find a1 knowing that a39=15 and d=4

The number of burger sam bought = x

Let the number of burgers for mike be = y

the equation for the total number of burgers will be

Mike brought 5 more than 2 times as many burgers as sam will be represented as

By substituting Eqn 2 in Eqn 1 we will have

Therefore,

The value of x= 15

To calculate the number of burgers mike brought to the BBQ =y,

We will substitute the value of x in (Eqn 1) above

In mathematics, differentiation refers to the process of finding the derivative of a function. The basic means of differentiation include:

Limit definition: The derivative of a function is defined as the limit of the difference quotient as the interval over which the quotient is taken approaches zero.

Power rule: The derivative of a function of the form f(x) = xⁿ is given by f'(x) = nx⁽ⁿ⁻¹⁾

Product rule: The derivative of a product of two functions u(x) and v(x) is given by (u × v)'(x) = u'(x) × v(x) + u(x) × v'(x).

Quotient rule: The derivative of a quotient of two functions u(x) and v(x) is given by (u/v)'(x) = [u'(x) × v(x) - u(x) × v'(x)] / v(x)².

Chain rule: The derivative of a composition of functions f(g(x)) is given by f'(g(x)) × g'(x).

These basic means of differentiation are essential tools for analyzing and modeling functions in calculus and related fields.

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According to the question For ( a ) the amount and concentration of salt at any time \(\(t\)\) can be \(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\) . For ( b ) the limiting concentration of salt in the tank is 0.25 kg/L.

To determine the amount and concentration of salt at any time in the tank, we need to consider the inflow of saltwater, outflow of water, and evaporation. Let's denote the time as \(\(t\)\) in hours.

a. Amount and Concentration of Salt at any time:

Let's denote the amount of salt in the tank at time \(\(t\) as \(S(t)\)\) in kg and the concentration of salt in the tank at time \(\(t\) as \(C(t)\) in kg/L.\)

Initially, the tank contains 100 L of water with a salt concentration of 0.1 kg/L. Therefore, at \(\(t = 0\)\), we have:

\(\[S(0) = 100 \times 0.1 = 10 \text{ kg}\]\)

\(\[C(0) = 0.1 \text{ kg/L}\]\)

Considering the inflow, outflow, and evaporation rates, the amount of salt in the tank at any time \(\(t\)\) can be calculated as:

\(\[S(t) = S(0) + \text{Inflow} - \text{Outflow} - \text{Evaporation}\]\)

The inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L. Thus, the amount of salt entering the tank per hour is:

\(\[\text{Inflow} = \text{Inflow rate} \times \text{Concentration} = 55 \times 0.2 = 11 \text{ kg/h}\]\)

The outflow rate is 44 L/h, so the amount of salt leaving the tank per hour is:

\(\[\text{Outflow} = \text{Outflow rate} \times C(t) = 44 \times C(t) \text{ kg/h}\]\)

The evaporation rate is 11 L/h, and as only water evaporates, it does not affect the salt concentration in the tank.

Therefore, the amount and concentration of salt at any time \(\(t\)\) can be expressed as follows:

\(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)

\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\)

b. Limiting Concentration:

The limiting concentration refers to the concentration reached when the inflow and outflow rates balance each other, resulting in a stable concentration. In this case, the inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L, and the outflow rate is 44 L/h. To find the limiting concentration, we equate the inflow and outflow rates:

\(\[\text{Inflow rate} \times \text{Concentration} = \text{Outflow rate} \times C_{\text{limiting}}\]\)

\(\[55 \times 0.2 = 44 \times C_{\text{limiting}}\]\)

\(\[C_{\text{limiting}} = \frac{55 \times 0.2}{44} = 0.25 \text{ kg/L}\]\)

Therefore, the limiting concentration of salt in the tank is 0.25 kg/L.

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Yes, the equation y = 5x represents a proportional relationship

Two or more expressions with an Equal sign is called as Equation.

The given equation is y=5x.

In a proportional relationship, the ratio of y to x is constant.

In the given equation the variable x and y has a proportional relationship.

The equation is in the form of y=mx+b

the ratio of y to x is 5, meaning that for every unit increase in x, y increases by 5 units.

Hence,  Yes, the equation y = 5x represents a proportional relationship

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Answer:

5

Step-by-step explanation:

A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.

B. The source of the variability is due to chance or sampling error, which arises from taking a sample instead of surveying the entire population.

