The sum of 2 numbers is 150.One number is 12 more than the other number.What is the smaller number?​

This is just an algebraic problem, the correct option is:

"Myra should have multiplied 4.5 and 2.1 first."

Here we want to evaluate the expression:

-31.7 + 4.5*x

in x = 2.1

This just means that we need to replace x by 2.1 in the given equation.

Now, what Myra does is:

-31.7 + 4.5*2.1 = -27.2*2.1

So she took the sum between -31.7 and 4.5 first, this is her mistake, you only would do that if the expression was:

(-31.7 + 4.5)*2.1

But in our expression:

-31.7 + 4.5*2.1

The first thing you need to solve is the product in the second term, so we get:

-31.7 + 4.5*2.1 = -31.7 + 9.45 = -22.25

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From the given numbers, the greatest number is 23 × 10^126

The first number = 23 × 10^126

The second number = 23 × 10^86

The third number = 23 × 10^66

The fourth number = 23 × 10^3

The scientific notation is defined as the easiest method to represents the very smallest or the largest number. The scientific notation consist of a whole number multiplied by the power of ten

Here, the whole number is same in all cases, only the power of the 10 is different . To find the largest number we have to find the number with largest power of 10

The number with largest power of 10 = 23 × 10^126

Hence, the greatest number is 23 × 10^126

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Answer:

There are about 118868 employees at the company.

Step-by-step explanation:

When dealing with percentage problems, we can use the following equation:

P%x = y, where P% of x is y.

Since we're told that 25200 is 21.2% of the total number of employees, we substitute 21.2% for P and 25200 for y in the formula to solve for x, the total number of employees.

Furthermore, we must first convert the percentage to a decimal by dividing 21.2 by 100:  21.2 / 100 = 0.212

0.212x = 25200

Step 1:  Divide both sides by 0.212 to solve for x:

(0.212x = 25200) / 0.212

x = 118867.9245

Step 2:  Round to the nearest whole number to get the final answer.

118867.9245 rounded to the nearest whole number is 118868.  Thus, the company has about 118867 employees in total.

Step 3:  Check that 21.2% of 118868 is (exactly or approximately) 25200:

0.212 * 118868 = 25200

25200.016 > 25200

Although 25200.016 is slightly larger than 25200, we can still trust that our answer is 11868 since it's rounded and an approximation.  A more exact number like 118867.9245 would give us exactly 25200.

The solution for x is x ∈ (-∞, 11] ∪ (9, ∞)

We are given that;

The inequality − 36 < − 3− 9 or −36<−3x−9or − 42 ≥ − 3 − 9 −42≥−3x−9

Now,

You can solve this inequality by first adding 9 to both sides of each inequality to get:

-27 < -3x or -33 >= -3x

Then, divide both sides of each inequality by -3, remembering to reverse the inequality symbol when dividing by a negative number:

9 > x or 11 <= x

Therefore, by inequality the answer will be x ∈ (-∞, 11] ∪ (9, ∞).

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The task is to find the convolution of the marginal distributions of two independent random variables x and y with identical geometric distributions.

To find the convolution of the marginal distributions of x and y, we need to calculate the probability distribution function of the sum of x and y. Since x and y have identical geometric distributions, we know that the probability of x=k and y=m is given by p(x=k, y=m) = (1-p)^k * p * (1-p)^m * p = p^2 * (1-p)^(k+m), where p is the probability of success in each trial of the geometric distribution.

To find the probability distribution function of the sum Z=x+y, we need to compute the probability of each possible value of Z. That is, P(Z=k) = Σ P(X=i, Y=k-i) for all i from 0 to k. Plugging in the probability distribution function of x and y, we get P(Z=k) = Σ p^2 * (1-p)^(i+k-i) = p^2 * (1-p)^k * Σ 1. The summation is over all i from 0 to k, and is equal to k+1. Therefore, we have P(Z=k) = (k+1) * p^2 * (1-p)^k. This is the probability distribution function of the sum of two independent random variables x and y with identical geometric distributions, and is the convolution of the marginal distributions of x and y.

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Answer:

5. p (6) = -6

6. f (-9) = -3

7. g (-4) = 15

8. h (5) = 19

9. u answered already

10. p (-9) = 9

11. f (-11) = -5

12. g (1) = 0

13. h(-4) = -8

14. k (10) = 181

15. p (11) = 11

16. f(-8) = -2

17. g (-10) = 99

18. h (3) = 13

19. k (6) = 49

20. p (99) = -99

21. f(0) = 6

22. g (2) = 3

23. h(0) = 4

24. k(3) = 7

25. p(-1/2) = 1/2

26. f (0.4) = 6.4

27. g (1/2) = -3/4

28. h (-1.2) = 0.4

29. k (1/2) = -1/2

30. p (\(\sqrt{6}\)) = -\(\sqrt{6}\)

Hope this helps! If it does, please mark me Brainliest. Remember to report any answer that copies mine. Thanks!

The required, Mmusi borrowed R3000 from Aggie as per the given conditions.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.

Amount = Principal [1 + rate×time]

Let's call the amount Mmusi borrowed from Aggie "P".

After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P

So if he has to pay back R4080, we can set up an equation to solve for P:

1.36P = 4080

To find P, we can divide both sides by 1.36:

P = 4080 / 1.36 = 3000

So Mmusi borrowed R3000 from Aggie.

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Answer:

B. √2

Step-by-step explanation:

First, rationalise the fraction so that the denominator is a whole number.

10 *  √50

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

√50 * √50

 10 √50

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

    50

√50 can be simplified as 5√2

10 *5√2 = 50√2

50√2

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

 50

- The 50's cancel out and you are left with √2

Answer:

7.5 kilometers

Step-by-step explanation:

i took the test

Answer:

The answer will be A

hope this helps :)

Algebraic properties can be applied to any mathematical equation.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

There are several algebraic properties; they include:

Distributive property

Additive property

Inverse property

Commutative property

All these properties can be applied in a mathematical equation.

An instance is as follows:

3(x + 2) = 18

Method 1

Apply the distributive property

3x + 6 = 18

Apply the subtraction property of equality

3x = 12

Apply the division property of equality

x = 4

Method 2

Apply the division property of equality

x + 2 = 6

Apply the subtraction property of equality

x = 4

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Answer:

they are the same

Step-by-step explanation:

as you said, they both weigh a ton, there would just be more feathers and less bricks

The above obtained relation can be used to find df(0) / dz as we now have df/dr (dr/dz) evaluated at z=0. Thus,df(0) / dz = 2 * 0 / (-dx - 2jdx) = 0. Hence, the required solution is df(0) / dz = 0.

Given complex function is f(z) = x2 + jy2. We are supposed to find df(0) / dz.Solution:To find df(0) / dz, we need to first find f(z) as a function of z. Since, f(z) = x2 + jy2, we have, f(z) = |z|2. Now, we have, |z|2 = (x+iy) (x-iy) = x2 + y2 = r2. Differentiating this with respect to z, we get,df / dz (|z|2) = df / dz (r2) = 2r dr/dz. Now, we need to find dz. This can be found using the following relation, dz = dx + jdy.

Thus, we have,dz = dx + jdy = 1/2 (dz + d\bar{z}) + j 1/2 (dz - d\bar{z}) = (dx - dy)/2 + j (dx + dy)/2. 

Therefore,

df/dz = df/dr (dr/dz)

= 2r / (dx - dy - 2jdx). T

he above obtained relation can be used to find df(0) / dz as we now have df/dr (dr/dz) evaluated at z=0.

Thus, df(0) / dz = 2 * 0 / (-dx - 2jdx) = 0. Hence, the required solution is df(0) / dz = 0.

To find df(0) / dz, we need to first find f(z) as a function of z.

Since, f(z) = x2 + jy2,

we have, f(z) = |z|2.

Now, we have, |z|2 = (x+iy) (x-iy) = x2 + y2 = r2.

Differentiating this with respect to z, we get,

df / dz (|z|2) = df / dz (r2) = 2r dr/dz. 

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Answer:

Total time: 67 minutes

Step-by-step explanation:

35m + 4(8m) = 67m

Answer:

READING TIME :- 35 MINUTES

GAME TIME. :- 32 MINUTES

HOPE IT HELPS U!!!!

The rental charge, denoted as "y," is determined based on the duration of time, denoted as "x," for which the item or service is rented. Factors such as costs, demand, competition, and desired profit margins influence the specific pricing structure.

The rental charge, denoted as "y," is determined based on the amount of time, denoted as "x," that the item or service is rented for. The longer the duration of rental, the higher the rental charge tends to be. The specific pricing structure for rental charges varies depending on the industry, location, and specific rental service being provided.

Rental charges are typically set by the rental company or service provider and can be influenced by several factors. These factors may include the cost of acquiring and maintaining the rental item, overhead expenses such as storage or transportation costs, demand and market conditions, competition, and desired profit margins.

For example, in the context of car rentals, the rental charge may be based on a fixed rate per hour or may involve different rates for specific time increments (e.g., hourly, daily, weekly). Additionally, there may be additional fees or surcharges based on factors such as mileage, fuel usage, insurance coverage, or any optional extras chosen by the customer.

