What degree of rotation about the origin will cause the triangle below to map
onto itself?

A. 90 degrees
B. 360 degrees
C. 180 degrees
D. 270 degrees

Answer:

1/3

Step-by-step explanation:

There are 3 cards and out of the three you only have one one third chance of picking each number

Answer: 0.66 ft

Step-by-step explanation:

Let assume that the initial position of the worker is x.

Given that the worker walks away with a constant speed of 2 ft/s. Therefore, dx/dt = 2

As the worker moves away, the rope makes a triangle, with width length x and the height length will be 30.

Using pythagorean theorem, the length of rope on this side of the pulley will be √(x² + 30²)

Also, the length of rope on the other side will be 60 - √(x² + 30²),

and the height h of the weight will be 30 - (60 - √(x² + 30²)) = √(x² + 30²) - 30

dh/dt = dx/dt × x/√(x² + 30²)

= 4x/√(x² + 30²)

dh/dt = 4x/√(x² + 30²)

If the worker moves 5ft away, then

dh/dt = (4×5)/√(5² + 30²)

dh/dt = 20/√(25 + 900)

dh/dt = 0.66 ft

Answer:

work is shown and pictured

Answer:

P = 0.1764

The events are dependent

Step-by-step explanation:

We have a total of 9 + 6 + 3 = 18 stuffed animals.

The probability of the first animal pulled being a bear is:

P(bear) = N(bear) / N(total)

P(bear) = 9 / 18 = 0.5

Then, for the second animal, we now have only 17 stuffed animals in total.

So the probability of the second animal pulled being a lion, given the first animal was a bear, is:

P(lion | bear) = N(lion) / N(total)

P(lion | bear) = 6 / 17 = 0.3529

So the final probability is the product of these probabilities:

P = P(bear) * P(lion | bear) = 0.5 * 0.3529 = 0.1764

To find if the events are dependent or independent, let's find the probability of the first pick being a lion:

P(lion) = N(lion) / N(total)

P(lion) = 6 / 18 = 0.3333

The probability of picking a lion is different from the probability of picking a lion given we already picked a bear, so the events are dependent.

Answer:

work is shown and pictured

Answer:

The question is not complete, as the table containing the data is missing, but I found a matching table that can be used to answer the question.

The Question is:

Which is the highest rated, of the four European cities under consideration, using the table.

The correct answer is: City A is the highest rated European city.

Step-by-step explanation:

The highest rated European city can be found by multiplying the factor and the importance of the factors, and summing up their final values. the cty with the highest number is the one with the highest rated city. Having this in mind, let us calculate the ratings for each of the cities as follows:

City A:

(70 × 20) + (80 × 20) + (100 × 20) + (80 × 10) + (90 × 10) + (65 × 10) + (70 × 10) = 1400 + 1600 + 2000 + 800 + 900 + 650 + 700 = 8050

City B:

(70 × 20) + (60 × 20) + (50 × 20) + (90 × 10) + (60 × 10) + (75 × 10) + (60 × 10) = 1400 + 1200 + 1000 + 900 + 600 + 750 + 600 = 6450

City C:

(60 × 20) + (90 × 20) + (75 × 20) + (65 × 10) + (50 × 10) + (85 × 10) + (65 × 10) = 1200 + 1800 + 1500 + 650 + 500 + 850 + 650 = 7150

City D:

(90 × 20) + (75 × 20) + (90 × 20) + (65 × 10) + (70 × 10) + (70 × 10) + (80 × 10)   = 1800 + 1500 + 1800 + 650 + 700 + 700 + 800 =7950

Therefore, from the ratings computed above, City A with a rating of 8050, is the highest rated, while City B with a rating of 6450, is the lowest rated.

Answer:

Answer:

The total is: $ 1345.5

Step-by-step explanation:

It is given that:

I would like to purchase 20 products at a cost 65.00 per product.

This means that the cost of 20 products will be:

Also, there is a sales tax of 3.5%

This means that a person has to pay a extra 3.5% on the total cost of the items he purchased.

i.e. he need to pay 3/5% on $ 1300

This means that the amount of tax he need to pay is: 3.5% of 1300

                                                                             =  3.5%×1300

                                                                            = 0.035×1300

                                                                           = $ 45.5.

Hence, the total cost is: $ 1300+$ 45.5

This means that the total cost is: $ 134.5

Answer:

(B) 0.7%

Step-by-step explanation:

X = Land Elevation (in ,000 feet)

Y = Unidentified Artifacts (in %)

The hypothetical theory says that:

The higher the elevation, the higher the percentage of unidentified artifacts in the location.

To find the percentage of variation in Y that can be explained by variations in X, we find the slope of the graph of X on Y.

