T/F : The absolute value of the determinant of A equals the volume of the parallelepiped determined by the columns of A

Answer:

(ax+1) = ( ax+89) -12 +1

Step-by-step explanation

add all of it up then subtract by 12 add 1 theres your answer

Answer:

don't say that

Step-by-step explanation:

I am l o

Answer:

Below

Step-by-step explanation:

There is an image uploaded below of the stem-and-leaf plot of the video game scores!

The graph of the system of linear equation is attached below

The graph of a linear equation is a line. Each point on the line is a solution to the equation. For a system of two equations, we will graph two lines. Then we can see all the points that are solutions to each equation. And, by finding what the lines have in common, we’ll find the solution to the system.

In this given problem, we can use a graphing calculator to plot the lines of the graph as well as find the point of intersection which will give us our solution.

The equations given are;

5x + 2y = -3 ...eq(i)

8x - 6y = -14 ...eq(ii)

Plotting this in a graphing calculator;

We can see that the solution to this graph which is the point of intersection is at (1, 1)

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Answer:

15

Step-by-step explanation:

1.4 x 15 equals 21 so if you round the question it equals 15 if not then 14.

If you wanted to measure satisfaction with this course on a scale from 1, not very satisfied, to 7, very satisfied, you would use an ordinal scale.

An ordinal scale is a type of scale used to measure variables that have an inherent order or ranking, such as the level of satisfaction in this case. However, the differences between the categories are not necessarily equal or measurable, which rules out the use of an interval or ratio scale. A nominal scale is used for variables that are categorical and cannot be ranked or ordered, which is not appropriate for this scenario.

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Answer: 9/4

Step-by-step explanation:

since each cube measure 1/2 of a centimeter on one side, the dimension is calculated first

length = 2 x 1/2 cm

width = 3 x 1/2 cm

height = 3 x 1/2 cm

The height of the right triangular prism whose surface are is 480 square inches is equal to 9 inches.

Total surface area of the right prism = 480 square inches

Surface area of a right triangular prism is,

S = 2B + Ph

where S is the surface area,

B is the area of the triangular base,

P is the perimeter of the base,

and h is the height of the prism.

First, area of the triangular base.

Use the formula for the area of a triangle,

B = (1/2)bh

where b is the base of the triangle

and h is the height of the triangle.

⇒ B = (1/2) × 8 × 15

⇒ B = 60 in²

Since the base is a right triangle,

Use the Pythagorean theorem to find the length of the third side,

c² = 8² + 15²

⇒ c² = 64 + 225

⇒ c² = 289

⇒ c = 17

Perimeter of the base is,

⇒ P = 8 + 15 + 17

⇒ P = 40 inches

Surface area of right prism = 480

⇒ 2B +Ph = 480

⇒ 2×60 + 40h = 480

⇒40h = 480 - 120

⇒ h = 360 /40

⇒ h = 9 inches.

Therefore, the height of the right prism is equal to 9inches.

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The cost of each pair of socks is $1.14 if Isabella paid $30 and gets $7.20 as a change for 5 pairs of socks.

The cost of 5 pairs of socks is given by the change she receives when subtracted from the total amount she paid.

Amount paid = $30

Change = $7.20

Cost of 5 pairs of socks = Amount paid - change

= 30 - 7.20

= $22.80

The cost of one pair of socks is calculated by dividing the cost of 5 pairs of socks by 5.

Cost of one pair of socks = 22.80 ÷ 5

= $ 1.14

Thus, the cost of one pair of socks is $1.14

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The complete question is 'Isabella gave the cashier $30 to pay for 5 pairs of socks. The cashier gave her $7. 20 in change. Each pair of socks cost the same amount. Find the cost of a single pair of socks.'

The value of the side x = 114. 34

We have that the six different trigonometric identities in mathematics are listed thus;

We also have that their ratios are given as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram, we have;

Adjacent side = 98

Hypotenuse = x

Angle = 31

cos 31 = 98/x

cross multiply

x = 114. 34

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The coupon give Shanice 75 percent off the original price of the pair of jeans.

At a clothing store, a pair of jeans costs $40. Using a coupon, Shanice is

able to pay $10 less than the original price. Therefore, the percentage off  the original price the coupon represents can be calculated as follows:

Therefore,

Price Shanice bought the jeans = 40 - 10 = 30 dollars

Hence,

let

x = percentage off the original price

Therefore,

x / 100 × 40 = 30

40x / 100 = 30

cross multiply

3000 = 40x

divide both sides by 40

x = 3000 / 40

x = 75%

Therefore,  the coupon gives Shanice 75% off of the original price.

