What’s the next 3 numbers after 1, -3, 9, -27

Answer:

16

Step-by-step explanation:

(1/4) ^-2

We know that a^-b = 1/a^b

(1/4) ^-2 = 1/(1/4) ^2 = 1/(1/16)

We know that 1/ (1/a) = a

1/ ( 1/16) = 16

Answer:

2/3xy.

Step-by-step explanation:

8x/12x^2y

The 8 and 12 simplify to 2/3 and x and x^2 simplify to 1/x so we have:

= 2/3xy.

Let's label the 8 questions as Q1, Q2, Q3, Q4, Q5, Q6, Q7, and Q8.

Let's label the 8 students as A, B, C, D, E, F, G, and H.

Since each problem has been correctly solved by exactly 5 students, we can say that the following is true:

Q1: A, B, C, D, E

Q2

Answer:

4) in question it should be triangleMNP and NOP

reason by SSS axiom

5) reason is as the angles of congurent triangles are equal)

Answer: 50 - 10m or 10(5 - m)

Step-by-step explanation:

Since Lily starts a savings account with $50 and each month, m, she withdraws $10 from her account, the expression that can be used to determine the amount left in her savings account after a certain number of months will be:

= 50 - 10(m)

= 50 - 10m

For example, the amount that'll be left in her account after two months will be:

= 50 - 10m

= 50 - 10(2)

= 50 - 20

= 30

She'll have $30 in her account after two months.

Based on the fact that Jessica and her best friend split the money and were able to get $16.32, the total amount that they found was $32.64

The fact that they split the money evenly means that they split it in half which each person getting the same amount.

This means that the total amount they found was twice the amount that Jessica and her best friend got.

The total amount found is therefore:

= Jessica's share + Best friend's share

= 16.32 + 16.32

= $32.64

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Answer:

X+22°=90°

X=90°-22°

X=68°

The formula to calculate the area of a circle is:

Where r is the raidus. Remember that the radius is one half of the diameter.

Thereby, the area of the bottom of the pool is:

Thereby, we can conclude that:

To calculate the wavelength λ1 for gamma rays of frequency f1 = 5.60×1021 hz, we can use the formula:
λ1 = c / f1, where c is the speed of light in a vacuum, which is approximately 3.00 × 108 m/s.
Plugging in the values, we get:
λ1 = (3.00 × 108 m/s) / (5.60×1021 hz) = 5.36 × 10^-14 m

Therefore, the wavelength λ1 for gamma rays of frequency f1 = 5.60×1021 hz is approximately 5.36 × 10^-14 meters.
To calculate the wavelength λ1 of gamma rays with frequency f1 = 5.60×10²¹ Hz, we can use the formula:

λ = c / f

Where λ is the wavelength, c is the speed of light (approximately 3.00×10^8 meters per second), and f is the frequency.

Step 1: Write down the given frequency:
f1 = 5.60×10²¹ Hz

Step 2: Write down the speed of light:
c = 3.00×10^8 m/s

Step 3: Use the formula to calculate the wavelength:
λ1 = c / f1
λ1 = (3.00×10^8 m/s) / (5.60×10²¹ Hz)

Step 4: Calculate λ1:
λ1 ≈ 5.36×10^-14 meters

So, the wavelength λ1 for gamma rays of frequency f1 = 5.60×10²¹ Hz is approximately 5.36×10^-14 meters.

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Answer:

6a

Step-by-step explanation:

There isnt a b in 18a and 18a isn't a factor of 24.

Get yourself some food, Yao Yao :)

1. The value of x should be such that the lengths of the hypotenuse and leg in triangle ABC are equal to the corresponding lengths in triangle A'B'C'.

2. We cannot determine if ΔFGH is congruent to ΔFJH without additional information about their sides or angles.

3. Translation, rotation, and reflection can be used to map triangle RST onto triangle VWX.

4. Translation, rotation, and reflection can be used to map triangle ABC onto triangle DEC.

5. Translation, rotation, reflection, and dilation can be used to map one triangle onto the other.

6. The value of x is irrelevant for the triangles to be congruent by SSS. As long as the lengths of the corresponding sides in both triangles are equal, they will be congruent.

