Isabel plans to watch 3 movies each month. Write an equation to represent the total number of movies
In that she will watch in m months

Veremos que el area del banderín es 930cm^2, entonces la opción correcta es A.

Luego de una pequeña busqueda online, pude ver que el banderin es un triangulo isósceles con base de 31cm y altura de 60 cm.

Recordar que para un triangulo de base b y altura h, el area es:

A = b*h/2

Entonces el area del banderín va a ser:

A = (31cm)*(60cm)/2 = 930cm^2

Entonces la opción correcta es A.

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To find the linear approximation, we use the formula

:f(x) = f(a) + f'(a) (x-a)

where, a is the point of approximation, and f'(a) is the derivative of the function f(x) at the point a.We have

√6.379 = f(x),

which is the function that we need to approximate.

f(a) = f(6) = √6f'(x) = (1/2) (x^(-1/2))f'(a) = f'(6) = (1/2) (6^(-1/2)) = 1/4√6.379 ≈ f(6) + f'(6) (√6.379 - 6)= √6 + (1/4) (√6.379 - 6) = 2.449625

approximated to 3 decimal places Hence, the value of √6.379 using linear approximation to three decimal places is 2.450.

The given length of a rectangle is increasing at the rate of 5 in./sec while the width is decreasing at the rate of 4 in./sec. We need to find how fast is the area changing at the instant the rectangle is a square each of whose sides is 6 in. We can solve this question using the formula

dA/dt

= (∂A/∂l) dl/dt + (∂A/∂w) dw/dt

We know that when the rectangle is a square each of whose sides is 6 in, then the length and width of the rectangle will be equal,

i.e. l

= w

= 6 in. Hence, A

= lw

= 36 sq

in Differentiating both sides with respect to time t, we get d

A/dt

= 2l (dl/dt) + 2w (dw/dt)Since l

= w

= 6 in,

dl/dt

= 5 in./sec and dw/dt

= -4 in./sec (since the width is decreasing), we have

dA/dt

= 2(6)(5) + 2(6)(-4)

= 12 in²/sec

Therefore, the area is changing at the rate of 12 in²/sec when the rectangle is a square each of whose sides is 6 in.Linear approximation: Linear approximation is an estimation technique that is used to find the approximate value of a function near a particular point. It is a method of approximating a value of a function by using a tangent line at a point near the one of interest. This method can be useful when exact calculations are difficult or time-consuming. Here, we need to find the value of √6.379 using linear approximation to three decimal places.

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Based on the given data, the solution to the system of equations is x1 = 5, x2 = 7, x3 = -8, and x4 = -1.

To solve the system of equations using an augmented matrix, we can perform row operations to transform the augmented matrix into row-echelon form or reduced row-echelon form. Let's denote the variables as x1, x2, x3, and x4.

The given system of equations is:

x1 + x2 + 2x3 + x4 = 3

x1 + 2x2 + x3 + x4 = 2

x1 + x2 + x3 + 2x4 = 12

2x1 + x2 + x3 + x4 = 4

We can represent this system of equations using an augmented matrix:

[1 1 2 1 | 3]

[1 2 1 1 | 2]

[1 1 1 2 | 12]

[2 1 1 1 | 4]

Now, let's perform row operations to transform the augmented matrix into row-echelon form or reduced row-echelon form. I'll use the Gaussian elimination method:

Subtract the first row from the second row:

R2 = R2 - R1

[1 1 2 1 | 3]

[0 1 -1 0 | -1]

[1 1 1 2 | 12]

[2 1 1 1 | 4]

Subtract the first row from the third row:

R3 = R3 - R1

[1 1 2 1 | 3]

[0 1 -1 0 | -1]

[0 0 -1 1 | 9]

[2 1 1 1 | 4]

Subtract twice the first row from the fourth row:

R4 = R4 - 2R1

[1 1 2 1 | 3]

[0 1 -1 0 | -1]

[0 0 -1 1 | 9]

[0 -1 -3 -1 | -2]

Subtract the second row from the third row:

R3 = R3 - R2

[1 1 2 1 | 3]

[0 1 -1 0 | -1]

[0 0 -1 1 | 9]

[0 -1 -3 -1 | -2]

Subtract three times the second row from the fourth row:

R4 = R4 - 3R2

[1 1 2 1 | 3]

[0 1 -1 0 | -1]

[0 0 -1 1 | 9]

[0 0 0 -1 | 1]

The augmented matrix is now in row-echelon form. Now, we can perform back substitution to find the values of the variables.

From the last row, we have:

-1x4 = 1, which implies x4 = -1.

Substituting x4 = -1 into the third row, we have:

-1x3 + x4 = 9, which gives -1x3 - 1 = 9, and thus x3 = -8.

Substituting x3 = -8 and x4 = -1 into the second row, we have:

1x2 - x3 = -1, which gives 1x2 - (-8) = -1, and thus x2 = 7.

Finally, substituting x2 = 7, x3 = -8, and x4 = -1 into the first row, we have:

x1 + x2 + 2x3 + x4 = 3, which gives x1 + 7 + 2(-8) + (-1) = 3, and thus x1 = 5.

Therefore, the solution to the system of equations is:

x1 = 5, x2 = 7, x3 = -8, and x4 = -1.

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In a sample of 10,000 observations from a normal population, about 27 would be expected to lie beyond three standard deviations of the mean, therefore, the correct option is b.

For a normal distribution, about 99.7% of the data is expected to lie within three standard deviations of the mean. This is known as the empirical rule or the 68-95-99.7 rule.

Using this rule, we can estimate the number of observations beyond three standard deviations of the mean for a sample of 10,000. Since the distribution is normal, we know that the mean and standard deviation completely describe the distribution.

Assuming the sample is representative of the population, we can use the empirical rule to estimate the number of observations beyond three standard deviations of the mean. Since three standard deviations from the mean cover 99.7% of the data, the remaining 0.3% of the data would be expected to lie beyond three standard deviations.

Therefore, the correct answer is c. about 27, since 0.3% of 10,000 is approximately 27.

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apply the absolute rule,

solve each inequality independently,

find the intersection of both solutions

Answer:

The solution to the inequality in interval notation is:

Answer: 4b+2

Step-by-step

(7b+1)-(3b-1)

7b+1-3b+1

4b+2

When (7b -1) - (3b - 1) is substrate then final value will be 4b.

Answer is 4b and correct option is a.

Subtraction would be the operation as well as process of determining the difference among two numbers or quantities. Subtracting one amount from another is however known as 'taking one number aside from another'.

Here given that,

(7b-1)-(3b-1)

we need to subtraction , so first we need to open brackets,

7b-1-3b+1= 4b

7b-3b will be equal to 4b.

so  got the answer 4b and option a is correct according to this answer.

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To find the probability of accepting a lot with a defect rate of 4% using an acceptance sampling plan with n = 27 and c = 0, we need to calculate the binomial probability of having zero defects in a sample of 27 items.

The probability of accepting a lot is equal to the probability of having zero defects, which can be calculated using the binomial probability formula. The formula is P(X = k) = C(n, k) * p^k * (1 - p)^(n - k), where P(X = k) is the probability of getting k successes, n is the sample size, p is the probability of success (defect rate), and C(n, k) is the binomial coefficient.

In this case, we want to find P(X = 0) where n = 27 and p = 0.04 (4% defect rate). Substituting these values into the binomial probability formula and calculating it will give us the desired probability of accepting the lot with zero defects.

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Answer:

4    1    1/8

Step-by-step explanation:

(1/2)^-2 = 2^2 = 4

(1/2)^0 = 1

(1/2)^3 = 1/(2^3) = 1/8

Answer:

At x=-2:
y=16

At x=0:
y=1

At x=3:
y=1/64

Step-by-step explanation:

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Assuming y[-1] = 0, we can solve this equation recursively for n ≥ 0.

To find the unit-pulse response h[n] for the given discrete-time systems, we can solve for y[n] when the input x[n] is a unit pulse.

For the system y[n+1] + 0.5y[n] = x[n+1]:

We can substitute x[n] = δ[n], where δ[n] is the unit pulse.

y[n+1] + 0.5y[n] = δ[n+1]

Next, we can express y[n+1] in terms of y[n] and solve the equation.

y[n+1] = -0.5y[n] + δ[n+1]

Since the initial condition is not provided, we assume y[-1] = 0.

For n = 0, the equation becomes:

y[1] = -0.5y[0] + δ[1]

For n = 1, the equation becomes:

y[2] = -0.5y[1] + δ[2]

By substituting the value of y[1] from the previous equation, we can continue this process recursively to find y[n] for n ≥ 0.

For the system y[n+1] + 1.5y[n] = x[n]:

Following the same procedure, we substitute x[n] = δ[n] into the equation:

y[n+1] + 1.5y[n] = δ[n]

Again, assuming y[-1] = 0, we can solve this equation recursively for n ≥ 0.

