If the number were written in scientific notation, the exponent will be -2.
What is scientific notation?Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form.
The number of times a number is multiplied by itself is referred to as its exponent.
In this case, the mass of a textbook is approximately 0.0165 metric tons. It should be noted that this will be 1.65 × 10^-2. The exponent is -2.
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The table shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine What is the rate of change of the distance in feet below sea level with respect to time that the submarine traveled? Record your answer
The rate of change of the distance in feet below the sea level over time is: 8 ft/sec.
What is the Rate of Change of a Linear Relationship?The rate of change of a linear relationship between variables x and y is calculated as:
Rate of change = change in y / change in x.
From the table given, we have:
x = time (in seconds)y = distance below sea level (in feet)Using any two points from the table, (0, 460) and (18, 604):
Rate of change of the linear relationship = change in y / change in x = (604 - 460)/(18 - 0)
Rate of change of the linear relationship = 144/18
Rate of change of the linear relationship = 8 ft/sec.
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An asteroid travels 25 kilometres per second how far does it travel in a hour
Answer:
The asteroid will travel 90000 km in an hourStep-by-step explanation:
GivenThe speed of the asteroid is 25 km/secTo find The distance traveled in an hour.SolutionFirst, convert hour into seconds:
1 hour = 60 min = 60*60 sec = 3600 secNow find the distance:
25 km/sec * 3600 sec = 90000 kmAt a local print shop, 10 copies can be made for $4. At this rate, how much would it
cost to make 75 copies?
Answer: $30 for 75 copies.
Step-by-step explanation:
We will set up a proportion to help us solve. Let x be equal to the amount for 75 copies.
[tex]\displaystyle \frac{10 \ copies}{\$4} = \frac{75 \ copies}{\$x}[/tex]
Cross-multiply:
10 * x = 75 * 4
10x = 300
Divide:
x = $30
(1 - 3k) - 4(2 + 2.5k)
HELP!! Quick answer pls
The answer is -13k - 7
Answer:
1 - 3k - 8 + 10k
1 - 3k + 10k - 8
1 - 13k - 8
1 - 8 - 13k
-7 - 13k or -7 + (-13k)
verify that real number can be a complex number but a complex number can not be a real number. Also verify that the lengths of the complex number and its conjugate are equal but the converse is not necessarily true.
real number can be a complex number but a complex number can not be a real number, verified.
the lengths of the complex number and its conjugate are equal but the converse is not necessarily true., verified.
Not all complex numbers are real numbers, despite the fact that every complex number is a real number.
In fact, determining whether the complex number z = a + bi is real is one of the complex conjugate's most useful applications. If and only if z = a + 0i, a complex number is real. In other words, a complex number is real if it contains an imaginary part.
Mathematical proof:
Let z = a+bi, where a and b = real numbers.
Let z* =complex conjugate of z.
Then the magnitude (absolute value) of z is:
|z| = √(a²+b²).
And the value of z* is:
|z*| = √[a²+(-b)²] = √(a²+b²).
So |z| = |z*|.
This Completes the Proof.
what are real numbers?
its a quantity whose decimal expansion has an endless range. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilised in measurements of continuously altering quantities such as size and time.
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Find two integers that add up to 2 and multiply to make -15
Answer:
5 and -3
Step-by-step explanation:
You want two integers that have a sum of 2 and a product of -15.
Factor pairsSolving a problem like this can often be done fairly quickly by listing the factor pairs that make up the product. Only the pairs need be listed that have a sum with the same sign as the sum you're looking for.
Divisors of 15 are 1, 3, 5, and 15. You want a negative product with the largest factor being positive:
-15 = 15(-1) = 5(-3)
The sums of these factor pairs are 14 and 2. The latter pair is the one of interest.
The two integers are 5 and -3.
__
Additional comment
The desired relations can be expressed as a quadratic equation. It generally works well to solve it by completing the square.
