Quick algebra 1 assignment for 50 points!

Experts please help, Only answer if you know the answer! :)

There are infinitely many such choices of (m - n) linearly independent vectors, so there are infinitely many such matrices X.

Since the rank of the matrix A is n, there exist n linearly independent rows in A. Without loss of generality, we can assume that the first n rows of A are linearly independent.

Let B be the matrix consisting of the first n rows of A. Then, B is an n × m matrix of rank n. By the rank-nullity theorem, the null space of B is of dimension m - n.

We can choose any m - n linearly independent vectors in R^m that are orthogonal to the rows of B. Let these vectors be v_1, v_2, ..., v_{m-n}. Then, we can form an m × n matrix X as follows:

The first n columns of X are the columns of B^(-1), where B^(-1) is the inverse of B.

The remaining m - n columns of X are the vectors v_1, v_2, ..., v_{m-n}.

Then, we have:

AX = [B | V] X = [B^(-1)B | B^(-1)V] = [I | 0] = I_n,

where V is the matrix whose columns are the vectors v_1, v_2, ..., v_{m-n}. Therefore, X is an m × n matrix such that AX = I_n.

If n < m, then there are infinitely many such matrices X. To see this, note that we can choose any (m - n) linearly independent vectors in R^m that are orthogonal to the rows of B, and use them to form the last (m - n) columns of X. There are infinitely many such choices of (m - n) linearly independent vectors, so there are infinitely many such matrices X.

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The structure indicated by: 10a, 15t, 3g, 7c? is a structure related to the composition of a DNA or RNA sequence.

The given information "10a, 15t, 3g, 7c" suggests a pattern or structure related to the composition of a DNA or RNA sequence.

In molecular biology, DNA and RNA are made up of nucleotides, which consist of a nitrogenous base (adenine, thymine/uracil, guanine, or cytosine) and a sugar-phosphate backbone.

Based on the provided data, it appears that the numbers preceding each letter indicate the count or frequency of that particular nucleotide in the sequence.

Therefore, the structure indicated by "10a, 15t, 3g, 7c" implies the composition of a DNA or RNA sequence with the following nucleotide counts:

10 adenine (A) nucleotides (abbreviated as 10a)

15 thymine (T) nucleotides (abbreviated as 15t)

3 guanine (G) nucleotides (abbreviated as 3g)

7 cytosine (C) nucleotides (abbreviated as 7c)

Together, these nucleotides make up a portion of the DNA or RNA sequence, indicating the presence and quantity of each base in that particular section.

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Answer:

The numbers can be 2,4,6,8,0

Step-by-step explanation:

Apparently, using these numbers, the last 3 digits become divisible with 8. Therefore, 2,4,6,8,0 is the numbers that can fit in the hundredth's place.

Hoped this helped.

Therefore, The final answer is a sum of terms with increasing powers of 2x and decreasing powers of 2/3.

Using the binomial theorem, we can expand (2x - 2/3)^10 to get:
(2x)^10 - 10(2x)^9(2/3) + 45(2x)^8(2/3)^2 - 120(2x)^7(2/3)^3 + 210(2x)^6(2/3)^4 - 252(2x)^5(2/3)^5 + 210(2x)^4(2/3)^6 - 120(2x)^3(2/3)^7 + 45(2x)^2(2/3)^8 - 10(2x)(2/3)^9 + (2/3)^10

We use the formula for the binomial theorem, which states that (a + b)^n = ∑(k=0 to n) [n choose k] * a^(n-k) * b^k, where [n choose k] = n! / (k! * (n-k)!) is the binomial coefficient. In this case, a = 2x and b = -2/3, so we plug these values into the formula and simplify.
The binomial theorem is used to expand expressions of the form (a+b)^n. To expand (2x - 2/3)^10, we plug in a = 2x and b = -2/3, and apply the formula to get the expanded expression. This involves finding the coefficients of each term, which depend on the binomial coefficients.

Therefore, The final answer is a sum of terms with increasing powers of 2x and decreasing powers of 2/3.

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Answer:

the answer is -2

Step-by-step explanation:

3-(-1)

= -3--1

= -3+1

= -2

The value of SSE (sum squared error) is 40 in the given analysis of the variance problem if SST = 120 and SSR = 80. Option b is correct.

Here the words SSE means Sum Squared Error, SST means Sum of Squares Total and SSR means Sum of Square Regression.

In the SSE accuracy measure, errors are squared and then added. It is used when the data points are similar in magnitude.

The formula is SST = SSR + SSE ⇒ SSE = SST - SSR

The given values of the analysis of the variance problem are

SST = 120; SSR = 80

Then, the value of SSE = SST - SSR = 120 - 80 = 40

So, option b is correct.

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When using a significance level of 0.1, the probability of making a Type I error is closely associated with that level. In this case, the probability of committing a Type I error, which means incorrectly rejecting a true null hypothesis, is 10% or 0.1.

When conducting a hypothesis test, the significance level is the probability of rejecting the null hypothesis when it is actually true. In other words, it is the probability of making a type I error.

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Answer:

D. 6x+18

Step-by-step explanation:

Answer:

a) x = 70

Step-by-step explanation:

70 (2) +20 +20

140 + 40

180

Answer:

flkajd;lfaj;sldjk;fasjkd ;flaksjd fklsdj ;faklsjd falkd fasdfaks;ldfja;lsdkf

Step-by-step explanation:

༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ༼ つ ◕_◕ ༽つ

The equation representing the minimum and maximum number of fishes which would fit into the tank is : 5 ≤ x ≤ 9

From the table given ;

To represent the maximum and minimum number of fish that will fit into the tank;

We could use an inequality expression to represent these range :

Let x represent the Number of fishes that would fit into the tank :

Therefore, the equation can be written thus :

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Answer:

Step-by-step explanation:

As all edges of a cube are expanding at a rate of 2 centimeters per second.

i.e ds/dt = 2 cm/s

The formula of volume of cube: V = s³

Differentiating the volume:

dv/dt = 3s²

Write ds/dt following derivative of volume

dv/dt = 3s² ds/dt

plug in the value: ds/dt = 2 cm/s

dv/dt = (3s²) (2)

dv/dt = 6s²

Given the edge is 2cm.

so plug in the value: s=2

dv/dt = 6s²

          = 6(2)²=6(4)=24 cm³/per second

SIMILARLY,

When the edge is 14cm

dv/dt = 6s²

plug in the value: s=14

dv/dt = 6s²

         = 6(14)²=6(196)=1176 cm³/per second

Thus,

The volume will be:

(a) 24 cm³

(b) 1176 cm³

Given:

Expanding rate,

Let,

(a)

When,

then,

→ \(\frac{dx}{dt} = 2 \ cm/sec\)

Let,

→ \(V = x^3\)

→ \(\frac{dV}{dt} = 3x^2 \frac{dx}{dt}\)

        \(= 3\times 2^2\times 2\)

        \(= 3\times 4\times 2\)

        \(= 24 \ cm^3\)

(b)

When,

then,

→ \(\frac{dx}{dt} = 2 \ cm/sec\)

Let,

→ \(V = x^3\)

→ \(\frac{dV}{dt} = 3x^2 \frac{dx}{dt}\)

        \(=3\times 14^2\times 2\)

        \(= 1176 \ cm^3\)

Thus the above answer is correct.

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Answer:

y = 6

Step-by-step explanation:

4y + 2x = 8 → (1)

5y + 2x = 14 → (2)

subtracting (1) from (2) term by term will eliminate x

y + 0 = 6

y = 6

Answer:

the first one, no

the second one, yes I think?(its def not no)

the third one, yes

Step-by-step explanation:

The exact answers in simplified radical form is,

x = \(3+2\sqrt{2}\)       or      x = \(3-2\sqrt{2}\) by using quadratic formula.

Based on the given conditions,

x^2-6x+1=0

Identify the coefficients,

a = 1 , b = -6 , c = 1

The quadratic equations is,

x = [-b ± \(\sqrt{b^{2} -4ac}\) ]/2a        (Equatoion-1)

We can substitute a, b, c values in equation-1,

So,

We can write,

x = [ -(-6) ± \(\sqrt{(-6)^{2}-4*1*1 }\) ]/2*1

x = [ 6 + \(\sqrt{(-6)^{2}-4 }\) ]/2      or

x = [ 6 - \(\sqrt{(-6)^{2}-4 }\) ]/2  

Determine the sign for exponential or radical expressions ,

x = [ 6 + \(\sqrt{6^{2} -4}\) ]/2

Calculate the power,

x = [ 6 + \(\sqrt{36-4}\) ]/2

Calculate the sum or difference,

x = [ 6 + \(\sqrt{32\) ]/2

Factor and rewrite the radicand in exponential form,

x = [ 6 + \(\sqrt{4^{2} *2}\) ]/2

Rewrite the expression using ,

\(\sqrt[n]{ab} =\sqrt[n]{a} *\sqrt[n]{b}\)

x = [ 6 + \(\sqrt{4^{2} } *\sqrt{2}\) ]/2

Simplify the radical expression,

x = \(\frac{6+4\sqrt{2} }{2}\)

Factor the expression,

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

Reduce the fraction,

x = \(3+2\sqrt{2}\)

Determine the sign for exponential or radical expressions,

x = [ 6 - \(\sqrt{6^{2} -4}\) ]/2

Calculate the power,

x = [ 6 - \(\sqrt{36-4}\) ]/2

Calculate the sum or difference,

x = [ 6 - \(\sqrt{32\) ]/2

Factor and rewrite the radicand in exponential form,

x = [ 6 - \(\sqrt{4^{2} *2}\) ]/2

Rewrite the expression using ,

\(\sqrt[n]{ab} =\sqrt[n]{a} *\sqrt[n]{b}\)

x = [ 6 - \(\sqrt{4^{2} } *\sqrt{2}\) ]/2

Simplify the radical expression,

x = \(\frac{6-4\sqrt{2} }{2}\)

Factor the expression,

x = \(\frac{2*(3-2\sqrt{2}) }{2}\)

Reduce the fraction,

x = \(3-2\sqrt{2}\)

Combine the results,

x = \(3+2\sqrt{2}\)       or      x = \(3-2\sqrt{2}\)

Therefore,

The exact answers in simplified radical form is,

x = \(3+2\sqrt{2}\)       or      x = \(3-2\sqrt{2}\) by using quadratic formula.

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Answer:

Step-by-step explanation:

cosx=(adjacent side)/(hypotenuse)

cosB=3/5

Answer:

16÷3×4

Step-by-step explanation:

Answer:

πd = 56, so d = 56/π

P = 28 + 3(56/π) = 28 + 168/π = 81.5 cm

The perimeter of the shape is approximately 81.46 cm. In other words, the required perimeter of composite shapes  is 81.46 cm.

To find the perimeter of the shape, we need to determine the lengths of the straight sides and the curved portion of the semicircle.

The semicircle has an arc length of 28 cm. Since the arc length is half the circumference of the full circle, we can find the circumference of the full circle by doubling the arc length: 28 cm × 2 = 56 cm.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. Since we have the circumference, we can rearrange the formula to solve for the radius:

r = C / (2π)

r = 56 cm / (2π)

r ≈ 8.91 cm (rounded to 2 decimal places).

The straight sides of the square have the same length as the diameter of the semicircle, which is twice the radius. Therefore, the length of each side of the square is 2 × 8.91 cm = 17.82 cm.

The perimeter of the shape is the sum of the lengths of all sides, which is the sum of the two straight sides and the curved portion of the semicircle.

Perimeter = Perimeter = 3 × (length of straight side) + length of arc

= 3 × 17.82 cm + 28 cm

= 53.46 cm + 28 cm

= 81.46 cm

Therefore, the perimeter of the shape is approximately 81.46 cm. In other words, the required perimeter of composite shapes  is 81.46 cm.

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The forecast for the next period using the following weights: 0.3, 2, 0.5 is Option d. 421.

To compute the forecast for the next period, we'll use the weighted moving average (WMA) formula.WMA formula:

WMA = W1Yt-1 + W2Yt-2 + ... + WnYt-n

Where, WMA is the weighted moving average

W1, W2, ..., Wn are the weights (must sum to 1)

Yt-n is the demand in the n-th period before the current period

As we know Month 1 – 381, Month 2-366, and Month 3 - 348.

Weights: 0.3, 2, 0.5

We'll compute the forecast for the next period (month 4) using the data:

WMA = W1Yt-1 + W2Yt-2 + W3Yt-3WMA

= 0.3(381) + 2(366) + 0.5(348)WMA

= 114.3 + 732 + 174WMA

= 1020.3

Therefore, the forecast for the next period is 1020.3, which rounds to 421. Hence, option d is correct.

