The equation which could be used to find the length of the hypothenuse is; 5 squared + 8 squared = c squared.
Which equation could be used to find the length of the hypothenuse?.It follows from the task content that the equation which could be used to find the length of the third side be determined.
Hence, since it follows from Pythagoras theorem that the square of the hypothenuse is equivalent to the sum of the squares of the two other sides of a right triangle.
Hence, the required equation is; 5 squared + 8 squared = c squared.
Read more on hypothenuse;
https://brainly.com/question/2217700
#SPJ1
Answer:
The answer is A
5 squared + 8 squared = c squared
Step-by-step explanation:
The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds
The correct option is (c) h = 10sin(π15t)+35.
The equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds is h = 10sin(π15t)+35.
How do windmills rotate?The blades of a turbine, which resemble propellers and function much like an airplane wing, capture the wind's energy.
A pocket of low-pressure air develops on one side of the blade when the wind blows. The blade is subsequently drawn toward the low-pressure air pocket, which turns the rotor.
Calculation for the equation of the model height-
Let's now review each choice individually and select the best one.
The blade is horizontal at time t = 0. As a result, h = 35 at t = 0 is valid for all of the possibilities in this situation.
They accomplish two spins in a minute. The blades will so complete one rotation in 30 seconds. and they will complete a quarter rotation in 15/2 seconds. Because of this, the blade will be vertically up from time t = 0 to t = 15/2. Its height in this instance should be 35 + 10 = 45 ft. Let's now examine the available possibilities.
If we put t=15/2 in the options
Option (a) gives h = 25
Option (b) gives h = -10sin(15/2) + 35
Option (c) gives h = 45
Option (d) gives h = 10sin(15/2) + 35
Therefore, the correct equation is given in option c.
To know more about windmill, here
https://brainly.com/question/2031508
#SPJ4
The complete question is -
The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.
a) h = −10sin(π15t)+35
b) h = −10sin(πt)+35
c) h = 10sin(π15t)+35
d) h = 10sin(πt)+35
Devon made a mosaic in art class with different-shaped tiles. She started by putting 2 rows of t triangle tiles at the top of the mosaic and 2 rows of c circle tiles at the bottom. She finished by putting 20 square tiles in between the triangle and circle tiles.
The expressions that represent number of tiles that Devon used on her mosaic:
A. 20 + 2t + 2c
D. 20 + t + t + c + c
What is an expression?An expression refers to a mathematical equation which shows the relationship between two or more numerical quantities or variables.
For the expressions that represent number of tiles that Devon used on her mosaic:
Let the triangle tiles be t.Let the circle tiles be c.Two rows of t triangle tiles = t + t = 2t.Two rows of c circle tiles = c + c = 2t.Mathematically, the expression is given by:
Total tiles = 20 + t + t + c + c
Total tiles = 20 + 2t + 2c.
Read more on expressions here: brainly.com/question/12189823
#SPJ1
Complete Question:
Devon made a mosaic in art class with different-shaped tiles. She started by putting 2 rows of t triangle tiles at the top of the mosaic and 2 rows of c circle tiles at the bottom. She finished by putting 20 square tiles in between the triangle and circle tiles.
Pick all the expressions that represent how many tiles Devon used on her mosaic.
A. 20 + 2t + 2c
B. 20 + 4 ( t + c )
C. 2 ( 20 + t + c )
D. 20 + t + t + c + c
What is the area of parallelogram that has a base of 15 meters and a height of 9 meters
The area of the parallelogram is 135 square meters.
What is parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal).
Properties of parallelogram are-
A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.The area of parallelogram = Base×Height
A = B×H
Calculation for the area of the given parallelogram.
The base is 15 meters.
The height is 9 meters
Area = 15×9
= 135
Therefore, the area of the parallelogram is 135 square meter.
To know more about the parallelogram, here
https://brainly.com/question/970600
#SPJ4
The lateral surface area of cone A is exactly 1/2 the lateral surface area of the cylinder B.
A. True
B. False
The statement, "the lateral surface area of cone A is exactly half of that of cylinder B" is: A. True.
