The function y=60+25sin(pi/6)t, where t is in months and t=0 corresponds to April 15, models the average high temperature in degrees Fahrenheit in Centerville.
b.) What is the maximum high temperature and when does this occur?
NOTE: I found the answer online, I just don't understand how to get there. It's July 15, 85 degrees.
Answer:
The maximum temperature will be of 85 degrees, on July 15.
Step-by-step explanation:
Sine function:
The sine function oscilates between -1 and 1, and it's maximum value is:
[tex]\sin{(\frac{\pi}{2})} = 1[/tex]
y=60+25sin(pi/6)t
The maximum value will occur when [tex]\sin{(\frac{\pi t}{6}}) = 1[/tex], and it will be of 60 + 25 = 85 degrees.
When will it occur?
First we find the value of t for which the value inside the function sine is [tex]\frac{\pi}{2}[/tex]. So
[tex]\frac{\pi t}{6} = \frac{\pi}{2}[/tex]
[tex]\frac{t}{6} = \frac{1}{2}[/tex]
[tex]2t = 6[/tex]
[tex]t = \frac{6}{2} = 3[/tex]
That is the number of months after April 15, which is 3 months. So July 15.
John is 3 years older than Susan and khalid is 5 years younger than her . The sum of their ages is 40 .
Find their ages.
Answer:
John is 17,
Susan is 14,
and Khalid is 9.
Step-by-step explanation:
a = John's age
b = Susan's age
c = Khalid's age
Let's set our rules from the given information.
a = b + 3
c = b - 5
a + b + c = 40
Now, we can solve for b through substitution.
(b + 3) + b + (b - 5) = 40
3b - 2 = 40
3b = 42
b = 14
So, now that we have Susan's age, we can follow the rules and see if it holds.
17 + 14 + 9 = 40 Viola!
[tex]if x^2 = 17x + y \: and \: y {}^{2} = 17y + x \: then \: find \sqrt{x {?}^ + {y { }^{2} + 1 } } [/tex]
Answer:
Bro wat
Step-by-step explanation:
Can someone help me plead
Answer:
a. 2^3
b. 3^4
c. 4^3 × 5^2
d. 9^4 × 7^2
Step-by-step explanation:
The following equations are given
a. 2 × 2× 2
b. 3 × 3 × 3 × 3
c. 4 × 4 × 4 × 5 × 5
d. 9 × 7 × 9 × 9 × 7 × 9
We need to find the index notation for the above equations
a. 2^3
b. 3^4
c. 4^3 × 5^2
d. 9^4 × 7^2
In this way it should be done
The same would be relevant
Which table represents a linear function?
1) f(x)
2) g(x)
3 h(x)
4 k(x)
Answer: f(x)
Step-by-step explanation:
Find the exact circumference of a circle with diameter equal to 8 ft.
Answer:
C = 8π ft
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = πd ( d is the diameter ) , then
C = 8π
Please answer if you can
Answer:
y = 15°
∠A = 78°
∠B = 68°
∠BAC = 34°
Step-by-step explanation:
∠BAC = 180° - 146° = 34°
the sum of the interior angles of any triangle is 180°
5y + 3 + 4y + 8 + 34° = 180°
combine like terms:
9y + 45° = 180°
subtract 45° from each side of the equation:
9y = 135°
divide both sides by 9:
y = 15°
∠A = 5(15) + 3 = 78°
∠B = 4(15) + 8 = 68°
Question 20
Penny is the manager of a nursery for pre-school children.
She knows that the ratio of the number of adults to the number of children
must be 1:8
Penny has 56 children at the nursery.
(a) Work out the number of adults Penny needs for 56 children.
Answer: 7
Step-by-step explanation:
We know that the ratio adults: children must be 1:8.
So if there are 58 children the ration is x: 56
56/8 (to find the number of adults) = 7
7:56 = 1:8
Two students went shopping and bought $150 worth of clothes they had to pay an additional $14.78 in tax. Estimate the tax rate they had to pay.
Answer:
10.15
Step-by-step explanation:
I divided the worth of clothe and the tax
ryan deposited $1,000 into an accontthat earns 5% simple annual interest. how much does ryan have total after 10 years
Answer:
$500
Step-by-step explanation:
1000x.05=50 per year
50/year x 10 years =500
round to nearest 1000 place
5932
26148
527061
Answer:
5932-6000
26148-26000
527061-527000
Which line is parallel to 2x - y = -3 and goes through (5, 5)?
Answer:
G. y=2x-5
Step-by-step explanation:
First, find the slope from 2x-y=-3
-y=-2x-3
y=2x+3, which means that the slope is 2
Since it is parallel, the given equation and the line we are finding has the same slope.
let y=mx+b, where m=2, y=5, x=5
5=2(5)+b
5=10+b
-5=b
Thus, y=2x-5
Answer:
F Y=1x+5 G Y=2x-5 H Y =x-3 J Y=2x+5
Find the area of the polygon.
42 m
26 m
21 m
52 m
The area of the polygon is _
square meters.
Answer:
1327
Step-by-step explanation:
Please check the attachment for explanation.
what is the slope of the line.
Answer:
1 ..................or 1/1
Answer:
-1 is the slope
..................
NO LINKS I WILL REPORT YOU
What are the missing numbers
A weapons manufacturer uses a liquid propellant to produce gun car- tridges. During the manufacturing process, the propellant can get mixed with another liquid to produce a contaminated cartridge. A University of South Florida statistician, hired by the company to inves- tigate the level of contamination in the stored cartridges, found that 23% of cartridges in a particular lot were contaminated. Suppose you randomly sample (without replacement) gun cartridges from this lot until you nd a contaminated one. Let x be the number of cartridges sampled until a contaminated one is found. It is known that the probability distribution for x is given by the formula:
P(x) = (.23)(.77)x-1, x = 1,2,3,....
A. Find p1.
B. Find p5.
C, Find P{xk's are greater than or equal to 2}.
Answer:
[tex]P(1) = 0.23[/tex]
[tex]P(5) = 0.0809[/tex]
[tex]P(x\ge 2) = 0.471[/tex]
Step-by-step explanation:
Given
[tex]P(x) = 0.23 * 0.77^{x-1}[/tex]
Solving (a): P(1)
This gives:
[tex]P(x) = 0.23 * 0.77^{x-1}[/tex]
[tex]P(1) = 0.23 * 0.77^{1-1}[/tex]
[tex]P(1) = 0.23 * 0.77^0[/tex]
[tex]P(1) = 0.23 * 1[/tex]
[tex]P(1) = 0.23[/tex]
Solving (b): P(5)
This gives:
[tex]P(x) = 0.23 * 0.77^{x-1}[/tex]
[tex]P(5) = 0.23 * 0.77^{5-1}[/tex]
[tex]P(5) = 0.23 * 0.77^{4}[/tex]
[tex]P(5) = 0.23 * 0.35153041[/tex]
[tex]P(5) = 0.0809[/tex]
Solving (c): [tex]P(x \ge 2)[/tex]
To do this, we make use of complement rule
[tex]P(x \ge 2) = 1 - P(x < 2)[/tex]
[tex]P(x < 2)[/tex] is calculated as:
[tex]P(x < 2) = P(0) +P(1)[/tex]
Calculate P(0)
[tex]P(x) = 0.23 * 0.77^{x-1}[/tex]
[tex]P(0) = 0.23 * 0.77^{0-1}[/tex]
[tex]P(0) = 0.23 * 0.77^{-1}[/tex]
[tex]P(0) = 0.299[/tex]
In (a):
[tex]P(1) = 0.23[/tex]
So:
[tex]P(x < 2) = P(0) +P(1)[/tex]
[tex]P(x < 2) = 0.299 + 0.23[/tex]
[tex]P(x < 2) = 0.529[/tex]
So:
[tex]P(x \ge 2) = 1 - P(x < 2)[/tex]
[tex]P(x\ge 2) = 1 - 0.529[/tex]
[tex]P(x\ge 2) = 0.471[/tex]
Jeremiah wants to estimate the mean age of students at his large university. He'll sample n students and make a 95%, percent confidence interval for the mean age. He is willing to use σ=3 years as an estimate of the standard deviation, and he wants the margin of error to be no more than 1 year. Which of these is the smallest approximate sample size required to obtain the desired margin of error?
Answer:
35 students
Step-by-step explanation:
khan
betty closes the nozzle and fills it completely with a liquid. She then opens the nozzle. If the liquid drips at the rate of 14 cubic inches per minute, how long will it take for all the liquid in the nozzle to pass through(Use Pi = 3.14
Answer:
4.71 minutes
Step-by-step explanation:
Incomplete question [See comment for complete question]
Given
Shape: Cone
[tex]r = 3[/tex] -- radius
[tex]h = 7[/tex] --- height
[tex]Rate = 14in^3/min[/tex]
Required
Time to pass out all liquid
First, calculate the volume of the cone.
This is calculated as:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
This gives:
[tex]V = \frac{1}{3} * 3.14 * 3^2 * 7[/tex]
[tex]V = \frac{1}{3} * 197.82[/tex]
[tex]V = 65.94in^3[/tex]
To calculate the time, we make use of the following rate formula.
[tex]Rate = \frac{Volume}{Time}[/tex]
Make Time the subject
[tex]Time= \frac{Volume}{Rate }[/tex]
This gives:
[tex]Time= \frac{65.94in^3}{14in^3/min}[/tex]
[tex]Time= \frac{65.94in^3}{14in^3}min[/tex]
Cancel out the units
[tex]Time= \frac{65.94}{14} min[/tex]
[tex]Time= 4.71 min\\[/tex]
Answer:
The time it will take for all the liquid to pass through is 4.71 minutes.
-Don't worry it's been already verified by myself .
please help with this problem
Answer:
C. equilateral
Step-by-step explanation:
Since each of the angles of Triangle ABC have equivalent values (each are 60 degrees), each of the sides also must have equivalent values.
Thus, since all three sides are the same length, the triangle created is equilateral.
Have a nice day! ^-^
What is the equation of this line?
Y=3x
Y=3
Y=-3
X=3
Please help
the diagram shows a cube and a cuboid
Answer:
2197 cm³
Step-by-step explanation:
surface area of cuboid = 2 * (5*9 + 33*9 + 33*5) = 1014
surface area of cube = 6 * x² .... x: side length of cube
6x² = 1014
x² = 169
x = 13
volume of cube = x³ = 13³ = 2197 cm³
The linear factors of a quadratic expression are (x + a) and (2x + b), where a and b are
positive, odd integers. Which statement about the zeros of this expression's related
quadratic function is FALSE?
A. Both of the zeros are located on the x-axis.
B. One zero is an integer, and the other is a fraction.
C. The zeros are the opposites of the constants in the linear factors.
D. The zeros can be found by setting each factor equal to 0 and solving.
Answer: The answer is C
Which negative angle is equivalent to a 75° angle?
Answer:
A) -285
Step-by-step explanation:
360-75=285
Which are dependent events?
A. rolling two number cubes
B. tossing the same coin two times
C. spinning a spinner and rolling a number cube
D. taking two marbles from a box without replacing the first marble
Answer:
D. taking two marbles from a box without replacing the first marble are dependent events
[tex]----------[/tex]
hope it helps
have a great day!!
The manager of a fleet of automobiles is testing two brands of radial tires and assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear out. The data (in kilometers) follow. Find a 99% confidence interval on the difference in the mean life.
Car Brand 1 Brand 2
1 36663 33866
2 43509 41829
3 36240 35500
4 32100 31950
5 37210 38015
6 48360 47800
7 38200 37810
8 33500 33215
a) Calculate SD =
b) Calculate a 99% two-sided confidence interval on the difference in mean life.
c) Which brand would you prefer? (brand 1/ no difference /brand 2)_____
Answer:
a) σ = 4933,64
b) CI 99% = ( - 5746 ; 7194 )
c) No difference in brands
Step-by-step explanation:
Brand 1:
n₁ = 8
x₁ = 38222
s₁ = 4974
Brand 2:
n₂ = 8
x₂ = 37498
s₂ = 4893
As n₁ = n₂ = 8 Small sample we work with t -student table
degree of freedom df = n₁ + n₂ - 2 df = 8 +8 -2 df = 14
CI = 99 % CI = 0,99
From t-student table we find t(c) = 2,624
CI = ( x₁ - x₂ ) ± t(c) * √σ²/n₁ + σ²/n₂
σ² = [( n₁ - 1 ) *s₁² + ( n₂ - 1 ) * s₂² ] / n₁ +n₂ -2
σ² = 7* (4974)² + 7*( 4893)² / 14
σ² = 24340783 σ = 4933,64
√ σ²/n₁ + σ²/n₂ = √ 24340783/8 + 24340783/8
√ σ²/n₁ + σ²/n₂ = 2466
CI 99% = ( x₁ - x₂ ) ± 2,624* 2466
CI 99% = 724 ± 6470
CI 99% = ( - 5746 ; 7194 )
As we can see CI 99% contains 0 and that means that there is not statistical difference between mean life of the two groups
The sum of a number, n, and 6.05 is 12.4. What is n?
Answer:
2.04
Step-by-step explanation:
Equation: 6.05n=12.4=
Answer:
n = 6.35
Step-by-step explanation:
Okay, so this is a basic algebraic expression, so you'd set it up like:
n + 6.05 = 12.4
And now you have to do the inverse operations thing:
12.4 - 6.05 = 6.35
So, n = 6.35
hope this helps:)
Factor the expression shown below completely.
18.12
603 + 50
OA. 2(31 – 5)2
OB. 2(6.1 – 5)2
OC. 3(2x - 5)
OD. 6(3.1 – 5)
RIGHT ANSWERS ONLY
A. 2(3x-5)²
Step-by-step explanation:
18x² - 60x + 50
= 2 (9x² - 30x + 25 ) ⇒⇒⇒ take 2 as common from all terms
note: 9x² = 3x * 3x and 25 = 5*5 and
3x * 5 *2 = 30x
so, this is a complete square
= 2(3x-5)(3x-5)
= 2(3x-5)²
Can someone please help
Answer:
16.989
Step-by-step explanation:
Cosine angle = adjacent/ hypnosis
Cos 28 = 15/x Multiply both sides by x
xCos 28 = 15x/x x/x is 1
xCos 28 = 15(1) Divide both sides by Cos 28
xCos 28/Cos 28 = 15 / Cos 28 Cos 28 / Cos 28 = 1
x = 15/Cos 28
x = 16.989
Which statement about the relationship between different types of triangles is true? (2 points)
An equilateral triangle is never an obtuse triangle.
An equilateral triangle is never an isosceles triangle.
A right triangle is always an isosceles triangle.
An obtuse triangle is always an acute triangle.
Answer:
A right triangle is always an isosceles triangle.An equilateral triangle is never an obtuse triangle.
Answer:
A right triangle is always an isosceles triangle.
Step-by-step explanation:
Students are voting on the color of T-shirts to wear on their field trip. There are 160 students-65 boys and 95 girls- going on the field trip. A random sample of students is chosen. Surveying the random sample produced a representative sample of the population. Which was most likely true of the representative sample? The representative sample contained all 160 students. The representative sample contained more boys than girls. The representative sample contained more girls than boys. The representative sample contained an equal number of boys and girls.
Answer:
The representative sample contained more girls than boys.
The true representative sample:
The representative sample contained more girls than boys.
The correct option is C.
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of potential experiment results. Depending on the experiment, a sample area could contain a variety of results.
Given:
Students are voting on the color of T-shirts to wear on their field trip. There are 160 students-65 boys and 95 girls- going on the field trip.
A random sample of students is chosen.
Surveying the random sample produced a representative sample of the population.
The total number of students = 160
The number of girls = 95
The number of boys = 65
Clearly, the number of girls is more than the number of boys.
Therefore, the sample should contain more girls than boys.
To learn more about the sample space;
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