How do science textbooks emphasis on individual scientists distort how science really works

Answer:

  D. r = -0.905 represents a stronger correlation because |-0.905| > |0.727|

Step-by-step explanation:

You want to know which value of r indicates a stronger​ correlation: r= 0.727 or r= - 0.905.

The correlation coefficient r is ±1 when the response variable value is perfectly predicted by the explanatory variable value. The closer the magnitude of r is to 1, the stronger the correlation. A value of r near zero indicates there is no correlation at all, and the explanatory variable has no predictive power with respect to the response variable.

  r = -0.905 indicates a stronger correlation than r = 0.727

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\(\text{If there are no real roots, then}\\\\~~~~~\text{Discriminant} < 0\\\\\implies b^2 -4ac < 0\\\\\implies (-8)^2 -4 \cdot 3 k < 0\\\\\implies 64-12k < 0\\\\\ \implies 12k > 64\\\\\implies k > \dfrac{64}{12}\\\\\implies k > \dfrac{16}3\\\\\text{Interval,}~ \left( \dfrac{16}3, ~\infty\right)\)

Answer:

all of them together or eahc seperate

Step-by-step explanation:

Explanation:

Point slope form in general is

y-y1 = m(x-x1)

Where m is the slope and (x1,y1) is the given point. From here you plug in the slope m = -3/4 and the point (x1,y1) = (4,2). There's not much to do from here.

Side note: parallel lines have equal slopes, but different y intercepts.

The inflection point is a point on a curve where the curvature changes sign.

In mathematics, an inflection point is a point on a curve where the curvature changes sign. More precisely, it is a point where the second derivative of the curve changes sign.

Intuitively, an inflection point marks a transition from a concave to a convex shape, or vice versa. In other words, the curve goes from curving downward to curving upward, or vice versa, at an inflection point.

Inflection points can have physical significance in various contexts. Inflection points are also important in the study of functions in calculus. In particular, they can be used to determine the concavity of a function and to find the intervals on which the function is concave up or down.

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The appropriate inference procedure for this scenario would be a hypothesis test for a proportion. Specifically, we want to test whether the true proportion of times a spun penny will land on heads is significantly different from a hypothesized value (usually 0.5, assuming the penny is fair).

To conduct this hypothesis test, we first need to specify the null and alternative hypotheses. The null hypothesis (H0) in this case would be that the true proportion of times the penny will land on heads is equal to some hypothesized value p0 (e.g., 0.5). The alternative hypothesis (Ha) would be that the true proportion is not equal to p0.

We can then use the sample proportion (i.e., the number of heads observed in the 50 spins divided by 50) to calculate a test statistic and p-value. The test statistic would typically be a z-score calculated as:

z = (p_hat - p0) / sqrt(p0*(1-p0)/n)

where p_hat is the sample proportion, n is the sample size (in this case, 50), and sqrt() denotes the square root function.

The p-value would then be calculated as the probability (under the null hypothesis) of observing a test statistic as extreme or more extreme than the one calculated from the data. This can be obtained using a standard normal distribution table or calculator.

If the p-value is less than a pre-specified significance level (e.g., alpha = 0.05), we reject the null hypothesis and conclude that there is evidence that the true proportion of times the penny lands on heads is different from p0. If the p-value is greater than alpha, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest that the true proportion is different from p0.

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tThe population in this scenario refers to the entire group of policyholders of the large automobile insurance company.

Set up the hypotheses ; Null hypothesis (H0): The mean age in the population of policyholders is 50.  Alternative hypothesis (Ha): The mean age in the population of policyholders is different from 50. Determine the significance level: The significance level is given as 5%.  Calculate the test statistic: The test statistic for a two-sample t-test is given by:
    t = (sample mean - hypothesized mean) / (standard error)

 In this case, the sample mean is 47.2, and the hypothesized mean is 50. The standard error can be calculated using the formula: standard error = sqrt(variance / sample size).  In this case, the variance is 121 and the sample size is 361. Calculate the degrees of freedom:  For a two-sample t-test, the degrees of freedom is calculated as the sum of the sample sizes minus 2.  In this case, the sample size is 361.  Determine the critical value:  Since the alternative hypothesis is two-tailed (different from 50), we divide the significance level by 2 (5% / 2) to get the critical value for each tail.

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The vector field is conservative and calculates its potential function does not exist as a function f F = ∇f.

To determine whether or not F is a conservative vector field, we need to check if the mixed partial derivatives of its components are equal. The vector field F can be written as F(x,y) = (2x - 3y)i + (-3x + 4y - 8)j.

To compute the mixed partial derivatives, we take the partial derivative of the y-component with respect to x, and the partial derivative of the x-component with respect to y. Doing so, we get:

∂Fy/∂x = -3

∂Fx/∂y = -3

Since these partial derivatives are not equal, we can conclude that F is not a conservative vector field.

