We will have the following:
First, we recall that the simple interest formula is given by:
[tex]A=P(1+rt)[/tex]Now, for the accounts that are described in the problem we will have that:
[tex]\begin{gathered} A_1+2P=2P(1+(0.04)(1))\Rightarrow A_1+2P=2P(1.04) \\ \\ A_2+P=P(1+(0.12)(1))\Rightarrow A_2+P=P(1.12) \end{gathered}[/tex]Now, we have that:
[tex]A_1+A_2=8740[/tex]Then:
[tex]\begin{gathered} A_1+A_2+2P+P=2P(1.04)+P(1.12) \\ \\ \Rightarrow8740+3P=3.2P\Rightarrow8740=0.2P \\ \\ \Rightarrow P=43710 \end{gathered}[/tex]So, the amount invested at 4% interest is $87 420.
And, the amount invested at 12% interest is $43 710.
What is the slope of the equation: 2x + 3y = 12?
Given the equation : 2x + 3y = 12?
We will find the slope of the equation by re-arranging the equation into the standard form of slope intercept formula:
[tex]\begin{gathered} y\text{ = mx + b } \\ where\text{ m represent a slope } \\ \text{ and b represents y -intercept } \end{gathered}[/tex]Re-arranging the equation will be :
[tex]\begin{gathered} 2x+3y=\text{ 12 } \\ 3y\text{ = -2x + 12 } \\ \frac{3y}{3\text{ }}=\text{ }\frac{-2x\text{ +12}}{3} \\ \therefore\text{ y = }\frac{-2}{3}x\text{ +4 } \end{gathered}[/tex]Therefore the equation will be : y = -2/3x +4 Meaning the slope = -2/3one step equations b+0.25=1.15
You will need to make b the subject of the formula:
This you do by subtracting 0.25 from both sides of the equation:
b + 0.25 = 1.15 becomes:
[tex]\begin{gathered} b+0.25-0.25=1.15-0.25\text{ which turns to become:} \\ b=1.15-0.25 \\ b=0.9 \end{gathered}[/tex]At Everton Middle School, there are 7 students who ride the bus to school for every 4 students who do not ride the bus.
The number of people who ride the bus is 70 students.
How to calculate the value?From the information, at the school, there are 7 students who ride the bus to school for every 4 students who do not ride the bus.
Therefore, the number of people who ride the bus if there are 40 people who do not take the bus will be represented by x.
This will be illustrated as:
4/7 = 40/x
Cross multiply
4x = 40 × 7
4x = 280
Divide
x = 280/4
x = 70
Therefore there are 70 students.
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At Everton Middle School, there are 7 students who ride the bus to school for every 4 students who do not ride the bus. How many people ride the bus of there are 40 people who do not take the bus?
Vector vector v equals vector RS has points R(−2, 12) and S(−7, 6). What are the magnitude and direction of vector RS question mark Round the answers to the thousandths place.
Take into account that vector v can be written as follow:
[tex]\vec{v}=(x-x_o)\hat{i}+(y-y_o)\hat{j}[/tex]where (x,y) and (xo,yo) are two points on the vector.
In this case, we can use (xo,yo) = R(-2,12) and (x,y) = S(-7,6). By replacing these values into the expression for vector v, we obtain:
[tex]\begin{gathered} \vec{v}=(-7-(-2))\hat{i}+(6-12)\hat{j} \\ \vec{v}=-5\hat{i}-6\hat{j} \end{gathered}[/tex]Now, consider that the magnitude of v is the square root of the sum of the squares of the components. Then, we have for the magnitud of v:
[tex]v=\sqrt[]{(-5)^2+(-6)^2}=\sqrt[]{25+36}=\sqrt[]{61}\approx7.810[/tex]Hence, the magnitude of v is approximately 7.810.
Now, consider that the tangent of the angle of the direction of the vector is equal to the quotient between the y component over the x component of the vector:
[tex]\begin{gathered} \tan \theta=\frac{-6}{-5} \\ \theta=\tan ^{-1}(\frac{-6}{-5})\approx230.194 \end{gathered}[/tex]Hence, the direction of vector v is approximately 230.194 degrees.
diagram 10 shows a straight line PQ with point P(-4,9) and Q(12,1).
We have a line defined by two points, P(-4,9) and Q(12,1).
Knowing two points of the line, we can calculate the slope with the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, the slope will be:
[tex]\begin{gathered} m=\frac{y_Q-y_P}{x_Q-x_P} \\ m=\frac{1-9}{12-(-4)}=\frac{-8}{12+4}=-\frac{8}{16}=-\frac{1}{2} \end{gathered}[/tex]With the slope and one point we can express the equation in slope-point form:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-y_Q=m(x-x_Q) \\ y-1=-\frac{1}{2}(x-12) \\ y=-\frac{1}{2}x+\frac{12\cdot1}{2}+1 \\ y=-\frac{1}{2}x+6+1 \\ y=-\frac{1}{2}x+7 \end{gathered}[/tex]The x-intercept is the value of x that makes the function f(x) become 0.
In this case, we have to find x so that y = 0.
We can replace y in the equation and calculate x as:
[tex]\begin{gathered} y=0 \\ -\frac{1}{2}x+7=0 \\ -\frac{1}{2}x=-7 \\ x=-7\cdot(-2) \\ x=14 \end{gathered}[/tex]Then, for the x-intercept is x = 14.
Answer:
a) The equation of the line is y = (-1/2)*x+7
b) The x-intercept is x = 14.
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 42 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 3000 aspirin tablets actually has a 6% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
The probability that the entire cargo will be approved is 0.078 = 7.8% using the Binomial probability distribution, while 92.2% will be refused. As a result, many will be rejected.
By Binomial probability distribution,
P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]
[tex]C_{n,x}[/tex] , various combinations of x items from a collection of n elements given by,
[tex]C_{n,x}[/tex] = n! ÷ x! (n - x)!
n=42, as 42 tablets are tested.
p=0.06 as 6% is defective.
If at most there is 1 defective piece then it will be accepted.
Therefore,
P(X ≤ 1) = P(X = 0) + P(X = 1)
P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]
P(X = 0) = [tex]C_{42,0}[/tex] × [tex](0.06)^{0}[/tex] × [tex](0.94)^{42}[/tex] = 0.074
P(X = 1) = [tex]C_{42,1}[/tex] × [tex](0.06)^{1}[/tex] × [tex](0.94)^{41}[/tex] = 0.0047
Thus,
P(X ≤ 1) = P(X = 0) + P(X = 1)
P(X ≤ 1) = 0.074 + 0.0047
P(X ≤ 1) = 0.0787
The probability that the entire shipment will be approved is 0.078 = 7.8%, while 92.2% will be refused.
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True or false?
Raising prices is the quickest way to resolve excess demand.
Answer:
this is true
Step-by-step explanation:
The formula for the volume of a cylinder is V=²2h. The cylinder to the right has an exact volume of 480 cubic meters. Find its height.
The height of the cylinder is
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(Simplify your answer.)
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The height of cylinder when volume of 480 cubic meters is 480/r^2.
What is volume?Volume serves as a measure for an object's storage capacity. For instance, a cup's volume is said to be 100 ml if it can hold 100 ml of water when filled to the brim. The amount of space a three-dimensional object occupies is another way to define volume.
A solid's volume can be calculated by counting how many unit cubes it contains, such as in the case of a cube or cuboid. The best way to understand volume is to think of it as the area surrounded or occupied by any solid object or object with three dimensions. This can be seen by performing the following easy exercise at home:
volume of cylinder V is = πr²h
where, r = radius of cylinder
h = height of cylinder
V = 480π cubic meters
Now, calculate its height in terms of cylinder radius using the volume of cylinder formula:
V = πr²h
480π = πr²h
h = 480π/ πr²2
h = 480/r²
Therefore, The height of cylinder when volume of 480π is 480/r².
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Find all X such that -13 < 5x - 3 ≤ 17.
Answer:
-5 < x < 17/5
Step-by-step explanation:
add three onto all sides -10 < 5x < 17
then divide all sides by -5 < x < 17/5
A model of Spaceship Earth, a major tourist attraction at Epcot Center in Florida, is a sphere whose diameter is approximately 5 inches.The volume of the model sphere is approximately ___ cubic inches.Use 3.14 for pi. Round only your final answer to the nearest hundredth.
The Volume of the model sphere is given as
[tex]V_{\text{sphere}}=\frac{4}{3}\pi r^3[/tex]Given that the diameter is 5inches, the radius will be
[tex]\begin{gathered} \text{diameter,d}=2\times radius \\ r=\frac{d}{2}=\frac{5}{2}\text{inches} \\ r=2.5\text{inches} \end{gathered}[/tex]substituting r in the formula will give
[tex]\begin{gathered} V_{\text{sphere}}=\frac{4}{3}\times3.14\times(2.5)^3 \\ =\frac{4}{3}\times3.14\times76.765625 \\ =\frac{964.17625}{3} \\ =321.3922\text{cubic inches} \end{gathered}[/tex][tex]V_{\text{sphere}}=321.39\text{cubic inches}[/tex]Hence, the volume of the model sphere is approximately 321.39 cubic inches
can somebody please help me with this question
Answer:
U'(12, 15)
Step-by-step explanation:
Given point U(4, 5) is part of figure STUVW that is dilated by a factor of 3 about the origin, you want the coordinates of U'.
DilationDilation about the origin multiplies each coordinate value by the scale factor:
U' = 3U
U' = 3(4, 5) = (12, 15)
The coordinates of U' are (12, 15).
what is the derivative of sqrt(9x^2-1)
Answer:
900
Step-by-step explanation:
because I know answer
is set of even number closed under operation of addition ?
Answer:
Yes
Explanation:
A set S is said to be closed under addition if:
For a, b in S, a+b is in S.
If we add two even numbers, the result will always be an even number.
Therefore, the set of even number is closed under the operation of addition
Part A find the value of each variable
x=14, y=15
x=14, y=-5
x=24, y=-10
x=24, y-5
Part B
the angle measures?
100°
50°
80°
130°
Answer:
Part A:
Option 1
3x + 8 = 5x - 20 (vertically opposite angles)
2x = 28
x = 14
3x + 8 + 5x + 4y = 180° (adjacent angles on a straight line)
8x + 4y = 172
Substitute x = 14 into equation to find y.
8(14) + 4y = 172
4y = 60
y = 15
Hence, x = 14 and y = 15.
Part B:
Option 4
Unlabeled angle = 5x + 4y (vertically opposite angles)
Substitute x and y to find angle measure.
5(14) + 4(15) = 130°
Hence, measure of unlabeled angle is 130°.
Given a pair of points on each line. use the slope formula to determine whether AB and CD are para el perpendicular, or neither. GH: G(14, 13) and H(-11,0) RS: R(-3, 7) and S(-4,-5)
1) Picking points G( 14,13) , H (-11, 0) and R(-3,7) , S(-4,-5) let's find their slopes using the slope formula
And R(-3,7) , S(-4,-5)
Since the condition to be parallel is share the same slope, and to be perpendicular one line must have the reciprocal and opposite slope in comparison to the first one. We can state that neither that line is parallel nor perpendicular.
3) So the answer is GH is not parallel nor perpendicular.
(4b) If you know that you can drive 230 miles withthat much gas, how many miles per gallon doesyour bus get?Round your answer to the nearest tenth of a mile.The bus gets miles per gallon,
Given the following question:
Part A:
75 dollars to spend on gaS
Gas per gallon costs $2.80
[tex]\begin{gathered} 75\div2.80=26.7857143 \\ 26.7857143 \\ 8>5 \\ 26.8\text{ gallons of gas} \end{gathered}[/tex]With 75 dollars you can buy "26.8 gallons of gas."
Part B:
We know we can travel 230 miles with 26.8 gallons of gas, now we have to find out how many miles can we travel PER gallon of gas.
[tex]\begin{gathered} 230\div26.8=10.4477612 \\ 10.4477612 \\ 4<5 \\ 10.4\text{ miles per gallons} \end{gathered}[/tex]"10.4 miles" per gallon
3 out of 20 cars passing through an intersection did not fully stop, what is the probability that a car arriving at this intersection will not fully stop
Step 1: State the given in the question
Given that 3 out 20 cars passing through an intersection did not fully stop
Step 2: State what to be determined
We are to determine the probability that a car arriving at this intersection that will not fully stop
Step 3: State the formula for finding probability
The formula for finding the probability of an en event, E, from a sample S, is the ratio of the number of elements of event E to the total number of elements in the sample S.
This can be represented mathematically as
[tex]\begin{gathered} P(E)=\frac{n(E)}{n(S)} \\ \text{Where} \\ P(E)=\text{Probability of an event E occuring} \\ n(E)=\text{Number of element in event E} \\ n(S)=\text{Total number of elements in the sample} \end{gathered}[/tex]Step 4: Use the formula to solve the probability
If the event E is cars passing through an intersection did not fully stop. Then, the number of elements in the event E is given as 3. That is:
[tex]n(E)=3[/tex]The sample is the total number of cars, which is given as 20. This means that
[tex]n(S)=20[/tex]Therefore, the probability of the event occuring would be P(E). This is as calculated below:
[tex]\begin{gathered} P(E)=\frac{n(E)}{n(S)} \\ n(E)=3 \\ n(S)=20 \\ P(E)=\frac{3}{20} \\ P(E)=0.15 \end{gathered}[/tex]Hence, the probability that a car arriving at this intersection will not fully stop is 3/20 or 0.15
Identify which method for solving systems is being described by this fact:
The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations.
For the description "The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations." Graphing method for solving systems is in play. Option A
This is further explained below.
What is Graphing method for solving systems?Generally, Construct a graph using the first equation.
Create a graph using the same rectangular coordinate system for the second equation.
Find out whether the lines overlap, if they run parallel to one another, or if they are the same line.
In conclusion, Find a solution to the problem that we are having. In the event that the lines meet, locate the location where they do so.
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CQ.
Identify which method for solving systems is being described by this fact:
The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations.
answer choices
Graphing
Substitution
Elimination (adding or multiplying)
HELP ASAP
Solve 21 ≤ −4z − 21.
z ≤ −10.5
z ≥ −10.5
z ≤ 0
z ≥ 0
[tex]21 + 21 \leqslant - 4z \\ - 4z \geqslant 42 \\ \frac{ - 4z}{ - 4} \geqslant \frac{42}{ - 4} \\ z \leqslant - 10.5[/tex]
ATTACHED IS THE SOLUTION
BE AWARE THE SIGNS <> ONLY CHANGE SIGN WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
A relationship between two expressions or values that are not equal to each other is called 'inequality. Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is twenty one lesser or equal to minus four z minus twenty one.
21 ≤ −4z − 21.
We need to solve for z
Let us add twenty one on both sides
21+21≤ −4z − 21+21
42≤ −4z
Divide both sides by 4
10.5≤ -Z
-10.5≥Z
Z≤ -10.5
Hence Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.
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The number of legislators has increased approximately linearly from 1138 positions in 2003 to 1222 positions in 2009 . Let n be the number of legislators at t years since 2000. Find an equation of a linear model to describe the data.
The equation of a linear model to describe the data is 14x - y = 26904
To find a linear equation of the provided data,
Let us put the number of legislature on the y axis and the year corresponding at the x axis,
According to provided information,
In year 2003, the number of legislature is 1138.
In year 2009, the number of legislature is 1222.
So here we have two points,
A(2003,1138) and B(2009,1222).
As we have two points now,
We can use the two point form of the line to find the equation of line,
It says if we have two point (a,b) and (c,d), then the equation of line is,
(y-b)/(x-a) = (d-b)/(c-a)
So, our equation of line is with points A and B is,
(y - 1138)/(x-2003) = (1222-1138)/(2009-2003)
(y-1138)/(x-2003) = 14
y - 1138 = 14x - 28042
14x - y = 26904
When,
x = 2000, y = n,
14(2000) - n = 26904
n = 1096.
The Linear Equation is 14x - y = 26904
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
t = 0: 372t = 4 hours: 24,382,480Step-by-step explanation:
You want the initial population and the population after 4 hours if its doubling time is 15 minutes, and the population is 60,000 after 110 minutes.
EquationWe like to use the numbers in the problem when writing the exponential equation. Here, we are given a doubling time and a population that is ...
(minutes, population) = (110, 60000)
We can put these numbers in the form ...
p(t) = (value at t1) · (growth factor)^((t -t1)/(growth period))
where the growth factor (2) is applicable over the growth period (15 minutes).
This makes our equation ...
p(t) = 60000(2^((t-110)/15))
ValuesWe want to find p(0) and p(240). (240 is the number of minutes in 4 hours). The attachment shows the calculations.
The population at t=0 was about 372.
The population after 4 hours will be 24,382,480.
__
Additional comment
A lot of times, you'll see this rewritten as an exponential equation with 'e' as the base. Here, that would be ...
p(t) = 372·e^(0.0452098t)
where 372 = p(0) = 60000·2^(-110/15), and 0.0452098 ≈ ln(2)/15
These rounded numbers don't give the problem statement values exactly:
p(110) = 53743, not 60000, for example. You would get a population of 60000 after 112.4 minutes (approximately).
<95141404393>
Mrs. long bought 4 types of fruits at the market. she bought 2 cantaloupes that weighed 2.3 pounds each 6 peaches that weighed a total of 1.7 pounds 4 apples that weighed a total of 1.25 pounds and 3 pounds and 3 pounds of grapes. what was the total weigh of the four fruits she bought?
Mrs. long bought 4 types of fruits at the market:
- 2 cantaloupes that weighed 2.3 pounds each:
that is, a total of 2.3x2 = 4.6
- 6 peaches that weighed a total of 1.7 pounds.
- 4 apples that weighed a total of 1.25 pounds.
- and 3 pounds of grapes.
The total weight of the four fruits is:
4.6 + 1.7 + 1.25 + 3 = 10.55 pounds.
If AB = 10 ft, AC = 14 ft, and BC = 20 ft, what is RS?
O 10 ft
14 ft
20 ft
24 ft
The sides of a scalene triangle have measures that are consecutive even integers. If the perimeter of this
triangle is 60 inches, what is the length of the longest side of the triangle?
Answer: 22
Step-by-step explanation:
Let the sides have lengths [tex]x-4, x-2, x[/tex]. Since the perimeter is 60,
[tex]x-4+x-2+x=60\\\\3x-6=60\\\\3x=66\\\\x=22[/tex]
So, the length of the longest side is 22 units.
-3x^2-24x+7=0 is written in the form (x-p)^2=q
[tex] ({x}^{2} + 8x + 16) \\ bring \: out \: the \: x \: and \: ivide \: the \: 8 \: by \: 2[/tex]
customer account “numbers” for a certain company consists of 4 letters followed by 2 single digit numbers. how many different account numbers are possible if repetitions of letters and digits are allowed?
Sport
Soccer
Jogging
Walking
Skiing
Football
Total
72
Hrs
5
20
10
5
10
50
Calculate the portion for soccer in degrees.
[?]°
5 hrs.
Total Sport Hours
Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.
How to find the soccer portion of the pie chart?
In mathematics, the complete pie chart is 360° and to calculate the soccer portion using standard formula which states that the division of the total hours spent on soccer and total sports hours multiply with 360°.
According to the question, the given data states that the pie chart is 360° which represents the total sports hours as 50 hours.
Therefore, the soccer portion is:
= Total hours spent on walking / Total sports hours x 360°
= 10 / 50 x 360°
= 72°
Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.
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Function g is a transformation of the parent function f(x) = x2. The graph of fis reflected across the x-axis, and then translated left 4 units anddown 2 units to form the graph of gWrite the equation for g in the form y = ax2 + bx + cO A. y = -x2 + 8x + 14O B. y = -x2 - 8x - 18O C. y = x2 - 8x + 18O D. y = -x2 - 8x + 14
The parent function is given as:
f(x) = x²
y = x²
The graph is reflected across the x - axis
The x axis remains the same but the y axis is negated
g(x) = -x²
It is translated 4 units left
The function g(x) becomes
g(x) = -(x - 4)²
It is the translated 2 units down
g(x) = -(x - 4)² - 2
Simplifying the above equation:
g(x) = - (x² - 8x + 16) - 2
g(x) = -x² + 8x - 16 - 2
g(x) = -x² + 8x - 18
A bird is flying above a tree. You are standing 40 feet away from the tree. The angle of elevation to the top of the tree is 32°, and the angle of elevation to the bird is 42°. What is the distance from the bird to the top of the tree?
A bird is flying above a tree. You are standing 40 feet away from the tree. The angle of elevation to the top of the tree is 32°, and the angle of elevation to the bird is 42°. What is the distance from the bird to the top of the tree?
Let
A -----> you
B-----> a bird
C-----> top of the tree
see the following image
step 1
In the right triangle ABD
tan(42)=BD/AD
substitute given values
tan(42)=BD/40
BD=40*tan(42)
BD=36 ft
step 2
In the right triangle ACD
tan(32)=CD/AD
CD=AD*tan(32)
CD=40*tan(32)
CD=25 ft
step 3
Find the difference BD-CD
36-25=11 ft
therefore
the answer is 11 ftOn a recent trip, Carol's car used 7/8 of a tank of gasoline. Which decimal and percentrepresents this amount?
The fraction of gasoline used is:
[tex]\frac{7}{8}[/tex]We need to convert this fraction to decimal and to percentage to find the answer.
Converting 7/8 to decimal:
For this we have to do the division between 7 and 8:
Thus, the decimal form of 7/8 is 0.875
Converting 7/8 to percentage:
we use the result that we previously get of 7/8 as a decimal: 0.875, and to convert it to percentage we multiply it by 100:
[tex]0.875\times100=87.5[/tex]7/8 to percentage is equal to 87.5%
Answer: 0.875 and 87.5%