Answer:
Step-by-step explanation:
Point-slope equation for line of slope m that passes through (x₀, y₀):
y-y₀ = m(x-x₀)
apply your data
y-2 = 4(x-6)
Answer:
y−2= −2(x−7)
Step-by-step explanation:
khan academy says its right
Find the area of the composite figure in terms of the figure (use 3.14 for pi)
Answer:
105.12 ft²
Step-by-step explanation:
Let's first find the area of the rectangle.
[tex]10\cdot8=80[/tex] ft², so the rectangle has an area of 80ft².
To find the area of the semi-circle, we find the area of a whole circle and divide by two.
The formula to find the area of a circle is [tex]\pi r^2[/tex]. The radius is 4, as the diameter is 8.
[tex]3.14\cdot4^2[/tex]
[tex]3.14\cdot16[/tex]
[tex]50.24\div2=25.12[/tex]
Add 80 and 25.12:
[tex]80+25.12=105.12[/tex]
Hope this helped!
Find the greatest common factor of 65a3b4 and 39a4b5.
Step-by-step explanation: Let's begin by finding the
greatest common factor for the numbers 65 and 39.
I would make a factor tree and break up 65 and 39.
So 65 is 13 x 5 and 39 is 13 x 3.
Since the 13's match up, the greatest
common factor between 65 and 39 is 13.
For the variables, we use the smallest power on each of them.
So we use a^3 and b^4 to get 13a^3b^4 as our GCF.
The value (in dollars) of an airplane depends on the flight hours as given by the formula V= 1,800,000 - 250x . After one year, the value of the plane is between $1,200,000 and $1,300,000. Which range for the flight hours does this correspond to?
a. 1800 <= x <= 2100
b. 2200<= x <= 2500
c. 1500<= x <= 1800
d. 2000<= x <= 2400
Answer:
D
Step-by-step explanation:
To determine the range we must solve this inequality;
● 1200000<1800000-250x<1300000
Substract 1800000 from both sides.
● 1200000-1800000<1800000-250x<1300000-1800000
● -600000< -250x < -500000
Divide both sides by 250
● -600000/250 < -250x/250 < -500000/250
● -2400 < -x < -2000
Multiply both sides by -1 and switch the signs
● 2000 < x < 2400
The correct option is D. 2000<= x <= 2400
Given, the value of an airplane depends on the flight hours,
[tex]V= 1800000-250x[/tex], here x is the flight hours.
We have to calculate the range of x After one year.
Since, [tex]V= 1800000-250x[/tex]
[tex]250x=1800000-V\\\\x=\dfrac{1800000-V}{250}[/tex]
Since the value of the plane is between $1,200,000 and $1,300,000. So,
[tex]x=\dfrac{1800000-1200000}{250}[/tex]
[tex]x=\dfrac{600000}{250}[/tex]
[tex]x=2400\\[/tex]
When V is 1300000 then x will be,
[tex]x=\dfrac{1800000-1300000}{250} \\[/tex]
[tex]x=\dfrac{500000}{250}[/tex]
[tex]x=2000[/tex]
Hence the range of x will be from 2000 to 2400.
The correct option is D. 2000<= x <= 2400.
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Which expression is equivalent to RootIndex 4 StartRoot x Superscript 10 Baseline EndRoot?
Answer:x2.2
Step-by-step explanation:
Question 5 of 10
Which of these groups of values plugged into the TVM Solver of a graphing
calculator will return the amount of a 20-year loan with an APR of 19.2%,
compounded monthly, that is paidoff with monthly payments of $510?
A. N=20; 1%=19.2; PV = ; PMT=-510; FV=0; P/Y=12; C/Y=12;
PMT:END
B. N=240; 1%=19.2; PV = ; PMT=-510; FV=0; P/Y=12; C/Y=12;
PMT:END
C. N=240; 1%=1.6; PV = ; PMT=-510; FV=0; P/Y=12; C/Y=12;
PMT:END
O D. N=20; 1%=1.6; PV = ; PMT=-510; FV=0; P/Y=12; C/Y=12; PMT:END
Answer:
N=240;I%=5.6=-205000;PMT=;Fv=0;P/Y=12;C/Y=12;PMT:END
Step-by-step explanation:
A P E X
The group of values to be plugged into TVM solver is
N=240 ; I % = 19.2% , P = -205000 , PMT= -$510, Fv =0 , P/Y =12.
