Common sources of caffeine in the diet are coffee and tea. suppose that 75 people were surveyed: 50 adults drink coffee, 30 adults drink tea, and 15 drink both coffee and tea. what percentage of adults drink either coffee or tea?

Answer:

yes

Step-by-step explanation:

First we should find a GCF for the number of boys and girls.

The gcf for the two would be 4.

Divide.

20/4 = 5

28/4= 7

therefore the ratio for boys to girls would be 5 to 7

Answer:

48

Step-by-step explanation:

18% of 1500 is 270

270x18% is 48.6 since it increased by 18%

Answer:

Step-by-step explanation:

Where we have "x" must replace for the number shown on table

We have for "x" tha numbers: 0; 1; 2; 3; 4 and 5

Equation:

1.y = x+4

y = x + 4

For x = 0

y = x + 4

y = 0 + 4

y = 4

For x = 1

y = x + 4

y = 1 + 4

y = 5

For x = 2

y = x + 4

y = 2 + 4

y = 6

For x = 3

y = x + 4

y = 3 + 4

y = 7

For x = 4

y = x + 4

y = 4 + 4

y = 8

For x = 5

y = x + 4

y = 5 + 4

y = 9

So:

x     y

0    4

1     5

2    6

3    7

4    8

5    9

I hope help you.

Using sampling concepts, it is found that a systematic sampling of 500 words would be achieved as follows:

B. Randomly select one of the first 200 words and then every 200th word thereafter for the sample.

Samples may be classified as:

In this problem, he wants a systematic sampling, hence he should choose every kth word, which means that the answer is between options a and b.

He will choose 500 words out of 100,000, hence the value of k is given by:

k = 100000/500 = 200.

Which means that option B is correct.

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Answer:

B

Step-by-step explanation:

khan

Answer:

13/4 inches

Step-by-step explanation:

3.25 inches

325/100 inches

13/4 inches

Answer:

Step-by-step explanation:

Answer:

90%

Step-by-step explanation:

50%×2 100%

5%×2 10%

45%×2 90%

When there are precisely two outcomes of a trial that are mutually exclusive, the binomial distribution is used.

A discrete distribution is the binomial distribution. It is a probability distribution that is frequently utilised. It is then designed to represent a variety of distinct phenomena that appear in business, social sciences, natural sciences, and medical research.

The probability of achieving a specific number of successes, such as successful basketball shots, out of a fixed number of trials can be determined using the binomial distribution. To determine discrete probabilities, we use the binomial distribution.

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Answer:

Your answer is 20

Step-by-step explanation:

as the formula 1/2*4*10=20.

hope it help you if yes then please make me the brainiest.

Thank you

parshv

Answer:

k = 6

Step-by-step explanation:

\(\frac{3k}{2}\) - \(\frac{k+3}{3}\) = 8 - \(\frac{k+2}{4}\)

multiply through by 12 ( the LCM of 2, 3 and 4 ) to clear the fractions

18k - 4(k + 3) = 96 - 3(k + 2) ← distribute parenthesis on both sides

18k - 4k - 12 = 96 - 3k - 6

14k - 12 = - 3k + 90 ( add 3k to both sides )

17k - 12 = 90 ( add 12 to both sides )

17k = 102 ( divide both sides by 17 )

k = 6

Weighing the available information and assigning a probability.

A sort of probability called subjective probability is one that is based on a person's subjective assessment or personal knowledge of the likelihood of a particular result. It solely represents the subject's thoughts and prior experience and does not include any formal computations. A "gut instinct" used when making a deal is an illustration of subjective probability.

So, as per the definition of subjective probability

Dividing the number of favourable events by the number of possible events and Studying the fraction of times in the past a particular event has happened, both can be determined through calculations mathematically accurate but for Weighing the available information and assigning a probability we might use a "gut instinct". Thus

Weighing the available information and assigning a probability.

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The correct option regarding whether the sum of a rational number and an irrational number is always irrational is given by:

Yes. The claim is correct because √ 16 + π = 4 + π , and 4 + π is an irrational number.

The sum of a terminating decimal with a non-terminating decimal always results in a non terminating decimal, that is, the sum of a rational number with an irrational number is always irrational, and the correct option is given by:

Yes. The claim is correct because √ 16 + π = 4 + π , and 4 + π is an irrational number.

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Answer: -152

Step-by-step explanation:

(-4)(-19)(-2)=

(-4)*(38)=

-152

Explanation:

Given point: (2, -4)

A movement to the right will be an addition to the x coordinate

y coordinate = -4

x coordinate = 2

8 units to the right implies an addition of 8 units to the x-coordiante

new x - coordinate = 2 + 8 = 10

The new coordinate (x, y) = (10, -4)

plotting on the graph:

The probability that the sample mean will be between 181 and 185 is 0.3039.

