Since the function is h(t) = −5t² + 15t, the domain of the function h(t) is 0 ≤ t ≤ 3
What is the domain of a function?The domain of a function is the range of input values that make the function have real values.
Now given the function h(t) = −5t² + 15t, it will have real values when
h(t) ≥ 0
So, h(t) ≥ 0
⇒ −5t² + 15t ≥ 0
Factorizing, we have
-5t(t - 3) ≥ 0
5t(t - 3) ≤ 0
t(t - 3) ≤ 0
t ≤ 0 and t - 3 ≤ 0
t ≤ 0 and t ≤ 3
For t ≤ 0, say -1, t(t - 3) = -1(-1 - 3) = -1(-4) = 4 ≥ 0
For 0 ≤ t ≤ 3, say 2, t(t - 3) = 2(2 - 3) = 2(-1) = -2 ≤ 0
For t ≥ 3, say 4, t(t - 3) = 4(4 - 3) = 4(1) = 4 ≥ 0
Since we require t(t - 3) ≤ 0, the domain of t is thus 0 ≤ t ≤ 3
So, the domain of the function h(t) is 0 ≤ t ≤ 3
Learn more about domain of a function here:
https://brainly.com/question/204418
#SPJ1
A manufacturer has a steady annual demand for 38016 cases of sugar. It costs $9 to store 1 for 1 year, $33 in set up cost to produce each batch, and $18 to produce each case. Find the number of cases per batch that should be produced to minimize cost.
Based on the setup costs, the steady annual demand, and the costs to store, the number of cases to produce to minimize cost is 528 units .
How many cases should be produced to minimize cost?This can be found by using the Economic Order Quantity.
= √ ( (2 x Setup costs x annual demand) / holding costs for the year)
Solving gives:
= √ ( ( 2 x 33 x 38,016) / 9)
= √278,784
= 528 units
Find out the economic order quantity at https://brainly.com/question/26814787.
#SPJ1
Calculate the geometric center of the graph the function
The geometric center of the graph under the function is 5/3
How to determine the geometric center of the graph under the function?The equation of the function is given as:
f(x) = 3 - |x - 2|
The interval is given as:
x ∈ [0, 3]
The geometric center (gc) of the graph under the function is calculated using
gc = ∫x f(x) dx/∫f(x) dx
Substitute the known values in the above equation
gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx
Integrate the numerator and the denominator of the above equation
gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]
Recall that the interval is given as x ∈ [0, 3]
Substitute the interval values in the above equation.
The equation is then simplified using a graphing calculator.
So, we have
gc = (65/6)/(13/2)
Express the quotient expression as a product
gc = (65/6) * (2/13)
Divide 65 by 13
gc = 5/6 * 2
Divide 2 by 6
gc = 5/3
Hence, the geometric center of the graph under the function is 5/3
Read more about geometric center at:
https://brainly.com/question/28099595
#SPJ1
a seller sold his house $240,000, which was 92 percent of the list price. what did the house list for?
The list price of the house is $260,869.57
What is a list price?
This is the price the property is valued to sell at in an arm's length transaction in a transaction that occurs between independent parties.
In this case, the property was sold for 92% of its list price, which means the sales price is 92% multiplied by the list price.
sales price=92%* list price
sales price=$240,000
list price=unknown(assume it is X)
$240,000=92%*X
X=$240,000/92%
X=$260,869.57
Find additional guidance on list price in the link below:
https://brainly.com/question/23103804
#SPJ1
Divide. (7x − 6x^2 + x^3 − 1) ÷ (x − 1)
Hope that helps...........................
At first it decreased by 60 percent and it increased by 80 percent
The quantity reported an equivalent net percentage change of 28 percent.
How to calculate the net change of a quantity in percentages
In this problem we must determine the simple percentage change equivalent to two consecutive percentual changes. The formula that describes the situation is:
1 + r/100 = (1 - 60/100) · (1 + 80/100)
1 + r/100 = 72/100
r/100 = - 28/100
r = - 28
The quantity reported an equivalent net percentage change of 28 percent.
Remark
The statement is incomplete. Complete form is presented below:
A quantity is changing. At first it descreased by 60 percent and it increased by 80 percent. What is net change of the quantity in percentage?
To learn more on percentages: https://brainly.com/question/13450942
#SPJ1
How should I solve this?
Inscribed angles that are formed by segments which extend from one side of the hypotenuse to the other are right angles.
Therefore, angle PRQ is a right angle and is equal to 90 degrees.
53y - 16 = 90
53y = 106
y = 2
Hope this helps!
Answer:
y=2
Step-by-step explanation:
the angle is 90 degrees which is equal to (53y-16).therefore find a number which you can substitute to get 90 which is y=2
please fill in the blanks of the question i sent a pic of
The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.
What is the center and the radius of the circle?
In this question we must determine the location of the center and the measure of the radius of a circle. According to Euclidean geometry, diameters are the longest possible chords of a circle. First, we determine the location of the center by definition of midpoint:
(h, k) = (1/2) · (4, 5.5) + (1/2) · (4, 10.5)
(h, k) = (4, 8)
And the radius is found by Pythagorean theorem:
[tex]d = \sqrt{(4 - 4)^{2}+(10.5-5.5)^{2}}[/tex]
d = 5
r = 0.5 · 5
r = 2.5
The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.
To learn more on circles: https://brainly.com/question/11833983
#SPJ1
Factories completely 2x * (2x + 1) ^ 2 + (2x + 1)(4x ^ 2 - 3)
The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).
How to factor an algebraic equation
In this question we have an algebraic expression to be expanded by means of algebraic properties, the purpose of this handling is to modify the polynomial until its standard form is finally obtained and later we find its factor form by Cardano's method. Now we proceed to show the procedure in detail:
2 · x · (2 · x + 1)² + (2 · x + 1) · (4 · x² - 3) Given
2 · x · (4 · x² + 4 · x + 1) + (2 · x + 1) · (4 · x²) + (2 · x + 1) · (- 3) Perfect square trinomial/Distributive property
8 · x³ + 4 · x² + 2 · x + 8 · x³ + 4 · x² - 6 · x - 3 Distributive property/(- 1) · a = - a
16 · x³ + 8 · x² - 4 · x - 3 Distributive property/Definitions of addition and subtraction
(x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242) Cardano's method/Result
The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).
To learn more on polynomials: https://brainly.com/question/11536910
#SPJ1
A university freshman class has 9900 students 4554 of thoses students are majoring in computer science what percentage of the class is computer science majors
Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.
What percentage of the class is computer science majors?Percentage is simply number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
Given the data in the question;
Total number of students or Whole = 9900Number of students majoring in computer science or Part = 4554Percentage of the class majoring in computer science = ?We substitute the given values into the above equation.
Percentage = ( Part / Whole ) × 100%
Percentage = ( 4554 / 9900 ) × 100%
Percentage = ( 0.46 ) × 100%
Percentage = 46%
Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.
Learn more about Percentages here: brainly.com/question/24159063
#SPJ1
answers for these? pls
Answer:
6a. 13.5m
6b. 12.4m
Step-by-step explanation:
We can use trig identities to solve these problems because each triangle is a right triangle.
6a. Find the measure of the hypotenuse.
Using the angle in the top corner, which is defined as 66 degrees and its adjacent side, we can find the hypotenuse. Remember that the hypotenuse is the longest side, which in this case would be AB. The adjacent side is the side next to the angle that is not the hypotenuse, in this case it would be AC, which is shown to be 5.5m.
The trig identity cos(x) is defined as adjacent/hypotenuse, or the value of the adjacent side divided by the value of the hypotenuse, where x is the degrees of the angle.
So we can set up the equation:
cos(x)=adj/hyp
If we know that x=66 (the degree of the angle) and adj=5.5m, we can substitute this into the equation. Let c represent the hypotenuse.
cos(66)=5.5/c
Then we can multiply by c:
c*cos(66)=5.5
Then divide by cos(66):
c=5.5/cos(66)
Use a calculator to estimate that c approximately equals 13.5m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).
6b. Find the measure of side a.
Side a is the side opposite to angle A. This can also be known as side CB or the bottom of the triangle.
Method 1: Use trig identity tan(x)tan(x)=opp/adj
Remember x=66 and adj=5.5m. Let a represent the opposite side. Plug in these values into the equation:
tan(66)=a/5.5
Multiply both sides by 5.5:
a=tan(66)*5.5
Use a calculator to estimate that a approximately equals 12.4m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).
Method 2 (I would recommend method 1, however because you are basing this answer off of the first answer, and in a test or a quiz, you might not be sure if your first answer was correct):
Use Pythagorean Theorem:
a^2+b^2=c^2
c, or the hypotenuse is 13.5m as found in out last problem, and b, the adjacent side is 5.5m which was a given. Substitute these values into the equation:
a^2+5.5^2=13.5^2
a^2+30.25=182.25
a^2=152a=sqrt(152) which rounds to 12.3m, which is almost the same as Method 1, however our answers are different because we used a rounded value of b, rather than the approximate.
Sketch the graph of y = (x-3)^2 -25, than select the graph that corresponds to your sketch.
Answer: graph c
Hope I was able to help
The difference of the square of a number and 8 is equal to 8 times that number. Find the positive solution.
Answer:
[tex]2\sqrt{6} +4[/tex]
Step-by-step explanation:
Let x be that unknown number.
From the information given from the question, we can deduce:
[tex]x^{2} -8=8x[/tex]
From here, we can solve for x to find what is the number.
[tex]x^{2} -8=8x\\x^{2} -8x-8=0[/tex] (Quadratic Equation)
From here we can use the Quadratic Formula to solve for x.
[tex]x=\frac{-b+/-\sqrt{b^{2} -4ac} }{2a}[/tex]
In this case,
a = 1, b = -8 , c = -8
We substitute a, b and c to find x.
[tex]x=\frac{-(-8)+/-\sqrt{(-8)^{2}-4(1)(-8) } }{2(1)} \\= 2\sqrt{6} +4[/tex]
(Reject the negative solution)
Please help ASAP
What of the secants below is a secant?
The secant in the diagram is [tex]\overline{AD}[/tex]
Segment AD intersect the circle at two points. So it can be a secant.
We have been given that a circle of center O. We have to find the segment that is secant.
What is Secant?Secant : If a line which intersect the circle at two points.Then the line segment is called secant.
If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.
(line segment has 2 fixed ends, whereas a ray has one end only, other end is not fixed)
Segment OB intersect the circle at one point B only. so OB cannot be a Secant.
Segment AD intersect the circle at two points. So it can be a secant.
Learn more about secant here;
https://brainly.com/question/7513459
#SPJ2
Which ordered pair is in the inverse of
the relation given by p?y + 5y= 0?
Remember that an ordered pair is of the form (x, y), then the ordered pairs on the inverse of the relation are (x, -x/5).
Which ordered pair is in the inverse of the relation given?Assuming the given relation is:
y + 5x = 0
We can rewrite it to:
y = -5x
Then the inverse will be a function g(x) such that:
y = -5*g(x) = x
Solving for g(x):
g(x) = (-x/5).
Then the inverse of the relation is:
y = -x/5
Remember that an ordered pair is of the form (x, y), then the ordered pairs on the inverse of the relation are (x, -x/5).
If you want to learn more about inverses:
https://brainly.com/question/14391067
#SPJ1
ANSWER ONLY THANK YOU
A. (1,4)
EXPALINATION :
IF WE WRITE THE VALUE x = -1 AND y = 4
THEN, y= -8x - 4
4= -8×-1-4
4= 8-4
AND SECOND EQUATION IS : y = x+5
y = -1 +5
y = 4
hence, solved and explained
thank you And mark me brainlist if you understand And hopes so
answer as soon as possible
The area of the equilateral triangle is 110.9 cm
How to find area of a triangle?area of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
tan 60 = opposite / adjacent
tan 60 = 8√3 / x
x = 8√3 / √3
x = 8
hence,
b = 8 + 8 = 16
Therefore,
area of a triangle = 1 / 2 × 16 × 8√3
area of a triangle = 64√3
area of a triangle = 110.851251684
area of a triangle = 110.9 cm
learn more on triangle here: https://brainly.com/question/20593575
#SPJ1
Find the dimensions of the rectangle
Answer:
length: 12 mwidth: 4.5 mStep-by-step explanation:
The given relation between length and width can be used with the area formula to write an equation for the dimensions of the rectangle.
SetupLet w represent the width of the rectangle. The length is 3 more than twice that, so is (2w+3). The area is the product of length and width.
A = LW
54 = (2w +3)(w)
SolutionRewriting this equation to standard form gives ...
2w² +3w -54 = 0
(2w -9)(w +6) = 0 . . . . factored
w = 9/2, -6 . . . . . . . . . values that make the equation true
Only the positive width makes sense in a geometry problem, so we have ...
w = 9/2
length = 2w +3 = 12
The length of the rectangle is 12 meters; its width is 4.5 meters.
The scatterplot to the left shows the cost, CCC, in thousands of dollars, and living space, xxx, in square feet (\text{ft}^2)(ft
2
)left parenthesis, start text, f, t, end text, squared, right parenthesis for several houses in a certain neighborhood. According to the data, which of the following best approximates the cost for an additional square foot of living space for homes in this neighborhood?
Choose 1 answer:
\$80$80dollar sign, 80
\$300$300dollar sign, 300
\$1{,}000$1,000dollar sign, 1, comma, 000
\$13{,}000$13,000dollar sign, 13, comma, 000
According to the data, the cost of this house would increase by 0.08 thousand dollars ($80) for each additional square foot of living space.
How to determine the cost for an additional square foot?By critically observing the scatter plot, we can logically deduce that it shows a linear trend. Thus, the slope of the line of best fit is given by a ratio of change in cost to the change in living space.
Next, we would approximate two points on the line of best fit and then find the slope as follows:
Slope, m = ΔC/Δx
Slope, m = (C₂ - C₁)/(x₂ - x₁)
Slope, m = (400 - 200)/(4000 - 1500)
Slope, m = 0.08.
Therefore, the cost of this house would increase by approximately 0.08 thousand dollars ($80) for each additional square foot of living space.
Read more on scatterplot here: brainly.com/question/6592115
#SPJ1
Reflect the given triangle over the line y=-X
TOP (3 6 3)
BOTTOM (-3 3 3)
The equation rule for the reflection of the triangle over the line y = -x is given as (x, y) ⇒ (-y, -x)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
The equation rule for the reflection of the triangle over the line y = -x is given as (x, y) ⇒ (-y, -x)
Find out more on transformation at: https://brainly.com/question/4289712
#SPJ1
1. The correlation coefficient on a scatter plot representing the variables for the amount of weight a body builder can lift in a gym and the amount of protein the body builder takes each day is 0.76. Describe the meaning of this correlation coefficient.
A
very Strong positive linear relationship between the two variables
B
very Strong negative linear relationship between the two variables
C
moderate positive linear relationship between the two variables
D
no relationship between the two variables
A correlation coefficient of 0.76 indicates a very strong positive linear relationship between the two variables.
What does the correlation coefficient mean?Correlation is a statistical measure used to measure the linear relationship that exists between two variables.
If the sign of the correlation coefficient is positive, it means that the two variables exhibits a positive correlation. The closer to 1, the correlation coefficient is, the stronger the linear relationship.
To learn more about correlation, please check: https://brainly.com/question/27246345
#SPJ1
The quantities xxx and yyy are proportional. xxx yyy 777 353535 121212 606060 202020 100100100 Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x. r =r=r, equals
The constant of proportionality of our given tables is; 5.
How to find the constant of Proportionality?We are given that x and y are proportional, and this means that:
y = r*x
where;
r is the constant of proportionality.
We are given the table;
x y
7 35
12 60
20 100
Now, we can replace those values in our equation and get, for the first pair: 35 = r*7
r = 35/7 = 5
For the second pair:
60 = r*12
60/12 = r
r = 5
Thus, we can conclude that the constant of proportionality is 5.
Read more about Constant of Proportionality at; https://brainly.com/question/20290730
#SPJ1
Answer: 3
Step-by-step explanation:
Rectangle A has side lengths of 6\text{ cm}6 cm6, start text, space, c, m, end text and 3.5\text{ cm}3.5 cm3, point, 5, start text, space, c, m, end text. The side lengths of rectangle B are proportional to the side lengths of rectangle A.
What could be the side lengths of rectangle B?
Choose 2 answers:
The side lengths of rectangle is 3 cm and 1.75 cm and 5.25 cm and 9 cm.
According to the statement
we have given that Rectangle A has side lengths of 6 cm and 3.5 cm
And The side lengths of rectangle B are proportional to the side lengths of rectangle A.
And we have to Find that the What could be the side lengths of rectangle B?
A 3 cm and 1.75 cm
B 5 cm and 2.5 cm
C 7 cm and 7 cm
D 12 cm and 5 cm
E 5.25 cm and 9 cm
Here we see that the side B are proportional to side length A of rectangle.
So,
Let say sides of rectangle B are a and b corresponding to sides 6 and 3.5 cm
=> a/6 = b/3.5
=> a/b = 6/3.5
=> a/b = 12/7
A 3 cm and 1.75 cm
3/1.75 = 12/7
Hence this is proportional
B 5 cm and 2.5 cm
5/2.5 = 2 ≠ 12/7
Not Proportional
C 7 cm and 7 cm
7/7 = 1 ≠ 12/7
Not Proportional
D 12 cm and 5 cm
12/5 ≠ 12/7
Not Proportional
E 5.25 cm and 9 cm
9/5.25 = 36/21 = 12/7
Hence this is proportional
So, 3 cm and 1.75 cm and 5.25 cm and 9 cm could be the side lengths of rectangle B.
Learn more about Rectangles here https://brainly.com/question/18019422
#SPJ1
Robert can mow a 600 square lawn in 1 hour and 20 minutes. How many lawns in the same size's can he mow in 8 hours?
the time between customer visits to the bank from midday to 1pm is evenly distributed over the period from 0 to 120 seconds. what is the standard deviation of the timeout?
Using the uniform distribution, the standard deviation of the timeout is of 34.64 seconds.
What is the uniform probability distribution?It is a distribution with two bounds, a and b, in which each outcome is equally as likely.
The standard deviation is:
[tex]S = \sqrt{\frac{(b - a)^2}{12}}[/tex].
For this problem, the bounds are:
a = 0, b = 120.
Hence the standard deviation is found as follows:
[tex]S = \sqrt{\frac{(120 - 0)^2}{12}} = 34.64[/tex].
More can be learned about the uniform distribution at https://brainly.com/question/13889040
#SPJ1
The company stock you are monitoring for your Economics class increases five-eighths point the first week and then it increases one- half point the second week and one-quarter point the third week. What is the total increase during the three weeks?
Based on the change in the company stock over the three weeks, the total increase in those three weeks is 1.38%.
how much did the stock increase by?assuming the stock has a value of $1, the value in the third week would be:
= 1 x (1 + 5/8%) x (1 + 1/2%) x (1 + 1/4%)
= $1.013809453125
the total increase is:
= (1.013809453125 - 1) / 1
= 1.38%
find out more on stock price change at https://brainly.com/question/23856103.
#SPJ1
In Fig. 6.39, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.
[tex] \: [/tex]
[tex] \leadsto \sf{ \pink{Pls \: give \: me \: correct \: answer!!}}[/tex]
Thank u :)
[tex] \huge{↬ \boxed{ \sf{ \pink{A\green{n \blue{s \color{yellow}w \red{e \orange{r}}}}}}}}[/tex]
Given: ∠SPR = 135° and ∠PQT = 110°To find: ∠PRQ[tex] \leadsto[/tex]According to Angle sum property of a triangle , sum of the interior angles of a triangle is 180°.
➱ ∠SPR + ∠QPR = 180° [Linear pair]
➱ 135° + ∠QPR = 180°
➱ ∠QPR = 180° - 135°
➱ ∠QPR = 45°.....(i)
➱ ∠PQT + ∠PQR = 180° [Linear pair]
➱ 110° + ∠PQR = 180°
➱ ∠PQR = 180° - 110°
➱ ∠PQR = 70°.....(ii)
Now,➛ ∠PQR + ∠QPR + ∠PRQ = 180° [Angle sum property of a triangle]
➱ 70°+ 45° + ∠PRQ = 180° [from (i) and (ii)]
➱ ∠PRQ = 180° - 115°
➥ ∠PRQ = 65°
hope it's help u!! :D
Which of the following are true?
Children learn to duplicate patterns when they can identify the rule, that is, when the unit repeats and the pattern becomes predictable.
a. True
b. False
Children learning to duplicate patterns when they can identify the rule, that is, when the unit repeats and the pattern becomes predictable is a true statement.
What are Patterns?
This involves the regularity or repeated way in which something is done or arranged.
Children are very inquisitive and tend to make logical connections when dealing with patterns due to their reasoning skills thereby aiding their learning process.
Read more about Patterns here https://brainly.com/question/17386984
#SPJ1
Rate:
168 ounces
14 boxes
How much does the spaghetti in each box weigh? Find the unit rate.
Answer:
12 ounces
Step-by-step explanation:
168 divided by 14 = 12
Question 19 of 25
f(x)=√x-6. Find the inverse of f(x) and its domain.
Answer:
f¯¹(x)=x²+12x+36
Step-by-step explanation:
[tex]f(x) = \sqrt{x} - 6 \\ substitute \: y \: for \: f {}^{ - 1} (x) \\ y = \sqrt{x} - 6 \\ interchange \: x \: and \: y \\ x = \sqrt{y} - 6 \\ swap \: the \: side \: of \: the \: equation \\ \sqrt{y } - 6 = x \\ move \: the \: constant \: to \: the \: right \: hand \: side \\ \sqrt{y} = x + 6 \\ square \: both \: sides \: of \: the \: equation \\ y = x {}^{2} + 12x + 36 \\ substitute \: f \frac{}{ -1} (x) \: for \: y \\ f {}^{ - 1} (x) = x {}^{2} + 12x + 36 \\ domain \: x∈R[/tex]