Determine the density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm3.

The value of cot θ is -3/2, which corresponds to option C) in the given choices. To find the value of cot θ, we can use the given information that tan θ = √7/3 and θ is in quadrant III. By using the appropriate trigonometric identity, we can determine that cot θ = -3/√7, which is equivalent to option C) -3/2.

We are given that tan θ = √7/3 and θ is in quadrant III. In quadrant III, both the sine and cosine functions are negative. We can use the fundamental identity for tangent:

tan θ = sin θ / cos θ

Since sin θ is positive (√7/3) and cos θ is negative in quadrant III, we can write:

√7/3 = sin θ / (-cos θ)

To find cot θ, which is the reciprocal of tan θ, we can invert both sides of the equation:

1 / (√7/3) = -cos θ / sin θ

Simplifying the left side gives:

3 / √7 = -cos θ / sin θ

Next, we can use the reciprocal identity for sine and cosine:

sin θ = 1 / csc θ

cos θ = 1 / sec θ

Substituting these identities into the equation, we get:

3 / √7 = -1 / (cos θ / sin θ)

Multiplying both sides by sin θ gives:

(3sin θ) / √7 = -1 / cos θ

Since sin θ = √7/6 (given), we can substitute this value:

(3√7/6) / √7 = -1 / cos θ

Simplifying the left side gives:

(3/2) / √7 = -1 / cos θ

Multiplying both sides by √7 gives:

(3/2√7) = -√7 / cos θ

We can see that the denominator of the left side is 2√7, which matches the denominator of the cot θ. So we have:

cot θ = -√7 / 2√7

Simplifying the expression, we get:

cot θ = -1 / 2

Therefore, the value of cot θ is -3/2, which corresponds to option C) in the given choices.

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The exact value of this integral may require advanced techniques or numerical methods, but the integral has been successfully transformed into polar coordinates.

To evaluate the integral ∬R arctan(y/x) dA using polar coordinates, we first need to convert the given rectangular region R and the integrand into polar form. The region R can be represented as 1≤r²≤4, which implies 1≤r≤2, and 0≤θ≤π/4. The integrand arctan(y/x) in polar form becomes arctan(rsinθ/(rcosθ)) or arctan(tanθ). The dA term in polar coordinates is r dr dθ.
Now we have the integral in polar coordinates:
∬R arctan(y/x) dA = ∫(θ=0 to π/4) ∫(r=1 to 2) arctan(tanθ) × r dr dθ
Evaluate the integral with respect to r first:
∫(θ=0 to π/4) [0.5r² arctan(tanθ)] (from r=1 to 2) dθ = ∫(θ=0 to π/4) (2arctan(tanθ) - 0.5arctan(tanθ)) dθ
Next, evaluate the integral with respect to θ:
∫(θ=0 to π/4) (1.5arctan(tanθ)) dθ

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Answer:

Style A shoes sold : 152

Style B shoes sold : 88

Step-by-step explanation:

Let :

Forming equations :

Substitute the value of x from 1 in 2.

Finding x :

Solution :

\(f(f^-1(x)) = f^-1(f(x)) = x\), which confirms that we have found the correct inverse function.

To find the inverse of a function f(x), we need to switch the roles of x and y in the equation and then solve for y. In other words, we replace f(x) with y, then swap the positions of x and y in the equation and solve for y.

For the function f(x) = x/8 + 3, we can write:

y = f(x) = x/8 + 3

\(To find f^-1(x),\) we swap the positions of x and y and solve for y:

x = y/8 + 3

Subtracting 3 from both sides, we get:

x - 3 = y/8

Multiplying both sides by 8, we get:

8(x - 3) = y

Therefore, the inverse of the function f(x) is:

\(f^-1(x) = 8(x - 3)\)

We can also check our answer by composing the two functions and verifying that we get the identity function:

\(f(f^-1(x)) = f(8(x - 3)) = 8(x - 3)/8 + 3 = x - 3 + 3 = x\\f^-1(f(x)) = f^-1(x/8 + 3) = 8((x/8 + 3) - 3) = x/8\)

As expected, we have \(f(f^-1(x)) = f^-1(f(x)) = x\), which confirms that we have found the correct inverse function.