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To find the p-value for the test examining the positive linear relationship between speed and jump height, you need to calculate the Pearson correlation coefficient, determine the degrees of freedom, and then find the corresponding p-value.

To determine the p-value for this test, we would need to conduct a hypothesis test using a linear regression model. The null hypothesis would be that there is no linear relationship between speed and jump height, while the alternative hypothesis would be that there is a positive linear relationship between the two variables.

After running the regression model and performing the hypothesis test, we would look for the p-value associated with the slope coefficient for speed. If this p-value is less than the chosen significance level (usually 0.05), we can conclude that there is convincing evidence of a positive linear relationship between speed and jump height for students like these.

Without actually running the regression model and hypothesis test, it is not possible to provide an exact p-value for this scenario.

To determine if there is convincing evidence of a positive linear relationship between speed (mph) and jump height (in) for students like these, you need to conduct a correlation test, specifically a Pearson correlation test. The p-value will help you determine the significance of the relationship.

Step-by-step explanation:

1. Gather the data: Obtain the values for speed (mph) and jump height (in) for each student.

2. Calculate the Pearson correlation coefficient (r): This value will help you measure the strength and direction of the linear relationship between the two variables. You can use statistical software or a calculator for this.

3. Determine the degrees of freedom (df): Calculate this by subtracting 2 from the total number of data points (n). Formula: df = n - 2.

4. Calculate the p-value: Using the Pearson correlation coefficient (r) and the degrees of freedom (df), you can find the p-value in a t-distribution table or by using statistical software.

5. Interpret the p-value: If the p-value is less than your chosen significance level (commonly 0.05), there is convincing evidence of a positive linear relationship between speed and jump height. If the p-value is greater than 0.05, there is not enough evidence to suggest a significant positive linear relationship.

In summary, to find the p-value for the test examining the positive linear relationship between speed and jump height, you need to calculate the Pearson correlation coefficient, determine the degrees of freedom, and then find the corresponding p-value. Comparing this p-value to your chosen significance level will help you conclude if there is convincing evidence of a positive linear relationship between the two variables.

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The surface area, A, is changing at a rate of 288 km/min decreasing.

Given,

Base length, l = 6 km

Height, h = 10 km

dl/dt = -9 km/min

dh/dt = 12 km/min

Surface area of a prism, A = 2 × (lw + lh + wh)

For a square prism,

Length, l = width, w = 6km

A = 2 × (l² + lh + lh)

= 2(l²) + 4lh

A = 2(l²) + 4 lh

= 2 × (l² + 2lh)

dA/dt = 2 × (2I × dI/dt + 0 × dh/dt + 2 × 2h × dl/dt + 2l × dh/dt)

dA/dt = 2 × (2l × dl/dt + 0 + 2 × 2h × dl/dt + 2l × dh/dt)

= 2 × (2(6) × (-9) + 2(10) × (-9) + 2(6) × (12))

= 2 × (- 108 + -180 + 144)

= 2 × -144

= -288 km/min

The rate of change of the surface area, A is decreasing by 288 km/min.

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Question is incomplete. Completed question is given below;

The length s(t)s(t)s, (, t, )of the side of the base of a square prism is decreasing at a rate of 9 kilometers per minute and the height h(t)h(t)h, (, t, )of the prism is increasing at a rate of 12 kilometers per minute. At a certain instant t_0t 0 ​ t, start subscript, 0, end subscript, the base's side is 6 kilometers and the height is 10 kilometers. What is the rate of change of the surface area A(t)A(t)A, (, t, )of the prism at that instant?

Answer:

145.62

Step-by-step explanation:

sin 18° = 45/z

z sin 18° = 45

z = 45/sin 18°

z = 145.62

Answer:

1/6

Step-by-step explanation:

Since we don't care what appears on the first roll

P( outcome) = 1

Second roll

P(1 or 2) = number of 1 or 2 / total number of outcomes

              =2/6 = 1/2

Third roll

odd numbers 1,3,5

P( odd number)= number of odd numbers/ total

                          =3/6 =1/2

P( outcome, 1or 2, odd)  = P( outcome) *P(1 or 2) *P( odd number)

                                       = 1* 1/3 * 1/2

                                       = 1/6

Answer:

Approximately 0.0364

Idk if this is right... :(

Step-by-step explanation:

4 dice with 12 sides

7 dice without 121 sides.

There is a \(\frac{4}{11}\) chance that the first dice has 12 sides.

There is a \(\frac{3}{10}\) chance that the second dice has 12 sides.

There is a \(\frac{7}{9}\) chance that the third dice doesn't have 12 sides.

There is a \(\frac{3}{4}\) chance that the fourth dice doesn't have 12 sides.

Multiply them up:

\(\frac{4}{11}*\frac{3}{10}*\frac{7}{9}*\frac{3}{4}=\frac{252}{3960}=0.0363636363636...\)

So approximately 0.0364

To find the five-number summary of the given data, we have to arrange the data in order:5, 11, 12, 17, 17, 21, 22, 28, 32, 35, 38, 42

Minimum value = 5

Q1 = 16 (Average of 5 and 12),(Q2) = 21 (Average of 17 and 22),Q3 = 35 (Average of 32 and 38)

Maximum value = 42

The five-point summary of the thefts per 1000 individuals for Worcester county during the evening hours from 6 pm to 2 am is as follows:

Minimum value = 8

Q1 = 10,Q2 = 12,Q3 = 17

Maximum value = 41

The box plot of the evening hours data is as follows:

Comparing the box plots of the two data sets, we can see that the evening hours data is skewed towards the right, which implies that the data is more spread out towards the higher values. While the daytime data is somewhat normally distributed with no outliers.

The median of the daytime data is 21, and the median of the evening hours data is 12. The maximum value of the daytime data is 42, and the maximum value of the evening hours data is 41.

Hence, we can conclude that the number of thefts is more in the day time than the evening hours in Worcester County.

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The missing coordinates for K, L, and M are (10, 25), (5, 20), and (30, 25), respectively.

THE LINE is a cultural resolution that main people and offers urban dwellers a unique experience while protected the natural environment. It defines the idea of  development and the design of future cities.

A coordinate system in geometry is the method for determining the location of points or other geometric objects on a manifold, In  Euclidean space, uniquely using one or more numbers or coordinates.

To find the missing coordinates for K, L, and M, we need to know the direction in which the line is going. If we assume that the line is going from left to right, then we can use the coordinates of K, L, and M to determine the missing values.

For K (10, ||), we know that the x-coordinate is 10, but we don't know the y-coordinate. Since K is between L and M, we can assume that its y-coordinate is somewhere between 20 and 30. If we take the average of 20 and 30, we get 25. Therefore, the missing coordinate for K is (10, 25).

For L (||, 20), we know that the y-coordinate is 20, but we don't know the x-coordinate. Since L is to the left of K, we can assume that its x-coordinate is somewhere between 0 and 10. If we take the average of 0 and 10, we get 5. Therefore, the missing coordinate for L is (5, 20).

For M (30, ||), we know that the x-coordinate is 30, but we don't know the y-coordinate. Since M is to the right of L, we can assume that its y-coordinate is somewhere between 20 and 30. If we take the average of 20 and 30, we get 25. Therefore, the missing coordinate for M is (30, 25).

Therefore, the missing coordinates for K, L, and M are (10, 25), (5, 20), and (30, 25), respectively.

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Answer:

ready-steady paint

Step-by-step explanation:

if he needs 12 tins, and purchased from paint -O  mine, he would spend (12/3) X 7.50 = 4 x 7.50 = £30

from ready steady, he can buy 4 for £11. he needs 12.

so he will spend (12/4) X 11 = 3 X 11 = £33. but he can get 15% off. 15% off is the same as multiplying by 0.85.

33 X 0.85 = £28.05.

so he his better purchasing from ready steady paint

Angle 4 and 7= Interior angles

Angle 12 and 16= Corresponding angles

Angle 1 and 14= Alternate exterior angles

Angle 5 and 10=Alternate angles

angle 6 and 7 are alternate angles I think.

Answer:

30

Step-by-step explanation:

So we know that there are 292 people and 9.9% attended one play so you just find 10% of 300(approximated) which is the same thing as 30.

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  9 cups

Step-by-step explanation:

If x represents the number of cups of dark chocolate needed for 60 candies, the proportion can be ...

  cups/candies = 3/20 = x/60

Multiplying by 60 gives ...

  x = 60(3/20) = 9

You need 9 cups of chocolate for 60 candies.