1. Divide 6/13 by 6/12
A. 12/13
B. 1/12
C. 13/12
D.916

Answer:

The 95​% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).

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 = 185, \pi = \frac{100}{185} = 0.5405[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 - 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.4687[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 + 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.6123[/tex]

The 95​% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).

Answer:

spinner green or blue

Step-by-step explanation:

Flipping a coin is 1/2 probability

Rolling a die and getting a number less than 4 is 1/2 probability

spinner green or blue is (4/6) = 2/3

Marbles is 1/2

Answer:

17000

Step-by-step explanation:

we can use the equation I=PRT

I=10,000(10)(0.07)

I=100,000(0.07)

i=7000

7000+ the initial 10,000=17000

Answer:

Step-by-step explanation:

(35 units three times a day) comes out to (35 units / day)(3 times per day), or

105 units per day

Answer:

[tex]x^{4} -11x^{2} +28[/tex]

Step-by-step explanation:

[tex](x^{2} -7)(x^{2} -4)[/tex]

[tex]x^{4} -4x^{2} -7x^{2} +28[/tex]

[tex]x^{4} -11x^{2} +28[/tex]

Answer:

Step-by-step explanation:

This is a test of the mean difference between 2 independent groups or populations.

Let μ1 be the mean annual bonus of Company A's employees and μ2 be the mean annual bonus of Company B's employees.

The random variable is μ1 - μ2 = difference in the mean annual bonus of Company A's employees and the mean annual bonus of Company B's employees

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 ≤ μ2 H0 : μ1 - μ2 ≤ 100

The alternative hypothesis is

H1 : μ1 > μ2 H1 : μ1 - μ2 > 100

This is a right tailed test because of the inequality sign at the alternative hypothesis. We need to take samples of annual bonuses from both company's employees and find the averages. Then we would determine the test statistic as well as the p value. We would use the p value with the level of significance to make decisions

Answer:

P = 4/13

Step-by-step explanation:

In a deck of 52 cards, there are 3 aces(spade, heart, diamond), 1 club ace, and 12 remaining club cards

=> The probability of randomly drawing 1 card that is an ace card or a club card:

P = number of elements/total number of elements

P = (3 + 1 + 12)/52

P = 16/52

P = 4/13

=> Option A is correct

Answer:

1) -4/5,3 Decimal form x= -0.8,3

2) ?

3)sq (x+2)(x+3)+sq x^2 +5x-4=0

Step-by-step explanation:

Hope this helps

Answer:

1/6

Question: Scott made a casserole for dinner he gave equal portions of 1/2 the casserole to 3 friends what diagram could scott use to find the fraction of the whole casserole that each friend got?

Step-by-step explanation:

Find attached the diagram Scott used to find the portion each friend got.

The shaded part indicate the portion of the casserole.

When Scott prepared the dinner = 1 portion of casserole

He shared 1/2 the portion to 3 of his friends:

Divide the diagram of the full portion into 2 to get ½ of the casserole

1/2 of the casserole = ½ × 1 portion = ½ portion

Each of his 3 friends would have equal portions = ⅓ of the ½ portion

The diagram of the ½ portion would be divided into 3 equal part

In terms of calculation = ½ × ⅓

= 1/6

Each of his friends would have 1/6 portion of the casserole.

Hello! I provided the answer to your problem in a picture.

Ex. (3/6)

Answer:

  9/8

Step-by-step explanation:

time A / time B = (3/2)/(4/3) = (3/2)(3/4) = (3·3)/(4·2)

time A / time B = 9/8

Answer:

The margin of error for a 95% confidence interval for the population mean is of 1.05 years.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population(square root of the variance) and n is the size of the sample.

What is the margin of error for a 95% confidence interval for the population mean

36 students, so [tex]n = 36[/tex]

Variance of 10.24, so [tex]\sigma = \sqrt{10.24} = 3.2[/tex]

[tex]M = 1.96*\frac{3.2}{\sqrt{36}} = 1.05[/tex]

The margin of error for a 95% confidence interval for the population mean is of 1.05 years.

Answer:

112 ounces

Step-by-step explanation:

Clay weighs 9 times as much as his baby sister .

Clay weighs 63 pounds.

His baby sister weigh 63/9.

His baby sister weighs 7 pounds.

But to be converted to ounce.

1 pound = 16 ounces

7 pounds = 7*16 ounces

7 pounds = 112 ounces

Answer:

- Only Drawing D has KL being a symmetrical segment.

