What are the slope and y-intercept of the line?
slope = -170. y-intercept = 1020
Step-by-step explanation:
Let [tex]P_1(0, 1020)[/tex] and [tex]P_2(6, 0).[/tex] The slope can be calculated as
[tex]m = \dfrac{0 - 1020}{6 - 0} = -170\:\text{m/hr}[/tex]
So the equation can be written as
[tex]y = -170x + b[/tex]
To solve for b, let's use the values for P2:
[tex]0 = -170(6) + b \Rightarrow b = 1020[/tex]
Therefore,
[tex]y = -170x + 1020[/tex]
To find the y-intercept, let x = 0. then the y-intercept is
[tex]y = -170(0) + 1020[/tex]
or
[tex](0, 1020).[/tex]
A group of ten people includes six men and four women. If five of these people are randomly selected to fill out a questionnaire, how many different samples of five people are possible?
The table shows the mass of a substance decreasing over a period of time during a chemical experiment.
Identify a quadratic model for the mass M, given the time t. Then use the model to predict the mass at t = 11
seconds
Time (s) Mass (g)
2
94.8
5
87.9
8
81.3
B
O M(x) = -0.02x2 - 2.42x + 99.57
M(11) - 75 g
O M(x) = 0.02x2 - 2.42x + 99.57
M(11) - 1299
O M(x) = -0.02x2 - 2.42X + 99.57
M(11) = 129 g
O M(x) = 0.02x2 - 2.42x + 99.57
M(11) = 75 g
So from a table, we want to find an equation that models the mass as a function of time, we will get the equation:
M(t) = 0.02*t^2 - 2.42*t + 99.57
And with that equation, we will find that the mass after 11 seconds is 75 grams.
From the table we have the points:
(2, 94.8)
(5, 87.9)
(8, 81.3)
And we know that this follows a quadratic model, then we have:
M(t) = a*t^2 + b*t + c
Notice that from the known points, we have 3 equations:
94.8 = a*2^2 + b*2 + c
87.9 = a*5^2 + b*5 + c
81.3 = a*8^2 + b*8 + c
So we have a system of equations, we can simplify the equations to get:
94.8 = a*4 + b*2 + c
87.9 = a*25 + b*5 + c
81.3 = a*64 + b*8 + c
To solve this, we start by isolating one of the variables in one of the equations, let's isolate c in the first one.
c = 94.8 - a*4 - b*2
now we replace this in the other two equations to get:
87.9 = a*25 + b*5 + (94.8 - a*4 - b*2)
81.3 = a*64 + b*8 + ( 94.8 - a*4 - b*2)
Now we simplify these two equations to get:
-6.9 = a*21 + b*3
-13.5 = a*60 + b*6
Now we do the same thing, I will isolate b in the first equation:
b = (-6.9 - a*21)/3 = -2.3 - a*7
Now we replace this in the other equation:
-13.5 = a*60 + (-2.3 - a*7)*6
Now we can just solve this for a:
-13.5 = a*(60 - 7*6) - 2.3*6
0.3 = a*18
0.3/18 = a = 0.016
Wich can be rounded to:
a = 0.02
Then the value of b is:
b = -2.3 - a*7 = -2.3 - 0.016*7 = -2.42
And the value of c is:
c = 94.8 - a*4 - b*2 = 94.8 - 0.016*4 - (-2.42)*2 = 99.57
So the equation is:
M(t) = 0.02*t^2 - 2.42*t + 99.57
Now we can evaluate this in t = 11s to get:
M(11) = 0.02*11^2 - 2.42*11 + 99.57 = 75.37
Wich can be rounded to 75 grams.
If you want to learn more, you can read:
https://brainly.com/question/20067450
Suppose you invest 18,400.00 into an account earning an interest rate of 2.991% compounded continuously for 2 year(s) and thereafter earning an interest rate of 4.192%compounded yearly. How much money is in the account after 9 years?
[tex]~~~~~~ \stackrel{\textit{for the first 2 years}}{\textit{Continuously Compounding Interest Earned Amount}} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$18400\\ r=rate\to 2.991\%\to \frac{2.991}{100}\dotfill &0.02991\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 18400e^{0.02991\cdot 2}\implies A = 18400e^{0.05982}\implies A\approx 19534.276[/tex]
now let's grab that amount and invest it for the remaining 7 years at 4.192% compounded.
[tex]~~~~~~ \stackrel{\textit{for the last 7 years}}{\textit{Compound Interest Earned Amount}}\\\\A=P\left(1+\frac{r}{n}\right)^{nt}\quad\begin{cases}A=\textit{accumulated amount}\\P=\textit{original amount deposited}\dotfill &\$19534.276\\r=rate\to 4.192\%\to \frac{4.192}{100}\dotfill &0.04192\\n=\begin{array}{llll}\textit{times it compounds per year}\\\textit{yearly meaning once}\end{array}\dotfill &\\t=years\dotfill &7\end{cases}[/tex]
[tex]A=19534.276\left(1+\frac{0.04192}{1} \right)^{1\cdot 7}\implies \boxed{A\approx 26039.82}[/tex]
30 percent of a number is 48 what is 50 percent of the same number
0.3x = 48
So x is 48/0.3
Therefore, 0.5 times 48/0.3 is the answer
100.000.000x30
Kaçtır?
Answer:
the answer is 3000000000
A pound of fertilizer covers 39 square feet lawn.Vivian Bulgakov lawn measures 7072.7 square feet,How much fertilizer,to the nearest tenth of a pound does she need to buy?
Answer: 275835.5
because 7072.7 times 39
Add the polynomials (-4x^3 + x^2y - xy^2), (3x^3 - xy^2 + 5x^2y) and (7xy^2 + 3y^3)
Answer:
4x³+x²
Step-by-step explanation:
to I was awesome and u too go to north and u too go home with he sister or talk
find DEC
pls give through explanation
[tex]\large{\rm{\underline{\underline{Answer:}}}}[/tex]
Angle AEB and Angle DEC are opposite angles which means they are equal in measure. Hence,
⇛ Angle AEB = Angle DEC
⇛ 9x + 8° = 3x + 42°
⇛ 9x - 3x = 42° - 8°
⇛ 6x = 34°
⇛ x = (34/6)°
To find: Angle DEC = 3(
34/6 °) + 42° = 59° (Ans)
A store manager is marking down cameras from $300 to $150. What percentage is the discount?
Write your answer using a percent sign (%).
Answer:
the discount is 50% the previous price
The fraction 1/16 can correctly be read as
Question 5 options:
one divided by sixteen.
sixteen divided by 1.
one sixth.
one and one sixth.
The given fraction [tex](\frac{1}{16} )[/tex] can correctly be read as one divided by sixteen.
A fraction can be defined as a numerical quantity that isn't a whole number and as such has two (2) parts.
Hence, a fraction is simply a part of a whole number.
Generally, a fraction comprises two (2) main parts and these include:
Denominator: this refers to the lower part of a fraction.Numerator: this is the upper part of a fraction.Mathematically, a fraction is represented as:
[tex]Fraction \;A = \frac{1}{16}[/tex]In order to read a fraction, you will start by naming the numerator (upper part) followed by the denominator (lower part).
In this scenario, the given fraction [tex](\frac{1}{16} )[/tex] can correctly be read as one divided by sixteen.
Read more: https://brainly.com/question/6201432
i need help with 32
Answer: See the drawing below
Explanation:
The region to the left of x = -3 has f(x) > 0, aka f(x) is positive. This is due to the sign chart indicating this with a + sign. The same applies from the region between x = -3 and x = -2. The graph will show f(x) above the x axis for these two regions.
When -2 < x < 0, f(x) is now negative and below the x axis. It goes above the x axis for the interval 0 < x < 2. Then it dips back down below the x axis again once it passes x = 2.
The graph below visually summarizes everything talked about. Keep in mind that there are infinitely many ways to draw a graph like this. There's not enough info to pin down one exact answer.
Can someone please help me thank you
36 is the answer, hope this helps.
write the solution in interval notation: 1/4x−3≥−1 and −3(x−2)≥2
Answer:Mark me as Brainliest please
Step-by-step explanation:
Let's solve your inequality step-by-step.
[tex]\frac{1}{4}x-3\geq -1[/tex]
Step 1: Add 3 to both sides.
[tex]\frac{1}{4} x-3+3\geq -1+3[/tex]
[tex]\frac{1}{4} x\geq 2[/tex]
Step 2: Multiply both sides by 4.
[tex]4*(\frac{1}{4} x)\geq (4)*(2)[/tex]
Answer:x≥8
Let's solve your inequality step-by-step.
−3(x−2)≥2
Step 1: Simplify both sides of the inequality.
−3x+6≥2
Step 2: Subtract 6 from both sides.
−3x+6−6≥2−6
−3x≥−4
Step 3: Divide both sides by -3.
[tex]\frac{-3x}{-3} \geq \frac{-4}{-3}[/tex]
Answer:=[tex]x\leq \frac{4}{3}[/tex]Give an example of a function.
example:
Input 9 9 4 5 and output: 3 -3 2 -2
give examples plz
I will make the brainliest.
Choose the correct answers.
Jane Dilford gets a student rate of $30.00 a month for health Insurance. There is a $250 deductible, but no coinsurance
payment. She recently recelved treatment for a covered condition. The bill was $2,550.00 Jane's Insurance company
provided payment of 80% of the bill less the deductible.
What was the company's payment? $2,040 or $1,840
V
What was Jane's total cost (not including monthly premium)? $510 or 710
Answer:
1840 amd 710
Step-by-step explanation:
hard one wat is 500-45=
good luck
Answer:
EASY the awnser is about 15
Answer:
455
Step-by-step explanation:
Add.
45+3110
Enter the sum in the box as a mixed number in simplest form.
Answer:
3110+45=3155
Step-by-step explanation:
just add them to
A line has a rise of 3 and a run of 12. What is the slope?
4
1/4
1/3
Answer:
1/4
Step-by-step explanation:
Rise/run=3/12 divided by 3 = 1/4
Dina and masha started out on a 12 mi bike path at the same time. when dina reached the end of the 12 mi, masha still had 4 mi left to bike. if dina's biking speed is 10 mph, find masha's biking speed. HELP NOWWW
Answer:
Dina took 12/8 = 3/2 hrs
So, if Masha's speed was x
3/2 x = 12-3
x = 6 mi/hr
Answer:
Step-by-step explanation:
Dina finished in a time of
12 mi / 10 mi/hr = 1.2 hr
Masha's speed is (12 - 4 mi) / 1.2 hr = 6⅔ mph
Can someone please help me?
$120; Markup: 35%
What's the final price? pls show how u got the answer...
Answer: 162
Step-by-step explanation:
So you will need to find the Markup. The original cost is $120.
Divide the number by 100 is 1.2. $1.2 is 1% of the $120.Now times the number by 35. $1.2 x 35 is $42.Finally, add the number. 120 + 42 = 162.I hope this is the answer you are looking for.
Can someone help please
Answer:
0.3 miles per hour
Step-by-step explanation:
Speed is distance divided by time so your equation is 45 divided by 150. 45 divided by 60 plus 60 plus 30 = 150 45 divided by 150= 0.3
1.25 is closer to 1.04 or not ?
plz heelp
Answer:
Yes 1.25 is closer to 1.04
Step-by-step explanation:
Hope this helps!
Answer:
1.25 is not closer to 1.04 because it's like, 1 dollar and 4 cents; compared to 1 dollar and 25 cents. Obviously 25 cents is more than 4 cents.
1.25 rounded:
1.30
1.04 rounded:
1.00
Write the slope of the line passing through the two points: (7,8) and (0,5)
Answer:
3/7
Step-by-step explanation:
slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex] = [tex]\frac{5-8}{0-7}[/tex] = -3/-7 = 3/7
Steve bicycles 3 mi to school everyday at 15 mph. If school starts at 8:30 am and he needs 15 min to lock his bike and get to his desk then what time should he leave his house
Answer:
8:03
Step-by-step explanation:
time=speedxdistance
t=1/15x3
t=3/15hr
t=.2hr
t=12 mins
plus 15 mins to lock up bike, 27 mins
27 mins before 8:30 is 8:03
pls mark branliest
Given ABCD, what is the measure of
Answer:
srry dude this isn't rly a quesiton
which prime number is found in between 70 and 80 and is made up of two odd digits which add up to 10
Answer:71
71, 73 and 79
Step-by-step explanation:
A prime number is a number that can only be divided by 1 or itself. Otherwise, it is a composite numbers.
There are three numbers between
70
and
80
that fit this criteria,
71
,
73
, and
79
Please help me ASAP
Answer:
New points:
N: (4,-5)
X: (2,-3)
B: (-1,-4)
Step-by-step explanation:
Rotate about the origin (0,0) counter clockwise 90 degrees
solve the equation 6= A/2 + 2
Answer:
A = 8
Step-by-step explanation:
A/2 + 2 = 6
subtract 2 from each side to get:
A/2 = 4
multiply each side by 2 to get:
A = 8