The given conditions are true:
law of contrapositive
Use long division or a calculator to write 4/99 as a decimal. Then tell whether the decimal is terminating or repeating
0.0404
Repeating decimal (periodic)
1) Let's proceed with the long division of 4 by 99:
1.1) Since 4 is way smaller than 99 let's add one zero to the dividend and another for the quotient followed by a dot.
But 40 is still lesser than 99, so let's add another zero after the dot to make it 400. Now we can divide 400 by 99
1.2) Again to proceed with that division we'll need to write a zero at that 4 and another one in the quotient.
As and we can see already this a repeating decimal or periodic. This division will yield 0.0404040404.....
2) Hence, the answer is 0.0404
Sonia opened a savings account and then added the same amount to the savings account every week. After 5 weeks, her savings account had a total of $45. After 10 weeks, her savings account had a total of $70. Which equation represents the amount of money (y), in dollars, in Sonia's savings account after x weeks?
First let's find the amount Sonia puts in her account each week.
To do so, let's find the amount increased between weeks 5 and 10:
[tex]70-45=25[/tex]The account increased $25 in 5 weeks, so for each week, we have:
[tex]\frac{25}{5}=5[/tex]So Sonia puts $5 in her account each week. Now, we need to find the initial value in the account. If after 5 weeks the account has $45, we can subtract $45 by 5 times the amount per week:
[tex]45-5\cdot5=45-25=20[/tex]So the initial amount is $20.
Now that we have the initial amount and the amount she puts per week, we have the following equation for the amount of money y after x weeks:
[tex]y=5x+20_{}[/tex]So the correct option is the third one.
Rectangle ABCD has vertex coordinates
A(1, -2), B(4, -2), C(4, -4), and D(1,
-4). It is translated 1 unit to the left and 1 3 units up. What are the coordinates
of B?
A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.
Response: C
What is a graph's vertex?A node of a graph, or one of the points on which the graph is defined and which may be connected by graph edges, is referred to as a "vertex" in computing.
For instance, a rectangle's four sides result in its four vertices.
Response: C . The coordinates are obtained by first subtracting 1 from 4 to obtain 3 and then adding 3 to -2 to obtain 1. (3, 1)
The vertex is the collective endpoint. Vertex, on the other hand, refers to the common terminal point where two rays converge to make an angle. In a similar manner, we must understand an angle's arm. The term "arm of an angle" refers to the two rays that unite to make an angle.
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Two cars are driving on the same road, in the same
direction. They start driving from the same place and are
traveling at a constant speed. The second car started
driving 1.5 hours after the first car started driving. If the
second car drives 60 miles per hour and the first drives 40
miles per hour, how many miles will each car have
traveled when the second car catches up to the first?
Answer:
180 miles
Step-by-step explanation:
distance = rate x time
t = time
1st car:
distance = 40t
2nd car:
distance = 60(t - 1,5)
When the car catch up to each other the distances will be the same, so set the equation equal to each other. Calculate the time and then put the time back into either equation and solve for the distance.
40t = 60(t-1.5) Distribute the 60
40t = 60t -(60)1.5
40t = 60t - 90 Subtract 60t from both sides of the equation
-20t = -90 Divide both sides by -20
t = 4.5
Now that we know the time, substitue that back into either equaiton and solve for the time
distance = 40 (4.5)
180 miles
Find an equation for the line that passes through the points (-2,-6) and (6,-4).
Answer:
[tex](y+6)=\frac{2}{8} (x+2)[/tex]
Step-by-step explanation:
First, find the slope
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
-4+6=2
6+2=8
m=2/8
With the slop, you have everything you need to stick one of your points in point-slope form. I chose (-2,-6)
[tex](y-y1)=m(x-x1)\\(y+6)=\frac{2}{8} (x+2)[/tex]
Really, that's all you need as it is not an equation of a line. Not the most useful form, but works as an answer.
Hooke's Law says that the force exerted by the spring in a spring scale varies directly with the distance that the spring is stretched. If a 20 pound mass suspended on a spring scale stretches the spring 20 inches, how far will a 29 pound mass stretch the spring? Round your answer to one decimal place if necessary.
The Hooke's law is given by:
F = k*x
Where:
F = force
k = constant factor
x = distance
If F = 20 and x = 20
20 = k*20
Solving for k:
20/20 = k
k = 1
So: how far will a 29 pound mass stretch the spring?
