A proportion is an equation in which two ratios are set equal to each other and the large sample size required is [tex]0.75[/tex].
What is population proportion?
A fraction is represented in the form of [tex]\frac{a}{b}[/tex], a while ratio [tex]a:b[/tex], then a proportion states that two ratios are equal. Here, [tex]a[/tex] and [tex]b[/tex] are any two integers.
Here, we are determining the minimum sample size for the determination of the population proportion. So, the general formula is of the form is:-
[tex]n=(\frac{z_\frac{x}{2}.x}{E})^{2}[/tex]
Here given values are:-
σ[tex]=76[/tex], population standard deviation
[tex]1-x=0.95\\[/tex], Confidence level
[tex]E=4.5[/tex], Error
Determining the critical value, we get
[tex]z_\frac{x}{2}\\P(z\leq z_\frac{x}{2})=1-\frac{x}{2}\\1-x=0.95\\x=1-0.95\\x=0.05\\\frac{x}{2}=\frac{0.5}{2}\\\frac{x}{2}=0.25\\1-\frac{x}{2}=1-0.25\\\\=0.75[/tex]
Hence, a large sample size is required is [tex]0.75[/tex].
To know more about proportion
https://brainly.com/question/16879541
#SPJ1
Which inequality is represented by the graph?
Answer:
x<1
Step-by-step explanation:
since the circle is not filled it will not be equal to one but either grater or equal to it
Since the arrow is pointing left than x is less than 1
x<1
hopes this helps please mark brainliest
The measures of the angles of a triangle are shown in the figure below. Find the measure of the largest angle.
The measure of the Largest angle using the angle sum property of a triangle is: 80°
What is the Angle sum property of a triangle?
According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.
One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.
In the given figure, we have:
Measure of 1st angle = 64°
Measure of 2nd angle = (2x + 14)°
Measure of 3rd angle = (6x + 14)°
and we know the angle of the property,
using the angle of property,
64° + (2x + 14)° + (6x + 14)° = 180°
⇒64° + 8x + 14° + 14° = 180°
⇒92° + 8x = 180°
⇒ 8x = 180° - 92°
⇒8x = 88°
⇒ x = 11°
So,
Measure of 2nd angle = (2x11 + 14)°
Measure of 2nd angle = (36)°
Measure of 3rdangle = (6x11 + 14)°
Measure of 2nd angle = (80)°
Hence,
The measure of the Largest angle using the angle sum property of a triangle is: 80°
To learn more about Angle sum property, visit:
https://brainly.com/question/22262639
#SPJ1
On rectangle ABCD below, if A is located at (3,4) and B is located at (7, 6), what is the slope of BC?
If A is located at (3,4) and B is located at (7,6) , then the slope of BC is -2 .
In the question ,
it is given that ,
In the rectangle ABCD , the coordinate of the point A is (3,4) and the coordinate of the point B is (7,6) .
since the sides of the rectangle are at 90° , that means they are perpendicular .
which means AB⊥BC ,
the slope of AB = (6-4)/(7-3)
slope = 2/4
slope = 1/2
Since , AB⊥BC ,
(slope of AB)×(slope of BC) = -1
substituting the values , we get
(1/2)×(slope of BC) = -1
slope of BC = -1/(1/2)
slope of BC = -2 .
Therefore , If A is located at (3,4) and B is located at (7,6) , then the slope of BC is -2 .
The given question is incomplete , the complete question is
On rectangle ABCD, if A is located at (3,4) and B is located at (7, 6), what is the slope of BC ?
Learn more about Slope here
https://brainly.com/question/15023791
#SPJ1
Use the calculator below to approximate √59 as a decimal to the tenths place.
Note that you must do the approximation without using a square root button.
Your answer must be within a tenth of the actual value.
The approximate of √59 is 7.7 when rounded off to the nearest tenth place.
Given, √59
we are asked to determine the approximation without using a square root button.
√59 is a decimal number since it is not a perfect square. Therefore, rather than finding a precise value, we will need to obtain a near approximation of 59 in decimal form.
the square root of the number 59 is:
7.6811
You rounded to the nearest tenths place. The 6 in the tenths place rounds up to 7 because the digit to the right in the hundredths place is 8.
= 7.7
When the digit to the right is 5 or greater we round away from 0.
7.6811 was rounded up and away from zero to 7.7
Hence we get the required approximation.
Learn more about Square root here:
brainly.com/question/98314
#SPJ1
A survey of 780 was conducted while visiting Sonoma county on vacation. Each person was asked if they drank wine on their trip. 532 people responded "Yes".
What proportion of people did NOT drink wine in the survey? Round your answer to two decimal places.
