how to solve the birth rate in a certain country in 1994 was 14.6 births per thousand population. in 2004 the birth rate was 14.32 births per thousand. let x represent years after 1994 and y represent the birth rate. assume the relationship is linear

Answer:

12,000

Step-by-step explanation:

The machine fills the containers at a rate of 50+5t milliliters (mL) per second.

Therefore, the rate of change of the number of containers, N is:

[tex]\dfrac{dN}{dt}=50+5t, 0\leq t\leq 60[/tex]

[tex]dN=(50+5t)dt\\$Taking integrals of both sides\\\int dN=\int (50+5t)dt\\N(t)=50t+\frac{5t^2}{2}+C $(C a constant of integration)\\\\When t=0, , No containers are filled, therefore:$ N(t)=0\\0=50(0)+\frac{5(0)^2}{2}+C\\C=0\\$Therefore, N(t)=50t+2.5t^2[/tex]

When t=60 seconds

[tex]N(60)=50(60)+2.5(60)^2\\N(60)=12000$ mL[/tex]

Therefore, 12,000 milliliters of acid solution are put into a container in 60 seconds.

Answer:

50,000

Step-by-step explanation:

ten thousand  thousand  hundreds   tens ones

4                            7                 5            9       2

When rounding to the ten thousands, we look at the thousands place

If it is 5 or higher we round the ten thousands place up

7 is five or higher so we round the 4 up one place  4 becomes 5 and the rest becomes 0

5 0 0 0 0

Answer:

$50,000

Step-by-step explanation:

=> $47,592

While rounding off to the nearest thousand, we check the thousands place. If the digit in the thousands place is greater than 5, 1 will be added to the T. Th. place while if its less than 5, there will be no change and The digits except the ten thousands place will all become zero.

So,

=> $50,000

Answer: the probability that the tires will fail within three years of the date of purchase is 0.12

Step-by-step explanation:

The average lifetime of a set of tires is 3.4 years. It means that μ = 3.4

Decay parameter, m = 1/3.4 = 0.294

The probability density function is

f(x) = me^-mx

Where x is a continuous random variable representing the time interval of interest(the reliability period that we are testing)

Since x = 3 years,

Therefore, the probability that the tires will fail within three years of the date of purchase is

f(3) = 0.294e^-(0.294 × 3)

f(3) = 0.294e^- 0.882

f(3) = 0.12

Answer:

the step-by-step explanation for height first :

[tex]h=\sqrt{h^{2} } +r^{2} =26[/tex]

[tex]h=\sqrt{h^{2} } +10^{2} =676[/tex]

[tex]h=\sqrt{h^{2} } + 100 = 676[/tex]

[tex]100-100 = 0[/tex]

[tex]676-100=576[/tex]

[tex]\sqrt{576}[/tex]

[tex]height =[/tex] 24 m

________________

step-by-step explanation for the problem :

FORMULA :  [tex]v = \frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]

v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]10^{2}[/tex] · [tex]24[/tex] = [tex]800\pi[/tex] = [tex]2513.27412[/tex] = 2513

Answer:

[tex]\boxed{\sf \ \ 9x^2-18x-7 \ \ divided \ by \ (3x+1) \ is \ (3x-7) \ }[/tex]

Step-by-step explanation:

Hello,

let's find a and b reals so that

[tex]9x^2-18x-7=(3x+1)(ax+b)[/tex]

[tex](3x+1)(ax+b)=3ax^2+(3b+a)x+b[/tex]

we identify the terms in [tex]x^2[/tex]

   9 = 3a

we identify the terms in x

   -18 = 3b + a

we identify the constant terms

   -7 = b

so ti goes with a = 9/3 = 3, b = -7

so we can write

[tex]9x^2-18x-7=(3x+1)(3x-7)[/tex]

so [tex]9x^2-18x-7 \ divided \ by \ (3x+1) \ is \ (3x-7)[/tex]

hope this helps

Answer:

$23.64

Step-by-step explanation:

12 * $1.97 = $23.64

Answer:

Read below

Step-by-step explanation:

To copy a segment, you have to open your compass to the length of the given segment. The instructions say to have an endpoint at R, so, with the compass open to the length of the given line segment, place one end of the compass at R and draw an arc that intersects the line that R lies on. This new segment is congruent to the given segment.