Note that finding a closed-form solution for the pattern of y[n] might not be straightforward, as it depends on the initial conditions and the specific values of the unit pulse at different time indices.

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The correct solution to this problem is option e. 1/e. We can find it in the following manner.

The time constant of an RC circuit is the time in which the current decreases to 1/e (approximately 0.368) of its initial value.

This can be derived from the equation for the current in an RC circuit:

\(I=10 * e^({-t/RC} )\)

where I is current at time t, I0 is the initial current, R is the resistance, C is the capacitance, and e is the mathematical constant approximately equal to 2.71828.

To find the time constant, we set the exponent to -1:

\(e^({-t/RC} ) = 1 /e\)

Solving for t/RC, we get:

t/RC = 1

Therefore, the time constant is equal to RC, and the current decreases to 1/e of its initial value in one time constant.

So the answer is e. 1/e.

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Answer:

6

Step-by-step explanation:

Answer:

The value of x is 30 degrees.

Step-by-step explanation:

We know that angle 1 is 60 degrees, and that angle two is a right angle (meaning 90 degrees.) 60+90 is equal to 150 degrees. 180 degrees - 150 degrees is equal to 30 degrees. I hope this helps! :)

\(~~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\\implies \sin 60^{\circ} = \dfrac{x}{8}\\\\\\\implies x = 8 \sin 60^{\circ}\\\\\\\implies x = 8 \cdot \dfrac {\sqrt3}2\\\\\\\implies x = 4\sqrt 3\)

Answer:

twenty five square meters

Step-by-step explanation:

100 divided by four

Using a system of equations, the quantity of Type A coffee that Trey's Coffee Shop blended with Type B coffee was 78 pounds.

A system of equations or simultaneous equations is two or more equations solved concurrently, simultaneously, or at the same time.

Unit Cost Per Pound:

Type A coffee = $5.80

Type B coffee = $4.25

The total quantity of pounds of the blend = 142 pounds

The total cost of 142 pounds = $724.40

Let the number of Type A coffee = x

Let the number of Type B coffee = y

x + y = 142 ... Equation 1

5.8x + 4.25y = 724.40 ... Equation 2

Multiply Equation 1 by 4.25:

4.25x + 4.25y = 603.5 ... Equation 3

Subtract Equation 3 from Equation 2:

5.8x + 4.25y = 724.40

-

4.25x + 4.25y = 603.5

1.55x = 120.9

x = 78

Substitute x = 78 in either equation:

x + y = 142

78 + y = 142

y = 64

Thus, 78 pounds of Type A coffee was used for the mixture.

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To determine the 95% energy bandwidth (B) of the signal g(t) = [0.5sinc²(0.5 t) cos(2 t)], we can apply Parseval's Theorem. Parseval's Theorem states that the total energy of a signal in the time domain is equal to the total energy of the signal in the frequency domain. Mathematically, it can be expressed as:

∫ |g(t)|² dt = ∫ |G(f)|² df

In this case, we want to find the frequency range within which 95% of the energy of the signal is concentrated. So we can rewrite the equation as: 0.95 * ∫ |g(t)|² dt = ∫ |G(f)|² df

Now, we need to evaluate the integral on both sides of the equation. Since the given signal is in the form of a product of two functions, we can separate the terms and evaluate them individually. By applying the Fourier transform properties and integrating, we can find the value of B.

For part (b), when we consider g(2t), the time domain signal is compressed by a factor of 2. This compression results in a corresponding expansion in the frequency domain. Therefore, the 95% energy bandwidth of g(2t) will be twice the value of B determined in part (a). This can be justified by considering the relationship between time and frequency domains in Fourier analysis, where time compression corresponds to frequency expansion and vice versa.

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Answer:

okokookokokokjfdgugv

A 70% chance of rain means that there is a higher likelihood of rain occurring compared to other possible weather conditions, but it is not a guarantee.

When a forecaster says there is a 70% chance of rain, it means that, based on their analysis of various weather factors, they believe there is a 70% probability of rain occurring. This percentage represents the likelihood or chance of rain happening.

It's important to note that this is not a definitive prediction that it will rain. Weather forecasting is not an exact science, and there is always some level of uncertainty involved. The forecaster is indicating that, given the current conditions and their expertise, rain is more likely to happen than not.

To put it into perspective, if this weather scenario were repeated 100 times, it is expected that rain would occur in approximately 70 of those instances. The remaining 30 instances would not experience rain.

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Answer:

Step-by-step explanation:

Assuming you have access to the standard normal distribution table, you can use the normalcdf function on a graphing calculator to find the probability that a data value in a normal distribution is between a z-score of 0.18 and 1.99.

To use the normalcdf function, you need to enter the lower and upper bounds of the z-score range, as well as the mean and standard deviation of the normal distribution.

Assuming the mean is 0 and the standard deviation is 1 (since we are dealing with the standard normal distribution), the expression to enter into the calculator would be:

normalcdf(0.18, 1.99, 0, 1)

This will return the probability that a data value in the normal distribution is between the z-scores of 0.18 and 1.99.

Answer:

12

Step-by-step explanation:

I just did the math on how much 30% is in 40 and I got the answer 12 I hope this helps you!

The frequency distribution of the digits indicates that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements.

Frequency Distribution:

Digit Frequency

0 3

1 5

2 9

3 5

4 3

5 4

6 4

7 4

8 2

9 1

From the distribution of the digits, it appears that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements.

The frequency distribution of the digits indicates that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements. For example, the frequency of the digit '2' is more than twice as high as the frequency of the digits '1' and '3', which is not likely to occur in a set of actual measurements.

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the slope of the tangent line to f(x) = x³ at any point (x, f(x)) is 3x².

The derivative of f(x) = x³ can be found using the power rule of differentiation. According to the power rule, the derivative of xⁿ is \(nx^(n-1).\)

Applying the power rule to f(x) = x³, we get:

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

f'(x) = 3x²

Now, to find the slope of the tangent line at a specific point (x, f(x)), we substitute the x-coordinate of the point into the derivative function f'(x).

So, the slope of the tangent line to f(x) = x³ at the point (x, f(x)) is given by:

slope = f'(x) = 3x²

Therefore, the slope of the tangent line to f(x) = x³ at any point (x, f(x)) is 3x².

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The number of students that voted is given as follows:

5 students.

The number of students that voted is obtained applying the proportions in the context of this problem, multiplying the total number of students by the decimal equivalent of the percentage.

The total number of students is given as follows:

20 students.

The decimal equivalent of the percentage is given as follows:

25/100 = 0.25.

Hence the number of students that voted is given as follows:

0.25 x 20 = 20/4 = 5 students.

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To estimate the mean per capita income for a major city in California with an error of at most $0.56 at the 85% confidence level, the economist needs to determine the required sample size.

To calculate the required sample size, we can use the formula: \(n = \left(\frac{{Z \cdot \sigma}}{{E}}\right)^2\), where \(n\) is the sample size, \(Z\) is the Z-score corresponding to the desired confidence level (in this case, for 85% confidence level, \(Z \approx 1.44\)), \(\sigma\) is the known standard deviation (\$6.6), and \(E\) is the desired margin of error (\$0.56). Plugging in the values, we have \(n = \left(\frac{{1.44 \cdot 6.6}}{{0.56}}\right)^2 \approx 52\). Therefore, a sample size of approximately 52 would be required to estimate the mean per capita income with an error of at most $0.56 at the 85% confidence level.

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\((5xy ^{2} {)}^{3} \\ = {5}^{3} \times {x}^{3} \times y ^{2 \times 3} \\ = 125 {x}^{3} {y}^{6} \)

Answer:

\(125 {x}^{3} {y}^{6} \)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

125x^3y^6

Step-by-step explanation:

Distribute the 3 exponent on the outside to the 5, x^1 and y^2

5^3 = 125

1 * 3 = 3

2 * 3 = 6

125x^3y^6

Answer:

-1/3

Step-by-step explanation:

Answer:

0.64

Step-by-step explanation:

4 out of 5 free throws is 0.8 as a decimal.

The probability that Brian will make 2 free throws is 0.8 for the first one, and then 0.8 of that for the second one. That means you multiply the two to get your answer and 0.8 times 0.8 = 0.64.

Answer:

I do believe The Answer Is 0.625

Answer:

5/8 or 0.625

Step-by-step explanation:

Hope this helps!

Answer:

B(9) = 11 means the depth of the water in the bathtub, 9 minutes after Tyler began to fill the bathtub is 11 inches

Step-by-step explanation:

Whereby the function is expressed as B(t) = d,

Where;

d = The depth of the water

Therefore, when we have B(9) = 11, by comparing with the general form of the function, B(t) = d, we have;

t = 9 = The time in minutes after Tyler began to fill the bathtub = 9 minutes

d = The depth of the water = 11 inches

Which gives the meaning of the equation, B(9) = 11 as the depth of the water in the bathtub, 9 minutes after Tyler began to fill the bathtub is 11 inches.