Answer:
Divide each term in Y i = 4 + 1.5 X i by i and simplify.
Y = − 4 i + 1.5 X
Step-by-step explanation:
how to graph quadratic relationship for h(x)=(x-1)^2-9
Answer:
use the formula y = a(x-h)^2 + k
the a stretches or flattens the parabola,
The h shifts left to right , and the k shifts up/down
Step-by-step explanation:
write 342 to 1 significant figure
Answer:
300
Step-by-step explanation:
A significant figure is the most important (largest) number you can round it to.
As it wants 1 significant figure, you count 1 to the left and round the 4 down.
Hope this helps :)
What are four ways an inequality can be written?
Answer:
There are four ways to represent an inequality: Equation notation, set notation, interval notation, and solution graph.
The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 45 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 45?
Do not enter the percent symbol.
ans = %
Answer:
34%
Step-by-step explanation:
Given that the distribution of daily light bulb request replacement is approximately bell shaped with ;
Mean , μ = 45 ; standard deviation, σ = 3
Using the empirical formula where ;
68% of the distribution is within 1 standard deviation from the mean ;
95% of the distribution is within 2 standard deviation from the mean
Lightbulb replacement numbering between ;
42 and 45
Number of standard deviations from the mean /
Z = (x - μ) / σ
(x - μ) / σ < Z < (x - μ) / σ
(42 - 45) / 3 = -1
This lies between - 1 standard deviation a d the mean :
Hence, the approximate percentage is : 68% / 2 = 34%
In a model, a submarine is located at point (0, 0) on the coordinate plane. The submarine’s radar range has an equation of 2x2 + 2y2 = 128
Draw the figure on a graph and label the location of the submarine. Make sure your name is on the paper, and label this activity Part 2.
Can the submarine’s radar detect a ship located at the point (6, 6) ? Mark that location on your graph, and explain how you know whether or not the ship will be detected in the space provided on the Circles Portfolio Worksheet.
Answer:
Remember that for a circle centered in the point (a, b) and with a radius R, the equation is:
(x - a)^2 + (y - b)^2 = R^2
Here we know that the submarine is located at the point (0, 0)
And the radar range has the equation:
2*x^2 + 2*y^2 = 128
You can see that this seems like a circle equation.
If we divide both sides by 2, we get:
x^2 + y^2 = 128/2
x^2 + y^2 = 64 = 8^2
This is the equation for a circle centered in the point (0, 0) (which is the position of the submarine) of radius R = 8 units.
The graph can be seen below, this is just a circle of radius 8.
We also want to see if the submarine's radar can detect a ship located in the point (6, 6)
In the graph, this point is graphed, and you can see that it is outside the circle.
This means that it is outside the range of the radar, thus the radar can not detect the ship.
The population of Americans age 55 and older as a percentage of the total population is approximated by the function f(t) = 10.72(0.9t + 10)^0.3 (0 <= t < = 20)
where t is measured in years, with t=0 corresponding to the year 2000.
Required:
a. At what rate was the percentage of Americans age 55 and older changing at the beginning of 2002?
b. At what rate will the percentage of Americans age 55 and older be changing in 2017?
c. What will be the percentage of the population of Americans age 55 and older in 2017?
Answer:
Part A)
About 0.51% per year.
Part B)
About 0.30% per year.
Part C)
About 28.26%.
Step-by-step explanation:
We are given that the population of Americans age 55 and older as a percentange of the total population is approximated by the function:
[tex]f(t) = 10.72(0.9t+10)^{0.3}\text{ where } 0 \leq t \leq 20[/tex]
Where t is measured in years with t = 0 being the year 2000.
Part A)
Recall that the rate of change of a function at a point is given by its derivative. Thus, find the derivative of our function:
[tex]\displaystyle f'(t) = \frac{d}{dt} \left[ 10.72\left(0.9t+10\right)^{0.3}\right][/tex]
Rewrite:
[tex]\displaystyle f'(t) = 10.72\frac{d}{dt} \left[(0.9t+10)^{0.3}\right][/tex]
We can use the chain rule. Recall that:
[tex]\displaystyle \frac{d}{dx} [u(v(x))] = u'(v(x)) \cdot v'(x)[/tex]
Let:
[tex]\displaystyle u(t) = t^{0.3}\text{ and } v(t) = 0.9t+10 \text{ (so } u(v(t)) = (0.9t+10)^{0.3}\text{)}[/tex]
Then from the Power Rule:
[tex]\displaystyle u'(t) = 0.3t^{-0.7}\text{ and } v'(t) = 0.9[/tex]
Thus:
[tex]\displaystyle \frac{d}{dt}\left[(0.9t+10)^{0.3}\right]= 0.3(0.9t+10)^{-0.7}\cdot 0.9[/tex]
Substitute:
[tex]\displaystyle f'(t) = 10.72\left( 0.3(0.9t+10)^{-0.7}\cdot 0.9 \right)[/tex]
And simplify:
[tex]\displaystyle f'(t) = 2.8944(0.9t+10)^{-0.7}[/tex]
For 2002, t = 2. Then the rate at which the percentage is changing will be:
[tex]\displaystyle f'(2) = 2.8944(0.9(2)+10)^{-0.7} = 0.5143...\approx 0.51[/tex]
Contextually, this means the percentage is increasing by about 0.51% per year.
Part B)
Evaluate f'(t) when t = 17. This yields:
[tex]\displaystyle f'(17) = 2.8944(0.9(17)+10)^{-0.7} =0.3015...\approx 0.30[/tex]
Contextually, this means the percetange is increasing by about 0.30% per year.
Part C)
For this question, we will simply use the original function since it outputs the percentage of the American population 55 and older. Thus, evaluate f(t) when t = 17:
[tex]\displaystyle f(17) = 10.72(0.9(17)+10)^{0.3}=28.2573...\approx 28.26[/tex]
So, about 28.26% of the American population in 2017 are age 55 and older.
A cylinder with a base diameter of x units has a volume of excubic units.
Which statements about the cylinder are true,Select
two options.
1)The radius of the cylinder is 2x units.
2)The area of the cylinder's base is 1/4 piex^2square units.
3)The area of the cylinder's base is 1/2 piex^2 square units.
4)The height of the cylinder is 2x units.
5)The height of the cylinder is 4x units.
Answer:3 and 4
Step-by-step explanation:
Find the missing Side of the triangle
Answer:
2√15
Step-by-step explanation:
Use the Pythagorean theorem.
2² + x² = 8²
x² + 4 = 64
x² = 60
x² = 4 * 15
x = 2√15
The ratio of total interior angles to total exterior angles of a quadrilateral is
Select one:
a. 3:1
b. 1:2
c. 1:1
d. 2:1
9514 1404 393
Answer:
c. 1 : 1
Step-by-step explanation:
The total of exterior angles of any convex polygon is 360°. The total of interior angles of a quadrilateral is 360°. So, the ratio of interest is ...
interior : exterior = 360° : 360° = 1 : 1
The length of a rectangular field is 25 m more than its width. The perimeter of the field is 450 m. What is the actual width and length?
Answer:
length= 125
width= 100
Step-by-step explanation:
let width have a length of x m
therefore length= (x+25)m
perimeter=2(length +width)
p=2((x+25)+x)
p=4x+50
but we have perimeter to be 450,, we equate it to 4x+50 above,
450=4x+50
4x=400
x=100 m
length= 125
width= 100
In Waterville, the average daily rainfall in July is 10 mm with a standard deviation of 1.5 mm. Assume that this data is normally distributed. How many days in July would you expect the daily rainfall to be more than 11.5 mm
Answer:
You should expect 5 days in July with daily rainfall of more than 11.5 mm.
Step-by-step explanation:
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.
In Waterville, the average daily rainfall in July is 10 mm with a standard deviation of 1.5 mm.
This means that [tex]\mu = 10, \sigma = 1.5[/tex]
Proportion of days with the daily rainfall above 11.5 mm.
1 subtracted by the p-value of Z when X = 11.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{11.5 - 10}{1.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.84.
1 - 0.84 = 0.16.
How many days in July would you expect the daily rainfall to be more than 11.5 mm?
July has 31 days, so this is 0.16 of 31.
0.16*31 = 4.96, rounding to the nearest whole number, 5.
You should expect 5 days in July with daily rainfall of more than 11.5 mm.
