Hello!
[tex]\large\boxed{y = 13(2)^x}}[/tex]
y = abˣ
We know that at x = 0, b = 1 because any number to the power of 0 = 1.
Therefore:
13 = a(1)
13 = a
Now, plug in this value to solve for b:
y = 13bˣ
Substitute in the next point:
416 = 13(b)⁵
Divide both sides by 13:
32 = b⁵
Take the 5th root of both sides:
2 = b
Rewrite:
y = 13(2)ˣ
Suppose that all of the points on the circular dartboard shown are equally likely to be hit by a dart. If the radius of the shaded center circle is 1 and the radius of the entire dartboard is 4, what is the probability of throwing a dart and hitting the white part of the board? Round your answer to the nearest whole number.
6%
34%
67%
94%
Answer:
94%
Step-by-step explanation:
what is the difference between dot product and cross product?
Answer:
A dot product is the product of the magnitude of the vectors and the cos of the angle between them. A cross product is the product of the magnitude of the vectors and the sine of the angle that they subtend on each other.
Step-by-step explanation:
A point is selected at random from a line segment of length l, dividing it into two line segments. What is the probability that the longer line segment is at least three times as long as the shorter segment
Answer:
3/4
Step-by-step explanation:
Let a be the length of the shorter line segment and b be the length of the longer line segment.
Since the length of the line segment is l, we have that the length of the line segment equals length of shorter line segment + length of longer line segment.
So, l = a + b
Since we require that the longer line segment be at least three times longer than the shorter line segment, we have that b = 3a
So, l = a + b
l = a + 3a
l = 4a
The probability that the shorter line segment will be a(or 3 times shorter than b) is P(a) = length of shorter line segment/length of line segment = a/l
Since l = 4a.
a/l = 1/4
So, P(a) = 1/4
The probability that a will be less than 3 times shorter that b is P(a ≤ 1) = P(0) + P(a) = 0 + 1/4 = 1/4
The probability that b will be 3 times or more greater than a is thus P(b ≥ 3) = 1 - P(a ≤ 1) = 1 - 1/4 = 3/4
B
13 ft.
5 ft.
A
C
12 ft.
Find the value of Cos (B) =
Answer: the answer is 12/13
a plant grows by 1.67cm in its first week. each week it grows by 4% more than it did the week before. by how much will grow in nine weeks, including the first week?
Answer: Approximately 2.29 cm
Step-by-step explanation:
Week 1 = 1.67 or [tex]1.67(1.04)^{0}[/tex]Week 2 = 1.67 + (1.67 · 4%) = 1.67 + 1.67 · 0.04 = 1.67(1 + 0.04) = 1.67(1.04)¹Week 3 = 1.67(1.04) + [1.67(1.04) · 0.04] = 1.67(1.04)(1.04) = 1.67(1.04)² Week 4 = 1.67(1.04)² + [1.67(1.04)² · 0.04] = 1.67(1.04)²(1.04) = 1.67(1.04)³See a pattern?
Number of week = xPlant growth = [tex]1.67(1.04)^{x-1}[/tex]Week 9 = [tex]1.67(1.04)^{9-1} =1.67(1.04)^{8} =1.67(1.3686)=2.2855[/tex]
Gieo 120 hạt giống của một loại cây thấy có 15 hạt nảy mầm. Với độ tin cậy 95% hãy tìm ước lượng khoảng cho tỷ lệ nảy mầm của loại hạt giống đó.
Mn giúp mình với ạ
Answer:
sorry can't understand the language
f(x) =x-4/x+5
and g(x) = 2x-1
Find the composition f•g
Step-by-step explanation:
2x-1 - (4/(2x-1)) + 5
2x^2 -4x -2 -4 + 10x - 5
2x^2 +6x -11
Suppose X and Y are two independent exponential variables. The mean of X is twice the mean of Y. If the probability of X exceeding 50 is 0.7788, what is the probability of Y exceeding 40
If X ~ Exponential(µ), then the mean of X is 1/µ. So if the mean of X is twice the mean of Y, then the mean of Y is 1/(2µ), so that Y ~ Exponential(2µ).
We're given that
P(X > 50) = 1 - P(X ≤ 50) = 1 - Fx (50) ≈ 0.7788
==> Fx (50) = P(X ≤ 50) ≈ 0.2212
where Fx is the CDF of X, which is given for 0 ≤ x < ∞ to be
Fx (x) = 1 - exp(-µx)
Solve for µ :
1 - exp(-50µ) ≈ 0.2212 ==> µ ≈ -ln(0.7788)/50 ≈ 0.005
Then we have
P (Y > 40) = 1 - P (Y ≤ 40) = 1 - Fy (40)
where Fy is the CDF of Y,
Fy (y) = 1 - exp(-2µy)
so that
P (Y > 40) ≈ 1 - exp(-2 × 0.005 × 40) ≈ 0.3297
In an examination every student took history or geography or both of 500 candidates 60% took history whiles 72% took geography. How many students took both subjects
Answer:
80 students
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
60% of 500 = 300
72% of 500 = 360
40% of 500 = 200
28% of 500 = 140
300+360 = 660
660 - 2x = 500
660 - 500 = 2x
160 = 2x
2x = 160
x = 80
If P = (2,-1), find the image
of P under the following rotation.
270° counterclockwise about the origin
([?], [])
Enter the number that belongs in
the green box.
9514 1404 393
Answer:
P'(-1, -2)
Step-by-step explanation:
The transformation for 270° CCW rotation is ...
(x, y) ⇒ (y, -x)
Then the image of the given point is ...
P(2, -1) ⇒ P'(-1, -2)
Please help ASAP!!! Thank you!!!
Due to a sale at Macy's you only have to pay 2/3 of the original price of a blouse. your price AFTER the discount $120. What was the original price? Explain how you arrived at this answer.
9514 1404 393
Answer:
$180
Step-by-step explanation:
The relationship between the prices is said to be ...
(amount you pay) = 2/3 × (original price)
To find the original price, multiply the equation by the reciprocal of the coefficient of the (original price).
(3/2)×(amount you pay) = (3/2)(2/3)(original price) = (original price)
(3/2)×$120 = original price = $180
3p + 2q = 14
10p + 6q = 44
What is p and what is q
Answer:
p = 2 ; q = 4
Step-by-step explanation:
Given tbe equation :
3p + 2q = 14 - - - (1)
10p + 6q = 44 - - -(2)
What is p and what is q
This is a simultaneous equation ; using elimination method :
Multiply (1) by 6 and (2) by 2
18p + 12q = 84 - - - - (3)
20p + 12q = 88 - - - (4)
Subtract (3) and (4)
-2p = - 4
p = 4/2
p = 2
Put p = 2 in (1)
3p + 2q = 14
3(2) + 2q = 14
6 + 2q = 14
2q = 14 - 6
2q = 8
q = 8/2
q = 4
p = 2 ; q = 4
Using the graph below, if f(x) = 4, find x.
The radius of a circle is 5 yd.
Answer the parts below. Make sure that you use the correct units in your answers.
If necessary, refer to the list of geometry formulas.
Answer:
Circumference =10 pi yard
Area =25 pi yard squared
Step-by-step explanation:
C=2*pi*r
Circumfrance =10 pi
A=pi r^2
Area =25 pi
For the estimate just sub in pi on the calculator for pi, then round to the hundreth.
Circumfrence= just the unit
Area= squared
Exactly how many planes contain points J, K, and N?
a - 0
b - 1
c - 2
d - 3
The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.7 millimeters and a standard deviation of 0.08 millimeters. Find the two diameters that separate the top 3% and the bottom 3%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.
Answer:
The diameter that separates the top 3% is of 5.85 millimeters, and the one which separates the bottom 3% is of 5.55 millimeters.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 5.7 millimeters and a standard deviation of 0.08 millimeters.
This means that [tex]\mu = 5.7, \sigma = 0.08[/tex]
Top 3%
The 100 - 3 = 97th percentile, which is X when Z has a p-value of 0.97, so X when Z = 1.88.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.88 = \frac{X - 5.7}{0.08}[/tex]
[tex]X - 5.7 = 1.88*0.08[/tex]
[tex]X = 5.85[/tex]
Bottom 3%
The 3rd percentile, which is X when Z has a p-value of 0.03, so X when Z = -1.88.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.88 = \frac{X - 5.7}{0.08}[/tex]
[tex]X - 5.7 = -1.88*0.08[/tex]
[tex]X = 5.55[/tex]
The diameter that separates the top 3% is of 5.85 millimeters, and the one which separates the bottom 3% is of 5.55 millimeters.
For each one of the following statements, indicate whether it is true or false.
(a) If X = Y (i.e., the two random variables always take the same values), then Van X | Y = 0.
(b) If X = Y (the two random variables always take the same values), then Var (X | Y) = Var (X).
(c) If Y takes on the value y, then the random variable Var (X | Y) takes the value E[(X – E[X | Y = y])2 |Y = y].
(d) If Y takes on the value y, then the random variable Var (X | Y) takes the value E[(X - E[X | Y])2 | Y = y].
(e) If Y takes on the value y, then the random variable Var ( X | Y) takes the value E[(X – E[X])2 | Y = y].
Solution :
a). [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y)$[/tex]
Now, if X = Y, then :
[tex]P(X|Y)=\left\{\begin{matrix} 1,& \text{if } x=y \\ 0, & \text{otherwise }\end{matrix}\right.[/tex]
Then, E[X|Y] = x = y
So, [tex]$\text{Var} (X|Y) =E((X-X)^2 |Y)$[/tex]
[tex]$=E(0|Y)$[/tex]
= 0
Therefore, this statement is TRUE.
b). If X = Y , then Var (X) = Var (Y)
And as Var (X|Y) = 0, so Var (X|Y) ≠ Var (X), except when all the elements of Y are same.
So this statement is FALSE.
c). As defined earlier,
[tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y=y)$[/tex]
So, this statement is also TRUE.
d). The statement is TRUE because [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y=y)$[/tex].
e). FALSE
Because, [tex]$\text{Var} (X|Y) =E ((X-E(X|Y=y))^2 |Y=y)$[/tex]
You and Michael have a total of $19.75. If Michael has $8.25, how much
money do you have?
$27.00
$28.00
$11.50
$12.00
Answer:
You have a total of $11.50
Step-by-step explanation:
We first subtract $19.75 by $8.25 and the result will be $11.50
Answer:
11.50
Step-by-step explanation:
19.75-8.35= 11.50
May I have the brainiest?
for the equation (x+3)(x+1)=1 explain why the solutions are not -3 and -1
Answer:
Step-by-step explanation:
(x+3)(x+1)=1
x²+3x+x+3=1
x²+4x+2=0
x²+4x+4=-2+4
(x+2)²=2
x+2=±√2
x=2+√2
and x=2-√2
so x≠-3
and x≠-1
(a) The heights of male students in a college are thought to be normally distributed with mean 170 cm and standard deviation 7.
The heights of 5 male students from this college are measured and the sample mean was 174 cm.
Determine, at 5% level of significance, whether there is evidence that the mean height of the male students of this college is higher than 170 cm.
[6]
(b) (i) The result of a fitness trial is a random variable X which is normally distributed with mean μ and standard deviation 2.4 . A researcher uses the results from a random sample of 90 trials to calculate a
98% confidence interval for μ . What is the width of this interval?
[4]
(ii) Packets of fish food have weights that are distributed with standard deviation 2.3 g. A random sample of 200 packets is taken. The mean weight of this sample is found to be 99.2 g. Calculate a 99% confidence interval for the population mean weight.
[4]
(c) (i) Explain the difference between a point estimate and an interval
Estimate. [2]
(ii) The daily takings, $ x, for a shop were noted on 30 randomly chosen days. The takings are summarized by Σ x=31 500 and
Σ x2=33 141 816 .
Calculate unbiased estimates of the population mean and variance of the shop’s daily taking. [4
Answer:
the answer is 50 but I don't know if
4g+r=2r-2x
I need someone’s help if you can help me
Answer:
4g+2x=r
Step-by-step explanation:
4g+r=2r-2x
collecting like terms
4g+2x=2r-r
4g+2x=r
The mean of 19 numbers is 1600. If 2000 is added in the number. Find the new mean
Answer:
Here's your answer .
hope it helps you
An expression to convert 50 miles per hour to miles per minute is shown.
What value can be entered in the box to correctly make this conversion?
Answer:
[tex]{ \tt{ = \frac{50}{1 \times 60} }}[/tex]
Step-by-step explanation:
50 miles=50 miles
1 hour=60 minutes
50÷60
0.8333333333333333mile per minute
~1.0 mile per minute
Suppose your dean of admissions is considering surveying high school seniors about their perceptions of your school to design better informational brochures for them. What are the advantages and disadvantages of doing (a) telephone interviews and (b) an Internet survey of seniors who have requested information about the school
Answer and explanation:
Advantages of telephone interviews:
They are more convenient than face to face interviews
They are alot more cost-effective
There is a wider geographical access as you can reach people in other countries too
Disadvantages of telephone interviews:
Questions become has limited complexity as opposed to face to face interviews
It may be somewhat intrusive for customers and there could also be interference from noise in the background. Also bad connection issues.
Advantages of internet survey:
Increased geographical access leading to high response rate.
Alot more convenient and flexible than face to face interviews
Low cost advantages
Disadvantages of internet survey:
Inability for individuals who are not online to participate
Non response bias
Limited complexity of questions, usually close ended questions
What is the domain of the given
set of ordered pairs?
(2, 4), (5,5), (8, 6), (11, 7)
Answer:
2, 5, 8, 11
Step-by-step explanation:
The domian is the x axis points thingy
Questions 24-25. In 1963, postage was 5 cents per ounce. In 1981, postage was 18 cents per ounce.
If the trend had continued through to 2015, what would the postage per ounce be?
(round to the nearest central
The answer posted "42.55" is incorrect.
Answer:
The postage per ounce would be of $2.02.
Step-by-step explanation:
Exponential model:
The postage, in t years after 1963, follows the following format:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial value and r is the growth rate, as a decimal.
In 1963, postage was 5 cents per ounce.
This means that [tex]P(0) = 5[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 5(1+r)^t[/tex]
In 1981, postage was 18 cents per ounce.
This means that [tex]P(1981 - 1963) = P(18) = 18[/tex]. We use this to find r. So
[tex]P(t) = 5(1+r)^t[/tex]
[tex]18 = 5(1+r)^{18}[/tex]
[tex](1+r)^{18} = \frac{18}{5}[/tex]
[tex]\sqrt[18]{(1+r)^{18}} = \sqrt[18]{3.6}[/tex]
[tex]1 + r = (3.6)^{\frac{1}{18}}[/tex]
[tex]1 + r = 1.0738[/tex]
So
[tex]P(t) = 5(1.0738)^t[/tex]
If the trend had continued through to 2015, what would the postage per ounce be?
2015 - 1963 = 52, so this is P(52).
[tex]P(52) = 5(1.0738)^{52} = 202[/tex]
202 cents, so $2.02.
Question 2
A force F=5i+3j-2k is applied to move a block of cement from A(0,1,1) to B(4.-1,3).
Determine the work done by the force.
The work is simply the dot product of the force and displacement (which I assume are given in Newtons and meters, respectively):
W = F • d
W = (5i + 3j - 2k) N • ((4i - j + 3k) m - (j + k) m)
W = (5i + 3j - 2k) • (4i - 2j + 2k) Nm
W = (20 - 6 - 4) Nm
W = 10 J
Identify the percent, amount, and base in this problem.
What percent of 80 is 40?
Answer:
50Step-by-step explanation:
40: 80x100 =100 =(40x100): 80 =100): 80 =4000: 80 = 50The percentage of the number 80 is 40 will be 50%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The percentage is given as,
P = [(80 - 40) / 80] x 100
P = (40 / 80) x 100
P = 0.50 x 100
P = 50%
The percentage of the number 80 is 40 will be 50%.
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ2
A charter school did a local beach cleanup. They collected a total of 55 pounds of plastic bottles and aluminum cans. The California refund value for plastic is $1.60 per pound and $1.28 per pound for aluminum. The school recycled a total of $77.60 worth of plastic and aluminum. How many pounds of each, plastic and aluminum, did the class collect?
Answer:
Plastic is 22.5 pounds and aluminum is 32.5 pounds.
Step-by-step explanation:
total junk = 55 pounds
Value of plastic = $ 1.60 per pound
Value of aluminum = $ 1.28 per pound
Total value= $ 77.60
Let the plastic is p and the aluminum is 55 - p.
Total cost
77.60 = 1.6 p + (55 - p) x 1.28
77.60 = 1.6 p + 70.4 - 1.28 p
7.2 = 0.32 p
p = 22.5 pounds
So, plastic is 22.5 pounds and aluminum is 32.5 pounds.