The standard form of the expression 25×10 to the power of -3 is 2.5×10⁻⁴
What exactly is meant by "scientific notation"?Scientific notation can be employed to reduce exceptionally large figures to positive exponential values, as well as very small figures to negative exponential values.When writing a number in m10n scientific notation, you can use decimal numbers and positive exponents to transform a long number to a shorter one.The Index Power Rule:
According to this formula, when the power of a number is raised to another power, this same indices are multiplied.This is the fourth index law, and it's the Index Law for Powers.For the given expression;
25×10 to the power of -3
This can be written as follows;
= 25×10⁻³
To write the expression in standard form, shift the decimal to the left of the number and add one more power to base 10.
= 2.5×10⁻⁴
Thus, the expression in the standard form becomes 2.5×10⁻⁴.
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I Need help with this
STEP - BY - STEP EXPLANATION
A quality control company was hired to study the length of meter sticks produced by a certain company. The team carefully measured the length of many many meter sticks, and the distribution seems to be slightly skewed to the right with a mean of 100.06 cm and a standard deviation of 0.1 cm. (a) What is the probability of finding a meter stick with a length of more than 100.17 cm?
(b) What is the probability of finding a group of 10 meter sticks with a mean length of less than 100.03 cm?
(c) What is the probability of finding a group of 44 meter sticks with a mean length of more than 100.08 cm?
(d) What is the probability of finding a group of 50 meter sticks with a mean length of between 100.05 and 100.07 cm?
(e) For a random sample of 24 meter sticks, what mean length would be at the 92nd percentile?
Using the normal distribution and the central limit theorem, the probabilities are calculated as follows:
a) One meter stick greater than 100.17 cm: 0.1357 = 13.57%.
b) Group of 10 with mean less than 100.3: 0.1711 = 17.11%.
c) Group of 44 with mean greater than 100.08: 0.0918 = 9.18%.
d) Group of 50 with mean between 100.05 and 100.07: 0.5222 = 52.22%.
e) 92nd percentile of sample of 24: 100.09.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
Considering the Central Limit Theorem, the z-score formula can be given as follows:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The mean and the standard deviation of the lengths are given as follows:
[tex]\mu = 100.06, \sigma = 0.1[/tex]
For item a, we have that n = 1 and the probability is one subtracted by the p-value of z when X = 100.17, hence:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{100.17 - 100.06}{\frac{0.1}{\sqrt{1}}}[/tex]
Z = 1.1
Z = 1.1 has a p-value of 0.8643.
1 - 0.8643 = 0.1357.
For item b, we have that n = 10 and the probability is the p-value of Z when X = 100.03, hence:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{100.03 - 100.06}{\frac{0.1}{\sqrt{10}}}[/tex]
Z = -0.95
Z = -0.95 has a p-value of 0.1711.
For item c, we have that n = 44 and the probability is one subtracted by the p-value of Z when X = 100.08, hence:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{100.08 - 100.06}{\frac{0.1}{\sqrt{44}}}[/tex]
Z = 1.33.
Z = 1.33 has a p-value of 0.9082.
1 - 0.9082 = 0.0918 = 9.18%.
For item d, we have that n = 50 and the probability is the p-value of Z when X = 100.07 subtracted by the p-value of Z when X = 100.05, hence:
X = 100.07:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{100.07 - 100.06}{\frac{0.1}{\sqrt{50}}}[/tex]
Z = 0.71.
Z = 0.71 has a p-value of 0.7611.
X = 100.05:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{100.05 - 100.06}{\frac{0.1}{\sqrt{50}}}[/tex]
Z = -0.71.
Z = -0.71 has a p-value of 0.2389.
0.7611 - 0.2389 = 0.5222 = 52.22%.
For item e, we have that n = 24, and the 92th percentile is X when Z = 1.405, hence;
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]1.405 = \frac{x - 100.06}{\frac{0.1}{\sqrt{24}}}[/tex]
x - 100.06 = 1.405 x 0.0204
X = 100.09.
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Find the first four terms of the binomial series for the function shown below
(1+x^3)^-1/5
The first four terms of the binomial series are 1, x³/5, (12/25)x⁶ and respectively.
The binomial provided to us is (1+x^3)^-1/5.
