the width of a rectangle is 2 in less than its length the area is 24 square inches find the dimensions of the rectangle

Answer:

See below

Step-by-step explanation:

The first one scales UP from 4 to 6     F'G'/FG =    factor is  6/4 = 1.5

second one scales DOWN from 4 to 3  

        F'G' / FG = scale factor is 3/4

Third one is scaled DOWN

F'G' / FG =    2/4 = 1/2

Note when scale is DOWN the factor is less than one

  when scale is UP , factor is more than one

The probability of selecting a student who is either female or a physics major is 0.375.

The given problem is asking to determine the probability that a randomly selected student is female or a physics major.

 We will use the formula for probability of union to solve this problem, where we will add the probability of female students and the probability of physics majors and subtract the probability of the intersection of these two events.

Formula for probability of union:P(A U B) = P(A) + P(B) - P(A ∩ B).

Given:Total number of students in the class = 40Number of physics majors = 15,

Number of female students = 18Number of female physics majors = 3Now, let's calculate the probability that a randomly selected student is a physics major:

P(A) = Probability of selecting a physics major out of 40 students= 15/40 = 3/8.

The probability that a student is female is:P(B) = Probability of selecting a female student out of 40 students= 18/40 = 9/20The probability that a student is both female and a physics major is:

P(A ∩ B) = Probability of selecting a female physics major out of 40 students= 3/40.

Using the formula of probability of union to get the probability of selecting a student who is either female or a physics major:P(A U B) = P(A) + P(B) - P(A ∩ B)= (3/8) + (9/20) - (3/40)= 15/40 = 0.375.

So, the probability of selecting a student who is either female or a physics major is 0.375.The answer should not be more than 100 words.

The conclusion to the above problem is that the probability of selecting a student who is either female or a physics major is 0.375. The solution involves the use of the formula for probability of union which is P(A U B) = P(A) + P(B) - P(A ∩ B), where we add the probability of female students and the probability of physics majors and subtract the probability of the intersection of these two events. The final answer is 0.375, which means there is a 37.5% chance of selecting a student who is either female or a physics major out of a total of 40 students.

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Answer:

x = 4

Step-by-step explanation:

6x - 8 = 4x

subtract 4x from both sides of the equation

6x - 4x -8 = 4x - 4x

2x - 8 = 0

add 8 to both sides of the equation

2x - 8 + 8 = 0 + 8

2x = 8

divide both sides of the equation by 2

2x/2 = 8/2

x = 4

Answer:

x = 4.

Step-by-step explanation:

6x - 8 = 4x

6x - 4x - 8 = 0

6x - 4x = 8

2x = 8

x = 4.

We can use the normal distribution to determine the value that is larger than roughly 55% of the population. So the value that is closest to the value larger than roughly 55% of the population is 89.24.

We can use a standard normal distribution table or a calculator to find that the z-score is approximately -0.1257.

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation.

x = z * σ + μ

x = (-0.1257) * 6 + 90

x ≈ 89.24

So the value that is closest to the value larger than roughly 55% of the population is 89.24.

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The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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Answer:

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = - 120\)

Step-by-step explanation:

By the rule of Integer multiplications,

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = [ (-1) \times (-2) ] \times [(-3) \times (-4)] \times (-5)\)

                                                      \(= [2] \times [12] \times (-5)\)

                                                      \(= -120\)

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Answer:

Step-by-step explanation:

To determine if the data give convincing evidence at the alpha = 0.05 significance level that the counselor's belief is correct, we can conduct a hypothesis test.

The null hypothesis is that the proportion of students at the school who have sent or posted suggestive images is equal to 20%, which is the national figure.

The alternate hypothesis is that the proportion of students at the school who have sent or posted suggestive images is greater than 20%

Using a one-sample proportion test and assuming the conditions are met, we can calculate the test statistic and p-value. The p-value can then be compared to the significance level (alpha) to determine if the results are statistically significant. If the p-value is less than the significance level, we can reject the null hypothesis and conclude that the counselor's belief is correct.

Otherwise, we fail to reject the null hypothesis and we cannot conclude that the counselor's belief is correct.

Answer:

C

Step-by-step explanation:

Answer:

Since it's increasing add 3.5% to 100%

= 103.5% of £16470.45

= 103.5/100 × 16470.45

= 17046.92

= £17046.92

Hope this helps.

Considering a growth factor of 10, the values of the exponential function are given as follows:

An exponential function is a function in which when the input x is increased by one, the output y is multiplied by the growth factor.

From the table given in the problem, the growth factor is of 8, meaning that when the input variable representing the number of hours is increased by one, the output is always multiplied by 8.

For the second table, which we have to fill, the growth factor is of 10, meaning that for each hour, the number of bacteria is given by the number of bacteria in the previous hour multiplied by 10, then:

And so on...

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Answer: -34

Step-by-step explanation:

66 minus 100 is negative 34.

Answer: 2.5, 5.3

Step-by-step explanation:

\(-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3\)

(a) The vectors a = ⟨-7, 3, 7⟩ and b = ⟨6, -8, 2⟩ are neither orthogonal nor parallel. Their dot product is -52, indicating they are not perpendicular. Additionally, their magnitudes, √147 and √104, are not proportional, ruling out parallelism.

(b) The vectors a = ⟨4, 2⟩ and b = ⟨-1, 2⟩ are orthogonal since their dot product is 0. However, they are not parallel as their magnitudes, 2√5 and √5, are not proportional.

(c) The vectors a = -i + 3j + 4k and b = 5i + 3j - k are orthogonal with a dot product of 0, but they are not parallel due to their differing magnitudes.

(d) The vectors a = 2i + 4j - 8k and b = -3i - 6j + 12k are neither orthogonal nor parallel since their dot product is -126 and their magnitudes, √84 and √189, are not proportional.

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Consider a "point" dipole with dipole moment p = pz placed at the origin of a grounded conducting spherical shell of radius a. When we ignore the conducting shell, the electrostatic potential (r, ) at distances large compared to the charge separation.

r is the distance from the origin and θ is the angle between the z-axis and r. The distance r is greater than the dipole moment distance d.

r >> d. The potential can be written as: The potential can be further expressed as to find the potential, we integrate over the entire charge distribution.

We have to integrate over the z-coordinate. For z > d, the potential is: For z < -d, the potential is When we substitute the limits of integration, the integral evaluates to: The potential is the electrostatic potential at distances large compared to the charge separation but small compared to the radius of the shell when we ignore the conducting shell is given by the expression

V(r,θ) = p cosθ/(4πε0r²).

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Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.

A slope field, which displays the slope of a differential equation along specific vertical and horizontal axes of the x-y plane, can be used to estimate the tangent slope at a particular point on a curve, where the curve is one possible solution to the differential equation.

Here,

For figure 1 slope field=

\(\frac{dy}{dx}=\frac{-17x-2y}{y}\)

For figure 2 slope field=

\(\frac{dy}{dx} = xy-3\\\)

For figure 1 a solution passing through the point (0,-1)

therefore,

slope=

\(\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(0)-2(-1)}{-1}=-2\)

so slope comes out to be negative

For figure 1 a solution passing through the point (-2,2)

\(\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(-2)-2(2)}{-1}=-30\)

so slope comes out to be negative

For the slope field in figure 2. a solution passing through the point (1.-3)

\(\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(1*-3)-3=-6\)

so slope comes out to be negative

\(\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(0*4)-3=-3\)

so slope comes out to be negative.

Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.

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A researcher looking to estimate the percentage of teenagers in the US who support the legalization of recreational marijuana should employ descriptive statistics, specifically using a proportion or percentage to summarize the data collected from a representative sample of teenagers.

The researcher should employ inferential statistics to obtain the answer to her question. She could use survey sampling methods to collect data from a representative sample of teenagers in the US and use statistical analysis techniques such as hypothesis testing and confidence intervals to estimate the percentage of teenagers who support the legalization of recreational marijuana in the entire population of US teenagers.

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Answer:

9 units

Step-by-step explanation:

(- 5, 3 ) and (4, 3 )

since the points have the same y- coordinate 3 , then the points lie on the same horizontal line.

the distance d can be calculated by finding the absolute value in the difference of the x- coordinates , that is

d = | - 5 - 4 | = | - 9 | = 9 units

or

d = | 4 - (- 5) | = | 4 + 5 | = | 9 | = 9 units

Answer:

217 days.

Step-by-step explanation:

The option that best explains how to minimize response bias is E. carefully word and field-test survey questions.

Response bias describes a number of variables that may cause someone to give a false or inaccurate answer to a question. This kind of bias is especially common in self-report questions, like those found on surveys and in structured interviews.

Response bias is a term that encompasses a wide range of participant tendencies to give false or inaccurate answers to questions. In research involving participant self-report, such as structured interviews or surveys, these biases are pervasive.

In conclusion, the correct option is E.

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Confidence interval refers to a statistical measure that helps quantify the amount of uncertainty present in a sample's estimate of a population parameter.

This measure expresses the degree of confidence in the estimated interval that can be calculated from a given set of data. In this scenario, the task is to build a 95% confidence interval for the regression line's slope. The regression analysis output has already been given. According to the output given, the estimated regression model is:y = 25,000 + 9,000 x, where x represents the number of miles the car has been driven and y represents the car's selling price.

The formula to calculate the 95% confidence interval for the slope is:Slope ± t · SE, where Slope is the point estimate for the slope, t represents the critical t-value for a given level of confidence and degrees of freedom, and SE represents the standard error of the estimate. The value of t can be calculated using the degrees of freedom and a t-table. Here, the number of pairs in the sample size is 20, and the model uses two parameters.

Therefore, the degrees of freedom would be 20 - 2 = 18.The critical t-value for a 95% confidence interval and 18 degrees of freedom is 2.101. Using the formula given above, we can calculate the 95% confidence interval for the slope as follows:Slope ± t · SE= 9000 ± (2.101)(700) ≈ 9000 ± 1,467.7 = [7,532.3, 10,467.7]Therefore, the 95% confidence interval for the slope is [7,532.3, 10,467.7]. This means that we are 95% confident that the true value of the slope for this model falls within the interval [7,532.3, 10,467.7].

It implies that the price of the car increases by $7,532.3 to $10,467.7 for each mile driven by the car. In conclusion, a 95% confidence interval has been calculated for the regression line's slope, which indicates that the actual slope of the model lies between the range [7,532.3, 10,467.7].

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Answer:

138

Step-by-step explanation:

x is an exterior angle of a triangle.

If you didn't know, an exterior angle of a triangle is equal to the sum of its opposite interior angles.

The opposite interior angles of x have measures of 80 degrees and 58 degrees.

Hence, x = 80 + 58 = 138

Answer:

138

80+58 = 138

180 - 138 = 42

42+x = 180

x = 180-42 = 138

Step-by-step explanation:

Answer: It's in the picture

Step-by-step explanation:

Answer:

The dimensions are thus 4 by 10 units

Step-by-step explanation:

Rewrite w(w + 6) = 40 in standard quadratic form ax^2 + bx + c = 0:

w^2 + 6w - 40 = 0

This factors as follows:

w^2 + 6w - 40 = 0  =>  (w + 10)(w - 4) = 0.

Solving for w, we get w = 4 (and also the unhelpful w = -10).

The width of the rectangle is 4 and the length is 4 + 6, or 10.

The dimensions are thus 4 by 10 units, with area = 40 units^2

Answer:

\(x = 5 + \sqrt{17 } \\ 4\)

Answer:

  (-2, -2.5)

Step-by-step explanation:

There are an infinite number of such points. One of the easiest to write coordinates for is the one that is on the same horizontal line. Its x-value will be 4 less that that of Q.

  (-2, -2.5) is one such point

_____

Additional comment

All of the points that could be solutions are on that portion of a circle with radius 4 and center Q that lies in quadrant III. They make up the red arc in the attachment.

Answer: 1.8 L/h

Step-by-step explanation:

To convert the rate of water dripping from a tap from millilitres per second (ml/sec) to litres per hour (L/h), we need to use conversion factors.

Step 1:

First, let's convert the rate from millilitres per second to litres per second.

There are 1000 millilitres in a litre, so we can divide the rate in millilitres per second by 1000 to get the rate in litres per second:

\(\LARGE \boxed{\textsf{0.5 ml/sec $\div$ 1000 = 0.0005 L/sec}}\)

Step 2:

We can convert the rate from litres per second to litres per hour. There are 3600 seconds in an hour, so we can multiply the rate in litres per second by 3600 to get the rate in litres per hour:

\(\LARGE \boxed{\textsf{0.0005 L/sec $\times$ 3600 = 1.8 L/h}}\)

Therefore, the rate of water dripping from the tap is 1.8 L/h.

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In the above scenario, it can be estimated with 95% confidence that the true proportion of young adult novels that include a love triangle are between 0.6854 and 0.8890

First we compute the Point Estimate

PE = 59/75 = 0.7867

Next we compute the standard error

SE = √((- - hat x (1 - p- hat) )/n)

= √( (o.7867 x (1 - 0.7867 ))/ 75
= 0. 509

Since the expected confidence level is 95%,

Margin of error = t - critical x S E

= 1.99 x 0.0509
= 0.101291

Thus,

point estimate ± margin of error

0.7867  ±  0.1013

(0.6854, 0.8880)

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Answer:

not similar

Step-by-step explanation:

hope it help