$151.31. Not proportional.
y= 9.17 +1.65x
1) Gathering the data
1996 Retired $ 9.17
9.17(1.65)^x
2) Since the value of that card has been increasing 1.65 yearly, then we can write the following equation:
[tex]y=9.17+1.65x[/tex]For y= Value, and x =years
Let's find out the value of the card in 2006, i.e. 10 years later. Plug x=10 into the above function:
[tex]\begin{gathered} y=9.17+1.65x \\ y=9.17+1.65(10) \\ y=9.17+16.5 \\ y=151.305\approx y=151.31 \end{gathered}[/tex]3) Hence, the value of the card in 2006 is $151.31
(rounded off to the nearest hundredth)
And since the initial value is $9.17, then it is not a proportional relationship since an initial value of a proportional is always 0.
If the factors of a polynomial are x-4 and x-5, which value of x make that polynomial 0?
Given a polynomial of factors below,
[tex]f(x)=(x-4)(x-5)[/tex]To find the values of x at f(x) = 0, substitute for f(x) into the equation above,
[tex]\begin{gathered} (x-4)(x-5)=0 \\ x-4=0 \\ x=4 \\ x-5=0 \\ x=5 \\ x=4\text{ and 5} \end{gathered}[/tex]C is the right option
Bradley rolls two fair 6-sided dice with faces numbered 1 through 6. What is the probability that the sum of her two rolls has an odd number of factors?
Answer:
The probability that the sum of her two rolls has an odd number of factors will be;
[tex]P=\frac{7}{36}[/tex]Explanation:
We want to find the probability that the sum of her two rolls has an odd number of factors.
For the two rolls the total number of possible outcomes is;
[tex]6\times6=36[/tex]Let us list out the possible outcomes of the two rolls;
[tex]\begin{gathered} (\text{outcome)= sum= number of factors of the sum} \\ \mleft(1,1\mright)=2=2\text{ factors} \\ (1,2)=3=2\text{ factors} \\ (1,3)=4=3\text{ factors} \\ (1,4)=5=2\text{ factors} \\ (1,5)=6=4\text{ factors} \\ (1,6)=7=2\text{ factors} \\ \end{gathered}[/tex][tex]\begin{gathered} (2,1)=3=2\text{ factors} \\ (2,2)=4=3\text{ factors} \\ (2,3)=5=2\text{ factors} \\ (2,4)=6=4\text{ factors} \\ (2,5)=7=2\text{ factors} \\ (2,6)=8=4\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (3,1)=4=3\text{ factors} \\ (3,2)=5=2\text{ factors} \\ (3,3)=6=4\text{ factors} \\ (3,4)=7=2\text{ factors} \\ (3,5)=8=4\text{ factors} \\ (3,6)=9=3\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (4,1)=5=2\text{ factors} \\ (4,2)=6=4\text{ factors} \\ (4,3)=7=2\text{ factors} \\ (4,4)=8=4\text{ factors} \\ (4,5)=9=3\text{ factors} \\ (4,6)=10=4\text{ factors} \\ \end{gathered}[/tex][tex]\begin{gathered} (5,1)=6=4\text{ factors} \\ (5,2)=7=2\text{ factors} \\ (5,3)=8=4\text{ factors} \\ (5,4)=9=3\text{ factors} \\ (5,5)=10=4\text{ factors} \\ (5,6)=11=2\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (6,1)=7=2\text{ factors} \\ (6,2)=8=4\text{ factors} \\ (6,3)=9=3\text{ factors} \\ (6,4)=10=4\text{ factors} \\ (6,5)=11=2\text{ factors} \\ (6,6)=12=6\text{ factors} \end{gathered}[/tex]From the listed possible outcomes, the number of oucomes with odd number of factors of the sum is;
[tex]n_A=7[/tex]Total number of possibles outcomes is;
[tex]n_T=36[/tex]The probability that the sum of her two rolls has an odd number of factors will be;
[tex]\begin{gathered} P=\frac{n_A}{n_T}=\frac{7}{36} \\ P=\frac{7}{36} \end{gathered}[/tex]I need help solving this problem any help is appreciated
If we want to solve this problem we first need to list a few properties of trigonometric functions:
[tex]\begin{gathered} \text{cot }\theta=\frac{\cos\theta}{\sin\theta} \\ \sin^2\theta+\cos^2\theta=1 \end{gathered}[/tex]We are told that cot(θ)=1/2. Using the first equation and this data we obtain the following:
[tex]\frac{1}{2}=\frac{\cos\theta}{\sin\theta}[/tex]We multiply both sides and we get an expression for the cosine of θ:
[tex]\begin{gathered} \frac{1}{2}\sin\theta=\frac{\cos\theta}{\sin\theta}\cdot\sin\theta \\ \cos\theta=\frac{1}{2}\sin\theta \end{gathered}[/tex]Now we are going to take the second property I wrote in the begining and replace the cosine of θ with this new expression that we found:
[tex]\begin{gathered} \sin^2\theta+\cos^2\theta=\sin^2\theta+(\frac{1}{2}\sin\theta)^2=1 \\ \sin^2\theta+\frac{1}{4}\sin^2\theta=1 \\ \frac{5}{4}\sin^2\theta=1 \end{gathered}[/tex]We must solve this equation for the sine of θ. We can multiply both sides by 4/5:
[tex]\begin{gathered} \frac{4}{5}\cdot\frac{5}{4}\sin^2\theta=1\cdot\frac{4}{5} \\ \sin^2\theta=\frac{4}{5} \end{gathered}[/tex]And we apply a square root to both sides:
[tex]\begin{gathered} \sqrt{\sin^2\theta}=\sqrt{\frac{4}{5}} \\ |\sin\theta|=\frac{2}{\sqrt{5}} \end{gathered}[/tex]We are told that θ is located in quadrant I which means that its sine is positive. Therefore we get:
[tex]\sin\theta=\frac{2}{\sqrt{5}}[/tex]AnswerThen the answer is 2/√5
The quotient of forty three abs a number m
Explanations:
Answer:
The original price of a pair ofjeans was $40. The price wasmarked down to $35. What is thepercent of decrease in the price?
SOLUTION
From the question, the original price of the jeans was $40, then the price was reduced to $35. Decrease in price becomes
[tex]40-35=5\text{ dollars }[/tex]Percent decrease becomes
[tex]\begin{gathered} =\frac{decrease\text{ in price}}{original\text{ price}}\times100 \\ =\frac{5}{40}\times100 \\ =\frac{1}{8}\times100 \\ =12.5 \end{gathered}[/tex]hence the answer is 12.5%
Decide whether enough information is given to prove that △RSV≅△UTV. If so, state the theorem you would use.
In the diagram we are given that angle S = angle T
We are given that side SV = side TV
We know that vertical angles are equal so angle RVT = angle UVT
WE have 2 angles and the included side so we can use the ASA Congruence theorem which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
There is enough information to use the ASA Congruence Theorem.
Solve the following system of equations. How many solutions are there? x + y = 2 5x + 5y = 10 a) There is no solution. b) There are infinite solutions. c) There is one solution.
we are given the following system of equations:
[tex]\begin{gathered} x+y=2,\text{ (1)} \\ 5x+5y=10,\text{ (2)} \end{gathered}[/tex]Equation (2) can be rewritten dividing by 5 on both sides as:
[tex]\frac{5x}{5}+\frac{5y}{5}=\frac{10}{5}[/tex]Solving the operations:
[tex]x+y=2,\text{ (2)}[/tex]Since equation (2) is the same equation as equation(1), this means that the system has infinite solutions.
Change 0.005 to equivalent fraction. ANS. _________.
You can identify that the following is a Decimal number:
[tex]0.005[/tex]In order to convert a Decimal number to an Equivalent fraction, you can follow the steps shown below:
1. You need to write the Decimal number 0.005 as the numerator of the fraction and the denominator must be 1:
[tex]=\frac{0.005}{1}[/tex]2. Now you can multiply the numerator and the denominator by 1,000, in order to remove the decimal places of the numerator (notice that it has three decimal places):
[tex]=\frac{0.005\cdot1,000}{1\cdot1,000}=\frac{5}{1,000}[/tex]3. Finally, you have to reduce the fraction. Notice that you can divide the numerator and the denominator by 5. Then, you get:
[tex]=\frac{1}{200}[/tex]The answer is:
[tex]\frac{1}{200}[/tex]Jack has $205 and he is spending $2 each day. Which algebraic expression describes this situation, where d represents the number of days?
M= 205 - 2d
1) We can write a mathematical sentence for that situation, considering Jack's initial amount of money: $205 and the fact that we don't know the number of days (d). But we do know that each day costs Jack $2, i.e. minus 2 dollars per day.
2) Therefore, we can write out the following:
[tex]M_{}=205-2d[/tex]Where M stands for Jack's money and "d" stands for the number of days.
3) Hence the answer is
M= 205 - 2d
Use elimination to solve eachsystem of equations3x - y = -56x - 2y = 8
Solution
We are given the pair of simultaneous equation
[tex]\begin{gathered} 3x-y=-5\ldots\ldots\ldots\ldots\ldots(1) \\ 6x-2y=8\ldots\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]we solve using elimination method
equation (1) x 2
[tex]\begin{gathered} 6x-2y=-10\ldots\ldots\ldots\ldots\ldots(1) \\ 6x-2y=8\ldots\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]Equation (2) - equation (1)
We have
[tex]\begin{gathered} (6x-6x)+(-2y+2y)=8-(-10) \\ 0=18 \end{gathered}[/tex]Which is impossible because 0 (zero) can never be equal to 18
Therefore, the simultaneous is not consistent or it degenerate and thus, there is no solution
the number of employees Forrester company of vindication each year by 4% of the company currently k670 employees and this rate continues from the number of employees in 16 years
The expression for number of employee after n year if population, P decreases at rate of r % is,
[tex]p=P(1-\frac{r}{100})^n[/tex]Substitute the values in the formula to determine the population after 16 years.
[tex]undefined[/tex]Darnell is running a short experiment on probability. He chooses one block at random from each of the two groups shown below. What is the probabilitythat he will choose a Z from Group 1 and a T from Group 2?
Answer
P(Z and T)= 8/121
Explanation
The total out come in group 1 = 11
The number of z = 4
Probability of picking a Z in group 1 = 4 / 11
Group 2
The total out comes = 11
Number of T outcomes = 2
Probability of picking a T = 2/11
Therefore, P( Z and T) = P(Z) x P(T)
P(Z and T) = P(Z) x P(T)
P(Z) = 4/11
P(T) = 2/11
P(Z and T) = 4/11 x 2/11
P(z and T) = 8/121
Therefore, the probability of picking a Z and aT is 8/121
mason used a 30% coupon to buy a new computer. after the discount, the cost of the computer was $728. determine the original price of the computer . show your work . calculate how much money Mason saved by using the coupon . show your work .
Let's call x to the original price.
Given that Mason used a 30% coupon, then he paid 0.3x dollars less.
After the discount, the cost of the computer was $728, then
x - 0.3x = 728
0.7x = 728
x = 728/0.7
x = 1040
The original price of the computer was $1040
Mason saves 30% of $1040, which is computed as follows:
[tex]1040\cdot\frac{30}{100}=312[/tex]Mason saves $312
Rewrite the following equation y - 7 = -4(x + 1)
1.question The preimage was(-3, 4) and after the rotation the image was (3, -4). What many degrees counterclockwise did the point rotate?a) 90b) 270c) none aboved) 1802. question
Answer:
Question 1
d) 180
Question 2:
b T <8, 14>
Explanation:
Here is a graph of the two points.
As can be seen, the two points are on the opposite sides of teacher other, meaning the point (-3,4) has to rotate 180 degrees to get to (3, -4) and vice versa.
Question 2
The coordinates of A and B are
A = (5, 6)
B = (-3, -8 )
If we want to go from B to A, we need to add 8 to the x-coordinate and 14 to the y-coordinate.
Therefore, the translation
[tex]B\rightarrow A\text{ is T<8,14>}[/tex]
Drag the tiles to the boxes to form correct pairs.
Given that
The vertices of the polygon ABCD are A(1,1), B(2,3), C(3,2), and D(2,1). ANd it is reflected about the x-axis.
So we have to find the vertices of the polygon A'B'C'D'.
Explanation -
Since the reflection is about the x-axis, the x-axis will be unchanged and the y-axis will be changed.(sign will be changed)
And it will be changed by the factor +2 in upwards directions.
So if A, B, C, D are reflected across x-axis.
The new points will be A' = (1,-1)
B' = (2,-3)
C' = (3,-2)
D' = (2,-1)
Now we have to add 2 in the y axis as they move upwards.
Then, the required points will be
A' = (1, -1+2) = (1,1)B' = (2, -3+2) = (2,-1)C' = (3,-2+2) = (3,0)D' = (2, -1+2) = (2,1)So these are the required answers.
In 2 years, Ariel wants to buy a bicycle that costs 1,000.00. If she opens a savings account that earns 9%interest compounded quarterly, how much will she have to deposit as principal to have enough money in 2 years to buy the bike?
Let's first list down the information given in the scenario:
a.) In 2 years ariel wants to buy a bicycle that costs 1,000.00
b.) She opens a savings account that earns 9% interest compounded quarterly
Question: How much will she have to deposit as principal to have enough money in 2 years to buy the bike?
To be able to determine the principal amount Ariel will need to deposit, let's use this formula for Compound Interest:
[tex]\text{ A = }P(1\text{ + }\frac{\frac{r}{n}}{100})^{nt}[/tex]Where:
A = Is the final amount/ cost of the bicycle = 1,000
n = Number of times the interest is being compounded = 4
r = Interest rate = 9%
t = No. of periods elapsed/ No. years the principal money be deposited
P = Principal amount/ amount to be deposited
Let's now find the principal amount:
[tex]\text{ A = }P(1\text{ + }\frac{\frac{4}{n}}{100})^{nt}\text{ }\rightarrow\text{ 1,000 = }P(1\text{ + }\frac{\frac{9}{4}}{100})^{4(2)}[/tex][tex]\text{1,000 = }P(1\text{ + }\frac{2.25}{100})^8\text{ }\rightarrow\text{ 1,000 = }P(1\text{ + }0.0225)^8\text{ }\rightarrow1,000=P(1.0225)^8[/tex][tex]\text{ P = }\frac{1,000}{(1.0225)^8}\rightarrow\text{ P = }\frac{1,000}{1.19483114181}[/tex][tex]\text{ P = 836.93835 }\cong\text{ 836.94}[/tex]Therefore, Ariel must deposit a principal amount of 836.94 for her to be able to buy the bike in 2 years.
What is the inverse operation for addition?additionsubtractiondivisionmultiplication
The inverse operation for addition is subtraction.
Hence, the answer is Subtraction.
find the value 24÷(1 to the 5th power+5)
Given
[tex]\frac{24}{(1^5+5)}[/tex]When you power a number by a determined exponent "n" it means that you are multiplying said number n-times by itself. We know that if you multiply 1 by 1 the result is 1, no matter how many times you do it, then 1 multiplied 5 times by itself is also equal to 1:
[tex]1^5=1\cdot1\cdot1\cdot1\cdot1=1[/tex]Then, you can write the calculation as:
[tex]\frac{24}{(1+5)}[/tex]Solve the addition in the denominator's place and then solve the division
[tex]\frac{24}{6}=4[/tex]The result of the calculation is 4
8 and 7 are like terms true or false
8 and 7 are like terms, because they share the same power of x:
[tex]\begin{gathered} 8x^0\rightarrow8 \\ 7x^0\rightarrow7 \end{gathered}[/tex]which expression is equivalent to 7y + 7y?
Evaluate the value of expression.
[tex]7y+7y=14y[/tex]So answer is 14y.
What is the Center and radius of x2+67+y2=8y+20x
Let's rewrite the expression as:
[tex]\begin{gathered} x^2+67+y^2-8y-20x=0 \\ so\colon \\ (x-10)^2+(y-4)^2-49=0 \\ (x-10)^2+(y-4)^2=49 \end{gathered}[/tex]Which is the standard equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h,k) is the coordinates of center of the circle and r is the radius
Therefore, the center is:
[tex]\begin{gathered} (h,k)=(10,4) \\ \end{gathered}[/tex]And the radius is:
[tex]r=\sqrt[]{49}=7[/tex]11 Jamal has a sudden medical emergency, and although his doctors do not agree, he is sure that it was caused by an antibiotic he took to prepare for a tooth extraction. Jamal posts a picture of himself in the hospital on his social media with the hashtag #antibioticskill. Although hashtags can raise awareness of important issues, what might happen if Jamal’s post were to go viral? A. People could be influenced into groupthink and reject antibiotics without knowing the facts. B. People would be encouraged to research the side effects that antibiotics cause before accepting them. C. Jamal would be investigated for making unfounded claims about a product online. D. Jamal could cause people to be more willing to listen to their doctor’s advice.
Answer:
A.
Step-by-step explanation:
A. People could be influenced into groupthink and reject antibiotics without knowing the facts.
which of the following equations has only one solution? x^2 - 8x + 16 = 0x ( x - 1 ) = 8 x^2 = 16
Simplify the equation x^2 - 8x + 16 = 0 to obtain the value of x.
[tex]\begin{gathered} x^2-8x+16=0 \\ x^2-2\cdot4\cdot x+(4)^2=0 \\ (x-4)^2=0 \\ (x-4)(x-4)=0 \\ x=4 \end{gathered}[/tex]Equation has one solution, x = 4.
Simplify the equation x ( x - 1 ) = 8 to obtain the value of x.
[tex]\begin{gathered} x(x-1)=8 \\ x^2-x-8=0 \end{gathered}[/tex]This is a quadratic equation which is not a perfect square so it has two solutions.
Simplify the equation x^2 = 16 to obtain the value of x.
[tex]\begin{gathered} x^2=16 \\ x=\sqrt[]{16} \\ =\pm4 \end{gathered}[/tex]Thes equation has two solution x = 4 and x = -4.
So equation x^2 - 8x + 16 = 0 has only one solution and remaining equation has two solutions.
(3x-3)
[6(x - 10)] What is the value of x?
one to the sixth power
sixth power is the exponent of 1.
To obtain the result, multiply 1 by itself 6 times:
1x1x1x1x1x1=1
1^6 = 1
Express the difference in medians as a multiple of the IQR of EACH dataset.Class A.Class B440506070Height (inches)
From the given box plot, let's express the difference in the medians of the IQR of each data.
Given:
Median of class A = 56
Q1 of class A = 50
Q3 of class A = 58
Median of class B = 52
Q1 of class B = 48
Q3 of class B = 54
Thus, we have:
IQR for class A = Q3 - Q1 = 58 - 50 = 8
IQR for class B = Q3 - Q1 = 54 - 48 = 6
Diffrence in median = 56 - 52 = 4
Thus, to find the expression of the difference in medians as a multiple of IQR of each data, we have:
[tex]\begin{gathered} \text{Difference class A: 4 = 8}\ast n \\ \\ \text{Difference class B: 4 = 6 }\ast n \end{gathered}[/tex]Let's solve for each difference.
Difference class A:
[tex]n=\frac{4}{8}=\frac{1}{2}[/tex]Difference class B:
[tex]n=\frac{4}{6}=\frac{2}{3}[/tex]ANSWER:
[tex]\begin{gathered} \text{CLass A = }\frac{1}{2} \\ \\ \text{Class B = }\frac{2}{3} \end{gathered}[/tex]If a normally distributed data set has a mean of81 and a standard deviation of 6, which of thefollowing represents approximately 95% of thedata?
95% of the data is represented as 69 to 93 (option G)
Explanation:Given:
mean of data = 81
standard deviation = 6
To find:
The option that represents 95% of the data
To determine the right option, we will apply the empirical rule (68-95-99.7%):
68% of the data will fall within 1 standard deviation
95% of the data will fall within 2 standard deviation
99.5% of the data will fall within 3 standard deviation
[tex]\begin{gathered} 2\text{ standard deviation is represented as:} \\ \mu\text{ }\pm\text{ 2\sigma} \\ where\text{ \mu = mean, \sigma = standard deviation} \end{gathered}[/tex]substitute the values:
[tex]\begin{gathered} μ\pm2σ\text{ = 81 }\pm\text{ 2\lparen6\rparen} \\ =\text{ 81 }\pm\text{ 12} \\ 81\text{ }\pm\text{ 12 means 81 - 12 , 81 + 12} \\ =\text{ 69, 93} \\ This\text{ means 95\% of the data is represented from 69 to 93 \lparen option G\rparen} \end{gathered}[/tex]Solve the system: y = 12 + 4x y = -33 - 5x
The equation system is:
[tex]\begin{gathered} y=12+4x \\ y=-33-5x \end{gathered}[/tex]So we can made the equation equal so:
[tex]\begin{gathered} 12+4x=-33-5x \\ 4x+5x=-33-12 \\ 9x=-45 \\ x=-\frac{45}{9} \\ x=-5 \end{gathered}[/tex]Now we can replace the value of x to find y in the first equation so:
[tex]\begin{gathered} y=12+4(-5) \\ y=12-20 \\ y=-8 \end{gathered}[/tex]so the solution is:
[tex](-5,-8)[/tex]i gave away 10% of my summer job earnings. If i give away $256, how much did i earn over the summer?
ok
$256 --------------------------- 10%
x --------------------------100%
x = (100 x 256) / 10
x = 25600 / 10
x = $2560
I earned $2560 over the summer