19. In each part, let TA: R2 → R2 be multiplication by A, and let u = (1, 2) and u2 = (-1,1). Determine whether the set {TA(u), TA(uz)} spans R2. 1 1 (a) A = -[ (b) A = --[- :) 0 2 2 -2

The value of arc XZW is determined as 310⁰.

The value of arc XZW is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

The value of arc XZW is calculated as follows;

arc XZW = 360 - arc WX (sum of angles in a circle)

arc XZW = 360 - 50

arx XZW = 310⁰

Thus, The value of arc XZW is calculated by applying intersecting chord theorem.

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The numbers on the mailboxes could be considered either categorical or quantitative data. The correct Option is C: Either categorical or quantitative data.

The numbers on the mailboxes can be considered either categorical or quantitative data, depending on the context in which they are being used.

If the numbers are simply labels for the mailboxes, with no inherent numerical value or order, then they can be considered categorical data. In this case, the numbers would be treated as labels for the different categories or groups, rather than as measurements with numerical significance.

On the other hand, if the numbers are being used to represent a quantity or a position in a sequence, then they can be considered quantitative data. For example, if the numbers represent the physical location of the mailbox within a building, or the order in which mail is sorted and delivered, then they can be treated as numerical measurements.

Therefore, without further context, the numbers on the mailboxes could be considered either categorical or quantitative data.

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Answer:

3x^2+17x-20

Step-by-step explanation:

Answer:

7 pm is the answer

15±45=60

then 7pm

Answer:

7

Step-by-step explanation:

12. In the figure given, we have x, y, z parallel lines. The answers are given below.

                                    Parallel lines                               Converse

a. ∠8≅∠20                  x, z                                           x and z are parallel lines

b. ∠1≅∠9                     x, y                                           x and y are parallel lines

c. m∠3+m∠10=180°     x, y                                          x and y are parallel lines

d. ∠11≅∠16                   -                                         Opposite angles are equal

e. m∠6+m∠24=180°    x, z                                     x and z are parallel lines

f. ∠14≅∠23                  y, z                                     Opposite angles are equal

g. ∠4≅∠21                   x, z                                     x and z are parallel lines

h. m∠8+m∠18=180°     x, z                                     x and z are parallel lines

i. ∠5≅∠15                     x, y                                     x and y are parallel lines

The figure shows that x, y, z are parallel lines. m and n are trasversals drawn intersecting these parallel lines. When a transversal intersects two lines, the opposite angles are equal and the consecutive angles on the same side sum upto 180.

The corresponding angles are equal when a transversal intersects parallel lines. For example, ∠2 = ∠10 = ∠18 as they are corresponding angles and ∠2 = ∠4 and ∠4 = ∠10 as they are opposite angles.

∠2 +∠3 = 180° as they are on the same side of the transversal and are consecutive angles.

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Answer:

$3066.58

Step-by-step explanation:

$2893 x 1.06= $3066.58

Hope this helps!

There is a 2 in 12 chance of drawing a penny

Step-by-step explanation:

Answer: 2/12

Step-by-step explanation:

There are 12 coins all together, and 2 pennies which means there is a 2/12 chance to draw a penny. Then they replace the penny and draw another time, so by replacing the penny the probability doesn't change and there is still a 2/12 chance of drawing a penny.

Answer:

(12,-6)

Step-by-step explanation:

Answer:

(12,-6)

Step-by-step explanation:

When dilating points, you multiply both coordinates (x and y) by the scale factor.

The point we are given is: (4,-2) and the scale factor is 3.

Multiply each coordinate by the scale factor of 3.

X-coordinate: 4

     4* 3= 12

New X-coordinate: 12

Y-coordinate : -2

    -2 * 3= -6

New Y-coordinate: -6

Our new x-coordinate is 12 and y-coordinate is -6. Therefore, our point is (12,-6). So, the image of point (4,-2) after a dilation of 3 is (12, -6).

Answer: (2, -2)

x=2, y=-2

Answer:

(2, -2)

Step-by-step explanation:

4x + y = 6

x - 2y = 6

x = 2y + 6

4(2y + 6) + y = 6

8y + 24 + y = 6

9y + 24 = 6

9y = 6 - 24

9y = -18

y = -18 ÷ 9

y = -2

4x + (-2) = 6

4x - 2 = 6

4x = 6 + 2

4x = 8

x = 8 ÷ 4

x = 2

Confirm:

4x + y = 6

4(2) - 2 = 6

8 - 2 = 6

6 = 6 (Correct)

(2, -2)

Answer:

Ok so right now that is in standard form (Ax+by=C) and we want to get this into y=mx+b form so that we can easily identify the slope. To do that we need to get y alone by folowing these steps:

9x-3y=81

9x-9x-3y=81-9x (in this step we are just getting rid of the x's from the left side so we can get y alone but since we subtract x from that side we need to subtract the same amount of x's on the other)

-3y=81-9x

-3y/-3=81-9x/-3 (finally to get y alone we need to divide by a -3. This is because any negative number multiplied or divided by another negative will give us a positive. If we divide by 3 then y will be negative which is incorrect. We have to divide by -3 on each side)\

y=81-9x/-3 -----> y=-27+3x ( in this part we have to divide everything on the right side of the equation by -3 as we did on the left side. 81/-3 = -27 and -9x/-3 = +3x.

our new equation is y=-27+3x although the proper form is y=mx+b.

all we need to do now is flip the 3x and -27 for this equation to match y-mx+b form. M in the equation represents the slope of an equation.

y=-27+3x---> y=3x-27

in this equation 3 is m and m represents the slope. For an line to be parralel to one another they must have the same slope. Therefore the slope of a line parallel to that equation is 3.

Step-by-step explanation:

The Slope of a line parallel to the line whose equation is 9x – 3y = 81 is 3.

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

Given that the slope of a line parallel to the line whose equation is

9x – 3y = 81

Reducing the Equation in form of y = mx + c, where m is the slope,

9x - 3y = 81

3y = 9x - 81

y = 3x - 27

Since, two line when parallel have equal slope, so the slope of the given line is 3.

Hence, The Slope of a line parallel to the line whose equation is

9x – 3y = 81 is 3.

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The value of the probability density function (pdf) at 0 for a uniform random variable between 5 and 15 is 0, because the pdf for a uniform distribution is constant between its minimum and maximum values, and is 0 elsewhere.

To explain further, a uniform distribution is a continuous probability distribution where every value within a certain range has an equal chance of being selected. In this case, the range is between 5 and 15. The pdf for a uniform distribution is constant within the range of the distribution and is 0 outside of it.

Since 0 is not within the range of the uniform distribution, the pdf at 0 is 0. This means that the probability of selecting a value of 0 from this uniform distribution is 0. The area under the pdf curve between 5 and 15 is equal to 1, which means that the probability of selecting a value within this range is 1.

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According to the question, The annual rate of interest is 5% for the first 5 years and 7% for the last 11 years. the present value of the annuity at time 0 is approximately $802.34.

To calculate the present value (PV) of the annuity, we need to determine the present value of each individual cash flow and sum them up.

For the first 5 years, the effective annual interest rate is 5%. Using the formula for the present value of an annuity:

\(\[ PV = PMT \times \frac{{(1 - (1 + r)^{-n})}}{{r}} \]\)

where PV is the present value, PMT is the annual deposit, r is the interest rate per period, and n is the number of periods.

Plugging in the values:

\(\[ PMT = \$50, \quad r = 5\% = 0.05, \quad n = 5 \text{ years} \]\)

we can calculate:

\(\[ PV_1 = 50 \times \frac{{(1 - (1 + 0.05)^{-5})}}{{0.05}} \]\)

For the next 11 years, the effective annual interest rate is 7%. Using the same formula:

\(\[ PMT = \$50, \quad r = 7\% = 0.07, \quad n = 11 \text{ years} \]\)

we can calculate:

\(\[ PV_2 = 50 \times \frac{{(1 - (1 + 0.07)^{-11})}}{{0.07}} \]\)

To find the total present value, we sum \(\(PV_1\) and \(PV_2\)\):

\(\[ PV = PV_1 + PV_2 \]\)

Calculating the values:

\(\[ PV_1 \approx 50 \times \frac{{(1 - 0.78353)}}{{0.05}} \approx \$432.94 \]\)

\(\[ PV_2 \approx 50 \times \frac{{(1 - 0.51316)}}{{0.07}} \approx \$369.40 \]\)

\(\[ PV \approx 432.94 + 369.40 \approx \$802.34 \]\)

Therefore, the present value of the annuity at time 0 is approximately $802.34."

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Answer:

I would choose a coin from the case containing half gold coins and half silver coins, because if you get a gold coin then you are going to know the chest only contains cold coins. From this we can deduce that the chest marked silver coins is really the 50/50, and the chest marked gold is really silver.  Step-by-step explanation:

Answer:

f(-9) = -119

Step-by-step explanation:

Hello!

You can evaluate for f(-9) by substituting -9 for x in the equation f(x) = -11 + 12x.

The evaluated value is -119.

By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

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Answer:

64 : 1.

Step-by-step explanation:

Ratio of the volumes is 16^3 to 4^3

= 4096 : 64

= 64 : 1.

Answer:

  y = 150x^2 -60x +6

Step-by-step explanation:

Do what the problem statement tells you: substitute for u.

  y = 6u^2

  y = 6(5x -1)^2 . . . . . . . . . . substitute 5x-1 for u

  y = 6(25x^2 -10x +1) . . . . expand the square

  y = 150x^2 -60x +6 . . . use the distributive property

Answer:

The ratio between Roberto and David is 3:11

Step-by-step explanation:

If Roberto were to have 18 cards when we start, then David would have 24. Roberto has 3/4 the amount that David has. Then Roberto gives half of his cards (9) to David. Roberto now has 9 cards and David has 33.

The ratio of Roberto's cards to David's cards will be 3:11.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

The number of Roberto's baseball cards is 3/4 the number of David's cards. If Roberto gives 1/2 of his cards to David.

If Roberto were to have 18 cards when we start, then David would have 24.

Roberto has 3/4 the amount that David has. Then Roberto gives half of his cards (9) to David. Roberto now has 9 cards and David has 33.

The ratio between Roberto and David is 3:11

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The exponential generating function for the sequence of factorials is x! = Γ(x+1) = \(\int\limits^{infinity}_0 {t}^{x}{e}^{-t} \, dt\).

We are given a sequence. A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It has members, just like a set. The length of the sequence is defined by the number of elements. The given sequence consists of factorials. The product of all positive integers less than or equal to n, denoted by n!, is the factorial of a non-negative integer n. We need to find the exponential generating function for the given sequence. The sequence is 0!, 1!, 2!, …, n!. The exponential generating function for the sequence of factorials is given below.

x! = Γ(x+1) = \(\int\limits^{infinity}_0 {t}^{x}{e}^{-t} \, dt\)

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Answer:

25/72

Step-by-step explanation:

Total outcomes :

P (red twice) :

P (blue twice) :

P (green twice) :

Adding :

Answer:

D

Step-by-step explanation:

To subtract a negative is basically adding because the negatives cancel out.

Answer:

f(x)=x+2

Step-by-step explanation:

Slope= (7-0)/(5-(-2)) = 7/7 = 1

Y-intercept= 2

substitute the slope, 1, for m and the y-intercept, 2, for b to get:

f(x)=x+2

hope this helps!

The linear function f with f(5)=7 and F(-2)=0 is f(x) = x + 2

f(5) = 7

This means when x = 5 , y = 7

(5, 7)

f(-2) = 0

(-2, 0)

This implies when x = -2 , y = 0

Using the linear function formula,

y = mx + b

where

m = slope

b = y-intercept

Therefore, the function can be represented as follows:

m = 0 - 7 / -2 - 5 = -7 / -7 = 1

Therefore,

y = x + b

0 = -2 + b

b = 2

The function in relation to x can be represented as follows:

f(x) = x + 2

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The Normal model is a good approximation for the sampling distribution.

a) According to the Central Limit Theorem, the theoretical mean and standard deviation for a sample size of 20 should be 0.05 and 0.02, respectively. For a sample size of 100, the theoretical mean and standard deviation should be 0.05 and 0.01, respectively.

b) The observed mean and standard deviation for a sample size of 20 was 0.052 and 0.021, respectively. For a sample size of 100, the observed mean and standard deviation was 0.051 and 0.012, respectively. These values are fairly close to the theoretical values.

c) Looking at the histograms in Exercise 1, I would be comfortable using the Normal model as an approximation for the sampling distribution at a sample size of 100.

d) The Success/Failure Condition states that the sample size should be large enough for the sampling distribution of the sample proportions to be approximately normal. Since I chose a sample size of 100, which satisfied the condition, I can be confident that the Normal model is a good approximation for the sampling distribution.

The sample size of 100 is large enough for the sampling distribution of the sample proportions to be approximately normal, and the observed mean and standard deviation is close to the theoretical values. Therefore, the Normal model is a good approximation for the sampling distribution.

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A sample size of 60 schoolgirls would be needed to estimate the mean IQ score within +5 points with 99% confidence.

Define mean ?

In statistics, the mean is a measure of central tendency that represents the average value of a set of numbers.

To estimate the required sample size to estimate the mean IQ score within +5 points with 99% confidence, we can use the formula:

\(n = (z^* * \sigma / E)^2\)

Where:

n = required sample size

z* = z-score corresponding to the desired confidence level (99% confidence level in this case, z* = 2.576)

σ = standard deviation of the population (given as 15 in this case)

E = margin of error (desired precision or half the confidence interval, which is 5 in this case)

Substituting the values into the formula, we get:

\(n = (2.576 * 15 / 5)^2\)

\(n = (38.64 / 5)^2\)

\(n = (7.728)^2\)

n ≈ 59.62

Rounding up to the nearest whole number, the required sample size is 60 schoolgirls.

Therefore, a sample size of 60 schoolgirls would be needed to estimate the mean IQ score within +5 points with 99% confidence, assuming a standard deviation of 15 in the population.

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The complete question is :

Estimating mean IQ. IQ scores are typically Normally distributed within a homogeneous population. How large a sample of schoolgirls in Example 14.3 (page 354) would be needed to estimate the mean IQ score u within +5 points with 99% confidence, assuming that o = 15 in this population? (Note that the z multiplier for a 99% confidence level is z* = 2.576.)

Answer:

y = 2

Step-by-step explanation:

use slope formula:

(4 - y) / (3 - 10) = -2/7

4-y / -7 = -2 /7

cross-multiply:

7(4 - y) = (-7)(-2)

28 - 7y = 14

-7y = -14

y = 2

Answer:

Options (B), (C) and (F) are correct.

Step-by-step explanation:

Properties of a rhombus,

1). All sides of a rhombus are equal in measure.

2). Both the diagonals of a rhombus are the perpendicular.

3). Diagonals bisect the vertex angles.

By these properties of a rhombus,

Option (B): PR is perpendicular to QS.

Option (C): ∠QPR ≅ ∠SPR

Option (F): PQ ≅ QR

Therefore, options (B), (C) and (F) are correct.

Answer:

B, C, F, and E are all correct.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

In B, the oranges is always 3 times the cups of juice. So it always follows the ratio 3:1.

A variant expression is a mathematical expression used to analyze the progress of a recursive function and ensure its termination. To guarantee that a recursive function terminates, a variant expression must have two essential properties which are Boundedness and monotonicity.

1. Boundedness: A variant expression must be bounded, which means that it has an upper or lower limit. This limit is often a non-negative integer value, such as 0. The boundedness property ensures that the variant expression cannot grow indefinitely, which would lead to non-termination of the recursive function.

2. Monotonicity: A variant expression must be monotonically decreasing, meaning that its value strictly decreases with each recursive call. Monotonicity ensures that the variant expression is always moving closer to the bound, eventually reaching the limit and causing the function to terminate.

To guarantee the termination of a recursive function, follow these steps:

Step 1: Identify a suitable variant expression for the function. The expression should be related to the problem size or input parameters of the function and should reflect the progress towards the function's termination.

Step 2: Verify the boundedness property of the variant expression. Ensure that the expression has an upper or lower limit, typically a non-negative integer, which it cannot exceed.

Step 3: Verify the monotonicity property of the variant expression. Check that the expression's value strictly decreases with each recursive call, moving closer to the bound.

Step 4: Ensure that the recursive function terminates when the variant expression reaches the bound. This condition is usually implemented as the base case of the function, which prevents further recursive calls and initiates the return process.

In summary, a variant expression must have boundedness and monotonicity properties to guarantee that a recursive function terminates. By verifying these properties and incorporating them into the recursive function, you can ensure that the function will reach its termination condition and not result in infinite recursion.

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Answer: 18

Step-by-step explanation: Use PEMDAS

Answer:

0

Step-by-step explanation:

i used a calculator & it was 0 meters