The area of the entire figure below is 111 square unit.
A rectangle that has been split into 24 parts, set in 4 rows of 6 parts each. The parts in the top 3 rows have been shaded blue. The parts in the left 5 columns have been shaded purple. The first 5 parts in the top 3 rows are striped to show they are shaded both blue and purple. Along the top of the rectangle, the columns are labeled one-sixth. Along the left side of the rectangle, the rows are labeled one-fourth.










A rectangle that has been split into 24 parts, set in 4 rows of 6 parts each. The parts in the top 3 rows have been shaded blue. The parts in the left 5 columns have been shaded purple. The first 5 parts in the top 3 rows are striped to show they are shaded both blue and purple. Along the top of the rectangle, the columns are labeled one-sixth. Along the left side of the rectangle, the rows are labeled one-fourth.
What is the area of the striped rectangle?

Answer: B: (1-5x²)³, all real numbers

Step-by-step explanation:

The notation [tex]f\circ g(x)[/tex] is called function composition, which is where you pass one function in as the value of another function. In other words, [tex]\( f\circ g(x)=f(g(x)) \)[/tex].

Since we have the values for f(x) and g(x), let's plug them in.

[tex]f(g(x))\\f(1-5x^2)\\(1-5x^2)^3[/tex]

Hence, the best answer choice is B, as all real numbers would work and it is the cube of 1 - 5x².

Answer:[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]

Step-by-step explanation:

Given the system of equations

[tex]1)~xy=2[/tex]

[tex]2)~x+y=4[/tex]

Divide x on both sides of the 1) equation

[tex]xy=2[/tex]

[tex]xy\div x=2\div x[/tex]

[tex]y=\dfrac{2}{x}[/tex]

Current system

[tex]1)~y=\dfrac{2}{x}[/tex]

[tex]2)~x+y=4[/tex]

Substitute the 1) equation into the 2) equation

[tex]x+(\dfrac{2}{x} )=4[/tex]

Multiply x on both sides

[tex]x\times x+\dfrac{2}{x}\times x=4\times x[/tex]

[tex]x^2+2=4x[/tex]

Subtract 4x on both sides

[tex]x^2+2-4x=4x-4x[/tex]

[tex]x^2-4x+2=0[/tex]

Use the quadratic formula to solve for the x value

[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(2)} }{2(1)}[/tex]

[tex]x=2\pm\sqrt{2}[/tex]

Substitute the x value into one of the equations to find the y value

[tex]xy=2[/tex]

[tex](2+\sqrt{2} )y=2[/tex]

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

[tex]OR[/tex]

[tex]xy=2[/tex]

[tex](2-\sqrt{2} )y=2[/tex]

[tex]y=2+\sqrt{2}[/tex]

Therefore, the points of intersection are

[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

(2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) and (2 + [tex]\sqrt{2}[/tex], 2 - [tex]\sqrt{2}[/tex] )

Step-by-step explanation:

xy = 2 → (1)

x + y = 4 ( subtract x from both sides )

y = 4 - x → (2)

substitute y = 4 - x into (1)

x(4 - x) = 2

4x - x² = 2 ( multiply through by - 1 )

x² - 4x = - 2

using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 2)x + 4 = - 2 + 4

(x - 2)² = 2 ( take square root of both sides )

x - 2 = ± [tex]\sqrt{2}[/tex] ( add 2 to both sides )

x = 2 ± [tex]\sqrt{2}[/tex] , that is

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

substitute these values of x into (2) for corresponding values of y

x = 2 - [tex]\sqrt{2}[/tex] , then

y = 4 - (2 - [tex]\sqrt{2}[/tex])

  = 4 - 2 + [tex]\sqrt{2}[/tex]

  = 2 + [tex]\sqrt{2}[/tex] ⇒ (2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) ← 1 point of intersection

x = 2 + [tex]\sqrt{2}[/tex] , then

y = 4 - (2 + [tex]\sqrt{2}[/tex] )

   = 4 - 2 - [tex]\sqrt{2}[/tex]

   = 2 - [tex]\sqrt{2}[/tex] ⇒ (2 + [tex]\sqrt{2}[/tex] , 2 - [tex]\sqrt{2}[/tex] ) ← 2nd point of intersection

6,800 to get a total interest of Rs 6,800 and keep the balance for 3 years.

