Answer: The correct option is
(E) 70.
Step-by-step explanation: We are given to find the number of triangles and quadrilaterals altogether that can be formed using the vertices of a 7-sided regular polygon.
To form a triangle, we need any 3 vertices of the 7-sided regular polygon. So, the number of triangles that can be formed is
[tex]n_t=^7C_3=\dfrac{7!}{3!(7-3)!}=\dfrac{7\times6\times5\times4!}{3\times2\times1\times4!}=35.[/tex]
Also, to form a quadrilateral, we need any 4 vertices of the 7-sided regular polygon. So, the number of quadrilateral that can be formed is
[tex]n_q=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.[/tex]
Therefore, the total number of triangles and quadrilaterals is
[tex]n=n_t+n_q=35+35=70.[/tex]
Thus, option (E) is CORRECT.
What is the slope of the line through (-10,1)(−10,1)left parenthesis, minus, 10, comma, 1, right parenthesis and (0,-4)(0,−4)left parenthesis, 0, comma, minus, 4, right parenthesis?
Answer:
-1/2
Step-by-step explanation:
Slope is calculated as ...
(change in y)/(change in x) = (y2 -y1)/(x2 -x1)
= (-4 -1)/(0 -(-10)) = -5/10 = -1/2
The slope of the line is -1/2.
If A, B, and C are integers between 1 and 10 (inclusive), how many different combinations of A, B, and C exist such that A
[tex]\fontsize{18}{10}{\textup{\textbf{The number of different combinations is 120.}}}[/tex]
Step-by-step explanation:
A, B and C are integers between 1 and 10 such that A<B<C.
The value of A can be minimum 1 and maximum 8.
If A = 1, B = 2, then C can be one of 3, 4, 5, 6, 7, 8, 9, 10 (8 options).
If A = 1, B = 3, then C has 7 options (4, 5, 6, 7, 8, 9, 10).
If A = 1, B = 4, then C has 6 options (5, 6, 7, 8, 9, 10).
If A = 1, B = 5, then C has 5 options (6, 7, 8, 10).
If A = 1, B = 6, then C has 4 options (7, 8, 9, 10).
If A = 1, B = 7, then C has 3 options (8, 9, 10).
If A = 1, B = 8, then C has 2 options (9, 10).
If A = 1, B = 9, then C has 1 option (10).
So, if A = 1, then the number of combinations is
[tex]n_1=1+2+3+4+5+6+7+8=\dfrac{8(8+1)}{2}=36.[/tex]
Similarly, if A = 2, then the number of combinations is
[tex]n_2=1+2+3+4+5+6+7=\dfrac{7(7+1)}{2}=28.[/tex]
If A = 3, then the number of combinations is
[tex]n_3=1+2+3+4+5+6=\dfrac{6(6+1)}{2}=21.[/tex]
If A = 4, then the number of combinations is
[tex]n_4=1+2+3+4+5=\dfrac{5(5+1)}{2}=15.[/tex]
If A = 5, then the number of combinations is
[tex]n_5=1+2+3+4=\dfrac{4(4+1)}{2}=10.[/tex]
If A = 6, then the number of combinations is
[tex]n_6=1+2+3=\dfrac{3(3+1)}{2}=6.[/tex]
If A = 7, then the number of combinations is
[tex]n_7=1+2=\dfrac{2(2+1)}{2}=3.[/tex]
If A = 3, then the number of combinations is
[tex]n_8=1.[/tex]
Therefore, the total number of combinations is
[tex]n\\\\=n_1+n_2+n_3+n_4+n_5+n_6+n_7+n_8\\\\=36+28+21+15+10+6+3+1\\\\=120.[/tex]
Thus, the required number of different combinations is 120.
Learn more#
Question : ow many types of zygotic combinations are possible between a cross AaBBCcDd × AAbbCcDD?
Link : https://brainly.in/question/4909567.
The base of a solid in the region bounded by the graphs of y = e-x y = 0, and x = 0, and x = 1. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid?
a) π /16 e^2
b) π /16 (1-1/e^2)
c) π/4(1-1/e^2)
d) π/16(e^2-1)
Answer:
b) π /16 (1-1/e^2)
Step-by-step explanation:
For this case we have the following limits:
[tex]y =e^{-x} , y=0, x=0, x=1[/tex]
And we have semicircles perpendicular cross sections.
