Find the value of x
a. 13 b. 14/5 c. 5 d. 8

The z-score for a data value of 98 in a normal distribution with a mean of 80 and a standard deviation of 5 is approximately 3.60.

The z-score is a measure of how many standard deviations a data value is away from the mean in a normal distribution. It is calculated by subtracting the mean from the data value and then dividing the result by the standard deviation. In this case, the data value is 98, the mean is 80, and the standard deviation is 5.

Using the formula for calculating the z-score, we have:

z = (data value - mean) / standard deviation

 = (98 - 80) / 5

 = 18 / 5

 = 3.60

Rounding the z-score to two decimal places, we find that the z-score for a data value of 98 is approximately 3.60. This means that the data value of 98 is 3.60 standard deviations above the mean. The positive value indicates that the data value is above the mean.

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To find a numerical solution of this initial value problem (IVP), we need to use a numerical method such as Euler's method or the Runge-Kutta method. Let's use the Runge-Kutta method with a step size of h=0.1.

The given IVP can be written as:

x''(t) - x(t) = 0,

with initial conditions x(1) = 1 and x'(1) = 2.

We can rewrite this second-order ODE as a system of first-order ODEs:

x'(t) = v(t),
v'(t) = x(t).

Now, using the Runge-Kutta method with h=0.1, we can approximate the solution at t=1.1, 1.2, 1.3, 1.4, and 1.5.

Let's define the function F(t, y) that represents the system of first-order ODEs:

F(t, y) = [y[1], y[0]]

where y[0] = x(t) and y[1] = v(t).

Then, we can apply the Runge-Kutta method to approximate the solution as follows:

t_0 = 1
y_0 = [1, 2]

for i = 1 to 5 do
 k1 = h * F(t_i-1, y_i-1)
 k2 = h * F(t_i-1 + h/2, y_i-1 + k1/2)
 k3 = h * F(t_i-1 + h/2, y_i-1 + k2/2)
 k4 = h * F(t_i-1 + h, y_i-1 + k3)
 y_i = y_i-1 + 1/6 * (k1 + 2*k2 + 2*k3 + k4)
 t_i = t_i-1 + h

The values of x(t) at t=1.1, 1.2, 1.3, 1.4, and 1.5 are then given by y_i[0] for i = 1 to 5:

y_1 = [1.2, 2.2]
y_2 = [1.442, 2.44]
y_3 = [1.721, 2.868]
y_4 = [2.041, 3.572]
y_5 = [2.408, 4.609]

Therefore, the numerical solution of the IVP is:

x(1.1) ≈ 1.2
x(1.2) ≈ 1.442
x(1.3) ≈ 1.721
x(1.4) ≈ 2.041
x(1.5) ≈ 2.408

Note that we only approximated the solution using a step size of h=0.1. The accuracy of the numerical solution can be improved by using a smaller step size.

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Answer:

0.125 times larger

Step-by-step explanation:

given the scale factor of 2 solids is k , then the volume  factor = k³

here k = 0.5 , so

volume factor = (0.5)³ = 0.125

Answer:

Step-by-step explanation:

(14 + 7)/2 = 21/2= 10.5

(-2 + (-8))/2= -10/2= -5

Midpoint(10.5, -5)

Dividing the number by 2 gives half of the number which is less than the original number.

Given that,
To specify dividing by 2 always produces a number less than the original number.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Dividing the number by 2 gives half of the number which is less than the original number.
Let the number be x,
Dividing the number by 2
Gives, x / 2 = 0.5 * x
Imply,
Dividing the number by 2 gives half of the number which is less than the original number.

Thus, dividing the number by 2 gives half of the number which is less than the original number.

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a The revenue obtained from selling x pizzas is 25x - x²

b The profit obtained from selling x pizzas, is x² + 21x - 109.25

c The break-even points are approximately x = 9.94 and x = 11.06.

d The vertex of the demand equation is (12.5, 12.5).

e The marginal profit at a production level of 1000 pizzas is $11.

f Increasing x by one at a production level of 1000 pizzas will result in a marginal profit of $10.

a) Find R(x), the revenue obtained from selling x pizzas.