It's important to note that rental charges can vary significantly across different industries and types of rental services. For instance, the rental charges for equipment rentals, housing rentals, or event space rentals may have different pricing structures and factors influencing the overall cost.

Ultimately, the rental charge is determined by considering various factors that contribute to the cost of providing the rental service and the duration of time for which the item or service is rented.

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Answer:

slope is undefined

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, 4 ) and (x₂, y₂ ) = (- 3, - 7 )

m = \(\frac{-7-4}{-3+3}\) = \(\frac{-11}{0}\)

Since division by zero is undefined then the slope is undefined

This indicates the line is vertical and parallel to the y- axis

Therefore , the solution of the given problem of velocity comes out to be  33.94 ft/sec is the velocity.

Looking at something from a distance allows us to calculate its speed. An object's speed determines how far it can travel in a certain amount of time. Utilizing the equation velocity = distance/time, velocity is computed. Miles per hour (mph), kilometers an hour (km/h), and meters a second (m/s) are the three most common units of speed (mph).

Here,

Given :

=>  v = (8h) ^ 1/2

=>  v = √8h

We separate the variables whose values we want to be determined in the aforementioned problems.

(1) We change the variable to become

  v = √8h  in order to solve for v.

Using the supplied as a replacement,

v = √8 * 144 = 33.94 ft/sec

Therefore , the solution of the given problem of velocity comes out to be  33.94 ft/sec is the velocity.

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a. 30.15% of the employees cost more than $1,500 per year for dental expenses.

b. 65.49% of the employees cost between $1,500 and $2,000 per year for dental expenses.

c. The percentage of employees who did not have any dental expense is 0.1%.

d. The cost of the 10% of employees who incurred the highest dental expenses is $1,796.4 (approx).

a. Probability that dental expenses cost more than $1,500 per year

So, we have to find the probability of employees costing more than $1,500 per year for dental expenses.

Let X be the amount paid per year for dental expenses. X follows normal distribution with mean μ = $1,280 and standard deviation σ = $420.

We have to find P(X > $1,500).Here, z = (X - μ) / σ = ($1,500 - $1,280) / $420 = 0.52P(X > $1,500) = P(Z > 0.52) = 0.3015 or 30.15%.

Therefore, 30.15% of the employees cost more than $1,500 per year for dental expenses.

b. Probability that dental expenses cost between $1,500 and $2,000 per year

Now we have to find the probability of the employees who cost between $1,500 and $2,000 per year for dental expenses.

Let X be the amount paid per year for dental expenses. X follows a normal distribution with mean μ = $1,280 and standard deviation σ = $420.

We have to find P($1,500 < X < $2,000).Here, z1 = (X1 - μ) / σ = ($1,500 - $1,280) / $420 = 0.52z2 = (X2 - μ) / σ = ($2,000 - $1,280) / $420 = 1.71P(0.52 < Z < 1.71) = P(Z < 1.71) - P(Z < 0.52) = 0.9564 - 0.3015 = 0.6549 or 65.49%.

Therefore, 65.49% of the employees cost between $1,500 and $2,000 per year for dental expenses.

c. Probability of employees having no dental expenses.Now we have to find the probability of employees having no dental expenses.

Let X be the amount paid per year for dental expenses. X follows normal distribution with mean μ = $1,280 and standard deviation σ = $420. We have to find P(X = 0).

Here, z = (X - μ) / σ = (0 - $1,280) / $420 = -3.05Now, P(X = 0) is P(X < 0.5), which is same as P(Z < -3.05 + 0.0013) = P(Z < -3.05) = 0.001 or 0.1%.

Therefore, the percentage of employees who did not have any dental expense is 0.1%.

d. Cost of the 10% of employees who incurred the highest dental expenses

We have to find the dental expenses of the 10% of employees who incurred the highest dental expenses.

Let X be the amount paid per year for dental expenses. X follows a normal distribution with mean μ = $1,280 and standard deviation σ = $420.

We have to find the 90th percentile, z0.9.

Using standard normal table, we can find the z-score corresponding to 0.9, which is 1.28.

The amount, X corresponding to z0.9 is:X = μ + z0.9 σ = $1,280 + 1.28 × $420 = $1,796.4

Therefore, the cost of the 10% of employees who incurred the highest dental expenses is $1,796.4 (approx).

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Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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Answer:

2/3

Step-by-step explanation:

Slope = (-1-(-3))/(3-0) = 2/3

Answer:

slope = 2/3

Step-by-step explanation:

equation: y = x2/3 -3

A. We would expect approximately 115 students to be members of the band in 2005.

B. We would expect the band to have 85 members in the year 2000.

a. To determine the number of students expected to be members of the band in 2005, we need to substitute the value of x = 2005 - 1990 = 15 into the equation y = 6x + 25:

y = 6(15) + 25

y = 90 + 25

y = 115

Therefore, we would expect approximately 115 students to be members of the band in 2005.

b. To find the year when the band is expected to have 85 members, we can rearrange the equation y = 6x + 25 to solve for x:

y = 6x + 25

85 = 6x + 25

Subtracting 25 from both sides:

60 = 6x

Dividing both sides by 6:

x = 10

This tells us that x = 10 represents the number of years since 1990. To find the year, we add 10 to 1990:

Year = 1990 + 10

Year = 2000

Therefore, we would expect the band to have 85 members in the year 2000.

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Answer:

1 and 11/15.

Step-by-step explanation:

To solve, we can separate the integers from the fractions.

(6 - 4) + (2/5 - 2/3)

= 2 + (6/15 - 10/15)

= 2 + (-4/15)

= 1 + 15/15 - 4/15

= 1 + 11/15

= 1 and 11/15

Hope this helps!

Given:

The number is 93.

To find:

The square root of 93.

Solution:

We need to find the square root of 93.

The square root of 93 by division method is:

         9.6436

_____________

9     |     93

9     |      81

__________

186 |    1200

  6 |      1116

___________

1924 |  8400

    4  | 7696

__________

19283 | 70400

       3 | 57849

____________

192686 | 1255100

         6 | 1156116

______________

192692 | 98984

And so on.

\(\sqrt{93}\approx 9.645\)

Therefore, the square root of 93 is about 9.645.

Answer:

9.643

Step-by-step explanation:

Got it right, checked answer on calculator

Therefore, the value of d for the given function is 144x^2 + 100.

To evaluate the expression d = f_xxf_yy - [fxy]^2 for the given function f(x, y) = 2x^4 + 3y^2 - 10xy - 3, we need to calculate the second-order partial derivatives and substitute them into the formula.

First, let's find the first-order partial derivatives:

f_x = 8x^3 - 10y

f_y = 6y - 10x

Now, let's find the second-order partial derivatives:

f_xx = d/dx (f_x) = d/dx (8x^3 - 10y) = 24x^2

f_yy = d/dy (f_y) = d/dy (6y - 10x) = 6

f_xy = d/dx (f_y) = d/dx (6y - 10x) = -10

f_yx = d/dy (f_x) = d/dy (8x^3 - 10y) = -10

Substituting these values into the expression:

d = f_xxf_yy - [fxy]^2

= (24x^2)(6) - (-10)^2

= 144x^2 + 100

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Answer:

101 sq. ft

Step-by-step explanation:

Answer: 9.8 feet!

Step-by-step explanation:

the equation Pr[A] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bi]] provides a general formula for calculating the probability of event A based on the given partition B1, B2, ..., Bt of the sample space.

(a) To prove the equation Pr[A] = Σ[Pr[A | Bx] Pr[Bx]], we start by using the law of total probability. The law of total probability states that for any event A and a partition B1, B2, ..., Bt of the sample space, we have Pr[A] = Σ[Pr[A | Bi] Pr[Bi]], where Pr[A | Bi] is the conditional probability of A given Bi.

By rearranging the terms, we get Pr[A] = Σ[Pr[A | Bi] Pr[Bi]] = Σ[Pr[A | Bi] Pr[Bi] / Pr[Bk] Pr[Bk]], where Pr[Bk] is the probability of the event Bk.

Next, we multiply and divide Pr[A | Bi] by Pr[Bk], giving us Pr[A] = Σ[(Pr[A | Bi] Pr[Bk]) / Pr[Bk] Pr[Bi]].

Since the summands have the same denominator Pr[Bk] Pr[Bi], we can write Pr[A] = Σ[(Pr[A | Bi] Pr[Bk]) / Pr[Bk] Pr[Bi]] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bk] Pr[Bi]].

Finally, by canceling out the common factor Pr[Bk], we obtain Pr[A] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bi]], which proves the equation.

(b) From the equation Pr[A] = Σ[Pr[A | Bi] Pr[Bk] / Pr[Bi]], we can see that Pr[A] can be expressed as a sum of terms involving the conditional probabilities Pr[A | Bi] and the probabilities of the partition sets Pr[Bi]. This equation allows us to compute the probability of A by considering the conditional probabilities and the probabilities of the partition sets.

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