Answer:
Final answer is given by x=-4, y=3
Step-by-step explanation:
Question says to use the given graph to determine the number of solutions the system where given system is x = - 4, y = - x - 1
Graph is missing but we can still find the solution.
plug first equation x=-4 into other equation y=-x-1
y=-x-1
y=-(-4)-1
y=4-1
y=3
Hence final answer is given by x=-4, y=3
or we can also write that as (-4,3)
In triangle ABC, how long is side c if A = 103°, C = 17°, and a = 21?
Answer:
c=6.30 units
Step-by-step explanation:
we know that
Applying the law of sines
a/sin(A)=c/sin(C)
Solve for c
c=a*sin(C)/sin(A)
substitute the values
c=21*sin(17°)/sin(103°)=6.30 units
If Joe drives 186.83 miles on a business trip, and the reimbursement from his company is $13.08. At what rate is Joe's employer reimbursing travel miles? (round to the nearest cent)
Please show work
Answer:
7 cents/mile
Step-by-step explanation:
You are looking for a unit rate of cents per mile.
Change the dollar amount to cents, and divide by the number of miles.
$13.08 * (100 cents)/$ = 1308 cents
(1308 cents)/(183 miles) = 7.001 cents/mile
The perimeter of a rectangular field is 328 yards. If the length of the field is 89 yards, what is its width?
Set up an equation based on the information given
[tex]89 + 89 + x + x = 328[/tex]
Combine like terms
[tex]89 + 89 = 178[/tex]
[tex]x + x = 2x[/tex]
[tex]2x + 178 = 328[/tex]
Solve
[tex]2x + 178 = 328[/tex]
[tex]328 - 178 = 150[/tex]
[tex]2x = 150[/tex]
[tex]x = 75[/tex]
Answer
The width of the rectangular field is 75 yards.
Lines a and b are parallel Line cis perpendicular to both line a and line b. Which
statement about lines a, b, and is NOT true?
CLEARCH
Line a and line b have the same slope.
The sum of the slopes of line b and line cis 0.
The product of the slopes of line cand line bis -1.
The product of the slopes of line a and line cis -1.
Answer:
see below
Step-by-step explanation:
The slopes of parallel lines are the same. The slopes of perpendicular lines are negative reciprocals of each other, hence their product is -1.
___
For the most part, the concept of adding slopes of lines does not relate to parallel or perpendicular lines in any way.
Answer:
c
Step-by-step explanation:
Which could be the area of one face of the rectangular prism?Check all that apply
Answer: 24, 44, and 66 [tex]cm^{2}[/tex]
Step-by-step explanation:
Check all of the possible combinations of the faces:
6 × 4 = 24
11 × 4 = 44
11 × 6 = 66
So the answers are 24, 44, and 66 [tex]cm^{2}[/tex]
Answer:
option B 24 cm² option C 44 cm² and option E 66 cm² are the correct options
Step-by-step explanation:
A rectangular prism has 6 faces, in which opposite faces are always similar.
So a rectangular prism has 3 different faces
(1) From the figure given
for face (1) Area = 11 × 4
= 44 cm²
For face (2) Area = 4 × 6
= 24 cm²
For face (3) Area = 11 × 6
=66 cm²
Now we can say that option B 24 cm² option C 44 cm² and option E 66 cm² are the correct options
1. Draw the image of ABC under the dilation with scale factor 2 and center of dilation (-4,-3). Label the
image A'B'C'.
Answer:
-4
-
21
2
3
4
5
Answer:
see below
Step-by-step explanation:
Each point moves to twice its original distance from (-4, -3). The point (-4, -3) remains unmoved.
Answer: (-4,1) ; (2,-3) ; (-4,-3)
PLEASE HELP
I marked the ones I'm stuck on
must show work
Use Slide method for some of them, some are perfect squares:
Watch this video and try it a few times, pay attention to the signs when you are seeing which one will be negative when you multiply it out, in picture is me working out all problems requested.
Ask your brother for further help!
New York City covers an area of 302.6 square miles. There are 8.54 million people living in New York City. Los Angeles has an area of 503 square miles and has a population of 3.98 million people. How many more people, per square mile, live in New York City verses Los Angeles? Round to the nearest person per square mile.
Answer:
20,309 people more people per sq mile.
Step-by-step explanation:
First step is to calculate the population density of both cities, then we'll be able to answer the question.
We're looking for a number of people per sq mile... so we'll divide the population by the area.
New York City: 8.54 million people on 302.6 sq miles
DensityNYC = 8,540,000 / 302.6 = 28,222 persons/sq mile
Los Angeles: 3.98 million people on 503 sq miles
DensityLA = 3,980,000 / 503 = 7,913 persons/sq mile
Then we do the difference... 28,222 - 7,913 = 20,309 people more people per sq mile.
If we were to make the ratio, we'd get 3.57, 3.57 more people in NYC per sq mile compare to LA.
Final answer:
New York City has approximately 20,309 more people per square mile than Los Angeles when rounded to the nearest person, based on their population densities.
Explanation:
To calculate how many more people per square mile live in New York City versus Los Angeles, we need to find the population density for each city and then subtract Los Angeles's density from New York City's density.
New York City's population density: 8.54 million people ÷ 302.6 square miles = approximately 28,220 people per square mile.
Los Angeles's population density: 3.98 million people ÷ 503 square miles = approximately 7,911 people per square mile.
The difference in population density: 28,220 people per square mile (NYC) - 7,911 people per square mile (LA) = approximately 20,309 people per square mile.Therefore, about 20,309 more people per square mile live in New York City than in Los Angeles, when rounded to the nearest person.
based on the pattern table what is the value of a?
A. -64
B. -12
C. 1/16
D. 1/64
Based on the pattern table, the value of a is 1/64.
What is the value of a?Given:
[tex]2^{-1} =\frac{1}{2}[/tex][tex]2^{-2} =\frac{1}{4}[/tex][tex]2^{-3} =\frac{1}{8}[/tex][tex]2^{-4} =\frac{1}{16}[/tex][tex]2^{-5} =\frac{1}{32}[/tex]Find:
The value of [tex]2^{-6}[/tex] which is represented by a.Solution:
The negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice versa.
So, [tex]2^{-6} = \frac{1}{2^{6} } = \frac{1}{64}[/tex]
As, [tex]2^{6} = 64[/tex].
So, a = 1/64
Hence, the value of a is 1/64
To learn more about patterns, refer to:
https://brainly.com/question/854376
#SPJ2
Solve (x + 1 < 4) ∩ (x - 8 > -7).
1 < x < 3 because
( x < 3 ) intersecting ( x > 1)
For this case we must find the intersection of the following inequations:
[tex]x + 1 <4\\x-8> -7[/tex]
So:
[tex]x + 1 <4\\x <4-1\\x <3[/tex]
All values of "x" less than 3.
[tex]x-8> -7\\x> -7 + 8\\x> 1[/tex]
All values of "x" greater than 1.
Thus, the intersection of the equations will be given by the values of "x" greater than 1 and less than 3.
[tex](1 <x <3)[/tex]
ANswer:[tex](1 <x <3)[/tex]
Sally got the following solutions when three different systems of linear equations. Tell which indicates one solution, no solution, and infinitely many solutions.
System #1
x=13
System #2
0=13
System #3
0=0
answer honestly and right il give you brainleist
Try this:
if x=13 it means 'one solution'; the only point;
if 0=13 it means 'no solution'; wrong equation = no points;
if 0=0 it means 'many solutions'; no variable in the equation = much points.
Finally:
System #1 - one solution;
System #2 - no solution;
System #3 - many solutions.
Membership to a national running club is shown in the table. Which answer describes the average rate of change from Year 3 to Year 5? Year: 1, 2, 3, 4, 5 Members(thousands): 87.5, 88.3, 96.8, 87.2, 83.6
answers:
Membership decreased by an average of 6,600 people per year from Year 3 to Year 5.
Membership increased by an average of 13,200 people per year from Year 3 to Year 5.
Membership decreased by an average of 13,200 people per year from Year 3 to Year 5.
Membership increased by an average of 6,600 people per year from Year 3 to Year 5.
Answer:
Membership decreased by an average of 6,600 people per year from Year 3 to Year 5
Step-by-step explanation:
The average rate of change from Year 3 to Year 5 will be given by the slope of the line joining the points;
(3, 96.8) and (5, 83.6)
The slope of a line given two points is calculated as;
( change in y)/( change in x)
In this case y is the number of members for a given year x.
average rate of change = (83.6-96.8)/(5-3)
= -6.6
Since the number of members is given in thousands, we have;
-6,600
The negative sign implies a decrease in the number of members. Therefore, membership decreased by an average of 6,600 people per year from Year 3 to Year 5
A storage box with a square base must have a volume of 80 cubic centimeters. The top and bottom cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter. Find the dimensions that will minimize cost.
Answer:
The dimensions that will minimize cost are 3.42 cm and 6.84 cm
Step-by-step explanation:
* Lets explain how to solve this problem
- We have a storage box with a square base
- The volume of the box is 80 cm³
* From the information above we can find relation between the two
dimensions of the box
∵ The base of the box is a square with side length L cm
∵ The height of the box is H cm
∵ The volume of the box = area of its base × its height
- The base is a square and area the square = L² cm²
∴ The volume of the box = L² × H
∵ The volume of the box = 80 cm³
∴ L² × H = 80
- Lets find H in terms of L by divide both sides by L²
∴ H = 80/L² ⇒ (1)
- The cost of the top and bottom is $0.20 per cm²
- We can find the cost of top and bottom by multiplying the area of
them by the cost per cm²
∵ The top and the bottom are squares with side length L cm
∴ The area of them = 2 × L² = 2L² cm²
∵ The cost per cm² is $0.20
∴ The cost of top and bottom = 2L² × 0.20 = 0.40L² ⇒ (2)
- Now we can find the cost of the lateral area (area of the 4 side faces)
by multiplying the area of them by the cost per cm²
∵ The lateral area = the perimeter of its base × its height
∵ The base is a square with side length L cm
∴ The perimeter of the base = 4 × L = 4L cm
∵ The height of the box is H cm
∴ The lateral area = 4L × H
- Now lets replace H by L using equation (1)
∴ The lateral area = 4L × 80/L²
- To simplify it : 4 × 80 = 320 and L/L² = 1/L
∴ The lateral area = 320/L cm²
∵ The cost of the sides is $0.10 per cm²
∴ The cost of the lateral area = 320/L × 0.10 = 32/L ⇒ (3)
- Now lets find the total cost of the box by adding (2) and (3)
∴ The total cost (C) = 0.40L² + 32/L
* For the minimize cost we will differentiate the equation of the
cost C with respect to the dimension L (dC/dL) and equate it
by 0 to find the value of L which makes the cost minimum
- In differentiation we multiply the coefficient of L by its power and
subtract 1 from the power
∵ C = 0.40L² + 32/L
- Lets change 32/L to 32L^(-1) ⇒ (we change the sign of the power by
reciprocal it)
∴ C = 0.40L² + 32L^(-1)
- Lets differentiate
∴ dC/dL = (0.40 × 2)L^(2 - 1) + (32 × -1)L^(-1 - 1)
∴ dC/dL = 0.80L - 32L^(-2)
- For the minimum cost put dC/dL = 0
∴ 0.80L - 32L^(-2) = 0 ⇒ add 32L^(-1) to both sides
∴ 0.80L = 32L^(-2)
- Change 32L^(-2) to 32/L² (we change the sign of the power by
reciprocal it)
∴ 0.80L = 32/L² ⇒ use cross multiplication to solve it
∴ L³ = 32/0.80 = 40 ⇒ take ∛ for both sides
∴ L = ∛40 = 3.41995 ≅ 3.42 cm ⇒ to the nearest 2 decimal place
- Substitute this value of L in equation (1) to find H
∵ H = 80/L²
∴ H = 80/(∛40)² = 6.8399 ≅ 6.84 cm ⇒ to the nearest 2 decimal place
* The dimensions that will minimize cost are 3.42 cm and 6.84 cm
You have $50 in your bank account.
You make $8 per hour mowing lawns.
How many hours must you mow lawns to have a total of $130 in your account?
Use the drop-down menus to complete the sentences below.
Answer:
10 hours
Step-by-step explanation:
If I have $50 in my bank account, and I want to have a total of $130 in my account. It means that I need to work enough hours to make $130 - $50 = $80.
If I make $8 per hour, and I need to make $80, then I just have to work 10 hours. ($80/8 = 10)
The area of a rectangular flower bed is 24 square feet. The perimeter of the same flower bed is 22 feet. What are the dimensions of the flower bed? A. 2 ft by 12 ft B. 3 ft by 8 ft C. 3 ft by 6 ft D. 4 ft by 6 ft
ANSWER
B. 3 ft by 8 ft
EXPLANATION
The area is given as 24 square feet.
This implies that,
[tex]l \times w = 24[/tex]
The perimeter of the rectangular field is given as 22 feet.
This implies that,
[tex]2(l + w) = 22[/tex]
Or
[tex]l + w = 11[/tex]
We make w the subject in this last equation and put it inside the first equation.
[tex]w = 11 - l[/tex]
When we substitute into the first equation we get;
[tex]l(11 - l) = 24[/tex]
[tex]11l - {l}^{2} = 24[/tex]
This implies that,
[tex] {l}^{2} - 11l + 24 = 0[/tex]
[tex](l - 3)(l - 8) = 24[/tex]
[tex]l = 3 \: or \: 8[/tex]
When l=3, w=24
Therefore the dimension is 3 ft by 8 ft
Answer:
The correct answer is option B. 3 ft by 8 ft
Step-by-step explanation:
Points to remember
Area of rectangle = length * breadth
Perimeter of rectangle = 2(Length + Breadth)
It is given that, The area of a rectangular flower bed is 24 square feet. The perimeter of the same flower bed is 22 feet
To find the correct option
1). Check option A
Area = 2 * 12 = 24
Perimeter = 2( 2 + 12 ) = 28
False
2) Check option B
Area = 3 * 8 = 24
Perimeter = 2(3 + 8 ) = 22
True
3). Check option C
Area = 3 * 6 = 18
Perimeter = 2( 3 + 6 ) = 18
False
4). Check option D
Area = 4 * 6 = 24
Perimeter = 2( 4 +6 ) = 20
False
The correct answer is option B. 3 ft by 8 ft
Max sneezes every 5 minutes, Lina coughs every 6 minutes, and their dog barks every 3 minutes. If there was sneezing, barking, and coughing at 3:15 PM, when is the next time that these three sounds will happen simultaneously?
Answer:
3:45 PM
Step-by-step explanation:
The least common multiple of 3, 5, and 6 is 30, so the next occurrence will be 30 minutes after 3:15 PM, at 3:45 PM.
Answer: The next time at which the three sounds will happen simultaneously at 3 : 45 PM.
Step-by-step explanation: Given that Max sneezes every 5 minutes, Lina coughs every 6 minutes and their dog barks every 3 minutes.
We are to find the time at which these three sounds will happen simultaneously if there was sneezing, barking, and coughing at 3:15 PM.
We have
the sneezing, barking and coughing happen simultaneously at an interval that is equal to the L.C.M. of 5, 6 and 3 minutes.
Now,
L.C.M. (5, 6, 3) = 30.
Therefore, the sneezing, barking and coughing happen simultaneously at an interval of 30 minutes.
Since there was sneezing, barking, and coughing at 3:15 PM, so the next time at which the three sounds will happen simultaneously is
3 : 15 PM + 30 min = 3 : 45 PM.
Thus, the next time at which the three sounds will happen simultaneously is 3 : 45 PM.
A culture started with 1,500 bacteria. After 5 hours it grew to 2,300 bacteria. How many bacteria with be present after 12 hours? PLSSS
Answer:
4185
Step-by-step explanation:
A culture of bacteria grows exponentially according to the following general exponential growth function;
[tex]P_{t}=P_{0}e^{kt}[/tex]
where;
p(t) is the population at any given time t.
p(0) is the initial population
k is the growth constant
From the information given we have;
p(0) = 1500
at t = 5, p(t) = 2300; p(5) = 2300
We shall use this information to determine the value of k;
[tex]2300=1500e^{5k}[/tex]
Divide both sides by 1500;
[tex]\frac{23}{15}=e^{5k}\\\\ln(\frac{23}{15})=5k\\\\k=0.08549[/tex]
Therefore, the population of the bacteria at any time t is given by;
[tex]P_{t}=1500e^{0.08549t}\\\\P(12)=1500e^{0.08549(12)}=4184.3[/tex]
The null and alternate hypotheses are: H0: π1 ≤ π2 H1: π1 > π2 A sample of 100 observations from the first population indicated that X1 is 70. A sample of 150 observations from the second population revealed X2 to be 90. Use the .05 significance level to test the hypothesis. a. State the decision rule. (Round your answer to 2 decimal places.) H0 is rejected if z > b. Compute the pooled proportion. (Round your answer to 2 decimal places.) Pooled proportion c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding the null hypothesis? H0 is
Answer:
365
Step-by-step explanation:
Heeeeeelp
Find the z score that corresponds to P99, the 99th percentile of a standard normal distribution curve.
Answer:
about 2.33
Step-by-step explanation:
The value can be found from a probability table, any of several web sites, your graphing calculator, most spreadsheet programs, or any of several phone or tablet apps.
A web site result is shown below. (I have had trouble in the past reconciling its results with other sources.) One of my phone apps gives the z-value as about ...
2.26347874
which is in agreement with my graphing calculator.
Answer:
[tex]Z = 2.325[/tex].
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Find the z score that corresponds to P99, the 99th percentile of a standard normal distribution curve.
This is the value of Z when X has a pvalue of 0.99. This is between 2.32 and 2.33, so the answer is [tex]Z = 2.325[/tex].
Look at the sequence given below.
4, 0, -4, -8, ...
If n = 1 represents the first term in the sequence above, which of the following describes the nth term of the sequence?
A. -3n + 4
B. n + 3
C. -4n + 8
D. -4n + 3
Answer:
C. -4n + 8
Step-by-step explanation:
Try the formulas and see which works.
__
The common difference is -4, so the coefficient of n in the explicit formula is -4. Every term is divisible by 4, so there won't be 3 anywhere in the formula.
__
-4·1 +8 = 4
-4·2 +8 = 0
-4·3 +8 = -4
-4·4 +8 = -8
The formula -4n+8 reproduces the sequence exactly.
Solve the following system: y = x + 3
3x + y = 19
(7, 4)
(−4, 7)
(4, 7)
(4, −7)
Answer:
(4,7)
Step-by-step explanation:
3x+x+3=19
4x=16
x=4
so y=7
c. (4,7)
What are the solution(s) to the quadratic equation 50 – x2 = 0?
x = ±2
x = ±6
x = ±5
no real solution
Answer:
No real solution
Step-by-step explanation:
Work is on another question for this. You have asked it multiple times
For this case we must find the solution of the following quadratic equation:
[tex]50-x ^ 2 = 0[/tex]
Subtracting 50 from both sides of the equation:
[tex]-x ^ 2 = -50[/tex]
Multiplying by -1 on both sides of the equation:
[tex]x ^ 2 = 50[/tex]
We apply square root on both sides to eliminate the exponent:
[tex]x = \sqrt {50}\\x = \pm \sqrt {25 * 2}\\x = \pm \sqrt {5 ^ 2 * 2}\\x = \pm5 \sqrt {2}[/tex]
ANswer:
[tex]x = \pm5 \sqrt {2}[/tex]
Find the limit of the function algebraically. limit as x approaches zero of quantity x cubed plus one divided by x to the fifth power.