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Answer:

3√2

Step-by-step explanation:

2√2-3√2+2^2√2

2√2-3√2+4√2

3√2

Answer:

\(3 \sqrt{2} \)

Step-by-step explanation:

Simplify

\( \sqrt{8} - \sqrt{18} + \sqrt{32} \)

Evaluate

\(2 \sqrt{2} - 3 \sqrt{2} + 2 {}^{2} \sqrt{2} \)

Collect like terms

\(2 \sqrt{2} - 3 \sqrt{2} + 4 \sqrt{2} \)

Finish

\(3 \sqrt{2} \)

Hope it helped;)

A one-sample t-test was conducted to determine if the temperature increased in the first week of October 2019 compared to the average temperature from the previous 10 years. The result showed a p-value of 0.032, indicating a significant increase in temperature.

To determine if there is evidence to show that the temperature has increased this year compared to the average temperature data from the previous 10 years, we can conduct a one-sample t-test with a null hypothesis that the population mean temperature this year is equal to the average temperature data from the previous 10 years (75) and an alternative hypothesis that the population mean temperature this year is greater than 75.

Using a statistical software, the calculated t-value is 2.17 with a corresponding p-value of 0.032. Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is evidence to show that the temperature has increased this year compared to the average temperature data from the previous 10 years. The p-value of 0.032 indicates that the probability of observing a sample mean temperature as extreme as 79.29 (the calculated sample mean temperature this year) or greater, assuming that the population mean temperature is equal to 75, is 0.032.

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Answer:

C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 5.

Step-by-step explanation:

The given integral ∭[2³(x + y)³] dz dy dx over the region -4 is a triple integral. It involves integrating the function 2³(x + y)³ with respect to z, y, and x, over the given region. The final result will be a single value.

The integral ∭[2³(x + y)³] dz dy dx represents a triple integral, where we integrate the function 2³(x + y)³ with respect to z, y, and x over the given region. To evaluate this integral, we follow the order of integration from the innermost variable to the outermost.

First, we integrate with respect to z. Since there is no z-dependence in the integrand, the integral of 2³(x + y)³ with respect to z gives us 2³(x + y)³z.

Next, we integrate with respect to y. The integral becomes ∫[from -4 to 0] 2³(x + y)³z dy. This involves treating z as a constant and integrating 2³(x + y)³ with respect to y. The result of this integration will be a function of x and z.

Finally, we integrate with respect to x. The integral becomes ∫[from -4 to 0] ∫[from -4 to 0] 2³(x + y)³z dx dy. This involves treating z as a constant and integrating the function obtained from the previous step with respect to x.

After performing the integration with respect to x, we obtain the final result, which will be a single value.

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Let the selling price for walnuts be x and the selling price for the almonds be y.

On the first day, Erick sold 2 pounds of walnuts and 4 pounds of almonds for $28. This implies that

On the second day, 4 pounds of walnuts and 3 pounds of almonds for $31.

Answer: y= -2x+9

Step-by-step explanation:

m is the increase each time the x axis goes up one

We can see that it goes down 2 every time so the m value is -2

the b value is the number when the x axis is at 0, we can see on the y axis this number is 9

The equation is:

y = -2x + 9

Work and explanation:

We should first find the slope of the graphed line.

Remember that :

\(\boldsymbol{m=\dfrac{rise}{run}}\)

rise = how many units we move up/down the y axis

run = how far we move on the x axis

The given slope goes "down 2, over 1" so:

That makes the slope:

\(\boldsymbol{m=-\dfrac{2}{1}}\)

If simplified, it gives us -2. So we have figured out the slope, m. Now, to figure out the y intercept, we should look at where the graphed line intercepts the y axis. This happens at (0, 9).