I hope this helps!

Answer:

20gallons

Step-by-step explanation:

Answer:

To find it's percentage divide $5.60 by

$17.50 and multiply it by 100%

That is

5.60/ 17.50 × 100%

= 32%

Hope this helps you

Answer:

a) Percentage of standardized test takers that scored 550 or less = 76.4%

b) Percentage of standardized test takers that scored 524 = 0.782%

Step-by-step explanation:

This is a normal distribution problem with

Mean = μ = 514

Standard deviation = σ = 50

a) Percentage of standardized test takers scored 550 or less = P(x ≤ 550)

We first normalize or standardize 550

The standardized score for any is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (550 - 514)/50 = 0.72

To determine the required probability

P(x ≤ 550) = P(z ≤ 0.72)

We'll use data from the normal distribution table for these probabilities

P(x ≤ 550) = P(z ≤ 0.72) = 0.76424 = 76.424%

The normal curve for this question and the b part are sketched in the first attached image to this solution.

b) Percentage of standardized test takers that scored 524 = P(x = 524)

On standardizing,

z = (x - μ)/σ = (524 - 514)/50 = 0.20

For this part, since it's an exact probability, we will use the normal distribution formula

P(z = Z) = [1/(σ√2π)] × e^(-z²/2)

Since z = (x - μ)/σ

It can be written properly as presented in the second attached image to this question.

Putting x = 524 or z = 0.20 in this expression, we get

P(x = 524) = P(z = 0.20) = 0.0078208539 = 0.782%

Hope this Helps!!!

Answer:

The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]

Step-by-step explanation:

A nth order polynomial f(x) has roots [tex]x_{1}, x_{2}, ..., x_{n}[/tex] such that [tex]f(x) = (x - x_{1})*(x - x_{2})*...*(x - x_{n}}[/tex],

Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2?

So

[tex]x_{1} = x_{2} = \sqrt{3}[/tex]

[tex]x_{3} = -2[/tex]

Then

[tex](x - \sqrt{3})^{2}*(x - (-2)) = (x - \sqrt{3})^{2}*(x + 2) = (x^{2} -2x\sqrt{3} + 3)*(x + 2) = x^{3} + 2x^{2} - 2x^{2}\sqrt{3} - 4x\sqrt{3} + 3x + 6[/tex]

Since [tex]\sqrt{3} = 1.73[/tex]

[tex]x^{3} + 2x^{2} - 3.46x^{2} - 6.93x + 3x + 6 = x^{3} - 1.46x^{2} - 3.93x + 6[/tex]

The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]

Answer:

196x^2y

Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.

Answer:

1:6, 7:36, 2:9

Step-by-step explanation:

2 : 9 → 8 : 36

1 : 6 → 6 : 36

7 : 36

Least → Greatest

1:6, 7:36, 2:9

Answer:

c. The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

A variable is said to be continuous if it can take on any value in an interval. Examples are lengths, temperature, etc

A discrete variable, on the other hand, can only take on specific values. Examples of discrete variables are the number of students and age.

The exact lengths (in kilometers) of the ocean coastlines of different countries is a continuous variable because it can take on any value in an interval.

A stated earlier, Lengths are in general, continuous variables.

Answer:

[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]    

[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]    

So on this case the 95% confidence interval would be given by (155.301;159.299)    

And the best option would be:

B. (155.3, 159,3)

Step-by-step explanation:

Information given

[tex]\bar X=157.3[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma =15.6[/tex] represent the population standard deviation

n=234 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The Confidence level is is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value for this case would be [tex]z_{\alpha/2}=1.96[/tex]

And replacing we got:

[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]    

[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]    

So on this case the 95% confidence interval would be given by (155.301;159.299)    

And the best option would be:

B. (155.3, 159,3)

Answer:

[tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex]

B.

B.

[tex]y = \frac{17}{8}e^4^x - \frac{1}{8}e^-^4^x[/tex]

Step-by-step explanation:

Question 1:

- We are given a homogeneous second order linear ODE as follows:

                                [tex]y'' + 49y = 0[/tex]

- A pair of independent functions are given as ( y1 ) and ( y2 ):

                               [tex]y_1 = cos ( 7x )\\\\y_2 = sin ( 7x )[/tex]

- The given ODE is subjected to following initial conditions as follows:

                               [tex]y ( 0 ) = 10\\\\y ' ( 0 ) = -4[/tex]

- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:

                               [tex]y = c_1y_1 + c_2y_2[/tex]

Solution:-

- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.

