ok, If she did not initially have anything on the account, this is the process
[tex]\begin{gathered} +35 \\ -12.5 \\ -35 \\ -12.50 \\ -35 \\ +12.50 \\ -------- \\ -47.50 \end{gathered}[/tex]his bank account is at -47.50 dollars
You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You neverwithdraw money from the account. How much money will be in the account after 4 years?
The formula to calculate the amount for compound interest is given to be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
From the question provided, we have the following parameters:
[tex]\begin{gathered} P=2000 \\ r=5\%=0.05 \\ n=1(annual\text{ }compounding) \\ t=4 \end{gathered}[/tex]Therefore, we can solve as follows:
[tex]\begin{gathered} A=2000(1+\frac{0.05}{1})^{1\times4}=2000(1.05)^4 \\ A=2431.01 \end{gathered}[/tex]The amount after 4 years is $2,431.01.
Huilan is 8 years younger than Thomas. The sum of their ages is 76. What is Thomas's age?
Let H denote the age of Hullan.
Let T denote the age of Thomas.
Huilan is 8 years younger than Thomas
Mathematically,
[tex]H=T-8\qquad eq.1[/tex]The sum of their ages is 76.
Mathematically,
[tex]H+T=76\qquad eq.2[/tex]Now let us substitute eq. 1 into eq. 2
[tex]\begin{gathered} H+T=76 \\ (T-8)+T=76 \\ T-8+T=76 \\ 2T-8=76 \\ 2T=76+8 \\ 2T=84 \\ T=\frac{84}{2} \\ T=42 \end{gathered}[/tex]Therefore, the age of Thomas is 42 years.
given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=590(1.061)^x
Given the exponential function:
[tex]y=590(1.061)^x[/tex]Let's determine if the exponential function represents growth or decay.
Take the exponential function:
[tex]y=a(b)^x[/tex]Where b is the base.
• If the base of an exponential function is greater than one, the exponential function represents growth
• If the base of an exponential function is between 0 and 1, the function represents a decay function.
Here, the base of the exponential function, b is 1.061 which is greater than 1, the function represents a growth function.
SInce it is represents a growth function, let's determine the percentage rate of increase.
The general formula for exponential growth is:
[tex]y=a(1+r)^x[/tex]Where r is the growth rate.
Thus, we have:
[tex]\begin{gathered} y=590(1+(1-1.061)^x \\ \\ y=590(1+0.061)^x \end{gathered}[/tex]The growth rate, r is = 0.061
The percentage rate of increase is:
[tex]\text{percentage rate of increase = }0.061\ast100=6.1\text{\%}[/tex]Therefore, the percentage rate of increase is 6.1%
ANSWER:
The function represents growth
Percentage rate of increase = 6.1%
In the figure below, pentagon RSTYZ is a regular polygon and m/RST = 108⁰.If m/UTY = 115°, what is m/STU?A137°OB. 223°OC. 108°OD. 115°
ANSWER
[tex]223[/tex]Option B
EXPLANATION
Given;
[tex]\begin{gathered} m\angle RST=108⁰. \\ m\angle UTY=115° \end{gathered}[/tex]Note that the pentagon is a regular polygon (all the angles are equal).
Hence;
[tex]m\angle RST=m\angle STY=108[/tex]The measure of angle STU is;
[tex]\angle STU=\angle STY+\angle UTY[/tex]Hence, substitute the values of the angles;
[tex]\begin{gathered} \operatorname{\angle}STU=\operatorname{\angle}STY+\operatorname{\angle}UTY \\ =108+115 \\ =223 \end{gathered}[/tex]Therefore, the measure of angle STU is 223 degrees
The graph shows the projections in total enrollment at degree granting institutions from Fall 2003 to Fall2012The linear model, y= .2145x + 15.79, provides the approximate enrollment, in millions, between the years 2003 and 2012,to 2004, and so on, and y is in millions of students(a) Use the model to determine projected enrollment for Fall 2008.The projected enrollment for Fall 2008 is 16.9 millions. This is answered. (Type an integer or decimal rounded to the nearest tenth as needed.)(b) Use the model to determine the year in which enrollment is projected to reach 17 million.(Round down to the nearest year)2008. This is answered(c) they are quite close. This is answered. This is the one i need help with part D.(d) The enrollment in Fall 1993 was 14.3 million. The model here is based on data from 2003 to 2012. If you were to use the model for 1993, what would the enrollment be?
Solution
We are given the relation
[tex]y=0.2145x+15.79[/tex]Need ASAP, explanation if you can :)
The probability of the complement of event E is 0.56,
How to find the probability?For any event A, we define the complement of A as:
[tex]A^c[/tex]
Where the complement refers to all the elements in the sample space that are not A, and the relation between the probabilities is:
P([tex]A^c[/tex]) = 1 - P(A).
In this case, we have an event E and we know that:
P(E) = 0.44
Then the probability of the complement will be:
P([tex]E^c[/tex]) = 1 - P(E) = 1 - 0.44 = 0.56
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A dog breeder has 14 puppies for sale, of which 7 are yellow Labrador retrievers. If 2 puppies are selected at random,
determine the probability they are all yellow Labrador retrievers. Assume that selection is to be done without
replacement.
Set up the problem as if it were to be solved, but do not solve.
P(2 yellow Labradors selected) =
The total probability that 2 randomly selected dogs are yellow Labradors without replacement is 3/13.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.So, the probability that the randomly selected dogs are yellow Labradors:
Probability formula: P(E) = Favourable events/Total eventsProbability in 1st selection:
P(E) = Favourable events/Total eventsP(E) = 7/14P(E) = 1/2Probability in 2nd selection: Without replacement
P(E) = Favourable events/Total eventsP(E) = 6/13Total Probability: 1/2 × 6/13 = 6/26 ⇒ 3/13
Therefore, the total probability that 2 randomly selected dogs are yellow Labradors without replacement is 3/13.
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PLEASE ANSWER QUICK I WILL GIVE BRAINLIEST IF ITS RIGHT
Step-by-step explanation:
try this option, all the details are in the attachment.
Help needed! please help math
Answer:
4.163 × 10^7
Step-by-step explanation:
The step by step explanation is in the image attached
hope this helps!!
I dont understand what to do for this I have 5 questions of this and I dont understand how to do this please help me!
1) Whenever we're asked to find out something of like 1/7 of 35 we must proceed with a multiplication. This way:
2)
[tex]\frac{1}{7}\times35=\frac{35}{7}\text{ = 5}[/tex]3) Hence, the answer is 5
The markdown of a bicycle is Php1500.00 which is 20% of the original selling price. Find (a) the original selling price and (b) the new selling price.
Given:
The markdown of a bicycle = $1500
Which is 20% of the original selling price
Let the original selling price = x
so, 20% of x = 1500
so,
[tex]\begin{gathered} \frac{20}{100}\cdot x=1500 \\ \\ x=\frac{1500\cdot100}{20}=7500 \end{gathered}[/tex]so, the answer will be:
a) the original selling price = $7,500
b) the new selling price = 7500 - 1500 = $6,000
(05.01 MC)A store sells cooking oil of two different brands in bottles of the same size. The table below and the equation each show the price (y), in dollars, of different number of bottles of oil (x):Brand ANumber of Bottles, x Price (dollars), y2 243 364 485 60Brand By = 15xHow many dollars more is the price of 9 bottles of brand B oil than the price of 9 bottles of brand A oil? (5 points)1. $32. $93. $184. $27
Solution
Step by step explanation:
Using the data, we can calculate the price per bottle for Brand A, which is:
24 / 2
= $12 per bottle
We also know that the slope of a line shows the rate of change, so the price per bottle for Brand B is $15.
The difference per bottle is 15 - 12 = Brand B is cost $3 more per bottle
The difference for 9 bottles will be: 9 * 3 = $27.
Therefore the answer will be $27
About how many times greater is the area ofthe Pacific Ocean than the Atlantic Ocean?Ocean Area (square kilometers)Pacific161.8 × 106Atlantic85,133,000
Given:
Area of Pacific ocean = 161.8 12 x 10⁶ square kilometers
Area of Atlantic ocean = 85133000 square kilometers
Let's find how many times greater is the area of the pacific ocean than the Atlantic ocean.
To find how many times greater, divide the area of the Pacific ocean by the area of the Atlantic ocean.
Thus, we have:
[tex]\begin{gathered} \frac{161.8\times10^6}{85133000} \\ \\ =\frac{161.8\times10^6}{85.133\times10^6} \\ \\ =1.9 \end{gathered}[/tex]Therefore, the area of the Pacific ocean is 1.9 times greater than the area of the Atlantic ocean.
ANSWER:
1.9 times
i need help with figures and dilations
What are the coordinates of the point on the directed line segment from (-9, 2) to
(5,-10) that partitions the segment into a ratio of 1 to 3?
[1.5, 4] are the coordinates that divide the section into a 3 to 1 ratio.
Using a 3:1 partitioning ratio
#Multiply the ratio by the length of the x-coordinate:
5 + 9 = 14;
1/4 of 14 is 3.5;
we take this value out of the x-max to get the point, which is 5 - 3.5 = 1.5.
#Multiply the ratio by the length of the y-coordinate:
We subtract -2 from the y-max to obtain the point,
which is equal to 2 + 2 = 4.
x length -10 + 2
=> 1/4 x -8 = - 2
Consequently, [1.5, 4] are the coordinates that divide the section into a 3 to 1 ratio.
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Proving the Congruent Supplements Theorem
Given <1 and <2 are suplements
By using the supplementary relations and the fact that angle 2 is congruent to angle 3, we will get that:
∠1 ≈ ∠4
How to prove this?Here we know that:
∠1 and ∠2 are supplements.∠3 and ∠4 are supplements.∠2 ≈ ∠3With the first two, we can write the equations:
∠1 + ∠2 = 180°
∠3 + ∠4 = 180°
Both equations have the same value in the right, then we can write:
∠1 + ∠2 = ∠3 + ∠4
Now, we know that ∠2 ≈ ∠3, then we can rewrite the equation as:
∠1 + ∠2 = ∠3 + ∠4
∠1 + ∠2 - ∠3 = ∠4
And ∠2 - ∠3 ≈ 0, then:
∠1 + ∠2 - ∠3 = ∠4
∠1 + 0 ≈ ∠4
∠1 ≈ ∠4
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How many solution does 19x=5x have?
Answer:
it doesn't have a solution
Step-by-step explanation:
Simplify the expression (x¹2)3.
Answer:
3x¹²
Step-by-step explanation:
1. Rule (x) = x
2. (x¹²) = x¹²
3. x¹²*3
4. 3x¹²
Did you get the same sum for both sets of angle measurements? What do you think that means? Create an equation to represent the situation.
If we know the measure of two of the three angles of a triangle, since the sum of the angles in a triangle aways is 180º, we can write the equation for angles a, b and c:
[tex]\begin{gathered} m\angle a=x \\ m\angle b=y \\ m\angle c=z \\ \text{Then,} \\ 180º=x+y+z \end{gathered}[/tex]Let's suppose we know x and y, then z is:
[tex]z=180º-x-y[/tex]what is 1,988 times 130
5,9460.
1) Let's multiply 1988 by 30:
Notice that we multiplied the units, 0 x 1988 and then 3 x 1988 and then we added both numbers.
2) Hence, 1,988x 30 is equal to 5,9460.
The function describes the spread of a rumor among a group of people in an enclosed space. N represents the number of people who have heard the rumor, and t is measured in minutes since the rumor was started. Which of the following statements are true?Check all that apply.A.There are 299 people in the enclosed space.B.The rumor spreads at a constant rate of 0.36 people per minute.C.It will take approximately 14 minutes for 100 people to hear the rumor.D.Initially, only one person had heard the rumor.
The statements which are true about this exponential function include the following:
C. It will take approximately 14 minutes for 100 people to hear the rumor.
D. Initially, only one person had heard the rumor.
What is an exponential function?Mathematically, an exponential function can be modeled by using this equation:
f(x) = abˣ
Where:
a represents the initial value.b represents the rate of change.At the initial time (t₀), the value of t₀ is zero (0) and the number of people who heard the rumor is given by:
N(t) = 300/(1 + 299e^{-0.36t})
Substituting the initial time (t₀) into this exponential function, we have;
N(t₀) = 300/(1 + 299e^{-0.36t₀})
N(0) = 300/(1 + 299e^{-0.36 × 0})
N(0) = 300/(1 + 299e^{0})
N(0) = 300/(1 + 299)
N(0) = 300/300
N(0) = 1 person.
At t = 14, the number of people who heard the rumor is given by:
N(t₁₄) = 300/(1 + 299e^{-0.36t₁₄})
N(14) = 300/(1 + 299e^{-0.36 × 14})
N(14) = 300/(1 + 299e^{-5.04})
N(14) = 300/(1 + 299(0.00647374831))
N(14) = 100 people.
In conclusion, there are 300 people in the enclosed space rather than 299 people.
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Coordinate of point x on the coordinate plane for each situation
The horizontal distance between points A and B is:
[tex]x_B-x_A=2-(-5)=7[/tex]1/5 of this distance is:
[tex]\frac{1}{5}\cdot7=\frac{7}{5}[/tex]Then, the x-coordinate of point X is:
[tex]x_X=x_A+\frac{7}{5}=-5+\frac{7}{5}=-3.6[/tex]The vertical distance between points A and B is:
[tex]y_B-y_A=9-(-5)=14[/tex]1/5 of this distance is:
[tex]\frac{1}{5}\cdot14=\frac{14}{5}[/tex]Then, the y-coordinate of point X is:
[tex]y_X=y_A+\frac{14}{5}=-5+\frac{14}{5}=-2.2[/tex]Finally, the coordinates of X are (-3.6, -2.2)
Use the compound interest formulas A=P(1+r/n)^nt and A=Pe^rt to solve. Find the accumulated value of $20,000 for 5 years at an interest rate of 6.5% if the money is compounded monthly. What is the accumulated value if the money is compounded monthly?
Given: An investment of $20000 for 5 years at an interest rate of 6.5%.
Required: To determine the accumulated value if the money is compounded monthly.
Explanation: The formula for compound interest is as follows-
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here, n=12 as the money is compounded monthly in a year. Also
[tex]\begin{gathered} P=20000 \\ t=5 \\ r=\frac{6.5}{100} \\ =0.065 \end{gathered}[/tex]Substituting the values into the formula as-
[tex]A=20000(1+\frac{0.065}{12})^{12\times5}[/tex]Further solving-
[tex]A=27,656.35[/tex]Final Answer: The accumulated value is $27,656.35
For f(2)=2-2, which gives an output of 4B?O f(-8)of()O f(4)Of(8)
For f(x)= x ^3 - x ^2 , which gives an output of 48?
_____________________
replace values directly in the expression
x ^3 - x ^2
f(2)= 2 ^3 - 2 ^2
______________________________________
f(-8) = -572
f(-4) = -80
f(4) = 48
f(8) = 448
____________________________
Answer f(4) = 48
7. The relationship between the latitude Lof a city in the Northern Hemisphere and its average annual temperature Tis modeled by the function T = -0.68L + 89.5. The slope of this linear function means (A) That temperature at the equator would be 89.5°. (B) For every degree increase in latitude, the average annual temperature increases by 89.5º. (C) For every degree increase in latitude, the average annual temperature increases by 0.68 (D) For every degree increase in latitude the average annual temperature decreases by 0.68º.
We are given the following function that models the temperature T as a function of the latitude L:
T = - 0.68 L + 89.5
We see that the temperature is in fact a linear function of slope -0.68 degrees/latitude.
Since the latitude of the Equator is 0 degrees, then, the equation tells us that the temperature at the Equator is:
T = - 0.68 (0) + 89.5 = 89.5 degrees of annual temperature. But this is NOT related to the slope.
The other two statements (B and C) are not correct,
The last statement D is correct, since for every degree increase in latitude, there is an annual decrease of temperature by 0.68 degrees, and this is what the slope expresses.
Please select answer D.
Exit Ticket in the triangles below, name all corresponding parts AND find "y. A ABD ACDB. Find y. A 7 y B D 3y + 20 C С tudents, write your response! Pear Deck In
Given that triangle ABD= traingle CDB then;
side AB= DC and
side AD = BC
thus equate side AB and DC as;
7y =3y +20
collect like terms as;
7y-3y = 20
4y = 20
y= 20/4 = 5
Find the probability of getting two or more heads.
Answer:
Step-by-step explanation: 0.50+0.25=0.75
so your answer would be 1/4 of a probability
if you borrow 500 dollars for 4 years at a 6 percent intrest rate how musch will you pay all together
Altogether, you will pay $631.24 if the interest is compounded at the end of every year for 4 years or $620 if it is based on simple interest.
What is the difference between compound interest and simple interest?Compound interest accumulates the interest and adds it to the principal for calculating subsequent interest.
On the other hand, simple interest does not accumulate the interest to add to the principal before computing the next year's.
N (# of periods) = 4 years
I/Y (Interest per year) = 6%
PV (Present Value) = $500
PMT (Periodic Payment) = $0
Results:
FV = $631.24
Total Interest = $131.24
Simple interest = $120 ($500 x 6% x 4)
Future value at simple interest = $620 ($500 + $120)
Thus, depending on how interest is calculated, you will repay between $620 and $631.24.
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11
Determine if the lines are parallel, perpendicular, or neither
y = 5 and y = -1
Parallel
Perpendicular
Neither
Answer:
its parallel
Step-by-step explanation:
because it is
given triangle ABC with C= 90 degree is given and B = 30 degree, then we have to calculate the value of sin 30 degree
Answer:
do you have picture if the question so I can help I
