In 2014, the population of India1 was 1.236 billion people and increasing at a rate proportional to its population. If the population is measured in billions of people and time is measured in years, the constant of proportionality is 0.0125. Define P to be the population of India, in billions of people, in the year t, where t represents the number of years since 2014. (a) Write a differential equation to describe the relationship.\

Answer:

65.8

Step-by-step explanation:

Use the sin formula

100/sin (28) = x/ sin (18)

(sin (18) (100))/ sin (28) = x

x = 65.8223

x = 65.8

Answer:

65.8

Step-by-step explanation:

Accellus Correct

Answer:

6

Step-by-step explanation:

Hello, please consider the following.

[tex](4+x)^2=4^2+2\cdot 4\cdot x+x^2=16+\boxed{8}x+x^2\\\\\text{ ... and not ...}\\\\16+\boxed{4}x+x^2[/tex]

So the correct equation becomes.

[tex]x^2+64=16+8x+x^2\\\\8x=64-16=48\\\\\text{ we divide by 8 both sides of the equation.}\\\\x=\dfrac{45}{8}=6[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Error : The expression ( 4 + x )² was expanded incorrectly.

Correct Solution : x = 6

Step-by-step explanation:

The planning of the solution is correct, by Pythagorean Theorem you can say that PQ² + QO² = PO², and hence through substitution x² + 8² = ( 4 + x )². Let's look into the calculations.

PQ² + QO² = PO²,

x² + 8² = ( 4 + x )²,

x² + 8² = 16 + 8x + x²,

64 = 16 + 8x,

48 = 8x,

x = 48 / 8 = 6, x = 6

As you can see, the only error in the calculations was expanding the expression ( 4 + x )². ( 4 + x )² = 4² + 2 [tex]*[/tex] 4 [tex]*[/tex] x + x² = 4² + 8x + x² = 16 + 8x + x², not 16 + 4x + x².

Answer:

A consistent of equations has at least one solution,and an inconsistent system has no solution, watch an example of analyzing a system to see if its consistent or inconsistent.

Answer:  see below

Step-by-step explanation:

Consider the standard form of a linear equation in Slope-Intercept form:

        y = mx + b    where

A CONSISTENT system of equations is where the equations have different slopes OR the same slope and y-intercept.

This results in the lines crossing so they have at least one solution.

An INCONSISTENT system of equations is where the equations have the same slope but different y-intercepts.

This results in parallel lines so they have no solutions.

Answer:

Step-by-step explanation:

Given the equation solved by savanah expressed as [tex]3+4|\frac{x}{2} + 3| = 11[/tex], IF she solved for one of the solution and got x = -2, we are to solve for the other value of x.

Note that the expression in modulus can be expressed as a positive expression and negative expression.

For the positive value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]\frac{x}{2} + 3[/tex], the expression becomes;

[tex]3+4(\frac{x}{2} + 3) = 11[/tex]

On simplification;

[tex]3+4(\frac{x}{2} + 3) = 11\\\\3 + 4(\frac{x}{2} )+4(3) = 11\\\\3 + \frac{4x}{2}+ 12 = 11\\\\3 + 2x+12 = 11\\\\2x+15 = 11\\\\Subtract \ 15 \ from \ both \ sides\\\\2x+15-15 = 11-15\\\\2x = -4\\\\x = -2[/tex]

For the negative value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]-(\frac{x}{2} + 3)[/tex], the expression becomes;

[tex]3+4[-(\frac{x}{2} + 3)] = 11[/tex]

On simplifying;

[tex]3+4[-(\frac{x}{2} + 3)] = 11\\\\3+4(-\frac{x}{2} - 3)= 11\\\\3-4(\frac{x}{2}) -12 = 11\\\\3 - \frac{4x}{2} - 12 = 11\\\\3 - 2x-12 = 11\\\\-2x-9 = 11\\\\add \ 9 \ to \ both \ sides\\\\-2x-9+9 = 11+9\\-2x = 20\\\\x = -20/2\\\\x = -10[/tex]

Hence her other solution of x is -10

Answer:

Error in calculated area = [tex]\pm 10.3 cm^2[/tex]

Step-by-step explanation:

x = 58 cm

y = 45 cm

A = x*y

delta A

= delta (x*y)

= y delta x + x delta y  (neglecting small qty delta x * delta y = 0.01)

= 45(0.1) + 58(0.1)

= 103(0.1)

= 10.3 cm^2

Answer:

The value of 1/3x-3/4 when x=1/4 is 0.08333 repeated.