How long should she keep the remaining amount to get a total interest of Rs 6,800 from the beginning:

The rate of 8% p.a. in her saving account.

20,000 at 8% interest for 2 years:

= 20,000*2*8/100

= 3200

5000 was withdrawn after 2 years and earned interest.

After 2 years, the new principal:

= 20000- 5000

=15000

She needs to get interested of 6800–3200 =3600 for the next N years.

N= 100* I /PR

= 100*3600/(15000*8)

=3

6,800 to get a total interest of Rs 6,800 and keep the balance for 3 years.

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Sajina should keep the remaining amount for 3 years to get a total interest of Rs 6,800 from the beginning.

For the principal [tex]P[/tex] and the rate of interest [tex]r\%[/tex] per annum, the total interest after [tex]t[/tex] years is given by the formula: [tex]I=\dfrac{Prt}{100}[/tex].

Given that Sajina deposited Rs 20,000 at the rate of 8% p.a. in her savings account.

So, [tex]P=20,000[/tex] and [tex]r=8[/tex].

Thus, after t=2 years the total interest would be

[tex]I=\dfrac{Prt}{100}\\\Longrightarrow I=\dfrac{20000\times 8\times 2}{100}\\\therefore I=3200[/tex]

So, the total interest after 2 years would be Rs 3,200.

Given that Sajina withdrew Rs 5,000 and the total interest of 2 years.

So, the new principal will be [tex]P'=20,000-5,000=\test{Rs}\hspace{1mm}15,000[/tex].

The total interest she wanted to gain is Rs 6,800. She had already gained Rs 3,200.

so, the remaining interest [tex]I'=6,800-3,200=\text{Rs}\hspace{1mm}3,600[/tex].

Let the required time be [tex]t'[/tex] years after how many years she got a total interest of Rs 6,800 from the beginning.

For principal [tex]P'=15,000[/tex], rate of interest [tex]r=8\%[/tex]; the total interest after [tex]t'[/tex] years would be [tex]I'=\dfrac{P'rt'}{100}=\dfrac{15000\times 8\times t'}{100}=1200t'[/tex]. But given that [tex]I'=3600[/tex].

So, we must have

[tex]1200t'=3600\\\Longrightarrow t'=\dfrac{3600}{1200}\\\therefore t'=3[/tex]

Therefore, Sajina should keep the remaining amount for 3 years to get a total interest of Rs 6,800 from the beginning.

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The equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.

To find the equation of a line, we can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁),

where (x₁, y₁) is the given point on the line and m is the slope.

In this case, the given point is (-5, -7) and the slope is 2/5. Substituting these values into the equation, we have:

y - (-7) = (2/5)(x - (-5)).

Simplifying further:

y + 7 = (2/5)(x + 5).

Distributing the 2/5:

y + 7 = (2/5)x + 2.

Subtracting 7 from both sides:

y = (2/5)x - 5.

Therefore, the equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.

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Answer:

[tex]u = x^{7} +8[/tex]     [tex]du = 7x^{6} dx[/tex]   result is [tex]\frac{1}{7} \sqrt[4]{u}[/tex]

Step-by-step explanation:

Answer: C, E

Step-by-step explanation:

These are polynomials by the definition of a polynomial.

Answer:

SR = 5

Step-by-step explanation:

We know that the two lines are equal to each other and thus TS + SR = 13

So, we can simply set the two equations of the first line equal to 13:

x + 2 + 2x - 7 = 13

3x - 5 = 13

3x = 18

x = 6

Now we plug in 6 for x in the SR equation:

2 * 6 = 12 - 7 = 5

The probability is p = 2/5, the correct option is the third one.

There is a total of 6 socks, such that 4 are black and 2 are blue.

Then the probability of first getting a black sock is the quotient between the number of black socks and the number of blue socks, which gives:

P = 4/6

Now there are 5 socks in total, such that 3 are black and 2 blue.

Then the probability of getting another black one is:

Q = 3/5

The joint probability (getting the two black socks) is given by the product of the individual probabilities:

p = (4/6)*(3/5) = 2/5

The correct option is the third one.

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El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.

En esta pregunta debemos encontrar el volumen remanente entre el espacio de una caja cúbica y una esfera introducida en el elemento anterior. El volumen remanente es igual a sustraer el volumen de la pelota del volumen de la caja.

Primero, se calcula los volúmenes del cubo y la esfera mediante las ecuaciones geométricas correspondientes:

Cubo

V = l³

V = (4 cm)³

V = 64 cm³

Esfera

V' = (4π / 3) · R³

V' = (4π / 3) · (2 cm)³

V' ≈ 33.5103 cm³

Segundo, determinamos la diferencia de volumen entre los dos elementos:

V'' = V - V'

V'' = 64 cm³ - 33.5103 cm³

V'' = 30.4897 cm³

El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.

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Considering the given function, it is found that:

Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.

The function is:

d = 5t².

Hence:

Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.

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The two positive numbers whose difference is 9 and whose product is 2950 are 50 and 59

As a general rule, it should be noted that positive numbers are numbers that have their value greater than 0

So, we start by representing the two positive numbers with x and y.

So, we have the following equations

x - y = 9

xy = 2950

Make x the subject in the first equation x - y = 9

x = y + 9

Substitute y + 9 for x in the second equation

(y + 9) * y = 2950

Expand the equation

y^2 + 9y - 2950 = 0

Using a graphing tool, we  have the solution of the above equation to be

y = 50

Recall that:

x = 9 + y

So, we have:

x = 9 + 50

Evaluate

x = 59

Hence, the two positive numbers whose difference is 9 and whose product is 2950 are 50 and 59

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An airplane is heading north at an airspeed of 640 km/hr, but there is a wind blowing from the southwest at 90 km/hr. degrees off course will be 6.25°

Generally, the equation for the velocity of the plane with reference to the ground is  mathematically given as

Vp=  velocity of the plane with reference to wind+  velocity of the wind with reference to ground

Therefore

Vp=Vp'+Vw

[tex]mVp=\sqrt{(640)^2+(90)^2-2*640*90cos45}[/tex]

mVp=579.8km/h

where

[tex]\frac{sintheta}{90}=\frac{sin45}{Vp'}[/tex]

[tex]sin \theta=\frac{90}{579.8}*sin45[/tex]

sin[tex]\theta=0.109[/tex]

[tex]\theta=sin^{-1}(0.109)=6.25[/tex]

In conclusion,  degrees off course will be 6.25

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The value of the given expression is approximate equal to 1.021 × 10⁴ OR 10207.8

From the question, we are to determine the value of the given expression

The given expression is

10 to the 4th times the square root of 1.042

That is,

10⁴ × √1.042

The expression can be evaluated as shown below

10⁴ × √1.042

= 10⁴ × 1.02078

= 1.02078 × 10⁴

≈ 1.021 × 10⁴

OR

= 1.02078 × 10⁴ = 10207.8

Hence, the value of the given expression is approximate equal to 1.021 × 10⁴ OR 10207.8

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The answer is no.

Always remember when converting from percent to decimal, divide by 100%.

Hence, the student's thinking is not correct.

Answer:

no

Step-by-step explanation:

0.3 = 30% not 3%

to change a percentage to a decimal fraction, divide by 100

3% = [tex]\frac{3}{100}[/tex] = 0.03

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

For two lines to be parallel, there should be angles that follow some specific properties that is usually observed with parallel lines.

We can clearly see that :

[tex] \qquad❖ \: \sf \: \angle7 \cong \angle16[/tex]

( by Alternate interior angle pair )

[tex] \qquad \large \sf {Conclusion} : [/tex]

Lines l and m are parallel to each other.

Answer:

Fufusyyigywngd, hdj4snwhsjtc

Bahr Ltd flu not ld6wlw

The slope of the curve described by the equation at the given point (0,1) as in the task content is; 4.

According to the task content, it follows that the slope of the curve can be determined by means of implicit differentiation as follows;

y⁵+ x³ = y² + 12x

5y⁴(dy/dx) -2y(dy/dx) = 12 - 3x²

(dy/dx) = (12 -3x²)/(5y⁴-2y)

Hence, since the slope corresponds at the point given; (0, 1); we have;

(dy/dx) = (12 -3(0)²)/(5(1)⁴-2(1))

dy/dx = 12/3 = 4.

Hence, slope, m = 4.

Consequent to the mathematical computation above, it can then be concluded that the slope of the curve, the line tangent to the curve at the given point is; 4.

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Solving a system of equations we will see that Hari has 800 and Ram has 600.

Let's define the variables:

We know that:

(2/3)*R = (1/2)*H

We also know that in total they have 1400, then:

R + H = 1400.

So we have the system of equations:

(2/3)*R = (1/2)*H

R + H = 1400.

In the first equation we can isolate R.

R = (3/2)*(1/2)*H = (3/4)*H

Now we can replace that in the other equation:

(3/4)*H + H  =1400

H*(7/4) = 1400

H = (4/7)*1400 = 800

So Hari has 800, and:

R + H = 1400

R = 1400 - H = 1400 - 800 = 600

Hari has 800 and Ram has 600.

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July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165

This is further explained below.

Generally, The term "cumulative balance" refers to the total amount of money left over at the end of a fiscal year after all surplus amounts have been subtracted from deficit amounts. If there is a negative amount in the Cumulative Balance at the conclusion of a fiscal year, then that balance will be carried forward and used as the opening balance for the next fiscal year.

The term "cumulative account" refers to the total amount of an employee's account under a defined contribution plan (for an unaggregated plan) or the total amount of an employee's account under all defined contribution plans included in an Aggregation Group (for aggregated plans), both of which are determined as of the most recent plan valuation date within the most recent 12-month period that ends on the...

In conclusion, for the following data  July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165

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[tex]x^3[/tex] is strictly increasing on [0, 5], so

[tex]\max\{x^3 \mid 0\le x\le5\} = 5^3 = 125[/tex]

and

[tex]\min\{x^3 \mid 0 \le x\le5\} = 0^3 = 0[/tex]

so the integral is bounded between

[tex]\displaystyle \boxed{0} \le \int_0^5x^3\,dx \le \boxed{125}[/tex]

Answer: no real solution

Thus, the function has no x- intercept

Step-by-step explanation:

1. To determine the better option between a 10% off coupon versus a $10 off coupon, it is necessary to determine the coupon price.

2. On the other hand, the $10 off coupon becomes better when the coupon price is less than $100.

3. The 10% off coupon and the $10 off coupon do not give the same amount of discount unless the coupon or list price is $100 in both situations.

A discount is a monetary reduction in the cost of a good or service offered to customers to increase trade.

Offering discounts enhances sales but not profitability.  So, there is a trade-off that must be considered properly.

Ordinarily, if the coupon price is more than $100, the 10% off coupon becomes better than the $10 off coupon.

For instance, if the coupon price is $110, the 10% off coupon will yield a discount amount of $11 ($110 x 10%), which is more than $10.

For instance, if the coupon price is $99, the discount amount will be $9.90, which is less than $10.

Thus, a 10% off coupon and a $10 off coupon do not offer the same discount amount unless the list price is $100, no more, no less.

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Compare the discounts you would receive with a 10% off coupon versus a $10 off coupon.

To estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:

T = R

825 + 0.06x = 1350 + 0.02x

Simplifying the equation, we get

x = 13125

We require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.

For this case, we can assume that the total salary for Teresa T is given by T = 825 + 0.06x

Where x represents the number of sales. And similarly the total salary of Ramon we have:

R = 1350 + 0.02x

We want to estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:

T= R

825 + 0.06x = 1350 + 0.02x

Multiply both sides by 100

[tex]$825 \cdot 100+0.06 x \cdot 100=1350 \cdot 100+0.02 x \cdot 100$[/tex]

82500 + 6x = 135000 + 2 x

Subtract 82500 from both sides

82500 + 6x - 82500 = 135000 + 2x - 82500

6x = 2x + 52500

Subtract 2x from both sides

6x - 2x = 2x + 52500 - 2x

4x = 52500

Divide both sides by 4

[tex]$\frac{4 x}{4}=\frac{52500}{4}$[/tex]

x = 13125

So then we require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.

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Answer:

22

Step-by-step explanation: