7.48 x 105 - 4.7 x 104​

a)

The value of k is 0.61.

b)

The population in 2010 is 739013.

The population in 2015 is 15604434.

c)

In 5.2 years, the population will reach 2.5 million.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

P = 1657.5 \(e^{kt}\)

P is the population in t years.

Now,

In 2000, t = 0,

a)

In 2005, t = 5 and P = 1940,000

So,

P = 1657.5 \(e^{kt}\)

1,940,000 = 1657.5 \(e^{5k}\)

1940000/1657.5 = \(e^{5k}\)

1170.44 = \(e^{5k}\)

Taking logs on both sides.

log 1170.44 = 5k

3.07 = 5k

k = 0.61

b)

In 2010, t = 10

So,

kt = 0.61 x 10 = 6.1

P = 1657.5 \(e^{6.1}\)

P = 1657.5 x 445.86

P = 739012.95

P = 739013

In 2015, t = 15

So,

P = 1657.5 \(e^{9.15}\)

P = 1657.5 x 9414.44

P = 15604434

c)

P = 2.5 million = 2,500,000

Now,

P = 1657.5 \(e^{6.1}\)

Solve for t.

2,500,000 = 1657.5 \(e^{0.61t}\)

2500000/1657.5 = \(e^{0.61t}\)

1508 = \(e^{0.61t}\)

Taking logs on both sides.

log 1508 = 0.61t

3.18 = 0.61t

t = 3.18/0.61

t = 5.21

t = 5.2

Thus,

a)

k = 0.61

b)

P = 739013 in 2010

P = 15604434 in 2015

c)

In 5.2 years, the population will reach 2.5 million.

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Answer:

Jul 11, 2016 · - Gush Tela, a 54-year-old man who was forced to flee with his family after the town of Humera, located in Ethiopia's Tigray region, was shelled by the Ethiopian Army. He was describing the scene he encountered as he returned to the town several days later; he and his family are now in a refugee camp in Sudan (as quoted on The Guardian )

Step-by-step explanation:

Answer:

(3, -2) is the correct choice.

200.60 interest does andy’s account earn.

Let x be the amount of interest earned by Andy's account.

According to the problem, Andy's account earns 0.3% more interest than Marty's account, which means that Andy's account earns the same amount plus an additional 0.3% of that amount. Mathematically, we can express this as:

x = 200 + 0.3% of 200

Simplifying the right-hand side of the equation, we get:

x = 200 + 0.003 × 200

x = 200.60

Therefore, the answer is option 1: 200.60.

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The required matrix is \(\left[\begin{array}{ccc}1&1&4\\0&1&2\\0&0&1\end{array}\right]\)

Let \(P^2\) be the vector space of Polynomials of degree at most 2.

We assume ordered basis of \(P^2\)

\(E = \{e_1, e_2, e_3 \} = \{1,t,t^2\}\)

\(\text{Let } L: P^2 \rightarrow P^2\) be linear transformation

\(L(P(t)) = 2P^{''}(t) + 1.P^{'}(t) + P(t)\)

\(L(1) = 2 \times 0 + 0 + 1 = 1 = 1.e_1 + 0.e_2 + 0.e_3\)

\(L(t) = 2 \times 0 + 1 + t = 1+t = 1.e_1 + 1.e_2 + 0.e_3\)

\(L(t^2) = 2.2 + 2.t + t^2 = 4e_1 + 2e_2 + 1.e_3\)

Now, we can write \(L_{ee} = A\)

\(\therefore A = \left[\begin{array}{ccc}1&1&4\\0&1&2\\0&0&1\end{array}\right]\)

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Answer:

the  possible number would be 159 in

Step-by-step explanation:

Answer:

032.0 yd2 de nada corona por favor

Answer:

A≈121
A= π r^2 (formula)

Step-by-step explanation:

A = π r^2
R=6.2
r^2 = 38.44

38.44 * 3.14 (simple π)
120.7 ---> 121 (rounded)

Answer:

The answer is the last one choice,letter D

Step-by-step explanation:

Answer:

Step-by-step explanation:

SEE EXAMPLE p. 323 Find each measure. 3. NA 4. XZ. ... Find each measure. 3. NA 4. XZ 10.2 5. NZ 5.6 M M 7. mZYXZ 6. m LMN 8. mZXLM N 29° Z ...

Answer:

Kohl = $42

Target = $51.30

Best deal is at Kohl's

Step-by-step explanation:

Given ;

At Kohl's:

Selling price = $60

Friend's and family discount = 30% off

(100 - 30)% * $60

0.7 * 60 = $42

At target :

Purchase price = $38

Markup = 35%

Selling price = (100 + 35)% * $38 = 1.35 * 38 = $51.3

Mrs. Clason will get the best deal at Kohl's.