29 = 1* x
Solving for x:
29/1 = x
x = 29 in
The recursive rule for a sequence and one of the specific terms is given. Find the position of the giving term. f(1)= 8 1/2; f(n)= f(n-1) - 1/2; 5 1/2
f(7) gives 5 1/2.
the position is the 7th term
Explanation:
f(1)= 8 1/2
f(n)= f(n-1) - 1/2
we are looking for the function that gives 5 1/2
We have been given f(1), this means n = 1
f(1) = f(1-1) - 1/2
8 1/2 = f(0) - 1/2
f(0) = 8 1/2 + 1/2
f(0) = 8 + 1 = 9
when n = 2
f(2) = f(2-1) - 1/2
f(2) = f(1) - 1/2
f(2) = 8 1/2 - 1/2
f(2) = 8
when n = 3
f(3) = f(3-1) - 1/2
f(3) = f(2) - 1/2
f(3) = 8 - 1/2
f(3) = 7 1/2
when x = 4
f(4) = f(4-1) - 1/2
f(4) = f(3) - 1/2
f(4) = 7 1/2 - 1/2
f(4) = 7
when n = 5
f(5) = f(5-1) - 1/2
f(5) = f(4) - 1/2
f(5) = 7 - 1/2
f(5) = 6 1/2
f(6) = f(6-1) - 1/2
f(6) = f(5) - 1/2
f(6) = 6 1/2 - 1/2 = 6
when n = 7
f(7) = f(7-1) - 1/2
f(7) = f(6) - 1/2
f(7) = 6 -1/2 = 5 1/2
f(7) gives 5 1/2.
Hence, the position is the 7th term
Solve the following inequality. Graph the solution set and then write it in interval notation .
Given:
-2x ≥ 6
Solve for x
Divide both sides by -2
-2x/-2 ≤ 6/-2
x ≤ -3
Graph:
Interval notation (-∞, -3 ]
#11 When you were born, your grandparents deposited $10,000 in a CD. for your college education. If theaccount earns 5% interest, compounded monthly, how much will be in the account for your collegeeducation?
Replacing with the values we already know, we have:
PV = 10,000
i = 5% or 0.05 but it is compounded monthly, then it is 0.05/12
n = 18 years or 216 months
10,000 = FV * 0.4073
FV = 10,000/0.4073
FV = $ 24,551.93
It is very close to option D, where the term "about" is included.
james harmon pays 850.80 per year for his life insurance. if he where to the premiums quarterly, the payments would would be 221.21 what percentage more is mr hamrmon paying for the year using yhe quarterly rate
Percent is given by the expression:
[tex]\begin{gathered} \text{Total}\cdot\frac{\text{percent}}{100}=\text{Equivalent number to the percent} \\ 850.8\cdot\frac{x}{100}=221.21 \\ x=\frac{221.21\cdot100}{850.8} \\ x=26\text{ percent} \end{gathered}[/tex]So, he is paying 74% more using the quarterly rate
Write each of the following products (the result to a multiplication problem) using exponents to express the results in a simpler form.(3a)(5a) __________(5p)(2p) ___________(3 inches)(5 inches)___________(5 feet)(2 feet)_________
Let's do the mutiplications:
(3a)(5a) = 15a²
(5p)(2p) = 10p²
(3 inches)(5 inches) = 15 inches²
(5 feet)(2 feet) = 10 feet²mutiplic
Solve this system of linear equations. Separatethe x- and y-values with a comma.18x - 10y = 749x - 9y = 45
Given,
[tex]\begin{gathered} \text{The system of pair of linear equation is,} \\ 18x-10y=74\ldots\ldots\ldots\ldots\ldots.\ldots.(i) \\ 9x-9y=45\ldots\ldots\ldots..\ldots\ldots\ldots.(ii) \end{gathered}[/tex]Multiplying equation (ii) by 2 as it make the coefficent of x in both equation equal.
[tex]\begin{gathered} 18x-10y=74\ldots\ldots\ldots\ldots\ldots.\ldots.(i) \\ 18x-18y=90\ldots\ldots\ldots..\ldots\ldots\ldots.(iii) \\ \end{gathered}[/tex]Substracting equation (i) from equation (iii) then we get,
[tex]\begin{gathered} 18x-18y-(18x-10y)=90-74 \\ 18x-18y-18x+10y=16 \\ -8y=16 \\ y=-2 \end{gathered}[/tex]The value of y is -2.
Substituting the value of y in equation (i) then,
[tex]\begin{gathered} 18x-10y=74 \\ 18x+20=74 \\ 18x=54 \\ x=3 \end{gathered}[/tex]Hence, the solution of the linear pair (x, y) is (3, -2).
what number is divisible by 5 ? 86,764,670,or27
The number divisible by 5 is 670.
Numbers divisible by 5 have their last digits as 0 or 5
Answer : 670
Solving Equations ** Reminder need to show ALL work **
solution
For this case we have the following equation:
[tex]\frac{3}{4}x-5=4[/tex]Then we can add 5 in both sides and we got:
[tex]\frac{3}{4}x=9[/tex]Then we can multiply both sides by 4/3 and we got:
[tex]x=9\cdot\frac{4}{3}=12[/tex]And the final solution for this case is x= 12
A firm incurs $70,000 in interest expenses each year. If the tax rate of the firm is 30%, what is the effective after-tax interest rate expense for the firm?