What is the Lateral Surface Area of a Cone and a Cylinder?Lateral surface area of cone = πrl
Lateral surface area of cylinder = 2πrh
Lateral surface area of cone A = πrl = πrh
Lateral surface area of cylinder B = 2πrh
This means the lateral surface area of cylinder B is twice that of cone A. Thus, lateral surface area of cone A is exactly half of that of cylinder B.
The answer is: A. True.
Learn more about the lateral surface area of a cone and cylinder on:
https://brainly.com/question/28071721
#SPJ1
The standard deviation tells us a. the average value of the scores. b. the relative standing of a particular score. c. the skewness of the distribution. d. the dispersion of the scores.
Answer:
D.
Step-by-step explanation:
Standard deviation tells us the dispersion of data/scores around the mean.
We can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.
What is the standard deviation?A standard deviation (or σ) is a measure of how widely distributed the data is about the mean (μ). A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out. A standard deviation around 0 suggests that data points are close to the mean, whereas a high or low standard deviation indicates that data points are above or below the mean, respectively.
We use the following formula to compute the standard deviation:
[tex]\sigma = \sqrt\frac{{\sum_{i=1}^{N}\left | x_i - \mu \right | }^2}{N}[/tex]
In this formula, σ is the standard deviation, [tex]x_i[/tex] is the data point in the set we are solving for, μ is the mean, and N is the total number of data points.
How to solve the question?In the question, we are asked to tell what standard deviations tell us from the given options.
From the above discussion, we can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.
Learn more about the standard deviation at
https://brainly.com/question/475676
#SPJ2
Cost of 4 tables and 3 chairs is $225 and 3 tables and 4
chairs cost $195. Find the cost of 2 chairs and 1 table.
The cost of 2 chairs is = $30
The cost of 1 table = $60
Step-by-step explanation:
Let a table represent x
A chair represents y
4x + 3y = 225.......eq 1
3x + 4y = 195........eq 2
Use elimination method
x - y = 30
x= 30 + y...... Eq 3
Substitute the value of x into equation 1
4(30+ y) + 3y= 225
120 + 4y + 3y= 225
7y + 120= 225
7y= 225-120
7y= 105
y= 15
Substitute the value of y in eq 2
3x + 15 = 195
3x= 195-15
3x= 180
x= 60
Therefore, the cost of 2 chairs is 15 * 2= $30
The cost of 1 table = $60
Answer:
65
Step-by-step explanation:
A private tutoring company charges $20 for a 1-hour session. Currently, 300 students are each tutored for an hour each week. Since the company is losing money, the owner has decided to increase the price. For each 50¢ increase, she estimates that 5 fewer students will participate. If the company needs to bring in $6,210 per week to stay in business, what price must be charged for a 1-hour tutoring session to produce this amount of revenue?
The price that must be charged for a 1-hour tutoring session to produce this amount of revenue is 24.5 dollars
How to solve Word ProblemThe first thing to do with word problem is to understand the question. After that, make analysis of the question.
It is given that a A private tutoring company charges $20 for a 1-hour session. Currently, 300 students are each tutored for an hour each week. Since the company is losing money, the owner has decided to increase the price. For each 50¢ increase, That is $20.5 for each students.
If she estimates that 5 fewer students will participate, that is, 295 students, and the company needs to bring in $6,210 per week to stay in business.
Let us assume that 1 hour per day. And there are 7 days in a week.
Divide the money by 7 to know the value per day
6210/7 = 887.14
Now, divide the amount per day by 250 students to know the amount per student per hour
887.14/295 = 3.007
The price that must be charged for a 1-hour tutoring session to produce this amount of revenue should be 20.5 + 4 = 24.5 dollars
Therefore, each student will pay $24.5 per hour
Learn more about Word Problem here: https://brainly.com/question/13818690
#SPJ1
The write right company manufactures ballpoint pens and has been experiencing a 5% rate of defective pens. modifications are made to the manufacturing process in an attempt to improve quality, and the manager claims that the modified procedure is better, because a test of 50 pens shows that only one is defective. a. assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, exactly one is defective. b. assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, none are defective. c. what probability value should be used for determining whether the modified process results in a defect rate that is less than 5%? d. what do you conclude about the effectiveness of the modified production process?
a. The probability that exactly one is defective is 0.2025
b. The probability that none will be defective is 0.0769
c. The probability rate that should be used is 2%
d. The modified production process is better.
