Answer:
x = 1/4
Step-by-step explanation:
Solve for x:
1 - 2 (1 - 2 x) = 0
Hint: | Distribute -2 over 1 - 2 x.
-2 (1 - 2 x) = 4 x - 2:
4 x - 2 + 1 = 0
Hint: | Group like terms in 4 x - 2 + 1.
Grouping like terms, 4 x - 2 + 1 = 4 x + (1 - 2):
4 x + (1 - 2) = 0
Hint: | Evaluate 1 - 2.
1 - 2 = -1:
4 x + -1 = 0
Hint: | Isolate terms with x to the left hand side.
Add 1 to both sides:
4 x + (1 - 1) = 1
Hint: | Look for the difference of two identical terms.
1 - 1 = 0:
4 x = 1
Hint: | Solve for x.
Divide both sides by 4:
Answer: x = 1/4
can some pls help me with this
100 + 55x > 150 + 51x
Answer:
x>25/2
(25/2,∞)
Step-by-step explanation:
I think it’s A but I think that I am incorrect. I’m in desperate need of the answer.
Answer:
It would be D
Step-by-step explanation:
The population of a city is P(t)=9e "
P(t)=9 e^{0.05 t} (in millions), where t is measured in years. (a) Calculate the doubling time of the population. (b) How long does it take for the population to triple in size? (c) How long does it take for the population to quadruple in size? (a) (b) (c)
(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.
To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.
(a) Doubling Time:
Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.
2P(0) = P(t)
Substituting P(t) = 9e^(0.05t), we have:
2 * 9 = 9e^(0.05t)
Dividing both sides by 9:
2 = e^(0.05t)
To solve for t, we take the natural logarithm (ln) of both sides:
ln(2) = 0.05t
Now, we can isolate t by dividing both sides by 0.05:
t = ln(2) / 0.05
Using a calculator, we find:
t ≈ 13.86
Therefore, the doubling time of the population is approximately 13.86 years.
(b) Time to Triple the Population:
Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.
3P(0) = P(t)
3 * 9 = 9e^(0.05t)
Dividing both sides by 9:
3 = e^(0.05t)
Taking the natural logarithm of both sides:
ln(3) = 0.05t
Isolating t:
t = ln(3) / 0.05
Using a calculator, we find:
t ≈ 23.10
Therefore, it takes approximately 23.10 years for the population to triple in size.
(c) Time to Quadruple the Population:
Similarly, we need to find the time it takes for the population to quadruple from its initial value.
4P(0) = P(t)
4 * 9 = 9e^(0.05t)
Dividing both sides by 9:
4 = e^(0.05t)
Taking the natural logarithm of both sides:
ln(4) = 0.05t
Isolating t:
t = ln(4) / 0.05
Using a calculator, we find:
t ≈ 27.72
Therefore, it takes approximately 27.72 years for the population to quadruple in size.
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the slope of the line is
Answer:
what line
Step-by-step explanation:
what line cause i dont see one
Put the following equation of a line into slope-intercept form, simplifying all fractions 2x + 6y = 36
Answer:
y=-\(\frac{1}{3} x+6\)
Step-by-step explanation:
Slope intercept form is y=mx+b. So, you solve for y by putting x to the other side and dividing by 6. In order it looks something like:
2x+6y=36
2x -2x +6y = 36 =2x
6y=36-2x
y=6-2/6x
y=6-1/3x
Hannah has a bag containing 6 yellow, 7
black, 8 green, 15 blue, and 9 white marbles
8
that are all the same size and shape. What
is the probability of randomly choosing a
blue marble on the first pick, NOT replacing
it, and then randomly choosing a white
marble on the second pick?
Answer:
Step-by-step explanation:
Convert 7.34 X 10-3 kg to mg
Answer:
51380000 mg
Step-by-step explanation:
10 - 3 = 7
7.34 x 7 = 51.38
1 kg = 1000000 mg
51.38 x 1000000 = 51380000
When \(7.34 \times 10^{-3} kg\) is converted to milligrams the result is 7340 mg.
Given, that kilograms to be converted to milligrams.
Multiplication: It is the basic mathematical operation among subtraction, division and addition. Multiplication follows associative and distributive property.
Exponential multiplication:
a) \(10^{-3} = \frac{1}{1000}\)
b) \(10^3 = 1000\)
Conversion factors:
1 Kg = 1000 grams
1 Gram = 100 milligrams
1 kg = 1000000 mg
Apply unitary method to convert Kg to mg.