Therefore, there does not exist a function f such that F = ∇f.

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The sampling method in which every nth member of the population is chosen to be a part of the process is known as systematic sampling. The value of n is calculated by dividing the total population by the sample size. It is a statistical method of selecting elements from a population.

Systematic sampling is one of the probability sampling techniques in which a sample is selected from a larger population. It is a form of non-random sampling that allows researchers to establish an ordered, systematic way of selecting subjects from a population.Systematic sampling is often used when there is a large population and a need for simplicity in selecting a sample. This method is advantageous in terms of its ease of implementation and efficient sampling.

A disadvantage of this method is the possibility of a skewed sample if the periodicity of the population is not taken into account.A systematic sample can be obtained by arranging the population elements in a particular order, for instance, alphabetical or chronological order, and then selecting every kth element, where k = population size / sample size. This method of sampling has been proven to be more efficient than other sampling methods when there is a need to cover a large population.

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The solution to the Equations is    x = 3, x = 7, x = 11,  x = -9,  x = 1.3,               x = -4, x = -4,x = -2,x = 11, x = 3.33,x = 7, x = 5,x = -4.

1. To solve 3(x+2)=15, we first distribute the 3 and get 3x + 6 = 15. Then, we subtract 6 from both sides and get 3x = 9. Finally, we divide both sides by 3 and get x = 3.

2. To solve 2(x+5)=24, we first distribute the 2 and get 2x + 10 = 24. Then, we subtract 10 from both sides and get 2x = 14. Finally, we divide both sides by 2 and get x = 7.

3. To solve 6(x-9)=12, we first distribute the 6 and get 6x - 54 = 12. Then, we add 54 to both sides and get 6x = 66. Finally, we divide both sides by 6 and get x = 11.

4. To solve 2(3x+5)= -44, we first distribute the 2 and get 6x + 10 = -44. Then, we subtract 10 from both sides and get 6x = -54. Finally, we divide both sides by 6 and get x = -9.

5. To solve 5(4x-3)=11, we first distribute the 5 and get 20x - 15 = 11. Then, we add 15 to both sides and get 20x = 26. Finally, we divide both sides by 20 and get x = 1.3.

6. To solve -3(2x+1)=21, we first distribute the -3 and get -6x - 3 = 21. Then, we add 3 to both sides and get -6x = 24. Finally, we divide both sides by -6 and get x = -4.

7. To solve -9(x-4)=54, we first distribute the -9 and get -9x + 36 = 54. Then, we subtract 36 from both sides and get -9x = 18. Finally, we divide both sides by -9 and get x = -2.

8. To solve 7(x-4)-3=46, we first distribute the 7 and get 7x - 28 - 3 = 46. Then, we combine like terms and get 7x - 31 = 46. Then, we add 31 to both sides and get 7x = 77. Finally, we divide both sides by 7 and get x = 11.

9. To solve 2(3x-1)+3=21, we first distribute the 2 and get 6x - 2 + 3 = 21. Then, we combine like terms and get 6x + 1 = 21. Then, we subtract 1 from both sides and get 6x = 20. Finally, we divide both sides by 6 and get x = 3.33.

10. To solve 2(x+1)+3x=37, we first distribute the 2 and get 2x + 2 + 3x = 37. Then, we combine like terms and get 5x + 2 = 37. Then, we subtract 2 from both sides and get 5x = 35. Finally, we divide both sides by 5 and get x = 7.

11. To solve 12+4(2x+4)=68, we first distribute the 4 and get 12 + 8x + 16 = 68. Then, we combine like terms  x = 5.

12.To solve 3x - 2(6x - 3) = 42, we first distribute the -2 and get:3x - 12x + 6 = 42,9x + 6 = 42Then, we subtract 6 from both sides:-9x = 36Finally, we divide both sides by -9 and get:x = -4Therefore, the solution to the equation is x = -4.

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The solution to the algebraic expressions are:

1. x = 3

2. x = 7

3. x = 13

4. x = -9

5. x = 1.3

6. x = -4

7. x = -2

8. x = 11

9. x = 10/3

10. x = 5

11. x = 5

12. x = -4

1. 3(x + 2) = 15,

Using distributive property, we get 3x + 6 = 15.

