Solution:
We are required to find the mean median and mode of 1,2,2,6,5,1,1.
[tex]Mean=\frac{1+2+2+6+5+1+1}{7}=\frac{18}{7}=2.5714[/tex]Median:
Sort the data
1, 1, 1, 2, 2, 5, 6
The median = 2
Mode = 1 (because it appears the most (3 times) )
Choose the best selection for thequadrilateral with vertices at thefollowing points:(4,0), (8,0), (4,-4), (8,-4)Hint: Start by graphing the points.Distance Formula: d= (x2 – x1)2 + (y2 - y1)2A. RectangleB. SquareC. RhombusD. Trapezoid
We are given coordinates of four points and we are asked to find the best selection of the shape.
In order to know what shape this is, we simply graph all the points and see what shape we get.
Using a graphing calculator, the points make up the following shape:
Now that we have the shape, we know that it can either be a Rectangle or a Square.
If the shape is a rectangle, the lengths x and y are not equal. If the shape is a square, lengths x and y are equal.
In order to find x and y, we use the distance formula given to us as:
[tex]\begin{gathered} |d|=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where,} \\ (x_2,y_2)\to\text{ Second point} \\ (x_1,y_1)\to\text{ First point} \end{gathered}[/tex]Now let us find x and y.
x:
The points that make up the length x are:
(4, 0), and (4, -4)
Therefore, length x can be gotten as:
[tex]\begin{gathered} x_2=4,y_2=0,x_1=4,y_1=-4 \\ |x|=\sqrt[]{(4-4)^2+(0--4)^2} \\ |x|=\sqrt[]{4^2} \\ \\ \therefore|x|=4 \end{gathered}[/tex]Now we find y.
y:
The points that make up the length y are:
(4, 0) and (8, 0)
Therefore, length y can be gotten as:
[tex]\begin{gathered} x_2=4,y_2=0,x_1=4,y_1=-4 \\ |x|=\sqrt[]{(4-4)^2+(0--4)^2} \\ |x|=\sqrt[]{4^2} \\ \\ \therefore|x|=4 \end{gathered}[/tex]O GEOMETRY Perimeter involving rectangles and circles A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 88 m long and 67 m wide. What is the length of a training track running around the field? (Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.) 88 m 1 67 m 1 0 m X m² S m³ 1/5 ?
Step 1
to know the full distance for the track running we need to add twilce the length of the rectangle to the perimeter of the circel, so
so
a) find the circumference of the circle , it is given by
[tex]\begin{gathered} C=\text{ }\pi d\text{ } \\ where\text{ d is the diameter} \end{gathered}[/tex]hence
[tex]\begin{gathered} let\text{ d=67 m} \\ so \\ C=\pi *67\text{ m=210.38 m} \end{gathered}[/tex]finally, add twice the length of the rectangle, so
[tex]\begin{gathered} traininin\text{ track = 210.38+\lparen2*88\rparen=210.38+176} \\ traininin\text{ track = 386.38} \end{gathered}[/tex]therefore, the answer is
[tex]386.38\text{ m}[/tex]I hope this helps you
Construct a Venn diagram where U={a,b,c,d,e,f,g}, A={b,d,f,g}, and B={b}.Move each of the lettered points to an appropriate region on the Venn diagram.
Explanation:
Given the universal set, U and subsets A and B as follows:
• U={a,b,c,d,e,f,g}
,• A={b,d,f,g}
,• B={b}
Answer:
The Venn diagram representing the sets is given below:
Note:
• The ,letter b is common to both A and B,, so we put it in the intersection of both sets.
,• The ,letters a, c, and e do not belong to either A or B,, so we place it outside of the two sets.
Determine the domain and range of the function shown below. Assume the entire function is shown. Domain: Range:
The function is made of the following ordered pairs:
(-1,-3) (1, -5) (2, 3) (3, 6) (5, 6) (7, -1)
The first coordinate of the ordered pairs is the input value and the second coordinate is the output value of the function.
The domain is the set of all the input values as shown below:
Domain: {-1, 1, 2, 3, 5, 7}
Range: {-3, -5, 3, 6, -1}
Sorting the values of the range.
Range: {-5, -3, -1, 3, 6}
radical 9 cubed times radical -24 cubed=?
we can easily calculate that -6 times -6 times- 6 =- 216 it is why we can do this equality
because we have an exponent 3 and a cubic root we can cancel both so the answer of
[tex]\sqrt[3]{9}\text{ }\cdot\sqrt[3]{-24}=\text{ -6}[/tex]The half-life of a certain substance is 27 years. How long will it take for a sample of this substance to decay to 66% of its original amount? for the sample of the substance to decay to 66% of its original amount
This is a type of radioactive decay problem. Given an initial amount of N0, the amount at t years is given by
[tex]N(t)=N_0e^{-\lambda t}[/tex]The information "27 years is the half-life of the substance" means that if we replace t by 27, we will get exactly half of the initial amount we had. That is
[tex]N_0e^{-\lambda\cdot27}=\frac{N_0}{2}[/tex]We can cancell out N0 on both sides, so we get
[tex]e^{-\lambda\cdot27}=\frac{1}{2}[/tex]using the properties of exponentials, we have the equivalent equation
[tex]\frac{1}{2}=\frac{1}{e^{\lambda\cdot27}}[/tex]which is also equivalent to
[tex]e^{\lambda\cdot27}=2[/tex]If we apply natural logarithm on both sides, we get
[tex]\ln (e^{\lambda\cdot27})=\lambda\cdot27=\ln (2)[/tex]Finally, we can divide both sides by 27, to get
[tex]\lambda=\frac{\ln (2)}{27}[/tex]So, the function that describes the amount of the subtances at time t is given as
[tex]N(t)=N_0e^{\frac{-\ln (2)\cdot t}{27}}[/tex]Now, we want to calculate the value of t, for which the amount we have at year t is exactly 66% of what we have at t=0. That is
[tex]\frac{N_0e^{-\frac{\ln (2)\cdot t}{27}}}{N_0}=0.66[/tex]We can cancell out N0 and, by equivalence by using the properties of exponents, we get
[tex]\frac{1}{e^{\frac{\ln(2)}{27}\cdot t}}=0.66[/tex]which is also equivalent to
[tex]\frac{1}{0.66}=e^{\frac{\ln (2)t}{27}}[/tex]if we apply the natural logarithm on both sides, we get
[tex]\ln (\frac{1}{0.66})=\ln (e^{\frac{\ln(2)\cdot t}{27}})=\ln (2)\cdot\frac{t}{27}[/tex]Finally, we want to solve for t. To do so, we can multiply by 27 and then divide by ln(2). So we get
[tex]t=\frac{27}{\ln(2)}\cdot\ln (\frac{1}{0.66})[/tex]with help of a calculator, we have that t is approximately 16.185. That is, about after 16 years, we will have 66% of the initial amount.
What is thX= ら*e coefficient of the term x³y5 in the expansion of the binomial expression (2x − y)³?
The coefficient of the term x²y in the binomial expansion of (2x − y)³ is -12.
The expression (2x − y)³ can be simplified as
8x³−12x²y+6xy²−y³ .
Thus the coefficient of the binomial expansion is -12.
Of the use of the binomial theorem, it is possible to determine the expanded value of either formula with the form (x + y)ⁿ.
The values of (x + y)², (x + y)³, and (a + b + c)² can be easily determined by adding the integers algebraically in accordance with the exponent value.
The binomial theorem was first mentioned by a well-known Greek mathematician by the name of Euclid in the fourth century BC.
According to the binomial theorem, which represents it as a sum of terms using distinct exponents of the variables x and y, the algebraic statement (x + y)ⁿ can be expanded. A coefficient, or numerical value, is assigned to each word in a binomial expansion.
