Answer:
Step-by-step explanation:
We know a total of 6000 is being turned into 510, in two accounts which equal to 15%, to find how much is in each account we can create the following equation:
[tex]5x+10x=510[/tex]
Solve for x
[tex]15x=510\\x=34[/tex]
Now multiply x by the corresponding percentages to find how much was invested into each percentage.
[tex]34*5=170[/tex]
[tex]34*10=340[/tex]
Therefore we now know that 170 dollars was invested into the 5% division, and 340 dollars was invested into the 10% division.
We can of course check our answer by adding 170+340 which equals our original investment of 510.
$1800 is invested at 5% and the remainder, $4200, is invested at 10%.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let us consider the amount invested at 5% x.
The amount invested at 10% is then the remainder, which is:
$6000 - x
Now we can set up an equation for the total interest earned:
0.05x + 0.10($6000 - x) = $510
Simplifying and solving for x:
0.05x + $600 - 0.10x = $510
-0.05x + $600 = $510
-0.05x = -$90
Divide both sides by 0.05
x = $1800
Hence, $1800 is invested at 5% and the remainder, $4200, is invested at 10%.
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A cube shaped box has a side length of 15 inches and contains 27 identical cube shaped blocks. what is the surface area of all 27 blocks compared to the surface area of the box?
The surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.
What is a cube?A cube is a three-dimensional solid object with six square faces, facets, or sides, three of which meet at each vertex.To find the total surface area of the 27 blocks:
A cube's surface area
SA = 6s² (where s is the side length)Given that the box's side length is 15 inches:
SA of box = 6152 = 1350 in2Surface Area of 3-inch side length blocks:
⇒ SA = 6 · 3² = 54 in²27 blocks SA = 27 54 = 1458 in2Surface Area of 4-inch side length blocks:
⇒ SA = 6 · 4² = 96 in²27 96 = 2592 in2 SA of 27 blocksSurface Area of 5-inch side length blocks:
⇒ SA = 6 · 5² = 150 in²27 blocks SA = 27 150 = 4050 in2Therefore, from the given answer options for the total surface area of the 27 blocks, the side length of the blocks must be 5 inches.
To calculate how many times the total surface area of the 27 blocks is to the surface area of the box:
So,
The side length of the blocks is 5 inches.
The total surface area of the 27 blocks is 4050 square inches.
This is 3 times the surface area of the box.
Therefore, the surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.
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A 10-acre parcel was sold for $3.50 per square foot. What was the total selling price for the parcel
Answer:
The total selling price for the parcel is 1,524,600 dollars.
Step-by-step explanation:
We are given that 10 acre parcel was sold for $3.50.
First we need to figure out how many square foot is in 10 acres.
when we convert 10 acres we get 435600 square feet.
Since we know that parcel was sold for $3.50 per square foot we simply multiply 435600 by 3.5 = 1,524,600
FIND the smallest number by which 576 mus be divided to make it perfect cube
Answer:
9
Step-by-step explanation:
when you divide 576 by 9 you get 64 which is a perfect cube
cbrt(64) = 4
so your answer is 9
3. Use the image to answer the following questions.
will brainiest if correct. try ur best!
(a) The angle pitch of a roof is safest when measuring between 18° – 27°. According to these guidelines, is the roof pictured in the image safe? (Note:
(b) What is length of the roof line (segment PR)? Round answer to the nearest tenth of a foot and show all your work.
Answer:
Answer:
Step-by-step explanation:
For missing hypotenuse: [tex]\sqrt({a^{2} + b^{2})[/tex]
Plug in the side lengths that are known to find the hypotenuse.
1. No, the angle is less than 18 degrees (closer to 15), so it is not safe
2. The length rounded to the nearest tenth is approximately 15.5 feet.
Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $48 and costs an additional $0.15 per mile driven.
The second plan has an initial fee of $53 and costs an additional $0.10 per mile driven. For what amount of driving do the two plans cost the same?What is the cost when the two plans cost the same?
Answer:
100 miles
Cost = $63
Step-by-step explanation:
Let us assume that the distance driven for both plans when they both equal in cost is X miles
Plan 1
Cost = 48 + 0.15X
Plan2
Cost = 53 + 0.1X
If they are both equal then
48 + 0.15X = 53 + 0.10X
Collecting like terms
0.15X - 0.10X = 53 - 48
0.05X = 5
X 5/0.05 = 100 miles
Plan 1 Cost = 48 + 0.15(100) = 48 + 15 = $63
Plan 2 Cost = 53 + 0.1(100) = 53 + 20 = $63
A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. if a marble is randomly selected from the bag, what is the probability that it is blue?
3/12, or 1/4 is the probability that it is blue.
What is probability?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .Probability = number of successes / total number of outcomes
Total marbels in bag = 4+ 3 + 5 = 12
A total of 12 marbles are in the bag.
3 blue marbles are in the bag.
Therefore, the probability of picking a blue is 3/12, or 1/4.
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Solve the following systems of equations algebraically:
[tex]\left \{ {{y=\frac{1}{2}*2^x } \atop {y=5x+2}} \right.[/tex]
The value of x in the system of equation is 6
How to solve the system of equations?The system of equations is given as:
y = 1/2 * 2^x
y = 5x + 2
Substitute y = 1/2 * 2^x in y = 5x + 2
1/2 * 2^x = 5x + 2
Multiply through by 2
2^x = 10x + 4
Next, we use the trial by error.
Set x = 6
This gives
2^6 = 10 * 6 + 4
Evaluate the product and the exponent
64 = 60 + 4
Evaluate the sum
64 = 64
Hence, the value of x in the system of equation is 6
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QUICK HELP PLSSSS
Find the probabilities of the events described and arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability of occurrence.
The probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.
Given A)Number of green marbles=5,number of red marbles=3, number of blue marbles=4,
B) Number of peaches=7,number of apples=3,
C) Number of red token=10, number of blue token=6,green tokens=4,
D)Number of golf balls=13, number of tennis balls=2.
We are required to find the following probabilities:
A) Probability of getting red marble=Number of red marbles/ Total marbles.
=3/12
=1/4
=0.25
B) Probability of getting peaches=Number of peaches/Total fruits.
=7/10
=0.7
C) Probability of getting green tokens=Number of green tokens/Total tokens
=4/20
=1/5
=0.2
D)Probability of getting golf balls= Number of golf balls/ Total balls.
=13/15
=0.867
The sequence will be from C-A-B-D.
Hence the probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.
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4. Joe has five times as much money as Bill. However, Joe pays Bill $5 he owes him, after which Joe has just twice the amount Bill now has. How much money did each have in the beginning?
Answer:
Bill starts with $5 and Joe starts with $25Step-by-step explanation:Let Ji and Bi represent the initial amounts that Joe and Bill have at the start. Number after J and B will be used to indicate subsequent steps in the problem.
We are told that "Joe has five times as much money as Bill," which we can write as:
1) Ji = 5Bi
We learn that "Joe pays Bill $5," which we can represent as:
2) J1 = Ji - 5
This would mean that Bill has added $5:
3) B1 = Bi + 5
We are then told that "Joe has just twice the amount Bill now has," which we can write as:
4) J1 = 2B1
===
We can rearrnage and substitute the above relationships to eliminate one of the two variables (B1 or J1)
J1 = Ji - 5 [from 2]
2B1 = Ji - 5 [Substitute 4 to eliminate J1]
Ji = 5Bi [from 1]
2B1 = 5Bi - 5 [Substitute 1 to eliminate Ji]
B1 = Bi + 5 [Rearrange]
2(Bi + 5) = 5Bi - 5 [Use the above expression in the previous equation to eliminate B1]
2Bi + 10 = 5Bi - 5 [Simplify]
-3Bi = -15 [Simplify]
Bi = $5 [Solve]
Ji = 5Bi [from 1]
Ji = 5*(5) [Since Bi = $5]
Ji = $25 [Solve]
Bi = $5 and Ji = $25===
CHECK:
Does Joe has five times as much money as Bill?
Ji = $25 and Bi = $5 YES
When Joe pays Bill $5 he owes him, does Joe has just twice the amount Bill now has?
J1 = $25 - $5 = $20
B1 = $5 + $5 = $10 YES
30. You want to simulate an experiment to draw cards out of a deck. You
plan to draw 35 cards (with replacement), and list which card you drew. How
many times would you expect to draw a face card?
6
8
12
10
Using the binomial distribution, we have that you would expected to draw a face card 8 times.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
For this problem, the parameters are given as follows:
n = 35, as the experiment will be repeated 35 times.p = 0.2308, as of the 52 cards, there are 12 faces, hence 12/52 = 0.2308.Then the expected value is found as follows:
E(X) = np = 35 x 0.2308 = 8
You would expected to draw a face card 8 times.
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The Fruit Juice Company sold 5,909,999,222 cans of juice last year. This
year the company sold 3,999,002,135 cans. Which is the best estimate of
how many more cans were sold last year than this year?
OA) 2,000,000,000
OB) 3,000,000,000
OC) 9,000,000,000
OD) 10,000,000,000
Question 1: The population of Ohio's three largest cities are: Cleveland, 479,459; Columbus, 715,230; and Cincinnati, 367,000. The average population of Ohio's three largest cities is:
a. 520,563
b. 620,563
c. 502,563
d. 602,563
Q2: Mr. Gorski bases each student's grade on 4 tests. On the first 3 tests, Horace scored 84, 93, and 88. What must he score on the final test to make his average 90?
a. 85
b. 88
c. 92
d. 95
The points A(-3, 4), B(3, 2), C(1,4), and D(-5, -2) form quadrilateral ABCDin the coordinate plane. What condition verifies that the
diagonals are perpendicular?
PLEASED HELP
The diagonals of the qudrilateral will not be perpendicular to each other.
What is a quadrilateral?A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.
Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. If two segments are perpendicular, the multiplication of their slopes is -1.
The slope of a coordinate pair is given by the change in y divided by the change in x, that is:
For the diagonal AD the slope will be:-
Slope = ( -5 + 3 ) / ( -2 - 4) = ( 1 / 3 )
For the diagonal BC, the slope will be:-
Slope= ( 1 - 3) / ( 4 - 2 ) = ( -2 / 2) = -1
The multiplication of the two slopes will be,
M = ( 1 / 3 ) x -1 = ( - 1 / 3 )
Therefore, the diagonals of the quadrilateral will not be perpendicular to each other. Because the product of the slope is not equal to -1.
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Answer:
The product of the slopes of the diagonals is -1.
Step-by-step explanation:
I had the question and got it right.
One of the famous Grand Prix races takes place in Monaco, a small country south of France and West of Italy. Each Spring, racers from around the world come to this prestigious event. Currently, the race has 78 laps through the town of Monte Carlo (you may have seen this famous event in Iron Man 2). Each lap of the race has a distance of 3.34 km.
The computation shows that the total distance will be 260.52km.
How to compute the value?From the information given, it was stated that the race has 78 laps through the town of Monte Carlo and that each lap of the race has a distance of 3.34 km.
Therefore, the total distance will be:
= 78 × 3.34
= 260.52 km
Therefore, the distance is 260.52km.
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A toy store retailer charges $26.88 for a board game. He marks up his goods by 25% before selling them. What was the cost of the game before the markup?
The price of the board game before the markup is $21.50.
What is the cost before the markup?
Percentage can be described as a fraction an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.
When the price of an item is marked up, it means that the price of the item has been increased by a predetermined percentage. In this question, the price of the board game is increased by 25%.
Price of the item before the mark up = price the retailer sells / ( 1 + percentage)
$26.88 / 1.25 = $21.50
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Find a power series for the function, centered at c. g(x) = 4x x2 2x − 3 , c = 0
The power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]
For given question,
We have been given a function g(x) = 4x / (x² + 2x - 3)
We need to find a power series for the function, centered at c, for c = 0.
First we factorize the denominator of function g(x), we have:
[tex]\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}[/tex]
We can write g(x) as,
[tex]\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\[/tex]
We know that, [tex]\frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n}[/tex] if |x| < 1
and [tex]\frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n[/tex] if [tex]|\frac{x}{6}| < 1[/tex]
[tex]\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\[/tex] if |x| < 1 and if [tex]|\frac{x}{6}| < 1[/tex]
[tex]\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex] if |x| < 1
Therefore, the power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]
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im having trouble with this question! pls help
Using a proportional relationship, it is found that the unit rate of change is of 9.
The relation d = 9t is graphed at the end of the answer.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, we have d as a function of t, hence the relationship is:
d = kt.
When t increases by 0.2, d increases by 1.8, hence the constant is given as follows:
k = d/t = 1.8/0.2 = 9
The relation d = 9t is graphed at the end of the answer.
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Which term is not possible in the domain of a sequence?
The term that is not possible in the domain of a sequence is:
-5.
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexes of the terms, starting at 0 and going until the nth term.
For example, suppose we have the following sequence: 3, 5, 7, ...
The term with index 0 is 3.The term with index 1 is 5.The term with index 2 is 7.From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:
-5.
Which is the only negative number of the options.
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suppose sin(A) = 2/5. use the trig identity sin^2(A)+cos^2(A)=1 to find cos(A) in quadrant I. show all steps and round to ten-thousandth
In quadrant I, [tex]\cos(A)[/tex] is positive. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} = \dfrac{\sqrt{21}}5 \approx \boxed{0.9165}[/tex]
how many days will he cut the last section?
Solving a linear equation, we will see that after 9 days he cuts the last section.
how many days will he cut the last section?We know that the initial length of the piece of cloth is 20m, and the taylor each day cuts a piece of 2 meters of it.
So, the length as a function on the number of days, is:
L(x) = 20m - 2m*x
Here we just need to solve:
L(x) = 2m
Because the last cut is when the long piece measures 4 meters (in that case he does one cut and has the two final pieces of 2 meters).
Solving that, we get:
20m - 2m*x = 2m
20m - 2m = 2m*x
18m/2m = x = 9
After 9 days he cuts the last section.
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Get every whole number from 0-10 using exactly five 3's, and any arithmetic operations and parentheses
See below for the combination of the arithmetic operations and exactly five 3's
How to determine the operations?The conditions are given as:
Exactly five 3'sAny arithmetic operation or combination of operationsThere are no direct rules to this, except by trial and error.
After several trials, we have the following operations:
(3 * 3 - 3 * 3)/3 = 0
3 - 3/3 - 3/3 = 1
(3 + 3 - 3 / 3)-3 = 2
(3 * 3 - 3 + 3)/3 = 3
3 *3/3 + 3/3 = 4
3 +3/3 + 3/3= 5
3 + 3 + (3 - 3)/3 = 6
(3^3 - 3 - 3)/3 = 7
3 + 3 + (3 + 3)/3 = 8
3 + 3 + 3+ 3 -3 =9
3 + 3 + 3 + 3/3 = 10
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My car uses 8.5L of petrol per 100km travelled. If petrol costs $2.05 per litre, how much will the petrol cost for my trip?
Answer:
$0.17425/Km
Step-by-step explanation:
8.5L/100Km*$2.05/L
= $0.17425/Km
find the total surface area and volume, then multiply by 0.0004
The Total surface area of the rectangular prism = 168 in.²
The Volume of the rectangular prism = 108 in.³
What is the Total Surface Area of a Rectangular Prism?The total surface area of a rectangular prism is given as: SA = 2(wl + hl + hw), where:
w = width of the rectangular prism
h = height of the rectangular prism
l = length of the rectangular prism
What is the Volume of a Rectangular Prism?The volume of a rectangular prism = l × w × h
Find the Total surface area of the rectangular prism:
Length (l) = 9 in.
Width (w) = 2 in.
Height (h) = 6 in.
Total surface area of the rectangular prism = 2(wl+hl+hw) = 2·(2·9+6·9+6·2) = 168 in.²
Find the volume of the rectangular prism:
Length (l) = 9 in.
Width (w) = 2 in.
Height (h) = 6 in.
Volume of the rectangular prism = l × w × h = 9 × 2 × 6
Volume of the rectangular prism = 108 in.³
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(a+b)^2-2(a+b)
Factorise (please explain)
Answer:
(a + b)(a + b - 2)
Step-by-step explanation:
(a + b)² - 2(a + b) ← factor out (a + b) from each term
= (a + b)(a + b - 2)
Pls help I’ll brainlest
Asap
Answer:
C. slope
Greetings !
The symbol for slope is "m". Slope can be calculated by taking any two locations along a line and calculating the ratio of the RISE to the RUN (the ratio of the difference between vertical positions of the locations to the difference between horizontal positions of the locations).
Answer: slope.
Step-by-step explanation:
Hurry show your work
24- 4 to rhe power of 2 x 3+15
the expression is simplified to give - 39
How to simply the expression
Given the expression;
= 24- 4 to the power of 2 x 3+15
= 24 - (4^2 × 3 ) + 15
First, expand the bracket
= 24 - ( 16 × 3) + 15
Find the product of the bracket
= 24 - 48 + 15
From our knowledge of BODMAS, we add before we subtract
Now, let's add first
= 24 - 63
The, subtract
= - 39
The expression is simplified to - 39
Thus, the expression is simplified to give - 39
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3. What is the greatest common factor for the two expressions? Use ^ to mean an exponent (use Shift +6 key). For example, 3x2 would be written as 3x^2. 15v³ and 12v² Write your response on the line below. Do not use any spaces or words.
The greatest common factor of the two expressions given as in the task content is; 3v².
What is the greatest common factor of the two expressions given?It follows from the task content that the terms whose greatest common factor are to be determined are: 15v³ and 12 v².
15v³ and 12v²
= 3v²(5v) and 3v²(4)
= 3v²(5v) and (4)
Consequently, in a bid to factorise the two expressions by means of their greatest Common factor, the greatest common factor can be determined as; 3v².
The correct answer choice which therefore represents the greatest common factor as required in the task content is; 3v².
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Hypotenuse: The ________ side of a right triangle; side ________ from the right angle.
The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.
According to the statement
we have given that the property of the hypotenuse of the triangle and we have to complete it.
So, For this purpose, we know that the
A hypotenuse is the longest side of a right-angled triangle, and The length of the hypotenuse can be found using the Pythagorean theorem.
Now we discuss about the properties of the hypotenuse;
The hypotenuse is the longest side in a right angled triangle. The hypotenuse is opposite the right angle. The midpoint of the hypotenuse is the circumference.And from these properties we have to complete the given property.
So, The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.
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What is the value of y¹ when y = 5 and x - 10?
Answer:
5
Step-by-step explanation:
y^1 = 5^1 (y = 5)
Anything raised to the power of 1 is just itself.
So, 5^1 = 5
Use the diagram to answer each part of the question. The image is not drawn to scale.
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In the afternoon, the person (who is 1.6 m tall) casts a shadow that is 8 m. The distance along the ground from the person (H) to the tree (G) is 30 m, and the distance from the tree (G) to the building (F) is 105 m. Calculate the height of the tree and the building. Round answers to the nearest tenth of a meter and show all your work.
The height of the tree and the building are 7.6 m and 28.6 m respectively.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Two triangles are similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.
Triangle BGD, CHD and AFD are similar triangles.
CH = 1.6, DH = 8, GH = 30, GF = 105
FH = GF + GH = 105 + 30 = 135
FD = FH + DH = 135 + 8 = 143; GD = 30 + 8 = 38
Hence, using similar triangles:
BG/CH = GD / DH
BG / 1.6 = 38/8
BG = 7.6 m
Also:
building/CH = DF / DH
building / 1.6 = 143/8
building = 28.6 m
The height of the tree and the building are 7.6 m and 28.6 m respectively.
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