by the factor 'a'. If a < 0, the graph is reflected across the x-axis.

The values 'h' and 'k' in the equation for p(x) represent a right shift of the graph by 'h' units and a shift up by 'k' units. That is, the graph is translated by (h, k).

We have h = 8. The graph is shifted right 8 units.

We have (h, k) = (-4, 12). The graph is shifted left 4 units and up 12 units.

The values of the transformation parameters are a = -1/2 and k = 8. The vertical compression and reflection do not affect the vertex. The vertex is shifted up 8 units.

Step-by-step explanation:

A. To calculate the monthly payment, we can use the formula for a fixed-rate mortgage:

M = P * (r*(1+r)^n) / ((1+r)^n - 1)

where:

M = monthly payment

P = principal (amount borrowed) = $213,000

r = monthly interest rate = APR / 12 = 0.0375 / 12 = 0.003125

n = total number of payments = 30 years * 12 months/year = 360

Plugging in these values, we get:

M = 213000 * (0.003125*(1+0.003125)^360) / ((1+0.003125)^360 - 1)

M ≈ $988.32

So the monthly payment, rounded to the nearest 10th, is $988.30.

B. The total amount paid over the 30-year period would be the monthly payment multiplied by the total number of payments:

Total = M * n

Total = $988.30 * 360

Total = $355,788.00

So the total amount paid over 30 years would be $355,788.00.

C. To calculate the total interest paid over the 30-year period, we can subtract the principal from the total amount paid:

Total Interest = Total - P

Total Interest = $355,788.00 - $213,000

Total Interest = $142,788.00

So the total interest paid over the 30-year period would be $142,788.00.

Thus, the expression [1 - 4sin²a] written in the product of its values is:

(1 + 2sina)(1 - 2sina).

We can solve mathematical equations thanks to algebra's inherent characteristics. Take note that both addition and multiplication adhere to these characteristics.

This Order of Operations is a set of rules that enables mathematicians to solve issues uniformly. In this order:

using the algebraic formula:

(a² - b²) = (a + b)(a - b)

Given expression:

= 1 - 4sin²a

This can be written as:

= 1² - (2sina)²

Now, using identity:

= (1 + 2sina)(1 - 2sina)

Thus, the expression [1 - 4sin²a] written in the product of its values is:

(1 + 2sina)(1 - 2sina).

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Complete question-

Express the given as the product of both values.

1 - 4sin²a

Answer:

x=6 and x=−5.

Answer:

20

Step-by-step explanation:

7 computers every 5 printers

7/5 = 28/x

Cross multiply

7x = 5*28

7x = 140

x = 20

Or in words,

7 times 4 is 28

5 times 4 is 20, which is your answer

We know that the sum of the angles of a triangle is 180 degrees. So, we can find the value of angle LNM as follows:

m/L + m/M + m/N = 180 degrees

Substituting the given values, we get:

40 + 41 + m/N = 180

m/N = 99

Now, we can see that angle LNM is greater than both angles L and M. So, we can conclude that:

OMN > NL > LM