PLZ HELP ME ITS 30 POINTS

The nature of the roots of a given quadratic equation √3x²+10x+7√3=0 is real and distinct because of the value of b²-4ac>0.

where a, b, and c are the coefficients in the standard form of the quadratic equation ax²+bx+c=0

Given quadratic equation is  √3x²+10x+7√3=0   on comparing with the standard form of a quadratic equation ax²+bx+c=0. Hence a=√3,b=10,

and c=7√3

Now  b²-4ac=10²-4×√3×7√3=100-28×3=16>0.

here the value of b²-4ac is greater than 0.

We know if the value of b²-4ac then the roots of the given equations are real and distinct.

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If EFGH is a parallelogram. The measures of FG and EG​ will be 44 and 59.46 respectively.

It is a four-sided plane shape in two dimensions where two pairs of sides are equal in length and parallel to one another. A parallelogram has 360° of angles total.

It is given that, in parallelogram EFGH, EH=5z-16 FG=3z+8, EF=4w+4, GH=2w+22

As we know that the opposite sides of the parallelograms are equal.

EH=FG

5z-16=3z+8

5z-3z=8+16

2z=24

z=12

EF=FG

4w+4=2w+22

4w-2w=22-4

2w=18

w=9

The measure of FG and EG is,

FG=3z+8

FG=3(12)+8

FG=44

EG=√EH²+HG²

EG=√(5z-16)²+(2w+22)²

EG=√(5×12-16)²+(2×9+22)²

EG=√(44)²+(40)²

EG=59.46

Thus, the measures of FG and EG​ will be 44 and 59.46 respectively.

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Answer:

a. h = A/w = 2 ³/₄ ft

b. A'/A = 2/3

Step-by-step explanation:

a. What is the total height of the wall? Write an equation to represent the situation. Then solve.

The wall is a rectangle and its area is A = wh where w = width and h = height of wall.

Making h subject of the formula,

h = A/w

Now, Since the area of the retaining wall, A is 23 ³/₈ ft² and its width is the length of the portion of the wall which is brick w is 8 ¹/₂ ft, then

h = A/w

= 23 ³/₈ ft² ÷ 8 ¹/₂ ft

= 187/8 ft² ÷ 17/2 ft

= 187/8 ft² × 2/17 ft

= 187/4 ft² × 1/17 ft

= 187/68 ft

= 2 ³/₄ ft

b. If the area of the brick portion of the wall is 15(7/12), what fraction of the wall is brick? Write an equation to show your work.

Since the area of the brick portion of the wall is A' = 15 ⁷/₁₂ ft²  and the total are of the retaining wall is A =  23 ³/₈ ft²

The fraction of the wall that is brick = A'/A

= 15 ⁷/₁₂ ft² ÷ 23 ³/₈ ft²

= 187/12 ÷ 187/8

= 187/12 × 8/187

= 8/12

= 2/3

Answer with Step-by-step explanation:

a) 2 3/4 ÷ 3 = 11/12 feet

11/12 + 11/12 = 1 5/6

Or, you could write an algebraic equation:

2 3/4 ÷ 3 = x.  (3x = 2 3/4)

x = 11/12

The height of the brick proportion of the wall is 1 5/6

b)

You know that 8 x 2 is 16. Well, you already know that the whole total of fractions, multiplied together, would probably be less that 1 and less than 1/2.

So, your rounded answer should be 16. Or 16 1/2

c)  

Area = 8 1/2 x 2 3/4.

Use Distributive Property to solve the area.

(8 x 2) + (3/4 x 1/2) = x

8 x 2 = 16

3/4 x 1/2 = 3/8

16 + 3/8 = 16 3/8

x = 16 3/8

I think my answer is reasonable because I estimated 16, and 1/2. 3/8 is close to 1/2. That's why my answer is reasonable.

-kiniwih426

No, p(x=5) = f(5) = 1/10 is not correct.

If x is a continuous random variable on the interval [0, 10], then the probability of x taking on any specific value (such as 5) is zero.

This is because there are infinitely many possible values that x can take on within the interval, and the probability of x taking on any one specific value is vanishingly small.

Instead, the probability of x falling within a certain range of values is what is meaningful.

This is typically represented by the probability density function (PDF) of the random variable, denoted as f(x). The probability of x falling within a range [a, b] is then given by the integral of the PDF over that range:

P(a <= x <= b) = integral from a to b of f(x) dx

For a continuous uniform distribution over the interval [0, 10], the PDF is a constant function:

f(x) = 1/10 for 0 <= x <= 10

f(x) = 0 otherwise

Using this PDF, we can find the probability of x falling within a specific range, but the probability of x taking on any one specific value is always zero:

P(x = 5) = 0

So, the statement "p(x=5) = f(5) = 1/10" is not correct for a continuous random variable.

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Answer:

The weight of the dog = 12 Pounds.

The weight of the cat = 3× Of dogs weight.

= 3×12 = 36 Pounds.

Therefore cat is 36 Pounds.

By using  the sum or difference formula of cosine to solve cos(525°) we get cos(525°) = -0.465

The formula to find the value of cos(A ± B) is given as,

cos(A + B) = cosA cosB − sinA sinBcos(A − B) = cosA cosB + sinA sinB

Here, A = 450° and B = 75°

We can write 525° as the sum of 450° and 75°.

Therefore,cos(525°) = cos(450° + 75°)

Now, we can apply the formula for cos(A + B) and solve it.

cos(A + B) = cosA cosB − sinA sinBcos(450° + 75°) = cos450° cos75° − sin450° sin75°= 0.707 × 0.259 − 0.707 × 0.966= -0.465

Substituting the values in the above equation, we get

cos(525°) = 0.707 × 0.259 − 0.707 × 0.966= -0.465

Thus, cos(525°) = -0.465.

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The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. The theorem can be proven using various methods, one of which is the geometric proof.

Geometric Proof of the Pythagorean Theorem:

Consider a right-angled triangle with sides of lengths a, b, and c, where c is the hypotenuse. By drawing squares on each side, we create four congruent right-angled triangles within the larger square formed by the hypotenuse. The area of the larger square is equal to the sum of the areas of the four smaller squares.

The area of the larger square is c^2, and the area of each smaller square is a^2, b^2, a^2, and b^2, respectively. Therefore, we have c^2 = a^2 + b^2, which is the Pythagorean theorem.

Converse of the Pythagorean Theorem:

The converse of the Pythagorean theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right-angled triangle.

To prove the converse, we assume that a triangle with sides of lengths a, b, and c satisfies the condition c^2 = a^2 + b^2. By comparing this equation to the Pythagorean theorem, we can conclude that the triangle must have a right angle opposite the side of length c.

This is one way to prove the Pythagorean theorem and its converse, demonstrating the relationship between the lengths of the sides in a right-angled triangle.

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Using the scale 1/4 inch = 1 foot, a room that is 10 feet by 20 feet would be represented by a scale drawing that is 2.5 inches by 5 inches.

The dimensions of the room in the scale drawing would be:

Width: 2.5 inches

Length: 5 inches

Please find the sketch below.

A scale drawing is a drawing that represents an object or space in proportion to its actual size.

It is used to show the relationship between different parts of an object or space, and to provide accurate measurements of its dimensions.

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A rough sketch of what the room might look like in scale:

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Please note that this is a rough sketch and the furniture placement is just an approximation.

Also, the furniture is not to scale, but just a representation of where it might be placed in the room.

Answer:

I think the answer is C.

Step-by-step explanation:

A triangle inside always has to add up to 180. So of you subtract 78 and 41 from 180 it wil give you 61

a. The number of passengers for each cruise line in thousands:

4,133,000 passengers ÷ 1,000 = 4,133 passengers

2,369,000 passengers ÷ 1,000 = 2,369 passengers

1,295,000 passengers ÷ 1,000 = 1,295 passengers

928,000 passengers ÷ 1,000 = 928 passengers

679,000 passengers ÷ 1,000 = 679 passengers

So, the answer is 4,133; 2,369; 1,295; 928; 679.

b. The mean number of passengers can be found by adding the number of passengers for each cruise line and then dividing the total by the number of cruise lines, which is 5.

(4,133 + 2,369 + 1,295 + 928 + 679) ÷ 5 = 10,514 ÷ 5 = 2,102.8 passengers

So, the mean number of passengers is 2,102.8 passengers.

c. The range is the difference between the highest and lowest number of passengers, which is:

4,133 - 679 = 3,454 passengers

So, the range is 3,454 passengers.

d. The standard deviation can be calculated using the formula for the standard deviation of a sample. However, this calculation is quite complex and requires a significant amount of mathematical knowledge and computational resources. Without access to those resources, the standard deviation cannot be calculated

The standard deviation is a measure of the amount of variation or dispersion from the mean. It shows how spread out the values in a set of data are. To calculate the standard deviation, the difference of each value from the mean is squared and then divided by the number of items in the set. The standard deviation provides a way to quantify the degree of variation of the values around the mean. It is a useful tool for understanding how much each value in a set deviates from the average.