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*only do question 14*diagrams are not drawn to scale. i only care about the answers & the steps you did to get the answers.don’t be slow pls (:
∠KU and ∠LE are vertically opposite angles, which means that they are congruent, so that:
[tex]\angle KU=\angle LE=60º[/tex]∠LUE and ∠LKE intersect the same arc mLE, which means that they are congruent:
[tex]\angle\text{LUE}=\angle\text{LKE}=32º[/tex]∠KU and the vertex angle marked in blue are supplementary angles, which means that they add up to 180º:
[tex]\begin{gathered} 60+x=180º \\ x=180-60 \\ x=120º \end{gathered}[/tex]Knowing two of the three angles of the upper triangle, you can calculate the measure of the missing one, ∠ULK:
[tex]\begin{gathered} 32+120+\angle\text{ULK}=180 \\ 152+\angle\text{ULK}=180 \\ \angle\text{ULK}=180-152 \\ \angle\text{ULK}=28º \end{gathered}[/tex]∠ULK and ∠UEK intercept the same arc mKU, so they are congruent:
[tex]\angle\text{ULK}=\angle\text{UEK}=28º[/tex]10 ydFind the surface area of the closed hemisphere.Enter your answer in terms of A and rounded to thenearest tenth.The surface area is ]# yd? or approximatelyyd?
We have the following:
[tex]A=2\cdot\pi\cdot r^2[/tex]we have that the radius is half the diameter, therefore
[tex]\begin{gathered} r=\frac{d}{2}=\frac{10}{2} \\ r=5 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} A=2\cdot\pi\cdot5^2 \\ A=50\pi\cong157 \end{gathered}[/tex]The surface area is 50*pi yd^2 or approximately 157 yd^2
Vihaan got 38/48 on his geography test. Sahaj got 80% on his geography test. Jada got 0.8125 on her geography test. Quinn thinks that Vihaan got a higher mark on his test than Sahaj and Jada.Is Quinn right? Prove whether he is right or wrong by showing your work (5 marks)
Vihaan got 38 in her geography test
Since the geography test has a total score of 48
Since Sahaj got 80% of it, then multiply 80/100 by 48 to find his score
[tex]\frac{80}{100}\times48=38.4[/tex]Sahaj got 38.4 on the geography test
Since Jada got 0.8125 on her geography test, then multiply 0.8125 by 48 to find her score
[tex]0.8125\times48=39[/tex]Jada got 39 on the geography test
The greatest one is Jada, then Sahaj, then Vihaan
Quinn thinks that Vihaan got the higher score
But Jada the one who got the higher score
Then Quinn is not right
what do factors 12 and 24 have in common
Mcd (max common divisor) of 12, 24 = 12
(Because 24/12= 2 )
are
2,3,4,6,12
A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 50 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answer:
See below
Step-by-step explanation:
Final amount of pure antifreeze = .75 (50)
amount of 70 % that is pure antifreeze = .70 x
amount of 95 % that is pure antifreeze = .95 (50-x)
ingredients in = ingredients out
.70x + .95 (50-x) = .75 (50)
x = 40 gal this is the amount of 70 %
then 95 % = 50 - 40 = 10 gal
Simplify the following expression. 7m+7(4m+2)
Given the expression:
7m + 7(4m + 2)
Use distributive property to expand the parenthesis:
= 7m + 7*4m + 7*2
= 7m + 28m + 14
Sum up like terms:
= 35m + 14
ANSWER:
35m + 14
Simplify the expression 8h + (-7.3d) - 14 + 5d - 3.2h
The expression is:
8h + (-7.3d) - 14 + 5d - 3.2h
collecting like terms, we have:
8h - 3.2h +(-7.3d) + 5d - 14
= 4.8h - 7.3d + 5d - 14
= 4.8h - 2.3d - 14
That is the expression simplified
Mr. Cumme bought the amount of clay listed for his class.- 2.2 kilograms- 1.5 kilograms- 850 grams - 700 gramshow many grams of clay did Mr.Cumme buy?