To find out the first four terms of the binomial, we shall first extend the standard binomial (1+x)^n.
[tex](1+x)^n = 1 + nx + [n(n - 1)/2!] x^{2} + [n(n - 1)(n - 2)/3!] x^{3} +...[/tex]
As we can see here,
The value of x = x³,
The value of n = -1/5.
We get,
[tex](1+x^{3})^{-\frac{1}{5} } = 1 - \frac{1}{5} (x^{3} ) + [\frac{-1}{5} (\frac{-1}{5} -1)/2!]x^{6} + [\frac{-1}{5} (\frac{-1}{5} -1)(\frac{-1}{5} -2)/3!]x^{27} +[/tex]
From the expansion, we can see,
First term = 1
Second term = x³/5
Third term = (12/25)x⁶
Fourth term = (-13/125)x²⁷
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About how much is 1224.53 divided by 36.02?
determine the coordinates of S(-7,1)after a reflection in the line y=3
This just means that the y coordinate will always be 3 for all coordinates of x that means that the y coordinate of the point ( -7,1) will change to
(-7,3)
Use the given special right triangle to find the value of cos 7 21 XV3 3 T
We have:
[tex]\cos (\frac{\pi}{6})=\frac{\sqrt[]{3}}{2}[/tex]And
[tex]\cos (\frac{\pi}{3})=\frac{1}{2}[/tex]After that, we proceed as follows:
[tex]\sin (\frac{\pi}{3})=\frac{x\sqrt[]{3}}{2x}\Rightarrow\sin (\frac{\pi}{3})=\frac{\sqrt[]{3}}{2}[/tex][tex]\cos (\frac{\pi}{3})=\frac{x}{2x}\Rightarrow\cos (\frac{\pi}{3})=\frac{1}{2}[/tex][tex]undefined[/tex]What is the sum of the first 5 numbers in the series 1+2+4+8+16+32+...?16313263
Given data:
The series is 1 + 2 + 4 + 8 + 16 + 32 + ....
The given series is G.P because the common ratio for GP is,
[tex]C\mathrm{}R\text{ = }\frac{a_2}{a_1}[/tex]Here, the common ratio is 2.
Sum of the first five numbers ,
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]Here, a is first term that is 1
r is common ratio that is 2
n is the number
Therefore, sum is given as
[tex]S_5=\frac{1(2^5-1)}{2-1}[/tex][tex]\begin{gathered} S_5=\frac{32-1}{1} \\ \text{ = 31} \end{gathered}[/tex]Thus, the sum of first five terms is 31
The correct option is (2).
Warm-UpMatch the math vocabulary to parts of the expression w+ 5w. Two tiles will not be used.TilestermexponentconstantexpressionequationvariablecoefficientPairsw2 + 5wthe win w2 + 5wthe 2 in w2 + 5Wthe 5 in w2 + 5wthe w? or the 5w in w2 + 5wSubmit
We are given w^2 + 5w and we are asked to identify the terms for each of its parts.
First, let's start with w. The letter w is used to represent an unknown value. Thus, it is called a variable.
ext, 2. Here, 2 is useda as an exponent of w in the first term.
Meanwhile, 5 is used as a multiplier or a numerical coefficient of w in the second term.
Finally, the expression w^2 + 5w is
(5-9i)-(2-6i)+(3-4i)
Hello! So...
We are given the following:
[tex](5-9i)-(2-6i)+(3-4i)[/tex]
_____________________________________________
1. Simplify the given expression.
[tex](5-9i)-(2-6i)+(3-4i)=5-9i-(2-6i)+3-4i[/tex]
_____________________________________________
2. Group the like terms.
[tex]-9i-4i(-2-6i)+5+3[/tex]
_____________________________________________
3. Add similar elements ( [tex]-9i-4i=-13i[/tex] ).
[tex]=-13i-(2-6i)+5+3[/tex]
_____________________________________________
4. Add the numbers ( [tex]5+3=8[/tex] ).
[tex]-13i-(2-6i)+8[/tex]
_____________________________________________
5. Remove the parentheses ( [tex]-(a+bi)=-a-bi[/tex] ).
[tex]-13i+-2-(-6)i+8[/tex]
_____________________________________________
6. Group the like terms.
[tex]-13i-(-6)i-2+8[/tex]
_____________________________________________
7. Add similar elements ( [tex]-13i-(-6)i=-7i[/tex] ).
[tex]-7i-2+8[/tex]
_____________________________________________
8. Add the numbers ( [tex]-2+8=6[/tex] ).
[tex]-7i+6[/tex]
_____________________________________________
9. Rewrite in standard complex form.
[tex]6-7i[/tex]
^Hence, our solution.
_______________________________________________________
Hope this helps! If so, lmk! If you need anything else, feel free to comment below and I'll see what else I can do to assist you further. But for now, thank you for your time and good luck!
Which of the following rational fractions is graphed below?
Help please!
The following rational fractions is graphed below?
f(x) = 1/ is the rational function seen in the given graph (x - 4)
How Are Graphs of Asymptotes Functions Interpreted?
The vertical asymptote of the graph is located at x = 4.
Let's determine each function's vertical asymptote.
We set the denominator equal to 0 to determine the vertical asymptote.
A) x + 4 = 0\sx = -4
That's incorrect
B) 4x = 0 x = 0 Invalid
C) The denominator is erroneous since it lacks a variable.
D) x - 4 = 0\sx = 4
So, this is true.
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An angle measures 88.8° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:Hence, the measure of angle whose measure is 32∘ less than its supplement is 74∘.
Step-by-step explanation:
What else would need to be congruent to show that ABC=DEF by SAS?
Answer:
D). Angle B ≈ Angle E
Step-by-step explanation:
ASA means that for the relation to be true, there not only has to be the 3 given proportionate values, but 2 have to be angles and 1 has to be a side.
Since we already have the 1 side, option 1 and 2 are voided.
Then since we already have Angle A and D option 3 is as well, so through this we know the answer is number 4 or Angle B = Angle E
Hope this helps.
Please show work
I will mark brainliest
Answer:
A: y = 10
B: ∠A = 42; ∠C = ∠D = 138
Step-by-step explanation:
Given vertical angles A and B, with A marked 5y-8 and B marked 42, you want to know the value of y and the measures of supplementary angles C and D.
A. Value of yVertical angles A and B are congruent, so we have ...
∠A = ∠B
5y -8 = 42
5y = 50 . . . . . . . add 8
y = 10 . . . . . . . divide by 5
B. Angle measuresAs we noted above, angle A has the same measure as vertical angle B:
∠A = 42
Angle C forms a linear pair with angle B, so is supplementary:
∠C = 180 -∠B = 180 -42
∠C = 138
Angle D is a vertical angle to angle C (and is also supplementary to angle B).
∠D = 138
Please help me correct my problem
Answer:
you accidentally put x+6 for the 1st part
95 divided by 60 step by step
DEEPER The scales shown are used to compare the weights of apples, tangerines, grapefruits, and bananas. How many tangerines
will balance one apple?
Justify your answer using a linear system. Let the weights of apples, tangerines, grapefruits, and bananas be represented by a, t,
g, and b respectively.
Equation for first picture:
Equation for second picture:
Equation for third picture:
Using a system of equations, it is found that 4 tangerines will balance one apple.
The equations are given as follows:
First balance: a + t = g.Second balance: b + t = a.Third balance: 2g = 3b.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.
For this problem, the variables are given as follows, considering the situation described:
Variable a: weight of an apple.Variable t: weight of a tangerine.Variable g: weight of an grapefruit.Variable b: weight of an banana.For the first picture, one apple and one tangerine balance one grapefruit, hence:
a + t = g.
For the second picture, one banana and one tangerine balance one apple, hence:
b + t = a.
For the third picture, two grapefruits balance three bananas, hence:
2g = 3b.
g = 1.5b.
Replacing on the first equation, we have that:
a + t = 1.5b.
From the second equation, we have that:
b = a - t.
Hence, replacing on the first:
a + t = 1.5(a - t)
1.5a - 1.5t = a + t
0.5a = 2t
a = 4t
Hence 4 tangerines will balance one apple.
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In a certain science experiment, it was required to estimate the nitrogen
content of the blood plasma of a certain colony of rats at their 37th day of age.
A sample of 9 rats was taken at random and the following data was obtained
(grams per 100cc of plasma):
0.98, 0.83, 0.99, 0.86, 0.90, 0.81, 0.94, 0.92, and 0.87.
Find the estimates for the average content and the variation in nitrogen
content in the colony.
The estimates for the average content is 0.9.
The variation in nitrogen content in the colony is 0.0036.
What is the average of a data set?
The average of a data set or the mean of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The sum of the data set is calculated as follows;
total = 0.98 + 0.83 + 0.99 + 0.86 + 0.9 + 0.81 + 0.94 + 0.92 + 0.87
total = 8.1
The estimated average of the nitrogen content = 8.1/9 = 0.9
The deviation of each data from the mean;
= (0.98 - 0.9), (0.83 - 0.9), (0.99 - 0.9), (0.86 - 0.9), (0.9 - 0.9), (0.81 - 0.9), (0.94 - 0.9), (0.92 - 0.9), (0.87 - 0.9)
= 0.08, -0.07, 0.09, -0.04, 0, -0.09, 0.04, 0.02, -0.03
The sum of the square of each data from the mean;
= (0.08)² + (-0.07)² + (0.09)² + (-0.04)² + (0.0)² + (-0.09)² + (0.04)² + (0.02)² + (-0.03)²
= 0.032
The variation of the data sample = (0.032)/9 = 0.0036
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Find the volume of this triangular prism.
Be sure to include the correct unit in your answer.
8 yd
K
5
7 yd
7 yd
➜
The volume of this triangular prism 7yd x 7yd x 8yd is calculated as 196 [tex]yd^3\\[/tex] as per answered with the correct unit.
What is a prism?A prism is a kind of a polyhedron in geometry that has n number of parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the present first base, and the n faces.
The bases are all translated into all cross-sections that are parallel to them.
The volume of this prism can be found by applying the formula
1/2 Area x Height
= 1/2 x 7 x 7 x 8
= 196 [tex]yd^3\\[/tex]
What is the equation for a prism’s volume?V=Bh
V=Bh, where B can be said as the base area and h as the height, is the formula for a prism’s volume. The prism has a rectangular base.
The total area that any kind of prism takes up in three dimensions is known as its volume. It is defined in mathematically as the result of the base’s area and length.
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h(t) = − 4.9 t^2 + 226t + 283
The Maximum height of the object is 2888.9 feet which is at 23.06 seconds
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Let h represent the height of an object after t seconds. Given that:
h(t) = -4.9t² + 226t + 283
The maximum height is at h'(t) = 0, hence:
h'(t) = -9.8t + 226
-9.8t + 226 = 0
9.8t = 226
t = 23.06 s
h(23.06) = -4.9(23.06)² + 226(23.06) + 283 = 2888.9
Maximum height is 2888.9 ft
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Suppose an account pays 6% interest that is compounded annually. At the beginning of each year, $2,000 is deposited into the account (starting with $2,000 for the first year).
Using the future value formula, it is found that the value of the account after the tenth deposit is of $26,361.59.
What is the future value formula?The future value formula is given by:
[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]
In which:
P is the payment.n is the number of payments.r is the interest rate.For this problem, the parameters are given as follows:
P = 2000, r = 0.06, n = 10.
Hence the value of the account will be of:
[tex]V(10) = 2000\left[\frac{(1 + 0.06)^{10} - 1}{0.06}\right][/tex]
V(10) = $26,361.59.
What is the missing information?The complete problem is:
"Suppose that there is an account that pays 6% interest that is compounded annually. At the beginning of each year, $2,000 is deposited into the account (starting with $2,000 for the first year).
What will be the value of the account after the tenth deposit if no withdrawals or additional deposits are made?"
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4: (x+5)=1:2
[tex]4 \div x + 5 = 1 \div 2[/tex]
4 is to (x + 5) and 1 is to 2
Step-by-step explanation:
i2o2k2wkekekekk2k2o2o2o2o2o292
The depth of a local lake averages 26 ft, which is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|. What is the difference between the depths in February and July?
21 feet
23 feet
8 feet
13 feet
The difference between the depths in February and July is D. 13 feet.
How to illustrate the information?From the information illustrated, it was stated that the depth of a local lake average 26 ft is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|.
Therefore, it should be noted that the depth in July is -18.
Therefore, the difference between the depths in February and July will be:
= -5 - (-18)
= -5 + 18
= 13
Therefore, the depth is 13 feet.
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Solve for x.
5x - 4 > 12
OR 12x + 5 ≤ -4
By using the method of addition, the equation is 12x + 1.
What is addition?Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. The sum is the entire value, and the addends are the integers that are being added. The mathematical operation of addition is the process of adding two or more numbers together to determine the total, or sum.
Given that,
5x - 4 > 12 adding 4 to both sides;
5x - 4+ 4 > 12 + 4
5x > 16 dividing both sides by 5;
x > 16/5
12x + 5-4
12x + 1
Therefore, the equation is 12x + 1.
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This year nelson planted 6 more than one fifth of the tomato plants he planted last year. which expression represents the number of tomato plants he planted this year?
a 1/5x-6
b 1/5x+6
c 5x+6
d 5x-6
The expression to represent the number of tomato plants he planted this year 1 / 5 x + 6.
How to represent expression?This year Nelson planted 6 more than one fifth of the tomato plants he planted last year.
The expression that can be used to represent the number of tomato plant he planted this year can calculated as follows:
Therefore,
let
x = number of tomato he planted last year.
Hence, the final expression is as follows:
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Which values of a make the solution of the equation 3(2x-4)=4(ax-2) positive? Select all that apply
PLEASE HELP!!!!
Answer:
u did not addd the pic
Step-by-step explanation:
Answer: 1.3660254037844
-0.36602540378444
Step-by-step explanation:
Consider the following total revenue function for a hammer. R = 36x − 0.01x2 (a) The sale of how many hammers, x, will maximize the total revenue in dollars? x = hammers Find the maximum revenue. $ (b) Find the maximum revenue if production is limited to at most 1000 hammers. $
The sales of the number of hammers that give the maximum revenue of 32400 is 1800
How to determine the number of sale of hammersThe equation of the revenue function is given as
R = 36x − 0.01x2
Rewrite the equation properly as a quadratic function
So, we have the following equation
R = 36x − 0.01x^2
Differentiate the above function
So, we have the following equation
R' = 36 - 0.02x
Set the differentiated function to 0
So, we have the following equation
36 - 0.02x = 0
This gives
0.02x = 36
Divide both sides by 0.02
So, we have
x = 1800
How to find the maximum revenue?In (a), we have
36 - 0.02x = 0
0.02x = 36
x = 1800
Substitute x = 1800 in R = 36x − 0.01x^2
So, we have
R = 36 x 1800 − 0.01 * 1800^2
Evaluate
R = 32400
Hence, the maximum revenue is 32400
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hello! here is my question! the histogram shows the range of salary for employees at a company . if the mediansalary increased by $10,000 per year, what would be the new median salary?
Increasing amount = $10000
Median = Middle value = $40000
then
New median salary = $40000 + $10000 = $50000
Then answer is
OPTION C) $50-59 thousand
F(x)=(1/2)=2^x
exponential functions
[tex] \frac{1}{2} = {2}^{x} \\ {2}^{ - 1} = {2}^{x} \\ x = - 1[/tex]
ATTACHED IS THE SOLUTION
Using truth tables
24) All businessmen wear suits.
Aaron wears a suit.
Therefore, Aaron is a businessman.
A) Valid
B) Invalid
What is the mathematical model of different dimensions but same volume?
Prism is the mathematical model with different dimensions but same volume.
As given in the question,
Mathematical model represent different dimensions but same volume.
Prism is the mathematical model with different dimensions but same volume.
To prove it consider two different dimensions of prism.
Prism 1
length = 4cm
Width = 4cm
Height = 4cm
Surface area of the prism1 = 2( 4×4 + 4×4 +4×4)
= 2(48)
= 96cm²
Volume of prism1 = 4×4×4
= 64cm³
Prism 2
length = 8cm
Width = 2cm
Height = 4cm
Surface area of the prism1 = 2( 8×2 + 2×4 +4×8)
= 2(56)
= 112cm²
Volume of prism1 = 8×2×4
= 64cm³
Therefore, prism is the mathematical model with different dimensions but same volume.
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