Let T:V→W be a linear transformation from a vector space V into a vector space W. Prove that the range of T is a subspace of W.

Answer:

R4 ≤ 0.00008

R4 = 0.00001

Step-by-step explanation:

Given: sinh( 0.4 ) ≈ [tex]1 - \frac{(0.4)^2}{2!} + \frac{(0.4)^2}{4!}[/tex]

using Taylor's Theorem

R4 ≤ 0.00008

R4 = 0.00001

attached is the detailed solution

Answer:

yards of carpet you need: 4*10/3=40/3=13.3333 yd^2

Step-by-step explanation:

convert feet to yard:

1 yard=3 feet so

12 feet=4 yards

10 feet=10/3 yard=3.33333 yard

yards of carpet you need: 4*10/3=40/3=13.3333 yd^2

Answer:

Option A is the correct option

Step-by-step explanation:

Since, we know that angle at center is double that of the circumference.

JL = 2 × 84°

calculate the product

= 168°

Hope this helps..

Best regards!!

Answer:

Option A is the correct answer.

Step-by-step explanation:

By the incribed angle theorem, we have

1/2of angle JKL.

so, JL = 84°×2

Therefore, the answer is 168°.

Hope it helps..

Answer:

Children: $13

Adults: $18

Step-by-step explanation:

Well for both sets we can set up the following system of equations,

[tex]\left \{ {{3a + 4c = 106} \atop {2a + 3c = 75}} \right.[/tex]

So first we need to solve for a in the first equation.

3a + 4c = 106

-4c to both sides

3a = -4c + 106

Divide 3 by both sides

a = -4/3c + 35 1/3

Now we plug in that a for a in 2a + 3c = 75.

2(-4/3c + 35 1/3) + 3c = 75

-8/3c + 70 2/3 + 3c = 75

Combine like terms

1/3c + 70 2/3 = 75

-70 2/3 to both sides

1/3c = 4 1/3

Divide 1/3 to both sides

c = 13

Now we can plug in 13 for c in 3a + 4c = 106,

3a + 4(13) = 106

3a + 52 = 106

-52 to both sides

3a = 54

Divide 3 by both sides.

a = 18

Thus,

an adult ticket is $18 and a children's ticket is $13.

Hope this helps :)

Answer:

Adults pay $18 and children pay $13.5

Step-by-step explanation:

Hello!

You need to calculate the price of the tickets for adults and children for the group trip to New York.

If X represents adult and Y represents children, then you can express the given information as two equations with two unknown values:

Three adults and four children must pay $106. ⇒ 3X + 4Y= $106

Two adults and three children must pay $75. ⇒ 2X + 3Y= $75

I) First step, in one of the equations you have to clear one of the unknown values, I'll clear the value of Y:

3X + 4Y= 106

4Y= 106 - 3X

[tex]Y= \frac{106-3X}{4}[/tex]

II) Second step you have to replace it in the second equation:

2X + 3Y= 75

[tex]2X + 3(\frac{106-3X}{4} )= 75[/tex]

[tex]2X + \frac{3}{4}(106-3X)= 75[/tex]

[tex]2X + (\frac{3}{4}*106 - \frac{3}{4}*3X )= 75[/tex]

[tex]2X + 79.5 -\frac{9}{4}X =75[/tex]

[tex]2X - \frac{9}{4}X= 75 - 79.5[/tex]

[tex]-\frac{1}{4} X= -\frac{9}{2}[/tex]

[tex]X= -\frac{9}{2} * -4= 18[/tex]

The price for adult tickets is $18.

III) Third step, using the calculated value of X, you replace it on the formula obtained in I) yo calculate the price for the children Y:

[tex]Y= \frac{106-3X}{4}= \frac{106-(3*18)}{4} = \frac{27}{2}= 13.5[/tex]

The ticket price for children is $13.5

I hope this helps!

Answer:

18+18 as point XYZ is in centroid of Q

Step-by-step explanation:

so it's equal.

36.which is option A.

Answer:

15

Step-by-step explanation:

4! +3! /2

4!=4*3*2*1=24

3!=3*2*1=6

24+6/2=30/2=15

Answer:

0.8390

Step-by-step explanation:

From the question,

Z score = (Value-mean)/standard deviation

Z score = (150.2-160.5)/10.4

Z score = -0.9904.

