Solve this system. Write your answer as an ordered pair.

-5x + y = -3

3x - 8y = 24

a. Let [tex]d[/tex] be the number of daytime calls Eshwa makes, and [tex]e[/tex] the number of evening calls. Then the cost [tex]C[/tex] (in pence) of making [tex]d+e[/tex] calls is

[tex]C = \boxed{50d + 40e}[/tex]

b. £1 = 100p, so the cost [tex]C'[/tex] (in £) is 1/100 of the cost found in part (a),

[tex]C' = \dfrac{50d + 40e}{100} = \boxed{\dfrac d2 + \dfrac{2e}5}[/tex]

c. If Eshwa makes 30 of each type of call in a month, then the total cost (in £) is

[tex]C' = \dfrac{30}2 + \dfrac{2\cdot30}5 = \boxed{27}[/tex]

c2. If Eshwa makes 20 daytime calls and 50 evening calls, then the total cost (in £) is

[tex]C' = \dfrac{20}2 + \dfrac{2\cdot50}5 = \boxed{30}[/tex]

d. Let [tex]e=40[/tex] and [tex]C'=42[/tex]. Solve for [tex]d[/tex].

[tex]42 = \dfrac d2 + \dfrac{2\cdot40}5[/tex]

[tex]42 = \dfrac d2 + 16[/tex]

[tex]\dfrac d2 = 26[/tex]

[tex]d = \boxed{52}[/tex]

The probability that of 6 randomly selected patients, 4 will recover is 0.03295

The chance of an event occurring is defined by probability.

Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative.

The ratio of good outcomes to all possible outcomes of an event is known as the probability.

Let X represent the binomial random variable that represents the patient count. Let p represent the likelihood that the patient will survive, and q represent the probability that they will pass away. The solution to the problem is q = 75% = 0.75, p = 25% = 0.25, and n = 6.

Required probability = 6C4[tex](0.25)^{4} (0.75)^{2}[/tex]

                                = 0.03295

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The rule of the translation of point P(–5, –4) to point P′(–8, –7) is:

(x,y) -> (x - 3, y - 3).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, from point P to point P', 3 was subtracted from both the x-coordinate and the y-coordinate, hence the rule is given by:

(x,y) -> (x - 3, y - 3).

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Answer:

[tex] \frac{27}{8} cm {}^{3} [/tex]

Is the volume of this right rectangular prism.

Step-by-step explanation:

Rectangular prism volume formula is:-

Answer:

[tex]V=\frac{27}{8}\: cm^3[/tex]

Step-by-step explanation:

The formula to find the volume of a rectangular prism is:

V = length × height × width

Let us find now.

[tex]V = length \:* height \:* width\\\\V =\frac{3}{2} *\frac{3}{2} *\frac{3}{2} \\\\V=\frac{9}{4}*\frac{3}{2} \\\\ V=\frac{27}{8}\: cm^3[/tex]

Check the picture below.

Answer: 28 [tex]units^{2}[/tex]

Step-by-step explanation:

Answer:

2^1 × 5^2 × 7^1 = 350

Step-by-step explanation:

2, 5, 7 are prime

first step is to divide the number 350 with the prime factor 2

continue dividing the number 175 by the next smallest prime factor

stop until you can't divide anymore

https://www.cuemath.com/numbers/factors-of-350/

Answer:

[tex]\sf b) \quad \dfrac{y^3}{4x}[/tex]

Explanation:

[tex]\sf \left(\dfrac{6x^2}{5y}\right) \left(?}\right) = \left(\dfrac{3xy^2}{10}\right)[/tex]

cross multiply variables

[tex]\sf ? = \left(\dfrac{3xy^2 (5y)}{10(6x^2)}\right)[/tex]

distribute inside parenthesis

[tex]\sf ? = \left(\dfrac{15xy^3}{60x^2}\right)[/tex]

remove parenthesis and simplify

[tex]\sf ? = \dfrac{y^3}{4x}[/tex]

Answer:

-1

Step-by-step explanation:

0.35 - 0.8 = -0.45

-0.1 - 0.35 = -0.45

-0.55 - 0.45 = -1

Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies

An equation is an expression that shows the relationship between two or more numbers and variables.

In his piggy bank, Neil has three times as many dimes as nickels and he has four more quarters than nickels. The coins total are 4.60. How many of each coin does he have.

Let x represent dimes (0.1), y represent nickels (0.5) and z represent quarter (0.25)

Hence:

0.1x + 0.05y + 0.25z = 4.6   (1)

Also:

x = 3y   (2)

And:

z = y + 4  (3)

From the equations:

x = 18, y = 6, z = 10

Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies

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Answer:

7.61577310586

Step-by-step explanation:

Pythagoras Theorem 7 squared + 3 squared= 49+9=58

[tex]\sqrt{58}[/tex]

The probability that the value of p(x) is greater than 315 is 0.063754

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (315 - 283)/21

Evaluate the difference of 315 and 283

z = 32/21

Evaluate the quotient of 32 and 21

z = 1.524

The probability that the value of p(x) is greater than 315 is then calculated as:

P(x > 315) = P(z > 1.524)

From the z table of probabilities, we have;

P(x > 315) = 0.063754

Hence, the probability that the value of p(x) is greater than 315 is 0.063754

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The sum of the first 7 terms of the geometric series is 15.180

The formula for calculating the sum of geometric series is expressed according to the formula. below;

GM = a(1-r^n)/1-r

where

r is the common ratio

n is the number of terms

a is the first term

Given the following parameters from the sequence

a = 1/36

r = -3

n = 7

Substitute

S = (1/36)(1-(-3)^7)/1+3
S = 1/36(1-2187)/4
S = 15.180

Hence the sum of the first 7 terms of the geometric series is 15.180

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Answer:

Step-by-step explanation:

If it is not Monday, then there are students in the gym.

Negation: It is not Monday and there are not students in the gym.

Statement: It is Monday or there are students in the gym.

Equivalent: If there are not students in the gym, then it is Monday.

Neither: There are not students in the gym or it is not Monday.

We conclude that 375 portions can be sold.

We know that 500 portions have been ordered, but only 5/6 of that was delivered, so the number of delivered portions is:

p = (5/6)*500 = 416.6

Which we can round to the next whole number, 417.

Now we know that 10% of these are given to the players and staff, then the number of portions that can be sold is the 90% of 417, which is:

N = 417*(90%/100%) = 417*0.9 = 375

We conclude that 375 portions can be sold.

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Answer:

5,526

Step-by-step explanation:

Mean of scores = Total Value of Scores / Number of Values

= [tex]\frac{3820+5500+8560+4400+5350}{5} \\[/tex]

= 5,526

Answer:5526

Step-by-step explanation: Add everything up and divide by 5 because there are 5 numbers

Answer: C, E

Step-by-step explanation:

These are polynomials by the definition of a polynomial.

Answer:

(the figure is poorly drawn)

Step-by-step explanation:

find y

180 - 120 = 60°

find x

180 - 60 - 30 = 90°

Answer:

y=-1/2n+44

Step-by-step explanation:

The number of bean stalks, n, represents the x values

The yield, y, represents the y values

After reading the problem, we have two coordinates: (30,29) and (32, 28) Because this problem is asking for y=mn+b, we have to find the slope. How do we find the slope? We do so by using the slope formula y2-y1/x2-x1. Now let's input the coordinates into this formula.

1.) 28-29/32-30 = -1/2

Let's plug -1/2 into y=mn +b

2.) y=-1/2n+b

Now we have to find what b ( y intercept) equals. To find B, we plug a coordinate into x and y. Let's use (30,29)

3.) 29 = -1/2(30)+b

29 = -15 +b

44 = b

We have now found the linear relationship form for this problem: y=-1/2n +44

The following linear system has [[12], [11], [4]] matrix of constants,

x + y + z = 12

x - y = 11

x - y + z = 4  

(Option D)

Verification of the Choice:

The given linear system is,

x + y + z = 12

x - y = 11

x - y + z = 4  

This can be written in the form of matrix as follows,

[tex]\left[\begin{array}{ccc}1&1&1\\1&-1&0\\1&-1&1\end{array}\right][/tex] [tex]\left[\begin{array}{}x&y&z\end{array}\right][/tex] = [tex]\left[\begin{array}{}12&11&4\end{array}\right][/tex]

Hence, option D is the correct linear system as it contains the desired matrix.

About the Other Options:

The RHS matrix in option A would be,

[tex]\left[\begin{array}{}26&17&23\end{array}\right][/tex] which is not the desired matrix.

Similarly, the linear systems in the options B and C contain the matrix [tex]\left[\begin{array}{}23&17&26\end{array}\right][/tex] and the matrix  [tex]\left[\begin{array}{}4&11&12\end{array}\right][/tex] on the RHS of the equality, which are not desired.

Thus, option D is correct.

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Answer:

I think its A

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

You have six choices and you want to pick only 1 of those choices.

1/6

[tex]\displaystyle\frac{1}{6}[/tex]

Probability explains the likelihood of an event occurring. The outcome you are finding the probability for is the successful outcome. The sample size is the total number of possible outcomes.

Simple Probability

Simple probability is when there is only one single event. In this situation, the cube is only being rolled once, so it's a simple probability question. To solve this question as a fraction, the numerator should be the number of successful outcomes and the denominator should be the sample size.

Solving for P(B)

Since there are 6 sides with 6 letters, the sample size is 6. So, 6 should be the denominator. We are finding the probability of "B", which means there is 1 successful outcome. Thus, the numerator should be 1.

This means as a fraction the probability is [tex]\frac{1}{6}[/tex].

Answer: 5/36

Step-by-step explanation:

Given that the graph shows P as a function of n, we have:

a. The more hot dogs that is sold, his profit increases.

b. Jimmy sells the hot dog for $1 each.

c. Jimmy needs to sell 16 hot dogs to recover the $8 he invested.

d. He would make a profit of $7.

e. The number of hot dogs he needs to sell is: 20.

A linear  function is expressed as, y = mx + b, where y is a function of x, m is the unit rate, and b is the starting value or initial value of the function.

We are given that profit, P, is a function of the number of hot dogs sold, n.

a. The graph of the function slopes upwards, so this means that the more hot dogs that is sold, his profit increases.

b. Cost of 1 hot dog = Unit rate = change in y / change in x = 2 units/2 units

Cost of 1 hot dog = Unit rate = 1

Thus, Jimmy sells the hot dog for $1 each.

c. If you trace profit (P) on the graph when it is $8, the corresponding number of hot dogs, n, would be 16.

So, Jimmy needs to sell 16 hot dogs to recover the $8 he invested.

d. When n = 15, P, from the graph would be 7.

Thus, if Jimmy sells 15 hot dogs, he would make a profit of $7.

e. When P = 12, from the graph, the corresponding n value is 20.

Therefore for Jimmy to make $12, the number of hot dogs he needs to sell is: 20.

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Answer:

  x = {π/6, π/2, 5π/6, 3π/2}

Step-by-step explanation:

The equation can be solved using a double-angle trig identity and factoring.

Dividing the equation by 7 and substituting for sin(2x), we have ...

  7sin(2x) = 7cos(x)

  sin(2x) = cos(x)

  2sin(x)cos(x) = cos(x)

  2sin(x)cos(x) -cos(x) = 0

  cos(x)(2sin(x) -1) = 0

The product of factors is zero when one or more of the factors is zero.

  cos(x) = 0   ⇒   x = {π/2, 3π/2}

  2sin(x) -1 = 0   ⇒   x = arcsin(1/2) = {π/6, 5π/6}

Solutions in the given interval are ...

  x = {π/6, π/2, 5π/6, 3π/2}

__

Additional comment

When the equation is of the form f(x) = 0, then the x-intercepts of f(x) are its solutions. We can rearrange this one to ...

  sin(2x) -cos(x) = 0

The solutions identified above match those shown in the graph.

6 decks of cards = 60 cards

---> 60/8 = 15/2 = 7.5

7.5 cards = 0.75 decks of cards

Therefore, each student will get 0.75 decks of cards.

Answer:

1

Step-by-step explanation:

Everyone gets 1 and there's 2 left over

The initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.

From the information given, we have the function to be;

a(t)=2400(1/2)^t/14

Where

To determine the initial amount, we have that t = 0

Substitute into the function, we have

[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{0}{14}[/tex]

[tex]A (t) = 2400[/tex]  × [tex]\frac{1}{2} ^0[/tex]

[tex]A (t) = 2400[/tex]

The initial amount is 2400 grams

For the amount remaining after 40 years, t = 40 years

A(t)=2400(1/2)^t/14

Substitute into the function, we have

[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{40}{14}[/tex]

[tex]A(t) = 2400[/tex] × [tex](0. 5) ^2^.^8^5^7[/tex]

[tex]A(t) = 2400[/tex] × [tex]0. 1380[/tex]

A(t) = 331. 26

A(t) = 331 grams in the nearest gram

Thus, the initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.

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Answer: They are the same

Step-by-step explanation: We convert both to $ per hour. Call center A is $15 per hour. Call center B is $.25 per minute. .25 per minute means $1.00 every 4 minutes. There are 15 4 minutes in an hour so they both offer the same wage.

A  value of 24 is 2.5 standard deviations away from the mean

The given parameters about the distribution are:

Mean = 18

Standard deviation = 4

Value = 24

Let the number of standard deviations away from the mean be x.

The value of x is calculated using

Mean + Standard deviation * x = Value

Substitute the known values in the above equation

18 + 4 * x = 24

Subtract 18 from both sides of the equation

4 * x = 6

Divide both sides of the equation by 4

x = 1.5

Hence, a value of 24 is 2.5 standard deviations away from the mean

So, the complete parameters about the distribution are:

Mean = 18

Standard deviation = 4

Value = 24

24 is 2.5 standard deviations away from the mean

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Answer:

To solve the problem we have to take 4 percent of 5000 and multiply it by 8 years and the final result is 1600 dollars, which would be the final result.

Así, concluimos que la posición final del buzo será 7 metros bajo la superficie del agua.

Primero, vamos a definir la superficie del agua como el 0 metros.

Sí sabemos que primero el buzo se sumerge 4 metros, entonces en este punto la posición del buzo es:

P = 0m - 4m = -4m

Luego el buzo sube 2 metros, entonces la nueva posición será:

P = -4m + 2m = -2m

Finalmente, el buzo desciende otros 5 metros, entonces la posición final del buzo será:

P = -2m - 5m = -7m

Así, concluimos que la posición final del buzo será 7 metros bajo la superficie del agua.

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