Answer:
[tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big) = \text{und} \text{efined}[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big)[/tex]
Step 2: Evaluate
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big) = 0^3 + \frac{1}{0^5}[/tex]Simplify: [tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big) = \text{und} \text{efined}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Verify that the line integral and the surface integral of Stokes' Theorem are equal for the following vector field, surface S, and closed curve C. Assume that C has counterclockwise orientation and S has a consistent orientation. Fequals=left angle y comma font size decreased by 6 minus x comma font size decreased by 6 14 right angley, −x, 14; S is the upper half of the sphere x squaredx2plus+y squaredy2plus+z squaredz2equals=44 and C is the circle x squaredx2plus+y squaredy2equals=44 in the xy-plane.
As near as I can tell, you're given the vector field
[tex]\vec F(x,y,z)=\langle y,-x,14\rangle[/tex]
and that [tex]S[/tex] is the part of the upper half of the sphere with equation
[tex]x^2+y^2+z^2=4[/tex]
with boundary [tex]C[/tex] the circle in the plane [tex]z=0[/tex].
Line integral:Parameterize [tex]C[/tex] by
[tex]\vec r(t)=\langle2\cos t,2\sin t,0\rangle[/tex]
with [tex]0\le t\le2\pi[/tex]. Then the line integral of [tex]\vec F(x,y,z)[/tex] along [tex]C[/tex] is
[tex]\displaystyle\int_C\vec F(x,y,z)\cdot\mathrm d\vec r=\int_0^{2\pi}\langle2\sin t,-2\cos t,14\rangle\cdot\langle-2\sin t,2\cos t,0\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle-4\int_0^{2\pi}(\sin^2t+\cos^2t)\,\mathrm dt=\boxed{-8\pi}[/tex]
Surface integral:Parameterize [tex]S[/tex] by
[tex]\vec s(u,v)=\langle2\cos u\sin v,2\sin u\sin v,2\cos v\rangle[/tex]
with [tex]0\le u\le2\pi[/tex] and [tex]0\le v\le\dfrac\pi2[/tex]. We have
[tex]\nabla\times\vec F(x,y,z)=\langle0,0,-2\rangle[/tex]
Take the normal vector to [tex]S[/tex] to be
[tex]\vec s_v\times\vec s_u=\langle4\cos u\sin^2v,4\sin u\sin^2v,2\sin2v\rangle[/tex]
Then the surface integral of the curl of [tex]\vec F(x,y,z)[/tex] across [tex]S[/tex] is
[tex]\displaystyle\iint_S(\nabla\times\vec F(x,y,z))\cdot\mathrm d\vec S=\iint_S(\nabla\times\vec F(x(u,v),y(u,v),z(u,v)))\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle\int_0^{\pi/2}\int_0^{2\pi}\langle0,0,-2\rangle\cdot\langle4\cos u\sin^2v,4\sin u\sin^2v,2\sin2v\rangle\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle-4\int_0^{\pi/2}\int_0^{2\pi}\sin2v\,\mathrm du\,\mathrm dv=\boxed{-8\pi}[/tex]
By United States cultural standards, it has been determined that 6 people live comfortably in 1500 square feet of living space. Based on this standard, how many people could be comfortably accommodated with 27,000 square feet of living space? Enter the number only.
I'm unsure about this answer, but I got 108 people. I just did a simple proportion of 6/1500 = x/27000 and solved for x.
Answer:
108 people
Step-by-step explanation:
We can write a proportion to solve this problem. Take the number of people over the living space
6 people x people
------------ = ------------------
1500 ft^2 27000 ft^2
Using cross products
6 * 27000 = 1500 x
Divide each side by 1500
6 * 27000/1500 = 1500x/1500
108 = x
108 people can be reasonably accommodated
a person invest $1,700 in an account that earns 3.97% annual interest. find when the value of the investment reaches $3,200
Answer:
16 1/4 years
Step-by-step explanation:
Assuming interest is compounded annually, the account balance (A) after t years will be ...
A = P(1 +r)^t
3200 = 1700·1.0397^t
log(3200) = log(1700) +t·log(1.0397)
t = (log(3200) -log(1700))/log(1.0397) ≈ 16.247
The account will reach a balance of $3200 after about 16 1/4 years.
___
You may be asked to round your answer to the nearest integer or tenth. We leave that exercise to the student.
A cube-shaped tank that measures 4.64.6 meters on each side is full of water. If some water is drained to fill a cone with a height of 66 meters and a radius of 2.52.5 meters, approximately how much water is left in the tank? Use 3.143.14 for ππ and round your answer to the nearest tenth. The amount of water left in the tank is approximately __________ cubic meters.
Answer:
The amount of water left in the tank is approximately 58.1 cubic meters
Step-by-step explanation:
step 1
Find the volume of the a cube shape tank
The volume is equal to
[tex]V=b^{3}[/tex]
we have
[tex]b=4.6\ m[/tex]
substitute
[tex]V=4.6^{3}=97.336\ m^{3}[/tex]
step 2
Find the volume of cone
The volume is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]r=2.5\ m[/tex]
[tex]h=6\ m[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]V=\frac{1}{3}(3.14)(2.5)^{2}(6)[/tex]
[tex]V=39.25\ m^{3}[/tex]
step 3
Find the difference of the volumes
[tex]97.336\ m^{3}-39.25\ m^{3}=58.1\ m^{3}[/tex]
What is the greatest common factor of 24s3, 12s4, and 18s?
3
6
3s
6s
Answer:
=> 6s
Step-by-step explanation:
Given terms
24s^3 ,12s^4 and 18s
GCF consists of the common factors from all the terms whose GCF has to be found.
In order to find GCF, factors of each term has to be made:
The factors of 24s^3:
24s^3=2*2*2*3*s*s*s
The factors of 12s^4:
12s^4=2*2*3*s*s*s*s
The factors of 18s:
18s=2*3*3*s
The common factors are(written in bold):
GCF=2*3*s
=6s
So the GCF is 6s ..
Answer:
6s
Step-by-step explanation:
Officials project that between 2010 and 2050, the population of a certain city will drastically change. The model below gives the projection of the city's population , P, in thousands, with respect to time, t, in years, where 2010 corresponds to t = 0.P=175 + (11/2)tWhat does the 175 mean in the equationin 2010 the population of the city was 175 thousand
in 2050 the population of the city will be 175 thousand
Between 2010 and 2050, the population of the city will increase by 175 thousand
Between 2010 and 2050 the population of the city will decrease by 175 thousand
Answer:
In the year 2010, the population of the city was 175,000
Step-by-step explanation:
If we rewrote this as a linear expression in standard form (it is linear, btw), it would look like this:
[tex]P(t)=\frac{11}{2}t+175[/tex]
The rate of change, the slope of this line, is 11/2. If the year 2010 is our time zero (in other words, we start the clock at that year), then 0 time has gone by in the year 2010. In the year 2011, t = 1 (one year goes by from 2010 to 2011); in the year 2012, t = 2 (two years have gone by from 2010 to 2012), etc. If we plug in a 0 for t we get that y = 175,000. That is our y-intercept, which also serves to give us the starting amount of something time-related when NO time has gone by.
Select the correct answer. Find the slope and the y-intercept of the equation y − 3(x − 1) = 0. A. slope = -3 and y-intercept = -3 B. slope = 3 and y-intercept = 3 C. slope = -3 and y-intercept = 3 D. slope = 3 and y-intercept = -3
Answer:
D. slope = 3 and y-intercept = -3
Step-by-step explanation:
The equation can be rearranged by adding the opposite of the term with parentheses:
y = 3(x -1)
Expanding this to slope-intercept form gives ...
y = 3x -3 . . . . . . . . slope = 3, y-intercept = -3
_____
Slope-intercept form is ...
y = mx +b . . . . . . . . slope = m, y-intercept = b