Four horizontal forces of magnitudes 1 N, 2 N, 3N and 4N act at a point in the direction whose bearings are 000, 060, 120 and 270 respectively. a Calculate the magnitude of their resultant. b. A 5th horizontal force of magnitude 3 N now acts at the same points so that the resultant of all five forces has a bearing of 090. Find the bearing of the 5th force

Answer:

x=30

Step-by-step explanation:

Find the value of x that will make A and B parallel

For A & B to be parallel, the interior angles must be supplementary, i.e.

4x+2x = 180

6x=180

x=30

When x=30, the interior angles are 120 and 60 which are supplementary.

Answer:

  35.98

Step-by-step explanation:

Fill in the numbers and do the arithmetic.

  y = a + bx . . . . . . a=4.95, b=0.29, x=107

  y = 4.95 + 0.29(107) = 35.98

The predicted price is 35.98.

Answer:

  Rn ≈ 0.6345

  Ln ≈ 0.7595

Step-by-step explanation:

The interval from -1 to 2 has a width of (2 -(-1)) = 3. Dividing that into 4 equal intervals means each of those smaller intervals has width 3/4.

It can be useful to use a spreadsheet or graphing calculator to evaluate the function at all of the points that define these intervals:

  x = -1, -.25, 0.50, 1.25, 2

Of course, the spreadsheet can easily compute the sum of products for you.

__

The approximation using right end-points will be the sum of products of the interval width (3/4) and the function value at the right end-points:

  Rn = (3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25) +(3/4)f(2)

  Rn ≈ 0.6345

__

The approximation using left end-points will be the sum of products of the interval width (3/4) and the function value at the left end-points:

  Ln = (3/4)f(-1) +(3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25)

  Ln ≈ 0.7595

_____

It is usually convenient to factor out the interval width, so only one multiplication needs to be done: (interval width)(sum of function values).

Answer:

11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet

Step-by-step explanation:

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

Permutations of four letters from a set of 12 letters. So

[tex]P_{(12,4)} = \frac{12!}{(12-4)!} = 11800[/tex]

11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet

Answer: it’s 11,880

not 11800

Answer:

The x-intercepts as shown on this graph are: (-3,0), (1,0), and (3,0). The y-intercept as shown on this graph is: (0,2).

Step-by-step explanation:

The intercepts refer to where the function intersects with either the x-axis or y-axis. Since the line crosses the y-axis at (0,2), that's the y-intercept. The same thing applies to the x-intercepts. On this graph, it's easier to identify because the intercepts are marked with dots.

Hey there! :)

Answer:

Last choice. a= 6.

Step-by-step explanation:

Starting with:

-6(2 + a) = -48

Distribute the -6:

-6(2) -6(a) = -48

Simplify:

-12 - 6a = -48

Add 12 to both sides:

-12 + 12 - 6a = -48 + 12

-6a = -36

Divide both sides by -6:

a = 6. Therefore, the last choice is correct.

Answer:

a = 6

Step-by-step explanation:

Solve the one-variable equation using the distributive property and properties of equality.

–6(2 + a) = –48

What is the value of a?

a = –6

a = –3

a = 5

a = 6

Answer:

1. JG (Jim gets first prize, George gets second prize)

2. JH (Jim gets first prize, Helen gets second prize)

3. JM (Jim gets first prize, Maggie gets second prize)

4. GH (George gets first prize, Helen gets second prize)

5. GJ (George gets first prize, Jim gets second prize)

6. GM (George gets first prize, Maggie gets second prize)

7. MJ (Maggie gets first prize, Jim gets second prize)

8. MG (Maggie gets first prize, George gets second prize)

9. MH (Maggie gets first prize, Helen gets second prize)

Step-by-step explanation:

The question asks for the list of outcomes in the event "Not A". We are looking for the reverse or negative of Event A.

The above given list is the list of outcomes in the event where Helen DOES NOT get first prize.

Answer:

a. AEB

b. BEC

c. CED

d. AED

Step-by-step explanation:

Each angle is made up of three points. All three points in order is the name of the angle.

Answer:

a. ∠1 = ∠AEB or ∠BEA

b. ∠2 = ∠BEC or ∠CEB

c. ∠3 = ∠CED or ∠DEC

d. ∠4 = ∠DEA or ∠AED

Step-by-step explanation: Penn <3

Answer:

C. 120 m²

Step-by-step explanation:

The surface area is equal to the area of 4 rectangles + area of 4 triangles + area of base.

Area of 4 rectangles:

4(5 × 4)

4(20) = 80

Area of 4 triangles:

4(3 × 4 × 1/2)

4(6) = 24

Area of base:

4² = 16

Add the areas.

16 + 24 + 80

= 120

The surface area of the composite solid is 120 m².

The surface area of this composite solid would be, 136 m². Hence, option D is true.

Used the formula for the surface area of the cuboid and the surface area of the 4 triangles,

The surface area of the cuboid = 2 (LW + LH + HW)

And, The surface area of the 4 triangles = 4 (1/2 × Base × Height)

Given that,

In a triangle,

Base = 4 m

Height = 3 m

And, In a Cuboid,

Length = 4 m

Width = 4 m

Height = 5 m

Hence, we get;

The surface area of the 4 triangles = 4 (1/2 × Base × Height)

= 4 (1/2 × 4 × 3)

= 4 × 6

= 24 m²

The surface area of the cuboid = 2 (LW + LH + HW)

= 2 (4 × 4 + 4 × 5 + 5 × 4)

= 2 (16 + 20 + 20)

= 112 m²

Therefore, The surface area of this composite solid would be,

24 m² + 112 m² = 136 m²

So, Option D is true.

To learn more about the triangle visit;

brainly.com/question/1058720

#SPJ4

Answer:

Critical value: b. 2.33

As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]

The significance level is 0.01.

The sample 1 (women), of size n1=150 has a proportion of p1=0.62.

The sample 2 (men), of size n2=200 has a proportion of p2=0.24.

The difference between proportions is (p1-p2)=0.38.

[tex]p_d=p_1-p_2=0.62-0.24=0.38[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{93+48}{150+200}=\dfrac{141}{350}=0.403[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.403*0.597}{150}+\dfrac{0.403*0.597}{200}}\\\\\\s_{p1-p2}=\sqrt{0.001604+0.001203}=\sqrt{0.002807}=0.053[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.38-0}{0.053}=\dfrac{0.38}{0.053}=7.17[/tex]

The critical value for a right-tailed test with a signficance level of 0.01 is zc=2.33 (see picture attached).

As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

Answer:

Option D is correct.

1/4 completes the square.

Step-by-step explanation:

To complete the square for a quadratic function, we require a third term that will enable the solutions of the quadrstic equation to be 2 repeated roots.

For that to be so for the quadratic equation

ax² + bx + c = 0,

b² has to be equal to 4ac

For this question, x² - x + c

From b² = 4ac

c = (b²/4a)

a = 1

b = -1, b² = 1

c = ?

c = (1/4)

Hence, (1/4) is the number that must be added to the expression to complete the square.

Hope this Helps!!!

Answer:

1

Step-by-step explanation:

We will use polynomial remainder theorem or little Bézout's theorem. It states that reminder p(x) divided by (x - a) is p(a). In our case (a = 3) it is p(3) = 1

Answer:

c. dividing is the inverse of multiplying because it doesn't really relate the equation like the others do.

hope it helps uh.......

Answer:

Step-by-step explanation:

The second is correct

f(x) <0 on ( _ infinit, -2.7) and ( -1, 0.8)

Answer:

192 m^2.

Step-by-step explanation:

We can split this up into 3 rectangles:

Area of the bottom rectangle = 27 * (9-3)

= 27 * 6 = 162 m^2.

Area of rectangle on the left = (18-6)*2

= 24 m^2

Area of small rectangle on the right = 3*2

= 6 m^2

Total area = 162+24+6

192 m^2.

Answer:

a) P(male=blue or female=blue) = 0.71

b) P(female=blue | male=blue) = 0.68

c) P(female=blue | male=brown) = 0.35

d) P(female=blue | male=green) = 0.31

e) We can conclude that the eye colors of male respondents and their partners are not independent.

Step-by-step explanation:

We are given following information about eye colors of 204 Scandinavian men and their female partners.

              Blue    Brown     Green    Total

Blue        78         23            13          114

Brown     19         23            12          54

Green     11           9             16          36

Total      108       55            41          204

a) What is the probability that a randomly chosen male respondent or his partner has blue eyes?

Using the addition rule of probability,

∵ P(A or B) = P(A) + P(B) - P(A and B)

For the given case,

P(male=blue or female=blue) = P(male=blue) + P(female=blue) - P(male=blue and female=blue)

P(male=blue or female=blue) = 114/204 + 108/204 − 78/204

P(male=blue or female=blue) = 0.71

b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=blue) = 78/114

P(female=blue | male=blue) = 0.68

c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=brown) = 19/54

P(female=blue | male=brown) = 0.35

d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=green) = 11/36

P(female=blue | male=green) = 0.31

e) Does it appear that the eye colors of male respondents and their partners are independent? Explain

If the following relation holds true then we can conclude that the eye colors of male respondents and their partners are independent.

∵ P(B | A) = P(B)

P(female=blue | male=brown) = P(female=blue)

or alternatively, you can also test

P(female=blue | male=green) = P(female=blue)

P(female=blue | male=blue) = P(female=blue)

But

P(female=blue | male=brown) ≠ P(female=blue)

19/54 ≠ 108/204

0.35 ≠ 0.53

Therefore, we can conclude that the eye colors of male respondents and their partners are not independent.

Answer:

1 1/8

Step-by-step explanation:

1/4 + 7/8

Make denominators equal.

2/8 + 7/8

Add the fractions.

9/8

Convert to a mixed fraction.

1 1/8

Answer:

1  1/8

Step-by-step explanation:

1/4 + 7/8

Get a common denominator

1/4 * 2/2 + 7/8

2/8 + 7/8

9/8

Change to a mixed number

8/8+ 1/8

1  1/8

Answer:

a) The domain of the function is [tex]x \geq 0\,s[/tex] [tex]\wedge[/tex]  [tex]x \leq 5.112\,s[/tex]. [tex][0\,s, 5.112\,s][/tex], [tex]\forall x \in \mathbb{R}[/tex], b) The range of the function is [tex]0\,m \leq y \leq 100\,m[/tex]. [tex][0\,m,100\,m][/tex], [tex]\forall y\in \mathbb{R}[/tex], c) The ball is 73 meters off of the ground at x = 3 seconds.

Step-by-step explanation:

The complete statement is: A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function [tex]f(x) = -5\cdot x^{2} + 6\cdot x + 100[/tex] represents this situation where x is time and y is the distance off of the ground.

a) What domain does the function make sense?

b) What range does the function make sense ?

c) How far off the ground is the ball at time x = 3 seconds?

a) Let [tex]x[/tex] and [tex]f(x)[/tex] be the time, measured in seconds, and the distance of the ground, measured in meters, respectively. Time is a positive variable, so domain corresponds to the interval when [tex]f(x) \geq 0[/tex] and [tex]t \geq 0[/tex]. That is:

[tex]-5\cdot x^{2} + 6\cdot x + 100 \geq 0[/tex]

[tex]-(x-5.112\,s)\cdot (x+3.912\,s) \geq 0[/tex]

Therefore, the domain of the function is [tex]x \geq 0\,s[/tex] [tex]\wedge[/tex]  [tex]x \leq 5.112\,s[/tex]. [tex][0\,s, 5.112\,s][/tex], [tex]\forall x \in \mathbb{R}[/tex]

b) The distance off of the ground is also a positive variable, where ball is thrown upward at a height of 100 meters and hits the ground at a height of 0 meters. Hence, the range of the function is [tex]0\,m \leq y \leq 100\,m[/tex]. [tex][0\,m,100\,m][/tex], [tex]\forall y\in \mathbb{R}[/tex]

c) The distance of the ball off of the ground at x = 3 seconds is found by evaluating the function:

[tex]f(3\,s) = -5\cdot (3\,s)^{2} + 6\cdot (3\,s) + 100[/tex]

[tex]f(3\,s) = 73\,m[/tex]

The ball is 73 meters off of the ground at x = 3 seconds.

Answer:

40 miles per hr.

Step-by-step explanation:

alll u have to do is divide the number of miles by the hrs.

ex.80/2=40

140/3.5=40

200/8=40

300/7.5=40

Answer:

32.5861

Step-by-step explanation:

I interpreted it this way:

20 - stop at n = 20 (inclusive)

1 - start at n = 1

4(8/9)^(n - 1) - geometric expression

Answer:

D

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

8/x+2=2/x-4

8/x=2/x-6

8=2-6x

6=-6x

-1=x

Answer:

x=6

Step-by-step explanation:

8/x+2=2/x-4

Using cross products

8*(x-4) = 2 (x+2)

Distribute

8x - 32 = 2x+4

Subtract 2x

8x-2x -32 = 2x-2x+4

6x-32 = 4

Add 32

6x-32+32 = 4+32

6x = 36

Divide by 6

6x/6 = 36/6

x = 6

Answer:

Step-by-step explanation:

Hello!

*Full text*

A fisheries biologist has been studying horseshoe crabs. She has sampled 100 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). The proposed regression equation is

weight = b + width * m

This model was fit to the data using the method of the least squares. The following results were obtained from statistical software.

(See attachment for output)

R2 = 0.423

A.) What is the regression equation for this example?

The estimate for the y-intercepts is b= 2.3013 and the estimate for the slope is m= 0.7963

In general, we can symbolize the estimated regression equation as ^Y= b + m*Xi. For this example you have to replace it with the calculated values of the regression coefficients to obtain the estimated regression equation:

^Y= 2.3013 + 0.7963Xi

B.) What is the explanatory, or predictor, variable in this study?

The explanatory or predictor variable is the variable that is suspected to have an effect over the response variable. In this example the predictor variable is:

X: Width of a horseshoe crab (cm)

C.) If the researcher wanted to test whether there is a statistically significant relationship between these two variables, what would the test statistic be? Calculate it from the table above.

To test if the regression is significant, the parameter of study will be the slope of the regression equation, symbolically: β. If the slope is equal to zero "β=0" then there is no linear regression between the response and explanatory variable. If the slope is different from zero "β≠0" then the regression is significant and the explanatory variable affects the response variable.

The hypotheses are:

H₀: β=0

H₁: β≠0

α: 0.05

[tex]t= \frac{m-\beta }{S_m} ~t_{n-2}[/tex]

[tex]t_{H_0}= \frac{0.7963-0}{0.0939}= 8.48[/tex]

The value of the statistic under the null hypothesis is t= 8.48

D.) What can we say about the p-value?

This test is two-tailed and so is the p-value, remember that the p-value is the probabulity of obtaining a value as extreme as the value of the statistic under the null hypothesis. The distribution for this test is a t with n-2= 100-2= 98 degrees of freedom. You can calculate the p-value as:

P(t₉₈≤-8.48) + P(t₉₈≥8.48)= P(t₉₈ ≤ -8.48) + (1 - P(t₉₈ < 8.48) ≅ 0.00001

E.) Ultimately, the reason that we find test statistics is so that we can compare them to a null distribution. For regression, that is a t-distribution based on the degrees of freedom. With 98 degrees of freedom (100-2), we can safely say that the critical t (or the confidence multiplier) is what?

As mentioned before, this test is two tailed, meaning that the rejection region is divided in two:

Critical values ±[tex]t_{n-2;1-\alpha /2}[/tex] = ± [tex]t_{98; 0.975}[/tex] = ± 1.984

This means that you'll reject the null hypothesis when the statistic is t ≤ -1.984 or if the statistic is t ≥ 1.984-

F.) Find the confidence interval for the slope.

Using a 95% confidence level, the interval for the slope is:

[m ± [tex]t_{n-2;1-\alpha /2}[/tex] Sm]

[0.7963 ± 1.984 * 0.0939]

[0.61; 0.98]

G.) Is there a statistically significant relationship? Answer with the test statistic and the confidence interval.

Yes, there is a significant relationship between the width and weight of the horseshoe crabs.

Using the critical value approach:

The calculated statistic is 8.48 and the critical value is ± 1.984, since the statistic is greater than the positive critical value, the decision is to reject the null hypothesis.

If you pay attention to the confidence interval, which was made at a confidence level complementary to the significance level of the hypothesis test, this interval [0.61; 0.98] doesn't include the "zero". Since the interval doesn't include the value of the parameter stated in the null hypothesis, you can conclude that this hypothesis is not true and therefore reject it.

I hope this helps!

Answer:

Radius = 6.5cm

Diameter = 13cm

Step-by-step explanation:

The diameter is given (13)

Radius is half the diameter (13/2=6.5)

Answer:

Explanation

The straight line is drawn from the centre of a circle to a point on its circumference is called radius of the circle. The radius of a circle is half of its diameter.

The chord that passes through the centre of a circle is called diameter of circle. Diameter is also called the largest chord of any circle. The length of diameter of a circle is two times it's radius.

Hope this helps...

Good luck on your assignment...

Answer:

Step-by-step explanation:

Hello!

The variable of interest is X: time it takes a customer from Andrew's computer store to pay his invoices.

You have the information of a sample of n= 17 customers

19, 15, 43, 39, 35, 31, 27, 34, 34, 30, 30, 26, 26, 26, 21, 21, 17

To determine the class width of the intervals for the divide the difference between the ending and initial class boundaries by the number of intervals that you want to determine:

Class width: (49.5-14.5)/5= 7

Then, starting from the initial class boundary, you have to add the class width to determine the next boundary, and so on until the ending class boundary:

Initial class boundary: 14.5

14.5 + 5.6= 20.1

1st interval: [14.5; 21.5]

and so on:

[21.5; 28.5]

[28.5; 35.5]

[35.5; 42.5]

[42.5; 49.5]

Once you determined all class intervals, you have to order the values of the data set from least to greatest and then count how many observations correspond to each interval and arrange it in a frequency table.

15, 17, 19, 21, 21, 26, 26, 26, 27, 30, 30, 31, 34, 34, 35, 39, 43

[14.5; 21.5] ⇒ 5

[21.5; 28.5] ⇒ 4

[28.5; 35.5] ⇒ 6

[35.5; 42.5] ⇒ 1

[42.5; 49.5] ⇒ 1

Once you have the data set organized in the table, you can proceed to draw the histogram.

(See attachment)

I hope this helps!

Answer:

[tex]\frac{C}{2r}[/tex]=pi

Answer:

π= C/2r

Step-by-step explanation:

In order to solve for pi, we must get pi by itself on one side of the equation.

C= 2πr

Let's rearrange the right side of the equation. We can do this because of the commutative property of multiplication.

C= 2πr

C= 2r* π

pi is now being multiplied by 2r. The inverse of multiplication is division. Divide both sides of the equation by 2r.

C/2r= 2r*π/2r

C/2r= π

π=C/2r

The required length of the line is given as 14.4 feet, as of the given conditions.

As given in the question, A kite is flying 12 ft off the ground. Its line is pulled taut and casts an 8 -ft shadow, to determine the length of the line.

In a right-angled triangle, its side, such as the hypotenuse, is perpendicular, and the base is Pythagorean triplets.

Here,
let the length of the line be x,
The scenario formed is right angle triangle,
Apply Pythagoras' theorem,
x² = 12² + 8²
x = √208
x = 14.4

Thus, the required length of the line is given as 14.4 feet, as of the given conditions.

Learn  more about Pythagorean triplets here:

brainly.com/question/22160915

#SPJ2

Answer:

4% is a statistic and 1% is a parameter

Step-by-step explanation:

First, let's remember the differences between parameters and statistics:

Parameters are values that describe data of the entire population.

Statistics are values that describe data from a sample.

The value of 1% refers to "all of the parts", which is the population of over 1 million parts, thus 1% is a parameter.

The value of 4% refers to the "100 selected", which is the sample of 100 parts, thus 4% is a statistic.

Therefore, 4% is a statistic and 1% is a parameter.

Answer:

$80

Step-by-step explanation:

Let the number of hours required to make a mailbox = x

Let the number of hours required to make a toy = y

Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita.

Each toy requires 1 hour of work from Carlo and 1 hour from Anita.

The table below summarizes the information for ease of understanding.

[tex]\left|\begin{array}{c|c|c|c}&$Mailbox(x)&$Toy(y)&$Maximum Number of Hours\\--&--&--&------------\\$Carlo&1&1&12\\$Anita&4&1&24\end{array}\right|[/tex]

We have the constraints:

[tex]x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0[/tex]

Each mailbox sells for $10 and each toy sells for $5.

Therefore, Revenue, R(x,y)=10x+5y

The given problem is to:

Maximize, R(x,y)=10x+5y

Subject to the constraints

[tex]x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0[/tex]

The graph is plotted and attached below.

From the graph, the feasible region are:

(0,0), (6,0), (4,8) and (0,12)

At (6,0), 10x+5y=10(6)+5(0)=60

At (4,8), 10(4)+5(8)=80

At (0,12), 10(0)+5(12)=60

The maximum revenue occurs when they use 4 hours on mailboxes and 8 hours on toys.

The maximum possible revenue is $80.