Answer
The shape of sampling distribution of ^p is approximately normal because n < greater than 0.05N and np (1-p) > less than 10.
Step-by-step explanation:
The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.
What is defined by the Central Limit Theorem?The distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n is defined by the central limit theorem, where:
The mean is [tex]\mu[/tex] = 9.The standard deviation is √p (1-p)/ n The shape is approximately normal.As long as these two conditions are respected:
n≤ N
np(1-p) > 10.
Here, we have the parameters
n= 700, p = 0.172, N= 15, 000
So, n/N = 0.0466 < 0.05
and, np(1-p)
= 700 x 0.172 ( 1- 0.172)
= 99.69 >10
Then the shape is approximately normal.
Learn more about Central Limit Theorem here: brainly.com/question/25800303
#SPJ1
Element X decays radioactively with a half life of 8 minutes. If there are 470 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 10 grams? y
The decay of Element X can be modeled by the equation:
N = N0 * (1/2)^(t/t1/2)
where N is the amount of Element X remaining after time t, N0 is the initial amount of Element X, t1/2 is the half-life of Element X, and ^(t/t1/2) denotes exponentiation with base 1/2.
We know that the initial amount of Element X is 470 grams, the half-life is 8 minutes, and we want to find the time it takes for Element X to decay to 10 grams. Let t be the time in minutes.
Then, we can set up the following equation:
10 = 470 * (1/2)^(t/8)
Dividing both sides by 470, we get:
(1/47) = (1/2)^(t/8)
Taking the natural logarithm of both sides, we get:
ln(1/47) = (t/8) * ln(1/2)
Solving for t, we get:
t = -8 * ln(47)/ln(2)
t ≈ 59.3
Therefore, it would take about 59.3 minutes, to the nearest tenth of a minute, for Element X to decay to 10 grams.
Find m < G in the image below (help asap please!!!)
Answer: m∠G = 41°
Step-by-step explanation:
Opposite angles of parallelograms are congruent. This means that m∠G = m∠E, so we can write an equation using the given information.
Given:
m∠G = m∠E
Substitue:
5x - 9 = 3x + 11
Add 9 to both sides of the equation:
5x = 3x + 20
Subtract 3x from both sides of the equation:
2x = 20
Divide both sides of the equation by 2:
x = 10
Then, we will substitute this value of x back into the expression for m∠G.
5x - 9 = 5(10) - 9 = 50 - 9 = 41°
Calculate the trade discount (in $). Round your answer to the nearest cent.
The trade discount is $15.75.
What is trade discount?A trade discount is a regular reduction from a product's regular, established price. The use of trade discounts allows a company to adjust the final price based on the volume or status of each customer.
It is important to note that trade discounts are not the same as early-payment discounts. (Early-payment discounts of 1% or 2% are typically recorded by the seller in an account such as Sales Discounts and by the buyer in an account such as Purchase Discounts using the periodic inventory method.) Neither the seller nor the buyer keeps a separate account for trade discounts.
We must first determine the product's list price in order to determine the trade discount.
List price: $75 plus $3.75 equals $78.75
As the trade discount rate is 20%, the following discount is offered:
Discount = 0.2 times List price = 0.2 times $78.75 = $15.75
The trade discount is therefore $15.75.
To know more about Discount visit:
brainly.com/question/3541148
#SPJ1
Is 5 9/10 bigger than 5 5/6?
Answer:
5 9/10
Step-by-step explanation:
find the same denominator
in this case 30
9x3=27 and 5x5=25
since 27 is bigger, the fraction is also bigger
Answer:
5\6 is smaller than 9\10
Step-by-step explanation:
Find the least common denominator or LCM of the two denominators:
LCM of 6 and 10 are 30
Next, find the equivalent fraction of both fractional numbers with denominator 30
For the 1st fraction, since 6 × 5 = 30,
[tex]\frac{5}{6} = \frac{5.5}{6.5} =\frac{25}{30}[/tex]
Likewise, for the 2nd fraction, since 10 × 3 = 30,
[tex]\frac{9}{10} =\frac{9.3}{10.3} =\frac{27}{30}[/tex]
Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction
[tex]\frac{25}{30} < \frac{27}{30} 0r \frac{5}{6} < \frac{9}{10}[/tex]
Dion bought 3 pounds of oranges and 2 pounds of grapefruit. Write an expression to represent the amount of money Dion spent on the fruit. Then evaluate the expression. How much did Dion spend?
Answer:
eeeeejjbbvvv g gyuuu u grrtyyu
Can someone help me please i really need help with this.
use the Remainder Theorem and synthetic division please
The value of the polynomial equations are
f ( -10 ) = 20201
f ( 2 ) = 17
f ( 3 ) = 142
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the polynomial equation be represented as A
Now , the value of A is
f ( x ) = 2x⁴ + x² - 10x + 1 be equation (1)
Now , when the value of x = -10
f ( -10 ) = 2 ( -10 )⁴ + ( -10 )² - 10 ( -10 ) + 1
On simplifying , we get
f ( -10 ) = 2 ( 10000 ) + 100 + 100 + 1
f ( -10 ) = 20000 + 201
f ( -10 ) = 20201
Now , when the value of x = 2
f ( 2 ) = 2 ( 2 )⁴ + ( 2 )² - 10 ( 2 ) + 1
On simplifying , we get
f ( 2 ) = 2 ( 16 ) + 4 - 20 + 1
f ( 2 ) = 32 - 15
f ( 2 ) = 17
Now , when the value of x = 3 , we get
f ( 3 ) = 2 ( 3 )⁴ + ( 3 )² - 10 ( 3 ) + 1
f ( 3 ) = 2 ( 81 ) + 9 - 30 + 1
f ( 3 ) = 162 - 20
f ( 3 ) = 142
Hence , the polynomial equations are solved
To learn more about polynomial equations click :
https://brainly.com/question/13199883
#SPJ1
Which correctly renames
7
8
and
5
6
using a common denominator?
A.
42
48
and
40
48
B.
42
48
and
30
48
C.
14
16
and
15
18
D.
28
24
and
20
24
Because the denominators of both fraction have been changed to 7/8=21/24 and 5/6=20/24, respectively,
What does it mean to be a denominator?In mathematics, a denominator is the lowest number in such a fraction that indicates how many equal parts are split into a whole. It is a fraction's divisor.
What term do you use instead of denominator?Divisor is another synonym for denominator. In a common fraction, the integer under the line is described by both of these terms. Similar to this, when discussing statistical values, the term "denominator" refers to the entire population or number out of which samples are selected.
Common denominator is going to be [tex]24[/tex]
[tex]8=2*2*2\\6=2*3\\24=2*2*2*3[/tex]
[tex]8[/tex] should be multiplied by [tex]3[/tex]
[tex]6[/tex] should be multiplied by [tex]4[/tex]
[tex]7/8=(7*3)/(8*3)=21/3\\5/6=(5*4)/(6*4)=20/24\\7/8=21/24\\5/6=20/24[/tex]
To know more about denominator visit:
https://brainly.com/question/9368188
#SPJ1
On a coordinate plane, the x-axis is labeled Number of Days and the y-axis is labeled Number of Computers. A line goes through points (3, 36), (4, 48), (5, 60). The graph shows a proportional relationship between the number of computers produced at a factory per day. In three days, 36 computers are produced; 48 computers are produced in 4 days; and 60 computers are produced in 5 days. Find the unit rate of computers per day using the graph. Unit rate: computers per da
The unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day.
What are computers?Computers are electronic devices that are used to store, process, and output data. They are used to perform a variety of tasks, from simple calculations to complex research projects. Computers consist of hardware, such as processors, memory, and storage devices, and software, which provides instructions for the hardware to follow.
The unit rate is the number of units produced per unit of time. To calculate the unit rate of computers per day using the graph, divide the number of computers produced by the number of days. Using the graph, 36 computers are produced in 3 days, 48 computers are produced in 4 days, and 60 computers are produced in 5 days.
Therefore, the unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day. The graph produced shows a proportional relationship between the number of computers produced at a factory per day.
For more questions related to graph,
https://brainly.com/question/17267403
#SPJ1
if x = 6 what is the value of x( 15 - x
Answer:
54
Step-by-step explanation:
I'm assuming you are referring to x = 6, then to find the value of x(15 - x).
If x = 6, we can substitute this value into the expression x(15 - x) to find its value:
x(15 - x) = 6(15 - 6) = 6(9) = 54
Therefore, if x = 6, then x(15 - x) = 54.
Hey there!
x(15 - x)
= 6(15 - 6)
= 6(15) + 6(-6)
= 90 - 36
= 54
Therefore, the answer should be about:
54
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
1. What is (f⋅g)(x)?
f(x)=x^2+2x−6
g(x)=x^4+3
Enter your answer in standard form in the box.
2. Question
WHAT IS : (f−g)(x)? its not the same question as 1
f(x)=x^4−x^2+9
g(x)=x^3+3x^2+12
Enter your answer in standard form in the box.
Answer:
[tex]\textsf{1.} \quad \left(f \cdot g \right)(x)=x^6+2x^5 -6x^4+3x^2+6x -18[/tex]
[tex]\textsf{2.} \quad\left(f -g \right)(x)=- x^4+x^2+2x-9[/tex]
Step-by-step explanation:
To calculate (f ⋅ g)(x), multiply function f(x) by function g(x) by distributing the parentheses:
[tex]\begin{aligned}\left(f \cdot g \right)(x)&=(x^2+2x-6)(x^4+3)\\&=x^2 \cdot x^4 +x^2 \cdot 3+2x \cdot x^4+2x \cdot 3 -6 \cdot x^4 -6 \cdot 3\\&=x^6+3x^2+2x^5+6x -6x^4 -18\\&=x^6+2x^5 -6x^4+3x^2+6x -18\\\end{aligned}[/tex]
To calculate (f - g)(x), subtract function g(x) from function f(x) by applying the distributive law -(a + b) = -a - b:
[tex]\begin{aligned}\left(f -g \right)(x)&=(x^2+2x-6) - (x^4+3)\\&=x^2+2x-6 - x^4-3\\&=- x^4+x^2+2x-6 -3\\&=- x^4+x^2+2x-9\end{aligned}[/tex]
Note: The standard form of a polynomial is expressed by writing the term with the highest degree first, followed by the other terms in order of decreasing powers.
A radioactive substance has a half-life of 8 years. How much of the original 3.2 grams of the substance would be left after 36 years? Which equation best models this situation?
The exponential function [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex] determines the amοunt of substance after 36 years to be 0.2 grams.
What is an exponential function?The fοrmula for an exponential functiοn is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The amοunt of a radioactive substance left after a certain number of half-lives can be calculated using the expοnential equation formula -
[tex]A = A_0 \times \frac{1}{2}^{\frac{t}{T}}[/tex]
where -
A0 is the initial amοunt of the substance
A is the amοunt of the substance remaining after t years
T is the half-life οf the substance
In this case, the half-life is 8 years, sο T = 8.
We want tο know how much of the original 3.2 grams of the substance wοuld be left after 36 years, so t = 36.
We can plug these values intο the formula to get -
[tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex]
A ≈ 0.2 grams
Therefοre, after 36 years, only about 0.2 grams of the original 3.2 grams of the substance wοuld be left.
The equation that best mοdels this situation is -
[tex]A = 3.3 \times \frac{1}{2}^{\frac{t}{8}}[/tex]
where A represents the amοunt of the substance remaining after t years, in grams.
Therefοre, the equation is [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex].
To learn mοre about exponential function from the given link
brainly.com/question/12626186
#SPJ1
Mr. Hamstra’s car holds 14 2/5 gallons of gas and averages 20 miles per gallon. About how far can Mr. Hamstra travel when his tank is 1/4 full?
Mr. Hamstra can travel about 70 miles when his tank is 1/4 full.
How is gas mileage calculated? What is it?The distance a car can go on a given quantity of gasoline is measured as gas mileage, also known as fuel efficiency. By dividing the distance driven by the amount of gasoline used, one may determine gas mileage. For instance, a car's gas mileage is 25 mpg (300/12 = 25) if it can go 300 miles on 12 gallons of petrol. Many variables, including traffic, speed, weather, road gradient, and vehicle maintenance, can have an impact on gas mileage.
Given that, Mr. Hamstra’s car holds 14 2/5 gallons of gas and averages 20 miles per gallon.
Thus, when his tank is 1/4 full, it contains:
1/4 * 14 2/5 = 14 2/5 / 4 = 3 1/2 gallons.
Hence, Mr. Hamstra can travel about 70 miles when his tank is 1/4 full.
Learn more about average here:
https://brainly.com/question/17661499
#SPJ1
what do right angles look like
The right angles would be named as:
3. ∠PNL 4. ∠PNO
How to Name Right Angles?Right angles can be named in a few different ways, depending on the context in which they are being used. One common way is:
Using three points: use the names of the three points that form the angle, with the vertex of the angle in the middle. For example, if the right angle is formed by the line segments AB and BC, you could name it angle ABC.
The sign "∠" means angle, therefore, it can be named also as ∠ABC.
Thus, the right angles in the given diagram can be named accordingly as:
∠PNL and ∠PNO
Learn more about right angles on:
https://brainly.com/question/64787
#SPJ1
Solve the right triangle. Round decimal answers to the nearest tenth.
Step-by-step explanation:
1) length of YZ:
[tex]YZ=\sqrt{XZ^2-XY^2} ;= > \ YZ=8.485=8.5;[/tex]
2) angle X:
[tex]m \angle X=arccos(\frac{XY}{XZ});= > \ m \angle X=arccos\frac{1}{3}=70.6 к;[/tex]
3) angle Z:
[tex]m \angle Z=arcsin(\frac{XY}{XZ});= > \ m \angle Z=arcsin\frac{1}{3}=19.4 к;[/tex]
Explain how you would find the area of the figure below
Any help will be awesome
The question in is the image
Find the measurment of line segement
DE and EF?
Answer:
Step-by-step explanation:
[tex]n\sqrt{2}=10[/tex]
Solve for n.
[tex]n\sqrt{2} =10\\\\\frac{n\sqrt{2} }{\sqrt{2} }=\frac{10}{\sqrt{2} }[/tex]
Rationalize the denominator.
[tex]n=\frac{10}{\sqrt{2} }\cdot \frac{\sqrt{2} }{\sqrt{2} }\\\\n=\frac{10\sqrt{2} }{2}[/tex]
Reduce to lowest terms.
[tex]n=\frac{10\sqrt{2} }{2} \div\frac{2}{2}\\\\n=5\sqrt{2}[/tex]
Yesterday, Dustin biked 4 1/2 miles, jogged 2 3/4 miles, and swam 3 1/8 miles. How many miles did he travel while exercising?
10 3/8. I had this exact question for homework and answered this and got it correct, so I'm pretty sure this is correct :)
70 points! Complete each proof using the most appropriate method.
All statements and reasons are shown below.
What is triangle?A triangle is a closed two-dimensional geometric shape that has three sides, three angles, and three vertices. Triangles are one of the basic shapes in geometry and can be classified according to the length of their sides (scalene, isosceles, or equilateral) or the size of their angles (acute, right, or obtuse). The sum of the angles of a triangle is always 180 degrees, and the Pythagorean theorem can be used to find the length of one side if the other two sides are known in a right triangle.
According to the given figure:
4. In ΔFGH and ΔFJH,
Statement Reason
GH = JH (Given)∠FGH = ∠FJH (each 90°)FH = FH (Common)ΔFGH ≅ ΔFJH (by R.H.S rule)5. In ΔTVY and ΔXWY,
Statement Reason
TY = XY (Given)∠TVY = ∠XWY (Given)∠VYT = ∠WYX (Vertically opposite angle)ΔTVY ≅ ΔXWY (by A.A.A rule) angle-angle-angle ruleTV = XW (by C.P.C.T)6. In ΔKML and ΔPMN,
Statement Reason
KL = PN (Given)∠KLM = ∠PNM (KL║NP and LN is transversal line, so this is alternate interior angle)∠LKM = ∠NPM (Alternate interior angle)ΔKML ≅ ΔPMN (by A.S.A rule) angle-side-angle ruleLM = NM (by C.P.C.T)To know more about types of triangle, visit:
https://brainly.com/question/1058720
#SPJ1
Question: What price should the restaurant sell the large square pizza (12 inch side) for, so that both pizzas cost the same amount per square inch?
According to the question the height of Ruben’s school is 360 inches.
What is school?School is a place where students can learn and grow in their knowledge. It is a place where students can gain an education and become well-rounded individuals. School is a place where people can make friends, learn from each other, and explore new ideas and topics. School is a place where teachers and staff provide guidance to help students succeed in their academics and extracurricular activities.
To find the height of Ruben’s school using similar triangles and a mirror, we can use the following formula:
height of school / height of Ruben = distance from mirror to school / distance from mirror to Ruben
Plugging in the given values, we get:
height of school / 72 = 425 / 85
Cross-multiplying and solving for height of school, we get:
height of school = 72 x 425 / 85
height of school = 360 inches
Therefore, the height of Ruben’s school is 360 inches.
To learn more about school
https://brainly.com/question/17145398
#SPJ1
Between ecery pair of distinct points, there is a positive unique number called the , which can be determined as the of the corresponding real numbers of the two points
The missing term of question is "distance".
Define distinct points?Distinct points refer to points that are not the same. In other words, if two or more points have different locations or coordinates, they are considered distinct points.
Distance is a measure of the length or space between two points, lines, or other objects. It is typically expressed as a non-negative number and can be determined using various formulas depending on the context and the nature of the objects being measured.
The missing term in the question is "distance". The sentence can be completed as:
"Between every pair of distinct points, there is a positive unique number called the "distance", which can be determined as the "absolute value of the difference" of the corresponding real numbers of the two points."