Answer:
After tax interest expenses = Interest expenses x (100 - Tax Rate)
= 70000 x (100 - 30)%
= 70000 x 70%
= $49,000.00
Step-by-step explanation:
740In the table on the right there are grades that were earned by students on a midtermbusiness math exam What percent of the students earned a grade below 80?83977084986685687783958879648890859396The percent of students with grade below 80 is(Round to the nearest whole number as needed)
Notice that the number of students that got a grade below 80 is:
[tex]7,[/tex]and the total number of students is:
[tex]20.[/tex]Therefore, we have to determine what percentage 7 represents from 20. To determine the percentage that x represents from y, we can use the following expression:
[tex]\frac{x}{y}*100.[/tex]Finally, we get that 7 represents the
[tex]\frac{7}{20}*100=35\%,[/tex]of 20.
Answer:
[tex]35\%.[/tex]Brian is looking to add tile to one wall in his kitchen, each tile is a rectangle that measures
14 inches by 2 inches. The wall that Brian wants to tile is a rectangle that measures
44.25inches by 51 inches. How many bie's will Brian need to cover the wall?
Using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.
What is a rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can also be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.So, tiles needed to cover the wall:
The formula for the area of a rectangle: l × bCalculate the area of a tile as follows:
l × b14 × 228 in²Now, calculate the area of the wall as follows:
l × b44.25 × 512,256.75 in²Then, tiles needed to cover the wall:
2,256.75/2880.59Which means: 80½
Therefore, using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.
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what is the solution to the system 3x-y+5=02x+3y-4=0A. X= -1, Y= -2B. X= -1, Y= 2C. X= 2, Y= -1D. X= 2, Y= 1
To find the solution to the system of equation
we will use the elimination method
3x - y = - 5 ----------------------------(1)
2x + 3y = 4 -------------------------------(2)
We will eliminate y and solve for x
multiply equation (1) through by 3
9x - 3y = - 15 ------------------------------------(3)
add equation (2) and equation (3)
11x = -11
divide both-side of the equation by 11
x = -1
substitute x = -1 in equation (1) and solve for y
3x - y = - 5
3(-1) - y = -5
-3 - y = -5
add 3 to both-side of the equation
- y = -5 +3
-y = -2
multiply through byb -1
y = 2
Hence, the correct option is B
Find a.Round to the nearest tenth:a10 cm150°12°с=a = [ ? ]cmLaw of Sines: sin A=sin Bbasin cСEnter
Answer:
24.0 cm
Explanation:
To find the value of a, we will use the Law of sines, so
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}[/tex]So, replacing A = 150°, B = 12°, and b = 10 cm, we get:
[tex]\frac{\sin150}{a}=\frac{\sin 12}{10}[/tex]Now, we need to solve for a. First, cross multiply
[tex]10\cdot\sin 150=a\cdot\sin 12[/tex]Then, divide by sin12
[tex]\begin{gathered} \frac{10\cdot\sin150}{\sin12}=\frac{a\cdot\sin 12}{\sin 12} \\ \frac{10\cdot(0.5)}{0.208}=a \\ 24.0=a \end{gathered}[/tex]Therefore, a = 24.0 cm
Given that angle A lies in Quadrant IV and cos(A)= 7/10, evaluate sin(A).
The value of the trigonometric function is; sin(A) =√51/10.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We have been given that angle A lies in Quadrant IV and cos(A)= 7/10 then;
cos(A)= 7/10
Hence, base = 7
hypotenuse = 10
Therefore, perpendicular
h² = b² + p²
10² = 7² + p²
100 = 49 + p²
p = √51
Then sin(A = perpedicular/ hypotenuse
sin(A) = √51/10
Hence, the value of the trigonometric function is; sin(A) =√51/10.
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polynomials: classifying, simplifying adding and subtracting polynomials write in standard formplease do minimum steps
do an addition in binary (inverse code) on following numbers:
00011101
+ 111111101
please, help asap thank u
The first complement of the binary addition is 00011111.
The binary addition operation works similarly to the base 10 decimal system, except that it is a base 2 system. The binary system consists of only two digits, 1 and 0.
Given that, the addition of the given number
00011101 + 11111101
In the binary addition,
0+1 = 1
1+0 = 1
1+1 = 0
00011101 + 11111101 = 11100000
Then inverse code means first complement of the answer.
In the first complement, 0 is the inverse of 1 and 1 is inverse of 0.
11100000 = 00011111
Hence, The first complement of the binary addition is 00011111.
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By using the substitution u = 4 + 3x^2, or otherwise, find
Solution
We have the following integral:
[tex]\int \frac{2x}{(4+3x^{2})^{2}}dx[/tex]We can use the substitution u= 4 +3x² and we have du= 6x dx, then we have this:
[tex]\int \frac{2x}{(u^{})^2}\cdot\frac{du}{6x}=\frac{1}{3}\int u^{-2}du=\frac{1}{3}\cdot\frac{u^{-1}}{-1}+C=-\frac{1}{3u}+C=-\frac{1}{3(4+3x^{2})}+C[/tex]Joe bought 8 comic books for $36. How much does 1 comic book cost?
Answer:
1 comic book costs $4.5
Explanation:
Given that 8 comic books cost $36
To know how much 1 comic book costs, let x be the cost of 1 comic book, then, we have:
8 comic books = $36
1 comic book = x
Then we have the equation
8x = 36
where we can solve for x
Divide both sides by 8
8x/8 = 36/8
x = 4.5
Therefore, 1 comic book costs $4.5
The area of a rectangular garden is 1,432 meters. If the length of the garden is 40 meters,
what is the width of the garden?
Answer: 35.8
Step-by-step explanation: 40x?=1432
40x35.8=1432
Hello! I need some help with this homework question, please? The question is posted in the image below. Q17
The function being one-to-one implies that every value of x, has one one vaue of y, and every value of y, has one value of x.
The inverse uses the output(y value) as an input(x value) and spits it out to get the original x value inputted into f.
Using the given point ( 2, -5 ), it implies of f(2) = -5. Since the function is one-to-one, this implies that:
[tex]f^{-1}(-5)=2[/tex][tex]\text{Thus, the point on the graph of f}^{-1}\text{ is }(-5,2\text{ )}[/tex]Hence, the correct option is option B
. Identify the difference. -2-(-6)
In this case,
This difference is made this way:
-2 - (-6) =
-2 +6 = 4
So there we have this identity. The minus before the parentheses turns the minus into plus sign.
Select the correct answer.Using long division, what is the quotient of 3r4 + 2023 + 1422 + 17= + 30 and I + 67
EXPLANATION
we are asked to use the long division method to solve the division
[tex]\frac{3x^4+20x^3+14x^2+17x+30}{x+6}[/tex]We will have
Perform the indicated operation by removing the parentheses and combining like terms.(5x + 3) + (x2 – 8x + 4)
Given the sum of the functions expressed as:
[tex]\mleft(5x+3\mright)+x^2-8x+4[/tex]Collecting the like terms:
[tex]x^2+5x-8x+3+4[/tex]Group the terms based on their degrees
[tex]x^2+(5x-8x)+(3+4)[/tex]Simplify the result to determine the final answer:
[tex]\begin{gathered} x^2+(5x-8x)+(3+4) \\ x^2+(-3x)+7 \\ x^2-3x+7 \end{gathered}[/tex]Hence the required sum of the functions is x^2 - 3x + 7
The probability that a tourist- will spot a Cheetah in Kruger National park is 0.4, the probability that he will spot a Tiger, is 0.7, and the probability that he will spot a Cheetah, or a Tiger or both is 0.5. What is the probability that the tourist will spot: (a) both animals? (b) neither of the animals? (c) Determine with appropriate reason whether the event of spotting a Cheetah and a Tiger are independent or not?
Since the probability of Cheetah is 0.4
Since the probability of Tiger is 0.7
Since the probability of Cheetah or Tiger or both is 0.5
Let us draw a figure to show this information
Then we need to find both animals (x)
Since
[tex]0.5+x=0.7+0.4-x[/tex]Add x to both sides and subtract 0.5 from both sides
[tex]\begin{gathered} 0.5+x+x=0.7+0.4-x+x \\ 0.5+2x=1.1 \\ 0.5-0.5+2x=1.1-0.5 \\ 2x=0.6 \end{gathered}[/tex]Divide both sides by 2 to find x
[tex]\begin{gathered} \frac{2x}{2}=\frac{0.6}{2} \\ x=0.3 \end{gathered}[/tex]a) The probability of both animals is 0.3
Since the total of probability is 1, then to find the neither subtract (0.4 + 0.7 - 0.3) from 1
[tex]\begin{gathered} N=1-(0.4+0.7-0.3) \\ N=1-0.8 \\ N=0.2 \end{gathered}[/tex]b) the probability of neither is 0.2
Events A and B are independent if the equation P(A∩B) = P(A) · P(B)
Since
[tex]P(Ch\cap T)=0.3[/tex]Since P(Ch) . P(T) = 0.4 x 0.7 = 0.28
Then
[tex]P(Ch\cap T)\ne P(Ch).P(T)[/tex]c) The events are not independent