Charles used a chain which was 12.5 metres long, 12 times to measure the breadth of his garden. Stephen used a chain of different length 10 times to cover the breadth of Charles' garden and 18 times to cover its length. What is the area of Charles' garden to the nearest one tenth of a hectare?
A. 4.05 m^2
B. 5.4 m^2
C. 3.6 m^2
D. 4.1 m^2​

The probability of getting a Club given that the card is a Ten is 0.25.

According to the statement

we have given that the there is a deck of the 52 cards and we have to find the conditional probability that the card is a club and the given card is a 10 number card.

So, For this purpose we know that the

Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.

And according to this,

The probability P is

P(Club) = 13/52 = 1/4

P(Ten) = 4/52 = 1/13

P(Club and Ten) = (1/4)(1/13) = 1/52

And we know that the

P(Club|Ten) = P(Club and Ten)/P(Ten)

And then substitute the values and it become

= (1/52)/(1/13) = (1/52)(13/1)

= 13/52 = 1/4

= 0.25

So, The probability of getting a Club given that the card is a Ten is 0.25.

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A data value is considered significantly low or significantly high  if its​ z-score is less than -2 or greater than 2.

What does it mean if z-score is 2?

What does a standard deviation of 2 mean?

         deviations of the mean.

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The correct question is -

A data value is considered​ _______ if its​ z-score is less than minus−2 or greater than 2.

Answer:

Step-by-step explanation:

let the ratio of men women and children be 13x 5x and 7x

now

13x + 5x + 7x = 4152

25x = 4152

x = 4152/25

x = 166.08

The equation that represents the function is y = -x - 1

The complete question is added as an attachment

From the table of values, we have the following points

(x, y) = (-1,0) and (0,-1)

Calculate the slope (m) using

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (-1 -0)/(0 + 1)

Evaluate the exponent

m = -1

The equation is then calculated as:

y = mx + c

This gives

y = -x + c

Using the point (0,-1), we have:

0 = 1 + c

Solve for c

c = -1

So, we have

y = -x - 1

Hence, the equation that represents the function is y = -x - 1

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Answer:

Step-by-step explanation:

the expected profit should be 2 dollars a drink

Answer:

The second option.
y > x^2 + 4x -2

y < 3x +4

Step-by-step explanation:

First off, we can eliminate the last option because the graph shows that both inequalities are greater than or less than, but not equal to. We come to this conclusion because both lines on the graph are dashed meaning not equal to. Look at the attached image below (1).

Next, we can input the point (0,0) and test to see if the inequality works. If we input the point (0,0) into the second equation in the second option, we end up with 0 < 4. This is factual meaning that this is your answer.
Hope this helps! If I wasn’t clear enough or you need more information, please let me know in the comments. Have an amazing day!

Answer:

no solution

Step-by-step explanation:

We can think of an absolute value as the magnitude of the number. We can also define it as how far the number is from 0 on the number line. Thus, absolute value must always be positive (or 0).

Start by adding 1 to both sides:

[tex]\frac{|m|}{2}=-2[/tex]

Multiply both sides by 2:

[tex]|m|=-4[/tex]

The absolute value of a number is always positive (with the exception of 0), therefore there is no solution.

Notice we can only add/multiply (or subtract/divide) an equation because of the Addition/Subtraction/Multiplication/Division Property of Equality which state that if you add/subtract/multiply/divide one side of the equation by a certain value, you must do the same to the other side of the equation.

Answer:

17

Step-by-step explanation:

the pattern

x is the blank

1+5 = 6

5+6 = 11

6+11 = x

11 + x = 28

so x = 17

There is a minimum value of -81 located at (x, y) = (6, -3).

The function given to us is f(x, y) = 3y² - 3x².

The constraint given to us is 2x + y = 9.

Rearranging the constraint, we get:

2x + y = 9,

or, y = 9 - 2x.

