A scale factor that is less than 1, but greater than 0 is​

Answer: 5

Step-by-step explanation: f(3) = 2x - 1

substitute the x with 3. 2(3)-1

6-1

5

Answer:

The answer is 5, hope you like!

The value 0.9413 indicates a strong positive correlation between x and y.

What is probability?

Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.

a. First, we need to calculate the sample means of x and y:

x = (1+3+4+4+6+8+10+10+11+13)/10 = 6.0

y = (80+97+92+102+103+111+119+123+117+136)/10 = 105.2

Then, we can use the following formulas to calculate SST, SSR, and SSE:

SST = Σ(yi - y)2 = (80-105.2)2 + (97-105.2)2 + (92-105.2)2 + (102-105.2)2 + (103-105.2)2 + (111-105.2)2 + (119-105.2)2 + (123-105.2)2 + (117-105.2)2 + (136-105.2)2 = 1786.96

SSR = Σ(yi - y)2 = Σ(b0 + b1xi - y)2 = Σ(b0 + b1xi - (b0 + b1x))2 = b12Σ(xi - x)2 = 16.8(94) = 1581.6

SSE = Σ(yi - i)y2 = Σ(yi - b0 - b1xi)2 = SST - SSR = 1786.96 - 1581.6 = 205.36

b. The coefficient of determination r² is given by SSR/SST, so:

r² = SSR/SST = 1581.6/1786.96 = 0.8857

This means that 88.57% of the variation in y can be explained by the linear relationship with x. This is a relatively strong fit.

c. The sample correlation coefficient r can be calculated as the square root of r², so:

r = √0.8857 = 0.9413

Hence, the value 0.9413 indicates a strong positive correlation between x and y.

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As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.

Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB

Diameter is twice of radius.

The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius

According to the criteria of isosceles triangle angle OAB =OBA =40°

hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]

                  angle AOB= 100 degrees.

We get, AOB = 100 degrees

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Answer:

\(a \approx 30.00^\)

Step-by-step explanation:

Main concepts:

Concept 1: Angle of elevation

Concept 2: Right Triangle trigonometry

Concept 1: Angle of elevation

An angle of elevation is the angle measured between two rays, starting from straight-ahead, to another ray pointing upward.

If she stands 40m from the base of the tower, and the tower is 23.09m tall, then the diagram can be drawn as attached.

Concept 2: Right Triangle trigonometry

The three basic trigonometric functions are Sine, Cosine, and Tangent.  Each of these functions, when applied to an angle, gives the ratio of two sides of a right triangle that contains that angle:

\(sin(\theta)=\dfrac{opposite~side}{hypotenuse}\)

\(cos(\theta)=\dfrac{adjacent~side}{hypotenuse}\)

\(tan(\theta)=\dfrac{opposite~side}{adjacent~side}\)

These relationships are often memorized with SoaCahToa, where, the S, C, or T, represent the Sine, Cosine, and Tangent, functions, and the "o", "a", or "h", represent the opposite side, the adjacent side, or the hypotenuse (the side across from the right angle).

Picking up from the diagram, we're trying to find the angle "a", and we know two sides of a right triangle, so we need to identify which trigonometric function uses the two given sides, relative to angle "a".

For angle "a", the 40m distance to the tower is the adjacent side of the triangle (touching both the right angle, and the angle "a"), and the 23.09m tower height is the opposite side (touching the right angle, but not touching the angle "a").

Given that the known sides are "opposite" and "adjacent", we'll need to use the Tangent function:

\(\tan(\theta)=\dfrac{opposite}{adjacent}\)

substituting known values...

\(\tan(a^o)=\dfrac{(23.09~m)}{(40~m)}\)

simplifying units...

\(\tan(a^o)=\dfrac{23.09}{40}\)

applying arctan to both sides to undo the tangent function, and evaluating ...

\(\arctan ( ~tan(a^o)~)=\arctan \left (\dfrac{23.09}{40} \right)\)

\(a^o=\arctan \left (\dfrac{23.09}{40} \right)\)

\(a^o=29.99569...^o\)

Rounding to the nearest hundredth...

\(a^o \approx 30.00^o\)

Noting that the problem says that the angle of elevation is "a degrees", so "a" is just a number (without degrees).

