Answer:
3.375 °C
Step-by-step explanation:
Mean temperature for first 7 days = 4 °C
⇒ Total temperature over first 7 days = 4 °C × 7 = 28 °C
Temperature on 8th day = -1 °C
[tex]\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]
Therefore, mean temperature for first 8 days:
= [28 - 1] ÷ 8
= 27 ÷ 8
= 3.375 °C
Question 2 Determine if (x-3) is a factor to the polynomial P(x) = 2x³ +5x²-28x - 15. (3 marks)
Answer:
(x - 3) is a factor of P(x)
Step-by-step explanation:
if (x - 3) is a factor of P(x) then P(3) = 0
P(3) = 2(3)³ + 5(3)² - 28(3) - 15
= 2(27) + 5(9) - 84 - 15
= 54 + 45 - 99
= 99 - 99
= 0
since P(3) = 0 then (x - 3) is a factor of P(x)
a) What is the population of interest? Approximately, how many people are in the population of interest? (Recall, the definition of a population is: The collection of all outcomes, responses, measurements, or counts that are of interest.)
b) What is the best data collection method to use for the study (explain)? (Recall, data collection methods are: Observation, Survey, Experiment, Simulation).
c) For one of the three studies, a census is possible. Determine which one and then explain why a census is possible for that study and is not possible for the other two studies. (A census means that we are able to collect data from every unit in the population. Most of the time the population is too large for a census to be feasible)
d) For the two studies where a census is not possible, how many people, students, or cars would you sample out of the population? What sampling technique would you use (see section 1.3)? (Explain your reasoning)
The What is the population of interest are:
GMC students People who own Cars in Macon, GA.People who eat oatmeal in Georgia.The data collection method according to the group below
SurveySurveyExperiment What is the statistical studies about?The best data collection method for the first one oatmeal and GMC students is survey because the population is large and opinions may differ.
The best data collection method for the cars is Experiment as one needs to study the cars that pass the red lights
For one of the three studies, a census is possible in the first one because the study population is the Georgia which is very large.
For the two studies the one that a census is not needed is GMC students and cars at red light because the population is not too big.
Based on the study I will use 500 people, 200 students, or 300 cars and the sampling technique would be Systematic sampling, Simple random sampling and Judgmental/purposive sampling.
A Simple random sampling is known to be the easiest method of selecting a sample as every member is known to have an equal chance of being selected in the sample.
See the other part of the question below
Write a reply
Consider the following statistical studies:
1. A study (in Georgia) of the effect of eating oatmeal on lowering cholesterol.
2. A study of current GMC students next career move after graduating or transferring from GMC.
3. A study of how many cars run the red light at a certain intersection in Macon, GA.
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A motorboat travels 464 kilometers in 8 hours going upstream and 644 kilometers in 7 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Rate of boat in still water ______km/h
Rate of current: _______ km/h
Let's say you are paddling at 5mph and the current is 3 mph. Going upstream, you are going 2 mph and downstream, 8 mph.
8(b - c) = 464
7(b + c) = 644
b - c = 58
b + c = 92
Adding the two together
2b = 150
b = 75
75 - c = 58
c = 17
The boat's speed is 75 mph and the current's speed is 17 mph.
Identify the first five terms of the sequence in which an = 3n − 1 + 1.
The first five terms of the sequence represented as an = 3(n -1) + 1 are 1,4, 7, 10 and 13
How to determine the first five terms?The formula of the sequence is given as:
an = 3(n -1) + 1
The above sequence is an arithmetic sequence, and the first five terms are the values of the sequence when the value of n is from 1 to 5
i.e. n = 1, 2, 3, 4 and 5
Next, we set n = 1, 2, 3, 4 and 5, and substitute these values for n in an = 3(n -1) + 1
So, we have the following equations
First term
a1 = 3(1 -1) + 1 = 1
Second term
a2 = 3(2 -1) + 1 = 4
Third term
a3 = 3(3 -1) + 1 = 7
Fourth term
a4 = 3(4 -1) + 1 = 10
Fifth term
a5 = 3(5 -1) + 1 = 13
Hence, the first five terms of the sequence represented as an = 3(n -1) + 1 are 1,4, 7, 10 and 13
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Eleanor is working her way through school. She works two part-time jobs for a total of 24 hours a week. Job A pays $5.80 per hour, and Job B pays
$7.40 per hour. How many hours did she work at each job the week that she made $158.40.
Step-by-step explanation:
a = hours at job A
b = hours at job B
a + b = 24
a = 24 - b
5.8a + 7.4b = 158.4
note we can use the a = 24 - b identity in the second equation :
5.8×(24 - b) + 7.4b = 158.4
139.2 - 5.8b + 7.4b = 158.4
1.6b = 19.2
b = 12 hours
a = 24 - b = 24 - 12 = 12 hours
she worked 12 hours on job A and 12 hours on job B.
The graph below represents which system of inequalities?
A) y > 2x − 3
y > −x − 3
b) y < 2x − 2
y < −x + 3
C) y ≤ 2x − 2
y > −x + 3
D) None of the above
The system of inequalities that represents the graph are y > -x + 3 and y ≤ 2x - 2
Equation of a lineA line is the shortest distance between two points. The equation of a line in slope-intercept form is y = mx + b
For the broken line, the coordinate points will be(0, 3) and (3, 0)
m = -3/3
m = -1
The equation of the line will be y > -x + 3
For the solid line, the coordinate points will be(0, -2) and (1, 0)
m = 2/1
m = 2
The equation of the line will be y ≤ 2x - 2
Hence the system of inequalities that represents the graph are y > -x + 3 and y ≤ 2x - 2
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Review the graph of complex number z.
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (negative 3, 1).
What is the modulus of z?
2
2StartRoot 2 EndRoot
3
StartRoot 10 EndRoot
Answer:
√10Step-by-step explanation:
[tex]\text {modulus of z } = =\sqrt{\left( -3\right)^{2} +\left( 1\right)^{2} } =\sqrt{9+1} =\sqrt{10}[/tex]
Answer:
square root of 10
Step-by-step explanation:
The cost of a ticket to the circus is $22.00 for children and $46.00 for adults. On a certain day, attendance at the circus was 1,400 and the total gate revenue was $52,400. How many children and how many adults bought tickets?
The number of children and adults who bought the tickets at the circus was 500 and 900 respectively.
How to write and solve equation?let
x = number of childreny = number of adultsx + y = 1400
22x + 46y = 52,400
From equation (1)
x = 1400 - y
Substitute into (2)
22(1400 - y) + 46y = 52,400
30,800 - 22y + 46y = 52,400
- 22y + 46y = 52,400 - 30,800
24y = 21,600
y = 21,600 / 24
y = 900
substitute y into
x + y = 1400
x + 900 = 1400
x = 1400 - 900
x = 500
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The number of children's ticket that was bought is 500.
The number of adult's ticket that was bought is 900.
What is the linear equation that represents the question?a + b = 1400 equation 1
22a + 46b = 52,400 equation 2
Where:
a - number of children's ticket b = number of adult's ticketWhat is the number of adult's ticket?Multiply equation 1 by 22
22a + 22b = 30800 equation 3
Subtract equation 3 from equation 2
21,600 = 24b
b = 21,600 / 24
b = 900
What is the number of children's ticket?Subtract 900 from 1400
1400 - 900 = 500
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if the volume of a cube is 27cm³ what are the dimensions of the cube
Answer:
3 cmStep-by-step explanation:
if the volume of a cube is 27cm³ what are the dimensions of the cube
Cube Volume = l³
we use the inverse formula
∛V = l
so
∛27 =
3 cm
√y18
please solve this one for me with explication
Answer: [tex]y^9[/tex]
This is the same as saying y^9
===================================================
Explanation:
When we apply the square root to the expression [tex]a^{2b}[/tex], we end up with [tex]a^b[/tex]
[tex]\sqrt{a^{2b}} = a^b[/tex]
The exponent 2b divides in half to get b
Based on that rule, we can then say:
[tex]\sqrt{y^{18}} = y^{18/2} = y^9[/tex]
Graph the function y = 4x4 – 8x2 + 4. Which lists all of the turning points of the graph?
(0, 4)
(–1, 0) and (1, 0)
(–1, 0), (0, 4), and (1, 0)
(–4, 0), (–1, 0), (0, 4), and (1, 0)
A function assigns the values. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
If we plot the function, y = 4x⁴ - 8x² + 4, then it can be observed that the lists all of the turning points of the graphs are (–1, 0), (0, 4), and (1, 0).
Hence, the correct option is C.
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What value correctly fills in the blank so that the expressions are equivalent?
18+45 = x (2+5)
A 2
B O3
C 07
D 9
Answer:
D, x = 9
Step-by-step explanation:
[tex]x\left(2+5\right)=63[/tex]
=> divide both side by 7
[tex]\frac{x\left(2+5\right)}{7}=\frac{63}{7}[/tex]
x=9
Answer:
D) 9
Step-by-step explanation:
Given :
⇒ 18 + 45 = x (2 + 5)
=============================================================
Simplify both sides :
⇒ 18 + 45 = x (2 + 5)
⇒ 63 = 7x
⇒ 7x = 63
=============================================================
Divide both sides by 7 :
⇒ 7x/7 = 63/7
⇒ x = 9
Line segment AB with endpoints A (5, 8) and B (7, 8) is translated 2 units down and 2
units left. Identify the coordinates of the endpoints of the translated line segment?
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of objects. The coordinates of the translated line segment will be A' (3,6) and B' (5,6).
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
Since AB is a line segment the changes will occur on both the coordinates, therefore, if the line segment is translated 2 units down and 2 units left, the coordinates will be,
A = (5,8) → 2 units down ⇒ (5, 8-2) → 2 units left ⇒ (5-2, 8-2) = (3, 6)
B = (7,8) → 2 units down ⇒ (7, 8-2) → 2 units left ⇒ (7-2, 8-2) = (5, 6)
Hence, the coordinates of the translated line segment will be A' (3,6) and B' (5,6).
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what would be the answer to this ?
Solve. 5x=15
Interpretation 1:
[tex]5x = 15 \\ [/tex]
Divide both sides by 5:
[tex]\implies \boxed{x = 3}[/tex]
(Which is the final answer.)
[tex]\huge\mathfrak\colorbox{white}{}[/tex]
Interpretation 2:
[tex] 5^{x}=15[/tex]
Take logarithm to the base 5 on both sides:
[tex]\implies log_5(5^{x})=log_5(15)\\\implies x=log_5 (15) \\\implies x= \frac{ln(15)}{ln(5)} \\\implies \boxed{x≈1.683} [/tex]
(Which is a thing too!)
[tex]\huge\mathfrak\colorbox{white}{}[/tex]
P. S.: Now please don't tell me that this is a PhD level question and this is referring to the Knuth's Up-Arrow Notation. Which translates the question into something like: [tex]^{5}x=15[/tex]
Answer:
x = 3Step-by-step explanation:
what would be the answer to this ?
Solve.
5x=15
x = 15 : 5
x = 3
--------------
check
5 * 3 = 15
the answer is good
Simplify 5/8+9/2+(-4/5)+7/8+(-5/2)+7/5
please answer
how to find the value of x and z
Answer:
z = 86 °
and, x = 2
Step-by-step explanation:
We know that a straight line is a 180 degree-angle. So, we know that
94 + z must equal 180, because they are the only two angles that make up the straight line.
from this information, (that 94 + z = 180) we can easily find z.
(this is typically an intuitive method of subtracting 94 from 180)
94 + z = 180
-94 -94
z = 86 °
-- we know that the relation between z and (10x + 74) must also be equal to 180, as they make up a straight line
if z = 86, then we can know that (10x + 74) must be equal to
(10x + 74) + 86 = 180
- 86 -86
(10x + 74) = 94
10x + 74 = 94
- 74 - 74
10 x = 20
÷ 10 ÷ 10
x = 2
so, z = 86 °
and, x = 2
(I am assuming that this "unprotected placement assessment" has already taken place, and you would like to understand a question. Or, this is a practice assessment. Because there is no point to cheating on a placement assessment--you will just skip over material you don't know. And, it wouldn't align with Brainly's honor policy. Hope you learn from this!!)
help asap please
Which of the points shown below are on the line given by the equation y = x + 4? Check all that apply
A) -1, 3
B) 2, 6
C) -2, -2
D) 2, 4
The points on the line are points B and D
How to determine the points on the line?The equation is given as:
y = x + 4
The above means that the output value is 4 more than the input value
Using the above rule, the points that satisfy the equation are:
B) 2, 6 and D) 2, 4
This is so because:
6 = 2 + 4
4 = 2 + 2
Hence, the points on the line are points B and D
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A scale model of a building is 3 inches tall. If the building is 90 feet tall, find the scale of the model.
The scale model of a building 3 inches tall if the building is 90 feet tall is 2:5
Scaling of measurementScaling is the way of enlarging or reducing the image of an object.
Given scale model of a building is 3 inches, if the building is 90feet tall, to write the scale;
Convert both measures to same units
Since 1 feet. = 12 in
90 feet = 90/12 in = 7.5 in
Take the ratio
3 : 7.5 = 30: 75
Reduce to lowest term
30: 75 = 2 : 5
Hence the scale model of a building 3 inches tall if the building is 90 feet tall is 2:5
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Suppose a normal distribution has a mean of 38 and a standard deviation of 2. What is the probability that a data value is between 36 and 43? Round your answer to the nearest tenth of a percent.
Answer:
[tex]P(36 < X < 43)\approx83.5\%[/tex]
Step-by-step explanation:
Use a TI-84 to calculate the probability
[tex]P(\text{Lower} < X < \text{Upper})=\text{normalcdf}(\text{Lower},\text{Upper},\mu,\sigma)\\\\P(36 < X < 43)=\text{normalcdf}(36,43,38,2)\approx0.8351\approx83.5\%[/tex]
A square is drawn below.
What is the value of x?
(2x + 15)°
(6x-45°) .
Answer:
2x+15 =6x-45 [Alternate Angles]
or, 15+45 =6x-2x
or, 60 =4x
or 60/4 =x
or 15 = x
# x=15
The total area of town C and town D is 120,000 square miles. The area of town C is 30,000 square miles more than that of town D. Find the area land of each town.
Answer:
Find the area land of each town.
Let x be the area of town D
then, x+ 30000 is the area of town C
we know that,
the total area of town C and town D is 120,000 square miles.
x+x+30000=120000
2x= 90000
x=45000
Area of town D= 45000 square miles
Area of town C= 45000+30000= 75000 square miles.
Solve. Be sure to eliminate any extraneous solutions. X= square -2x+48
Answer: X = 6
Step-by-step explanation:
Substitute the x’s in the equation for the answer options that are provided.
Solutions of quadratic equation x = √(-2x + 48) are x = -8 and x = 6.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given, quadratic equation;
x = √(-2x + 48)
Squaring on both sides,
x² = -2x + 48
x² + 2x - 48 = 0
Now, we have to solve for x.
Simplifying,
x² + 8x - 6x - 48 = 0
(x + 8)(x -6) = 0
(x + 8) = 0 and (x -6) = 0
x = -8 and x = 6
After eliminating the extraneous solutions;
we have,
x = -8 and x = 6.
Therefore, the solutions are x = -8 and x = 6.
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What is the Length of CG
Answer: 32
Step-by-step explanation:
Since [tex]\overline{FG} \parallel \overline{AC}[/tex], we know that by the corresponding angles theorem, [tex]\angle BFG \cong \angle BAC[/tex] and [tex]\angle BGF \cong \angle BCA[/tex].
Thus, [tex]\triangle BFG \sim \triangle BAC[/tex] by AA.
It follows that since corresponding sides of similar triangles are proportional,
[tex]\frac{36+90}{90}=\frac{CG+80}{80}\\ \\\frac{126}{90}=\frac{CG+80}{80}\\\left(\frac{126}{90} \right)(80)=CG+80\\112=CG+80\\CG=\boxed{32}[/tex]
find the midpoint of the line segment between the points (11, -5) and (-3, -7)
Answer:
(4, -6)
Step-by-step explanation:
(x1+x2)/2 + (y1+y2)/2 = midpoint
(11+-3)/2 = 8/2 = 4. x = 4
(-5 + -7)/2 = -12/2. y = -6
4, -6 is the midpoint
give brainliest please! hope this helps :)
Help me plsss helpppppppppp
Step-by-step explanation:
this is very easy u can do urself
The sides of a triangle measure 10 feet, 13 feet, and 17 feet.
How would you explain to a friend that the triangle is not a right triangle?
Step-by-step explanation:
if the squares of the two shorter sides add up to the square of the hypotenuse, the triangle contains a right angle
bbc
10 squared = 100
13 squared = 169
17 squared = 289
100 + 169 = 269 NOT 289 so
there is no right angle and so its not a right triangle
Choose two number sentences below that equal 39:
A) 71 - 32
B) 49 - 20
C) 85 - 46
D) 50 - 29
The box plots show the average wind speeds, in miles per hour, for two different islands.
Average Wind Speeds on Island A
H
++
2 3 4 5 6 7 8 9 10 11
Average Wind Speeds on Island B
Which explains, on a given day, which island is more likely to have a wind speed close to its median
the answer would be 240 because wind speed is close to its median
A rain drop hitting a lake makes a circular ripple.. if the radius, in inches,, grows as a function of time in minutes according to R(t)=20sqrt(t+2), find the area of the ripple as a function of time. What is the area of the circular ripple at t=2?
Answer:
Step-by-step explanation:
Area A(t) = πR² = π x 400 (t + 2) = 400π (t + 2)
A(2) = 400π (2 + 2) = 1600π = 5026.5 in²
|2/13t-11|-10=-16
solve for t
[tex]\left|\dfrac{2}{13}t-11\right|-10=-16\\\\\left|\dfrac{2}{13}t-11\right|=-6\\\\x\in\emptyset[/tex]