Answer:
103/28
Step-by-step explanation:
Let the number be 'x'
Equation:-
7x - 3/4 = 25
7x = 25 + 3/4
7x = 100/4 + 3/4
7x = 103/4
x = 103/(4 x 7)
x = 103/28
Answer:
if we make this a algebraic equation it will look like this
7x-3/4x=25
6.25x=25
25 divided by 6.25=4
x=4
to check
28-3=25
Hope This Helps!!!
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.
In a carnival game, there are 8 identical boxes, one of which contains a prize. Contestants guess which box contains the prize. The game is played until one of the contestants guesses it correctly. A contestant with the smaller number of guesses wins the prize. Before each game, a new prize is placed at random in one of the 8 boxes.
Requried:
Is it appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game that day several times wins exactly 4 times?
Since there is a fixed number of trials and the trials are independent, it is appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game that day several times wins exactly 4 times.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
The game is played n times.In each game, each of the 8 participants is equally as likely to win the game, hence p = 1/8.Thus, the binomial distribution is appropriate.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
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
Please help me with this question!!! I'm
desperate!
Solve the following system of equations by graphing.
- 4x + 3y -12
- 2x + 3y -18
Answer:
The solution of the graph is at (-3,-8).
Step-by-step explanation:
The given equations are :
-4x+3y=-12
and
-2x+3y=-18
These are the system of equations in two variables.
The graphs for the equations are :
The solution of the graph is at (-3,-8).
Seema is travelling to Guernsey. She travels a distance of 3,800 km by plane to London and then another 400 km to Guernsey. Both planes fly at an average speed of 900 kmh-1.
What is her total flight time in hours and minutes, to the nearest minute?
9514 1404 393
Answer:
4 hours 40 minutes
Step-by-step explanation:
The appropriate relation is ...
time = distance/speed
time = (3800 km)/(900 km/h) +(400 km)/(900 km/h) = (38+4)/9 h
= 14/3 h = 4 2/3 h
Seema's flight time is 4 hours 40 minutes.
__
2/3 of 60 minutes is 40 minutes
How many different 5 digit natural numbers are there starting with odd numbers or ending with even numbers.
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]
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
WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST
Answer:
height = (3x + 3)
Step-by-step explanation:
area of rectangular prism = length *breadth
2x^2 + 3x = length*breadth
volume of a rectangular prism = length * breadth *height
6x^3 + 13x^2 + 6x = (2x^2 + 3x) *height
x(6x^2 + 13x + 6) = x(2x + 3) *height
a nd x gets cancel . So,
(6x^2 + 13x + 6) = (2x + 3) *height
6x^2 + (9 + 4)x + 6 = (2x + 3) *height
6x^2 + 9x + 4x + 6 = (2x + 3) *height
3x(2x +3) +2(2x +3) = (2x + 3) *height
(3x + 2)(2x + 3) = (2x + 3)*height
(3x + 2)(2x + 3) / (2x + 3) = height
(2x + 3 ) of numerator and (2x + 3) of denominator gets cancel
(3x + 3) / 1 = height
(3x + 3) = height
can anyone help me in this questions
Step-by-step explanation:
3.
1.4191919... = 1405/990
4.
√(2/5) and √(1/2)
What is the cube root of -1,000p12q3?
O-1004
O - 10pta
O 1004
O 10pta
Answer:
Your options are not clear
Step-by-step explanation:
[tex]\sqrt[3]{-1000 \times p^{12} \times q^3} \\\\(-1 \times 10^3 \times p^{12} \times q^3)^{\frac{1}{3} }\\\\(-1^3)^{\frac{1}{3} }\times 10^{3 \times \frac{1}{3} } \times p^{12 \times \frac{1}{3}} \times q^{3 \times \frac{1}{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (-1)^3 = - 1 \ ] \\\\- 1 \times 10 \times p^4 \times q\\\\-10p^4q[/tex]
Tính (1,5)4; ((-2)/3)3; (√3)5.
Step-by-step explanation:
câu trả lời là trong bức ảnh trên
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)
Learn more about functions here:
https://brainly.com/question/28533782
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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.
Learn more about linear equations here -
https://brainly.com/question/25058584
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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:
Find the length of X ( IN THE PICTURE)
Answer:
x=3
Step-by-step explanation:
The triangles are similar so we can use ratios to solve
x 4
----- = -----------
4.5 6
Using cross products
6x = 4.5 * 4
6x =18
Divide by 6
6x/6 = 18/6
x = 3
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
Select all the numbers that are rational.
Answer:
-14/2 , 1/3 and 0.325 are the rational numbers
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]
Could you help me answer 2a, b, c and d? See the image below.
Answer:
2a. 1/4
2b. 2/8
2c. yes, 1/4 = 2/8 because
2 / 8 = 2 ÷ 2 / 8 ÷ 2 = 1 / 4.
2d. the total number of parts doubled in the denominator, the number of parts represented in the numerator doubled as well.
The operations of division and multiplication are made proportionally to the numerator and denominator.
Which of the following represents a function?
The girls in Lana’s troop set a goal to sell 1,000 boxes of cookies this year. There are 13 girls in the troop. At least how many boxes of cookies should each girl sell to reach their goal?
Answer:
77 boxes
Step-by-step explanation:
Take the total number of boxes to be sold and divide by the number of girls in the troop
1000/13
76.92307692
Round up
77
Each girl must sell 77
77*13 =1001
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.
WILL MARK BRAINIEST Evaluate the 6 trigonometric functions at
Step-by-step explanation:
the Adjacent = √15²-9²=√225-81=√144=12
sin 0 = 9/15 = 3/5
cos 0 = 12/15 = 4/5
tan 0 = 9/12 = ¾
sec 0 = 15/12 = 5/4
csc 0 = 15/9 = 5/3
cot 0 = 12/9 = 4/3
Have a stack of quarters
from the floor to the top of
your head OR $225?
Answer:
225 quarters are easy to loose and who will accept that many quarters
Step-by-step explanation:
Answer:
quarters
You will get more money
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]
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]
62.5% of a number is 25. What is half of the same number.
let the number be b
62.5/100 x b = 25
0.625 x b = 25
b =25/0.625
b=40
half of b= 40/2 = 20
