The population of Atlanta is 5,949,951. It is said to be growing at a rate of 1.3% yearly. What will the population be in 10 years? *

Answer:

90 pounds, 210 pounds

Step-by-step explanation:

Given:

A storekeeper wants to mix two types of flour to get 300 pounds, so he can sell it by 2.50$ per pound.

He uses flour worth $2.40 a pound with another flour worth $3.00 a pound.

Question:

How many pounds of each does he use?

Solution:

Let pounds of one type of flour mixed = [tex]x[/tex]

Then pounds of another type of flour mixed = [tex]300-x[/tex]

Cost of 1 pound of one type of flour = $2.40

Cost of [tex]x[/tex] pounds of one type of flour = [tex]2.4x[/tex]

Similarly,

Cost of 1 pound of another type of flour = $3

Cost of  [tex]300-x[/tex] pounds of another type of flour = [tex]3(300-x)=900-3x[/tex]

Cost of mixed flour per pound = $2.5

Total cost of mixed flour per pound = $2.5 [tex]\times[/tex] 300 = $750

Cost of [tex]x[/tex] pounds of one type + Cost of  [tex]300-x[/tex] pounds of another type = $750

[tex]2.4x+900-3x=750\\\\ -0.6x+900=750\\ \\ Subtracting\ both\ sides\ by\ 900\\ \\ -0.6x+900-900=750-900\\ \\ -0.6x=-150\\ \\ Minus\ canceled\ by\by\ minus\\ \\ 0.6x=150\\ \\ Dividing\ both\ sides\ by\ 0.6\\ \\ x=90[/tex]

Pounds of one type of flour mixed = [tex]x[/tex] = 90 pounds

Pounds of another type of flour mixed = [tex]300-x[/tex] = 300 - 90 = 210 pounds

Thus, 90 pounds of one and 210 pound of another type of flour mixed.

Answer:

50lb of 3.00

250lb of 2.40

Step-by-step explanation:

Answer:

I think the answer is B

Step-by-step explanation:

180 - 104 - 36 = 40

Answer:

cookies

Step-by-step explanation:

Answer:

$508.41

Step-by-step explanation:

Compound interest is calculated with the formula:

[tex]CI = P(1 + R)^T - P[/tex]

where P = Principal/ Initial amount = $850

R = Rate = 4.8% = 0.048

T = Time elapsed = 10 years

Hence, the compound interest is:

[tex]CI = 850(1 +0.048)^{10} - 850\\\\\\CI = 850(1.048)^{10} - 850\\\\\\CI = (850 * 1.598) - 850\\\\\\CI = 1358.41 - 850\\\\\\[/tex]

CI = $508.41

The interest after the first 10 years is $508.41

The first account with an initial deposit of $850 at a 4.8% interest rate compounded annually will earn approximately $510.87 in interest over 10 years.

The student asked how much interest the first account, which is a college savings account with an initial deposit of $850 at a 4.8% interest rate compounded annually, will earn in 10 years. To calculate this, we can use the formula for compound interest:

A = P(1 + r/n)^nt

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for, in years.

In this case, P = $850, r = 4.8/100 = 0.048, n = 1 (since the interest is compounded annually), and t = 10 years. So, the calculation is:

A = 850(1 + 0.048/1)1*10

A = 850(1 + 0.048)10

A = 850(1.048)10
A ≈ 850(1.60103)
The total amount in the account after 10 years will be approximately $1,360.87.

To find the interest earned, we subtract the original principal from the total amount:

Interest Earned = Total Amount - Original Principal
Interest Earned ≈ $1,360.87 - $850
Interest Earned ≈ $510.87
Therefore, the interest earned in the first account after 10 years is approximately $510.87.

Answer:

A  y = 3x

Step-by-step explanation:

We can check each line to see if the point is on it

A  y = 3x  6 = 2*3  6=6  this is true so the point is one the line

B  y = 4-x   6 = 2-4  6 = -2  false

C  y = -3x   6 = -3(2)  6=-6  false

D  y =-x+4   6 = -2+4   6 = 2  false

Equivalent expression are expressions that have equal values, when expanded. The equivalent expression of ln(2x)^4  is 4ln(2) + 4ln(x))

The expression is given as:

[tex]\ln(2x)^4[/tex]

Apply the following logarithmic rule to the above equation

[tex]\ln(a)^b = b\ln(a)[/tex]

So, we have:

ln(2x)^4  = 4ln(2x)

Next, apply the following product rule of logarithm to the above equation

ln(ab) = ln(a) + ln(b)

So, we have:

ln(2x)^4  = 4 * [ln(2) + ln(x)]

Expand the bracket

ln(2x)^4  = 4ln(2) + 4ln(x))

Hence, the equivalent expression of ln(2x)^4  is 4ln(2) + 4ln(x))

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Answer:

ln (2x)4

✅ 4 ln 2 + 4 ln x

❎ 4 ln 2 + ln x

❎ 8 ln x

ln

4y5

x2

❎ ln 4 - 2 ln x - 5 ln y

✅ ln 4 - 2 ln x + 5 ln y

❎ -8 ln x + 5 ln y

Answer:

y = x^2 - 4x - 5

y = (x + 1)(x - 5)

Answer:

[tex] Standard \: form :\:y= {x}^{2} - 4x - 5\\

Factored\: from:\:y = (x + 1) (x - 5)[/tex]

Step-by-step explanation:

[tex]y = (x - 2)^{2} - 9 \\ y= {x}^{2} - 4x + 4 - 9 \\ \red{ \boxed{ \bold{y= {x}^{2} - 4x - 5}}} \\ is \: in \: standard \: form \\ \\ y = (x - 2)^{2} - 9 \\ y = (x - 2)^{2} - {3}^{2} \\ y = \{(x - 2) + 3\} \{(x - 2) - 3 \} \\ y = \{x - 2 + 3\} \{x - 2- 3 \} \\ \purple{ \boxed{ \bold{y = (x + 1) (x - 5)}}} \\ is \: in \: factored \: form[/tex]

Answer:

Step-by-step explanation:

Kevin’s verbal score is 610 is 140 points above the mean,which is 470. the standard deviation is 121 so his verbal score is 140/121≈1.16 standard deviations above the mean. Kevins quantitative score of 700 is 150 points above the mean, which is 500. The standard deviation is 148, so his quantitative score is 150/148 ≈ 1.01 standard deviation above the mean.Thus, Kevins verbal score is better than his quantitative score.

Answer:

75+150=225 in^2

Step-by-step explanation:

Separate each layer.

Area1+Area2= Total area

A1= a*b*d

A2=a*c*d

A1=5*5*3=75 in^2

A2=5*10*3=150 in^2

75+150=225 in^2

Answer:

210

Step-by-step explanation:

Answer:

∠ABC=[tex]70^0[/tex]

Step-by-step explanation:

In the attached diagram,

If Angle ADC =[tex]35^0[/tex]

Since the center of the circle is at B

∠ABC is the angle subtended at the center by arc AC.

∠ADC is the angle subtended at the circumference by arc AC.

Theorem

The angle subtended by an arc at the center of a circle is double the size of the angle subtended by the same arc at the circle's circumference.

Therefore by the theorem above

∠ABC = 2 X ∠ADC

=2 X 35

∠ABC=[tex]70^0[/tex]

The cost of filling the planter with soil is $6.24. option C

What is the cost of filling the planter with soil?

Length = 2 ft

Width = 2 ft

Height = 6 ft

Volume of the square based pyramid = ⅓ × length × Width × height

= ⅓ × 2 × 2 × 6

= ⅓ × 24

= 8 cubic feet

Cost of soil per cubic foot = $0.78

Therefore,

Cost of filling the planter with soil = Volume of the square based pyramid × Cost of soil per cubic foot

= 8 × $0.78

= $6.24

Complete question:

A planter in the shape of a square pyramid with dimensions 2 ft by 2 ft by 6 ft is being filled with soil. Soil cost $0.78 per cubit cubic foot What is the cost of filling the planter with soil?

a $24.00

b $8.00

c. $6 24

d. $18.72

Answer:

Determinant of matrix = 12

Step-by-step explanation:

rewrite this system with matrices

[{4   ,   -3]

[8,     -3]]

determinant =   4*(-3)  -  (-3)*8 =  -12 + 24 = 12

are you finding the inverse too?

the  system should look like   A* v  =  C

where matrix A is

[{4   ,   -3]

[8,     -3]]

and  V = [x  , y]  vector

C = [-8, 12]  vector

Answer:

Explanation: When the determinant of the coefficient matrix of a system of linear equations equals zero it means that at least one equation in the system is a scalar multiple of another equation. Hence it is not possible to find the inverse matrix and so the system cannot be solved.

Step-by-step explanation:

Answer:

x = -5

Step-by-step explanation:

Get 2x by itself, so subtract to the other side. 2x = -10. Then get x alone, so divide by 2. Then your answer is -5

Answer:

I think you meant a "=" instead of a "+"

Step-by-step explanation:

10 = 2x

10 = 2x

2      2

5  =  x

I hope this helps!

- sincerelynini

Answer:

C (I'm not 100% sure that this is correct)

Step-by-step explanation:

I don't think that an act of genocide in the regions of Africa occurred recently.

Answer:

I think you might get a better answer if you put this question under the social studies category instead of math.

Answer:

12 boys

Step-by-step explanation:

boys : girls

4      : 5

Add a total column

boys : girls: total

4      : 5     : 4+5 =9

To get to a total of 27 we multiply each term by 3

boys : girls: total

4*3      : 5*3  : 9*3

12        :15     :27

There are 12 boys

Final answer:

There are 12 boys in the class of 27 students.

Explanation:

The ratio of boys to girls in the class is 4:5, which means for every 4 boys, there are 5 girls. To find out how many boys there are, if there are 27 students in total, we need to work with this ratio.

Step-by-step Solution:

Therefore, there are 12 boys in the class of 27 students.

Answer:

x/2=87.2

Step-by-step explanation:

Pip was thinking of a number - Let's call this number x

Pip halve the number - So half of x = x/2  (or 1/2 x)

And gets an answer of 87.2  - x/2=87.2

So your equation would be x/2=87.2

I hope this helps :)

Final answer:

Pip's mystery number is found by taking the equation x / 2 = 87.2, where x is the original number. By solving it, we find that x = 174.4.

Explanation:

Pip is thinking of a number. When Pip halves this number, the result is 87.2. To formulate an equation with x based on this information, we consider that halving a number is equivalent to multiplying that number by 0.5 or dividing it by 2.

Therefore, we can represent the situation with the equation x / 2 = 87.2. This equation states that half of Pip's unknown number (x) equals 87.2.

To solve for x, we multiply both sides of the equation by 2:

x = 87.2 × 2

Which simplifies to:

x = 174.4

This means that Pip was thinking of the number 174.4.

Answer:

39 feet

Step-by-step explanation:

In this problem, the height of the football at time t is modelled by the equation:

[tex]h(t)=-16t^2+vt+s[/tex]

where:

s = 3 ft is the initial height of the ball

v = 48 ft/s is the initial vertical velocity of the ball

[tex]-32 ft/s^2[/tex] is the acceleration due to gravity (downward)

Substituting these values, we can rewrite the expression as

[tex]h(t)=-16t^2+48t+3[/tex]

Here we want to find the maximum height reached by the ball.

This is equivalent to find the maximum of the function h(t): the maximum of a function can be found requiring that the first derivative of the function is zero, so

[tex]h'(t)=0[/tex]

Calculating the derivative of h(t), we find:

[tex]h'(t)=-32 t+48[/tex]

And imposing it equal to zero, we find the time t at which this occurs:

[tex]0=-32t+48\\t=-\frac{48}{-32}=1.5 s[/tex]

And substituting back into h(t), we can find the maximum height of the ball:

[tex]h(1.5)=-16\cdot (1.5)^2 + 48\cdot 1.5 +3=39 ft[/tex]

Using the vertical motion model, the time when the football reaches maximum height is calculated to be 1.5 seconds. Substituting this into the model, the maximum height of the football is found to be 39 feet.

To find the maximum height, we consider the vertical motion model h = -16t^2 + vt + s, where v is initial velocity in feet per second and s is the initial height of the football. The information provided include: initial velocity v = 48 feet/sec and initial height s = 3 feet.

The maximum height reached by the football is achieved when the velocity becomes zero (time at which the ball reaches its highest point). This time can be calculated using the formula t = v / (2 * g), with g being half the coefficient of t^2 (g = 16 feet/sec^2 in this case). Substituting v and g gives us approximately t = 1.5 seconds.

We then substitute this time into our initial equation to find the maximum height. This gives: h = -16*(1.5)^2 + 48*1.5 + 3 = 39 feet. Therefore, the maximum height reached by the football is 39 feet.

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Answer:

ok the anwer is C= 34

16^2+30^2=1156

√1156=34

so double check

16^2+30^2=34^2

256+900=1156

√1156=34

Step-by-step explanation:

Substituting the given values of Simple Algebra 'a' and 'b' into the equation a+b=c we get 16 + 30 = c. This simplifies to c = 46, so the answer is C) 46.

We are given that a is equal to 16 and b is equal to 30. The equation given is a+b=c. Substituting the given values of 'a' and 'b' into the equation, we get 16 + 30 = c. This simplifies to c = 46. Therefore, the answer is C) 46.

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The probable question may be:

If a is equal to 16, b is equal to 30, what is the value of c in the equation a+b=c?

Additional Information: In this question, we have two known values, a and b, which are 16 and 30, respectively. To find the value of c, we'll use the equation a+b=c Solving this equation will give us the equivalent value of c.

Options:

A) 14

B) 36

C) 46

D) 62

Answer:

12.57

Step-by-step explanation:

hope this helps

Answer:

3.14 x 4 = 12.57

Step-by-step explanation:

Answer:

i think:

A number times four minus nine is one

Answer:

The length of the actual lawn is 56 meters.

Step-by-step explanation:

Given:

The scale of the drawing was 1 millimeters : 2 meters, in the drawing the lawn in the backyard is 28 millimeters long,

Now, to find the length of the actual lawn.

Let the length of the actual lawn be [tex]x.[/tex]

The length of the lawn in the drawing = 28 millimeters.

The scale of the drawing was 1 millimeters : 2 meters.

So, 1 millimeters is equivalent to 2 meters.

Thus, 28 millimeters is equivalent to [tex]x.[/tex]

Now, to get the length of the actual lawn by using cross multiplication method:

[tex]\frac{1}{2} =\frac{28}{x}[/tex]

By cross multiplying we get:

[tex]x=56\ meters.[/tex]

Therefore, the length of the actual lawn is 56 meters.

Answer:

There's one solution to this equation and that is 2

Step-by-step explanation:

5 (2x-3) = 5 multiply inside the parenthesis by 5

10x - 15 = 5 add 15 to both sides

10x - 15 + 15 = 15 + 5

10x = 20 divide both sides by 10

x = 2

Answer:

The answer should be 6 miles..

3(6)x2=20

Step-by-step explanation:

Answer:

Which ones

Step-by-step explanation:

11.a

Range: 16

To find the range, you subtract the biggest number(52) from the smallest number(36)

52-36=16

11.b

Mean: 43.75

To find the mean, you have to add all the numbers, then divide by the total amount of numbers

(36+45+52+40+38+41+50+48)/2 = 43.75

Median: 43

To find the median, the numbers must be put in either ascending or descending order and the middle must be found. In this case, there were 2 numbers(41 and 45) so you add the two and divide by 2.

36,38,40,41,45,48,50,52       (41+45)/2=43

Mode: N/A

The mode is the number that occurs the most and in this case each number is only seen once , so there is no mode

I am going to put the answers for the rest since I've explained the process

12a.

Range: 3655

12b.

Mean: 1014.166667 = 1014.17

Median: 608.5

Mode: N/A

13a.

Mean: You: 4  Friend: 8

Median: You: 17 Friend: 17

Mode: You: N/A   Friend: 20

13b.

Your Friend

Answer:

a)  P (  1100 < X < 1400 ) = 0.755

b) P (  X < 1000 ) = 0.755

c) proportion ( X > 1200 ) = 65.66%

d) 5.87% percentile

Step-by-step explanation:

Solution:-

- Denote a random variable X: The number of chocolate chip in an 18-ounce bag of chocolate chip cookies.

- The RV is normally distributed with the parameters mean ( u ) and standard deviation ( s ) given:

                               u = 1252

                               s = 129

- The RV ( X ) follows normal distribution:

                       X ~ Norm ( 1252 , 129^2 )  

a) what is the probability that a randomly selected bag contains between 1100 and 1400 chocolate​ chips?

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( x1 < X < x2 ) = P ( [ x1 - u ] / s < Z <  [ x2 - u ] / s )

- Taking the limits x1 = 1100 and x2 = 1400. The standard normal values are:

     P (  1100 < X < 1400 ) = P ( [ 1100 - 1252 ] / 129 < Z <  [ 1400 - 1252 ] / 129 )

                                        = P ( - 1.1783 < Z < 1.14728 )

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( -1.1783 < Z < 1.14728 ) = 0.755

Hence,

      P (  1100 < X < 1400 ) = 0.755   ... Answer

b) what is the probability that a randomly selected bag contains fewer than 1000 chocolate​ chips?

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( X < x2 ) = P ( Z <  [ x2 - u ] / s )

- Taking the limit x2 = 1000. The standard normal values are:

     P (  X < 1000 ) = P ( Z <  [ 1000 - 1252 ] / 129 )

                                        = P ( Z < -1.9535 )

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( Z < -1.9535 ) = 0.0254

Hence,

       P (  X < 1000 ) = 0.755   ... Answer

​(c) what proportion of bags contains more than 1200 chocolate​ chips?

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( X > x1 ) = P ( Z >  [ x1 - u ] / s )

- Taking the limit x1 = 1200. The standard normal values are:

     P (  X > 1200 ) = P ( Z >  [ 1200 - 1252 ] / 129 )

                                        = P ( Z > 0.4031 )

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( Z > 0.4031 ) = 0.6566

Hence,

      proportion of X > 1200 = P (  X > 1200 )*100 = 65.66%   ... Answer

d) what is the percentile rank of a bag that contains 1050 chocolate​ chips?

- The percentile rank is defined by the proportion of chocolate less than the desired value.

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( X < x2 ) = P ( Z <  [ x2 - u ] / s )

- Taking the limit x2 = 1050. The standard normal values are:

     P (  X < 1050 ) = P ( Z <  [ 1050 - 1252 ] / 129 )

                                        = P ( Z < 1.5659 )

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( Z < 1.5659 ) = 0.0587

Hence,

       Rank = proportion of X < 1050 = P (  X < 1050 )*100

                 = 0.0587*100 %  

                 = 5.87 % ... Answer

Answer:

[tex]b^6z^612a^5[/tex]

Step-by-step explanation:

The first step is to combine like terms, and multiply them together first. Since multiplication is commutative, it doesn't matter in what order you do it. Therefore, this can be rewritten as [tex](2a^2\cdot 6a^3)\cdot(b^4\cdot b^2)\cdot(z\cdot z^5)=(12a^5)\cdot(b^6)\cdot(z^6)=b^6z^612a^5[/tex]. Hope this helps!

Answer:

Step-by-step explanation:

(2a²b⁴z)(6a³b²z⁵ = 2*6*a²⁺³ b⁴⁺² z¹⁺⁵

= 12a⁵b⁶z⁶

Answer:

-0.9231

Step-by-step explanation:

Given cos theta = 0.3846 within the range 3π/2<theta<2π

Costheta = 0.3846

Theta = arccos(0.3846)

Theta = 67.38°

Since 67.38° didn't fall within the range of theta, we will locate our theta using the quadrant.

Since cos is positive in the 4th quadrant,

Theta = 360-67.38°

Theta = 292.62°

Sin(theta) = sin(292.62°)

= -0.9231