Transforming X to thousand feets, we have 5220, 5690, 6250, 6750, 7250. This is in the attachment, plotted against 17, 12, 33, 37 and 62 respectively.

Further calculations, along with the graph, are in the attachment below. The answer therein is (B) 0.7%

Answer: B. although none are exactly 0.3 B is closest

Step-by-step explanation:

a. 35/999 = .0350

b. 31/99 = .3153

c. 105/7333 = .0143

d. 35/111 = .3135

Answer:

174

Step-by-step explanation:

l x w

5x20

8x4

6x7

174

Answer:

(a) The probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.

(b) The probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.

Step-by-step explanation:

The  cumulative distribution function of the random variable X, the waiting time, in hours, between successive speeders spotted by a radar unit is:

[tex]F(x)=\left \{ {{0;\ x<0} \atop {1-e^{-9x};\ x\geq 0}} \right.[/tex]

(a)

Compute the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function as follows:

[tex]12\ \text{minutes}=\frac{12}{60}=0.20\ \text{hours}[/tex]

The probability is:

[tex]P(X<0.20)=|F (x)|_{x=0.20}[/tex]

                  [tex]=(1-e^{-8x})|_{x=0.20}\\\\=1-e^{-8\times 0.20}\\\\=0.7981[/tex]

Thus, the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.

(b)

The probability density function of X is:

[tex]f_{X}(x)=\frac{d F (x)}{dx}=\left \{ {{0;\ x<0} \atop {8e^{-8x};\ x\geq 0}} \right.[/tex]

Compute the probability of waiting less than 12 minutes between successive speeders using the probability density function as follows:

[tex]P(X<0.20)=\int\limits^{0.20}_{0} {8e^{-8x}} \, dx[/tex]

                  [tex]=8\times [\frac{-e^{-8x}}{8}]^{0.20}_{0}\\\\=[-e^{-8x}]^{0.20}_{0}\\\\=(-e^{-8\times 0.20})-(-e^{-8\times 0})\\\\=-0.2019+1\\\\=0.7981[/tex]

Thus, the probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.

Answer:

A. or every 1 ton increase in precompression stress, the shear strength of the joint is estimated to increase by 0.987 tons.

Step-by-step explanation:

Hello!

The engineers created a regression model to estimate the relationship between the "shear strength of masonry joints" (Y), measured in tons, and the "precompression stress" (X), measured in tons.

^Y= a + bXi

Using the regression output:

Estimate of the y-intercept: a= 1.192

Estimate of the slope: b= 0.987

In general terms you can interpret the slope as:

"Is the modification of the estimated mean of Y when X increases one unit"

In this case it means that every time the precompression stress increases one ton, the shear strength of the joint is estimated to increase 0.987 tons.

I hope this helps!

Answer:

80 milk chocolates

Step-by-step explanation:

Probability of choosing a dark chocolate= number of dark

chocolate/number of total

chocolate

But the probability of choosing dark chocolate= 2/9

The number of dark chocolate= 24

Total chocolate= number of dark

chocolate/probability

of choosing dark

chocolate

Total chocolate= 24/(2/9)

Total chocolate=( 24*9)/2

Total chocolate= 108

Number of milk chocolate= total- dark

Number of milk chocolate

= 108-28

= 80

Answer:

B. 0.0043

Step-by-step explanation:

The null and alternative hypothesis of this one-tailed test are:

[tex]H_0: p_1-p_2=0\\\\H_a:p_1-p_2> 0[/tex]

The output of proportions_ztest method from statsmodels is a size-2 vector with the value of the test statistic and the P-value.

Then, if the output is (3.25, 0.0043), the P-value for this one-tailed test is 0.0043.

Answer:

  D.  x is all real numbers

Step-by-step explanation:

The graph only goes from -11 to +11 in the horizontal direction, but that domain is not a choice. Apparently, we're to assume the graph extends to infinity both to the left and the right.

The domain is the horizontal extent of the function, so is ...

  x is all real numbers

Answer: F.) 7 triangles

Step-by-step explanation:

Congruent means completely equal in side lengths and angles. Think of this weird figure like 4 triangles that are see through and are covering a diamond underneath

Of those 4 "see through triangles", there are 3 equal to ΔABC

Now on the diamond underneath, there is another 4. Its hard to actually explain what I mean, but take two triangles from that dimaond. Theyre gonna be congruent to ΔABC.

That's 4 + 3 = 7 total triangles

Answer:

Time = X = 37.14 minutes

Distance they covered= 33.42 miles.

Step-by-step explanation:

Distance= speed * time

And the distance traveled by the two need to be equal.

Speed of storm = 33 mph

Speed of van = 54 mph

But storm is 13 miles away from van.

