OI need help with geometry

a. True. The Extreme Value Theorem states that if a function is continuous on a closed interval, it must have both an absolute maximum and an absolute minimum on that interval.

b. False. There can't be a function for which every point on the graph is both an absolute maximum and absolute minimum. However, there can be a function with a single point that is both an absolute maximum and minimum, like a constant function, but not every point.

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The SAT prep class has no influence on the mean difference in SAT writing scores, hence the null-hypothesis (H0) states that the mean difference is zero.

The alternative theory (Ha) states that the SAT prep course has a positive impact on the mean difference in SAT writing scores, resulting in a mean difference that is greater than zero.

The sample size of 50 is sufficient for us to do the hypothesis test using the t-distribution.

The estimated t-test statistic is 1.96, and at the 5% level of significance, it is significant only if it is in the rejection zone of the null hypothesis (1.677 is the crucial value for a one-tailed test with 49 degrees of freedom).

The calculated p-value of 0.028 is less than the threshold of 0.05, the null hypothesis is also rejected in favour of the alternative hypothesis.

To draw the conclusion that the SAT prep course has a favourable impact on the mean difference in SAT writing scores. Particularly, at the 5% level of significance, the sample-mean difference of 5 is statistically significantly greater than zero.

Therefore, it is reasonable.

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In linear regression, we are trying to forecast the dependent variable based on the independent variable.

Option C is the correct answer.

We have,

In linear regression, the dependent variable is the outcome variable or the response variable that we want to predict or explain, while the independent variable is the predictor variable or explanatory variable that helps us in predicting the dependent variable.

The beta parameter and y-intercept are coefficients of the linear regression equation that help in determining the relationship between the dependent and independent variables.

Thus,

In linear regression, we are trying to forecast the dependent variable based on the independent variable.

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The equation of the line through \((1,2)\) which make equal intercepts on the axis \(x+y=3\)

The equation of the line through (1,2) makes an equal intercept on the axis

The formula of the intercept form is

\(\frac{x}{a} +\frac{y}{b} =1\)

If they make an equal intercept

\(a=b\\\frac{x}{a} +\frac{y}{a} =1\\x+y=a\)

Put the value of the point in the axis, and we get.

\(1+2=a\\a=3\)

Put the value in the equation, and we get.

\(x+y=3\)

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Three different vectors are [-8, 14],  [-6, 16], and [15, -18].

To find three different vectors that are in the span of the given vectors \(u_1\) = [-3, 8] and \(u_2\) = [-5, 6], we can use linear combinations of these vectors.

Let's call the three different vectors \(v_1\), \(v_2\), and \(v_3\). We can express them as follows:

\(v_1\) = \(u_1\) + \(u_2\) = [-3, 8] + [-5, 6] = [-3 + (-5), 8 + 6] = [-8, 14]

\(v_2\) = 2\(u_1\) = 2[-3, 8] = [-6, 16]

\(v_3\) = -3\(u_2\) = -3[-5, 6] = [15, -18]

Therefore, three different vectors that are in the span of \(u_1\) and \(u_2\) are \(v_1\) = [-8, 14], \(v_2\) = [-6, 16], and \(v_3\) = [15, -18].

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Answer:

6y-5

Step-by-step explanation:

(48y- 40)/8 because an octagon has 8 equal sides.

-hope this helps:)

\(\dfrac{4e^2+16e-9}{2ef+12e-f-6}\)

⇒ First, factor the numerator by grouping:

\(=\dfrac{4e^2-2e+18e-9}{2ef+12e-f-6}\\\\\\=\dfrac{2e(2e-1)+9(2e-1)}{2ef+12e-f-6}\\\\\\=\dfrac{(2e+9)(2e-1)}{2ef+12e-f-6}\)

⇒ Now, factor the denominator by grouping:

\(=\dfrac{(2e+9)(2e-1)}{2e(f+6)-(f+6)}\\\\\\=\dfrac{(2e+9)(2e-1)}{(2e-1)(f+6)}\)

⇒ We must determine which values of e and f are unacceptable, meaning, will make this expression undefined. These will be the values of e and f that make the denominator equal to 0.

