A study was performed on a type of bearing to find the relationship of amount of wear y to x1 = oil viscosity and x2 = load. The following data were obtained. Estimate the unknown parameter for x1 of the multiple linear regression equation. Use 4 decimal places.
y x1 x2 y x1 x2
193 1.6 851 230 15.5 816
172 22.0 1058 91 43.0 1201
113 33.0 1357 125 40.0 1115

x<5-3

x<2

so your answer is

\( - \infty < x < 2\)

Question:

x + 3 < 5, Find x.

Answer

⟹ x + 3 < 5

( Subtracting 3 from both the sides of the inequality )

⟹ ( x + 3) - 3 < 5 - 3

⟹ x < 5 - 3

⟹ x < 2

It means that any number that is smaller than 2 will satisfy the inequality.

Answer:

Step-by-step explanation:

There are 10 cubes all together.

You want blue and then red with replacement.

Blue

P(B then red) = 3/10 * 4/10 = 12 / 100

12/100 reduces to 3/25

The answer is A

Answer:

A?

Step-by-step explanation:

The values for c and d are c=4 and d=2, and the answer is B.

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

A line with slope 2 passes through the points P(-3,-2), A(0,c), and B(d,8).

What are the values for c and d?

A. c=3 and d=9

B. c=4 and d=2

C. c=4 and d=4

D. c=7 and d=5

To solve for c and d, we can use the fact that the line passes through two points: P and A. The slope of the line is given as 2, so we can write the equation of the line using point-slope form:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. Using point P(-3,-2) and slope m=2, we get:

y - (-2) = 2(x - (-3))

y + 2 = 2(x + 3)

y + 2 = 2x + 6

y = 2x + 4

Now we can use the fact that the line passes through point A(0,c) to solve for c:

c = 2(0) + 4

c = 4

To solve for d, we can use the fact that the line also passes through point B(d,8). We know that the y-coordinate of point B is 8, so we can substitute this into the equation of the line:

8 = 2d + 4

4 = 2d

d = 2

Therefore, the values for c and d are c=4 and d=2, and the answer is B.

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Answer:

r=8

Step-by-step explanation:

The number we are looking for is represented by 'r' which is multiplied by 8

Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

Answer:

A. One point greater than the last test grade.

Step-by-step explanation:

One point greater than the last test grade can be written as an expression:n + 1

The difference of Gina’s score and one can be written as an expression:

n - 1

The total cost less one dollar can be written as an expression: n - 1

One minute less than Mickey’s previous time can be written as an expression: n - 1

Answer:

Step-by-step explanation:

its A

Answer:

x = 1 1/4

Step-by-step explanation:

6x - 1 = -2x + 9

Move the x to one side and the numbers to the other side:

8x = 10

Simplify:

x = 10/8 = 5/4 = 1 1/4

The difference quotient of \(f(x) = x^2 - 6x + 5\) is is 2x - 6 + h.

To find the difference quotient for the function \(f(x) = x^2 - 6x + 5\), we need to evaluate

(f(x + h) - f(x)) / h, where h is not equal to 0.

First, let's find f(x + h):

\(f(x + h) = (x + h)^2 - 6(x + h) + 5\)

\(= x^2 + 2hx + h^2 - 6x - 6h + 5\)

\(= x^2 - 6x + 5 + 2hx - 6h + h^2\)

Now, we can substitute the values of f(x + h) and f(x) into the difference quotient:

\((f(x + h) - f(x)) / h = ((x^2 - 6x + 5 + 2hx - 6h + h^2) - (x^2 - 6x + 5)) / h\)

= (2hx - 6h + h^2) / h

= 2x - 6 + h

Therefore, the difference quotient of \(f(x) = x^2 - 6x + 5\) is 2x - 6 + h.

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a) This study is observational because the researchers are observing and comparing groups based on self-reported apple consumption, without actively manipulating the variables.

b) Confounding occurs when an additional variable associated with both the exposure and outcome introduces bias. An example could be oral hygiene habits, which could confound the relationship between apple consumption and cavities.

c) No, one cannot conclude that lower cavities are solely due to eating an apple a day. Other factors or confounding variables could be at play. Experimental studies are needed to establish causality.