We have 20 year loan then the number of periods will be
N = 20 x 12
N= 240
and, the Monthly payment is $510 then
PMT = - 510
and, Interest = 19.2%
and, PV = - 205, 000
Thus, N=240 ; I % = 19.2% , P = -205000 , PMT= -$510, Fv =0 , P/Y =12.
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BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?
Answer:
$935.76
Step-by-step explanation:
BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?
Step 1
We find the Present value factor of sum
The formula =
(1 + i)^n
Where
i = maturity rate = 9% = 0.09
n = number of years = 10 years
Present Value = ( 1 + 0.09)^-10
= 0.4224
Step 2
We find the present value factor of annuity
The formula is given as:
1 - (1+i)^-n / i
i = maturity rate = 9% = 0.09
n = number of years = 10 years
= 1 - (1 + 0.09)^-10 /0.09
= 1 - 0.4224 /0.09
= 0.5775 /0.09
= 6.417
Step 3
The bond's current market price is calculated as:
= PV factor of Sum × Par Value + PV factor of annuity × coupon payment
Coupon payment is calculated as:
= Coupon interest × par value
= 8% × 1000
= 80
Hence,
= 0.4224 × 1,000 + 6.417 × 80
= 422.4 + 513.36
= 935.76
In this exercise we have to use the knowledge of finance to calculate the corrective value of the market place, in this way we find that:
[tex]\$935.76[/tex]
We find the Present value factor of sum, by the formula of:
[tex](1 + i)^n[/tex]
Where:
i = maturity rate = 9% = 0.09 n = number of years = 10 years
Substituting the values in the formula as;
[tex]Present \ Value = ( 1 + 0.09)^{-10} = 0.4224[/tex]
We find the present value factor of annuity, by the formula as:
[tex]1 - (1+i)^{-n} / i[/tex]
Where:
i = maturity rate = 9% = 0.09 n = number of years = 10 years
Substituting the values in the formula as;
[tex]= 1 - (1 + 0.09)^{-10} /0.09\\= 1 - 0.4224 /0.09\\= 0.5775 /0.09\\= 6.417[/tex]
The bond's current market price is calculated as:
[tex]= PV \ factor\ of\ Sum * Par\ Value + PV\ factor\ of\ annuity * coupon\ payment[/tex]
Coupon payment is calculated as:
[tex]= Coupon\ interest * par\ value\\= 8\% * 1000= 80[/tex]
So continue the calcule;
[tex]= 0.4224 *1,000 + 6.417 * 80\\= 422.4 + 513.36\\= 935.76[/tex]
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Hurry quick i have more questions answer then all for a total of about 100 points
Answer:
1/5
Step-by-step explanation:
.7555555(repeating )
writing as a fraction
x = .755555555
10 x = 7.555555
Subtract the two
10x = 7.555555
-x = .75555555
--------------------------
9x =6.8
Divide each side by 9
x = 6.8/9
x = 68/90
Divide by 2
x = 34/45
We do the same for .555555 repeating
y = .5555 repeating
10 y = 5.5 repeating
10y = 5.5
-y = .555
-------------------
9y = 5
y = 5/9
Subtract x - y
34/45 - 5/9
Get a common denominator
34/45 - 25/45
9/45
1/5
A collection of 30 coins consists of dimes and nickels. The total value is $1. 95How many dimes are there?
find the value of x? please help
Answer:
49
Step-by-step explanation:
With these types of problems, you have to subtract the outer and inner values and then divide by 2. So, (125-27)/2 = 49. Hope this helps!
The function g(x) = x2 is transformed to obtain function h:
h(x) = g(x) – 5.
Which statement describes how the graph of his different from the graph of g?
A.
The graph of h is the graph of g horizontally shifted right 5 units.
B.
The graph of h is the graph of g vertically shifted up 5 units.
C.
The graph of h is the graph of g vertically shifted down 5 units.
OD.
The graph of h is the graph of ghorizontally shifted left 5 units.
Answer:
Option C
The graph of g is vertically shifted 5 units down
(3) In a group of 60 seldiers have enough food for
20 days - How many soldiers should leave the group
so that the food is enough for 100 days ? Find it.
Answer:
48 soldiers
Step-by-step explanation:
60 soldiers 20 days
x soldiers 100 days
60 x 20 = 1200 = 100x
Therefore x = 1200/100 = 12
60 - 12 = 48
Hope that helped!!! k
Answer:
30 Soldiers
Step-by-step explanation:
Given:
1) No of soldiers=60
No of days=20
2) No of days=100
No of soldiers=?
No of soldiers to leave=?
Solution:
Let us use the cross multiplication method.
Let x be the no of soldiers.
No of days No of soldiers
1) 20 60
2) 100 x
by cross multiplying,
20x=100 x 60
20x=600
x=600/20
x=30 soldiers
Therefore, No of soldiers to leave =60-30=30 soldiers
John receives a perpetuity paying 2 at the end of year 4, 4 at the end of year 6, 6 at the end of year 8, etc. The present value of this perpetuity at an annual effective rate of 10% equals X. Calculate X
Answer:
45.35
Step-by-step explanation:
From the above question, we are told that the annual effective rate = 10% = 0.10
Note also that payment is been made every 2 years
Hence , we apply the formula of effective interest rate for a period of 2 years.
Effective Interest rate(j) = (1 + r)² - 1
= (1 + 0.10)² - 1
= 1.10² - 1
= 1.21
= 0.21
Present value of perpetuality = t/[j × j/(1 + r)²]
Where t = time in years = 2
r = 0.10
= 2/ [0.21 × 0.21/(1 + 0.10)²
= 54.87528
Present value at time t = 0
= 54.87528(1 + r)^-2
= 54.87528(1 + 0.10) ^-2
= 54.87528(1.10)^-2
= 45.35
Therefore, the present value at time (t) is 0 = 45.35
a day? 6. If 18 pumps can raise 2150 tonnes of water in 50 days, working 8 hours a day, how much water will be raised in 60 days by 16 out of which 10 are working 9 hours a day and the rest 7 hours a day?
if ella earns x dollars, she is taxed x%. How much money should she earn to maximize her income?
Answer:
just devide it. after that ÷ with 100 per time
find the probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10, all of the same suit. What is the probability of being dealt this hand is
Answer: 20/52 x 4/51 x 3/50 x 2/49 x 1/48 = .00000153908
Step-by-step explanation:
The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10 of the same suit is 0.00000153908
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
The value of probability lies between 0 and 1
Given data ,
Let the number of cards in deck be = 52 cards
Total number of cards selected = 5
The number of ways of choosing 5 cards = ⁵²C₅
The cards selected are of the same suit
So , there are 4 ways to select them , Hearts , Clubs , Spades and Diamonds = ⁴C₁
And there is only one way to select the cards 6 , 7 , 8 , 9 , 10 = 1
Now , we use combination to select the cards in a deck,
So,
The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10, all of the same suit is calculated by,
P ( x ) = 1 / ⁵²C₅ x ⁴C₁ x 1
P ( x ) = 1 / 52! / ( 47! x 5! ) x 4! / 3! x 1
P ( x ) = 1 / ( 52 x 51 x 50 x 49 x 48 ) / ( 2 x 3 x 4 x 5 ) x 4
P ( x ) = 1 / ( 2598966 ) x 4
P ( x ) = 4 / 2598966
P ( x ) = 0.00000153908
Hence , The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10 of the same suit is 0.00000153908
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PLEASE HELP!!! Determine the domain and range of the following function. Record your answers in set notation.
Answer:
Ok so to help you out, first, off you need to be sure that the sets domain and range use the proper variable. After that, you are going to want to just plug it into the equation. I am going to link a screenshot to the correct answer if you are still have trouble finding it.
Anyways hoped this helped and I got to this question in time c:
Please help! Make sure to simplify
[tex] \frac{5b^{5}c}{4c^4} \times \frac{8c}{b^4}[/tex]
[tex]\frac{40b^{5}c^2}{4b^{4}c^4}[/tex]
[tex]{10b^{5-4}c^{2-4}}[/tex]
[tex]10bc^-2[/tex]
[tex]\frac{10b}{c^2}[/tex]
Step-by-step explanation:
[tex] \frac{5 {b}^{5} c}{ 4{c}^{4} } \times \frac{8c}{ {b}^{4} } [/tex]
First reduce the expression with b⁴
b⁴ will cancel b^5 remaining with one b
That's
[tex] \frac{5bc}{4 {c}^{4} } \times 8c[/tex]Next reduce 8 and 4 with their GCF which is 4
We have
[tex] \frac{5bc}{ {c}^{4} } \times 2c[/tex]Reduce the expression with c .
c will go into c⁴ remaining with c³
That's
[tex] \frac{5bc}{ {c}^{3} } \times 2[/tex]Simplify the expression again with c
That's
[tex] \frac{5b}{ {c}^{2} } \times 2[/tex]Multiply the expression
We have the final answer as
[tex] \frac{10b}{ {c}^{2} } [/tex]Hope this helps you
A population is estimated to have a standard deviation of 9. We want to estimate the population mean within 2, with a 99% level of confidence. How large a sample is required? (Round up your answer to the next whole number.)
Answer:
The sample required is [tex]n = 135[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 9[/tex]
The margin of error is [tex]E = 2[/tex]
Given that the confidence level is 99% then the level of significance is mathematically evaluated as
[tex]\alpha = 100-99[/tex]
[tex]\alpha = 1 \%[/tex]
[tex]\alpha = 0.01[/tex]
Next we will obtain the critical value [tex]\frac{\alpha }{2}[/tex] from the normal distribution table(reference math dot armstrong dot edu) , the value is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 2.58[/tex]
The sample size is mathematically represented as
[tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]
substituting values
[tex]n = [ \frac{ 2.58 * 9 }{2} ]^2[/tex]
[tex]n = 135[/tex]
given the circle find the arc measure
9514 1404 393
Answer:
87°
Step-by-step explanation:
Call the circle center point X. The measure of arc FG is the measure of central angle FXG, which is the supplement of central angle GXH.
arc FG = 180° -93° = 87°
what is the average rate of change from 1 to 3 of the function represented by the graph? the graph is attached.
Answer: -4
At 1, the parabola is at (1, 3). And at 3, it's at (3, -5). The rate of change is -4, since each time it moves right 1, it goes down 4.
Hope that helped,
-sirswagger21
Solve for x using the
distributive property.
6(2 - 6x) = -24
X ?
⇛6(2 - 6x) = -24
⇛12 - 36x = -24
⇛-36x = -24 - 12
⇛-36x = -36
⇛x = -36/-36
⇛x = 1
Instructions: The polygons in each pair are similar. Find the
missing side length.
Answer:
45/27=30/18=x/24
x = 30×24/18
or, x = 40
Answer:
? = 40
Step-by-step explanation:
Since the polygons are similar then the corresponding sides are in proportion, that is
[tex]\frac{?}{24}[/tex] = [tex]\frac{?}{24}[/tex] = [tex]\frac{30}{18}[/tex] ( cross- multiply )
18 ? = 720 ( divide both sides by 18 )
? = 40
which best defines a service
Answer:
A service could be multiple things.
Step-by-step explanation:
Like, working as a scribe in a nursing home helping old people. Or, being part of a leadership club at school that funds food banks and things like that
Answer:
a
Step-by-step explanation:
The average person lives for about 78 years. Does the average person live for at least 1,000,000 days? (Hint: There are 367 days in each year.)
what i
Answer:
[tex]\large \boxed{\sf No}[/tex]
Step-by-step explanation:
There are 365 days in 1 year.
The average person lives for about 78 years.
Multiply 78 by 365 to find the value in days.
[tex]78 \times 365= 28470[/tex]
The average person lives for about 28470 days.
-7y=-91 show your work
Answer:
[tex] \boxed{ \bold{\sf{y = 13}}}[/tex]Step-by-step explanation:
[tex] \sf{ - 7y = - 91}[/tex]
Divide both sides of the equation by -7
⇒[tex] \sf{ \frac{ - 7y}{ - 7} = \frac{ - 91}{ - 7} }[/tex]
Calculate
⇒[tex] \sf{y = 13}[/tex]
Hope I helped!
Best regards!!
Answer:
[tex] \boxed{\sf y = 13} [/tex]
Step-by-step explanation:
Solve for y:
[tex] \sf \implies - 7y = - 91[/tex]
Divide both sides of -7y = -91 by -7:
[tex] \sf \implies \frac{ - 7y}{ - 7} = \frac{ - 91}{ - 7} [/tex]
[tex] \sf \frac{ - 7}{ - 7} = 1 : [/tex]
[tex] \sf \implies y = \frac{ - 91}{ - 7} [/tex]
[tex] \sf \implies y = \frac{ \cancel{ - 7} \times 13}{ \cancel{ - 7}} [/tex]
[tex] \sf \implies y = 13[/tex]
Which best describes the relationship between the line that passes through the points (9, -1) and (11,3) and the line that passes through
the points (-6, 4) and (-4,0)?
Answer:
Option B, parallel
Step-by-step explanation:
for the first line,
[3-(-1)]/[11-9]
= 4/2 = 2
for the second line,
(0-(-4))/(-4-(-6))
= 4/2 = 2
Both has same slope so they're parallel but it doesn't seem like they are the same line
Verify the identity algebraically:
Csc(-x)tanx =-secx
Step-by-step explanation:
Recall that
[tex]\sin(-x) = -\sin x[/tex]
Therefore,
[tex]\csc(-x) = \dfrac{1}{\sin(-x)} = -\dfrac{1}{\sin x}[/tex]
so
[tex]\csc(-x)\tan x = \left(-\dfrac{1}{\sin x}\right)\left(\dfrac{\sin x}{\cos x}\right)[/tex]
[tex]\:\:\:\:\:\:\:\:\:= -\dfrac{1}{\cos x} = -\sec x[/tex]
Sam have worked these hours during the week: 4.5, 8.75, 9.5, 10, and 4.25 hours. How many hours did Sam work?
Answer:
37 hours
Step-by-step explanation:
4.5 + 8.75 + 9.5 + 10 + 4.25 = 37 hours
Answer:
37 hours
Step-by-step explanation:
4.5 hours = 4 hrs and 30 mins
8.75 hrs = 8 hrs and 45 mins
9.5 hrs = 9 hrs and 30 mins
10 hrs = 10 hrs and 0 min
4.25 hrs = 4 hrs and 15 mins
(30 + 45 + 30 + 15) mins = 2 hrs
Therefore, total hours Sam worked = (4 + 8 + 9 + 10 + 4 + 2) hrs = 37 hours
A publishing company claims that in fall 2019, the average price of college textbooks for a single semester is $385. Suppose you decide to collect data from a random sample of students to assess whether the publisher's claim is reasonable, and you find that in a random sample of 22 college students, the mean price of textbooks for the fall 2019 semester was $433.50 with a standard deviation of $86.92. At the 0.01 significance level, is there sufficient evidence to conclude that the mean price of college textbooks for a single semester is different from the value claimed by the publisher?
Answer:
We accept H₀ . We don´t have enough evidence to express the publisher claim is not true
Step by Step explanation:
We must evaluate if the mean of the price of college textbooks is different from the value claimed by the publisher
n < 30 then we must use t - distrbution
degree of freedom n - 1 df = 22 - 1 df = 21
As the question mentions " different " that means, a two-tail test
At 0,01 significance level α = 0,01 α/2 = 0,005
and t(c) = 2,831
Test Hypothesis
Null Hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ ≠ μ₀
To calculate t(s)
t(s) = ( μ - μ₀ ) /σ/√n
t(s) = ( 433,50 - 385 ) / 86,92 / √22
t(s) = 2,6171
Comparing t(c) and t(s)
t(s) < t(c)
Then t(s) is in the acceptance region we accept H₀. We don´t have enough evidence to claim that mean price differs from publisher claim
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x + 3y = -9
Answer:
[tex]y = -x - 3[/tex]
Step-by-step explanation:
We are trying to get the equation [tex]3x + 3y = -9[/tex] into the form [tex]y = mx+b[/tex], aka slope-intercept form.
To do this we are trying to isolate y.
[tex]3x + 3y = -9[/tex]
Subtract 3x from both sides:
[tex]3y = -9 - 3x[/tex]
Rearrange the terms:
[tex]3y = -3x - 9[/tex]
Divide both sides by 3:
[tex]y = -x - 3[/tex]
Hope this helped!