- Drawings A, B and C have no axis of symmetry.

- Tylko rysunek D ma KL będący segmentem symetrycznym.

- Rysunki A, B i C nie mają osi symetrii.

Step-by-step explanation:

English Translation

In which drawing was the symmetrical segment of KL drawn? Which of these letters has no axis of symmetry?

Solution

The attached image to the question is presented in the attached image to this Solution.

Symmetry is a concept where a figure/shape has half of its part being a mirror image of the other part.

About the line or axis of symmetry, the structure or figure can be rotated at right angles or whole number multiples of right angles and the resulting structure is still the same as the one we started with.

Of the 4 drawings, only drawing D satisfies this conditions/criteria. And Hence, it is the only drawing amongst the four with an axis of symmetry.

In Polish/Po polsku

Załączony obraz do pytania jest przedstawiony na załączonym obrazku do tego rozwiązania.

Symetria to koncepcja, w której figura / kształt ma połowę swojej części stanowiącą odbicie lustrzane drugiej części.

W odniesieniu do linii lub osi symetrii, strukturę lub figurę można obracać pod kątem prostym lub wielokrotności liczby całkowitej pod kątem prostym, a wynikowa struktura jest nadal taka sama jak ta, od której zaczęliśmy.

Z 4 rysunków tylko rysunek D spełnia te warunki / kryteria. I dlatego jest to jedyny rysunek wśród czterech z osią symetrii.

Hope this Helps!!!

Mam nadzieję że to pomoże!!!

Answer:

AP = 10

Step-by-step explanation:

According to secant-secant theorem

(PB)(AP)=(PD)(PC)

6(AP) = (5)(12)

AP = 60/6

AP = 10

Answer:

10

Step-by-step explanation:

Applying the secant theorem, we get:

(PB) * (AP) = (PD) * (PC)

6 * (AP) = (5) * (12)

AP = 60/6

= 10

Hope this helps!

Answer:

a) 0.6628 = 66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance

b) 0.5141 = 51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

c) 0.5596 = 55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

d) 0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 175[/tex]

(a) What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?

46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows. This means that [tex]p = 0.467[/tex]. So

[tex]\mu = E(X) = np = 175*0.467 = 81.725[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.467*0.533} = 6.6[/tex]

This probability, using continuity correction, is [tex]P(X \geq 85 - 0.5) = P(X \geq 84.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 84.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{84.5 - 81.725}{6.6}[/tex]

[tex]Z = 0.42[/tex]

[tex]Z = 0.42[/tex] has a pvalue of 0.6628.

66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance.

(b) What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?

Using continuity correction, this is [tex]P(80 - 0.5 \leq X <  90 - 0.5) = P(79.5 \leq X \leq 89.5)[/tex], which is the pvalue of Z when X = 89.5 subtracted by the pvalue of Z when X = 79.5. So

X = 89.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{89.5 - 81.725}{6.6}[/tex]

[tex]Z = 1.18[/tex]

[tex]Z = 1.18[/tex] has a pvalue of 0.8810.

X = 79.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{79.5 - 81.725}{6.6}[/tex]

[tex]Z = -0.34[/tex]

[tex]Z = -0.34[/tex] has a pvalue of 0.3669.

0.8810 - 0.3669 = 0.5141

51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

(c) What is the probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance?

6.3% of visitors entered through the Grand Lake park entrance, which means that [tex]p = 0.063[/tex]

[tex]\mu = E(X) = np = 175*0.063 = 11.025[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.063*0.937} = 3.2141[/tex]

This probability, using continuity correction, is [tex]P(X < 12 - 0.5) = P(X < 11.5)[/tex], which is the pvalue of Z when X = 11.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{11.5 - 11.025}{3.2141}[/tex]

[tex]Z = 0.15[/tex]

[tex]Z = 0.15[/tex] has a pvalue of 0.5596.

55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

(d) What is the probability that more than 55 visitors have no recorded point of entry?

22.7% of visitors had no recorded point of entry to the park. This means that [tex]p = 0.227[/tex]

[tex]\mu = E(X) = np = 175*0.227 = 39.725[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.227*0.773} = 5.54[/tex]

Using continuity correction, this probability is [tex]P(X \leq 55 + 0.5) = P(X \leq 55.5)[/tex], which is the pvalue of Z when X = 55.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55.5 - 39.725}{5.54}[/tex]

[tex]Z = 2.85[/tex]

[tex]Z = 2.85[/tex] has a pvalue of 0.9978

0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

Answer:

Answers are below in bold.

Step-by-step explanation:

The first answer is correct. 1 m² = 10,000cm²

A=2(wl+hl+hw)        To find the surface area of the package, use this equation

A=2(18*50+20*50+20*18)      Multiply in the parentheses

A=2(900+1000+360)             Add in the parentheses

A=2(2260)                              Multiply

A=4520

The package has a surface area of 4520 cm²

The area of the package is less than the area of the wrapping paper.

So, Dayson can completely cover the package with the wrapping paper.

Answer:

Dimensions 30 in x 30 in x 15 in

Surface Area = 2,700 in²

Step-by-step explanation:

Let 'r' be the length of the side of the square base, and 'h' be the height of the bin. The volume is given by:

[tex]V=13,500=h*r^2\\h=\frac{13,500}{r^2}[/tex]

The total surface area is given by:

[tex]A=4*hr+r^2[/tex]

Rewriting the surface area function as a function of 'r':

[tex]A=4*\frac{13,500}{r^2} *r+r^2\\A=\frac{54,000}{r}+r^2[/tex]

The value of 'r' for which the derivate of the surface area function is zero, is the length for which the area is minimized:

[tex]A=54,000*r^{-1}+r^2\\\frac{dA}{dr}=0= -54,000*r^{-2}+2r\\\frac{54,000}{r^2}=2r\\ r=\sqrt[3]{27,000}\\r=30\ in[/tex]

The value of 'h' is:

[tex]h=\frac{13,500}{30^2}\\ h=15\ in[/tex]

The dimensions that will ensure the minimum surface area are 30 in x 30 in x 15 in.

The surface area is:

[tex]A=4*15*30+30^2\\A=2,700\ in^2[/tex]

Answer:

[tex]2p=348 cm\: S=6726 cm^{2}[/tex]

Step-by-step explanation:

Ciao, come stai?

1) Per prima cosa, dobbiamo trovare la misura della base più grande. Scomponendo la figura possiamo visualizzare un triangolo e un quadrato. Ci sono somiglianze con gli angoli. Quindi è un triangolo rettangolo. Applichiamo il teorema di Pitagora:

[tex]a^2=b^2+c^2\\95^2=b^2+76^2\\57=b[/tex]

2) Perimetro:

[tex]2p=60+57+76+60+95\\2p=348 cm[/tex]

3) L' area

[tex]\frac{(B+b)h}{2} =\frac{(117+60)76}{2} =6726 \:cm^{2}[/tex]

Answer:

y = -x + 3

Step-by-step explanation:

I graphed the equation on the graph below to show you that it goes through (-1,4) and is perpendicular to y = x.

Answer:

1/3

Step-by-step explanation:

The slope of a perpendicular line is always the negative reciprocal of the slope of the original line.

-1/-3 = 1/3

Answer:

I have two types of packages that i sell. one has 3 apples and 10 pears, another one has 5 apples and 20 pears. what are the minumum quantitys of each do i have to buy so i can make either all package #1 or only make package#2 with oout any left over pears and apples?

Step-by-step explanation:

i don't know how to explain it but i;ll try. you take the lcm i beleive of the two. i think i may have done it wrong

Answer:

no solution

Step-by-step explanation:

4( − 11) = 15 − 4

-44 = 11

Since this iS FALSE, it means that the equation given has no solution

Answer:

c. 0.80

Step-by-step explanation:

Probability from relative frequency:

The probability is the number of desired outcomes divided by the number of total outcomes.

What is the probability that the next bus sold will be yellow or green?

250+150+100 = 500 buses sold

Of those, 250+150 = 400 are yellow or green.

400/500 = 0.8

So the correct answer is:

c. 0.80

Answer:

27.41%

Step-by-step explanation:

Data provided in the question

The staffed of Alpha company = 79%

The staffed of Beta company = 62%

Based on the above information, the relative change of staffing from Alpha to beta company is

As we know that

[tex]\bold {\ Relative \ change = \frac{\alpha- \beta }{\beta }}[/tex]

[tex]= \frac{(79 -62)}{62} \% \\\\= \frac{17}{62} \times 100\\\\=0.2741 \times 100\\\\=27.41\ \%[/tex]

By applying the above formula we can get the relative change and the same is to be applied so that the correct percentage could come

Answer:

the graph of y=f(x)will shift up 9 units

Answer:

The area of the large circle is 16π

The area of one small circle is 4π

The total area of the two small circles will be one-half of the area of the large circle

Step by step explanation:

Area if circle = πr²

area of one large circle with a diameter of 8:

r = diameter/2 = 8/2 = 4

Area = π×4² = 16π

total area of 2 smaller diameter one-half that of the large circle.

