In 1960, the population of Colombia was about 16 million and the population of Argentina was about 20.6 million. Between 1960 and 2010, the population of Colombia increased by about 530,000 people per year, and the population of Argentina increased by about 340,000 people per year. Let P represent the population, in millions, and t represent the number of years since 1960. Which of the following system of equations can be used to find the year when both countries had approximately the same population?


A. P = 16 + 0.34t
P= 20.6 + 0.53t

B. P = 16 + 0.53t
P = 20.6 + 0.34t

C. P = 16 + 530,000t
P = 20.6 + 340,000t

D. P = 16t + 340,000
P= 20.6t+ 530,000

24 millennials will use blogs to make a purchase and 60 millennials will  never buy anything without reading a review first.

Here, we are given that 33% of millennials rely on blogs before making a purchase and eight out of 10 millennials never buy anything without reading a review first.

a. If there is a sample of 75 Millennials, out of these 33% will use blogs to make a purchase.

Thus,

33% of 75

= 33/100 × 75

= 33/4 × 3

= 99/4

= 24.75

Since, the number of millennials cannot be a decimal number, we approximate it to the lowest integer, that is, 24.

Thus, 24 millennials will use blogs to make a purchase.

b. Now, if there is a sample of 75 Millennials, out of these 8 out of 10 will never buy anything without reading a review first.

8 out of 10 in percentage terms will be-

8/10 × 100

= 80%

Thus,

80% of 75

= 80/100 × 75

= 80/4 × 3

= 20 × 3

= 60

Thus, 60 millennials will never buy anything without reading a

review first.

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Answer:

RS.20

Step-by-step explanation:

1 pen costs R5.20 and is sold for RS5 so profit is RS.20 per pen

The integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is: \(8 * (1/3)tan^2\theta(1 + tan^2\theta)^(3/2) + C\), where θ is determined by x = 2tanθ, and C represents the constant of integration

What is integration?

Integration is a fundamental concept in calculus that involves finding the integral of a function.

To integrate the function \(\int(x^3/\sqrt(x^2+4))\) dx using a trigonometric substitution, we can use the substitution x = 2tanθ. Let's go through the steps:

Substitute x = 2tanθ. This implies \(dx = 2sec^2\theta d\theta.\)

Rewrite the integral in terms of θ:

\(\int((8tan^3\theta)/(\sqrt(4tan^2\theta+4))) * 2sec^2\theta d\theta.\)

Simplify the expression inside the square root:

\(\int((8tan^3\theta)/(2sec\theta)) * 2sec^2\theta d\theta.\\\\\int(8tan^3\theta) * sec\theta d\theta.\)

Simplify further:

\(16\int tan^3\theta sec\theta d\theta.\)

Apply the trigonometric identity: \(sec^2\theta = 1 + tan^2\theta\). Rearranging, we get: \(sec\theta = \sqrt(1 + tan^2\theta).\)

Substitute \(sec\theta = \sqrt(1 + tan^2\theta)\) in the integral:

\(16\int tan^3\theta * \sqrt(1 + tan^2\theta) d\theta.\)

Let u = tanθ, which implies \(du = sec^2\theta d\theta\). We can rewrite the integral in terms of u:

\(16\int u^3 * \sqrt(1 + u^2) du.\)

Now we have a rational power of u. We can use the substitution \(v = 1 + u^2\) to simplify it:

\(v = 1 + u^2\), which implies dv = 2u du.

Rewrite the integral using v:

\(16\int (u^3 * \sqrt v) * (1/2u) dv.\\\\8\int (u^2\sqrt v) dv.\)

Simplify and integrate:

\(8\int (u^2\sqrt v) dv = 8\int(u^2 * v^{(1/2)}) dv = 8\int u^2v^{(1/2)} dv.\)

Integrate \(u^2v^{(1/2)\) with respect to v:

\(8 * (1/3)u^2v^{(3/2)} + C.\)

Replace v with \(1 + u^2\):

\(8 * (1/3)u^2(1 + u^2)^{(3/2)} + C.\)

Substitute u = tanθ back into the expression:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C.\)

So, the integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C,\)

where θ is determined by x = 2tanθ, and C represents the constant of integration

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120 of the 200 dentists that participated in the survey and recommended Sparkle toothpaste.

If 60% of dentists recommended Sparkle toothpaste, then the remaining 40% did not.

To find out how many dentists recommended Sparkle toothpaste, we can multiply the total number of dentists in the survey (200) by the percentage who recommended it (60% or 0.6):

To solve for x, we can cross-multiply and simplify:

100x = 60 * 200

x = (60 * 200)/100

x = 120

Number of dentists who recommended Sparkle = 0.6 * 200 = 120

Therefore, 120 of the 200 dentists who took part in the survey recommended Sparkle toothpaste.

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y=30 x=60 that should be the answer sorry if it isnt

Answer:

Step-by-step explanation:

\( - \frac{1}{8} t = 4\)

\( = > \frac{- t}{8} = 4\)

\( = > \frac{-t}{8} × 8 = 4 × 8\)

=> -t = 32

=> t = - 32 (Ans)

Answer:

\( \boxed{\huge\underline{\it \: t = \bf \: - 32}}\)

Step-by-step explanation:

\( \bf \: Equation \: Given :-\)

\( \tt \: \dfrac{ - 1}{ 8} t = 4\)

It is an equation.We need to find the value of T of this equation.

\( \huge \underline{\bf \: Solution:-}\)

The given Equation may be rewritten as,

\( : \implies \tt \: - \dfrac{ 1}{8} t = 4\)

\( \bf \: Firstly, multiply \: both \: sides \: by \: 8/-1 : \)

\( : \implies \tt \dfrac{8}{ - 1} \times \dfrac{ - 1}{8} t = \dfrac{8}{ - 1} \times 4\)

Now cancel Left hand side's 8 and 8 and -1 and -1 . (Result is 1 t)

That is:-

\( : \implies \tt \dfrac{ \cancel8}{ \cancel{ - 1}} \times \dfrac{ \cancel{ - 1}}{ \cancel8}t \: = \dfrac{8}{ - 1} \times4\)

\( : \implies \tt 1 t = \dfrac{8}{ - 1} \times4\)

Simply multiply :-

\( : \implies \tt \: t \: = - 8 \times 4\)

\( : \implies \tt \: t = - 32\)

_____________________________________

\( \underline{\bf \huge \: Verification :} \)

Put the value of T on this equation :-

\( : \implies \tt \: \dfrac{ - 1}{8} t \: = 4\)

Putting 32 (The value of t we got) instead of t :-

As we know t is multiplied with -1/8 so,

\( : \implies \tt \: \dfrac{ - 1}{8} \times - 32 = 4\)

Simplifying this equation :

Cancel 8 and 32,and cancel the minus sign of -1 and minus sign of -32, That is:-

\( : \implies \tt \: \dfrac{ \cancel - 1}{ \cancel8} \times \cancel{ - 32} {}^{ \huge4} = 4\)

4 is the result.

\( : \implies \tt \: 4 = 4\)

\( : \implies \it\: LHS = RHS\)

\( \bf \: Hence, verified.\)

________________________________

I hope this helps!

Please let me know if you have any questions.

The correct solution for the given differential equation is: C. y=(4x+c1)³/²/24+c2

To solve the differential equation, you can follow these steps:
Step:1. Rewrite the equation as Y" = 4/Y'.
Step:2. Integrate both sides with respect to x:
  ∫ Y" dx = ∫ 4/Y' dx
Step:3. The left side will result in Y', while the right side will give (4x + c1):
  Y' = 4x + c1
Step:4. Integrate both sides again with respect to x:
  ∫ Y' dx = ∫ (4x + c1) dx
Step:5. The left side will result in Y, and the right side will give (4x+c1)³/²/24+c2:
  Y = (4x+c1)³/²/24+c2

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The error term is a random variable with an expected value of zero.2. The error term is normally distributed

The assumptions underlying the simple linear regression model `y = Bo + B1x + e` are: 1.

The variance of the error term e is constant across all values of x.Thus, the assumptions that are underlying the simple linear regression model `y = Bo + B1x + e` are the second and the third options, which are "The error term is normally distributed." and "The variance of the error term e is constant across all values of x." respectively.

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The standard deviation of the sampling distribution of sample means, with 69 children, would be of 0.11 years, using the Central Limit Theorem.

The Central Limit Theorem defines the distribution of the sampling distribution of sample means with size n of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\).

For the sampling distribution, the mean and the standard deviation are given as follows:

In the context of this problem, the parameters are given as follows:

Hence the standard deviation of the sampling distribution of sample means, with 69 children is calculated as follows:

\(s = \frac{0.9}{\sqrt{69}} = 0.11\)

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Answer:

B. \(y=-sin\ x-2\)

Step-by-step explanation:

We all suck at math... just lmk if you need more help...

Answer:

a = -2  

Step-by-step explanation:

Ok, so for parallel lines you need to make slopes for both the lines equal. So for line y = x + 4 the slope is 1. (slope is the coefficent infront of the x value while in y=mx+b form. To make the other line have a slope of 1 a needs to be a number as so that 2a+5 = 1

2a+5 = 1

2a = 1 - 5

a = -4/2

a = -2  

Answer:

$445

Step-by-step explanation:

Linear regression line y=2.1x+130 predicts sales based on the money spent on advertising.