R(x) = x * p

R(x) = x * (25 - x)

R(x) = 25x - x²

b) Find P(x), the profit obtained from selling x pizzas, and simplify.

Profit is calculated as revenue minus cost.

P(x) = R(x) - C(x)

P(x) = (25x - x²) - (109.25 + 4x)

P(x) = -x² + 21x - 109.25

c) Find the Break-Even point(s) for P(x).

The break-even point is where the profit is zero.

Setting P(x) = 0:

x² + 21x - 109.25 = 0

x = (-b ± ✓(b² - 4ac)) / (2a)

For our equation:

a = -1, b = 21, c = -109.25

x = (-21 ± ✓(21² - 4(-1)(-109.25))) / (2(-1))

x = (-21 ± ✓(441 - 436.5)) / (-2)

x = (-21 ± ✓(4.5)) / (-2)

x = (-21 ± 2.121) / (-2)

x1 = (-21 + 2.121) / (-2) ≈ 9.94

x2 = (-21 - 2.121) / (-2)

≈ 11.06

The break-even points are approximately x = 9.94 and x = 11.06 (rounded to two decimal places).

d) Using the formula x = -b/2a, we can calculate the x-coordinate of the vertex:

x = -(25)/(2*(-1)) = -25/-2 = 12.5

p = 25 - x = 25 - 12.5

= 12.5

Therefore, the vertex of the demand equation is (12.5, 12.5).

e To find the marginal profit, we need to calculate the derivative of the profit function. The profit function is given by P(x) = xp - C(x).

P'(x) = p - C'(x)

C'(x) = 4

Substituting the values into the formula for marginal profit:

MP = p - C'(x) = 25 - x - 4

= 21 - x

To find the marginal profit at a production level of 1000 pizzas (x = 10), we substitute x = 10 into the marginal profit equation:

MP = 21 - 10 = 11

Therefore, the marginal profit at a production level of 1000 pizzas is $11.

f. Increasing x by one at a production level of 1000 pizzas means x will become 11. To find the new marginal profit, we substitute x = 11 into the marginal profit equation:

MP = 21 - 11

= 10

Therefore, increasing x by one at a production level of 1000 pizzas will result in a marginal profit of $10.

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Answer: $13875

Step-by-step explanation:

The interest in capital for X will be:

= 10% × $50000

= $5000

The interest in capital for Y will be:

= 10% × $30000

= $3000

The total amount credited to Y's current account will be:

= 3000/(3000 + 5000) × $37000

= 3/8 × $37000

= $13875

The total amount credited to Y's current account at the end of the year will be $13875

Answer:

The answer is F(2) is equal to 15

Step-by-step explanation:

My knowledge is so powerful my brain hurts when I think.

Hope this helped

this was easy!

let me know if you want help with anything else

\( \Large{\boxed{\sf (10 + 6i)(-2 - 4i) = 4 - 52i}} \)

\( \\ \)

To find the algebraic form, also called 'a + bi form', of the given complex number, we will have to expand its expression using FOIL method.

\( \\ \)

\( \Large{ \sf \: \underline{FOIL \: method \text{:}}} \\ \\ \Large{\boxed{\sf (A + B)(C + D) = AC + AD + BC + BD}} \)

\( \\ \)

Let's identify our coefficients and expand the given expression:

\( \sf (\underbrace{\sf 10}_{A} + \overbrace{\sf 6i}^{B})(\underbrace{\sf -2}_{C} \overbrace{\sf -4i}^{D}) = 10 \times (-2) + 10 \times (-4i) + 6i \times (-2) + 6i \times (-4i) \\ \\ \\ \sf = -20 - 40i - 12i - 24i^2 = -20 - 52i - 24i^2 \)

\( \\ \)

In the complex number system, i² = -1. Therefore, our final answer is:

\( \sf (10 + 6i)(- 2 - 4i) = -20 - 52i - 24(-1)= \boxed{\boxed{\sf 4 - 52i}} \)

\( \\ \\ \)

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Answer:

1)55,44

2)6,4

3)49,8

4)11,7

5)12,444

6)23,04

7)12,46

8)15,06

9)31,68

10)30,4

Step-by-step explanation:

Recheck them and make sure there are no mistakes

I'm not sure about questions 7-10 tho, very sorry

Step-by-step explanation:

11) 5/7

12) 1/4

13) 7/10

14) 3/4

15) 2/9

16) 2/5

17) 13/30

18) 27/50

19) 5/16

20) 4/15

21) 1/24

22) 7/12

23) 1/20

24) 8/15

25) 11/45

1

Step-by-step explanation:

The trick is to recognize a few things.

1. These are similar triangles, so the ratio of BU to BC is the same as BT to BA and UT to CA.

    \(\dfrac{BU}{BC}=\dfrac{BT}{BA}=\dfrac{UT}{CA}\)

2. BC = 2 BUs and BA = 2 BTs

This means the sides of the short triangle are half the length of the sides of the big triangle.

Put in other words, CA = 2 UT

Put into an equation x+29 = 2(x+19).

   x + 29 = 2x + 38

        –9  = x

So that means UT = 10 and CA = 20

List the first multiples of each number:

Multiples of 10

Multiples of 29:

Answer:

B

Step-by-step explanation:

The distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The time, t = π / 2 sec,

Calculate the distance by using the formula given below,

\(Distance = r\times time\)

So, for distance, a = 1 × π / 2 =  π / 2

for distance, b = 1 × π =  π

for distance, c = 1 × 3 π / 2 =  3 π / 2

Therefore, the distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

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Given:

Amount Marty spent per day = $3

Number of days = 14

Remaining amount = $68

Since the amount left depends on the number

The amount of border that Roberto will need to put around the edges of the platform, given the area is 16 units.

The platform is given in the figure and to find the amount of border that Roberto needs to cover it if the area is 12 square units, you need to count the number of dots all along the edges of the platforms.

Counting this would give us 16 dots. This then means that Roberto needs sixteen units of border to be able to put up a border around the edges of the platform.

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Answer:

Explanation:

Given the sum:

The sum (in base 3) is evaluated below:

The answer is 10110 (in base 3).

Answer: 1 amd -3

Step-by-step explanation:

(1)*(-3) = -3

(1)+(-3)= -2

Step-by-step explanation:

2 numbers multiplied equals -3

a × b = -3

the same 2 numbers added is -2

a + b = -2

a = -2 - b

we use this in the first equation

(-2 - b) × b = -3

we can see already here that one solution must be b=1 and a=-3.

but let's continue formally

-2b - b² = -3

-b² - 2b + 3 = 0

solving that quadratic equation based on the general formula

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x is named b (but is not the b of the general formula).

a = -1

b = -2

c = 3

b = (- -2 ± sqrt(-2² - 4×-1×3))/(2×-1) =

= (2 ± sqrt(4 + 12))/-2 = (2 ± sqrt(16))/-2 =

= (2 ± 4)/-2

b1 = (2+4)/-2 = 6/-2 = -3

b2 = (2-4)/-2 = -2/-2 = 1

for b1 we get an a1 :

a1 = -2 - b1 = -2 - -3 = -2 + 3 = 1

for b2 we get an a2 :

a2 = -2 - b2 = -2 - 1 = -3

so, there is only one combination of 2 numbers that fulfill the description : one has to be 1, and the other has to be -3

The value of that makes the volume of the parallelepiped with edges oa, ob, and oc equal to 3 units is  α = 1

The volume of a parallelopiped with sides a, b and c is V = a.(b × c)

Now, consider the parallelepiped with edges oa, ob, and oc, where a(2,1,0), (1,2,0), and c(0,1,α). To find the real number α>0 such that the volume of the parallelepiped is 3 units, we proceed as follows.

We know that the volume of the parallelopiped with sides a, b and c is  a.(b × c) where

Now  a.(b × c) =det \(\left[\begin{array}{ccc}2&1&0\\1&2&0\\0&1&\alpha \end{array}\right]\)

So,  a.(b × c) = 2(2 × α - 1 × 0) - 1(1 × α - 0 × 0) + 0(1 × 1 - 2 × 0)

= 2(2α - 0) - (α - 0) + 0(1 - 0)

= 2(2α) - (α) + 0(1)

= 4α - α + 0

= 3α + 0

= 3α

Now since the volume of the parallelopied is 3 units, we have that

a.(b × c) = 3

3α = 3

α = 3/3

α = 1

So, α = 1

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The value of the vector is : 3b - 2c + d is equal to [6, 14, -2].

Here, we have,

To compute the vector 3b - 2c + d, we need to perform scalar multiplication and vector addition.

Given:

b = [3, 2, 1]

c = [1, -4, 1]

d = [-1, -1, -3]

We can now compute 3b - 2c + d as follows:

3b = 3 * [3, 2, 1] = [9, 6, 3]

2c = 2 * [1, -4, 1] = [2, -8, 2]

d = [-1, -1, -3]

Now, let's perform vector addition:

3b - 2c + d = [9, 6, 3] - [2, -8, 2] + [-1, -1, -3]

Performing the addition component-wise:

3b - 2c + d

= [9 - 2 - 1, 6 - (-8) - 1, 3 - 2 - 3]

= [6, 14, -2]

Therefore, 3b - 2c + d is equal to [6, 14, -2].

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The amount of the markup is $48 + $48 (0.55) .

Option (C) is correct .

Mark up refers to the value that a player adds to the cost price of a product. The value added is called the mark-up. The mark-up added to the cost price usually equals retail price.

As given

An item is purchased for a wholesale price of $48 and will be sold at a 55 percent markup.

55% is written in the decimal form .

                                              = 55/100

                                              = 0.55

Markup price = 0.55 × wholesale price of item .

                      = 0.55 × $48

                     = $48 (0.55)

Price of item after markup = Wholesale price of item + Markup price

                                           = $48 + $48 (0.55)

Thus, the amount of the markup is $48 + $48 (0.55) .

Option (C) is correct .

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Answer:The answer is A

Step-by-step explanation:

Edg 2022 (sometimes the verified ones are wrong)

Answer:

12

Step-by-step explanation:

If we know that hanj is a decreasing sequence and all its terms lie between the numbers 5 and 8, it can be explained as follows:

Decreasing Sequence: The term "decreasing sequence" means that each subsequent term in the sequence is smaller than its preceding term. In the case of hanj, this implies that each hanj term is smaller than the one that comes before it. This information establishes the order and pattern of the sequence.

Upper Bound: The fact that all the terms of hanj lie between the numbers 5 and 8 indicates that no term in the sequence exceeds the value of 8. This upper bound of 8 sets a limit on the magnitude of the hanj terms, ensuring they do not exceed this value.

Lower Bound: Similarly, the statement suggests that none of the hanj terms is less than the number 5. This establishes a lower bound for the sequence, indicating that the terms are not smaller than 5.

Combining these two bounds (5 and 8) along with the decreasing nature of the sequence, we can conclude that the hanj sequence is a monotonically decreasing sequence with terms ranging from 5 to 8, inclusive.

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Answer:

29

Step-by-step explanation:

The angle represented with 2x and the angle with the measure 32 are complementary so their sum is equal to 90 degrees

We know this because it's seen in the figure that the angle is a right angle

2x + 32 = 90 subtract 32 from both sides

2x = 58 divide both sides by 2

x = 29