Solve
[tex]\begin{gathered} -12=3-2k-3k \\ \text{Collect like terms} \\ -12-3=-2k-3k \\ \text{Note that when a positive value crosses the equality sign, it becomes negative} \\ \text{Similarly when a negative value crosses the equality sign it becomes positive} \\ \text{Hence, 3 crosses over and becomes negative} \\ -12-3=-2k-3k \\ -15=-5k \\ \text{Divide both sides by -5} \\ \frac{-15}{-5}=\frac{-5k}{-5} \\ 3=k \end{gathered}[/tex]2. (5 points) A very special island is inhabited only by knights and knaves. Knights always tell
the truth, and knaves always lie. You meet two inhabitants: Sue and Marge. Sue says that
Marge is a knave. Marge claims. "Sue and I are not the same." Determine who is a knight and
who is a knave.
Answer:
Sue is knave and Marge be knightStep-by-step explanation:
Let Sue be knight and Marge be knave.
Sue says: "Marge is a knave". Since Sue is knight, she is right and Marge should lie.
Marge says: "Sue and I are not the same." - this is right answer too, so this is not a correct response and our assumption is wrong.
Now, let Sue be knave and Marge be knight. Then Marge's response is right and Sue's is wrong. This is a match and this assumption is correct.
The padlock for your gym locker uses a 3 number sequence to open the lock. If the numbers go from 1 to 27, how many different sequences are there on the dial without repeating a number?A. 17,550B. 33,696C. 16,848D. 8,775
SOLUTION:
We want to the different sequences possible without repeating a number.
For the first number, there are 27 ways to select it.
Since we aren't allowed to repeat numbers;
There are 26 ways to select the second number.
There are also 25 ways to select the third number.
Therefore, the different sequences possible are;
[tex]No\text{. of ways =}27\times26\times25=17550\text{ ways}[/tex]Given that p = 6 and q = 2, which yields a quotient greater than -9? ОА -3 a -р B 3 O a O С Зр. (-9) (0) D (-p) (-39)
Good evening, I need help on this questions. Thanks :)
Answer:
A and B ---> decreasing
B and C ---> constant
C and D ---> decreasing
D and E ---> increasing
Explanation:
A function is increasing if we go from left to right and the graph goes up, it is constant when it is a horizontal line and it is decreasing if when we go from left to right the graph goes down.
Therefore, for each part of the function, we get
A and B ---> decreasing
B and C ---> constant
C and D ---> decreasing
D and E ---> increasing
QUESTION 31 POINTThe area of a triangle is 18. The base is 6 inches. What is the height? Do not include units in your answer.
ANSWER:
6
STEP-BY-STEP EXPLANATION:
The area of a triangle is given by the following equation:
[tex]A=\frac{b\cdot h}{2}[/tex]We replace and solve for h (height)
[tex]\begin{gathered} 18=\frac{6\cdot h}{2} \\ h=\frac{18\cdot2}{6} \\ h=6 \end{gathered}[/tex]The height of the triangle is 6 inches
How many modes does the following dataset have? 9,29,13,4,2,16,10,14,27
Given:
[tex]9,29,13,4,2,16,10,14,27[/tex]To find- the mode of the given dataset.
Explanation-
We know that the mode is the most occuring frequency of the dataset. Let us arrange the data in ascending order first, and we get
[tex]2,4,9,10,13,14,16,27,29[/tex]Since there is no repeated frequency, we can say that there is no mode for the given data set.
The answer is 0.
2.) Part A: complete the following table for the functions
Complete the following table for the functions:
[tex]\begin{gathered} f(x)=x^2+1 \\ g(x)=f(x-5) \\ h(x)=f(x+3) \end{gathered}[/tex]The below function represents the transformation of the independent variables:
[tex]\begin{gathered} f(x)=x^2+1 \\ g(x)=f(x-5)\ldots\ldots\text{.f(x) will decrease by 5 units} \\ h(x)=f(x+3)\ldots\ldots.f(x)\text{ will increase by 3 units} \end{gathered}[/tex]NEED ASAP ILL GIVE BRAINLIEST IF CORRECT
Suppose you are choosing at random from the numbers 1 through 12 (inclusive). If the event E is "the number is even," find the set representing E. Express your answer as a bracketed set in the form {a,b,c,d}.
The set numbers from 1 to 12(inclusive) is:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
The set even numbers are:
2, 4, 6, 8, 10, 12
Given that the event E is "the number is even"
Therefore, the set representing the event E as a bracketed set is:
[tex]E=\mleft\lbrace2,4,6,8,10,12\mright\rbrace[/tex]
Melissa wants to rent a boat and spend at most $38. The boat costs $6 per hour, and Melissa has a discount coupon for $4 off. What are the possible numbers of hours Melissa could rent the boat?Use t for the number of hours.Write your answer as an inequality solved for t.
ANSWER:
[tex]t\leq7[/tex]EXPLANATION:
Given:
Melissa wants to rent a boat and spend at most $38
Cost of boat per hour = $6
Discount coupon off = $4
Let t represent the number of hours
We can go ahead and set up the below inequality;
[tex]6t-4\leq38[/tex]Let's add 4 to both sides of the inequality;
[tex]\begin{gathered} 6t-4+4\leq38+4 \\ 6t\leq42 \end{gathered}[/tex]Let's divide both sides by 6;
[tex]\begin{gathered} \frac{6t}{6}\leq\frac{42}{6} \\ t\leq6 \end{gathered}[/tex]So Melissa can rent the boat for up to 7 hours
a^2 - b^4 Evaluate is a= -5 and b= 2
21
Explanations:Given the expression
[tex]a^2-b^4[/tex]We are to find the resulting value given that a = -5 and b = 2
[tex]\begin{gathered} =(-5)^2-(2)^2 \\ =25-4 \\ =21 \end{gathered}[/tex]Hence the value of the expression if a = -5 and b = 2 is 21
when graphed on a coordinate plane,Bumby Avenue can be represented by the equation y=-4x-7. primrose can be represented by the equation 8x+2y=17. Are these streets parallel ?
Answer:
The lines are not parallel because their slopes are opposite reciprocals.
Explanation:
The lines:
[tex]\begin{gathered} y=-4x-7 \\ \text{and} \\ 8x+2y=17 \end{gathered}[/tex]are not parallel because their slopes are not the same
Note:
Two straight lines are said to be parallel when their slopes are the same, and have different y-intercepts.
-2(6.× -8 - 8 × 4)^0
Every number raised to the power of zero is equal to one.
[tex]-2\cdot1=-2[/tex]The final expression is -2
what is the solution set for the inequality
A. x ≤ -5
B. x ≤ 5
C. x ≤ 1
d. x ≤ -14
The solution set to the inequality, 4x + 12 ≤ -8, is determined as: A. x ≤ -5.
How to Find the Solution Set of an Inequality?The solution set is the value of x that would make an inequality statement true. To find the value of x, solve as you would solve a normal equation.
Using the key to the given model in the diagram, we can write the inequality as follows:
On the left, we would have, 4x + 12.
On the right, we would have, -8.
The inequality would be expressed as:
4x + 12 ≤ -8
Solve for x
4x + 12 - 12 ≤ -8 - 12 [subtraction property of equality]
4x ≤ -20
4x/4 ≤ -20/4
x ≤ -5
The solution set is: A. x ≤ -5.
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Use the times and corresponding closing prices of the stock to create coordinate pairs. Let X represent the number of weeks since the first at a point, and Y represent the closing price of each time. So, X equals zero represents the data point from five years ago. There are 52 weeks in a year, and you can write the time for each closing price recorded in terms of weeks that have passed since five years ago, when X equals zero. Fill in the table to represent your data as coordinate pairs
Combining both tables we get:
Jodie is an event planner who believeseach person requires 3.75 feet ofpersonal space at her events. Her nextevent will be at a venue that measures40 feet by 75 feet. How many peopleshould she include on the guest list?
The venue measures 40 ft by 75 ft . This means the venue has the shape of a rectangle. A rectangle
a triangular lot is 130 ft on one side and has a property line of length 700 ft. Find the area of the lot in acres.
Area of the lot = 1.03 acres
Explanations:The line length of the triangular lot = 700 ft
The height of the triangular lot = 130 ft
Note:
Area of a triangle = 0.5 x base x height
Calculate the base of the triangular lot using the Pythagora's theorem
[tex]\begin{gathered} \text{Length}^2=Height^2+Base^2 \\ 700^2=130^2+Base^2 \\ \text{Base}^2=700^2-130^2 \\ \text{Base}^2\text{ = }490000\text{ - }16900 \\ \text{Base}^2\text{ = }473100 \\ \text{Base = }\sqrt[]{473100} \\ \text{Base = }687.82 \end{gathered}[/tex]The base of the triangular lot = 687.82 ft
Area of the triangular lot = 0.5 x 687.82 x 130
Area of the triangular lot = 44708.3 ft²
NB
1 ft² = 2.3 x 10^(-5) Acres
44708.3 ft² = 44708.3 x 2.3 x 10^(-5)
44708.3 ft² = 1.03 acres
Therefore:
Area of the lot = 1.03 acres
Find an equation for the line that passes through the points (1, -3) and (-5,5).=X$?
To answer this question we will use the following two-point formula for the equation of a line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1).[/tex]Therefore the equation of the line that passes through the points (1, -3) and (-5,5) is:
[tex]y-(-3)=\frac{5-(-3)}{-5-1}(x-1).[/tex]Simplifying the above result we get:
[tex]\begin{gathered} y+3=\frac{8}{-6}(x-1), \\ y+3=-\frac{4}{3}x+\frac{4}{3}. \end{gathered}[/tex]Subtracting 3 from the above result we get:
[tex]\begin{gathered} y+3-3=-\frac{4}{3}x+\frac{4}{3}-3. \\ y=-\frac{4}{3}x-\frac{5}{3}. \end{gathered}[/tex]Answer:
[tex]y=-\frac{4}{3}x-\frac{5}{3}.[/tex]Section 5.2-10. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).-2x+3y = 15-x-3y = 12
1)-2x2)
[tex]-2x+3y-(-2x-6y)=15-2\times12\Rightarrow-2x+3y+2x+6y=15-24\Rightarrow9y=-9\Rightarrow y=-1[/tex]y=-1 implies
[tex]-2x+3\times(-1)=15\Rightarrow-2x-3=15\Rightarrow-2x=18\Rightarrow x=-9[/tex]Hence the solution is
[tex](-9,-1)[/tex]A loaded S-sided de is loaded so that the number 4 occurs 3/10 of the time while the other numbers occur with equal frequency. What is the expected value of this die? CASS 08.44 OC.48 Next O My
The probablity of obtain a 4 is= 3/10
The probablity of obtain a 1,2,3,5,6,7,8= 1-3/10=7/10
The expect value is:
[tex]E(p)=X1*p1+X2*p2+X3*p3+...+X8*p8[/tex]And p(1)=p(2)=p(3)=p(5)=p(6)=7/10
All have the same frequency, therefore
p(1,2,3,5,6,7,8)=7/10*1/5=7/50=1/10
Where x=1, 2 ,3,4,5,6 and p=3/10 if is 4 and 7/10 for any other number.
Replacing:
[tex]\begin{gathered} E=(1+2+3+5+6)*\frac{7}{50}+4*\frac{3}{10} \\ \\ E=2.38+1.2=3.58\approx4 \end{gathered}[/tex]hi, can you help me answer this question please, thank you!
The correct option is B
Explanation:The given statement shows that there is a 95% chance that the mean of a sample of 29 gadgets will be between 12.8 and 34.9
CASSANDRA WENT FOR A JO9.SHE RAN AT A PACE OF 7.3 MILESPER HOUR. IF SHE RAN FOR 0.75HOURS, HOW FAR DID CASSANDRARUN?
We can use one simple formula, that is d=vt
d=distance
v=pace
t=time
So,
d=(7.3miles per hour)(0.75 hours)=5.475 miles
Your brother is buying textbooks for college. He has to buy 3 math textbooks and 2 science textbooks. The total cost of his textbooks is $487. Write a linear equation to represent the cost of his textbooks.
Let's define the following variables,
x: cost of a math textbook
y: cost of a science textbook
He has to buy 3 math textbooks and 2 science textbooks, that is,
Total cost = 3x + 2y
The total cost of his textbooks is $487, then the linear equation is,
487 = 3x + 2y
The order in which you write the ratio is ____ to the meaning.
The ratio is defined as fraction in which one number is numertor and other number is denominator.
For example the ratio 2/3 has 2 in numerator and 3 in denominator, but if we write the ratio as 3/2 then it is different from previous ratio 2/3. So in ratio order is important in which you write the ratio.
Thus answer is,
The order in which you write the ratio is important to the meaning.
this lettuce i have is 25 calories per serving. serving size is 85 grams. i had 27 grams. how many calories would that be??
Answer:
7.94117647059 Calories
Step-by-step explanation:
25 Calories = 85 Grams
25/85 = 0.294117647059
0.294117647059 = 1 Gram
0.294117647059 times 27 = 7.94117647059
find two vectors each of norm 1 that I perpendicular to vector A={3,2}
(2√13/13 , 3√13/13) and (-2√13/13 , -3√13/13) are two vectors of norm 1 that are perpendicular to A = (3 , 2) .
What is perpendicular vectors ?In Cartesian coordinates, the given vector can be represented by the line y = -2x/3. The vector is the line segment that connects (0,0) and (3,-2).y = 3x/2 can be used to represent the normal.
If the vector is represented by a line connecting (0,0) to a point (p,q), then,p2 + q2 = 1 because the normal is one length, and q = 3p/2.
As a result,p² + 9p²/4 = 1, 13p²/4 = 1, p = ±√(4/13) = ±2/√13, q = ±3/√13.
After rationalization, one normal vector is (2√13/13 , 3√13/13) and the other is (-2√13/13 , -3√13/13).The two vectors of norm 1 perpendicular to A = (3 , 2) is :
(2√13/13 , 3√13/13) and (-2√13/13 , -3√13/13).
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247474647447x4747474747
Answer:
1174879639277360520909 in exact form
or
in decimal form 1.17487963 x 10^21
Step-by-step explanation:
Solve the following/3x=7-3/x
Value of x is 8.46 for equation 3x=7-3/x
What is Equation?Two or more expressions with an Equal sign is called as Equation
The given equation is 3x=7-3/x
3x+3/x=7
3x²+3=7x
3x²-7x+3=0
Use quadratic equation formula
a=3, b=-7, c=3
x=-b±√b²-4ac/2a
x=7±√49-4(3)(3)/2(3)
x=7±√49-36/6
x=7±√13/6
x=7±√2.16
x=7+1.46
x=8.46
Hence value of x is 8.46 for equation 3x=7-3/x
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Debra will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs anadditional $0.15 per mile driven. The second plan has an initial fee of $59 and costs an additional $0.11 per mile driven.for what amount of driving do the two plans cost the same? i need the answer for miles and cost
First plan cost is modeled as:
50 + 0.15x
where x are the miles driven
Second plan cost is modeled as:
59 + 0.11x
If the two plans cost the same, then:
50 + 0.15x = 59 + 0.11x
0.15x - 0.11x = 59 - 50
0.04x = 9
x = 9/0.04
x = 225 miles
which corresponds to a cost of:
50 + 0.15*225 = $83.75
For an arc length s, area of sector A, and central angle θ of a circle of radius r, find the indicated quantity for the given value. r= 6.45 in, θ= 5 pi\6, s=?
Calculate the arc length by using the following formula:
[tex]s=r\theta[/tex]Replace the values of r and θ and simplify:
[tex]\begin{gathered} s=(6.45in)(5\frac{\pi}{6})=(6.45)(\frac{5}{6})(3.14) \\ s=16.8775in \end{gathered}[/tex]Hence, the arc length is 16.8775 in