What should you know about the slopes of perpendicular lines? SOMEONE HELP ME

The probability that a selected individual's height will be less than 45 inches is approximately 0.0228.

We can use the normal distribution to find the probability that a selected individual's height will be less than 45 inches. We'll need to first calculate the z-score for a height of 45 inches, and then use a standard normal distribution table or calculator to find the corresponding probability.

The formula for calculating the z-score is:

z = (x - μ) / σ

Where x is the height we're interested in, μ is the population mean (given as 53 inches), and σ is the population standard deviation (given as 4 inches).

Plugging in the values, we get:

z = (45 - 53) / 4 = -2

Now, we can use a standard normal distribution table or calculator to find the probability of a z-score less than -2. Using a table, we find that the probability is approximately 0.0228.

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Answer:

a(first term)=4

d(common difference)=6

sum of first 6 terms=114

The sum of the first 6 terms is given by 114

An Arithmetic progression (AP) is a special type of progression in which the difference between two consecutive terms is always a constant. The terms of an arithmetic progression series is a a+d, a + 2d, a + 3d, a + 4d, a + 5d,…

Given here The 3rd and the 6th terms of an Arithmetic Progression (A.P) are 16 and 34 respectively. Here on increase in 3 terms the value changes by  34-16=18 Thus if we move by +1 term the common difference must be 18/3=6 and thus the common difference is equal to 3.

∴ The Arithmetic progression is given by:

4,10,16,22,28,34 . . . .

∴ The sum of the first 6 terms is 4+10+16+22+28+34=114

Hence, The sum of the first 6 terms is given by 114

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The optimal level of Y is option a) 23

TB = \(300Y - 6Y^2\)

MB or Marginal Benefit will result from the first derivative

MB=300-12Y

and TC = 24Y + 108

Marginal Cost, or MC, will result from the first derivative.

MC=24

MC=MB is the level of Y that is ideal.

300-12Y=24

12Y=276

Y=23

The expense that a business incurs when it needs to produce extra units of any goods or services is referred to as a marginal cost.

It is computed by taking into consideration the whole cost of creating the extra items and dividing that sum by the variation in the overall quantity of the produced goods.

Variable costs like materials and labor are included in marginal costs. Additionally, it takes into account any increases in fixed expenses like selling, administration, and overhead.

When a change in production volume is required, the cost change is referred to as the change in the cost of production. More labor and raw resources are needed to produce additional units, changing the overall cost of production.

The volume of output either increases or decreases, which affects quantity. With an increase or decrease in production, there will be a variation in cost.

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Answer:

3y

Step-by-step explanation:

Sqrt of 9 = ±3

-±3\(\sqrt{y^{2} }\)

the square and sqrt cancel leaving you with -±3y

Since y < 0, the sqrt of 9 should be -3 to cancel out the - sign in front.

Hope that helps

The regression equation for predicting the height of girls at age 18 based on their height at age 2 is:

y ≈ 68.953 + 1.210x

The correlation coefficient illustrates how closely two variables are related to one another. This coefficient's range is from -1 to +1. This coefficient demonstrates the degree to which the observed data for two variables are significantly associated.

Based on the given information, we can use the linear regression model to predict the height of girls at age 18 based on their height at age 2. Here are the summary statistics:

n = 70 (sample size)

x = 87.25 (mean height at age 2 in cm)

y = 166.54 (mean height at age 18 in cm)

R = 0.664 (correlation coefficient)

S = 3.33 (standard deviation of height at age 2 in cm)

\(S_y\) = 6.07 (standard deviation of height at age 18 in cm)

To predict the height of girls at age 18 (y) based on their height at age 2 (x), we can use the regression equation:

y = a + bx

where a is the y-intercept (predicted height at age 18 when x = 0) and b is the slope of the regression line.

From the given information, we have the following values:

x = 87.25

y = 166.54

R = 0.664

Using these values, we can calculate the slope (b) of the regression line:

b = R * (\(S_y\) / S)

 = 0.664 * (6.07 / 3.33)

 ≈ 1.210

Next, we can calculate the y-intercept (a) using the formula:

a = y - b * x

 = 166.54 - 1.210 * 87.25

 ≈ 68.953

Therefore, the regression equation for predicting the height of girls at age 18 based on their height at age 2 is:

y ≈ 68.953 + 1.210x

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Answer:

Step-by-step explanation:

Let's call the width of the rectangle "w". Then, the length of the rectangle would be 3 + 4w. The area of a rectangle is found by multiplying the length and width: A = l * wSo, using the values we found for the length and width, the polynomial in a standard form that represents the area of the rectangle would be: A = (3 + 4w) * expanding the expression, we get: A = 3w + 4w^2So, the polynomial in a standard form that represents the area of the rectangle is: A = 4w^2 + 3w

Step-by-step explanation:

7y = 7

y = 1

2(1) + 4x = 14

4x = 12

x = 3

The best estimate for the subtraction operation in this problem is given as follows:

C. 270-150=120

The subtraction operation in the context of this problem is defined as follows:

267 - 154 = 113.

We can round each of the terms of the subtraction to the nearest tens, hence:

Hence the estimate is given as follows:

270 - 150 = 120.

Hence option C is the correct option for this problem.

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Answer:

6^2 - (3*-4)+20

6^2 - (-12)+20

36+12+20

48+20

68

Let me know if this helps!

Answer:

68

Step-by-step explanation:

The answer choices which are solutions to the given equation as required are Choice D; 6 and Choice E; -4.

Given; x² - 2x -24 = 0.

By factorisation;

x² - 6x + 4x - 24 = 0

(x - 6) (x + 4) = 0

x - 6 = 0 or x + 4 = 0

Consequently, x = 6 or x = -4

Therefore, the solutions to the given equation are; Choice D; 6 and Choice E; -4.

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The efficiency of the pump (in %) is 0.35%. Hence, option (c) is correct.

Efficiency of the pump:

According to the question, a centrifugal pump with a performance curve is given. For H, the performance curve is given as,

H = 340 - 1.2(Q²) in feetAnd for BP, the performance curve is given as,

BP = 0.0521(Q³) + 1.25(Q²) + 11.042(Q) + 134.5 in horsepower (HP)

Where Q is the flow rate in ft³/s.

We have to find the efficiency of the pump which can deliver 8 ft³/s.

The specific weight of water is given as 62.4 lbf/ft³.

Efficiency of the pump,η = (output power/input power)

Where input power = power supplied to the

pump = g × Q × H × w

Where g is acceleration due to gravity, w is the specific weight of the water.

Given, g = 32.2 ft/s², w = 62.4 lbf/ft³ = 32.2 × 62.4 = 2009.28 lbf/ft³'

Using the performance curves,

H = 340 - 1.2(Q²)BP = 0.0521(Q³) + 1.25(Q²) + 11.042(Q) + 134.5

Substituting Q = 8 ft³/s, we get

H = 304 ftBP = 77.87 HP Power supplied to the pump = g × Q × H × w

= 32.2 × 8 × 304 × 2009.28

= 16.57 × 10^6 ft-lbf/s

Output power of the

pump = BP × 746

= 77.87 × 746

= 58.17 × 10^3 ft-lbf/s

Efficiency of the pump,η = (output power/input power)η

= (58.17 × 10³)/(16.57 × 10^6)η

= 0.003509

= 0.3509%.

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Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

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The proved oil reserves in the globe were projected to be 1,000 billion barrels by the World Resources Institute in 1997, while the eventually recoverable reserves were predicted to be 2,000 billion barrels. 75 years old

The World Resources Institute (WRI) has offices abroad in Brazil, China, India, Indonesia, Mexico, and the United States. The organization's goal is to advance human health and wellbeing, economic opportunity, and environmental sustainability.  WRI collaborates with regional and federal governments, private businesses, publicly traded firms, and other non-profit organizations to provide services addressing challenges such as the global climate change, sustainable markets, ecosystem protection, and environmentally conscious governance.  Since the first of October 2008, WRI has maintained a Charity Navigator rating of 4 out of 4.

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Answer:

x=9  x=-5

Step-by-step explanation:

x² − 4x + 4 = 49

(x-2)²= 49

x-2= 7  or    x-2=-7  

x=9  or    x=-5

The value should be reported as follows:

25.1 ± 0.1

In this case, the value has been rounded to the same decimal place as the uncertainty, which is the first decimal place. The uncertainty is rounded to one significant figure to reflect the precision of the measurement. The value is reported with one decimal place, which is the same as the uncertainty, to maintain consistency.

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The value of y is, \(y=\frac{2\sqrt{6}-6}{5},\:y=\frac{-2\sqrt{6}-6}{5}\)

We have given that,

\(\left(5y+6\right)^2=24\)

We have to determine the value of y,

\(\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\)

Therefore,we get

\(5y+6=\sqrt{24}\)

\(5y+6=2\sqrt{6}\)

\(\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\)

\(5y+6-6=2\sqrt{6}-6\)

\(5y=2\sqrt{6}-6\)

\(\frac{5y}{5}=\frac{2\sqrt{6}}{5}-\frac{6}{5}\)

\(y=\frac{2\sqrt{6}-6}{5}\)

\(y=\frac{2\sqrt{6}-6}{5},\:y=\frac{-2\sqrt{6}-6}{5}\)

Therefore the value of y is,

\(y=\frac{2\sqrt{6}-6}{5},\:y=\frac{-2\sqrt{6}-6}{5}\)

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The cost of one apple is $0.70.

Let's assume that the cost of one apple is "a" dollars and the cost of one banana is "b" dollars. We can create two equations based on the information given:

4a + 9b = 12.70 ...(1)

8a + 11b = 17.70 ...(2)

To solve for "a", we can use elimination method by multiplying equation (1) by 8 and equation (2) by -4, so that the coefficients of "a" in both equations will be equal and opposite:

32a + 72b = 101.60

-32a - 44b = -70.80

Adding these two equations, we get:

28b = 30.80

Simplifying and solving for "b", we get:

b = 1.10

Now, we can substitute the value of "b" in equation (1) and solve for "a":

4a + 9(1.10) = 12.70

4a + 9.90 = 12.70

4a = 2.80

a = 0.70

Therefore, the cost of one apple is $0.70.

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The angle of elevation of the ramp to the nearest degree is 34°.

we can use trigonometry to determine the angle of elevation of the ramp.To begin, we need to draw a diagram to visualize the problem.

Let's assume that the height of the end of the ramp is h, and the horizontal distance from the bottom of the ramp to the building is d.

From the diagram, we can see that we have a right-angled triangle where the height of the triangle is h, the base of the triangle is d, and the hypotenuse of the triangle is the length of the ramp.

Using the tangent ratio, we can write:

tanθ = opposite/adjacent

where opposite is the height of the triangle, and adjacent is the base of the triangle. Substituting the values we have, we get:

tanθ = h/d

Rearranging this formula, we can write:

θ = tan⁻¹(h/d)

Substituting the values we have, we get:θ = tan⁻¹(10/15)θ = 33.69°

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The area of the shaped portion of the given diagram(circle) would be = 153.86cm²

The formula which is used to calculate the area of a circle = πr²

where π = 3.14

radius = 7 cm

Therefore the area of the shaded part of the circle ;

= 3.14 × 7²

= 3.14 × 49

= 153.86cm²

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Answer:

third option

Step-by-step explanation:

(4x + 3)² = 18 ( take square root of both sides )

4x + 3 = ± \(\sqrt{18}\) = ± \(\sqrt{9(2)}\) = ± (\(\sqrt{9}\) × \(\sqrt{2}\) ) = ± 3\(\sqrt{2}\) ( subtract 3 from both sides )

4x = - 3 ± 3\(\sqrt{2}\) ( divide both sides by 4 )

x = \(\frac{-3+3\sqrt{2} }{4}\) , x = \(\frac{-3-3\sqrt{2} }{4}\)

Answer is d. The testable proposed relationship between the variables in the research hypothesis is: "Then people with a high exposure to UV light will have a higher frequency of skin cancer." This portion of the hypothesis specifically establishes the expected connection between UV light exposure and the occurrence of skin cancer, allowing for investigation and data collection to either support or refute the hypothesis.