Step-by-step explanation:

1 inch = four 1/4’s

1 inch = 4 feet

6 X 4 = 24 feet

3/4 inches = 3 feet.

6 3/4 inches = 27 feet

4 x 4 = 16

1/2 inch = 2 feet

4 1/2 inches = 18 feet

Room is 27 feet x 18 feet

Answer:

a. 17

Step-by-step explanation:

The pattern is add 5 then subtract 2

Answer:

[tex] {(x - 3)}^{2} + {(y + 5)}^{2} = {5}^{2} [/tex]

Step-by-step explanation:

First find the radius

Which is the distance between the 2 points.

Radius =5

The answer in the standad form is above.

The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25

The standard equation of a circle is given as:

(x - a)² + (y - b)² = r²

where (a, b) is the center of the circle and r is the radius of the circle.

Given the center as (3, -5) hence the radius of the circle is the distance between (3, -5) and (-1, -8). Hence:

[tex]Radius=\sqrt{(-8-(-5))^2+(-1-3)^2} \\\\Radius=5\ units\\[/tex]

hence:

(x - 3)² + (y - (-5))² = 5²

(x - 3)² + (y + 5)² = 25

The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25

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Answer:

b

Step-by-step explanation:

y = x + 1

The correct answer is (B). The slope-intercept form of a line is y = mx + b. Since the line passes through (−1,2), there are three possibilities: the line will have a slope (the "m" in front of the "x" variable), it will be vertical (x = −1), or it will be horizontal (y = 2). Plug x = −1 into all four equations to see which equation is not satisfied. The only answer choice that doesn't give us y = 2 is (B).

Option B is correct.

Given:

Line A passes through the point [tex](-1,2)[/tex].

To find:

Which of the given equations cannot be the equation of line A.

Solution:

If Line A passes through the point [tex](-1,2)[/tex], it means the equation of Line A must be satisfied by the point

In option A, consider the given equation is:

[tex]y=1-x[/tex]

Substituting [tex]x=-1,y=2[/tex], we get

[tex]2=1-(-1)[/tex]

[tex]2=1+1[/tex]

[tex]2=2[/tex]

This statement is true. So, [tex]y=1-x[/tex] can be the equation of line A.

Similarly, check for the other options.

In option B,

[tex]y=x+1[/tex]

Substituting [tex]x=-1,y=2[/tex], we get

[tex]2=-1+1[/tex]

[tex]2=0[/tex]

This statement is false. So, [tex]y=x+1[/tex] cannot be the equation of line A.

In option C,

[tex]x=-1[/tex]

It is a vertical line and it passes through the point [tex](-1,2)[/tex] because the x-coordinate is [tex]-1[/tex]. So, [tex]x=-1[/tex] can be the equation of line A.

In option D,

[tex]y=x+3[/tex]

Substituting [tex]x=-1,y=2[/tex], we get

[tex]2=-1+3[/tex]

[tex]2=2[/tex]

This statement is true. So, [tex]y=x+3[/tex] can be the equation of line A.

Therefore, the correct option is B.

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Answer:

151 9/19

Step-by-step explanation:

Step-by-step explanation:

Option A is the correct answer because it is equal to 151.47

Answer:

a) Means: 24 and 2; Extremes: 4 and 12

b) Means: 6 and 16; Extremes: 24 and 4

c) Means: 8 and 8; Extremes: 4 and 16

d) Means: 50 and 3; Extremes: 6 and 25

Step-by-step explanation:

The Means and Extremes in a proportion are defined based on the writing the proportion in one lie using colons the indicate the fraction, like in:

a : b = c : d The extremes values here are those that you see at the extreme left and extreme right of that expression. That is: a, and d.

The Means are the values that appear in the middle of the one line expression, that is: b and c.

Recall as well that the proportion can also be written with fractions:

a : b = c : d  is the same as:   a / b = c / d

so convert the expression to a one line with colons when the question comes in fraction form, and that way you can answer.

