We can calculate the interest as the difference between the future and the present value of the investment:
[tex]I=FV-PV[/tex]The present value is $4780.
The annual interest rate is r=1.25/100=0.0125.
The number of years is 8, so n=8.
We can calculate the future value as:
[tex]\begin{gathered} FV=PV(1+r)^n \\ FV=4780\cdot(1+0.0125)^8 \\ FV=4780\cdot1.0125^8 \\ FV\approx4780\cdot1.1045 \\ FV\approx5279.44 \end{gathered}[/tex]Then, we can calculate the interest as:
[tex]I=FV-PV=5279.44-4780=499.44[/tex]Answer: D. $499.44
Is (2,7) a solution to the system of equations: y= x + 5 y= 4x + 1 Part 1 (circle 1) Yes No Part 2 Shows a proof of your answer
Answer
(2, 7) is not a solution to this system of equations.
The ordered pair doesn't fit into the second equation
Explanation
To check if the given ordered pair is a solution to this, we will insert the values into the two equations and if they fit into rach equation, then, the ordered pair is a solution for this.
y = x + 5
y = 4x + 1
(2, 7) means x = 2, y = 7
y = x + 5
7 = 2 + 5
7 = 7
y = 4x + 1
7 = 4(2) + 1
7 = 8 + 1
7 ≠ 9
The ordered pair doesn't fit into the second equation, hence, (2, 7) is not a solution to this system of equations.
Hope this Helps!!!
A regular hexagon has perimeter 72m. Find the area
A regular hexagon has six equal sides:
If you notice, a regular hexagon has exactly six equilateral triangles inside of it.
So, to find the area we could find the area of a triangle and then multiply this result by 6. This seems to be a little bit complicated to do, so, there's a formula to find the area of a regular hexagon, which is:
[tex]\begin{gathered} A=\frac{3\sqrt{3}s^2}{2} \\ Where: \\ s:Measure\text{ of a side of the regular hexagon} \end{gathered}[/tex]We know that the measure of any side of our regular hexagon equals 12m, so, we could just replace in the equation:
[tex]A=\frac{3\sqrt{3}(12m)^2}{2}\rightarrow A=\frac{3\sqrt{3}(144m^2)}{2}\rightarrow A=216\sqrt{3}m^2[/tex]Simplified, that's about 374.1 m2.
in a particular hospital, newborn babies were delivered yesterday. here are their weights (in ounces). 121 ,101 ,97 121,124 ,112 assuming that these weights constitute an entire population, find the standard deviation of the population. round your answer to two decimal places.
The standard population formula is:
[tex]\sigma=\sqrt[]{\frac{\sum ^{}_{}(x_{}-\mu)^2}{n}}[/tex]where
x is the data points
μ is the mean of the data
and n is the number of data points
The mean is computed as follows:
[tex]\mu=\frac{\Sigma x}{n}[/tex]In this case, the mean is:
[tex]\mu=\frac{121+101+97+121+124+112}{6}=\frac{676}{6}=112.67[/tex]Then, the standard deviation of the population is:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(121-112.67)^2+(101-112.67)^2+(97-112.67)^2+(121-112.67)^2+(124-112.67)^2+(112-112.67)^2}{6}} \\ \sigma=\sqrt[]{\frac{69.39+136.19+245.55+69.39+128.37+0.045}{6}} \\ \sigma=\sqrt[]{108.22} \\ \sigma=10.4 \end{gathered}[/tex]Flying against the wind, an airplane travels 2010 kilometers in 3 hours. Flying with the wind, the same plane travels 10,530 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?
it is given that,
the distance travel against wind = 2010
time = 3 hrs
so, the relative speed is = distance/ time = 2010/3 = 670 km/hr
the distance travel with wind is 10,530
time 9 hrs
so,the relative speed is,= 10 530/9 = 1170 km/hr
let a = speed of plane ,
b = speed of wind
so, when plane travel with wind the the relative speed is ,
a + b = 1170
when travel against wind then the relative speed,
a - b = 670
sum the equation
a + b + a - b = 1170 + 670
2a = 1840
a = 920
put a = 920 in equation a + b = 1170
920 + b = 1170
b = 1170 - 920
b = 250
thus, the rate of plane is 920
rate of wind is 250
What is the determinant of H= 0 2 3-1 3 56 3 -2
1) Since this is a Matrix 3x3 we can make use of the Sarrus Rule to find the determinant of this Matrix:
[tex]\begin{bmatrix}0 & 2 & 3 \\ -1 & 3 & 5 \\ 6 & 3 & -2 \\ \end{bmatrix}[/tex]2) We can do that by copying two columns to the right of the Matrix, and multiplying the entries, this way:
Now, let's add algebraically each diagonal and subtract from the other like this:
[tex]\begin{gathered} \det (H)=\lbrack60-9+0\rbrack-\lbrack54+4+0\rbrack \\ \det H)=51-58 \\ \det (H)=-7 \end{gathered}[/tex]The sum of two numbers is30. The sum of4 times the larger and6 times the smaller is128. Find the numbers.
let
the smaller number = x
the larger number = y
x + y = 30
4y + 6x = 128
[tex]\begin{gathered} x+y=30 \\ 4y+6x=128 \\ x=30-y \\ 4y+6(30-y)=128 \\ 4y+180-6y=128 \\ -2y=128-180 \\ -2y=-52 \\ y=\frac{52}{2} \\ y=26 \\ x+y=30 \\ x+26=30 \\ x=30-26 \\ x=4 \end{gathered}[/tex]
The numbers are 4 and 26.
GEOMETRY: Express the volume of each cube below as a monomialNeeded fast!
Remember that
The volume of a cube is equal to
[tex]V=b^3[/tex]where b is the long side of the cube
so
Part 19
we have that
[tex]b=7c^6d^2[/tex]substitute in the formula
[tex]V=(7c^6d^2)^3[/tex]Applying property of exponents
[tex]\begin{gathered} V=(7^3)(c^{(6\cdot3)})(d^{(2\cdot3)}) \\ V=342c^{(18)}d^6 \end{gathered}[/tex]Part 20
we have
[tex]b=6r^7s^8[/tex]substitute in the formula
[tex]\begin{gathered} V=(6r^7s^8)^3 \\ V=216r^{(21)}s^{(24)} \end{gathered}[/tex]find the slope of the line
Solution
We can use the following points from the graph:
(0,-2) and (2,1)
And we can find the slope on this way:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{1+2}{2-0}=\frac{3}{2}[/tex]Then we can find the intercept on this way:
1= 3/2 (2)+b
b= 1-3= -2
Then the equation would be:
y= 3/2 x -2
How do I know if 6.209 is greater or lesser than 6.29
Since,
[tex]6.29-6.209=0.081[/tex]The difference gives us a positive value.
So, 6.29 is grater than 6.209
Answer: Add a 0 to 6.29 and compare the numbers to see which one is greater
6.29 (or 6.290) is greater than 6.209 since the hundrenth in 6.29 is 9 and the other hundrenth for 6.209 is 0.
A landscaper's truck is filled with ton of gravel.The gravel is shared equally among 3 projects.3. Write and solve a division equation to find how muchgravel each project will get. Explain your reasoning.
Step 1
Let n represent the weight of tons of gravel.
Step 2
The gravel is shared equally among the 3 projects.
Step 3
Write the division equation
Each project will get
[tex]=\text{ }\frac{n}{3}\text{ tons of gravel}[/tex]What is the value of X?
Check the picture below.
Make sure your calculator is in Degree mode.
Geometry- Need help` brainly logged me out w my other tutor who explained it so if u see this miss tutor my bad
"Reason" means a mathematical justification for the assert on the left. "Given" means something that doesn't need justification; it's an assumption.
The first statement,
[tex]\bar{FG}\cong\bar{FJ},[/tex]is given.
The second reason is Base Angles Theorem. Note the word angles in the middle. Its corresponding statement on the left must involve angles. There is only one option involving angles:
[tex]\measuredangle G\cong\measuredangle J.[/tex]Finally, statement 3 is also in the assumptions made above (tagged by Given:). It's also Given.
AnswerThe reason #1 is Given.
The statement 2 is
[tex]\measuredangle G\cong\measuredangle J.[/tex]The reason #3 is Given.
Jim stocks shelves at a grocery store. He aerns $8.60 per hour for 37.5 hours each week. One week a large shipment arrives late and Jim is asked to work overtime at 1.5 times his regular rate. He works 4.5 hours for overtime. What are his total earnings for the week?
