The solution of (2.3 x 10^3) + (6.9 x 10^3) is [tex]9.2 \times 10^3[/tex] that is 9200
Solution:Need to solve the following expression:
[tex]\left(2.3 \times 10^{3}\right)+\left(6.9 \times 10^{3}\right)[/tex]
There are two terms in given expression
Let’s find GCF for this two terms
The greatest number that is a factor of two (or more) other numbers. When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.
[tex]\begin{array}{l}{2.3 \times 10^{3}=2.3 \times 10^{3}} \\\\ {6.9 \times 10^{3}=3 \times 2.3 \times 10^{3}}\end{array}[/tex]
[tex]\text {So GCF between two terms is } 2.3 \times 10^{3}[/tex]
Let’s bring GCF out of the bracket in expression for sake of simplicity.
[tex]\begin{array}{l}{=>2.3 \times 10^{3}(1+3)} \\\\ {=>2.3 \times 10^{3} \times 4} \\\\ {=>9.2 \times 10^{3}} \\\\ {=>9200}\end{array}[/tex]
Hence on solving the expression (2.3 x 10^3) + (6.9 x 10^3) the result we get is [tex]9.2 \times 10^3[/tex] that is 9200
The rule which allows us to change the sign of an exponent is called the ____ rule.
Answer:
The rule which allows us to change the sign of an exponent is called the negative exponent rule.
Step-by-step explanation:
Consider the provided information.
The negative exponent rule is the rule which allows to change the sign of an exponent.
[tex]x^{-1}=\frac{1}{x}[/tex]
According to negative exponent rule: A negative exponents in the numerator moved to the denominator and become positive exponents.
If A negative exponents in the denominator moved to the numerator and become positive exponents.
Hence, the required statement is: The rule which allows us to change the sign of an exponent is called the negative exponent rule.
On a 95-degree day with 80% humidity, the amount of time it takes an air-conditioning unit to cool a 2000-square-foot home 1 degree follows a normal distribution with mean time of 24 minutes and standard deviation of 1 minute. What is the probability it takes an air-conditioning unit longer than 25 minutes to cool the house 1 degree? (Use the Empirical Rule.)
There's a 16% probability that the air-conditioning unit will take longer than 25 minutes to cool a 2000-square-foot home by 1 degree on a 95-degree day with 80% humidity, based on the empirical rule of normal distribution.
Explanation:To find the probability of the air-conditioning unit taking longer than 25 minutes to cool the house 1 degree, you first have to understand that the situation described follows a normal distribution with a mean (μ) of 24 minutes and a standard deviation (σ) of 1 minute.
Using the Empirical Rule, also known as the 68-95-99.7 rule, we can assess probabilities for normal distributions.
According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Since we are interested in the time more than 25 minutes, we are looking at the area to the right of the mean plus 1 standard deviation (24 + 1 = 25 minutes).
Approximately 68% of the data falls within one standard deviation (between 23 and 25 minutes), so about 34% is below 25 minutes, and another 34% is above. However, we're interested in the portion beyond 25 minutes, falling in the tail.
Because 50% of the distribution falls above the mean (by definition of a normal distribution), and we account for the 34% within one standard deviation above the mean, this leaves us with 50% - 34% = 16% of data points (times in this case) falling beyond 25 minutes on a 95-degree day with 80% humidity.
how do i do this???????
Answer:
2y-4-6y-12=4
-4y=20
y= -5
Step-by-step explanation:
because (y+2)(y-2)=y^2-4
so we have the step to let the every part have the same denominator y^2-4
2(y-2)/(y+2)(y-2) -6(y+2)/(y-2)(y+2)=4/(y-2)(y+2)
the denominators are the same so the equality .we just need the part over be the same 2y-4-6y-12=4
y= -5
There is a total of 2,512 people attending the fun fair. 5/8 of sttemdees are students and 1/4 of attendees are parents. the rest of the attendees are people living ioin the neigbourhood. How mnay o fthe attendees are people living in the neighbouhood?
Answer:
314 of the people attending the fun fair are people living in the neighborhood
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Number of people attending the fun fair = 2,512
Fraction of people attending the fun fair that are students = 5/8
Fraction of people attending the fun fair that are parents = 1/4
Rest of the people attending the fun fair lives in the neighborhood
2. Let's calculate the number of students, parents and people living in the neighborhood
Students:
Fraction of people attending the fun fair that are students = 5/8
5/8 * 2,512 = 1,570
1,570 of the people attending the fun fair are students
Parents:
Fraction of people attending the fun fair that are parents = 1/4
1/4 * 2,512 = 628
628 of the people attending the fun fair are parents
People living in the neighborhood
2,512 - 1,570 - 628 = 314
314 of the people attending the fun fair are people living in the neighborhood
Which expression has a value of 35 when p = 7?
49/p
5p
45-p
25+ p
Answer: the answer is B. 5p
Step-by-step explanation:
just did it so i know its right:)
comment if so!
The sum of three integers is 12
12
. The sum of the first and second integers exceeds the third by 32
32
. The third integer is 15
15
less than the first. Find the three integers.
The three integers are 5,17 and -10
Step-by-step explanation:
Let x, y and z be three integers then
[tex]x+y+z=12 \ \ \Eqn\ 1[/tex]
'The sum of the first and second integers exceeds the third by 32'
[tex]x+y=z+32\ \ \ \ Eqn\ 2[/tex]
The third integer is 15 less than the first.
[tex]z=x-15\ \ \ \ Eqn\ 3[/tex]
From Eqn 2:
[tex]x+y=z + 32\\x+y-z=32[/tex]
Subtracting Eqn 1 from eqn 2
[tex]x+y-z-(x+y+z)=32-12\\x+y-z-x-y-z=20\\-2z=20[/tex]
Dividing both sides by -2
[tex]\frac{-2z}{-2}=\frac{20}{-2}\\z=-10[/tex]
Putting z=-10 in Eqn 3
[tex]z=x-15\\-10=x-15\\x=15-10\\x=5[/tex]
Putting x=5 and z=-10 in Eqn 1
[tex]x+y+z=12\\5+y-10=12\\y-5=12\\y=12+5\\y=17\\[/tex]
Hence,
The three integers are 5,17 and -10
Keywords: Linear Equations, Variables
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Answer:
First = 5, second = 17, third = -10
Step-by-step explanation:
First integer = x
The third integer is 15 less than the first, so
Third integer = x - 15
The second integer = y
The sum of the first and second integers exceeds the third by 32, so
The sum of the first and second integers = x + y
The third integer = x - 15
x + y is 32 more than x - 15, hence
x + y - 32 = x - 15
y - 32 = -15
y = 32 - 15
y = 17
The second integer = 17
The sum of three integers is 12, so
x + 17 + x - 15 = 12
2x + 2 = 12
2x = 12 - 2
2x = 10
x = 5
x - 15 = 5 - 15 = -10
What is the surface area of the right prism?
Answer:
The surface area of right prism is 12 feet² , option D
Step-by-step explanation:
Given as :
The measure of base = 4 ft
The height of base = 0.5 ft
The surface area of right prism = perimeter of base × height + 2 × base
Now ,
Perimeter of base = 4 + 4 = 8 ft
So, The surface area of right prism = 8 × 0.5 + 2 × 4
Or, The surface area of right prism = 4 + 8
∴ , The surface area of right prism = 12 feet²
Hence The surface area of right prism is 12 feet² . Answer
Answer:
17.5 ft2
Step-by-step explanation:
Write the number 9.359 × 105 in standard form.
Answer:
982.695
Step-by-step explanation:
9.359 x 105 = 982.695
a woman is walking at the rate of 90 yards per minute. How fast is she going in feet per second?
Answer:
She is going at the rate of 4.5 feet per second.
Step-by-step explanation:
Given:
The rate of walking is 90 yards per minute.
Now, to find the rate in feet per second.
1 yard = 3 foot.
1 minute = 60 seconds.
So, first we find the rate of walking per second in yard = [tex]90\div 60[/tex]
Therefore by dividing we get = [tex]1.5 yard[/tex]
Now, we find the rate of walking per second in feet = [tex]1.5\times 3[/tex]
So, by multiplying we get = [tex]4.5 feet[/tex]
Therefore, she is going at the rate of 4.5 feet per second.
Solve x2 – 8x = 3 by completing the square. Which is the solution set of the equation?
