Find the solution of the system of equations
shown on the graph.

At the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].

Here, the initial population is [tex]P=1.23\times 10[/tex] and the growth rate is [tex]r=6.7\%[/tex].

So the population after [tex]t=4[/tex] years will be:

[tex]A=P(1+\frac{r}{100})^t\\\Longrightarrow A=1.23\times 10\times(1+\frac{6.7}{100})^4\\\Longrightarrow A=1.23\times 10\times(1.067)^4[/tex]

Therefore, at the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].

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Answer:

3 hours

Step-by-step explanation:

When the ships meet each other, that means the the distance travelled for both ships are the same, that is where the 2nd ship will overtake the ship.

Distance = Speed * Time

So, given information from the question, and letting x be the time in hours (from when the 1st ship departs), we can deduce:

Distance travelled of 1st ship = Distance travelled of 2nd ship

30x = 40(x-1)

30x = 40x - 40

-10x = - 40

x = [tex]\frac{-40}{-10}[/tex]

= 4

Since we are calculating based on the 2nd ship,

Time taken for 2nd ship to overtake first ship = x - 1 = 4 - 1 = 3 hours.

Answer:

sorry i thought i knew it

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

using the rules of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] : nm > n

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex] : n > m

[tex]\frac{6a^2b^{-2} }{8a^{-3b^3} }[/tex] ← separate the variables

= [tex]\frac{6}{8}[/tex] × [tex]\frac{a^2}{a^{-3} }[/tex] × [tex]\frac{b^{-2} }{b^3}[/tex]

= [tex]\frac{3}{4}[/tex] × [tex]a^{2-(-3)}[/tex] × [tex]\frac{1}{b^{3-(-2)} }[/tex]

= [tex]\frac{3}{4}[/tex] × [tex]a^{2+3}[/tex] × [tex]\frac{1}{b^{3+2} }[/tex]

= [tex]\frac{3}{4}[/tex] × [tex]a^{5}[/tex] × [tex]\frac{1}{b^{5} }[/tex]

= [tex]\frac{3a^{5} }{4b^{5} }[/tex]

Answer:

45.7 kilometers = 45,700 meters

Explanation:

Hi!
Okay, so basically, in one kilometer, there are 1000 meters.
Using this problem, all you have to do is multiply 45.7 by 1000, which is 45,700.

Whatever value is used for kilometers (ex. 2), just multiply by 1000, and you’ll get the value as meters (ex. 2 x 1000 = 2000 meters).

Hope this helps!

To convert kilometers to meters, multiply the kilometer value by 1000 meters which is equal to 1 km.

Convert 45.7 kilometers to meters:

               [tex]\boldsymbol{\sf{Therefore \ \ \longmapsto \ \ 45.7\not{km}*\left(\dfrac{1000 \ m}{1\not{km}}\right)=45700 \ m }}[/tex]

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The following classification of quadratic equations is presented below:

In this problem we have quadratic equations in factored form, whose form is presented below:

y = a · (x - r₁) · (x - r₂)      (1)

Where r₁ and r₂ are the roots of the equation and a is the leading coefficient. A value of x is a root if and only if y is zero. Besides, we must located all the quadratic equations according to their roots.

x = - 2 and x = 3

h(x) = (x + 2) · (x - 3)

k(x) = - 3 · (x + 2) · (x - 3)

x = 2 and x = - 3

g(x) = 8 · (x + 3) · (x - 2)

m(x) = (x + 3) · (x - 2)

Neither

f(x) = 3 · (x - 1) · (x + 2)

j(x) = (x - 2) · (x - 3)

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The answer is 756 m³.

The formula to find volume is : length × width × height

To estimate, round each dimension to the nearest whole number.

⇒ 12.3 ≅ 12

⇒ 7.2 ≅ 7

⇒ 8.6 ≅ 9

Volume = 12 × 7 × 9

Volume = 84 × 9

Volume = 756 m³

Answer:

The ans to this question is 756 which is Option (B)

Step-by-step explanation:

Estimate volume = rounding every digit

= 12.3 = 12

= 7.2 = 7

= 8.6 = 9

= 12x7x9 = 756

The sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2

The sum notation is given as:

∞Σn=1 2(1/5)^n-1

The above notation is a geometric sequence with the following parameters

The sum is then calculated as

S = a/(1 - r)

The equation becomes

S = 2/(1 - 1/5)

Evaluate the difference

S = 2/(4/5)

Express the equation as products

S = 2 * 5/4

Solve the expression

S= 5/2

Hence, the sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2

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Answer:

S = 5/2

Thank me later

Yes, companies that provide mobile wifi hotspots can see your history.

A Wi-Fi hotspots can be defined as  the hotspots that makes it possible for other mobile user connected to a wifi hotspots to browse or to connect to the internet.

For a mobile user to connect to the internet through the mobile wifi hotspot, the mobile hotspot wifi owner must have giving access to mobile user to browse .