1. For the triangles to be congruent by HL (Hypotenuse-Leg), the value of x must be such that the corresponding hypotenuse and leg lengths are equal in both triangles. The HL theorem states that if the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the two triangles are congruent. Therefore, the value of x should be such that the lengths of the hypotenuse and leg in triangle ABC are equal to the corresponding lengths in triangle A'B'C'.

2. To determine if triangles ΔFGH and ΔFJH are congruent, we need to compare their corresponding sides and angles. The HL theorem is specifically for right triangles, so we cannot apply it here since the triangles mentioned are not right triangles. We would need more information to determine if ΔFGH is congruent to ΔFJH, such as the lengths of their sides or the measures of their angles.

3. The transformations that can be used to map triangle RST onto triangle VWX are translation, rotation, and reflection. Translation involves moving the triangle without changing its shape or orientation. Rotation involves rotating the triangle around a point. Reflection involves flipping the triangle over a line. Any combination of these transformations can be used to map one triangle onto the other, depending on the specific instructions or requirements given.

4. The rigid transformations that can map triangle ABC onto triangle DEC are translation, rotation, and reflection. Translation involves moving the triangle without changing its shape or orientation. Rotation involves rotating the triangle around a point. Reflection involves flipping the triangle over a line. Any combination of these transformations can be used to map triangle ABC onto triangle DEC, depending on the specific instructions or requirements given.

5. The transformations that can be used to map one triangle onto the other are translation, rotation, reflection, and dilation. Translation involves moving the triangle without changing its shape or orientation. Rotation involves rotating the triangle around a point. Reflection involves flipping the triangle over a line. Dilation involves changing the size of the triangle. Any combination of these transformations can be used to map one triangle onto the other, depending on the specific instructions or requirements given.

6. For the triangles to be congruent by SSS (Side-Side-Side), the value of x is not specified in the question. The SSS congruence theorem states that if the lengths of the corresponding sides of two triangles are equal, then the triangles are congruent. Therefore, the value of x is irrelevant for the triangles to be congruent by SSS. As long as the lengths of the corresponding sides in both triangles are equal, they will be congruent.

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Answer:

-3(2t - 1) = t + t + t + 3

-6t + 3 = 3t + 3

-6t -3t = 3t - 3t +3

-9t + 3 - 3 = 0

9t = 0

t = 0

Step-by-step explanation:

The line joining the points (0, 2) and (-5,-4) divides the line segment joining the point (6, 3) and (-2, 1) in the ratio 2:1.

Let the point of intersection of the two lines be (x, y). Using point-slope form, the equation of the line joining the points (0, 2) and (-5,-4) is y-2 = -3/5(x-0), and the equation of the line segment joining the points (6, 3) and (-2, 1) is y-3 = -2/8(x-6).

Solving for x and y, we get x = 8/5 and y = 4/5.

So, the distance from (x, y) to (0, 2) is 2/5 and the distance from (x, y) to (6, 3) is 6/5.

Hence, the ratio of the distances is 2/5 : 6/5 = 2 : 1.

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Answer:

\( \frac{ {11}^{4} }{ {11}^{11} } < \frac{1}{ {11}^{ - 4} } < {11}^{5} . {11}^{2} < ( {11}^{ - 3} )^{ - 3} \)

Step-by-step explanation:

\(A) \frac{ {11}^{4} }{ {11}^{11} } = {11}^{4 - 11} = {11}^{ - 7} \\ \\ B)\frac{1}{ {11}^{ - 4} } = {11}^{4} \\ \\C) ( {11}^{ - 3} )^{ - 3} = {11}^{ - 3( - 3)} = {11}^{9} \\ \\ D){11}^{5} . {11}^{2} = {11}^{5 + 2} = {11}^{7} \\ \\ \because \: {11}^{ - 7} < {11}^{4} < {11}^{7} < {11}^{9} \\ \\ \therefore \: \frac{ {11}^{4} }{ {11}^{11} } < \frac{1}{ {11}^{ - 4} } < {11}^{5} . {11}^{2} < ( {11}^{ - 3} )^{ - 3} \)

Answer:

A.11^4/11^11

Step-by-step explanation:

The symbols p,x, and s represent sample statistics.