If one of the numbers is x, the other is 2-x. Their product is -15:
x(2 -x) = -15
2x -x^2 = -15 . . . . . eliminate parentheses
x^2 -2x = 15 . . . . . . make the leading coefficient positive
Complete the square by adding the square of half the x-coefficient
x^2 -2x +1 = 15 +1
(x -1)^2 = 16
x -1 = √16 = 4 . . . . . . take the square root
x = 5 . . . . . . . . . . . add 1
2-x = 2 -5 = -3 . . . . the other number
4*10^8 -9*10^7 pls work it out
Answer:
Answer down below!
Step-by-step explanation:
Answer: 310000000
Step-by-step is provided in the picture below!
The perimeter of a rectangular room is 60.5 feet. Let x be the width of the room (in feet) and let y be the length of the room (in feet). Select the equation that could model this situation.
A. y=−2x+60.5
B. y=−x+30.25
C. 2x+y=30.25
D. x+2y=60.5
The equation that could model the given situation is y = -x + 30.25. The correct option is B. y = -x + 30.25
Perimeter of a rectangle and equationsFrom the question, we are to determine the equation that could model the given situation
The perimeter, P, of a rectangle is given by the formula,
P = 2(l + w)
Where P is the perimeter
l is the length
and w is the width
From the given information,
The perimeter of a rectangular room is 60.5 feet.
∴ P = 60.5 feet
Also,
x is the width of the room and y is the length of the room
That is,
l = y
and
w = x
Thus,
The equation becomes
60.5 = 2(y + x)
2(y + x) = 60.5
Divide through by 2
y + x = 30.25
y = -x + 30.25
Hence,
y = -x + 30.25 is the equation that might be used to model the circumstance.
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using ordinary interest, calculate the missing information for the following simple discount
Face Value $50,000. Discount Rate (%) 13. Date of Note Apr. 5. Term (days) — Maturity Date, Aug. 14. Bank Discount — Proceeds —
The Bank discount and proceeds of the given information is:
$2365.27 and $47634.73 respectively.
Given the face value is $50,000
Discount rate = 13%
No.of term days = April 5 to August 14
= 131 days.
Bank discount = ?
Proceeds = ?
First calculate the bank discount using the formula:
Bank discount = face value × discount rate × time
Bank discount = $50,000 × 0.13 × 131/360
= 50,000×0.13×0.36388
= $2365.27
now calculate the proceeds using the formula :
Proceeds = face value - bank discount
= 50,000 - 2365.27
= $47634.73
Hence the bank discount and proceeds are $2365.27 and $47634.73 respectively.
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What is the equation of the line that is perpendicular to y = 3x + 3 and passes through the point (−6, 9)?
y equals negative one-third times x plus 3
y equals negative one-third times x plus 7
y = 3x − 33
y = 3x + 27
Answer:
y=-1/3x+7
Step-by-step explanation:
put it in y-y1=m(x-x1)
perpendicular means the slope is opposite
slope is -1/3
y-9=-1/3 (x+6)
y-9=-1/3x -2
+9 +9
y=-1/3x +7
evaluate the expression when x=-5. x² + 6x - 9
Answer:
- 14
Step-by-step explanation:
substitute x = - 5 into the expression
x² + 6x - 9
= (- 5)² + 6(- 5) - 9
= 25 - 30 - 9
= - 5 - 9
= - 14
Answer:
-14
Step-by-step explanation:
Step 1: Substitute x = -5
[tex]\displaystyle{x^2+6x-9\to (-5)^2+6(-5)-9}[/tex]
Step 2: Evaluate
Keep in mind that negative times negative is positive and positive times negative is negative.
[tex]\displaystyle{=(-5)(-5)+6(-5)-9}\\\\\displaystyle{=25-30-9}\\\\\displaystyle{=-14}[/tex]
Please let me know if you have any questions!