Area = πr²

Diameter of small circle = 1/2(bigger circle diameter)

Diameter = 8/2 = 4

radius = 4/2 = 2

Area of one small circle = π×(2)² = 4π

Total Area of Two smaller circles= 2(4π) = 8π

Area of two smaller circle = 1/2(area of bigger circle) = 1/2(16π) 8π

Therefore, based on the answer:

The area of the large circle is 16π

The area of one small circle is 4π

The total area of the two small circles will be one-half of the area of the large circle

Answer:

The area of the large circle is 16 pi.

The area of one small circle is 4 pi.

The total area of the two small circles will be one-half of the area of the large circle.

Step-by-step explanation:

To shorten this down for ya lazy people like me the answers are 1, 2, and 5!!!

I got this right on my UNit test review!!!!!

I hope this helps!!!!!!

Answer:

y = 4.5x

Step-by-step explanation:

y=ax is form of proportional relationship

checking the first pair of numbers:

checking other lines

So the equation is:

Answer:

11.49 dogs/ square mile

Step-by-step explanation:

Population density of any place is number of living being living in that area per unit area.

Population density = number of living being/ area of the place

given

number of dogs= 43,600,000

area = 3,794,083 square miles

population density of domesticated dogs = 43,600,000 /3,794,083

                                                              = 11.4915 dogs/ square mile

population density of domesticated dogs, rounded to the nearest 10th

                                                              is  11.49 dogs/ square mile.

Answer:

Step-by-step explanation:

Since we know that for a distribution be a probability density function sum of all the probability events should be equal to 1 and all individual events should have probability between 0 and 1

a. x P(X=x)

0 -----3/8

1 -----1/4

2 -----3/8

P(X=0)+P(X=1)+P(X=2) = 3/8 + 1/4 + 3/8

P(X=0)+P(X=1)+P(X=2) = 6/8 + 2/8 = 1

This is a probability density function

b. x P(X=x)

0 ----0.2

1 ----0.1

2 ----0.35

3 ----0.17

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.2 + 0.1 + 0.35 + 0.17

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.65 + 0.17 = 0.82 ≠ 1

Therefore this is NOT a probability density function

c. x P(X=x)

0---- 9/10

1 ---- −3/10

2 ---- 3/10

3 ---- 1/10

Since P(X=1) is not between 0 and 1

Therefore this is NOT a probability density function

d. x P(X=x)

0 ----0.06

1 ----0.01

2 ----0.07

3 ----0.86

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.06 + 0.01 + 0.07 + 0.86

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.14 + 0.86 = 1

Therefore this is a probability density function

e. x P(X=x)

0 ----1/2

1 ----1/8

2 ----1/4

3 ----1/8

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/2 + 1/8 + 1/4 + 1/8

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/2 + 1/2 = 1

Therefore this is a probability density function

f. x P(X=x)

0 ----1/10

1 ----1/10

2 ----3/10

3 ----1/5

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/10 + 1/10 + 3/10 + 1/5

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 2/10 + 5/10 = 7/10 ≠ 1

Answer:

[tex]P(52<X<70)=P(\frac{52-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{70-\mu}{\sigma})=P(\frac{52-60}{9.4}<Z<\frac{70-60}{9.4})=P(-0.851<z<1.064)[/tex]

And we can find this probability with this difference:

[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)[/tex]

And if we use the normal standard distribution or excel we got:

[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)=0.856-0.197=0.659[/tex]

Step-by-step explanation:

Let X the random variable that represent the time required to construct and test a particular component of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(60,9.4)[/tex]  

Where [tex]\mu=60[/tex] and [tex]\sigma=9.4[/tex]

We want to find this probability:

[tex]P(52<X<70)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we got:

[tex]P(52<X<70)=P(\frac{52-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{70-\mu}{\sigma})=P(\frac{52-60}{9.4}<Z<\frac{70-60}{9.4})=P(-0.851<z<1.064)[/tex]

And we can find this probability with this difference:

[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)[/tex]

And if we use the normal standard distribution or excel we got:

[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)=0.856-0.197=0.659[/tex]