The percent change if a city that used to produce 2050 kilowatt hours has reduced their consumption to 1125 kilowatt hours is 45.122% decrease.
What is percentage change?Percent increase and percent decrease are measures of percent change, which is the extent to which a variable gains or loses intensity, magnitude, extent, or value.
we know,
% change = (final- initial) / initial * 100
=(1125-2050)/1125 *100
=45.122%
Hence, percentage change be 45.122% decrease.
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A sinusoidal function whose period is 4π, maximum value is 6, and minimum value is -2 has
a y intercept of 6.
What is the equation of the function described?
The equation for the sinusoidal function described is given as follows:
[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]
What is a sinusoidal function?We want a function with a y-intercept at it's maximum value, hence we use the cosine equation, given by:
[tex]y = A\cos{\left(\frac{2\pi}{B}x\right)} + C[/tex]
In which:
2A is the amplitude, which is the difference between the largest and smallest value.B is the period.C is the vertical shift, considering that the standard cosine function has range between -A and A.The amplitude is of 8, hence 2A = 8 -> A = 4. This would represent a function between -4 and 4, but we want between -2 and 6, hence the vertical shift is of C = 2.
As for the period, we have that:
[tex]B = 4\pi[/tex]
Then, the equation is given by:
[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]
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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 :)
use mathematics to calculate [tex] Ilan \ ang \ asawa \ ni \ Sheryl [/tex]
[tex] 4x² - 12x + 9 = 0 [/tex]
[tex]~~~~~~~4x^2-12x+9=0\\\\\implies (2x)^2-2 \cdot 2x \cdot 3+3^2 = 0\\\\\implies (2x-3)^2 = 0\\\\\implies 2x -3 = 0\\\\\implies x =\dfrac 32[/tex]
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]
Find area in square units
Step-by-step explanation:
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(05.03 LC)A polygon is shown:
The area of polygon MNOPQR = Area of a rectangle that is 9 square units + Area of a rectangle that is ___ square units. (Input whole numbers only, such as 8.)
The figure is the combination of the rectangle and square. Then the area of the figure will be 13 square units.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Then the area of the geometry will be
The figure is the combination of the rectangle and square.
Then we have
Area = 3 x 3 + 4 x 1
Area = 9 + 4
Area = 13 square units
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√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]
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 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.
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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(15 pts) Help me out with this please!
Answer:
18
Step-by-step explanation:
my answer is correct,try to read the question,
if the length of larger triangle is 6 times so it means 6 ×5= 30 and you will times 3 to 6=18
so that's why it has lenght of 30
because the. larger triangle is 6 times bigger than smaller rectangle
100%✓sure answer
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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
Given u = −8i − 3j and v = −12i − 7j, what is projvu?
−4.845i − 1.819j
−7.275i − 4.244j
−7.886i − 2.957j
−11.828i − 6.900j
Answer:
(b) -7.275i -4.244j
Step-by-step explanation:
The projection of vector u onto vector v is the product of the unit vector v, the magnitude of vector u, and the cosine of the angle between them.
__
The dot product gives the product of the magnitudes of the two vectors and the cosine of the angle between them. To find the projection, we must divide the dot product by the magnitude of v and multiply by the unit vector in the direction of v.
[tex]proj(u,v)=(\vec{u}\cdot\vec{v})\cdot\dfrac{\vec{v}}{|\vec{v}|^2}=\dfrac{((-8)(-12)+(-3)(-7))(-12\vec{i}-7\vec{j})}{(-12)^2+(-7)^2}\\\\=\dfrac{-(96+21)(12\vec{i}+7\vec{j})}{144+49}=-\dfrac{117}{193}(12\vec{i}+7\vec{j})\approx\boxed{-7.275\vec{i}-4.244\vec{j}}[/tex]
calculates the sum of the first 8 terms of an arithmetic progression starting with 3/5 and ending with 1/4
We conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.
How to get the sum of the first 8 terms?
In an arithmetic sequence, the difference between any two consecutive terms is a constant.
Here we know that:
[tex]a_1 = 3/5\\a_8 = 1/4[/tex]
There are 7 times the common difference between these two values, so if d is the common difference:
[tex]a_1 + 7*d = a_8\\\\3/5 + 7*d = 1/4\\\\7*d = 1/4 - 3/5 = (5 - 12)/20 = -7/20\\\\d = -1/20[/tex]
Then the sum of the first 8 terms is given by:
[tex]3/5 + (3/5 - 1/20) + (3/5 - 2/20) + ... + (3/5 - 7/20)\\\\8*(3/5) - (1/20)*(1 + 2 + 3+ 4 + 5 + 6 + 7) = 3.4 = 34/10 = 17/5[/tex]
So we conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.
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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:
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.
Please help me with this math problem and I will help you.
In a survey, 60% of those questioned chose winter as their favorite season.
If 48 people chose winter, then how many people were surveyed?
A.29
B.32
C.80
D.128
Answer:
C. 80Step-by-step explanation:
Let the number of people were surveyed is x.
We have 60% of x is 48 people.
Set this as equation and solve:
60% of x = 48x*60/100 = 480.6x = 48x = 48/0.6x = 80Correct choice is C.
Answer:
C. 80
Step-by-step explanation:
Given:
60% = 48 peopleLet x be the total number of people surveyed.
Set up a ratio of people to percentage and solve for x:
[tex]\implies \sf 48 : 60 = x : 100[/tex]
[tex]\implies \sf \dfrac{48}{60}=\dfrac{x}{100}[/tex]
[tex]\implies \sf x=100 \cdot \dfrac{48}{60}[/tex]
[tex]\implies \sf x=\dfrac{4800}{60}[/tex]
[tex]\implies \sf x=\dfrac{480}{6}[/tex]
[tex]\implies \sf x=80[/tex]
Therefore, the total number of people who were surveyed was 80.
The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend?
6d5 – 2c3d2 + 5c2d3 – 12cd4 + 8
6d5 – 4c3d2 + 3c2d3 – 4cd4 + 8
6d5 – 4c3d2 + 5c2d3 – 12cd4 + 8
6d5 – 2c3d2 – 3c2d3 – 4cd4 + 8
By subtracting the given addend to the sum, we see that the other addend is:
[tex]6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]
How to get the other addend?
We know that the sum of two polynomials is:
[tex]8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9[/tex]
One of the addends is:
[tex]2d^5 - c^3d^2 + 8cd^4 + 1[/tex]
To get the other addend, we can subtract the given addend to the sum:
[tex]8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9 - (2d^5 - c^3d^2 + 8cd^4 + 1)\\\\6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]
Then we can conclude that the other addend is:
[tex]6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]
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Which is an x-intercept of the continuous function in the table ? (0, - 6); (3, 0); (- 6, 0) O (0, 3)
An x-intercept of the continuous function in the table is (-1, 0)
Intercept of a lineThe x-intercept of a line is the point where the line crossed the x-axis or the point where the value of y is zero.
From the table, the x-intercept are all the point where the value of f(x) is zero. Hence the Which is an x-intercept of the continuous function in the table is (-1, 0)
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Which of the following is a linear equation?
a. 4x² +9y² = 25
b. 2+6= 15
c. 2x-3y=7
d. 4x+6=30
2x - 3y = 7 can be rewritten as y = 2/3x - 7/3, therefore, the equation that is a linear equation is: C. 2x - 3y = 7.
What is a Linear Equation?A linear equation is expressed in the slope-intercept form as y = mx + b.
2x - 3y = 7, rewritten in slope-intercept form would be:
-3y = -2x + 7
y = -2x/-3 + 7/-3
y = 2/3x - 7/3
m = 2/3 and b = -7/3
Therefore, the equation that is a linear equation is: C. 2x - 3y = 7.
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Help me plsss helpppppppppp
Step-by-step explanation:
this is very easy u can do urself
Find the value of x so that (x,-2) satisfies 3y - 4x = 6, x=
Step-by-step explanation:
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Please help me find the volume
The formula for calculating the volume of a cube is expressed as V = L³. The volume of the cube is 1/27 cubic meters
How to find the volume of the cube?The formula for calculating the volume of a cube is expressed as:
V = L³
where:
L = 1/3cm
Substitute
V = (1/3)³
V = 1/3³
V = 1/27 cubic meters
Hence the volume of the cube is 1/27 cubic meters
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12 is what percent of 24? What percent of 35 is 7? What percent of 90 is 9? 20 out of 60 is what percent?
Answer:
12 is 50% of 24
7 is 20% of 35
9 is 10% of 90
20/60 is 33.33%
A rectangular prism has a length of 7 m, a height of 5 m, and a volume of 140 m3. What is the width?
Which steps are correct? Check all that apply.
Substitute the known values into the formula:
140 = 7(w)(5).
Substitute the known values into the formula:
7 = 140(w)(5).
Substitute the known values into the formula:
5 = 7(w)(140).
Solve for the unknown: w = 4 m.
Solve for the unknown: w = 7 m.
Solve for the unknown: w = 2 m.
The question is incomplete because it was not properly and correctly arranged
Complete Question:
A rectangular prism has a length of 7 m, a height of 5 m, and a volume of 140 m³. What is the width? A prism has a length of 7 meters, width of w, and height of 5 meters.
Which steps are correct? Check all that apply.
a) Substitute the known values into the formula: 140 = 7(w)(5).
b) Substitute the known values into the formula: 7 = 140(w)(5).
c) Substitute the known values into the formula: 5 = 7(w)(140).
d) Solve for the unknown: w = 4 m.
e) Solve for the unknown: w = 7 m.
f) Solve for the unknown: w = 2 m.
Answer:
a) Substitute the known values into the formula: 140 = 7(w)(5).
d) Solve for the unknown: w = 4 m.
Step-by-step explanation:
The steps that are correct are Options a) and d). This is because:
Step 1
The volume of a rectangular prism is calculated as:
Volume of a rectangular prism = Length (l) × Width(w) × Height(h)
The unit of the volume or a rectangular prism is in cubic metres (m³)
In the question, we are asked to find the unknown value which is the width and we were given the following known values:
Length = 7 m,
Height = 5 m
Volume = 140 m³
Step 2
Solve for the unknown value( Width)
Volume of a rectangular prism = Length (L) × Width(W) × Height(H)
140m³ = 7m × Width(m) × 5m
140m³ = 35m² × Width(m)
Width(w) = 140m³ ÷ 35m²
Width(w) = 4m
Hence, the unknown Width(w) = 4m
From the above explanation we can see that the correct steps is Option a) and Option d)
Answer:
Step-by-step explanation:
Volume of rectangular prism= Length x width x height
V=L x W x H
140=7 x W x 5
140= 35 x w
W= 140/35
W= 4
3x – 2y = -4
4x + 2y = 25
Answer:
(-21, 54.5)
Step-by-step explanation:
Hello there!
We have two methods to solve this problem.
Substitution methodElimination method.We will limit ourself to Substitution method.
3x – 2y = -4.................... 1.
4x + 2y = 25................... 2.
First lets manipulate eq.2 in terms of y.
4x + 2y = 25
2y = 25 - 4x
y = 25/2 - 2x .............. eq.3
Substitute eq.3 into eq.1
3x – 2(25/2 -2x) = -4
Solve for x.
Opening the brackets
3x - 25 - 4x = -4
-x = 21
x = -21
Substitute x into equation 3
y = 25/2 - 2x
=> y = 25/2 - 2(-21)
= 54.5
In terms of x and y; (x,y)
= (-21, 54.5)
I hope this helps.
Have a nice studies.
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
similarities between the Product Rule and Quotient Rule?
Step-by-step explanation:
Use the product rule for finding the derivative of a product of functions. Use the quotient rule for finding the derivative of a quotient of functions.
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!!)
Kendra is researching the lowest recorded temperatures in four different cities. She wants to plot the lowest temperatures on a vertical number line. The lowest recorded temperatures of the cities are shown in the table below.
City Lowest Recorded Temperature
Morgantown 7°F below 0
Charlotte 6°F above 0
Huntsville 4°F above 0
Bluefield 8°F below 0
On a vertical number line, the point representing Morgantown's lowest recorded temperature should be plotted above the point representing
lowest recorded temperature.
On a vertical number line, the point representing Huntsville's lowest recorded temperature should be plotted below the point representing
lowest recorded temperature.
The attached number line represents points of the lowest recorded temperatures
How to represent the points on a number line?The table is given as:
City Lowest Recorded Temperature
Morgantown 7°F below 0
Charlotte 6°F above 0
Huntsville 4°F above 0
Bluefield 8°F below 0
To rewrite the table, we use the following representations:
Above 0 means positiveBelow 0 means negativeSo, we have:
City Lowest Recorded Temperature
Morgantown -7
Charlotte 6
Huntsville 4
Bluefield -8
See attachment for the number line that represents the above points
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