Distance using absolute value for each example are given below:
205916147555104328346916807227323816As given in the question,
Distance Using Absolute Value
Difference between each set of points on the number line and also confirming it by writing an absolute value statement for each.
1) –15 and 35
Distance Using Number Line –15 – (–35) = –15 + 35 = 20
Absolute Value Statement |–15 – (–35)| = 20
2) 47 and –12
Distance Using Number Line 47 – (–12) = 47 + 12 = 59
Absolute Value Statement |47 – (–12)| = 59
3) –43 and 27
Distance Using Number Line –43 – (–27) = –43+27 = – 16
Absolute Value Statement |–43 – (–27)| = 16
4) –10 and 4
Distance Using Number Line –10 – 4 = –14
Absolute Value Statement |–10 – 4| = 14
5) 50 and –25
Distance Using Number Line 50 – (–25) = 50 + 25 = 75
Absolute Value Statement |50 – (–25)| = 75
6) 36 and –19
Distance Using Number Line 36 – (–19) = 36+19 = 55
Absolute Value Statement |36 – (–19)| = 55
7) –30 and –40
Distance Using Number Line –30 – (–40) = –30 + 40 = 10
Absolute Value Statement |–30 – (–40)| = 10
8) –2 and –45
Distance Using Number Line –2 – (–45) = –2 + 45 = 43
Absolute Value Statement |–2 – (–45)| = 43
9) 18 and 46
Distance Using Number Line 18 – 46 = –28
Absolute Value Statement |18 – 46| = 28
10) –10 and –44
Distance Using Number Line –10 – (–44) = –10 + 44 = 34
Absolute Value Statement |–10 – (–44)| = 34
11) –28 and 41
Distance Using Number Line –28 – 41 = –69
Absolute Value Statement |–28 – 41| = 69
12) 7 and –9
Distance Using Number Line 7 – (–9) = 7+9 = 16
Absolute Value Statement |7 – (–9)| = 16
13) –52 and 28
Distance Using Number Line –52 – 28 = –80
Absolute Value Statement |–52 – 28| = 80
14) 22 and –50
Distance Using Number Line 22 – (–50) = 22 + 50 = 72
Absolute Value Statement |22 – (–50)| = 72
15) –4 and –31
Distance Using Number Line –4 – (–31) = –4 + 31 = 27
Absolute Value Statement |–4 – (–31)| = 27
16) 19 and 51
Distance Using Number Line 19 – 51 = –32
Absolute Value Statement |19 – 51| = 32
17) 0 and –38
Distance Using Number Line 0 – (–38) = 0+ 38 = 38
Absolute Value Statement |0 – (–38)| = 38
18) 2 and –14
Distance Using Number Line 2 – (–14) = 2+14 = 16
Absolute Value Statement |2 – (–14)| = 16
Therefore, distance using absolute value for each example are given below:
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Which of the following equations best represents "y is inversely related to x"?
y = kx
y = kx2
y = k(1/x)
y = k(1/x2)
and i dont think it is c
The equations best represents "y is inversely related to x" is y = k(1/x).
What is an inverse proportionality?The inverse proportionality can be described as the relationship that exist between two or more quantities whereby when one of the quantities is increasing in value, then the the second quantity will be decreasing in value however there will be a proportionality constant that would be found in the equation.
Considering the chosen option D, we can see that when the value of y is increasing then the value of x will be decreasing, and when the value of x is decreasing , them the value of y will be increasing.
Therefore, option C is correct.
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X+4y=10 and 3x-y=-9 find the value of x/y
[tex]x = 10 - 4y.....(3)[/tex]
I WILL SOVE BY SUBSTITUTION.
[tex]3(10 - 4y) - y = - 9 \\ 30 - 12y - y = - 9 \\ - 13y = -9 - 30 \\ - 13y = - 39 \\ \frac{ - 13y}{ - 13} = \frac{ - 39}{ - 13} \\ y = 3 \\ [/tex]
[tex] x= 10 - 4(3) \\ x = 10 - 12 \\ x = - 2[/tex]
we have (-2,3)
ATTACHED IS THE SOLUTION
A zookeeper is 6 14 feet tall. A young giraffe in his care is 93/8 feet tall. How many times as tall as the zookeeper is the giraffe?