Let us analyze in a detailed way:

a) This study is an observational study rather than an experiment because the researchers are not actively manipulating the variables. They are observing and comparing the number of new cavities in two groups of people based on their self-reported apple consumption. The individuals in each group already have their eating habits established, and the researchers are merely observing and recording the outcomes.

b) In the context of the study, confounding refers to the presence of an additional variable that is associated with both the exposure (eating an apple a day) and the outcome (number of new cavities), leading to a potential bias in the results. It can be challenging to determine whether the observed effect is solely due to the apple consumption or if it is influenced by the confounding variable. An example of a possible confounding variable in this study could be oral hygiene habits. If individuals who eat an apple a day also have better oral hygiene practices, such as regular brushing and flossing, this could confound the relationship between apple consumption and the number of new cavities.

c) No, one cannot conclude that the lower number of cavities can be attributed solely to eating an apple a day. Even if the mean number of new cavities is significantly smaller in the group that eats an apple a day, there may be confounding factors or other variables at play that contribute to the observed difference. In order to establish a causal relationship between apple consumption and the number of new cavities, a randomized controlled trial or an experimental study would be needed, where participants are randomly assigned to the apple consumption groups and other potential confounding variables are controlled.

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An observational study is being conducted to determine if there is a difference in the number of new cavities between people who eat an apple a day and those who eat less than one apple a week. confounding is a concept in observational studies where an extraneous variable associated with both the exposure (apple consumption) and the outcome (number of new cavities) can distort the relationship. The mean number of new cavities being significantly smaller in the group that eats an apple a day does not establish causation. Additional research, such as a randomized controlled experiment, is needed to determine if the lower number of cavities can be attributed to eating an apple a day.

In this dental study, the dentists are conducting an observational study to determine if there is a difference in the number of new cavities between people who eat an apple a day and those who eat less than one apple a week. An observational study is a type of study where researchers observe and collect data on individuals without intervening or manipulating any variables. In this case, the dentists are not assigning people to specific groups or controlling their apple consumption; instead, they are simply observing and comparing the number of new cavities in two groups of people based on their self-reported apple consumption.

confounding is a concept in observational studies where an extraneous variable, known as a confounding variable, is associated with both the exposure (apple consumption) and the outcome (number of new cavities). This confounding variable can distort the relationship between the exposure and the outcome, leading to incorrect conclusions. For example, a possible confounding variable in this study could be oral hygiene habits. If people who eat an apple a day also have better oral hygiene habits, it could be the oral hygiene habits rather than the apple consumption that is responsible for the lower number of cavities.

To determine if the lower number of cavities can be attributed to eating an apple a day, additional research is needed. The mean number of new cavities being significantly smaller in the group that eats an apple a day compared to the group that eats less than one apple a week suggests an association, but it does not establish causation. Other factors, such as oral hygiene habits, diet, genetics, or socioeconomic status, could be confounding variables that contribute to the observed difference. To establish a causal relationship, a randomized controlled experiment would be necessary, where participants are randomly assigned to either eat an apple a day or not and their cavities are monitored over time.

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Answer:

2.025, 2.25, 2.2582, 2.4

Step-by-step explanation:

The standard deviation for the given data is c. 0.024 cm.

Let's calculate the standard deviation using the given data:

Diameters: 0.493, 0.534, 0.527, 0.511, 0.565, 0.559, 0.519, 0.562, 0.551, and 0.530.

Find the mean:

Mean = (0.493 + 0.534 + 0.527 + 0.511 + 0.565 + 0.559 + 0.519 + 0.562 + 0.551 + 0.530) / 10

Mean ≈ 0.5411 cm

Calculate the squared differences:

\((0.493 - 0.5411)^2, (0.534 - 0.5411)^2, (0.527 - 0.5411)^2, (0.511 - 0.5411)^2, (0.565 - 0.5411)^2, (0.559 - 0.5411)^2, (0.519 - 0.5411)^2, (0.562 - 0.5411)^2, (0.551 - 0.5411)^2, (0.530 - 0.5411)^2\)

Find the average of the squared differences:

Average = (sum of squared differences) / 10

Take the square root of the average to get the standard deviation.

By calculating the above steps, the standard deviation of the given data set is approximately 0.024 cm.

Therefore, the correct answer is c. 0.024 cm.

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Answer:

It decreases.

Step-by-step explanation:

$4.28 will go up because it is greater.

Answer:

Image result for Three vertices of a rectangle are (6,1), (3,1), and (3,8). What are the coordinates of the fourth vertex?

One would be to divide the rectangle into two triangles, then use the Pythagorean Theorem to find the distances between the points, and finally use Heron's formula to find the areas of the two triangles.

To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2.

Step-by-step explanation:

The number of squares of the given scales required to make a square of 1 m is:

a) 1 square: 1 m = 1.

b) 1 square: 25 cm = 16.

c) 1 square: 20 cm = 25.

d) 1 square: 0.5 m = 4.

In the question, we are asked the number of squares of the given scales required to make a square of 1 m.

The area of the square of 1 m is 1 m * 1 m = 1 m² = 10000 cm².

a) 1 square: 1 m

The area of the given square = 1 m * 1 m = 1 m².

The area of the required square = 1 m².

The number of squares required = The area of the required square/The area of the given square,

or, the number of squares required = 1 m²/1 m² = 1.

b) 1 square: 25 cm.

The area of the given square = 25 cm * 25 cm = 625 cm².

The area of the required square = 10000 cm².

The number of squares required = The area of the required square/The area of the given square,

or, the number of squares required = 10000 cm²/625 cm² = 16.

c) 1 square: 20 cm.

The area of the given square = 20 cm * 20 cm = 400 cm².

The area of the required square = 10000 cm².

The number of squares required = The area of the required square/The area of the given square,

or, the number of squares required = 10000 cm²/400 cm² = 25.

d) 1 square: 0.5 m

The area of the given square = 0.5 m * 0.5 m = 0.25 m².

The area of the required square = 1 m².

The number of squares required = The area of the required square/The area of the given square,

or, the number of squares required = 1 m²/0.25 m² = 4.

Thus, the number of squares of the given scales required to make a square of 1 m is:

a) 1 square: 1 m = 1.

b) 1 square: 25 cm = 16.

c) 1 square: 20 cm = 25.

d) 1 square: 0.5 m = 4.

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Answer:

x = 20°

explanation:

solve:

5x + 35 + 45 = 180°

5x + 80° = 180°

5x = 100°

x = 20°

-:x less than or equal to-7.8

-3x -2 is less than or equal to 6

collect like terms

-3x is less than or equal to 8

x= 8/-3

x is less than or equal to -7.8

This restricted portion of the fundamental niche that Chthamalus can effectively utilize in the presence of competition is referred to as its realized niche.

The weaker competitor is forced to retreat to a more restricted niche (its realized niche) than it would inhabit in the absence of the competition when interspecific interactions result in competitive exclusion.

For Chthamalus, a typical intertidal barnacle animal categories, its key specialty alludes to the full scope of ecological circumstances and assets it is hypothetically fit for taking advantage of without rivalry. Chthamalus would occupy its entire fundamental niche in the absence of competition.

However, Chthamalus is outcompeted and forced to withdraw from a portion of its fundamental niche when competing with a stronger competitor, such as Balanus, the dominant barnacle species. This limited part of the essential specialty that Chthamalus can actually use within the sight of contest is alluded to as its acknowledged specialty.

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The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.

A number can be obtained by multiplying the square root by itself. Square root is represented by the symbol sqrt, which stands for square root of, end square root. The reverse of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number can be found by looking for a number that, when squared, yields the original value. If 'a' is the square root of 'b,' then a a = b.

given

Use the average rate of change formula to substitute.

(√1)−(√−4) / (1)−(−4)

Condense the phrase.

1/5−2i/5

The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.

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π/16 is the area enclosed by the curve r= sin(4θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)

where a and b is the boundary at which r=0

so after equation r=0

sin(4θ) =0

=> sin(4θ) =0

=> 4θ = 0,π

=> θ = 0, π/4

so a=0 , b= π/4

now  

  A =  \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)   ------(i)

so   \(r^2\) = (sin(4θ))^2

=>   \(sin^2\)( 4θ )

ans we know that

cos(2α) = 1 -  \(2sin^2\)2 α

so     \(sin^2\)= (1- cos(8θ) )/2

putting the value of r in the equation (i) we get :-

A = \(\int\limits^b_a {\frac{1}{4} *(1-cos8\theta) } \, d\theta\)

=> 1/4*  \(\int\limits^b_a {(1-cos8\theta) } \, d\theta\)

here a=0 and b=π/4

after putting the value and solving the integral

A = π/16

so A is the area enclosed by r=sin(4θ) is π/16

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The experiment involves a 200 g air-track glider attached to a spring, which is pushed in 9.20 cm and released. The glider undergoes oscillations, and a student measures that 11.0 oscillations take 13.0 s.

Using this data, the period, frequency, and spring constant of the oscillation can be calculated.

The period of the oscillation is the time it takes for one complete oscillation. It can be calculated by dividing the total time by the number of oscillations. In this case, the period is 1.18 s. The frequency of the oscillation is the number of oscillations per unit time, and can be calculated by taking the reciprocal of the period. The frequency is 0.85 Hz.

The spring constant can be calculated using the equation for the period of a mass-spring system: T = 2π√(m/k), where T is the period, m is the mass of the glider, and k is the spring constant. Rearranging this equation, we get k = (4π^2m)/T^2. Substituting the values for m and T, we can find the spring constant to be 4.36 N/m.

The experiment demonstrates the principles of simpe harmonic motion, which is the motion of an object back and forth around its equilibriulm position under the influence of a restoring force, such as the force exerted by a spring. The period and frequency of the oscillation depend on the mass of the object and the spring constant. The larger the mass or the smaller the spring constant, the longer the period and the lower the frequency. Conversely, the smaller the mass or the larger the spring constant, the shorter the period and the higher the frequency. The experiment also shows the importance of measuring and analyzing data accurately in order to make valid conclusions about physical phenomena.

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Answer:

100 3/13

Step-by-step explanation:

1,303 ÷ 13= 100 3/13

Answer:

=6×3/4×3

Now, 3cut3

=6×4

=24

Answer:

A is correct

Step-by-step explanation:

The required solution for the given inequality is -17 ≤ x ≤ 10, and this solution to inequality is represented by number line A.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given expression,
|2x + 7| ≤ 27

-27 ≤ 2x+7 ≤ 27
-34 ≤ 2x ≤ 20
-17 ≤ x ≤ 10

Thus, the required solution for the given inequality is -17 ≤ x ≤ 10, and this solution to inequality is represented by number line A.

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Answer:

The Great Western Trail = 4,455 miles

Step-by-step explanation:

The Iditarod Trail = 1,025 miles long

The Great Western Trail is 355 miles longer than 4 times the length of the Iditarod Trail.

The Great Western Trail = (4 × 1,025) miles + 355 miles

= 4,100 miles + 355 miles

= 4,455 miles

The Great Western Trail = 4,455 miles

Step-by-step explanation:

Prove the LHS

Using trigonometric identities

That's

Rewrite the expression

We have

So we have

Using trigonometric identities

Rewrite the expression

That's

Reduce the expression with cos a

We have the final answer as

As proven

Hope this helps you

Leading coefficient means the number that goes multiplicating the bigger exponent ,in this case is -9 because -9 multiplies x^3

Leading coefficient is the bigger exponent in a polynomial. In this case is 3 ,because -9x^3 is the biggest number in exponent.

So finally is a third degree equation.

Answer:

See Explanation

Step-by-step explanation:

\(15 = 3 \times \bold{ \red{ \boxed5}} \\ \\ 40 = 2 \times 2 \times 2 \times \bold{ \purple{ \boxed5}} \\ \\ common \: factor \: of \: 15 \: and \: 40= 5 \\ \\ \therefore \: gcf \: of \: 15 \: and \: 40 = 5\)

A vector is in the direction 39.0∘ clockwise from the −y-axis. The x-component of A is Ax = -18.0 m. What is the y-component of A? To determine the y-component of A, we will use the trigonometric ratio.

sinθ = opposite/hypotenuse where θ = 39.0°, hypotenuse = |A|, and opposite = Ay. Therefore, sinθ = opposite/hypotenuse Ay/|A| = sinθ ⟹ Ay = |A| sinθSince A is in the third quadrant, its y-component is negative.

Ay = - |A| sinθWe know the x-component and we know that it is negative, so the vector is in the third quadrant, and the y-component is negative.

Ax = -18.0 m, θ = 39.0°We know that the magnitude of A is:

A = √(Ax² + Ay²)Since Ax = -18.0 m, we can substitute it into the equation:

A = √((-18.0)² + Ay²)B) The magnitude of A is |A| = 19.4 m.

We can conclude that the y-component of A is -11.5 m, and the magnitude of A is 19.4 m.

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The y-component of vector A, given that the vector is pointing 39 degrees clockwise from the -y axis and has an x-component of -18 m, is approximately -14.67 m. The magnitude of this vector is about 23.03 m.

Firstly, since the vector A is pointing 39 degrees clockwise from the -y axis, it means our angle with respect to the standard x-axis is 180-39 = 141 degrees. We use the trigonometric relation cos(α) = Ax/A or Ax = A cos(α) to isolate A in the equation (magnitude of A), we get that A = Ax/cos(α). Substituting given values, we get A approximately equal to 23.03 m.

Then, the y-component can be found using sine relation: Ay = A sin(α). Substituting A=23.03 m and α= 141 degrees gives us Ay approximately equal to -14.67 m. Therefore, the y-component of A is -14.67 m and the magnitude of A is approximately 23.03 m.

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