Use the diagram to the right to find x.

a.
470
b. 29°
C.) 181°

Answer:

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ \)

where

(x1 , y1) and (x2 , y2) are the points

We have

\(m = \frac{4 - 7}{3 - - 1} = \frac{ - 3}{3 + 1} = - \frac{3}{4} \\ \)

We have the final answer as

\( - \frac{3}{4} \\ \)

Hope this helps you

The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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Answer: The dimensions of the rectangular part of the Norman window that would allow in as much light as possible, given 12 feet of framing material available, are approximately 4 feet by 8 feet.

Explanation:

Let's assume that the height of the rectangular part of the Norman window is "h" and the width is "w". Then the diameter of the semicircle is also "w". The total amount of framing material needed is the sum of the perimeter of the rectangular part and half the circumference of the semicircle:

Perimeter of rectangular part = 2h + 2w

Circumference of semicircle = 1/2πw

Total framing material = 2h + 2w + 1/2πw

We want to maximize the amount of light entering the window, which is proportional to the area of the rectangular part of the window. The area of the rectangular part is given by:

Area of rectangular part = hw

Now we can use the constraint that there is only 12 feet of framing material available:

2h + 2w + 1/2πw = 12

Solving for h in terms of w:

h = (12 - 2w - 1/2πw)/2

Substituting this expression for h into the formula for the area of the rectangular part:

Area of rectangular part = w(12 - 2w - 1/2πw)/2

We can now use calculus to find the value of w that maximizes this area. Taking the derivative of the area with respect to w and setting it equal to zero:

d/dw[w(12 - 2w - 1/2πw)/2] = 0

Simplifying and solving for w:

w = 4π/(4 + π)

Substituting this value of w into the expression for h:

h = (12 - 2w - 1/2πw)/2

h ≈ 8

Therefore, the dimensions of the rectangular part of the Norman window that allow in as much light as possible, given 12 feet of framing material available, are approximately 4 feet by 8 feet.

In summary, using Z scores and a Z table, we can find that approximately 51% of respondents were married for the first time between the ages of 20 and 30, and an individual married for the first time at the age of 35 is in approximately the 97th percentile.

(a) To calculate the Z score for an observed age of 25.50, we use the formula Z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation. Substituting the given values, we get Z = (25.50 - 23.33) / 6.13 ≈ 0.36. The Z score tells us that the observed age is approximately 0.36 standard deviations above the mean. (b) To find the observed age associated with a Z score of -0.72, we rearrange the formula and solve for X: X = Z * σ + μ. Substituting the values, we get X = -0.72 * 6.13 + 23.33 ≈ 20.95. Thus, an observed age of approximately 20.95 corresponds to a Z score of -0.72.

(c) To calculate the proportion of respondents married between the ages of 20 and 30, we need to convert the age range to Z scores. The Z score for 20 is (20 - 23.33) / 6.13 ≈ -0.54, and the Z score for 30 is (30 - 23.33) / 6.13 ≈ 1.09. We then calculate the area under the normal distribution curve between these Z scores using a Z-table or a statistical software. This proportion represents the proportion of respondents married for the first time between the ages of 20 and 30.

(d) To determine the percentile rank for an individual married at the age of 35, we need to calculate the area under the normal distribution curve to the left of the corresponding Z score. The Z score for 35 is (35 - 23.33) / 6.13 ≈ 1.90. We then look up the corresponding percentile in a Z-table or use statistical software to find the percentage of the population with a Z score less than 1.90. This percentage represents the percentile rank for an individual married at the age of 35.

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Answer:

x = -4,-2

Step-by-step explanation:

x² + 6x + 8 = 0

Factor the equation

(x+4)(x+2) =0

Using the zero product property

x+4 =0   x+2 =0

x=-4  x=-2

x = -4,-2

Answer:

\( \sf \: x = - 2 \: \: or \: \: - 4\)

Step-by-step explanation:

\( \sf {x}^{2} + 6x + 8 = 0\)

Factorise.

\( \sf {x}^{2} + 6x + 8 = 0 \\ \sf {x}^{2} + 4x + 2x + 8 = 0\)

\( \sf x(x + 4) + 2(x + 4) = 0 \\ \sf(x + 2)(x + 4) = 0\)

Use the zero product property.

