Please help:) calculus asking about delta functions

By using the substitution method, the value of x is equal to -1.94 and the value of y is 2.71.

In order to solve the given system of linear equations, we would apply the substitution method. From the information provided in the question above, we have the following system of linear equations:

y = 5x - 7      .......equation 1.

3y - 2x = -12          .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

-3(5x - 7) - 2x = -12

-15x + 21 - 2x = -12

-17x = -12 - 21

17x = -33

x = -33/17 or -1.94

For the value of y, we have:

y = 5(-33/17) - 7

y = -165/17 - 7

y = 2.71

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Weighed averages show that the student has a grade point average of 2.33.

The grade point average (GPA) is calculated by multiplying the unit value for each course in which a student receives one of the aforementioned grades by the grade point total for that grade. Divide the total of these products by the total number of units. By dividing the total grade points by the total number of units, the cumulative GPA is determined.

A. The student's weighted mean grade point score is (3 classes) × (3 credits per class) × (3 points for a B) ÷ (9 total credits) = 3.00.

B. The student's weighted mean grade point score is (1 class) × (3 credits) × (1 point for a D) ÷ (3 total credits) = 1.00.

C. The student's weighted mean grade point score is (1 class) × (4 credits) × (2 points for a C) ÷ (4 total credits) = 2.00.

D. The student's weighted mean grade point score is (1 class) × (2 credits) × (2 points for a C) ÷ (2 total credits) = 2.00.

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The perimeter of the parallelogram is 10units

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.

To obtain the perimeter of the parallelogram , we add all the sides together.

P = 2(l+b)

P= 2( c-2+12-c)

P = 2( c-c -2 +12 )

P = 2( 10)

P = 20

therefore the perimeter of the parallelogram is 20

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Step-by-step explanation:

The average rate of change of a function on an interval [x, x + h] is given by the formula:

(F(x + h) - F(x)) / h

For the function F(x) = 6x^2 + 5, the average rate of change on the interval [x, x + h] is:

(F(x + h) - F(x)) / h = (6(x + h)^2 + 5 - (6x^2 + 5)) / h = (6(x^2 + 2xh + h^2) - 6x^2 + 5) / h = (6(2xh + h^2)) / h = (12xh + 6h^2) / h

So the average rate of change of the function on the interval [x, x + h] is (12xh + 6h^2) / h for a real number h.

Answer:

The equation that matches the number of zombies after 2 hours would be:

23 × 4^2 = 23 × 16 = 368

So after 2 hours, there would be 368 aggressive zombies.

Answer:

To solve this problem, we can use the formula for exponential growth:

V(t) = V0 * (1 + r)^t

where:

V(t) is the value of the equipment at time t

V0 is the initial value of the equipment ($15,000)

r is the annual growth rate (15.9% or 0.159)

t is the time in years

We want to find the time t when the value of the equipment will be less than $7500. So we can set up the following inequality:

V(t) < 7500

Substituting the formula for V(t), we get:

V0 * (1 + r)^t < 7500

Substituting the given values, we get:

15000 * (1 + 0.159)^t < 7500

Simplifying and solving for t,

we get:(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

So the company's new equipment will be worth less than $7500 after about 2.64 years.

Step-by-step explanation:

If a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.

What is inequality?

In mathematics, an inequality is a statement that describes a relationship between two values, expressing that one value is greater than, less than, or equal to the other value. Inequalities are denoted by symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).

The inequality 10 < y means that "y" is greater than 10. To determine whether a given value of "y" is a solution to this inequality, we simply need to check whether that value is indeed greater than 10.

For example:

If y = 11, then 10 < y is true, because 11 is greater than 10.

If y = 10, then 10 < y is false, because 10 is not greater than 10 (they are equal).

If y = 9, then 10 < y is false, because 9 is not greater than 10.

Hence, if a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.

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68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.

What is a circle graph?

A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarise a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments.

Let's say the total number of students = X.

From the circle graph, we can say that 15% of students chose cinnamon twists and their count is 12.

Which means that

[tex]X*\frac{15}{100}=12\\ X=80[/tex]

Therefore the total number of students is 80.

Among the 80 students except for 12 students, the remaining students asked for jumbo chocolate chip cookies.

Which is equal to 80-12=68.

Therefore 68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.

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Sure! To reduce the fraction 5 to its lowest terms, we need to find the greatest common factor of 5 and divide both the numerator and denominator by it.

The greatest common factor of 5 and 5 is 5, so we divide both the numerator and denominator by 5 to get:

5 / 5 = 1

So, 5 reduced to its lowest terms is 1.

To make it kid-friendly, you could explain it like this: "We can simplify the fraction 5 by dividing the top and bottom by the biggest number that they both share. In this case, 5 is the biggest number that 5 and 5 share, so we divide both 5 and 5 by 5 to get 1."

Answer:

96 stamps

Step-by-step explanation:

We know

Connor collected 80 stamps last year. This year he increased his collection by 20%.

80 stamps = 100%

100% + 20% = 120%

So, this year he collected 120% of the number of stamps from last year.

120% = 1.2

How many stamps are in his collection?

We take

80 times 1.2 = 96 stamps

So, there are 96 stamps in his collection.

8. The center and radius of the circle given the following equation:

(x + 4)^2 + (y - 2) ^ 2 = 5 is

9. The  equation for the circle is

10. The length of arc AB is

Information given in the question

a circle whose equation is (x + 4)^2 + (y - 2) ^ 2 = 5

Equation of a circle is given as:

(x - h)² + (y - k)² = r²

Where

r = radius

h and k are coordinates of the center

x and y is the coordinate of point on the circumference

The equation of the circle is compared with the given equation and this shows that

Using the graph the centers are (-5, -2) and the radius is 3, this will give equation  (x + 5)² + (y + 2)² = 3²

If angle ACB = 60 deg and the radius is 12 cm,  length of arc

= 60 / 360 * 2 * π * 12

= 4π

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Answer

[tex] - 95.783[/tex]

Answer:

To find the coefficient of variation (CV) of a sample, we divide the standard deviation by the mean and multiply by 100 to get the percentage.

1. For the systolic sample:

•Find the mean:

mean = (116 + 130 + 157 + 94 + 155 + 122 + 115 + 138 + 124 + 122) / 10 = 130

•Find the standard deviation:

sum = (116 - 130)^2 + (130 - 130)^2 + (157 - 130)^2 + (94 - 130)^2 + (155 - 130)^2 + (122 - 130)^2 + (115 - 130)^2 + (138 - 130)^2 + (124 - 130)^2 + (122 - 130)^2

sum = 165.4

std = sqrt(sum/9) = 7.3

•Calculate the coefficient of variation:

CV = (std / mean) × 100 = (7.3 / 130) × 100 = 5.62%

2. For the diastolic sample:

•Find the mean:

mean = (82 + 78 + 74 + 51 + 89 + 88 + 56 + 63 + 72 + 83) / 10 = 72.5

•Find the standard deviation:

sum = (82 - 72.5)^2 + (78 - 72.5)^2 + (74 - 72.5)^2 + (51 - 72.5)^2 + (89 - 72.5)^2 + (88 - 72.5)^2 + (56 - 72.5)^2 + (63 - 72.5)^2 + (72 - 72.5)^2 + (83 - 72.5)^2

sum = 624.75

std = sqrt(sum/9) = 12.24

•Calculate the coefficient of variation:

CV = (std / mean) × 100 = (12.24 / 72.5) × 100 = 16.82%

So the CV for systolic is 5.62% and the CV for diastolic is 16.82%. We can see that the diastolic measurement has higher variation than the systolic measurement.

Answer: 2 hours babysitting

Step-by-step explanation:

18 x 9 = 162

180-162= 18

meaning he'd have to work 2 hours babysitting to get to meet his requirement.

hours used = 11

hours left= 3

The number of times it is not land on the blue color sector is 7-1 = 6

A probability is defined as the ratio to the number of required outcomes to the total number of outcomes of an event.

The spinner is divided into 7 sectors, in which each sector is equal in size.

Among 7 sectors two of of them are blue in color.

We have to calculate that how many times the spinner not landing on the blue color sector.

For that we have to calculate the possible outcome for the blue color sector for 1 spin.

For 1 spin , the number of possible outcomes = 7.

Number of required outcomes = 2.

Probability of number of spins on blue sector for 1 spin = 2/7.

Probability of number of spins on blue sector for 7 spin = 7*(2/7) = 2.

Standard deviation = [tex]\sqrt{\frac{2}{7} *\frac{5}{7} }[/tex]= 0.4518.≅0.452.

Standard error=root(7)*0.452= 1.19≅1.2

Expected value =2-1.2 = 0.8 ≅1

Therefore the expected value is 1.

Number of times it will land on the blue color sector is 1.

Hence, the number of times it is not land on the blue color sector is 7-1 = 6.

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Answer:

-

Step-by-step explanation:

the question isn't clear enough to answer it

Answer:

Step-by-step explanation:

here's a step-by-step explanation with more detail:

The equation X^2 + X + 8 = 0 can be solved using the Quadratic Formula:

X = (-b ± √(b^2 - 4ac)) / 2a,

where a = 1, b = 1, and c = 8.

Plugging in the values, we get:

X = (-1 ± √(1^2 - 4 * 1 * 8)) / 2 * 1

X = (-1 ± √(-31)) / 2

Since the square root of a negative number is not a real number, the solution to the equation must be expressed using complex numbers. In this case, the square root of -31 can be expressed as the imaginary unit i times the square root of 31.

X = (-1 ± i * √31) / 2

So, the two solutions to the equation are:

X = (-1 + i * √31) / 2 and X = (-1 - i * √31) / 2

And these are the two solutions expressed in terms of the imaginary unit i.

The function g(x) = (x - 3)³ is shown in the graph. The solution has been obtained by using the concept of transformation.

What is transformation?

Any action that moves a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation.

Translation, rotation, reflection, and dilation are all methods of transformation.

We are given a graph, from which we can say that when x = 3, then y = 0

The function must satisfy these values.

The functions g(x) = (x + 3)³ , g(x) = x³ + 3 and g(x) = x³ − 3 does not satisfy the point (3,0).

Also, the translation is 3 units to the right.

So the function shown in the graph is g(x) = (x - 3)³.

Hence, the transformed function is g(x) = (x - 3)³.

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Question: If the parent function is f(x) = x³, which transformed function is show in the graph?

g(x) = (x − 3)³ , g(x) = (x + 3)³ , g(x) = x³ + 3 , g(x) = x³ − 3

x^2 - 2x + 1 is the required quadratic equation using the completing the square

Given the quadratic expression below

x^2 - 2x

We need to determine the constant that will make the expression a perfect square.

The constant will be the half of the square of coefficient of 'x'

Coefficient of 'x' = -2

Half of the coefficient of 'x' = -2/2 = -1

Square of the coefficient = (-2/2)^2

Square of the coefficient = 1

Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1

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Answer:

EF this is the correct answer

Answer:

  1625

Step-by-step explanation:

You want the sum of the first 25 terms of the series 5 +10 +15 +....

The first term is 5, the common difference is 5, so the general term is ...

  an = a1 +d(n -1)

  an = 5 +5(n -1)

The last term of the sum is ...

  a25 = 5 +5(25 -1) = 125

The sum of the series is the average of the first and last terms, multiplied by the number of terms:

  S25 = (a1 +a25)/2 · 25 = (5 +125)/2 · 25 = 65·25 = 1625

The sum of 25 terms of the series is 1625.

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The two possible locations of the fourth vertex are (4, -1) and (-6, 9). The solution has been obtained by using the properties of parallelogram.

What is a parallelogram?

A parallelogram has two sets of parallel sides, making it a quadrilateral. A parallelogram's opposing sides and angles are both the same length.

Finding the vector that depicts the shift from one of the given vertices to another is necessary in order to determine the fourth vertex of a parallelogram.

The third given vertex must then be added to the vector.

We know that the opposite sides of a parallelogram are parallel and equal in length, we may determine the coordinates of the other two vertices by adding the same displacement vector to two of the given vertices.

The difference between the first and second provided vertices i.e.

(1 - (-4), -2 - 3), is one potential displacement vector which is (5, -5).

On adding this vector to the third vertex, we get the fourth vertex as (4,-1).

Similarly, the difference between the second and third vertices i.e.

(-1 - 1, 4 - (-2))  is another potential displacement vector which is (-2, 6).

On adding this vector to the third vertex, we get the fourth vertex as

(-6, 9).

Hence, the two possible locations of the fourth vertex are (4, -1) and

(-6, 9).

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Answer:

a. The probability that a married couple watches the show can be calculated by multiplying the probabilities that each spouse watches the show:

P(Married couple watches the show) = P(Husband watches the show) * P(Wife watches the show) = 0.4 * 0.5 = 0.2

Step-by-step explanation:

b. The probability that a wife watches the show, given that her husband does, can be calculated using Bayes' theorem:

P(Wife watches the show | Husband watches the show) = P(Husband watches the show | Wife watches the show) * P(Wife watches the show) / P(Husband watches the show)

P(Wife watches the show | Husband watches the show) = 0.7 * 0.5 / 0.4 = 0.875

c. The probability that at least one member of a married couple will watch the show can be calculated as the sum of the probabilities that either the husband or the wife watches the show:

P(At least one member of a married couple watches the show) = P(Husband watches the show) + P(Wife watches the show) - P(Married couple watches the show) = 0.4 + 0.5 - 0.2 = 0.7

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

The first order derivative of the given function is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

The given function is [tex]f(x)=\sqrt{x+\sqrt{x+\sqrt{x} } }[/tex].

The derivative using the chain and power rules is

f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex]

Therefore, the first order derivative is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].

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Answer:

m = -4

Step-by-step explanation:

-2 ( m + 1 ) = 10

( m + 1 ) = 10 / -2

m + 1 = -5

m = -4

The distance at which Allison should stand to catch the ball will be 8.32 m.

What is speed?

Speed of an object is defined as the ratio of distance covered by the object to the time taken by the object to cover that distance. In other words its tell how much times an object takes to cover a particular distance.

Now for the given question:

Emily throw the ball at 30° below the horizontal towards Allison at a speed of 12m/s. So here we will calculate the Horizontal and Vertical components of the speed.

[tex]v_{x}[/tex]=12cos30°=10.4 m/s

[tex]v_{y}[/tex]=12sin30°=6 m/s

Vertical distance between Alice and Emily according the question is 8 m.

s= 8 m.

Now by applying Second equation of motion to calculate time take by ball to move from Emily to Allison.

s=[tex]v_{y}[/tex]×t+[tex]\frac{1}{2}[/tex]×a×[tex]t^{2}[/tex]

4= 6×t+[tex]\frac{1}{2}[/tex]×9.8×[tex]t^{2}[/tex]           (a=9.8 m/[tex]s^{2}[/tex] acc. due to gravity a constant)

By solving above quadratic equation we get

t= 0.8 s

To find horizontal distance

d= [tex]v_{x}[/tex]×t

d=10.4×0.8

d= 8.32 m

Hence Allison should stand at a distance of 8.32 m to catch the ball.

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The values are a = 16.69, c=16.68 ad m∠C = 22.07°.

What are trigonometric ratios?

Trigonometric ratios are mathematical functions that describe the relationship between the angles and sides of a right triangle. The three main trigonometric ratios are the sine, cosine, and tangent.

In the given figure, by using trigonometric ratios, we can find

sin68° = a/18

18 sin 68° = a

Using a calculator, we can find that sin 68° is approximately 0.9272. Multiplying 18 by 0.9272 gives us:

a ≈ 16.69

Therefore, a is approximately 16.69.

cos68° = c/18

18 cos 68° = c

Using a calculator, we can find that cos 68° is approximately 0.3714. Multiplying 18 by 0.3714 gives us:

c ≈ 6.68

Now

sinC = c/18

[tex]C = sin^{-1}(\frac{6.68}{18})\\\\C = sin^{-1}(0.3714)\\\\C = 22.07\degree[/tex]

Hence, the values are a = 16.69, c=16.68 ad m∠C = 22.07°.

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