Compare Hopi and Navajo Groups differences

Daycare center earns $180 from x preschoolers and y infants/toddlers.

The equation given is 3x + 4y = 180, where x represents the number of preschoolers and y represents the number of infants and toddlers at the daycare center in an hour when it earns $180.

To find the values of x and y, we can use algebraic techniques such as substitution or elimination. For example, we can solve for y in terms of x by subtracting 3x from both sides and dividing by 4, giving us y = (180-3x)/4. We can then plug in different values of x to find the corresponding values of y.

Alternatively, we can solve for x in terms of y and use the same process. Ultimately, the goal is to find the values of x and y that satisfy the equation and make sense in the context of the problem.

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The quadrilateral with vertices at (1, -2, 3), (4, 3, -1), (2, 2, 1), and (5, 7, -3) is a parallelogram, and its area can be found using the cross product of two adjacent sides.

1

To show that the quadrilateral is a parallelogram, we need to demonstrate that opposite sides are parallel. Two vectors are parallel if and only if their cross product is the zero vector.

Let's consider the vectors formed by two adjacent sides of the quadrilateral: v1 = (4, 3, -1) - (1, -2, 3) = (3, 5, -4) and v2 = (2, 2, 1) - (1, -2, 3) = (1, 4, -2).

Now, we calculate their cross product: v1 × v2 = (3, 5, -4) × (1, 4, -2) = (-12, -2, 22).

Since the cross product is not the zero vector, we can conclude that the quadrilateral is indeed a parallelogram.

To find the area of the parallelogram, we can calculate the magnitude of the cross product: |v1 × v2| = √((-12)² + (-2)² + 22²) = √(144 + 4 + 484) = √632 = 2√158.

Therefore, the area of the quadrilateral is 2√158 square units.

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Answer: 12 no caculator needed

Step-by-step explanation:

As a result, the provided equation has two solutions: -2,1. That is option B.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

Taking the given equation ,

x = 2/(x +1)

x²+x-2=0

Simplify ,

x²+2x-x-2=0

x(x+2)-1(x+2)=0

x=-2,1

Hence the given equation has two solutions that is -2,1.

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The general solution to the given system of differential equations is \((x(t), y(t)) = (C - 9, -5 + 5Ce^{5t})\), where C is an arbitrary constant.

To find the general solution of the given system of differential equations:

dx/dt = 9x - y

dy/dt = 5x + 5y

Solve these equations simultaneously.

Step 1: Solve the first equation, dx/dt = 9x - y.

To do this,  rearrange the equation as follows:

dx/dt + y = 9x

This is a first-order linear ordinary differential equation. Solve it using an integrating factor. The integrating factor is given by \(e^{\int1 \,dt}= e^t\).

Multiply both sides of the equation by \(e^t\):

\(e^{t}dx/dt + e^t y = 9x e^t\)

Now, notice that the left side is the derivative of the product \(e^t\) x with respect to t:

d/dt \((e^t x)\) = 9x \(e^t\)

Integrating both sides with respect to t:

\(\int{d/dt (e^t x)}\, dt = \int{9x e^t}\, dt\)

\(e^t x = 9 \int{x e^t}\, dt\)

integrating by parts.

\(e^t x = 9 (x e^t - \int{ e^t}\, dx\)

\(e^t x = 9x e^t - 9 \int{e^t}\, dx\)

\(e^t x + 9 \int{ e^t}\, dx = 9x e^t\)

\(e^t x + 9 e^t = C e^t\)  (where C is the constant of integration)

\(x + 9 = C\)

\(x = C - 9\)

Step 2: Solve the second equation,\(dy/dt = 5x + 5y\).

This equation is separable. Rearrange it as:

\(dy/dt - 5y = 5x\)

Multiply both sides by \(e^{(-5t)}\):\(e^{-5t} dy/dt - 5e^{-5t} y = 5x e^{-5t}\)

Again, notice that the left side is the derivative of the product \(e^{(-5t)}y\) with respect to t:

\(d/dt (e^{(-5t)} y)= 5x e^{-5t}\)

Integrating both sides with respect to t:

\(\int{ d/dt (e^{(-5t)} y) dt = ∫ 5x e^{(-5t)} dt\)

\(e^{(-5t)} y = 5 \intx e^{(-5t)} \,dt\)

Adding zero for symmetry

\(e^{-5t} y = 5 (\int x e^{-5t} \,dt + \int 0\, dt)\)

\(e^{-5t} y = 5 (\int x e^{-5t}\, dt + C)\)

\(e^{-5t} y = 5 (\int x e^{-5t}\, dt) + 5C\)

Using substitution: u = -5t, du = -5dt

\(e^{-5t} y = 5 (-\int e^{-5t} \,dx) + 5C\)

\(e^{-5t} y = -5 \int e^u \,dx + 5C\)

\(e^{-5t} y = -5e^u + 5C\)

\(e^{-5t} y = -5e^{-5t} + 5C\)

\(y = -5 + 5Ce^{5t}\)

Combining the results from Step 1 and Step 2, we have:

\(x(t) = C - 9\)

\(y(t) = -5 + 5Ce^{5t}\)

Therefore, the general solution to the given system of differential equations is \((x(t), y(t)) = (C - 9, -5 + 5Ce^{5t})\), where C is an arbitrary constant.

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0.735

Answer: For every 60 light bulbs, 3 light bulbs are defective. Then, we can find out the probability of a light bulb being defective as 3/60 = 0.05.Now, we need to find the probability that more than 6 bulbs will need to be tested before finding the first defective bulb. Here, we can use the geometric distribution formula: P(X = k) = (1 - p)^(k - 1) * p where p is the probability of success, which is the probability that a light bulb is defective. So, p = 0.05Here, we need to find the probability of more than 6 trials. So, we need to find the probability that the first defective bulb is found at 7th trial or later. P(X > 6) = P(X = 7) + P(X = 8) + ...+ P(X = ∞)P(X > 6) = (1 - 0.05)^(7 - 1) * 0.05 + (1 - 0.05)^(8 - 1) * 0.05 + ...+ (1 - 0.05)^(∞ - 1) * 0.05Here, we can observe that this is a geometric series. So, we can find the sum of an infinite geometric series as follows: S = a/(1 - r), where S is the sum, a is the first term, and r is the common ratio. Now, we can apply this formula to find the sum of the geometric series of probabilities. S = (1 - 0.05)^(7 - 1) * 0.05/(1 - (1 - 0.05))S = 0.95^6 * 0.05/0.05S = 0.95^6Now, we can round off this value to 3 decimal places. P(X > 6) = 0.735Thus, the required probability is 0.735, rounded off to 3 decimal places.

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Answer:

144 days

Step-by-step explanation:

160 · 0.9

The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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We can say with 90% confidence that the true mean GPA of all accounting students at this university lies between 2.7107 and 3.0493.

We are given:

Sample size n = 21

Sample mean X = 2.88

Sample standard deviation s = 0.16

Confidence level = 90% or α = 0.10 (since α = 1 - confidence level)

Since the sample size is small and population standard deviation is unknown, we will use a t-distribution to construct the confidence interval.

The formula for the confidence interval is given by:

X ± t(α/2, n-1) * s/√n

where t(α/2, n-1) is the t-score with (n-1) degrees of freedom, corresponding to the upper α/2 percentage point of the t-distribution.

Using a t-table with (n-1) = 20 degrees of freedom and α/2 = 0.05, we find the t-score to be 1.725.

Plugging in the values, we get:

2.88 ± 1.725 * 0.16/√21

= (2.7107, 3.0493)

Therefore, we can say with 90% confidence that the true mean GPA of all accounting students at this university lies between 2.7107 and 3.0493.

Note: The confidence interval can also be written as [2.71, 3.05] rounding to two decimal places.

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Answer:

Step-by-step explanation:

Square

519450.2

Holes

Semi-circle: 1/2*pi*r^2

diameter = 700/2 = 350 =radius

1/2*pi*350 = 175*pi

Triangle

1/2 b*h

1/2 200*400

100*400

40000

Take out the semi circle and triangle

560000-40000-175*pi

520000-175*pi = 519450.2

Answer:

40%

Step-by-step explanation:

60/150 = 40% (0.4 * 100)

Step-by-step explanation:

area of rhombus =1/2(d1×d2)

=1/2(4.25×4.25)

=1/2×18.0625

=9.03cm^2

Answer:divideing by the whole number

Step-by-step explanation:

The scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

What is dilation?

A dilation is a transformation that creates an image that has the same shape as the original but is larger.

• An enlargement is a dilation that produces a larger image.

• A reduction is a dilation that produces a smaller image.

• A dilation expands or contracts the original figure.

A dilation is a stretch or a shrink in the size and location of a figure or point.

The scale factor in a dilation is the amount by which the figure is stretched or shrunk.

The center of dilation is a reference point used to appropriately scale the dilation of a figure. Given a point on the pre-image, \((x_1, y_1)\)and a corresponding point on the dilated image \((x_2, y_2)\)and the scale factor,

k, the location of the center of dilation, \((x_0,y_0)\) is

\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\)

Hence, the scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

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Answer:

x = 7,    x = -3

Step-by-step explanation:

(x - 2)^2 = 25

Take the square root of each side

sqrt((x - 2)^2) =±sqrt( 25)

x-2 = ±5

Add 2 to each side

x-2+2 = 2±5

x =  2±5

x = 2+5,  x=2-5

x = 7,    x = -3

This is a binomial experiment because it satisfies all the conditions for a binomial experiment. In this case, the experiment involves randomly selecting 15 adults and recording whether they are satisfied or not with the job the major airlines are doing.

The two mutually exclusive outcomes for each trial are either an adult is satisfied or not satisfied. The fixed number of trials is 15 since we are selecting 15 adults.

The outcome of one trial does not affect the outcome of another, as each adult is selected independently. Finally, the probability of success (being satisfied) remains constant for each trial, as the given information does not indicate any changes in the satisfaction rate. Therefore, this experiment meets all the criteria for a binomial experiment.

The given scenario satisfies the conditions for a binomial experiment because it involves randomly selecting 15 adults and recording their satisfaction with the major airlines.

The experiment meets the requirements of having two mutually exclusive outcomes, a fixed number of trials, independent trials, and a constant probability of success.

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Answer:

3.3

Step-by-step explanation:

Hour : H

subtract the 75 from both sidesso the variable would be on one side and the knowns would be on the other side

45H + 75 = 225

        -75      -75

Divide by 45 from both sides

45H = 150

÷45     ÷45

3.33

Answer: Slope: 3/2

Step-by-step explanation:

Coordinates: (1, -3), (3, 0)

Slope formula: m=(y2-y1)/(x2-x1)

m=(0-(-3))/(3-1)

m=(0+3)/2

m=3/2 ==> Slope: 3/2

The probability that he would have done at least this well if he had no ESP is 0.4335,

The probability of a man correctly predicting the outcome of a coin flip without having extrasensory perception (ESP) can be calculated by using probability theory.

In this case, we can calculate the probability of correctly predicting 16 or more coin flips out of 22, given that the man has no ESP. To do this, we first need to calculate the probability of correctly predicting each coin flip individually. Since each coin flip is an independent event, the probability of correctly predicting each coin flip is 0.5, or 50%.

Therefore, the probability of correctly predicting 16 or more coin flips out of 22 can be calculated as the sum of the probabilities of correctly predicting each coin flip, multiplied by the number of ways in which 16 or more coin flips can be correctly predicted. This can be expressed as

=> P(x ≥ 16) = 0.5²² x C(22, 16) + 0.5²² x C(22, 17) +…+ 0.5²² x C(22, 22),

where C is the combination operator.

Using this formula, the probability of correctly predicting 16 or more coin flips out of 22 without having ESP is 0.4335, meaning that it is highly unlikely that the man has ESP

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Answer:

1. To determine whether there is a significant difference between the population mean and the sample mean, we can use a one-sample t-test. The null hypothesis (H0) is that there is no significant difference between the population mean and sample mean, while the alternative hypothesis (Ha) is that there is a significant difference.

Using a significance level of 5%, and assuming the population standard deviation is unknown, we can calculate the t-statistic as:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

t = (24000 - μ) / (5000 / sqrt(25))

t = (24000 - μ) / 1000

At a significance level of 5% with 24 degrees of freedom (25-1), the critical t-value is ±2.064.

If the calculated t-value falls outside this range, then we reject the null hypothesis in favor of the alternative hypothesis.

