a) Suppose you want to find the average weight of an adult emperor penguin. The weight of five penguins
are 46, 52, 49, 50, and 54 pounds. What is the point estimate for the average weight?

Answer:

88.99

Step-by-step explanation:

his plan includes 800 minutes for 79.99, all we need to do is calculate the cost of the extra 50mins he used and add it to 79.99. this is ((850-800)*0.18) +79.99 and this is equal to 88.99

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Your all choices are correct ~

Question 1 : A right triangle always has obtuse exterior angles at two vertices :

Question 2 : The sum of measures of exterior angles minus the sum of measures of interior Angle is 180° :

Question 3 : The sum of exterior Angle and the two non - adjacent interior angles is 180°

Question 4 : An obtuse triangle has only one vertex with an acute exterior angle

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

D

Step-by-step explanation:

None of the others make sense. In answer D x+y is the same as x-y+2y because you add the y's and its the same thing as x+y.

Hope It Helped :)

Yes, there is an analogous ratio between 2:1 and 20:10.

We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.

By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.

As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.

The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:

20 ÷ 10 : 10 ÷ 10

= 2 : 1

As a result, both ratios have the same reduced form, 2:1, making them equal.

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The variance of X-bar is 12.25.

To find the variance of the sample mean (X-bar) for a normally distributed population, we can use the formula:

Variance of X-bar = (Population Variance) / (Sample Size)

In this case, the population mean (μ) is 138 and the standard deviation (σ) is 14. The population variance (σ^2) can be calculated as the square of the standard deviation, which gives us 14^2 = 196.

Since we are sampling with a batch size of 16, the sample size is also 16.

Now we can substitute these values into the formula:

Variance of X-bar = 196 / 16 = 12.25

Therefore, the variance of X-bar is 12.25.

It's important to note that the sample mean (X-bar) is an unbiased estimator of the population mean (μ). The smaller the sample size, the greater the variability of X-bar around the population mean.

As the sample size increases, the variance of X-bar decreases, indicating a more precise estimate of the population mean.

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∠A = 41.81°

To get measure of angle A, we would apply trigonometry ratio SOHCAHTOA:

opposite = side opposite the angle = 4

hypotenuse = 6

adjacent = base = AC = ?

Since we have been given the opposite and the hypotenuse, we would use the sine ratio:

Sin A = opposite/hypotenuse

Sin A = 4/6

sin A = 0.6667

A = 41.8129 degrees

To the nearest hundredth, ∠A = 41.81°

Answer:

A. 24

Step-by-step explanation:

aₙ=a₁+d(n-1)

aₙ= -20 + 1/2(n-1)

a₉= -20 + 1/2(9-1)

  = -20 + 1/2(8)

   = -20 + 4

  = -16

Answer:

9a-2=7

Step-by-step explanation:

4a+ 5a-2=5+3-1

To simplify each side, combine like terms.

4a+5a = 9a

5+3-1 = 7

The equation becomes:

9a-2=7

The approximate difference in the circumferences of the two circles is: C. 61 cm.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, the circumference of the small circle is;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 4.5

Circumference of circle, C = 14.13 cm.

For the larger circle, we have:

Circumference of circle, C = 3.14 × 24

Circumference of circle, C = 75.36 cm.

Difference = 75.36 cm - 14.13 cm.

Difference = 61.23 ≈ 61 cm.

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To Find :

How many of the smallest 200 positive integers are divisible by 3,5 and 7 .

Solution :

We have to find number which are divisible by all 3,5 and 7 .

So , we will find numbers which are divisible by their H.C.F .

Since , 3 ,5 and 7 are prime numbers .

Therefore , their H.C.F is \(3\times 5\times 7=105\) .

Now , we can see that HCF is 105 , so the next number which is divisible by all of them are \(105\times 2=210\) which is greater than 200 .

Therefore , their is only 1 number i.e 105 less than 200 which is divisible by 3,5 and 7 .

Hence , this is the required solution .

Answer: 108 integers!

Hope this helped!

The probability is closer to one than zero.

Probability theory is used to analyze and predict the likelihood of events happening in various fields such as statistics, gambling, physics, finance, and more. It allows us to make informed decisions based on the likelihood of different outcomes. In probability theory, the total number of possible outcomes is important to determine the probability of a single event occurring. By comparing the favorable outcomes to the total outcomes, we can calculate the probability of an event happening.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But when two coins are tossed then there will be four possible outcomes,  i.e {(H, H), (H, T), (T, H), (T, T)}.

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Answer:

yes

Step-by-step explanation:

the ratio of 28 : 36 can be simplifeid by dividing both sides of the ratio by 4.

28/4=7

36/4=9

so the ratio of 28 : 36 is equal to 7 : 9

Answer:

18.559 km/min

Step-by-step explanation:

Horizontal and vertical velocities of the plane:

Vx = 19*cos(35) = 15.5639

Vy = 19*sin(35) = 10.898

Location of plane after 3 minutes will be:

X-component = Vx * 2 = 15.5639 * 2 = 31.1278 km

Y-component = 12 + (Vy * 2) = 12 + (10.898 * 2) = 33.796 km

Angle to the radar station (measured relative to ground) will be given as;

Angle = tan^(-1) (Y-component/X-component) = tan^(-1) (33.796/31.1278) = 47.35°

Thus;

Velocity component along the line between the radar and the plane:

Vt = 19 * cos (47.3534° - 35°)

Vt = 19 * cos 12.3534

Vt = 19 * 0.9768

Vt = 18.559 km/min

Answer: A≈201.06ft²

D: 8ft

HOPE THIS HELPS

Answer:

Because you are using x which equals to -6.

Answer:

Question one: 2
Question two: 3

Step-by-step explanation:

Given the following questions:

\(\frac{1}{2} \times4\)
\(\frac{3}{4} \times4\)

In order to find the answers, we need to remember that every integer has an invisible denominator of one. Then we simply multiply the numerators by the numerators and the denominators by the denominators.

Question one:
\(\frac{1}{2} \times4\)
\(4=\frac{4}{1}\)
\(\frac{1}{2} \times\frac{4}{1}\)
\(1\times4=4\)
\(2\times1=2\)
\(=\frac{4}{2}\)

Simplify by reducing:
\(\frac{4}{2}\)
\(\frac{4}{2} \div2=\frac{2}{1} =2\)
\(=2\)

Question two:
\(\frac{3}{4}\times4\)
\(4=\frac{4}{1}\)
\(\frac{3}{4} \times\frac{4}{1}\)
\(3\times4=12\)
\(4\times1=4\)
\(=\frac{12}{4}\)

Simplify by reducing:
\(\frac{12}{4}\)
\(=\frac{12}{4}\div4=\frac{3}{1} =3\)

Your answers are "2 and 3."

Hope this helps.

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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Answer: 0.0965

Step-by-step explanation:

This would happen if:

First toss: Here we must have any number that is not 6.

the options are 1, 2, 3, 4, 5 so the probablity is p1 = 5/6

The same happens for the second toss, p2 = 5/6

and for the third one: p3 = 5/6

for the fourth toss, person B must roll a 6, so the probability here is p4 = 1/6

Now, the joint probability is equal to the product of the probabilities for each toss, this is:

P = p1*p2*p3*p4 = (5/6)^3*(1/6) = 0.0965

Answer:

Step-by-step explanation:

If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.

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: X=3

Step-by-step explanation:

The limit of (tan(6t)) / (sin(2t)) as t approaches 0 is 0.

The limit lim(t→0) (tan(6t)) / (sin(2t))

We'll use trigonometric identities to simplify the expression.

lim(t→0) sin(t) / t = 1

Using this identity, let's manipulate the expression:

lim(t→0) (tan(6t)) / (sin(2t))

= lim(t→0) [(sin(6t) / cos(6t))] / (sin(2t))

Now, let's simplify further by using the double-angle identities:

sin(2t) = 2sin(t)cos(t)

cos(6t) = cos(2t + 4t) = cos(2t)cos(4t) - sin(2t)sin(4t)

Substituting these identities back into the expression:

lim(t→0) [(sin(6t) / (cos(2t)cos(4t) - sin(2t)sin(4t)))] / (2sin(t)cos(t))

Let us apply the trigonometric identity sin(t) / t = 1:

lim(t→0) [(sin(6t) / (cos(2t)cos(4t) - sin(2t)sin(4t)))] / (2(1)cos(t))

lim(t→0) [(sin(6t)) / (cos(2t)cos(4t) - sin(2t)sin(4t)))] / (2cos(t))

As t approaches 0, the value of cos(t) approaches 1.

Therefore, we can simplify the expression to [(sin(0)) / (cos(0)cos(0) - sin(0)sin(0)))] / (2(1))

= 0 / 2

= 0

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Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

Answer: Use the figures to complete the statements.

The height of the triangle h is

✔ 12

in.

The area of the triangle is

✔ 48

in.2.

The area of the parallelogram is

✔ 80

in.2.

The area of the irregular figure is

✔ 128

in.2.

Step-by-step explanation: I js now got it right by the power of guessing

Answer:

27.7142857143 this is the awnser