Answer:
D.lines that lie in the same plane but will never intersect
Step-by-step explanation:
parallel lie in the same plane but never meet
A bacteria culture is growing at a rate of
r(t) = 7e^0.6t
thousand bacteria per hour after t hours. How much did the bacteria population increase during the first two hours? (Round your answer to three decimal places.)
Answer:
[tex]{ \bf{r(t) = 7e {}^{0.6t} }} \\ { \tt{r(2) = 7 {e}^{0.6 \times 2} }} \\ = { \tt{7 {e}^{1.2} }} \\ = 23.241 \: thiusand bacteria \: per \: hour[/tex]
X+ 5
If m(x) =x-1 and n(x) = x-3, which function has the same domain as (mon)(x)?
X+5
O (x)=
11
11
o h(x)=
X-1
11
O (X)=
X-4
11
Oh(x) =
X-3
Answer:
third option
Step-by-step explanation:
m(n(x)) =
[tex] \frac{x - 3 + 5}{x - 3 - 1} = \frac{x + 2}{x - 4} [/tex]
the domain of this is R/(4)
so as the third option
The function that has the same domain as (m o n)(x) is
h(x) = 11 / (x - 3)
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
m(x) = (x + 5)/ (x - 1) and n(x) = x - 3,
Now,
(m o n)(x)
= m (n(x)
= m (x - 3)
= (x - 3 + 5) / (x - 3 - 1)
= (x + 2) / (x - 3)
We can not have x = 3.
So,
The domain can not have x = 3.
From the options,
h(x) = 11 / (x - 3) can not have x = 3.
Thus,
The function that has the same domain as (m o n)(x) is
h(x) = 11 / (x - 3)
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How many different 5 digit natural numbers are there starting with odd numbers or ending with even numbers.
the single discount of two successive discounts 10% and 5% is
Answer:
14.5%
Step-by-step explanation:
Use the number 100 as an example to find the single discount.
Take a 10% discount off of this:
100(0.9)
= 90
Take a 5% discount:
90(0.95)
= 85.5
So, after the successive discounts, $14.5 was discounted.
This means that the single discount is 14.5%.
So, the answer is 14.5%
Given m n, find the value of X.
Answer:
x = 62
Step-by-step explanation:
62 and x are alternate exterior angles and alternate exterior angles are equal when the lines are parallel
a number added to 3 is equal to negative 5, find the number
Answer:
-8
Step-by-step explanation:
An equation at represents this situation is:
-5 = 3 + x
Find x by;
-5 - 3 = -8
So x is -8:
-5 = 3 + -8 (TRUE)
Hope this helps
[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]
Sum of the two numbers = [tex]-5[/tex]
One of the number = [tex]3[/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The other number.
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
The other number is [tex]\sf\blue{-8}[/tex].
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
Let the other number be [tex]x[/tex].
As per the question, we have
[tex]Sum \: \: of \: \: the \: \: two \: \: numbers = -5 [/tex]
[tex]➺ \: 3 + x = - 5[/tex]
[tex]➺ \: x = - 5 - 3[/tex]
[tex]➺ \: x = - 8[/tex]
[tex]\sf\purple{Therefore,\:the\:other\:number\:is\:-8.}[/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex] ➪ \: 3 + ( - 8) = - 5[/tex]
[tex] ➪ \: 3 - 8 = - 5[/tex]
[tex] ➪ \: - 5 = - 5[/tex]
➪ L. H. S. = R. H. S.
[tex]\sf\orange{Hence\:verified.}[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35\:ヅ}}}}}[/tex]
Write down the equation of the function whose graph is shown.
will mark brainliest
Answer:
y = 1(x - 5)² + 3
Step-by-step explanation:
The general formula of a quadratic equation is written as;
y = a(x − h)² + k
Where (h, k) are the x and y coordinates at the vertex.
Our vertex coordinate is (5, 3)
Thus;
y = a(x - 5)² + 3
Now,we are given another coordinate as (8, 12)
Thus;
12 = a(8 - 5)² + 3
12 = 9a + 3
9a = 12 - 3
9a = 9
a = 9/9
a = 1
Thus,the equation is;
y = 1(x - 5)² + 3
HELP ME PLEASE!!!
GIVEN sin0= √23/12
tan0= √23/11
Find cos0
Answer:
[tex]cos \theta = \frac{11}{12}[/tex]
Step-by-step explanation:
[tex]sin \theta = \frac{\sqrt{23}}{12} \ , \ tan \theta = \frac{\sqrt{23}}{11}\\\\tan \theta = \frac{sin \theta }{cos \theta }\\\\ \frac{\sqrt{23}}{11} = \frac{\frac{\sqrt{23}}{12} }{cos \theta}\\\\cos \theta = \frac{\frac{\sqrt{23}}{12} }{\frac{\sqrt{23}}{11} }\\\\cos \theta = \frac{\sqrt{23}}{12 } \times \frac{11}{\sqrt{23}}\\\\cos \theta = \frac{11}{12}[/tex]
pleaseeeee solve thissss pleaseeee
Answer:
a.) 15 feet
b.) 3.25 seconds
c.) 17.1125 feet
d.) 12.5 seconds
Step-by-step explanation:
a
This is just asking for the y intercept
to get this just do h(0)= 15
b
This is asking for the x value of the vertex
solve that through -b/2a
-1.3/(2*-.2)= 3.25
c
This is asking for the y value of the vertex
to solve this plug in the x value from b
-.2*3.25²+1.3*3.25+15= 17.1125
d
This is asking for an x intercept
using the quadratic formula...
[tex]\frac{-b(+-)\sqrt{b^2-4*a*c}}{2a}=\frac{-1.3(+-)\sqrt{1.3^2-4*-.2*15}}{2*-.2}= -6, 12.5[/tex]
*note the (+-) before the radical is ± *
logic will tell us that a negative x intercept doesn't make any sense so we only take the positive value, 12.5
At the start of a month, Sasha and Natalia each have a certain amount of money.
Sasha has $400 and saves $20 each week. The graph below shows the amount of money in Natalia's account each week
Whose monthly activity shows a greater rate of change, and by how much?
A) Sasha, by $10/week
B)Sasha, by $19/week
C) Natalia, by $10/week
D) Natalia, by $19/week
Answer:
Option (A)
Step-by-step explanation:
Sasha has an amount of $400 and saves $20 per week.
If we graph the savings of Sasha, her savings per week will be defined by the slope of the line = $20 per week
Similarly, from the graph attached,
Slope of the line given in the graph = Per week savings of Natalia
Slope of line passing through (0, 190) and (2, 210) will be,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{210-190}{2-0}[/tex]
= 10
Therefore, per week savings of Natalia = $10
Difference in savings of Sasha and Natalia = 20 - 10 = $10 per week
Here, Sasha shows the greater rate of change by $10 per week
Therefore, Option (A) will be the answer.
If "u" varies directly with "v," and u = 6
when v = -7, what is "u" when v = 4
9514 1404 393
Answer:
u = -3 3/7
Step-by-step explanation:
The new value of v is 4/-7 = -4/7 of the old value. Because u varies directly, its new value will also be -4/7 of the old value.
u = -4/7(6) = -24/7
u = -3 3/7
Trong một lớp học có 50 sinh viên. Hỏi có bao nhiêu cách bầu ra một ban cán sự lớp gồm 3 người: 1 lớp trưởng, 1 lớp phó, 1 bí thư và không kiêm nhiệm chức vụ.
Answe
SI Si olla amigo lel just spammin here
Step-by-step explanation:
If 12 girls can sweep a room in 20hours, how many hours will it take 8 girls to perform the same task, assuming they are sweeping at the same rate?
Answer:
30 hour
Step-by-step explanation:
girls time
12 20 hour
8 x(let)
now,
12/8=x/20
12×20=8×x
240=8x
x=240/8
x=30,,
Use the drawing tools to form the correct answer on the graph. Graph this function. - 2 + 8 = Reset ® Delet Undo Drawing Tools Click on a tool to begin drawing. Select Point 10 Line 8 3 6- 4 2 2 4 6 -2 8 10 -4 -10 -8 -6 -2 7071 Frmentum. All rights reserved.
Answer:
we have,AD=x cmBC=AD=x cmAB=2AD=2x cmDC=4 cm+AB=(4+2x)cmPerimeter of the trapezium, p=38 cm
The graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8
The function is given as:
[tex]f(x) = -2x + 8[/tex]
The above function is a linear function.
A linear function is represented as:
[tex]y =mx + c[/tex]
Where:
m represents the slope, and c represents the y-intercept.
So, by comparison;
[tex]m =-2[/tex]
[tex]c = 8[/tex]
This means that the graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8
See attachment for the graph of the function
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A customer buys a different book that has an original selling price of $38. The book is discounted 25%. The customer must pay a 6% sales tax on the discounted price of the book.
What is the total amount, in dollars, the customer pays for the discounted book? Explain and SHOW how you arrived at your answer.
Answer:
$30.21
Step-by-step explanation:
100% -25%= 75%
Discounted price of the book
= 75% ×$38
= $28.50
Since the customer must pay an additional 6% of the discounted price,
percentage of discounted price paid
= 100% +6%
= 106%
Total amount paid
= 106% × $28.50
= $30.21
_________________________________
Alternative working:
Original selling price= $38
Since the book is discounted 25%,
100% ----- $38
1% ----- $0.38
75% ----- 75 ×$0.38= $28.50
Since the sales tax is based on the discounted price, we let the discounted price be 100%.
100% ----- $28.50
1% ----- $0.285
106% ----- 106 ×$0.285= $30.21
∴ The total amount the customer pays for the discounted book is $30.21.
The 12th term of GP whose
1
first term is 1/8 and second
term is 1/2is
Answer:
jjanation:jdgjdjgdjgjkdkidjgjghdjjghhkd
Suppose b is any integer. If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 4b is divided by 12? Fill in the blanks to show that the same answer will be obtained no matter what integer is used for b at the start. Because b mod 12 = 7, there is an integer m such that b = 12m + . Multiply both sides of this equation by 4 and then simplify the right-hand side to find values of q and r such that 4b = 12q + r with 0 ≤ r < 12. The result is q = and r = . Now 0 ≤ r < 12, and q is an integer because ---Select--- . So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 4b is divided by 12 is . Need Help?
Answer:
4b mod 12 = 4
Step-by-step explanation:
Since b mod 12 = 7, it implies that there is an integer, m such that
b = 12m + 7.
We desire to find 4b mod 12
So, multiplying b by 4, we have
4b = 4(12m + 7)
4b = 4 × 12 m + 4 × 7
4b = 4 × 12 m + 28
4b = 4 × 12 m + 24 + 4
4b = 4 × 12 m + 12 × 2 + 4
Factorizing 12 out, we have
4b = 12(4m + 2) + 4
Since m is an integer 4m + 2 is an integer since the operation of adding and multiplication is closed for the set of integers.
comparing 4b = 12q + r with 4b = 12(4m + 2) + 4,
q = 4m + 2 and r = 4
So 4b mod 12 = 4, that is the remainder when 4b is divided by 12 is 4.
In this exercise we have to calculate the value of the unknown, so we have:
the value is 4
we know that the equation will be given as:
[tex]b = 12m + 7\\[/tex]
we need to multiply both sides by 4 to become another known equation, like this:
[tex]4b = 4(12m + 7)\\4b = 4 * 12 m + 4 * 7\\4b = 4 * 12 m + 28\\4b = 4 * 12 m + 24 + 4\\4b = 4 * 12 m + 12 * 2 + 4[/tex]
So factoring this equation we will find that:
[tex]4b = 12(4m + 2) + 4[/tex]
Thus, when making a comparison between the two equations, we have that:
[tex]4b = 12q + r \\4b = 12(4m + 2) + 4\\q = 4m + 2\\r = 4[/tex]
See more about factoring at brainly.com/question/6810544
Find an equation for the line with the given property. (a) It passes through the point (2, −6) and is parallel to the line 4x + y − 10 = 0.
It has x-intercept 6 and y-intercept 4.
Answer:
[tex]y = -4x + 2[/tex]
Step-by-step explanation:
Required
Determine the equation
From the question, we understand that, it is parallel to:
[tex]4x + y -10 = 0[/tex]
This means that they have the same slope.
Make y the subject to calculate the slope of: [tex]4x + y -10 = 0[/tex]
[tex]y = -4x + 10[/tex]
The slope of a line with equation [tex]y =mx + c[/tex] is m
By comparison:
[tex]m = -4[/tex]
So, the slope of the required equation is -4.
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where:
[tex](x_1.y_1) = (2,-6)[/tex]
So, we have:
[tex]y = -4(x - 2) -6[/tex]
Open bracket
[tex]y = -4x + 8 -6[/tex]
[tex]y = -4x + 2[/tex]
My sister’s house is 1 2/4 times as high as my house. My house is 5 feet high. How high is my sister’s house?
Answer:
Sister's house is 7.5 feet high
Step-by-step explanation:
Given :
My house = 5 feet
Sisters house = [tex]1\frac{2}{4}[/tex] [tex]times[/tex] [tex]my \ house[/tex]
= [tex]\frac{6}{4} \times 5[/tex]
[tex]=\frac{30}{4}\\\\=\frac{15}{2}\\\\= 7 . 5 \ feet[/tex]
[tex]8 \times {2}^{n + 2} = 32[/tex]
What is the value of n
Step-by-step explanation:
2³×2^n+2=32
2^3+n+2=2⁵
n+5=5
n=0
[tex]_____________________________________[/tex]
[tex]\sf\huge\underline\red{ANSWER:}[/tex]
[tex]\tt n = 0[/tex]
[tex]\sf\huge\underline\red{SOLUTION:}[/tex]
[tex]\tt8 \times {2}^{n + 2} = 32 \\ = \tt {2}^{3} \times {2}^{n + 2} = 32 \\ = \tt {2}^{n + 5} = 32 \\ = \tt {2}^{n + 5} = {2}^{5} \\ = \tt n + 5 = 5 \\ = \tt n = 5 - 5 \\ = \large\boxed{\tt{\green{n = 0}}}[/tex]
[tex]_____________________________________[/tex]
[tex]\large\boxed{\sf{\green{CarryOnLearning}}}[/tex]
[tex]\large\boxed{\sf{\red{MathDemonQueenシ︎✌︎}}}[/tex]
[tex]\large\boxed{\sf{\green{ItsMoreFunInThePhilippines✌︎}}}[/tex]
A cone has a diameter of 4 inches and a height of 9 inches. Find the volume of the cone. Use 3.14 for \large \pi.
Answer:
37.68 in.^3
Step-by-step explanation:
diameter = 4 in.
radius = diameter/2 = 2 in.
height = 9 in.
[tex] V = \dfrac{1}{3}\pi r^2 h [/tex]
[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]
[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]
[tex] V = \blue{37.68~in.^3} [/tex]
How many solutions are there to the equation below?
8(x-3) = 7x- 20
Answer:
x = 4 (ONE solution)
Step-by-step explanation:
This is a first order linear equation, so we can expect 1 solution.
Multiplying out the left side, we get:
8x - 24 = 7x - 20, which simplifies to:
x = 4 (ONE solution)
Select all the numbers that are rational.
Answer:
-14/2 , 1/3 and 0.325 are the rational numbers
To solve the equation 6x + 3 = 9 for x, what operations must be
performed on both sides of the equation in order to isolate the variable
x?
Answer:
Subtraction, and then division.
Step-by-step explanation:
We would subtract 3 on each side to undo the '3', and then divide by 6 on both sides to isolate 'x'.
[tex]6x+3 = 9\\\\6x + 3 - 3 = 9 - 3\\\\ 6x = 6\\\\\frac{6x=6}{6}\\\\\boxed{x=1}[/tex]
Hope this helps.
To solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.
What is a linear equation?A linear equation in one variable has the standard form Px + Q = 0. In this equation, x is a variable, P is a coefficient, and Q is constant.
How to solve this problem?Given that 6x + 3 = 9.
First, we have to separate variable and constants. So, we have to subtract 3 from both sides.
6x + 3 - 3 = 9 - 3
i.e. 6x = 6
Now, to solve this equation, we use division.
x = 6/6 = 1
i.e. x = 1
Therefore, to solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.
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Neglecting air resistance and the weight of the propellant, determine the work done in propelling a five-ton satellite to a height of (a) 100 miles above Earth and (b) 300 miles above Earth.
Answer:
a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
Step-by-step explanation:
Given the data in the question;
We know that the weight of a body varies inversely as the square of its distance from the center of the earth.
⇒F(x) = c / x²
given that; F(x) = five-ton = 5 tons
we know that the radius of earth is approximately 4000 miles
so we substitute
5 = c / (4000)²
c = 5 × ( 4000 )²
c = 8 × 10⁷
∴ Increment of work is;
Δw = [ ( 8 × 10⁷ ) / x² ] Δx
a) For 100 miles above Earth;
W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4100}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4100}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]
= 487.8 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) For 300 miles above Earth.
W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4300}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4300}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]
= 1395.3 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
NEED HELP ASAP
So for this problem I got 10.8 by multiplying 0.60 x 18. However it stated that my answer is incorrect. How do I go about this problem because I am not sure what else to do?
We are looking for the total amount of the solution. We only know part of it, that there are 18 milliliters of the alcohol. We also know that the alcohol makes up only 60% of the solution.
To find the whole, we can set up a proportion using the information given.
60 / 100 <--- This is our percentage, which we were given.
18 / x <--- This is the part (alcohol - 60%) over the whole, which we don't know and which also corresponds to the 100.
Therefore, our proportion is as such:
60 / 100 = 18 / x
To solve, cross-multiply.
100 * 18 = 60 * x
1800 = 60x
x = 30 total milliliters of the solution
Hope this helps!
upandover has a great solution. Here's a slightly different approach.
x = total amount of solution (consisting of water and alcohol mixed)
0.60x = 60% of x = amount of pure alcohol
0.60x = 18 since we have 18 mL of pure alcohol
Divide both sides by 0.60 to isolate x
0.60x = 18
x = 18/0.60
x = 30
Answer: 30 mL of total solution (alcohol + water).
Explain why the work is not correct.
3.42x16.5 show your work plz
Answer:
= 56.43
Step-by-step explanation:
= 3.42 × 16.5
multiply the numbers= 56.43
The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2. (a) What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2
Answer:
0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.
This means that [tex]\mu = 14, \sigma = 2[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{2}{\sqrt{100}} = 0.2[/tex]
What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?
This is 1 subtracted by the p-value of Z when X = 14.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{14.2 - 14}{0.2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
1 - 0.8413 = 0.1587
0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.
simplify (1+3i) + (2-5i)
Answer:
3 - 2i
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsAlgebra II
Imaginary number i = √-1Step-by-step explanation:
Step 1: Define
Identify
(1 + 3i) + (2 - 5i)
Step 2: Simplify
[Addition] Combine like terms: 3 + 3i - 5i[Subtraction] Combine like terms (i): 3 - 2i