NO LINKS!! What is the equation shown in the smaller circle shown in the figure?​

Answer:

16 packages

Step-by-step explanation:

5 2/5 + 2 1/4  Use the common denominator of 20

5 8/20 + 2 5/20  

7  13/20

I know that I will need 14 packages for the 7 pounds.  For the fraction part, 10/20 would be half, so I would need to buy a half pound for that, but I need 13/20 which would be more than a half pound, so I will need to buy 2 more pounds for the fraction part.

14 + 2 = 16

Answer:Sanjay has 8

Step-by-step explanation: Because 8x4 equals 32 so thats how much tanya has a 32+8 equals 40. This is what I did I knew 10x4 is 40 so that couldn't be it so then I tried 8 because nine x four is 36 which would be to high so I tried 8 and it was perfect hope this helps.

If Combined, Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, then Sanjay have 8 pens.

Two or more expressions with an equal signs is called as Equation.

Given that Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, We need to find how many pens sanjay has.

Let sanjay has x number of pens.

Tanya has four times as many pens as Sanjay

So 4 times means four multiple of sanjay pens.

Tanya has four times as many pens as Sanjay can be write as 4x.

Combined of tanya and sanjay has 40 pens.

Combined means adding.

x+4x=40

Add the like terms

5x=40

Divide both sides by 5.

x=8

So Sanjay has eight pens and Tanya has 4(8)=32 pens.

Hence Sanjay have eight pens.

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Find where the two curves meet.

[tex]x^3 - x^2 + x + 8 = 5x^2 - 7x + 8 \\\\ \implies x^3 - 6x^2 + 8x = 0 \\\\ \implies x (x-2) (x - 4)= 0 \implies x=0, x=2, x=4[/tex]

The area between the curves is

[tex]\displaystyle \int_0^4 \left|\left(x^3-x^2+x+8\right) - \left(5x^2 - 7x + 8\right)\right| \, dx = \int_0^4 \left|x(x-2)(x-4)\right| \, dx[/tex]

When [tex]x[/tex] is between 0 and 2, [tex]x(x-2)(x-4)[/tex] is positive; when [tex]x[/tex] is between 2 and 4, [tex]x(x-2)(x-4)[/tex] is negative. So we split the integral at [tex]x=2[/tex] to get

[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_2^4 x(x-2)(x-4)\,dx[/tex]

In the second integral, substitute [tex]y=x-2[/tex] to get

[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_0^2 (y+2)y(y-2)\,dy[/tex]

[tex]\displaystyle \int_0^2 x(x-2) \bigg((x-4) - (x+2)\bigg) \, dx[/tex]

[tex]\displaystyle -6 \int_0^2 x(x-2) \, dx[/tex]

[tex]\displaystyle 6 \int_0^2 \left(2x - x^2\right) \, dx[/tex]

[tex]\displaystyle 6 \left(x^2 - \frac13x^3\right)\bigg|_0^2 = \boxed{8}[/tex]

Answer:

So this is all you need to do!

Hope it helped you:)

Answer: 44

Step-by-step explanation: Since 11 members are equal to 25% of the club, 11 members is 1/4 of the club because 25% = 1/4. There are four-fourths in a whole so 11x4 = 44 members. The ski club has 44 members.

The maximum area of a rectangular piece of metal with perimeter of 27.75 in² has length of 6.9375 in and width of 6.9375 in.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length and y represent the width. hence:

Perimeter = 2(x + y)

27.75 = 2(x + y)

y = 13.875 - x

Area (A) = xy

A = x(13.875 - x)

A = 13.875x - x²

Maximum area is at A' = 0, hence:

A' = 13.875 - 2x

13.875 - 2x = 0

x = 6.9375

y = 6.9375

The maximum area of a rectangular piece of metal with perimeter of 27.75 in² has length of 6.9375 in and width of 6.9375 in.

