The number of different choices for nine questions is 384, when at most one of questions 1 and 2 may be included among the nine.
Given, the exam instructions specify that at most one of questions 1 and 2 may be included among the nine.
We have to find the number of different choices for nine questions.
Now, using the concept of Permutation and Combinations we get
There will be three cases,
Case 1 : we include question 1
Case 2 : we include question 2
Case 3 : we neither include question 1 nor question 2
Case 1 :
question 1 is included, so question 2 can not be included and remaining 7 questions have 2 choices.
Case 2 :
question 2 is included, so question 1 can not be included and remaining 7 questions have 2 choices.
Case 3 :
neither question 1 nor question 2 is included and also remaining 7 questions have 2 choices.
Total choices = 2^7 + 2^7 + 2^7
So, the number of different choices of nine questions are 384.
Hence, the number of different choices of nine questions are 384, when at most one of questions 1 and 2 may be included among the nine.
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Select all the correct answers.
A pharmaceutical company claims that regular consumption of its new children's vitamin Increases the average number of hours that a
child sleeps each night. To test this claim, a researcher decided to conduct an experiment. The researcher randomly selected
500 children, grouped by age. Over the course of a year, half of the children received the children's vitamin and half of the children
received a placebo. At the end of the year, the researcher compared the average number of hours that the children in each group slept
each night.
Which statements about this study are true?
This study uses random sampling.
This study uses blinding.
This study uses blocking.
This study uses a repeated measures design.
This study uses a control group.
The statements that are true concerning the study that was carried out by the pharmaceutical company include the following: This study uses random sampling, This study uses blinding and This study uses a control group. That is option A, B and E.
What is a pharmaceutical company?A pharmaceutical company is defined as the company that has been certified to manufacture and distribute drugs such as the children's vitamin.
While selecting sample for the study, it was stated that 500 children grouped by age was randomly selected.
Out of the total samples, 250 was given the vitamin while the remaining half was given a placebo ( a blind) which would serve as concealment of the group allocation from them as they are serving as the control.
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Answer:
A,B,C,
Step-by-step explanation:
PLATO
How do you split a sentence into two simple sentences?
To split a sentence into two simple sentences, first, highlight the clauses while dividing sentences. When necessary, add subjects or other words in place of subordinating liners to make sub-clauses autonomous.
In the given question we have to explain how we split a sentence into two simple sentences.
As we know that;
A basic sentence typically consists of a subject, a verb, and maybe an object and modifiers. It only has one independent clause, though. Here are a few illustrations: She composed.
First, highlight the clauses while dividing sentences. When necessary, add subjects or other words in place of subordinating liners to make sub-clauses autonomous.
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1. In the figure below, segments LJ and A F are perpendicular. What is the value of x+y?
2. In the figure below, LJ is perpendicular-bisector of A F. What is the value of m + n?
1) The value of the expression x + y is; 30
2) The value of the expression m + n is; 16
How to solve Algebraic Expressions?1) We are told that segments LJ and A F are perpendicular. This means that; 4x + 50 = 90 and 7y - 50 = 90
Let us solve for x and y;
4x + 50 = 90
4x = 90 - 50
4x = 40
x = 10
Similarly;
7y - 50 = 90
7y = 90 + 50
7y = 140
y = 140/7
y = 20
Thus;
x + y = 10 + 20
x + y = 30
2) We are told that LJ is a perpendicular-bisector of A F. Thus;
AJ = FJ and AL = FL
Thus;
FL = AL gives;
3m = 42
m = 42/3
m = 14
Similarly;
2m + 3n = 34
2(14) + 3n = 34
28 + 3n = 34
3n = 6
n = 2
m + n = 14 + 2 = 16
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How long is the shortest route from Asheboro to Fort Jennings using the roads shown?
If necessary, round your answer to the nearest tenth.
miles
The shorted distance from Asheboro to Fort Jennings is, 20.4 miles.
What is Pythagorean theorem?
The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.
In this problem we have to find the shortest route from Asheboro to Fort Jennings using the roads shown.
From the given route the shorted distance from Asheboro to Fort Jennings is,
= 3 mi + 8 mi + (distance from North lean to Fort Jennings)
Let distance from North lean to Fort Jennings is x.
To find the value of x using Pythagorean theorem.
x^2 = 8^2 + 5^2
x^2 = 64 + 25
x^2 = 89
x = 9.433
x = 9.4
So, the total distance is, 3 mi + 8 mi + 9.4 mi =20.4 miles.