Substituting this in the function, we get:

f(x, y) = 3y² - 3x²,

or, f(x) = 3(9 - 2x)² - 3x² = 3(81 - 36x + 4x²) - 3x² = 243 - 108x + 12x² - 3x² = 243 - 108x + 9x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = - 108 + 18x ... (i)

Equating to 0, we get:

- 108 + 18x = 0,

or, 18x = 108,

or, x = 6.

Differentiating (i), with respect to x again, we get:

f''(x) = 18, which is greater than 0, showing f(x) is minimum at x = 6.

The value of y, when x = 6 is,

y = 9 - 2x,

or, y = 9 - 2*6 = 9 - 12 = -3.

The value of f(x, y) when (x, y) = (6, -3) is,

f(x, y) = 3y² - 3x²,

or, f(x, y) = 3*(-3)² - 3*6² = 3*9 - 3*36 = 27 - 108 = -81.

Thus, there is a minimum value of -81 located at (x, y) = (6, -3).

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Answer:

C

Step-by-step explanation:

Im going to be quick on this since your in a hurry, is AB is 3 and QR = 1  and their similar then BC would be 3 times the amount of RS which is 1.5 so the Answer is 4.5

Answer:

C

Step-by-step explanation:

　　＿＿＿　 AA

*～/■　■　⊂ P

　 |　■　■.（＿）

　 U U￣￣U U

The equation of a circle exists:

[tex]$(x-h)^2 + (y-k)^2 = r^2[/tex], where (h, k) be the center.

The center of the circle exists at (16, 30).

Let, the equation of a circle exists:

[tex]$(x-h)^2 + (y-k)^2 = r^2[/tex], where (h, k) be the center.

We rewrite the equation and set them equal :

[tex]$(x-h)^2 + (y-k)^2 - r^2 = x^2+y^2- 32x - 60y +1122=0[/tex]

[tex]$x^2 - 2hx + h^2 + y^2 - 2ky + k^2 - r^2 = x^2 + y^2 - 32x - 60y +1122 = 0[/tex]

We solve for each coefficient meaning if the term on the LHS contains an x then its coefficient exists exactly as the one on the RHS containing the x or y.

-2hx = -32x

h = -32/-2

⇒ h = 16.

-2ky = -60y

k = -60/-2

⇒ k = 30.

The center of the circle exists at (16, 30).

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There are only 13 multiples of both 3 and 5, since

[tex]200 = 3\cdot5\cdot13 + 5[/tex]

From these integers, we eliminate any that are also divisible by 4 or 7.

[tex]3\cdot5\cdot4 = 60 \implies \{60,120,180\}[/tex]

[tex]3\cdot5\cdot7 = 105 \implies \{105\}[/tex]

so there are 13 - 4 = 9 such integers.

Total charges from bank A exists $15.

Total charges on Bank B spending exists $45.

Given: Bank A charges a $15 monthly fee for a checking account and debit card, with unlimited transactions.

Shade 25 transactions.

Total charges from bank A = $15 monthly

Bank B charged a $35 monthly fee for a checking account and debit card, plus $ 0.70 for each transaction.

She made 25 transactions.

Total charges on bank B = $35 + (0.40)25

Total charges on bank B = $35+10

Total charges on bank B = $45

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Answer:

Step-by-step explanation:

Add the numbers and divide by 2 and you will find the average

(8.1 + 8.24) : 2 =

8.17

8.17 is exactly half way between them.

Answer:

12 m

Step-by-step explanation:

Well, imagine you got this nice room. How can it reach the other corner? It has to go along the 3 dimensions. So the shortest path would be: 5 + 4 + 3  12m

Answer:

3 + √(41) = 9.4 m (nearest tenth)

Step-by-step explanation:

The room can be modeled as a rectangular prism with:

If the ant is at the top of a corner of a room and crawls to the opposite bottom corner of the room, the shortest distance will be to travel down one vertical edge of the room then to travel the diagonal of the floor of the room (or to travel the diagonal of the ceiling and then one vertical edge).

Vertical edge = height of room = 3m

The diagonal of the floor (or ceiling) is the hypotenuse of a right triangle with legs of the width and length.  Therefore, to find the diagonal, use Pythagoras Theorem.

Pythagoras Theorem

[tex]a^2+b^2=c^2[/tex]

where:

Given:

Substitute the given values into the formula and solve for c:

[tex]\implies 4^2+5^2=c^2[/tex]

[tex]\implies c^2=41[/tex]

[tex]\implies c=\sqrt{41}[/tex]

Therefore, the shortest distance the ant can travel is:

⇒ 3 + √(41) = 9.4 m (nearest tenth)

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Step-by-step explanation:

x = the number of goals of the top scorer.

y = the number of goals of the second top scorer.

z = the number of goals of the third top scorer.

x + y + z = 98

x = y + 8

y = z + 15

using the third in the second equation we get

x = z + 15 + 8 = z + 23

and now using this and the third equation in the first equation gives us

z + 23 + z + 15 + z = 98

3z + 38 = 98

3z = 60

z = 20

y = z + 15 = 20 + 15 = 35

x = y + 8 = 35 + 8 = 43

the player with the most goals scored 43 goals.

Answer:

Work is incorrect

Step-by-step explanation:

I'm assuming this question is asking whether the work is correct or not? In which case the work is not correct.

The Pythagorean Theorem states: [tex]a^2+b^2=c^2[/tex] where c=hypotenuse, and "a" and "b" are the other two sides. The main thing to note here, is that the hypotenuse is the largest side of all three sides.

So the equation Arial set up: [tex]9^2+15^2=12^2[/tex] is incorrect, since the 15 would need to be on the right side. This forms the correct equation: [tex]9^2+12^2=15^2[/tex] which then simplifies to: [tex]81 + 144 =225 \implies 225=225[/tex].

Thus a right triangle can be formed using these side lengths. You can of course set up a similar equation to Ariels, where the "c" or hypotenuse is not isolated,  but you would have to rearrange the equation so that: [tex]a^2+b^2=c^2\implies b^2=c^2-a^2[/tex] but see how "a squared" is being subtracted from "c squared"? So it's a similar equation to Ariels, but not quite the same, and if she set it up like this, then she would reach the same conclussion

Answer:  [tex]\\ \lim\limits_{k \to \infty} (1+\frac{4}{k})^k =e^4.[/tex]

Step-by-step explanation:

[tex]\displaystyle\\ \lim_{k \to \infty} (1+\frac{4}{k})^k \\x=\frac{x}{4} *4\\So,\ \lim_{k \to \infty} (1+\frac{4}{k})^\frac{k}{4}*4 \\ \lim_{k \to \infty} ((1+\frac{4}{k})^\frac{k}{4} )^4.\\Use\ the\ second\ wonderful\ limit:\\\boxed { \lim_{x \to \infty} (1+\frac{1}{x})^x=e },\\\\So,\\ \lim_{k \to \infty} (1+\frac{4}{k})^k =e^4.[/tex]

We can also apply l'Hôpital's rule by first rewriting the limit as

[tex]\displaystyle \lim_{k\to\infty} \left(1 + \frac4k\right)^k = \lim_{k\to\infty} \exp\left(\ln \left(1 + \frac4k\right)^k\right) = \exp\left(\lim_{k\to\infty} \frac{\ln\left(1+\frac4k\right)}{\frac1k}\right)[/tex]

Applying the rule gives

[tex]\displaystyle \lim_{k\to\infty} \frac{\ln\left(1+\frac4k\right)}{\frac1k} = \lim_{k\to\infty} \frac{\left(-\frac4{k^2}\right)/\left(1+\frac4k\right)}{-\frac1{k^2}} = 4 \lim_{k\to\infty} \frac1{1 + 4k} = 4[/tex]

so that the overall limit is

[tex]\displaystyle \lim_{k\to\infty} \left(1 + \frac4k\right)^k = \lim_{k\to\infty} \exp(4) = \boxed{e^4}[/tex]

Use of identity for sum of cubes:

Change it as:

It is easy to notice that:

So the sum of cubes for the given expression will be:

Now substitute the values and calculate each of these:

(a) 4a + 5b = 5, ab = -1.

(b) 4a + 5b = -2, ab = 1/15.