Linear regression represents the relationship between two variables. the value of y depends on the value of x.

x represents the dollars spent in advertising and y represents the company sales in dollars.

We need to find out sales y when $150 spends on advertising.

Plug in 150 for x and find out y

y = 2.1 x + 130

y = 2.1 (150) + 130

y= 445

The company expects $445 in sales

The company expects $445 in sales.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Linear regression line y = 2.1x + 130 predicts sales based on the money spent on advertising.

Now, Linear regression represents the relationship between two variables. the value of y depends on the value of x.

Here, x represents the dollars spent in advertising and y represents the company sales in dollars.

We need to find out sales y when $150 spends on advertising.

Plug in 150 for x and find out y as;

y = 2.1 x + 130

y = 2.1 (150) + 130

y = 445

Thus, The company expects $445 in sales.

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Answer:x=2/3

Step-by-step explanation:

Answer:

It's around 459. So 460 if need to round

Step-by-step explanation:

So, 40 randomly chosen people do not represent  the whole school, but using the ratio 27:40 you are given in the equation, you can divide the number of students (680) by the surveyed students (40) to get 17. What this means is there is 17 groups of 40 in the school, so to distribute the amount of people who are in a after-school activity, you must multiply 17 x 27 to get the assumption of about 459 kids. Hopefully you understand =)

Step-by-step explanation:

Well they made 19 clay, where 12 were vases. That means 7 were not vases. She randomly chooses 16 clay objects, which then also means 3 were left behind. so if the vases are  12/19, which is approximately 63%, then 63% of the objects are vases. Makes sense, right? Well now we need to multiply that by the initial 11 in the question. After all of this work..

Answer: 6.9474 or 6.94736.

Please mark as Brainliest.

The cost of walking this guest is $190.

The cost of walking the guest can be calculated by adding up the expenses incurred by the hotel.

The guest was walked to another hotel that charged a room rate of $150. Therefore, the hotel incurred a cost of $150 for the room.

In addition to the room cost, the hotel also paid for the guest's Uber ride to the new hotel, which was $15.

Furthermore, the overbooked hotel gave the guest a gift card worth $25. Although the gift card does not directly represent an expense, it can be considered as an opportunity cost for the hotel, as they could have used that money to cover other costs.

Therefore, the total cost incurred by the hotel for walking the guest is:

$150 (room cost) + $15 (Uber cost) + $25 (gift card cost) = $190

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Answer:

200 Recyclables Items

Step-by-step explanation:

The first step is to find the common ratio using this formula

Common ratio= Numbers of recyclable items/Number of minutes it takes to sort the recyclable item

Let plug in the formula

Common ratio =150/3 = 50

This means that we have 50 Recyclables Items per minute.

Now let calculate how many recyclable items that Faye can sort in 4 minutes

This means we are going to multiply 4 minutes by the 50 recyclable items per minutes

Hence,

4 * 50 = 200 Recyclables Items

Therefore Based on the ratio shown in the double number line, this means that Faye can sort 200 recyclable item in 4 minutes

Answer: 200

Step-by-step explanation: Since 150 divided by 3 is 50 add a 50 to 150 and you get 200

Answer:

0.18

Step-by-step explanation:

5.2-5.02=0.18

Subtract the smaller number from the larger number. Difference always means you have to subtract.

Answer:

\(\sf\longmapsto0.18\)

Step-by-step explanation:

\(\sf\longmapsto \: 5.2 - 5.02\)

\(\sf\longmapsto \: 0.18\)

Note:

Difference means Subtract (–)

Answer:

D y=2x

Step-by-step explanation:

Using slope formula change in y over change in x

\( \frac{2}{1} \)

the slope is 2 and when we plug the x value in it gives us our corresponding y value so the answer is D

PLEASE GIVE BRAINLIEST!

thank you and have a good day :)

Answer:

b^5

Step-by-step explanation:

When you are multiplying exponents with the same letter base, you simply just add the exponents.

for example, x^2 * x^3 = x^5

another example, y^6 * y^8 = y^14

An expression equivalent to b^3 * b^2 would be b^5

I hope this helps!

To find the year during which the average cost of a new car was $11,600, we can set up the equation and solve for the value of t.

The given model is:

\(\sf C = 45.5t^2 + 6100 \\\)

We want to find the value of t when C is $11,600. So we can substitute C = $11,600 into the equation:

\(\sf 11,600 = 45.5t^2 + 6100 \\\)

Now, let's solve this equation for t.

Subtracting 6100 from both sides:

\(\sf 11,600 - 6100 = 45.5t^2 \\\)

Simplifying:

\(\sf 5500 = 45.5t^2 \\\)

Dividing both sides by 45.5:

\(\sf \frac{5500}{45.5} = t^2 \\\)

Calculating:

\(\sf 120.88 \approx t^2 \\\)

To find the value of t, we take the square root of both sides:

\(\sf t \approx \sqrt{120.88} \\\)

Calculating:

\(\sf t \approx 11.00 \\\)

Therefore, the average cost of a new car was $11,600 around the year 1991 (since 1980 + 11 years = 1991).

Thus, the average cost of a new car was $11,600 in the year 1991.

If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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Answer:

48

Step-by-step explanation:

n² +6n ÷ 3

Plug in n:

6^2+6x6 ÷ 3

Solve for exponent first (According to PEMDAS)

36+6x6 ÷ 3

Multiply next:

36+36 ÷ 3

Divide next:

36+12

Finally, add:

48

Answer: 48

Additional Note: For PEMDAS, M and D is first come first serve. So you read it left to right and if you see M first, you do M. If you see D first, you do D. Same goes for A and S. If you see A first, you do A. If you see S first, you do S. M and D ALWAYS does before A and S

P= Parenthesis

E= Exponent

M= Multiplication

D= Division

A= Addition

S= Subtraction

The rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

What is volume?

Volume refers to the amount of three-dimensional space occupied by an object or a substance.

To find the rate of increase in the volume V of a sphere when the surface area S becomes 100π square inches, we need to use the formulas relating the surface area and volume of a sphere to its radius.

The surface area S of a sphere is given by the formula:

\(S = 4\pi r^2,\)

where r is the radius of the sphere.

The volume V of a sphere is given by the formula:

\(V = (4/3)\pi r^3.\)

To find the rate of increase in volume with respect to time, we need to differentiate the volume formula with respect to time.

Given that the radius r is increasing at a uniform rate of 0.3 inches per second, we can write:

dr/dt = 0.3 inches per second.

Now, let's differentiate the volume formula with respect to time:

\(dV/dt = d/dt [(4/3)\pi r^3].\)

Using the power rule of differentiation, we get:

\(dV/dt = (4/3)\pi * 3r^2 * (dr/dt).\)

Simplifying further, we have:

\(dV/dt = 4\pi r^2 * (dr/dt).\)

Since we want to find the rate of increase in cubic inches per second, we need to express the volume in cubic inches.

Substituting the value of the surface area S = 100π square inches into the surface area formula:

\(100\pi = 4\pi r^2.\)

Dividing both sides by 4π, we get:

\(r^2 = 25.\)

Taking the square root of both sides, we find:

r = 5.

Now, we can substitute the value of r into the rate of increase formula:

\(dV/dt = 4\pi(5^2) * (0.3).\)

Simplifying the expression:

dV/dt = 4π(25) * 0.3.

dV/dt = 30π cubic inches per second.

Therefore, the rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

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Answer:

The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. For example, 8xyz2 and −5xyz2 are like terms because they have the same variables and power while 3abc and 3ghi are unlike terms because they have different variables.

Answer:

one, x = 7

Step-by-step explanation:

7(x - 2) + 5 = 3 (2x - 1) + 1

reduce:

7x - 14 + 5 = 6x - 3 + 1

x = 7

a. The sample mean is 3 and the sample standard deviation is approximately 1.53.

b. The estimated standard error for the sample mean is 0.765.

a. The sample mean is:

mean = (2 + 2 + 6 + 2)/4 = 3

The sample standard deviation can be calculated using the formula:

s = √(sum((xi - mean)²)/(n - 1))

where xi represents each score in the sample. Plugging in the values, we get:

s = √((2-3)² + (2-3)² + (6-3)² + (2-3)²)/3

s = √(14/3)

s ≈ 1.53

So, the sample mean is 3 and the sample standard deviation is approximately 1.53.

b. The estimated standard error for the sample mean can be calculated using the formula:

SE = s/√(n)

where s is the sample standard deviation and n is the sample size. Plugging in the values, we get:

SE = 1.53/√4)

SE = 0.765

So, the estimated standard error for the sample mean is 0.765.

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Answer:

T(c) = 100 + 3*c

Step-by-step explanation:

cost = fee + cost per chair * number of chairs

T(c) = 100 + 3*c

Answer:

T ( c)= $ 100 + $ 3 c

Step-by-step explanation:

Given that :-

To Find :-

Solution :-

Total Cost, T ( c) = Fee + cost per chair × no. of chairs.

T ( c) = $ 100 + $ 3 × c

T ( c) = $ 100 + $ 3 c

Answer:

formula for area is length × height

so we have 13+8 ×16+4

21×20 = 420m

Answer:

c

Step-by-step explanation:

I hope this helpssssssss