Since the question does not provide a specific value for μ (population mean), we cannot complete the calculation to determine whether there is a significant difference between the population and sample mean.

2. To determine whether there is enough evidence that the average amount of active ingredient in the drug is greater than 12 mg, we can use a one-sample t-test. The null hypothesis (H0) is that the average amount of active ingredient is equal to 12 mg, while the alternative hypothesis (Ha) is that it is greater than 12 mg.

Using a confidence level of 99%, and assuming the population standard deviation is unknown, we can calculate the t-statistic as:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

t = (12.1 - 12) / (0.5 / sqrt(30))

t = 2.12

At a confidence level of 99% with 29 degrees of freedom (30-1), the critical t-value is 2.462.

Since the calculated t-value (2.12) is less than the critical t-value (2.462), we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the average amount of active ingredient in the drug is greater than 12 mg at a confidence level of 99%.

3. To test whether the transaction fee is higher than the remittance center's claim, we can use a one-sample t-test. The null hypothesis (H0) is that the mean transaction cost is equal to or lower than 3%, while the alternative hypothesis (Ha) is that it is higher than 3%.

Using a significance level of 10%, and assuming the population standard deviation is unknown, we can calculate the t-statistic as:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

t = (3.4 - 3) / (0.5 / sqrt(20))

t = 4.38

At a significance level of 10% with 19 degrees of freedom (20-1), the critical t-value is 1.734.

Since the calculated t-value (4.38) is greater than the critical t-value (1.734), we reject the null hypothesis and conclude that there is enough evidence to suggest that the transaction fee is higher than the remittance center's claim at a significance level of 10%.

4. To test whether the average hours spent on school work is less than 7 hours, we can use a one-sample t-test. The null hypothesis (H0) is that the mean number of hours spent on school work is equal to or greater than 7, while the alternative hypothesis (Ha) is that it is less than 7.

Using a confidence level of 95%, and assuming the population standard deviation is unknown, we can calculate the t-statistic as:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

t = (6.5 - 7) / (0.8 / sqrt(100))

t = -3.125

At a confidence level of 95% with 99 degrees of freedom (100-1), the critical t-value is -1.984.

Since the calculated t-value (-3.125) falls outside the range of the critical t-value (-1.984 to 1.984), we reject the null hypothesis and conclude that there is enough evidence to suggest that the average hours spent on school work is less than 7 hours at a confidence level of 95%.

The information in the venn diagram have the following solution:

a) A ∪ B = {8,14,17,16,9,15}

b) A ∩ B = {14,17}

c) probability that one of the numbers chosen at random is A' = 0.7

Venn diagrams are commonly used in mathematics, statistics, and logic to illustrate relationships between sets of data. It consists of circles that overlap to show the similarities and differences between the sets like in the case of students data.

From the venn diagram we have that:

A = {8,14,17}

B = {14,17,16,9,15

A' = {13,10,11,12,16,9,15}

U = {13,10,11,12,8,14,17,16,9,15}

so;

A ∪ B = {8,14,17,16,9,15}

A ∩ B = {14,17}

A' = 7

U = 10

probability that one of the numbers chosen at random is A' = 7/10 or 0.7

Therefore, the information from the venn diagram have the following solutions for:

a) A ∪ B = {8,14,17,16,9,15}

b) A ∩ B = {14,17}

c) probability that one of the numbers chosen at random is A' = 0.7

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

17 units

Step-by-step explanation:

Because the triangle is isosceles, 2 of its sides are congruent; namely, the two sides that are opposite of the 2 congruent angles are contruent.

Because of the reason stated above, we can see that AC is congruent to BC, meaning that:

x+9=2x-8

-x      -x

9=x-8

+8  +8

17  = x

Notice that BC is equal to x, so 17 is our final answer.

The remainder when the sum of all three-digit positive integers with three distinct digits is divided by 10001000 is 549,450

To find the sum of all three-digit positive integers with three distinct digits, we can use the concept of arithmetic progression.

An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. In this case, the difference between consecutive three-digit positive integers is 1.

To find the sum of an arithmetic progression, we can use the formula: Sum = (first term + last term) * number of terms / 2

In this case, the first term is 100, the last term is 999 (the largest three-digit positive integer with three distinct digits), and the number of terms is the count of numbers between 100 and 999 inclusive.

To find the count of numbers between 100 and 999 inclusive, we subtract the starting number from the ending number and add 1:

(999 - 100) + 1 = 900.

Substituting the values into the formula, we get:

Sum = (100 + 999) * 900 / 2 = 549,450

Now, to find the remainder when the sum is divided by 10001000, we can use the modulo operation.

Remainder = 549,450 % 10001000

= 549,450

Therefore, the remainder when the sum is divided by 10001000 is 549,450.

The remainder is 549,450.

To find the sum of all three-digit positive integers with three distinct digits, we can use the concept of arithmetic progression.

The first term is 100, the last term is 999, and the difference between consecutive terms is 1.

The formula for the sum of an arithmetic progression is

(first term + last term) * number of terms / 2.

In this case, the number of terms is the count of numbers between 100 and 999 inclusive, which is

(999 - 100) + 1 = 900.

Substituting the values into the formula, we get a sum of 549,450. To find the remainder when the sum is divided by 10001000, we can use the modulo operation.

The remainder is 549,450.

The remainder when the sum of all three-digit positive integers with three distinct digits is divided by 10001000 is 549,450.

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Answer:

3 x + 24

Step-by-step explanation:

Answer:

X=52

Step-by-step explanation:

3X+24=180

3X=180-24

3X=156

X=156/3

X=52

Answer:

cos37= 9.4/BC,cos37=0.8

BC= 9.4/0.8

bc = 11.75

Answer:

BC ≈ 32.2

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos73° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{AB}{BC}\) = \(\frac{9.4}{BC}\) ( multiply both sides by BC )

BC × cos73° = 9.4 ( divide both sides by cos73° )

BC = \(\frac{9.4}{cos73}\) ≈ 32.2 ( to 3 sf )

Answer:

15y - x

Step-by-step explanation:

(-4x + 6y) - (-3x - 9y) = -4x + 6y + 3x + 9y

combine like terms:

15y - x

The slope of the graph of the function y = 8 + csc(x) / (7 - csc(x)) at the point (π/7, 2) is -1.

To find the slope at a given point, we need to compute the derivative of the function and evaluate it at that point. The derivative of y = 8 + csc(x) / (7 - csc(x)) can be found using the quotient rule of differentiation. Applying the quotient rule, we get:

dy/dx = [(-csc(x)(csc(x) + 7csc(x)cot(x))) - (csc(x)cos(x)(7 - csc(x)))] / (7 - csc(x))^2

Simplifying this expression, we have:

dy/dx = [csc(x)(8csc(x)cot(x) - 7cos(x))] / (7 - csc(x))^2

Now, we can substitute the x-coordinate of the given point, π/7, into the derivative expression to find the slope at that point:

dy/dx = [csc(π/7)(8csc(π/7)cot(π/7) - 7cos(π/7))] / (7 - csc(π/7))^2

Calculating this value, we find that the slope at the point (π/7, 2) is approximately -1. This can be confirmed by using the derivative feature of a graphing utility, which will provide a visual representation of the slope at the specified point.

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The answer is that statement 2 is true about the series ∑n=1[infinity]12n+1. This is because the integral test says that if an improper integral converges, then the corresponding series also converges. In this case, the improper integral converges, so the series converges.

For statement 1, that the limit comparison test compares the given series to a known series with a known convergence behavior. In this case, the comparison series is ∑n=1[infinity]1/n, which diverges. Since the limit of the ratio of the two series is 12, the given series also diverges.

For statement 3, the explanation is that the integral in question is the same as the one mentioned in statement 2, which we know converges. Therefore, statement 3 is false.
For statement 4, the explanation is that the n-th term test looks at the limit of the terms in the series to determine convergence or divergence. In this case, the limit of the terms is 0, which is inconclusive. Therefore, statement 4 is false.For statement 5, the explanation is that the limit test looks at the limit of the terms in the series to determine convergence or divergence. In this case, the limit of the terms is 0, which does not provide enough information to determine convergence or divergence. Therefore, statement 5 is false. Overall, the long answer is that the series converges due to statement 2 being true, and the other statements are either false or inconclusive.

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