Its saying 8/9= w-2 over 6 and the the problem says what is w and then shows improper fractions
To solve this problem we ned to isolate the "w" variable on the left side of the equation, as shown below:
[tex]\begin{gathered} \frac{8}{9}\text{ = }\frac{w}{6}\text{ - }\frac{2}{6} \\ \frac{8}{9}\text{ + }\frac{2}{6}\text{ = }\frac{w}{6} \\ \frac{w}{6}\text{ = }\frac{2\cdot8\text{ + 3}\cdot2}{18} \\ \frac{w}{6}\text{ = }\frac{16+6}{18} \\ \frac{w}{6}\text{ = }\frac{22}{18} \\ w\text{ =}\frac{6\cdot22}{18}\text{ = }\frac{22}{3} \end{gathered}[/tex]The correct answer is the second option.
5. Which of the following is a perfect square trinomial?
A. x^2 + 9x + 18
C. 3x²+ 10x +3
B. x²+ 6x +9
D. x²-4
Answer:
Step-by-step explanation:
B)
x² + 6*x + 9 = x² + 2*x*3 +3² = (x + 3)²
Write the equation of the circle given the following information.Center: (-4,3)Diameter: 9
The equation of a circle is given by:
[tex]\lparen x-h)\placeholder{⬚}^2+\left(y-k\right)^2=r^2[/tex]where (h,k) is the center and r is the radius.
In this case we know that the center of the circle is (-4,3). To find the radius we just need to remember that the radius is half the diameter, hence:
[tex]r=\frac{9}{2}[/tex]Plugging the values for the center and the radius we have that:
[tex]\begin{gathered} \lparen x-\left(-4\right))\placeholder{⬚}^2+\left(y-3\right)^2=\lparen\frac{9}{2})^2 \\ \lparen x+4)\placeholder{⬚}^2+\left(y-3\right)^2=\frac{81}{4} \end{gathered}[/tex]Therefore, the equation of the circle is:
[tex]\operatorname{\lparen}x+4)\placeholder{⬚}^2+\left(y-3\right)^2=\frac{81}{4}[/tex]Use these two representations of reflection at the right to sort each each statement below as the or false
The statements that are true are:
Statement A: Figure A was reflected from the third quadrant to the second quadrant
Statement B: Triangle DEF was reflected over the x-axis
The False statements are:
Statement C: The image of DEF is in quadrant 3
Statement D: The reflection of A can be represented by (-x, y)
Statement E: The reflection of DEF can be represented by (-x, y)
100 points ANSWER ASAP
Answer: Question 1: 113 & Question 2: 27
Step-by-step explanation:
For question 1 you would add 35+32=67,then you subtract 180-67 to get 113 for your answer & question 2 you would subtract 155-128 to get 27 for the answer
Angles in a triangle add up to 180 degrees.
[tex]180-35-32=113[/tex]
Angles on a line add up to 180 degrees.
[tex]p=180-113=67[/tex]
Angles on a line add up to 180 degrees.
[tex]180-155=25[/tex]
Angles in a triangle add up to 180 degrees.
[tex]q=180-128-25=27[/tex]
A group of people paid a total of $240 to see a concert. The tickets each cost the same amount. There are more than 2 and less than 10 people in the group. What are the possible number of people in the group and the possible amounts paid per ticket?
Using the properties of permutation and combination we can calculate that there are possible 3 ,4 ,5 ,6 or 8 people in the group.
A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already ordered, or arranging its members into a sequence or linear order.
The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."A combination is a choice of items from a group of different items where the order of the choices is irrelevant.There are 2 to 10 people in the group.
Lets us consider there are 3 people. Ticket price = 240 / 3= $80
Lets us consider there are 4 people. Ticket price = 240 / 4= $60
Lets us consider there are 5 people. Ticket price = 240 / 5= $48
Lets us consider there are 6 people. Ticket price = 240 / 6= $40
Lets us consider there are 8 people. Ticket price = 240 / 3= $30
Hence from the properties of permutation and combination we can see that there could be 3 ,4,5,6 or 8 people.
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7. It has been estimated that Halley's comet has a mass of 1 X 10"' tons.
This comet is estimated to lose 1 X 108 tons of material each time its orbit brings it close to the sun. With an orbital period of 76 years, what is the maximum remaining life span of Halley's comet?
The maximum remaining life span of Halley's Comet is 76000 years.
The formula for calculating maximum remaining life span of Halley's Comet is [tex]L = \frac{M}{m} \times t[/tex]
M = mass of comet = [tex]1 X 10^{11}[/tex] tons
m = Mass of material lost =[tex]1 X 10^{8}[/tex] tons
t=orbital period = 76 years
Equating values in the equation
L = [tex]\frac{1 X 10^{11}}{1 X 10^{8}} \times76[/tex]
L = 76000 years
What is life span?life span, is the time between the birth and death of an organism. It is normal for all organisms to die. Some die after a short existence, like the nymph fly, which returns to adult life in a day, and others, like the wrinkled fly, which live for thousands of years. It seems that the lifespan limits of each species are ultimately determined by heredity. Locked in the code of the genetic material are instructions that determine the age at which a species cannot survive even under the most favourable conditions. And many environmental factors reduce this upper age limit.
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Which best describes and corrects the error in finding the solution?
X
x+8 =
10
+8 +8
x = 18
The 10 should have been subtracted rather than added.
Correct answer: x = -2
The 8 should have been subtracted rather than added.
Correct answer: a = 2
The 8 should have been subtracted rather than added.
Correct answer: x = -2
The 10 should have been subtracted rather than added.
Correct answer: x = 2
Plssss help :(
Answer:
answer D is right. You need to substract,so that you can get x=2
If there are 6,500 tcf of reserves of natural gas in the world and we are consuming 123 tcf per year, how long until we run out?.
It takes 53 years until we run out of gas.
Given,
Reserves of natural gas = 6500 TCF
Consumption per year = 123 TCF
Therefore,
years left ( x )= Reserves of natural gas / Consumption per year
= 6500/123
= 52.8 years
x = 53 years approximately
So, it takes 53 years until we run out of gas at this rate of consumption.
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-2(4-3х)-6x = 10
Please show how to check work too
Answer:
No solution
Step-by-step explanation:
-2 ( 4 - 3x ) - 6x = 10
→ Expand brackets
-8 + 6x - 6x = 10
→ Simplify
-8 = 10 ⇒ No solution
how is g ( x ) = – | x + 2 | + is related to the graph of the parent function.
Answer: These linear functions can be represented by two lines y = 5x and y' = 5x' + 3
So when we shift line y = 5x by 3 units up on the y-axis then a new graph of
y = 5x + 3 will be formed.
Therefore, Option A is the answer.
Determine whether each function is an example of exponential growth or decay. Then, find the y-intercept. y=0.5(1/4)^x
Because the base is 1/4, which is smaller than 1, we conclude that this is an exponential decay.
Is the function an exponential growth or decay?
A general exponential function is of the form:
y = A*(b)^x
Where A is the initial value, b is the base, and x is the variable.
If 0 < b < 1, then we have an exponential decay.
if b > 1, then we have an exponential growth.
In this case, the function is:
y = 0.5*(1/4)^x
So b =1/4 < 1.
Then we have an exponential decay.
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As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution.
The standard normal distribution becomes smaller.
What is standard deviation?
Your dataset's average level of variability is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. A low standard deviation denotes that values are grouped close to the mean, whereas a large standard deviation shows that values are often far from the mean.Think about the following data: 2, 1, 3, 2, 4. The average and the sum of squares representing the observations' variances from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation.As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
becomes smaller.
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5. The monthly membership fee at a gym
increased by 10% this year. Last year,
the cost of a monthly membership was
$28.50. What is the total yearly cost for a
membership at the gym this year?
