8 × [tex]10^5[/tex] is 200 times greater than 4 × [tex]10^3[/tex] as according to multiplying and dividing as per the scientific notation of multiplication and division.
What is scientific notation?A kind of representation of number which is some power of 1/10 can also be expressed in as easily in scientific notation.
1/10 = [tex]10^{-1[/tex] (“ten to the minus one power”)
More generally, the expression “[tex]10^{-n[/tex]” (where n is a whole number) means (1/10) n. Thus
[tex]10^{-3[/tex] = [tex]\frac{1}{10}^{-3}[/tex]
= 1/1000
[tex]10^{-8[/tex] = [tex]\frac{1}{10}^{-8[/tex]
= 1/100,000,000
Scientific notation was invented to help scientists (and science students) deal with very large and very small numbers, without getting lost in all the zeros.
Herein this question
8 × [tex]10^5[/tex] can also thus be written as 2 x 4 × [tex]10^5[/tex]. On dividing with 4 × [tex]10^3[/tex] we get 2 x [tex]10^2[/tex]. Thus, it is 2 x [tex]10^2[/tex] i.e., 200 times larger than 4× [tex]10^3[/tex].
The expression “10n”, where n can be stated as a whole number, simply means that “10 is raised to the nth power,” or in other words, a number that is got by using 10 as a factor n times.
You can also notice that the number of zeros that are present in the ordinary decimal expression is absolutely equal to the power to which thus 10 is raised.
If any kind of number is expressed in words, first we have to write it down as an ordinary decimal number and then we have to convert it. Thus, the value “ten million” becomes 10,000,000. There are a total of seven zeros, so in powers of ten notation ten million is written [tex]10^7[/tex].
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I need helping finding out the answers … I’m confused.
To solve this problem, we will use the following formula for the area of a trapezoid:
[tex]A=\frac{a+b}{2}h,[/tex]where a, and b are the lengths of the bases and h is the height.
Now, we are given that ( we will omit the units to simplify the calculations):
[tex]\begin{gathered} h=\frac{1}{4}(a+b), \\ h=2\frac{1}{2}. \end{gathered}[/tex]Therefore:
[tex]\frac{(a+b)}{2}=2(\frac{a+b}{4})=2h=2(2+\frac{1}{2})=4+1=5.[/tex]Substituting in the above formula, we get:
[tex]A=\frac{5}{2}\times(2\frac{1}{2}).[/tex]Simplifying the above result, we get:
[tex]A=\frac{25}{4}ft^2.[/tex]Answer:
[tex]\begin{gathered} A=\frac{1}{2}(2\frac{1}{2})(2\frac{1}{2}\cdot2) \\ =\frac{1}{2}(\frac{5}{2})(\frac{5}{2}\cdot2) \\ =\frac{50}{8}=\frac{25}{4}=6.25ft^2. \end{gathered}[/tex]k (x)=6x-12 ; k(x)=15
The input value x in the function k( x ) = 6x - 12 when k( x ) = 15 is 9/2.
What is the input value (x) in the given function?A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.
Given the data in the question;
k( x ) = 6x - 12k( x ) = 15x = ?To determine the value of x, equate the function to 15 and solve for x.
k( x ) = 6x - 12
k( x ) = 15
15 = 6x - 12
Rearrange the equation
6x - 12 = 15
Collect like terms
6x = 15 + 12
6x = 27
Divide but sides by 6
6x/6 = 27/6
x = 27/6
x = 9/2
Therefore, the input value (x) is 9/2, this forms an ordered pair of ( 9/2, 15 ).
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what’s the inequality
17 < 9 + x
Answer:
x > 9
Step-by-step explanation:
Which of the following is the best estimate of the slope of the best -fit line for the graph at the right?
The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.
What is the slope?The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. A line that is moving up will have a positive slope, and a line that is moving down will have a negative slope if you view the line from left to right. A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x₁,y₁) and (x₂,y₂), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
Given Data
x coordinate = 4
y coordinate = 7
Slope = y-coordinate/ x-coordinate
Slope = 7/4
The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.
