solving equations: please help:)
-(x+7)-5= -3x-12+2x

Answer:

1.05263

explanation:

8 divided by 7.6

\(\hookrightarrow \dfrac{8}{7.6}\)

multiply both by 10

\(\hookrightarrow \dfrac{80}{76}\)

final answer

\(\hookrightarrow 1.05263\)

The statement "you will be expected to know the antiderivatives of the six trigonometric functions for the final" is false because it is subjective and dependent on the specific requirements and expectations of your course or exam.

While it is true that knowledge of the antiderivatives of the six trigonometric functions (sine, cosine, tangent, cotangent, secant, and cosecant) can be beneficial in calculus and integration.

Whether or not you will be specifically expected to know them for your final exam depends on your course syllabus and the instructions provided by your instructor.

It is important to consult your course materials, syllabus, or instructor to determine the specific content that will be covered on your final exam.

This will ensure that you allocate your study time and focus on the relevant topics that will be assessed.

Therefore, the correct option is (b) false, as the expectation of knowing specific antiderivatives of trigonometric functions for the final exam is not universally applicable and may vary depending on the course and instructor.

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The factory makes 125.8 ounces of noodles in each minute.  

The factory made 817.7 ounces of noodles in 6.5 minutes .

This simply means for every 6.5 minutes the factory made 817.7 ounces of

noodles.

Therefore,

The amount of noodles the factory made in each minute can be calculated as follows using rate:

Rate is the ratio of 2 quantities with different units.

Therefore,

rate = amount made(ounces) / time taken

amount made(ounces)  = 817.7 ounces

time taken = 6.5 minutes

rate = 817.7 / 6.5

rate = 125.8 ounces per minute

Therefore, the factory makes 125.8 ounces of noodles in each minute.  

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Answer:

(-1) & 4/3

Step-by-step explanation:

           3x² - x - 4

Sum = -1

Product = 3*(-4) = -12

Factors = -4 and 3       { (-4)*3 = -12 & (-4) + 3 = -1}

3x² - x - 4 = 3x² + 3x - 4x -4 {Rewrite the middle term using the factors}

               = 3x(x + 1) -4(x + 1)

               =(x + 1)(3x - 4)

x + 1 = 0   ;  3x - 4 = 0

     x = -1  ;          3x = 4

                            x = 4/3

\(\sf Zeroes \ of \ the \ polynomial \ are \ (-1) \ and \ \dfrac{4}{3}\)

Verification:

         \(\sf 3x^2 - x - 4 = 0\\\\Divide \ the \ entire \ equation \ by \ 3\\\\\\\dfrac{3x^2}{3}-\dfrac{x}{3}-\dfrac{4}{3}=0\\x^2 - \dfrac{x}{3}-\dfrac{4}{3}=0\)

       Coefficient of x = sum of the zeroes

                                  \(\sf = -1 + \dfrac{4}{3}\\\\=\dfrac{-3}{3}+\dfrac{4}{3}\\\\=\dfrac{1}{3}\\\\\)

Constant = product of the zeroes

               \(\sf = (-1)*\dfrac{4}{3}\\\\=\dfrac{-4}{3}\)

Thus verified.

Answer:

A) x + 5y = 20

B) x + 3y = 14

Multiplying A) by -1

A) -x -5y = -20 then adding B)

B) x + 3y = 14

-2y = -6

y = 3

x = 5

Step-by-step explanation:

No, x and y are not independent. The joint pdf contains a term that depends on both x and y, which means that the value of x affects the value of y and vice versa.

Therefore, they are not independent. To determine if random variables X and Y are independent, we can analyze their joint probability density function (PDF). If the joint PDF can be expressed as the product of their marginal PDFs, then X and Y are independent. In this case, you haven't provided the joint PDF function or the constant c. However, the general approach is to integrate the joint PDF over one variable to find the marginal PDFs. Next, multiply the marginal PDFs together and compare the result to the joint PDF. If they are equal, X and Y are independent. If not, they are dependent. Please provide the joint PDF for further assistance.

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Answer:

\(-8x + 6y = -180\)

Step-by-step explanation:

Given

\(\frac{4}{5} x-\frac{3}{5}y=18\)

\(8x + 12y = 11\)

Required

Equivalent form of the first equation that eliminates x when added to the second

To do this, we simply make the coefficients of x to be opposite in both equations.

In the second equation, the coefficient of x is 8.

So, we need to make the coefficient of x -8, in the first equation.

\(\frac{4}{5} x-\frac{3}{5}y=18\)

Multiply by -10

\(-10 * [\frac{4}{5} x-\frac{3}{5}y=18]\)

\(\frac{-40}{5} x+\frac{30}{5}y=-180\)

\(-8x + 6y = -180\)

When this is added to the first equation, the x terms becomes eliminated

Answer:

When you divide 1060 by 48, your answer will be 22.08333... ( decimal) but when rounded, it will either be 22, 22.1, or 22.08 (just for rounding, you do not have to put this in.)

Hope this helped!

Step-by-step explanation:

Answer:

22 1/12

Step-by-step explanation:

48*22=1056

1060-1056=4

=  22 4/48

= 22 1/12

So the answer is 22 1/12,

Hope this helps!

The smallest measurement used in the apothecary system for volume is the minim.

The apothecary system is an outdated system of measurements primarily used in pharmacy and medicine. It includes various units for measuring volume, weight, and other quantities.

In the apothecary system, the minim is the smallest unit of measurement for volume. It is equivalent to approximately 0.0616 milliliters.

The minim is a small unit of measurement and is typically used for precise dosing of liquids in the apothecary system. It is commonly used in pharmaceutical compounding and in the preparation of medications.

However, it's important to note that the apothecary system is no longer widely used in modern healthcare practices. The metric system, with units such as milliliters and liters, has become the standard for measuring volume in most countries.

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Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

The weight of a single chocolate selected at random from the production line P(X > 22.07) is  0.0400.

Given:

X~ N(21.37, 0.16). X ~ N(μ, σ²) Mean (μ) = 21.37 Standard Deviation (σ) = √0.16 = 0.40

To Find: P(x > 22.07)

z = (x-μ)/σ z = (22.07-21.37)/0.40  = 1.75

Now, P(x > 22.07) = 1 - P(x < 22.07) = 1 - P(z < z) = 1 - P(z < 1.75)

By Using Standard Normal Table, = 1 - 0.9599 P(x > 43) = 0.0400

P(x > 22.07) = 0.0400

Therefore, the weight of a single chocolate selected at random from the production line, P(x > 22.07) is 0.0400.

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Answer:

Step-by-step explanation:

f(x) = -4cos(3x-pi) +2

compare to f(x) = A cos (B(x+C))+D

A is amplitude =4

Period is 2pi/B so period = 2pi/3

Phase shift is C so phase shift = -pi (this could be positive if it shifted to the left)

Midline is at D so midline is y=2

Answer:

Step-by-step explanation:

1.5 feet                   x

======        =     ======  

250 miles           450

Multiply both sides by 450

1.5 * 450                  x

======        =      

250 miles          

x = 2.7 feet

1 foot = 12 inches

0.7 foot = x

x = 12 * 0.7

x = 8.4 inches

Answer

Either 2.7 feet

or 2 feet 8 inches.

The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.

To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.

For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.

In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.

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Answer:

3x-15

Step-by-step explanation:

> First start off by rewriting with each term that has the same variable beside each other

5x+ x -3x+xy+2xy-3xy-4-2-9

> Start to combine like terms

3x + 0xy - 15

> Rewrite

3x-15

The slope is -Ea/R and the intercept is equal to ln(A)

The Arrhenius equation is a mathematical equation that describes the relationship between the rate constant of a chemical reaction and temperature:

k = Ae^(-Ea/RT)

where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

The slope and intercept of the linear plot of the Arrhenius equation using a semilogarithmic (semilog) plot can be determined by transforming the equation into a linear form. The semilog plot is created by taking the logarithm of the rate constant (k) on the y-axis and the reciprocal of the temperature (1/T) on the x-axis:

ln(k) = ln(A) - Ea / RT

The slope of the plot is equal to -Ea/R and the intercept is equal to ln(A). By fitting a straight line to the semilog plot, the values of Ea and A can be determined.

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Answer: X=y/2-5/2

Step-by-step explanation:

Answer:

x=1/2y+(−5/2) or x=y-5/2

Step-by-step explanation:

Step 1: Flip the equation.

2x+5=y

Step 2: Add -5 to both sides.

2x+5+−5=y+−5

2x=y−5

Step 3: Divide both sides by 2.

2x/2=y−5/2

x=1/2y+(−5/2) or x=y-5/2

In the addition of another child in the process of making lemonade, the marginal productivity of the whole group was decreased that they started to make -6 cups than previous.

To compute the marginal product of adding the fourth kid, we must first determine the additional output produced by adding one more unit of input (the fourth child).

With three youngsters, the group's initial production is 40 glasses of lemonade per hour. This means that their average productivity per child is:

Average productivity per child = Total productivity / Number of children = 40 cups / 3 children

Average productivity per child = 13.33 cups/child

With the addition of a fourth youngster, the group's overall production rises to 34 cups per hour. This means that their average productivity per child with four children is:

Average productivity per child = Total productivity / Number of children = 34 cups / 4 children

Average productivity per child = 8.5 cups/child

To calculate the marginal product of adding a fourth kid, subtract the total production of the group with four children from the total productivity of the group with three children:

Marginal product = Total productivity with 4 children - Total productivity with 3 children

= 34 cups/hour - 40 cups/hour

Marginal product = -6 cups/hour

The negative sign indicates that adding the fourth child has resulted in a decrease in productivity. This could be due to factors such as coordination and communication challenges that arise when working in larger groups.

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The table shows a proportional relationship between the cups of milk used and number of tablespoons of chocolate syrup used. The scale factor shown is 3/2. The constant of proportionality for this relationship is 3/2. The units for the constant of proportionality are teaspoons of chocolate syrup used per cups of milk used.

When it comes to ratios and fractions, the concept of proportion is very connected. When two amounts with the same unit are compared, they form a ratio. When comparing two quantities, a ratio enables us to determine whether one is larger or smaller.

Two ratios or two fractions are equivalent when they are compared according to the proportional rule. To put it another way, two ratios are said to be proportional when they are equal. Performing arithmetic operations on both sides of the ratio taught us that a ratio can be expressed in a variety of ways.

Both the 3: 5 and 6: 10 are equivalent ratios. This indicates that these ratios are proportional. This proportionality can be expressed mathematically as follows:

                                                 \($ \frac{3}{5} = \frac{6}{10}\)

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Answer:Yes.

Step-by-step explanation:Because all X functions are paired with each Y axis and it isn't combined.

Answer: Not a function

Step-by-step explanation: A capacity is a connection for which each incentive from the set the primary parts of the arranged sets is related with precisely one incentive from the arrangement of second segments of the arranged pair.

Answer:

13x + 11y

Step-by-step explanation:

3x and 10x both have x so we can add them

5y and 6y both have y so we add 5 and 6

The assertion that which shows that P(k + 1) is true provided Pk in the Inductive step is true. Moreover, P(1) is also true. Hence, by induction principle, we can say that P(n) is true for all positive integer n.

What is Integer?

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Given that P(n) be the assertion

∑j² = n (n+1)(2n+1)/6

(a) For n = 3, we get

∑j² = 1² + 2²+3² =14

= 3(3+1)(6+1)/6

=14

Hence, P(3) is true.

(b) Expression for P(k) may take the form

∑j² = k (k+1)(2k+1)/6

(c) Expression for P(k + 1) may take the form

∑j² = (k+1) (k+2)(2k+3)/6

(d)Base case:

In base case, we must prove that P(1) is true.

(e) To prove P(n) will be true for every positive integer n, we need to prove that P(k + 1) is true in the inductive step, where k is a positive integer.

(f) In the Inductive step, the Inductive hypothesis is that Pk is true for positive integer k.

(g)Base case:

a) For n=1, we get

RHS= 1(1+1)(2+1)/6

=1

Hence, P(1) is true.

Inductive hypothesis:

Assume P(k) is true:

∑j² = k (k+1)(2k+1)/6

Inductive step:

Now,

∑j² = k (k+1)(2k+1)/6 +(K+1)²

which shows that P(k + 1) is true provided P(k) in the Inductive step is true. Moreover, P(1) is also true. Hence, by induction principle, we can say that P(n) is true for all positive integer n.

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The probability of exactly two dice having a face value of 6 when rolling three fair six-sided dice is 5/72.

To find the probability of exactly two dice having a face value of 6 when three fair six-sided dice are rolled, we can use the concept of combinations.

The total number of possible outcomes when rolling three dice is 6^3 = 216, as each die has 6 possible outcomes.

Now, let's determine the number of favorable outcomes where exactly two dice have a face value of 6.

We have three scenarios where exactly two dice show a 6:

The first die shows a 6, the second die shows a 6, and the third die does not show a 6.

The first die does not show a 6, the second die shows a 6, and the third die shows a 6.

The first die shows a 6, the second die does not show a 6, and the third die shows a 6.

In each scenario, the probability of rolling a 6 on one die is 1/6, and the probability of not rolling a 6 is 5/6.

Scenario 1:

Probability = (1/6) * (1/6) * (5/6) = 5/216

Scenario 2:

Probability = (5/6) * (1/6) * (1/6) = 5/216

Scenario 3:

Probability = (1/6) * (5/6) * (1/6) = 5/216

Adding up the probabilities from each scenario:

Total Probability = (5/216) + (5/216) + (5/216) = 15/216 = 5/72

Therefore, the probability of exactly two dice having a face value of 6 when rolling three fair six-sided dice is 5/72.

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Answer:

That means it will take you 1 and 1/3 hour to go a kilometer.

Answer:

Step-by-step explanation:

5x2-12=10-12=-2

Answer:

=-2 ( B.)

Step-by-step explanation:

f(x) = 5x-12

f(2)= 5(2)-12

=10-12

=-2

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Upper Control Limit (UCL) for R chart = D4 x Rbar = 2.282 x 0.347 = 0.792 and Lower Control Limit (LCL) for R chart = D3 x Rbar = 0 x 0.347 = 0.

To determine the trial central line and control limits for the X and R control charts, we need to first calculate the average and range of each subgroup.
Average (Xbar):
Subgroup 1: 20.35
Subgroup 2: 20.40
Subgroup 3: 20.36
Subgroup 4: 20.65
Subgroup 5: 20.20
Subgroup 6: 20.40
Subgroup 7: 20.43
Subgroup 8: 20.37
Subgroup 9: 20.48
Subgroup 10: 20.42
Subgroup 11: 20.39
Subgroup 12: 20.38
Subgroup 13: 20.40
Subgroup 14: 20.41
Subgroup 15: 20.45
Subgroup 16: 20.34
Subgroup 17: 20.36
Subgroup 18: 20.42
Subgroup 19: 20.50
Subgroup 20: 20.31
Subgroup 21: 20.39
Subgroup 22: 20.39
Subgroup 23: 20.40
Subgroup 24: 20.41
Subgroup 25: 20.40

Average (Xbar) = (20.35 + 20.40 + 20.36 + 20.65 + 20.20 + 20.40 + 20.43 + 20.37 + 20.48 + 20.42 + 20.39 + 20.38 + 20.40 + 20.41 + 20.45 + 20.34 + 20.36 + 20.42 + 20.50 + 20.31 + 20.39 + 20.39 + 20.40 + 20.41 + 20.40)/25 = 20.408
Range (R):
Subgroup 1: 0.34
Subgroup 2: 0.36
Subgroup 3: 0.32
Subgroup 4: 0.36
Subgroup 5: 0.36
Subgroup 6: 0.35
Subgroup 7: 0.31
Subgroup 8: 0.34
Subgroup 9: 0.30
Subgroup 10: 0.37
Subgroup 11: 0.29
Subgroup 12: 0.30
Subgroup 13: 0.33
Subgroup 14: 0.36
Subgroup 15: 0.34
Subgroup 16: 0.36
Subgroup 17: 0.37
Subgroup 18: 0.73
Subgroup 19: 0.38
Subgroup 20: 0.35
Subgroup 21: 0.33
Subgroup 22: 0.33
Subgroup 23: 0.30
Subgroup 24: 0.34
Subgroup 25: 0.30

Range (R) = max(Range of each subgroup) - min(Range of each subgroup) = 0.73 - 0.29 = 0.44
Using these values, we can now calculate the trial central line and control limits:
Central line (CL) for X chart = Xbar = 20.408
Upper Control Limit (UCL) for X chart = CL + (A2 x Rbar) = 20.408 + (0.577 x 0.44) = 20.672
Lower Control Limit (LCL) for X chart = CL - (A2 x Rbar) = 20.408 - (0.577 x 0.44) = 20.144
Central line (CL) for R chart = Rbar = (0.34 + 0.36 + 0.32 + 0.36 + 0.36 + 0.35 + 0.31 + 0.34 + 0.30 + 0.37 + 0.29 + 0.30 + 0.33 + 0.36 + 0.34 + 0.36 + 0.37 + 0.73 + 0.38 + 0.35 + 0.33 + 0.33 + 0.30 + 0.34 + 0.30)/25 = 0.347
Upper Control Limit (UCL) for R chart = D4 x Rbar = 2.282 x 0.347 = 0.792
Lower Control Limit (LCL) for R chart = D3 x Rbar = 0 x 0.347 = 0
If any points fall outside of these control limits, it suggests that the process is out of control and requires investigation for assignable causes. Upon investigating, any assignable causes should be removed and the control chart revised accordingly.

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To determine the points of intersection we first equate the expressions, then we solve for x. Once we have the values of x for which the functions are equal we plu them on one of the function to find its corresponding value of y.

a)

Let's equate the functions and solve for x:

Now we find the corresponding values of y for each value of x; to do this we use the second equation.

When x=3:

Hence the functions intersect at (3,11)

When x=2:

Hence the functions intersect at (2,6)

Therefore the function intersect at the points (3,11) and (2,6).

b)

Let's equate the functions and solve for x:

Now we find the corresponding values of y for each value of x; to do this we use the second equation.

When x=7:

Hence the functions intersect at (7,-26)

When x=-1:

Hence the functions intersect at (-1,-2)

Therefore the function intersect at the points (7,-26) and (-1,-2).

Based on these results, a reasonable conclusion about the productivities of corn variety 1 and corn variety 2 is that:  (c) No, because there may be other differences between the two years besides the corn variety.

In Science, a hypothesis is primarily considered to be a tentative or an educated guess and it can be defined as a testable explanation for an observation, result, or a specific experimentation (scientific) problem, especially by using the "if . . . then . . . because" format.

Even though the result showed that corn variety 1 yielded 140 bushels per acre while corn variety 2, planted in the same location, yielded only 110 bushels per acre, we can not reasonably conclude that corn variety 1 is much more productive than corn variety 2 because there might be other differences between them within the given period of time (2 years).

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1177.5 cubic cm is the volume of the cylinder.

The formula to calculate the volume of a cylinder is V = πr²h, where V represents the volume, r is the radius of the base, and h is the height of the cylinder.

In this case, the radius (r) is 5 cm and the height (h) is 15 cm. Let's calculate the volume:

V = π * (5 cm)² * 15 cm

V ≈ 3.14159 * 25 cm² * 15 cm

V ≈ 1177.5 cm³

Therefore, the volume of the cylinder is approximately 1177.5 cubic cm (rounded to the nearest tenths place).

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Answer: \(5\log(2)=\log(2^5)\)

Step-by-step explanation:

According to the properties of logarithms, we have

To rewrite : \(5\log (2)\) in the form of log(c).

Therefore,

\(\leq 5\log(2)=\log(2^5)\)   [\(\because\ n\log(m)=\log(m^n)\)]

Hence, \(5\log(2)=\log(2^5)\) .