The scientific notation of products of 4.5 x 10¹² and 5.12 x 10⁹ will be 2.304 x 10²² .
Given, the product of 4.5 x 10¹² and 5.12 x 10⁹
The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
If a number is written as exponents of 10 and decimal imposed after 1 digit then it is called scientific notation.
Therefore, product of 4.5 x 10¹² and 5.12 x 10⁹ = 4.5 x 10¹² × 5.12 x 10⁹
= (4.5 x 5.12)(10¹² x 10⁹)
= 23.04 x 10²¹
But in scientific notation, we only can put 1 digit before the decimal place.
So, 2.304 x 10²² will be correct.
Hence the scientific notation of products of 4.5 x 10¹² and 5.12 x 10⁹ will be 2.304 x 10²².
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Which expression is NOT equivalent to 60+20
A 10(6+2)
b 5(12+4)
c2(30+10)
d 10(6+1)
Determine which integer will make the inequality x − 3 > 15 true.
D: S:{15}
A: S:{17}
B: S:{18}
C: S:{30}
Answer:
c) S : {30}
Step-by-step explanation:
a) S : {17}
→ 17 - 3 > 15
→ 14 < 15
So, it is not suitable.
b) S : {18}
→ 18 - 3 > 15
→ 15 = 15
So, it is not suitable.
c) S : {30}
→ 30 - 3 > 15
→ 27 > 15
So, it is correct answer.
d) S : {15}
→ 15 - 3 > 15
→ 12 < 15
So, it is not suitable.
The equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost?
The total cost based on the equation illustrated as y= 10x is $230.
How to illustrate the information?It should be noted that from the information, the equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost.
Therefore, it should be noted that the total cost when x is 23 will be illustrated thus:
y = 10x
y = 10 (23)
y = 230
Therefore, the total cost based on the equation illustrated as y= 10x is $230.
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The equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost. Calculate the total cost when x is 23.
The table shows the approximate population and land area for several states. Order the states from least population density (top) to greatest population density (bottom). State Population Land Area (mi2) Arizona 6 . 83 × 10 6 113 , 594 Colorado 5 . 46 × 10 6 103 , 642 Kentucky 4 . 43 × 10 6 39 , 486 Minnesota 5 . 45 × 10 6 79 , 627
States from least population density (top) to greatest population density (bottom) are Colorado Arizona Minnesota Kentucky.
In the problem we are given with some datas
State Population Land Area
Arizona 6 . 83 × [tex]10^{6}[/tex] 113 , 594
Colorado 5 . 46 × [tex]10^{6}[/tex] 103 , 642
Kentucky 4 . 43 × [tex]10^{6}[/tex] 39 , 486
Minnesota 5 . 45 × [tex]10^{6}[/tex] 79 , 627
population density are for
Arizona (6 . 83 × [tex]10^{6}[/tex] )/113594=60.12
Colorado 52.68
Kentucky 112.19
Minnesota 68.44
States from least population density (top) to greatest population density (bottom) are Colorado Arizona Minnesota Kentucky.
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could someone help me understand what I need to do in this problem?
[tex]p(x-1)[/tex] is a quadratic in the form
[tex]a(x-1)^2 + b(x-1) + c[/tex]
We want to write [tex]p(x-1)[/tex] instead in the form
[tex]a' x^2 + b' x + c[/tex]
To do this, simply expand the first form completely.
[tex]a(x-1)^2 + b(x-1) + c = a(x^2 - 2x + 1) + b(x-1) + c \\\\ ~~~~~~~~ = ax^2 + (-2a + b)x + (a - b + c)[/tex]
Then [tex]a'=a[/tex], [tex]b'=-2a+b[/tex], and [tex]c'=a-b+c[/tex].
Given
[tex]p(x-1) = 2(x-1)^2 + 3(x-1) + 4[/tex]
(so [tex]a=2[/tex], [tex]b=3[/tex], and [tex]c=4[/tex]) it follows that
[tex]a' = a = 2[/tex]
[tex]b' = -2a + b = -2^2 + 3 = -1[/tex]
[tex]c' = a - b + c = 2 - 3 + 4 = 3[/tex]
[tex]\implies p(x-1) = \boxed{2}\,x^2 - \boxed{1}\,x + \boxed{3}[/tex]
g. Use a spreadsheet to solve the absolute value equations in part (f).
Explain your method.
123456
7
8
9
10
11
A
X
-8
-7
-6
-5
-4
-3
-2
-1
0
B
|x + 21
6
=abs(A2 + 2)
Pls help omg
Starting from the x-value (A column) for -7 and going down the y-values values (B column) are 5, 4, 3, 2, 1, 0, 1, 2
Step-by-step explanation:The function is given to us in the B column. We can use this to find the y-values without having to plug them in each time.
Finding the Vertex
In absolute value functions, there is a vertex. The vertex, in this case, is the minimum where the y-values change from decreasing to increasing. The absolute value formula is y = a|x - h| + k.
The vertex is equal to (h,k). The h-value in the function above is -2 and the k-value is 0. Thus, the vertex is at (-2,0).
Finding Slope
The slope of an absolute value function is written before the x. Since there isn't anything before the x in this function, the slope must be 1. So, the values either increase or decrease by 1.
Like all positive absolute value functions, the graph will decrease, reach 0, then begin to increase. The graph will reach 0 at the vertex.
Writing Out the Values
The table shows us that the y-values begin at 6. Then, we decrease by one until we get to 0.
So, the first values are 6, 5, 4, 3, 2, 1, 0Each of these x-values matches up with one of the y-values. Then, the graph begins to increase once again.
The next values are 1 and 2So together the y-values for the x-values -8 through 0 are 6, 5, 4, 3, 2, 1, 0, 1, 2.
Insert brackets in this expression
to make it correct:
8 – 2 + 1 × 5 – 3 = 2
Answer: 8 – (2 + 1) × (5 – 3) = 2
Step-by-step explanation:
8 – 2 + 1 × 5 – 3 = 2
8 – 2 + 1 × 5 – 3 = 2 ==> notice there is an '8-' in the equation, Let's solve for the difference between 8 and 2.
8 – (2 + 1 × 5 – 3)+(2 + 1 × 5 – 3) = 2 + (2 + 1 × 5 – 3)
8=2 + (2 + 1 × 5 – 3)
8-2=2-2+(2 + 1 × 5 – 3)
6=2 + 1 × 5 – 3 ==> 6 is a multiple of 2 and 3. Let's see how we can convert 2 + 1 × 5 – 3 into the product of 2 and 3
6=(2 + 1) × (5 – 3)
6=3 × 2
6=6√ ==> since this is right, let's substitute the parentheses to the original equation
8 – 2 + 1 × 5 – 3 = 2 ==> 8 – (2 + 1) × (5 – 3) = 2
You water your succulent every ninth day and your pothos every seventh
day. Today you water both plants. In how many days will you water both
plants on the same day again?
How many 250ml containers can fill a 5 litter container?
Answer:
20
Step-by-step explanation:
Someone please solve this for me and show your work
It should be noted that the multiplication of 2.102 × 12.62 is 25.39144.
How to illustrate the information?It should be noted that multiplication simply means the product of a number. It should be noted that this contains the number a specified number of times.
Therefore, it should be noted that the value of 2.012 multiplied by 12.62 will be illustrated thus:
= 2.102 × 12.62
= 25.39144
In conclusion, it should be noted that the multiplication of 2.102 × 12.62 is 25.39144.
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Use the appropriate compound interest formula to compute the balance in the account after the stated period of time $13,000 is invested for 7 years with an APR of 4% and quarterly compounding
Answer:
Step-by-step explanation:
Compound Interest Formula
The Amount A after t years due to a principle P invested at an annual interest rate r compounded n times per year
Compounded Quartely means 4 times per year
A = P(1 + r/n)^nt
A= 13000(1 + 0.04/4)^4(7)
A = 13000(1 + 0.01)^28
A = 13000(1.01)^28
A = 13000(1.321290967)
A = 17176.78|257
A ≈ 17,176.78
please help me in my maths question
Zen Have 20 Apples.. his weight is 45kg And have 2 shopping bags; then how many oranges he have
In this problem you have two unknowns: the weight of a bag of apples and the weight of a bag of oranges.
You have one given equation, which allows you to reduce the number of unknowns by one. This means that you will not be able to tell both the weight of the apples and the oranges, but find a line with possible solutions instead.
e.g. apples weigh 6+2x, oranges 7-3x where x is any real number.
You may narrow the problem down by assuming the weights to be non-negative, but to solve for x you need another piece of information that allows you to eliminate the last unknown.
A sample of 15 Girl Scouts was selected and their weights (in pounds) were recorded. The results are listed below. Construct a frequency histogram for the data using a class width of 10 and using 95 as the lower limit of the first class.
97 120 137 124 117
108 134 126 123 106
130 110 100 120 140
Frequency Histogram for the data using a class width of 10 and using 95 as the lower limit of the first class.
A histogram is a bar graph type of data representation in this representation the width of the class size is represented by the rectangle shapes reaching a particular height which describes the the number of frequency distribution.
The girls scouted got their weight recorded. The weights of the girls recorded are 97 120 137 124 117 108 134 126 123 106 130 110 100 120 140.
All the weights are measured in pounds.
The histogram is represented in the x axis and the y axis. The weight of the girls is represented on the y axis. The number of girls is represented on the x axis.
Each girl's weight is represented by a different color to understand the graph easily.
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A class has 6 boys and 15 girls. What is the raito of boys to girls
Boys: 2, Girls: 5
There are 6 boys and 15 girls.
If there were 5 boys and 15 girls, the ratio would go to 1 to 3
But this is 6 boys to 15 girls
Final answer: 2:5
A computer with software costs 2903 and Catherine stevens has agreed to pay a 20% per year finance charge on the cash price. If she contracts to pay the loan in 18 months, how much will she pay each month?
If she contracts to pay the loan in 18 months, Catherine would pay 209.66 in each month
What simple interest ?The simple interest on purchase finance is determined as the cost of the items purchased multiplied by the annual interest of 20% and the period the month payments would last:
I=PRT
Where:
I=simple interestP=principal=2903R=interest rate=20%T=time=18months/12 months=1.5So we have:
I=2903*20%*1.5
I= 870.90
total payments=2903+ 870.90
total payments= 3,773.90
monthly payment=3,773.90/18
monthly payment= 209.66
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A $25,000 machine depreciates linearly to 0 over a 10 year period. What is the value of the machine after 3 years?
The value of machine after 3 years which costs $25000 will be $17500.
What is the depreciation in value ?
An asset loses value over time as a result of use, damage, or obsolescence. This decline in value is known as depreciation.
The value of a machine is $25000.
The value of the machine after 3 years must be found.
Let y be the machine's price and x be its production time.
We are aware that the line's equation is y = mx + c.
Machine costs $25,000, therefore the point is (0,25000), and when it costs nothing after 10 years, the point becomes (10,0).
Regarding the first point (0 , 25000)
25000 = 0(x) + c
c = 25000
For a second point which is (10,0)
0 = 10(m) + 25000
m = -2500
As a result, y = -2500x + 25000 is the equation.
We know that , we have to find the value of machine after 3 years i.e., x = 3.
So ,
y = - 2500 × 3 + 25000
y = -7500 + 25000
y = $ 17500
Therefore , the value of machine after 3 years which costs $25000 will be $17500.
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The machine after 3 years when depreciates linearly to 0 over a 10 year period is 17500.
What is equation?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
A $25,000 machine depreciates linearly to 0 over a 10 year period.
According to given question we have
At the time of launch, its cost is $25,000 so the point becomes (0,25000) and after 10 years its cost becomes zero then the point becomes (10,0).
For the first point (0, 25000)
25000 = 0(x) + c
c = 25000
For second point (10,0)
0 = 10(m) + 25000
m = -2500
Thus the equation become y = -2500x + 25000.
When x=3
y = -2500x + 25000
y=-2500*3+25000
y=17500
Therefore, the machine after 3 years when depreciates linearly to 0 over a 10 year period is 17500.
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What was Fred Korematsu arrested for which sparked the Korematsu v. United States case?
A. Inciting violence against the military
B. Refusing to move to the detention center
C. Providing military secrets to the Japanese government
D. Leading the attack on Pearl Harbor
Correct answer is B. Fred Korematsu was arrested for Refusing to move to the detention center.
Fred Korematsu is detained on May 30, 1942, in San Leandro, California, for defying President Franklin Roosevelt's contentious Executive Order 9066, which called for the internment of almost all Japanese Americans in the US following Japan's assault on Pearl Harbor.
Korematsu, who was 23 at the time, sued in federal court after being found guilty and being imprisoned in a Utah camp. The U.S. Supreme Court ultimately heard his case, and in 1944 it affirmed the government's argument that the detention was necessary due to "military necessity."
However, a federal court overturned Korematsu's sentence for escape internment in 1983, declaring that he had been the victim of a "grave injustice."
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Length 10cm width 4 cm
30 points
The school that Jessica goes to is selling tickets to a fall musical. On the first day of ticket sales
the school sold 6 senior citizen tickets and 5 student tickets for a total of $50. The school took in
$44 on the second day by selling 8 senior citizen tickets and 1 student ticket. Find the price of a
senior citizen ticket and the price of a student ticket.
6C+ SS=50
8C+15=44
Answer:
The price of a senior citizen ticket to the fall musical is $6
The price of a student citizen ticket to the fall musical is $4
Step-by-step explanation:
C = the price of a senior citizen ticket to the fall musical
S = the price of a student citizen ticket to the fall musical
Day 1:
6C + 5S = 50
Day 2:
8C + 1S = 44
Manipulate the equations so that they have a common coefficient.
Multiple Day 2's equation by 5.
8C + 1S = 44
40C + 5S = 220
Subtract Day 2's equation from Day 1's
(40C + 5S = 220) - (6C + 5S = 50)
(40C + 5S) - (6C + 5S) = 220 - 50
(40C - 6C) + (5S - 5S) = 220 - 50
34C = 170
C = 5
Substitute C into either equation to solve for S.
Day 1:
6C + 5S = 50
6(5) + 5S = 50
30 + 5S = 50
5S = 50 - 30
5S = 20
S = 4
Day 2:
8C + 1S = 44
8(5) + 1S = 44
40 + 1S = 44
1S = 44 - 40
S = 4
I need help I give a lot of points and answer all of them for star
Step-by-step explanation:
1. 10.58
2. 15.87
3. 20.37
4 25.88
5. 8.89
6. 2.24
7. 9.95
8. 4.80
Solve x^2 + 4x = 1 for x by completing the square.
x = −3
x = −1
x equals plus or minus square root of 5 minus 2
x equals plus or minus square root of 5 plus 2
Answer:
x equals plus or minus square root of 5 minus 2
Step-by-step explanation:
Let's solve your equation step-by-step.
x²+4x=1
Step 1: Subtract 1 from both sides.
x²+4x−1=1−1
x²+4x−1=0
For this equation: a=1, b=4, c=-1
1x²+4x+−1=0
Step 2: Use quadratic formula with a=1, b=4, c=-1.
[tex] \sf \: x = \frac{−b± \sqrt{ b {}^{2} −4ac}}{2a}[/tex]
[tex]\sf \: x = \frac{−(4)± \sqrt{4 {}^{2} −4(1)( - 1)}}{2(1)}[/tex]
[tex] \sf \: x = \frac{−4±√20}{2} [/tex]
x=−2+√5 or x=−2−√5
\left|-c+12\right|=
∣−c+12∣= 14
The value of c from the equation is 2
What is absolute value?The absolute value of a number can be defined as the non -negative value of a number irrespective of its sign.
It is known as the distance of a number from zero without consideration of its sign.
It is also known as the modulus of a number.
It is denoted with the symbol, " | | "
Given the expression;
∣−c+12∣= 14
find the absolute value
c + 12 = 14
collect like terms
c = 14 - 12
c = 2
Thus, the value of c from the equation is 2
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What pages will be favored for the following search terms:
Chevrolet AND Corvette
The pages that will be favored for the search terms Chevrolet AND Corvette are Pages that include Chevrolet Corvette. Option B
This is further explained below.
What pages will be favored for the following search terms Chevrolet AND Corvette?Generally, We may think about AND as the intersection of two sets by applying the concept of the set union to it.
The intersection of two sets is a representation of the components that are included in or shared by both.
In conclusion, For the sake of this discussion, the sites that contain both Chevrolet and Corvette will be regarded as the most reliable resources.
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what pages will be favored for the following search terms:
Chevrolet AND Corvette
A. Pages about Chevrolet and pages about corvette
B. Pages that include Chevrolet Corvette
C. pages that include Chevrolet and pages that include Corvette plus pages about both.
D. Pages about chevrolet, pages about OR plus pages about corvette
3. 0.5b +4=2(b-2) (1 point)
O10
O5
Ono solution
O identity
Answer:
0.5b + 4 = 2(b + 2)
0.5b + 4 = 2b + 4
0.5b - 2b = 4 - 4
-1.5b = 0
b = 0/-1.5
b = 0
Give the slope and the y-intercept of the line with the
given equation. Then, graph the linear equation.
y = 3x +5
What is the slope? Select the correct choice below and
fill in any answer boxes within your choice.
OA. The slope is
(Simplify your answer.)
OB. The slope is undefined.
What is the y-intercept? Select the correct choice
below and fill in any answer boxes within your choice.
OA. The y-intercept is
(Type an integer or a simplified fraction.)
OB. There is no y-intercept.
Graph the equation.
Click to
enlarge
graph
The average temperature in the mountains is 62° in April. The average temperature in that same spot is −4° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.
62 − |−4| = 58°, 62° is the farthest from 0°
62 + |−4| = 66°, 62° is the farthest from 0°
62 − |−4| = 58°, −4° is the farthest from 0°
62 + |−4| = 66°, −4° is the farthest from 0°
Answer: 62 + |−4| = 66°, 62° is the farthest from 0°
I believe this is the correct answer.
The one that shows how much warmer this location is in April than in December, and which temperature is the farthest away from 0°. will be B Option 62 - |−4| = 566°, 62° is the farthest from 0°
How are Kelvin, Celsius, and Fahrenheit related?We have got an equation that can relate these three units of measurement of temperature, as given below:
[tex]\dfrac{C}{5} = \dfrac{F - 32}{9} = \dfrac{K - 273}{5}[/tex]
where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in fahrenheit, and K represents the measurement of equally intense temperature in kelvin.
Based on the information given, the value of warmer will be;
= 62 - (-4)
= 62 + 4.
= 66
Therefore, the correct option will be option B. 62 - |−4| = 566°, 62° is the farthest from 0°
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 19
Blue 20
Green 14
Yellow 8
Purple 10
Based on these results, express the probability that the next spin will land on blue or green or purple as a fraction in simplest form.
The probability that the next spin will land on blue or green or purple as a fraction in simplest form is 44/71.
Given that, a spinner is divided into five coloured sections that are not of equal size: red, blue, green, yellow, and purple.
What is probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favourable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
The spinner results are as follows:
Colour Frequency
Red 19
Blue 20
Green 14
Yellow 8
Purple 10
Total number of outcomes = 19+20+14+8+10=71
The probability of getting blue =20/71
The probability of getting green =14/71
The probability of getting purple =10/71
So, the probability of getting blue or green or purple = 20/71 + 14/71 + 10/71
=44/71
Therefore, the probability that the next spin will land on blue or green or purple as a fraction in simplest form is 44/71.
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5. Gasoline is priced at $3.39 per gallon. Write
an equation to represent the total cost, y, of
purchasing x number of gallons.
Answer:
3.39x=y
Step-by-step explanation:
This is because the 'y' part is supposed to be the answer for how much the gallons of gasoline would be.
The 'x' part of the equation represents how much gallons of gasoline you got and you can treat it as a normal number.
Pretend that x is 2 and so you are to find out how much 2 gallons of gasoline costs and to work this out you would do this: 3.39 x 2.
You just basically treat x as a normal number like so and it would look like:
3.39 x x=3.39x
Equation for the line that passes through the points (6,-5) and (-4,1)
Answer: Equation for the line that passes through the points (6,-5) and (-4,1) is equal to 3x+5y+7 = 0.
Step-by-step explanation:
The equation of a line can be written in slope intercept form:
y = mx + b where m is the slope and b is the y-intercept
You can use the two points to find the slope m:
m = (y2 - y1 ) / ( x2 - x1 )
Given that points (6,-5) and (-4,1)
It represents the values are,
x1 = 6
y1 = -5
x2 = -4
y2 = 1
so,
Replace with x1, x2, y1, y2 values in this equation,
we can write,
m=(1-(-5)) / (-4-(6))
m = (1+5) / (-4-6)
m= 6/-10
m = 3/-5
Now you can select either point and substitute the coordinates in the equation to determine b, the y intercept. Let's us (-4, 1):
y= mx + b
so, x = -4 and y = 1 and m = 3/-5
Replace with the values in this equation,
y= mx +b
1 = (-3/5)(-4) + b
1 = (0.6)(4) +b
1 = 2.4 +b
1-2.4 = b
-1.4 = b
b = -1.4
The equation will be:
y = mx +b
substitute m and b values,
Then,
y = (-3/5)x + (-1.4)
y = (-3/5)x -1.4
In standard form, the equation would be transformed as:
y = (-3x-7) / 5
5y = -3x-7
3x+5y = -7
3x+5y+7 = 0
In standard form, the equation would be transformed as: 3x+5y+7 = 0
Therefore,
Equation for the line that passes through the points (6,-5) and (-4,1) is equal to 3x+5y+7 = 0.
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PLEASE HELP AND HURRY
Solve for x: −6 < x − 1 < 9 5 < x < 10 −5 < x < 10 −5 > x > 10 5 > x > −10
Answer:
i want orange juice
Answer:
−5 > x > 10
Step-by-step explanation: