The amount earned, calculated using the formula for geometric progressions are as follows;
(A) The income on day 31 =$1,073,741,824
(B) Total income for 31 working days = $2,147,483,647
What is a geometric progression?A geometric progression is one in which each subsequent term is a constant multiple of the previous term
(A) The function that indicates the amount earned on the nth day is the formula for a geometric progression , which can be presented as follows;
[tex]a_n = a_1\cdot r^{n-1}[/tex]
The sum is presented as follows;
[tex]S_n =a_1\cdot \dfrac{1 - r^n}{1 - r}[/tex]
Therefore;
The common ratio, r = 2
The first term, a₁ = 1
The amount received on day 31 is therefore;
[tex]a_{31} = 1\times 2^{31-1} = 1,073,741,824[/tex]
Income on day 31 = $1,073,741,824
(B) The total income in 31 days is therefore;
[tex]S_{31} =a_1\cdot \dfrac{2^{31} - 1}{2- 1}== 2,147,483,647[/tex]
The total income in 31 working days = $2,147,183,647
Learn more about geometric progression in mathematics here::
https://brainly.com/question/15562660
#SPJ1
v+8 over v = 1 over 2
The given expression is
[tex]\frac{v+8}{v}=\frac{1}{2}[/tex]First, we multiply 2v on each side.
[tex]\begin{gathered} 2v\cdot\frac{v+8}{v}=2v\cdot\frac{1}{2} \\ 2v+16=v \end{gathered}[/tex]Then, we subtract v on each side.
[tex]\begin{gathered} 2v-v+16=v-v \\ v+16=0 \end{gathered}[/tex]At last, we subtract 16 on each side.
[tex]\begin{gathered} v+16-16=-16 \\ v=-16 \end{gathered}[/tex]Therefore, the solution is -16.The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.2. The initial population is 10.
Answer
Explanation
Using the formula for the population growth:
[tex]P(t)=P_0\cdot(1+r)^t[/tex]where P₀ is the initial population, r is the rate of growth, and t is the time.
From the given information, we know that:
• P₀ = 10
,• r = 0.2
1.
And we are asked to find P(50) (when t = 50), thus, by replacing the values we get:
[tex]P(50)=10\cdot(1+0.20)^{50}[/tex][tex]P(50)\approx91004.3815[/tex]2.
For the population to double, this would mean that P(t) = 2P₀. By replacing this we get:
[tex]2P_0=10e^{0.20t}[/tex][tex]2(10)=10e^{0.20t}[/tex][tex]20=10e^{0.20t}[/tex][tex]\frac{20}{10}=e^{0.20t}[/tex][tex]\ln\frac{2}{1}=\ln e^{0.20t}[/tex][tex]\ln2=0.20t[/tex][tex]t=\frac{\ln2}{0.20}\approx3.5days[/tex]place the letter of the angle relationship that beat represents the given angle pair in the box.
Angle relationship that best represents the given angle
Considering the angles in the attached diagram above
<6 and <13 has no relationship because they are not parallel
Hence NO relationship between <6 and <13
I need help with this please, I know that the opposite of 4.6 is -4.6 but I don’t know how to explain it.
Answer:
As a rational number is a fraction we had to convert our number to a fraction, and as the opposite number is the number with the same magnitude but a different sign, we had to change the sign.
[tex]-4\cdot\frac{3}{5}[/tex]
Explanation
• Rational numbers are the numbers that can be written as the fraction of two integers.
,• Additionally, opposite numbers are numbers with the same magnitude but different signs.
Thus, based on these definitions, we have to change the sign and search for a fraction.
Steps:
0. From 4.6 we go to -4.6.
,1. We convert -4.6 to a fraction: -4 is the whole number and we are left with -0.6, which is 6/10 (as it is in the tenth's place).
,2. Simplifying 6/10 to 3/5 dividing both numbers by 2.
Imagine you are working for Hasbro making Gummy Bear containers. On a day to day basis you fill up two different size containers with gummy bears. One of the containers is4.4x5.7 x 6.0 in dimensions and contains 385 gummy bears. The other is 8.1 x 8.1 x 8.3 in dimensions. About how many gummy bears would fit in the box? Round to the nearestwhole number
It is given that,
One of the containers is 4.4 x 5.7 x 6.0 in dimensions and contains 385 gummy bears.
So, 1 gummy bear occupies,
[tex]\frac{4.4\times5.7\times6.0}{385}=0.39086[/tex]The other is 8.1 x 8.1 x 8.3 in dimensions.
So, the number of gummy bears would fit in the box is,
[tex]\frac{8.1\times8.1\times8.3}{0.39086}=1393.24[/tex]Hence, the number of gummy bears is 1,393 (Rounded to the nearest whole number).
NO LINKS!! Use the method of to solve the system. (if there's no solution, enter no solution). Part 2z
Answer:
smaller x-value: (-4, 18)
larger x-value: (3, 11)
Step-by-step explanation:
Solving for x:
y = x^2 + 2
x + y = 14 ---> y = 14 - x
14 - x = x^2 + 2
0 = x^2 + x - 12
0 = (x + 4)(x - 3)
x = -4 or 3
Solving for y:
If x = -4
y = 14 + 4
y = 18
if x = 3
y = 14 - 3
y = 11
Answer:
[tex](x,y)=\left(\; \boxed{-4,18} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{3,11} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\phantom{bbbb}y=x^2+2\\x+y=14\end{cases}[/tex]
To solve by the method of substitution, rearrange the second equation to make y the subject:
[tex]\implies y=14-x[/tex]
Substitute the found expression for y into the first equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}y=14-x \implies 14-x&=x^2+2\\x^2+2&=14-x\\x^2+2+x&=14\\x^2+x-12&=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}x^2+x-12&=0\\x^2+4x-3x-12&=0\\x(x+4)-3(x+4)&=0\\(x-3)(x+4)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for x:
[tex]\implies x-3=0 \implies x=3[/tex]
[tex]\implies x+4=0 \implies x=-4[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}x=3 \implies 3+y&=14\\y&=14-3\\y&=11\end{aligned}[/tex]
[tex]\begin{aligned}x=-4 \implies -4+y&=14\\y&=14+4\\y&=18\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-4,18} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{3,11} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Please help me I don’t know if I’m right or missing any other to select.
The given equations are
[tex]-x+4y=7[/tex][tex]6x-3y=42[/tex]To find the answer we need to cancel out x or y.
so we have to find the LCM of the coefficients of the corresponding variable.
consider the coefficients of x is -1 in the first equation and 6 in the second equation .
Lcm of -1 and 6 is 6.
Multiplying the first equation by 6.
consider the coefficients of y is 4 in the first equation and -3 in the second equation .
Lcm of 4 and 3 is 12
Multiplying the first equation by 3 and the second equation by 4.
Either one of these is the first step to eliminate variables.
Amswer os
I am very confused can you help me please thanks!
Solution
For this case we know that :
1/8 of teaspoon for every 3 cups of frosting
Now the amount of cups increase to 4 cups then we can find the number teaspoon
We can use a proportional rule and we got:
[tex]\frac{\frac{1}{8}}{3}=\frac{x}{4}[/tex]The answer is:
C
Please helpIf the 100th term of an arithmetic sequence is 595, and its common difference is 6, thenits first term a1= ,its second term a2= ,its third term a3=
Given
100th term of an arithmetic sequence is 595 and common difference , d = 6
Find
First three terms of arithmetic sequences.
Explanation
As we know the general nth term of an arithmetic sequence is given by
[tex]a_n=a+(n-1)d[/tex]we have given 100th term = 595 , so
[tex]\begin{gathered} a_{100}=a+(100-1)6 \\ 595=a+99\times6 \\ 595-594=a \\ a=1 \end{gathered}[/tex]so , first term = 1
second term = a + 6 = 7
third term = a + 2d = 1 +2*6 = 13
Final Answer
Therefore , the first terms of an arithmetic sequences are
[tex]a_1=1,a_2=7,a_3=13[/tex]Heart Rates For a certain group of individuals, the average heart rate is 74 beats per minute. Assume the variable is normally distributed and the standarddeviation is 2 beats per minute. If a subject is selected at random, find the probability that the person has the following heart rate. Use a graphing calculator.Round the answers to four decimal places.Higher than 73 beats per minute,P (x> 73) =
we need to determine P (x> 73)
when
mean: μ = 74 beats/min
standard deviation: σ = 2 beats/min
First we need to use the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
x = 73
μ = 74
σ = 2
and
Z is the z-score
... therefore
[tex]z=\frac{73-74}{2}=-\frac{1}{2}=-0.5[/tex]If we check a table of z scores, we will find that when z = -0.5, then P = 0.3085
Now, since we need P(x>73)
therefore
[tex]P=1-0.3085=0.6915[/tex]P(x>73) = 0.6915
The triangular faces of the prism shown are equilateral triangles with perimeter 30 cm. Use a net to find the surface area of the prism.
Explanation:
[tex]\begin{gathered} The\text{ surface area is made up of the two equilateral triangles shown above as well as the three rectangles.} \\ Area\text{ of Triangles = 2\lparen}\frac{1}{2}b*h) \\ If\text{ the perimeter of the triangle is 30cm, the length of one side = 30/3 = 10 = base} \\ Area\text{ = 2\lparen}\frac{1}{2}*10*8.7) \\ \text{ =87} \\ Area\text{ of the three rectangles = 3\lparen length*width\rparen } \\ \text{ =3\lparen10*12\rparen} \\ \text{ =360} \\ Total\text{ Surface Area = 360 + 87 = 447} \end{gathered}[/tex]Surface Area of the two triangles in the net = 2*(0.5*b*h)
= 2*(0.5*10*8.7)
=87
Surface Area of three rectangles in the net = 3(l*b)
= 3*12*10
=360
Answer: Total Surface area = 360 + 87 = 447
Some of the tallest crystals in a cave in Mexico are 85 feet tall. Lin is 6 feet tall. About how many times as tall as Lin are the tallest crystals?
What is 85 / 6
/= divided by
14.16 ≈ 14 times as tall as Lin are the tallest crystals.
Given:
Some of the tallest crystals in a cave in Mexico are 85 feet tall.
Lin is 6 feet tall.
Number of times = tallest crystals height / lin height.
= 85 feet / 6 feet
= 14. 16 ≈ 14 times
14.16 is not represented in times so we take the nearest number which is 14.
Therefore 14 times as tall as Lin are the tallest crystals.
Learn more about the times and tallest crystals here:
https://brainly.com/question/12327373
#SPJ1
Which of the following statements about the graph of f (x)=(0.5)^x shown above are true? Select all that apply.
From the graph, the following are true
[tex]1)Thefunctionf(x)=(0.5)^xis\text{ a decay function.}[/tex][tex]2)\text{The range of the function is the set of all real numbers }>0[/tex][tex]3)\text{ The graph of the function intersects the x-axis at x = 5}[/tex]If you bought 12 gallons of gas for $26.00, how much did you pay per gallon?
To get pay per gallon, we divide the total payment by the total amount of gallons.
So,
Total Cost = 26
Total Gallons = 24
Pay Per Gallon = 26/24 = $1.08 per gallon
y = 2x – 2 y = -x + 7
Given the system of equations:
[tex]\begin{gathered} y=2x-2 \\ y=-x+7 \end{gathered}[/tex]We will find the solution of the system by the graph
To draw each line, we need to know 2 points
So, we will substitute with 2 values of x and calculate the corresponding value of y
For the first equation: y = 2x - 2
[tex]\begin{gathered} x=0\rightarrow y=2\cdot0-2=-2 \\ x=2\rightarrow y\rightarrow=2\cdot2-2=2 \end{gathered}[/tex]So, the line passes through the points ( 0, -2 ) and ( 2, 2)
For the second line: y = -x + 7
[tex]\begin{gathered} x=0\rightarrow y=0+7=7 \\ x=2\rightarrow y=-2+7=5 \end{gathered}[/tex]so, the line passes through the points ( 0, 7) and ( 2, 5)
The graph of the system will be as shown in the following figure:
As shown in the figure:
Equation 1 is the blue line
Equation 2 is the red line
The point of intersection = ( 3, 4)
So, the answer is the solution of the system = ( 3, 4 )
3. Write the tangent of angle Mas a fraction. Then write it as a decimal rounded to the nearest hundredth. tan M=
solution
For this case we can do the following:
[tex]\tan M=\frac{\sin M}{\cos M}=\frac{\text{opposite}}{\text{adjacent}}[/tex]For this case the opposite side is 8 and the adjacent is 6 so we got:
[tex]\tan M=\frac{8}{6}=\frac{4}{3}[/tex]Solve the following inequality. Write the solution set in interval notation
Given:
Inequality is
[tex]5(x-3)<2(3x-1)[/tex]To find:
The solution set of the given inequality:
Explanation:
[tex]\begin{gathered} 5(x-3)<2(3x-1) \\ 5x-15<6x-2 \\ 5x-6x<15-2 \\ -x<13 \\ x>-13 \end{gathered}[/tex]Therefore the solution set is
[tex](-13,\hat{\infty)}[/tex]Final answer:
The solution set is
[tex](-13,\infty)[/tex]LEVEL B 1.b) Solve for x angle relationship X+34" 2x-120
Answer
x = 46 degrees
Step-by-step explanation:
Alternate interior angles are equal
x + 34 = 2x - 12
Collect the like terms
x - 2x = -12 - 34
-x = -46
Divide both sides by -1
-x/-1 = -46/-1
x = 46 degrees
Hence, the value of x is 46 degrees
Use your compass to help with the direction. Also, the question is in the question box
1. Extending the dashed lines
2. Translating the triangle ABC in the direction EF
copy the vector in each vertice
then with the final points draw the new triangle a distance of EF
The blue triangle is the translated triangle (in your case you can your compass to help with the direction and protractor to verify the distance).
Additional and SubtractionAnswers should have only three significant figures.Question a) 86.5-0.07 ?Question b) 30.61-87.3-42.109 ?
a. 86.5-0.07
The result of the subtraction is:
[tex]\begin{gathered} 86.50 \\ -0.07 \\ ----- \\ 86.43 \end{gathered}[/tex]As the answer should have only three significant figures then, the result is: 86.4
b. 30.61-87.3-42.109
The subtraction is:
[tex]\begin{gathered} 30.61 \\ -87.30 \\ ----- \\ -56.690 \\ -42.109 \\ ------ \\ -98.799 \end{gathered}[/tex]As the answer should have only 3 significant figures, then the result is -98.8
Express: 12x-9x-4x+3 in factored form
SOLUTION:
Step 1:
In this question, we are given the following:
Expressing:
[tex]12\text{ x - 9x - 4x + 3}[/tex]Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} 12\text{ x -9x - 4 x + 3} \\ \text{= -x + 3} \\ =\text{ -\lparen x -3\rparen } \end{gathered}[/tex]CONCLUSION:
The final answer in factored form =
[tex]-(x-3)[/tex]Determine the measures of the unknown angle.
To find the measure of the unknown angle we can use the triangle sum theorem that states that the sum of the measures of the interior angle of a triangle is 180°. We know the measure of two of the interior angles of the triangle that are 50° and 88°, and we can use this information to find the unknown one:
[tex]\begin{gathered} 50+88+\measuredangle3=180 \\ 138+\measuredangle3=180 \\ \measuredangle3=180-138 \\ \measuredangle3=42 \end{gathered}[/tex]The correct answer is C. 42°.
Can you help me with this math question? it says "A cell phone plan costs $200 to start. Then there is a $50 charge each month, Write an expression that shows the total cost for x months on this plan" Is there a proportional relationship between time and cost of the cell phone plan?
Cost = 200 + 50x
The relationship between time and cost of the plan is not proportional. By definition, proportional ;relationships between two variables have equivalent ratio; one variable is always a constant value times the other which in this case is not .
To illustrate,
Month 1 Cost = 200 + 50(1) = 250 Ratio ( time:cost) = 1:250
Month2 Cost = 200 + 50(2) = 300 Ratio ( time:cost) = 2:300 = 1:150
Month 3 Cost = 200 + 50(3) = 350 Ratio ( time:cost) = 3:350
Month 4 Cost = 200 + 50(4)= 400 Ratio ( time:cost) = 4 :400 = 1:100
The ratios are not equivalent,thus the relationship is not proportional.
Lizzy is tiling a kitchen floor for the first time. She had a tough time at first and placed only 6 tiles the firstday. She started to go faster and by the end of day 4, she had placed 36 tiles. She worked at a steady rateafter the first day. Use an equation in point-slope form to determine how many days Lizzy took to placeall of the 100 tiles needed to finish the floor. Solve the problem using an equation in point-slope form.
We know that
• She placed 6 tiles on the first day.
,• By the end of day 4, she had placed 36 tiles.
Based on the given information, we can express the following equation.
[tex]y=3x+6[/tex]If she had placed 36 tiles in 3 days, it means she had placed 12 tiles per day, that's why the coefficient of x is 3. And the number 6 is the initial condition of the problem, that is, on day 0 she placed 6 tiles.
Now, for 100 tiles, we have to solve the equation when y = 100.
[tex]\begin{gathered} 100=3x+6 \\ 100-6=3x \\ 3x=94 \\ x=\frac{94}{3} \\ x=31.33333\ldots \end{gathered}[/tex]Therefore, she needs 32 days to place all the tiles.Notice that we cannot say 31 days, because it would be incomplete.
if triangle ABC has sides of length 9, 15, and 3x, between which two numbers must the value of x lie?
Let's employ the triangle inequality here.
If the sides were to form a triangle.
Then if 3x was the longest side, it must be less than the sum of 15 and 9, being the other 2 sides.
So;
[tex]\begin{gathered} 3x<15+9 \\ 3x<24 \\ x<8 \end{gathered}[/tex]If 3x was the shortest side, then 15 would be the longest side, and thus
3x plus 9 must be greater than 15,
So;
[tex]\begin{gathered} 3x+9>15 \\ 3x>15-9 \\ 3x>6 \\ x>2 \end{gathered}[/tex]So, the range of values for which x must lie is;
[tex]2i.e any values greater than 2 but less than 8.The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3628 grams and a variance of 408,321. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be greater than 4330 grams. Round your answer to four decimal places.
Answer:
0.13597 = 0.136
Step-by-step explanation:
using normal cd in calculator
Lower- 4330 (since we want weight above this)
Upper- 100000 (any large number will still be valid)
std deviation- [tex]\sqrt{408,321}[/tex]
mean- 3628
p- 0.13597
Hope this helps!
13. Rose's probability of successfully shooting a basketball is 2/5. What is the probability of hershooting in at least 1 if she makes 4 shots?
Answer:
0.8704
Explanation:
The probability of successfully shooting a basketball is 2/5, so the probability t3/o fail will be equal to:
[tex]P=1-\frac{2}{5}=\frac{3}{5}[/tex]Then, we will calculate the probability of failing the 4 shots. So, we need to multiply 3/5 by itself 4 times.
[tex]P(\text{fail all times) = }\frac{3}{5}\times\frac{3}{5}\times\frac{3}{5}\times\frac{3}{5}=0.1296[/tex]Finally, the probability of her shooting in at least 1 if the complement of the probability to fail all times, so, the answer is:
[tex]P(at\text{ least 1) = 1 - 0.1296 = 0.8704}[/tex]Therefore, the answer is 0.8704
The graph shows the number of gallons of white paint that were mixed with gallons of blue paint in various diffrent ratios:
From the graph, we can note that the points are in a line.
Hence, we must find the line equation for these points.
The general form of the straigh line equation is
[tex]y=mx+b[/tex]where m is the slope and b the y-intercept. The slope can be computed as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where,
[tex]\begin{gathered} (x_1,y_1)=(2,4) \\ (x_2,y_2)=(6,12) \end{gathered}[/tex]By substituying these values into m, we have
[tex]m=\frac{12-4}{6-2}[/tex]hence,
[tex]\begin{gathered} m=\frac{8}{4} \\ m=2 \end{gathered}[/tex]the form of the line equation is
[tex]y=2x+b[/tex]where x is the blue paint and y the white paint.
In order to find b, we can substitute one point into the above equation. For instance, the point
(2,4):
[tex]\begin{gathered} 4=2(2)+b \\ 4=4+b \\ b=0 \end{gathered}[/tex]Thefore, the line equation is
[tex]y=2x[/tex]Hence, the number of galons when we mix 1 gallon of blue pain is
[tex]\begin{gathered} y=2(1) \\ y=2 \end{gathered}[/tex]in other words, for 1 gallon of blue paint we must have 2 gallons of white paint
15. Deanna started a savings
account for her
when she was bom. She put
$1,500 in an account with a
simple 3.25% interest rate. What
will be the total amount in the
account after 18 years?
granddaughter
$23,775.00 will be the total amount in the account after 18 years, Formula of simple interest = A = P(1 + rt).
What is simple interest?
The straightforward interest formula makes figuring out how much interest will be applied to a loan quick and simple. Multiply the principle, this same number of days between payments, as well as the daily interest rate to determine simple interest.
Although this method of calculation is used in some mortgages, this type of interest is typically associated with auto loans as well as short-term loans.
Simple interest is calculated by multiplying the principle by the daily interest rate and number of days among payments.Simple interest rewards borrowers for making on-time or early monthly payments on their loans.Auto loans as well as short-term personal loans are two common uses for simple interest loans.A represents the total amount of accrued interest and principal.
P is the principal amount.
The interest rate is I.
The annual percentage real interest rate, abbreviated as r, is 1/10.
R is the interest rate in annual percentage terms; R = r * 100 t is the time period in months or years.
In light of the query
P=$1500
r=3.25%
=0.0325
t=18 years
simple interest = 1500(1+ 0.0325 x 18)
=$(1500+877.5)
=$ 23,775
Thus the simple interest is $23,775
Learn more about Simple interest from the link below
https://brainly.com/question/21020925
#SPJ1
Mason calculated the sales tax on his clothing purchase to be $5.57375. Round to the nearest hundredth. ANS $ __________
As per given by the question,
There are given that the sales tax is $5.57375.
Now,
For find the value nearest hundredth,
Nearest hundredth is the second digit after the decimal point.
That means,
If there is given that the value , x.yzw
Then, the nearest hundredth number is x.yz.
So,
From the given value.
The nearest hundredth value is, secon digit after the decima.
Here, second digit after the decimal is 57.
Then,
The nearest value of hundredth is 5.57.
Hence, the value is $5.57