Answers
Step-by-step explanation:
[tex] \frac{5}{4} = \frac{x}{6} \\ 4x = 30 \\ x = 7.5[/tex]
Related Questions
please help meeeee!!
Answers
Step-by-step explanation:
[tex]\begin{aligned} -5x+4y &= 3\\\\ x&=2y-15 \end{aligned}[/tex]
A small town experienced explosive population increase. Originally the town had population 170. Within 3 years, the town's population increased by 400%. What's the town's current population
Answers
Answer:
850
Step-by-step explanation:
Given that :
Initial population = 170
Percentage rise in population within 3 years = 400%
Hence, the current population of the town will be ;
Current population = Initial population * (1 + rate)
Current population = 170(1 + 400%)
Current population = 170(1 + 4)
Current population = 170(5)
Current population = 850
Differentiate the function. y = (3x - 1)^5(4-x^4)^5
Answers
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
Alec bakes spherical rolls of bread. Each roll is about 8cm
wide. What is the approximate volume of each roll? Use
3.14 to approximate a.
Answers
Answer:
Step-by-step explanation:
2143.57
the temperature at 6 pm in frost frozen antarctica was -37 if the tem dropped 8 1 /2 c uring the next hour what was the the temp at 7 pm
Answers
Answer:
-45 1/2
Step-by-step explanation:
Can someone tell me if its A,B, or C? Thanks besties.
Answers
Answer:
... ..... C is the answer
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!!
Answers
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.
Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per
year, compounded monthly. Give your answer accurate to 2 decimal places.
Preview
years.
Answers
Answer:
The time required is of 17.53 years.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per year, compounded monthly.
This is t for which [tex]A(t) = 14000[/tex], considering [tex]P = 7000, r = 0.04, n = 12[/tex]. So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]14000 = 7000(1 + \frac{0.04}{12})^{12t}[/tex]
[tex](1.0033)^{12t} = 2[/tex]
[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]
[tex]12t\log{1.0033} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]
[tex]t = 17.53[/tex]
The time required is of 17.53 years.
Q. A board that measures feet long is cut into 6 equal pieces. What is the length of each piece?
A. 1} inches
B. 3 inches
C. 3 inches
D. 9 inches
Answers
QUESTION :- . A board that measures feet long is cut into 6 equal pieces. What is the length of each piece?
A. 1 inches
B. 3 inches
C. 2 inches
D. 9 inches
ANSWER:- 1 FEET -->12 INCH
ATQ ->
1 FEET IS divided into 6 parts so
1 feet = 12 inches
[tex] \frac{1}{6} feet = \frac{12}{6} inches \\ \frac{1}{6} feet = 2 inches [/tex]
so each part will be equal to 2 inches
1 ft = 12 in
12 inch can be devided into 6 equal parts resulting in 2 inches each.
I guess you mistyped either B or C..
hope it helps
kind regards
Alex
You put $600 in a savings account. The account earns 6% simple interest per year.
a. What is the interest earned after 10 years?
b. What is the balance after 10 years?
Answers
50 + x + 10 + 8x + 2x =650
what is the value of x?
Answers
Answer:
x = 590/11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
50 + x + 10 + 8x + 2x = 650
Step 2: Solve for x
[Addition] Combine like terms: 11x + 60 = 650[Subtraction Property of Equality] Subtract 60 on both sides: 11x = 590[Division Property of Equality] Divide both sides by 11: x = 590/11Answer:
x= 590/11
Step-by-step explanation:
Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.
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°
Answers
X + Y + Z = 180
Z > X + Y so Z > 90
Answer:
M < X + M < Y < 90
Step-by-step explanation:
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
Answers
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
what type of data states that every value in the set is a number
Answers
Answer:
QUALITATIVE DATA-type of data states that every value in the set is a number.
Step-by-step explanation:
QUALITATIVE DATA-type of data states that every value in the set is a number.
Answer:
QUALITATIVE DATA-type of data states that every value in the set is a number.
Exhibit 11-10 n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 At 95% confidence, the null hypothesis _____. a. should not be rejected b. should be revised c. should be rejected d. None of these answers are correct
Answers
Answer:
Option C
Step-by-step explanation:
n = 81
s2 = 625
H0: σ2 = 500
Ha: σ2 ≠ 500
Test Statistics X^2 = (n-1)s^2/ σ2 = (81-1)*625/500
X^2 = 100
P value = 0.0646 for degree of freedom = 81-1 = 80
And X^2 = 100
At 95% confidence interval
Alpha = 0.05 , p value = 0.0646
p < alpha, we will reject the null hypothesis
At 95% confidence, the null hypothesis
3.42x16.5 show your work plz
Answers
Answer:
= 56.43
Step-by-step explanation:
= 3.42 × 16.5
multiply the numbers= 56.43
Explanation:
There’s an imaga attached showing the steps through ling multiplication. My handwriting is bad and these steps came from the web. Either way it is still correct.
Hope this absolutely helps!
If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x).
True or false?
Answers
Answer:
False
Step-by-step explanation:
Take the point (2, 3) = (x, y)
Rotated 90º clockwise (3, -2) = (y, -x)
Rotated 90º counter clockwise (-3, 2) = (-y, x)
Neither rotation becomes (-3, -2)
HELP ASAP I WILL GIVE BRAINLIST
A = {1, 3, 4, 5, 7, 9}
B = {1, 2, 4, 6, 8, 10}
List the outcomes of A ∪ B? What does this represent?
List the outcomes of A ∪ B? What does this represent?
Answers
Answer:
A U B={1,2,3,4,5,6,7,8,9,10} represents A union B
(includes all the members of set Sand the members of set Bout together, do not repeat anyone that comes twice)
A n B={1,4} represents A interception B( this refers to the members that sets A and B have in common)
Answer:
A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }
Step-by-step explanation:
A = { 1 , 3 , 4 , 5 , 7 , 9 }
B = { 1 , 2 , 4 , 6 , 8 , 10 }
A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }
It represents the whole numbers between 0 and 11
[ A ∪ B is the elements of both A and B , without any repetition ]
A ∩ B = { 1 , 4 }
It represents the common numbers in both A and B
What is the domain of the square root function graphed below?
Answers
Answer:
Set the expression inside the square root greater than or equal to zero. We do this because only nonnegative numbers have a real square root, in other words, we can not take the square root of a negative number and get a real number, which means we have to use numbers that are greater than or equal to zero.
Step 2: Solve the equation found in step 1. Remember that when you are solving equations involving inequalities, if you multiply or divide by a negative number, you must reverse the direction of the inequality symbol.
Step 3: Write the answer using interval notation.
What proportion of families own as opposed to rent their home? To find out, an urban planner selected a random
sample of 400 families in a large city to participate in a survey about homeownership. Of the 362 families that
responded to the survey, 42% reported that they own their home. Which of the following statements about the
survey results is true?
O A suitable estimate of all families who own their home is 42%.
The survey suffers from voluntary response bias and may not accurately represent the population.
O Only 362 responses cannot provide a suitable estimate of families who own their home.
O The survey suffers from undercoverage and may not provide a suitable estimate of homeownership.
Mark this and return
Save and Exit
fyext
Submit
Answers
Answer:
A suitable estimate of all families who own their home is 42%.
Step-by-step explanation:
42% reported that they own their home.
This means that the sample proportion is of 42%. So that an estimate for the percentage of all families who own their home is of 42%., and that the first option is correct.
Answer:
The correct answer is: The survey suffers from undercoverage and may not provide a suitable estimate of homeownership.
Step-by-step explanation:
I just took the review test. The person above me is wrong
Two angles are complementary. One angle measures 60 degrees. What is the measure of the other angle?
I'm not sure if its A.
Answers
Answer:
30
Step-by-step explanation:
Complementary angles add to 90
x+60 = 90
x+60-60 = 90-60
x = 30
Answer: A
Step-by-step explanation:
Complementary angles sum up to 90 degrees. Thus, we can write that:
90=angle1+angle2
90-angle1=angle2
90-60=angle2
angle2=30
for what value of x does 4x=(1/8)^x+6?
Answer please help
A. -15
B. -3
C. 3
D. 15
Answers
Im sorry but what I got was x=1.5 I don't know if this helps or not.
Consider a fishery in which harvesting is taking placeat a constant rateh. The population at the fisherywill be modeled by
dP/dt = kP- h
Required:
Find the general solution to this DE.
Answers
Answer:
The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
Step-by-step explanation:
We are given the following differential equation:
[tex]\frac{dP}{dt} = kP - h[/tex]
Solving by separation of variables:
[tex]\frac{dP}{kP-h} = dt[/tex]
Integrating both sides:
[tex]\int \frac{dP}{kP-h} = \int dt[/tex]
On the left side, by substitution, u = kP - h, du = kDp, Dp = du/k. Then
[tex]\frac{1}{k} \ln{kP-h} = t + K[/tex]
In which K is the constant of integration.
[tex]\ln{kP-h} = kt + K[/tex]
[tex]e^{\ln{kP-h}} = e^{kt + K}[/tex]
[tex]kP - h = Ke^{kt}[/tex]
[tex]kP = Ke^{kt} + h[/tex]
[tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
Please help me I am confused and i will give you anything you want just help me. SOS
Answers
Answer:
hope it helps you..........
PLEASE HELP ASAP!!! What is the range of the function shown on the graph?
(The graph is below)
Answers
Answer:
-6 < y < ∞
Step-by-step explanation:
The range is the values that y can take
y goes from almost -6 to infinity ( there is an asymptote at -6)
-6 < y < ∞
Which statement describes the sequence defined by a Subscript n Baseline = StartFraction n cubed minus n Over n squared + 5 n EndFraction?
Answers
Answer:
The answer is " The sequence converges to infinity. "
Step-by-step explanation:
Given:
[tex]\to a_n=\frac{n^3-n}{n^2+5n}[/tex]
[tex]\lim_{n \to \infty} a_n= \lim_{n \to \infty} \frac{n^3-n}{n^2+5n}[/tex]
[tex]= \lim_{n \to \infty} \frac{n(n^2-1)}{n(n+5)}\\\\= \lim_{n \to \infty} \frac{(n^2-1)}{(n+5)}\\\\= \lim_{n \to \infty} \frac{n(n-\frac{1}{n})}{n(1+\frac{5}{n})}\\\\= \lim_{n \to \infty} \frac{(n-\frac{1}{n})}{(1+\frac{5}{n})}\\\\[/tex]
Denominator[tex]= \lim_{n \to \infty} 1+\frac{5}{n}=1+\lim_{n\to \infty} \frac{5}{n}=1+0=1[/tex]
Numerator [tex]=\lim_{n\to \infty}n-\frac{1}{n}=\infty[/tex]
[tex]\therefore\\\\\lim_{n\to \infty}a_n=\frac{\infty}{1} =\infty[/tex]
which equation is correctly rewritten to solve for x?
Answers
explanation
Suppose that each student at a university has one of 4 expected graduation years and one of 21 majors. How many students must be enrolled to guarantee 2 graduations in the same year and major?
Answers
Answer:
The correct answer is "168 students".
Step-by-step explanation:
According to the question,
Graduation probability,
[tex]P_g=\frac{1}{4}[/tex]
Major probability,
[tex]P_m=\frac{1}{21}[/tex]
Now,
The probability of having both graduation as well as major will be:
= [tex]\frac{1}{4}\times \frac{1}{21}[/tex]
= [tex]\frac{1}{84}[/tex]
hence,
The number of students having guarantee two graduations throughout the same year and major will be:
⇒ [tex]\frac{x}{84}=2[/tex]
By applying cross-multiplication, we get
⇒ [tex]x = 84\times 2[/tex]
⇒ [tex]=168[/tex]
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°.
Answers
Answer:
1-90
2-80
3-033
Step-by-step explanation:
Solve the following system of equations and show all work. y = 2x2-3 y = 7x + 1 (10 points)
Answers
Answer:
x = -1/2 , y = -5/2
x = 4, y = 29
Step-by-step explanation:
y = 2x² - 3
y = 7x + 1
------------------
set equal
2x² - 3 = 7x + 1
Subtract 7x + 1 from both sides
2x² - 7x - 4 = 0
Factor
(2x + 1)(x - 4) = 0
x = {-1/2, 4}
For x = -1/2
y = 7(-1/2) + 1
y = -5/2
(-1/2 , -5/2)
For x = 4
y = 7(4) + 1
y = 29
(4, 29)