1 kg = 1000000 mg
Multiply both sides by \(7.34 \times 10^{-3} kg\)
\(7.34 \times 10^{-3} kg\) × 1 = \(7.34 \times 10^{-3} kg\) × 1000000
Here the kilograms is converted to equivalent milligrams.
\(7.34 \times 10^{-3} kg\) = 7340 milligrams
Thus the total milligrams in \(7.34 \times 10^{-3} kg\) are 7340 .
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help i’ll give brainly i’m being timed
Answer: 18 and 37
Step-by-step explanation:
The answers should be 18 and 37, I am very sorry if these answers are incorrect.
4 % З с. 43 D. 12 А. 3 4 В. 4 3 12 1 ОА ов G, с OD
To write a division as a fraction: In the numerator write the dividend and in the denominator write the divisor:
Then, 4 divided into 3 is:
\(\frac{4}{3}\)What is the next term of the geometric sequence?
32, 16, 8,
three consecutive integers have a sum of 83. find the integers.
Write a summary of how to get the area of a parallelogram.
Answer:
Opposite sides are equal in length and opposite angles are equal in measure. To find the area of a parallelogram, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply.
I hope it's helpful!
please help me solve this
Explanation:
The proof can be had by making use of the AAS congruence postulate (twice) and CPCTC.
We start by showing ΔPQY≅ΔPRX, then by showing ΔXQN≅ΔYRN. The proof is then a result of CPCTC.
Proof1. PQ≅PR, ∠Q≅∠R . . . . given
2. ∠P≅∠P . . . . reflexive property of congruence
3. ΔPQY≅ΔPRX . . . . AAS congruence postulate
4. PX≅PY . . . . CPCTC
5. PX+XQ=PQ, PY+YR=PR . . . . segment sum theorem
6. PX+XQ = PY +YR . . . . substitution property
7. PX +XQ = PX +YR . . . . substitution property
8. XQ = YR . . . . subtraction property of equality
9. ∠XNQ≅∠YNR . . . . vertical angles are congruent
10. ΔXNQ≅ΔYNR . . . . AAS congruence postulate
11. XN ≅ YN . . . . CPCTC
__
Additional comment
You probably did steps 1-3 in part (a) of the problem.
an agency has specialists who analyze the frequency of letters of the alphabet in an attempt to decipher intercepted messages. suppose a particular letter is used at a rate of 6.6%. what is the mean number of times this letter will be found on a typical page of 2650 characters? 174.9 what is the standard deviation for the number of times this letter will be found on a typical page of 2650 characters ? round your answer to 1 decimal place. in an intercepted message, a page of 2650 characters is found to have the letter occurring192 times. would you consider this unusual?
Standard deviation normal distribution table or calculator to determine the probability of observing a z-score of 1.3 or higher.
The probability is approximately 0.0968, or 9.68%.
To determine the mean number of times the letter appears on a page, we can multiply the probability of the letter appearing (0.066) by the total number of characters on the page (2650):
\(Mean = 0.066 \times 2650 = 174.9\)
To calculate the standard deviation, we can use the formula:
Standard deviation = \(\sqrt(n \times p \times q)\)
n is the sample size (2650), p is the probability of success (0.066), and q is the probability of failure \((1 - p = 0.934)\).
Standard deviation = \(sqrt(2650 \times 0.066 \times 0.934) = 13.2\) (rounded to 1 decimal place)
Determine whether 192 occurrences of the letter on a page is unusual, we can use the z-score formula:
z = (x - mean) / standard deviation
x is the observed number of occurrences (192), mean is the expected number of occurrences (174.9), and standard deviation is the standard deviation we just calculated (13.2).
\(z = (192 - 174.9) / 13.2 = 1.3\)
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which of the following expressions are equivalent to ∑i=12n(i 1)2 ?
Answer:
The expression (2n)(2n + 1)(4n + 1)/6 - 2n(2n + 1) + 2n is equivalent to ∑i=1 to 2n (i-1)².
Step-by-step explanation:
The expression ∑i=1 to 2n (i-1)² represents the sum of (i-1)² for values of i ranging from 1 to 2n. We can simplify and rewrite this expression using properties of summation:
∑i=1 to 2n (i-1)² = ∑i=1 to 2n (i² - 2i + 1)
= ∑i=1 to 2n i² - ∑i=1 to 2n 2i + ∑i=1 to 2n 1
Now let's evaluate each term separately:
∑i=1 to 2n i²:
This represents the sum of the squares of i for values of i ranging from 1 to 2n. This can be expressed as the formula for the sum of squares:
∑i=1 to 2n i² = (2n)(2n + 1)(4n + 1)/6
∑i=1 to 2n 2i:
This represents the sum of 2i for values of i ranging from 1 to 2n. We can factor out the 2 and use the formula for the sum of the first n positive integers:
∑i=1 to 2n 2i = 2(2n)(2n + 1)/2 = 2n(2n + 1)
∑i=1 to 2n 1:
This represents the sum of 1 for values of i ranging from 1 to 2n. Since we are summing 1 a total of 2n times, this is simply 2n.
Putting it all together, we have:
∑i=1 to 2n (i-1)² = ∑i=1 to 2n i² - ∑i=1 to 2n 2i + ∑i=1 to 2n 1
= (2n)(2n + 1)(4n + 1)/6 - 2n(2n + 1) + 2n
= (2n)(2n + 1)(4n + 1)/6 - 2n(2n + 1) + 2n
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The solution set of a linear system whose augmented matrix is [ 1 2 3 ] is the same as the solution set of =, if =[ 1 2 3 ].
x+2x+x=d is solution set of a linear system whose augmented matrix.
What does matrix mean?
A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.First statement
[ 1 2 3 | d][x]
[ 1 2 3]x=d
x+2x+3x=d
Second statement
Ax=d
Given that A = [ 1 2 3]
[ 1 2 3]x=d
x+2x+3x=d
x+2x+x=d
Then, they are going to have the same solution
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Plzz answer this question properly step by step
Answer:
54°
Step-by-step explanation:
∠A = 2x + 10, ∠C = 3x - 14
∠E + 266 = 360 (sum of angles around a point)
∠E = 360 - 266
∠E = 94°
AB is parallel to line BD. Lets draw a line cuts line AB and line BD to form ∠B and ∠D. Hence:
∠B + ∠D = 180° (sum of interior angles on the same side)
∠A + ∠B + ∠C + ∠D + ∠E = 540° (sum of angles in a pentagon)
2x + 10 + 3x - 14 + 94 + 180 = 540
5x + 270 = 540
5x = 540 - 270
5x = 270
x = 54°
Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement
Answer:
The answer is "\(\frac{3}{7}\)"
Step-by-step explanation:
Please find the complete question:
The dilation scale factor will be the same:
\(=\frac{\text{Picture to Center Gap}}{\text{Related pre-image distance to the middle}}\)
Throughout the picture, the distance is \(CP'=6\), while the equivalent distance is \(CP=14\). The factor of scale is then\(=\frac{CP'}{CP} =\frac{6}{14} =\frac{3}{7}\)
The decrease because if a factor of scale is below 1 and a factor of scale is higher than 1. Dilation is a reduction since \(\frac{3}{7}<1\), therefore the scale factor is \(\frac{3}{7}\).
The scale factor of the given dilation is; 6/14 and the dilation is a reduction
Transformations
The image of the object undergoing transformation is missing and so i have attached it.
From the attached object, we se that CP = 14.
Also CP' = 6
Thus; Scale factor is 6/14
Now, reduction is reducing the dimensions while enlargement is increasing the dimensions by a scale factor.
Since the denominator of the scale factor is greater than the numerator, then there is a reduction.
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Easy maths question please help
Answer:
12.649
Skills needed: Trigonometry
Step-by-step explanation:
1) We need to use one of the fundamentals of trigonometry, which is:
Soh Cah Toa
---> Soh = \(sin(\angle x) = \frac{opposite}{hypotenuse}\) (\(sin(\angle x) \) equals the side Opposite of it divided by the Hypotenuse -- sin is short for sine (pronounced as sign)
Soh = Sine Opposite Hypotenuse
---> Cah = \(cos(\angle x) = \frac{adjacent}{hypotenuse}\) (\(cos(\angle x)\) equals the side adjacent (not the hypotenuse) to the angle divided by the hypotenuse -- cos is short for cosine (pronounced as co-sign)
Cah = Cosine Adjacent Hypotenuse
---> Tan = \(tan(\angle x) = \frac{opposite}{adjacent}\) (\(tan(\angle x) \) equals the side opposite of it divided by the side (not hypotenuse) adjacent to it -- tan is short for tangent
Tan = Tangent Opposite Adjacent
2) In this case, we are solving for adjacent:
This is because \(\overline{BC}\) is next to \(\angle \theta\) and \(\overline{BC}\) is not the hypotenuse (\(\overline{AC}\) is the hypotenuse as it is opposite the right angle)
---> We are given opposite as side \(x\) is opposite \(\angle \theta\)
3) Let's plug it in:
\(\tan \angle x = \frac{opposite}{adjacent}\)
\(\angle \theta = 31, adjacent = 7.6, opposite = \overline{BC}\)
\(\tan 31 = \frac{7.6}{\overline{BC}}\) --> Here, we should multiply both sides by \(\overline{BC}\)
\(\overline{BC} * \tan 31 = 7.6\) --> To get \(\overline{BC}\) by itself, divide both sides by \(\tan 31\)
\(\overline{BC} = \frac{7.6}{tan 31}\)
You have to plug this into the calculator as you cannot mentally solve trig functions.
---> Plugging it into calc:\(\overline{BC} = \frac{7.6}{\tan 31} = 12.6485 \text{ rounded to the ten-thousandths place}\)
\(12.6485\) is rounded to the ten-thousandths, but the problem asks for 3 SF, so that would be \(12.649\) (rounded that 85 to 9 (or 90))
Sonji has $5.25 in nickels and dimes.The coin value can be modeled by the equation , where d represents the number of dimes and n represents the number of nickels. If Sonji has 21 dimes, how many nickels does she have
The number of nickels that Sonji has as per the given equation is 63.
What is the value of N mean?In mathematical operations, “n” is a variable, and it is often found in equations for accounting, physics and arithmetic sequences. A variable is a letter or symbol that stands for a number and is used in mathematical expressions and equations. In an arithmetic sequence, which is a list of numbers that follow a pattern, “n” is a variable representing the number of the term to find.For instance, if students want to find the value of the seventh term, “n” would be 7. In physics, an equation for standing waves uses “n” as an integer symbolizing the harmonic number or number of antinodes. The equation evaluates the length of the string in terms of its wavelength. In accounting, “n” is used in the equation for compound interest. It represents the number of compounding in 1 year.We are given the information that Sonji has 21 dimes (which means that d=21). We can use the equation to find the number of nickels n.
0.10d + 0.05n = 5.25
0.10(21) + 0.05n = 5.25
2.10 + 0.05n = 5.25
0.05n = 3.15
n = 3.15 / 0.05
n = 315 / 5
n = 63
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Parallelogram ABCD is placed on a coordinate grid. A (5, -1), B (7, 4), and C (7, 8).
Find the coordinates for D.
Answer:
(5, 3)
Step-by-step explanation:
\(\vec{AB}=(2, 5) \\ \\ \vec{CD}=-\vec{DC}=-\vec{AB}=(-2, -5) \\ \\ \therefore D(7-2, 8-5)=(5, 3)\)
hermes earns
6
6
$ an
hour
hour
for babysitting.he wants to earn at least $
168
168
for a new video game system. determine the number of
hours
hours
he must babysit to earn enough money for the video game system then interpret the solution
Answer:
6 × 28 = 168
Step-by-step explanation:
So, hermes have to work for 28 hours to get enough money for his video games system.
I need help on this equation
A kite and its tail total 48 ft in length. the tails is 7 times the length of the body. How long is the kite's tail?
Answer:
42 ft
Step-by-step explanation:
body = x
tail = 7x
x + 7x = 48
8x = 48
Divide both sides by 8
x = 6
Tail
7x = 7(6)
7x = 42
convert 7.25 kL to mL
The band boosters sell snickers bars for 75¢ each. Which of the following statements are true? Select all that apply.
A. If Tom spent $6.00 on snickers bars, he bought 9.
B. When the band boosters sell 10 snickers bars they make $7.50.
C. For every 4 snickers bars sold the band boosters earn $3.00.
D. If Tom bought 6 snickers bars, he paid $3.50. E. 75¢ is the unit price for a snickers bar.
Answer:
B, C, and E
Step-by-step explanation:
B because 0.75*10=7.5. C because 4*0.75=3. And E because 0.75 is how much each snickers bar is is that is the unit price
What is 35,070,000 expressed in scientific notation?
20 POINTS
Answer:
3.507 x 107 in scientific notation.
Answer:
3.507 x 10^7 is the answer to your question.
What is the factored form of x2 – x – 2?
(x – 2)(x + 1)
(x + 2)(x + 1)
(x – 2)(x – 1)
(x + 2)(x – 1)
If we are told ab=0, then what can we infer? by the zero product property we know = 0 = 0
If we are told that ab=0, then we can infer that either a or b (or both) must be equal to 0.
This is because when the product of two numbers is 0, at least one of the numbers must be 0 according to the zero product property.
One of the most crucial concepts for pupils to understand in maths and science is the zero product property.
The greatest educators, mathematicians, and recognized scientists in the fields of physics and chemistry have worked with Vedantu to provide their insights on the subject.
Their suggestions helped us develop materials for your understanding that would make it simple for you to put these ideas into practice.
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