F or G = { 5,6,7,8,9,10,11,12 } is probability  P(F or G) using the general addition rule.

What are examples and probability?

The likelihood that something will happen is called the probability. the total number of conceivable outcomes.

                                   For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). P(heads) = 12 is what we write.  the forerunners of the contemporary mathematical theory of probability (for example the "problem of points").

S={ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14},

event F={5, 6, 7, 8, 9}​, and

event G={9, 10, 11, 12}.

F or G = { 5,6,7,8,9,10,11,12 }

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Answer:

m = 30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

10 + 10 = 20

8 + 2 = 10

20 + 10 = 30

Answer:

Answer: 10.5

With out being rounded it’s 10.5417

Step-by-step explanation:

Looks like you're given

x cos(y/x) (y dx + x dy) = y sin(y/x) (x dy - y dx)

Like with your other equation, multiply by 1/x² on both sides:

cos(y/x) (y/x dx + dy) = y/x sin(y/x) (dy - y/x dx)

Then substitute z = y/x again, so y = xz and dy = x dz + z dx. You end up with a separable equation.

cos(z) (z dx + x dz + z dx) = z sin(z) (x dz + z dx - z dx)

cos(z) (2z dx + x dz) = xz sin(z) dz

2z cos(z) dx = x (z sin(z) - cos(z)) dz

(z sin(z) - cos(z)) / (z cos(z)) dz = 2/x dx

(tan(z) - 1/z) dz = 2/x dx

Integrate both sides:

∫(tan(z) - 1/z) dz = ∫ 2/x dx

-ln|cos(z)| - ln|z| = 2 ln|x| + C

ln|cos(z)| + ln|z| = -2 ln|x| + C

ln|z cos(z)| = ln(1/x²) + C

z cos(z) = C/x²

Solve in terms of y :

(y/x) cos(y/x) = C/x²

y cos(y/x) = C/x

Answer:

g(x) = f(x) - 5

Step-by-step explanation:

Answer for edgenuity

Answer:

A, g(x)=f(x)-5

Step-by-step explanation:

g(x) is 5 units lower than f(x) so -5  and inside the parentheses would mean moving on the x axis but it is five lower on the y axis of g(x)=f(x)-5 is correct.

By the fundamental theorem of calculus,

\(\displaystyle y = \int_0^v \sqrt{3+4t^2} \, dt \implies \boxed{\frac{dy}{dv} = \sqrt{3+4v^2}}\)

In general,

\(\displaystyle \frac{d}{dx} \int_0^{g(x)} f(u) \, du = f(g(x)) \frac{dg}{dx}\)

Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week \(\sf = 19 \times 40 = \$760\)

Now, according to option b, he will get 8% commission on weekly sales.

Let. x = the amount of weekly sales.

To earn the same amount of option A, he will have to equal the 8% of x to $760

So, \(\sf \dfrac{8x}{100}=760\)

Or, \(\sf 8x= 76000\)

Or, \(\sf x= \dfrac{76000}{8}=9500\)

the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.

About 80 necklaces have more than 28 beads. Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.

P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)

P(x > 28) = P(x - 24 / 4 > 1)

P(x > 28) = 1 - ∅1

P(x > 28) = 1 - 0.8413

P(x > 28) = 0.1587

Multiply both sides by 500, then we have

500 P(x > 28) = 0.1587 × 500

500 P(x > 28) = 79.35

500 P(x > 28) ≈ 80

About 80 necklaces have more than 28 beads. Then the correct option is C.

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The missing options are given below.

A. About 24 devices have more than 28 beads.

B. About 48 necklaces have more than 28 beads.

C. About 80 necklaces have more than 28 beads.

D. About 96 necklaces have more than 28 beads.

Answer:

slope intercept

y=6/5x+14/5

point slope=

y-4=6/5 (x-1)

therefore y-4/x-1=6/5 is the answer

The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:

The functions have the same range.

The functions have the same domain.

The functions have the same x-intercepts.

Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.

Here are the options:

The functions have the same graph.

The functions have the same range.

The functions have the same domain.

The functions have the same vertex.

The functions have the same y-intercept.

The functions have the same x-intercepts.

The functions have the same graph:

This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).

Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).

The functions have the same range:

This statement is true.

Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.

The functions have the same domain:

This statement is true.

The domain of both functions, unless restricted by any other factors, is all real numbers.

Quadratic functions have a domain of (-∞, ∞).

The functions have the same vertex:

This statement is false.

The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).

Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).

The functions have the same y-intercept:

This statement is false.

The y-intercept of a function is the value of y when x = 0.

For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.

For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3

= 3.

Their y-intercepts are different.

The functions have the same x-intercepts:

This statement is true.

To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.

The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.

Both functions have the same x-intercepts.

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Answer:

V = 314.2 ft^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h    r is the radius (5) and h is the height (4)

Using the pi button for pi

V = pi (5^2) (4)

V =314.1592654

Rounding to the nearest tenth

V = 314.2 ft^3

Answer: \(-\frac{5}{12}\)

Steps:

\(1\frac{1}{4}\times \left(-1\right)\frac{1}{3}\)

Convert mixed numbers to improper fractions: \(1\frac{1}{4}\)\(=\frac{5}{4}\)

\(=\frac{5}{4}\times \left(-1\right)\frac{1}{3}\)

\(\mathrm{Apply\:the\:rule}:\quad \:a\left(-b\right)=-ab\)

\(\frac{5}{4}\left(-1\right)=-\frac{5}{4}\times \:1\)

\(=-\frac{5}{4}\times \:1\times \frac{1}{3}\)

\(\mathrm{Apply\:rule}\:a\times 1=a\)

\(=-\frac{5}{4}\times \frac{1}{3}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}\)

\(\frac{5}{4}\times \frac{1}{3}=\frac{5\times \:1}{4\times \:3}\)

\(=-\frac{5\times \:1}{4\times \:3}\)

\(\mathrm{Multiply\:the\:numbers:}\:5\times \:1=5\)

\(=-\frac{5}{4\times \:3}\)

\(\mathrm{Multiply\:the\:numbers:}\:4\times \:3=12\)

\(=-\frac{5}{12}\)

Hope This Helps!

Answer:

To Express one quantity as a percentage of another.

Triangle DAC is congruent to triangle BCA by SAS congruence theorem.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that, AD = BC and AD || BC.

AD = BC (Given)

AD || BC (Given)

AC = AC (Reflexive property)

∠DAC=∠BCA (Interior alternate angles)

By SAS congruence theorem, ΔDAC≅ΔBCA

By CPCT, AB=CD

Therefore, triangle DAC is congruent to triangle BCA by SAS congruence theorem.

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The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

3:2.

Step-by-step explanation:

They have 15 - 6 = 9 problems to do, so it is:

9:6

= 3:2.

Answer:

9/15

Step-by-step explanation:

15 - 6 = 9 as a fraction would be 9 meaning what is left and 15 as meaning how much they started with so it is 9/15 also called 9 over 15

Hope This Helped

Answer:

Step-by-step explanation:

angle S+angle T+angle+angle R=180 degree(being sum of interior angle of a triangle)

4x^2-6x+40+18x+3+2x^2-7=180

6x^2+12x+36=180

6(x^2+2x+6)=180

x^2+2x+6=180/6

x^2+2x+6=30

x^2+2x=24

x(x+2)=24

x+2=24/x

x=24/x-2

x=24-2x/x

substitute the value of x^2 in angle R

2x^2-7

2(24-2x/x)^2-7(here x and x gets cancel)

2(24-2)^2-7

2*22^2-7

2*484-7

968-7

961

Answer:

Step-by-step explanation:

angle S+angle T+angle+angle R=180 degree(being sum of interior angle of a triangle)4x^2-6x+40+18x+3+2x^2-7=1806x^2+12x+36=1806(x^2+2x+6)=180x^2+2x+6=180/6x^2+2x+6=30x^2+2x=24x(x+2)=24x+2=24/xx=24/x-2x=24-2x/xsubstitute the value of x^2 in angle R2x^2-72(24-2x/x)^2-7(here x and x gets cancel)2(24-2)^2-72*22^2-72*484-7968-7961

Answer:

6

Step-by-step explanation:

6 times 6 = 36, so 6 is the answer

Hope this helps. Please mark me brainliest!

The answer to the question 36/12=3

The expression that represents the perimeter, in centimeters, of the rectangle is 18d + 10f

Option A is correct

Let the width of the rectangle be represented by w

w  =  (7d+8f) cm

Let the length of the rectangle be represented by l

l = (2d-3f) cm

The perimeter of a rectangle is given by the formula:

P  =  2(l  +  w)

P  =  2[(7d + 8f) + (2d - 3f)]

P  = 2[7d  +  2d  +  8f  -  3f]

P  = 2[9d  +  5f]

P  =  18d  +  10f

Therefore, the expression that represents the perimeter, in centimeters, of the rectangle is 18d + 10f

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