Hello there. To solve this question, we have to remember how to convert kilograms to grams.
Given an amount in kilograms, to determine its value in grams, we simply multiply it by 1000.
In this case, we know that Mr. Cume bought the amount of clay listed for his class:
- 2.2 kilograms
- 1.5 kilograms
- 850 grams
- 700 grams
To determine how many grams of clay he bought, we start converting the values from kilograms to grams
2.2 kilograms * 1000 = 2200 grams and
1.5 kilograms * 1000 = 1500 grams
Now, we add everything
2200 + 1500 + 850 + 700 = 5250 grams
This is the final answer to this question.
Find the number that belongsin the green boc
the value for green box is 7.61
It can be calculated using sine law
first we need to know the angle opposite of 5
using sine law
16 a.)Vivian approximated the square root of 15. What is the value of the square root of 15 to the nearest whole number? Show or explain how you got your answer.
ANSWER
3.872
EXPLANATION
Given:
A number 15
Desired Outcome:
Square root of the number
Square root of 15
Step 1:
Starting on the right, we'll put a bar above the digits to match them together.
Step 2:
Find a number that when multiplied by itself produces a result that is less than or equal to 15 and close to 15. So the answer is three. Using 3 as the divisor, we get 3 as the quotient (same as the divisor), and 6 as the remainder.
Step 3:
Enter the divisor twice with a blank on the right. Choose the largest possible digit to fill in the blank, which will become the new digit in the quotient, so that the resultant product is less than or equal to the dividend when the new divisor is multiplied by the new quotient. Divide the leftover and write it down. Repeat this method until you get the desired number of decimal places.
Hence, the square root of 15 is 3.872
A store makes a profit of $25 on each watch it sells. What solution setwill represent how many watches the store must sell to make a profitof at least $375?US
Here, the variable is the number of watches.
The profit on each watch it sells is, $25.
The least profit to be made is, $375.
Let x be the number of watches, Then we have, the total profit as,
[tex]25x[/tex]This profit should be atleast 375, therefore, we have,
[tex]\begin{gathered} 25x\ge375 \\ \frac{25x}{25}\ge\frac{375}{25} \\ x\ge15 \end{gathered}[/tex]Type the correct answer in each box. Spell all words correctly.
Two triangles are graphed in an x y plane. The vertices are as follows: first: A (negative 6, 2), B (negative 2, 6), and C (negative 4, 2); second: A prime (negative 6, negative 2), B (negative 2, negative 6), and C (negative 4, negative 2). A sequence of transformations maps ∆ABC onto ∆A″B″C″. The type of transformation that maps ∆ABC onto ∆A′B′C′ is a . When ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″, vertex of ∆A″B″C″ will have the same coordinates as B′.
Part A: Transformation which mapped ABC to A′B′C′; reflection along x-axis.
Part B: The coordinate of B" is the same as the coordinate of B'.
What is referred as the term transformation?A transformation is a broad term for four major methods of changing the form and/or position of the a point, line, as well as geometric figure. The Pre-Image is the original shape of a object, and the Image for under transformation is the final shape as well as position of the object.For the given question;
The coordinates are-
∆ABC; A(-6, 2), B(-2, 6), C(-4, 2).
∆A′B′C; A'(-6, - 2), B (-2, -6), C (-4, -2).
A) We are now told that ABC was transformed into
∆A′B′C. We can see from the coordinates that merely the y coordinate sign modified after the transformation.
As a result, the transformation which mapped ABC to A′B′C′ is a reflection along the x-axis.
B) A′B′C′ is now reflected all across line x = -2 to form A′′B′′C′′. Because the line x = -2 is vertical as well as the coordinate of B' in A′B′C′ has had an x - coordinate of -2,
Thus, the coordinate of B" is the same as the coordinate of B'.
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uueJUU Telp Find the area of the polygon. The area of the polygon is (Type a whole number.) 4 cm 7 cm 7 cm -14 cm 14 cm יד 4 cm
The area of the polygon = Sum of area of eight triangles + area of a square.
Area of the square
[tex]\begin{gathered} \\ \text{Length = 14cm} \\ \text{Area of the square = Length}^2 \\ \text{ = 14}^2 \\ =196cm^2 \end{gathered}[/tex]Area of one triangle
[tex]\begin{gathered} =\text{ }\frac{Base\text{ x Height}}{2} \\ \text{Base = 4cm} \\ \text{Height = 7cm} \\ =\text{ }\frac{4\text{ x 7}}{2} \\ =\text{ }\frac{28}{2} \\ =14cm^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the eight triangles = 8 x 14 } \\ \text{ = 112 cm}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the polygon = 196 + 112} \\ \text{ = 308 cm}^2 \end{gathered}[/tex]Use an alternative method to express the following set: {y:y is a person in your math class and also more than 100 years old.}
Let's use the letter M to label the math class. The fact that person y is in that class can be expressed by:
[tex]y\in M[/tex]We also have to show that is older than 100 so we have:
[tex]y>100[/tex]If we put all this information together we get:
[tex]\mleft\lbrace y\colon y\in M,y>100\mright\rbrace[/tex]And that's an alternative way to express the set.
Find the total amount in the compound interest account $10000 is compounded semiannually at a rate of 11% for 20 years. (Round to the nearest cent.)
The compound interest formula is:
[tex]A=P(1+\frac{r}{m})^{mt}\begin{cases}A=amount \\ P=initialValue \\ r=interest \\ m=\#timesCompounedPerYear \\ t=years\end{cases}[/tex]Therefore:
[tex]A=(10000)(1+\frac{0.11}{1})^{20}=80623.12[/tex]What are lim f(x) and lim f(x) if they exist?
SOLUTION:
Case: Limits
Method:
Right and left-sided limits.
The right sided limits is gotten from the right-hand side and gives an f(x) of 0 while the left sided limits gives an f(x) of 1.
Final answer: Option
[tex]\begin{gathered} \lim_{x\to0^-}f(x)=1 \\ \lim_{x\to0^+}f(x)=0 \end{gathered}[/tex]Question 6: a study of several cities show a positive correlation between the percent of people biking to work and percent of people spending their vacation time at home.What statement is most likely true? A. Correlation implies causation; therefore vacationing at home make people want to ride their bike.B. Correlation implies causation; therefore, bike riding makes people want to vacation at home.C. Correlstion does not imply causation; therefore,the correlation is due to a third. variable: cost of milk.D. Correlation does not imply correlation, therefore is due to a third variable: cost of gas.
If the study shows a positive correlation means that as people bike to work increase also the percentage of people spending their vacation time at home increases
since work happens before vacation one of the statemens that is most likely to be true will be B.
Write the point-slope form of an equation of the line that passes through (4, -3) and (2, 1).
Oa y-4-2
(x+3)
Oby+3=-2 (x-4)
OC y-3= -2(x-4)
y+3= =(x-4)
The point-slope form that passes through (4, -3) and (2, 1) is y+3 is −2(x−4). A slope of a line is the change in y coordinate with respect to the change in x coordinate.
How to calculate Point-slope form ?The slope of the line and any points on the line determine the point-slope form of a line. When given a point on the line and the slope, the form's purpose is to describe the equation of the entire line.
The slope of a line passing through the two points P=(x1,y1) and Q=(x2,y2) is given by m = y2−y1 / x2−x1
We have that x1=4, y1=−3, x2=2, y2=1.
Plug the given values into the formula for slope: m = (1)−(−3)/(2)−(4)
=4−2 =−2.
Now, the y-intercept is b=y1−m⋅x1 (or b=y2−m⋅x2, the result is the same).
b=−3−(−2)⋅(4)=5.