A $307.80
C $334.20
B $319.20
D $376.20
Answer:
D $376.20
Step-by-step explanation:
The monthly membership fee at a gym increased by 10% this year. Last year, the cost of a monthly membership was $28.50. What is the total yearly cost for a membership at the gym this year?
A $307.80
C $334.20
B $319.20
D $376.20
28.50 × 1.10 = $31.35 per month this year
there are 12 months per year so:
$31.35 × 12 = $376.20
Find each sum:
1. 4j+k, -3k+7, 5-2j, and j+k-8
2. 5x^2-9x+3 and -2x^3+4x^2+7
1. The sum for the algebraic expression 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4
2.The sum for the algebraic expression 5x^2-9x+3 and -2x^3+4x^2+7 is -2x³+9x²-9x+10
What is algebraic addition?The addition of two or more numbers or quantities taken with regard to their signs according to the rules of addition in algebra.
First we will find the sum of 4j+k, -3k+7, 5-2j, and j+k-8
0i + 4j + k + 0
0i + 0j - 3k + 7
0i - 2j + 0k + 5
0i + j + k- 8
So the sum of 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4
First we will find the sum of 5x²-9x+3 and -2x³+4x^2+7
0x³ + 5x² - 9x + 3
-2x³ + 4x² + 0x+ 7
So the sum of 5x²-9x+3 and -2x³+4x²+7 is -2x³+9x²-9x+10
Therefore, the sum of the given algebraic expressions 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4 and 5x²-9x+3 and -2x³+4x²+7 is -2x³+9x²-9x+10.
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For a given week, Tammy's Coffee House has available 1584 ounces of A grade coffee and 1536 ounces of B grade coffee. These are blended into 1-pound
packages as follows: an economy blend that contains 3 ounces of A grade coffee and 8 ounces of B grade coffee, and a superior blend that contains 9 ounces of
A grade coffee and 3 ounces of B grade coffee. (The remainder of each blend is made of filler ingredients.) There is a $3 profit on each economy blend package
sold and a $2 profit on each superior blend package sold. Assuming that the coffee house is able to sell as many blends as it makes, how many packages of
each blend should it make to maximize its profit for the week?
Note that the ALEKS graphing calculator can be used to make computations easier.
Economy blend:
Superior blend:
package(s)
package(s)
X
S
There is a requirement of 176 packets of economy blend and 96 packets of a superior blend to make maximum profit for the week.
Using the given data, calculate the x number of packages of the economy blend as well as the y number of packages of the superior mix.
3x + 11y =1584
6x + 4y = 1440
From the graph of these two equations, three extreme points are deduced: (240,0), (0,144), and (176,96).
The maximum (2x +4y) is the goal function.
Determine the aim function's value at all these extreme points,
The objective function value for (240,0) is 2 × 240 = 480
The objective function value for (0,144) is 4 × 144 = 576
The value of the objective function for (176,96) is 2 × 176 + 4 × 96 = 736
∴ The optimal point is (176,96) where x = 176 and y = 96.
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Write the sentence as an equation.
341 is the same as the product of k and 273, minus 79
Answer:
341 = 273k - 79 or 273k - 79 = 341
what is the monthly fee being charged? how do you know?
Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.
Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.
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A business breaks even when its production costs are equal to its revenue. The expression 120 + 4x represents the cost of producing x items. Decide on a selling price for each item, and write an expression for the revenue generated by selling x items. How many items would you need to sell at your chosen price to break even? Write an equation and solve it.
The number of items you would need to sell at your chosen price to break even is; 120 items
How to Solve Algebra Word Problems?
We are given the expression that represents the cost of producing x items as;
Cost of producing x units: C = 120 + 4x.
Now, we are told to decide on a selling price for each item. If we decide that the selling price for each item is $5, then it means that;
Revenue generated by selling x units at the rate of $5 per unit is;
R = 5x
For the chosen price to break even, it means that revenue must be equal to cost. Thus;
R = C
Thus;
5x = 120 + 4x
x = 120
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