Answer:
0.32
Step-by-step explanation:
[tex]\frac{780-532}{780}[/tex] = [tex]\frac{248}{780}[/tex] = 0.32 Rounded.
evaluate: p2(square) +3q2(square). p= -1/2. q= -2
Answer:
12 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
substitute the given values for p and q into the expression
p² + 3q²
= (- [tex]\frac{1}{2}[/tex] )² + 3(- 2)²
= [tex]\frac{1}{4}[/tex] + 3(4)
= [tex]\frac{1}{4}[/tex] + 12
= 12 [tex]\frac{1}{4}[/tex]
1. A circle is divided into 9 uneven pie shaped pieces. Each section is labeled 1, 2, ... 9. The circle is then spun and the number pointing north recorded. Estimate the probability that the next number pointing north will be between 2 and 7 inclusive.
4 3 2 1 9 8 5 6 7 4 3 2 1 5 8 6 5 4
13/18
5/18
5/8
8/5
2. How many shoppers made a purchase at a big-box store, or online, or at a locally- owned store?
250
359
380
400
3. How many shoppers made a purchase online and at a locally owned store, but not at a big box store?
38
56
109
179
The probability that the next number pointing north is between 2 and 7 is 13/18 .
1) The circle is divided into 9 parts.
Now the parts are uneven.
So the data about the spins is required to calculate the probability .
The total number of items in the box = 18
favorable outcomes (between 2 and 7) = 13 possible outcome.
Required probability
= favorable outcome / total outcome
= 13 / 18
2) Using the Venn diagram we can calculate the various parts of the problem:
Shoppers at big-box store or online or local store = sum of all the shoppers = 109+57+107+18+17+38+34 = 380 shoppers
3) Shoppers made purchase online or locally owned shop but not at a big box store = 107 + 38 + 34 = 179 shoppers.
To learn more about probability visit:
https://brainly.com/question/11234923
#SPJ1
The following table summarizes the results of a study on SAT prep courses, comparing SAT scores of students in a private preparation class, a high
school preparation class, and no preparation class. Use the information from the table to answer the remaining questions.
Treatment
Private prep class
High school prep class
No prep class
Number of Observations
Source
Between treatments
Within treatments
60
60
60
Using the data provided, complete the partial ANOVA summary table that follows. (Hint: T, the treatment total, can be calculated as the sample mean
times the number of observations. G, the grand total, can be calculated from the values of T once you have calculated them.)
Sum of Squares (SS)
21,000.00
442,500.00
df
2 ▼
Sample Mean
650
645
625
177
Sum of Squares (SS)
132,750.00
147,500.00
162,250.00
Mean Square (MS)
The F Test statistic is 1.58.
Given data is
Source SS df MS
between 21,000.00 2 6,000.00
within 442,500.00 117 3,782.00
The SStotal is sometimes easier to calculate than SSbetween Since ......
SSwithin +SSbetween = SStotal you can use SStotal to calculate SSbetween.
= 442,500+21,000 = 463,500
In ANOVA, the F test statistic is the ratio of the between - treatments variance and the within-treatments variance. The value of the F test statistic is 1.58 when the null hypothesis is true , the F test statistics is closer to 1, when the null hypothesis is false, the F test statistic is most likely large in general, you should reject null hypothesis for larger values of the F test statistic.
Hence the answer is the F Test statistic is 1.58.
To learn more about F test statistic, click here https://brainly.com/question/17256783
#SPJ9
At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh. Two hours later, the forecast for solar generation for 12 PM has changed from 4 GW to 4.5 GW. The market is currently bid at 95 pounds/MWh and offered at 105 pounds/MWh. What would you do, and why?
After 2 hours the plan needs to be changed, and purchase solar for the cost effect.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
It is given that:
At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh.
Total cost = 6x100 = 600 pounds
Total cost for 2 hours = 200 pounds
Two hours later, the forecast for solar generation for 12 PM has changed from 4 GW to 4.5 GW.
Total cost for this:
From 8 AM to 12 PM = Number of hours 4 hours
4.5 GW = 4500 MW
= 105 pounds/MWh
Total cost for 4 hours = 630 pounds for 4500 MW per hour
Thus, after 2 hours the plan needs to be changed, and purchase solar for the cost effect.
Learn more about the unit conversion here:
https://brainly.com/question/11543684
#SPJ1
The formula D = 5e -0.1h
can be used to find the number of milligrams D of a certain drug that is in a patient's
bloodstream h hours after the drug was administered. When the number of milligrams reaches 3, the drug is to be
administered again. What is the time between injections?