- p (pronounced "p-hat") is the sample proportion. It is used to estimate the population proportion. It is computed as the number of successes in the sample divided by the sample size.

-x (pronounced "x-bar") is the sample mean. It is used to estimate the population mean. It is computed as the sum of all the values in the sample divided by the sample size.

- s is the sample standard deviation. It is used to estimate the population standard deviation. It measures how spread out the data is in the sample. It is computed as the square root of the sum of the squared deviations from the sample mean divided by the sample size minus one.

These sample statistics are used to make inferences about the corresponding population parameters, which are denoted by Greek letters such as μ (mu) for the population mean and σ (sigma) for the population standard deviation.

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Answer:

The height of the balloon is 46 feet.

Step-by-step explanation:

Let the height from the ground to the top of the balloon be represented by x. Applying the appropriate trigonometric function, we have;

Looking at the top of the balloon,

Tan θ = \(\frac{opposite}{adjacent}\)

Tan 53° = \(\frac{x}{60}\)

x = 60 x Tan 53°

  = 79.6227

x = 79.62 feet

Looking at the bottom of the balloon, let the height from the ground to the bottom of the balloon be represented by y.

Tan θ = \(\frac{opposite}{adjacent}\)

Tan 29° = \(\frac{y}{60}\)

y = 60 x Tan 29°

  = 33.2585

y = 33.26 feet

The height of the balloon = x - y

                                           = 79.6227 - 33.2585

                                           = 46.3642

The height of the balloon is 46 feet.

Answer:

x² + 8

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 2x² + 1 - (x² - 7)

= 2x² + 1 - x² + 7 ← collect like terms

= x² + 8

The major assumption in factor analysis (but not PCA) is that the observed variables are caused by a smaller number of underlying, unobserved (latent) variables, which are called factors.

Factor analysis and principal component analysis (PCA) are both techniques used for data reduction and dimensionality reduction. However, they differ in their assumptions and goals.

In factor analysis, the focus is on identifying the underlying latent variables (called factors) that explain the observed correlations among a set of variables. The major assumption in factor analysis is that the observed variables are caused by a smaller number of underlying factors. These factors cannot be directly measured, but are inferred from patterns of correlations among the observed variables. The goal of factor analysis is to extract these factors and to estimate how much each factor contributes to each observed variable.

In contrast, PCA is a technique that focuses on finding a linear combination of the original variables that explain the maximum amount of variance in the data. The major assumption in PCA is that the observed variables are not caused by any underlying factors, but are simply linearly related to each other. The goal of PCA is to find a set of orthogonal (uncorrelated) principal components that capture the maximum amount of variance in the data.

Therefore, the major assumption in factor analysis (but not PCA) is that there are underlying latent variables (factors) that cause the observed correlations among the variables.

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Each element in the domain is mapped into only one element in the range, so this is a function, the correct option is D.

A relation maps inputs into outputs, such that the notation used is (input, output).

And a relation is a function only if each input is mapped into only one output.

Here we have the relation:

{(4, 7), (2, 8), (-2, 8), (0, 9)}

There we can see that no input is mapped into more than one output, so this is a function, the correct option is D.

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Answer:

the answer is

Answer:

the answer is c

Step-by-step explanation:

Carla will run on Sunday, November 12 and then run and swim on Thursday, November 16.

Carla runs every 3 days and swims every Thursday.

Carla ran and swam on Thursday 9 November.

The next time Carla will run will be 3 days later: Sunday, November 12.

The next Thursday after November 9 is November 16.

Therefore, Carla will run on Sunday, November 12 and then run and swim on Thursday, November 16.

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Answer:

60

Step-by-step explanation:

All angles = 180

All sides are equal

Therefore, 180/3 = angle degrees = 60

x is an opposite angle of bottom right angle therfore x = 60

Answer:

(a) x = 60°

(b) Angle x is alternate to the right base angle of the equilateral triangle.

Step-by-step explanation:

(a) The triangle in the figure above is an equilateral triangle in which all sides and angles are equal. The sum of angles in a triangle is 180°. Each angle in the equilateral triangle is 60° (180°/3 = 60°)

Therefore, angle x is 60°.

