Answer:
In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.
201
5. One flight took a total of 4.6 hours. Write this number as a mixed number
and as an improper fraction. Show your work in the space below. Remember
to check your solution.
The improper fraction is 25 / 6 hours
The mixed fraction is [tex]4\frac{1}{6}[/tex] hours.
What is the mixed fraction and the improper fraction?The time is written as a decimal. A decimal is a number that is made up of integers and non-integers. The integers are separated from the non-integers by a decimal point.
A mixed number is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a fraction whose numerator is less than the denominator. An improper fraction is a fraction whose numerator is greater than the denominator.
In order to convert 4.6 hours to a mixed fraction, the proper fraction has to be determined. To determine this value, multiply 0.6 by the minutes in an hour
0.6 x 60 minutes = 10 minutes
The decimal becomes : [tex]4\frac{10}{60}[/tex] hours
[tex]4\frac{1}{6}[/tex] hours
To convert the mixed fraction to an improper fraction, multiply the denominator by the whole number and add the numerator, then divide by the denominator
The improper fraction is : 25 / 6 hours
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Kari is preparing for a party and must have the perfect outfit with one
jacket and one jumpsuit. How many possible outcomes can she create if
she has a jean jacket, leather jacket, white jumpsuit, tan jumpsuit, green
jumpsuit, and a black jumpsuit?
Answer:
8
Step-by-step explanation:
Kari has 2 choices for jackets and 4 choices for jumpsuits. We'll multiply those together to find the number of options she has.
Since the numbers are very small, we can grind out this same number (but be organized):
Jean/white
Jean/tan
Jean/green
Jean/black
Leather/white
Leather/tan
Leather/green
Leather/black
These are the eight choices.
please help im sorry it is late but please i dont understand
Answer:
416 people
Step-by-step explanation:
The way you get the answer is by adding up the number of people from the sample, which gives you 175 people. After finding that you take the number of people who like pretzels (26) and divide it by 175, giving you 0.16 or 16%.
This means 16% of people will like pretzels, so you apply this to the actual number of people coming, 2600, and find 16% of 2600 (0.16 x 2600) which is 416 people. I hope this makes sense :)
Matt (180lb male) goes to a party and is served beer in a 16 oz red plastic cup. he has 3 cups of beer over a two hour period. What is Matt's BAC?
Matt's BAC the equation for is mathematically given as
X= 4 standard drinks
This is further explained below.
What is Matt's BAC?Blood Alcohol Content, sometimes known as BAC, is a measurement that expresses the amount of alcohol present in the blood as a percentage. Because it is measured in grams per 100 milliliters of blood, a blood alcohol concentration (BAC) of 0.08 indicates that your blood contains 0.08 percent alcohol by volume.
Generally, One standard drink is equal to twelve ounces of beer.
He drank a total of 48 ounces of beer since he had three cups of beer that were each 16 ounces.
In conclusion, the number of standard drinks that Matt consumed
X= 48/12
X= 4 standard drinks
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Amelia has a job baby-sitting for a neighbor. she is paid $20 plus $2.50 for each hour on the job. if amelia wants to earn $40 to buy a new sweater, how many hours would she need to work? a. 16 hours b. 9 hours c. 10 hours d. 8 hours please select the best answer from the choices provided a b c d
The correct option is option (d) 8 hours.
Amelia need to work for 8 hours to buy new sweater $40.
What is an equation and its solution?When two expressions are connected with the equals sign (=) in a math equation, it expresses the equality of the two expressions. A number that may be entered for the variable to produce a true number statement is the solution to an equation.
Let the hours Amelia need to work=h
Amalia paid=$20
Payment of each hour=$2.50
So, we can make an equation with given problem
40=20+2.50h
40-20=2.5h
20=2.5h
[tex]h=\frac{20}{2.5}[/tex]
h= 8
So, Amelia need to work for 8 hours to get $40.
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please help me with this question
Answer:
3,500 people
Step-by-step explanation:
10% of 35,000 is the same as .10 × 35,000, or 3,500.
What is the solution to the compound inequality in interval notation?
4(x+1)>−4 or 2x−4≤−10
(−∞, −3] or (2, ∞)
(−3, −2]
(−∞, −2) or [3, ∞)
(−∞, −3] or (−2, ∞)
Answer:
Step-by-step explanation:
Because of the word "or", this is a disjunction, or a union of all the solutions to the inequality as they present on a number line.
For the first inequality:
4(x + 1) > -4 we distribute through the parenthesis to get
4x + 4 > -4 and subtract 4 from both sides to get
4x > -8 and then divide both sides by 4 to get
x > -2. That will be graphed on a number line with an open hole over the -2 and the arrow will go to the right where the numbers are bigger than -2. This arrow continues into positive infinity.
For the other inequality:
2x - 4 ≤ -10 we add 4 to both sides to get
2x ≤ -6 and then divide by 2 to get
x ≤ -3. That is a closed hole over -3 and the arrow goes to negative infinity (to the left). Since one arrow goes off to the right forever, and the other arrow goes off to the left forever, and the arrows do not intersect at any point, the interval notation answer is
(-∞, -3] or (-2, ∞). The parenthesis mean that the number following it is not included (you can't include infinity, either negative or positive, because it's not actually a number) and the brackets mean that the number following it IS included. The hole is closed over the -3 so -3 is included in the solution, where the hole over the -2 is open and is not included.
Explain what is meant by intercepts with the axes give examples of y and x intercepts
Intercepts with the axes are where your line touches the x or y axis. An example is a straight line, say, y=4x+2. In this case, the y-intercept is 2 because the line touches the y-axis at (0, 2). With y=mx+b format, the y-intercept is b. To find the x-intercept of an equation in y=mx+b format, set y to zero and solve for x. In a parabola, the x-intercepts would be the roots. An example of this is x^2 - 5x + 4 = 0. The roots here are (4,0) and (1,0). Hopefully this helped.
The population of a town in 2007 is 113, 505
and is increasing at a rate of 1.2% per year.
What will the population be in 2012?
What number will you fill in for a to solve the
equation?
(Hint: For this one, how many years
after 2007 is 2012?
from 2007 to 2012 is only 5 years, so we can see this as a compound interest with a rate of 1.2% per annum for 5 years, so
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$113505\\ r=rate\to 1.2\%\to \frac{1.2}{100}\dotfill &0.012\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=113505\left(1+\frac{0.012}{1}\right)^{1\cdot 5}\implies A=113505(1.012)^5\implies A\approx 120481[/tex]
neeed help please pleasee
Answer:
Y = 2+- square root of 6
Step-by-step explanation:
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Lets solve ~
Let's calculate its discriminant ~
[tex]\qquad \sf \dashrightarrow \: {y}^{2} -4y - 2=0[/tex]
a = 1b = -4c = -2[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (-4) {}^{2} - (4 \times 1\times - 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 16 - ( - 8)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 24[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d }= 2 \sqrt{6} [/tex]
So, by quadratic formula :
[tex]\qquad \sf \dashrightarrow \: y= \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: y = \dfrac{ - {(-4)}^{} \pm 2\sqrt{6} }{2 ×1} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:y=\pm \cfrac{2(2\pm\sqrt{6} }{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:y= { 2+\sqrt{6}}{} \: \: and \: \: t = {2-\sqrt{6}}{} [/tex]
Select the correct answer from each drop-down menu.
-60
8-
6-
4
2-
-4-2 O
-2-
-4-
-6-
-8-
-N
4
2
-6
Quadrilateral 1 and quadrilateral 2 are polygons that can be mapped onto each other using similarity transformations. The
transformation that maps quadrilateral 1 onto quadrilateral 2 is a
followed by a dilation with a scale factor of
Reset
Nexts
The transformation that maps quadrilateral 1 onto quadrilateral 2 is a translation followed by a dilation with a scale factor of 2.
What is a transformation?A transformation can be defined as the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
The types of transformation.In Geometry, there are different types of transformation and these include the following:
DilationReflectionRotationTranslationBased on similarity transformation of both quadrilateral 1 and quadrilateral 2, we can infer and logically deduce that the transformation which directly maps quadrilateral 1 onto quadrilateral 2 is a translation followed by a dilation with a scale factor of 2, as shown in the image attached below.
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An oblique prism with a square base of edge length x units has a volume of x3 cubic units. which expression represents the height of the prism?x unitsx units2x unitsx units
The expression that represents the height of the oblique prism is: 1/2x.
What is the Volume of a Prism?
The volume of a prism is defined as the total space occupied by the three-dimensional object. Mathematically, it is defined as the product of the area of the base and the length.Prism Volume = base area × height of the prism
Given that the oblique prism has:
Volume = 1/2x³ cubic units
edge length = x units
Therefore,
base area = x²
Thus:
1/2x³ = (x²)(height)
Divide both sides by x²
1/2x³ ÷ x² = height
1/2x³ × 1/x² = height
x³/2 × 1/x² = height
height = x³/2x²
height = x/2
Therefore, the expression that represents the height of the oblique prism is: 1/2x.