P(x>Z) = 1- P(x<Z)

From the Z table,

P(x<Z) = 0.16099

Therefore,

P(x>Z) = 1-0.16099

P(x>Z) = 0.8390

Hence the probability that a person weighs more than 150.2 pounds = 0.8390

Answer:

The upper quartile is 20.5825

Step-by-step explanation:

In order to find the upper quartile we would have to use the following formula:

According to the given data:

value of a stock varies each day from $9.82 to $24.17

Hence, Q=upper quartile,

Therefore, ($24.17 - Q)/($24.17 - $9.82) = 25%

($24.17 - Q)/$14.35=25%

$24.17 - Q=3.5875

Q=20.5825

The upper quartile is 20.5825

Answer:

The answer is missing.

I think there is something wrong with the equation on its own

Step-by-step explanation:

Equation for the hovercraft

F(x)= X²+6x+2

Olivia catapult equation

F(x)= √2x

Differential of the both equation will give the velocity at x time

F(x)= X²+6x+2

DF(x)/Dx= 2x +6

F(x)= √2x

F(x)= (2x)^½

DF(x)/Dx= (2x)^-½

So the differential is the velocity of the both equation.

Let's equate both equation to find the value of x at which they have same velocity.

(2x)^-½=- 2x+6

(2x)^-1= (-2x+6)²

(2x)^-1= 4x² -24x +36

0= 8x³ - 48x² +72x -1

Correct Question:

5 (u + 1) - 7  = 3 (u - 1) + 2u.

Solve for u

Answer:

See explanation below

Step-by-step explanation:

In this given question, we are required to find u.

Given the equation:

5 (u + 1) - 7 = 3 (u - 1) + 2u​

Required:

Solve for u

To find u, first simplify both sides individually.

Simply 5 (u + 1) - 7:

Expand the parenthesis:

5u + 5 - 7

Collect like terms:

5u - 2

Simplify 3 (u - 1) + 2u​:

Expand the parenthesis:

3u - 3 + 2u

Collect like terms:

3u + 2u - 3

5u - 3

Bring both simplified equations together:

5u - 2 = 5u - 3

5u - 5u - 2 = -3

-2 = -3

Since -2 ≠ -3, there is no solution.

Therefore, we can say the equation is invalid.

Answer:

x = 50°

Step-by-step explanation:

Step 1.

180° - 80° (because there are 180 degrees in a triangle) = 100°

Step 2.

100° ÷ 2 = 50° (because the two angles on the bottom are identical, as this is an isosceles triangle - which we know because the two sides on the left and right are both the same length, 7 units)

Step 3.

Answer: x = 50°

We are given [tex]\triangle ABC \cong \triangle EFG[/tex]

The order of the letter sequence is important. The letters pair up based on how they are arranged. We see that A and E are the first letters of the sequences. So this means that angles A and E are the same measure

angle A = angle E

3x+20 = 5x-80

3x-5x = -80-20

-2x = -100

x = -100/(-2)

x = 50

Use this x value to find the measure of angle A

angle A = 3x+20

angle A = 3(50)+20

angle A = 150+20

angle A = 170 degrees

Answer:

a. Identify the population of interest in this study.

b. Identify the sample for the study.

c. Identify the parameter of interest in the study.

d. Find and interpret a 95​% confidence interval for the parameter of interest.

z score for a 95% confidence level = 1.96

margin of error (E) = z score x √{[0.4(1 - 0.4)] / 50} = 1.96 x 0.069282 = 0.13579

95% confidence level interval:

0.4 - 0.13579 = 0.26421

0.4 + 0.13579 = 0.53579

Answer:

In this question it is given that:

The cash account of a company had an ending balance of $6750. During the last month, the account was debited for a total of $11,350 and credited for a total of $10,500.

And we have to use the formula

Substituting the values , we will get

Therefore beginning cash balance is

Answer:

B) –3x – 6 = 21

Step-by-step explanation:

Well the distributive property is the multiplying of a number by more numbers in parenthesis.

For example  -3(x + 2) by using the distributive property we get,

-3x - 6

Thus,

the answer is B) -3x - 6 = 21 because it shows the aftermath of the distributive property.

Hope this helps :)

When distributive property applies on 3(x + 2) = 21 expression than it changes as 3x + 6 = 21.

Distributive property explains us how to solve expressions in the form of a(b + c).

After apply distributive property this term convert as ab+ac.

The given expression is,

3(x + 2) = 21

To solve the expression, use distributive property,

According to distributive property,

a(b + c) changes in the form of ab+ac.

Solve for the given expression,

3x + 2×3 = 21

3x + 6 = 21

Solve for the value of x,

3x = 21 - 6

3x = 15

x = 5

Hence, option (C) is correct.

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Answer:

-4.30

Step-by-step explanation:

The computation of the test statistic is shown below:

Data are given in the question

Sample = 55 night students

Sample mean = 2.3

Standard deviation = 0.02

Sample = 50 day students

Sample mean = 2.35

Standard deviation = 0.08

Based on the above information, the test statistic is

[tex]z = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma _1^2}{n_1} + {\sqrt{\frac{\sigma _2^2}{n_2}}}}}[/tex]

[tex]z = \frac{2.3 - 2.35}{\sqrt{\frac{(0.02)^2}{55} + {\sqrt{\frac{(0.08)^2}{50}}}}}[/tex]

= -4.30

Hence, the test statistic is -4.30

Answer:

Step-by-step explanation:

Suppose that at time [tex]t_0[/tex] we have x mold cells. We are told that after 12 minutes the amount present is double. That is a [tex]t= t_0+12[/tex] we have 2x cells. Then, at [tex]t = t_0+24[/tex] we have (2x)*2 = 4x. We can continue as follows

[tex]t: t_0+36[/tex] we have (4x)*2 = 8x.

[tex]t: t_0+48[/tex] we have (8x)*2 = 16x

[tex]t: t_0+60[/tex] (one hour later) we have (16x)*2 = 32x.

So after one hour from now we have 32x cells.

The no. of mold cells one hour from now will be 32[tex]x[/tex].

Given,

The number of mold cells doubles every 12 minutes.

Let at time [tex]t[/tex] we have x mold cells.

So, after 12 minutes, the no of molds at[tex],t_{12} =t+12[/tex]  the no. of mold will be[tex]2x.[/tex]

After further 12 minutes at, [tex]t_{24} =t+24[/tex], the no. of mould will be [tex]4x[/tex].

After further 12 minutes at, [tex]t_{36} =t+36[/tex], the no. of mold will be [tex]8x[/tex].

After further 12 minutes at, [tex]t_{48} =t+48[/tex], the no. of mold will be [tex]16x.[/tex]

After further 12 minutes at, [tex]t_{60} =t+60[/tex], the no. of mold will be [tex]32x[/tex].

Hence the no. of mold cells one hour from now will be 32[tex]x[/tex].

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Answer:

2 km

Step-by-step explanation:

Since we know that the TOTAL distance from Kensington to Greenville is 4.3 km, and we also that the distance from Kensington to Springfield is 2.3 km, we can subtract these values to find the distance from Springfield to Greenville.

[tex]4.3-2.3=2[/tex]

I hope this helped!

Answer:

Simple math, different numbers.

Step-by-step explanation:

Take the total distance, 4.3

And subtract it from the given segment of the road.

4.3 - 2.3 = 2.0

So the distance between Springfield and Greenville is 2 kilometers.

Answer: 14

Step-by-step explanation:

12/4 times 3 +5

= 3 times 3 + 5

= 9 + 5

= 14

[tex]\dfrac{3}{x^3y} +\dfrac{7}{xy^4}\\\\\\\dfrac{1}{xy}(\dfrac{3}{x^2} +\dfrac{7}{y^3})[/tex]

It's xy.

Answer:

A. The mean represents the center.

A. The median represents the center.

B. The mode does not represent the center because it is the smallest data value.

Step-by-step explanation:

Mean

(9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11)/13 = 120/13 = 9.2

The mean 9.2 and it represents the center of data.

Median

By arranging the set of data, the median, the median is the center number

8,8,8,8,8,8,(9),9,9,10,11,12,12

The median is 9 and it represents the center of data.

Mode

The mode is the number that appears most in the set of data.

The number that appears most in the set of data is 8 and does not represent the set of data.

Given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:

A. The mean does represents the center of the data set

Given the following data set:

9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8, 11

Let's find the mean, median, and mode.

Mean of the data set:

Mean = sum of all values / number of values

Mean = [tex]\frac{9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11}{13}[/tex]

Mean = [tex]\frac{120}{13} = 9.2[/tex]

Median of the data set:

Order the data from the least to the greatest then find the middle value.

8, 8, 8, 8, 8, 8, (9,) 9, 9, 10, 11, 12, 12

The middle value is 9.

Mode of the data set:

The mode = the data value that appears most

8 appeared the most, therefore, the mode = 8

If you observe, you will note that the mean and median of the data set are similar. We can as well conclude that the mean represents the center of the data set.

In summary, given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:

A. The mean does represents the center of the data set

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Answer: 9.52cm

Step-by-step explanation:

The data we have is:

Radius = 7cm

Angle of the arc = 1.36 rads

Now, the perimeter of a full circle is equal to:

P = 2*pi*r

Where 2*pi = 6.28 rads

Then the length of an arc of angle A is

P = A*r

then in our case:

P = 1.36*7cm = 9.52cm

Answer:

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Step-by-step explanation:

Coordinates of points A and C are (-8, 6) and (2, 5).

If a point B intersects the segment AB in the ratio of 2 : 5

Then coordinates of the point B will be,

x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]

and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]

where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.

For the coordinates of point B,

x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]

  = [tex]-\frac{36}{7}[/tex]

y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]

  = [tex]\frac{40}{7}[/tex]

Therefore, coordinates of pint B will be,

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Answer:

the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Step-by-step explanation:

Given that :

The mean value [tex]\mu[/tex] = 12

The standard deviation [tex]\sigma[/tex] = 3.5

Let Consider Q to be the weight of the parcel that is normally distributed .

Then;

Q [tex]\sim[/tex] Norm(12,3.5)

The objective is to determine thewight  value of c under which there is a surcharge

Also, let's not that 99% of all the parcels are below the surcharge

However ;

From the Percentiles table of Standard Normal Distribution;

At 99th percentile; the value for Z = 2.33

The formula for the Z-score is:

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

[tex]2.33 = \dfrac{X - 12}{3.5}[/tex]

2.33 × 3.5 = X - 12

8.155 = X - 12

- X = - 12 - 8.155

- X = -20.155

 X = 20.155

the weight  value of c under which there is a surcharge = X + 1 (0) since all the  pounds are below the surcharge

c = 20.155 + 1(0)

c = 20.155

Thus ; the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Answer:

6/5

Step-by-step explanation:

The reciprocal of 5/6 means flip it

6/5

Answer:

6/5

Step-by-step explanation:

The reciprocal of a fraction is switching the numerator with denominator.

5/6 ⇒ 6/5

Answer:

[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]

Step-by-step explanation:

To express the given product (108 X 125) as a product of prime factors

Step 1: Express each of the numbers as a product of its prime factors.

[tex]108=2^2 \times 3^3\\125=5^3[/tex]

Step 2: Write the product together, and combine any like terms if any

Therefore,

[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]

Answer:

D. 489

Step-by-step explanation:

489 has the number,

four - 4

eight - 8

and ONE nine - 9

Hope this helps :)

Answer:

6y +2x +7

Step-by-step explanation:

10 + 6y + 2x - 3​

The only like terms are the constant

6y+2x +10-3

6y +2x +7

Answer:

2x + 6y + 7.

Step-by-step explanation:

10 + 6y + 2x - 3

= 2x + 6y - 3 + 10

= 2x + 6y + 7.

Hope this helps!

Answer:

  5

Step-by-step explanation:

The 5 terms in the expression are ...

  6y

  3

  y

  4y

  5

__

If like terms were combined, the expression could be reduced to one with 2 terms:

  11y +8

Answer:

5 terms

Step-by-step explanation:

In an expression, a term can be a number, a variable, or a number and variable multiplied together. Terms are separated by addition or subtraction.

In the expression:

6y+3+y+4y+5

There are 5 terms. The 5 terms are:

1. 6y

2. 3

3. y

4. 4y

5. 5

We can simplify this expression by combining like terms. We can add the constants (just numbers) and the terms with variables being multiplied by numbers.

6y+3+y+4y+5

(6y+y+4y)+(3+5)

11y+(3+5)

11y+8

Step-by-step explanation:

5) a. x/2 = 7-5

x/2 = 2

x = 2×2

x=4

b.4x - 2 = 3x +7

4x - 3x = 7 + 2

x = 9

c. x+2 = 42 × 3

x+2 = 126

x = 124

d. 13x + 260 = 39

13x = 39 - 260

13x = -221

x = -17

6) a. 6x / 7 = 4 +2

6x = 6 × 7

6x = 42

x = 7

b. -49 = 7x + 7

-49 - 7 = 7x

7x = - 56

x = -8

c. -7 + 7x - 21 = 0

7x - 28 = 0

7x = 28

x = 4

d. 8x - 32 + 2 = 42

8x - 30 = 42

8x = 42 + 30

8x = 72

x = 9

e. 5x + 7 = 18

5x = 11

x = 2.5