(b) Alternate angles are equal. Angle x and the right base angle of the equilateral triangle are alternate angles. Therefore, angle x is 60°.

The solution of x in the equation 3^(x -4) = 6 is x = 5.63

The equation is given as

3^(x -4) = 6

Apply the law of indices on the expression 3^(x -4) to rewrite it

So, we have

3^x/3^4 = 6

The above equation becomes

3^x = 6 * 3^4

Evaluate the product

So, we have

3^x = 486

Take the logarithm of bot sides

xlog(3) = log(486)

Divide both sides by log(3)

x = log(486)/log(3)

Evaluate

x = 5.63

Hence, the solution of x in the equation 3^(x -4) = 6 is x = 5.63

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Answer:

3/0

Step-by-step explanation:

to find the slope use rise over run or y-y/x-x, in this case, 2-(-1)/-6-(-6)the negative and the subtraction sign cancel out resulting in something like this: 2+1/-6+6 equaling 3/0

I hope this helps have a nice day

The solution for this equation system is x= 29, y=53, (29, 53).

\((1)y=3x-34\\ \\(2)y=2x-5\)

\((2x-5)=3x-34\\\\2x-5=3x-34\)

\(2x-5+5=3x-34+5\\ \\2x=3x-29\)

\(2x-3x=3x-29-3x\\ \\-1x=-29\\ \\-x=-29\)

\(-x(-1)=-29(-1)\\ \\x=29\)

To find a value of "y", use the calculated value of "x" (29), and substitute in any of the two equations to find the value of "y". For this solution, we're going to use equation 2.

\(y=2(29)-5\\ \\y=58-5\\ \\y=53\)

On step 6 we proved that the value of "x=29" returns a value of "53" when evaluating with equation 2. Now, if equation 1 returns the same "y" value when evaluating "x=29", then the calculated values of both "x" and "y" are correct. Let's verify!

\(y=3(29)-34\\ \\y=87-34\\ \\y=53\)

Both of the equations return the same value of "y" (53) when evaluated with "x=29". Therefore, the solution for this equation system is x= 29, y=53, (29, 53).

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Based on the cost-to-cost trade-off calculations, the company should choose the 83 mph speed, resulting in a total cost of $764.

To evaluate the cost-to-cost trade-offs, we need to consider the fuel cost and the cost of delay due to slower mph. The distance to be covered is 720 miles. At a speed of 90 mph, the fuel efficiency is 8 miles per gallon, and at 83 mph, it is 10 miles per gallon. The diesel fuel cost is $8.64 per gallon, and the cost of delay due to slower mph is $630.
To calculate the total cost for each speed, we divide the distance by the miles per gallon to determine the number of gallons needed. Then, we multiply the number of gallons by the fuel cost per gallon and add the cost of delay, if applicable.
For 90 mph: Total fuel cost = (720 miles / 8 miles per gallon) * $8.64 per gallon = $777.60.
For 83 mph: Total fuel cost = (720 miles / 10 miles per gallon) * $8.64 per gallon = $622.08.
Adding the cost of delay for 83 mph: Total cost = $622.08 + $630 = $1252.08.
Therefore, choosing the 83 mph speed results in a total cost of $764, which is lower than the total cost of $1252.08 for the 90 mph speed. Thus, the company should choose the 83 mph speed according to the cost-to-cost trade-off calculations.

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On the arranged survey, the statistical margin of error is supposed to be 14.73 SEK.

In a large consumer survey, 610 randomly selected customers are interviewed in a large grocery store. They are asked, among other things, how much they have shopped for. On average, they have shopped for 412 SEK with a standard deviation of 181 SEK .

Estimate with a 95% confidence interval the average purchase amount in the entire population. The formula for finding the margin of error is given as;

Margin of Error = z * (σ/√n)

Where:

σ is the standard deviation

n is the sample size

z is the Z-score for the desired confidence level, which is 95%.

Z-score corresponding to 95% confidence level is 1.96

Margin of Error = 1.96 * (181/√610) = 14.73

The statistical margin of error is 14.73 SEK.