So

54*x = 33*x+ 13

54x-33x = 13

21x = 13

X= 0.62 hours

X = 37.14 minutes

54 *0.62= 33.42 miles.

Answer:

y=2x-4

Step-by-step explanation:

[tex]answer \\ a. \frac{2}{117} \\ b. 4 \\ solution \\ a. \: \frac{2}{9} \times \frac{1}{13} \\ = \frac{2 \times 1}{9 \times 13} \\ = \frac{2}{117} \\ b. \: \frac{12}{5} \times \frac{35}{21} \\ = divide \: 35 \: by \: 5 \: it \: becomes \\ = 12 \times \frac{7}{21} \\ divide \: 21 \: by \: 7 \: it \: becomes \\ = 12 \times \frac{1}{3} \\ divide \: 12 \: by \: 3 \: it \: becomes \\ = 4 \times 1 \\ = 4 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

[tex](a) \frac{2}{117} [/tex]

[tex](b)4[/tex]

Step-by-step explanation:

[tex](a) \frac{2}{9} \times \frac{1}{13} \\ = \frac{2}{117} [/tex]

[tex](b) \frac{12}{5} \times \frac{35}{21} \\ = \frac{84}{21} \\ = \frac{28}{7} \\ = 4[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

4 ( a+2)

Step-by-step explanation:

The average rate of change is

(f(a) - f(2))/(a-2)

f(a) = 4a^2 -8

f(2) = 4*2^2 -8 = 4*4 -8 = 16-8 = 8

(4a^2 - 8  - 8))/(a-2)

(4a^2 -16) / (a-2)

Factor the numerator

4( a^2 -4) / (a-2)

4( a-2)(a+2) / (a-2)

Cancel

4 ( a+2)

Answer:

a) The probability that the mean printing speed of the sample is greater than 17.55 ppm = 0.4247

b) The probability that more than 48.6% of the sampled printers operate at the advertised speed = 0.4197

Step-by-step explanation:

The central limit theorem explains that for an independent random sample, the mean of the sampling distribution is approximately equal to the population mean and the standard deviation of the distribution of sample is given as

σₓ = (σ/√n)

where σ = population standard deviation

n = sample size

So,

Mean of the distribution of samples = population mean

μₓ = μ = 17.35 ppm

σₓ = (σ/√n) = (3.25/√10) = 1.028 ppm

a) The probability that the mean printing speed of the sample is greater than 17.55 ppm.

P(x > 17 55)

We first normalize 17.55 ppm

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (17.55 - 17.35)/1.028 = 0.19

To determine the required probability

P(x > 17.55) = P(z > 0.19)

We'll use data from the normal probability table for these probabilities

P(x > 17.55) = P(z > 0.19) = 1 - P(z ≤ 0.19)

= 1 - 0.57535 = 0.42465 = 0.4247

b) The probability that more than 48.6% of the sampled printers operate at the advertised speed

We first find the probability that one randomly selected printer operates at the advertised speed.

Mean = 17.35 ppm

Standard deviation = 3.25 ppm

Advertised speed = 18 ppm

Required probability = P(x ≥ 18)

We standardize 18 ppm

z = (x - μ)/σ = (18 - 17.35)/3.25 = 0.20

To determine the required probability

P(x ≥ 18) = P(z ≥ 0.20)

We'll use data from the normal probability table for these probabilities

P(x ≥ 18) = P(z ≥ 0.20) = 1 - P(z < 0.20)

= 1 - 0.57926 = 0.42074

48.6% of the sample = 48.6% × 10 = 4.86

Greater than 4.86 printers out of 10 includes 5 upwards.

Probability that one printer operates at advertised speed = 0.42074

Probability that one printer does not operate at advertised speed = 1 - 0.42074 = 0.57926

probability that more than 48.6% of the sampled printers operate at the advertised speed will be obtained using binomial distribution formula since a binomial experiment is one in which the probability of success doesn't change with every run or number of trials. It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. The outcome of each trial/run of a binomial experiment is independent of one another.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 10

x = Number of successes required = greater than 4.86, that is, 5, 6, 7, 8, 9 and 10

p = probability of success = 0.42074

q = probability of failure = 0.57926

P(X > 4.86) = P(X ≥ 5) = P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10) = 0.4196798909 = 0.4197

Hope this Helps!!!

Answer:

y = -2x - 10

Step-by-step explanation:

1. rearrange to find the gradient.

the gradient of the original equation is 1/2 hence why a line PERPENDICULAR to that equation would have a gradient of -2.