(c) 4a + 5b = 1/3, ab = -1/9.

(d)  4a + 5b = -1, ab = 1.

Answer: D

Step-by-step explanation:

The first term is 3 and the common difference is 2.

Substituting into the explicit formula for an arithmetic sequence gives D as the correct answer.

Answer: 7 1/2 cups

Step-by-step explanation:

We first need to make both fractions have an equal denominator. Cross Multiply 3/4 and 1/10. You will end up with 30/40 and 4/40.

Next we divided 30 by 4, and we will end up with 7 1/2. 7 times 4 is 28, and half of 4 is 1/2, or in this case 2/10. John can fill 7 and 1/2 cups of orange juice.

The three parts weigh 27/112 pound ( letter B).

The question gives:

Therefore, each part will be  [tex]\frac{\frac{9}{16} }{7} =\frac{9}{16} *\frac{1}{7} =\frac{9}{112}[/tex].

For knowing the three parts weigh, you should mulitiply the previous value for 3. Thus,

[tex]\frac{9}{112}*3=\frac{27}{112}[/tex].

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The weight of three parts is 27/112 pounds

The weight of the chocolate bar is given as:

Weight = 9/16

When it is cut into 7 equal parts, the weight of each part is

Each = Weight/7

This gives

Each = 9/16 * 1/7

Evaluate the product

Each = 9/112

The weight of three parts is then calculated as:

Three parts = Each * 3

This gives

Three parts = 9/112 * 3

Evaluate the product

Three parts = 27/112

Hence, the weight of three parts is 27/112 pounds

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Answer:

1. to add 9 to both sides

2. to multiply by 2 to both sides (horrible English)

3. x = -8

Step-by-step explanation:

why do you feel you are terrible at this ?

this is like a riddle or puzzle to solve. like a magic cube or changing a match in a pattern of matches to create another pattern.

let's try and explain this to you.

an equation is like a balance, where both cups are in perfect balance.

whatever value is on the left side, is exactly also on the right side. although it is not plainly visible and explainable, why they are equal.

so, to find out we need to transform the equation. and to keep the balance while transforming you have to do the same changes on both sides of the balance. until you find out what makes the cups equal.

if we destroy the balance at any point, we have no more chance to find out what made both sides equal in the first place, because there is no more original balance.

we can do all mathematical operations in the transformation.

we can add things, subtract things, multiply by a factor, divide by something, ... - anything.

x/2 - 9 = -13

to get clarity in our search for the reason of the equality we try to combine the same type of terms on one side of the equation, and the other type (or types) on the other side.

what types of terms do we have here ?

there is one with a variable (x/2), and there are constant terms (-9, -13).

so, what do I need to do to get rid of the constant term (-9) on the side of the variable term (so that this becomes the side with only variable terms) ?

I need to add 9, so the constant term on that side turns 0 and therefore disappears in the sum. but remember, the action has to be done on both sides.

so,

x/2 - 9 = -13 | + 9 on both sides

x/2 - 9 + 9 = -13 + 9

x/2 = -4

what else is now blocking our view on what x is ?

there is this 1/2 factor of x.

how do we get rid of this 1/2 ? by multiplying by 2. because 2× 1/2 = 1, and a factor of 1 disappears in a multiplication.

x/2 = -4 | ×2 on both sides

x/2 × 2 = -4 × 2

x = -8

and now we see what it is that kept both cups or sides in balance : x = -8

The number of terms, 'n' is 8

Let's determine the common ratio;

common ratio, r = 3/1 = 3

The formula for sum of geometric series with 'r' greater than 1 is given as;  Sn = a( r^n - 1) / (r - 1)

n is unknown

Sn = 3280

Substitute the value

3280 = 1 ( 3^n - 1) / 3- 1

3280 = 3^n -1 /2

Cross multiply

3280 × 2 = 3^n - 1

6560 + 1 = 3^n

6561 = 3^n

This could be represented as;

3^8 = 3^n

like coefficient cancels out

n = 8

Thus, the number of terms, 'n' is 8

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Answer:

39 hours

Step-by-step explanation:

First solve for how much Taylor would earn per hour which is to divide 203.40 by 9

= 203.40÷9 = 22.6

Let x represent the unknown hours

If 22.6 = 1 hr

Then 881.40 = x solving this simultaneously becomes

881.40 ÷ 22.6 = 39

x = 39, hence it'll take Taylor 39 hours to earn $881.40

She have to work 39 hours the next week to earn $881.40.