\(=\dfrac{(2e+9)(2e-1)}{(2e-1)(f+6)}\)

⇒ Reduce values in the numerator and denominator:

\(=\dfrac{(2e+9)}{(f+6)}\\\\\\=\dfrac{2e+9}{f+6}\)

\(=\dfrac{2e+9}{f+6}\)

Step-by-step explanation:

this is you answer solved.

Answer:Lin

Step-by-step explanation: because it takes him less time for the mile

Answer:

let whole number be x

9+3x=45(according to the question this is a equation)

3x=45-9

x=36/3

x=12

Step-by-step explanation:

The probability that a continuous random variable equals any of its values is called Continuous probability distribution.

Continuous probability distribution:

A probability distribution in which the random variable X can take on any value (which is continuous). Since there are infinitely many possible values ​​for X, the probability that X takes on any particular value is zero. So we often talk about a range of values ​​[p(X >0] = 0.50).

An absolutely continuous probability distribution is a probability distribution of real numbers with an uncountable set of possible values, such as the full interval of a solid line, where the probability of any event can be expressed as an integral. More precisely, there exists a function f: R − [0, so that for each interval[ 0,∞] ⊂ R, the probability that X belongs to [a, b] is given by the integral of f over I.

\(P(a\leq X\leq b) = \int\limits^a_b {f(x)} \, dx\)

Since this is the definition of a probability density function, an absolutely continuous probability distribution is exactly equivalent to a probability density function. In particular, the probability that X takes any single value a (i.e. a≤X≤b) is zero because integrals with the same upper and lower bounds are always zero. If the interval [a, b] is replaced by the measurable set A, then the equivalence remains valid.

P(X ∈ A) = \(\int\limits^a_b {f(x)} \, dx\)

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Answer:

17 is added to both numerator and denominator.

Step-by-step explanation:

Given:

Fraction = 1/10

New fraction = 2/3

Find:

Number added to both numerator and denominator.

Computation:

Assume,

a is added to both numerator and denominator.

\(\frac{1+a}{10+a}=\frac{2}{3}\\\\3 + 3a=20+2a\\\\3a-2a=20-3\\\\a=17\)

Therefore, 17 is added to both numerator and denominator.

Answer:

$500

Step-by-step explanation:

100-12=88

88/100=440/x

88x=100(440)

88x=44000

/88.  /88

x=500

hopes this helps

Answer:

Y= 5

X=6

Step-by-step explanation:

Plug in the equation and you get

2(2y-4)-3y=-3

which gives you y=5

Plug in y to get x=2•5-4

Which gives you 6 for x

Answer: the second, third and fifth options.

Step-by-step explanation:

When an equation is set up in a y=mx+b format, the slope is always equal to the value m.

Answer:

What is step 6

Step-by-step explanation:

Answer:

here is ur midpoint

Step-by-step explanation:

(4, -7)

9614 1404 393

Answer:

  add up the gaps and divide by their number

Step-by-step explanation:

You find the average gap time the same way you find any average: divide the total of the gap times by the number of them.

The four gaps total 4 minutes 37 seconds, or 277 seconds. Their average is ...

  (277 s)/4 = 69.25 s

_____

Each gap is computed by subtracting the first cyclist's time from each of the others.

In a spreadsheet such as this one, time computation can be done fairly easily. For the final conversion to seconds, we have to account for the fact that the spreadsheet stores time internally as a number of days. The 0:04:37 is converted to 277 seconds by multiplying it by 86400, the number of seconds in a day.

Answer:

Think about it this way: The x axis goes from left to right, correct? So just try to visualize actually picking up the object and flipping it over that axis. So since one tip of the triangle is on the coordinate (1,1), after reflecting the shape that same tip would be on (1,-1). You understand?

The ratio of false positives to true positives is 8 over 54.

According to the Question

Results of a strep throat test performed on a sample of 400 ill people are displayed in the table's data. People who have the flu and those who don't are separated into two categories. The patients are then separated into groups based on whether they tested positive or negative for strep throat within each of these categories.

We must first define what a true positive and a false positive are in order to calculate the ratio of false positives to true positives. A patient who tests positive for strep throat but does not actually have the illness is said to have a false positive. The 8% of patients in this instance who tested positive for strep throat but did not have the flu would fall under that category. A patient who tests positive for strep throat and truly has the illness is said to have a true positive. That would be the 54% of patients who tested positive for both the flu and strep throat in this instance.

We divide the percentage of false positives (8%) by the percentage of true positives (54%), which gives us the ratio of false positives to true positives.

As a result, the ratio becomes 8% / 54%, or 8/54.

It's critical to remember that this ratio is dependent on the sample and test performed and may not be the same for different populations or testing methodologies.

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Answer:

B 25.2

Step-by-step explanation:

AB = AC - BC

= 51.8 - 26.6 = 25.2

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Part A: An open circle on a number line represents an excluded value, indicating that the endpoint is not included in the solution set of the inequality. It is used when the inequality includes the symbols < (less than) or > (greater than), which denote strict inequality.

Part B: A closed circle on a number line represents an included value, indicating that the endpoint is part of the solution set of the inequality. It is used when the inequality includes the symbols ≤ (less than or equal to) or ≥ (greater than or equal to), which denote inclusive inequality.

Part C: The shading on the number line represents the range of values that satisfy the given inequality. It indicates which values make the inequality true. Typically, the shading is done to the right or left of the circle(s) depending on whether the inequality is greater than or less than.

Part A:

For example, if we have the inequality x > 2, we would represent it with an open circle at 2 on the number line. This means that 2 itself is not a valid solution, but any value greater than 2 is included.

Part B:

For example, if we have the inequality x ≥ -3, we would represent it with a closed circle at -3 on the number line. This means that -3 itself is a valid solution, as well as any value greater than or equal to -3.

Part C:

For example, if we have the inequality x > 2, we would shade the portion of the number line to the right of the open circle at 2. The shaded region represents all the values greater than 2 that satisfy the inequality. The shading visually illustrates the solution set and helps identify the range of valid values for the variable in the given inequality.

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The width of the original piece of sheet metal is (w^2 - l^2)/(3w + 3l), and the length is (l^2 - w^2)/(3w + 3l).

To solve this problem, we can use the formula for the volume of a rectangular box, which is V = lwh, where l is the length, w is the width, and h is the height.

First, let's find the height of the box. Since we cut squares from each corner, the height of the box is the length of the square that was cut out. Let's call this length x.

The width of the box is the original width minus the lengths of the two squares that were cut out, which is w - 2x.

Similarly, the length of the box is the original length minus the lengths of the two squares that were cut out, which is l - 2x.

Now we can write the volume of the box in terms of x, w, and l:

V = (w - 2x)(l - 2x)(x)

Expanding this expression, we get:

V = x(4wl - 4wx - 4lx + 8x^2)

Simplifying further:

V = 4x^3 - 4wx^2 - 4lx^2 + 4wlx

To find the dimensions of the original piece of sheet metal, we need to maximize this volume. We can do this by taking the derivative of the volume with respect to x and setting it equal to zero:

dV/dx = 12x^2 - 8wx - 8lx + 4wl = 0

Solving for x, we get:

x = (2wl)/(3w + 3l)

Now we can use this value of x to find the width and length of the original piece of sheet metal:

w - 2x = w - 2(2wl)/(3w + 3l) = (w^2 - l^2)/(3w + 3l)

l - 2x = l - 2(2wl)/(3w + 3l) = (l^2 - w^2)/(3w + 3l)

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Answer:

C.5

Step-by-step explanation:

Fiona:

After t trials, she would have:

\(f(t) = 4.127(1.468)^t\)

Karl:

After t trials, he would have:

\(k(t) = 0.897(1.992)^t\)

At what number of trials would Fiona and Karl have the same number of beans?

This is t for which:

\(f(t) = k(t)\)

So

\(4.127(1.468)^t = 0.897(1.992)^t\)

\(0.897(1.992)^t = 4.127(1.468)^t\)

\(\frac{(1.992)^t}{(1.468)^t} = \frac{4.127}{0.897}\)

\((\frac{1.992}{1.468})^t = 4.6\)

\((1.35695)^t = 4.6\)

\(\log{(1.35695)^t} = \log{4.6}\)

\(t\log{1.35695} = \log{4.6}\)

\(t = \frac{\log{4.6}}{\log{1.35695}}\)

\(t = 5\)

So the correct answer is 5 trials, option C.

There are 1820 different groups of applicants for 4 management trainee positions, 126 different groups of trainees consisting entirely of women, and a 0.0692 probability that the trainee class will consist entirely of women.

The number of different groups of applicants that can be selected for the four management trainee positions can be calculated using the combination formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of applicants (16 in this case) and r is the number of positions to be filled (4 in this case).

So the number of different groups of applicants that can be selected is:

16C4 = 1820

Therefore, there are 1820 different groups of applicants that can be selected for the four management trainee positions.

The number of different groups of trainees that would consist entirely of women can be calculated using the combination formula again, but this time we are selecting all 4 positions from the 9 female applicants:

9C4 = 126

Therefore, there are 126 different groups of trainees that would consist entirely of women.

Assuming that all groups of four are equally likely to be selected, the probability that the trainee class will consist entirely of women can be calculated by dividing the number of different groups of trainees that consist entirely of women (126) by the total number of different groups of applicants (1820):

Probability = 126 / 1820 = 0.0692

So the probability that the trainee class will consist entirely of women is 0.0692 (rounded to four decimal places).

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Answer:

-2

Step-by-step explanation:

-2-4/3-0=-2

you basically take the y value of the first point subtract it from the y value of the 2nd point. you do the same for the x values

Answer:

-2

Step-by-step explanation:

You can use the equation rise over run, which is basically y2-y1 over x2-x1

Y2 is -2 and y4 is 4, x2 is 3  x1 is 0

-2-4 over 3-0=-6/3=-2

The height of the cone is approximately 28.867 units and the radius is approximately 21.65 units.

Let's denote the height of the cone as "h" and the radius as "r".

From the problem statement, we know that:

r = (3/4)h ...(1) (given)

The surface area of the cone is given as 3750 square units. The formula for the surface area of a cone is:

Surface Area of Cone = πr(r + l),

where "l" is the slant height of the cone. Since the slant height is not given in the problem, we need to express "l" in terms of "r" and "h" using the Pythagorean theorem:

l² = r² + h²

l² = (3/4)² h² + h²

l² = (9/16)h² + h²

l² = (25/16)h²

l = (5/4)h

Substituting this expression for "l" and the expression for "r" from equation (1) into the surface area formula, we get:

3750 = πr(r + l)

3750 = π[(3/4)h] [(3/4)h + (5/4)h]

3750 = π (9/16 + 15/16) h²

3750 = π (24/16) h²

3750 = (3/2) π h²

h² = (2500/3π)

h ≈ 28.867

Substituting this value of "h" into equation (1), we get:

r = (3/4)h

r ≈ 21.65

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Answer: Radius 37.5    &      height 50

Step-by-step explanation: correct in edmuntum/plato

Therefore, the correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

Based on the given information, D represents the null hypothesis (H₀) and E represents the alternative hypothesis (Hₐ).

The null hypothesis (H₀) is a statement that there is no significant difference between the observed data and the expected results. In this case, the null hypothesis is that the population mean (μ) is greater than or equal to 1000.

The alternative hypothesis (Hₐ) is a statement that there is a significant difference between the observed data and the expected results. In this case, the alternative hypothesis is that the population mean (μ) is less than 1000.

Correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

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