C.  The sampling distribution of p is approximately normal.

D. We find that the probability is 0.0912 or about 9.12%.

E. We get:z = (0.75 - 0.82) / sqrt[0.82(1-0.82)/100] = -2.29

a. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.

b. The sample proportion, p, is a random variable because it varies from sample to sample. The source of the variability is due to chance or sampling error, which arises from taking a sample instead of surveying the entire population.

c. The sampling distribution of p is approximately normal if the sample size is sufficiently large and if np ≥ 10 and n(1-p) ≥ 10, where n is the sample size and p is the population proportion. In this case, we have:

Sample size (n) = 100

Population proportion (p) = 0.82 Thus, np = 82 and n(1-p) = 18, both of which are greater than 10. Therefore, the sampling distribution of p is approximately normal.

d. To calculate the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.85, we need to find the z-score and then look up the corresponding probability from the standard normal distribution table. The formula for the z-score is:

z = (p - P) / sqrt[P(1-P)/n]

where p is the sample proportion, P is the population proportion, and n is the sample size. Substituting the given values, we get:

z = (0.85 - 0.82) / sqrt[0.82(1-0.82)/100] = 1.33

Looking up the corresponding probability from the standard normal distribution table, we find that the probability is 0.0912 or about 9.12%.

e. Yes, it would be unusual for a survey of 100 Americans to reveal that 75 or fewer are satisfied with the way things are going in their life. To check if it is unusual or not, we need to calculate the z-score and find its corresponding probability from the standard normal distribution table. The formula for the z-score is:

z = (p - P) / sqrt[P(1-P)/n]

where p is the sample proportion, P is the population proportion, and n is the sample size. Substituting the given values, we get:

z = (0.75 - 0.82) / sqrt[0.82(1-0.82)/100] = -2.29

Looking up the corresponding probability from the standard normal distribution table, we find that the probability is 0.0106 or about 1.06%. Since this probability is less than 5%, it would be considered unusual to observe 75 or fewer Americans being satisfied with the way things are going in their life.

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Answer:

(0,. 5 )

Step-by-step explanation:

Substitute the input x = 0 into the function for output y

y = 5 × \(2^{0}\) = 5 × 1 = 5 [ note \(a^{0}\) = 1 ]

Answer:

According to the statement, the equation is :

Sides of regular octagon T= 3 × the length of sides of regular octagon G

The required equation is x = 3y

Where x is the length of the sides of the octagon T and y is the length of the side of the octagon G.

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

Example:

2x + 5 - 9 is an equation.

We have,

Sides of regular octagon T = x

Sides of regular octagon G = y

Now,

The equation of the sides of regular octagon T is three times the length of the sides of regular octagon G can be written as:

x = 3y

Thus,

The equation is x = 3y.

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Given:

The function

Required:

What’s all the transformations that happened

Explanation:

The required concepts:

Now,

Answer:

Completed the answer.

The researcher is assessing item equivalence, If a study is in parallel forms of the measurement instrument to the same person. The correct option is C).

When a study introduces parallel forms, the researcher is assessing item equivalence. Item equivalence refers to the extent to which the different forms of the measurement instrument produce similar results for the same individual.

This assessment is crucial in research because it allows researchers to evaluate the consistency and reliability of the measurement instrument across different versions. By administering parallel forms to the same person, any differences in responses can be attributed to individual factors rather than variations in the instrument.

This helps ensure that the instrument is measuring the intended construct consistently and accurately. The correct option is C).

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The ordered pair (x,y) = (2,-1) is a solution to the equation 3x - y = 7.

The given equation is 3x - y = 7.

To find the ordered pair (x,y) that is a solution to the equation, we can choose any value of x and find the corresponding value of y that satisfies the equation.

Let's choose x = 2:

3x - y = 7

Substituting x = 2, we get:

3(2) - y = 76 - y

= 7

Subtracting 6 from both sides, we get:

-y = 1

Multiplying both sides by -1, we get:

y = -1

Therefore,

when x = 2,

y = -1 satisfies the equation.

Thus, the ordered pair (x,y) = (2,-1) is a solution to the equation 3x - y = 7.

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Answer:

\(\boxed{\sf \ \ YES \ \ }\)

Step-by-step explanation:

Hello

let's say that the price of the book was x

the price after a 20% discount is x - 20%*x = x*(1-20%)=x*(1-.20)=0.8*x

and this is $72 so we can write that

0.8*x=72

and then divide by 0.8 both parts

x = 72/0.8=90

So the list price value of the book is $90

and we can verify as 90 - 20%*90 = 90 - 18 = 72

Hope this helps

The statement is generally true.

In materials science, the close-packing of atoms in crystal structures can affect the mechanical properties of the material, such as its ductility and ability to undergo plastic deformation.

In general, structures with closely packed planes (i.e., structures with a higher atomic packing factor) are more likely to undergo plastic deformation because the closely packed planes allow for more slip planes for atoms to move along without disrupting the overall crystal structure.