The question has to do with binomial probability.
What is binomial probability?Binomial probability is probability in which the event can only have two values or is binary.
Given the binomial probability formula,
P(X = x) = ⁿCₓpˣ(1 - p)ⁿ ⁻ ˣ
where
p = probability of defective = 5% = 0.05 and n = 50a. Assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, exactly one is defective.For the probability that exactly one is defective, x = 1
So, P(x = 1) = ⁵⁰C₁p¹(1 - p)⁵⁰ ⁻ ¹
= ⁵⁰C₁p(1 - p)⁴⁹
= ⁵⁰C₁(0.05)(1 - 0.05)⁴⁹
= ⁵⁰C₁(0.05)(0.95)⁴⁹
= 50(0.05)(0.95)⁴⁹
= 50(0.05)(0.081)
= 0.2025
So, the probability that exactly one is defective is 0.2025
b. Assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, none are defective.For the probability that exactly one is defective, x = 0
So, P(x = 0) = ⁵⁰C₀p⁰(1 - p)⁵⁰ ⁻ ⁰
= ⁵⁰C₀(1 - p)⁵⁰
= ⁵⁰C₀(1 - 0.05)⁵⁰
= ⁵⁰C₀(0.95)⁵⁰
= 1 × (0.95)⁵⁰
= 0.0769
So, the probability that none will be defective is 0.0769
c. What probability value should be used for determining whether the modified process results in a defect rate that is less than 5%?
Since the modified result results in a defective rate of one out of 50 pens.
The probability rate that should be used is p = number of defective pens/total number of pens = 1/50
= 1/50 × 100 %
= 2%
The probability rate that should be used is 2%
d. What do you conclude about the effectiveness of the modified production?Since the defective rate of the modified production process is 2% which is less than that of the previous production process which is 5%, the modified production process is better.
So, the modified production process is better.
Learn more about binomial probability here:
https://brainly.com/question/13018489
#SPJ1
Instructions:Given the coordinates the translation (x,y)>(x-4,y).
Triangle JKL is graphed on the coordinate plane. -5 -4 -3 y B MD N In L 2 4 5 X What are the coordinates of its image, JKL, if this triangle is dilated by a factor of 5 with respect to the origin? O J(2, 7), K (8, 7), and L'(5, 1) O J'(-5, 2), K'(5, 2), and L'(0, -5) O J'(-3, 2), K'(8, 2), and L'(0, -9) O J'(-15, 10), K'(15, 10), and L'(0, -20)
The coordinate of the image of JKL when dilated by a factor of 5 with respect to the origin is J'(-15, 10), K'(15, 10) and L'(0, 20).
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
Let us assume that triangle JKL has vertices at J(-3, 2), K(3, 2) and L(0, 4).
The coordinate of the image of JKL when dilated by a factor of 5 with respect to the origin is J'(-15, 10), K'(15, 10) and L'(0, 20).
Find out more on transformation at: https://brainly.com/question/4289712
#SPJ1
Use the given transformation to evaluate the integral. double integral 9xy dA R , where R is the region in the first quadrant bounded by the lines y = 2 3 x and y = 3x and the hyperbolas xy = 2 3 and xy = 3; x = u/v, y = v
It looks like the boundaries of [tex]R[/tex] are the lines [tex]y=\dfrac23x [/tex] and [tex]y=3x[/tex], as well as the hyperbolas [tex]xy=\frac23[/tex] and [tex]xy=3[/tex]. Naturally, the domain of integration is the set
[tex]R = \left\{(x,y) ~:~ \dfrac{2x}3 \le y \le 3x \text{ and } \dfrac23 \le xy \le 3 \right\}[/tex]
By substituting [tex]x=\frac uv[/tex] and [tex]y=v[/tex], so [tex]xy=u[/tex], we have
[tex]\dfrac23 \le xy \le 3 \implies \dfrac23 \le u \le 3[/tex]
and
[tex]\dfrac{2x}3 \le y \le 3x \implies \dfrac{2u}{3v} \le v \le \dfrac{3u}v \implies \dfrac{2u}3 \le v^2 \le 3u \implies \sqrt{\dfrac{2u}3} \le v \le \sqrt{3u}[/tex]
so that
[tex]R = \left\{(u,v) ~:~ \dfrac23 \le u \le 3 \text{ and } \sqrt{\dfrac{2u}3 \le v \le \sqrt{3u}\right\}[/tex]
Compute the Jacobian for this transformation and its determinant.