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The amount more that the Penders budgeted for transportation than they spent on transportation is $ 3.30.

Looking at the Budget presented by the Penders, we see that they budgeted for Gasoline and Parking to the tune of :

= 85 + 70

= $ 155

The Penders however spent a different amount on transport to the tune of :

= 101. 70 + 50

= $151. 70

This then means that they spent less than they budgeted for transport and the difference was :

= 155 - 151. 70

= $ 3.30

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E[X] = 21.

E[f(X = n)] = 1.

a. To find the expected value of the random variable X, we need to use the formula:

E[X] = Σn P(X = n) * n

where Σn denotes the sum over all possible values of X.

Given that the pmf of X is given by:

f(X = n) = 4/(n(n+1)(n+2)),

we have:

P(X = n) = f(X = n) * 21 = 84/(n(n+1)(n+2))

Substituting this into the formula for E[X], we get:

E[X] = Σn P(X = n) * n
    = Σn (84/(n(n+1)(n+2))) * n
    = Σn (84/(n+1)(n+2)))
    = 84 * Σn (1/(n+1)(n+2))

Now, using partial fractions, we can write:

1/(n+1)(n+2) = (1/2) * [1/(n+1) - 1/(n+2)]

Substituting this back into the expression for E[X], we get:

E[X] = 84 * Σn [(1/2) * (1/(n+1) - 1/(n+2))]
    = 42 * Σn [1/(n+1) - 1/(n+2)]
    = 42 * [(1/2) - (1/3) + (1/3) - (1/4) + ...]
    = 42 * (1/2)
    = 21



b. To find the expected value of f(X = n), we simply need to substitute the pmf into the formula for expected value:

E[f(X = n)] = Σn f(X = n) * P(X = n)

Substituting the given pmf, we have:

E[f(X = n)] = Σn (4/(n(n+1)(n+2))) * 21

Using partial fractions as before, we can write:

4/(n(n+1)(n+2)) = (2/n) - (4/(n+1)) + (2/(n+2))

Substituting this into the expression for E[f(X = n)], we get:

E[f(X = n)] = Σn [(2/n) - (4/(n+1)) + (2/(n+2))] * 21
            = 2 * [1 - (4/2) + (2/3) - (4/3) + (2/4) - (4/4) + ...] * 21
            = 2 * [(1/2) + (1/3) + (1/4) + ...] * 21
            = 42 * [(1/2) + (1/3) + (1/4) + ...]

This is the harmonic series, which diverges. However, note that we are interested in the expected value of f(X = n), not the sum of f(X = n) over all possible values of X. Therefore, we can say that E[f(X = n)] = 1, since the pmf is normalized to sum to 1:

Σn f(X = n) = Σn (4/(n(n+1)(n+2))) * 21
            = 21 * Σn (2/n) - Σn (4/(n+1)) + Σn (2/(n+2))
            = 21 * (2 - 1 + 1/2)
            = 21

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Equivalent ways for chi-square statistic: statistically significant relationship between the variables, reject null hypothesis, suggesting that the relationship in the population is not due to chance, The probability of observing the data by chance is 5% or less, supporting the presence of a relationship in the population.

If the p-value is 0.05 or less and the chi-square statistic is at least 3.84, it can be concluded that there is a significant relationship in the population. Another way to state this result is that the null hypothesis (that there is no relationship) can be rejected at a significance level of 0.05.

Based on your question, you would like to know equivalent ways to state the result when the chi-square statistic is at least 3.84 and the p-value is 0.05 or less. Here's my answer:

When the chi-square statistic is at least 3.84 and the p-value is 0.05 or less, we can conclude that the relationship in the population is real. Equivalent ways to state this result are:

1. There is a statistically significant relationship between the variables in the population.
2. We reject the null hypothesis, suggesting that the relationship in the population is not due to chance.
3. The probability of observing the data by chance is 5% or less, supporting the presence of a relationship in the population.

I hope this helps! Let me know if you need any further clarification.

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The length of the arc intercepted by a central angle of 2.9 radians is 14.5 inches. Rounded to the nearest tenth, this is 14.5 inches.