Given,

The mean of a population, μ = 180

Standard deviation, σ = 36

Number of sample observations, n = 84

We have to find the probability that the sample mean will be between 181 and 185;

Lets convert 181 and 185 into z scores;

z = (x - μ) / (σ/√n)

z = (181 - 180) / (36/√84)

z = 1/3.93

z = 0.25

z = (185 - 180) / (36/√84)

z = 5 / 3.93

z = 1.27

Lets look z score table;

The area to the left of z = 0.25 is 0.5987

The area to the left of z = 1.27 is 0.8980

The probability that the z is between 0.25 and 1.27 would be 0.8980 – 0.5887 = 0.3039.

That is,

The probability that the sample mean will be between 181 and 185 is 0.3039.

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We were given a function with the following expression:

And we need to calculate the value of this function for a pair of inputs. In this case a = 4 and b = 5. So we have:

Answer:

2 seconds, assuming the "?" in the equation is supposed to be ^2 (the exponent of 2):  f(h) = -16x^2 +64x + 80

Step-by-step explanation:

You can either graph the functuion or take the first derivative to find the maximum height.  The first derivative will give us the slope for a values of x.  The slope at the top height of the rocket is zero, since it has stopped and is starting it's way back down.

First Derivative:

f(x) = -16x^2 +64x + 80

f'(x) = -32x + 64

Set this equal to zero and solve for x

0 = -32x + 64

x = 2 seconds.

Use 2 seconds in the original equation to find the height at 2 seconds.

f(2) = -16x^2 +64x + 80

f(2) = -16(2)^2 +64*(2) + 80

f(2) = 144 feet

Graph:

A graph is attached.  You can locate the maximum at (2,144)

Answer:

Step-by-step explanation:

No

The value of the line integral is 1/3.

To use Green's theorem to evaluate the line integral, we need first to find the curl of the vector field (M, N):

M = √(1-\(x^{3}\))dx

N = 2xydy

Taking partial derivatives of M and N with respect to x and y, respectively, we get:

∂M/∂y = 0

∂N/∂x = 2y

So the curl of (M, N) is:

curl(M,N) = ∂N/∂x - ∂M/∂y = 2y

Now we can apply Green's theorem:

∮C (M dx + N dy) = ∬R curl(M,N) dA

where C is the oriented boundary of the region R.

The region R is the triangle with vertices(0,0), (1,0), and (1,3).

We can express R as:

R = {(x,y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 3x}

The integral on the right-hand side of Green's theorem can be evaluated using iterated integrals:

∬R curl(M,N) dA

= ∫x=0..1 ∫y=0..3x 2y dy dx

= ∫x=0..1 \(x^{2}\) dx

= 1/3

So the line integral is:

∮C (M dx + N dy) = ∬R curl(M,N) dA = 1/3

Therefore, the value of the line integral is 1/3.

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Answer: 20 Minutes

Step-by-step explanation:

If you are traveling double the speed, the end time is going to be half of the original time.

dy/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x) + e*cos(x)

This is the derivative of the given function y with respect to x.

We want to find the derivative dy/dx of the function y = ln(e^(x^2)+1) + e*sin(x). To do this, we will apply the rules of differentiation.

First, we'll differentiate the function term-by-term. For the natural logarithm function, the derivative is (1/u) * du/dx, where u is the function inside the natural logarithm. In our case, u = e^(x^2) + 1.

The derivative of e^(x^2) is found by applying the chain rule, which gives us (e^(x^2) * 2x). The derivative of 1 is 0. Therefore, the derivative of u is (e^(x^2) * 2x). Now we can find the derivative of ln(u):

d[ln(u)]/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x)

Next, we will differentiate e*sin(x). The derivative of e*sin(x) is found by applying the product rule. The derivative of e is e, and the derivative of sin(x) is cos(x). Applying the product rule, we have:

d[e*sin(x)]/dx = e*cos(x) + e*sin(x) * 0 = e*cos(x)

Now, adding the derivatives of both terms, we get:

dy/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x) + e*cos(x)

This is the derivative of the given function y with respect to x.

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A substance is tested and has a Ph of 7.0. It would be a weak acid.

The correct option is (c) a weak acid .

What is the nature of substance if the pH is less than 7?

What is pH?

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During the winter season, a family sets up a hot chocolate stand near a local ice skating rink. They sell cups of hot chocolate for $1.50 each and typically sell 50 cups per day.

However, due to changes in weather conditions and customer preferences, the family decides to conduct a market experiment by varying the price of hot chocolate to assess the impact on sales volume. The experiment involves increasing the price to $2.00 per cup and monitoring the resulting sales.

By increasing the price of hot chocolate from $1.50 to $2.00 per cup, the family aims to observe how the change in price affects the demand for their product. The experiment helps them understand the price elasticity of demand, which measures the responsiveness of quantity demanded to changes in price. If the increase in price leads to a significant decrease in sales volume, it suggests that the demand for hot chocolate is elastic, meaning consumers are sensitive to price changes. Conversely, if sales remain relatively stable despite the price increase, it indicates that the demand is inelastic, indicating that consumers are less sensitive to price changes. The family can analyze the results of this experiment to make informed pricing decisions and optimize their profitability during the winter season.

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h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

The correct answer is A. The statement is false. If λ+5 is a factor of the characteristic polynomial of A, then −5 is an eigenvalue of A. In order for 5 to be an eigenvalue of A, the characteristic polynomial would need to have a factor of λ−5. This is because the eigenvalues of a matrix A are the roots of its characteristic polynomial, which is given by det(A-λI) where I is the identity matrix.

If λ+5 is a factor of the characteristic polynomial, then det(A-(λ+5)I)=0. This implies that A has an eigenvector corresponding to eigenvalue -(λ+5), which is -5 in this case. Therefore, 5 is not necessarily an eigenvalue of A. Moreover, the diagonal of A-λI contains the eigenvalues of A, not λ+5 as mentioned in option B. Option C is also incorrect because having λ+5 as a factor of the characteristic polynomial does not necessarily mean that λ=5 is a root of the polynomial. Option D is also incorrect because the factors of the characteristic polynomial are used to determine both the eigenvalues and eigenvectors of a matrix.

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The statement is false. If λ+5 is a factor of the characteristic polynomial of A, then it means that λ=-5 is an eigenvalue of A, not 5. This is because the characteristic polynomial is defined as det(A-λI), where I is the identity matrix and det is the determinant function. Setting λ+5 as a factor means that det(A-(-5)I) = 0, which implies that -5 is an eigenvalue of A.

Therefore, in order for 5 to be an eigenvalue of A, the characteristic polynomial would need to have a factor of λ-5, not λ+5. It is also important to note that while the characteristic polynomial is useful for determining both the eigenvalues and eigenvectors of a matrix, the factors of the polynomial only determine the eigenvalues, not the eigenvectors.

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Answer:

graphical method

of simultaneously linear equation

Answer:

58.480766068854

Step-by-step explanation:

hope it will help you

The instantaneous velocity of the object at t = 6 is 2.

Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 + h). s(6 + h) = 2(6 + h) - 7 = 12 + 2h - 7 = 2h + 5Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h.8(6+h) - s(6) h = 8(6 + h) - (2(6) - 7) h= 8h + 56

Then, to rationalize the numerator in the average velocity. (If it applies, simplify again.)$(6 + h) - $(6) h(h(h) + 56)/(h(h)) = (8h + 56)/h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero.s(6 + h) – $(6) v(6) lim h -0s(6 + h) – s(6) v(6) lim h -0Using the above calculation, we get:s(6 + h) – s(6) / h lim h -0s(6 + h) = 2(6 + h) - 7 = 2h + 5So,s(6 + h) – s(6) / h lim h -0(2h + 5 - (2(6) - 7)) / h= (2h + 5 - 5) / h = (2h / h) = 2

Therefore, the instantaneous velocity of the object at t = 6 is 2.

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To determine whether the series is convergent or divergent, we can use the integral test.

First, we note that the function f(x) = ln(x^2+3/8x^2+7) is continuous, positive, and decreasing for x ≥ 1.

Then, we take the integral of f(x) from 1 to infinity:

∫_1^∞ ln(x^2+3/8x^2+7) dx

We can evaluate this integral using integration by parts:

u = ln(x^2+3/8x^2+7)    dv = dx
du/dx = (2x)/(x^2+3/8x^2+7)    v = x

∫_1^∞ ln(x^2+3/8x^2+7) dx = [xln(x^2+3/8x^2+7)]_1^∞ - ∫_1^∞ (2x)/(x^2+3/8x^2+7) dx

We know that the limit of xln(x^2+3/8x^2+7) as x approaches infinity is infinity, so the first term evaluates to infinity.

For the second term, we can use the substitution u = x^2 to get:

∫_1^∞ (2x)/(x^2+3/8x^2+7) dx = ∫_1^∞ (2du)/(u+3/8u+7)

We can then use partial fractions to write the integrand as:

(2du)/((u/8)+7/8) - (2du)/(u+7)

We can now evaluate the integral:

∫_1^∞ (2du)/(u+3/8u+7) = [2ln(u/8+7/8)]_1^∞ = 2ln(∞/8+7/8) - 2ln(1/8+7/8) = ∞

∫_1^∞ (2du)/(u+7) = 2ln(u+7)]_1^∞ = ∞ - 2ln(8) = ∞

Since both integrals diverge, the original series diverges by the integral test. Therefore, the answer is divergent.

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