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The complete question is -
An oblique prism with a square base of edge length x units has a volume of x3 cubic units. Which expression represents the height of the prism?
Help me! mark brainliest 10 pts please!
Answer:
A) the fraction of the week that Jamaar spent in this garden.
When the sample evidence is sufficient to justify rejecting the null hypothesis in a goodness-of-fit test, can you tell exactly how the distribution of observed values over the specified categories differs from the expected distribution? explain your answer.
No, we can only suppose that the observed distribution deviates from the expected distribution when we reject the null hypothesis.
What is a null hypothesis?The null hypothesis exists as a specific mathematical theory that claims that there exists no statistical relationship and significance between two sets of observed data and estimated phenomena for each set of selected, single observable variables. The null hypothesis can be estimated to define whether or not there exists a relationship between two measured phenomena, which creates it useful. It can let the user comprehend if the outcomes exist as the product of random events or intentional manipulation of a phenomenon.
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Sloane kicked a soccer ball off the ground at a speed of 56 feet per second. the height of the ball can be represented by the function h(t) = −16t2 56t, where t is the time in seconds. how many seconds did the ball travel before returning the ground? t = 56 seconds t = 16 seconds t = 3.5 seconds t = 0.29 seconds
The time in seconds that it took the ball to travel would be = 0.25 seconds.
Calculation of speed timeSpeed can be defined as the distance covered by an object per unit time.
The speed used to kick the soccer off the ground = 56 feet per second.
The height equation= −16t² + 56t
The time= ?
The formula for speed = distance/time
56= −16t² + 56t/t
56t = −16t² + 56t/t
−16t² = -56t + 56t
−16t² = 0
Make t the subject formula,
t = √1/16
t = 0.25 seconds.
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helpp assignment due at 3:40
Question 17: B. A’ (1,2), B’ (3,2), C’ (3,5)
Translating 4 to the right means that you should add 4 to the x value of your coordinate point.
Question 18: C. (3,-5)
This is because reflecting over the x-axis would mean to move down the same amount of units above the x-axis the original point is (the original point is five units above the x-axis so you just move down five units). Look at the attached picture for more help.
Question 19: A. C’ (0,-2)
We can see that the triangle has been translated 1 unit to the right and 2 units up. This would mean you add 1 to the x-value of the coordinate and add 2 to the y-value of the coordinate. I can’t see point C clearly, but I’m guessing that it’s at (-1,-4). This would give point C’ as (0,-2)
Hope this helps! Let me know if you need more help! Have a fantastic day!
Find the rational roots of the following: \)3x^3-5x^2+15x-25=0\)
Answer:
possible: ±{1/3, 1, 5/3, 5, 25/3, 25}actual: 5/3Step-by-step explanation:
The rational root theorem tells you any rational roots of the expression will be found from the constant and the leading coefficient:
rational roots = ±{divisor of 25} / {divisor of 3}
Possible rootsThe list of divisors in each case is pretty short, so this is ...
rational roots = ±{1, 5, 25) / {1, 3} = ±{1/3, 1, 5/3, 5, 25/3, 25}
Actual roots
We find the only actual rational root is x = 5/3 when we graph the function.
(Factoring out that root, we find the remaining roots are ±i√5, irrational imaginary values.)
Sierra found that 15 meters is equivalent to 49.2 feet. Which of the following is an equivalent ratio?
3 to 8.84
5 to 18.22
7 to 22.96
9 to 25.32
Answer:
7 to 22.96
Step-by-step explanation:
Hello!
We can represent each ratio as a fraction:
Original: 15 to 49.2 = [tex]\frac{15}{49.2}[/tex]3 to 8.84 = [tex]\frac{3}{8.84}[/tex]5 to 18.22 = [tex]\frac{5}{18.22}[/tex]7 to 22.96 = [tex]\frac{7}{22.96}[/tex]9 to 25.32 = [tex]\frac{9}{25.32}[/tex]To find equivalent values, we can convert each fraction into a decimal by dividing them.
ConvertOriginal: [tex]\frac{15}{49.2} = 0.304878048780488[/tex][tex]\frac{3}{8.84} = 0.339366515837104[/tex][tex]\frac{5}{18.22} = 0.274423710208562[/tex][tex]\frac{7}{22.96} = 0.304878048780488[/tex][tex]\frac{9}{25.32} = 0.355450236966825[/tex]The ratio of 7 to 22.96 is equivalent to the ratio of 15 to 49.2.
Uan zhang bought a 10-year bond that pays 8. 25 percent semiannually for $911. 10. what is the yield to maturity on this bond? (roundyour percentage answer to two decimal places. )
The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.
According to the statement
we have given that the Uan zhang bought a 10-year bond that pays 8. 25 percent interest per 6 months.
And we have to find that the yield to maturity on this bond.
So, For this purpose,
The amount given is $911. 10.
Years to maturity = n = 10
Coupon rate = C = 8.25%
Semiannual coupon = $1,000 × (0.0825/2) = $41.25
Yield to maturity = i
Present value of bond = PB = $911.10
Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate.
Try YTM = 9.4%:
= $522.90 + 391.54 ≅ $914.43
The YTM is approximately 9.66 percent. Using a financial calculator provided an exact YTM of 9.656 percent (2 × 4.828%).
So, The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.
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I really need help ASAP! thx
Let f(z)=z-8 and g(z)=4z-9
Find (f+g)(2)
Answer:
(f +g)(2) = -7
Step-by-step explanation:
Functions are added by adding their values.
Application(f +g)(2) = f(2) +g(2)
= (2 -8) +(4(2) -9) . . . . . evaluate f and g with z=2
= -6 +(-1)
(f +g)(2) = -7
Valerie ran three and one-fourth laps yesterday, and her coach wants her to run two and one-half times that many laps today. how many laps will she need to run today? choose the expression needed to solve the problem.
Valerie needs to run [tex]8\frac{1}{8}[/tex] laps.
What are mixed fractions?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
You can divide any fraction into two pieces. These are the denominator and numerator. A improper fraction is one in which the numerator is greater than the denominator. The numerator must then be multiplied by the denominator by the students. They will then receive a specific form of a fraction. That is referred to as a mixed fraction.
Given,
Number of laps valerie ran = [tex]3\frac{1}{4}[/tex] laps
Number of times her coach wants her to run = [tex]2\frac{1}{2}[/tex] times
Therefore,
total number of laps she needs to run = [tex]3\frac{1}{4} \times 2\frac{1}{2}[/tex]
[tex]= \frac{13}{4} \times \frac{5}{2}[/tex]
[tex]= \frac{65}{8}[/tex] laps
[tex]=8\frac{1}{8}[/tex] laps.
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Amanda increased the amount of protein she eats everyday from 48g to 54 g By what percentage did Amanda increase the amount of protein she eats
Step-by-step explanation:
she increased the amount from 48g to 54g. that is 54-48 = 6g.
so, the question really is, how many % of 48 is 6 ?
100% = 48g
1% = 100%/100 = 48/100 = 0.48g
how many % are 6g ?
as many as how often 1% (0.48g) fits into 6g :
6 / 0.48 = 12.5%
Given any two events, e1 and e2, what does the probability p(e1 ∪ e2) represent?
The equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands one of the events occurs, or both occur.
What are Mutually Exclusive events?Mutually Exclusive events are described as in probability the particular addition rule exists practical when two occurrences exist incompatible with one another. It claims that the probability of either event exists equivalent to the probability of each possibility separately.
If e₁ and e₂ stand said to be mutually exclusive events then the probability of an event e₁ happening or the probability of event e₂ occurring exists given as P(e₁) + P(e₂) :
P(e₁ ∪ e₂) = P(e₁) + P(e₂)
Therefore, the equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands for one of the events that happens, or both happen.
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Paul teaches math to five classes in sixth grade. he wants to measure the variation in the performances of students of each class. which measures will help him?
The measures of variation that can be used by Paul are interquartile range and mean absolute deviation.
What are the measures of variation?
The interquartile range is the difference between the third quartile and the first quartile.
Third quartile = 3/4(n + 1)
First quartile = 1/4 x (n + 1)
The mean absolute deviation is the average of the distance of a data set from its mean.
Mean absolute deviation = ∑ l x - m(x) l
Mean, median and mode are measures of tendency. They are used to measure the number at the center of a dataset.
Here are the options:
Mean absolute deviation
mean
interquartile range
median
mode
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mean absolute deviation
mean
median
interquartile range
mode
subtract 2/9-2/15. enter your answer below as a fraction in lowest terms, using the slash (/) as the fraction bar.
Answer:
2/9 - 2/15
Solution
LCM = 45
45 ÷9 ×2 = 10
45÷ 15 ×2 = 6
10 - 6 = 4
ANSWER = 4/45
Answer:
l
Step-by-step explanation:
take the lcm of 9 and 15. it will be 45 . than continue
Help pls i cant answer and i need to get them right
The expression has 2 factors, and the second factor has 2 terms.
How many factors has the expression?We can write an expression of N factors as:
[tex]y = A_1*A_2*...*A_n[/tex]
Here, the expression is:
4*(8x + 5)
This expression has 2 factors, which are:
4 and (8x + 5)
Now, if we look at the only factor 8x + 5, we have two terms (the terms are the parts that are added), the terms are:
8x and 5.
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Which number is a rational number?
A. sqrt{15
B. 2.6457513110
C. 17.156
D. sqrt[3]{85}
From the given options, the rational numbers is:
17.156 = 17,156/100
Which is the one in option C.
Which of the given numbers is a rational number?
A rational number is a number that can be written as the quotient of two integer numbers.
When written in decimal form, a rational number has a finite number of digits after the decimal point. Now, for the given options we have:
A: √15
B: 2.6457513110...
C: 17.156
D: √3/85
Now, the square root of a number that is no square, is always an irrational number, so we can discard these two, and also we can see that the number in option B has infinite digits after the decimal point, so we also discard that one.
Now, if we look at the remaining option, which is:
17.156
We can multiply it and divide it by 100 to get:
(100/100)*17.156 = 17156/100
So the number can be written as the quotient of two integers, which means that it is a rational number.
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PLEASE HELP ASAP (AS SOON AS POSSIBLE)
A square has a perimeter of 29 meters. Amria wanted to find a unit so that she would obtain a whole number of units when she measured the side of the square. Which of the following is a possible length of the unit? A) 8 cm B) 33 cm C) 58 cm D) 145cm
The possible length of the unit in centimeters given a perimeter of 29 meters is 725 centimeters
Perimeter of a squarePerimeter of the square = 29 metersconvert to centimeters
1 meter = 100 centimeters29 meters = 2900 centimetersPerimeter of a square = 4a
where,
a = side lengthPerimeter of a square = 4a
2900 = 4a
divide both sides by 4
a = 2900/4
a = 725 centimeters
Therefore, the possible length of the unit in centimeters given a perimeter of 29 meters is 725 centimeters
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The mean, median, and mode of the 5 number 5, 7, 8, a, b are equal. (the list have a single mode.) find all the possibilities of a+b
The mean, median, and mode of the 5 number 5, 7, 8, a, b. are equal so
the possibilities of a+b is 20.
what is mean?The" mean" is the" average" you are used to, where you add up all the figures and also divide by the number of figures.
what is median?The" median" is the" middle" value in the list of figures. To know the median, your figures have to be listed in numerical order from lowest to largest, so you may have to rewrite your list before you can find the median.
what is mode?The" mode" is the value that occurs utmost often. However, also there's no mode for the list, If no number in the list is repeated.
According to the given Information:Given numbers are: 5, 7, 8, a, b
Total number =5
Then,
The mean = (5+7+8+a+b) / 5
Mean=(20+a+b) / 5 ------------------ (1)
Median=middle value in the list of figures
Median=8 ------------------(2)
According to the question ,mean and median are equal
Compare equation (1) and (2),
we get
= (20+a+b) / 5=8 20+a+b
=40a+b=20
there is no repetition of any number, so no mode is there
hence, all the possibilities of a+b is 20.
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If you are playing a game that has a pair of dice you have to roll, what is the
probability that the sum of the numbers you roll will be a 9?
Probabilities are stated as fractions. For instance, the probability that you will get
heads on a coin flip are "1 out of 2" or 1/2. State your answer as a fraction in
simplest form.
Answer:
1/9
Step-by-step explanation:
For each of the first die's 6 outcomes, the second die also has a possible 6 outcomes.
6 × 6 = 36
There are 36 different outcomes from
1, 1
1, 2
1, 3
...
6, 6
Many outcomes have the same sum. For example, 3, 4 and 4, 3 both add to 7.
How many outcomes add to 9?
3, 6
4, 5
5, 4
6, 3
4 different outcomes out of a possible 36 different outcomes add to 9.
p(sum of 9) = 4/36 = 1/9