2. substitute into y - y1 = m (x - x1)

y - (-2) = -2 (x - (-4))

y = -2x - 10

Answer:

514 square meters

Step-by-step explanation:

Consider the length of p;

[tex]11 * p * 3 = 528,\\33 * p = 528,\\p = 528 / 33 = 16 meters[/tex]

11, 3, and p act as the length, width, and height of this rectangular prism. We can apply the volume formula length * width * height, and thus made 11 * p * 3 equivalent to the volume 528. Now let us determine the surface area;

[tex]Area of Side 1 = 16 * 11 = 176 square meters,\\Area of Side 2 = 3 * 16 = 48 square meters,\\Area of Side 3 = 11 * 3 = 33 square meters,\\\\Surface Area = 2 * ( 176 ) + 2 * ( 48 ) + 2 * ( 33 ) = 352 + 96 + 66 = 514 square meters[/tex]

Hope that helps!

Answer:

514 square meters

Step-by-step explanation:

Since the volume of a rectangular prism is the product of the width, length, and height, 11*3*p=528. Therefore, p=528/(11*3)=16. Now, you can find the surface area. The surface of a rectangular prism is made up of 3 pairs of rectangles. One pair has dimensions of 11 by 3, one pair has dimensions of 16 by 3, and the last pair has dimensions of 16 by 11. The surface area of this figure is therefore:

[tex]2(11\cdot 3)+2(16\cdot 3) + 2(16\cdot 11)=66+96+352=514 m^2[/tex]

Hope this helps!

Answer: 30

Step-by-step explanation:

Q1: 120

Q3: 150

To find the interquartile range, subtract Q1 from Q3, which is 150-120. Therefore, the interquartile range  of the kitten's weight, is 30

Answer: 30 grams

Step-by-step explanation:

The interquartile range is the range within the boxed areaa. You subtract the minimum value from the maximum value.

150 - 120 = 30

Answer:

L(xyz) = ( 1 , 3 , -7 )

L = x + 3y - 7z -3

Step-by-step explanation:

f (x,y,z) = xy + 2yz - 3xz

f (3,1,0) = (3) (1) + 2 (1) (0) - 3 (3) (0)

f (3,1,0) = 3

fx = y - 3z

f (3,1,0) = (1) - 3 (0)

fx = 1

fy = x + 2z

f (3,1,0) = (3) - 2 (0)

fy = 3

fz = 2y - 3x

f (3,1,0) = 2 (1) - 3 (3)

fz = -7

Multiply 2 by 1/2 to get 1.

Multiply 1 by 2/3 to get 2/3.

Multiply 2/3 by 3/4 to get 6/12 = 1/2.

Multiply 1/2 by 4/5 to get 4/10 = 2/5.

Multiply 2/5 by 5/6 to get 10/30 = 1/3.

Multiply 1/3 by 6/7 to get 6/21 = 2/7. (I suspect there's a typo in the question.)

And so on, so that the nth term in the sequence is multiplied by n/(n + 1) to get the (n + 1)th term.

Recursively, the sequence is given by

[tex]\begin{cases}a_1=2\\a_n=\dfrac{n-1}na_{n-1}&\text{for }n>1\end{cases}[/tex]

We can solve this exactly by iterating:

[tex]a_n=\dfrac{n-1}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}{n-1}\dfrac{n-3}{n-2}a_{n-3}=\cdots[/tex]

and so on down to

[tex]a_n=\dfrac{(n-1)\cdot(n-2)\cdot(n-3)\cdot\cdots\cdot3\cdot2\cdot1}{n\cdot(n-1)\cdot(n-2)\cdot\cdots\cdot4\cdot3\cdot2}a_1[/tex]

or

[tex]a_n=\dfrac{(n-1)!}{n!}a_1[/tex]

and with lots of cancellation, we end up with

[tex]a_n=\dfrac{a_1}n=\boxed{\dfrac2n}[/tex]

Answer:

Divide 2 by n.

Step-by-step explanation:

Answer:

The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 150, \pi = \frac{17}{150} = 0.1133[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 - 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.0531[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 + 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.1735[/tex]

The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).

[tex]x^2+14x+40=0\\x^2+14x+40+9-9=0\\x^2+14x+49=9\\(x+7)^2=9\\\\D=7\\E=9[/tex]

Answer:

x^2+14x+40=0\\x^2+14x+40+9-9=0\\x^2+14x+49=9\\(x+7)^2=9\\\\D=7\\E=9

Step-by-step explanation:

Answer:

(7, -11)

Step-by-step explanation:

If the point is shifted 3 to the right and 2 down, you just have to add 3 to the x-coordinate and subtract 2 from the y-coordinate. 4+ 3 = 7 and -9 - 2 is -11. So, the new point will be (7, -11).

Answer:

(7, -11)

Step-by-step explanation:

The point is translated three units to the right, and 2 units down.

[tex](4,-9)=>(4+3,-9-2)=>(7,-11)[/tex]

Point " ' " should be (7,-11)