By Computing the Logarithmic Relation, we calculate that the time between injections is 5.1 hours or 5 hours and 6 minutes.
The given formula is
[tex]D = 5e^{-0.1h}[/tex]
where D is the amount of drug in milligrams in the patient's bloodstream and h is the number of hours after the drug was administered.
So, it is given that D = 3 and we need to evaluate the number of hours it took between the injections,
So, We have,
[tex]D = 5e^{-0.1h}[/tex]
[tex]\frac{D}{5} = e^{-0.1h}[/tex]
Taking Natural log on both sides, we have :
[tex]ln\frac{D}{5} =ln e^{-0.1h}\\\\ln\frac{D}{5} = -0.1h\\[/tex]
We have D = 3, putting it in the formula, we get
[tex]\ln\frac{3}{5} = -0.1h\\\\ln(0.6) = -0.1h\\\\-0.5108 = -0.1 h\\\\h = \frac{0.5108}{0.1} = 5.1[/tex]
Hence, the time between injections is 5.1 hours or 5 hours and 6 minutes.
To read more about Logarithmic Relations, visit https://brainly.com/question/12597250
#SPJ1
Draw and label the following figure.
Isosceles obtuse triangle with the obtuse vertex is angle T.
The Isosceles obtuse triangle in which the obtuse vertex is angle T is represented with the attached diagram.
What is an isosceles obtuse triangle?An isosceles obtuse triangle is a type of triangle which is formed by two equal sides of the triangle.
The vertex angle, which will be the obtuse one (x) can be x > 90°.The sum of the two base angles, y1 and y2, can be represented by y1 + y2 < 90 degrees.As long as the measures of the angles add up to 180°, it is an isosceles obtuse triangle.
An obtuse angle is an angle greater than 90 degrees but less than 180 degrees.
A triangle is a polygon with three sides and three angles. There are different types of triangle, which includes:
Equilateral triangleScalene triangleObtuse triangleIsosceles triangleRight angle triangleSo therefore, an isosceles obtuse triangle is formed by having two equal sides of a triangle.
Read more on isosceles triangle:
https://brainly.com/question/14368414
#SPJ1
Stefanie bought a package of pencils for \$ 1.75$1.75 and some erasers that cost \$ 0.25\$0.25 each. She paid a total of \$ 4.25$4.25 for these items, before tax
Exactly how many erasers did Stefanie buy?
The number of eraser Stefanie bought is 10.
How to find the number of eraser she bought?Stefanie bought a package of pencils for $1.75 and some erasers that cost $0.25 each. She paid a total of $4.25 for these items, before tax.
Therefore, the number of eraser Stefanie bought can be calculated as follows;
let
x = number of eraser bought
Therefore,
4.25 = 1.75 + 0.25x
subtract 1,75 from both sides of the equation
4.25 - 1.75 = 1.75 - 1.75 + 0.25x
2.5 = 0.25x
divide both sides by 0.25
x = 2.5 / 0.25
x = 10
Therefore,
number of eraser = 10
learn more on cost here: https://brainly.com/question/14132782
#SPJ1
3 years is to 4 , , ,
calculate the surface area of a cube that has a width of 25 centimeters
The surface area of a cube that has a width of 25 centimeters is 3750 cm².
What is surface area?It should be noted that surface area simply implies the measure of the total area that the surface of an object occupies.
In this case, the surface area of a cube is measured as 6a² where a = side
In this case, the side is 25. Therefore, the surface area will be:
= 6a²
= 6 × 25²
= 3750 cm²
Learn more about surface area on:
brainly.com/question/1297098
#SPJ1
Draw and label the following figure.
Scalene Right triangle RGH.
The scalene right triangle RGH is given by the image shown at the end of the answer.
What are the classification of triangles?There are two classifications of triangles, either regarding the side lengths or the angles.
Regarding the side lengths, the classifications are given as follows:
Scalene: Three different side lengths.Isosceles: Two equal side lengths.Equilateral: Three equal side lengths.Regarding the measure of the greatest angle, the classifications are given as follows:
Acute: The greatest angle has a measure that is less than 90º.Straight: The greatest angle has a measure that is exactly 90º.Obtuse: The greatest angle has a measure that is greater than 90º.In this problem, RGH is a scalene right triangle, hence:
The three sides have different lengths.There is an angle of 90º on the triangle.More can be learned about classification of triangles at https://brainly.com/question/16589630
#SPJ1
Find the distance between 7 and 18 on a number line.
Answer:
11
Step-by-step explanation:
Find the difference using subtraction:
18 - 7 = 11
So, the numbers are 11 units apart.
Which of the following is a disadvantage to a questionnaire?
A.
They are inexpensive to administer.
B.
The respondent controls the validity.
C.
The results can be confidential.
D.
They are time efficient.
A disadvantage of using a questionnaire is that B. The respondent controls the validity.
What is a disadvantage of using questionnaires?Questionnaires are a means of gathering data in research in order to find out more about a certain phenomenon. They involve writing questions and giving them to a respondent to fill out the answers.
Questionnaires are inexpensive to administer and can lead to confidential results which is good. However, they have the disadvantage that respondents control the validity of questionnaire results and can decide to lie if they feel it would make them look better, which would confuse the research results.
Find out more on questionnaires at https://brainly.com/question/15204986
#SPJ1
Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x = −7 and x = 5 and passes through the point (0, −2).
The formula of the parabola is y = 2/35(x + 7)(x - 5)
How to determine the formula of the parabola?The parameters in the question are given as
Horizontal intercepts (roots) at x = −7 and x = 5 Passes through the point (0, −2).These parameters can be represented as
x₁ = -7 and x₂ = 5
(x, y) = (0, -2)
The quadratic function can be represented as
y = a(x - x₁)(x - x₂)
Substitute the known values in the above equation So, we have the following equation
y = a(x + 7)(x - 5)
At (x, y) = (0, -2), we have
-2 = a(0 + 7)(0 - 5)
Evaluate
a = -2/-35
Divide
a = 2/35
So, we have
y = 2/35(x + 7)(x - 5)
Hence, the equation is y = 2/35(x + 7)(x - 5)
Read more about parabola at
https://brainly.com/question/1480401
#SPJ1
water is poured into a container in the shape of a right circular cone with a radius 4 inches and height 16 inches express the volume v of the water in the cone as a function of the height h of the water
The volume V of the water in the cone as a function of the height h of the water is,
V = (1/48)πh³
Given, water is poured into a container in the shape of a right circular cone with a radius 4 inches and height 16 inches.
We have to express the volume V of the water in the cone as a function of the height h of the water.
Now, at any instant let the height of the water in the cone be h and radius of the water in the cone be r,
So, using the concept of similarity in triangles
we get, r/4 = h/16
r = h/4
Now, the volume of the water in the cone be,
V = (1/3)πr²h
V = (1/3)π(h/4)²h
V = (1/48)πh³
So, the function expressing the volume of the water in the cone be,
V = (1/48)πh³
Hence, the volume V of the water in the cone as a function of the height h of the water is,
V = (1/48)πh³
Learn more about Volumes here https://brainly.com/question/463363
#SPJ9
Diego is solving this system of equations:
4x + 3y = 10
-4x + 5y = 6
Here is his work:
4x + 3y = 10
-4x + 5y =6
-4x + 5y = 6 +
0 + 8y = 16
y = 2
4x + 3(2) = 10
4x + 6 = 10
4x = 4
x = 1
The solutions of the equations are x = 1 and y = 2
The system of equations are
4x + 3y = 10
-4x + 5y = 6
Here we have to use the elimination method. Eliminate the x term and find the value of y term
Add both equation
3y + 5y = 10 +6
Add the like terms
8y = 16
y = 16 / 8
Divide the terms
y = 2
Substitute the value of x in the first equation
4x + 3y = 10
4x + 3×2 = 10
Multiply the terms
4x + 6 = 10
4x = 10 - 6
4x = 4
x = 4 / 4
Divide the terms
x = 1
Hence, the solutions of the equations are x = 1 and y = 2
Learn more about elimination method here
brainly.com/question/14619835
#SPJ1
a point lies on the line y=3x-2, its y coordinate is 25. what is the coordinates of this point?
Answer:
x=9 (9,25)
Step-by-step explanation:
9*7=27
27-2=25
Ordered pair for 2x+3y=5x-y
onsider the following equation:
3|x+3|−12=0
Step 1 of 4: Rewrite the equation above in standard form and determine if there is a solution.
The value of x in the following equation: 3|x+3|−12=0 is -7 and 1
The equation is 3|x+3|−12=0
We need to rewite the equation above in standard form
The modulus function can be positive and negative
Considering it to be negative,
the equation is
3((-1)(x + 3) - 12
3(-x - 3) - 12
-3x - 9 - 12 = 0
3x + 21 = 0
3x = -21
x = -7
3(x + 3) - 12
3x + 9 - 12
3x - 3 = 0
3x = 3
x = 1
Therefore, the value of x in the following equation: 3|x+3|−12=0 is -7 and 1
To learn more about the algebra refer here
brainly.com/question/4344214
#SPJ1
Triangles ABD and BCD are right-angled triangles.
A
5 cm
B
x cm
Work out the value of x.