Answer:

x =2

Step-by-step explanation:

(x+4) /3 = 2

Multiply each side by 3

(x+4) /3  *3= 2*3

x+4 = 6

Subtract 4

x+4-4 = 6-4

x =2

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 2

▹ Step-by-Step Explanation

[tex]\frac{x + 4}{3} = 2\\\\3 * 2 = 6\\\\x + 4 = 6\\\\x = 2[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

to provide interest in the subject

As per my experience,I used to hate math and always scored less marks,the moment I was going to high school I realized the importance of math towards the future, see you'll find maths in nearly all subjects like the 3 sciences, economics, geography, business e.t.c

Why did you write this question at first?, just take some free time and think about it,the only best way to learn maths is to take maths positively as the best and most valuable subject,if you want to ace math you have to race it, challenge math like you'd challenge anyone to a game, practice math if it's your weakest point, practice is very much needed to skill maths and never be shy to ask your teachers whether you are studying online/offline. You'll need to get the shy behaviour out of you whether you like /don't like your teacher or your an average student.

Concentrate while learning math, whether there's noise in you background or not, Nothing can stop you in excelling math if you have full concentration, positiveness and the "will" to do so.

if you're next to your exams then just one thing, Start now!!

hope this helps!

Answer:

£39.20

Step-by-step explanation:

→ Identify which ratio goes to each person

2 : 1 : 5

2 = Paul

1 = Colin

5 = Brian

→ Divide the total tip by the total sum of the ratio's

£78.40 ÷ ( 2 + 1 + 5 ) ⇔ £78.40 ÷ 8 = £9.80

→ Now we know one part is equal to £9.80 we multiply this number by each of the associated ratio's

Paul = £9.80 × 2 ⇔ £19.60

Colin = £9.80 × 1 ⇔ £9.80

Brian = £9.80 × 5 ⇔ £49

→ Minus Brian's tip against Colin's tip

£49 - £9.80 = £39.20

Answer: intersecting lines

Step-by-step explanation:

Answer:

The relationship of the lines would be Parallel.

Answer:

-12

Step-by-step explanation:

Answer:

a) dV(s)  =  15,386 cm³

b) dS(s) = 4,396 cm²

c) dV(s)/V(s) = 1,07 %    and   dS(s)/ S(s)  =  0,71 %

Step-by-step explanation:

a) The volume of the sphere is

V(s) = (4/3)*π*x³        where x is the radius

Taking derivatives on both sides of the equation we get:

dV(s)/ dr  =  4*π*x²    or

dV(s)  =  4*π*x² *dr

the possible propagated error in cm³ in computing the volume of the sphere is:

dV(s)  = 4*3,14*(7)²*(0,025)

dV(s)  =  15,386 cm³

b) Surface area of the sphere is:

V(s) = (4/3)*π*x³  

dV(s) /dx  =  S(s) = 4*π*x³

And

dS(s) /dx  = 8*π*x

dS(s) = 8*π*x*dx

dS(s) = 8*3,14*7*(0,025)

dS(s) = 4,396 cm²

c) The approximates errors in a and b are:

V(s) =  (4/3)*π*x³     then

V(s) = (4/3)*3,14*(7)³

V(s) = 1436,03 cm³

And  the possible propagated error in volume is from a)  is

dV(s)  =  15,386 cm³

dV(s)/V(s)  = [15,386 cm³/1436,03 cm³]* 100

dV(s)/V(s) = 1,07 %

And for case b)

dS(s) = 4,396 cm²

And the surface area of the sphere is:

S(s) =  4*π*x³        ⇒   S(s) =  4*3,14*(7)²    ⇒ S(s) = 615,44 cm²

dS(s) = 4,396 cm²

dS(s)/ S(s)  =  [ 4,396 cm²/615,44 cm² ] * 100

dS(s)/ S(s)  =  0,71

Answer:

B

Step-by-step explanation:

X must not be equal to -6, -1, 1 or 3

Answer:

Collinear occurs when the two points has the same gradient,

So, for this question any line that forms by any three points would be collinear.