To know more about distance, visit:
https://brainly.com/question/26550516
#SPJ1
What is the value of 8.3?
The answer is 6.03 did this help?
$650 is invested in an account at 3
simple interest per year. Write an
explicit formula representing the
account balance in any given year,
and use this formula to find the
balance in the 25th year.
5. The value of the account at yearly intervals is given below.
6. The balance in the 25th year in the account will be $1,137.5.
What is simple interest?Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,
The formula for interest is written as,
I = (PRT)/100
5. The simple interest is given as,
I = 650 x (3/100)
I = $19.5
End of first year = 650 + 19.5 - $669.50
End of second year = 669.5 + 19.5 = $689
End of third year = 689 + 19.5 = $708.50
End of fourth year = 708.50 + 19.5 = $728
End of fifth year =728 + 19.5 = $747.50
6. The balance after 25 years is given as,
A = $650 + ($650 x 3 x 25) / 100
A = $650 + $487.5
A = $1,137.5
More about the simple interest link is given below.
https://brainly.com/question/2793278
#SPJ1
Find the value of the given expression, and most importantly show the steps please.
Answer:
Step-by-step explanation:
[tex]16^\frac{1}{n}=2[/tex] (since by definition [tex]\sqrt[n]{16} =16^\frac{1}{n}[/tex])
[tex](2^4)^\frac{1}{n}=2[/tex]
[tex]2^\frac{4}{n}=2[/tex]
[tex]2^\frac{4}{n}=2^1[/tex]
∴[tex]\frac{4}{n} =1[/tex] (indices must be equal when bases are equal)
∴[tex]n=4[/tex]
y = 3x² - 24x + 57
find the coordinates of the vertex
Answer:
(4,9)
Step-by-step explanation:
The word "vertex" isn't clear here. I'm assuming the question is referring to finding the stationary (turning) point. This can be found by finding the derivative (dy/dx).
To find the derivative we use the following formula:
[tex]y = ax^{n}\\ \frac{dy}{dx} = nax^{n-1}[/tex]
What this means is that for each term of the equation, we multiply by the current power and then reduce the power by 1. In the case of the question's equation, this will be done like this:
[tex]y = 3x^{2} - 24x + 57\\\frac{dy}{dx} = 6x - 24[/tex]
Now we can use this to find the stationary point, as stationary points are where the derivative (dy/dx) = 0:
6x - 24 = 0
6x = 24
x = 4
Through this we have found the x-coordinate of the stationary point, however we still need to find the y coordinate. This is done by substituting our x value back into the original equation (not the derivative):
y = 3(4)² - 24(4) + 57
y = 9
Therefore, the coordinates of the stationary point are (4,9)
Rahul bought a pencil for Rs. 73.50, a pen for Rs. 68.75 and a paint box for Rs. 112.35. He gave Rs. 500 to the shopkeeper and got back Rs. 345.40. He, however, returned Rs. 100 back to the shopkeeper. Was Rahul correct in returning Rs. 100 to the shopkeeper?
Answer:
Yes he was correct in returning the 100
Step-by-step explanation:
Pen 68.75
Pencil 73.50
Paint box 112.35
Add all together, you get 254.60
If he paid 500 to the shopkeeper, he will collect (500.00-254.60) =245.40
If the shopkeeper gave him 345.40, then he had an excess and should give back the 100
inverse trig ratio can someone pls answer the rest of these i don’t understand them answers are already there but i need to see how they are done
We're given the angle measure to be 46 for No. 8. The length of 1 leg is x and the hypotenuse is 28.
We can use cosine to solve this. Since cosine is adjacent over hypotenuse, we can do cos(46) = x/28. Cross multiply to get cos(46)*28 = x. That solves to be 19.5
Using this principle allows us to solve the other ones. I'll let you figure them out.
TLDR: We can use the definition of trig functions to plug in what we know and place variables where we don't have enough information to find the length of a side.
A recipe uses 4 cups of milk to make 20 servings. If the same amount of milk is used for each serving, how many servings can be made from three quarts?
Answer:
4=20
3=?
so 20×3 divide by 4 = 15
Step-by-step explanation:
Answer:25
Step-by-step explanation: 25 25 25
Which transformations map the strip pattern onto itself?
b b
b
b b
P
a reflection across a vertical line
a horizontal translation only
a horizontal translation and a gidé refecion
a horizontal translation and a 180° rotation
Answer:
The strip pattern has a vertical axis of symmetry, so a reflection across a vertical line will map the strip pattern onto itself. Therefore, the correct answer is "a reflection across a vertical line."
Step-by-step explanation: