4) Graph the line 2x - 7y = 14 using X- and y-intercepts.
x-intercept y-intercept
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O
YA
6
5
4
3
2
1
-6-5-4-3-2
1 2 3 4
5 6
2
-3
-5
-6
10:45


a) The Sample size is calculated to be  4,272 U.S. adults and count is 897. (b) Sample proportion is 0.21 or 21%. (c)The sample proportion is an estimate of the population proportion.

The sample size is 4,272 U.S. adults, and the count of those who regularly wear a smart watch or fitness tracker is 897.

To calculate the sample proportion, we divide the count of those who regularly wear a smart watch or fitness tracker by the sample size:

sample proportion = count / sample size

sample proportion = 897 / 4,272

sample proportion = 0.21 or 21%

Therefore, the sample proportion of U.S. adults who regularly wear a smart watch or fitness tracker is 21%.

The population proportion is the proportion of all U.S. adults who regularly wear a smart watch or fitness tracker, while the sample proportion is the proportion of U.S. adults in the sample who regularly wear a smart watch or fitness tracker.

The relationship between the two proportions is that the sample proportion is an estimate of the population proportion. The sample proportion provides a rough idea of the proportion of all U.S. adults who regularly wear a smart watch or fitness tracker, but it may not be exactly the same as the population proportion due to sampling error.

To get a more accurate estimate of the population proportion, we would need to take a larger and more representative sample or survey the entire population.

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Answer:

$7650.44

Step-by-step explanation:

Annual interest rate = 4.02%

but compound 4 times per year, means quarterly compound

quarterly interest rate = 4.02%/4 = 1.005%

Account balance = 4734 * (1.01005)^48 [compound 4 times a year for 12 years]

= 4734 * 1.616

= 7650.44

Answer:

D) $7,650.44

Step-by-step explanation:

Compound Interest Formula

\(\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}\)

where:

Given:

Substituting the given values into the formula and solving for A:

\(\large \text{$ \sf \implies 4734\left(1+\frac{0.0402}{4}\right)^{4 \times 12} =7650.435473$}\)

The algorithm we will use to merge k sorted lists into one sorted list is called the "k-way merge algorithm."

Create a min heap of size k and insert the first element of each input list into the heap.

Repeat the following steps until the heap is empty Extract the minimum element from the heap and add it to the output list and If the input list from which the minimum element was extracted is not empty, insert the next element from that list into the heap.

The time complexity of this algorithm is O(n log k), where n is the total number of elements in all the input lists, and k is the number of input lists.

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If p and n are positive integers and p > n. 0, 1, 5, 6, 9, and 11 are the remainders when p² - n² is divided by 15.

To find the remainder whilst (p² - n²) is split with the aid of 15, we are able to think of the expression p² - n² the usage of the distinction of squares method.

The distinction of squares formula states that a² - b² can be factored as (a + b)(a - b).

Applying this method to p² - n²;

p² - n² = (p + n)(p - n)

Now, we recognize that p and n are positive integers and p > n. This way that p + n and p - n are both advantageous integers.

To locate the remainder whilst (p^2 - n^2) is split through 15, we will take a look at the remainders of (p + n) and (p - n) when divided with the aid of 15.

Let's don't forget the viable remainders when dividing an integer by means of 15:

zero, 1, 2, 3, 4, five, 6, 7, eight, 9, 10, 11, 12, 13, 14

Since p + n and p - n are both high-quality integers, the feasible remainders when dividing them by way of 15 could be:

zero, 1, 2, three, 4, 5, 6, 7, eight, 9, 10, eleven, 12, thirteen, 14

Now, permits take into account the viable products of (p + n) and (p - n) while the remainder is multiplied:

0 * 0 = 0

1 * 14 = 14

2 * 13 = 26 (that's equal to eleven modulo 15)

3 * 12 = 36 (that's equal to six modulo 15)

4 * eleven = 44 (that's equivalent to fourteen modulo 15)

5 * 10 = 50 (which is equivalent to five modulo 15)

6 * 9 = 54 (that is equivalent to nine modulo 15)

7 * eight = 56 (that's equal to 11 modulo 15)

8 * 7 = 56 (that is equivalent to eleven modulo 15)

9 * 6 = 54 (that's equal to nine modulo 15)

10 * 5 = 50 (which is equivalent to 5 modulo 15)

11 * 4 = 44 (that's equivalent to fourteen modulo 15)

12 * 3 = 36 (that is equal to 6 modulo 15)

13 * 2 = 26 (that's equivalent to 11 modulo 15)

14 * 1 = 14

From the above merchandise, we will see that (p + n)(p - n) will have remainders of zero, 1, five, 6, 9, and eleven when divided via 15.

Therefore, the feasible remainders whilst () is split through 15 are 0, 1, 5, 6, nine, and 11.

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Thus, the probability that two people picked at random both own a dog is 0.1296 or 1296/10000.

To solve this problem, we need to use the formula for calculating the probability of independent events: P(A and B) = P(A) x P(B).

In this case, let A be the event that the first person owns a dog and B be the event that the second person owns a dog.

We know that P(A) = 0.36, or 36% chance that the first person owns a dog. Since the events are independent, P(B) is also 0.36.

So, the probability of both events occurring (both people owning dogs) is:

P(A and B) = P(A) x P(B)
= 0.36 x 0.36
= 0.1296

This can also be expressed as a fraction:

P(A and B) = 36/100 x 36/100
= 1296/10000

Therefore, the probability that two people picked at random both own a dog is 0.1296 or 1296/10000.

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The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.

Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.

Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

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The rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.

We know that,

The Base is growing at the rate of 1 cm per sec.

Height is growing at the rate of 2 cm per sec.

Area of triangle: 1/2 × b × h

The rate of change will be:

1/2 × b × h

1/2 × 4/1 × 7/2

28/4

7 cm per sec

Therefore, the rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.

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The relative frequency of randomly selected students whose favorite exhibit was either butterflies or trains is 36% (third option)

Relative frequency is the ratio of the frequency of a class to the total frequency.  

Relative frequency of randomly selected students whose favorite exhibit was either butterflies or trains = (number of students that chose butterflies / total frequency) + (number of students that chose trains / total frequency)

Total frequency = 12 +  25 +  17 + 6 = 50

= (12/50) + (6/50) = 18/50

(18/50) x 100 = 36%

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the total area under the standard normal curve to the left of z1 = -1.645 and to the right of z2 = 1.645 is approximately 0.

To find the total area under the standard normal curve to the left of z1 = -1.645 and to the right of z2 = 1.645, we can use the properties of the standard normal distribution.

The area to the left of z1 represents the cumulative probability from negative infinity up to z1, and the area to the right of z2 represents the cumulative probability from z2 up to positive infinity.

Using a standard normal distribution table or a calculator, we can find the cumulative probabilities associated with these z-values.

The cumulative probability to the left of z1 = -1.645 is approximately 0.0500 (rounded to four decimal places).

The cumulative probability to the right of z2 = 1.645 is also approximately 0.0500 (rounded to four decimal places).

To find the total area between z1 and z2, we subtract the cumulative probability to the right of z2 from the cumulative probability to the left of z1:

Total area = 0.0500 - 0.0500 = 0

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The total price of the racket is $192.60 (first option).

A tax is a compulsory amount of money that is levied by the government or an agency of the government on goods and services. A sales tax is levied on the sales of goods and services.

The total price of the racket would include the amount of tax that would be paid.

Total price = (1 + tax/100) x initial price

Total price = (1 + 7%/100) x $180

Total price = (1 + 0.07) x $180

Total price = (1,07 x $180)  

Total price = $192.60

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Answer:

7

Step-by-step explanation:

If the mpc increases in value, the consumption function will become steeper.

What is MPC ?

MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.

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The figure illustrates four different growth patterns: exponential growth (Curve A), logarithmic decay (Curve B), linear growth (Curve C), and sigmoidal growth (Curve D).

Curve A represents an exponential growth pattern. It starts with a relatively slow increase but gradually accelerates over time. This type of growth is commonly observed in natural phenomena like population growth or the spread of infectious diseases.

Curve B depicts a logarithmic decay pattern. It begins with a steep decline but levels off over time. Logarithmic decay is often seen when a process initially experiences rapid changes but eventually approaches a stable state or limiting factor.

Curve C displays a linear growth trend. It shows a constant and consistent increase over time. Linear growth is characterized by a steady rate of change and is commonly observed in situations where there is a constant input or output.

Curve D represents a sigmoidal growth pattern. It starts with a slow initial growth, then experiences rapid expansion, and finally levels off. Sigmoidal growth is prevalent in various fields, such as biology, economics, and technology, where a system initially has limited resources, undergoes rapid development, and eventually reaches a saturation point.

The figure illustrates four different growth patterns: exponential growth (Curve A), logarithmic decay (Curve B), linear growth (Curve C), and sigmoidal growth (Curve D).

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Answer:

Step-by-step explanation:

-150

Answer: -15x + 30

Step-by-step explanation:

-3(5x) = -15x (positive x negative = negative)

-3(-10) = 30 (negative x (negative = positive)

(same symbols = positive)

(Different symbols = negative)

Answer:

b

Step-by-step explanation:

Answer:

108

Step-by-step explanation:

324 = 2 * 2 * 3 * 3 * 3 * 3

432 = 2 * 2 * 2 * 2 * 3 * 3 * 3

The HCF is 2 * 2 * 3 * 3 * 3 = 108

Answer:

B

Step-by-step explanation:

\( \frac{1}{40} + x = \frac{1}{8} \)

\(40( \frac{1}{40}) + (40)x = 40( \frac{1}{8} )\)

\(1 + 40x = 5 \times 1\)

\(1 + 40x = 5\)

\(40x = 5 - 1\)

\(40x = 4\)

\( \frac{40x}{40} = \frac{4}{40} \)

\(x = \frac{1}{10} \)

Answer:

1/10

Step-by-step explanation:

You fall asleep under the shade of the tree. When you wake up, you notice that your shadow is now half as long as it was before, but is in the opposite direction. So you have slept around 6 hours and 20 minutes

Since the length of the shadow is proportional to the height of the object producing the shadow, we can solve this problem with comparable triangles.

Let S be the length of your shadow before sleeping, and T be the length of the tree's shadow. Also, make H your height.

Then there are two triangles that are similar:

your shadow / distance = H / S

The shadow of a tree /distance = H/ T

Using the facts provided, we have:

H = 5'6"

S = 8

T = 48

H /S = 5'6"/8

= 5.5 feet / 8

= 0.6875

H /T = 5'6"/48

= 5.5 feet / 48

= 0.1146

When you wake up, your shadow is half the length it was before, resulting in:

0.6875/2 = 0.34375

Since the two triangles are still similar, we can use this knowledge to calculate S:

H / (S/2) = 5.5/ (S/2)

5.5S = 2H

S = 2H/5.5

S = 2(0.6875)/5.5

S = 0.25

So, your shadow is 0.25 feet long, or 3 inches after sleeping. Because your shadow was half as long as it had been before, you must have slept for half the time the sun was up:

(18:20 - 5:40)/2 = 6 hours and 20 minutes

You slept for 6 hours and 20 minutes as a result.

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Answer:

V = 3322.6 ft³

Step-by-step explanation:

V(rt cone) = \(\frac{\pi r^2h}{3}\)

V = [π(17.2/2)²(14.3)] ÷ 3

V = π(8.6)²(14.3)

V = 73.96(14.3)π

V = 3322.6

Answer:

12

200+50=250

3,000/250=12

Answer:

(0,1) , (1,3) , (2,5) , (3,7) , (4,9) , (5,11) are examples of  points on the line

y = 2x + 1.

TRUE. As one performs multiple separate hypothesis tests, the risk of committing a Type I error (rejecting a true null hypothesis) accumulates.

This overall risk is referred to as the experiment-wise alpha level or family-wise error rate (FWER). It represents the probability of making at least one Type I error among all the conducted tests.

When multiple hypothesis tests are performed simultaneously or sequentially, the individual alpha levels (typically set at 0.05) for each test may no longer be appropriate. This is because if we conduct, for example, 20 separate tests with an alpha level of 0.05 for each test, the cumulative chance of committing at least one Type I error can be much higher than the desired 5%.

To control the experiment-wise error rate, various multiple comparison procedures and adjustments can be employed, such as the Bonferroni correction or the Holm-Bonferroni method. These methods aim to maintain a desired level of significance for the entire set of tests, reducing the risk of accumulating Type I errors.

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Step-by-step explanation:

MUN={1,2,3,4,6,8}

M intersection N={1,2}

hope it helps.

Step-by-step explanation:

M intersection N = { 1 , 2 }

hope it is helpful to you

Answer:

you should take notes

Step-by-step explanation:

why you should know this your teacher probally already taught you this already you should go back and take notes = )

50 m  is dimensions will require the least amount of fencing .

What is rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. It is also known as an equiangular quadrilateral for this reason.

                                          Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let x = length of the side parallel to the river

     y = length of each of the other two sides

Then xy = 5,000, so y = 5,000/x

Minimize:  L = length of the fence

L = x + 2y

 = x + 10,000/x, where x > 0

L' = 1 - 10,000/x2 = (x2 - 10,000)/x2

L' = 0 when x = 100 or -100

Since x can't be negative, x must be 100.

When 0 < x < 100, L' < 0.  So, L is decreasing.

When x > 100, L' > 0.  So L is increasing.

Therefore, L has a relative and absolute minimum when x = 100 m

                                                                                    y = 5,000/x = 50 m

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In one sweep, the area covered by the sprinkler is 77.19 sq ft (approx). The area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

We know that a rotating sprinkler can reach up to 14 feet through a 300-degree angle. Area covered by the sprinkler in one sweep = area of the sector whose radius = 14 feet and angle = 300°Area of sector = (θ / 360) × πr²Where θ = 300°, r = 14 ftArea of sector = (300/360)× π(14)²= 77.19 sq ft (approx) Therefore, the area covered by the sprinkler in one sweep is 77.19 sq ft (approx).

We need to find the total area of the lawn that receives water from this sprinkler. The sprinkler rotates 360 degrees, so it will cover a full circle whose radius is 14 feet. Area of a circle = πr²= π(14)²= 615.752 sq ft (approx) Therefore, the area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

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Answer:

$540

Step-by-step explanation:

Multiply 10.80 by the 5 sisters then divide your answer by 10%