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A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

16 and -16

Step-by-step explanation:

Answer: D. 16 and -16

Step-by-step explanation: I dont think you need an explanation because it is multiple choice.

Answer:

A. i think

Step-by-step explanation:

because it can't be E. (there is no 3 in-between the circle) And it can't be D. Because there isn't a 16 inbetween the circle and plus etc! and it could be C. also, because it is 4 and 4 is in-between the circle but, the difference between the answer A and C is the plus sign or the minus sign so let's think about that, it could be A or C............A. says (x-3)2 + (y-3)2=4 that seems correct and C. says (x+3)2 + (y+3)2 = 4.......we do not add in this case so it is definitely A. :)

Answer:

(x − 3)2 + (y − 3)2 = 4

Step-by-step explanation:

Answer: 15m^2+22m-5

Use FOIL (first, outter, inner, last) to multiply the polynomials.

(3m + 5)(5m - 1)

= 15m^2-3m+25m-5

= 15m^2+22m-5

Therefore, the solution is: (a) Yes, x(1) is real.(b) No, x(1) is not even.(c) No, dx(t)/dt is not even.

(a) Yes, x(1) is real because the function x(t) is periodic and the given Fourier series coefficients are 2,

= {²¹4, ak = k = 0 otherwise}.

A real periodic function is the one whose imaginary part is zero.

Hence, x(t) is a real periodic function. Thus, x(1) is also real.(b) Is x(1) even?

To check whether x(1) is even or not, we need to check the symmetry of the function x(t).The function is even if x(t) = x(-t).x(t) = 2, = {²¹4, ak = k = 0 otherwise}.

x(-t) = 2, = {²¹4, ak = k = 0 otherwise}.Clearly, the given function is not even.

Hence, x(1) is not even.(c) Is dx(t)/dt even?

To check whether the function is even or not, we need to check the symmetry of the derivative of the function, dx(t)/dt.

The function is even if dx(t)/dt

= -dx(-t)/dt.x(t)

= 2,

= {²¹4, ak = k = 0 otherwise}.

dx(t)/dt = 0 + 4cos(t) - 8sin(2t) + 12cos(3t) - 16sin(4t) + ...dx(-t)/dt

= 0 + 4cos(-t) - 8sin(-2t) + 12cos(-3t) - 16sin(-4t) + ...

= 4cos(t) + 16sin(2t) + 12cos(3t) + 16sin(4t) + ...

Clearly, dx(t)/dt ≠ -dx(-t)/dt.

Hence, dx(t)/dt is not even.

The symbol "ak" is not visible in the question.

Hence, it is assumed that ak represents Fourier series coefficients.

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Answer:

4 my good sir

Step-by-step explanation:

Answer:

-4

Explanation:

Given any quadratic function of the form:

Its discriminant is obtained by using the formula:

Comparing our given equation with the form of a quadratic above, we have:

Therefore, the discriminant will be:

The value of the discriminant for the given quadratic is -4.

The given information is that 1.504 ÷ 4.7 equals 0.32. We can use this information to solve for the value of 320 * 0.7.

Let's start by rearranging the given equation:

1.504 ÷ 4.7 = 0.32

Next, we can multiply both sides of the equation by 4.7 to isolate 1.504:

1.504 = 0.32 * 4.7

Simplifying the right side of the equation gives us:

1.504 = 1.504

This shows that the equation is balanced, meaning the values are equal. Therefore, we can conclude that the value of 320 * 0.7 is also 1.504.

Based on the given equation 1.504 ÷ 4.7 = 0.32, we can deduce that the value of 320 * 0.7 is 1.504.

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Answer:

2

Step-by-step explanation:

h ( x ) = - x - 4

To find : h ( - 6 )

h ( - 6 ) = h ( x )

Here,

x = - 6

h ( - 6 ) = - x - 4

           = - ( - 6 ) - 4

           = 6 + 4

h ( - 6 ) = 2

The power series expansion of f(x) = ln(1 + x²) about a=0 can be found using geometric series, differentiation, and integration of power series. The expansion is given by:

ln(1 + x²) = x² - (1/2)x⁴ + (1/3)x⁶ - (1/4)x⁸ + ...

To find the power series expansion, we start by considering the geometric series expansion of ln(1 + x). Using the formula for the sum of an infinite geometric series, we have:

ln(1 + x) = x - (1/2)x² + (1/3)x³ - (1/4)x⁴ + ...