Finally, the equation of the line can be written in the form y=mx+b.
y=−2x+5.
The slope of the line is m=−2.
The equation of the line in the slope-intercept form is y=−2x+5.
The equation of the line in the point-slope form is y+3=−2(x−4).
The equation of the line in the point-slope form is y−1=−2(x−2).
The general equation of the line is 2x+y−5=0.
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Convert 15% to a fraction. Write in lowest terms.Convert 26% to a fraction. Write in lowest terms.Read the "Fractions, Decimals & Percents" lesson. Then answer each of the following questions to practice converting between fractions, decimals and percents.
Convert 15% to a fraction. Write in the lowest terms.
So,
[tex]15\%=\frac{15}{100}=\frac{5\times3}{5\times20}=\frac{3}{20}[/tex]So, the answer will be 15% = 3/20
=========================================================
Convert 26% to a fraction. Write in the lowest terms.
So,
[tex]\frac{26}{100}=\frac{2\times13}{2\times50}=\frac{13}{50}[/tex]So, the answer will be 26% = 13/50
Suppose Albers Elementary School has 26 teachers and Bothel Elementary School has 14 teachers. If thetotal number of teachers at Albers and Bothel combined is 27, how many teachers teach at both schools
Given:
Albers Elementary School has 26 teachers
Bothel Elementary School has 14 teachers
And the total number of teachers at Albers and Bothel combined is 27
Note, there a number of teachers working at both schools
We will let the following:
The number of teachers at Albers = x
The number of teachers at Bothel = y
The number of teachers at both = z
So, we can write the following system of equations:
x + z = 26 ⇒ (1)
y + z = 14 ⇒ (2)
x + y + z = 27 ⇒ (3)
Solving the system of equations to find x, y, and z
From (1) ⇒ x = 26 - z
From (2) ⇒ y = 14 - z
Substitute with (x) and (y) into equation (3)
[tex]\begin{gathered} (26-z)+(14-z)+z=27 \\ -z-z+z=27-14-26 \\ -z=-13 \\ z=13 \end{gathered}[/tex]So, the answer will be
The number of teachers teach at both schools = 13
8. (07.01 MC)If the sin 60º = 13, then which statement is true? =2cos 30º =V3, because the cosine and sine are complements523cos 120º =2because the cosine and sine are supplementscos 30º = 0, because the cosine and sine are complementscos 120º = 0, because the cosine and sine are supplements
Note that if the angles are complementary with each other, the sine and cosine are the same.
From the problem, sin 60 = √3/2, the complement of 60 degrees is 30,
so cos 30 is the same as sin 60.
The best answer is Choice A
In the game of Monopoly, a player is sent to jail if he or she rolls doubles with a pair of dice 3 times in a row.What is the probability of rolling doubles on a single turn? (Enter your probability as a fraction.) _______What is the probability of rolling doubles 3 times in succession? (Enter your probability as a fraction.) _______
The probability of rolling doubles on a single turn is the number of favorable cases over the number of total cases, the favorable cases are those when you get a double, the number of total cases is the number of total possible outcomes.
Now, the number of total possible outcomes is
[tex]6\times6=36.[/tex]The number of favorable cases is
[tex]6.[/tex]Therefore, the probability of rolling doubles is:
[tex]\frac{6}{36}=\frac{1}{6}\text{.}[/tex]Now, the probability of rolling double 3 times in succession is the product of rolling a double in a single turn, therefore:
[tex]P=\frac{1}{6}\times\frac{1}{6}\times\frac{1}{6}=\frac{1}{216}.[/tex]Answer:
The probability of rolling doubles on a single turn is:
[tex]\frac{1}{6}\text{.}[/tex]The probability of rolling doubles 3 times in succession is:
[tex]\frac{1}{216}\text{.}[/tex]fill in the blanks.30x8=3x_____x840x7=_____x10x7
Answer:
30x8=3x_10_x8
40x7=_4_x10x7
First one: 10
Second one: 4