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Please help me please I’m begging I WILL GIVE YOU BRAINLEST
The value of x is 54.
What is the Same Side Interior Angles Theorem?If a transversal meets two parallel lines, each pair of same-side interior angles is supplementary (their sum is 180°), according to the theorem for the "same-side interior angle theorem."
The given angles in the figure are 2x + 42° and x - 24°, which are interior angles formed on the same side of the transversal.
By Same Side Interior Angles Theorem,
2x + 42° + x - 24° = 180°
3x + 18° = 180°
3x = 180° - 18°
3x = 162°
x = 54
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Rebecca wants to prove that if the diagonals in a parallelogram are perpendicular, then it is a rhombus.
It is shown that if a parallelogram's diagonals are perpendicular, the parallelogram is a rhombus.
In mathematics, what is a parallelogram?A parallelogram is a quadrilateral with two parallel sides (and therefore opposite angles equal).
What exactly is a rhombus?A rhombus is a quadrilateral with all of its sides equal. Because opposite sides of a parallelogram are equal, a rhombus is a type of parallelogram in which all sides are equal.
We must demonstrate that if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
Let ABCD be a parallelogram .
Consider Δ AOD and Δ COD
Since, a parallelogram's diagonals bisect each other we can say that,
AO = CO
∠AOD = ∠COD = 90°
DO = OD
Δ AOD ≅ Δ COD [SAS rule]
∴ AD = CD
Because the parallelogram's adjacent sides are equal, we can conclude that all four sides are equal.
As a result, it is demonstrated that if the diagonals of a parallelogram are perpendicular, the parallelogram is a rhombus.
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your ethics professor decides to conduct a survey in your class about whether voluntary euthanasia should be legal in the united states. for her survey, she takes all 30 students' names and assigns them each a number. then she has a computer program indiscriminately choose 15 students. we could say that her survey will be:
Hence, the survey of professor will be representative survey.
What is survey?A survey is a technique for acquiring data from a sample of people by asking pertinent questions with the goal of comprehending populations as a whole.
Everyone involved in the information economy, from corporations to the media to the government and academia, relies on surveys as a vital source of information and insights.
The survey of professor will be representative survey.
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11. A researcher in a personal submarine begins at the surface of the ocean.
The submarine descends 20.6 meters and then ascends 57 meters. What
is the depth of the personal submarine?
A-26.3 meters
14.9 meters
B-14.9 meters
26.3 meters
The depth of the personal submarine is -14.9 meter.
What is an integer?An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.
Given that,
The submarine descends 20.6 meters and then ascends 5.7 meters. it means 20.6 is a negative number and 5.7 is a positive number.
Now,
To find the depth adding the -20.6+5.7
-20.6+5.7
-14.9
Hence, The depth of the personal submarine is -14.9 meter
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Solve the equation for the given variable. (type "no solution" if the equation has no solution and type "all
real numbers" if the equation is valid for all possible x-values)
4(4x + 2) + 2(9x + 4) + 3 = 34x + 19
Answer:
all real numbers
Step-by-step explanation:
4(4x+2)+2(9x+4)+3=34x+19
16x+8+18x+8+3=34x+19
34x+19=34x+19
all real numbers
:]
help me with this please!!
y -intercept #4 the starting value
(1 , 7.5) #3 the value after 1 year
because the x axis is the time (in years). When x = 0 (at the y-intercept) time = 0 or beginning time. When x = 1 one year has passed.
The figures below are congruent. Name the corresponding sides.
Answer:
KM
KL
LM
Step-by-step explanation:
A restaurant chain is measuring the levels of arsenic in chicken from its suppliers. The question is whether there is evidence that the mean level of arsenic is greater than 80 ppb, so we are testing vs , where represents the average level of arsenic in all chicken from a certain supplier. It takes money and time to test for arsenic so samples are often small. A sample of chickens from one supplier is tested, and the resulting sample mean is . Subtracting 11 from the sample data to move the mean down to the null mean of results in the following data: . 62, 78, 89, 95, 95, 137
The p-value of the test is 0.1515 which concludes that the average amount of arsenic in chicken from suppliers is 80 ppb.
The test hypothesis is as follows:
H₀: The mean amount of arsenic is 80 ppb, i.e. μ= 80.
Hₐ: The mean amount of arsenic is more significant than 80 ppb, i.e.μ > 80.
We will apply a t-test for a single mean because the population standard deviation is unknown,
It is assumed that the sample means [tex]\bar{x}[/tex] = 91.
The adjusted sample presented is:
S = { 62, 78, 89, 95, 95, 137}
Calculate the sample standard deviation as follows:
[tex]\bar{x}[/tex] = 62 + 78 + 89 + 95 + 95 + 137 =80
[tex]s =\sqrt{\frac{1}{6-1} \times [(62-80)^2 + (78-80)^2 + (89-80)^2 + (95-80)^2 + (95-80)^2 + (137-80)^2]}[/tex]
s =28.66
[tex]t =\dfrac{\bar{x}-\mu}{s/ \sqrt{n} } = \dfrac{{91}-80}{28.6/ \sqrt{6} }=0.94[/tex]
Thus, the test statistic value is 0.94.
Compute the p-value of the test as follows:
p-value = p(tₙ₋₁ < t)
p-value = p(t₆₋₁ < t)
p-value = p(t₅ < t)
*Make use of a t-table.
As a result, the test has a p-value of 0.1515.
Rule of decision:
The null hypothesis will be rejected if the p-value of the test is less than the significance threshold, and vice versa.
p-value = 0.1515 > α = 0.05
At 5% significance, the null hypothesis will not be rejected.
As a result, we may conclude that the average amount of arsenic in chicken from suppliers is 80 ppb.
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Last year, Lena biked 565 miles. This year, she biked k miles. Using k, write an expression for the total number of miles she biked
11. The price of a sweater changed from $20 to $12. By what percentage was the price of the sweater
changed?
The price of the sweater decreased by __ %
well, the change was 8 bucks.
if we take 20 to be the 100%, what is 8 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 20 & 100\\ 8& x \end{array} \implies \cfrac{20}{8}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2}=\cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40[/tex]
I'm doing linear equations and one if the things says y = -x so do i plug in the x that i have already and just switch it to the opposite integer????
To solve for y we will have to simply replace the value of x and the solution we write it in the equivalent palce for y, that is:
For x = -5:
[tex]y=-(-5)\Rightarrow y=5[/tex]For x = -2:
[tex]y=-(-2)\Rightarrow y=2[/tex]For x = 0:
[tex]y=0[/tex]For x = 3:
[tex]y=-3[/tex]write the equation of the line in a fully simplified slope-intercept form.
Slope intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptWe can identify two points on the given graph and solve for the slope and the y-intercept.
Solving the QuestionTwo clear points on the graph are (6,0) and (0,6).
First, we can solve for the slope by using the slope equation:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
⇒ Plug in the points (6,0) and (0,6):
[tex]m=\dfrac{0-6}{6-0}\\\\m=\dfrac{-6}{6}\\\\m=-1[/tex]
Therefore. the slope of the line is -1. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-x+b[/tex]
Now, we can find the y-intercept. It is the value of y when the line crosses the y-axis.
In this case, we can see on the graph that this is 6.
[tex]y=-x+6[/tex]
Answer[tex]y=-x+6[/tex]
the half-life of palladium-100 is 4 days. after 12 days a sample of palladium-100 has been reduced to a mass of 4 mg. what was the initial mass (in mg) of the sample? what is the mass (in mg) 7 weeks after the start? you may enter the exact value or round to 4 decimal places.
Using the half life of palladium, mass seven weeks after start was 0.7931 gm.
The half-life is the amount of time it takes for a quantity (of material) to fall to the cost. In nuclear physics, the phrase usually refers to how rapidly neutrons become radioactive atoms or how long stable atoms survive.
The term can also refer to any sort of hyperbolic (or, in rare situations, non-exponential) decay.
The half life of palladium 100 = 4 days
after 24 days sample has reduced to a mass of 5mg
standard exponential function is
[tex]P = P_o e^{kt}[/tex]
plugging P = P₀ /2
[tex]P_o/2 = P_o e^{4k }[/tex]
[tex]1/2 = e^{4k }[/tex]
ln (1/2) = 4k
k = -0.1733
function becomes
[tex]P = P_o e^{- 0.1733 t }[/tex]
plugging P = 5 and t = 24
[tex]5 = P_o e^{( - .1733\times 24 ) }[/tex]
P₀ = 320.10
In the medical sciences, for example, the biological half of drugs and other chemicals in the human body is referred to. The flipside of half-life is doubling time in exponential growth.
For the second part of the problem:
7 weeks = 5 × 7 =49 days
plugging t = 49
[tex]P = 320.10 e^{(-.1733 * 35 ) }[/tex]
mass 7 weeks after = 0.7431 mg
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pls help im faling geometry
5
8
of the staff are male. 5
12
of the staff works part time at
the aquarium. What fraction of the staff is female?
The fraction that are female in the company is 227/256
How to determine the fraction that are female?The given parameters are
Male staff = 58
Total number of staff = 512
Start by calculating the number of female staffs
So, we have
Female staff = Total number of staff - Male staff
Substitute the known values in the above equation
So, we have
Female staff = 512 - 58
Evaluate the like terms
Female staff = 454
The fraction that are female is
Fraction = Female staff/Total number of staff
This gives
Fraction = 454/512
Simplify
Fraction = 227/256
Hence, the fraction is 227/256
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60 cents as percent of $3
60 cents is 20% of $3.
What is the percentage?In essence, percentages are fractions with 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). The value of a number out of 100 is the percentage of that number. The terms "percent" and "cent" combine to make the word "percentage." Having Latin and French roots, the term "cent" means "hundred," while the word "percent" means "per hundred."
Given Data
60 cents as a percent of $3
1 dollar = 100 cents
$3 dollar = 300 cents
Percentage:
[tex]\frac{Value}{Total value}[/tex] × 100
[tex]\frac{60}{300}[/tex] ×100
20%
60 cents in 20% of $3.
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The complete question is:
"60 cents is what percent of $3."
Evaluate the arithmetic series described:
a (subscript 1) = 12
a (subscript n) = 64
Find S (subscript 14)
Answers:
541
532
1082
1064
...the subscript thing isn't working for some reason
Answer:
532
Step-by-step explanation:
Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac{n}{2}(a_1+a_n)}[/tex]
Where:
aₙ is the nth term.a₁ is the first term.n is the position of the term.Given terms:
[tex]a_1=12[/tex][tex]a_n=64[/tex]Substitute the given terms into the formula to create an equation for the nth term:
[tex]\implies S_n=\dfrac{n}{2}(12+64)[/tex]
[tex]\implies S_n=\dfrac{n}{2}(76)[/tex]
[tex]\implies S_n=38n[/tex]
To find S₁₄, substitute n = 14 into the found equation:
[tex]\begin{aligned}n=14 \implies S_{14}&=38(14)\\ & = 532\end{aligned}[/tex]
Find the value of p in the inequality.
three fourths times p plus 8 is greater than or equal to 3
The value of p that we get by solving the inequality given in the question is [tex]p\geq \frac{-20}{3}[/tex]
The given inequality is
[tex]\frac{3}{4}p+8\geq 3[/tex]
⇒[tex]\frac{3}{4}p\geq 3-8[/tex] (subtracting 8 on both sides)
⇒[tex]3p\geq -5*4[/tex] (multiplying both sides by 4)
⇒[tex]p\geq \frac{-20}{3}[/tex] (dividing both sides by 3)
⇒[tex]p\geq -6.667[/tex]
Therefore the value of p must be greater than or equal to -20/3 or -6.667
That is, [tex]p\geq -6.667[/tex]
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Find the quotient of.(4.617 × 10 ^3 ) ÷ (5,700 ÷ 10^ 2 )
The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The expression is;
(4.617 × 10³ ) ÷ (5,700 ÷ 10² )
Now, Solve the expression by using BODMAS rule;
= (4.617 × 10³ ) ÷ (5,700 ÷ 10² )
= 4,617 ÷ 57
= 81
Thus, The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.
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Which of these shapes are a trapezoid?
Answer: The Pink one
Step-by-step explanation: Trapezoids have 2 parallel sides and 2 non-parallel sides.
Solve each equation by factoring. Then solve the quadratic formula. (Show all work)
[tex] - {k}^{2} + 3k = 28 - 2 {k}^{2} \\ - {k}^{2} + 2 {k}^{2} + 3k - 28 = 0 \\ {k}^{2} + 3k - 28 = 0 \\ (k + 7)(k - 4) = 0 \\ \\ k + 7 = 0 \\ \\ ork - 4 = 0 \\ \\ k = - 7 \\ \\ or \\ \\ k = 4[/tex]
ATTACHED IS THE SOLUTION
I GROUPED THE LIKE TERMS TOGETHER FIRST AFTER THAT THEN FACTORISED.
HELP ME PLEASE! THIS IS URGENT!!
For what value of x will the line passing through the following pairs of points be veritcal? F(3-2x, 12) and G(x+9, 7)
By solving a linear equation, we will see that the points are vertical only if the value of x is -2.
For which value of x are the points vertical?
We say that two points (x₁, y₁) and (x₂, y₂) are vertical if the points have the same x-component and different y-component, so we must have:
x₁ = x₂
y₁ ≠ y₂
In this case, the two points are:
F(3-2x, 12) and G(x+9, 7)
The y-component is different, so we only need to have:
3 - 2x = x + 9
This is a linear equation, below I will solve it:
3 - 2x = x + 9
3 - 9 = x + 2x
-6 = 3x
-6/3 = x
-2 =x
The points are vertical if x = -2.
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find the values of a,b,c, and d so that h(x)=a|bx+c|+d is a translation 7 units up and 1 unit right, followed by a reflection in the y-axis of the graph of g(x)=1/3|x+3|-4
The translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.
What is translation and reflection?
In mathematics, the translation shift the coordinates either on the horizontal axis or on the vertical axis. It compress the expression also. Similarly, in reflection, the expression get reflected on the coordinate axis either on the upper side or downward side.
According to the question, the given expression for the translation as well as for the reflection are as follows:
h(x)=a |b(x) + c| + d
g(x)=1/3 | x + 3| - 4
And the given condition state that the translation is for 7 units and reflection is on the y-axis. Translation shift the expression and reflection reflects the expression.
Translation expression: h(x+7)=a |b(x+7) + c| + d
Reflection expression: g(-x)=1/3 | -x + 3| - 4 = 1/3 | x + 3| - 4
Therefore, the translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.
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Solve the system of linear equations using the substitution method.
4x + 7y = 19 and y = x + 9
A. (-4, 5)
B. (-6, 4)
C. (-1, 2)
D. (-4, 3)
Answer:D
Step-by-step explanation:
What is the answer: 4(3x+2)-2
Answer:
12x + 6Step-by-step explanation:
What is the answer:
4(3x+2)-2=
12x + 8 - 2 =
12x + 6
-2
-3
S
y = -2|x|
2
X
The function is positive when
The function is negative when
The function is increasing when
The function is decreasing when
Answer: Never, All real numbers, x<0, x>0
Step-by-step explanation:
The function is positive when it is above the x-axis.
The function is negative when it is below the x-axis.
The function is increasing when the graph is going up.
The function is decreasing when the graph is going down.