125.315 to two significant figures

The measure of <1 is 147 degree.

Given:

m∠2 = 12x - 15

m∠7 = 3x + 21

Since angles 2 and 7 are alternate Exterior angles, they are congruent.

So, 12x - 15 = 3x + 21

12x - 3x = 21 + 15

9x = 36

x = 4

So, <2 = 12x - 15= 48 - 15 = 33

Now, <1 + <2 = 180 (Linear Pair)

<1 + 33 = 180

<1 = 147 degree

Thus, the measure of <1 is 147 degree.

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Answer:

7x + y + 26

Step-by-step explanation:

5x+ 1 2 +3y+ 1 4 +2x−2y

5x + 2x + 3y - 2y + 12 + 14

7x + y + 26

Answer:

the slope, m, is 4 and that the y-intercept, b, is -8

Step-by-step explanation:

Compare the given equation to the slope-intercept form y = mx + b.  Here we see that the slope, m, is 4 and that the y-intercept, b, is -8.

Answer:

D i think

Step-by-step explanation:

The projection matrices for matrix A are P1 = [25, -5; -5, 1] and P2 = [1, 1; 1, 1]. The matrix exponential is\(e^{At\) = P1 * \(e^{(2t)\) + P2 * \(e^{(14t)\), and particular solution  x' = AX + f(t), x(a) = xa is X(t) =\(e^{At\) * x(a) + ∫[a to t] (\(e^{A(t-s)\)* f(s)) ds.

To find the projection matrix for matrix A, we need to calculate its eigenvalues and eigenvectors. Solving the characteristic equation, we find that the eigenvalues are 2 and 14. The corresponding eigenvectors are [1, 1] and [-1, 1]. Using these eigenvectors, we can construct the projection matrices P1 and P2 as P1 = [5, -1; -1, 1] and P2 = [1, 1; 1, 1].

Next, to find the matrix exponential e^At, we need to compute the exponential of each eigenvalue multiplied by the time variable t. We have \(e^{(2t)\) and \(e^{(14t)\). Multiplying these exponential terms by their respective projection matrices, we get P1 * \(e^{(2t)\) and P2 * e^(14t).

Finally, to find the particular solution X(t) to the initial value problem, we use the formula X(t) = \(e^{At\) * x(a) + ∫[a to t] (\(e^{A(t-s)\) * f(s)) ds. Here, x(a) represents the initial condition. By substituting the calculated values, we obtain the particular solution X(t) in terms of the exponential terms and the integral.

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The complete question is:

Use projection matrices to find the matrix exponential and particular solution of the given linear system x' = AX + f(t), x(a) = xa. 4 - 16 1612 x' = x, f(t) = X(0) = Do 1 - 4 4t 0 Find the projection matrix(matrices) for A. 1 0 The projection matrix(matrices) is/are 0 1 (Type exact answers, using radicals and i as needed. Use a comma to separate matrices as needed.) Find the matrix exponential. e At 1 +41 - 160 t 1-4 Find the particular solution to the initial value problem. X(t) =

Answer:

The rate of change of the weight of kitten A is greater than the rate of change of the weight of kitten B

Step-by-step explanation:

∵ The table shows the weight gain of kitten A

→ Choose two points from the table to find the slope

∵ Points (0, 3) and (1, 7) are two points in the table

∴ x1 = 0 and y1 = 3

∴ x2 = 1 and y2 = 7

→ Substitute them in the rule of the slope above

∵ m = \(\frac{7-3}{1-0}\) = \(\frac{4}{1}\) = 4

∵ The slope is the rate of change

∴ The rate of change of the weight of kitten A is 4 oz/week

∵ The graph shows the weight gain of kitten B

→ Choose two points on the line to find the slope

∵ Points (0, 4) and (2, 10) lies on the line

∴ x1 = 0 and y1 = 4

∴ x2 = 2 and y2 = 10

→ Substitute them in the rule of the slope above

∵ m = \(\frac{10-4}{2-0}\) = \(\frac{6}{2}\) = 3

∵ The slope is the rate of change

∴ The rate of change of the weight of kitten B is 3 oz/week

→ By comparing the two rates

∵ The rate of change of kitten A is 4 oz per week

∵ The rate of change of kitten B is 3 oz per week

∴ The rate of change of the weight of kitten A is greater than

   the rate of change of the weight of kitten B

It will take 40 days for 5 workers to construct the same house that 8 workers built in 25 days

The time required to build a house varies inversely as the number of people.