Hence, EBF,DGC,MGN,BGA are all collinears

Step-by-step explanation:

Answer:

No. of 1 pt free throws = 5, No. of 2 pt goals = 8, No. of 3 pt goals = 4

Step-by-step explanation:

Equations : x + y + z = 17 [ Total times taken to score ]

1x + 2y + 3z = 33 [ Total Score ]

Also, y = x + 3

Putting the value of 'y' in both equations :

x + (x + 3)+ z = 17 → 2x + 3 + z = 17 → 2x + z = 14  (i)

1x + 2 (x + 3) + 3z = 33 →  x + 2x + 6 + 3z = 33 → 3x + 3z = 27 (ii)

Solving these equations :

From (i), z = 14 - 2x

Putting this value in (ii), 3x + 3(14 - 2x) = 27 → 3x + 42 - 6x = 27

42 - 3x = 27 → 3x = 15 → x = 5

y = x + 3 = 5 + 3 → y = 8

z = 17 - x - y → z = 17 - 5 - 8 = 17 - 13 → z = 4

Answer:

4

Step-by-step explanation:

Answer:

Alpha (α) is used to measure the error for decisions concerning true null hypotheses, while beta (ß) is used to measure error for decisions concerning false null hypotheses.

Step-by-step explanation:

Suppose we have events X and Y.

1. If it is said that X equals Y, when X is actually not equal to Y, α is used in this case, the null hypotheses.

2. If X is said to not be equal to Y, when X is actually equal to Y, β is used in this case, the false null hypotheses.

Answer:

476 workers

Step-by-step explanation:

Men: women : total

3          4           3+4 = 7

We want 204 men

204/3 =68

Multiply each by 68

Men: women : total

3*68    4*68      7*68

204        272      476

Answer:

There are 476 workers

Step-by-step explanation:

Step-by-step explanation:

check the tile whose side length is divisible by both 150 and180 in such a way that you don't get decimal points

150÷4=37.5 so that is impossible

150÷8=18.75 so that is also impossible

150÷6=25 180÷6=30

so the six sided tile is applicable

Answer:

The P-Value is  0.07186  

Step-by-step explanation:

GIven that :

Mean = 70

standard deviation = 3.5

sample size n = 49

sample mean = 69.1

The null hypothesis and the alternative hypothesis can be computed as follows;

[tex]H_o : \mu = 70 \\ \\ H_1 : \mu \neq 70[/tex]

The standard z score formula can be expressed as follows;

[tex]\mathtt{z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}}[/tex]

[tex]\mathtt{z = \dfrac{69.1 - 70}{\dfrac{3.5}{\sqrt{49}}}}[/tex]

[tex]\mathtt{z = \dfrac{-0.9}{\dfrac{3.5}{7}}}[/tex]

z = -1.8

Since the test is two tailed and using the Level of significance = 0.05

P- value = 2 × P( Z< - 1.8)

From normal tables

P- value = 2 × (0.03593)

The P-Value is  0.07186  

Answer:

The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour

Step-by-step explanation:

Represent the bus average speed with x and the motorcycle average speed with y

Given

[tex]x = y + 2[/tex]

Distance covered by bus = 165 miles

Distance covered by motorcycle in same time = 155 miles

Required

Determine the speed of each

Average Speed is calculated as;

[tex]Average\ Speed = \frac{Distance}{Time}[/tex]

Since the two are measured with the same time, represent time with T

For the bus

[tex]Average\ Speed = \frac{Distance}{Time}[/tex] becomes

[tex]x = \frac{165}{T}[/tex]

Make T the subject of formula

[tex]T = \frac{165}{x}[/tex]

For the motorcycle

[tex]y = \frac{155}{T}[/tex]

Make T the subject of formula

[tex]T = \frac{155}{y}[/tex]

Since, T = T; we have that

[tex]\frac{165}{x} = \frac{155}{y}[/tex]

Cross Multiply

[tex]165y = 155x[/tex]

Substitute [tex]x = y + 2[/tex]

[tex]165y = 155(y+2)[/tex]

Open Bracket

[tex]165y = 155y - 310[/tex]

Collect Like Terms

[tex]165y - 155y = 310[/tex]

[tex]10y = 310[/tex]

Divide both sides by 10

[tex]y = 31[/tex]

Recall that [tex]x = y + 2[/tex]

[tex]x = 31 +2[/tex]

[tex]x = 33[/tex]

Hence;

The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour

Complete Question

In a genetic experiment on peas, one sample of offspring contained 436 green peas and 171 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was expected? The probability of getting a green pea is approximately: Is the probability reasonably close to 3/4?