\(a \approx 30.00^\)

Step-by-step explanation:

base is 12, hypotenuse is 20

so X² is h²-b²

so X=16

The given function, f(x) = x + 4 is increasing on the entire interval of 2≤x≤5

From the question, we are to determine if the given function is increasing or decreasing over the given interval

The given function is

f(x) = x + 4

To determine if the function f(x)=x+4 is increasing or decreasing on the interval of 2≤x≤5, we need to look at the sign of the first derivative of the function on that interval.

The first derivative of the function is

f'(x) = 1

Which is always positive

This means that the function is increasing on the entire interval of 2≤x≤5.

To justify this, we can also look at the graph of the function, which is a straight line with a positive slope. Any line with a positive slope is always increasing, so this confirms our conclusion that the function is increasing on the given interval.

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The main answer is that the infinite number of types of matter arises from the unique combinations of elements and their arrangements in terms of composition and geometry.

While the number of elements is limited, their combinations and arrangements allow for an infinite number of types of matter. Elements can combine in different ratios and configurations, forming various compounds and structures with distinct properties.

Additionally, the arrangement of atoms within a molecule or the spatial arrangement of molecules within a material can create different types of matter. These factors, along with the possibility of isotopes and different states of matter, contribute to the vast diversity and infinite types of matter despite the limited number of elements.

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Total possible arrangements are 55,450

Multiply the number of opportunities for each event by its own X times, where X equals the number of occurrences in the sequence.

A child possesses 12 blocks, six of that are black, three of which are red, two of which are white, and one of which is blue. If the child arranges the blocks in a line, we must determine the best possible arrangement.

If the child arranges the blocks in a line, the following arrangements are possible:

As a result, the arrangements could be as follows:

\(= > \frac{12!}{6!3!2!1!}\)

=> (12 × 11 × 10 × 9 × 8 × 7 × 6! )/ 3 × 2 × 1 ×2 × 6!

=> 55,440

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The combined present worth of the costs associated with the proposed bridge design, including construction and annual operating costs, is $10,583,333.

To calculate the combined present worth of costs, we need to consider the construction cost and the annual operating cost over the infinite life of the bridge. We will use the concept of present worth, which is the equivalent value of future costs in today's dollars.

The present worth of the construction cost is simply the initial cost itself, which is $9,000,000. This cost is already in present value terms.

For the annual operating cost, we need to calculate the present worth of perpetuity. A perpetuity is a series of equal payments that continue indefinitely. In this case, the annual operating cost of $700,000 represents an equal payment.

To calculate the present worth of the perpetuity, we can use the formula PW = A / MARR,

where PW is the present worth, A is the annual payment, and MARR is the minimum attractive rate of return (also known as the discount rate). Here, the MARR is given as 12%.

Plugging in the values, we have PW = $700,000 / 0.12 = $5,833,333.

Adding the present worth of the construction cost and the present worth of the perpetuity, we get $9,000,000 + $5,833,333 = $14,833,333.

However, since we are looking for the combined present worth, we need to subtract the salvage value, which is zero in this case. Therefore, the combined present worth of the costs associated with the proposed bridge design is $14,833,333 - $4,250,000 = $10,583,333, rounded to the nearest dollar.

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To determine the particle's position at time t = 0.6 s, we need to integrate the acceleration function with respect to time. Given that the initial position x₀ and initial velocity vₓ₀ are both zero, we can calculate the position using the following steps:

First, integrate the given acceleration function to obtain the velocity function:

vₓ(t) = ∫aₓ(t) dt

∫(8t³ - 500t⁵ + 6) dt = 2t⁴ - 100t⁶ + 6t + C₁

Next, integrate the velocity function to find the position function:

x(t) = ∫vₓ(t) dt

∫(2t⁴ - 100t⁶ + 6t + C₁) dt = (2/5)t⁵ - (100/7)t⁷ + 3t² + C₁t + C₂

Since we know that x₀ = 0 and vₓ₀ = 0 at t = 0, we can substitute these values to determine the constants C₁ and C₂:

x(0) = (2/5)(0)⁵ - (100/7)(0)⁷ + 3(0)² + C₁(0) + C₂

0 = 0 - 0 + 0 + 0 + C₂

C₂ = 0

Now, we can substitute the values of C₁ and C₂ back into the position function:

x(t) = (2/5)t⁵ - (100/7)t⁷ + 3t²

Finally, we can find the particle's position at t = 0.6 s:

x(0.6) = (2/5)(0.6)⁵ - (100/7)(0.6)⁷ + 3(0.6)²

Calculating this expression will give us the position of the particle at t = 0.6 s.

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Answer:

8

Step-by-step explanation:

357÷17=21

168÷21=8

so $357 divided by the 17 hours is 21

then you do the $21 per hour multiplied by the money is what he makes then divide 21 and 168

The solution to the equation f(x) - g(x)=0 is the x-intercept of the two lines, which is the point at which the two lines intersect.

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The midpoint formula and the normal vector of the plane can be used to determine the equation of the plane that contains all points equidistant from the points (1,0,-2) and (3,4,0).

Given by: The midpoint of the two points is:

M = [(1 + 3)/2, (0 + 4)/2, (-2 + 0)/2] = (2, 2, -1) (2, 2, -1)

The following vector runs between the two points:

V = (3 - 1, 4 - 0, 0 - (-2)) = (2, 4, 2) (2, 4, 2)

The cross product of two non-parallel plane vectors yields the normal vector to the plane. The midpoint M to a point on the plane is one such vector, while the other is the vector V. Consider the point P = (2, 2, -1) + t(2, 4, 2) as an illustration, where t is a scalar.

The normal vector is then provided by:

N = V x (P - M) = (2, 4, 2) x (2t, 4t, 2t -1), which equals (12t, -8t, 4t + 2)

The point-normal form, which makes use of the normal vector N and the point M, can be used to determine the equation for the plane:

(x - 2) * 12t = (y - 2) * -8t = (z + 1) * 4t + 2

The final equation of the plane is obtained by multiplying both sides of the equation by t and setting t 0.

12(x - 2) = -8(y - 2) = 4(z + 1) + 2

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The probability of winning in the described dice game can be calculated by considering the possible outcomes and their corresponding probabilities.

On the first roll, there are three favorable outcomes to win: rolling a total of 7 or 11. There are 36 equally likely outcomes in total (since each die has 6 faces and there are two dice), so the probability of winning on the first roll is 3/36 or 1/12.

If a point is established (any number other than 2, 3, 7, 11, or 12), the game continues. In this case, there are two ways to win: rolling the point value before rolling a 7. The probability of rolling the point before a 7 depends on the specific point value.

For example, if the point is 4, there are 3 ways to win (rolling a 4) and 6 ways to lose (rolling a 7), so the probability of winning in this case is 3/9 or 1/3.

To calculate the overall probability of winning, we need to consider both the probability of winning on the first roll and the probability of winning after establishing a point. These probabilities need to be weighted based on the likelihood of each scenario.

Since the probability of establishing a point on the first roll is 1 - (3/36 + 2/36) = 31/36, the overall probability of winning can be calculated as follows:

Probability of winning = (1/12) + (31/36) * (probability of winning after establishing a point)

The probability of winning after establishing a point depends on the specific point value and the number of ways to win and lose from that point. This probability varies depending on the point and can be calculated individually.

By combining the probabilities of winning from the first roll and winning after establishing a point for all possible point values, we can determine the overall probability of winning in the dice game.

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The option that is true based on the given information about the survey is; There is evidence of nonresponse bias in the survey results.

We are told that the researcher mails a survey to a random sample of 7,500 students out of all home-schooled students in the US.

Now, a total of 4,195 out of the 7,500 respond and 39% say they prefer to learn at home.

This means that not all those who received the mail responded and as such we can say that there is evidence of nonresponse bias because it occurs when survey participants are unwilling or unable to respond to a survey question or an entire survey.

In this case, those who failed to respond may be indifferent or even influenced by something else at home and as such this is not a true representation of the research.

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Each person buys a number of cakes

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy

So,

Andy has = x Cakes

Betty have = 4x Cakes

Clin has = x +3 Cakes

Since each cake costs 65p and the total cost of the cakes is £52.65

thus,

0.65( x + 4x + x +3) = 52.62

x + 4x + x +3 = 81

6x = 78

x = 13

Therefore,

Andy has = 13 cakes

Betty has = 4x = 4*13 = 52 cakes

Colin has = x + 3 = 16 cakes

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Answer:

if 5 people =1 hour. which is 60 minutes.

so 8people.52 minutes ...it wont take hours .since an hour is 60 min.

Answer:

Step-by-step explanation:

Let's solve:

\( \mathsf {people \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: time( \: in \: minutes) }\)

\( \mathsf{5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 hour = 60 minutes}\)

\( \mathsf{8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x}\)

Here, Let 8 people take x minutes to complete the work.

Since, the number of people and their working minutes are indirect proportional. So,

Here, the ratio of people = 5 : 8

The ratio of minutes = 60 : x

So,

\( \mathsf{ \frac{5}{8} = \frac{x}{60} }\)

Apply cross product property

⇒\( \mathsf{8x = 60 \times 5}\)

Multiply the numbers

⇒\( \mathsf{8x = 300}\)

Divide both sides of the equation by 8

⇒\( \mathsf {\frac{8x}{8} = \frac{300}{8} }\)

Calculate

⇒\( \mathsf{x = 37.5 \: minutes}\)

Hope I helped!

Best regards!

Test the hypothesis step of the scientific method is he performing.

Making conjectures (hypothetical explanations) is a step in the scientific method. Predictions are then derived from the hypotheses as logical conclusions, and experiments or actual observations are conducted based on those predictions.

Since at least the 17th century, the scientific method—an empirical approach to learning—has guided the advancement of science. Since one's interpretation of the observation may be distorted by cognitive presumptions, it requires careful observation and the application of severe skepticism regarding what is observed.

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Answer:

the probability is 25/144 or about 0.174

Step-by-step explanation:

his chance of not getting the shot is 5/12, so multiply 5/12×5/12 to get the chance of him missing both.

Mario usually makes 7 out of 12 shots, the probability that mario will NOT make either of his next 2 shots is 25/144

To solve the problem, let us define probability

This is the likelihood of an event. Probability is given mathematically as P(event) = no of required outcomes/total number of outcomes

Since Mario makes 7 out of 12 shots, the probability that he makes a shot is P(shot) = 7/12. The probability that he makes no shot is

P(no shot) = 1 - P(shot)

= 1 - 7/12

= 5/12

Since Mario's shots are independent events, the probability of his first shot does not affect that of the second. So, the probability that Mario will not make either ofhis next 2 shots is

P(no 2 shot) = P(no first shot) × P(no second shot)

= P(no shot) × P(no shot)

= 5/12 × 5/12

= 25/144

So, since Mario is practicing ice hockey and usually makes 7 out of 12 shots, the probability that mario will NOT make either of his next 2 shots is 25/144

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600ft³ will be the required volume

The formula for calculating the volume of the rectangular prism is expressed as:

Given the following information

l = 10 feet

w = 15feet

h = 12 feet

Get the volume

V = 1/3(10 * 15 *12)

V = 1/3(1800ft³)

V = 600ft³

Hence 600ft³ will be the required volume

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The probability that an outcome of 5 appears before an outcome of 7 is 1.

The probability of getting a 5 or a 7 in one roll of two fair dice is 6/36 = 1/6. The probability of getting a 5 before a 7 is equal to the sum of the infinite geometric series with the first term being 1/6 and common ratio 5/6:

1/6 + (5/6) * (1/6) + (5/6)² * (1/6) + ... = 1/6 / (1 - (5/6)) = 1/6 / (1/6) = 1.

So, the answer is 1.

The method used here is called the Geometric Series formula. It is used to calculate the sum of an infinite geometric series, which is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed constant called the common ratio. The formula for the sum of an infinite geometric series is:

S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.

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Answer:

\(volume = 2304\pi \ mm^3\\\\volume = 7234.56 \ mm^3\)

Step-by-step explanation:

Radius , r = 12mm

\(Volume = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (12^3)\\\\\)

                      \(=\frac{4}{3} \pi \times 1728\\\\= 4\pi \times 576\\\\= 2304 \pi \ mm^3\\\\or \\\\= 7234.56 \ mm^3\)

The number of significant figures that the digits given have are;

1) 3

2) 2

3) 4

Significant figures are defined as the number of digits in a value, which is often a measurement, that contributes to the degree of accuracy of the value.

Some of the rules for counting significant figures are;

- All non-zero  digits and any zeros contained between non - zero digits count e.g 300042 has 6 significant digits

- Leading zeros don't count e.g 0.000254 has only 3 significant figures.

- Trailing zeros count if there is a decimal point e.g 0.0002500 has 4 significant figures.

- Trailing zeros will not count if there is no decimal point e.g 180000 has only 2 significant figures.

1) 90500 Kg; This has only 3 significant figures when applying rule 1 and 4 above.

2) 7.1 x 10 ml = 71 ml; This clearly has 2 significant figures.

3) 0.004300; Applying rule 3 above, this has 4 significant figures.

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Laptop- 44, Tablet- 94, Desktop- 62, Percentage of tablets- 47%.

To calculate the percentage of devices that are tablets, we need to find the proportion of tablets among all devices. In this case, there are 94 tablets out of a total of 200 devices (44 laptops + 94 tablets + 62 desktops).

To find the proportion, we divide the number of tablets by the total number of devices: 94/200 = 0.47.

To convert this proportion to a percentage, we multiply by 100: 0.47 * 100 = 47%.

47% of the devices owned by the local company are tablets.

This means that nearly half of the devices fall into the tablet category, making it a significant portion of their device inventory.

It's important to note that this calculation assumes the given numbers accurately represent the actual device distribution and that there are no missing or unaccounted devices.

By determining the percentage of tablets, we gain insight into the composition of the device inventory, which can be useful for decision-making and resource allocation within the local company.

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Answer: 7 is the opposite of negative 7

Step-by-step explanation:

Hope this helps :)

Answer:

Elena made 10 batches.

Step-by-step explanation:

1 batch uses 2/3 cup

Elena used 6 2/3 cup

The number of batches is the quotient of 6 2/3 and 2/3.

We need to divide 6 2/3 by 2/3. First, we convert 6 2/3 into a fraction.

6 2/3 ÷ 2/3 = 20/3 ÷ 2/3 = 20/3 × 3/2 = 10

Answer: Elena made 10 batches.

Answer:

10

Step-by-step explanation:

2/3 for 1 cup if he used 6 2/3 of sugar then its 10.

if you times 2/3 by 10 its 6.66 and 6.66 is 2/3

1/3=33

2/3=66

3/3=100

Option B is the true statement based on the given information by solving the method of average.

In mathematics, the average (also called the arithmetic mean) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of values in the set.

Since both tests had a median score of 78, we know that there were nine scores below 78 and nine scores above 78 on each test.

If the original test had a range of 20, that means the highest score was 20 points above the lowest score. Therefore, the lowest score on the original test was 78 - 10 = 68, and the highest score was 68 + 20 = 88.

If the retest had a range of 2, that means the highest score was only 1 point above the lowest score. Therefore, the lowest score on the retest was 78 - 1 = 77, and the highest score was 77 + 2 = 79.

We don't know the mean score for either test, so we cannot determine if option A is true or false. We also don't know if any student scored exactly 78 on the retest, so we cannot determine if option C is true or false. Finally, we know that the highest score on the retest is 79, so option D is false.

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The normal approximation to the binomial distribution also implies that the sampling distribution of p is roughly bell-shaped, as the normal distribution is. Therefore, the answer is A) The shape.

The sampling distribution of the proportion is the distribution of all possible values of the sample proportion that can be calculated from all possible samples of a certain size taken from a particular population in statistical theory. The state of the examining dispersion of p is generally chime molded, as it is an illustration of a binomial conveyance with enormous n and moderate p.

The example size (n=900) is sufficiently enormous to legitimize utilizing an ordinary guess to the binomial dissemination, as indicated by as far as possible hypothesis. In order for the binomial distribution to be roughly normal, a sample size of at least 30 must be present, which is achieved.

Subsequently, the examining dispersion of p can be thought to be around ordinary with a mean of 0.532 and a standard deviation of roughly 0.0185 (involving the equation for the standard deviation of a binomial distribution).The typical estimate to the binomial dissemination likewise infers that the inspecting conveyance of p is generally chime molded, as the ordinary circulation is. As a result, A) The shape is the response.

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