Answer:
The equation is given by:
[tex]D(t) = 80 + 9\sin{0.2618t}[/tex]
Step-by-step explanation:
Sine function:
Has the following format:
[tex]y = A\sin{bx}[/tex]
In which A is the amplitude and [tex]\frac{2\pi}{b}[/tex] is the period.
Suppose you know the temperature is 80 degrees at midnight and the high and low temperature during the day are 89 and 71 degrees
This means that the amplitude of the sinusoidal variation function is 89 - 80 = 80 - 71 = 9. This means that [tex]A = 9[/tex]
During a 24-hour day, which means that the period is 24. So
[tex]\frac{2\pi}{b} = 24[/tex]
[tex]24b = 2\pi[/tex]
[tex]b = \frac{2\pi}{24}[/tex]
[tex]b = 0.2618[/tex]
So the variation is:
[tex]V(t) = 9\sin{0.2618t}[/tex]
Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
Initial temperature of 80, so:
[tex]D(t) = 80 + V(t) = 80 + 9\sin{0.2618t}[/tex]
An article describes a study in which a new type of ointment was applied to forearms of volunteers to study the rates of absorption into the skin. Eight locations on the forearm were designated for ointment application. The new ointment was applied to five locations, and a control was applied to the other 3. How many different choices were there for the five locations to apply the new ointment
Answer:
There were 56 different choices for the five locations to apply the new ointment.
Step-by-step explanation:
The order of the locations in which the new ointment was applied is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many different choices were there for the five locations to apply the new ointment
Five locations from a set of 8. So
[tex]C_{8,5} = \frac{8!}{5!(8-5)!} = 56[/tex]
There were 56 different choices for the five locations to apply the new ointment.
please help if your good at geometry. find a
Answer:
a = 1.8 to the nearest tenth.
Step-by-step explanation:
Remark
I don't think this case is ambiguous. It has only 1 solution, I think.
Step One
Find the top angle.
All triangles have 180 degrees.
15 + 105 + x = 180
120 + x = 180 Subtract 120 from both sides
x = 180 - 120
x = 60
Step Two: Find a
a/sin(60) = 2/Sin(105) Multiply both sides by sin(60)
a = 2 * Sin(60) / sin(105)
a = 2 * .8660 / 0.9659
a = 1.793
Match these together
1 similar figure
2 congruent
3 corresponding sides
4 corresponding angles
a. angles that have the same measure are _______.
b. sides in the same relative position. In similar figures they are proportional.
c. Figures with the same shape but no necessarily the same size
d. angles in the same relative position. in similar figures they are congruent
find the slopes of the line
Answer:
1/4
Step-by-step explanation:
Suppose X∼N(6.5,1.5), and x=3.5. Find and interpret the z-score of the standardized normal random variable. Provide your answer below:
Answer: x= 3.5 is -2. The mean is 6.5.
z score to the left is 2
Step-by-step explanation:
X is a normally distributed random variable with μ=6.5 (mean) and σ=1.5 (standard deviation). To calculate the z-score,
z=x−μσ=3.5−6.51.5=−31.5=−2
This means that x=3.5 is two standard deviations (2σ) below or to the left of the mean. This makes sense because the standard deviation is 1.5. So, two standard deviations would be (2)(1.5)=3, which is the distance between the mean (μ=6.5) and the value of x (3.5).
Using the normal distribution, it is found that x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.
--------------------------------
In a normal distribution 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 X is from the mean, above or below.
X∼N(6.5,1.5), which means that [tex]\mu = 6.5, \sigma = 1.5[/tex].The measure is [tex]X = 3.5[/tex]The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.5 - 6.5}{1.5}[/tex]
[tex]Z = -2[/tex]
The measure x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.
A similar problem is given at https://brainly.com/question/13383035
Which ordered pair is a solution of y>2x-3?
A. (-1,-5)
B. (1,-5)
C. (2,3)
D. (2,-2)
Answer:
C. (2, 3)Step-by-step explanation:
Given
y > 2x - 3Substitute the values to verify which is correct
A. (-1, -5)
-5 > 2(-1) - 3 ⇒ - 5 > -5 FalseB. (1, -5)
-5 > 2(1) - 3 ⇒ -5 > -1 FalseC. (2, 3)
3 > 2(2) - 3 ⇒ 3 > 1 TrueD. (2, -2)
-2 > 2(2) - 3 ⇒ - 2 > 1 FalseAnswer:
we have
y>2x-3
now
For
A. (-1,-5)
-5>-2-3
-5>-5
It is equal. So false.
B. (1,-5)
-5>2-3
-5>-1
-1 is not greater than -5
So false
For
C. (2,3)
3>2-3
3>-1
3 is greater than -1
So True
For
D. (2,-2)
-2>2-3
-2>-1
-2 is not greater than -1
So false
Determine the axis of symmetry of the Quadratic equation.
A. y=2
B. X=2
C. X=0
D. y=1
Answer:
option B : X=2
Step-by-step explanation:
Because the line U touches on X:2
At a bake sale, the soccer team had 50 packs of cookies to sell. At the end of the sale, they had 5 packs left.
What FRACTION of the cookies were sold?
Answer:
45/50= 9/10
Step-by-step explanation:
If 5 packs were left after the sale, then 50-5=45 is the number of packs sold
Then the fraction sold would be the number of packs sold divided by the total number of packs.
45 sold/50 total
i will mark brainliest !! write an exponential function for the set of points. picture is below
Answer:
[tex]y = 6(2^{x} )[/tex]
Step-by-step explanation:
Let
[tex]y = kb^{x}[/tex]
When x = 0, y = 6. So, [tex]6 = kb^{0}[/tex] = k(1 ) = k
Since k = 6 we have [tex]y = 6b^{x}[/tex]
When x = 1, y = 12.
So [tex]12 = 6b^{1} = 6b[/tex]
b = 2
Therefore, the exponential function is [tex]y = 6(2^{x} )[/tex]
What is the slope of the line shown in the graph?
A coordinate plane is shown. Points are graphed at −3 comma 2 and −1 comma −1. The points are connected by a line.
How many minutes does April jump rope in 1 day? 1 week?
Answer:
2 1/3 hours
Step-by-step explanation:
7/1 × 1/3 = 7/3 = 2 1/3 so the answer would be 7/3 or 2 1/3
BELE
What is the slope of the line represented by the equation y = -- 5x?
-5
Nm nm is
For each inequality, decide whether the solution is represented by x < 4.5 or x > 4.5.
-24 > -6(x - 0.5)
When factoring a expression, what's the easiest way to find a GCF
Answer:
Almost the same way you normally find it! :D
Step-by-step explanation:
To get the GCF multiply all common factors. You can use the greatest common factor to simplify fractions. A ratio is an expression that tells us the quotient of two numbers
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLS SHOW THE WORK!!!!!!!!
Answer:
The answer is (-4/11, -19/11)
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation. Hoped this helped!
Brainly, Please?
factor as the product of 2 binomials x² -10x + 21 =
Answer:
(x - 7) (x - 3)
Step-by-step explanation:
Did u want the actual answer? Cuz if u do I could do that too, jus lemme kno
Answer:
( X - 7) (X-3)
An airline claims that its average taxi time is 15 minutes, and the standard deviation is 1.4 minutes. The taxi time has a bell/mound shape distribution. On a flight with this airline, you observe that the taxi time is 18 minutes. Calculate the z score for your flight's taxi time. Round the final answer to 2 decimal places.
Answer:
The z score for your flight's taxi time is of 2.14.
Step-by-step explanation:
When the distribution is normal, we use 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.
An airline claims that its average taxi time is 15 minutes, and the standard deviation is 1.4 minutes.
This means that [tex]\mu = 15, \sigma = 1.4[/tex]
On a flight with this airline, you observe that the taxi time is 18 minutes. Calculate the z score for your flight's taxi time.
This is Z when [tex]X = 18[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18 - 15}{1.4}[/tex]
[tex]Z = 2.14[/tex]
The z score for your flight's taxi time is of 2.14.
You can convert the variate which tracks heights of trees to standard normal variate. That value of standard normal variate is called the z score and shows the area of the considered area in the plot of the standard normal distribution.
The z score for our flight's taxi time is approx 2.14286
How to convert a normal distribution variate to standard normal distribution variate?Suppose you have got a normal distribution variate with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] (let the variate is denoted by X), then we have
[tex]X \sim N(\mu, \sigma)[/tex]
To convert it to standard normal distribution with mean 0 and the standard deviation as 1 ( [tex]Z \sim N(0,1)[/tex] ), we have:
[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]
For the given case we have:
Let the average taxi time be tracked by random variable X, then, as the mean time is 15 minutes, and the standard deviation 1.4 minutes , thus,
[tex]X \sim N(15, 1.4)[/tex]
Converting it to standard variate:
[tex]Z = \dfrac{X - 15}{1.4}[/tex]
Since the observed taxi time was 18 minutes, thus, we have X = 18,
Getting the z score:
[tex]Z = \dfrac{18 - 15}{1.4} = \dfrac{3}{1.4} \approx 2.14286[/tex]
Thus,
The z score for our flight's taxi time is approx 2.14286
Learn more here about normal distribution here:
brainly.com/question/14989264
The sum of two numbers is twenty-one. One number is nineteen less than four times the other. Find the numbers.
9514 1404 393
Answer:
8, 13
Step-by-step explanation:
The given relationships can be put into two equations. Let x and y represent the numbers.
x + y = 21 . . . . . their sum is 21
y = 4x -19 . . . . .one is 19 less than 4 times the other
__
Substituting for y in the first equation, we get ...
x + (4x -19) = 21
5x = 40 . . . . . . . . . add 19
x = 8 . . . . . . . . . . . divide by 5
y = 4(8) -19 = 13
The two numbers are 8 and 13.
Here is a balanced hanger diagram. A circle has a mass of 6 grams and a square has a
mass of 4 grams. What is the mass of the triangle?
Answer:
7
Step-by-step explanation:
A medium of exchange ?
A.) People are willing to hold onto it because they’re confident that it will keep its value over time.
B.) Money simplifies the exchange process because it’s a mean of indicating how much something costs.
C.) To use money to buy the goods and services you want.
Answer:
B
Step-by-step explanation:
Five times a number decreased by 8 is less than 37. Write an algebraic inequality to represent this situation. Then solve algebraically & graph.
Answer:
5x - 8 < 37 and x < 9
Step-by-step explanation:
again, sorry if it's wrong.
5x - 8 < 37
+8 +8
5x < 45
---- -----
5 5
x < 9
-7r2 + 7r + 2 = 2
Find Discriminant
Answer:
r = 1 , 0
Step-by-step explanation:
-7[tex]r^{2}[/tex] + 7r + 2 = 2
-7r(r-1)=2-2
-7r(r-1)=0
r-1=0
r=1
Problem 3.39) Suppose that 10% of the adult population has blood chemistry parameters consistent with a diagnosis of a pre-diabetic condition. Of four volunteer participants in a health screening study, what is the probability that one of them is pre-diabetic
Answer:
0.2916 = 29.16% probability that one of them is pre-diabetic
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they have blood chemistry parameters consistent with a diagnosis of a pre-diabetic condition, or they do not. Each volunteer in independent of other volunteers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
10% of the adult population has blood chemistry parameters consistent with a diagnosis of a pre-diabetic condition.
This means that [tex]p = 0.1[/tex]
Of four volunteer participants in a health screening study, what is the probability that one of them is pre-diabetic
This is P(X = 1) when n = 4. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.1)^{1}.(0.9)^{3} = 0.2916[/tex]
0.2916 = 29.16% probability that one of them is pre-diabetic
Find the value of x.
60
3x
O A. 60
B. 10
O C. 20
D. 30
Answer:
the answer is D. 30
Step-by-step explanation:
I got it wright
What is the derivative of sech u with respect to x?
Answer:
[tex]\displaystyle \frac{dy}{dx} = -u'sech(u)tanh(u)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
*Note:
This is a known derivative (apply trigonometric differentiation).
Step 1: Define
Identify
[tex]\displaystyle y = sech(u)[/tex]
Step 2: Differentiate
Hyperbolic Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = -u'sech(u)tanh(u)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
A teacher evenly distributes 7 packages of markers to 3 groups of students.
Which two of the following represents how many packages of marker each
group receives?
A. 7/3
B. 3/7
C. 2 ⅓
D. 2.1
E. 21
Answer:
Step-by-step explanation:
2 1/3
Mr. V has 3 3/4 lbs of chocolate chips and he puts 3/4 lb in each batch. How many batches can
he make?
Answer:
5 batches
Step-by-step explanation:
Total chocolate chips = 3 3/4 = 15/4
15/4 ÷ 3/4
15/4 × 4/3
= 5 batches
At $.54 for a dozen oranges, what will 7 1/2 dozen cost?
9 is 15% of what number?
A.24
B.60
C.85
D.135
Answer: B.60
Step-by-step explanation:
9 divided by 15%=60
PLEASE HELP!!!
Greta currently works 45 hours per week and earns a weekly salary of $729. She
will soon be starting a new job where her salary will be increased by 10% and her hours reduced by 10%.
How much more will she be earning per hour at her new job?
Answer:
$7.29 per hour at her new job.
Step-by-step explanation:
Answer:
$3.60
Step-by-step explanation:
Her hourly wage at her old job is 729/45 or $16.20 per hour. If her salary is increased by 10% then her wage weekly is $801.90. If her hours are reduced by 10% then she has to work 40.5 hours per week. This means you have to do 801.90/40.5 to get $19.80 per hour. So according to my math here she will make $3.60 more per hour at her new job. (Double check to make sure I'm correct)