A hypothesis is a tentative explanation for a phenomenon that is based on prior knowledge and observations. It is essential to have a testable hypothesis to ensure that the research study can be conducted in a rigorous and systematic manner. A testable hypothesis allows researchers to design experiments that can collect data to support or refute the hypothesis. Without a testable hypothesis, researchers may not be able to generate meaningful results that contribute to scientific knowledge.

A critical aspect of hypothesis testing is making clear and specific predictions about the relationship between the variables. In this case, the researchers are predicting that people with a high exposure to UV light will have a higher frequency of skin cancer. This prediction is specific because it defines the level of UV light exposure that is expected to lead to a higher frequency of skin cancer. It is also measurable because the frequency of skin cancer can be quantified through data collection. By making this clear and specific prediction, the researchers can test their hypothesis and determine whether the data support or refute their hypothesis.

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The value of the line integral over the curve C: x=e−t cos(t), y=e−t sin(t), for the limits 0≤t≤π/2 ∫C\((x^2+y^2)\)ds is approximately √2/3.

To evaluate the line integral ∫C\((x^2 + y^2\)) ds over the curve C defined by x = \(e^{-t}\)cos(t), y = \(e^{-t}\)sin(t), with 0 ≤ t ≤ π/2, we can parameterize the curve C with respect to t.

The parameterization of C is given by:

r(t) = (\(e^{-t}\))cos(t), \(e^{-t}\)sin(t)).

We can express the differential arc length ds in terms of t by using the formula:

ds = √(dx/dt)² + (dy/dt)² dt.

Differentiating x and y with respect to t, we have:

dx/dt = \(-e^{-t}\))cos(t) \(-e^{-t}\))sin(t),

dy/dt = \(-e^{-t}\)sin(t) + \(e^{-t}\)cos(t).

Now, let's substitute the parameterization and the differentials into the line integral:

∫C\((x^2 + y^2)\) ds = ∫[0,π/2] \((x^2 + y^2)\)) √(dx/dt)² + (dy/dt)² dt.

Substituting the expressions for x, y, dx/dt, and dy/dt, we have:

∫[0,π/2] (\(e^{-2t}\))cos²(t) + \(e^(-2t)sin^2(t)\)) √(\((-e^(-t)\)cos(t) - \(e^(-t)\)sin(t))² + (-\(e^(-t)\)sin(t) + \(e^(-t)\)cos(t))²) dt.

Simplifying the integrand, we have:

∫[0,π/2] \(e^(-2t)\) √(\(e^(-2t)(2cos^2(t) + 2sin^2(t))\)) dt.

Notice that 2cos²(t) + 2sin²(t) simplifies to 2, so we have:

∫[0,π/2] \(e^(-2t)\) √(2\(e^(-2t)\)) dt.

Simplifying further, we obtain:

∫[0,π/2] √2 e^(-2t)\(e^(-2t)\)) dt.

Integrating with respect to t, we have:

∫[0,π/2] √2\(e^(-3t)\) dt = [-√2/3 \(e^(-3t)\)] from 0 to π/2.

Evaluating the limits, we get:

[-√2/3 \(e^(-3\)(π/2))] - [-√2/3 \(e^(-3\)(0))].

Simplifying:

[-√2/3 \(e^{-3\pi /2}\)] - [-√2/3].

Since e^(-3π/2) is very close to zero, the term -√2/3 \(e^{-3\pi /2}\) can be neglected. Therefore, we have:

[-√2/3 \(e^{-3\pi /2}\)] - [-√2/3] ≈ -[-√2/3] = √2/3.

Hence, the value of the line integral ∫C (\(x^2 + y^2\)) ds over the curve C is approximately √2/3.

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Using a two-sample Wilcoxon rank-sum test, we cannot reject the null hypothesis that the prices for the microwave oven are the same in Dallas and San Antonio.

To perform the hypothesis test, we can use a two-sample Wilcoxon rank-sum test because the data are not normally distributed and the sample sizes are different. First, we calculate the mean and standard deviation of the normal distribution that can be used for this statistical test. The mean is (10 + 13 + 1) / 2 = 12 and the standard deviation is √[(10 × 13 × (10 + 13 + 1)) / 12] ≈ 3.05.

Next, we rank all the prices from lowest to highest, combining the data from both cities. We calculate the sum of the ranks for Dallas to be 107.5. We then calculate the test statistic using the formula:

W = min(U1, U2) = min(107.5, 165.5) = 107.5

Using Table 1 of Appendix B with α = 0.05 and n1 = 10, n2 = 13, the critical value is 25. Since our test statistic (107.5) is greater than the critical value (25), we cannot reject the null hypothesis.

The p-value for the hypothesis test is the probability of obtaining a test statistic as extreme or more extreme than our observed test statistic under the null hypothesis. Since our test statistic is greater than the critical value, the p-value is less than 0.001.

Therefore, we do not have enough evidence to reject the null hypothesis that says there is no difference in the microwave prices in Dallas and San Antonio.

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Answer:

Step-by-step explanation:

We start by developing an equation for Line 1, and then use that to find the equation for Line 2.  We'll use the form of an equation for a straight line:

 y = mx + b,

where m is the slope and b the y-intercept (the value of y when x=0).

Line 1

Determine the slope, m, by calculating the "Rise/Run" between the two points (-3,-7) and (5,3).

Line up the two points from left to right (based on x) and then calculate:

  Rise:  (3 - (-7)) = 10

   Run:  (5 -(-3) = 8

The slope, m, is Rise/Run or (10/8)

The equation becomes y = (5/4)x + b

We could calculate b, the y-intercept, by entering one of the two given points and solving for b, but the only thing we need from this line is it's slope, m.  Slope is (5/4), which we'll use in the next step:  Line 2.

[Note:  Out of curiosity, here is the calculation for b:  Use point (5,3) in y = (5/4)x + b and solve for b.   3 = (5/4)*5 + b.  3 = (25/4) + b  b = -13/4.  This means that Line 1 is y = (5/4)x -(13/4)]

Line 2

The slope of a line perpendicular to the first is the "negative inverse" of the first line.  In this case, line 1's slope of (13/8) would become a slope of -(8/13) for line 2.

    Line 2:  y = -(8/13)x + b

We'll calculate b for this line by enetering the single point provided,  (-4,-2), and solving for b:

          y = -(8/13)x + b

        -2 = -(8/13)*(-4) + b

          -2 = (32/13) + b

          -2 - (32/13) =  b

b = -(26/13) - (32/13)

b = -(58/13)

The new line perpendicular to Line 1 and passing through (-4,-2) is:

          y = -(8/13)x -(58/13)

See attached graph.

Answer:

Sorry to say this... but neither of them have a solution of (2,1)

Step-by-step explanation:

The top one has a solution of (-2,-1). The one on the bottom has a solution of (-2,1). So... I'm not sure how this can help... but yeah...

Answer:

Step-by-step explanation:

24-6=18

now 2022 so

2022-18=2004

Answer:

The fifth answer is correct! have a great day

Answer:

3 and 4

Step-by-step explanation:

23x5= 115

115+35=150

23x2=46

46+35= 81

which gives us numbers 3 and 4

Please give me brainliest :)

Answer:

I think it's still going to be 2x+3. please let me know if I am wrong