The consumer price index (CPI), issued by the U.S. Bureau of Labor Statistics, provides a means of determining the purchasing power of the U.S. dollar from one year to the next. Using the period from 1982 to 1984 as a measure of 100.0, the CPI figures for selected years from 2002 to 2016 are shown here. Year Consumer Price Index 2002 179.9 2004 188.9 2006 201.6 2008 215.3 2010 218.1 2012 229.6 2014 236.7 2016 240.0 E. To use the CPI to predict a price in a particular year, we can set up a proportion and compare it with a known price in another year, as follows. price in year A index in year A price in year B index in year B
A parallel plate capacitor has an area of 1.5 cm
2
and the plates are separated a distance of 2.0 mm with air between them. How much charge does this capacitor store when connected to a 12V battery?
Step-by-step explanation:
Given:
[tex]A=1.5\:\text{cm}^2×\left(\frac{1\:\text{m}^2}{10^4\:\text{cm}^2}\right)=1.5×10^{-4}\:\text{m}^2[/tex]
[tex]d = 2.0\:\text{mm} = 2.0×10^{-3}\:\text{mm}[/tex]
The charge stored in a capacitor is given by [tex]Q = CV.[/tex] In the case of a parallel-plate capacitor, its capacitance C is given by
[tex]C = \epsilon_0\dfrac{A}{d}[/tex]
where [tex]\epsilon_0[/tex] = permittivity of free space. The amount of charge stored in the capacitor is then
[tex]Q = \left(\epsilon_0\dfrac{A}{d}\right)V[/tex]
[tex]\:\:\:\:\:=\left[\dfrac{(8.85×10^{-12}\:\text{F/m})(1.5×10^{-4}\:\text{m}^2)}{(2.0×10^{-3}\:\text{m})}\right](12\:\text{V})[/tex]
[tex]\:\:\:\:\:=8.0×10^{-12}\:\text{C}[/tex]
Find the length of AC on this triangle
Answer:
A
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan12° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{44}[/tex] ( multiply both sides by 44 )
44 × tan12° = AC , then
AC ≈ 9.35 ( to 2 dec. places )
Please i need to find the era bounded by the following curves
Answer:
10 2/3 or 32/ 3
Step-by-step explanation:
5 - x^2 - (2 - 2x) =
= -x^2 + 2x + 3
Integral of (-x^2 + 2x + 3)dx from -1 to 3 =
= -x^3/3 + 2x^2/2 + 3x from -1 to 3
= -x^3/3 + x^2 + 3x from -1 to 3
= -27/3 + 9 + 9 - (1/3 + 1 - 3)
= -9 + 9 + 9 - 1/3 - 1 + 3
= 11 - 1/3
= 10 2/3 = 32/3
Answer:
32/3
Step-by-step explanation:
Check the pdf :)
Please look below (Please Explain and NO LINKS)
Answer:
Mean = Sum of all numbers divided by the amount of numbers
[tex]Mean/Average=\frac{3+1+1.5+1.25+2.25+4+1+2}{8} =\frac{16}{8} =2[/tex]
Median = the middle number when the ordered from least to greatest.
From least to greatest: [tex]1, 1, 1.25, 1.5, 2, 2.25, 3, 4[/tex]The two middle numbers are 1.5 and 2.If there are two middle numbers, find the mean/average of those numbers:
[tex]\frac{1.5+2}{2} =\frac{3.5}{2} =1.75[/tex]
Therefore, the answer would be:
Mean = 2Median = 1.75Solve the equation.
1. For parentheses:
Distribute
4-2(x+7) = 3(x+5)
2. If necessary:
Combine Terms
3. Apply properties:
Add Subtract
Multiply
Divide
4. To start over:
Reset
Answer:
x = -5
Step-by-step explanation:
4-2(x+7) = 3(x+5)
Distribute
4 - 2x-14 = 3x+15
Combine like terms
-2x-10 = 3x+15
Add 2x to each side
-2x-10 +2x =3x+2x+15
-10 = 5x+15
Subtract 15 from each side
-10-15 = 5x+15-15
-25 = 5x
Divide by 5
-25/5 = 5x/5
-5 =x
If sum of first 6 digits of AP is 36 and that of the first 16 terms is 255,then find the sum of first ten terms.
•Please answer it correctly ( step by step)
Answer:
100
Step-by-step explanation:
We have the sum of first n terms of an AP,
Sn = n/2 [2a+(n−1)d]
Given,
36= 6/2 [2a+(6−1)d]
12=2a+5d ---------(1)
256= 16/2 [2a+(16−1)d]
32=2a+15d ---------(2)
Subtracting, (1) from (2)
32−12=2a+15d−(2a+5d)
20=10d ⟹d=2
Substituting for d in (1),
12=2a+5(2)=2(a+5)
6=a+5 ⟹a=1
∴ The sum of first 10 terms of an AP,
S10 = 10/2 [2(1)+(10−1)2]
S10 =5[2+18]
S10 =100
This is the sum of the first 10 terms.
Hope it will help.
[tex]\sf\underline{\underline{Question:}}[/tex]
If sum of first 6 digits of AP is 36 and that of the first 16 terms is 255,then find the sum of first ten terms.
$\sf\underline{\underline{Solution:}}$
$\sf\bold\purple{||100||}$$\space$
$\sf\underline\bold\red{||Step-by-Step||}$
$\sf\bold{Given:}$
$\sf\bold{S6=36}$ $\sf\bold{S16=255}$$\space$
$\sf\bold{To\:find:}$
$\sf\bold{The \: sum\:of\:the\:first\:ten\:numbers}$$\space$
$\sf\bold{Formula\:we\:are\:using:}$
$\implies$ $\sf{ Sn=}$ $\sf\dfrac{N}{2}$ $\sf\small{[2a+(n-1)d]}$
$\space$
$\sf\bold{Substituting\:the\:values:}$
→ $\sf{S6=}$ $\sf\dfrac{6}{2}$ $\sf\small{[2a+(6-1)d]}$
→ $\sf{36 = 3[2a+(6-1)d]}$
→$\sf{12=[2a+5d]}$ $\sf\bold\purple{(First \: equation)}$
$\space$
$\sf\bold{Again,Substituting \: the\:values:}$
→ $\sf{S16}$ $\sf\dfrac{16}{2}$ $\sf\small{[2a+(16-1)d]}$
→ $\sf{255=8[2a + (16-1)d]}$
:: $\sf\dfrac{255}{8}$ $\sf\small{=31.89=32}$
→ $\sf{32=[2a+15d]}$ $\sf\bold\purple{(Second\:equation)}$
$\space$
$\sf\bold{Now,Solve \: equation \: 1 \:and \:2:}$
→ $\sf{10=20}$
→ $\sf{d=}$ $\sf\dfrac{20}{10}$ $\sf{=2}$
$\space$
$\sf\bold{Putting \: d=2\: in \:equation - 1:}$
→ $\sf{12=2a+5\times 2}$
→ $\sf{a = 1}$
$\space$
$\sf\bold{All\:of\:the\:above\:eq\: In \: S10\:formula:}$
$\mapsto$ $\sf{S10=}$ $\sf\dfrac{10}{2}$ $\sf\small{[2\times1+(10-1)d]}$
$\mapsto$ $\sf{5(2\times1+9\times2)}$
$\mapsto$ $\sf\bold\purple{5(2+18)=100}$
$\space$
$\sf\small\red{||Hence , the \: sum\: of \: the \: first\:10\: terms\: is\:100||}$
_____________________________
Eli takes the 17 apples home, and he bakes as many apple pies
as he can. He uses 7 apples in each pie. How many apple pies does
Eli bake? How many apples are left?
Answer:
2 with 3 left over
Step-by-step explanation:
17 divided by 2 is 14 with 3 remaining
Answer:
2 pies
Step-by-step explanation:
Do number 6 plz thanks
Answer:
24cm
Step-by-step explanation:
Question: Find the length of side OR.
Answer + explanation:
24cm
Since PQ = 24 cm, OR = 24 cm because they're paralleled and congruent!
Answer:
<O = 125
OR = 24
Step-by-step explanation:
consecutive angles are supplementary in a parallelogram
<R + <O = 180
55 + <O =180
<O = 180-55
< O = 125
opposite sides are congruent in a parallelogram
PQ = OR = 24
Which statements describe the data in the bar graph? Check all that apply.
People prefer rock music to any other type of music.
People prefer pop music to any other type of music.
The least favorite genre of music is blues.
The least frequent favorite genre is country.
Four times as many people prefer pop music to blues.
Answer:
People prefer pop music to any other type of music.
The least favorite genre of music is blues.
Four times as many people prefer pop music to blues.
Answer:
People prefer pop music to any other type of music.
The least favorite genre of music is blues.
Four times as many people prefer pop music to blues.
Answer:
B) People prefer pop music to any other type of music.
C) The least favorite genre of music is blues.
E) Four times as many people prefer pop music to blues.
Step-by-step explanation:
edge 2023
Identify the decimals labeled with letters A B and C on the scale
Answer:
A. 37.39 B. 37.41 C. 37.27
Translate into an algebraic expression:
n-1 increased by 110%
Answer:
Step-by-step explanation:
(n-1)1.1
ifteen accounting majors had an average grade of 90 on a finance exam. Seven marketing majors averaged 85, while ten finance majors averaged 93 on the same exam. What is the weighted mean for the 32 students taking the exam? A. 89.84 B. 89.33 C. 89.48 D. Impossible to determine without more information
Answer:
A. 89.84
Step-by-step explanation:
Weighed mean:
Sum of the multiplications of each value by its weight, divided by the sum of the weights.
Weights:
15 had an average of 90.
7 averaged 85.
10 averaged 93.
What is the weighted mean for the 32 students taking the exam?
[tex]M = \frac{15*90 + 7*85 + 10*93}{15 + 7 + 10} = 89.84[/tex]
Thus the correct answer is given by option A.
A researcher records the repair cost for 27 randomly selected refrigerators. A sample mean of $60.52 and standard deviation of $23.29 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The critical value is [tex]T_c = 1.7056[/tex]
The 90% confidence interval for the mean repair cost for the refrigerators is ($52.875, $68.165).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 27 - 1 = 26
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7056, which means that the critical value is [tex]T_c = 1.7056[/tex]
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.7056\frac{23.29}{\sqrt{27}} = 7.645[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 60.52 - 7.645 = $52.875.
The upper end of the interval is the sample mean added to M. So it is 60.52 + 7.645 = $68.165.
The 90% confidence interval for the mean repair cost for the refrigerators is ($52.875, $68.165).
A car rental agency rents 480 cars per day at a rate of $20 per day. For each $1 increase in rate, 10 fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What is the maximum income?
Answer:
340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.
Step-by-step explanation:
Given that a car rental agency rents 480 cars per day at a rate of $ 20 per day, and for each $ 1 increase in rate, 10 fewer cars are rented, to determine at what rate should the cars be rented to produce the maximum income and what is the maximum income, the following calculations must be performed:
480 x 20 = 9600
400 x 28 = 11200
350 x 33 = 11550
300 x 38 = 11400
310 x 37 = 11470
320 x 36 = 11520
330 x 35 = 11550
340 x 34 = 11560
Therefore, 340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.
Determine the product of (46.2 × 10^-1) ⋅ (5.7 × 10^–6). Write your answer in scientific notation.
A)
2633.4 × 10^–5
B)
2.6334 × 10^–7
C)
2.6334 × 10^–1
D)
2.6334 × 10^–5
Step-by-step explanation:
here's the answer to your question
Find the missing length in the image below
Let it be x
Using basic proportionality theorem
[tex]\\ \sf\longmapsto \dfrac{x}{10}=\dfrac{14}{7}[/tex]
[tex]\\ \sf\longmapsto \dfrac{x}{10}=2[/tex]
[tex]\\ \sf\longmapsto x=10(2)[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
Find the measure of each angle in the problem. TO contains point H.
Answer:
The angles are 45 and 135
Step-by-step explanation:
The two angles form a straight line, which is 180 degrees
c+ 3c = 180
4c = 180
Divide by 4
4c/4 =180/4
c = 45
3c = 3(45) = 135
The angles are 45 and 135
Answer:
45 and 135 ...
Find the measures of angles 1 and 2. If necessary, round to the tenths place.
Hint: Do not assume that Point D is the center of the circle.
A. m<1 = 20 m<2= 20
B. m<1 =40 m<2 = 140
C. m<1 = 82.5 m<2 = 97.5
D. m<1 =97.5 m<2= 82.5
Answer:
Option C
Step-by-step explanation:
From the picture attached,
m∠ABC = 40° [Given]
Since, measure of the intercepted arc is double of the measure of the inscribed angle.
Therefore, m(arc AC) = 2(m∠ABC)
m(arc AC) = 2(40°)
= 80°
m(arc FB) = 115° [Given]
By applying theorem of the angles formed by the chords inside a circle,
m∠2 = [tex]\frac{1}{2}(\text{arc}AC+\text{arc}FB)[/tex]
= [tex]\frac{1}{2}(80^{\circ}+115^{\circ})[/tex]
= 97.5°
m∠1 + m∠2 = 180° [Linear pair of angles are supplementary]
m∠1 + 97.5° = 180°
m∠1 = 180° - 97.5°
= 82.5°
Option C is the answer.
