Answer:
y = 0.01(3ˣ)
Step-by-step explanation:
Solve by elimination Solve by elimination or substitution: 4x + 2y = 6 and x - 3y = 5
Step-by-step explanation:
since we need to multiply only one equation with something, elimination might be a good method here. we bring both equations to 4x terms and then subtract the second from the first equation :
4x + 2y = 6
- 4x - 12y = 20
-----------------------
0 14y = -14
y = -1
=> e.g. in the second original equation
x - 3×-1 = 5
x + 3 = 5
x = 2
what is the intercepts of the line?
x-intercept and y-intercept
4x-1=3y+5
Answer: X (3/2,0) Y (0,-2)
Step-by-step explanation:
6/11 = q/3
Pls help me!
A 300 m long wire is used to fence a rectangular plot whose length is twice it’s width. Find the length and breadth of the plot.
An internet service provider (ISP) has experienced rapid growth in the past five years. As part of its marketing strategy, the company promises fast connections dependable service. To achieve its objectives, the company constantly evaluates the capacity of its servers. One component of its evaluation is an analysis of the average amount of time a customer is connected and actively using the Internet daily. A random sample of 12 customer records shows the following daily usage times, in minutes.
274 347 283 307 327 314
303 285 280 391 359 325
Interpret the confidence interval estimate.
a. Based on the sample data, with 90% confidence, the ISP can conclude that the sample mean daily usage time is between _____ minute(s) and _____ minute(s).
b. Based on the sample data, with 90% confidence, the ISP can conclude that the true population mean daily usage time is between _____ minute(s) and _____ minute(s).
c. Based on the sample data, the ISP can conclude that 90% of daily usage times are between _____ minute(s) and _____ minute(s).
Using the t-distribution, it is found that the correct interpretation is:
b. Based on the sample data, with 90% confidence, the ISP can conclude that the true population mean daily usage time is between 297.75 minute(s) and 334.75 minute(s).
We can find the standard deviation for the sample, which is why the t-distribution is used to solve this question.
We are given a sample size of [tex]n = 64[/tex].Using a calculator, we find that:
The sample mean is [tex]\overline{x} = 316.25[/tex]The sample standard deviation is [tex]s = 35.68[/tex]The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 12 - 1 = 11 df, is t = 1.7959.
Then:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 316.25 - 1.7959\frac{35.68}{\sqrt{12}} = 297.75[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 316.25 + 1.7959\frac{35.68}{\sqrt{12}} = 334.75[/tex]
From the confidence interval, we can infer about the population mean, hence, the correct option is:
b. Based on the sample data, with 90% confidence, the ISP can conclude that the true population mean daily usage time is between 297.75 minute(s) and 334.75 minute(s).
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1 2/15 + -3 1/2 in simplest form
Find an equation for the perpendicular bisector of the line segment whose endpoints
are (2, -1) and (6, -9).
Answer:
x-2=y+1
Step-by-step explanation:
here is ur answer
If a recipe for a cake calls for 2 1/2 cups of flour and Mary wishes to make 3 cakes, how many cups of flour does she need A. 6 B. 6 1/2 C. 7 1/2 D. 9 E. 9 1/2
Answer:
option C 7½ is correct hope this answer helps you dear! take care
Henry is investing at a continuously compounded annual interest rate of 4.4%. How many years will it take for the balance to triple? Round your answer up to the nearest whole number, and do not include units in your answer.
The number of years it would take the amount to triple is 25 years.
The formula that would be used to determine the number of years it would take the balance to triple is:
FV = PV x [tex]e^{r}[/tex]N
Where:
n = number of years fv = future value PV = present value e = 2.7182818 r = interest rate3 = [tex]e^{0.044}[/tex]N
Take the log of both sides
log(3) / log(e) / (0.044) = 25 years
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What's the answer to this question?
[tex]3\dfrac 23 -1 \dfrac 45 = 3 \dfrac{10}{15} - 1 \dfrac{12}{15}[/tex]
5/8 x 3 1/4 using cancellation
Answer: 65/32
Step-by-step explanation:
Assume each choice is random and equally likely. What is the probability that someone gets a bowl of ice cream, with two scoops of vanilla?
Answer:
1/4
Step-by-step explanation:
Solution: as shown in the figure,
2/8 = 1/4
Answer:
3
Step-by-step explanation:
i thing
An indoor track is made up of a rectangular region with two semi-circles at the ends. The distance around the track is 400 meters. What dimensions for the rectangular region maximize the area of the rectangular region?
Answer:
width of rectangle = 2R = (200/π) = 400/π meters
length of rectangle = 400 - π(200/π) = 400 - 200 = 200 meters
Step-by-step explanation:
The distance around the track (400 m) has two parts: one is the circumference of the circle and the other is twice the length of the rectangle.
Let L represent the length of the rectangle, and R the radius of one of the circular ends. Then the length of the track (the distance around it) is:
Total = circumference of the circle + twice the length of the rectangle, or
= 2πR + 2L = 400 (meters)
This equation is a 'constraint.' It simplifies to πR + L = 400. This equation can be solved for R if we wish to find L first, or for L if we wish to find R first. Solving for L, we get L = 400 - πR.
We wish to maximize the area of the rectangular region. That area is represented by A = L·W, which is equivalent here to A = L·2R = 2RL. We are to maximize this area by finding the correct R and L values.
We have already solved the constraint equation for L: L = 400 - πR. We can substitute this 400 - πR for L in
the area formula given above: A = L·2R = 2RL = 2R)(400 - πR). This product has the form of a quadratic: A = 800R - 2πR². Because the coefficient of R² is negative, the graph of this parabola opens down. We need to find the vertex of this parabola to obtain the value of R that maximizes the area of the rectangle:
-b ± √(b² - 4ac)
Using the quadratic formula, we get R = ------------------------
2a
-800 ± √(6400 - 4(0)) -1600
or, in this particular case, R = ------------------------------------- = ---------------
2(-2π)
-800
or R = ----------- = 200/π
-4π
and so L = 400 - πR (see work done above)
These are the dimensions that result in max area of the rectangle:
width of rectangle = 2R = (200/π) = 400/π meters
length of rectangle = 400 - π(200/π) = 400 - 200 = 200 meters
You are studying a population of geese in which there are two color phases, brown and gray. Color in this species is controlled by a single gene, with brown dominant to gray. A random sample of 250 geese shows that 210 are brown. What percentage of the brown geese are heterozygous
Based on the information given the percentage of the brown geese that are heterozygous is 48%.
Random sample = 250
Brown color = 210
Gray color = 250 - 210 = 40
First step is to calculate the proportion of a alleles in the population
Proportion (a alleles)=√40/250
Proportion (a alleles)= √0.16
Proportion (a alleles)= 0.4
Second step is to calculate the proportion of A alleles in the population
p(A) = 1 - 0.4
p(A)= 0.6
Third step is to calculate brown heterozygous percentage using this formula
Brown heterozygous percentage=2pq(Aa)
Let plug in the formula
Brown heterozygous percentage= 2 x 0.6 x 0.4
Brown heterozygous percentage= 0.48 ×100
Brown heterozygous percentage= 48%
Inconclusion the percentage of the brown geese that are heterozygous is 48%.
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If you deposit $400 into an account that offers a 5% interest rate. How much interest will you earn after 1 year?
Answer:
Answer: The answer is $20
Multiply 400 by .05 or 5%.
If you wanna know 6 years it would be 536 usd
Explanation:
This would be an compound interest. Meaning that your gain every year would increase exponentially.
The equation to calculate this would be: Kn = K0⋅
(1+p100)n Kn is your savings after the period nK0 is your starting deposit p is the percentage n is the period of interest for your example we would have.
Kn=400⋅
(1+5100)6
Step-by-step explanation:
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calderonj4588
What are the zeros of the polynomial function f(x)=(x−2)(x+4)(x−5)?
Would appreciate the help
Answer:
The probability of obtaining exactly 3 tails is on the tosses is 1/8.
Step-by-step explanation:
P(all tails)= P(nickel tails)P(dime tails)P(quarter tails)
P(all tails)= (1/2)(1/2)(1/2)
P(all tails)= 1/8
cite a real life situation that describes the concept of direct and inverse variation. create your own word problem and answer it. present your answer with table of values, graph and equation
A need a appropriate answer, thanks...
Step-by-step explanation:
An example of direct variation would be the relationship of distance with time when speed is constant.
d = stLet's assume you travel at the speed of 60 mph. The distance at 0, 0.5, 1, 2 hours would be 0, 30, 60, 120 miles.
d = 60tThis is a linear relationship and produces a graph of line.
See the graph.
--------------------
An example of inverse variation would be the time to complete the same work as number of workers increase.
t = w/p, where w is work (constant), p- number of workersAssume 5 workers complete wok in 20 days, 10 workers do same in 10 days, 20 workers do in 5 days.
t = 100/pThis relationship produces a curved line.
See the graph.
Which of these functions would you use to represent the length, width or heigh of a box whose dime
O Quadratic
O 4th-degree polynomial
O Cubic
O Linear
Answer:
Cubic
Step-by-step explanation:
He has widht, heigh and length.
The cubic function is used to represent the length, width or height of a box. The correct option is C.
What is a cubic function?The cubic function is defined as a function having a degree of three. It is the same as that of cubic polynomials.
A cubic function is defined in mathematics as a function of form f(x)=ax³+bx²+cx+d, where the coefficients a, b, c, and d are complex numbers and the variable x takes real values.
The box has three dimensions that are length, width, and height. The volume of the box will be calculated by the product of the three sides of the box.
There are three dimensions involved in the calculation of the volume of the box. It means that the volume will be a cubic function.
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helpppppppppp WILLLL GIVE BRAINLISTTTTT
Solve | x+4| -5=6
A. x= -7 and = -15
B = 7 and = -7
C. x = 7 and = -15
D. x = -7 and = 15
Answer:
b
Step-by-step explanation:
1.8.3 practice - functions
3. Water freezes at 0 Celsius and 32 Fahrenheit. Water boils at 100 Celsius and 212 Fahrenheit.
Answer:
A. C(F) = 5/9F -(17 7/9)
B. slope: 5/9
C. y-intercept: -17 7/9
Step-by-step explanation:
A.The question tells us that the independent variable is the temperature in degrees Fahrenheit. Then the given ordered pairs are ...
(F, C) = (32, 0) and (212, 100)
The slope can be found from the slope formula:
m = (y2 -y1) / (x2 -x1)
m = (100 -0)/(212 -32) = 100/180 = 5/9
The y-intercept can be found from the slope-intercept equation for a line:
y = mx +b
b = y -mx
Using the first point, we have ...
b = 0 -(5/9)(32) = -160/9 = -17 7/9
Using the found values for m and b, the slope-intercept equation can be written ...
C(F) = 5/9F -(17 7/9)
__
B.The slope was found in part A to be 5/9. This means each degree Fahrenheit corresponds to 5/9 of a degree Celsius.
__
C.The y-intercept was found in part A to be -17 7/9. This means 0 °F corresponds to -17 7/9 °C.
Find the missing side of the triangle. Round to the nearest tenth where necessary find qr
Answer:
QR = 4.9 ft
Step-by-step explanation:
Since the triangle is a right triangle, use the Pythagorean Theorem (a² + b² = c²).
[tex]a^2+b^2=c^2\\\\a^2+1^2=5^2\\\\a^2+1=25\\\\a^2=24\\\\\sqrt{a^2}=\sqrt{24}\\\\a=4.9[/tex]
m 130 degrees n 130 degrees what is t
Answer:
50 degrees
Step-by-step explanation:
that line is a 180 degree and 180-130=50
When Lucia plays golf at the Rolling Hills golf course, she loses about 12 balls on average. When she plays golf at the Meandering Meadows golf course, she loses about 8 balls on average. If Lucia lost approximately 100 balls after playing at Rolling Hills rr times and Meandering Meadows mm times, which of the following equation best represents the relationship between rr and mm?
When Lucia plays golf at the Rolling Hills golf course, she loses about 12 balls on average. When she plays golf at the Meandering Meadows golf course, she loses about 8 balls on average. If Lucia lost approximately 100 balls after playing at Rolling Hills rr times and Meandering Meadows mm times, which of the following equation best represents the relationship between rr and mm?
8r+12m=1008r+12m=100
12r+8m=10012r+8m=100
12r-8m=10012r−8m=100
8r-12m=1008r−12m=100
The relationship between the number of balls Lucia lost at the golf
courses can be expressed as an equation.
The equation that best represents the relationship between r and m is; 12·r + 8·m = 100Reasons:
The given parameters are;
The number of balls Lucia loses at the Rolling Hills, r = 12 balls
The number of balls Lucia loses at the Meandering Meadows, m = 8 balls
The total number of balls Lucia lost after playin at Rolling Hills and Meandering Meadows = 100 balls
The relationship between r and m is therefore;
Number of balls lost at Rolling Hills + Number of balls lost at Meandering Meadows = 100
12 × r + 8 × m = 100
12·r + 8·m = 100
The equation that best represents the relationship between r and m is therefore; 12·r + 8·m = 100
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10. Is it possible for a regular polygon to have 240° as the measure of each of its interior
angles?
Step-by-step explanation:
No, it is not possible for a regular polygon to have 240° as the measure of each of
its interior angles.
according to the formula:
A = 180 - (360 /n)
where A is the interior angle
therefore, the A could be less than 180°
simplify √6+3√6 please and thank you
Answer:
4√6
Step-by-step explanation:
√6 is a common factor on either side of the plus sign.
Therefore you can use the distributive property to get it out as a common factor. If you do not know what the distributive property is, then you can just say that √6 is a common factor.
√6(1 + 3) Combine the like terms in the brackets.
√6(4) or
4√6
Answer:
Exact Form: 4√6
Decimal Form: 9.79795897...
Step-by-step explanation:
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Body surface area is calculated a) in m2 from weight and height. b) from height. c) from weight. d) in meters from weight and height.
Answer:
Body surface area is calculated a) in m2 from weight and height.
Step-by-step explanation:
Basically the surface has to be in m2, because you have two dimensions when you multiply: e.g. when you have a lawn 10m x 10m, then you multiply 10 times 10, and meters times meters, so
[tex]10m * 10m = 100m^2[/tex]
9w=8w-5
[tex]9w=8w-5[/tex]
Answer:
9w=8w-5
collect like terms
9w-8w=-5
w=-5
All of the points in the picture are on the same line *help asap*
Answer:
yes all of the points are on the same line
Step-by-step explanation: