Answer: she invested $17000 in the account earning 6% annual interest.
she invested $13000 in the account earning 7.5% annual interest.
Step-by-step explanation:
Let x represent the amount that she invested in the account earning 6% annual interest.
Let y represent the amount that she invested in the account earning 7.5% annual interest.
Marilyn Mallinson invested $30000, part at 6% annual interest and the rest at 7.5% annual interest. This means that
x + y = 30000
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering the account earning 6% annual interest.
P = x
R = 6%
T = 1 year
I = (x × 6 × 1)/100 = 0.06x
Considering the account earning 7.5% annual interest,
P = y
R = 7.5
T = 1
I = (y × 7.5 × 1)/100 = 0.075y
Last year she earned $1995 in interest. This means that
0.06x + 0.075y = 1995 - - - - - - - -
Substituting x = 30000 - y into equation 1, it becomes
0.06(30000 - y) + 0.075y = 1995
1800 - 0.06y + 0.075y = 1995
- 0.06y + 0.075y = 1995 - 1800
0.015y = 195
y = 195/0.015 = 13000
x = 30000 - y = 30000 - 13000
x = 17000
Define like terms. Give an example of like terms and then combine them
Answer:
Like terms are numbers with or without variables that have the same variables.
Step-by-step explanation:
5x and 3x are like terms because they have the same variable.
5x and 3y are not like terms because the variables are different.
To combine them, just add or subtract them. You cannot combine non-like terms!
Answer:
Definition: Like terms - Term in math that have the same variables or powers.
Ex. 2x, -5x, and 7x.
Combine Them: 2x + 7x = 9x - 5x = 4x
Step-by-step explanation:
Give the equation that you would use to solve for exterior angles. Solve for x.
Answer:
X = 93
Step-by-step explanation:
Angles of a polygon = (n - 1)180
The above polygon is heptagon (with 6 sides)
(6-1) × 180
5×180 = 900
Add the given Angles and equate it to 900 (as gotten above)
4x + 3x + 47 + 93 + 46 + 62 = 900
7x + 248 = 900
Collect like term of the number
7x = 900-248
7x = 652
Divide both side by the coefficient of x
7x/7 =652/7
X = 93.1429
please help this is complicated
Answer:
In order the sequences defined by the expressions on the left are ...
2, 4, 8, 164, 8, 16, 321/2, 1/4, 1/8, 1/161, 1/2, 14, 1/81, 2, 4, 81/4, 1/8, 1/16, 1/32Step-by-step explanation:
One of the first steps in working multiple choice questions (in any subject) is to look at the answers to see what you need to know to be able to tell a correct answer from an incorrect one.
Here, all of the first terms are different, except for the two sequences that both starts with 1. Those differ in the ratio between terms (1/2 vs 2).
This means you only have to evaluate the expression for the first domain value (x=1) and you can tell right away what the answer is. It is not complicated, and your calculator can help if you can't do it in your head.
___
Starting at the top of the list on the left, ...
2^1 = 2 . . . . matches 2, 4, 8, ...
2(2^1) = 4 . . . . matches 4, 8, 16, ...
(1/2)^1 = 1/2 . . . . matches 1/2, 1/4, 1/8, ...
2(1/2)^1 = 1 . . . . double the previous sequence, so 1, 1/2, 1/4, ...
1/2(2^1) = 1 . . . . half the first sequence, so 1, 2, 4, ...
1/2(1/2)^1 = 1/4 . . . . matches 1/4, 1/8, 1/16, ...
Riverside Elementary School is holding a school-wide election to choose a school color. 5/8 of the voters were for blue 5/9 of the remaining voters were for green. And the remaining 48 voters were for red. How many voters were for blue?
Answer:
There were 180 voters for blue color.
Step-by-step explanation:
Let the total number of voters be 'x'.
Given:
Number of Voters for blue color = [tex]\frac{5}{8}x[/tex]
Number of Voters for green color = [tex]\frac{5}{9}(x-\frac58x)=\frac59x(1-\frac58)[/tex]
Now we will use LCM to make the denominator common we get;
Number of Voters for green color = [tex]\frac59x(\frac88-\frac58)=\frac59x(\frac{8-5}{9})=\frac59x(\frac38)=\frac{15x}{72}[/tex]
Number of Voters for red color = 48
We need to find the number of voters for blue color.
