The equation which represents the equation for the temperature, D , in terms of t is D(t)=5°cos{(π/3)t}+67°.
Given that the high temperature is 72 degrees and low temperature is 62 degrees at 3 A.M.
We know that temperature is the intensity of the heat present around us.
We know that,
Maximum temperature=72 degrees,
Minimum temperature=62 degrees, which occurs at t=3 hours
Now we can write the equation as:
D(t)=A cos(ct)+B
Where A, c, B are constants.
We have a minimum at t=3 a minimum means cos(ct)=-1
then we have that D(3)=A cos(c*3)+B
=A*(-1)+b
=35°
Here we solve that ,
Cos(c*3)=-1
this means that
c*3=-1
c*3=π
c=π/3
We also know that the maximum temperature is 72°, the maximum temperature is when cos(c*t)=1
D(t)=0=A(t)+B=72
With this we can find that values of A and b
-A+B=62
A+B=72
B=67
A=5
Equation will be D(t)=5 cos{(π/3)t}+67°.
Hence the equation for the temperature is D(t)=5 cos{(π/3)t}+67°..
Learn more about equation at https://brainly.com/question/2972832
#SPJ1
please help me it is an easy question
Answer:
200 yd²
Step-by-step explanation:
A = 17 yd
B = 15 yd
C = 2 yd
D = 8 yd
b) Area of rectangle = length * width
[tex]\sf Area \ of \ 2 \ triangle = 2* \dfrac{1}{2}* base * height = base* height\\\\[/tex]
Area of right triangular prism = Areas of two triangle + area of the upper rectangle + area of middle rectangle + area of below rectangle
= 8 * 15 + 17 * 2 + 15 *2 + 8*2
= 120 + 34 + 30 + 16
= 200 yd²
#1) a normal distribution has a mean of 101 and a standard deviation of 4.2. what is the z-score of 105?
Step-by-step explanation:
z = (specific score - mean) / standard deviation
in our case
z = (105 - 101)/4.2 = 4/4.2 = 0.952380952... ≈ 0.95
as z-tables usually round the z-scores to hundredths.
The z-score of the normal distribution is 0.95.
What is normal distribution?A probability distribution which is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.
It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution shows as a "bell curve" on a graph.
Z-score: A Z-score is just a metric that quantifies how closely a value relates to a mean of a set of values. Standard deviations from of the mean are used to measure Z-score.
A Z-score of zero means the data point is actually score is the same as the mean score.
The formula for z-score is-
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
Z = standard score
x is observed value = 105
[tex]\mu[/tex] is mean of the sample 101.
[tex]\sigma[/tex] is standard deviation of the sample 4.2.
Substitute all the values in the z-score formula;
z = ( 105 - 101)/4.2
z = 0.9523..
z = 0.95
Therefore, the z-score the given normal distribution is 0.95.
To know more about characteristics of a normal distribution, here
https://brainly.com/question/23418254
#SPJ4
Evaluate the function when x=5
F(5)=?
Step-by-step explanation:
When evaluating piecewise function, make sure the x value satisfies the function we use.
since 5>3, we use the second equations
That function is a constant function, this means at any x>3, exclusive, we will have a y value of -1.
So
[tex]f(5) = - 1[/tex]
Help me please
6. Find the LCM of 22a³b³c4 and 55abc.
O 110abc
O 77a³b³c¹
O 110a³b³c4
O 11a³b³c4
Help pls, it’s urgent!! ASAP! (Geometry)
“Compete the proof”
1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AD} \cong \overline{CB}[/tex], [tex]\overline{AX} \perp \overline{BD}[/tex], [tex]\overline{CY} \perp\overline{BD}[/tex] (given)
2) [tex]\overline{BD} \cong \overline{BD}[/tex] (reflexive property)
3) [tex]\triangle ABD \cong \triangle ACDB[/tex] (SSS)
4) [tex]\angle ADB \cong \angle CBY[/tex] (CPCTC)
5) [tex]\angle CYB[/tex] and [tex]\angle AXD[/tex] are right angles (perpendicular lines form right angles)
6) [tex]\triangle CYB[/tex] and [tex]\triangle AXD[/tex] are right triangles (a triangle with a right angle is a right triangle)
7) [tex]\triangle AXD \cong \triangle CYB[/tex] (HA)
8) [tex]\overline{AX} \cong \overline{CY}[/tex] (CPCTC)
Which equation is the inverse of 5y+4= (x+3)²+?
