answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fed [463]
2 years ago
5

Amanda bought g gallons of paint for $16.55 per gallon and t pints of paint thinner for $5.97 per pint. Write an expression to r

epresent the total amount that amanda spent, if amanda bought 8 gallons of paint and 3 pints of paint thinner, how much did she spend? Explain? (A) 16.55t +5.97g...(B) 16.55t x 5.97g..(C) 16.55g + 5.97t..(D) 16.55g x 5.97t
Mathematics
1 answer:
Neporo4naja [7]2 years ago
3 0

Answer:

total \ cost =16.55(8) +5.97(3)=150.31

Step-by-step explanation:

Amanda bought g gallons of paint for $16.55 per gallon and t pints of paint thinner for $5.97 per pint

Total amount = rate per gallon times gallons + rate per pint times  pints

total amount =16.55 g +5.97 t

amanda bought 8 gallons of paint and 3 pints of paint thinner

g=8 and t=3, substitute the values and find total cost

total \ cost =16.55(8) +5.97(3)=150.31

You might be interested in
Where does the helix r(t) = cos(πt), sin(πt), t intersect the paraboloid z = x2 + y2? (x, y, z) = What is the angle of intersect
Colt1911 [192]

Answer:

Intersection at (-1, 0, 1).

Angle 0.6 radians

Step-by-step explanation:

The helix r(t) = (cos(πt), sin(πt), t) intersects the paraboloid  

z = x2 + y2 when the coordinates (x,y,z)=(cos(πt), sin(πt), t) of the helix satisfy the equation of the paraboloid. That is, when

\bf (cos(\pi t), sin(\pi t), t)

But  

\bf cos^2(\pi t)+sin^2(\pi t)=1

so, the helix intersects the paraboloid when t=1. This is the point

(cos(π), sin(π), 1) = (-1, 0, 1)

The angle of intersection between the helix and the paraboloid is the angle between the tangent vector to the curve and the tangent plane to the paraboloid.

The <em>tangent vector</em> to the helix in t=1 is

r'(t) when t=1

r'(t) = (-πsin(πt), πcos(πt), 1), hence

r'(1) = (0, -π, 1)

A normal vector to the tangent plane of the surface  

\bf z=x^2+y^2

at the point (-1, 0, 1) is given by

\bf (\frac{\partial f}{\partial x}(-1,0),\frac{\partial f}{\partial y}(-1,0),-1)

where

\bf f(x,y)=x^2+y^2

since

\bf \frac{\partial f}{\partial x}=2x,\;\frac{\partial f}{\partial y}=2y

so, a normal vector to the tangent plane is

(-2,0,-1)

Hence, <em>a vector in the same direction as the projection of the helix's tangent vector (0, -π, 1) onto the tangent plane </em>is given by

\bf (0,-\pi,1)-((0,-\pi,1)\bullet(-2,0,-1))(-2,0,1)=(0,-\pi,1)-(-2,0,1)=(2,-\pi,0)

The angle between the tangent vector to the curve and the tangent plane to the paraboloid equals the angle between the tangent vector to the curve and the vector we just found.  

But we now

\bf (2,-\pi,0)\bullet(0,-\pi,1)=\parallel(2,-\pi,0)\parallel\parallel(0,-\pi,1)\parallel cos\theta

where  

\bf \theta= angle between the tangent vector and its projection onto the tangent plane. So

\bf \pi^2=(\sqrt{4+\pi^2}\sqrt{\pi^2+1})cos\theta\rightarrow cos\theta=\frac{\pi^2}{\sqrt{4+\pi^2}\sqrt{\pi^2+1}}=0.8038

and

\bf \theta=arccos(0.8038)=0.6371\;radians

7 0
1 year ago
A town has a population of 5000 and grows 3.5% every year. To the nearest tenth of a year, how long will it be until the populat
oksano4ka [1.4K]

Answer:

Step-by-step explanation:

This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is

y=a(b)^x where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then

a = 5000

If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So

b = 1.035

Our function is

y=5000(1.035)^x where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.

7300=5000(1.035)^x and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.

Begin by dividing both sides by 5000 to get

1.46=1.035^x and take the natural log of both sides:

ln(1.46)=ln(1.035)^x

The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:

ln(1.46)=xln(1.035) To solve for x, we now divide both sides by ln(1.035):

\frac{ln(1.46)}{ln(1.035)}=x

Do that division on your calculator and get that

x = 11.0 years.

That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)

5 0
2 years ago
A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of
nydimaria [60]

This question is incomplete. I got the complete part (the boldened part) of it from google as:

The following 98% confidence interval was obtained for μ1 - μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B:

4.90 hrs < μ1 - μ2 < 17.50 hrs.

Answer:

A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A​ (the original​ paint) and 9 cans of type B​ (the modified​ paint) were selected and applied to similar surfaces. The drying​ times, in​ hours, were recorded. The summary statistics are as follows. Type A Type B x 1x1equals=76.3 hr x 2x2equals=65.1 hr s 1s1equals=4.5 hr s 2s2equals=5.1 hr n 1n1equals=11 n 2n2equals=9 The following​ 98% confidence interval was obtained for mu 1μ1minus−mu 2μ2​, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B. What does the confidence interval suggest about the population​ means?

The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.

Step-by-step explanation:

The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.

Only positive values comprise the confidence interval which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The modification appears to be effective in reducing drying times.

7 0
2 years ago
16
BlackZzzverrR [31]

Answer:

c.33.08

Step-by-step explanation:

add all of them together and you get 140.7 divded by 5 and get 33.08

6 0
2 years ago
Read 2 more answers
What value of x is in the solution set of 2(3x - 1) = 4x - 6?<br> EO<br> -10
tensa zangetsu [6.8K]

Answer:

D) -1

Step-by-step explanation:

6x-2≥4x-6

6x-4x≥-6+2

2x≥-4

x≥-4÷2

x≥-2

Only -1 is greater than -2 in the list.

5 0
2 years ago
Read 2 more answers
Other questions:
  • Leah decided to paint some of the rooms at her 51-room hotel. She needs 1/5 of a can of paint per room. If Leah had 6 cans of pa
    12·1 answer
  • What is the maximum number of times two planes can intersect? What is the minimum number of times they can intersect?
    10·1 answer
  • The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball
    11·1 answer
  • Lana is the oldest of four sisters. Her youngest sister is half her age. The other two sisters are twins $2$ years younger than
    8·1 answer
  • Mrs. Blair believes there is a relationship between the number of minutes students study and their test grades. She asked her hi
    14·2 answers
  • The scatterplot shows a linear relationship between the distance traveled and the time elapsed. What is the rate of change of th
    7·2 answers
  • Suppose that the regression equation y = 16.99 + 0.32 x1 + 0.41 x2 + 5.31 x3 predicts an adult’s height (y) given the individual
    8·1 answer
  • What is 12% sales tax on a $4.25 6-pack of soda?
    10·1 answer
  • Theresa has hired Chuck and Diana to paint a fence. Diana can paint 150 fence posts in the same time it takes Chuck to paint 130
    9·1 answer
  • 5. Write an equation for the line representing each of the following situations.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!