Explanation
Since Jim earns 8.60 per hour for 37.5 hours each week. His normal earnings for a week becomes,
[tex]earnings=8.60\times37.5=322.5\text{ dollars}[/tex]During the late shipment period, Jim had to earned an overtime payment at 1.5 times his regular rate. This means per overtime hour he would earn
[tex]1.5\times8.60=12.9[/tex]Therefore, for 4.5 hours for overtime, we will have;
[tex]12.9\times4.5=58.05\text{ dollars}[/tex]Hence, altogether, he would make;
[tex]322.5dollars+58.05dollars=380.55\text{ dollars}[/tex]Answer: 380.55 dollars
I have been stuck on this for a while, your help would be most appreciated!
Answer:I Don't Know What She Said
Step-by-step explanation:
Consider a triangle ABC like the one below. Suppose that A = 35°, C = 68°, b = 32. (The figure is not drawn to scale.) Solve the triangle. Round your answers to the nearest tenth.
Solution.
Given the triangle
[tex]\begin{gathered}Using sine rule,
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex][tex]\begin{gathered} \frac{a}{sin35}=\frac{32}{sin77} \\ a=\frac{32\text{ x sin35}}{sin77} \\ a=18.84 \\ a=18.8(nearest\text{ tenth\rparen} \end{gathered}[/tex][tex]\begin{gathered} \frac{a}{sinA}=\frac{c}{sinC} \\ \frac{18.84}{sin35}=\frac{c}{sin68} \\ \end{gathered}[/tex][tex]\begin{gathered} c=\frac{18.84\text{ x sin68}}{sin35} \\ c=30.45 \\ c=30.5(nearest\text{ tenth\rparen} \end{gathered}[/tex](MP Reason An internet company spends half their yearly profits on advertising for the next year. Of the remaining half, they spend 1/5 on new computers. What fraction of the total profits does the company spend on new computers? Use the number line to show how you can to make his bowl? Write an equati Harcourt Pub 4 find the fraction. 1 o Module 8. Lesson 3
Let the total profit be represented by 1
The internet company spends half their yearly profits on advertising for the next year. The amount of the profit spent on advertising is 1/2 = 0.5
The amount left is 1 - 0.5 = 0.5
Of the remaining half, they spend 1/5 on new computers. It means that the amount spent on new computers is
1/5 * 0.5 = 0.1 = 1/10
Therefore, the fraction of the total profits does the company spend on new computers is
0.1/1 = 0.1 = 1/10
The number line is shown below
The solutions to a quadratic equation are -2 and 6. What is the equation of its axisof symmetry?
General form of a quadratic equation is
[tex]ax^2+bx+c=0[/tex]another form is
[tex](x+h)(x+k_{})=0[/tex]where h and k are the number opposite by the sign of the solutions, then on this case the values of h and k are 2 and -6
[tex](x+2)(x-6)=0[/tex]Our equatio is a parabola then if we find the vertex we are finding the axis of simmetry
to find the vertex we trasnforme ou equation to the general form of a quadratic equation multipliying parenthesis
[tex]\begin{gathered} (x\times x)+(x\times-6)+(2\times x)+(2\times-6)=0 \\ x^2-6x+2x-12=0 \\ x^2-4x-12=0 \end{gathered}[/tex]now take the equation and derivate
[tex]\begin{gathered} 2x-4-0=0 \\ 2x-4=0 \end{gathered}[/tex]if we solve x we find the coordinate x of the vertex and the axis of simmetry
then
[tex]\begin{gathered} 2x-4=0 \\ 2x=4 \\ x=\frac{4}{2} \\ \\ x=2 \end{gathered}[/tex]axis of Symmetry is x=2
1 8. Matt wants to purchase a gasoline motor scooter. The gas mileage is 75 miles for each gallon of gasoline. How many miles will Matt be able drive on 5 gallons of gasoline? 2
Answer:
375 miles
Explanation:
The gas mileage of the scooter = 75 miles for each gallon of gasoline.
Therefore:
If 1 gallon will cover a distance of 75 miles
Then: 5 gallons will cover a distance of:
5 x 75 miles
=375 miles
Matt will be able to drive 375 miles on 5 gallons of gasoline.
Three cards are drawn from an ordinary deck and not replaced find the probability of the following P(getting 3 queens)P(getting an ace and king and queen)P(getting club and spade and heart)P(getting 3 diamonds)Answer the following problems using multiplication rule make sure to reduce your fraction
a) P(3 queens) ) = 4/52*3/51*2/50 = 1/5525
b) P(ace,king, queen) = 4/52*4/51*4/50 = 8/16575
c) P( ) = 10/52 * 10/51*10/50 = 5/663
d) P(3 diamonds) = 10/52 * 9/51* 8/50 = 6/1105
Really need help with 11 and 12 just started learning this today and I don't quite understand it would really appreciate it
11.
Given:
[tex]y=x^2[/tex]Differentiate with respect to x, we get
[tex]\frac{dy}{dx}=2x[/tex]The given point is (3,9)
Substitute x=3 in the derivative, we get
[tex]\frac{dy}{dx}=2\times\times3=6[/tex]Hence the slope is 3.
12.
Given:
[tex]y=x^2+4[/tex]Differentiate with respect to x, we get
[tex]\frac{dy}{dx}=2x+0[/tex]The given point is (0,4)
Substitute x=0 in the derivative, we get
[tex]\frac{dy}{dx}=2(0)+0=0[/tex]Hence the slope is 0.
Question: What is the solution to this system of linear equations? 8x + 2y = 2 and x + 3y 2 = 14 I NEED The claim, evidence and reasoning. Please I need help
help my brother the other one I tried was a scam
1. Given the integers a and b, a common multiple is a positive integer that is divisible by both a and b.
2. The Least Common Multiple (LCM ) is the smallest positive integer that is divisible by both a and b.
3. Multiples of 6: 6 (= 6x1), 12 (= 6x2), 18 (= 6x3), 24 (= 6x4), ...
Multiples of 4: 4 (= 4x1), 8 (= 4x2), 12 (= 4x3), 16 (= 4x4), ...
The smallest number of these two lists is 12, then the LCM between 6 and 4 is 12.
At the start of a research study, a colony of penguins had a population of 20,000. One year later, it had a population of 21,200.Assuming the population of the colony has grown exponentially, which expression best models thepopulation? Let t represent the time in years from the start of the research study.1,200(1.015)^t20,000 (1.06)^4t21,200 (1.012)^t20,000 (1.06)^tAssuming the colony continues to grow at the same rate, what will the population of the colony be 4 years after the start of the research study?Round your answer to the nearest whole number.
Solution:
An exponential function is generally expressed as
[tex]\begin{gathered} y=a(b)^t\text{ ----- equation 1} \\ \end{gathered}[/tex]Given that in a research study, a colony of penguins had a population of 20,000.
This implies that
[tex]\begin{gathered} when\text{ t=0,} \\ 20,000=ab^0 \\ \Rightarrow20000=a\times1\text{ \lparen where b}^0=1) \\ thus, \\ a=20000 \end{gathered}[/tex]Substitute the value of a into equation 1.
Thus,
[tex]y=20000(b)^t\text{ ----- equation 2}[/tex]One year later, it had a population of 21,200. This implies that when t equals 1, we substitute the values of 21200 and 1 for y and t respectively into equation 2.
This gives
[tex]\begin{gathered} 21200=20000(b)^1 \\ \Rightarrow21200=20000b \\ divide\text{ both sides by the coefficient of b, which is b.} \\ thus, \\ \frac{21200}{20000}=\frac{20000b}{20000} \\ \Rightarrow b=1.06 \end{gathered}[/tex]Substitute the obtained value of b into equation 2.
Thus, the expression that best models the population is
[tex]20,000(1.06)^t[/tex]Assuming the colony grows at the same rate, the population of the colony after 4 years is evaluated by solving for y when the value of t is 4.
Thus,
[tex]\begin{gathered} y=20,000(1.06)^t \\ when\text{ t=4, we have} \\ y=20,000(1.06)^4 \\ =20000\times(1.06)^4 \\ =20000\times1.26247696 \\ \Rightarrow y=25249.5392 \\ \therefore y=25250\text{ \lparen nearest whole number\rparen} \end{gathered}[/tex]Hence, after 4 years the population of the colony will be 25250 penguins (nearest whole number).
What type of number is 3 - 77iChoose all answers that apply:A. RealB. ImaginaryC. Complex
True or False? In a two column proof, the right column contains a series of deductions. (Geometry)
In a two column proof the left column contains a series of statements. The reasons why these statements are true are given in the right column. This reasons are deduction made from the data provided by the problem. Then the statement "In a two column proof, the right column contains a series of deductions." is True.
An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of drawing a queen ? Question content area bottomPart 1The probability of drawing a queen is enter your response here .(Type an integer or a simplified fraction.)
Given:
Total number of cards = 52
Number of cards drawn = 1
Then:
Number of ways of drawing a card from 52 cards
[tex]\begin{gathered} =^{52}C_1 \\ =52 \end{gathered}[/tex]Number of queens in a deck of cards = 4
Number of ways that one card is a queen
[tex]\begin{gathered} =^4C_1 \\ =4 \end{gathered}[/tex]Probability of drawing a queen
[tex]\begin{gathered} =\frac{\text{ Number of favorable cases}}{\text{ Total number of cases}} \\ =\frac{4}{52} \\ =\frac{1}{13} \end{gathered}[/tex]Final answer: 1/13
what is the answer to number 9 and how do i solve?
Given:
[tex]T=\frac{1}{r}\frac{N_{\infty}-N_0}{N_0}[/tex]From question (1)
[tex]r=2[/tex]and given:
[tex]\begin{gathered} N_{\infty}=3.3 \\ N_0=10 \end{gathered}[/tex]we will find the daily cases beak as follows:
[tex]undefined[/tex]The Senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High school A Rented and Filled 6 vans and 7 buses with 471 students. High School B rented and Filled 5 vans and 9 buses with 573 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many Students can a bus carry?
Answer: A van can carry 12 students
A bus can carry 57 students
Explanation:
Let x represent the number of students that a van can carry
Let y represent the number of students that a bus can carry.
The senior class at High school A Rented and Filled 6 vans and 7 buses. This means that
the number of senior class students that the van carried is 6 * x = 6x
the number of senior class students that the bus carried is 7 * y = 7y
If both vehicles were filled with 471 students, it means that
6x + 7y = 471 equation 1
High School B rented and Filled 5 vans and 9 buses. This means that
the number of High School B students that the van carried is 5 * x = 5x
the number of High School B students that the bus carried is 9 * y = 9y
If both vehicles were filled with 573 students, it means that
5x + 9y = 573 equation 2
We would solve both equations by applying the method of elimination. To eliminate x, we would multiply equation 1 by 5 and equation 2 by 6. The new equations are
30x + 35y = 2355 equation 3
30x + 54y = 3438 equation 4
Subtracting equation 3 from equation 4, we have
30x - 30x + 54y - 35y = 3438 - 2355
19y = 1083
y = 1083/19
y = 57
Substituting y = 57 into x equation 1, we have
6x + 7 * 57 = 471
6x + 399 = 471
6x = 471 - 399 = 72
x = 72/6
x = 12
Thus,
A van can carry 12 students
A bus can carry 57 students
If f(x)=x²-20 and g(x) = 4+3x, then f(g(-3)) =
The value of function f(g(-3)= 5.
What is composite function?
A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x).
Given, f(x)=x²-20 and g(x) = 4+3x
first we will find
f(g(x)) = f(4+3x)^2-20
=9x^2+16+24x-20
=9x^2+24x-4
Now to find, f(g(-3)), substitute x=-3,
= 9(9)+24(-3)-4
=81-72-4
=5
To know more about composite function, visit:
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Blair purchases the T-shirts from Company B. She needs to add a 75markup to her total cost to make a profit when she sells the shirts at thcarnival. How should Blair determine the selling price of each T-shirt athe carnival?Drag a number into each box to make the statements true.She canThe total cost Blair paid for one T-shirt is $calculate the markup by multiplying her total cost byBlair will sell each T-shirt at the carnival for $
Isolating selling price,
[tex]\begin{gathered} \frac{\text{ markup \% }}{100}\text{= }\frac{\text{ selling price - cost}}{\text{ cost}} \\ \frac{\text{ markup \% }}{100}\cdot\cos t=\text{selling price - cost} \\ \frac{\text{ markup \% }}{100}\cdot\cos t+cost=\text{selling price} \\ \cos t(\frac{\text{ markup \% }}{100}+1)=\text{ selling price} \end{gathered}[/tex]The markup is 75 %. Supposing that the cost of a T-shirt is $6.00, then the selling price will be:
[tex]\begin{gathered} \text{selling price = 6.00}\cdot(\frac{75}{100}+1) \\ \text{selling price = 6.00}\cdot(0.75+1) \\ \text{selling price = 6.00}\cdot1.75 \\ \text{selling price = \$}10.5 \end{gathered}[/tex]