Answer:
{±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24}
Step-by-step explanation:
Since the leading coefficient is 1, any rational zeros will be divisors of -24.
_____
Comment on rational zeros
If the leading coefficient is not one, then rational zeros will be the ratio of a divisor of 24 to a divisor of the leading coefficient.
What is the area of the parallelogram?
48 sqrt(3)cm2
48 cm2
24 sqrt (3) cm2
24 cm2
Answer: 48cm2
Step-by-step explanation:
area = base x height
a = 8 x 6
a = 48
Solve x − 5y = 6 for x.?
A) x = −5y + 6
B)x = −5y − 6
C) x = 5y + 6
D) x = 5y −6
Answer:
C.
Step-by-step explanation:
To solve for x you have to move the -5y to the other side of the equals sign. Since the opposite of subtracting is adding, we will add 5y to both sides to get
x = 5y + 6
Choice C
The value of x − 5y = 6 is x = 5y + 6.
Value of xGiven:
x − 5y = 6
To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Solve the value of x, then
x - 5y = 6
Simplifying the above equation, we get
x = 6 + 5y
Therefore, the correct answer is option C) x = 5y + 6.
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which statement about the following system is correct? y=-2x+5 and y=-2x+5
Answer:
Infinite number of solutions
Step-by-step explanation:
Since the equations are both the same, we have an infinite number of solutions! The solutions lie on the graph y = -2x+5.
The system of equations given represents the same line with infinitely many solutions,.
The system given is y = -2x + 5 and y = -2x + 5. Both equations are identical, which means they represent the same line. Therefore, every point on the line y = -2x + 5 will satisfy both equations, indicating that the system has infinitely many solutions. The slope of the line is -2 and the y-intercept is 5. This aligns with the standard form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
A sign language club made $627.50 from selling popcorn at a festival. The popcorn cost the club $95.00. Which expression represents the amount of money that was raised for each member of the club?
its D. 2.95x+39.95(12)
Answer:
$532.50 / (number of members)
Step-by-step explanation:
Let m represent the number of members.
The net income (after subtracting the cost of the popcorn) was $532.50.
Thus, the amount of $ raised per member of the club was $532.50/m
Answer
(627.50-95)/m
Step-by-step explanation:
got 100%
PLZZ! HELP WITH THIS! WILL GIVE BRAINLLEIST! PROMISE! AND 11 POINTS! FOR A SIMPLE ANSWER! THANKS TO ANYONE WHO ANSWERS THIS! HURRY!! PLZZ
A farm is to be built in the shape of quadrilateral ABCD, as shown below.
All four sides are equal. A rhombus ABCD is shown with diagonal AC equal to 12.6 feet and diagonal BD equal to 10.4 feet.
What is the area of the farm?
32.76 square feet
46 square feet
65.52 square feet
92 square feet
Answer:
65.52 square feet
Step-by-step explanation:
to find area of a rhombus with the diagonals multiply them together and divide by two.
10.4 x 12.6 = 131.04
131.04/2 = 65.52 square ft
Imagine if you're in a room filling up with water. there are no windows/doors and you can't break anything, how do you get out?
Answer:
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What is the image of point (9, -9) for mapping (x, y) , (x + 2, y + 2).
Answer:
(11 , -7)
Step-by-step explanation:
Note that x = 9, y = -9. Plug in the corresponding numbers to the corresponding variables.
(x + 2, y + 2)
(9 + 2, -9 + 2)
Simplify.
(11, -7)
(11 , -7) is your image point.
~
Help with this question, please!!
Answer:
12.85 inches
Step-by-step explanation:
Angle ACP = Angle DPB = 92 degrees
because they are vertical angles
We are finding arc length, which is circumference
C = 2* pi *r
but we are only find 92 degrees of the 360 in a circle
C = 2 * pi * r * 92/360
= 2 * pi *8 *92/360
= 4.09 pi inches
= 12.84562329
= 12.85 inches
Answer:
Last answer
4.09 π
Step-by-step explanation:
Assuming CD and AB are straight lines and P is the center of the circle,
∠BPD = ∠CPA = 92°
r = 8 in
Minor Arc Length BD,
= (92/360) * 2πr
= (92/360) * 2π(8)
= 4.09 π
Eight white balls and twenty black balls are in a bag. What is the probability of drawing a black ball in one draw?
01
O
2/5
O
5/7
Answer:
The correct answer is last option
5/7
Step-by-step explanation:
It is given that, eight white balls and twenty black balls are in a bag
To find the probability
From the above data we get,
number of white balls = 8
Number of black balls = 20
total number of balls = 8 + 20 = 28
Probability of getting black ball = number of black ball/Total number of balls
= 20/28 = 5/7
The correct answer is last option
5/7
The oblique prism has a rectangular base with a width of 10 units and a length of 13 units. The top base extends 8 units to the right of the bottom base. What is the volume of the prism?
Answer:
1950 cubic units
Answer:
[tex]1040[/tex] cubic units
Step-by-step explanation:
The volume of any oblique geometric shape is equal to the product of area of its base and the height from which its top extends to its bottom base.
Mathematically, it can be represented as -
[tex]V = (Area_{base} * height)\\[/tex]
Substituting the given values in above equation, we get -
[tex]V = (10 * 13) * 8 \\V = 1040\\[/tex] cubic unit.
Rodney is helping to make hamburgers for the football game. He's made 10 hamburgers so far. His coach asked him to make at least 30 hamburgers but no more than 80. Solve the inequality and interpret the solution.
30 ≤ x + 10 ≤ 80
20 ≥ x ≥ 70; Rodney needs to make less than 20 more hamburgers or more than 70.
40 ≤ x ≤ 90; Rodney needs to make at least 40 more hamburgers but no more than 90.
40 ≥ x ≥ 90; Rodney needs to make less than 40 more hamburgers or more than 90.
20 ≤ x ≤ 70; Rodney needs to make at least 20 more hamburgers but no more than 70.
Answer:
Option D (20 ≤ x ≤ 70; Rodney needs to make at least 20 more hamburgers but no more than 70).
Step-by-step explanation:
The given inequality is 30 ≤ x + 10 ≤ 80 . There are basically two inequalities. One is 30 ≤ x + 10 and x + 10 ≤ 80. x is the number of hamburgers that are to be made, 10 is the number of hamburgers already made, 30 is the lower limit of the hamburgers required, and 80 is the upper limit of the hamburgers required. The question requires to solve the inequality. To solve this, the inequality will be separated as done above.
1)
30 ≤ x + 10.
20 ≤ x.
2)
x + 10 ≤ 80.
x ≤ 70.
Now combining the two inequality gives:
20 ≤ x ≤ 70. So Rodney needs to make at least 20 more hamburgers but no more than 70. Therefore, Option D is the correct answer!!!
Answer:
20 ≤ x ≤ 70; Rodney needs to make at least 20 more hamburgers but no more than 70
Step-by-step explanation:
Let
x ----> the numbers of hamburgers that Rodney needs to make
we know that
[tex]x+10\geq 30[/tex] ----> inequality A
[tex]x+10\leq 80[/tex] -----> inequality B
Solve the inequality A
[tex]x\geq 30-10[/tex]
[tex]x\geq 20\ hamburgers[/tex]
Solve the inequality B
[tex]x\leq 80-10[/tex]
[tex]x\leq 70\ hamburgers[/tex]
so
The solution of the system of inequalities is the interval
[20,70]
[tex]20 \leq x \leq 70[/tex]
All whole numbers greater than or equal to 20 hamburgers and less than or equal to 70 hamburgers
therefore
Rodney needs to make at least 20 more hamburgers but no more than 70.
If you apply the changes below to the linear parent function f(x)=x what is the equation of the new function vertically compress by 1/4 over the y-axis
Answer: It moves the graph down by 1/4
Step-by-step explanation:
I used demos and the graph had a change making it lower coordinates by a fourth.
NEED HELP WITH A MATH QUESTION
Answer:
[tex]\dfrac{18}{5}<x<4\\ \\3.6<x<4[/tex]
Step-by-step explanation:
The picture shows three isosceles tirangles with the same legs. The base of each triangle is 12 units, 5x-3 units and 17 units.
Since the angles at vertex of each isosceles triangles are 27°, 28° and 29°, then the lengths of the bases satisfy the double inequality
15<5x-3<17
Add 3 to this inequality
15+3<5x-3+3<17+3
18<5x<20
Divide it by 5:
[tex]\dfrac{18}{5}<x<4\\ \\3.6<x<4[/tex]
please help asap will mark brainliest
Answer: 1/20, or 0.05
Step-by-step explanation: What we have to do is figure out how many times the blue shades area goes into the total area. Horizontally, it would be 5/10 squares, or 1/2. Vertically, it is 5/50 squares, or 1/10. Multiplying 1/2 and 1/10 gives us 1/20, or 0.05 as your answer.
URGENT PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
10.4 cm
Step-by-step explanation:
In this question apply the formulae for volume of a pyramid
General formulae for volume of a pyramid is = l*w*h /3 where l is base length, w is base width and h is height.
In this question l=w= 6cm, v=120 cm³ and h=? ,
Apply the formulae
[tex]V= l*w*h /3\\\\120=6*6*h/3\\\\120=12h\\\\120/12 =h\\\\10cm=h[/tex]
Slant height
The length = 6cm-----------------divide by 2 to get half the legth
a=6/2=3cm
h=b= 10cm
c=?
apply the Pythagorean relationship
a²+b²=c²
3² + 10²= c²
9+100=c²
√109=c²
c=10.44
slant height =10.4 cm
Answer:
Slant height of pyramid = 10.4 m
Step-by-step explanation:
Points to remember
Volume of square pyramid = a²h/3
Where 'a' is the side of base and h is the height of pyramid
To find the height of pyramid
It is given that volume of square pyramid = 120 cm³ and
base a = 6 cm
a²h/3 = 120
h = (120 * 3)/a²
= (120 * 3)/6²
=10 cm
Therefore h = 10 cm
To find the slant height of pyramid
By using Pythagorean theorem we can write,
slant height ² = (base/2)² + height²
l² = (a/2)² + h²
= (6/2)² + 10²
= 3² + 10²
= 9 + 100
=109
l = √109 = 10.44 ≈ 10.4
The volume of a box is 80 cubic feet with length x-3 and width x-1 and height x+5. What are the possible values of x? What are the possible dimensions?
Answer:
the only possible value of x is 5the dimensions are 2 × 4 × 10Step-by-step explanation:
The cubic equation ...
(x -3)(x -1)(x +5) = 80
has one real root: x = 5. Using that value for x, the dimensions become ...
length = 5 - 3 = 2
width = 5 - 1 = 4
height = 5 + 5 = 10
The dimensions are (length, width, height) = (2, 4, 10).
_____
We cannot tell the thrust of the problem, since it has only one solution. Perhaps you're supposed to write the cubic in standard form and use the Rational Root theorem to find possible values of x. That form can be found to be ...
(x -3)(x -1)(x +5) -80 = 0
x³ +x² -17x -65 = 0
Descartes' rule of signs tells you there is one positive real root. The rational root theorem tells you possible rational roots are factors of 65:
1, 5, 13, 65
We know that x must be greater than 3 (so all dimensions are positive). Thus possible values of x are 5, 13, 65, and we're pretty sure that 65 is way too large.
Please help, never had a question like this before
Answer:
22.3 km²
Step-by-step explanation:
you are given the diameter is 5[tex]\frac{1}{3}[/tex] km
radius = 1/2 x 5[tex]\frac{1}{3}[/tex] = 2.667 km
area = π * radius² = 3.142 * 2.667² = 22.3 km²
See attachment for solution steps and answer.
Factor the polynomial.
8g + 16h
Answer:
[tex]8g+16h=8(g+2h)[/tex]
Step-by-step explanation:
The given expression is
[tex]8g+16h[/tex]
To factor this polynomial, we just need to extract the common factor. Or you can see as the greatest common factor.
What is the greatest common factor between 8 and 16?
16: 1, 2, 4, 8, 16.
8: 1, 2, 4, 8.
You can observe that the greatest common factor is 8, so we extract it from both numbers
[tex]8g+16h=8(g+2h)[/tex]
Notice that we placed the GCM in the front as a product, if we don't do that, it would be completely wrong, because we can change the equivalence of the expression. Now, notice that each variable have different coefficients, that is because if you extract the GCM, you need to placed its quotients as coefficients.
Therefore, the factor of the polynomial is
[tex]8g+16h=8(g+2h)[/tex]
PLEASE HELP ME ON THIS, I WILL APPRECIATE IT SO MUCH!!!! TYSM
1.
[tex]|\Omega|=15^2=225\\|A|=5\cdot4=20\\\\P(A)=\dfrac{20}{225}=\dfrac{4}{45}[/tex]
2.
[tex]|\Omega|=15^2=225\\|A|=6\cdot5=30\\\\P(A)=\dfrac{30}{225}=\dfrac{2}{15}[/tex]
Annual high temperatures in a certain location have been tracked for several years. Let
X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).
y=________
x=________
Answer:
Y= 19.86 - 0.42b
Step-by-step explanation:
Step 1: Write the formula
Regression Line: Y = a + bx
a=(Total Y) x (Total X^2) - (Total X) x (Total XY)
n x (total X^2) - (Total X)^2
b= n x (Total XY) - (Total X) x (Total Y)
n x (total X^2) - (Total X)^2
Step 2: Make a table to find all values
X Y X^2 Y^2 XY
5 17.19 25 295.4961 85.95
6 19.12 36 365.5744 114.72
7 16.75 49 280.5625 117.25
8 15.58 64 242.7364 124.64
9 16.21 81 262.7641 145.89
10 14.14 100 199.9396 141.1
11 14.97 121 224.1009 164.67
12 16.2 144 262.44 194.4
68 130.16 620 2133.614 1088.62 TOTAL
Step 3: Substitute all values in the equation to find a and b
a=(Total Y) x (Total X^2) - (Total X) x (Total XY)
n x (total X^2) - (Total X)^2
a= (130.16 x 620) - (68 x 1088.62)
8 x (620) - (68)^2
a = 80699.2 - 74026.16
336
a = 19.86
b = n x (Total XY) - (Total X) x (Total Y)
n x (total X^2) - (Total X)^2
b = 8 x (1088.62) - (68 x 130.16)
8 x (620) - (68)^2
b = 8708.96 - 8850.88
336
b = -0.42
Step 4 : Apply values of a and b in the formula of the regression line.
Regression Line: Y = a + bx
Y= 19.86 + b (-0.42)
Y= 19.86 - 0.42b
The regression line is calculated using the 'least squares method'. The formula is Y=a+bX, where a is the Y-intercept and b is the slope. These are calculated from the X and Y data values using specific formulas.
Explanation:To calculate the regression line from the given X (year) and Y (high temperature) values, we first need to know the specific data. Unfortunately, the data isn't provided in the question. However, I can explain the process to you.
A regression line, also known as the line of best fit, is a straight line that best represents the data on a scatter plot. This line can be calculated using the 'least squares method'. This method minimizes the sum of the squares of the residuals (the differences between the actual and predicted Y values).
The formula for the regression line is Y=a+bX, where:
a is the Y-intercept, calculated as (average of Y Values) - b * (average of X Values) b is the slope of the line, calculated as [N * (sum of XY) - (sum of X) * (sum of Y)] / [N * (sum of X²) - (sum of X)²]. Note that N is the number of data points.
You can plug in your X and Y data values into these equations to find your regression line.
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Which of the following functions is represented by the graph below?
a. y = 3 cos (1/2)x
b. y = -3 cos (1/2)x
c. y = 2 sin (1/3)x
d. y = -2 sin (1/3)x
Answer:
A. y = 3 cos (1/2) x.
Step-by-step explanation:
The y-intercept is 3 so it will contain 3 cos x (because y = cos x passes through (0, 1).
The graph of 3 cos x has been stretched horizontally by a factor 2 ( 3 cos x would pass through (π/2, 0) whereas the given graph passes through (π, 0).
So the equation is 3 cos(1/2) x
The function which represents the graph is A. y = 3 cos (1/2) x.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The y-intercept is 3 so it will contain 3 cos x (because y = cos x passes through (0, 1).
The graph of 3 cos x has been stretched horizontally by a factor of 2 ( 3 cos x would pass through (π/2, 0) whereas the given graph passes through (π, 0).
Therefore the function which represents the graph is A. y = 3 cos (1/2) x.
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Which of the following equations is an example of inverse variation between
the variables x and y?
For this case we have that by definition, a direct variation is given by:
[tex]y = kx[/tex]
Where:
k: It is the constant of proportionality of the variables.
On the other hand, we have that the inverse variation is given by:
[tex]y = \frac {k} {x}[/tex]
Where:
k: It is the constant of proportionality of the variables.
In this way, the correct option is: [tex]y = \frac {9} {x}[/tex]
ANswer:
Option A
Answer: Option A
[tex]y = \frac{9}{x}[/tex]
Step-by-step explanation:
It is said that two variables x and y vary inversely if the increase of one of the variables causes the other to decrease.
This is represented by the following equation
[tex]y = \frac{k}{x}[/tex]
Where k is known as variation constant
To answer this question, identify among the options given that the form has
[tex]y = \frac{k}{x}[/tex]
The answer is the option A. with k = 9
find the equation of the line parallel to y=2x+6 passing through (4,5)
Answer:
y=2x-3
when two lines are parallel, they have the same slope.
in the formula y=mx+b, m=slope of the line
we know 2 will be the slope for the line passing through (4,5)
next plug in (4,5) into the formula with 2 as the slope
4=x 5=y
next 5=2(4)+b
and you end up with
y=2x-3 when you simplify
According to the SMART goals method, goals should be
A. Clearly defined.
B. Easy to achieve
C. Similar to your peers' goals.
D. Flexible.
According to the SMART goals method, goals should be clearly defined, aligning with the "Specific" attribute of the SMART acronym. This means having a clear and direct aim for the goal, which is essential for effective goal-setting.
Explanation:According to the SMART goals method, goals should be clearly defined. SMART is an acronym that stands for Specific, Measurable, Attainable, Relevant, and Time-bound. Each of these attributes plays a crucial role in the formulation of effective and actionable goals.
Specific means the goal should be clear and direct, detailing exactly what is expected to be achieved. A goal that is Measurable has quantifiable criteria to indicate progress or completion. Attainable refers to the goal being realistic and possible to achieve given current resources and constraints.
Being Relevant means the goal aligns with broader objectives and makes sense within the greater plan. Lastly, Time-bound means there is a specific deadline or period within which the goal should be accomplished.
Therefore, the correct choice is A. Clearly defined, as a SMART goal must be specific and this inherently means the goal should have a clear definition.
Given sinA=9/√97 and that angle A is in Quadrant I, find the exact value of cos A in simplest radical form using a rational denominator.
Answer:
cos(A) = (4√97)/97
Step-by-step explanation:
The cosine is related to the sine by ...
cos(A)² = 1 - sin(A)²
cos(A)² = 1 - (9/√97)² = 1 - 81/97 = 16/97 . . . . substitute for sin(A), simplify
Make the denominator a square:
cos(A)² = (16·97)/97²
cos(A) = (4√97)/97 . . . . . square root
The exact value of cos A can be determined using the Pythagorean identity. In this case, cosA = 4√97/97, which is the exact value of cos A in simplest radical form with a rational denominator.
Explanation:In mathematics, the exact value of cos A can be determined using the Pythagorean identity, sin²A + cos²A = 1.
According to the problem, sinA = 9/√97, which when squared gives 81/97. Using the Pythagorean identity, we can substitute the value of sin²A to get cos²A. Hence, cos²A = 1 - sin²A = 1 - 81/97 = 16/97. The exact value of cos A, then, is the square root of 16/97. As A is in Quadrant I where cosine is positive, this will be √(16/97).
In order to write this value with a rational denominator, multiply and divide by the square root of the denominator (√97). Hence, cosA = 4√97/97, which is the exact value of cos A in simplest radical form with a rational denominator.
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There are approximately 3.6 million deaths per year in country A. Express this quantity as deaths per minute.
Answer:
Approximately 7 deaths per minute.
Step-by-step explanation:
There's 365 days in a year, there's 24 hours in a day, and there's 60 minutes in one hour. 3.6 Million/ 365 days = 9,863 deaths per day 9,863 deaths per day/ 24 hours = 411 deaths per hour 411 deaths per hour/ 60 minutes = Approximately 7 deaths per minuteWhich statement could the expression 13+x represent? Andrea has 13 eggs and bought 13 more. Victoria has 13 flowers. This is greater than the number of flowers Elisa has. Prakhar is 13 years older than his youngest sister. Kai is 13 blocks from home. Jack is a greater distance away.
Answer:
Prakhar is 13 years older than his youngest sister.
Step-by-step explanation:
if we let his younger sisters age be x, and prakar is 13 years older,
then prakar's age is (13 + x)
The statement that represents the expression 13 + x is " Prakhar is 13 years older than his youngest sister".
What is an expression?The expression consists of at least one variable and constants with basic arithmetic operators.
Verifying the given statements with the given expression:Statement 1: Andrea has 13 eggs and bought 13 more
Here there is no use of variables. So, Andrea has a total of 26 eggs. "false"
Statement 2: Victoria has 13 flowers. This is greater than the number of flowers Elisa has.
The expression that represents this statement is V > E (the number of flowers that Victoria and Elisa have are denoted by V and E)
So, this also does not represent the given equation. "false"
Statement 3: Prakhar is 13 years older than his youngest sister.
Consider the age of Prakhar's younger sister = x
So. Prakhar's age becomes x + 13 or 13 + x
Thus, it represents the given expression. "true"
Statement 4: Kai is 13 blocks from home. Jack is a greater distance away.
These are not connected or related to one another. So, no variable is used and it doesn't form an expression. "false"
Therefore, statement 3 is a true expression and it is represented by the expression "13 + x".
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An urn contains different colored marbles. The probability of drawing two green marbles from the urn without replacement is 3/20 , and the probability of drawing one green marble is 2/5 .
What is the probability of drawing a second green marble, given that the first marble is green?
3/50
1/2
3/8
1/5
The probability of drawing a second green marble, given that the first marble is green is:
[tex]\dfrac{3}{8}[/tex]
Step-by-step explanation:Let A denote the event that first marble is green.
B denote the event that the second marble is green.
A∩B denote the event that both the marbles are green.
Let P denote the probability of an event.
We are asked to find:
P(B|A) i.e. probability of drawing a second green marble, given that the first marble is green.
We know that:
[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]
Probability of drawing one green marble is 2/5 i.e.
[tex]P(A)=\dfrac{2}{5}[/tex]
The probability of drawing two green marbles from the urn without replacement is 3/20 i.e.
[tex]P(A\bigcap B)=\dfrac{3}{20}[/tex]
Hence, we have:
[tex]P(B|A)=\dfrac{\dfrac{3}{20}}{\dfrac{2}{5}}\\\\\\i.e.\\\\\\P(B|A)=\dfrac{3\times 5}{20\times 2}\\\\\\P(B|A)=\dfrac{3}{8}[/tex]
Answer:
3/50
Step-by-step explanation:
Jalen says that the height, radius, and diameter of a cone lie entirely on the base of the cone. What is Jalen’s error?
Answer:
The height does not lie on the base because it is perpendicular to the base.
Step-by-step explanation:
Jalen's error is that the height of a cone does not lie entirely at the base of the cone. Only the diameter and the radius lie entirely on the base of a cone.
What is a cone?A cone is a three-dimensional object that tapers smoothly from a flat circular base to its vertex. The diameter of a circle is a straight line that touches two points on the circumference of a circle and also passes through the center. The radius is half of the diameter.
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If a preterm birth is anticipated, at what temperature should the room be set? 26ºc to 28ºc (79 ºf - 82 ºf) 20ºc to 30ºc (68 ºf - 86 ºf) 24ºc to 27ºc (75 ºf – 80 ºf) 23ºc to 25ºc (74° f – 77° f)
Answer:
23ºC to 25ºC (74° F - 77° F)