\( \sf \: x + 2 = 0 \\ \sf \: x = 0 - 2 \\ \sf x = - 2\)

Or

\( \sf \: x +4 = 0 \\ \sf \: x = 0 - 4 \\ \sf \: x = - 4\)

Therefore,

\( \sf \: x = - 2 \: or \: \: - 4\)

Answer:

y = 100 - 0.08^ x

Step-by-step explanation:

Answer:

B. v < - ⅙

Step-by-step explanation:

v + ⅚ < ⅔

v < ⅔ - ⅚

v < 4/6 - ⅚

v < - ⅙ (option B.)

Hope it helps ⚜

Q10

Q11

Answer:

9

Step-by-step explanation:

\(f(x) = x^4 +5x^3 -18x +1\\\\f(-4) = (-4)^4 +5(-4)^3 -18(-4) +1\\\\~~~~~~~~~=256+5(-64)+72+1\\\\~~~~~~~~~=329-320\\\\~~~~~~~~~=9\)

This means that the answer is D.

In everyday speech, the term "probability" refers to the likelihood that a specific event (or set of events) will take place, expressed as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of occurrences that follow a probability distribution.

The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

According to the given question:-

Even though there aren't any actual options for this question, figuring out the right response should be simple. The quantity of numbers that will be listed is the "probability of success" that is being discussed here. We simply need to select the option with 8 of the 10 mentioned numbers since an 80% likelihood is what is being sought. This indicates that the solution is D. Hope this is useful!

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Answer:

Step-by-step explanation:

Answer:

She has 27 quarters

Step-by-step explanation:

Let:

x = Number of nickels

y = Number of quarters

US$0.05 = 5 cents = monetary value of a nickel

US$0.25 = 25 cents = monetary value of a quarter

                      x + y = 68

                     x = 68 - y  ---- --------  (equation i)

                0.05x + 0.25y = 8.80----- (equation ii)

These two are linear simultaneous equations, which can be solved either by substitution, elimination or graphical method.

Substitution method:

Substitute (equation i) into (equation ii) to solve for y:

0.05(68 - y) + 0.25y = 8.80

Expand the brackets by applying the Distributive Law and then bring all the like terms together. y needs to be isolated and made the subject of the equation:

= 3.4 - 0.05y + 0.25y = 8.80

= 0.25y - 0.05y = 8.80 - 3.40

= 0.20y = 5.40

= y = \(\frac{5.40}{0.20}\)

∴ y = number of quarters = 27

Answer:

:(

Step-by-step explanation:

idek

Answer:  None of the above

The central bank of the US is the Federal Reserve.

Answer: 5 - 20 i

Step-by-step explanation:

Based on the information provided, the table that best matches the data in the scatter plot is shown below.

A scatter plot is a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

Based on the information provided, the table that best matches the data in the scatter plot is given by:

Data                       1    2    4    5.5    6.3

Height (cm)            1    2    3     4       5

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Answer:

the answer is 6

Step-by-step explanation:

Find what's 1/8 divided by 3/4 in fraction form?

step 1 Address formula, input parameters & values.

Input parameters & values:

1/8 and 3/4

Step 2: change the problem

Remember, always do KCF(Keep,Change,Flip)

First i keep 1/8

1/8 ÷ 3/4

Then I change the sign to multiplication because you need to need to find the answer and simplified it

1/8 x 3/4

Make sure u always flip the other fraction because you are multiplying

1/8 x 4/3

then you do the rest

Step 3:solve

1/8 x 4/3=4/24

Step 4: simplified

24/4=6

Now your answer is 6

Hope it helps :)

a. \(3\left[\begin{array}{ccc}2\\-3\\0\end{array}\right]+5\left[\begin{array}{ccc}-1\\0\\1\end{array}\right] = \left[\begin{array}{ccc}1\\-9\\5\end{array}\right]\) by using the algebraic properties of vectors.

b. A unit vector in the direction \(\overline{a} = \left[\begin{array}{ccc}1\frac{5}{\sqrt{34} } \\ \frac{-3}{\sqrt{34} }\\ \frac{0}{\sqrt{34} } \end{array}\right]\) of the vector \(\left[\begin{array}{ccc}5\\-3\\0\end{array}\right]\).

Given that,

Use the algebraic properties of vectors for solving the

a. \(3\left[\begin{array}{ccc}2\\-3\\0\end{array}\right]+5\left[\begin{array}{ccc}-1\\0\\1\end{array}\right]\)

We know that,

By using the algebraic properties of vectors as,

= 3(2i - 3j + 0k) + 5(-i + 0j + k)

= 6i - 9j + 0k -5i + 0j + 5k

= i - 9j + 5k

= \(\left[\begin{array}{ccc}1\\-9\\5\end{array}\right]\)

Therefore, \(3\left[\begin{array}{ccc}2\\-3\\0\end{array}\right]+5\left[\begin{array}{ccc}-1\\0\\1\end{array}\right] = \left[\begin{array}{ccc}1\\-9\\5\end{array}\right]\) by using the algebraic properties of vectors.

b. We have to find a unit vector in the direction of the vector \(\left[\begin{array}{ccc}5\\-3\\0\end{array}\right]\)

The unit vector formula is \(\overline{a}= \frac{\overrightarrow a }{|a|}\)

Let a = \(\left[\begin{array}{ccc}5\\-3\\0\end{array}\right]\)

Determinant of a is |a| = \(\sqrt{5^2 +(-3)^2 + (0)^2}\) = \(\sqrt{25 + 9}\) = \(\sqrt{34}\)

\(\overrightarrow a\) = 5i -3j + 0k

Now, we get

\(\overline{a}= \frac{\overrightarrow a }{|a|}\) = \(\frac{5i -3j + 0k}{\sqrt{34} }\) = \(\frac{5}{\sqrt{34} }i + \frac{-3}{\sqrt{34} }j + \frac{0}{\sqrt{34} } k\)

\(\overline{a} = \left[\begin{array}{ccc}1\frac{5}{\sqrt{34} } \\ \frac{-3}{\sqrt{34} }\\ \frac{0}{\sqrt{34} } \end{array}\right]\)

Therefore, a unit vector in the direction \(\overline{a} = \left[\begin{array}{ccc}1\frac{5}{\sqrt{34} } \\ \frac{-3}{\sqrt{34} }\\ \frac{0}{\sqrt{34} } \end{array}\right]\) of the vector \(\left[\begin{array}{ccc}5\\-3\\0\end{array}\right]\).

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Answer:

B

Step-by-step explanation:

since 5 is constant so you can take it out from the summation

Answer:

A)2/1

Step-by-step explanation:

the x is one apart ans it whent up 2 to the right 1

Answer:

2/1

Step-by-step explanation:

Slope is rise over run, or y2-y1/x2-x1

y2=5 y1=3 x2=2  x1=1

5-3/2-1=2/1

Answer:

t=  \(\frac{-2S}{u-v}\)

Step-by-step explanation:

Solve S=(v - u) t ÷ 2​

t=  \(\frac{-2S}{u-v}\)

The probability that a five-card hand will contain a straight = 5/1274

There are 52 cards in a deck from which each 13 cards are from 4 different suits (clubs, diamonds, spades and hearts) in a game of poker.

Each 13 cards from high to low are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. So a straight of five cards, i.e., five cards in unbroken numerical sequence would be got only from 10 cards in a sequence.

So the possible ways to get a single straight five from all four suits = \(4^5\)

Now as we doesn't need all 5 cards from a single suit, we can ignore 4 ways from the above number. i.e.,  \(4^5-4 = 1020\) ways.

Hence the possible ways to get a straight five from 10 cards from all four suits = 10 x 1020 = 10200 ways

Total number of ways to select 5 cards from 52 cards = 52C5

Thus,

The probability that a five-card hand will contain a straight = 10200 / 52C5

                                                                                                  = 5/1274                        Learn more about probability at https://brainly.com/question/5858025

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Answer:

14/23

Why:

P(A) = probability that the ball transferred from urn first to second is white

P(B) = probability that the ball drawn from second urn is black.

Case I: If white ball goes to urn II

P(C) = 5/12 x 9/13= 45/156

Case II: If black ball goes to urn II

P(D) = 7/12 x 10/13= 70/156

Thus, P(B) = P(C) + P(D) = 115/156

P(A/B) = Probability of event A when B has occurred = Probability that ball drawn from II urn is black = 14/23.

Given parameters:

Number of equally sized slices = 10

Red slices  = 2

Yellow slices  = 4

Blue slices  = 4

Unknown:

Probability that the dial stops on a red or yellow color  =?

Solution:

Probability is the likelihood of an event to occur.

   Probability  = \(\frac{Possible outcome }{Total outcome}\)  

   This probability cites a mutually exclusive event because if the dial stops on red, it cannot be on yellow.

Pr(red  or yellow) = Pr(red) + Pr(Yellow)

                             = \(\frac{2}{10}\)  + \(\frac{4}{10}\)

                              = \(\frac{6}{10}\)

                              = \(\frac{3}{5}\)

The probability of red or yellow is \(\frac{3}{5}\)

Questions that require responses at fixed intervals along a scale of answers are called scale questions.

Closed-ended questions, such as the Likert Scale, are one of the most popular methods for gauging public opinion. To gauge people's opinions, attitudes, and beliefs, they employ psychometric testing. Statements are used in the questions, and respondents are asked how much they agree or disagree with each assertion. Likert Scale questions typically have a scale from 0 to 10, while shorter scales are also conceivable.

Every sort of research has benefits and drawbacks, and this particular question type has both in spades. The fundamental benefit of Likert Scale questions is that they follow a standard way of data collection, making them simple to comprehend.

Hence, according to the definition questions that require responses at fixed intervals along a scale of answers are called scale questions.

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Answer:

\(\displaystyle{P(x)=x^3-x^2}\)

Step-by-step explanation:

Given the zeros of 0, 0, 1. We can write the polynomial in form of x-intersects:

\(\displaystyle{P(x) = (x-x_1)(x-x_2)(x-x_3)}\)

Hence:

\(\displaystyle{P(x)=(x-0)(x-0)(x-1)}\)

Which can be simplified to:

\(\displaystyle{P(x)=x\cdot x \cdot (x-1)}\\\\\displaystyle{P(x)=x^2(x-1)}\)

Convert to the standard form by distributing x²:

\(\displaystyle{P(x)=x^2\cdot x - x^2 \cdot 1}\\\\\displaystyle{P(x)=x^3-x^2}\)

The curvature \(\(\kappa(t)\)\) of the parametric equations \(\(x = 7 + t^2\)\) and \(\(y = 6 + t^3\)\)is given by:  \(\(\kappa(t) = \frac{2|3t^2 - 2|}{t^2(4 + 9t^2)^{3/2}}\)\)

To find the curvature, we need to calculate the second derivative of the parametric equations x = 7 + t² and y = 6 + t³, and then use the following formula:

\(\[ \kappa(t) = \frac{\left| \frac{d \vec{r}}{dt} \times \frac{d^2 \vec{r}}{dt^2} \right|}{\left| \frac{d \vec{r}}{dt} \right|^3} \]\)

where \(\(\vec{r}\)\) represents the vector-valued function with components x and y.

Let's start by finding the first derivative and the second derivative of\(\(\vec{r}\)\):

Given:

\(\[ x = 7 + t^2 \]\\\)

\(\[ y = 6 + t^3 \]\)

First derivative:

\(\[ \frac{d \vec{r}}{dt} = \left(\frac{dx}{dt}, \frac{dy}{dt}\right) \]\)

Differentiating x with respect to t:

\(\[ \frac{dx}{dt} = \frac{d}{dt}(7 + t^2) = 2t \]\)

Differentiating y with respect to t:

\(\[ \frac{dy}{dt} = \frac{d}{dt}(6 + t^3) = 3t^2 \]\)

So the first derivative of \(\(\vec{r}\)\)is:

\(\[ \frac{d \vec{r}}{dt} = (2t, 3t^2) \]\)

Now, let's find the second derivative of \(\(\vec{r}\)\):

Second derivative:

\(\[ \frac{d^2 \vec{r}}{dt^2} = \left(\frac{d^2 x}{dt^2}, \frac{d^2 y}{dt^2}\right) \]\)

Differentiating \(\(\frac{dx}{dt}\)\) with respect to t:

\(\[ \frac{d^2 x}{dt^2} = \frac{d}{dt}(2t) = 2 \]\)

Differentiating \(\(\frac{dy}{dt}\)\) with respect to t:

\(\[ \frac{d^2 y}{dt^2} = \frac{d}{dt}(3t^2) = 6t \]\)

So the second derivative of \(\(\vec{r}\)\) is: \(\[ \frac{d^2 \vec{r}}{dt^2} = (2, 6t) \]\)

Now, we can substitute these values into the curvature formula:

\(\[ \kappa(t) = \frac{\left| \frac{d \vec{r}}{dt} \times \frac{d^2 \vec{r}}{dt^2} \right|}{\left| \frac{d \vec{r}}{dt} \right|^3} \]\)

Calculating the cross product of \(\(\frac{d \vec{r}}{dt}\) and \(\frac{d^2 \vec{r}}{dt^2}\)\):

\(\[ \frac{d \vec{r}}{dt} \times \frac{d^2 \vec{r}}{dt^2} = (2t, 3t^2) \times (2, 6t) \]\[\)=

\(\begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 2t & 3t^2 & 0 \\ 2 & 6t & 0 \end{vmatrix} \]\)

\(\[ = (0, 0, 6t^3 - 4t) \]\)

Now, let's calculate the magnitudes of the vectors:\(\[ \left| \frac{d \vec{r}}{dt} \right| = \left| (2t, 3t^2) \right| = \sqrt{(2t)^2 + (3t^2)^2} = \sqrt{4t^2 + 9t^4} = t\sqrt{4 + 9t^2} \]\)

\(\[ \left| \frac{d \vec{r}}{dt} \times \frac{d^2 \vec{r}}{dt^2} \right| = \left| (0, 0, 6t^3 - 4t) \right| = \sqrt{(6t^3 - 4t)^2} = |2t(3t^2 - 2)| = 2t|3t^2 - 2| \]\)

Finally, substituting these values back into the curvature formula:\(\[ \kappa(t) = \frac{2t|3t^2 - 2|}{(t\sqrt{4 + 9t^2})^3} = \frac{2|3t^2 - 2|}{t^2(4 + 9t^2)^{3/2}} \]\)

That's the expression for the curvature \(\(\kappa(t)\)\)of the given parametric equations.

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Answer:

D)  Marty gets ten dollars for his allowance and then spends ten dollars at the movies.

Step-by-step explanation:

Answer: It is ten degrees below zero and then the temperature rises fifteen degrees.

Step-by-step explanation:

Answer:

60 mph

Step-by-step explanation:

Let 'S' be the velocity of the southbound car and 'E' be the velocity of the eastbound car. The distances traveled by each car are:

\(D_E=3E\\D_S=3S=3(E+15)\\D_S=3E+45\)

The distance between both cars is given by:

\(D^2=D_S^2+D_E^2\\225^2=(3E+45)^2+(3E)^2\\50,625=9E^2+270E+9E^2+2,025\\18E^2+270E-48,600=0\\\)

Solving the quadratic equation for the velocity of the eastbound car:

\(18E^2+270E-48,600=0\\E^2+15E-2,700\\E=\frac{-15\pm\sqrt{15^2-4*1*(-2,700)}}{2}\\E=45.0\ mph\)

The velocity of the southbound car is:

\(S=E+15=45+15\\S=60\ mph\)

The southbound car is driving at 60 mph.

The solution to the polynomial expression are: -√3 and √3.

The factored form of X⁴ - 2x² - 3 = 0 can be found by factoring a common factor of x² from the first two terms:

X²(x² - 2) - 3 = 0

Next, we can add 3 to both sides and factor out a common factor of X^2 - 2 from the right side:

X²(x² - 2) = 3

x² - 2)(x²) 3

x² = ±√3

Taking the square root of both sides, we find that X = ±√3. However, since we want to write the solutions in order from least to greatest with imaginary solutions last, we write the solutions as follows:

X = -√3, √3

So the solutions to X^4 - 2X^2 - 3 = 0 are -√3 and √3, written in order from least to greatest and with the imaginary solutions last.

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The pieces of cloth are beyond the standard at 0.05 level of significance.

We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.

The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:

H0: μ = 3.25

The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:

Ha: μ > 3.25

We can calculate the test statistic as:

t = (x - μ) / (s / √n)

where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).

Plugging in the values, we get:

t = (3.52 - 3.25) / (0.52 / √35) = 3.81

Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.

Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.

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