[tex]J = \begin{bmatrix}x_u & x_v \\ y_u & y_v\end{bmatrix} = \begin{bmatrix}\dfrac1v & -\dfrac u{v^2} \\\\ 0 & 1 \end{bmatrix} \implies \det(J) = \dfrac1v[/tex]
Then the area element under this change of variables is
[tex]dA = dx\,dy = \dfrac{du\,dv}v[/tex]
and the integral transforms to
[tex]\displaystyle \iint_R 9xy \, dA = \int_{2/3}^3 \int_{\sqrt{2u/3}}^{\sqrt{3u}} \frac{dv\,du}v[/tex]
Now compute it.
[tex]\displaystyle \iint_R 9xy \, dA = \int_{2/3}^3 \ln|v|\bigg|_{v=\sqrt{2u/3}}^{v=\sqrt{3u}} \,du \\\\ ~~~~~~~~ = \int_{2/3}^3 \ln\left(\sqrt{3u}\right) - \ln\left(\sqrt{\frac{2u}3}\right) \, du \\\\ ~~~~~~~~ = \frac12 \int_{2/3}^3 \ln(3u) - \ln\left(\frac{2u}3\right) \, du \\\\ ~~~~~~~~ = \frac12 \int_{2/3}^3 \ln\left(\frac{3u}{\frac{2u}3}\right) \, du \\\\ ~~~~~~~~ = \frac12 \ln\left(\frac92\right) \int_{2/3}^3 du \\\\ ~~~~~~~~ = \frac12 \ln\left(\frac92\right) \left(3-\frac23\right) = \boxed{\frac76 \ln\left(\frac92\right)}[/tex]
What is the domain and range of each function?
FIRST PERSON TO ANSWER GETS BRAINLIEST OR 5 STARS :D
A) f(x) = −2x
Domain:
Range:
g(x) = ½x2 + 5
Domain:
Range:
Answer:
Greetings!A) Domain: x∈R or in interval notation (- ∞, ∞)
Range: x∈R or in interval notation (- ∞, ∞)
Thus, they both the domain & the range of the first function are the same.
B) Domain: x∈R or in interval notation (- ∞, ∞)
Range: [-5,∞)
Using it's concepts, the domain and the range of the functions are given as follows:
a) Both all real numbers.
b) Domain all real numbers, range [tex]y \geq 5[/tex].
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In this problem, neither function has any impediment, such as an even root or denominator, hence the domain is all real numbers. As for the range, a linear function assumes all real values, while a concave up quadratic function assumes values of the vertex, in this case y = 5, and greater, hence the range of the second function is [tex]y \geq 5[/tex].
More can be learned about the domain and the range of functions at https://brainly.com/question/10891721
#SPJ1
How do I solve this problem 34=p+19
Hello,
[tex]34 = p + 19[/tex]
[tex]34 - 19 = p + 19 - 19[/tex]
[tex]15 = p[/tex]
[tex]p = 15[/tex]
If 111 is divided into pieces that are each \dfrac19
9
1
start fraction, 1, divided by, 9, end fraction of a whole, how many pieces are there?
1\div\dfrac19=1÷
9
1
=1, divided by, start fraction, 1, divided by, 9, end fraction, equals
The results of dividing 1 into pieces that are each 1/9 of a whole is 9
Division of fraction1 ÷ 1/9
multiply by the reciprocal of 1/9 which is 9/11 ÷ 1/9
= 1 × 9/1
= (1 × 9) / (1 × 1)
= 9/1
= 9
Complete question:
If 1 is divided into pieces that are each 1/9 of a whole, how many pieces are there
Learn more about fraction:
https://brainly.com/question/1622425
#SPJ1
An analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a
An analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a parameter.
What is a parameter?A parameter is used to describe the entire population under consideration. For example, we may be interested in the average length of a butterfly. This is a parameter since it contains information about the entire butterfly population.An arbitrary constant whose value identifies a system member (such as a family of curves) is a measure that describes a statistical population (such as a mean or variance).A named variable supplied into a function is referred to as a parameter. Arguments are imported into functions using parameter variables.Therefore, an analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a parameter.
Know more about a parameter here:
https://brainly.com/question/2292917
#SPJ4
To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? first equation: second equation:
Answer:
See below.
Step-by-step explanation:
Here is an example:-
Solve by elimination:
2x - 3y = 0
3x + 2y = 13
To eliminate the y terms Multiply the first equation by 2 and the second by 3. This gives:
4x - 6y = 0
9x + 6y = 39 Adding the 2 equations:
13x + 0 = 39
13x = 39
x = 39/13 = 3
Finally we find y by plugging x = 3 into the first equation:
2(3) - 3y = 0
3y = 2(3) = 6
y = 2.
please can someone tell me how to get the answer
The number of three-digit number you can make is 8
How to determine the number of digits?The usable digits are given as:
4 and 9
Since the two digits can be repeated, then we have
First = 2
Second = 2
Third = 2
So, we have:
Total = 2 * 2 * 2
Evaluate
Total = 8
Hence, the number of three-digit number you can make is 8
Read more about combination at:
https://brainly.com/question/11732255
#SPJ1
A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained 33 pounds per batch and fertilizer from distributor B contained 25 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is three pounds per batch and four pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let µ1 and µ2 represent the average amount of nitrogen per batch for fertilizer A and B, respectively. Which of the following is the correct value of the test statistic?
Based on the calculations, the correct value of the test statistic is equal to 3.2.
How to calculate value of the test statistic?For samples A and B, the hypothesis is given by:
H₀: μ₁ ≤ μ₂
H₁: μ₁ > μ₂
Since both samples have a normal distribution, we would use a pooled z-test to determine the value of the test statistic:
[tex]z = \frac{\bar{x_1} - \bar{x_2} -(\mu_1 - \mu_2) }{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_1^2}{n_1}} }[/tex]
Substituting the given parameters into the formula, we have;
[tex]z = \frac{33 - 25 -(0) }{\sqrt{\frac{3^2}{4} + \frac{4^2}{4}} }\\\\z = \frac{8 }{\sqrt{\frac{9}{4} + \frac{16}{4}} }\\\\z = \frac{8 }{\sqrt{\frac{25}{4} } }\\\\z = \frac{8 }{\frac{5}{2} }}\\\\z = 8 \times \frac{2}{5}[/tex]
z = 3.2.
Read more on standard deviation here: brainly.com/question/4302527
#SPJ1
Suppose a and b are independent events. if p(a) = .5 and p(b) = 0.45 what is p(a^b)
If P(a)=0.5 and P(b) =0.45, then P(a ∩ b) is 0.225.
What are independent events?Independent events are events such that the occurrence of one event won't affect the other.
Therefore,
P(a) × P(b) = P(a ∩ b)
Hence,
P(a) = 0.5
P(b) = 0.45
Therefore,
P(a ∩ b) = 0.5 × 0.45
P(a ∩ b) = 0.225
learn more on Independent event here: https://brainly.com/question/2840943
#SPJ1
the price for 5/6 l of liquid x is $80. what is the price per litre of liquid x
Answer:
$96.
Step-by-step explanation:
5/6 costs 80
Multiply both parts by 6/5:
5/6 * 6/5 ( = 1 ) costs 80 * 6/5
= 16 * 6
= $96.