Hence, the shorted distance from Asheboro to Fort Jennings is, 20.4 miles.
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Complete question:
Complete question is attached below.
What is the slope of the line that passes through the points (2, -4) and (5, 2)? Write
your answer in simplest form.
Answer:
used formula
Step-by-step explanation:
y-y1=m(x-x1)
What is the measure of one of the central angles in the regular Pentagon What is the measure of one of the congruent base angles in triangle ABC?
The measure of one of the central angles of a regular pentagon is 72° .
In the question ,
a regular pentagon is given ,
we have to find the measure of one of central angle ,
we know that a pentagon has 5 equal sides .
and the sum of the central angles is 360° .
it is given that the pentagon is regular , So , all the central angles are equal in measure .
The central angle can be calculated using the formula ,
central angle = 360°/n , where n is number of sides .
substituting the value of number of sides as = 5 ,
we get ,
central angle = 360°/5 = 72° .
Therefore , the central angle is = 72° .
The given question is incomplete , the complete question is
What is the measure of one of the central angles in the regular Pentagon ?
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There are about 2.54 centimeters in 1 inch. if a segment is 2.7 centimeters long, how many inches is it, rounded to the nearest hundredth?
The number of inches made by a segment of 2.7 centimeters long, where 1 inch is 2.54 centimeters is 236 inches.
What is the symbol for an inch?Please also notice that the sign for inches is the double prime ("), not the double quotation mark, the straight quotation mark, or even (gasp!) the two consecutive single quotation marks (").
What exactly is 1 inch?The inch was defined as "three dry, spherical grains of barley set end to end lengthwise" during the early 14th century under King Edward II. The lengths of 12 poppy seeds together have also been used at various periods to define one inch. Since 1959, 2.54 cm has been the official definition of an inch.
From the above definition, we get that
The number of inches made by a segment of 2.7 centimeters long, where 1 inch is 2.54 centimeters is 236 inches.
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Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 7.
The area of the surface is 5/3 [tex]\sqrt{14}[/tex][tex]\pi[/tex]
Consider that the part of the plane x+2y +3z=1 that lies inside the cylinder [tex]x^{2}[/tex] + [tex]y^{2}[/tex] =5
The surface area of an equation z= g(x,y) is given by the following formula:
[tex]\int\limits^d_d \sqrt {\alpha z/\alpha x]^{2} . [\alpha z/\alpha y]^{2} +1da[/tex]
where the D is the domain of integration.
Since the plane lies inside the cylinder[tex]x^{2}[/tex] + [tex]y^{2}[/tex] = 5, we have the domain of
D= ( (r,0) |0 [tex]\leq[/tex]r [tex]\leq[/tex][tex]\sqrt{5}[/tex],0[tex]\leq[/tex]θ[tex]\leq[/tex]2[tex]\pi[/tex])
The partial derivatives of z = 1/3 ( 1 - x - 2y) are
[tex]\alpha z/ \alpha x[/tex] = 1/3, [tex]\alpha z / \alpha y[/tex] = - 2/3
[tex]\int\limits^d_d \sqrt {[-1/3]^{2} . [-2/3]^{2} +1da[/tex]
= [tex]\int\limits^d_d \sqrt{14} / 9 da[/tex]
= [tex]\sqrt{14}/3 \int\limits^0_ {2^{\pi }[/tex] [tex]\int\limits^\sqrt{5[/tex]r dr dθ
Evaluating the integral we have
[tex]\sqrt{14}/3 \int\limits^0_ {2^{\pi }[/tex][tex]\int\limits^\sqrt{5[/tex]rdrdθ = [tex]\sqrt{14} /3[/tex] 2 [tex]\pi[/tex] [ 5/2]
= 5/3 [tex]\sqrt{14}[/tex][tex]\pi[/tex]
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1) x-2y=15
2) x-3=4y
A) rearrange equation (2) to make x the ubject
B) uing your anwer to part a) olve the imultaneou equation uing ubtitution
x= -9 and y= -3
What is equation?
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
A) rearranging equation (2) to make x the subject
[tex]x-3=4y\\x-4y=3[/tex]
Also,
[tex]4y=x-3\\y=(x-3)/4[/tex]
by subtitution method
putting this value of y in equation 1)
[tex]x-2((x-3)/4)=15\\\\x-2x+6=15\\x=-9\\y=(-9-3)/4\\y=-3[/tex]
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Solve for ttt:
-18 = -3t−18=−3t
Answer: 4z
Step-by-step explanation:
I need help with question number 10 the question says Ash has 61 toothpicks but do I keep increasing by 1 until I get 61?