0 y = x ² +
O
5
Oy=3±15x+
7
O y=-3±5x
11
10
O-5y-4--(x+3)²-1
72
4
Answer:eq
Step-by-step explanation:
Here is a list of numbers: 13, 15, -6, 8, -16, 2, -12 ,3 ,-18 ,-18 state the median.
The median of list of numbers is-2.
Given the list of numbers is 13,15,6,8,-16,2,-12,3,-18,-18.
The median is the median of a sorted list of numbers. To find the median of a sequence of numbers, the numbers must be sorted in order from lowest to highest or highest to lowest.
Firstly, we will arrange the number from ascending to descending, we get
-18,-18,-16,-12,-6,2,3,8,13,15.
Now, we will find the middle term of the sequence, we get
The middle terms are -6 and 2.
Further, we will find the median of it.
n=(-6+2)/2
n=-4/2
n=-2
Hence, the median of the list of numbers 13, 15, -6, 8, -16, 2, -12 ,3 ,-18 ,-18 is -2.
Learn more about median from here brainly.com/question/15796951
#SPJ4
A restaurant has the following items on its three-course menu.
List all the possible three-course meals that could be ordered, assuming diners must order one meal from each category.
Starters:
Salad
Garlic bread
Mains:
lamb
pizza
desserts:
cookie
brownie
Answer:
salad, lamb, cookie
salad, pizza, brownie
garlic bread, lamb, cookie.
garlic bread, pizza, brownie
The two-way table shows the number of students in a school who like hockey and/or football. like hockey do not like hockey total like football 50 25 75 do not like football 30 45 75 total 80 70 150
5 students like hockey more than football.
What is a table?A table is a collection of information or data that is commonly organized in rows and columns but can sometimes have a more sophisticated structure. Tables are common in communication, research, and data analysis. Tables can be found in a variety of media, including print media, handwritten notes, computer software, architectural ornamentation, traffic signs, and many more locations. The specific conventions and vocabulary used to describe tables differ depending on the situation. Tables also range greatly in terms of variety, structure, flexibility, nomenclature, representation, and use.To find out How many more students like hocket than football:
Refer to the given table -
Students who do not like football and like hockey = a = 30
Students who like football and do not like hockey = b = 25
Now,
[tex]=a-b\\=30-25\\=5[/tex]
Therefore, 5 students like hockey more than football.
Know more about a table here:
https://brainly.com/question/25630111
#SPJ4
The question you are looking for is shown below:
The two-way table shows the number of students in a school who like hockey and/or football. like hockey does not like hockey total like football 50 25 75 do not like football 30 45 75 total 80 70 150.
How many more students like hocket than football?
A car is valued at $35400 at the start of the year, and at $25700 at the end of that year. During that year, the car travelled 25000kms.
a) Find the total depreciation of the car in that year in dollars
b) Find the depreciation per kilometre for this car
c) Using (initial value) -> V₀ = 35400, write down a rule for the value of the car Vₙ after ₙ kilometres
d) How many kilometres are travelled when the value of the car is $6688?
e) Including the first year of travel, how many kilometres in total is this car expected to drive before it has a value of 0?
a. Total depreciation = $9700
b. Depreciation per kilometer = $0. 388 per kilometer
c. Vₙ = $35400 + ₙt
d. Distance = 4723. 16 kilometers
e. Total distance = 29723. 16 kilometers.
How to determine the depreciation
i. The formula for total depreciation is given as;
Total depreciation = Cost of asset - Residual value
Cost of car = $ 35400
Residual value = $25700
Total depreciation = $35400 - $25700
Total depreciation = $9700
b. Depreciation per kilometer = Total depreciation/ distance travelled in kilometers
Depreciation per kilometer = $ [tex]\frac{9700}{25000}[/tex]
Depreciation per kilometer = $0. 388 per kilometer
c. Vₙ = V₀ + ₙt
t = time of depreciation
V₀ = $35400
Vₙ = $35400 + ₙt
d. When the car costs $35400, it travelled 25000 kilometers
It costs $6688, it would travel 'x' kilometers
Cross multiply
$35400 × x = $ 6688 × 25000 kilometers
Make 'x' subject
x = [tex]\frac{6688 * 25000}{35400}[/tex]
x = [tex]\frac{167200000}{35400}[/tex]
x = [tex]4723. 16[/tex] kilometers
The car would travel 4723. 16 kilometers
e. To find the total distance
Total distance = 25000 + 4723. 16
Total distance = 29723. 16 kilometers.
Learn more about depreciation here:
https://brainly.com/question/25297296
#SPJ1
Order the set of numbers from least to greatest: -
--5, -√26.-31
6
Answer:
-31, /~26, -5, 6
Step-by-step explanation:
How do i find the value of y?
Answer: 65
Step-by-step explanation:
We know that from the 65-degree angle, x=130.
So, by the inscribed angle theorem, y=65.
Aubree's parents invested $500 into a mutual fund that paid 6.5% interest each year compounded annually when she was born. Find the value of the mutual fund in 18 years.
The value of the fund in 18 years as required by the task is; $1553.5.
What is the value of the fund in 18 years?Since, the interest rate is compounded annually as described, the value of the fund in 18 years can be calculated by means of the compound interest formula as;
Value = 500(1.065)^18.
Hence, we have; Value = $1553.5.
Read more on compound interest;
https://brainly.com/question/24924853
#SPJ1
Which algebraic expression has a term with a coefficient of 9?
• A. 6 + X- 9
• B. 6x - 9
C. 6(x + 5)
• D. 9x ÷ 6
Answer:
D
Step-by-step explanation:
Coefficient is the number next to the variable, and D is the only one where that number is 9. All the others are 6.
If you played 12 games but only won 7, what is the percent of the victories?
Answer:
58.3%
Step-by-step explanation:
7/12 = 0.583333333
0.583333333 simplified is 58.3%
Answer:
Approximately 58.3%.
Step-by-step explanation:
7/12 ≈ 0.583
0.583 = 58.3%
Help checking my answer (solving inequalities)
(-4x + 2) / 4 >= 6
-4x + 2 >= 24
-4x >= 22
x <= 22/4 OR x <= 5 1/2 OR x <= 5.5
Hope this helps!
State if the three side lengths 3 mi, 12 mi, 13 mi?
Since the sum of any two sides is greater than the third, hence the three sides for the sides of a triangle
What is a triangle?A triangle is a 2-D shape with 3sides and angles. According to the question, we are to determine whether the given measures form sides of a triangle.
For the following measure to form the sides of a triangle, the sum of any two sides must be equal to the third as shown:
3 + 12 = 15 > 13
3 + 13 = 16 > 12
13 + 12 = 25 > 3
Since the sum of any two sides is greater than the third, hence the three sides for the sides of a triangle
Learn more triangle here: https://brainly.com/question/2217700
#SPJ1
A rectangular equation that is a function will be a function in any coordinate system. true or false ?
Answer:
True.
Step-by-step explanation:
In this true or false question, the answer is true.
Hope this helps!
Answer:
False
Step-by-step explanation:
Not every function in a rectangular plane will be a function in every plane. Hope this helps
It cost Josiah $9.75 to send 65 text messages. How many text messages did he send if
he spent $28.20?
According to my calculation the answer is 188.
Convert the exponential to a logarithmic form: 10 ^ 4 = 10000
Answer:
10^4 = 10 × 10 × 10 × 10
= 10000
Jason deposited $18 000 in a bank that offers an interest rate of 5% per annum compounded
daily.
He kept the money in the bank for 20 days, before withdrawing an amount, H.
Given that, the balance in the bank after another 20 days is $16 093.41, find H.
Answer:
$1995.97.
Step-by-step explanation:
Amount in bank after 20 days =
18000(1 + 0.05/365)^20
= $18049.38
So H = 18049.38 - 16093.41
= $1995.97.
7-2x≥15
solve for inequality
graph the solution
shade the possible solutions
1 -12 13 -4 -42 4
The solution set of the inequality is x ≤ - 4. The graph of inequality is shown below and the points x = - 4, x = - 12, x = - 42 are part of the solution set.
How to solve an inequality
In this question we must use algebraic axioms and theorems to solve an inequality and graph the solution set with the help of a graphing tool. Now we proceed to present the procedure to solve for x:
7 - 2 · x ≥ 15
7 - 15 ≥ 2 · x
2 · x ≤ - 8
x ≤ - 4
Now we present the graph of the inequality. The points x = - 4, x = - 12, x = - 42 are part of the solution set.
To learn more on inequalities: https://brainly.com/question/20383699
#SPJ1
this is a question on a review assignment that i’m stuck on , my summer school teacher said i could get help if i needed. any help would be greatly appreciated
Answer:
may be 3549 cube inch while rounded up.
The power of the algebraic expression
7xy + 3xy² - x³y² + 4 is
The power of the algebraic expression 7xy + 3xy² - x³y² + 4 is 1.
How to estimate the power of algebraic expression?An expression that denotes repeated multiplication of the exact factor exists named a power. The number 5 stands named the base, and the number 2 exists named the exponent. The exponent equals the number of times the base exists utilized as a factor.
Given: 7xy + 3xy² - x³y² + 4
An expression that represents repeated multiplication of the same factor is called a power.
So, the power of the given expression will be 1.
Therefore, the correct answer is 1.
To learn more about algebraic expression refer to:
https://brainly.com/question/1527946
#SPJ9
What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89
The value of the sum of squares due to regression is 18.43.
Given the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89.
A common measure used in regression analysis is the sum of squares total (SST). The square of each difference is added to the sum of squares to obtain the squared disparities between individual data points and their mean. The variance is calculated using the sum of squares, which is also used to assess how well a regression curve fits the data.
We will use the total sum of squares (SST) is given as the summation of the sum of squares due to regression (SSR) and sum of squares error (SSE);
SST = SSR + SSE
Here, SST=25.32 and SSE=6.89
Substitute the values in the formula, we get
25.32=SSR+6.89
Now, we will subtract 6.89 from both sides, we get
25.32-6.89=SSR+6.89-6.89
18.43=SSR
Hence, the value of the sum of squares due to regression (SSR) when the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89 is 18.43.
Learn more about regression from here brainly.com/question/23438254
#SPJ4
Compute a value for t that satisfies the equation below. "-2/3" t - 2 = - 3
Answer:
t = 3/2
Step-by-step explanation:
Instead of randomly guessing values of "t" that will satisfy the equation, you can easily find the correct value by solving the equation in terms of "t". In other words, you can set the equation equal to "t" to find the final answer.
(-2/3)t - 2 = -3 <----- Original equation
(-2/3)t = -1 <----- Add 2 to both sides
t = 3/2 <----- Divide both sides by -2/3
You can check this value by plugging it into "t" and determining whether both sides of the equations will be equal.
(-2/3)t - 2 = -3 <----- Original equation
(-2/3)(3/2) - 2 = -3 <----- Plug 3/2 into "t"
-6/6 - 2 = -3 <----- Multiply -2/3 and 3/2
-1 - 2 = -3 <----- Simplify -6/6
-3 = -3 <----- Subtract
How many more times intense, to two decimal places, was the 2011 earthquake in Japan that measured 9.0 on the Richter scale than the 1905 earthquake in San Francisco that measured 8.1 on the Richter scale?
Using the properties of logarithms, it is found that the earthquake in Japan in 2011 was 12.92 times more severe.
How to find the ratios of the intensity of earthquakes?As given in the problem, the intensities of the earthquakes are given by logarithms of base 10. Then, supposing that the intensities are [tex]R_1, R_2 > 0, R_1 > R_2[/tex], the ratio of the intensities is given by:
[tex]10^{\frac{R_1}{R_2}}[/tex]
The intensities for this problem are [tex]R_1 = 9, R_2 = 8.1[/tex], hence the ratio is:
[tex]10^{\frac{9}{8.1}} = 12.92[/tex]
The earthquake in Japan in 2011 was 12.92 times more severe.
More can be learned about logarithms at brainly.com/question/20719486
#SPJ1
65. Find the perimeter & area:
13 cm
5 cm
12 cm
66.
Given, that the sides of a triangle are [tex]$5 \mathrm{~cm}, 12 \mathrm{~cm}$[/tex] and [tex]$13 \mathrm{~cm}$[/tex] semi-perimeter [tex]$=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}$[/tex]
[tex]$$\begin{aligned}&\mathrm{s}=\frac{(5+12+13)}{2} \\&\mathrm{~s}=\frac{30}{2} \\&\mathrm{~s}=15 \mathrm{~cm}\end{aligned}$$[/tex]
Area of the triangle (according to Heron's Formula)
[tex]$$\begin{aligned}&=\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})} \\&=\sqrt{15(15-5)(15-12)(15-13)} \\&=\sqrt{15(10)(3)(2)} \\&=\sqrt{900} \\&=30 \mathrm{~cm}^{2}\end{aligned}$$[/tex]
What is Heron's Formula?
Heron's formula was first given by Heron of Alexandria. It is used to calculate the area of various triangles such as equilateral, isosceles, and scalene triangles or quadrilaterals. When we know the sides of a triangle, we can use Heron's formula to find its area. Using Heron's formula, we find the area of a triangle by taking its semi-perimeter and side lengths.Heron's formula is used to calculate the area of triangles given the lengths of all their sides, as well as the area of quadrilaterals. It's also known as Hero's formula. This formula for calculating the area does not rely on the angles of a triangle. It is solely determined by the lengths of all triangle sides. It contains the term "s," which stands for semi-perimeter, which is obtained by halving a triangle's perimeter. Similarly, the concept of determining the area is extended to determine the area of quadrilaterals.To learn more about Hero's formula visit:
https://brainly.com/question/20934807
#SPJ1
The volume of a cylinder is given by the formula , where r is the radius of the cylinder and h is the height. Which expression represents the volume of this cylinder
The Volume of cylinder represented by the option B.
According to the statement
we have given that the volume formula of cylinder is V= (pi)r^2h, and we have to find that the which expression verify the volume formula for the cylinder given in diagram.
So,
We know that height of the cylinder is given by h = 2x + 7 and
radius r = x - 3.
We know that the formula of volume of cylinder is:
Volume of a cylinder = (pi)r^2h
and Substituting the given values in the above formula
And the volume becomes
Volume = (pi)r^2h
Volume = (pi)( x-3 )^2 (2x+7)
Volume = (pi) ( x^2 + 9 - 6x ) (2x+7)
Volume = (pi) ( 2x^3 + 7x^2 +18x +63 - 42x)
So, The Volume of cylinder represented by the option B.
Learn more about Volume here https://brainly.com/question/1972490
Disclaimer: This question is incomplete. Please find the full content below.
Question:
The volume of a cylinder is given by the formula V= pi^2h, where r is the radius of the cylinder and h is the height: which expression represents the volume of this cylinder?
a) Volume = (pi) ( 3x^3 + 7x^2 +14x +63 - 42x)
b) Volume = (pi) ( 2x^3 + 7x^2 +18x +63 - 42x)
c) Volume = (pi) ( 7x^3 + 7x^2 +11x +63 - 42x)
d) Volume = (pi) ( 11x^3 + 7x^2 +13x +63 - 42x)
#SPJ4
0.10x how much is the bill for a person who uses 600 kWh in a month
The total bill paid for a person who uses 600 kWh in a month is $60.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that the utility company charges $0.10 per kWh, hence:
Total charge in a month = 0.10 * 600 = $60
The total bill paid for a person who uses 600 kWh in a month is $60.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1