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Step-by-step explanation:

Let's solve for the first one,

[tex]R.H.S. = Cos²A + cos²A.cot²A[/tex]

Step 1- Take Cos²A common,

[tex] = Cos²A( 1+ cot²A)[/tex]

[tex] \small \sf \: Now \: we \: know \: that \\ \small (1 + Cot^{2} \theta = Cosec^{2} \theta)[/tex]

Step 2 - Substituting above value in step 1,

[tex] = Cos^{2} A(Cosec^2A)[/tex]

[tex] \small \sf \: We \: know \: that \: Cosec \theta= \frac{1}{Sin \theta} [/tex]

Step 3 - Substitute Cosec²A with 1/Sin²A

[tex] = \frac{Cos^2A}{Sin^2A} [/tex]

[tex] \small \sf \: Now \: the \: basic \: trigonometric \: function \: is \\ \small \frac{Cos\theta}{Sin \theta} = Cot\theta[/tex]

Step 4 - Replacing the product of step 3 with above function,

[tex] = {Cot}^{2} A[/tex]

Hence proved,

[tex]R.H.S = L.H.S[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Now let's prove the second relation,

[tex](1-sin²A)(1+cot²A)=cot²A[/tex]

Let's solve for R.H.S.,

[tex]R.H.S.= (1-sin^{2} A)(1+cot^{2} A)[/tex]

As I told above,

[tex]\small(1+cot^{2} \theta) = cosec^{2} \theta[/tex]

Another important relation is,

[tex] \small sin^2\theta + cos^2\theta= 1 \: or \: \\ \small cos^2\theta = 1 - sin^2\theta[/tex]

Replacing both the above brackets with this relation we get,

[tex] = Cos^2A \cdot Cosec^2A [/tex]

Now follow the step 3 and step 4 of first question and you will get,

[tex]R.H.S. = L.H.S.[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Some important trigonometric relations that you must learn,

[tex]Sin^2\theta + Cos^2\theta = 1 \\ 1 + Cot^2\theta = Cosec^2\theta \\ 1+Tan^2\theta = Sec^2\theta[/tex]

[tex] \small\sf \: Thanks \: for \: joining \: brainly \: community! [/tex]

1. D

2. B

3. E

4. C

5. B

From the three examples at the top of the page, the sum of the bottom two parts of the triangle equals to six times the value of the part at the top.

For example, the first one: 20, 10, 5 (Tip)

For example, the second one: 4, 14, 3 (Tip)

Question 1

Given information

Tip = 15

Bottom = ?, 51

Determine the sum

15 × 6 = 90

Find the other bottom part

90 - 51 = 39

[tex]\Large\boxed{D.~39}[/tex]

Question 2

Given information

Tip = 9

Bottom = 21, ?

Determine the sum

9 × 6 = 54

Find the other bottom part

54 - 21 = 33

[tex]\Large\boxed{B.~33}[/tex]

Question 3

Given information

Tip = ?

Bottom = 60, 60

Determine the sum

60 + 60 = 120

Find the tip

120 ÷ 6 = 20

[tex]\Large\boxed{E.~20}[/tex]

Question 4

Given information

Tip = ?

Bottom = 18, 30

Determine the sum

18 + 30 = 48

Find the tip

48 ÷ 6 = 8

[tex]\Large\boxed{C.~8}[/tex]

Question 5

Given information

Tip = 12

Bottom = ?, 38

Determine the sum

12 × 6 = 72

Find the other bottom part

72 - 38 = 34

[tex]\Large\boxed{B.~34}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Considering the given function, we have that:

The function is:

f(x) = 4 - 2x + 6x².

When x = a, we have that:

f(a) = 4 - 2a + 6a².

When x = a + h, we have that:

f(a + h) = 4 - 2(a + h) + 6(a + h)² = 6a² + 12ah + 6h² - 2a - 2h + 4.

For the fraction, we have that:

[f(a + h) - f(a)]/h = [6a² + 12ah + 6h² - 2a - 2h + 4 - 4 + 2a - 6a²]/h = [12ah + 6h² - 2h]/h = h(12a + 6h - 2)/h

Hence:

[f(a + h) - f(a)]/h = 12a + 6h - 2.

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The volume (in cubic centimeters) of a box) given the fixed base area of 6cm² and height of 6 cm is 36 cm³.

V = 6h

Where,

If the height = 6 cm

Fixed base area = 6 cm²

V = 6h

= 6 cm² × 6 cm

V = 36 cm³

Therefore, the volume of the box given the fixed base area of 6cm² and height of 6 cm is 36 cm³.

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Answer:

1) 13m, 2) 10ft, 3) 11.4ft, 4) 12.7m

Step-by-step explanation:

Since all of these triangles are right triangles, we can use the Pythagorean Theorem: a^2+b^2 = c^2

1) 5^2+12^2 = c^2 = 25+144 = c^2 = 169 = c^2 = 13 = c

2) 6^2+8^2 = c^2 = 36+64 = c^2 = 100 = c^2 = 10 = c

3) 5^2+10.3^2 = c^2 = 25+106.09 = c^2 = 131.09 = c^2 = 11.4494541 = 11.4 = c

4) 8.6^2+9.4^2 = c^2 = 73.96+88.36 = c^2 = 162.32 = c^2 = 12.7404866 = 12.7 = c

The answer to these questions are

How to find the point where the distribution lies at 99.7%. The data is 3 sd from mean

Hence

39 - 3*(5) = 24

39 + 3*(5) = 54

The widget lies between 24 and 54

c. P(29.0 < x < 54.0)

= 29 - 39 / 5 and 54 - 39 / 5

= -2.0 and 3.0

We have to find P(Z < 3.0) - P(Z < -2.0)

= 0.9987 - 0.0228

= 97.59%

d. x = 44

= 44 - 39/ 5

= 1

We are to find P(z < 1.0)  = 84.13%

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The series of fractions is 1, 2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.

The string lengths are fractions whose numerators are powers of 2 and denominators are powers of 3, and the fractions are larger than 1/2 but smaller than 1.

Some powers of 2 are:

2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32, 2⁶ = 64, 2⁷ = 128, 2⁸ = 256, 2⁹ = 512, 2¹⁰ = 1024, 2¹¹ = 2048, 2¹² = 4096, 2¹³ = 8192, 2¹⁴ = 16384,  2¹⁵ = 32768, 2¹⁶ = 65536, and 2¹⁷ = 131072.

Some powers of 3 are:

3⁰ = 1, 3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81, 3⁵ = 243, 3⁶ = 729, 3⁷ = 2187, 2⁸ = 6561, 3⁹ = 19683, 3¹⁰ = 59049, and 3¹¹ = 177147.

The fractions, for which the numerator is a power of 2, the denominator is a power of 3, and the value is between 1/2 and 1 are:

2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.

Thus, the series of fractions is 1, 2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.

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Considering the definition of mass volume percent, the percent composition of lactose in skim milk is 28%.

The concentration of solutions is the amount of solute contained in a given amount of solvent or solution. In other words, the relationship between the amount of solute and the amount of solvent is called concentration.

Mass volume percent (% m/V) is a measure of concentration that indicates the number of grams of solute in each 100 mL of solution.

In other words, mass-volume percent is an intensive property that is defined as the mass of solute (in grams) that there are in 100 mL of solution and it is calculated by applying the following equation:

[tex]Mass volume percent=\frac{mass solute (grams)}{volume solution (mL)}x100[/tex]

This is, mass volume percent is defined as the ratio of the mass of solute that is present in a solution, relative to the volume of the solution, as a whole.

In this case, you know:

Replacing in the definition of mass volume percent:

[tex]Mass volume percent=\frac{0.28 grams}{1 mL}x100[/tex]

Solving:

mass volume percent= 28 %

Finally, the percent composition of lactose in skim milk is 28%.

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Answer:

Step-by-step explanation:

answer: 47

add the heights then divide by 5

Answer: 4

Step-by-step explanation:

x - (1/3)x - (1/6)x = 2

(6x - 2x - x)/6 = 2

3x/6 = 2

x=4

She paid a simple interest of $3,125.00 on the borrowing of $25,000

What is simple interest?

The simple interest on a loan or an investment can be determined as the principal multiplied by interest multiplied by the number of periods.

This is quite different from compound interest where the interest earned previously would earn interest in the future alongside the principal

I=PRT

I=interest on loan=unknown

P=amount borrowed=$25,000

R=interest rate=1% per month

T=12.5 months( from December 2 2011 to December 1 2012 makes one year and from December 1-16 gives 15 days, which is 0.5 of one month)

I=$25,000*1%*12.5

I=$3,125.00

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Assuming that the company sells all that it produces, The profit function is: P(x)=-x^/2+50x -100 or P(x)=-0.5x²+50x -100.

Profit = R-C = -(x-100)^2/2 +5000 - 50x -100 =

-(x^2 -200x +10000)/2 -50x +4900 =

-x^2/2 +100x -5000 +5000 -50x +4900

Collect like terms

-x^/2+50x -100

Hence,

Profit function = P(x)=-0.5x²+50x -100

Maximum profit generating output  can be determine by taking the derivative and setting it equal to zero

R-C = -x^2/2 + 50x -100

R'-C' = -x + 50 =0

P(0)x = 50

Maximum profit  can be determine by substituting x=50 into the original profit equation, R-C

P(50) =-(1/2)(50)^2 +50(50) -100

P(50)= -1250 + 2500 -100

P(50) = $1150 profit

P(120) =-(1/2)(120)^2 +50(120) -100

P(120)= -3600 + 6000 -100

P(120) = $2300 profit

Therefore the profit function is: P(x)=-x^/2+50x -100 or P(x)=-0.5x²+50x -100.

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Answer: [tex]y+2=2(x-3)[/tex]

Step-by-step explanation:

Parallel lines have the same slope, so substituting into point-slope form, the equation is

[tex]y+2=2(x-3)[/tex]

The probability that the candidate will win is P = 0.357

We know that the odds against the particular candidate are 9 to 5.

The the odds for the candidate are 5 to 9, this means that in 5 cases the candidate will win, and in 9 cases the candidate will lose.

Then the candidate wins in 5 out of 14 cases, then the probability that the particular candidate wins the elections is given by the quotient:

P = 5/14 = 0.357

The probability that the candidate will win is P = 0.357

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Answer:

303.66 in²

Option 4 is the correct answer

Answer:

x+(x+5)=28

Step-by-step explanation:

girls(g)should be equal to x

boys(b) will therefore be x+5

x+(x+5)=28

Answer:

4x³ + 4x² + 5

Step-by-step explanation:

3x³ - 2x + 8 + 2x² + 5x + x³ + 2x² - 3x - 3.

4x³ - 2x + 8 + 2x² + 5x + 2x² - 3x - 3

4x³ + 4x² - 2x + 8 + 5x - 3x - 3

4x³ + 4x² + 8 - 3

4x³ + 4x² + 5

Part 1: Devon is able to contribute (a) $450 each month to a retirement plan.

a. The amount in Devon's retirement account if she makes the same monthly investment for 40 years is $733,253.26.

b. Overall, Devon's total contribution of her own money into the retirement account is $216,000.

c. The percent of the final balance in Devon's retirement account that was interest was 70.5%.

Part 2: Taylor will invest (b) $1,733.00 per month.

a. The amount that will be in Taylor's retirement account if she makes the same monthly investment for 20 years is $733,253.26.

b. By the time that Taylor retires, she will have contributed $415,920 of her own money into the account.

c. The percent of the final balance in Taylor's retirement account that will be interest is 43.3%.

3. Both Devon and Taylor had the same amount, $733,253.26, in their retirement accounts when they planned to retire.

a. None had more money at their retirement.

b. Taylor contributed more to her retirement account by $199,920 ($414,920 - $216,000).

Gross monthly income = $4,500

APR = 5.25% compounded monthly

N (# of periods) = 480 months (12 x 40 years)

I/Y (Interest per year) = 5.25%

PV (Present Value) = $0

PMT (Periodic Payment) = $450 ($4,500 x 10%)

Results:

FV = $733,253.26 ($517,253.26 + $216,000)

Sum of all periodic payments = $216,000 ($450 x 480)

Total Interest = $517,253.26

Percentage of interest out of the FV = 70.5% ($517,253.26/$733,253.26 x 100)

N (# of periods) = 240 months (12 x 20 years)

I/Y (Interest per year) = 5.25%

PV (Present Value) = $0

FV (Future Value) = $733,253.26

Results:

PMT = $1,733.00

Sum of all periodic payments = $415,920 ($1,733 x 240

Total Interest = $317,333.26

Percentage of interest out of the FV = 43.3% ($317,333.26/$733,253.26 x 100)

Thus, based on the time value of money of investments, it is more profitable to start investing early.