(4 minus StartRoot 19 EndRoot comma 4 + StartRoot 19 EndRoot)
(4 minus StartRoot 11 EndRoot comma 4 + StartRoot 11 EndRoot)
(4 minus StartRoot 8 EndRoot comma 4 + StartRoot 8 EndRoot)
(4 minus StartRoot 3 EndRoot comma 4 + StartRoot 3 EndRoot)
Answer:
[tex](4-\sqrt{19},4+\sqrt{19)[/tex]
Step-by-step explanation:
we have
[tex]x^{2} -8x=3[/tex]
Divide the coefficient of term x by 2
[tex]-8/2=-4[/tex]
Squared the number
[tex](-4)^2=16[/tex]
Adds the number 16 to the both sides
[tex]x^{2} -8x+16=3+16[/tex]
[tex]x^{2} -8x+16=19[/tex]
Rewrite as perfect squares
[tex](x-4)^{2}=19[/tex]
take square root both sides
[tex](x-4)=(+/-)\sqrt{19}[/tex]
[tex]x=4(+/-)\sqrt{19}[/tex]
[tex]x_1=4(+)\sqrt{19}[/tex]
[tex]x_2=4(-)\sqrt{19}[/tex]
therefore
The solution set is
[tex](4-\sqrt{19},4+\sqrt{19)[/tex]
Answer:
its A
Step-by-step explanation:
students at westbrook middle school hold green team meetings to plan ways to help protect the environment this week there are 144 at the meeting which is 90% of the total group
Answer:
160 member
Step-by-step explanation:
Here the question is, how many total member are there in the team?
Given: 144 member in the meeting is equal to 90% of the total group.
Let assume x be the total member in the green team.
Now, finding the number of member in the team, which is x.
[tex]\frac{90}{100} \times x = 144[/tex]
Next, cross multiply the number on both the side
⇒ [tex]x= \frac{144 \times 100}{90} = 16\times 10[/tex]
∴ x = 160
160 is the total number of member in green team.
Answer:
160 members
Step-by-step explanation:
How do I know this well 144/90 1.6 take away the decimal and it is 16 add a 0 from the 90 and 160
Solve the inequality. Graph the solution.
7z< -28
Answer: The answer is -9
Step-by-step explanation:
7z<-28= -9
Because we take the -28 and add 19 because that's the common denominator and we come up with -9
On a certain hot summer's day, 196 people used the public swimming pool. The daily prices are $ 1.50 for children and $ 2.00 for adults. The receipts for admission totaled $ 314.00 . How many children and how many adults swam at the public pool that day?
Number of adults = 40
Number of children = 156
Step-by-step explanation:
Let x be the number of adults and
y be the number of children
Then according to given statements
[tex]x+y=196\ \ \ Eqn\ 1\\2.0x+1.50y = 314\ \ \ Eqn\ 2\\[/tex]
From equation 1:
[tex]x+y = 196\\x = 196-y[/tex]
Putting in equation 2
[tex]2(196-y) + 1.50y = 314\\392-2y+1.50y = 314\\392-0.5y = 314\\-0.5y=314-392\\-0.5y=-78[/tex]
Dividing both sides by -0.5
[tex]\frac{-0.5y}{-0.5} = \frac{-78}{-0.5}\\y = 156[/tex]
Putting y = 156 in equation 1
[tex]x+156 = 196\\x = 196 - 156\\x = 40[/tex]
Hence,
Number of adults = 40
Number of children = 156
Keywords: Linear equations, Variables
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Write an equation of the line that passes through the points
(0, 3) and (-5, 0).
Answer:
y-3=3/5x
Step-by-step explanation:
y-y1=m(x-x1)
Where m=slope and (x1, y1) is a point on the line.
m=(y2-y1)/(x2-x1)
m=(0-3)/(-5-0)
m=-3/-5
m=3/5
y-3=3/5(x-0)
y-3=3/5(x)
y-3=3/5x
(0, 3) is the y-intercept as it passes through y = 3 at x = 0, or the y-axis.
Slope:
[tex] \frac{y1 - y0}{x1 - x0} = \frac{3 - 0}{0 - ( - 5)} = \frac{3}{5} [/tex]
Equation of a straight line:
y = mx + c
m = slope (3/5)
c = y value of y-intercept (3)
Equation:
[tex]y = \frac{3}{5} x + 3[/tex]
A 2 1/2 pound bag of grass seed cover 1/8 of an acre. How much grass seed is needed for 1 acre?
Answer:
8 times more 8*2 1/2 = 20 pounds.
Step-by-step explanation:
Answer:
20 pounds of grass seed is needed for one acre.
Step-by-step explanation:
You can set up a proportion to solve:
[tex]\frac{2.5 pounds}{1/8 acre}[/tex] = [tex]\frac{x pounds}{1 acre}[/tex]
Cross multiply:
[tex]\frac{1}{8}[/tex]x = 2.5
Divide both sides by [tex]\frac{1}{8}[/tex] or multiply both sides by 8.
x = 20
Write the equation of the line that passes through the point (4,3) and is perpendicular to the line y=2x-4
Answer:
y-3=-1/2(x-4)
Step-by-step explanation:
y-y1=m(x-x1)
perpendicular means negative reciprocal of the current slope,
and the negative reciprocal of 2 is -1/2.
y-3=-1/2(x-4)
Paul Hastings had a checkbook balance of $1345.00. His bank statement showed a deposit of $423.00 and he hadnt recorded a $15 service fee. What should his checkbook balance be?
Answer:
Paul Hastings checkbook balance be $1753
Explanation:
We are given Paul Hastings
current checkbook balance is equal to $1345.00
and a deposit of $423.00 is said to be made in the bank
so the new balance will be addition of this deposit in the current balance also there's a deduction of $15 as service fee.
So the total checkbook balance will be after subtracting $15 from sum of current balance and deposit.
So his checkbook balance = $1345 + $423 - $15
= $1753
which is the required value of checkbook.
what is the equation of a line parallel to y-2x=3 that passes through the point (3,1)
Answer:
y = 2x - 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange y - 2x = 3 into this form by adding 2x to both sides
y = 2x + 3 ← in slope- intercept form
with slope m = 2
Parallel lines have equal slopes, thus
y = 2x + c ← is the partial equation
To find c substitute (3, 1) into the partial equation
1 = 6 + c ⇒ c = 1 - 6 = - 5
y = 2x - 5 ← equation of line
What is (8x-30)+6x+(2x+10) simplified?
Answer:
16x-20
Step-by-step explanation:
(8x-30)+6x+(2x+10)
8x-30+6x+2x+10
8x+6x+2x-30+10
14x+2x-20
16x-20
2) Jim get $200 for 50 sales, $350 for 70 sales, and $500 for
85 sales. This is called
Answer:
salary based on how many sales are made
Step-by-step explanation:
A recipe for ice cream calls for 1.656 liters of milk.How many millimeters are in the recipe?
Answer:
In the recipe are 1,656 milliliters of milk
Step-by-step explanation:
The correct question is
A recipe for ice cream calls for 1.656 liters of milk.How many millimeters of milk are in the recipe?
Remember that
[tex]1\ liter=1,000\ milliliters[/tex]
To convert liters to milliliters multiply by 1,000
so
[tex]1.656\ L=1.656(1.000)=1,656\ mL[/tex]
therefore
In the recipe are 1,656 milliliters of milk
Rectangle PQRS is rotated 90 clockwise about the origin what are the coordinates of R
Since rectangle PQRS is rotated 90 clockwise about the origin what are the coordinates of R' are: A. R' (4, -1).
In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
By applying a rotation of 90° clockwise about the center (origin), the coordinates of triangle A'B'C' are as follows;
(x, y) → (y, -x)
Coordinate P (-3, -1) → Coordinate P' (-1, 3)
Coordinate Q (-1, -1) → Coordinate Q' (-1, 1)
Coordinate R (-1, -4) → Coordinate R' (-4, 1)
Coordinate S (-3, -4) → Coordinate S' (-4, 3)
Complete Question:
Rectangle PQRS is rotated 90 clockwise about the origin. What are the coordinates of R'?
If triangle ABC = DEF AB = 8 , BC = 19 , AC = 14 , EF = 4x - 1 and DE=y-6, what are the values of x,y, and z
Answer:
x = 5 and y = 14
Step-by-step explanation:
Given [tex]\triangle[/tex]ABC[tex]\cong \triangle[/tex]DEF.
Congruent triangles have congruent corresponding parts, so
[tex]AB\cong DE\\ \\AC\cong DF\\ \\BC\cong EF[/tex]
Since
[tex]AB=8\\ \\BC=19\\ \\AC=14\\ \\EF=4x-1\\ \\DE=y-6,[/tex]
then
[tex]4x-1=19\\ \\4x=19+1\\ \\4x=20\\ \\x=5[/tex]
and
[tex]y-6=8\\ \\y=8+6\\ \\y=14[/tex]
What is the name of a 21 sided polygon?
Answer:
We call a 21-sided polygon a Henacosagon.
Explanation:
See chart above
* 9 − nona-
I am joyous to assist you anytime.
The name of a 21 sided polygon is Henicosagon.
What is a polygon?A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. The interior of a solid polygon is its body.
Given that, what is the name of a 21 sided polygon,
Polygons have very simple names for the first twenty names.
They use a basic prefix naming system. Di, tri, tetra, penta, and so on.
But polygons with 21 to 99 sides have a different naming system.
First, we use a prefix for the tens (such as triaconta—30). Then we use a prefix for the ones (such as di—20).
At last, we put them together with a ‘kai’ between them. This would be formatted to look like (tens)kai(ones)gon.
In simpler words, a 32-sided polygon. We can normally refer to it as a 32-gon.
Hence, the name of a 21 sided polygon is Henicosagon.
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There is a pile of nickles and dimes. The whole pile has 82 coins and is worth 6.75. How many nickles are in the pile?
There are 29 nickles in the pile.
Step-by-step explanation:
Let,
nickles = x
dimes = y
Total coins = 82
Total worth = $6.75 = 6.75*100 = 675 cents
1 nickle = 5 cents
1 dime = 10 cents
According to given statement;
x+y=82 Eqn 1
5x+10y=675 Eqn 2
Multiplying Eqn 1 by 5;
[tex]5(x+y=82)\\5x+5y=410\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5x+10y)-(5x+5y)=675-410\\5x+10y-5x-5y=265\\5y=265[/tex]
Dividing both sides by 5;
[tex]\frac{5y}{5}=\frac{265}{5}\\y=53[/tex]
Putting y=53 in Eqn 1
[tex]x+53=82\\x=82-53\\x=29[/tex]
There are 29 nickles in the pile.
Keywords: linear equations, subtraction
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It took mady 26 minutes to do her math homework. It took Lola 3/5 of that amount of time to do her math homework. How much time did it take Lola to do her math homework?
Answer:15.6
Step-by-step explanation:
it takes one fourth of a gallon of paint covers one fifth of a car how much paint covers the whole car
Answer:
The volume of paint that covers the whole car is [tex]1\frac{1}{4}[/tex] gallons or one and a quarter gallons.
Step-by-step explanation:
Let the volume of paint required to cover whole car be 'x'.
Given:
Volume of paint to cover one-fifth of a car = one-fourth of a gallon.
We use unitary method to determine the volume of paint required.
∵ One-fifth of a car requires paint = [tex]\frac{1}{4}\ gal[/tex]
∴ Whole volume of car requires paint = [tex]\frac{\frac{1}{4}}{\frac{1}{5}}[/tex]
[tex]=\frac{1}{4}\times \frac{5}{1}\\=\frac{5}{4}\\=1\frac{1}{4}\ gal[/tex]
Therefore, the volume of paint that covers the whole car is [tex]1\frac{1}{4}[/tex] gallons or one and a quarter gallons.
Which expression is equivalent to 8-4(x-6)/4?n is equivalent to 8-4(x-6)/4?
Answer:
B) -x+8
Step-by-step explanation:
8-4(x-6)=8-4x+24=-4x+32
(-4x+32)/4=-x+8
Answer:
the answer is B did it on edge
Step-by-step explanation:
please give brainlist
If Carrie and Cory add on 18% tip to the bill after tax what does their lunch cost in total
Answer:
The cost of total lunch is 1.18 y ( 1+ 0.0 x )
Step-by-step explanation:
Given as :
The percentage of tip added tot he bill after tax = 18 %
Let the tax added to the bill = x % of total the lunch price
Let The total lunch cost = y
So, The cost of the lunch after tax = y + x % × y
I.e The cost of lunch after tax = y × ( 1 +x % )
Or. The bill of lunch after tax = y × ( 1 + 0.0 x )
Now the cost of lunch after tax and tip =18 % of y × ( 1 + 0.0 x ) + y × ( 1 + 0.0 x )
Or, the cost of lunch after tax and tip = y × ( 1 + 0.0 x ) (0.18 + 1 )
∴ The cost of lunch after tax and tip = y × ( 1 + 0.0 x ) × 1.18
Hence The cost of total lunch is 1.18 y ( 1+ 0.0 x ) Answer
11. Any company plans to connect a total of 20 pF of capacitance to a 7200-V
dine. To make this connection, four capacitors will be connected in series, What is
the capacitance of each capacitori
1 W
oche minimum ac
Answer:
C = 80pF
Step-by-step explanation:
The total capacitance of 4 capacitors connected in series is given by:
[tex]Ct = \frac{1}{1/C1 + /C2 + 1/C3 + 1/C4}[/tex]
[tex]Ct = \frac{1}{1/C + /C + 1/C + 1/C}[/tex]
[tex]Ct = \frac{1}{4/C}[/tex]
[tex]Ct = \frac{C}{4}=20pF[/tex]
Solving for C:
C = 4*20pF
C = 80pF