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a. the amplitude of the function \(E = 4 \cos (140 \pi t)\) is 4, and the period is \(\frac{1}{70}\). b. the frequency of the function \(E = 4 \cos (140 \pi t)\) is 70. c. when \(t = 0.07\), \(E\) is equal to -4. d. The graph will display a periodic wave that oscillates between the values -4 and 4 over the given interval of \(t\), with a period of \(\frac{1}{70}\) seconds.

(a) To find the amplitude and period of the function \(E = 4 \cos (140 \pi t)\), we can compare it to the general form of a cosine function, \(y = A \cos (Bx + C)\).

In our given function, the coefficient in front of the cosine function is 4, so the amplitude \(A\) is 4 (the absolute value of 4).

The value inside the cosine function is \(140 \pi t\). To find the period, we can determine the value of \(B\) in the general form.

The period of a cosine function is calculated using the formula \(T = \frac{2\pi}{|B|}\). In our case, \(B = 140 \pi\), so the period \(T\) can be found as follows:

\[T = \frac{2\pi}{|140 \pi|} = \frac{1}{70}\]

Therefore, the amplitude of the function \(E = 4 \cos (140 \pi t)\) is 4, and the period is \(\frac{1}{70}\).

(b) The frequency (\(f\)) of a function is the reciprocal of the period. So, in our case, the frequency \(f\) is:

\[f = \frac{1}{T} = \frac{1}{\frac{1}{70}} = 70\]

Therefore, the frequency of the function \(E = 4 \cos (140 \pi t)\) is 70.

(c) To find \(E\) when \(t = 0.07\), we can substitute the given value into the function:

\[E = 4 \cos (140 \pi \times 0.07) = 4 \cos (9.8 \pi)\]

Using the properties of the cosine function, we know that \(\cos (9.8 \pi)\) evaluates to -1. Therefore, we have:

\[E = 4 \times (-1) = -4\]

So, when \(t = 0.07\), \(E\) is equal to -4.

(d) To graph \(E\) for \(0 \leq t \leq 35\), we can plot points on a coordinate system by substituting various values of \(t\) into the function \(E = 4 \cos (140 \pi t)\). However, since we are dealing with a continuous function, it would be more suitable to use a graphing software or calculator to plot the graph accurately.

The graph will display a periodic wave that oscillates between the values -4 and 4 over the given interval of \(t\), with a period of \(\frac{1}{70}\) seconds.

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The number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.

To calculate the number of kilowatt-hours (kW-hrs) consumed by the air conditioner in a week, we need to consider the power rating of the air conditioner (850 Watts) and the duration it is left on each day.

Power of the air conditioner = 850 Watts

Duration of usage per day = 24 hours (left on all day)

Number of days in a week = 7 days

To calculate the energy consumption, we can use the formula:

Energy (kW-hrs) = Power (kW) * Time (hours)

First, let's convert the power from Watts to kilowatts by dividing it by 1000:

Power (kW) = 850 Watts / 1000 = 0.85 kW

Now we can calculate the energy consumption in a week:

Energy (kW-hrs) = Power (kW) * Time (hours)

Energy (kW-hrs) = 0.85 kW * 24 hours/day * 7 days

Energy (kW-hrs) = 14.28 kW-hrs

Therefore, the number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.

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Given statement solution is :- We cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

The given sequence is: 5 2 1 4 0 0 7 2 8 1 m m 7 m 5 m A.

To find the missing value, let's analyze the pattern in the sequence. We can observe the following pattern:

The first number, 5, is the sum of the second and third numbers (2 + 1).

The fourth number, 4, is the sum of the fifth and sixth numbers (0 + 0).

The seventh number, 7, is the sum of the eighth and ninth numbers (2 + 8).

The tenth number, 1, is the sum of the eleventh and twelfth numbers (m + m).

The thirteenth number, 7, is the sum of the fourteenth and fifteenth numbers (m + 5).

The sixteenth number, m, is the sum of the seventeenth and eighteenth numbers (m + A).

Based on this pattern, we can deduce that the missing values are 5 and A.

Now, let's calculate the missing value:

m + A = 5

To find a specific value for m and A, we need more information or equations. Without any additional information, we cannot determine the exact values of m and A. Therefore, we cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

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