Answer:
148.59
Step-by-step explanation:
Inflation is kind of similar to interest and with that bieng said we can (kind of ) use the same formula
the time between 2034 and 2014 is 2034-2014= 20
100(1.02)²⁰=148.5947396
which we can round to 148.59
148.5 is the cost in 2034 of an item that costs $100 in 2014
What is Simple Interest?Simple interest is a quick and easy method of calculating the interest charge on a loan
[tex]A=P(1+r)^{t}[/tex]
where A is the Actual amount
P is Initial amount
t is time period
r is rate of interest
Given,
The rate of inflation measures the percentage increase in the price of consumer goods
The rate of inflation in the year 2014 was 2% per year.
2% is converted to decimal by dividing with 100
2/100=0.02
The time gap between 2014 and 2034 is
2034-2014=20 years
The initial amount is 100
A=100(1+0.02)²⁰
A=100(1.02)²⁰
A=100×1.485
A=148.5
Hence 148.5 is the cost in 2034 of an item that costs $100 in 2014.
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For the data set 4, 5, 10, 11, 15, the mean, x, is 9. What is the standard
deviation?
The formula for the sample standard deviation is a -
Jo-;2(x-
z(x -- Hoje
Use the table to help you.
4.
5
10
11
15
X-8
(x - x?
-5
25
-4
16
1
1
2
4.
6
36
Sum= 82
Round your answer to the nearest tenth.
Answer:
4.53
Step-by-step explanation:
Given the data :
4, 5, 10, 11, 15
The mean = 9
The standard deviation of a sample :
s = √[Σ(x - mean)²/(n-1)]
s = √[((4-9)² + (5-9)²+(10-9)² + (11-9)² + (15-9)²) / (5-1)]
s = √(25+16+1+4+36)/4
s = √20.5
s = 4.527
s = 4.53
Answer:
4.5
Step-by-step explanation:
5.1.3
Please help me I am confused and i will give you anything you want just help me. SOS
Answer:
hope it helps you..........
The perimeter of a rectangle is 12cm the area is 5cm square what is the length of the sides?
Answer:
l=5, w=1
Step-by-step explanation:
5*1=5 for area
5+1+5+1=12 for perimeter
what is the value of this expression
log2^8 + log3(1/3)
Answer:
2
Step-by-step explanation:
log2^8 + log3(1/3)
=>3 + (-1)
=>2
A professor has been teaching introductory statistics for many years and the final exam performance has been very consistent from class to class and the scores have been normally distributed. Overall, the whole data base (i.e. population) of final scores has a mean (μ) of 24 points (out of a maximum of 30 points) and a standard deviation (Ï) of 5 points. The professor would like to revise the course design to see if student performance on the final could be improved.
The new course design was implemented in the most recent academic year. There were 100 students and the average final exam score was 24.7. The professor would like to run a hypothesis test to see if this sample of students in the recent academic year performed significantly better than the past population. In other words, the hypothesis was a comparison between the population taking the course with the new design (represented by the sample of 100 students) with the population taking the course with the old design. The professor is predicting an increase of final score with the new design, so the hypotheses should be directional, and the test should be one-tailed. The significance level is set at α = .1.
Required:
a. Identify the dependent variable for this study.
b. State the null hypothesis and alternative hypothesis using both words and symbol notation
Answer:
a) Independent variable - Design of the course
Dependent variable - Final score of the students
b) H0 - Final score >24.7
Alternate hypothesis - Final score is less than or equal to 24.7
Step-by-step explanation:
a) Independent variable - Design of the course
Dependent variable - Final score of the students
b) Null Hypothesis : Performance of student taking course with the new design is better as compared to the population of student taking the course with the old design.
H0 - Final score >24.7
Alternate hypothesis - Final score is less than or equal to 24.7
Differentiate the function. y = (3x - 1)^5(4-x^4)^5
Answer:
[tex]\displaystyle y' = -5(3x-1)^4(4 - x^4)^4(15x^4 - 4x^3 - 12)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (3x - 1)⁵(4 - x⁴)⁵
Step 2: Differentiate
Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[(3x - 1)^5](4 - x^4)^5 + (3x - 1)^5\frac{d}{dx}[(4 - x^4)^5][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' =[5(3x - 1)^{5-1} \cdot \frac{d}{dx}[3x - 1]](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^{5-1} \cdot \frac{d}{dx}[(4 - x^4)]][/tex]Simplify: [tex]\displaystyle y' =[5(3x - 1)^4 \cdot \frac{d}{dx}[3x - 1]](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot \frac{d}{dx}[(4 - x^4)]][/tex]Basic Power Rule: [tex]\displaystyle y' =[5(3x - 1)^4 \cdot 3x^{1 - 1}](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot -4x^{4-1}][/tex]Simplify: [tex]\displaystyle y' =[5(3x - 1)^4 \cdot 3](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot -4x^3][/tex]Multiply: [tex]\displaystyle y' = 15(3x - 1)^4(4 - x^4)^5 - 20x^3(3x - 1)^5(4 - x^4)^4[/tex]Factor: [tex]\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 3(4 - x^4) - 4x^3(3x - 1) \bigg][/tex][Distributive Property] Distribute 3: [tex]\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 12 - 3x^4 - 4x^3(3x - 1) \bigg][/tex][Distributive Property] Distribute -4x³: [tex]\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 12 - 3x^4 - 12x^4 + 4x^3 \bigg][/tex][Brackets] Combine like terms: [tex]\displaystyle y' = 5(3x-1)^4(4 - x^4)^4(-15x^4 + 4x^3 + 12)[/tex]Factor: [tex]\displaystyle y' = -5(3x-1)^4(4 - x^4)^4(15x^4 - 4x^3 - 12)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?
m∠X + m∠Z < 90°
m∠Y > 90°
∠X and∠Y are complementary
m∠X + m∠Y < 90°
Answer:
M < X + M < Y < 90
Step-by-step explanation:
characteristics of the median
Answer:
Median: The median is the middle value of the data set when the data is arranged in ranking order. It always lies at the center of the data set and not affected by the extreme values or outliers. For the calculation of median, the variable should be measured at least at the ordinal level.
What is the system of equations represented by the tables?
O A. y=2x-1
y = -x + 3
B. y = x + 2
y = x-1
O c. y=-3x-1
y = 3x + 2
O D. y = 2x-3
y = -x + 2
Answer:
C.
y = -3x - 1
y = 3x + 2
Step-by-step explanation:
Find the slope (m) and y-intercept (b) of each table to write an equation for each.
✔️First table:
Find the slope (m) = change in y/change in x
Using any two pair of values, say (0, -1) and (1, -4),
Slope (m) = (-4 - (-1))/(1 - 0) = -3/1
m = -3
Find the y-intercept:
y-intercept is the value of y when x = 0
From the table, y = -1 when x = 0. Therefore,
y-intercept (b) = -1
To write an equation for table 1, substitute m = -3 and b = -1 into y = mx + b
Equation for table 1:
y = -3x - 1
✔️ Second table:
Find the slope (m) = change in y/change in x
Using any two pair of values, say (0, 2) and (1, 5),
Slope (m) = (5 - 2)/(1 - 0) = 3/1
m = 3
Find the y-intercept:
y-intercept is the value of y when x = 0
From the table, y = 2 when x = 0. Therefore,
y-intercept (b) = 2
To write an equation for table 1, substitute m = 3 and b = 2 into y = mx + b
Equation for table 1:
y = 3x + 2
PLEASE HELP ASAP
Add the complex numbers: (4 + 8i) + (–2 – i)
Answer:
2 + 7i
Step-by-step explanation:
(4 + 8i) + (-2 - i)
open the brackets
4 + 8i - 2 - i
add or subtract like terms
2 + 7i
Answer:
2+7i
Step-by-step explanation:
Open the brackets.
4+8i-2-i
You will get…
2+7i
If a franchise company wanted to determine why sales were higher at some locations rather than others, what statistical process would be most appropriate? Group of answer choices Regression with sales as an independent variable Regression with sales as the dependent variable Use a confidence interval with the posted speed as the mean Hypothesis testing with a null hypothesis that the sales are less than or equal to the highest sales Hypothesis testing with a null hypothesis that the sales are more than the highest sales
Answer: Regression with sales as the dependent variable
Step-by-step explanation:
Since the franchise company wanted to determine why sales were higher at some locations rather than others, the statistical process that would be most appropriate is regression with sales as the dependent variable.
Regression will be used in determining the strength of the relationship that exist between one dependent variable and the independent variables. In this case, the dependent variable is sales.
What value of y makes the sentence true?
y + 3 = 30
Type your answer in the box below.
I
y =

Hey there!
y + 3 = 30
SUBTRACT 3 to BOTH SIDES
y + 3 - 3 = 30 - 3
CANCEL out: 3 - 3 because that gives you 0
KEEP: 30 - 3 because that gives you the value of y
y = 30 - 3
30 - 3 = y
y = 27
Answer: y = 27
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Name two characteristics of the Fibonacci Series that you observed.
Answer:
See the answers below
Step-by-step explanation:
Name two characteristics of the Fibonacci Series that you observed.
If we take a closer look at the Fibonacci series, we will notice the following characteristics
1.The next number is the sum of the two preceding numbers
2. Another interesting characteristic is evidenced in the convergence of the sequence
Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation of 0.2 feet. A sample of 41 men's step
lengths is taken
Step 2 of 2: Find the probability that the mean of the sample taken is less than 2.2 feet. Round your answer to 4 decimal places, if necessary,
Answer:
0% probability that the mean of the sample taken is less than 2.2 feet.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 2.5 feet and a standard deviation of 0.2 feet.
This means that [tex]\mu = 2.5, \sigma = 0.2[/tex]
Sample of 41
This means that [tex]n = 41, s = \frac{0.2}{\sqrt{41}}[/tex]
Find the probability that the mean of the sample taken is less than 2.2 feet.
This is the p-value of Z when X = 2.2 So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2.2 - 2.5}{\frac{0.2}{\sqrt{41}}}[/tex]
[tex]Z = -9.6[/tex]
[tex]Z = -9.6[/tex] has a p-value of 0.
0% probability that the mean of the sample taken is less than 2.2 feet.
An experienced teacher writes an exam so that, on average, about 5% of students will earn an A grade. If she has 50 students in her class and their performance is independent, what is the probability that at least one student gets an A
Answer:
[tex]P(x\geq 1) = 0.923[/tex]
Step-by-step explanation:
From the question we are told that:
Percentage of student to get A [tex]P(A)=\%5=0.05[/tex]
Sample size [tex]n=50[/tex]
Generally Number of student to get A is
[tex]N_a=n*P(A)[/tex]
[tex]N_a=50*0.05[/tex]
[tex]N_a=2.5[/tex]
Therefore
Probability that one student gets an A grade is mathematically by
[tex]^nPC_xP^x(1-P)^{n-x}[/tex]
[tex]P(x\geq 1)=1-P(x<1)[/tex]
[tex]P(x\geq 1) =1-P(x=0)[/tex]
[tex]P(x\geq 1) =^50C_0(0.05)^0(0.95)^50[/tex]
[tex]P(x\geq 1) = 0.923[/tex]
The harmonic mean of two real numbers x and y equals 2xy/(x + y). By computing the harmonic and geometric means of different pairs of positive real numbers, formulate a conjecture about their relative sizes and prove your conjecture.
Answer:
Conjecture : 2xy / ( x + y ) ≤ √xy
Step-by-step explanation:
Harmonic mean of x and y = 2xy/( x + y )
Formulate a conjecture about their relative sizes
we will achieve this by computing harmonic and geometric means
Geometric mean = √xy
harmonic mean = 2xy/( x + y )
Conjecture : 2xy / ( x + y ) ≤ √xy
attached below is the proof
Kaleigh wants to buy a car that costs $17360. She deposits $14,000 in a savings account that earns 8% simple interest. How long was Kaylee leave the money in the savings account to be able to buy the car?
Answer:
Kaylee must leave the money in the savings account for 3 years.
Step-by-step explanation:
Given that Kaylee wants to buy a car that costs $ 17,360, and she deposits $ 14,000 in a savings account that earns 8% simple interest, to determine how long was Kaylee leave the money in the savings account to be able to buy the car must be made the following calculation:
14,000 + (14,000 x 0.08 x X) = 17360
1,120X = 17,360 - 14,000
X = 3,360 / 1,120
X = 3
Therefore, Kaylee must leave the money in the savings account for 3 years.
Find the explicit general solution to the following differential equation.
(8+x) dy/dx = 5y
The explicit general solution to the equation is y:_______
Answer:
y = (8+x)^5 + C
Step-by-step explanation:
Given the differential equation
(8+x) dy/dx = 5y
Using the variable separable method
(8+x) dy = 5ydx
dx/8+x = dy/5y
Integrate both sides
[tex]\int\limits^ {} \, \frac{dx}{8+x} = \int\limits^ {} \, \frac{dy}{5y} \\ln(8+x) = \frac{1}{5}lny\\5ln(8+x)= lny\\ln(8+x)^5 = lny\\ (8+x)^5 = y\\Swap\\y = (8+x)^5 + C[/tex]
This gives the required solution
The explicit general solution to the following differential equation[tex](8+x)\dfrac{dy}{dx} = 5y[/tex] is [tex](8+x)^5 +C[/tex], where [tex]C[/tex] is a constant.
The relationship between the unknown function and its derivative is called the differential equation.
The differential equation in which variables are separated from each other is called the variable separable method.
Now, separate the variables using the variable separable method:
[tex](8+x){dy} = 5y \ dx[/tex]
[tex]\dfrac{dx}{8x} = \dfrac{dy}{5y}[/tex]
Integrating both sides,
[tex]\int \dfrac{dx}{x+8} = \int \dfrac{dy}{5y}\\log(x+8) = \dfrac{1}{5} log y\\ 5 log(x+8) = log y\\log(x+8)^{5} = log y \ \ \\y = ( x+8)^{5} +C[/tex]
Thus, the explicit general solution to the equation is [tex](8+x)^5 +C[/tex].
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A team of researchers wants to determine whether pet owners are generally more satisfied with their lives than non-pet owners. To test their theory, the researchers randomly select 500 pet owners and 500 non-pet owners from several major metropolitan areas in the country. The researchers then interview the individuals, asking them a series of questions. Each response is assessed with a point value that is later translated to a satisfaction indicator. Of the pet owners surveyed, 380 of the 500 were found to be satisfied with their lives, while 336 of the 500 non-pet owners were found to be satisfied.
Would this study be considered an experiment or an observational study?
Answer:
observational study
Step-by-step explanation:
A cyclist travels at a rate of 12 kilometers per hour. What is the rate in kilometers per minute? How many kilometers will the cyclist travel in 20 minutes? Do not round your answer.
Answer:
0.2&4
Step-by-step explanation:
There are 60 minutes in one hour, so 12 divided by 60 is the answer.
0.2 kilometers * 20 = 4
Find the value for the side marked below.
Round your answer to the nearest tenth.
50°
122
y
y = [?
Enter
Answer:
y = 189.8
Step-by-step explanation:
Apply trigonometric function to find y.
Reference angle (θ) = 50°
Adjacent side = 122
Hypotenuse = y
Apply CAH, since the Hypotenuse and the Adjacent are involved.
Thus:
Cos θ = Adj/Hypo
Plug in the values
Cos 50° = 122/y
y*Cos 50° = 122
y = 122/cos 50°
y = 189.8 (beater tenth)
I need a math genius please
!!WILL MARK BRAINLIEST!! PLEASE SOMEONE HELP!! IM TRYING TO PREPARE FOR MATH CAMP AND THEY GAVE US THIS PROBLEM AND I CANT FIND ANYTHING LIKE IT!!
Answer:
How long is the [shirt] in the air? 3 seconds
How many seconds after launching is the t-shirt at 17 feet? 0.25 seconds
Step-by-step explanation:
Formula to represent the shirt's flight path (given): [tex]h=-16t^2+vt+c[/tex], where [tex]h[/tex] is the height of the shirt, [tex]v[/tex] is the initial velocity of the shirt, [tex]c[/tex] is the shirt's starting height, and [tex]t[/tex] is elapsed time since launch.
The function forms a parabola concave down. Since the shirt is caught at 17 feet, we want to second x-coordinate of a point with a y-coordinate of 17 that the function passes through. This is because the shirt was caught going down, not up.
Therefore, let [tex]h=17[/tex]:
[tex]17=-16t^2+52t+5,\\\\-16t^2+52t-12=0,\\\\ y= \frac{-52\pm\sqrt{52^2-4(-16)(-12)}}{2(-16)},\\\\y=\frac{1}{4},\boxed{y=3}[/tex].
The second x-coordinate is the larger of the two and therefore the shirt was in the air for 3 seconds.
However, the first time the shirt reaches a height of 17 feet is on its way up, which occurs at 1/4 or 0.25 seconds (the first x-coordinate). Therefore, the t-shirt reached a height of 17 feet 0.25 seconds after launching.
work out 8^2/3
^2/3 means to the power of 2/3
Hi there!
»»————- ★ ————-««
I believe your answer is:
4
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Answer...}}\\\\8^{\frac{2}{3}}\\-----------\\\text{Recall the Exponent Rule: }} a^{\frac{b}{c}} = \sqrt[c]{a^b}\\\\\rightarrow {\frac{\text{Power}}{\text{Root Index}}\\\\[/tex]
[tex]-----------[/tex]
[tex]\rightarrow 8^{\frac{2}{3}}\\\\\rightarrow \sqrt[3]{(8^2)}\\\\\rightarrow\sqrt[3]{64}\\\\\rightarrow \boxed{4}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
4
Step-by-step explanation:
[tex]8^{\frac{2}{3} }[/tex]
=[tex](2)^3*\frac{2}{3}[/tex]
=[tex](2)^\frac{3*2}{2}[/tex]
=[tex](2)^\frac{6}{3}[/tex]
=[tex]2^2[/tex]
=4
Choose the Athat seems to be congruent to the given one.
R.
F
D
B
AEGFA
OEGD
o CGD
BGC
Answer:
a. ∆EGF ≅ ∆EGD
Step-by-step explanation:
Congruent triangles would have the same side lengths and the same measure of angles.
From the figure given:
EG in ∆EGF ≅ EG in ∆EGD
GF in ∆EGF ≅ GD in ∆EGD, also
EF ≅ ED.
The three angles in ∆EFG are also congruent to the three angles in ∆EGD.
Therefore, ∆EGD is congruent to ∆EGF.
∆EGF ≅ ∆EGD
Can someone tell me if its A,B, or C? Thanks besties.
Answer:
... ..... C is the answer
brainliest answer po yung tama
nk tym for nega NEED HELP PK TALAG
A
A
B
C
A
D
B
C
May choices po yan saamen
Step-by-step explanation:
Love you
Find the 23rd term of the arithmetic sequence with the terms a1 27 and d = 16.
Answer:
379
Step-by-step explanation:
a23 = 27 + (23-1)(16)
= 27 + (22)(16)
= 27 + 352
= 379
Consider the given statements below.
• A central angle in a circle measures 70°.
An inscribed angle in the same circle also measures 70°.
Which statement best describes the relationship between the arcs
intersected by these angles?
.
1 of 4 QUESTIONS
The inscribed angle intersects an arc that is twice the measure of the arc
intersected by the central angle. The inscribed angle's arc measures 70°,
and the central angle's arc measures 35º.
The inscribed angle intersects an arc that is half the measure of the arc
intersected by the central angle. The inscribed angle's arc measures 35º,
and the central angle's arc measures 70°.
The inscribed angle intersects an arc that is half the measure of the arc
O intersected by the central angle. The inscribed angle's arc measures 70°
and the central angle's arc measures 140°.
The inscribed angle intersects an arc that is twice the measure of the arc
O intersected by the central angle. The inscribed angle's arc measures 140°,
and the central angle's arc measures 70°.
Answer:
1-90
2-80
3-033
Step-by-step explanation:
How tall is the table?
120cm
90cm
I
The values of variables, such as the height of the table can be found by writing equations of their relationships
The height of the table is 105 cm
The reason the above height value is correct is as follows;
Known parameters:
The diagram shows a table, a cat and a mice
Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice
From the given diagram, we have;
Height of the table + Height of the cat - Height of the mice = 120 cm
∴ x + y - z = 120...(1)
Height of the table + Height of the mice - Height of the cat = 90 cm
∴ x + z - y = 90...(2)
Adding equation (1) to equation (2) gives;
x + y - z + (x + z - y) = 120 + 90 = 210
x + y - z + (x + z - y) = 210
However;
x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x
∴ x + y - z + (x + z - y) = 2·x = 210
x = 210/2 = 105
Therefore;
The height of the table, x = 105 cm
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(x-2)(-5x^2+x)=(x)(-5x^2)+(x)(x)+(-2)(-5x^2)+(-2)(x) is an exsample of
this is an example of linear equations is one variable