Hence, companies that provide mobile wifi hotspots can see your history of the site you visit.

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Solve the second equation for [tex]t[/tex], then substitute it into the first equation.

[tex]y = t + 2 \implies t = y-2[/tex]

[tex]x = t^2 - 3 \implies \boxed{x = (y-2)^2 - 3}[/tex]

Answer: 8 x 10^2

Step-by-step explanation:

scientific notation has to be greater than 1, less than 10

therefore:

0.08 = 8 x 10^2

Answer:

d 1-12-3-5 is the answer

Usando la distribución hipergeométrica,  la probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es: 0.2 = 20%.

La fórmula es:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Los parámetros son:

Los valores de los parámetros son:

N = 6, k = 3, n = 2.

La probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es P(X = 2), por eso:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,6,2,3) = \frac{C_{3,2}C_{3,0}}{C_{6,2}} = 0.2[/tex]

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Using the given definition and [tex]\Delta x=\frac{0-(-2)}n=\frac2n[/tex], we have

[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \sum_{i=1}^n \left(7\left(-2+\frac{2i}n\right)^2 + 7\left(-2+\frac{2i}n\right)\right) \frac2n \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac2n \sum_{i=1}^n \left(14 - \frac{42i}n + \frac{28i^2}{n^2}\right)[/tex]

Recall the well-known power sum formulas,

[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]

[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + 9 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]

Reducing our sum leads to

[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \frac2n \left(\frac{7n}3 - 7 + \frac{14}{3n}\right) = \lim_{n\to\infty} \left(\frac{14}3 - \frac{14}n + \frac{28}{3n^2}\right)[/tex]

As [tex]n[/tex] goes to ∞, the rational terms containing [tex]n[/tex] will converge to 0, and the definite integral converges to

[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \boxed{\frac{14}3}[/tex]

The best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.

It should be noted that conjecture simply means a conclusion that's proffered on a tentative basis without any proof.

From the information, Charlie used construction paper, scissors and a ruler to construct an isosceles triangle with a pair of sides each 3 inches long and an acute angle on top.

Here, the best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.

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Factorization refers to the process by which the terms that are common in an expression are obtained.

Factorization refers to the process by which the terms that are common in an expression are obtained.

Given the trinomials, the correct binomial factors are;

1) (x−1)(x+7)

2) (x−2)(x−3)

3) (x+1)(x−7)

4) (x−1)(x+6)

5) (x−3)(x+4)

6) (x+2)(x−4)

7) (x+1)(x−5)

8) (x−1)(x+3)

9) (x+4)(x−4)

10) (x+3)(x−4)

11) (x−3)(x−6)

12) (x+2)(x−7)

13) (x−2)(x−5)

14) (x−3)(x−8)

15) (x+5)(x−6)

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Option A. The total share expense that the company would share would be given as 512,000

These are the necessary expenses that are needed for the smooth functioning of a particular business that are not within the confinement of the O and M agreement. It has to do with shared facilities.

The total number of the employees that are knwon to satistfy condition are given as

800 * 0.8

= 640

The options that are estmated that would be exercised

This is given as the employees * share option

= 640×50

=32000.

The total shae for the company would be gotten as

= 32000× $16

This gives us $512,000.

Hence it can be concluded that the total share of the company if they have 80 percent meeting the condition is $512000.

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Answer:

z = [tex]\sqrt{30}[/tex]

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

z² = 3 × (3 + 7) = 3 × 10 = 30 ( take square root of both sides )

z = [tex]\sqrt{30}[/tex]

The decision is to fail to reject the null given that p value is not ≤ 0.05.

The hypothesis

H0 = p = 0.63

H1 = p < 0.63

α = 0.05

sample proportion = 71/125 = 0.568

x = 71

n = 125

standard error of the proportion

√0.63(1-0.63)/125

= 0.0431

The null hypothesis follows a standard normal distribution. This is a left tailed test.

We are to reject the null if the p value is less than 0.05

p < 0.05

This probability test is a z probability test.

Z test = 0.568 - 0.63 / 0.0431

test statistic = -1.436

-Z0.05 =

Critical value =  -1.645

p(z < -1.436)

p value = 0.0755

The decision would be to fail to reject the null hypothesis. The reason would be due to the fact that p value is greater than significance.

P-value is not ≤ α 0.05

0.0755 > 0.05

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The value of x in the equation is 26.7

0.75x + 1.5y = 40

−1.5x − 1.5y = −60

add both equation to eliminate y .

Therefore,

−1.5x + 0.75x = -0.75x

1.5y + (- 1.5y) = 0

40 + (-60) = -20

Hence,

-0.75x  = - 20

divide both sides by -0.75

-0.75x / -0/75 = - 20 / -0.75

x = - 20 / -0.75

x = 26.6666666667

x = 26.7

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The true statement is (c) the function f(x) is an exponential function

From the table, we can see that:

This means that the table represents an exponential function

The rate is then calculated as:

f(n) = f(1) * r^n-1

Using f(3), we have

102 = 17 * r^3-1

This gives

r^2 = 6

Take the square roots

r = 2.45

Hence, the true statement is (c) the function f(x) is an exponential function

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The variable overhead rate variance is: c. $6,052 U.

First step is to calculate variable component of the predetermined overhead rate using this formula

Variable component of the predetermined overhead rate= Budgeted variable manufacturing overhead/Budgeted hours

Let plug in the formula

Variable component of the predetermined overhead rate=$ 28,200/12,000 labor-hours

Variable component of the predetermined overhead rate=$2.35 per labor-hour

Second step is to calculate  variable overhead rate variance using this formula

Variable overhead rate variance=(AH×AR)-(AH×SR)

Let plug in the formula

Variable overhead rate variance= $ 26,967- ( 8,900 labor-hours×$2.35 per labor-hour)

Variable overhead rate variance= $ 26,967- $20,915

Variable overhead rate variance= $6,052 U (Unfavorable)

Therefore the variable overhead rate variance is: c. $6,052 U.

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By the chain rule,

[tex]g(x) = f(4 - x^2) \\\\ \implies g'(x) = -2x f'(4 - x^2) \\\\ \implies g''(x) = -2 f'(4 - x^2) + 4x^2 f''(4 - x^2)[/tex]

Observe that

[tex]4 - x^2 = 1 \implies x^2 = 3 \implies x = \pm\sqrt3[/tex]

Then

[tex]g''(\sqrt3) = -2 f'(1) + 4\left(\sqrt3\right)^2 f''(1) = -2(-5) + 4(3)(-1) = \boxed{-2}[/tex]

Converting the portions to decimal, the grade that has the greatest portion of students is: 3rd grade.

The bigger the digit that is close to the decimal point, the bigger the number given.

Also, percentage can be converted to decimal by dividing the given percent by 100. Percent means over 100.

Fractions can also be converted to decimals by simply dividing the numerator by the denominator.

To compare the portion of students interested in playing an instrument in each grade, let all the portions be in decimals.

Converting 25/36 to decimal, we have: 0.694 (3rd grade)

Converting 61.24% to decimal, we have: 61.24/100 = 0.6124 (4th grade)

From the rest of the portions given, 0.694 is greater than the others.

Therefore, the grade that has the greatest portion of students is: 3rd grade.

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Answer:

Step-by-step explanation:

2x + 5y = 8

      -5    -5

2x = 8 - 5y

divide both sides by 2

[tex]\frac{2x}{2} = \frac{8-5y}{2}[/tex]

divide by 2 undoes the multiplication by 2

x = [tex]\frac{8- 5y}{2}[/tex]

divide 8 - 5y by 2

x = - [tex]\frac{5}{2}[/tex] y + 4

The equation 15x + 5y = 0  is a direct variation and the constant of variation is -3 while the equation -5x + 8y = 3 is neither a direct variation nor an inverse variation

As a general rule, we have the following forms of equation:

Direct variation: y =kx

Inverse variation: y = k/x

Where k represents the constant of variation

The equations 15x + 5y = 0 can be rewritten as:

5y = -15x

Divide by 5

y = -3x

The above equation take the form y = kx

This means that k = -3

Hence, the equation 15x + 5y = 0  is a direct variation and the constant of variation is -3

However, the equation -5x + 8y = 3 do not take any of the given forms

Hence, the equation -5x + 8y = 3 is neither a direct variation nor an inverse variation

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Answer:

Step-by-step explanation:

Answer:

12 and 14

Step-by-step explanation:

12 * 14 = 168

Answer:

12 & 14

Step-by-step explanation:

the work: x = first even number, (x+2) = second even number

The equation

[tex]x(x+2)=168[/tex]

[tex]x^{2} +2x=168[/tex]

[tex]x^{2} +2x-168=0[/tex]

Factoring

[tex](x-12)(x+14)=0[/tex]

first factor

[tex]x-12=0\\x=12[/tex]

Second factor

[tex]x+14=0\\x=-14[/tex]

The solution is the positive number

x = 12     is the first even number

x + 2 = 12 + 2 = 14    is the second even number

Hope this helps

Answer: 8.7 the mean is 20

Step-by-step explanation:

When we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.

Given two expressions be [tex]x^{3} +6x^{2} +3x+1[/tex] and (x-2).

We are required to divide the first expression by second expression.

Division means distributing parts of something. The number which is being divided is known as quotient.Divisor is a number which divides the number.

Expressions refers to the combination of numbers, fractions, coefficients, determinants, indeterminants. It expresses some relationship or show equation of line.

We know that  relationship between quotient, divisor, divident and remainder is as under:

Dividend=Divisor*Quotient+Remainder

[tex]x^{3} +6x^{2} +3x+1[/tex]=(x-2)*([tex]x^{2} +8x+19[/tex])+39

Quotient=[tex]x^{2} +8x+19[/tex]

Remainder=39

Hence when we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.

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