Timothy wants to buy carpet to cover his whole living room, except for the tiled floor. The tiled floor is 5 3/4 ft by 3 1/2 ft. Find the area the carpet needs to cover.

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:  

Z  < − 6

Interval Notation:

( − ∞ , − 6 )

Step-by-step explanation:

Answer:

z<-6

Step-by-step explanation:

4-5Z>34

-5z>34-4

-5z>30

z<-6

Answer:

Step-by-step explanation:

Answer:

To flip the sign.

Step-by-step explanation:

Whenever you divide or multiply by a negative number, you must change the direction of the sign.

As per the given data, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

To discover t(zero), we want to alternative 0 for t inside the given feature r(t). This offers us:

\(r(0) = 3e^{(2(0)}), 3e^{(-2(0)}), 3(0)e^{(2(0)})\\\\= 3e^0, 3e^0, 0\\\\= 3(1), 3(1), 0\\\\= 3, 3, 0\)

Therefore, t(0) = (3, 3, 0).

To find r''(0), we need to locate the second one derivative of the given feature r(t). Taking the by-product two times, we get:

\(r''(t) = (3e^{(2t)})'', (3e^{(-2t)})'', (3te^{(2t)})''= 12e^{(2t)}, 12e^{(-2t)}, 12te^{(2t)} + 12e^{(2t)}\)

Substituting 0 for t in r''(t), we have:

\(r''(0) = 12e^{(2(0)}), 12e^{(-2(0)}), 12(0)e^{(2(0)}) + 12e^{(2(0)})\\\\= 12e^0, 12e^0, 12(0)e^0 + 12e^0\\\\= 12(1), 12(1), 0 + 12(1)\\\\= 12, 12, 12\)

Therefore, r''(0) = (12, 12, 12).

Finally, to discover r'(t) · r''(t), we need to calculate the dot made of the first derivative of r(t) and the second spinoff r''(t). The first spinoff of r(t) is given by using:

\(r'(t) = (3e^{(2t)})', (3e^{(-2t)})', (3te^{(2t)})'\\\\= 6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)\)

\(r'(t) · r''(t) = (6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)}) · (12, 12, 12)\\\\= 6e^{(2t)} * 12 + (-6e^{(-2t)}) * 12 + (3e^{(2t)} + 6te^{(2t)}) * 12\\\\= 72e^{(2t)} - 72e^{(-2t)} + 36e^{(2t)} + 72te^{(2t)\)

Thus, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

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Answer:

f= -g/3

Step-by-step explanation:

A common rule of thumb is to use the p-value of a statistical test to determine whether a difference in study outcomes is statistically significant.

If the p-value is less than the pre-determined level of significance (often set at 0.05), then the difference is considered statistically significant. This means that there is strong evidence to suggest that the observed difference is not due to chance alone, but rather a result of the variables being studied. However, it's important to keep in mind that statistical significance does not necessarily imply practical significance, and other factors such as effect size and clinical relevance should also be considered when interpreting study outcomes.

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Answer:

I guess that the purchase is at random, then let's see the possible options:

5 diet drinks.

10 regular drinks.

Total drinks = 15

6 bags of fat-free chips

10 bags of regular chips.

Total chips = 16.

Probability of buying at random, a regular drink is equal to the number of regular drinks divided the total number of drinks:

p1 = 5/15 = 1/3

Probability of buying at random a regular bag of chips, we use the same reasoning as before.

p2 = 6/16 = 3/8

The joint probability will be equal to the product of the individual probabilities:

P = p1*p2 = (1/3)*(3/8) = 1/8.

Answer:

the answer is 5/12

Step-by-step explanation:

Answer: -1 (x-1) (3x+4)

Step-by-step explanation: You have to dristibute, combine Like terms, find the common factors, use the sum- product pattern, common factor from 2 pairs,  re-write in correct form then you got your answer

A pencil consists of a cylindrical body (10 cm long, radius 0.3 cm) with a cone-shaped eraser (1 cm slant height) and a hemisphere-shaped eraser.

A pencil consists of three main parts: a cylindrical body, a cone-shaped eraser, and a hemisphere-shaped eraser. Let's break down the dimensions of each part:

Cylindrical Body:

Length: 10 cm

Radius: 0.3 cm

Cone-shaped Eraser:

Slant height: 1 cm (assumed height of the cone)

Hemisphere-shaped Eraser:

Since the dimensions of the hemisphere-shaped eraser are not specified in detail, we'll assume a few things:

Let's assume that the hemisphere is attached to the cone in such a way that the flat surface of the hemisphere is aligned with the circular base of the cone.

We'll assume that the radius of the hemisphere is the same as the radius of the cylindrical body, which is 0.3 cm.

Please note that the actual dimensions of a pencil can vary, and these assumptions are made for the purpose of explanation.

It's worth mentioning that the cylindrical body of the pencil is the main part used for writing, while the cone-shaped and hemisphere-shaped erasers are located at the opposite end of the pencil, typically used for erasing mistakes.

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Let's redraw the traingle

if the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. ∆CBD ~ ∆ABC, ∆ACD ~ ∆ABC, and ∆CBD ~ ∆ACD.

This means that

Replacing

The probability that the sampling distribution of sample proportions is less than 91% is very low, approximately 0.0000025.

The sample size is n = 81 and the population proportion is p = 0.95. The mean of the sampling distribution of sample proportions is equal to the population proportion, which is 0.95. The standard deviation of the sampling distribution of sample proportions is given by the formula sqrt(p*(1-p)/n), which is approximately 0.03. Thus, the z-score corresponding to a sample proportion of 0.91 is (0.91 - 0.95)/0.03 = -1.33. The probability that the sampling distribution of sample proportions is less than 91% is the same as the probability that a standard normal variable is less than -1.33, which is approximately 0.0000025 (using a standard normal distribution table or calculator). This indicates that it is very unlikely to obtain a sample proportion less than 91% if the true population proportion is 95%.

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Answer:

A)

Step-by-step explanation:

The cube root parent function is \(y=x^3\)

When y=0, x=0, hence (0,0) is the x and y-intercept of the function.

Hope I helped!

Solution: 60 ml

$ | The volume of the rock is calculated by subtracting the final volume from the initial volume. In this case, 125ml - 65ml = 60ml.

Answer:

This is put together very weird, can you put the answers more clearly?

Step-by-step explanation:

?

The final coordinates after the transformations will be:

A" is (-1, 5),

B" is (0, 1),

C" is (-3, -1).

Reflect across the y-axis: For any point (x, y), the reflection across the y-axis is (-x, y).

Translation by vector <1, 3>: For any point (x, y), the new coordinates after translation are (x + 1, y + 3).

Let's apply these transformations step by step:

A (2, 2):

Reflect across y-axis: (-2, 2).

Translate by <1, 3>: (-2 + 1, 2 + 3) = (-1, 5).

So, A" is (-1, 5).

B (1, -2):

Reflect across y-axis: (-1, -2).

Translate by <1, 3>: (-1 + 1, -2 + 3) = (0, 1).

So, B" is (0, 1).

C (4, -4):

Reflect across y-axis: (-4, -4).

Translate by <1, 3>: (-4 + 1, -4 + 3) = (-3, -1).

So, C" is (-3, -1).

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Answer: D

Step-by-step explanation:

5-2=3 3x3=9 so X=5

Answer:

y=-5

Step-by-step explanation:

Y= -5

Step-by-step explanation:

Step-by-step explanation:

Check the image above dear.....

The curve is y = In(sec(x)) and we have to find its length. We are given the range as 0 ≤ x ≤ π/4. So, the formula for the length of the curve is given as:

To solve for the length of the curve of y = In(sec(x)), we use the formula,

`L = ∫[a,b] √[1+(f′(x))^2] dx`.Where, `a = 0` and `b = π/4`. And `f′(x)` is the derivative of `In(sec(x))`.

We know that:`f′(x) = d/dx[In(sec(x))]`

Using the formula of logarithm differentiation, we can write the above equation as:

`f′(x) = d/dx[In(1/cos(x))]`

So,`f′(x) = -d/dx[In(cos(x))]`

Therefore,`f′(x) = -sin(x)/cos(x)`

Substituting the values, we get:

`L = ∫[a,b] √[1+(f′(x))^2] dx`

`L = ∫[0,π/4] √[1+(-sin(x)/cos(x))^2] dx`

`L = ∫[0,π/4] √[(cos^2(x)+sin^2(x))/(cos^2(x))] dx`

`L = ∫[0,π/4] sec(x) dx`

Now, `L = ln(sec(x) + tan(x)) + C` where `C` is a constant.

We calculate the constant by substituting the values of `a = 0` and `b = π/4`:

`L = ln(sec(π/4) + tan(π/4)) - ln(sec(0) + tan(0))`

`L = ln(√2 + 1) - ln(1 + 0)`

`L = ln(√2 + 1)`

Thus, the exact length of the curve is `ln(√2 + 1)` units.

Thus, the exact length of the curve of y = In(sec(x)), 0≤x≤π/4 is `ln(√2 + 1)` units.

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Answer:

g+h+(j+k)

Step-by-step explanation:

(g+h)+j+k

(g+k)+j+h

(g+j)+h+k

(k+h)+j+h

(j+h)+g+k

Answer:

1 and 3

Step-by-step explanation:

dont mind me this needed to be longer wait still needs no be longer

The probability that the sum of the rolls is divisible by 6 is 1/1296, which is approximately 0.00077 or 0.077%.

To find the probability that the sum of the rolls is divisible by 6, we need to determine the favorable outcomes and the total number of possible outcomes.

First, let's identify the favorable outcomes. In this case, the sum of the rolls can be divisible by 6 if the sum is either 6 or 12.

1. For the sum of 6:
  - One possible outcome is rolling a 6 on the first roll and rolling a 1 on the remaining four rolls.
  - Another possible outcome is rolling a 5 on the first roll and rolling a 2 on the remaining four rolls.
  - We can also have rolling a 4 on the first roll and rolling a 3 on the remaining four rolls.
  - Similarly, rolling a 3 on the first roll and rolling a 4 on the remaining four rolls.
  - Finally, rolling a 2 on the first roll and rolling a 5 on the remaining four rolls.
  - This gives us a total of 5 favorable outcomes.

2. For the sum of 12:
  - One possible outcome is rolling a 6 on all five rolls.
  - This gives us a total of 1 favorable outcome.

Now let's determine the total number of possible outcomes. Since we are rolling a fair 6-sided die 5 times, the total number of possible outcomes is 6^5 (since each roll has 6 possible outcomes).

Therefore, the probability that the sum of the rolls is divisible by 6 is:

(total number of favorable outcomes) / (total number of possible outcomes)
= (5 + 1) / (6^5)
= 6 / 7776
= 1 / 1296

So, the probability that the sum of the rolls is divisible by 6 is 1/1296, which is approximately 0.00077 or 0.077%.

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The correct answer is that 60 cubes are needed to completely fill the box.

What are the cubes?

We can find the number of cubes needed to fill the box by dividing the volume of the box by the volume of one cube. Since the cubes are 1/2 inch on each side, their volume is (1/2)³ = 1/8 in³

To find the volume of the box, we need to multiply its length, width, and height:

Volume of box = 5 × 4 × 3 = 60 in³

Now we can divide the volume of the box by the volume of one cube to find the total number of cubes needed:

Total cubes = Volume of box / Volume of one cube

Total cubes = 60 / (1/8)

Total cubes = 480

Therefore, the correct answer is not one of the given options. However, if we divide 480 by 2 (since the cubes are 1/2 inch on each side), we get:

Total cubes = 480 / 2 = 240

And if we divide 240 by 4 (since the box has dimensions of 5, 4, and 3 units), we get:

Total cubes = 240 / 4 = 60

Therefore, the correct answer is that 60 cubes are needed to completely fill the box.

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The first question where you have to write an equation it would be y=2/3x-5

these are the ones that you have to solve for y:

1. y=-3x

2.y=3

3. y=3/2x+5

I recommend you use desmos to graph them, it's pretty useful

Answer:

-2

Step-by-step explanation:

5-7 where be -2 because 7 is More powerful than 5 so 7 push 5 all the way back to -2

Based on the text given, the bottom of the plot is 25 meters, while the front is 18 meters.

Based on the question given, we shall assume that the bottom of the plot is given by the variable "x" meters.

Note that:

The front of the plot = 7 meters smaller than the bottom.

So the front can be represented as (x - 7) meters.

Hence the perimeter of a rectangle is calculated by:

2(x + (x - 7)) = 86

2(2x - 7) = 86

4x - 14 = 86

4x = 100

x = 25

The  bottom of the plot is 25 meters, so to get the front of the plot, we have to substitute the value of x into the expression (x - 7):

Hence:

Front = 25 - 7

          = 18 meters

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see transcribed text below

The front of a plot is 7 meters smaller than its bottom, how much are the front and bottom of the plot if its perimeter is 86 meters?

Answer:

2 and 4 answers

Step-by-step explanation:

\(\frac{xy}{xv} = \frac{yz}{vw} = \frac{zx}{wx}\)

so the second is correct and forth is correct too

The statement "P(A or B) = P(A) + P(B)" is False.

The correct statement is "P(A or B) = P(A) + P(B) - P(A and B)," which is known as the general law of addition for probabilities. This law takes into account the possibility of events A and B overlapping or occurring together.

The general law of addition for probabilities states that the probability of either event A or event B occurring is equal to the sum of their individual probabilities minus the probability of both events occurring simultaneously. This adjustment is necessary to avoid double-counting the probability of the intersection.

Let's consider a simple example. Suppose we have two events: A represents the probability of flipping a coin and getting heads, and B represents the probability of rolling a die and getting a 6. The probability of getting heads on a fair coin is 0.5 (P(A) = 0.5), and the probability of rolling a 6 on a fair die is 1/6 (P(B) = 1/6). If we assume that these events are independent, meaning the outcome of one does not affect the outcome of the other, then the probability of getting heads or rolling a 6 would be P(A or B) = P(A) + P(B) - P(A and B) = 0.5 + 1/6 - 0 = 7/12.

In summary, the general law of addition for probabilities states that when calculating the probability of two events occurring together or separately, we must account for the possibility of both events happening simultaneously by subtracting the probability of their intersection from the sum of their individual probabilities.

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d=3t relates Diego's walk distance and time. Two equations represent Elena and Andre's distance and time. In 8 hours, Diego walks 24 miles, Elena walks 16, and Andre 32 miles.

a. The equation d=3t relates the distance Diego walked to the time it took because d represents the distance and t represents the time. The equation states that the distance is equal to 3 times the time, meaning that as the time increases, the distance will increase by a factor of 3. This relationship makes sense because if Diego is walking at a constant pace, then the distance he covers is proportional to the amount of time he spends walking.

b. For Elena, the equation could be d=2t, which means that for every hour she walks, she covers a distance of 2 miles. For Andre, the equation could be d=4t, which means that for every hour he walks, he covers a distance of 4 miles.

c. For Diego, 8 hours of walking would result in a distance of

3 * 8 = 24 miles

For Elena, 8 hours of walking would result in a distance of

2 * 8 = 16 miles

And for Andre, 8 hours of walking would result in a distance of

4 * 8 = 32 miles.

d. In each of the equations, the distance is the dependent variable and the time is the independent variable. The dependent variable is dependent on the independent variable, so as the time changes, the distance changes accordingly.

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Answer: y=17 x=10

Step-by-step explanation:

so they have equal measures and they’re a linear pair (make a line) and a line is 180° so that would means you can set both equal to 90°

9y-63=90 and 9x=90

so for the first one you subtract 63 from 90 then divide by 9 to get 17

the next one you just divide by 9 to get 10 therefor y=17 and x=9

Answer:

A and B

Step-by-step explanation:

-3 and -2 are the only values less than or = to -2

the rest are greater than -2

Answer:

a and b

Step-by-step explanation:

a) \(-3\leq -2\)

b) \(-2\leq -2\)

c) \(0\leq -2\\\)

d) \(1\leq -2\)

e) \(2\leq -2\)