Solution:
Now we can say that;
total number of voters is equal to sum of Number of Voters for blue color, Number of Voters for green color and Number of Voters for red color.
framing in equation form we get;
[tex]x=\frac58x+\frac{15x}{72}+48[/tex]
Combining like terms we get;
[tex]x-\frac58x-\frac{15x}{72} = 48[/tex]
Now we will make denominators common using LCM we get;
[tex]\frac{72x}{72}-\frac{5x\times9}{8\times9}-\frac{15x\times1}{72\times 1} = 48\\\\\frac{72x}{72}-\frac{45x}{72}-\frac{15x}{72} = 48[/tex]
Now denominators are common so we will solve the numerators we get;
[tex]\frac{72x-45x-15x}{72}=48\\\\\frac{12x}{72}=48\\\\\frac{x}{6}=48[/tex]
Now multiplying both side by 6 we get;
[tex]\frac{1}{6}x\times6=48\times6\\\\x = 288[/tex]
Number of voters for blue color = [tex]\frac{5}{8}x=\frac{5}{8}\times 288= 180[/tex]
Hence There were 180 voters for blue color.
Can anyone answer this question?
It's confusing and i'd like explanation as well!
Answer:
D. 286 deg
Step-by-step explanation:
Think of both triangles as just one single large triangle.
The exterior angles at the bottom have measure 127 deg.
That means the two interior angles at the bottom have measure
180 deg - 127 deg = 53 deg
The measures of the interior angles of triangle add to 180 deg.
The upper interior angle has measure:
180 deg - 53 deg - 53 deg = 74 deg
A full circle has 360 degrees.
Angle r is a full circle minus the upper interior angle of the combined triangle.
r = 360 deg - 74 deg
r = 286 deg
Which equation can be used to solve for x, the side length of the original square? x2 − 2x − 120 = 0 x2 + 2x − 120 = 0 x2 − 2x + 120 = 0 x2 + 2x + 120 = 0
Question:
A square piece of paper has an area of x2 square units. A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper. The remaining piece of paper has an area of 120 square units.
Which equation can be used to solve for x, the side length of the original square?
x2 − 2x − 120 = 0
x2 + 2x − 120 = 0
x2 − 2x + 120 = 0
x2 + 2x + 120 = 0
Answer:
Option a: [tex]x^{2} -2x-120=0[/tex] is the equation
Explanation:
It is given that the area of the square paper is [tex]x^{2}[/tex] square units.
The area of the remaining piece of paper is 120 square units.
It is also given that the area of the remaining piece of paper is [tex]x^{2}-2 x[/tex]
Thus, equating the area of the remaining piece of paper, we have,
[tex]x^{2} -2x=120[/tex]
Subtracting 120 from both sides of the equation, we have,
[tex]x^{2} -2x-120=0[/tex]
Thus, the equation [tex]x^{2} -2x-120=0[/tex] can be used to solve for x.
Hence, Option a is the correct answer.
According to the 2016 study by the Pew research 74 percent of adults American have read at least one book in the past 12 months a sample of 10 adult americans is randomly selected le t x be the randem variable representing the number of people who have read at least on book explain why x is a binomial random variable by filling the blanks below in this problem a trial is------------- the number of trials n=--------------
Answer:
x is a binomial random variable because a trial is independent and number of trials, n = 10.
Step-by-step explanation:
We are given the following information:
We treat adult reading at least one book in the past 12 months as a success.
P(Adult reading atleast one book) = 74% = 0.74
Then the number of adults follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
If x is a random variable representing the number of people who have read at least on book, then x follows a binomial distribution because:
There are n independent trials. Here, n = 10.Each trial have two possible outcome either a success(read atleast one book) or a failure(not read atleast one book)The probability of success is same for each trial. Here p = 0.74Thus,
x is a binomial random variable because a trial is independent and number of trials, n = 10.
Apply the distributive property and the greatest common factor to write an equivalent expression. Enter your answers in the boxes.