The sum of a number and 4
The solution for x in the equation x + 4 = 12 is 8.
Given,
Sum of two numbers is 12
Take the first number as x
Second number is given as 4
We have to find the value of x.
The equation will be like:
x + 4 = 12
Solve for x in the equation.
Add -4 to both sides
x + 4 - 4 = 12 - 4
x = 8
That is, the solution for x in the equation x + 4 = 12 is 8.
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The question is incomplete. Completed question is given below.
The sum of a number and 4 is 12. Find the number.
convert 0.43 to a percent
Answer:
43%
Step-by-step explanation:
To convert a decimal to a percent, you have to move the decimal over 2 times to the right.
Rhianna drew a scale drawing of a house and its lot. She used the scale 9 inches = 5 feet. What is the scale factor of the drawing?
Simplify your answer and write it as a fraction.
The scale factor that was used for the drawing is 1 inch represents [tex]\frac{5}{9}[/tex] feet.
What is the scale factor?A fraction is a non-integer that has a numerator and a denominator. An example of a fraction is 2/9. 2 is the numerator and 9 is the denominator.
A scale drawing is either a smaller or a bigger version of another image. If the scale used in the drawing is smaller in relation to the dimension of the original image, the scale drawing is a reduced image. If this is not the case, then it is a bigger scale drawing.
The scale drawing is usually reduced at a constant dimensions using a scale factor. In order to determine the scale factor, divide both dimensions provided by 9.
(9 / 9) = (5 / 9)
1 inch = 5/9 feet
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Use the square root property to solve the equation.(x + 8)² = 2Select one:O A. (-8+√√2)OB. √2-√√8O C. (√2+8,-√2+8}O D. (-8± √2)
Answer: D
Jason made a spherical cake pop that is 1.3 inches in diameter. He coated the whole cake pop with sprinkles.What is the approximate area Jason covered with sprinkles?
Given:
The diameter of the sphere is 1.3 inches.
The surface area of the sphere is given as,
[tex]\begin{gathered} SA=4\pi\times r^2 \\ SA=4\pi\times(\frac{d}{2})^2 \\ SA=4\pi\times(\frac{1.3}{2})^2 \\ SA=1.69\pi \\ SA=1.69\times3.14\ldots\ldots\pi=3.14 \\ SA=5.3066 \\ SA\approx5.3\text{ square inches} \end{gathered}[/tex]Answer: area covered with sprinkles is 5.3 square inches
18 is 50% of what????????
Let the unknown value be x.
18 is 50% of ________n can also be written as;
18 = 50% of x
of means multiplication;
18 = 50% * x
18 = 50/100 * x
18 = 50x/100
cross multiply
18 * 100 = 50x
1800 = 50x
Divide both sides by 50
1800/50 = 50x/50
180/5 = x
x = 180/5
x = 36
Hence 18 is 50% of 36
Solve similar triangles (advanced) khan academy. solve for x
Answer:
that would be X=22, i had the same thing today, and got it right :D
Step-by-step explanation:
The Stingrays at the zoo requires the 196 gallon tank to be 4% salt. After a period of time, some water evaporated, raising the salinity to 7%.
How many gallons of water must be resupplied in order to bring the salinity back down to 4%?
Answer:
196 x 3 / 100 = 5,88
Step-by-step explanation:
7% - 4% = 3%
So we need to had 3% t have again 4%
Find the measure of arc indicated using the inscribed angle given in thecircle below.X91 0YZ?
SOLUTION
The correct option is A (the first option)
We are asked to find the measure of the angle at the center.
Circle theorem:
The angle at the center of a circle = 2 x Angle at the circumference
The angle at the center of the circle = 2 x = 2 x 91 degrees
=182 degrees
The value for the angle at the center (?) of this circle is
[tex]182^o[/tex]The correct option is A (the first option)
Which expression does not belong with the other three? justify your response.
To find the equation that does not belong with the other three we have to solve each equation.
Given the equation:
[tex]4\cdot x\cdot7=56[/tex]Dividing by 4 at both sides:
[tex]\begin{gathered} \frac{4\cdot x\cdot7}{4}=\frac{56}{4} \\ x\cdot7=14 \end{gathered}[/tex]7:
[tex]\begin{gathered} \frac{x\cdot7}{7}=\frac{14}{7} \\ x=2 \end{gathered}[/tex][tex]5\cdot2\cdot x=40[/tex]Simplifying on the left:
[tex]10\cdot x=40[/tex]10:
[tex]\begin{gathered} \frac{10\cdot x}{10}=\frac{40}{10} \\ x=4 \end{gathered}[/tex]:
[tex]x\cdot3\cdot9=54[/tex][tex]x\cdot27=54[/tex]27:
[tex]\begin{gathered} \frac{x\cdot27}{27}=\frac{54}{27} \\ x=2 \end{gathered}[/tex][tex]4\cdot x\cdot5=40[/tex]4 :
[tex]\begin{gathered} \frac{4\cdot x\cdot5}{4}=\frac{40}{4} \\ x\cdot5=10 \end{gathered}[/tex]5
[tex]\begin{gathered} \frac{x\cdot5}{5}=\frac{10}{5} \\ x=2 \end{gathered}[/tex]In consequence, the equation that does not belong with the other three is:
[tex]5\cdot2\cdot x=40[/tex]because its solution, 4, is different from the solution to the other equations (2).
If we change the 5 in the equation by a 10 and solve the equation we get:
[tex]\begin{gathered} 10\cdot2\cdot x=40 \\ \frac{10\cdot2\cdot x}{10}=\frac{40}{10} \\ 2\cdot x=4 \\ \frac{2\cdot x}{2}=\frac{4}{2} \\ x=2 \end{gathered}[/tex]And now the equation (with a 10) belongs with the other three
In a recent year, there were 29,757 traffic fatalities in the United States. Of these, 9001 were alcohol related.
(a) What is the probability that a bandomly selected traffic fatality in this year was alcohol related?
(b) What is the probability that a randomly selected traffic fatality in this year was not alcohol related?
(c) What is the probability that two randomly selected traffic fatalities in this year were both alcohol related?
(d) What is the probability that neither of two randomly selected traffic fatalities in this year were alcohol related?
(e) What is the probability that of two randomly selected traffic fatalities in this year, at least one was alcohol related?
we have found out the probability for different cases when there were 29,757 traffic fatalities in the United States and of these, 9001 were alcohol related.
Total traffic fatalities = 29,757
Alcohol related = 9001
(a) probability that a randomly selected traffic fatality in this year was alcohol related:
P = 9001 / 29,757 = 0.302
(b) probability that a randomly selected traffic fatality in this year was not alcohol related:
P = 1 - 0.302 = 0.698
(c) probability that two randomly selected traffic fatalities in this year were both alcohol related:
P = 0.302 × (9000 / 29756)
P = 0.091
(d)What is the probability that neither of two randomly selected traffic fatalities in this year were alcohol related:
P = 1 - 0.091
P = 0.909
(e) probability that of two randomly selected traffic fatalities in this year, at least one was alcohol related
P = 0.302 + 0.302 = 0.604
Therefore, we have found out the probability for different cases when there were 29,757 traffic fatalities in the United States and of these, 9001 were alcohol related.
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Heights of 10-year old's, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches.
(a). The height requirement for Batman the Ride is 54 inches. What percent of 10 year old's cannot go on this ride?
(b). Suppose there are four ten year olds. What is the chance that at least two of them will be able to ride Batman the Ride?
(c). Suppose you work at the park to help them better understand their customers demoghraphics, and you are counting people as they enter the park. What is the chance that the first 10 year old you see who can ride Batman the Ride is the 3rd 10 year old who enters the park?
(d). What is the chance that the 5th 10 year old you see who can ride Batman the Ride is the 12th 10 year old who enters the park?
Using the normal distribution and the binomial distribution, it is found that:
a) 43.25% of 10 year old's cannot go on this ride.
b) There is a 0.7814 = 78.14% probability that at least two of them will be able to ride Batman the Ride.
c) There is a 0.1062 = 10.62% probability that the first 10 year old you see who can ride Batman the Ride is the 3rd 10 year old who enters the park.
d) There is a 0.0834 = 8.34% probability that the 5th 10 year old you see who can ride Batman the Ride is the 12th 10 year old who enters the park.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.In the context of this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 55, \sigma = 6[/tex]
For item a, the proportion is the p-value of Z when X = 54, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (54 - 55)/6
Z = -0.17.
Z = -0.17 has a p-value of 0.4325.
Hence the percentage is of 43.25%.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.For item b, the parameters of the binomial distribution are given as follows:
p = 0.5675, n = 4.
Hence:
P(X = 2) = 6 x (0.5675)² x (0.4325)² = 0.3615.P(X = 3) = 4 x (0.5675)³ x (0.4325)¹ = 0.3162.P(X = 4) = (0.5675)^4 = 0.1037.Hence:
P(X >= 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.3615 + 0.3162 + 0.1037 = 0.7814.
Which is the probability.
For item c, the probability is given as follows:
p x P(X = 0 with n = 2).
Hence:
p = 0.5675 x (0.4325)² = 0.1062.
For item d, the probability is given as follows:
p x P(X = 4 with n = 11). (inverse binomial).
Hence:
0.5675 x (11!)/(5! x 6!) x (0.5675)^4 x (0.4375)^7 = 0.0834.
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15. Over what range of angles does the value of sin(O) consistently increase?
A. 45° to 135°
B. 90° to 180°
C. 0° to 180°
D. 0° to 90°
The value of sin(O) will at the range of 0° to 90° consistently increase. This makes option D the correct options.
how to find the range of values where sin will consistently increaseIn trigonometry, the first basic functions are the sin, cos and tan.
In a right angle triangle the sin is represented as the ratio of opposite to hypotenuse. cos is represented as the ratio of the adjacent to hypotenuse, while tan is the ratio of opposite to adjacent or ratio of sin to cos.
Plotting the graph of sin functions, the pattern forms a sinusoidal pattern which bears its maximum value at sin 90degrees and the minimum value at sin 0 degrees.
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A pedestrian signal at a crosswalk has the following cycle: "WALK” for 45 seconds, "DON'TSTART" for 30 seconds and "DONT WALK" for 40 seconds. What is the probability the signalwill show "DON'T START" if you arrive at a random time? Write your answer as a percentagerounded to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
The probability is represented by the following equation:
[tex]undefined[/tex]what picture can you draw to show a thinking about 9÷4?
Think of
[tex]\frac{Green}{Red}[/tex]In a standard normal distribution, the range of values of z is from _____.
In a standard normal distribution, the range of values of z is from: D. d. -∞ to ∞.
What is a z-score?A z-score is also known as a standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
What is a normal distribution?A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than the data that are far from the mean.
In conclusion, the range of values of z in a standard normal distribution are all real numbers which typically ranges from negative infinity (-∞) to positive infinity (∞).
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Complete Question:
In a standard normal distribution, the range of values of z is from ______.
a. -3.09 to 3.09
b. -1 to 1
c. 0 to 1
d. -∞ to ∞
Where do you find a vertical shift in the exponential parent function?
What happens when (x-4) is in the exponent?
What happens when (x+9) is in the exponent?
Where do you find a horizontal shift in the exponential parent function?
What happens when there is a +7 at the end of the exponential parent function?
What happens when there is a -6 at the end of the exponential parent function?
For the given expressions we will have:
y = exp(x - 4) →we have a shift of 4 units to the right.
y = exp (x +9) → we have a shift of 9 units to the left.
y = exp(x) + 7 → we have a shift of 7 units up.
y = exp(x) - 6 → we have a shift of 6 units down.
How to work with vertical and horizontal shifts?
Remember that the shifts work as follows.
For a function f(x), we define a vertical shift of N units as:
g(x) = f(x) + N
If N > 0, the shift is upwards.If N < 0, the shift is downwards.For a function f(x), we define a horizontal shift of N units as:
g(x) = f(x + N)
If N > 0, the shift is to the left.If N < 0, the shift is to the right.Then, if we have:
exp(x - 4) we have a shift of 4 units to the right.
exp (x +9) we have a shift of 9 units to the left.
exp(x) + 7 we have a shift of 7 units up.
exp(x) - 6 we have a shift of 6 units down.
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Two numbers are respectively 60% and 20% of a third number, second number exepress ss as a perentage of first is?
Answer:
10%
Step-by-step explanation:
this is because the total number is supposed to be 100%
and 60%+20%=90%. 100%-90%=10%.
So 10% is the final answer
Help
Simplify the negative exponent. Please show your work.
4 ⁻⁴
Answer: 0.0625
Step-by-Step Explanation: positive exponents = multiply the number by itself however many times the exponent demands.
negative exponents: multiply the reciprocal of the base number by itself however many times the exponent demands.
The area of a circle is 100π cm². What is the circumference, in centimeters? Express your answer in terms of \piπ. THE ACTUAL ANSWER PLEASE
Answer:
35.45
Step-by-step explanation:
C=2πA=2·π·100≈35.44908
13. Making an argument. Your friend claims that a line always represents a function. Is your friend
correct? Explain your reasoning
Based on the given argument, it is concluded that my friend's reasoning was incorrect.
What is a Linear Function?This refers to the type of function that represents one line on a linear plane in cartesian mathematics.
With this in mind and from the claim of my friend that a line always represents a function, my friend is incorrect because If the line was vertical, then it could not pass through and as such, cannot represent a function.
Therefore, the answer to the question is that my friend is incorrect in his claim about lines and functions.
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HELP ME PLEASE SOON NEED RN
Answer:
x = + or - 8
Step-by-step explanation:
2x^2 = 128
solve for x
hope this helped have a great day ^^
The proof is converted to paragraph form.
Which parts of the paragraph proof are incorrect?
The part "since ∠ AMC is a right angle, ∠BMC and ∠CMD will be complementary" and "since ∠ BMC is a right angle, ∠BMC and ∠AMB will be complementary" , the paragraph proof is incorrect.
We are given that,
∠ AMC and ∠BMC are right angles.
Since,
∠ AMC = ∠ AMB + ∠ BMC
The paragraph part should have been ∠ AMB and ∠ BMC are complementary angles and,
Since,
∠ BMD = ∠ BMC + ∠ CMD
The paragraph part should have been ∠ CMD and ∠ BMC are complementary angles instead of the part given in the paragraph proof.
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Write .24 as a fraction
in lowest terms.
Answer:
.24 as a fraction is 6/25
Step-by-step explanation:
1) Let convert our decimal into a percentage so we could write it in the not simplified fraction of 0.24:
.24 = 24% = 24/100
2) Now since we have 24/100, we could now simplify:
24/100 = 12/50 = 6/25
We can't simplify anymore.
Answer: 6/25
Step-by-step explanation:
I need help with this
Answer:
[tex]\text{ 78 miles per hour}[/tex]Step-by-step explanation:
Given the linear function for the traffic fines:
[tex]f(s)=14(s-60)+40[/tex]If a fine comes to $292, substitute f(s)=292 and solve for "s" to find the speed of the person:
[tex]\begin{gathered} 292=14(s-60)+40 \\ 292=14s-840+40 \\ 14s=292+840-40 \\ 14s=1092 \\ s=\frac{1092}{14} \\ s=78\text{ miles per hour} \end{gathered}[/tex]what does this mean 3|-3| the whole |-3| thing I'm confused please help
|-3| means "the absolute value of 3", which is a way of saying how far away from zero the number -3 is on the number line.
The definition of absolute value goes like this:
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
In other words, if the number [tex]x[/tex] inside the absolute value bars is already positive or zero, we leave it alone. If instead [tex]x[/tex] is negative, we multiply it by -1 to recover the positive version of that number.
Since -3 is negative, it follows that |-3| = -(-3) = 3. So the expression 3 |-3| is equivalent to 3 • 3 = 3² = 9.
The length of a rectangle is 3 cm less than twice the width of the rectangle. If the perimeter is 75 cm, what are the dimensions of the rectangle?
If the length of a rectangle is 3 cm less than twice the width of the rectangle and the perimeter is 75 cm, then the length is 24 cm and width is 13.5 cm
Consider the width of the rectangle as w
The length of a rectangle is 3 cm less than twice the width of the rectangle
The length of the rectangle = 2w-3
Perimeter of the rectangle = 75 cm
Perimeter of the rectangle =2(l+w)
Where l is the length and w is the width of the rectangle
Substitute the values in the equation
2(2w-3+w) = 75
2(3w-3) = 75
6w-6 = 75
6w = 81
w = 13.5 cm
The length of the rectangle = 2(13.5)-3
=24 cm
Hence, If the length of a rectangle is 3 cm less than twice the width of the rectangle and the perimeter is 75 cm, then the length is 24 cm and width is 13.5 cm
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