To find the length (s) of the arc intercepted by a central angle of 2.9 radians in a circle with a radius of 5 inches, you can use the following formula:

Arc length (s) = radius × central angle (in radians)

In this case, the radius is 5 inches, and the central angle is 2.9 radians. Plugging these values into the formula, we get:

s = 5 × 2.9

s ≈ 14.5 inches

Therefore, the length of the arc intercepted by a central angle of 2.9 radians in a circle with a radius of 5 inches is approximately 14.5 inches, rounded to the nearest tenth.

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The equation which represent the price as a function of year (t) is: p = 7562t + 156100

The average price of a home today would be $352,712.

The equation to represent the price (p) of a house can be found using the slope-intercept form of the equation of a line:

p = mt + b

We have two points given:

(0, 156100)

(13, 254400)

where 13 corresponds to the year 2010 since t=0 is 1997.

slope (m) = (change in y)/(change in x)

slope (m) = (254400-156100)/(13-0)

slope (m) = 98300 / 13

slope (m) = 7562

We will substitute the slope and one of the points into the equation and solve for b:

156100 = 7562(0) + b

b = 156100

Now, our equation to represent the price as a function of year (t) is:

p = 7562t + 156100

From 1997 up to today (2023) is:

= 2023 - 1997

= 26 years

Using our function:

p = 7562*(26) + 156100

p = 352712

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The answer is (d.) (x - 2)^2 = 9, which is equivalent to the original equation when completing the square.  To solve the given quadratic equation using the completing the square method, we'll rewrite the equation in the form (x - h)² = k.

Given equation: 0 = 3x² - 12x - 15

First, let's divide by 3 to simplify the equation:

0 = x² - 4x - 5

Next, let's complete the square by adding and subtracting the square of half the coefficient of x:

0 = (x² - 4x + 4) - 5 - 4

Now, we can rewrite the left side as a perfect square:

0 = (x - 2)² - 9

Finally, add 9 to both sides to get the equation in the desired form:

(x - 2)² = 9

So the correct answer is (d.) (x - 2)² = 9.

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The amount of brown sugar called for in the recipe is 1134.0 grams, tenths of a gram rounded up. By dividing 40 ounces by the conversion value of 28.35 grams per ounce, you can calculate this and get 1134.0 grams.

Rounding to the closest tenth of a gram is necessary to convert 40 ounces to grams. To do this, multiply the weight in ounces by the conversion factor of 28.35 (1 ounce = 28.35 grams).

Therefore, 40 ounces of brown sugar are equivalent to:

40 ounces x 28.35 grams per ounce = 1134 grams

Because 1 gram only roughly equates to 0.04 ounces, it is vital to keep in mind that this is an estimation. This conversion factor may change based on the situation and the material being measured.

Hence, The amount of brown sugar required for the recipe is roughly 1134 grams.

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To use the alternating series estimation theorem, we need to check that the series alternates in sign and that the absolute value of the terms decreases monotonically.

Assuming these conditions are met, the alternating series estimation theorem tells us that the error in approximating the sum of the series by the sum of the first n terms is bounded by the absolute value of the (n+1)th term.

To determine the minimum number of terms we need to add in order to find the sum with an error less than 0.00005, we can set the absolute value of the (n+1)th term to be less than or equal to 0.00005 and solve for n. If such an n exists, then we know that adding n terms will give us an approximation with the desired level of accuracy. If no such n exists, then the series diverges and we cannot find an approximation with the desired level of accuracy.

Note that the alternating series estimation theorem only applies to alternating series, so if the given series is not alternating, then we cannot use this theorem to determine the minimum number of terms needed for a desired level of accuracy.

The Alternating Series Estimation Theorem states that for a convergent alternating series with decreasing positive terms, the error in the partial sum is less than the first omitted term.

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The intersection change has significantly increased the number of traffic accidents. If not, you would fail to reject the null hypothesis and not have enough evidence to claim a significant increase in accidents due to the intersection change.

A) The Null Hypothesis (H0) is that the intersection change has not significantly increased the number of traffic accidents.

B) Without specific data, I cannot calculate the exact Test Statistic value. You'll need to perform a hypothesis test using the appropriate formula for your data set.

C) The Critical Value also depends on your data and the level of significance (alpha) you choose, typically 0.05 or 0.01. Use a statistical table or software to find the critical value based on your chosen level of significance and the degrees of freedom.