Answer:
12 (5x - 2)
Step-by-step explanation:
First to know if we can get a common factor we have to find a number by which it is divisible on 24 and 60
first we will try with 2
60/2 = 30 both are divisible by 2
24 /2 = 12
then we will take common factor 2
60x - 24
we multiply and divide by 2
2 (60x - 24)/2
we distribute the 2
2(60x/2 - 24/2)
and solve
2(30x - 12)
Now we continue with the same procedure until there is no more number in common to divide
we will try with 2
30/2 = 15 both are divisible by 2
12 /2 = 6
then we will take common factor 2
2(30x - 12)
we multiply and divide by 2
2*2 (30x - 12)/2
we distribute the 2
4(30x/2 - 12/2)
and solve
4(15x - 6)
continue with the same procedure
we will try with 2
15/2 = X only one is divisible by 2
6 /2 = 3
we will try with 3
15/3 = 5 both are divisible by 3
6 /3 = 2
then we will take common factor 3
4(15x - 6)
we multiply and divide by 3
4*3 (15x - 6)/3
we distribute the 3
12(30x/3 - 6/3)
and solve
12(5x - 2)
there is no number other than 1 by which we can divide 5 and 2
12(5x - 2)
Suppose you want to determine the distance d that light travels in h hours. The speed of light is approximately 670,616,629 miles per hour. Which direct variation equation represents this situation? d = 670,616,629h h = 670,616,629d
Answer:
[tex]d = 670,616,629h \ mi[/tex]
Step-by-step explanation:
Given:
Speed of the light = 670,616,629 mi\hr
We need to find the direct variation equation represents given situation.
Solution:
Speed is defined as the ratio of distance and time. So, the equation of the speed is as follows:
[tex]Speed = \frac{Distance}{Time}[/tex]
And also written as.
[tex]S = \frac{d}{h}[/tex]
Now, we write the above equation for distance.
[tex]d = S\times h[/tex] ------------(1)
Where:
d = distance travel by object.
S = speed of the object.
h = Total time taken
Substitute S = 670,616,629 mi\hr in equation 1.
[tex]d = 670,616,629h \ mi[/tex]
Therefore, direct variation equation to represents the given situation
[tex]d = 670,616,629h \ mi[/tex]
PLZ HURRY IT'S URGENT!!
Which equation can be used to find the two numbers whose ratio is 4 to 3 and that have a sum of 42?
4x + 3x = 42
34x=42
43x=42
4x−3x=42
Answer:
4x + 3x = 42
Step-by-step explanation:
Point A(-7, - 2) is rotated 270 counterclockwise and then shifted down 3 units.
What are the coordinates of A'?
A. (2,4)
B. (-2,-7)
C. (-2,4)
D. (7,-5)
The coordinates of A' after rotation of 270 counterclockwise and then shifted down 3 units are (2, 4).
To find the coordinates of point A' after a 270-degree counterclockwise rotation around the origin and then shifting down 3 units, we first perform the rotation.
A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. So, when we rotate point A(-7, -2) 90 degrees clockwise, we swap the coordinates and change the sign of the former x-coordinate, which gives us the new point A''(2, 7). Next, we shift A'' down 3 units, which means we subtract 3 from the y-coordinate, resulting in A'(2, 4).
A researcher is gathering data on the 50 states. She wants to actually enter the name of the state into the data matrix as one of the variables in her data set. What type of SPSS variable should that be?
Answer: String variables
Step-by-step explanation:
SPSS means Statistical Package for Social Sciences.
The SPSS has only two variables namely:
1. String variables which includes numbers,letters and other characters.
The string variables cannot perform calculations. It is basically used to type names of people, age,occupation,home addresses,email addresses e.t.c Which is what is what the researcher was trying to do.
2. Numeric variables which include only numbers. It can perform calculations too using mathematical operations like addition,multiplication,division and subtraction.
5. A survey of student pizza preferences showed that 43 students preferred cheese, 56 preferred sausage, 39 preferred pepperoni, 28 preferred supreme, 31 preferred another kind, and 19 did not like any type of pizza. Make your own probability distribution in order to answer the question. Match the probability of each outcome given to the correct outcome.