This means that when a force is applied to the material, the planes can slide more easily past one another, leading to plastic deformation.

In contrast, structures that are not closely packed (i.e., structures with a lower atomic packing factor) have fewer slip planes and are less likely to undergo plastic deformation. Instead, they may experience brittle fracture or other types of failure when subjected to stress.

However, it is important to note that the relationship between atomic packing and plastic deformation is complex and depends on a variety of factors, including the type of crystal structure, the presence of defects or impurities in the material, and the conditions under which the material is being deformed.

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Answer:

The answer is 10.16

Step-by-step explanation:

I do the asigment

Answer:

y = -5(x-5)^2+1125

Step-by-step explanation:

To prove that min(a, min(b, c)) = min(min(a, b), c), we need to consider two cases:

Case 1: a is the smallest of the three integers
If a is the smallest, then min(a, b) = a and min(a, c) = a. Therefore, min(min(a, b), c) = min(a, c) = a. On the other hand, min(b, c) could be either b or c, depending on which is smaller. Therefore, min(a, min(b, c)) could be either a or min(b, c). However, since we know that a is the smallest of the three integers, it follows that min(a, min(b, c)) = a. Hence, in this case, both sides of the equation are equal.

Case 2: a is not the smallest of the three integers
If a is not the smallest, then either b or c is smaller than a. Without loss of generality, assume that b is smaller than a. Then, min(a, min(b, c)) = min(a, b) = b. On the other hand, min(min(a, b), c) could be either a or b, depending on which is smaller. Therefore, we have two sub-cases:

Sub-case 2.1: b is smaller than c
If b is smaller than c, then min(min(a, b), c) = min(a, b) = b. Hence, both sides of the equation are equal.

Sub-case 2.2: c is smaller than or equal to b
If c is smaller than or equal to b, then min(min(a, b), c) = min(a, c) = c. Therefore, we need to compare this to min(a, min(b, c)). Since c is smaller than or equal to b, it follows that min(b, c) = c. Therefore, min(a, min(b, c)) = min(a, c) = c. Hence, in this sub-case as well, both sides of the equation are equal.

Since we have shown that both sides of the equation are equal in all possible cases, we can conclude that min(a, min(b, c)) = min(min(a, b), c) for all integers a, b, and c.

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The value of (tanx+2cosx) = \(2\frac{7}{20}\).

Given that

sinx = \(\frac{3}{5}\)

sinx = \(\frac{opp}{hyp}\)

Using the Pythagoras' theorem

\(hyp^{2} = opp^{2} + adj^{2} \\\\adj^{2} = 5^{2}- 3^{2} \\ \\= 25-9\\\\adj^{2} = 16\\ \\adj = \sqrt{16} \\\)

adj = 4.

Now we have to find out tanx and cosx

\(tanx = \frac{opp}{adj}\)

\(= \frac{3}{4}\)

\(cosx = \frac{adj}{hyp}\\ \\= \frac{4}{5}\)

Now we have to find out the given equation (tanx+2cox)

\(= \frac{3}{4} +2(\frac{4}{5})\\ \\= \frac{15+32}{20} \\\\= \frac{47}{20} \\\\or\\\\= 2\frac{7}{20}\)

Hence the answer is the value of (tanx+2cosx) = \(2\frac{7}{20}\).

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The area of the picture frame is 15x² + 8x + 3 = 0

Note that the formula for calculating the area of a rectangle is expressed as;

A = lw

Such that the parameters are given as;

Also, the picture frame takes the shape of a rectangle

Substitute the expressions

Area = (5x + 3)(3x + 1)

expand the bracket

Area = 15x² + 5x + 3x + 3

collect the like terms

Area = 15x² + 8x + 3

In standard form, the area is 15x² + 8x + 3 = 0

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Answer:

27

Step-by-step explanation:

I broke the figure up into 3 rectangles.

5x2 = 10

2x3 = 6

4x5 = 20

This adds to 36.  Then subtract out the green square of 9

36 - 9 = 27

The volume of cuboid with dimensions 9cm × 4cm × 5cm is 180 cm³

We know that the formula for the volume of the cuboid is:

V = l × w × h

where, V is the volume of the cuboid

l is the length of the cuboid

w is the  width of the cuboid

and h is the height of the cuboid

Here, the length of the cuboid is l = 9 cm,

the width of the cuboid is w = 4 cm

and the height of the cuboid is h = 5 cm

Using above formula,

V = l × w × h

V = 9 × 4 × 5

V = 180 cubic cm

Therefore, the required volume is 180 cubic centimeters

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Opposite angles of a cyclic quadrilateral are supplementary, so

\(x+17+6x-5=180 \\ \\ 7x+12=180 \\ \\ 7x=168 \\ \\ x=24 \\ \\ \\ \implies \angle QRO=2(24)+19=\boxed{67^{\circ}}\)

Answer:

15

Step-by-step explanation:

distance formula

\(\sqrt{((x2-x1)^2 + (y2-y1)^2)}\)

\(\sqrt{(9-0)^2 + (-6-6)^2}\)

\(\sqrt{81 + 144}\)

\(\sqrt{225}\)

15

Answer:

40

Step-by-step explanation:

The surface area of the composite figure is 1,665.04 in².

The volume of composite figure is 1,079.66 in³.

The volume  and surface area of the composite figure is calculated by applying the following formula as shown below;

The surface area = area of cone + area of hemisphere

S.A = πr(r + l) + 3πr²

S.A = π x 10 (10 + 13)  +  3π(10²)

S.A = 1,665.04 in²

The volume of composite figure is calculated as follows;

V = ¹/₃πr²h  +  ²/₃πr²

The height of the cone is calculated;

h = √(13² - 10²)

h = 8.31 in

V = ¹/₃π(10)²(8.31)  +  ²/₃π(10)²

V = 870.22 + 209.44

V = 1,079.66 in³

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EVENT 1 has a probability value of 0.5.

EVENT 2 has a probability value of 0.5.

There is an equal chance of getting a HEAD or a TAIL when flipping a fair coin.

A coin has two faces: Head and Tail, and the total probability is always 1

1/2 = 0.5 is the likelihood of getting a head.

1/2 = 0.5 is the probability of receiving a tail.

When the coin is tossed for the first time, E1 is the event when TAIL comes up.

When the coin is tossed a second time, E2 represents the circumstance in which HEAD appears.

EVENT 1 has a probability value of 0.5.

EVENT 2 has a probability value of 0.5.

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Answer:

need a image to answer this

Answer:

4:1

Step-by-step explanation:

The ratio at first would be 48:12, after this to simplify it we need to find the gcf (greatest/biggest common factor), which is 12. Dividing 48 by 12 gives us 4 and dividing 12 by 12 gives us 1, thus making the ratio 4:1

Answer:

Equation A: x = -1 and y = 3

Equation B: x = 12 and y = 16

Step-by-step explanation:

In the complex numbers (a + bi) and (x + yi)

Equation A

∵ (x + yi) + (4 – 7i) = 3 – 4i

∴ (x + 4) + (y - 7)i = 3 - 4i

→ Compare the real parts and compare the imaginary parts

∴ x + 4 = 3 and y - 7 = -4

∵ x + 4 = 3

→ Subtract 4 from both sides

∴ x + 4 - 4 = 3 - 4

∴ x = -1

∵ y - 7 = -4

→ Add 7 to both sides

∴ y - 7 + 7 = -4 + 7

∴ y = 3

Equation B

∵ (x + yi) - (-6 + 14i) = 18 + 2i

∴ (x - -6) + (y - 14)i = 18 + 2i

→ (-)(-) = (+)

∴ (x + 6) + (y - 14)i = 18 + 2i

→ Compare the real parts and compare the imaginary parts

∴ x + 6 = 18 and y - 14 = 2

∵ x + 6 = 18

→ Subtract 6 from both sides

∴ x + 6 - 6 = 18 - 6

∴ x = 12

∵ y - 14 = 2

→ Add 14 to both sides

∴ y - 14 + 14 = 2 + 14

∴ y = 16

Answer: In equation A,  -1  and  3 .  In equation B,  12  and  16 .

picture below

Step-by-step explanation:

Answer: B

Step-by-step explanation:

The question asks for [n≥-5] to be true, which means any value that is greater or equal to -5 will be considered.

A. {-5, -5.5, -6}

-5 TRUE

-5.5 FALSE

-6 FALSE

B. {-5, -4.5, -3}

-5 TRUE

-4.5 TRUE

-3 TRUE

C. {-6, 0, 5}

-6 FALSE

0 TRUE

5 TRUE

D. {-6, -7, -8}

-6 FALSE

-7 FALSE

-8 FALSE

As shown above, we can clearly see that Set B is the set that makes the inequality true.

Answer:

No

Step-by-step explanation:

The coordinates in an ordered pair are listed (x,y).  So, in (8,3)  The 8 is the x coordinate and the 3 is the y coordinate.  Plug those numbers into the equation and see if it makes a true statement.  If it does, then that point is on the line and it is a solution

y = 17x + 7

3 = 17(8) + 7

3 = 136 + 7

3 \(\neq\) 143, so this point is not a solution