The algebraic expression for each phrase would be the following:
a. the product of 9 and a number t would be expressed as:
9*t
b. the difference of a number x and 1/2 would be expressed as:
x - 1/2
c. the sum of a number m and 7.1 would be expressed as:
m + 7.1
d. the quotient of 207 and a number n would be expressed as:
207 / n
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]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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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]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
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
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
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.
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
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]247474647447x4747474747
Answer:
1174879639277360520909 in exact form
or
in decimal form 1.17487963 x 10^21
Step-by-step explanation:
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 $487, then the linear equation is,
487 = 3x + 2y
2. (5 points) A very special island is inhabited only by knights and knaves. Knights always tell
the truth, and knaves always lie. You meet two inhabitants: Sue and Marge. Sue says that
Marge is a knave. Marge claims. "Sue and I are not the same." Determine who is a knight and
who is a knave.
Answer:
Sue is knave and Marge be knightStep-by-step explanation:
Let Sue be knight and Marge be knave.
Sue says: "Marge is a knave". Since Sue is knight, she is right and Marge should lie.
Marge says: "Sue and I are not the same." - this is right answer too, so this is not a correct response and our assumption is wrong.
Now, let Sue be knave and Marge be knight. Then Marge's response is right and Sue's is wrong. This is a match and this assumption is correct.
Jodie is an event planner who believeseach person requires 3.75 feet ofpersonal space at her events. Her nextevent will be at a venue that measures40 feet by 75 feet. How many peopleshould she include on the guest list?
The venue measures 40 ft by 75 ft . This means the venue has the shape of a rectangle. A rectangle
Find an equation for the line that passes through the points (1, -3) and (-5,5).=X$?
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]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
Janet has a scale drawing in her room
Using the scale drawing, we can see that dimensions of the room are 17 feet by 14 feet.
So the correct option is A.
What are the actual dimensions of the room?
We know that each inch in the scale drawing is equal to 5 feet in the real room, in this case we know that the length of the drawing is 3.4 inches, then the real length is:
L = 3.4*5 ft = 17ft
And the width in the drawing is 2.8 inches, then the real width is:
W = 2.8*5 ft = 14ft
Then the dimensions of the room are 17 feet by 14 feet.
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Samantha received a loan from the bank for $4,500. She plans on payinyoff the loan in 4 years. At the end of 4 years, Samantha will have paid$900 in interest. What is the simple interest rate on the bank loan?
The simple interest rate formular is;
I = A - P
A= I + P
A = P ( 1 + rt )
A is the amount after t years
P is the initial amount = $4,500
r is the rate in percent = ?
t is the time in years = 4
A = $4,500 + $900 = $5,400
Therefore to obtain the rate (r)
5400 = 4500 (1 + r x 4 )
1 + 4r = 5400/4500
1 + 4r = 1.2
4r = 1.2 - 1
4r = 0.2
r = 0.2/4 = 0.05
In percentage;
r = 0.05 x 100 = 5%
Thus, the simple interest rate is 5%
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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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]
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
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)
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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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
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(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
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
A kite is flying 95 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 48º. Find the length ofthe string. Round your answer to the nearest tenth.
Given data:
Kite is flying off the ground = 95ft. ( Perpendicular)
Angle = 48 degree
[tex]\sin 48^{\circ}=\frac{Perpendicular}{Hypotenues}[/tex][tex]\text{Hypotenues}=\frac{Perpendicular}{\sin 48^{\circ}}[/tex][tex]\begin{gathered} H=\frac{95}{0.7431} \\ H=127.84ft \end{gathered}[/tex]Thus, the length of the string is 127.8 ft.
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
Simplify. 3 6 4 2m n 4 6m Write your answer using only positive exponents. . X Х ?
we have the expression
[tex](\frac{2m^6n^4}{6m^4})^3[/tex][tex](\frac{2m^6n^4}{6m^4})^3=\frac{(2^3)(m^{(18)})(n^{(12)})}{(6^3)(m^{(12)})}[/tex]simplify
[tex]\frac{(8)(m^{(18-12)})(n^{(12)})}{216}=\frac{(m^6)(n^{(12)})}{27}[/tex]