The largest figure that Ash can built with 61 toothpicks is of:
A composition of 12 hexagons.
How to obtain the largest figure?The number of toothpicks needed is modeled with a linear function, defined as follows:
y = mx + b.
The coefficients of the function are given as follows:
m is the slope, representing the number of toothpicks per new figure.b is the y-intercept, representing the number of toothpicks of the first figure.The number of toothpicks in each figure is represented by the following sequence:
(6, 11, 16, ...).
Hence the parameters are given as follows:
m = 5, b = 6.
Thus the definition of the function is of:
T(n) = 5(n - 1) + 6. (as the first figure is with n = 1).
T(n) = 5n + 1.
Then the number of hexagons with 61 toothpicks is obtained as follows:
5n + 1 = 61
5n = 60
n = 60/5
n = 12 hexagons.
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Which president proposed the creation of the Environmental Protection Agency ?
President Richard Nixon proposed the creation of The Environmental Protection Agency (EPA).
What is the Environmental Protection Agency?
The Environmental Protection Agency is an independent government agency of the United States, which was considered mandatory by the government for environmental issues.
The Agency followed a series of measures to improve air quality, decrease greenhouse gas emissions, forbid water pollution, and invest in oil spill control measures.
The EPA had many obligations in the United States, two of which were to set industry standards to reduce their impact on the environment and investigate air pollution.
How did the EPA launch?
The operation of the agency began on December 2, 1970, after President Nixon had signed an executive order. The order established by the EPA was made official by signing by the committee hearings in the House and Senate.
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You plug your phone in to charge. After 10 mins your phone is at 30%. If your phone is charging at a rate of 5% every 2 minutes, write an equation in point slope form representing the battery percent,y, after x minutes.
y-5=3(x-2) is the equation in point slope form representing the battery percent, y, after x minutes.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
After 10 mins your phone is at 30%.
If your phone is charging at a rate of 5% every 2 minutes,
4 minutes=10%
6 minutes=15%
8 minutes=20%
10 minutes=25 %
The equation of point slope form.
y-5=3(x-2)
Hence, y-5=3(x-2) is the equation in point slope form representing the battery percent, y, after x minutes.
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I need help please. I’m struggling.
option 3
The mean is the same as the average.
Use the information to answer the following question.
Carolyn was asked to solve the following system of equations.
Her work is shown.
Step 1: 3x – 2y = 7
Step 2: 3x – 2(x + 2) = 7
Step 3: 3x – 2x + 4 = 7
Step 4: x + 4 = 7
Step 5: x = 3
Step 6: y = x + 2
Step 7: y = 3 + 2
Step 8: y = 5
Solution: (3, 5)
Did Carolyn make an error in her work?
Yes, Carolyn did not correctly combine like terms in Step 2.
Yes, Carolyn should have substituted the x-value into the first equation in Step 6.
No, Carolyn solved the system of equations correctly.
Yes, Carolyn did not correctly distribute the negative in Step 3.
Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.
System of EquationsA system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.
3x – 2y = 7
3x – 2(x + 2) = 7
3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).
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Help with question 3
Answer:
3.75
Step-by-step explanation:
I BELIVE YOUR ANSWER IS 3.75
Answer:
3.75
Step-by-step explanation:
How do you dilate an image with a scale factor?
To dilate an image with a scale factor, multiply the scale factor with the dimensions of the image
The dilation is the process of changing the size of the given shape or figure ,the shape of the figure will be always same. Therefore dilation is one form transformation of shapes
The scale factor is the ratio of the measurement of the new shape to the measurement of the original shape.
We can use the scale factor for the dilation
To get the dilate and image with scale factor, we have to multiply the scale factor with the measurement of the original shape
The equation will be
The dimension after dilation = scale factor × original dimensions
Therefore, to dilate an image, multiply the scale factor and the original dimensions
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c(1) = -20
c(n) = c(n − 1) + 10
Find the 2nd term in the sequence.
Answer:
-10
Step-by-step explanation:
So we are going to find c(2)
c(2)=c(1)+10
c(2)=-20+10
c(2)=-10
Which graph represents y=^3square root x
a combination lock requires three selections of numbers, each from 1 through 35. suppose the lock is constructed in such a way that no number may be used twice in a row, but the same number may occur both first and third. for example, 20 13 20 would be acceptable, but 20 20 13 would not. how many different combinations are possible? to answer this question, note that some combinations will consist of three different numbers, whereas in others the first and third numbers can be the same. the total number of combinations is
Answer:
Below
Step-by-step explanation:
35 choices for first number
34 choices for second number (because it cannot be same as first)
34 choices for third number ( because it cannot be same a second)
35 x 34 x 34 = 40 460 combos
Rewrite the function by completeing the square x^2-x-20
By algebra properties, the quadratic function x² - x - 20 = 0 is equivalent to the quadratic function (x + 1 / 2)² - 81 / 4 = 0.
How to complete the quadratic function
In this problem we have a quadratic function whose form does not correspond with a perfect square trinomial, that is, a polynomial of the form (x + a)² = x² + 2 · a · x + a². Herein we can modify part of the function by means of completing the square, an application of algebra properties.
First, write the quadratic function described in the statement:
x² - x - 20 = 0
Second, use algebra properties until the square is complete:
x² - x - 20 = 0
x² - x = 20
x² - x + 1 / 4 = 20 + 1 / 4
(x + 1 / 2)² = 81 / 4
(x + 1 / 2)² - 81 / 4 = 0
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There are about 2.54 centimeters in 1 inch. if a segment is 2.7 centimeters long, how many inches is it, rounded to the nearest hundredth?
The number of inches of a segment is 1.06 inches if a segment is 2.7 centimeters long.
What is meant by line segment?In geometry, a line segment is a portion of a straight line that is bounded by two distinct end points and includes all of the points on the line that fall inside those endpoints. A line segment's length is determined by the Euclidean distance between its endpoints.
In geometry, a line segment is a portion of a straight line that is bounded by two distinct end points and includes all of the points on the line that fall inside those endpoints. A line segment's length is determined by the Euclidean distance between its endpoints.
Given,
In 1 inch there are about 2.54centimeters
And the segment is 2.7 centimeters long
The number of inches=?
2.7/2.54=1.0629
When it is rounded to the nearest 100, we get
1.06 inches.
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What is the mode when mean is 15 and median is 10?
The mode in this situation is not defined because there is only one value for each of the mean and median.
Mean (15) and median (10) are two different measures of central tendency. The mean is the average of all values, while the median is the middle value when all the values are arranged in order. The mode is the most frequent value in a set of data, and there can be more than one mode. Since there is only one value for both the mean and median, there is no mode in this situation.
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Idenify the slope and y-intercept
Answer:
The slope is -2 and the y-intercept is (0,1)
H(t)= 50- t/5
H(35)=
Please explain it
The value of the function H(t) = 50 - t / 5 at t = 35 will be 43.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
H(t) = 50 - t / 5
At t = 35, the value of the function will be given as,
H(35) = 50 - 35 / 5
H(35) = 50 - 7
H(35) = 43
The value of the function H(t) = 50 - t / 5 at t = 35 will be 43.
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30.9 divided by 100
PLEASE I NEED HELP ASAP
Answer:
0.309
Step-by-step explanation:
How do you solve an equation with 2 answers?
The quadratic formula x = [-b (b2 - 4ac)] / 2a] provides the solutions to the quadratic equation ax2 + bx + c = 0. (2a).
Given,
Equation with two answers are quadratic equations.
Quadratic equation;
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).
The solution for quadratic equation;
The quadratic formula x = [-b (b2 - 4ac)] / 2a]gives the solutions to the quadratic equation ax2 + bx + c = 0. (2a). Get the problem into standard form, ax2 + bx + c = 0, and then use the quadratic formula to solve the quadratic equation.
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9(-2)
Help I don't get it :'(
So, let's think about what it's asking
it next to the parentheses means to distribute, or multiply into.
Multiply 9 * -2
A negative times a positive is a negative.
9 * 2 = 9 + 9 = 18
Make the final answer negative because its a positive and a negative multiplied. A positive and a positive multiplied gives you a positive. A negative and a negative multiplied gives you a positive too.
-18
PLS HELP AND PLS PUT THE WORK!!!!****, PLS ASAP
In a game, the probability of winning is 20%. If i play 48 times, how many times should I expect to win?
Answer:
Step-by-step explanation:
I will try to get the answer for you just give me a minute.!
Which function is used to calculate maximum value?
Derivatives is used to calculate the maximum value of a function.
We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.
Derivatives
The rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.
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