The y intercept is the second number; therefore the y intercept is 9.

Therefore, the equation is y = -2x + 9.

Answer:

0.0637

Step-by-step explanation:

hope this helps :)

6.37 x 10⁻² in the standard form is 0.0637.

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.

We have an expression,

6.37 x 10⁻².

Simplifying to standard form.

6.37 x 10⁻²,

= 6.37 x 1/100

= 6.37/100

= 0.0637

Therefore, 0.0637 is the standard form.

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Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).

Answer:

What? I think you forgot to attach the picture.

Answer:

The answer is 6:8

Step-by-step explanation:

It is the closest to being a whole number.

Hope that helps!

6:8 is greater than 6:9

You can cross multiply the 2 equation to get the same denominator. That way you can now compare them. You would get 48:72 (6:9) and 54:72 (6:8). There for 6:8 is larger than 6:9.

The chart has been completed and the information has been given below:

Annually $9200 6% 15 9200(1+0.06)15 $22084.34

Semi-Annually $9200 6/2 = 3% 15*2 = 30 9200(1+0.03)30 $22330.81

Quaterly $9200 6/4 = 1.5% 15*4 = 60 9200(1+0.015)​​​​​60 $22477.62

Monthly $9200 6/(12*15) = 1/30 %

15*12*15 = 2700

9200(1+1/(30*100))2700

$22624.96

Weekly $9200 6/(15*52) = 1/130 15*52*15 = 11700

9200(1+1/(130*100))11700

$22627.57

Daily $9200 6/(15*365) = 2/1825

15*365*15 = 82125

9200(1+2/(1825*100))82125

$22628.24

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Answer: 1/6

Step-by-step explanation:

Answer:

There is a 1 out of 6 probability the die shows a one.

Step-by-step explanation:

Although there are only 3 odd numbers in a die (1,3,5) , the die still only has 6 numbers. (1,2,3,4,5,6)

These means that the probability of getting 1, is 1 out of the 6 numbers.

Because of this it's a 1 out of 6 probability that this would happen. (or you can write 1/6 same answer)

Hope this helps, good luck!! :)

The statement is true. The mean of all possible differences between the two sample means does equal the difference between the two population means, regardless of the distributions of the variable on the two populations.

This concept is known as the Central Limit Theorem (CLT) and holds under certain assumptions.

The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. This means that even if the populations have different distributions, as long as the sample sizes are large enough, the distribution of the sample means will be normally distributed.

When comparing two independent samples from two populations, the difference between the sample means represents an estimate of the difference between the population means. The mean of all possible differences between the sample means represents the average difference that would be obtained if we were to repeatedly take samples from the populations and calculate the differences each time.

Due to the Central Limit Theorem, the sampling distribution of the sample mean differences will be approximately normally distributed, regardless of the distributions of the variables in the populations. Therefore, the mean of all possible differences will converge to the difference between the population means.

It's important to note that the Central Limit Theorem assumes random sampling, independence between the samples, and sufficiently large sample sizes. If these assumptions are violated, the Central Limit Theorem may not hold, and the statement may not be true. However, under the given conditions, the statement holds true.

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Step-by-step explanation:

( √6-6²)/√6

(√6-6²)×√6/√6×√6

(√6)²-√6(6)²/(√6)²

6-36√6/6

1-6√6

Answer:10

Step-by-step explanation:

I would say 10 because she is sacrificing that 1 hour of pay

Answer:

5 cameras they sell

Step-by-step explanation:

P = 3x² – 3x + 10       p = 70

3x² – 3x + 10 = 70

3x² – 3x - 60 = 0

x² - x -20 = 0

(x + 4) (x - 5) = 0

x can't be negative, x = 5

The no of cameras sold if A camera shop's daily profit is given by P = 3x² – 3x + 10, where x is the total number of cameras sold in the day. If they only had a profit of $70 today is 5.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in, 3x + 5 Equals 15, instances. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

Given:

The equation, P = 3x² - 3x + 10,

If P = 70 then,

70 =  3x² - 3x + 10

x = 5 and -4 but the number of cameras can not be negative

Therefore, The no of cameras sold if A camera shop's daily profit is given by P = 3x2 – 3x + 10, where x is the total number of cameras sold in the day. If they only had a profit of $70 today is 5.

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The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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Answer:

70%

Step-by-step explanation:

Simply do 14÷20

0.7

70% passed

Answer:

domain and range below

Step-by-step explanation:

domain: [-5,1) or 1>x≥-5

range: [-4,7) or -4≥x<7

these are due to the domain being the possible x-values and range being the possible y-values.

hope this helps! comment below my response if you need further clarification.

sin θ = 3 / 7 = .429

sin^2 θ + cos^2 θ = 1      trig identity

9/49 + cos^2 θ = 1

cos^2 θ = 40 / 49 = .816       cos θ = .903

Check .429^2 + .903^2 = 1

cos .903 = 25.4 deg

In the second quadrant sin = +, cos = -, tan = -

So 25.4 deg in the second quadrant = 180 - 25.4 = 154.6 deg

Check:

sin 154.6 = .428

cos 154.6 = -.903

tan 154.6 = -.475

Answer:

B

Step-by-step explanation:

this is really simple. Just multiply the exponents to get rid of the parenthesis.

(-2 times 2 is -4)

(7 times 2 is 14)

so you get a to the power of -4 times 8 to the power of 14.

the answer is B

Answer:

B a⁻¹⁴ · 8¹⁴

Step-by-step explanation:

(a⁻² · 8⁷)²

= a⁽⁻²⁾⁽²⁾ · 8⁽⁷⁾⁽²⁾

= a⁻⁴ . 8¹⁴

A sequence is arithmetic sequence when the first differences are all the same non-zero number.

An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a defined number. The common difference of the series, which is a constant value, is the same for all following pairs of terms.

As a result, a sequence can be said to be arithmetic if its first differences all contain the same non-zero value. For instance, the arithmetic sequence 3, 6, 9, 12, 15,... has a common difference of 3.

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Answer: Sara would earn  $478 for that week

Step-by-step explanation:

1. Sara's weekly salaries is $400, and she gets 6.5% on sales at her work.

2. In order to find how much she would get from the commission of $1200 worth of merchandise they sold, we need to find the 6.5% of 1200

Step 1: Our output value is 1200.

Step 2: We represent the unknown value with x.

Step 3: From step 1 above, 1200=100%.

Step 4: Similarly, x=6.5%.

Step 5: This results in a pair of simple equations:

1200=100%(1).

x=6.5%(2).

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both  equations have the same unit (%); we have

\(\frac{1200}{x} = \frac{100}{6.5}\)

Step 7: Again, the reciprocal of both sides gives

\(\frac{x}{1200} =\frac{6.5}{100}\)

⇒\(x=78\)

Therefore, 6.5% of $1200 is $78

3. you would then need to add 400 + 78 and you get a total of $478

Answer:

the value of X is 13..

Thank you ☺️

Answer:

the value of X is 13..

Step-by-step explanation:

The buffer will probably be destroyed by the addition of HCN.

A weak acid and the conjugate base of the weak acid, or a weak base and the conjugate acid of the weak base, are combined to form the buffer solution, a water-based solvent solution. They withstand being diluted or having modest amounts of acid or alkali added to them without changing their pH.

Given that a 1.0 l buffer solution is 0.15 m in HCN and 0.10 m in NaCN.

We need to find a action which one destroy the buffer solution.

A buffer is a substance made of salt and a weak acid that is beneficial. From the aforementioned chemicals, HCN is a potent acid and NaCN is a salt between HF and NaCN. Therefore, the buffer will probably be destroyed by the addition of HCN.

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