Now, we substitute x² for x in the above series to get the power series expansion for ln(1 + x²):

ln(1 + x²) = x² - (1/2)(x²)² + (1/3)(x²)³ - (1/4)(x²)⁴ + ...

Simplifying the terms, we have:

ln(1 + x²) = x² - (1/2)x² + (1/3)x⁶  - (1/4)x⁸ + ...

The interval of convergence for this power series expansion is -1 < x < 1, which means the expansion is valid for values of x within this interval. The radius of convergence is 1, which indicates that the series converges absolutely for values of x within the interval -1 < x < 1.

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Answer: Yes.

Step-by-step explanation:

600 x 0.41 or 41% = 246, which yes is different from 0.41.

Answer:

$3.15

Step-by-step explanation:

Divide the total amount of money Marisa earned by the number of days.

Hope this is helpful!!! :)

Answer:

Marisa earned $3.15 a day.

Step-by-step explanation:

To find this, first we must identify our info. We know that the total for the 5 days of walking a dog was $15.75. So, to find out how much money she earned each day, simply divide $15.75 by 5.

You will get $3.15. That means that Marisa earned $3.15 a day for walking the dog.

The probability that the first card is an odd number and the second card is less than 4 is 3/20.

We have,

To calculate the probability, we need to determine the number of favorable outcomes (the desired outcomes) and the total number of possible outcomes.

Favorable outcomes:

The first card is an odd number and has a probability of 5/10 since there are 5 odd-numbered cards (1, 3, 5, 7, 9) out of a total of 10 cards.

The second card is less than 4 and also has a probability of 3/10 since there are 3 cards (1, 2, 3) less than 4 out of a total of 10 cards.

Total number of possible outcomes:

Since we replace the first card before selecting the second card, the total number of possible outcomes for each selection is still 10.

Now, to find the probability of both events happening, we multiply the probabilities of each event:

Probability = (Probability of the first card being odd) * (Probability of the second card being less than 4)

= (5/10) x (3/10)

= 15/100

= 3/20

Therefore,

The probability that the first card is an odd number and the second card is less than 4 is 3/20.

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The Euclidean inner product of the given vectors is 25.

The Euclidean inner product of two vectors u and v is defined as the sum of the products of the corresponding entries of the vectors. In mathematical terms, it is given by:

Euclidean inner product = u[1]*v[1] + u[2]*v[2] + u[3]*v[3]

Given the vectors u=[[5],[3],[-4]] and v=[[1],[0],[-5]], we can find the Euclidean inner product by substituting the values into the formula:

Euclidean inner product = (5)*(1) + (3)*(0) + (-4)*(-5)
= 5 + 0 + 20
= 25

Therefore, the Euclidean inner product of the given vectors is 25.

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Answer:

a) y = -2/5x + 3   b) (20, 19)

Step-by-step explanation:

a) slope of PQ => 24-9/22-16 = 15/6 = 5/2

perpendicular line have negative reciprocal slope = -2/5

substitute the new slope -2/5(m) and (5, 1) into the equation: y = mx + c  to find the value of c

=> 1 = -2/5(5) + c

=> c = 3

plug in both the slope -2/5(m) and b = 3 into the equation: y = mx + c

=> y = -2/5x + 3

b) (2/3(22 -16), 2/3(24 - 9))=> (4, 10)

(16, 9) + (4, 10) = (20, 19)

Answer:

the answe r is I because it does not mirror the other side

\( {3}^{ - 2} \times {3}^{ - 5} = {3}^{ - 7} \)

Answer:

A) 3^-7

Step-by-step explanation:

The probability that exactly 10 are yellow out of 9 random selections is 0.

To calculate the probability of exactly 10 jelly beans being yellow out of 9 selected at random, we need to consider the total number of favorable outcomes (selecting exactly 10 yellow jelly beans) divided by the total number of possible outcomes (selecting any 9 jelly beans).

The total number of jelly beans in the box is 23 (yellow) + 33 (green) + 37 (red) = 93.

The number of ways to select exactly 10 yellow jelly beans out of 9 is 0, as we have fewer yellow jelly beans than the required number.

Therefore, the probability of exactly 10 yellow jelly beans is 0.

In this case, it is not possible to have exactly 10 yellow jelly beans out of the 9 selected because there are not enough yellow jelly beans available in the box.

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A box contains 23 yellow, 33 green and 37 red jelly beans. if 9 jelly beans are selected at random, what is the probability that: exactly 10 are yellow?