Solve for x sim b (10, 0.75) for x = 5
The value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06
How to solve the probability?The expression is given as:
[tex]x \sim B (10, 0.75)[/tex]
This means that:
n = 10
p = 0.75
The probability is then calculated as
[tex]P(x)= ^nC_x * p^x *(1 - p)^{n-x[/tex]
This gives
[tex]P(5)= ^{10}C_5 * 0.75^5 *(1 - 0.75)^5[/tex]
Evaluate the combination expression
[tex]P(5)= 252 * 0.75^5 *0.25^5[/tex]
Evaluate
P(5)= 0.06
Hence, the value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06
Read more about probability at:
https://brainly.com/question/24756209
#SPJ1
A group of people hoping to win tickets
to a concert includes 15 people over age 30,
14 people between 20 and 30 years old,
and 10 people under 20. If a 14-year-old
enters the pool of applicants, what will be the
probability of someone over age 30
winning the tickets?
Probability of someone over age 30 winning the tickets is; 38.46%
How to find the probability of winning?We are given;
Number of People over 30 years of age = 15
Number of people between 20 and 30 years old = 14
Number of People under 20 years old = 10
Total number of people in the group = 15 + 14 + 10 = 39
Thus;
Probability of someone over age 30 winning the tickets = 15/39 = 38.46%
Read more about Winning probability at; https://brainly.com/question/24756209
#SPJ1
Find the dependent value
for the graph
y = 5x + 30
when the independent value is - 5.
y = [?]
SOLVE ASAP
X + x/3 = 4/9
solve for x!!
The value of 'x' from the expression is 1/3
How to determine the value
Given the expression;
[tex]x + \frac{x}{3} = \frac{4}{9}[/tex]
Find the LCM of the left side, we have
[tex]\frac{3x + x}{3} = \frac{4}{9}[/tex]
Cross multiply
[tex]9(4x) = 4 *3[/tex]
[tex]36x = 12[/tex]
Make 'x' the subject
[tex]x = \frac{12}{36}[/tex]
x = [tex]\frac{1}{3}[/tex]
Thus, the value of 'x' from the expression is 1/3
Learn more about algebraic expressions here:
https://brainly.com/question/723406
#SPJ1
Hello !
Answer:
[tex]\boxed{\sf x=\dfrac{1}{3} }[/tex]
Step-by-step explanation:
Our aim is to find the value of x that verifies the following equation :
[tex]\sf x+\frac{x}{3} =\frac{4}{9}[/tex]
Let's isolate x :
Multiply both sides by 3 :
[tex]\sf 3(x+\frac{x}{3} )=\frac{4}{9}\times 3\\ \sf 3x+x=\frac{4}{3}[/tex]
Now we can combine like terms :
[tex]\sf 4x=\frac{4}{3}[/tex]
Finally, let's divide both sides by 4 :
[tex]\sf \frac{4x}{4} =\frac{4}{3} \times \frac{1}{4} \\\boxed{\sf x=\dfrac{1}{3} }[/tex]
Have a nice day ;)
An allergy medication is successful in treating 60% of all patients who use it. The medication is given to 200 patients. Let X
The mean is μ=140.
The standard deviation is σ = 6.4807.
The probability that X (number of successful treatments) is 128 or less is 0.0322.
What is normal distribution curve?In statistics, a normal distribution's probability density function is represented by a symmetrical bell-shaped curve. The likelihood that the random variable will fall between two values that define a vertical portion of the curve is represented by the area of the section.
According to the question,
An allergy medication is successful in treating 70%
The medication is given to 200 patients.
Thus,
The random variable X is a binomial random variable with n = 200 (there were 200 patients).
The probability that a medication is successful in treating a randomly selected patient is 0.7.
p = 0.7 (the medication was successful in 70% cases).
Step 1: Use the formulas for mean and standard deviation of a binomial random variable X.
[tex]\begin{gathered}\mu=E(X)=n \cdot p \\\sigma=\sqrt{n \cdot p \cdot(1-p)}\end{gathered}[/tex]
Substitute values of 'n' and 'p' to get the result,
[tex]\begin{gathered}\mu=200 \cdot 0.7=140 \\\sigma=\sqrt{200 \cdot 0.7 \cdot 0.3}=\sqrt{42}=6.4807 .\end{gathered}[/tex]
Thus, the mean is obtained as 140.
The standard deviation is 6.4807.
Step 2: find P(X≤128)
As a result, the prerequisites for a normal approximation to the binomial distribution are satisfied.
[tex]$n \cdot p=200 \cdot 0.7=140 \geq 10$$$n \cdot(1-p)=200 \cdot 0.3=60 \geq 10 .$$[/tex]
[tex]\begin{aligned}P(X \leq 128) & \approx P\left(Z \leq \frac{128-n \cdot p}{\sqrt{n \cdot p \cdot(1-p)}}\right)=P\left(Z \leq \frac{128-200 \cdot 0.7}{\sqrt{200 \cdot 0.7 \cdot(1-0.7)}}\right) \\&=P(Z \leq-1.85)=0.0322\end{aligned}[/tex]
Therefore, the probability that X is 128 or less. is 0.0322.
To know more about the normal distribution, here
https://brainly.com/question/23418254
#SPJ4
The complete question is-
An allergy medication is successful in treating 70% of all patients who use it. The medication is given to 200 patients. Let X = number of successful treatments. What are the mean and standard deviation of X? Use the normal curve to approximate the probability that X is 128 or less.
Which algebraic expression has a term with a coefficient of 9?
• A. 6 + X- 9
• B. 6x - 9
C. 6(x + 5)
• D. 9x ÷ 6
[tex]\textbf{ Heya !}[/tex]
Your Answer Is:-
[tex]\sf{9x\div6}[/tex]
because,
it has a coefficient of 9 (a number that comes before a variable)
`hope that was helpful to u ~
Anna is reading a 300-page book. She can read a page in two minutes. If she has finished reading 75 percent of the pages, how many minutes of reading does she have left
Answer:
150 minutes
Step-by-step explanation:
If Anna read 75% of her 300-page book, then she has already read:
300 × 75%
= 300×0.75
= 225
225 pages.
If Anna has already read 225 pages, then she has:
300 - 225 = 75
75 pages left still to read.
If Anna reads 2 minutes per page, then she has
75 × 2 = 150 minutes.
She has 150 minutes of reading left to finish her book.
By the way, it's weird to say you have 150 minutes of something to do. In real life 150 minutes = 2 1/2 hours. jfyi. Have a great day!
Can someone please explain how [tex](3^{\frac{1}{5} } )^{2}[/tex] can be written as the radical expression [tex]\sqrt[5]{9}[/tex] ???
We can to convert the expression [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression [tex]\sqrt[5]{9}[/tex]. by using the laws of indices.
What is a radical expression?A radical expression is an expression of the form ⁿ√x where it is called the nth root of x.
Now, to write [tex](3^{\frac{1}{5} } )^{2}[/tex] as the radical expression [tex]\sqrt[5]{9}[/tex], we use following laws of indices
The power law of indices. [tex](x^{\frac{1}{b} } )^{a} = (x^{a} )^{\frac{1}{b} }[/tex] and root law of indices [tex]x^{\frac{1}{a} } = \sqrt[a]{x}[/tex]So, [tex](3^{\frac{1}{5} } )^{2} = (3^{2} )^{\frac{1}{5} }[/tex]
[tex](3^{2} )^{\frac{1}{5} } = 9^{\frac{1}{5} } = \sqrt[5]{9}[/tex]
Thus, we can to convert the expression [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression [tex]\sqrt[5]{9}[/tex]. by using the laws of indices.
Learn more about radical expression here:
https://brainly.com/question/3005248
#SPJ1
A certain university recently calculated the number of days that its students took to complete their master's degrees. It took 100 of the students 800 days. In contrast, it took 150 of the students 600 days. What is the average number of days that these students took to complete their master's degrees? a) 620 days b) 680 days c) 700 days d) 720 days?
Answer:
c) 700
Step-by-step explanation:
Add 800 and 600, and then divide by the number of number, or in this case, two. This should give you 700.
please put it in expanded form and solve it
Answer:
1/xyz^3
Step-by-step explanation:
exponents are subtracted when divided
x^0 is 1
negative exponents are positive in the denominator
(4x^0y^-2z^-3) / (4xy-1)
(4xy^-2z^-3) / (4xy^-1)
x-1y^-1z^-3
1/xyz^3