In simple terms, the unitary method is used to find the value of a single unit from a given multiple. For example, the price of 40 pens is Rs. 400, then how to find the value of one pen here. It can be done using the unitary method. Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit.

In 9 hours she earned  $203.40

∴ In 1 hour she earned $203.40/9 = $22.6

Let number of hours she worked to earn  $881.40  be x.

∴ x =   $881.40/ $22.6

x = 39 hours

Thus she have to work 39 hours the next week to earn $881.40.

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We've got a negative slope, but it doesn't look steep enough to go through 6 on the y-axis.

So, it's the last option:

y = - 1.25x + 5.75

Hope this helps!

Answer:

x=1 and y=−5

Step-by-step explanation:

Problem:

Solve y=−5x;y=x−6

Steps:

I will solve your system by substitution.

y=−5x;y=x−6

Step: Solve y=−5x for y:

Step: Substitute −5x for y in y=x−6:

y=x−6

−5x=x−6

−5x+−x=x−6+−x (Add -x to both sides)

−6x=−6

−6x/−6=−6/−6 (Divide both sides by -6)

x = 1

Step: Substitute 1 for x in y=−5x:

y=−5x

y=(−5)(1)

y=−5(Simplify both sides of the equation)

Answer:

x=1 and y=−5

Thank you,

Eddie

The value of w is 12.5 when x = 5 , y= 5  and z = 10.

What is Equation of variation?

Equation of variation w = [tex]\frac{kxy^{2} }{z}[/tex]

Constant of variation  k = [tex]\frac{wz}{xy^{2} }[/tex]

Find k when w = 1/2, x = 2 and z = 36

k = [tex]\frac{wz}{xy^{2} }[/tex]

[tex]k = \frac{\frac{1}{2} * 36 }{2 * 3^{2} }[/tex]

[tex]k = \frac{18}{2 * 9}[/tex]

[tex]k = \frac{18}{18}[/tex]

k= 1

find the value of w when x = 5 , y = 5 and z = 10

[tex]w = \frac{kxy^{2} }{z} \\w= \frac{1 * 5 * 5^{2} }{10}[/tex]

[tex]w = \frac{5^{3} }{10}[/tex]

w = 125 /10

w = 25 /2

w = 12 . 5

Therefore, the value of w is 12.5 when x = 5 , y= 5  and z = 10

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Answer:

9

Step-by-step explanation:

you have to plug in the numbers and solve it, so it would go as follows:

-(-3^2)- 2(-5)(2) - /2/

-9 + 20 - 2 =

9

i hope this helps

Based on the dimensions of the support for the slides, the missing length and slide length is 15 yards.

The number of 3-yard straight pieces needed is 15 straight pieces.

The length of a single slide is the hypotenuse of the triangle which can be found using the Pythagoras theorem as:

Hypotenuse² = 9² + 12²

Hypotenuse = √(81 + 144)

= 15 yards

If a single slide is 15 yards, then 3 slides would be:

= 15 x 3

= 45 yards

The number of 3-yard straight pieces needed are:

= 45 / 3

= 15 pieces

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Answer: 39

Explain:

The length of each slanted area for each slide is 15 yards. The length of each straight piece is 3 yards. So, the number of straight pieces needed for 15 yards is 15 - 3, or 5. There are two slanted areas on each slide.

The number of straight pieces required for the flat area at the bottom of each slide is 3.

Adding them up, the total number of straight pieces required for one slide is 5 + 5 + 3, or 13. Because there are three slides, the total number of straight pieces needed is 13 • 3, or 39

Vince needs 39 straight pieces to build the three slides.

From ED