D) Similar to B and C, the p-value cannot be calculated without specific data. Compare the calculated p-value to the chosen level of significance (alpha) to determine whether to reject or fail to reject the null hypothesis.

E) Based on the Test Statistic, Critical Value, and p-value, you can draw conclusions about the null hypothesis. If the Test Statistic is greater than the Critical Value or the p-value is less than the chosen level of significance (alpha), you would reject the null hypothesis.

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Answer:

6log 2

Step-by-step explanation:

log 16 + log 4 = log 2⁴ + log 2² = 4log 2 + 2log 2 = 6log 2

The probability of randomly picking out a book of poetry from a bookshelf depends on the total number of books on the shelf and the number of poetry books among them. If there are 10 books on the shelf and 2 of them are poetry books, then the probability of randomly picking out a poetry book is 2/10 or 1/5.

To calculate the odds in favor of choosing a book of poetry, we need to compare the number of favorable outcomes (picking a poetry book) to the number of unfavorable outcomes (picking a non-poetry book). In this case, the odds in favor of choosing a book of poetry would be 2:8 or 1:4, since there are 2 favorable outcomes (picking a poetry book) and 8 unfavorable outcomes (picking a non-poetry book) out of a total of 10 books.

In summary, the probability of randomly picking out a book of poetry from a bookshelf depends on the number of poetry books among the total number of books. The odds in favor of choosing a book of poetry can be calculated by comparing the number of favorable outcomes to the number of unfavorable outcomes.

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The volume of the rectangular pyramid is 130.7 cubic units.

The volume of a rectangular pyramid can be calculated as:

V = 1/3 × l × w × h

where l, w, and h are the length, width, and height of the rectangular pyramid, respectively.

Given that a rectangular pyramid with a length of 7 units, a width of 7 units, and a height of 8 units.

To find the volume of a given pyramid,  substitute the values into the formula:

V = 1/3 × l × w × h

V = 1/3 × 7 × 7 × 8

V = 130.7 units³

Therefore, the volume of the rectangular pyramid is 130.7 cubic units.

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The missing figure has been attached below.

The required decrease in dollars was $1222 and the amount of money in Bob's account at the end of last year was $3978.

To find the decrease in dollars and the amount of money in Bob's account at the end of last year, we can use the following steps:

Calculate the amount of the decrease. We can do this by multiplying the original amount by the percentage decrease as a decimal:

Decrease = 0.235 x $5200 = $1222

So, the decrease in dollars is $1222.

Calculate the amount of money in Bob's account at the end of last year. We can do this by subtracting the decrease from the original amount:

Amount at end of last year = $5200 - $1222 = $3978

So, the amount of money in Bob's account at the end of last year was $3978.

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John Doe was killed approximately 4.06 hours ago.

To determine the time of death for John Doe, we will use the given formula: [tex]T = T0 + (T1 - T0)(0.97)^t[/tex],[/tex]where T is the body temperature at time t, T0 is the air temperature (74°F), and T1 is the body temperature at the time of death (93°F).

We are trying to find the time (t) when John Doe's body temperature was 98.6°F (normal body temperature). So, we'll set T equal to 98.6°F and solve for t:

[tex]98.6 = 74 + (93 - 74)(0.97)^t[/tex]

To solve for t, follow these steps:

1. Subtract 74 from both sides:
[tex]24.6 = 19(0.97)^t[/tex]

2. Divide by 19:
[tex]1.2947 ≈ (0.97)^t[/tex]

3. Take the natural logarithm of both sides:
ln(1.2947) ≈ [tex]ln((0.97)^t)[/tex]

4. Apply the logarithm power rule:
ln(1.2947) ≈ t * ln(0.97)

5. Divide by ln(0.97):
t ≈ ln(1.2947) / ln(0.97)

6. Calculate t:
t ≈ 4.06

So, John Doe was killed approximately 4.06 hours ago.

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To compute Paasche's index for 2018 using 2010 as the base period, we need to use the formula:

Paasche's index = (current year prices * current year quantities) / (base year prices * current year quantities)

Using the given information, we have:

For Margarine:
- Current year prices: $2.00
- Current year quantities: 26
- Base year prices: $0.81
- Base year quantities: 20

Paasche's index for Margarine = (2.00 * 26) / (0.81 * 20) = 2.54

For Shortening:
- Current year prices: $1.88
- Current year quantities: 8
- Base year prices: $0.84
- Base year quantities: 1

Paasche's index for Shortening = (1.88 * 8) / (0.84 * 1) = 17.71

For Milk:
- Current year prices: $2.89
- Current year quantities: 63
- Base year prices: $1.44
- Base year quantities: 74

Paasche's index for Milk = (2.89 * 63) / (1.44 * 74) = 2.26

For Potato chips:
- Current year prices: $3.99
- Current year quantities: 34
- Base year prices: $2.91
- Base year quantities: 28

Paasche's index for Potato chips = (3.99 * 34) / (2.91 * 28) = 1.87

Therefore, the Paasche's index for 2018 using 2010 as the base period is:

Paasche's index = (2.54 + 17.71 + 2.26 + 1.87) / 4 = 6.34 (rounded to 2 decimal places)

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Answer:

Step-by-step explanation:

c because just add 64 and 46

Answer:

x = 1.08 and x = -2.08

Step-by-step explanation:

We can solve this equation using the quadratic formula.

[tex]ax^2+bx+c=0[/tex]

Thus, in the equation given, 4 is our a value, 4 is (also) our b value and -9 is our c value.

The formula for the positive solution of the quadratic formula is

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]

The formula for the negative solution of the quadratic formula is

[tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

Positive solution:

[tex]x=\frac{-4+\sqrt{4^2-4(4)(-9)} }{2(4)}\\ \\x=\frac{-4+\sqrt{160} }{8}\\ \\x=1.08113883\\\\x=1.08[/tex]

Negative solution:

[tex]x=\frac{-4-\sqrt{4^2-4(4)(-9)} }{2(4)}\\ \\x=\frac{-4-\sqrt{160} }{8}\\ \\x=-2.08113883\\\\x=-2.08[/tex]

Answer: B

Step-by-step explanation:

(x,y) (-3,0) look for the point located at -3 on the x-axis and 0 on the y-axis

Answer:

  24.1 square units

Step-by-step explanation:

You want the base area of a prism with height 9 units and volume 216.9 units³.

The formula for the volume of a prism is ...

  V = Bh

where B is the area of the base, and h is the height. Solving for the base area, we have ...

  B = V/h = (216.9 u³)/(9 u) = 24.1 u²

The area of one of the bases is 24.1 square units.

The probability that an arrival does not have to wait before service is 0.7 (Option B).

To calculate the probability that an arrival does not have to wait before service, we need to use the Poisson and exponential distributions.

First, we can calculate the average number of arrivals per hour:

60 minutes / 10 minutes per arrival = 6 arrivals per hour

Next, we can use the exponential distribution to calculate the probability that a phone call is less than or equal to 10 minutes (the time between arrivals):

P(call length ≤ 10 minutes) = 1 - e^(-10/3) ≈ 0.957

This means that there is a 95.7% chance that a phone call will end before the next arrival.

Finally, we can use the Poisson distribution to calculate the probability that there are no arrivals in the 10-minute window between the end of a phone call and the next arrival:

P(no arrivals in 10 minutes) = e^(-6) ≈ 0.002

So the probability that an arrival does not have to wait before service is:

P(no wait) = P(call length ≤ 10 minutes) * P(no arrivals in 10 minutes)

P(no wait) = 0.957 * 0.002

P(no wait) ≈ 0.002

Therefore, the answer is A) 0.3.

We're given that arrivals at a telephone booth follow a Poisson distribution with an average time of 10 minutes between arrivals, and the length of a phone call is exponentially distributed with a mean of 3 minutes. We need to find the probability that an arrival does not have to wait before service.

Step 1: Calculate the arrival rate (λ) and service rate (μ)
The average time between arrivals is 10 minutes, so the arrival rate λ is 1/10 arrivals per minute.
The average length of a phone call is 3 minutes, so the service rate μ is 1/3 calls per minute.

Step 2: Calculate the traffic intensity (ρ)
The traffic intensity ρ is the ratio of the arrival rate to the service rate.
ρ = λ/μ = (1/10) / (1/3) = 3/10 = 0.3

Step 3: Calculate the probability that an arrival does not have to wait (P_0)
For an M/M/1 queue (Poisson arrivals and exponential service times with a single server), the probability that an arrival does not have to wait before service is given by P_0 = 1 - ρ.
P_0 = 1 - 0.3 = 0.7

So, the probability that an arrival does not have to wait before service is 0.7 (Option B).

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