3x = 9

x = 9/3

x = 3

2. 2(x + 5) = 24

Using distributive property, we get:

2x + 10 = 24

2x = 14

x = 7

3. 6(x - 9) = 12

Using distributive property, we get:

6x - 54 = 24

6x = 78

x = 78/6

x = 13

4. 2(3x + 5) = -44

Using distributive property, we get:

6x + 10 = -44

6x = -54

x = -9

5. 5(4x - 3) = 11

Using distributive property, we get:

20x - 15 = 11

20x = 26

x = 1.3

6. -3(2x + 1) = 21

-6x - 3 = 21

-6x = 24

x = -4

7. -9(x - 4) = 54

Using distributive property, we get:

-9x + 36 = 54

-9x = 54 - 36

-9x = 18

x = -2

8. 7(x - 4) - 3 = 46

Using distributive property, we get:

7x - 28 - 3 = 46

7x = 77

x = 11

9) 2(3x - 1) + 3 = 21

Using distributive property, we get:

6x - 2 + 3 = 21

6x = 20

x = 20/6

x = 10/3

10) 2(x + 1) + 3x = 37

2x + 2 + 3x = 37

5x = 35

x = 5

11) 12 + 4(2x + 4) = 68

12 + 8x + 16 = 68

8x = 40

x = 5

12) 3x - 2(6x - 3) = 42

3x - 12x + 6 = 42

6 - 9x = 42

9x = -36

x = -36/9

x = -4

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Answer: C 24

Step-by-step explanation:

The measure of the length of EF in a right-angle triangle is 24 units, then the correct option is C.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.

The right-angle triangle is shown in a diagram. Then by the Pythagoras theorem, we have

P² = H² - B²

P² = 25² - 7²

P² = 625 - 49

P² = 576

 P = 24

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The probability of getting four or more answers correct by random guessing on a multiple-choice exam with four answers per question is approximately 0.0039 or 0.39%.

To calculate the probability of getting four or more answers correct by random guessing on a multiple-choice exam with four answers per question, we need to consider the probability of each possible outcome.

The probability of guessing a single answer correctly is 1 out of 4, or 1/4. Since there are four answers per question, the probability of guessing all answers correctly by random guessing is (1/4) * (1/4) * (1/4) * (1/4), which simplifies to (1/4)^4.

To calculate the probability of getting exactly four answers correct, we multiply the probability of getting four answers correct by the number of different combinations of questions that can result in this outcome. The number of different combinations can be calculated using the binomial coefficient.

The binomial coefficient for "n choose k" is calculated as n! / (k! * (n - k)!), where n is the total number of questions and k is the number of correct answers.

In this case, we have:

n = total number of questions = 4

k = number of correct answers = 4

Using the binomial coefficient, we have:

(4 choose 4) = 4! / (4! * (4 - 4)!) = 1

Therefore, the probability of getting exactly four answers correct is (1/4)^4 * 1 = (1/4)^4 = 1/256.

To calculate the probability of getting four or more answers correct, we need to consider all possible outcomes where the number of correct answers is four, five, six, seven, or eight (since there are only eight questions in total). We then sum up the individual probabilities for each outcome:

P(4 or more correct) = P(4 correct) + P(5 correct) + P(6 correct) + P(7 correct) + P(8 correct)

P(4 or more correct) = (1/4)^4 + (1/4)^5 + (1/4)^6 + (1/4)^7 + (1/4)^8

Calculating this expression, we find that the probability of getting four or more answers correct by random guessing is approximately 0.0039 or 0.39%.

Therefore, the probability of getting four or more answers correct by random guessing on a multiple-choice exam with four answers per question is approximately 0.0039 or 0.39%.

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The fundamental set of solutions for the given differential equation L[y]=y''-7y'+12y=0 with initial point t0=0 that also specifies y1(t0)=1, y′1(t0)=0, y2(t0)=0 and y′2(t0)=1 can be solved using the method of variation of parameters.

The general solution of the differential equation is given by:
y = C1y1 + C2y2
where C1 and C2 are constants and y1 and y2 are the two linearly independent solutions of the given equation.

The initial values of y1(t0) = 1 and y′1(t0) = 0 and y2(t0) = 0 and y′2(t0) = 1 give the equations
y1(t0) = 1 = C1y1(t0) + C2y2(t0)
y′1(t0) = 0 = C1y′1(t0) + C2y′2(t0)

These two equations can be solved simultaneously to obtain
C1 = 1 and C2 = -1

Therefore, the fundamental set of solutions is given by
y(t) = y1(t) - y2(t)

y1(t) is the solution of the equation y′′-7y′+12y=0 satisfying the initial conditions y1(t0) = 1 and y′1(t0) = 0
y2(t) is the solution of the equation y′′-7y′+12y=0 satisfying the initial conditions y2(t0) = 0 and y′2(t0) = 1

Hence, the fundamental set of solutions is given by
y(t) = y1(t) - y2(t) = 1 - e7t + te7t

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Answer:

slope = 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

9x - 3y = - 54 ( subtract 9x from both sides )

- 3y = - 9x - 54 ( divide all terms by 0 3 )

y = 3x + 18 ← in slope- intercept form

with slope m = 3

Parallel lines have equal slopes, thus

slope of parallel line is 3

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The graph of the linear equation, 5x - 9y = -7, is in the attachment below.

