Twenty individual seals were weighed, giving the following data (in pounds). 
902 920 925 931 936 940 945 948 949 951 956 958 960 966 968 970 974 982 987 991 Calculate the mean, median, standard deviation, and IQR. 
(Round your answers to one decimal place.) mean = ........lbs
median =..... lbs
standard deviation = ….lbs 
IQR =...... Ibs 

Answer:

11:27 am.

Step-by-step explanation:

The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked

1.25 * 4.8

= 6 km.

So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes

= 0.6 hrs.

So, Tom's speed is 6/0.6 = 10 km/hr.

,

and Tom will take 18/10 = 1.8 hours to finish the route,

= 1 hr 48 minutes

So he finishes the route at

9:39 + 1:48

= 11:27 am.

Answer:

Find the negative reciprocal of the slope of the original line and use the point-slope formula y−y1=m(x−x1) to find the line perpendicular to y=3x−5. y=−13x−2

Step-by-step explanation:

Answer:

10 teenagers

Step-by-step explanation:

using the formula i took the sample size of 30, then added all of the cumulative frequency to get to 650

no of teenagers = 10

When Danny has lots of energy, his mom tells him to do laps around the block. His block is 66 yards wide and 80 yards long. There are 292 yards are in one lap around Danny's block.

The perimeter of a rectangle is the total length or distance from its border on all sides. The perimeter of a rectangle is a linear measurement expressed in linear units such as meters, feet, inches, or meters

The block is a rectangle with 80 yd length and 66 yd width. We need the perimeter of the block, which is the perimeter of the rectangle.

P = 2L + 2W

P = 2(80 yd) + 2(66 yd)

P = 160 yd + 132 yd

P = 292 yard

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Answer:

Lana has 6 more candy bars than Markus.

Step-by-step explanation:

Lana has 6 bags, each with 3 candy bars. To find the total amount you multiply 6 by 3 which is 18. Markus has 3 bags, each with 4 candy bars, to find the total amount you also multiply 3 by 4 which is 12. Now you subtract:       18-12=6. So Lana has 6 more candy bars than Markus.

Answer:

Lana has 6 candy bars more than Markus

Step-by-step explanation:

6 x 3 = 18

3 x 4 = 12

18 - 12 = 6

The Taylor polynomial T₅(x) is 0.99500416 and by use the Error Bound the maximum possible size of the error is 49943.1 × 10⁻⁷.

What is Taylor Series?

The Taylor series or Taylor expansion of a function in mathematics is the infinite sum of terms represented in terms of the function's derivatives at one particular point. The function and the sum of its Taylor series are roughly equivalent for the majority of typical functions at this point.

Taylor series or Taylor expansion:

Infinity ∑ (n = 0) fⁿ(a)/n! (x - a)ⁿ

Where,

n! = factorial of n

a = real or complex number

fⁿ(a) = nth derivative of function f evaluated at the point a.

As given function is,

f(x) = cosx, a = 0, x = 0.1

Taylor polynomial of degree 'n' for f(x) center a,

Tₙ(x) = f(a) + f'(a)(x - a) + f''(a)/2 (x - a)² + f'''(a)/3 (x - a)³ + ......+ fⁿ⁻¹(a)/(n - 1)! (x - a)ⁿ⁻¹ + fⁿ(a)/n! (x - a)ⁿ

Evaluate values as follows:

f(x) = cosx ⇒ f(0) = 1

f'(x) = -sinx ⇒ f'(0) = 0

f''(x) = -cosx ⇒ f''(0) = -1

f'''(x) = sinx ⇒ f'''(0) = 0

f⁴(x) = cosx ⇒ f⁴(0) = 1

f⁵(x) = -sinx ⇒ f⁵(0) = 0

Substitute obtained values in Taylor series,

T₅(x) = 1 + (0) (x - 0) + (-1)/2 (x - 0)² + 0 + 1/24(x - 0)⁴ + 0

T₅(x) = 1 -1/2x² + 1/24x⁴

At x = 0.1

T₅(0.1) = 1 -1/2(0.1)² + 1/24(0.1)⁴

T₅(0.1) = 1 - 0.005 + 4.16 × 10⁻⁶

T₅(0.1) = 0.99500416

Hence, the Taylor polynomial T₅(x) is 0.99500416.

Evaluate the maximum possible size of the error:

cos(0.1) = 0.99999847

T₅(0.1) = 0.99500416

Icos(0.1) - T₅(0.1)I = 0.99999847 - 0.99500416

Icos(0.1) - T₅(0.1)I = 0.00499431

Icos(0.1) - T₅(0.1)I = 49943.1 × 10⁻⁷.

Hence, the Error Bound the maximum possible size of the error is 49943.1 × 10⁻⁷.

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Answer:

Bala = 279$

Peter = 1395$

Step-by-step explanation:

Peter has 5 times as much Money as Bala.

They have $1674 in total.

How much more money has Peter than bala

Bala has 1 unity

Peter has 5 unity

total unity = 6

Find 1 unity

1674 : 6 = 279

Bala = 279

Peter = 5 * 279 = 1395

Answer:  4/9

Step-by-step explanation:

Let x represent the denominator. Then the fraction is: (x - 5)/x

Add 1 to the numerator and denominator   →     (x - 5 + 1)/(x + 1) = 1/2

Cross Multiply:                   1(x + 1) = 2(x - 4)

Distribute:                             x + 1 = 2x - 8

Subtract x from both sides:       1 = x - 8

Add 9 to both sides:                  9 = x

Numerator:  x - 5    →     9 - 5 = 4

Denominator:  x     →     9

So the fraction is: 4/9

The marginal rate of substitution (MRS) for u(x) = 5x^2 is 10x.

The marginal rate of substitution (MRS) represents the rate at which a consumer is willing to trade off one good for another while keeping their utility constant. In the given utility function u(x) = 5x², where x represents the quantity of a particular good, we can determine the MRS by taking the derivative of the utility function with respect to x.

Taking the derivative of u(x) = 5x² with respect to x, we get du/dx = 10x. This derivative represents the MRS. The coefficient 10 indicates that for each unit increase in x, the MRS increases by a factor of 10.

The MRS of 10x implies that the consumer is willing to give up 10 units of the other good in exchange for an additional unit of x while maintaining the same level of utility. This indicates a constant rate of substitution between the two goods.

In summary, the marginal rate of substitution (MRS) for the utility function u(x) = 5x² is 10x, indicating the consumer's willingness to trade off the other good for x at a constant rate of substitution.

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Answer:

D, 3/13 simplified from 12/52

Step-by-step explanation:

the reason that it would be 3/13 is because its simplified from 12/52, which is 12 of the possibly of face cards over 52 the amount of cards in the deck, so the possibility was 12/52, but simplified would be 3/13 ! love you !

                     BE SAFE !!!!                      HOPE THIS HELPS!!!!

                                              <3 <3 <3 <3 <3

The probability that the card drawn is a face card is 3/13.

Option D is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

There are 3 face cards.

Number of jack = 4

Number of queen = 4

Number of king = 4

Total number of cards = 52

The probability that the card drawn is Jack.

= 4/52

The probability that the card drawn is Queen.

= 4/52

The probability that the card drawn is King.

= 4/52

The probability that the card drawn is a face card.
= 4/52 + 4/52 + 4/52

= 3 x 4/52

=  3 x 1/13

= 3/13

Thus,

The probability that the card drawn is a face card is 3/13.

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Answer:

A

Step-by-step explanation:

a line parallel to the y- axis is a vertical line with equation

x = c ( c is the value of the x- coordinates the line passes through )

the only line in this form is

x = - 2

Answer:

x = -2

Step-by-step explanation:

Since x = -2 is a vertical line, there is no y-

Hence, x = -2 is a parallel line to y - axis

The ratio of nonfiction to fiction books is 49 : 2.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

Given, The number of fiction books is 2/7 times the number of nonfiction books.

So, If we have 7 nonfiction books then we have 2/7 fiction books.

Therefore, The ratio Nonfiction : Fiction = 7 : 2/7.

Nonfiction : Fiction = 49 : 2.

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Answer:

CBD = 82°

Step-by-step explanation:

From the chords relations in a circle, we have that when two chords intersects, we have the following angles:

CBF = DBE =  (1/2) * (arc(CF) + arc(DE))

CBD = FBE = (1/2) * (arc(CD) + arc(EF))

So, using the second equation to find the value of the angle CBD, we have that:

CBD = (1/2) * (100 + 64)

CBD = (1/2) * 164

CBD = 82°

Answer: 0

Step-by-step explanation:

Since m is with x, you don't need to care about y

We would get 2x - 6x + 4x = mx

0x = mx

m is 0

Answer:

m=3/4

Step-by-step explanation:

use y=mx+b formula

One would earn more if one apprenticed for Sara as a professional artist as evident judging from the current sales ratio and commission rates.

As evident in the task content; the current ratio of Sara's sales to Ravi's sale is 100 : 2.

Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.

Hence, since the commission rate is 60%, it follows that the commission earned on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.

Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.

Hence, since the commission rate for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.

Ultimately, one would earn more if one apprenticed for Sara.

Complete question; Sara's pieces of art sell for $25 each your commission is 60%.

Ravi's pieces of art sell for $2000 each and your commission is 25%.

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Step-by-step explanation:

3

???

is that really the answer you are looking for ? there are infinite possibilities.

Answer:

\(\bold{Infinitely~many!}\)

Step-by-step explanation:

Hi there!

Remember. there are infinitely many numbers.

Here are some numbers greater than 2:

3, 4, ...400, ...5000, ...

It goes on for ever...

Hope it helps! Enjoy your day!
~Just a teenager girl willing to help

\(\bold{Besties4Ever}\)

Answer:

(5,6) and (8,3)

Step-by-step explanation:

A and C are two of the corners of the square.

Imagine the top LEFT corner. If you drew a line straight UP from A and to the LEFT of C, it would meet at (5,6).

Now picture the bottom RIGHT corner. If you drew a line from A to the RIGHT and then another line from C DOWN, those lines would meet at (8,3).

I drew a pic showing the square you are trying to create! See attached.

In given word problem the number of cards Alan has is 13 and Number of cards Calvin has is 13.

What is word problem?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order  to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here , Let us take Number of card Alan has as A and Number of card bill has as B and Number of cards does Calvin has as C.

Now Alan has 11 less than 2 times the number of cards Bill has then,

=> A = 2B-11 ------------->1

And Calvin has 1 more than 1 times the number of cards Bill has then,

=> C =  B+1 ----------> 2

Here Alan and Calvin has same number of cards then

=> 1 = 2

=> 2B - 11 = B +1

=> 2B-B = 11+1

=> B = 12

Now put B= 12 into 1 then

=> A = 2(12)-11= 24-11 = 13

Now put B= 12 into 2 then

=> C = 12+1 = 13

Hence the number of cards Alan has is 13 and Number of cards Calvin has is 13.

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\(\huge\text{Hey there!}\)

\(\large\boxed{\mathsf{\dfrac{1}{2}a = 7}}\\\\\large\text{MULTIPLY 2 to BOTH SIDES}\\\\\large\boxed{\mathsf{2\times\dfrac{1}{2}a= 2\times7}}\\\\\large\text{CANCEL out: }\rm{2\times\dfrac{1}{2}}\large\text{ because it gives you 1.}\\\large\text{KEEP: }\rm{2\times7}\large\text{ because it helps you get your a-value}\\\\\large\boxed{\mathsf{a = 2\times7}}\\\\\\\large\text{SIMPLIFY IT!}\\\\\large\boxed{\mathsf{a = 14}}\\\\\\\huge\boxed{\text{Therefore, your answer is: \boxed{\mathsf{a = 14}}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

Answer 1

Because the alphabet can end,it is not unlimited

Given that Mr. Townsend needs to make 13 pairs of butterfly wings for costumes for a play. Each pair of wings is made with 3/4 yards of fabric. The fabric costs $8 per yard. The total cost of the fabric is $78.

The total cost formula is used to get a total by combining the variable and fixed expenses of delivering commodities.

The step-by-step is given as follows:

1) Total cost  (TC) = 3/4 (P) x 13

2) 1 pair of wings = 3/4 yard fabric

Recall that the price of 1 yard of fabric = $8

3) 1 pair of wings = $8 x 3/4 = $6

4) Therefore total cost = $6 x 13 = $78

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The Equation of circle is (x+3)² + (y-5)² = (√20)².

We have,

Center = (-3, 5)

Point = (1, 7)

We know the standard form of Equation of circle

(x-h)² + (y-k)² = r²

where (x, y) is any point on the circle, (h, k) is the center

So, (x+3)² + (y-5)² = r²

Put the point (1, 7) in above equation we get

(1+3)² + (7-5)² = r²

(4)² + (2)² = r²

16 + 4= r²

r= √20

Thus, the Equation of circle is

(x+3)² + (y-5)² = (√20)²

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Answer:

a^2 + 2ab + b^2

Step-by-step explanation:

Answer:

(-5,-8)

Step-by-step explanation:

Answer: 49 degrees

Step-by-step explanation:

The solution to each of the arithmetic sequence are:

1) a₁₀ = 56

2) a₁₀ = 87

3) missing term is 13

4) missing term is 14

The formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

n is nth term

d is common difference

1) a = 2

d = 6

a₁₀ = 2 + (10 - 1)6

a₁₀ = 2 + 54

a₁₀ = 56

2) a = 15

d = 8

a₁₀ = 15 + (10 - 1)8

a₁₀ = 87

3) The missing term will be gotten by finding the common difference.

d = (22 - 4)/2

d = 18/2

d = 9

missing term = 4 + 9 = 13

4) The missing term will be gotten by finding the common difference.

d = (53 - 25)/2

d = 28/2

d = 14

missing term = 4 + 9 = 14

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Answer:

\(:\implies\tt \dfrac{n + 1}{2} = -\dfrac{3}{4} \\ \\ \\ \)

⚽ Cross multiplying both the sides we get :

\(:\implies\tt (n + 1) \times 4= -3 \times 2 \\ \\ \\ \)

\(:\implies\tt 4n + 4= -6 \\ \\ \\ \)

\(:\implies\tt 4n = -6 - 4 \\ \\ \\ \)

\(:\implies\tt 4n = -10 \\ \\ \\ \)

\(:\implies\tt n = \dfrac{-10}{4}\\ \\ \\ \)

\(:\implies\tt n = \dfrac{-5}{2}\\ \\ \\ \)

\(:\implies \ddag \: \gray{ \underline{ \boxed{\tt n = - 2.5}}} \: \ddag\\ \\ \\ \)

The decomposition of  713 × 49 has been provided below

To multiply 713 and 49, we can use the distributive property and decompose the second number as follows:

49 = 40 + 9

Then, we can multiply each part of the sum by 713:

713 × 40 + 713 × 9

To calculate this, we can use the multiplication table and then add the results:

713

x 40

28520

713

x 9

6417

Then, we add the two results:

713 × 40 = 28520

713 × 9 = 6417

34997

Therefore, the multiplication 713 × 49, decomposed as 713 × 40 + 713 × 9, equals 34,997.

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