Answer:
P (Cheese) = 0.199, P (Sausage) = 0.259, P (Pepperoni) = 0.181,
P (Supreme) = 0.130, P (Another Kind) = 0.144
and P (Does not like any kind) = 0.088
Step-by-step explanation:
Given:
Number of students who prefer cheese = 43
Number of students who prefer sausage = 56
Number of students who prefer pepperoni = 39
Number of students who prefer supreme = 28
Number of students who prefer another kind = 31
Number of students who did not like any kind = 19
∴ The total number of students surveyed = [tex]43+56+39+28+31+19=216[/tex] The number of students who prefer pizza = [tex]43+56+39+28+31=197[/tex]
The probability that a students likes pizza is,
[tex]P(Student\ likes\ pizza)=\frac{No.\ of\ students\ who\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{197}{216} \\=0.912[/tex]
The probability that a students does not likes pizza is,
[tex]P(Student\ does\ not\ likes\ pizza)=\frac{No.\ of\ students\ who\ does\ not\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{19}{216} \\=0.088[/tex]
The probability distribution of students who prefer different kinds of pizza is:
The probability that a student likes cheese:[tex]P(A\ Student\ prefers\ cheese)=\frac{No.\ of\ students\ who\ prefer\ cheese}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{43}{216}\\=0.199[/tex]
The probability that a student likes sausage:[tex]P(A\ Student\ prefers\ sausage)=\frac{No.\ of\ students\ who\ prefer\ sausage}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{56}{216}\\=0.259[/tex]
The probability that a student likes pepperoni:[tex]P(A\ Student\ prefers\ pepperoni)=\frac{No.\ of\ students\ who\ prefer\ pepperoni}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{39}{216}\\=0.181[/tex]
The probability that a student likes supreme:[tex]P(A\ Student\ prefers\ supreme)=\frac{No.\ of\ students\ who\ prefer\ supreme}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{28}{216}\\=0.130[/tex]
The probability that a student likes another kind:[tex]P(A\ Student\ prefers\ another\ kind)=\frac{No.\ of\ students\ who\ prefer\ another\ kind}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{31}{216}\\=0.144[/tex]
Thus, the probability distribution table is displayed below:
At And Easter egg hunt there were a total of 4680 eggs hidden the number of real eggs what's 2/3 the number of chocolate eggs how many eggs were chocolate
Answer:
There are 3120 chocolate eggs.
Step-by-step explanation:
We are given the following in the question:
Total number of eggs = 4680
Number f chocolate eggs =
[tex]\dfrac{2}{3}[/tex] the number of real eggs
We have to find the number of chocolate eggs.
Number of chocolate eggs =
[tex]\dfrac{2}{3}\times \text{Total number of eggs}[/tex]
[tex]=\dfrac{2}{3}\times 4680\\\\=3120[/tex]
Thus, there are 3120 chocolate eggs.
Why shouldn't classes overlap when summarizing continuous data in a frequency or relative frequency distribution?
Answer:
Step-by-step explanation:
Why shouldn't classes overlap when one summarizes continuous data? If classes overlap, then some observations will be counted in more than one class. This means that certain observations will end up in more than one bar of a histogram, which will misrepresent the data!
Jenny plans to invest $9,000. America's Bank offers a 10 year CD at an annual interest rate of 3.8% compounding interest semi-annually. How much is her investment worth at the end of the 10 years?
Group of answer choices
$9,000
$13,114
$15,840
$18,000
Answer: $13,114
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 9000
r = 3.8% = 3.8/100 = 0.038
n = 2 because it was compounded 2 times in a year.
t = 10 years
Therefore,.
A = 9000(1+0.038/2)^2 × 10
A = 9000(1+0.019)^20
A = 9000(1.019)^20
A = $13114
The final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B: $13114 approx.
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]
For this case, we are given that:
Initial amount Jenny invested = $9,000 = PThe rate of interest = 3.8% semi annually (0.5 years) = 3.8/2 = 1.9% per 0.5 years = R Thus, unit of time = half yearTime for which investment was made= 10 years = 20 half years =TThus, the final amount at the end of 10 years is given by:
[tex]A = P(1 +\dfrac{1.9}{100})^T\\\\A = 9000(1 + \dfrac{1.9}{100})^{20} = 9000(1.019)^{20} \approx 13114 \text{\: \: (in dollars)}[/tex]
Thus, the final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B: $13114 approx.
Learn more about compound interest here:
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what equivalent expression was used
3y+4y
Answer:
7y²
Step-by-step explanation:
First u group them like 4+3+y+y=7y²
The product of two numbers is 21. If the first number is -3, which equation represents this situation and what is the second number? A. The equation that represents this situation is x − 3 = 21. The second number is 24. B. The equation that represents this situation is 3x = 21. The second number is 7. C. The equation that represents this situation is -3x = 21. The second number is -7. D. The equation that represents this situation is -3 + x = 21. The second number is 18.
Option C
The equation that represents this situation is -3x = 21
The second number is -7
Solution:
The first number is -3
The product of two numbers is 21
Let the second number be "x"
The equation that represents this situation is:
Product of first and second number = 21
[tex]-3 \times x = 21\\\\-3x = 21[/tex]
Thus the equation is found
Solve the equation
-3x = 21
Divide both sides by -3
[tex]x = \frac{21}{-3}\\\\x = -7[/tex]
Thus the second number is -7
Answer:
C.
The equation that represents this situation is -3x = 21. The second number is -7.
Step-by-step explanation:
I just did it and got it right on edmentum/plato
hope this helps good luck
Two of the vertices of a rectangle are (1, -6) and ( -8, -6 ) if the rectangle has a perimeter of 26 units what are the coordinates of it's other vertices?
Answer:
(1, -2)
(-8, -2)
Step-by-step explanation:
(1 , -6) and (-8 , -6)
1 - (-8) = 9
we know that the length of the side that we know the vertices is 9
from there we make an equation with the sum of the sides equal to the perimeter
we will have 2 times 9 and 2 times x beacause it is a rectangle
x + x + 9 +9 = 26
2x + 18 = 26
2x = 26 - 18
2x = 8
x = 8/2
x = 4
Now that we know the missing side we just have to add or subtract this value to the coordinate in and of the vertices we have and we will obtain the missing vertices
(1, -6 + 4)
(1, -2)
( -8, -6+4 )
(-8, -2)
The coordinates of the other two vertices of the rectangle are (1, -2) and (-8, -2), found by calculating the length of one side using the given vertices and then applying the rectangle's perimeter to find the length of the adjacent sides.
Explanation:The subject of the question is to find the other two vertices of a rectangle given two of its vertices and the perimeter. We know that the opposite sides of a rectangle are equal in length. So, to solve this, we can use the distance formula to find the length of one side with the two given points (1, -6) and (-8, -6). The length of this side is the absolute value of the difference in the x-coordinates, which is 9 units. Since the perimeter is 26, and this length is 9, the sum of the lengths of the other two sides is 26 - 2*9 = 8 units. Therefore, each of these sides is 4 units long. Because the given points have the same y-coordinate, they lie on a horizontal side of the rectangle, so the other two vertices will have the same x-coordinates as the given ones and will be 4 units vertically away. If we add and subtract 4 units from the y-coordinate of the given points, we get the other two vertices: (1, -6 +4) and (-8, -6 +4). So the coordinates of the other two vertices are: (1, -2) and (-8, -2).
Jorge soccer team is having its annual fundraiser. The team hopes to earn three times as much as it did last year. The team earned $87. What is the team's goal for this year
Answer:
$261
Step-by-step explanation:
The team hopes to earn three times more than it did last year
Last year the team earned $ 87
We are required to determine the team's goal this year.
Therefore;
Since they hope to raise three times than last year;
Then;
Goal this year = 3 × last year's earnings
= 3 × $ 87
= $261
Therefore, the team's goal this year is $261
Hi, does anyone know how to solve this. If so, please show the working out too. Thanks.
See the explanation
Explanation:I have corrected your diagram so ∅ is the angle at the top of the diagram. In order to solve this problem we have to use Pythagorean theorem and the law of sines. Moreover, I have named two sides as w and z so those variables will help us to solve this problem. So:
The triangle at the bottom is right, so by Pythagorean theorem is true that:
[tex]w^2=4^2+(2\sqrt{2})^2 \\ \\ w^2=24 \\ \\ w=\sqrt{24} \\ \\ w=2\sqrt{6}[/tex]
By law of sines:
[tex]\frac{z}{sin\theta}=\frac{w}{sin60^{\circ}} \\ \\ z=\frac{wsin\theta}{sin60^{\circ}} \\ \\ z=\frac{2\sqrt{6}sin\theta}{\sqrt{3}/2} \\ \\ z=4\sqrt{2}sin\theta[/tex]
By law of sines again:
[tex]\frac{y}{sin45^{\circ}}=\frac{z}{sin\phi} \\ \\ y=\frac{zsin45^{\circ}}{sin\phi} \\ \\ y=\frac{4\sqrt{2}sin\theta \sqrt{2}/2}{sin\phi} \\ \\ \\ Finally: \\ \\ \boxed{y=\frac{4sin\theta}{sin\phi}}[/tex]
Learn more:Classification of triangles: https://brainly.com/question/10379190
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Circles M and K are congruent, segment QR is congruent to arc LN . Find the length of segment QR .
Answer:
26/3 or 8.67
Step-by-step explanation:
Arc lengths are congruent and the radii are the same implies angle at the centre is also equal,
Hence length of the chords are equal too
4x+2 = x+7
3x = 5
x = 5/3 or 1.67
Length of QR = 4x+2
= 4(5/3) +2
= 20/3 + 2
= 26/3 = 8.67
Answer:
8.67
Step-by-step explanation:
La patinoar au venit dimineața 136 de copii, iar după-amiază de 3 ori mai mulți. Câți bani s-au încasat pe biletele vândute, dacă un bilet de intrare costă 15 lei?
Answer:
8,160 lei
Step-by-step explanation:
The question in English is
136 children came to the ice rink in the morning, and three times in the afternoon. How much money was collected on the tickets sold, if an entrance ticket costs 15 lei?
step 1
Find the total number of children that came to the ice rink
we know that
The number of children that came to the ice rink in the morning was 136
The number of children that came to the ice rink in the afternoon was (136*3)=408
To find out the total number of children that came to the ice rink , adds the number of children that came in the morning plus the number of children that came in the afternoon
so
[tex]136+408=544\ children[/tex]
step 2
To find out the total money collected, multiply the total number of children by the cost of one ticket entrance
so
[tex]544(15)=8,160\ lei[/tex]
Travel Ez sells dollars at a rate of ($1.40)/(1 euro) and buys dollars at a rate of ($1.80)/(1 euro). At the beginning of a trip, Sophie exchanged $540 to get 300 euros. At the end of the trip she is left with 40 euros, so she exchanges the 40 euros back to dollars. How many dollars will Sophie get in exchange?
a. $72.
b. $22.
c. $56.
d. $28.
Answer:
C
Step-by-step explanation:
In the first instance, he wanted buying euros in exchange for his dollars. He had $540 and wanted to buy euros. The conversion factor here is that for every 1 euro, he pays $1.80
Now at the second instance, he wanted buying dollars with his left over euros. This means for every 1 euro, he gets $1.4
Since, he is having 40 euros, the total amount in dollars he would get will be 40 * $1.4 = $56
How do you do this on the calculator?
Answer:
B) -3.464
Step-by-step explanation:
∫₀³ g'(x) cos²(2g(x) + 1) dx
Using u substitution:
u = 2g(x) + 1
du = 2g'(x) dx
½ du = g'(x) dx
When x = 0, u = 11.
When x = 3, u = -3.
½ ∫₁₁⁻³ cos²(u) du
You can use a calculator to solve this, or you can evaluate algebraically.
Use power reduction formula:
½ ∫ (½ + ½ cos(2u)) du
¼ ∫ du + ¼ ∫ cos(2u) du
¼ ∫ du + ⅛ ∫ 2 cos(2u) du
¼ u + ⅛ sin(2u) + C
Evaluating from u = 11 to u = -3:
[¼ (-3) + ⅛ sin(-6) + C] − [¼ (11) + ⅛ sin(22) + C]
-⁷/₂ + ⅛ sin(-6) − ⅛ sin(22)
−3.464
Liam opened a savings account with a $400
deposit and a simple interest rate of 7.5%. If
the balance of the account is now $670 and
there were no deposits or withdrawls, how
long ago did he open the account
Answer: he open the account 9 years ago.
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount deposited.
P represents the principal or amount deposited.
R represents interest rate
T represents the time for which the amount deposited was left in the account.
From the information given,
P = 400
R = 7.5%
I = 670 - 400 = $270
Therefore,
270 = (400 × 7.5 × T)/100 = 30T
T = 270/30
T = 9 years
Step-by-step explanation:
9 years thank you yw bubye
Scientists are studying hurricanes to determine the number of hurricanes in the past 50 years that have caused greater than $1 million in damages. Which best describes the population?
Answer:
Hurricanes
Step-by-step explanation:
We are given the following in the question:
Scientists are studying hurricanes to determine the number of hurricanes in the past 50 years that have caused greater than $1 million in damages.
Population:
It is the collection of all possible values of the variable of interest or individual of interest.The population is always greater than sample.A sample is a subset of population.Thus, for the given scenario
Population of interest:
Hurricanes
From this population a sample of hurricanes that have caused greater than $1 million in damages is taken.
Answer:
A)Hurricanes
Step-by-step explanation:
Write the equation of the function.
is it y = x2 / 6 - 3x /2 + 13/3 ?
Yo sup??
Since there is an x^2 term therefore this equation is of a parabola
By taking LCM and then cross multiplying it.
6y=x^2-9x+26
6y=x^2-9x+(9/2)^2+23/4
6y-23/4=(x-9/2)^2
we see that this is of the form
X^2=4AY
(x-9/2)^2=4(3y/2-23/16)
Hope this helps.
Answer:
[tex]f(x) =- \sqrt{x-1}+3[/tex]
Step-by-step explanation:
This looks like a square root function [tex]f(x) = \sqrt{x}[/tex] but symmetric with respect to the x axis and shifted to the right for 1 and up for 3:
Lets take [tex]f(x) = \sqrt{x}[/tex] . The function symmetric with respect to the x axis would be [tex]-f(x)[/tex], so now we have:
[tex]f(x) = -\sqrt{x}[/tex]
Lets take [tex]f(x) = -\sqrt{x}[/tex] and shift it up for y = 3. Now we have:
[tex]f(x) =- \sqrt{x}+3[/tex]
Lets take [tex]f(x) = -\sqrt{x}+3[/tex] and shift it right for x = 1. That means that instead of x we will have x-1:
[tex]f(x) =- \sqrt{x-1}+3[/tex]
if the number of students at a particular High School who participate in after-school drama programs increases at a rate of 8% per year, how long will it take for the number of students participating in the after-school programs to double?
a. about 25 years
b. about 12.5 years
c. about 3.6 years
d. about 9 years
Answer:
d. about 9 years
Step-by-step explanation:
There is a "rule of thumb" for doubling time* that says the product of the percentage rate of change per year and the doubling time in years is about 72. Here, that means the doubling time is about ...
72/8 = 9 . . . . years
_____
You can write the exponential equation ...
multiplier = (1 +.08)^n
and solve for multiplier = 2:
2 = 1.08^n
log(2) = n·log(1.08) . . . . . take logs
log(2)/log(1.08) = n . . . . . divide by the coefficient of n
9.00647 ≈ n
It will take about 9 years for the participation to double.
_____
* The farther away from 8% the rate of change is, or the more times per year it is compounded, the less accurate is the "rule of 72." When compounding is continuous, the "rule of 72" becomes the "rule of 69.4". For this problem, answer choices are sufficiently far apart that the rule of thumb is adequate for making a correct choice.
At a car dealership, there are three times as many sedans as SUVs. If there are a combined 24 sedans and SUVs, how many sedans are there at the dealership?
Answer:
There are 18 Sedans in the dealership shop.
Step-by-step explanation:
Let x represent the number of Sedans in the dealership shop.
Let y represent the number of SUV's in the dealership shop.
If there are a combined 24 sedans and SUVs, it means that
x + y = 24 - - - - - - - - - - - -1
At a car dealership, there are three times as many sedans as SUVs. This means that
x = 3y
Substituting x = 3y into equation 1, it becomes
3y + y = 24
4y = 24
y = 24/4 = 6
x = 3y = 6 × 3
x = 18