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a. The area on [0, 10] is that of a trapezoid with bases 5 and 15 and height 10, so

[tex]\displaystyle \int_0^{10} f(x) \, dx = \frac{5+15}2\cdot10 = \boxed{100}[/tex]

b. By linearity of the definite integral, we have

[tex]\displaystyle \int_0^{25} f(x)\,dx = \int_0^{10} f(x)\,dx + \int_{10}^{25} f(x)\,dx[/tex]

and the area on [10, 25] is another trapezoid with bases 15 and 7.5 and height 15, so that

[tex]\displaystyle \int_{10}^{25} f(x)\,dx = \frac{15+7.5}2\cdot15 = 168.75[/tex]

Then the total area on [0, 25] is

[tex]\displaystyle \int_0^{25} f(x)\,dx = \boxed{268.75}[/tex]

c. The area on [25, 35] is that of a triangle with base 10 and height 15. However, [tex]f(x)<0[/tex] on this interval, so we multiply this area by -1 to get

[tex]\displaystyle \int_{25}^{35} f(x)\,dx = -\frac{10\cdot15}2 = \boxed{-75}[/tex]

d. The area on [15, 25] is the same as the area on [25, 35] because it's another triangle with the same dimensions. But the area on [15, 25] lies above the horizontal axis, so

[tex]\displaystyle \int_{15}^{25} f(x)\,dx = \int_{15}^{25} f(x)\,dx + \int_{25}^{35} f(x)\,dx = \boxed{0}[/tex]

e. The plot of [tex]|f(x)|[/tex] lies above the horizontal axis. We know the area on [15, 25] is the same as the area on [25, 35], but now both areas are positive, so

[tex]\displaystyle \int_{15}^{35} |f(x)| \, dx = \int_{15}^{25} f(x)\,dx - \int_{25}^{35} f(x)\,dx = 2 \int_{15}^{25} f(x)\,dx = \boxed{150}[/tex]

f. Changing the order of the limits in the integral swaps the sign of the overall integral, so

[tex]\displaystyle \int_{10}^0 f(x)\,dx = -\int_0^{10} f(x)\,dx = \boxed{-100}[/tex]

The dimensions of the pool would give a quadratic equation x² + 28x - 770 = 0

For the pool, we have that;

Let the width = x feet

Length = (x+8) feet

The pool alongside the walkway gives;

Width = x + 5 + 5 = (x + 10) feet

Length = x + 8 + 5 + 5 = (x + 18) feet

Total area of the pool with walkway = 950 square feet

Note that formula for area is given as

Area = length * width = 950

Equate the length and width

(x+18)  × (x + 10) = 950

Using the  FOIL method, we have;

(x × x )+ (x × 10) + (18 × x) + (18 × 10) = 950

x² + 10x + 18x + 180 -950 = 0  

collect like terms

x² + 28x - 770 = 0

Thus, the dimensions of the pool would give a quadratic equation x² + 28x - 770 = 0

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Answer:

Step-by-step explanation:

According to the construction we have:

It gives us:

Then, corresponding angles of congruent triangles are congruent:

So,

Then,

Answer:

- [tex]\sqrt{2}[/tex]

Step-by-step explanation:

cos90° - 2sin45° + 2tan180°

= 0 - ( 2 × [tex]\frac{\sqrt{2} }{2}[/tex] ) + 2(0)

= 0 - [tex]\sqrt{2}[/tex] + 0

= - [tex]\sqrt{2}[/tex]

The z-score for a data value of 19 if the mean of a set of data is 37 and the standard deviation is 8.6 is -2.09

From the question, the given parameters about the distribution are

Mean value of the set of data = 37

Standard deviation value of the set of data = 8.6

The actual data value = 19

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (19 - 37)/8.6

Evaluate the difference of 19 and 37

z = -18/8.6

Evaluate the quotient of -18 and 8.6

z = -2.09

Hence, the z-score for a data value of 19 if the mean of a set of data is 37 and the standard deviation is 8.6 is -2.09

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Answer:

x ≤ 4

Step-by-step explanation:

the solid dot at 4 indicates that x can equal 4

the arrow points to the left indicating values less than 4 , then

x ≤ 4