The linear equation that models a graph can be written in  slope-intercept equation as y = mx + b. The value of the slope, which is the rise over the run of the line is represented as m, while the value of b, which is where the line intercepts the y-axis is b.

Given the linear equation, 5x - 9y = -7, rewrite in slope-intercept form:

5x - 9y = -7

-9y = -5x - 7

-9y/-9 = -5x/-9 - 7/-9

y = 5/9x + 7/9

This means the rise over the run of the line, m is 5/9, while the y-intercept of the graph, b is 7/9.

The graph is shown below.

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a.  If we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

b. Michael's substitution satisfies the requirement for u to be differentiable.

(a) i. Kayla's proposed substitution of u as (3 - 2x) will not work in this case. The reason is that when using the u-substitution method, it is necessary for the chosen u to be differentiable, meaning that its derivative du/dx should exist and be non-zero. However, if we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

ii. Kayla's idea of always picking the most inside factor as u does not work for all u-substitutions. There can be cases where choosing the most inside factor may not lead to a valid substitution that simplifies the problem or makes integration easier. It is important to consider the properties of the function and choose a suitable substitution accordingly.

(b) i. Michael's proposed substitution of u as 3√3 - 2x will work in this case. If we let u = 3√3 - 2x, then the derivative du/dx would be -2, which is non-zero. Therefore, Michael's substitution satisfies the requirement for u to be differentiable.

ii. Michael's idea of always picking the most complicated factor as u also does not hold true for all u-substitutions. The choice of u depends on various factors, including the structure of the function, simplification possibilities, and making the integration process more manageable. It is not necessarily the case that the most complex factor will always result in a successful substitution.

It is important to consider the specific characteristics of the function and apply appropriate judgment in choosing the substitution u to simplify the problem effectively.

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Answer:

225 tons is the total

Step-by-step explanation:

Let the total amount be x

Given that,

32% of x = 72tons

32x/100 = 72tons

32x = 7200tons

x = 225 tons

To verify,

32% of 225 = 72tons

32/100 * 225 = 72 tons

72 = 72

Hence, verified.

Answer:

yes

Step-by-step explanation:

Answer:

34.16 Miles Traveled

Step-by-step explanation:

If she rode around the 8.54 mile park four times you would multiply four by 8.54 to get your answer. Hope this helps!

Answer:

B - 7.75(x+y)+282.97

Step-by-step explanation:

7.75x + 7.75y is the same as distributing 7.75 to x + y. 153.95+129.02 also is equivalent to 282.97, so B should be the answer. The other answers either don't have enough steps or the wrong operation.

hope this helped!! <3

The critical t-value is approximately 1.753.

To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).

In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.

This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.

It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.

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Answer:

A) Cube

Explanation:

Quadrilateral just means "four sides"

Examples: square, rhombus, parallelogram, rectangle.

Hope that helps

Answer:

24

Step-by-step explanation

-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|--|-|-|-|

50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.

The ratio of sparkling water to grape juice is,

1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) =  2 : 1

The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is

2/3 · 75quarts = 50 quarts

Then the grape juice content is,

1/3 · 75 quarts = 25 quarts

Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

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The values of a, h and k on the function are given as follows:

The meaning of the transformations is given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

y = 1/x.

Hence the meaning of the transformations is given as follows:

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each large envelope costs $1.60.

What did we do?

Let's represent the cost of a postcard by "p" and the cost of a large envelope by "e".

From the information given, we can create a system of equations:

17p + 4e = 13.88 (equation 1)

10p + 12e = 23.60 (equation 2)

To solve for "e", we can use the method of elimination.

First, let's multiply equation 1 by 3:

51p + 12e = 41.64 (equation 3)

Now, we can subtract equation 3 from equation 2:

10p + 12e = 23.60

-(51p + 12e = 41.64)

-41p = -18.04

Dividing both sides by -41, we get:

p = 0.44

Substituting this value into equation 1:

17(0.44) + 4e = 13.88

7.48 + 4e = 13.88

4e = 6.4

Therefore, the cost of each large envelope is:

e = 6.4/4 = 1.6

So each large envelope costs $1.60.

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The value of det(b) cannot be determined based on the given information.

To find det(b) based on the given information, let's analyze the equation det(2a - 2bt) = 1.

We know that det(2a - 2bt) = (2\(^n\)) * det(a - bt), where n is the size of the matrix (in this case, n = 4).

Given that det(a) = 2, we can rewrite the equation as follows:

(2\(^n\)) * det(a - bt) = 1

Substituting n = 4 and det(a) = 2, we have:

(2\(^4\)) * det(a - bt) = 1

16 * det(a - bt) = 1

Now, we are given that det(a - bt) = 1, so we can rewrite the equation as:

16 * 1 = 1

This equation is not possible, as it contradicts the given information.

Therefore, there is no specific value that can be determined for det(b) based on the provided information.

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