Answer:

The  probability is  [tex]P(g) =0.72[/tex]

Yes the result is reasonably close

Step-by-step explanation:

From the question we are told that

   The  number of  of  green peas is  [tex]g = 436[/tex]

     The number of yellow peas is  [tex]y = 171[/tex]

   The sample size is  [tex]n = 171 + 436 = 607[/tex]

The probability of getting an offspring pea that is green is mathematically represented as

       [tex]P(g) = \frac{g}{n}[/tex]

        [tex]P(g) = \frac{436}{607}[/tex]

        [tex]P(g) =0.72[/tex]

Comparing  [tex]P(g) =0.72[/tex]  to   [tex]\frac{3}{4} = 0.75[/tex] we see that the result is reasonably close

Answer:

See attachment for Venn diagram

Percentage of only TV owners is 16%

Step-by-step explanation:

Given

[tex]TV\ Owners = 68\%[/tex]

[tex]Radio\ Owners = 72\%[/tex]

[tex]None = 12\%[/tex]

Required

Represent with a Venn Diagram

What percentage owned television

From the Venn Diagram and In sets theory; we have that

Total = (TV Owners - Radio and TV Owners) + (Radio Owner - Radio and TV Owners) + Radio and TV Owners + None

Represent Radio and TV Owners with y

[tex]Total = (TV\ Owners - y) + (Radio\ Owner - y) + y + None[/tex]

Substitute 68% for TV Owners, 72% for Radio Owners, 12& for None:

[tex]Total = 68\% - y + 72\%- y + y + 12\%[/tex]

Collect Like Terms

[tex]Total = 68\% + 72\%+ 12\%- y + y - y[/tex]

[tex]Total = 152\% - y[/tex]

In Sets, Total represents 100%; So, we have

[tex]100\% = 152\% - y[/tex]

Make y the subject of formula  

[tex]y = 152\% - 100\%[/tex]

[tex]y = 52\%[/tex]

The percentage of only TV owners is calculated by subtracting y from TV owners

[tex]\%P = 68\% - 52\%[/tex]

[tex]\%P = 16\%[/tex]

Answer:

The answer is 90%

Step-by-step explanation:

Answer:

17h+1.75m=522 m=40h

Step-by-step explanation:

Let h=  {the number of hours the driver drove}

Let m=  the number of miles driven

The driver makes $17 for each hour working, so if the driver worked for hh hours, Luke would have to pay him 17h17h dollars. The cost of gas and maintenance is $1.75 per mile, so for mm miles Luke's costs would be 1.75m1.75m dollars. The total cost of the route 17h+1.75m17h+1.75m equals \$522:$522:

17h+1.75m=522

17h+1.75m=522

Since the driver drove an avearge of 40 miles per hour, if the driver drove  hour, he would have driven 40 miles, and if the driver drove hh hours, he would have driven 40h40h miles, therefore mm equals 40h:40h:

m=40h

m=40h

Write System of Equations:

​  

17h+1.75m= 522

m=40h

The truck is going for a run for 6 hours and the system of the equation to solve a further problem related to this is [tex]\rm{Cost}=17x+1.75y[/tex]

The following are the different costs of the truck that Luke must be pay while running a truck:

Let ' x ' be the total time of driving a truck in hours.

and ' y ' be the total mile distance that is covered by the truck.

Therefore, the system of the equation for the overall running cost for a truck is given below.

[tex]\rm{Cost}=17x+1.75y[/tex]

Now, On one particular day, the driver drove an average of 40 miles per hour, and Luke's total expenses for the driver, gas and truck maintenance were $522.

Thus,

The total distance traveled by truck is 40x.

That is,

[tex]y=40x[/tex]

Substitute the values and solve them further.

[tex]522=17x+1.75y\\522=17x+1.75 \times 40x\\522=17x+70x\\522=87x\\x=6[/tex]

Thus, the truck is going for a run for 6 hours and the system of the equation to solve the further problems related to this is [tex]\rm{Cost}=17x+1.75y[/tex]

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