Give your answer correct to 2 decimal places.
10 cm
D
4 cm
C
Let f(x) = -4x + 3 and g(x) = 6+ 7x Find the function. f/g (f/g)(x) =
The solution of the composite function (f/g)(x) is [tex]\frac{-4x+3}{6+7x}[/tex]
How to solve composite function?Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Composite function involves the composition of functions is combining two or more functions as a single function.
Therefore, let's solve the function below:
f(x) = -4x + 3
g(x) = 6 + 7x
Hence,
(f/g)(x) = f(x) / g(x)
Therefore,
f(x) / g(x) = [tex]\frac{-4x+3}{6+7x}[/tex]
learn more on function here: https://brainly.com/question/12375190
#SPJ1
Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four
Answer: 2(x+4) >3(x+7)-4
Step-by-step explanation:
Hope this helps
Answer:
2(n+4)≤3(n+7)-4
Step-by-step explanation:
The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4
What is a solution set to an inequality or an equation?
If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality.
We need to find the inequality of the statement given;
"Two times the sum of a number and four is no more; than three times the sum of the number and seven decreased by four"
Let n be the unknown number
Then it would be;
2(n+4) ≤ 3(n+ 7) - 4
Hence, The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4
Learn more about inequalities here:
brainly.com/question/27425770
...........................................PLEASE HELP ME
Answer:
They should pay AED 180 as interest.
Step-by-step explanation:
Simple interest:
P = The amount borrowed = AED 3000
R = rate of interest = 3% per year
t = time = 24 months = 24 ÷ 12 = 2 years
[tex]\sf \boxed{Interest = PRt}[/tex]
Substitute the values,
[tex]\sf = 3000 * \dfrac{3}{100}*2\\\\ = 30*3*2\\\\=AED \ 180[/tex]
Please show your work:
-5/2(8a - 2b) =
[tex]-\frac{5}{2} (8a - 2b) = ...[/tex] the answer for this question is zero (0)
How can the answer is zero?
The first thing that we should do is simplify questions.
[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (- 2b)\\= - 20a + 5b[/tex]
After that, we will search for "a" and "b" to solve the question. For me, i will search for "b" first.
[tex]- 20a + 5b \\5b = 20a\\b = \frac{20}{5} a\\b = 4a[/tex]
Next step is find the "a" by enter the "b" into the same question.
[tex]- 20a + 5b =\\20a = 5b\\20a = 5 (4a)\\20a = 20a\\a = 1[/tex]
After we find the "a" and "b", the next step is to enter it into the main question to find the right answer.
[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a - 2[4a]) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (-8a)\\= - 4a + 4a\\= -4 (1) + 4 (1)\\= -4 + 4\\= 0[/tex]
So, the answer is zero (0).
Learn more about algebra and variabel here: https://brainly.com/question/24389362?referrer=searchResults
#SPJ1
Answer:
[tex] - 20a + 5b[/tex]
Step-by-step explanation:
[tex] - \frac{5}{2} (8a - 2b)[/tex]
[tex] - \frac{5}{2} (8a) - \frac{5}{2} ( - 2b)[/tex]
[tex] - 20a + 5b[/tex]
given f(x)=2x-2, find f (-3)
Answer:
-8
Step-by-step explanation:
f(-3) = 2(-3)-2
f(-3) = -6 -2
f(-3) = -8
Answer:
[tex] \huge{f( - 3) = - 8}[/tex]
Step-by-step explanation:
[tex]f(x) = 2x - 2[/tex]
In order to find f(-3) we substitute the value of x that's -3 into f(x) that's wherever we find x in f(x) we substitute it with -3 and solve for f(-3).
We have
[tex]f( - 3) = 2( - 3) - 2 \\ = - 6 - 2 \\ = - 8[/tex]
We have the final answer as
[tex] \bold{f( - 3) = - 8}[/tex]
Hope this helps you
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 33 miles. If the two airplanes are 55 miles apart, how far has the eastbound airplane traveled?
The eastbound airplane traveled 44 miles far.
Given:
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 33 miles. If the two airplanes are 55 miles apart.
Let x be the eastbound airplane traveled.
we know that,
north and east direction are perpendicular and with hypotenuse 55 miles it forms a right angle triangle with side = 33 miles.
According to pythagorean theorem:
[tex]33^2+x^2=55^2[/tex]
[tex]x^{2} =55^2-33^2[/tex]
= 3025 - 1089
x = [tex]\sqrt{1936}[/tex]
= 44 miles.
Therefore The eastbound airplane traveled 44 miles far.
Learn more about the east traveled here:
https://brainly.com/question/20299363
#SPJ1