The area of interest is the enclosed on the picture attached.
So we are assuming that the diameter for any cross section on the region of interest have a diameter of [tex]D=e^{-x}[/tex]
And then we can find the volume of a semicircular cross section with the following formula:
[tex]V= \frac{1}{2}\pi (\frac{e^{-x}}{2})^2 dx= \frac{1}{8} \pi e^{-2x}[/tex]
And for th volum we can integrate respect to x and the limits for x are from 0 to 1, so then the volume would be given by this:
[tex]V= \pi \int_0^{1} \frac{1}{8} \pi e^{-2x} dx[/tex]
[tex] V= -\frac{\pi}{16} e^{-2x} \Big|_0^1 [/tex]
And evaluating the integral using the fundamental theorem of calculus we got:
[tex]V = -\frac{\pi}{16} (e^{-2} -1)= \frac{\pi}{16}(e^{-2} -1)=\frac{\pi}{16} (1-\frac{1}{e^2})[/tex]
And then the best option would be:
b) π /16 (1-1/e^2)
Suppose an oligopoly consists of two firms. Firm A lowers price and Firm B responds by lowering its price by the same amount. If average costs and industry output remain the same, which of the following will occur?
Answer:
The profits for firma A and B will decrease.
Step-by-step explanation:
Oligopoly by definition "is a market structure with a small number of firms, none of which can keep the others from having significant influence. The concentration ratio measures the market share of the largest firms".
If the costs remain the same for both companies and both firms decrease the prices then we will have a decrease of profits, we can see this on the figure attached.
We have an equilibrium price (let's assume X) and when we decrease a price and we have the same level of output the area below the curve would be lower and then we will have less profits for both companies.
Indra baked and frosted a rectangular cake to sell at a bake sale for the Model UN club. The cake, including frosting, was 4 inches high, 16 inches wide, and 12 inches long. She centered the cake on a circular tray. The circular tray had a radius of 10 inches. What is the area, to the nearest square inch, of the tray that is not covered by the cake?
A. 100
B. 114
C. 122
D. 314
E. 192
Answer:
C. 122
Step-by-step explanation:
Given,
Dimension of the cake:
Length = 12 in Width = 16 in Height = 4 in
We have to find out the area of the tray that is not covered by the cake.
Indra centered the cake on a circular tray.
Radius of the tray = 10 in.
So area of the tray is equal to π times square of the radius.
Framing in equation form, we get;
Area of tray =[tex]\pi\times r^2=3.14\times{10}^2=3.14\times 100=314\ in^2[/tex]
Since the cake is placed in circular tray.
That means only base area of cake has covered the tray.
Base Area of cake = [tex]length\times width=12\times 16=192\ in^2[/tex]
Area of the tray that is not covered by the cake is calculated by subtracting area of base of cake from area of circular tray.
We can frame it in equation form as;
Area of the tray that is not covered by the cake = Area of tray - Base Area of cake
Area of the tray that is not covered by the cake =[tex]314-192=122\ in^2[/tex]
Hence The area of the tray that is not covered by the cake is 122 sq. in.
When the results of an experiment can be applied to real-world conditions, that experiment is said to have _____
Answer:
Ecological validity
Step-by-step explanation:
Well, to complete the sentence, first we need to be aware of types of validity of experiments such as criterion validity, ecological validity, content validity , factorial validity, etc.
In this particular example, it is stated that the results of an experiment can be applied to real-world conditions. Therefore, the experiment is said to have ecological validity considering the fact that results applied to real-world conditions.
When the results of an experiment can be applied to real-world conditions, that experiment is said to have external validity.
External validity refers to the degree to which the findings of a study can be generalised beyond the study's specific conditions to real-world situations. It's crucial for research to have external validity to ensure its applicability and relevance outside of the laboratory setting.
And international calling plan charges a rate per minute plus a flat fee. A 10 minute call to France costs $4.29. Right and solve a linear equation to find the cost of a 12 minute call to France
Answer:
The cost of a 12 minute call to France is $ 3.63
Step-by-step explanation:
given:
The cost of 15 minute call to France = $ 4.29
The cost of 10 minute call to France = $ 3.19
To Find :
The cost of a 12 minute call to France = ?
Solution:
Let the flat fee be X
and the cost per minute be Y
so the 15 minute call to France will be
X + 15(Y) = 4.29---------------------------(1)
the 10 minute call to France will be
X + 10(X) = 3.19----------------------------(2)
Subtracting (2) from (1)
X + 15(Y) = 4.29
X + 10(Y) = 3.19
- - -
---------------------------------
5Y = 1.10
--------------------------------
[tex]Y =\frac{1.10}{5}[/tex]
Y = 0.22
So the cost per minute of a call = $0.22
substituting the values in (1)
X + 15(0.22) = 4.29
X + 3.3 = 4.29
X = 4.29 -3.3
X = 0.99
Now the cost of 12 minute call is
=>X + 12(Y)
=> 0.99 + 12(0.22)
=> 0.99 + 2.64
=> 3.63
. Jane is practicing solving systems of equations by inspection. She thinks that y = 5 6 x + 2 and y = 5 6 x – 2 would have exactly one solution. Is she correct? Why or why not?
Answer:
No solution , The line's are parallel
Step-by-step explanation:
Given set of equations are y = 56x + 2 and y = 56x - 2
If we observe carefully these lines are in the form of y=mx+c where m is the slope of the line and c is the y-intercept
Here both the line's have slope m = 56
We also know that two lines are parallel only if their slopes are equal ie m1=m2
Here the two line's have same slope, so the giventwo line's are parallel And they don't have a solution So jane is wrong.
Do men and women differ, on average, in terms of the amount of television that they watch each day? A researcher conducted a hypothetical study in which he randomly selected 50 men and 50 women and recorded the number of minutes of television watched during the previous day. The researcher wanted to determine whether there is a difference in mean number of minutes of television viewing between men and women. What hypothesis testing technique should the researcher use to analyze the data?
Answer: Two-sample t-test
Step-by-step explanation:
The Two-sample t-test is used to test the difference between two random and distinct population means. It help test whether the difference between the two populations is statistically significant.
In the case above the researcher wants to determine whether there is a difference in mean number of minutes of television viewing between men and women which makes it a Two-sample t-test.
.
The number -13 can be classified as:
real and natural
real and whole
real and integer
real and irrational
Number -13 is classified as real and integer
Solution:
Given that The number -13 can be classified as
Let us first understand about real numbers, whole numbers, Integers and irrational numbers
Whole numbers:Whole numbers are positive numbers, including zero, without any decimal or fractional parts. Negative numbers are not considered "whole numbers."
But -13 is a negative number. Therefore -13 is not a whole number
Real numbers:Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers. They are called "Real Numbers" because they are not Imaginary Numbers.
Therefore -13 is a real number
Integers:An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043.
Therefore -13 is a integer
Irrational number:An irrational number is real number that cannot be expressed as a ratio of two integers. An irrational number is not able to be written as a simple fraction because the numbers in the decimal of a fraction would go on forever
But -13 can be expressed in fraction as [tex]-13 \div 1[/tex]
Therefore -13 is not a irrational number
Thus we can conclude that number -13 is classified as real and integer
Mandy is building a rectangular garden pond with the area on 12ft^2. The length of the pool needs to be 2ft more than twice that width. What are the dimensions of the pool
Answer: the length is 6 feet. The width is 2 feet
Step-by-step explanation:
The garden pool is rectangular in shape.
Let L represent the length of the rectangular garden.
Let W represent the width of the rectangular garden.
The area of a rectangle is expressed as L× W. The area of the rectangular garden pond is 12ft^2. It means that
L× W = 12 - - - - - - - - - - 1
The length of the pool needs to be 2ft more than twice that width. This means that
L = 2W + 2 - - - - - - - - - - - 2
Substituting equation 2 into equation 1, it becomes
W(2W + 2) = 12
2W^2 + 2W = 12
2W^2 + 2W - 12 = 0
W^2 + W - 6 = 0
W^2 + 3W - 2W - 6 = 0
W(W + 3) - 2(W + 3) = 0
W - 2 = 0 or W + 3 = 0
W = 2 or W = - 3
Since the Width cannot be negative, then the width is 2 feet
Substituting W = 2 into equation 2. It becomes
L = 2×2 + 2 = 6 feet
K12: Graph the image of this triangle after a dilation with a scale factor of 3 centered at the origin.
Use the polygon tool to graph the triangle.
The points after Dilation are (0,0), (9,-3), and (9,9).
Step-by-step explanation:
The given points are A(0,0), B(3,-1), and C(3,3).
The scale factor is 3.
[tex]D_{new}[/tex]([tex]p_{x} , p_{y}[/tex]) = scale factor × ([tex]p_{x} , p_{y}[/tex]) .
If the triangle starts form the origin (0,0) retains the same after the dilation.
[tex]D_{Anew}(p_{x} , p_{y})[/tex]= (0,0).
For point B(-1,3),
[tex]D_{Bnew}(p_{x} , p_{y})[/tex] = 3 × (3,-1).
[tex]D_{Bnew}(p_{x} , p_{y})[/tex] = (9,-3).
For Point C(3,3),
[tex]D_{Cnew}(p_{x} , p_{y})[/tex] = 3 × ( 3,3).
[tex]D_{Cnew}(p_{x} , p_{y})[/tex] = ( 9,9).
Refer the graph for dilated triangle.
Rachel is collecting donations for the local animal shelter. So far she has collected $245, which is 70% of what she hopes to collect. How much money does Rachel plan to collect for the shelter? Show your work.
Answer:
The money Rachael plan to collect for the shelter is $350.
Step-by-step explanation:
Given:
Rachel is collecting donations for the local animal shelter.
So far she has collected $245, which is 70% of what she hopes to collect.
Now, to find the money Rachael plan to collect for the shelter.
Let the total amount Rachael plan to collect be [tex]x[/tex].
Amount she collected = $245.
Percentage of amount she collected = 70%.
Now, to get the amount Rachael plan to collect we put an equation:
[tex]70\%\ of\ x=\$245.[/tex]
⇒ [tex]\frac{70}{100} \times x=245[/tex]
⇒ [tex]0.70\times x=245[/tex]
⇒ [tex]0.70x=245[/tex]
Dividing both sides by 0.70 we get:
⇒ [tex]x=\$350.[/tex]
Therefore, the money Rachael plan to collect for the shelter is $350.
90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?A. 125B. 150C. 225D. 250E. 500
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
90 students represent x percent of the boys at Jones Elementary School.
So, it is expressed as
[tex]90=\dfrac{x}{100}[/tex]
If the boys at Jones Elementary make up 40% of the total school population of x students,
[tex]90=\dfrac{x}{100}\times 0.4x\\\\9000=0.4x^2\\\\\dfrac{9000}{0.4}=x^2\\\\22500=x^2\\\\x=\sqrt{22500}\\\\x=150[/tex]
Hence, the value of x is 150.
Therefore, Option 'B' is correct.
HELP PLEASE:
Sketch the graph of the given function. Then state the function’s domain and range. f(x)= (1/3)^x+2
Answer:
Domain: set of all real numbers; (-∞, ∞)
Range : {y | y f > 2}
Check the attached figure to visualize the graph.
Step-by-step explanation:
The graph of the given function is attached. Please check the attached figure.
As the function is given as:
[tex]f(x) = (\frac{1}{3})^{x} +2[/tex]
As the table of some of the values of x and y values for [tex]f(x) = (\frac{1}{3})^{x} +2[/tex] is given as follows:
x y-2 11
-1 5
0 3
1 2.33
2 2.111
Hence, it is clear that the function is defined for every input value of x. So, domain is the set of all real numbers.
Domain: set of all real numbers; (-∞, ∞)
If we carefully analyze the graph of this function, it is clear that no matter what input value of x we put, range or y-value of this function would always be be greater than 2. Check the attached graph figure to better visualize the range of the function.
Range can also be denoted as: Range : {y | y f > 2}
Keywords: graph, function, domain and range
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Chris uncle from japan promised to give him 42 g of gold .The local jewelry exchange will buy gold for $1286 per once.How much money can Chris get for selling the gold?
Answer:
Chris will make $1905.22 by selling gold.
Step-by-step explanation:
Amount of gold Chris will have = 42 g
Current rate of gold = $1286 per ounce
We need to find the amount Chris will make after selling the gold.
Now we will first find Current rate of gold in grams.
We know that 1 ounce = 28.3495 grams.
So we can say that
28.3495 g = $1286
So 1 g = Rate of gold for 1 gram.
By Using Unitary method we get;
Rate of gold for 1 gram = [tex]\frac{1286}{28.3495} \approx \$45.3624[/tex]
Now we will find the amount for 42 g of gold
if 1 g = $45.3624
so 42 g = Amount of money for 42 g
Again by using Unitary method we get;
Amount of money for 42 g = [tex]42 \times 45.3624 \approx \$1905.22[/tex]
Hence Chris will make $1905.22 by selling gold.
Chris can get $1,736.10 by selling 42 grams of gold.
Chris's uncle from Japan has promised to give him 42 grams of gold. The local jewellery exchange will buy gold for $1286 per ounce. To find out how much money Chris can get for selling the gold, we need to convert grams to ounces and then multiply by the price per ounce. There are approximately 31.1035 grams in an ounce. So, to convert grams to ounces we use the following formula:
Divide the amount of gold in grams by the number of grams per ounce. 42 grams ÷ 31.1035 grams/ounce = 1.35 ounces.
Multiply the amount of gold in ounces by the current price of gold per ounce. 1.35 ounces × $1286/ounce = $1,736.10.
Bob drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Bob drove home, there was no traffic and the trip only took 5 hours. If his average rate was 21 miles per hour faster on the trip home, how far away does Bob live from the mountains? Do not do any rounding.
Answer:280 miles
let x=rate of speed on the way to mountains
x+21=rate of speed on the way home
travel time*rate=distance
8x=5(x+21)
8x=5x+105
3x=105
x=35
8x=280
how far away does Bob live from the mountains? =280 miles
Final answer:
Bob lives 280 miles away from the mountains. We solved for the slower speed and then calculated the distance using the time it took Bob to get to the mountains and his average speed during that trip.
Explanation:
Finding the Distance to the Mountains
To find out how far Bob lives from the mountains, we need to set up an equation based on the information given about time and average speed. Since the average rate was 21 miles per hour faster on the return trip and the times for the trips are known (8 hours to the mountains and 5 hours returning), we can let the slower speed be 's' and the faster speed be s' + 21'.
We can now create two equations based on the definition that Distance = Speed *Time:
Coming back home (faster speed): Distance = (s + 21) *5 hours
Since the distance to the mountains and back home is the same, we can equate these two expressions:
s * 8 = (s + 21)* 5
Calculating the Speed and Distance
Now we solve for 's':
8s = 5s + 105
8s - 5s = 105
3s = 105
s = 35
Thus, the slower speed was 35 miles per hour. We can plug this back into either equation to find the distance:
Distance = 35 miles/hour * 8 hours
Distance = 280 miles
Therefore, Bob lives 280 miles away from the mountains.
(5-4i)-(2-4i)
Complex numbers
Need to show work
Answer:
3
Step-by-step explanation:
Simplify :
(5-4i)-(2-4i)
5-4i-(2-4i)
=3
A combination lock uses a 3-digit code. Each digit can be any one of the ten available integers 0-9. How many different combinations are possible?
Answer:
1000
Step-by-step explanation:
Each value of the first digit can be paired with any value of the second digit, so there are 10×10 = 100 possible pairs of the first two digits. Each of those can be combined with any third digit to give a total of ...
10×10×10 = 1000
possible combinations.
Final answer:
A combination lock with a 3-digit code where each digit can be 0-9 allows for 1000 different combinations, as calculated by 10 x 10 x 10, which equals 10³ or 1000.
Explanation:
The question asks how many different 3-digit combinations are possible with a combination lock where each digit can range from 0-9. Each digit of the code is independent and can take any of the ten possible values (0-9), leading to a total combination of possibilities calculated by multiplying the number of choices for each digit position. Given that there are three digit positions and each can be any of the ten digits, the calculation is as follows:
10 (choices for first digit) × 10 (choices for second digit) × 10 (choices for third digit) = 10³
Therefore, there are 1000 different possible combinations for the lock, ranging from 000 to 999.
What is the value of secant theta given the diagram below? A unit circle is shown. A ray intersects point (negative 3, 6) in quadrant 2. Theta is the angle formed by the ray and the x-axis in quadrant 1. Negative StartRoot 5 EndRoot Negative StartFraction StartRoot 5 EndRoot Over 2 EndFraction StartFraction StartRoot 5 EndRoot Over 2 EndFraction StartRoot 5 EndRoot
Answer:
- √5
Step-by-step explanation:
Given that, a ray intersects point (negative 3, 6) in quadrant 2 and we are told to find the value of secant theta.
To get the answer to the question,
The first step is to find the hypotenuse, we have to use the Pythagoras theorem where, Hypotenuse = opposite raise to power two + adjacent raise to power.
(I.e. h= O² + A²)
H = 6² + (-3)2
H = 36 + 9
H = 45
We then convert the answer to surds form.
H = 3√5
The next step is to find the value of secant theta.
To get the value of secant theta we will have to divide the hypotenuse by adjacent with a negative sign because of the negative sign in the second quadrant
We have
Sec ø = - (hypotenuse/adjacent)
Sec ø = - (3√5/ 3)
Sec ø = - √5
Answer:
-√5
Step-by-step explanation:
in triangle abc shown below side ab is 6 and side ac is 4
which statement is needed to prove that segment DE is parallel to segment BC and half its length?
Question is Incomplete, Complete question is given below:
In Triangle ABC shown below, side AB is 6 and side AC is 4.
Which statement is needed to prove that segment DE is parallel to segment BC and half its length?
Answer
Segment AD is 3 and segment AE is 2.
Segment AD is 3 and segment AE is 4.
Segment AD is 12 and segment AE is 4.
Segment AD is 12 and segment AE is 8.
Answer:
Segment AD is 3 and segment AE is 2.
Step-by-step explanation:
Given:
side AB = 6
side AC = 4
Now we need to prove that segment DE is parallel to segment BC and half its length.
Solution:
Now AD + DB = AB also AE + EC = AC
DB = AB - AD also EC = AC - AE
Now we take first option Segment AD is 3 and segment AE is 2.
Substituting we get;
DB = 6-3 = 3 also EC = 4-2 =2
From above we can say that;
AD = DB and EC = AE
So we can say that segment DE bisects Segment AB and AC equally.
Hence From Midpoint theorem which states that;
"The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side."
Hence Proved.
If 2, 4, 6, and 9 are the digits of two 2-digit integers, what is the least possible positive difference between the integers? A28 B27
Answer: 13
Step-by-step explanation: first we have to know what an integer, which is a single whole number without fractions or decimal numbers e.g. 1,2,3,4,5,6,7,8,9
So now we are to find the least possible positive difference between two digit integers with combination of 2,4,6,9
So first, since it has to be the lowest difference, we have to look between these numbers for the lowest difference between the given integers, 6-4 = 2, 4-2 = 2, now the rest of the combination will give numbers higher that 2, e.g. 9-6 = 3, 6-2 = 4, 9-4 = 5, 9-2 = 7, so we can say our two digit integers can start with either 4 and 2, or 6 and 4, which is the tens in the two digit integers, so to get the least difference in this values, the units number of the bigger two digit integer will be smaller than the units number of the smaller two digit integers
So let's take the number 2, and 4
The bigger two digit integer will obviously start will 4, and since it's supposed to have the smaller units number, the two digit integer will be 46, and the second two digit integer will be 29, the finding the difference
We have 46-29=17
The taking the other combination of integer to give the smallest value, which was 2, (6 and 4) then giving the units number of the bigger integer which will be the smaller units number value (2), that two digit integer will be 62, and the other 49, finding the difference
62-49= 13
So therefore the least possible positive difference = 13
Find the midpoint of the line segment with the given points, (3, -7), (-2, 3)
Answer:
The answer to your question is Midpoint ( [tex]\frac{1}{2} , -2)[/tex]
Step-by-step explanation:
Data
A (3, -7)
B (-2, 3)
Formula
[tex]Xm = \frac{x1 + x2}{2}[/tex]
[tex]Ym = \frac{y1 + y2}{2}[/tex]
Substitution and simplification
[tex]Xm = \frac{3 - 2}{2}[/tex]
[tex]Xm = \frac{1}{2}[/tex]
[tex]Ym = \frac{-7 + 3}{2}[/tex]
[tex]Ym = \frac{-4}{2}[/tex]
[tex]Ym = -2[/tex]
Solution
Midpoint ( [tex]\frac{1}{2} , -2)[/tex]
A set of logically interrelated concepts, statements, propositions, and definitions supported by data, testing, and verification to account for or characterize some phenomena is called ______.
Answer:
Theory
Step-by-step explanation:
The term theory is associated to a "set of logical interrelated concepts, statements, propositions, and definitions", who are "derived from philosophical and logical beliefs from scientific data and from which questions and hypotheses can be deduced, characterize, tested and verified".
So then we can conclude that :
A set of logically interrelated concepts, statements, propositions, and definitions supported by data, testing, and verification to account for or characterize some phenomena is called theory.
Final answer:
A theory is a comprehensive explanation for observed phenomena that is supported by evidence and repeated validation. It is a core component of scientific understanding, which relies on the scientific method for development and verification.
Explanation:
A set of logically interrelated concepts, statements, propositions, and definitions supported by data, testing, and verification to account for or characterize some phenomena is called a theory. In science, a theory is a well-developed set of ideas that propose an explanation for observed phenomena. It involves a hypothesis, or group of hypotheses, that has been substantiated through repeated experiments or empirical observations. Theories are used to make predictions about future observations and can be revised as new evidence is discovered.
The validity of a theory is determined by the accuracy of its predictions and the extent to which it can measure what it is designed to measure. A robust theory not only explains the phenomena in question but is also supported by a wide range of scientific evidence and has been verified multiple times by various groups of researchers using the scientific method.
In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?A. 0.9B. 0.7C. 0.45D. 0.3E. 0.25
Answer:
Option B is right
Step-by-step explanation:
Given that in the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older.
Males Females
48% 52%
25 or more
age 40% 20%
One student in the class is randomly selected,
to find the probability that he or she will be less than 25 years old
= Prob (male and less than 25 years old)+Prob (female and less than 25 years old)
(since mutually exclusive and exhaustive)
= [tex]0.48(1-0.4) + 0.52(1-0.20)\\= 0.288+ 0.416\\= 0.704\\[/tex]
After rounding off to 1 one decimal
we get 0.7
Option B is right
The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours.
Answer:
Step-by-step explanation:
Since the length of time taken on the SAT for a group of students is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - u)/s
Where
x = length of time
u = mean time
s = standard deviation
From the information given,
u = 2.5 hours
s = 0.25 hours
We want to find the probability that the sample mean is between two hours and three hours.. It is expressed as
P(2 lesser than or equal to x lesser than or equal to 3)
For x = 2,
z = (2 - 2.5)/0.25 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.02275
For x = 3,
z = (3 - 2.5)/0.25 = 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.97725
P(2 lesser than or equal to x lesser than or equal to 3)
= 0.97725 - 0.02275 = 0.9545
Final answer:
The probability that the sample mean is between two and three hours is practically 1, or 100%.
Explanation:
To find the probability that the SAT exam completion time sample mean for a group of students is between two and three hours, we need to calculate the z-scores for 2 hours and 3 hours and then use these z-scores to determine the corresponding probabilities.
Given:
- Population mean (= 2.5 hurs
- Standard deviation = 0.25 hours
- Sample size = 60
We'll use the z-score formula:
[tex]\[ z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}} \][/tex]
For X = 2 hours:
[tex]\[ z = \frac{2 - 2.5}{\frac{0.25}{\sqrt{60}}} \][/tex]
[tex]\[ z = \frac{-0.5}{\frac{0.25}{\sqrt{60}}} \][/tex]
[tex]\[ z \approx \frac{-0.5}{\frac{0.25}{7.746}} \][/tex]
[tex]\[ z \approx \frac{-0.5}{0.0323} \][/tex]
[tex]\[ z \approx -15.49 \][/tex]
For X = 3 hours:
[tex]\[ z = \frac{3 - 2.5}{\frac{0.25}{\sqrt{60}}} \][/tex]
[tex]\[ z = \frac{0.5}{\frac{0.25}{\sqrt{60}}} \][/tex]
[tex]\[ z \approx \frac{0.5}{\frac{0.25}{\sqrt{60}}} \][/tex]
[tex]\[ z \approx \frac{0.5}{0.0323} \][/tex]
[tex]\[ z \approx 15.49 \][/tex]
Using the z-scores, we consult a standard normal distribution table or use a calculator to find the corresponding probabilities. Then, we calculate the difference between the two probabilities to get the probability that the sample mean is between two and three hours. Let me calculate the exact probabilities.
Using the z-scores calculated:
For z = -15.49 , the corresponding probability is practically 0 (since it's far in the left tail of the distribution).
For z = 15.49, the corresponding probability is practically 1 (since it's far in the right tail of the distribution).
Therefore, the probability that the sample mean is between two and three hours is practically 1, or 100%.
Andrew and Sarah are tracking the number of steps they walk. Andrew records that he can walk 6000 steps in 50 minutes. Sarah writes the equation y=118x where y is the number of steps and x is the number of minutes she walks, to describe her step rate.
Answer:
Andrew walks more steps than Sarah.
Step-by-step explanation:
The question is incomplete. The complete question is :
Andrew and Sarah are tracking the number of steps they walk. Andrew records that he can walk 6000 steps in 50 minutes. Sarah writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andrew and Sarah each walk for a total of 5 hours. Who walks more steps?
Solution:
Given:
Andrew walks 6000 steps in 50 minutes.
Number of steps Sarah walks is given by the equation :
[tex]y=118x[/tex]
where [tex]y[/tex] is the number of steps and [tex]x[/tex] is the number of minutes she walks.
Finding the number of steps each walks in 5 hours.
Total number of minutes in 5 hours = [tex]5\times 60 = 300\ min[/tex]
For Andrew:
Using unitary method:
If in 50 minutes Andrew walks = 6000 steps.
In 1 minute he will walk = [tex]\frac{6000}{50}[/tex] = 120 steps
In 300 minutes he will walk = [tex]120\times 300 = 36000[/tex] steps
Thus, Andrew will walk 36,000 steps in 5 hours.
For Sarah:
We will plugin [tex]x=300[/tex] in the equation and solve for [tex]y[/tex].
We have:
[tex]y=118(300)[/tex]
∴ [tex]y=35400[/tex]
Thus, Sarah will walk 35,400 steps in 5 hours.
Therefore, Andrew walks more steps than Sarah as [tex]36,000>35,400[/tex].
At a movie theater, the ticket prices to see a movie in 3-D are $18 for an adult and $12 for a child. The owner of the theater wants to make at least $300 when a movie is shown in 3-D. Choose the inequality that shows the numbers of tickets that must be sold.
Answer:
[tex]18x+12y\geq 300[/tex]
Step-by-step explanation:
Let
x ---> the number of an adult tickets
y ---> the number of a child tickets
Remember that the word "at least" means "greater than or equal to"
so
The number of an adult tickets multiplied by its price ($18) plus the number of a child tickets multiplied by its price ($12) must be greater than or equal to $300
The inequality that represent this situation is
[tex]18x+12y\geq 300[/tex]
using a graphing tool
the solution is the shaded area
Remember that the number of tickets cannot be a negative number
see the attached figure
Write an algebraic expression for the verbal expression, "17 less than k and 12"
Answer:
k-5
Step-by-step explanation:
"k and 12" : (k + 12)
"17 less than k and 12" : (k + 12) - 17
simplifying:
(k + 12) - 17
= k + 12 - 17
= k-5
the length of a rectangle increases at a rate of 0.5 cm/sec and the width decreases at a rate of 0.5 cm/sec at the time when the length is 10cm and the width is 7 cm what is the rate of change in the area of the rectangle?
Answer:
Step-by-step explanation:
let length=x
width=y
area A=xy
[tex]\frac{dA}{dt}=x\frac{dy}{dt}+y\frac{dx}{dt}\\ \frac{dx}{dt}=0.5 ~cm/sec\\\frac{dy}{dt}=-0.5~cm/sec\\\frac{dA}{dt}=10*(-0.5)+7(0.5)=-5+3.5=-1.5[/tex]
area is decreasing at the rate of 1.5 cm^2/sec
The rate of change in the area of the rectangle when the length is 10 cm and the width is 7 cm, with their rates of change being 0.5 cm/sec and -0.5 cm/sec respectively, is -1.5 cm²/sec.
Explanation:To determine the rate of change in the area of a rectangle where the length is increasing at 0.5 cm/sec and the width is decreasing at 0.5 cm/sec, we can use the concept of derivatives from calculus.
Let L be the length and W be the width of the rectangle. The area A of the rectangle is given by A = L * W. Given that the length is increasing at 0.5 cm/sec (dL/dt = 0.5 cm/sec) and the width is decreasing at 0.5 cm/sec (dW/dt = -0.5 cm/sec) the rate of change of the area with respect to time can be found using the product rule for derivatives: dA/dt = (dL/dt) * W + L * (dW/dt).
At the moment when the length L is 10 cm and the width W is 7 cm, we can plug these values into the formula: dA/dt = (0.5 cm/sec) * 7 cm + 10 cm * (-0.5 cm/sec). This simplifies to dA/dt = 3.5 cm2/sec - 5 cm2/sec, giving us the rate of change in the area as dA/dt = -1.5 cm2/sec.