- Formulate the second derivatives of both functions y1 and y2 as follows:

                           [tex]y'_1 = -7sin(7x) , y''_1 = -49cos(7x)\\\\y'_2 = -7cos(7x) , y''_2 = -49sin(7x)\[/tex]

- Now plug the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.

                           [tex]y''_1 + 49y_1 = 0\\\\-49cos(7x) + 49cos ( 7x ) = 0\\0 = 0\\\\y''_2 + 49y_2 = 0\\\\-49sin(7x) + 49sin ( 7x ) = 0\\0 = 0\\\\[/tex]

- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.

- The complete solution to a homogeneous ODE is given in the form as follows:

                            [tex]y = c_1y_1 + c_2y_2\\\\y = c_1*cos(7x) + c_2*sin(7x)\\[/tex]

- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,

                           [tex]y (0) = c_1cos ( 0 ) + c_2sin ( 0 ) = 10\\\\y'(0) = -7c_1*sin(0) + 7c_2*cos(0) = -4\\\\c_1 ( 1 ) + c_2 ( 0 ) = 10, c_1 = 10\\\\-7c_1(0) + 7c_2( 1 ) = -4 , c_2 = -\frac{4}{7}[/tex]

- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:

                           [tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex]    .... Answer

Question 2

- We are given a homogeneous second order linear ODE as follows:

                               [tex]y'' -16y =0[/tex]

- A pair of independent functions are given as ( y1 ) and ( y2 ):

                               [tex]y_1 = e^4^x\\\\y_2 = e^-^4^x[/tex]

- The given ODE is subjected to following initial conditions as follows:

                               [tex]y( 0 ) = 2\\y'( 0 ) = 9[/tex]

- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:

                               [tex]y = c_1y_1 + c_2y_2[/tex]

Solution:-

- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.

- Formulate the second derivatives of both functions y1 and y2 as follows:

                         [tex]y'_1 = 4e^4^x , y''_1 = 16e^4^x\\\\y'_2 = -4e^-^4^x , y''_2 = 16e^-^4^x[/tex]  

- Now substitute the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.

                           [tex]y''_1 - 16y_1 = 0\\\\16e^4^x - 16e^4^x = 0\\\\0 = 0\\\\y''_2 - 16y_2 = 0\\\\16e^-^4^x - 16e^-^4^x = 0\\\\0 = 0[/tex]

- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.

- The complete solution to a homogeneous ODE is given in the form as follows:

                            [tex]y = c_1y_1 + c_2y_2\\\\y = c_1*e^4^x + c_2*e^-^4^x[/tex]

- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,

                           [tex]y ( 0 ) = c_1 * e^0 + c_2 * e^0 = 2\\\\y' ( 0 ) = 4 c_1 * e^0 - 4c_2 * e^0 = 9\\\\c_1 + c_2 = 2 , 4c_1 - 4c_2 = 9\\\\c_1 = \frac{17}{8} , c_2 = -\frac{1}{8}[/tex]

- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:

                           [tex]y = \frac{17}{8} e^4^x - \frac{1}{8}e^-^4^x[/tex]   .... Answer

Answer : The correct statements are,

AC = 5 cm

BA = 4 cm

The perimeter of triangle ABC is 12 cm.

Step-by-step explanation :

As we know that a, b, and c are midpoints of the sides of right triangle that means midpoint divide the side in equal parts.

Now we have to calculate the sides of triangle ABC by using Pythagoras theorem.

Using Pythagoras theorem in ΔACF :

[tex](AC)^2=(FA)^2+(CF)^2[/tex]

Now put all the values in the above expression, we get the value of side AC.

[tex](AC)^2=(3)^2+(4)^2[/tex]

[tex]AC=\sqrt{(9)^2+(16)^2}[/tex]

[tex]AC=5cm[/tex]

Using Pythagoras theorem in ΔDAB :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](BD)^2=(AD)^2+(BA)^2[/tex]

Now put all the values in the above expression, we get the value of side BA.

[tex](5)^2=(3)^2+(BA)^2[/tex]

[tex]BA=\sqrt{(5)^2-(3)^2}[/tex]

[tex]BA=4cm[/tex]

Using Pythagoras theorem in ΔBEC :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](BE)^2=(CE)^2+(CB)^2[/tex]

Now put all the values in the above expression, we get the value of side CB.

[tex](5)^2=(4)^2+(CB)^2[/tex]

[tex]CB=\sqrt{(5)^2-(4)^2}[/tex]

[tex]CB=3cm[/tex]

Now we have to calculate the perimeter of ΔABC.

Perimeter of ΔABC = Side AB + Side CB+ Side AC

Perimeter of ΔABC = 4 + 3 + 5

Perimeter of ΔABC = 12 cm

Now we have to calculate the area of ΔABC.

Area of ΔABC = [tex]\frac{1}{2}\times 4\times 3=6cm^2[/tex]

Now we have to calculate the area of ΔDEF.

Area of ΔDEF = [tex]\frac{1}{2}\times 8\times 6=24cm^2[/tex]

Area of ΔABC = [tex]\frac{6}{24}\times[/tex] Area of ΔDEF

Area of ΔABC = [tex]\frac{1}{4}[/tex] Area of ΔDEF

Answer:

x=2√2 is the answer

Step-by-step explanation:

x²=8

TAKING SQUARE ROOT ON BOTH SIDES

√x²=√8

x=√2×2×2

x=√2²×√2

x=2√2

i hope this will help you

Answer:

The value of x is -2.828 or 2.828

Step-by-step explanation:

In order to eliminate of square of x, you have to square root both sides :

[tex] {x}^{2} = 8[/tex]

[tex] \sqrt{ {x}^{2} } = ± \sqrt{8} [/tex]

[tex]x = \sqrt{8} \\ x = 2 \sqrt{2} \: or \: 2.828[/tex]

[tex]x = - \sqrt{8} \\ x = - 2 \sqrt{2} \: or \: - 2.828[/tex]

Answer/Step-by-step explanation:

==>Given:

=>Rectangular Pyramid:

L = 5mm

W = 3mm

H = 4mm

=>Rectangular prism:

L = 5mm

W = 3mm

H = 4mm

==>Required:

a. Volume of pyramid:

Formula for calculating volume of a rectangular pyramid us given as L*W*H

V = 5*3*4

V = 60 mm³

b. Volume of prism = ⅓*L*W*H

thus,

Volume of rectangular prism given = ⅓*5*3*4

= ⅓*60

= 20mm³

c. Volume of the prism = ⅓ x volume of the pyramid

Thus, 20 = ⅓ × 60

As we can observe from our calculation of the solid shapes given, the equation written above is true for all rectangular prism and rectangular pyramid of the same length, width and height.

Answer:

[tex] = \frac{3}{2} [/tex]

Step-by-step explanation:

[tex]y = mx + c[/tex]

Here,

In this equation ,

[tex]2y - 3x = 8[/tex]

to find the value of m or the value of slope we have to solve for y

Let's solve,

[tex]2y - 3x = 8 \\ 2y = 8 + 3x \\ \frac{2y}{2} = \frac{8 + 3x}{2} \\ y = 4 + \frac{3x}{2} \\ y = \frac{3x}{2} + 4[/tex]

So, the slope is,

[tex] = \frac{3}{2}[/tex]

Answer:

0.0013

Step-by-step explanation:

The probability of selling a property is 40%, so the probability of not selling it is 60%.

To find the probability of selling at least 11 properties, we can calculate the following cases:

Selling 11:

P(11) = C(13,11) * P(sell)^11 * P(not sell)^2

P(11) = (13! / (11! * 2!)) * 0.4^11 * 0.6^2

P(11) = 13*12/2 * 0.4^11 * 0.6^2 = 0.001178

Selling 12:

P(12) = C(13,12) * P(sell)^12 * P(not sell)^1

P(11) = (13! / (12! * 1!)) * 0.4^12 * 0.6^1

P(11) = 13 * 0.4^12 * 0.6 = 0.000131

Selling 13:

P(13) = C(13,13) * P(sell)^13 * P(not sell)^0

P(11) = 1 * 0.4^13 * 0.6^0

P(11) = 1 * 0.4^13 * 1 = 0.000007

Final probability:

P(at least 11) = P(11) + P(12) + P(13)

P(at least 11) = 0.001178 + 0.000131 + 0.000007 = 0.001316

P(at least 11) = 0.0013

Answer:

13 students

Step-by-step explanation:

At least 30 and fewer than 67 makes it 30-66

So,

30-66 => 13 students

Answer:

16

Step-by-step explanation:

There are two columns in the diagram.

The column headed stem represents tens while the column headed leaf represents units. e.g. 2 3 = 23

So we just have to count how many of the numbers are less than 8 in the 6th Stem column and all the numbers below it, which are:

20, 23, 28, 31, 31, 34, 38, 40, 44, 50, 51, 53, 54, 65, 65, 66

Answer:

(x-1) ( x -i) (x+i)

Step-by-step explanation:

x^3 -2x^2 +x-2

Factor by grouping

x^3 -2x^2      +x-2

x^2(x-2)      +1(x-2)

Factor out (x-2)

(x-2) (x^2+1)

Rewriting

(x-1) ( x^2 - (-1)^2)

(x-1) ( x -i) (x+i)

Answer:

Should be b

Step-by-step explanation:

Since it's a multiple choice question you know that -2 or 2 has to be a root for the cubic.

You can test both -2 and 2 and see that replacing x for 2 has the expression evaluate to 0.

Then, since you know the imaginary roots have to be conjugates, you get B.

Answer:

D. No, because the differential equation does not have constant coefficients.

Step-by-step explanation:

The undetermined coefficient method cannot be applied to non homogeneous variables. The differential equation does not have constant variables therefore the method of undetermined superposition can not be applied. To complete a solution of non homogeneous equation the particular solution must be added to the homogeneous equation.

Answer:

3.784

Step-by-step explanation:

Answer:

x=-4

Step-by-step explanation:

[tex]2x^2+8x=x^2-16[/tex]

Move everything to one side:

[tex]x^2+8x+16=0[/tex]

Factor:

[tex](x+4)^2=0[/tex]

By the zero product rule, x=-4. Hope this helps!

Answer:

x=-4

Step-by-step explanation:

Move everything to one side and combine like-terms

x²+8x+16

Factor

(x+4)²

x=-4

Answer:

[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]

Step-by-step explanation:

You have the following differential equation:

[tex]3y''+12y=0[/tex]     (1)

In order to find the solution to the equation, you can use the method of the characteristic polynomial.

The characteristic polynomial of the given differential equation is:

[tex]3m^2+12=0\\\\m^2=-\frac{12}{3}=-4\\\\m_{1,2}=\pm2\sqrt{-1}=\pm2i[/tex]

The solution of the differential equation is:

[tex]y(x)=c_1e^{m_1x}+c_2e^{m_2x}[/tex]   (2)

where m1 and m2 are the roots of the characteristic polynomial.

You replace the values obtained for m1 and m2 in the equation (2). Then, the solution to the differential equation is:

[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]

Answer:

-0.28

Step-by-step explanation:

(1/5) : (-5/7)=(1*5)/(5*(-5))=-(7/25)=-0.28

Answer:

[tex]-7/25[/tex]

Step-by-step explanation:

[tex]1/5 \div -5/7[/tex]

Do the reciprocal of the second fraction.

[tex]1/5 \times 7/-5[/tex]

Multiply the first fraction by the reciprocal of the second fraction.

[tex]7/-25=-0.28[/tex]

The answer in decimal form is -0.28.

Answer:

[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.102[/tex]    

[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]    

And the best option would be:

C. (77.1, 78.3)

Step-by-step explanation:

Information given

[tex]\bar X=77.7[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=3.6 represent the sample standard deviation

n=100 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=100-1=99[/tex]

Since the Confidence is 0.90 or 90%, the significance would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value for this case would be [tex]t_{\alpha/2}=1.66[/tex]

And replacing we got:

[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.10[/tex]    

[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]    

And the best option would be:

C. (77.1, 78.3)

Answer:

Step-by-step explanation:

its B

Answer:

the answer is B

Step-by-step explanation: