An increasing exponential function is modeled as follows:
A(t) = A(0)(1 + r)^t.
The parameters of the exponential function are given as follows:
A(0) is the initial value of the exponential function.r is the growth rate of the exponential function, as a decimal.She borrows 12,000 at 12% annual percentage rate, hence the initial value and the growth rate are given as follows:
A(0) = 12,000, r = 0.12.
Then the function that describes her loan is given as follows:
A(t) = 12000(1.12)^t.
After six years, the value of the loan is calculated as follows:
A(6) = 12000(1.12)^6 = $23,686.
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Aniyah invests $2300 in one account and $1400 in an account paying 4 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest
The rate of interest in one account whose investment is $2300 will be 3.21%.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Aniyah puts $2300 in one record and $1400 in a record paying 4 % higher interest. Toward the finish of one year, she had procured $130 in interest.
Let 'x' be the interest. Then the equation is given as,
(2300 × x × 1)/100 + (1400 × 4 × 1) / 100 = 130
Simplify the equation, then we have
23x + 56 = 130
23x = 74
x = 3.21%
The pace of revenue in one record whose speculation is $2300 will be 3.21%.
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Need help with this equation and graphing table asap!! Look at the image
first 2;
a) 7(2) + 8 = 22 > 16, 7(4) + 8 = 36>32
36 - 22 = 14/2 = 7
32 - 16 = 16/2 = 8
7<8
the table has a greater rate of change
y intercept
equation; 8
table; 0
8> 0
the equation has a greater y intercept
Please help me with this question!
Answer:
Step-by-step explanation:
the answer is 11/12
Cora plans to buy some calligraphy pens priced at $5 each. Write an equation that shows how the total cost, y, depends on the number of calligraphy pens Cora buys, x. Do not include dollar signs in the equation.
Answer: y = 5x
Step-by-step explanation:
Find x in the equation. 4 times x plus one half equals one half times x plus 4
After solving the equation, the value obtained for x will be equal to 1.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the information given in the question,
4 times x plus one-half equals one-half times x plus 4.
Let's write it in mathematical form,
4x + 1/2 = 1/2x + 4
Now, solve the equation for x,
4x - 1/2x = 4 - 1/2
(8x - x)/2 = (8 - 1)/2
7x/2 = 7/2
x = (7 × 2)/(2 × 7)
x = 14/14
x = 1
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Ms. Hall is buying Ms. Ward some gifts for Christmas. She is buying one big gift that
will cost $90 as well as some small gifts that cost $7 each.
1+90 +7
What is its :
Constant:
Coefficient
Equation:
When Ms. Hall is buying Ms. Ward some gifts for Christmas as described in the problem,
the Constant: $90 and $7
the Coefficient: $7
the Equation: $90 + $7x
How to find the constantInformation form the problem shows that
one big gift that will cost $90
some small gifts that cost $7 each
the constant in this case is the price of the gifts
$90 and $7
the coefficient is $7
the equation is
$90 + $7x
where x is the number of the small gifts
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Fátima, Gabriel y José tienen un total de $1080 en sus carteras. Gabriel tiene 3 veces lo que José tiene. Fátima tiene $70 menos
que José. ¿Cuanto dinero tienen en sus carteras?
Fátima tiene un total de $ 160, Gabriel tiene un total de $ 690 y José tiene un total de $ 230.
¿Cómo determinar el dinero requerido en sus carteras?
En este problema tenemos a tres personas, Fátima, Gabriel y José, que reúnen un total de $ 1.080. A continuación, traducimos las variables y ecuaciones asociadas a la situación:
x - Cantidad de dinero de Fátima.
y - Cantidad de dinero de Gabriel.
z - Cantidad de dinero de José.
Ecuaciones: Fátima, Gabriel y José tienen un total de $ 1080.
x + y + z = 1080
Gabriel tiene 3 veces lo que José tiene.
y = 3 · z
Fátima tiene $ 70 menos que José.
x = z - 70
A continuación, resolvemos el sistema de ecuaciones lineales:
x + y + z = 1080
(z - 70) + 3 · z + z = 1080
5 · z - 70 = 1080
5 · z = 1150
z = 1150 / 5
z = 230
x = z - 70
x = 230 - 70
x = 160
y = 3 · z
y = 3 · 230
y = 690
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Elevation (meters) -2 , 2 , -4 which is higher ???
Answer:
2
Step-by-step explanation:
-2 and -4 are less than 0
2 is greater than
If you write down in descending order ===> 2, -2 , -4
What is the smallest prime number that is the sum of two other distinct prime numbers?
Answer:
5
Step-by-step explanation:
2 +3 = 5
Jill made a popcorn container that is shaped like a cone. The diameter of the opening is 8 inches and the height is 9 inches. What is the volume of the popcorn container? Leave answer alone, do not round.
in a hypothetical case-control study of female participants regarding exposure to emf's and breast cancer, the following data were obtained: 11 cases exposed, 108 controls exposed, 5 cases not exposed, 436 controls not exposed. what is the odds ratio for the association between exposure to emf's and breast cancer?
The odds ratio for the association between exposure to emf's and breast cancer would be (11/5) / (108/436) = 2.2.
1. Calculate the odds of exposure for cases: 11/5 = 2.2
2. Calculate the odds of exposure for controls: 108/436 = 0.25
3. Divide the odds of exposure for cases by the odds of exposure for controls: 2.2/0.25 = 8.8
4. Finally, the odds ratio for the association between exposure to EMF's and breast cancer is 2.2.
The odds ratio for the association between exposure to EMF's and breast cancer can be calculated by dividing the odds of exposure for cases by the odds of exposure for controls. To calculate this, first take the number of cases exposed (11) and divide it by the number of cases not exposed (5). This will give the odds of exposure for cases (2.2). Second, take the number of controls exposed (108) and divide it by the number of controls not exposed (436). This will give the odds of exposure for controls (0.25). Finally, divide the odds of exposure for cases (2.2) by the odds of exposure for controls (0.25). This will give the odds ratio for the association between exposure to EMF's and breast cancer (2.2).
Odds ratio = (11/5) / (108/436) = 2.2
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a line passes through point (1, 6) and has a slope of 2. what is the y-intercept?
A line passes through point (1, 6) and has a slope is y=8x-14 We want to write the equation of the line that passes through (1, -6) and has a slope of 8 in slope-intercept form
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
As we are already given the slope (8), we can immediately plug that into the equation
So far, the equation of the line is:
y=8x+b
Now we need to find b
The line passes through the point (1, -6), which means that the point is a solution to the equation; when plugged into the equation, it'll create a true statement. This can help us find unknown variables, like b
Substitute 1 as x and -6 as y in the equation to solve for b
-6=8(1)+b
Multiply
-6=8+b
Subtract 8 from both sides
-14=b
Substitute -14 as b into the equation
y=8x-14
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(x-14)÷7=12 I just need help
Answer:
x = 98
Step-by-step explanation:
Solve for x:
(x - 14)/7 = 12
Multiply both sides of (x - 14)/7 = 12 by 7:
(7 (x - 14))/7 = 7×12
(7 (x - 14))/7 = 7/7×(x - 14) = x - 14:
x - 14 = 7×12
7×12 = 84:
x - 14 = 84
Add 14 to both sides:
x + (14 - 14) = 14 + 84
14 - 14 = 0:
x = 84 + 14
84 + 14 = 98:
Answer: x = 98
∠Cis a right angle and AB=14 miles, determine the length of BC and AC.
The length of BC is approximately 5.72 miles and the length of AC is approximately 12.67 miles.
Let's represent the length of the side opposite angle A "BC" and the length of the side adjacent to angle A "AC". We can then use the sine function to find BC:
sin(A) = BC / AC
Substituting the given values, we get:
sin(24°) = BC / 14
We can use a calculator or look up the value of sin(24°) to get:
sin(24°) ≈ 0.406
Solving for BC, we get:
BC = 14 * sin(24°) ≈ 5.72
To find AC, we can use the cosine function:
cos(A) = AC / AC
Substituting the given values, we get:
cos(24°) = AC / 14
We can use a calculator or look up the value of cos(24°) to get:
cos(24°) ≈ 0.913
Solving for AC, we get:
AC = 14 x cos(24°) ≈ 12.67
Thus, BC is about 5.72 miles long while AC is about 12.67 miles in length.
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help i need perimeter of these
Answer: A= 52cm B= 94mm C= 9m D= 17cm
Step-by-step explanation:
A) You first need to find the missing sides by doing
11-9= 2
and 15-9= 6
you then add it all together
6+2+9+9+15+11=52cm
B) You first need to find the missing sides by doing
25-18=7
and 22-6= 16
you then add it all together
25+22+18+16+7+6=94mm
C) You first need to find the missing sides by doing
0.5+1=1.5 then 2.5-1.5=1
and 1.2+0.8=2 then 2-0.5=1.5
you then add the numbers all together
1+1.5+0.8+1+0.5+0.5+1.2+2.5=9m
D) You first need to find the missing sides by doing
2.5+1= 3.5 then 3.5-2=1.5
and 1.5+2.5=4 then 5-4=1
you then add all the numbers together
2.5+2.5+1.5+1+5+2+1+1.5=17cm
Type the correct answer in each box. Use numerals instead of words. If necessary, round to the nearest hundredth.
The relationship between the values of two different currencies is modeled by a linear function that varies depending on the current value of each currency. The table shows the relationship between an amount in U.S. dollars, x, and the equivalent amount in euros, f(x), where f(x) = x/1.06.
The inverse function is given by f⁻¹(x) = 1.06x. 2 euros is equivalent to 2.12 U.S. dollars. 4 euros is equivalent to 4.24 U.S. dollars
How to find the inverse function?Given that: the two different currencies is modeled by a linear function f(x) = x/1.06
where, x = an amount in U.S. dollars and f(x) = the equivalent amount in euros
To find the inverse function f⁻¹(x). Let y = f(x):
y = x/1.06
x = 1.06y
Since x = f⁻¹(y) = 1.06y
Thus, f⁻¹(x) = 1.06x
Note: f⁻¹(x) will help you convert from euros to dollar
2 euros to dollars will be:
f⁻¹(x) = 1.06x
f⁻¹(2) = 1.06(2) = 2.12
Thus, 2 euros is equivalent to 2.12 U.S. dollars
4 euros to dollars will be:
f⁻¹(x) = 1.06x
f⁻¹(4) = 1.06(4) = 4.24
Thus, 4 euros is equivalent to 4.24U.S. dollars
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Billy pulled a number of colored marbles from a large bag. green 1 orange 4 red 1 yellow 9 white 3 Based on experimental probability, how many of the next 20 marbles selected should you expect to be yellow marbles?
The likelihood that the next 20 marbles picked will be yellow marbles is 9/20.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
The probability that of the next 20 marbles selected it is expect to be yellow marbles,
=9/20
The probability that of the next 20 marbles selected it is expect to be yellow marbles will be 9/20.
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Answer:
the answer is 10
Step-by-step explanation:
ixl says its ten
The equation 4(2x 1) = 6x − 12 models the change in water level in a lake in one month. solve for x, which is change in height in inches. x equals negative thirteen halves x = −8 x = 8 x equals eleven halves
From the given options, option 2. x= -8 is the correct option. Here, the x is change in height in inches so the, change in height is -8 inches.
A linear equation is simply an equation with the highest degree always being 1. The standard form of a linear equation in one variable is Ax + B = 0. x is a variable in this equation, and A and B are constants. A two-variable linear equation has the standard form Ax + By = C. The variables x and y are variables, their coefficients A and B are variables, and C is a constant.
Given, linear equation is
[tex]4(2x+1)=6x-12\\\\8x+4=6x-12\\\\8x-6x=-4-12\\\\2x=-16\\\\x=-8[/tex]
Hence, the x equals to -8.
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1. Which of the following is a perfect cube. (A) 100 (B) 68600 (C) 343000 (D) 400
Answer: 68600
hope it helps!
Express 80 as the product of its prime factors.
Write the prime factors in ascending order.
Answer: [tex]2^4 \times 5[/tex]
Step-by-step explanation:
[tex]80=2 \times 40\\\\80=2 \times 2 \times 20\\\\80=2 \times 2 \times 2 \times 10\\\\80=2 \times 2 \times 2 \times 2 \times 5\\\\80=2^4 \times 5[/tex]
I need help please ok okokokookokook
Answer:
should be angle 7, 1, and 3
hope i could helpppp
Answer: 1 , 7 , 3
Step-by-step explanation:
The angles that habe the same measurement of angle 5 are;
1 , 7 , 3
Because the lines are parallel, these angles correspond to angle 5.
Is this true or false?
TRUE: The given contrapositive statement are correct,
If m ≤ 3, then, m < 5.
Explain the contrapositive statement?An inference rule called proof by contrapositive, also known as proof by contraposition, is used in proofs to infer a conditional assertion from its contrapositive. To put it another way, the assertion "if B, then not A" is proven rather than the conclusion "if A, then B."When you reverse the hypothesis as well as the conclusion in a statement and reject both of them, you have a contrapositive statement.For the stated conditional statement -
If m ≤ 3, then, m < 5.
Then, contrapositive statement for the given statement will be
(m < 5)' ⇒ (m ≤ 3)'
That is;
(m > 5) ⇒ (m > 3)
That is, if m> 5 then, m > 3, which is true.
Thus, the contrapositive statement for the given conditional statement is true.
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Pleaseeee help I’m so confused
Answer:
D
Step-by-step explanation:
if you move the preimage on the image you can see that the two figures are equals
1.
The band and the orchestra are each having a party to celebrate the
results of their latest competition. The band would like to order cupcakes
from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee
The orchestra would like to order cupcakes from Publix at $2.90 each
and a $22.50 order fee. This system {2.90c +22.50 represents the
total cost, T, and the number of cupcakes. Determine how many
cupcakes each club can order if they both have the same amount of
money to spend. Is the solution viable or not viable?
By solving a linear equation, it can be calculated that
Each club can order 21.1 cupcakes if they both have the same amount of
money to spend
What is a linear equation?
Equation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by an equal to sign
A one degree equation is called linear equation
Let the number of cupcakes ordered by each club be c
The band would like to order cupcakes from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee
Total amount spent = $(13 + 3.35c)
The orchestra would like to order cupcakes from Publix at $2.90 each
and a $22.50 order fee
Total amount spent = $(22.5 + 2.90c)
By the problem,
The linear equation is
13 + 3.35c = 22.5 + 2.90c
3.35c - 2.90c = 22.5 - 13
0.45c = 9.5
c = 21.1
This solution is not viable as the number of cupcakes must be an integer not a decimal.
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Identify the pattern.
-4. -5.5, -7, -8.5, -10, -11.5, -13,..
Answer:
The pattern is that each number in the sequence is the previous number minus 1.5. For example, -5.5 is -4 minus 1.5, -7 is -5.5 minus 1.5, and so on.
Answer:
-1.5
Step-by-step explanation:
You take two of the variables in the pattern and subtract them with the second one being the minuend, and the first being the subtrahend.
For example we will use -4 and -5.5
(-5.5) - (-4) = -1.5
There is a negative sign present so it indicates subtraction towards the pattern.
Hence, the pattern change rate is -1.5
How to solve this problem? I need the answer quick as possible!
Consider the following three systems of linear equations. Answer the questions below.
For each, choose the transformation and then fill in the blank with the correct number.
The arrow → means the expression on the left becomes the expression on the right.
Answer:
24 Inches
Step-by-step explanation:
The length of a piece of wood that uses 8 nails as required in the task content is; 24 inches.
What is the length of a piece of wood that uses 8 nails?
It follows from the task content that the length of a piece of wood that uses 8 nails is to be determined from the task content.
Julie buys a pair of earrings for $7. Now she would like to buy the same earrings for 2 of her friends. How much will she spend for all 3 pairs of earrings
1. The equation, 687.5 = 550(1 + 0.05t), represents the amount of money earned on a simple interest savings account. What does the value 550 represent?
The value 550 represents the initial balance in the account, which means the account started with $550.
The value 550 represents the final balance in the account, which means the account balance ended with $550.
The value 550 represents the final balance in the account, which means the account balance started with $550.
The value 550 represents the amount of interest earned, which means $550 was added to the initial balance.
2. A savings account is opened with an initial deposit of $425.00. Determine the account balance after 9 years if the account earns 2.7% simple interest annually.
$3,928.28
$1,457.75
$528.28
$103.28
3. An arithmetic sequence begins with 56, 59, 62, 65, 68, …
Which option below represents the formula for the sequence?
f(n) = 56 + 3(n − 1)
f(n) = 53 + 3(n − 1)
f(n) = 56 + 3(n)
f(n) = 53 + 3(n + 1)
4. The equation, 816 = 600(1 + 9r), represents the amount of money earned on a simple interest savings account. Solve for r.
r = 0.04
r = 0.14
r = 0.26
r = 0.40
Answer:
Answers below
Step-by-step explanation:
1. The value 550 represents the initial balance in the account, which means the account started with $550.
2. 528.28
425.00 x 2.7% x 9 = 103.275
Then we add 103.275 to the initial deposit of $425.00
425.00 + 103.275 = 528.275
Therefore the answer is $528.28
3. The answer for this one is f(n) = 56 + 3(n − 1)
So, as we can see the first value is 56 and the common difference is 3 and the rule for the nth term is [tex]a_{n} =a_{1} +d(n-1)[/tex]
Therefore, its 56 + 3(n − 1)
4. For this one we solve for r and using a calculator its r = 0.04
The value of r from the given equation is 0.04. Therefore, option A is the correct answer.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
1) The given equation is 687.5=550(1+0.05t)
Here, amount=$687.5, principal (initial balance)=$550 and rate of interest =0.05×100 =5%
So, the value 550 represents the initial balance in the account, which means the account started with $550.
2) Given that, principal=$425.00, time period=9 years and rate of interest=2.7%
We know that, S.I=(P×T×R)/100
= (425×9×2.7)/100
= 103.275
Amount=103.275+425
= 528.275
≈ $528.28
3) The given arithmetic sequence is 56, 59, 62, 65, 68,.…
Here, first term (a)=56 and common difference=59-56=3
We know that, general form of arithmetic sequence is aₙ=a+(n-1)d
Now, f(n)=56+(n-1)3
4) The given equation is 816=600(1+9r)
1+9r =816/600
1+9r =1.36
9r=0.36
r=0.04
The value of r from the given equation is 0.04. Therefore, option A is the correct answer.
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2) Given that Y and P are two events and P(Y) = 0.57, P(P) = 0.5 and P(Y UP) = 0.84,
Draw a Venn Diagram and find:
a) P(Yn P)
b) P(Y|P)
c) P(P|Y)
d) P(Y/P')
a) The value of P(Y∩P) =0.23
b) The value of (Y|P) = 0.34
c) The value of (P|Y) = 0.27
d) The value of P(Y/P') = 0.68
What is Venn diagram?
A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it. A subset of whole numbers, which is a subset of integers, is a collection of natural numbers, as an example.
Given that there are two events Y and P.
P(Y) = 0.57
P(P) = 0.5
P(Y∪P) = 0.84
The formula of intersection is P(Y∩P) = P(P) + P(Y) - P(Y∪P)
Putting P(Y) = 0.57, P(P) = 0.5, P(Y∪P) = 0.84
P(Y∩P) = 0.5 + 0.57 - 0.84
P(Y∩P) = 0.23.
b)
P(Y|P) = P(Y) - P(Y∩P)
P(Y|P) = 0.57 - 0.23
P(Y|P) = 0.34
c)
P(P|Y) = P(P) - P(Y∩P)
P(P|Y) = 0.5 - 0.23
P(P|Y) = 0.27
d) P(Y/P') = P(Y∩P') / P(P')
P(Y/P') = P(Y|P)/[1 - P(P)]
P(Y/P') = 0.34/(1- 0.5)
P(Y/P') = 0.68
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the manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a variance equal to 1,456. based on this information, what are the chances that the revenue on the first show will exceed $800?
The chances that the revenue on the first show will exceed $800 when mean revenue is $336.25 and standard deviation is $38.16 is essentially zero. i.e. 0
A normal distribution is a type of continuous probability distribution in which the majority of data points cluster in the middle of the range, while the remainder taper off symmetrically toward either extreme. The mean of the distribution is also known as the middle of the range.
The normal distribution is primarily used to calculate the likelihood of an observation in a distribution falling above or below a given value.
Given,
Mean, [tex]\mu[/tex] = 336.25
variance, [tex]\sigma^2[/tex]= 1456
then,
standard deviation, [tex]\sigma = \sqrt{1456}[/tex] = 38.16
To determine the chances that the revenue on the first show will exceed 800 is1:
[tex]1-p(z=\frac{x-\mu}{\sigma})\\\\=1-p(z=\frac{800-336.25}{38.16})\\\\=1-p(z=\frac{436.75}{38.16})\\\\=1-p(z=12.15)\\\\=1-1=0[/tex]
Hence, there is no chance that the revenue will exceed $800 on the first show.
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