Which means if the number of workers is decreased by a component of k, the time required to construct the house might be improved by using a component of k.

let's use the formulation for inverse variation:

t = k/w

in which t is the time required to construct the house, w is the variety of workers, and okay is a consistent of proportionality.

we can use the given information to discover the value of k:

25 = k/8

k = 200

Now we are able to use the value of k to discover the time required to construct the house with 5 workers:

t = 200/5

t = 40

Therefore, it'd take 40 days for 5 workers to construct the same house that 8 workers built in 25 days

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The area of the 125 degree sector for a circle with a radius of 12 m is approximately 158 square meters.

To find the area of a 125 degree sector of a circle with a radius of 12 m, we need to use the formula for the area of a sector:

Area of sector = (θ/360) x πr², where θ is the central angle of the sector, r is the radius of the circle, and π is a constant equal to approximately 3.14.

Substituting the given values, we get: Area of sector = (125/360) x π x 12² = (0.3472) x π x 144 = 158.03

Rounding to the nearest whole number, we get the area of the sector as 158 square meters. Therefore, the area of the 125 degree sector for a circle with a radius of 12 m is approximately 158 square meters.

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Justice is using a technique known as chunking.

Short-term memory can function more effectively thanks to chunking, however the quantity of chunks that can be stored efficiently declines as chunk size grows.

Large pieces of information may be divided into smaller bits and then grouped together using relevant information or attributes before being stored in order to improve retention of that information in the short term memory. To establish relational information or similarity between the information to be stored in order to improve retention and recall in the short term memory, information must be broken down before being regrouped. However, as chunk size grows, so does the efficiency of information chunking.

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Answer:

D. x > -3 and x < 1

Step-by-step explanation:

There is an absolute value in this inequality, so we have to solve for 2 instances -- where the quantity in the absolute value is positive, and where it is negative.

First, we will isolate the absolute value by dividing by 3:

3|x + 1| < 6

|x + 1| < 2

Then, because this is a less-than case of the absolute value, we can put it in between the positive and negative absolute values of the other side:

-|2| < x + 1 < |2|

-2 < x + 1 < 2

and solve.

-3 < x < 1

(this can also be written as x > -3 and x < 1)

Answer:

See below

Step-by-step explanation:

a) The solution for b in the equation 2b × 3 = 6 is b = 1.

b) The solution for b in the equation 32 - 3b = 2 is b = 10.

c) The solution for b in the equation 6 + 7b = 41 is b = 5.

d) The solution for b in the equation 100/5b = 2 is b = 10.

a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.

2b × 3 = 6

(2b × 3) / 2 = 6 / 2

3b = 3

b = 3/3

b = 1

Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.

c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.

6 + 7b - 6 = 41 - 6

7b = 35

b = 35/7

b = 5

Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.

b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.

32 - 3b - 32 = 2 - 32

-3b = -30

b = (-30)/(-3)

b = 10

Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.

d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.

(100/5b) × 5b = 2 × 5b

100 = 10b

b = 100/10

b = 10.

Therefore, the solution for b in the equation 100/5b = 2 is b = 10.

In summary, the solutions for b in the given equations are:

a) b = 1

c) b = 5

b) b = 10

d) b = 10

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Answer:

2.5 hours

Step-by-step explanation:

The total amount of time studying by students who spent 1/2 an hour studying is the product of the number of students who spent 1/2 an hour studying by 1/2 an hour.

Hence, counting the number of dots on the point marked 1/2 gives the count of students who spent 1/2 an hour studying and multiply this number by 1/2.

Total amount of hours spent = 1/2 * 5 = 2.5 hours

In summary, when the two new children (ages four and twelve) are added to the existing group, the mean age increases from 8 to 8, and the standard deviation changes from its original value to approximately 3.74.

To determine the effect of adding two children (ages four and twelve) to the existing group of five children (ages five, six, eight, nine, and twelve) on the mean and standard deviation of ages, we need to calculate the new values.

Let's calculate the mean first:

Calculate the sum of the ages of the initial five children:

5 + 6 + 8 + 9 + 12 = 40

Add the ages of the two new children:

40 + 4 + 12 = 56

Calculate the new mean by dividing the sum by the total number of children (5 initial + 2 new):

56 / 7 = 8

Therefore, the new mean age is 8.

Now let's calculate the standard deviation:

Calculate the squared difference between each age and the mean for the initial five children:

\((5 - 8)^2 + (6 - 8)^2 + (8 - 8)^2 + (9 - 8)^2 + (12 - 8)^2 = 54\)

Calculate the squared difference between each new age and the new mean:

\((4 - 8)^2 + (12 - 8)^2 = 80\)

Calculate the sum of the squared differences for the initial five children and the new children:

54 + 80 = 134

Divide the sum of squared differences by the total number of children (5 initial + 2 new) and take the square root:

√(134 / 7) ≈ 3.74

Therefore, the new standard deviation is approximately 3.74.

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Answer:

3 Months.

Step-by-step explanation:

1 Month: J = $160 P = $200

2 Months: J = $200 P = $220

3 Months: J = $240 P = $240

Answer:

x=3 y=1

x=4 y=2

x=5 y=3

x=6 y=4

Step-by-step explanation:

add y to both sides to get:

2x-4=y

pull out the 2 from 2x-4 to get:

2(x-2)-y = 0

We need to know that x-2 cannot equal 0 or else the solution will be negative. So we need to make x-2 equal to any other number that is not negative and make y the inverse of x-2 so they cancel out and be zero. so some solutions are:

x=3 y=1

x=4 y=2

x=5 y=3

x=6 y=4

Answer:

14

Step-by-step explanation:

Area is base times height, so to find the height, divide the area by the base. 168/12=14

Answer:18.75

Step-by-step explanation:

When throwing a pair of dice, there are a total of 6 sides on each die, which gives us 6 x 6 = 36 possible outcomes. The total number of spots (the sum of the numbers on the dice) can range from 2 to 12.

When a pair of dice are thrown, there are three possible outcomes for the total number of spots: 1) The sum of the spots on both dice is less than 7. This occurs when the first dice lands on a number between 1 and 6, and the second dice lands on a number that will make the total less than 7 (e.g. if the first dice lands on 3, then the second dice must land on a number less than or equal to 3).  2) The sum of the spots on both dice is exactly 7. This occurs when the first dice lands on a number between 1 and 6, and the second dice lands on the number that will make the total equal to 7 (e.g. if the first dice lands on 2, then the second dice must land on 5).  3) The sum of the spots on both dice is greater than 7. This occurs when the first dice lands on a number between 1 and 6, and the second dice lands on a number that will make the total greater than 7 (e.g. if the first dice lands on 4, then the second dice must land on a number greater than 3).

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Answer:

5(2z +9)

Step-by-step explanation:

factor out 5 of 10z +45

A)  ln(8): x = ln(2) / ln(8)

B)  x = ln(1/4).

C) There is no solution for this equation.

A) The equation 8^x = 2 can be solved using the natural logarithm. Taking the natural logarithm (ln) of both sides, we have ln(8^x) = ln(2). Applying the logarithm property, which states that ln(a^b) = b * ln(a), we can rewrite the equation as x * ln(8) = ln(2). Finally, we solve for x by dividing both sides by ln(8): x = ln(2) / ln(8). The exact value of x can be obtained by evaluating the logarithms.

B) Similarly, the equation 8e^x = 2 can be solved using the natural logarithm. Dividing both sides by 8, we get e^x = 2/8 = 1/4. Taking the natural logarithm of both sides, ln(e^x) = ln(1/4), which simplifies to x = ln(1/4). Again, we can evaluate the natural logarithm to obtain the exact value of x.

C) The equation 2 * 2^x = 2e^(5x) can be solved using the natural logarithm as well. Dividing both sides by 2, we have 2^x = e^(5x). Taking the natural logarithm of both sides, ln(2^x) = ln(e^(5x)). Using the logarithm property, we rewrite the equation as x * ln(2) = 5x * ln(e). Since ln(e) is equal to 1, the equation simplifies to x * ln(2) = 5x. Dividing both sides by x (assuming x ≠ 0), we get ln(2) = 5. However, this leads to a contradiction since ln(2) is not equal to 5. Therefore, there is no solution for this equation.

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The estimation of 0.000007328 is \(7\times10^{-6\).

Estimation is he ability to guess the amount of anything without actual measurement.

The number (n) is given as:

\(\text{n}=0.000007328\)

Multiply by 1

\(\text{n}=0.000007328\times1\)

The number is to be rounded to the nearest millionth.

So, we substitute \(\frac{1000000}{1000000}\) for 1

\(\text{n}=0.000007328\times1\)

\(\text{n}=0.000007328\times\dfrac{1000000}{1000000}\)

This becomes

\(\text{n}=7.328\times\dfrac{1}{1000000}\)

Express the fraction as a power of 10

\(\text{n}=7.328\times10^{-6\)

Approximate to a single digit

\(\rightarrow\bold{n=7\times10^{-6}}\)

Therefore, the estimation of 0.000007328 is \(7\times10^{-6}\).

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Answer:

Anything in the bottom center portion, under both diagonal lines, works. An example is (-2, 0)

Step-by-step explanation:

Answer:

(-3,9)

Step-by-step explanation:

The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

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According to the information, it can be inferred that on Thursday the farmers picked 8 1/2 barrels of tomatoes, or 4 barrels of tomatoes.

To find the number of tomatoes that the farmers picked on Wednesday we must look at the reference number that they picked on Wednesday. In this case it would be 8 barrels.

Additionally, if on Thursday they collected half, we can express this number with a fraction:

8 1/2 Due to the fact that half of each of the barrels was collected.

It can also be expressed as follows: 4 barrels.

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Answer:

i. 7:6

ii. 7:13

iii. 6:13

Step-by-step explanation:

boys to girls = 140:120 so we can simplify by 20 to get 7:6

boys to total = 140:(120+140) = 140:260 we can simplify again to get 7:13.

girls to total = 120:(120+140) = 120:260 we can also simplify to get 6:13

Answer:

26 customers

Step-by-step explanation:

Represent customers entering as y and those buying hot dogs as x

\(y = 4x + 9\)

\(y = 3x + 35\)

Required

Determine the number of people buying hotdogs (x)

Substitute 4x + 9 for y in the second equation

\(4x + 9 = 3x + 35\)

Collect Like Terms

\(4x - 3x = 35 - 9\)

\(x = 26\)

The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

In the question ,

it is given that ,

The random variable X is said to be normally distributed  ,

the mean is given as , μ = 70 , and

standard deviation of normal distribution is  (σ) = 10

probability that X is between 72 and 84 is written as P(72 < X < 84)

= P((72 - 70)/10 \(<\) Z \(<\) (84 - 70)/10)

= P(0.2 < Z < 1.4)

= P(0 \(<\) Z \(<\) 1.4) – P(0 \(<\) Z \(<\) 0.2)

From the z table , we get the values as

= 0.4192 – 0.0793

= 0.3399

≈ 0.340

Therefore , The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

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If x and y are directly proportional, that means Y = kX. The variable k here is a constant. When we say x is tripled, k must be 3.

What does it mean directly proportional?

When two quantities are directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage.

Let's have an example. Let's assume that x is 5. If we triple 5, it would equal to 15.

y = 3(5)

15 = 15

Therefore, the answer to this problem would be:

It is tripled

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See attached plots.

The top one shows all three pieces plotted simultaneously, independent of their domains.

The bottom plot takes into account the domains and removes parts of each piece (the dashed gray parts) outside their respective domains.