The inverse of +5 as calculated is found to be +1 / 5.
To find the inverse of +5 we can simply reciprocate it and the result will be the required answer.
reciprocal of +5 = 1 / 5.
Therefore, the answer is 1 / 5.
The opposite or reciprocal of a number or term in math is known as it's inverse. There are two types of inverse in math, the additive inverse and the multiplicative inverse.
The multiplicative inverse of a number for any n is given as 1/n. It is also called as the reciprocal of a number and 1 is called the multiplicative identity. On the other hand subtraction is the inverse of addition.
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O. Test Practice Alaska has the longest coastline in the United States. Traveling at 62 miles per hour, how many hours would it take to travel along the Pacific Coast? A 17 hours B 89 hours 90 hours D 100 hours Alaska Coastline Coast Pacific Arctic Miles 5,580 1,060
Answer:
17
Step-by-step explanation:
What is another name for angle 1?
∠JNL
∠N
∠MNK
∠NLJ
Answer: JNL
Step-by-step explanation: We can give angle 1 another name by using 3 letters which include the letter of the vertex point in the middle, and two other letters of the two rays that meet at the vertex point.
Lily purchases 3 gallons and two quarts of ice cream. How much ice cream did she purchase, in QUARTS
Answer:
14 Quarts
Step-by-step explanation:
1 Gallon = 4 Quarts.
3x4 = 12 + 2 = 14 Quarts.
Eric went for a drive in his new car. He drove for 182.4 miles at a speed for 57 miles per hour. For how many hours did he drive?
Answer:
3.2 hours
Step-by-step explanation:
182.4÷57=3.2
time divided by speed equals time
Which pairs of events are independent? Select all that apply.
Answer:the last one is right, because you cannot control when rain happens, or where at that matter.
If you are doing a linear regression, what is the slope of the line predicted by the null hypothesis?
Therefore , the solution of the given problem of slope comes out to be the slope won't be equal to zero if the independent variable X and the dependent variable Y have a substantial linear connection.
Define slope.
The slope-intercept formulation of an equation is used to represent each time the formula of a line is stated as y = mx + b. The line slope is represented by the m. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in
the formula y = 3x - 7.
Here,
The slope won't be equal to zero if the independent variable X and the dependent variable Y have a substantial linear connection.
:
: B not equal to 0
The slope is equal to zero according to the null hypothesis, however the slope is not equal to zero according to the alternative hypothesis.
The alternative hypothesis therefore asserts that the slope is not equal to zero, whereas the null hypothesis asserts that the slope is equal to zero.
Therefore , the solution of the given problem of slope comes out to be the slope won't be equal to zero if the independent variable X and the dependent variable Y have a substantial linear connection.
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How do you solve equivalent questions?
One of the way by which we can solve equivalent questions is by multiplying both the numerator and the denominator by a same number .
The number chosen for the purpose should be same and should be a non zero number. Example, if we want to find the equivalent of 2/8 then we can simply multiply 2 and 8 which are the numerator and the denominator by a same number say 3 .
Then we will get the result as 2 x 3 /8 x 3 = 6 / 24 .
The result will be a number equivalent to the given fraction. This can be checked by reducing the result to its lowest terms.
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the normal body temperature for an adult horse is 100 degrees F, but it can vary by as much as 1.2 degrees. which inequality could be used to determine the range of body temperature?
The requried inequality to determine the range of body temperature is given as 98.8 ≤ x ≤ 101.2.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
The normal body temperature for an adult horse is 100 degrees F, but it can vary by as much as 1.2 degrees.
Let x be the average temperature of the horse,
100 - 1.2 ≤ x ≤ 100 + 1.2
98.8 ≤ x ≤ 101.2
Thus, the requried inequality determines the range of body temperature is given as 98.8 ≤ x ≤ 101.2.
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A parallelogram has three of its vertices at $(-1,0)$, $(2,4)$ and $(2,-4)$. What is the positive difference between the greatest possible perimeter and the least possible perimeter of the parallelogram
The difference in perimeters is 6.
We have 3 possible points for the last vertex.
These are
[ -1 + 2 , 0 + 4 ] - [ 2 , -4 ] = [ [ 1 , 4] - [2 , - 4 ] = ( -1, 8 )
The perimeter of this parallelogram = [tex]2 [ \sqrt{(-1-2)^{2} + (8-4)^2]} + 8][/tex]
= [tex]2 [ \sqrt{9+16}+ 8 ][/tex]
= 2 [ 5 + 8 ]
= 26
Another possible point is
[ 2 + 2, 4 - 4] - [-1,0] = [ 4, 0] - [ -1,0] = (5,0)
The perimeter of this parallelogram
= [tex]2 [ \sqrt{(5-2)^{2} +(0-4)^{2} } + \sqrt{(2+1)^{2}+ (4-0)^{2} } ][/tex]
= [tex]2 [ \sqrt{3^{2}+ 4^{2} } + \sqrt{3^{2}+ 4^{2} }][/tex]
= [tex]2(\sqrt{25} +\sqrt{25})[/tex]
= 2(5 + 5)
= 20
The third feasible point won't change either the largest perimeter of 26 or the smallest perimeter of 20; therefore, we don't need to calculate it.
Difference = 26-20
= 6
Hence, the difference in perimeters is 6.
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On a negatively skewed curve, which is true?a.The median is lower than the mode which is lower than the mean. b.The mean, median, and mode are the same. c.The mean is lower than the median which is lower than the mode. d.The mode is lower than the mean which is lower than the median. e.The mean is lower than the mode which is lower than the median.
A distribution is negatively skewed if the mode is larger than the mean. The final answer is C.
In a negatively skewed distribution:
A. the median is larger than the mode.
B. the mean is larger than the mode.
C. the mode is larger than the mean.
D. the mean is larger than the median.
Negatively Skewed Distribution:
left skewed distributions occur when the long tail is on the left side of the distribution. Statisticians also refer to them as negatively skewed. This condition occurs because probabilities taper off more slowly for lower values. Therefore, you’ll find extreme values far from the peak on the low side more frequently than the high side.
The distribution is negatively skewed if the data values are clustered on the right side of the curve causing it to have a peak on the right but a flatter tail on the left side. This happens when the data set has more frequently occurring higher values than lower values.
When the median is closer to the box’s higher values and the lower whisker is longer, it’s a left skewed distribution. Notice that the longer tail extends towards the lower values, making it negatively skewed.
To find out if the data set follows a normal or skewed distribution, the three measures of central tendency (mean, median, and mode) can be compared.
The mean is greater than the median. The mean overestimates the most common values in a positively skewed distribution
The distribution is negatively skewed if the mean is lesser than the median and the median is lesser than the mode.
The given scenario is the same as negatively skewed I if the mode is larger than the mean. The final answer is C.
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Carlos bought two packages of rope, each containing 12 feet of
rope. He needs to cut pieces of rope that are each 20 inches in
length. What is the greatest number of pieces that he can cut
from these two packages of rope?
1 foot = 12 inches
Answer: 14 pieces.
Step-by-step explanation: 1 foot = 12 inches
12 feet of rope = 144 inches of rope
144 / 20 = 7.2 = 7 sections can be cut from each package.
The greatest number of pieces from 2 packages = 14 pieces
Answer
14 pieces
Step-by-step explanation:
First you need to convert the 24 feet into inches. Do this by multiplying 24 (feet) by 12 (inches) since 1 foot has 12 inches in it and you have 12 feet. This means he has 288 inches of rope. Then divide 288 by 20 since he wants to see how many 20 inch pieces he can cut. You should get 14.4 but since it asks for the greatest number of pieces you need to round it down to 14 since he wants full 20 inch pieces.
A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 4 reproductions and the population
standard deviation is known to be 1.9. If a sample of 283 was used for the study, construct the 95% confidence interval for the true mean number of reproductions
per hour for the bacteria. Round your answers to one decimal place.
The 95% confidence interval for the true mean number of reproductions per hour for the bacteria is given as follows:
(3.78, 4.22)
What is a z-distribution confidence interval?The bounds of the confidence interval are calculated according to the equation presented as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The remaining parameters are given as follows:
[tex]\overline{x} = 4, \sigma = 1.9, n = 283[/tex]
Hence the lower bound of the confidence interval is of:
[tex]4 - 1.96\frac{1.9}{\sqrt{283}} = 3.78[/tex]
The upper bound of the confidence interval is of:
[tex]4 + 1.96\frac{1.9}{\sqrt{283}} = 4.22[/tex]
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Is 2x³ a polynomial?
[tex]2xA^{3}[/tex] is a polynomial as a result. Constants, variables, and exponents can all be included in a polynomial, but variable division is never permitted.
what is a polynomial ?In mathematics, a polynomial is an expression made up of variables (also known as indeterminates) and coefficients that exclusively uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).
given
[tex]2xA^{3}[/tex] is a polynomial as a result. Constants, variables, and exponents can all be included in a polynomial, but variable division is never permitted.
It is impossible to classify an expression as a polynomial if it contains a variable with exponents that are negative or fractional, divides by a variable, or is included inside a radical.
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Blanca runs 8 laps around the track each day to train for an endurance race. She times each lap to practice her pacing for the race. The table shows the lap times, in seconds, for three days of practice. Which histogram represents Blanca’s lap times for the three days of practice?
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds
What is endurance race?
A type of motorsport racing known as endurance racing is designed to test both the participants' and the equipment's endurance. Teams of several drivers attempt to travel a long distance in a single race while being allowed to change drivers at any time.
The given table is attached below.
The number of laps in the range 82 to 84 seconds = 1
The number of laps in the range 84 to 86 seconds = 4
The number of laps in the range 86 to 88 seconds = 2
The number of laps in the range 88 to 90 seconds = 4
The number of laps in the range 90 to 92 seconds = 6
The number of laps in the range 92 to 94 seconds = 5
The number of laps in the range 94 to 96 seconds = 2
The number of laps in the range 96 to 98 seconds = 0
Therefore, the histogram that represents Blanca's lap times for the three days of practice is described as follows;
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds.
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Answer:A
Step-by-step explanation:
Please help me, find the circumference of the circle use 3.14
A 20% acid solution is mixed with a 70% acid solution to get 50 liters of a 40% solution.
How much of the 70% solution is used?
A)30 liters
B)20 liters
C)25 liters
x = liters of solution at 20%
y = liters of solution at 70%
[tex]\begin{array}{lcccl} &\stackrel{liters}{quantity}&\stackrel{\textit{\% of liters that is}}{\textit{acid only}}&\stackrel{\textit{liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{Sol'n at 20\%}&x&0.2&0.2x\\ \textit{Sol'n at 70\%}&y&0.7&0.7y\\ \cline{2-4}&\\ mixture&50&0.4&20 \end{array}~\hfill \begin{cases} x + y = 50\\\\ 0.2x+0.7y=20 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies x=50-y}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{0.2(50-y) + 0.7y=20} \\\\\\ 10-0.2y+0.7y=20\implies -0.2y+0.7y=10\implies 0.5y=10 \\\\\\ y=\cfrac{10}{0.5}\implies \boxed{y=20}[/tex]
1.) Each row of the grocery store parking lot has 10 parking spots of equal width. What is the width for each spot?
2.) How many space is given for each parking spot at the mall parking lot if each spot has an equal width?
3.) Which location gives the greatest space for each parking lot?
(Ik this is a lot but can someone help me please I’m so confused)
When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.
what is equation ?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." The three main types of linear equations are the slope-intercept form, standard form, and point-slope form. An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.
given
The grocery store is 31.92 wide overall, with 10 equally wide parking spaces.
If you assume that the width of these 10 parking spaces is equal to the width of the grocery store as a whole, you will have:
10x=31.92
on both sides of the equation, multiply by 10.
10x/10 = 31.92/10
x = 3.192
When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.
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Manish and Ravi are reading the same series of books. As of today, Manish has read a total of 544 pages. If he reads at the same pace, after 8 days he will read a total of 928 pages.
The total number of pages that Ravi has read is modeled by the equation y=51x+594, where x is the number of days after today, and y is the total number of pages read.
Who will finish the series first? Why?
Select the response that correctly answers both questions.
Responses
Ravi will finish first, because he has already read more than Manish as of today, and he reads more than Manish each day.
Ravi will finish first, because he has already read more than Manish as of today, and he reads more than Manish each day.
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
Manish, because even though Ravi has read more as of today, Manish reads faster overall.
Manish, because even though Ravi has read more as of today, Manish reads faster overall.
Manish will finish first because he has already read more than Ravi as of today, and he reads more than Ravi each day.
The person that will finish the series first is;
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
How to interpret Linear Equation Problems?The general equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Total pages manish has read as at today = 544 pages
He reads at the same pace and after 8 days he has read 928 pages. Thus, the equation that represents the number of pages that Manish has read is; 928 = 8m + 544
922 - 544 = 8m
m = 378/8
m = 47.25
Thus, his rate is 47.25 pages per day
The equation for Ravi is y = 51x + 594
This shows a rate of 51 pages per day
Thus, Ravi will finish first
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It takes a train of a certain length 15 seconds to pass under a sign, and it takes the same train 40 seconds to pass under a bridge that is 100 meters wide.What is the length (in meters) of the train
After solving, the length of the trains in meters is 60 meters.
In the given question, it takes a train of a certain length 15 seconds to pass under a sign, and it takes the same train 40 seconds to pass under a bridge that is 100 meters wide.
We have to find the length (in meters) of the train.
Let the length of the train is x.
The length of the bridge is 100 meters.
As we know that the formula of the speed is the ratio of distance that he traveled in the certain duration of time.
So Speed = Distance/Time
So according to the question;
(x + 100)/40 = x/15
Now solving the expression using the cross multiplication
15x + 1500 = 40x
Subtract 15x on both side, we get
25x = 1500
Divide by 25 on both side, we get
x = 60 meters
Hence, the length of the trains in meters is 60 meters.
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Give 2 numercial expressions that can be compared without calculating the values. Explain.
The numercial expressions that can be compared without calculating the values include:
3x^2 + 4x - 5 > 2x^2 + x - 3
2/x < 4/x
How to illustrate the expressionIn 3x^2 + 4x - 5 > 2x^2 + x - 3. This expression can be compared without calculating the values because it is a comparison of polynomials of the same degree (both are quadratics). The degree of a polynomial (in this case 2) is the highest power of the variable in the expression. Since the degree is the same, we can directly compare the coefficients of the highest degree term (x^2) and the second highest degree term (x) without calculating the values. In this case, 3x^2 > 2x^2 and 4x > x, therefore the polynomial on the left side is greater than the polynomial on the right side.
For 2/x < 4/x, this expression can be compared without calculating the values because it is a comparison of two different fractions, both of which have a common denominator of x^2. Since the denominators are the same, we can directly compare the numerators. In this case, 2 < 4, therefore the fraction on the left side is less than the fraction on the right side.
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Please help me with these two questions
The expression for area of the rectangles are obtained as x² + 10x + 21 and x² - 9x + 8 respectively. The correct options for both parts are (C) and (B) respectively.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The dimension of both the rectangles are given as,
First rectangle : (x + 3) and (x + 7)
Second rectangle : (x - 1) and (x - 8)
Since, the area of a rectangle is product of its dimensions.
It can be obtained as,
Area of first rectangle is given as,
⇒ (x + 3) × (x + 7)
⇒ x² + 10x + 21
Area of second rectangle is given as,
⇒ (x - 1) × (x - 8)
⇒ x² - 9x + 8
Hence, the area of both the rectangles are obtained as x² + 10x + 21 and x² - 9x + 8 respectively.
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NEED THIS ASAP!
(picture below)
is it
A
B
C
or D ?
(this is Fractions and Whole Numbers)
(100 Points)
Answer:
C) 4 2/3------------------------------
The product of 7/9 and 6 is:
7/9 × 6 = Simplify by cancelling 37/3 × 2 = Multiply 14/3 = Convert to mixed number4 2/3 AnswerAnswer:
[tex]\textsf{C)} \quad 4\frac{2}{3}[/tex]
Step-by-step explanation:
To find the product of two numbers, multiply them.
[tex]\implies \dfrac{7}{9} \times 6[/tex]
To multiply a fraction by a whole number, first rewrite the whole number as a fraction by dividing it by 1:
[tex]\implies \dfrac{7}{9} \times \dfrac{6}{1}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{a \times b}{c \times d}[/tex]
[tex]\implies \dfrac{7 \times 6}{9 \times 1}[/tex]
Simplify:
[tex]\implies \dfrac{42}{9}[/tex]
Reduce the fraction by dividing the numerator and denominator by the common factor of 3:
[tex]\implies \dfrac{42 \div 3}{9 \div 3}[/tex]
[tex]\implies \dfrac{14}{3}[/tex]
Divide the numerator by the denominator:
[tex]\implies 14 \div 3=4\;\rm remainder\;2[/tex]
The mixed number answer is the whole number and the remainder divided by the denominator:
[tex]\implies 4\frac{2}{3}[/tex]
(i) Six donkeys are each given 5 ml spoons of medicine three times each day.
Calculate the number of whole days a 2 L bottle of medicine will last.
pls I really need the answer
Hello there!
Answer:
33 days
Step-by-step explanation:
Every day you give 5 ml of medicine to 6 donkeys. So you spent 5 ml * 6 = 30 ml per day
1 L = 1000 ml
To find the answer you should volume of bottle divide by 30 ml per day:
1000 ml / 30 = 33.333...
It means that if will be possible to use the bottle 33 days but then it will be left
What is 3 and 2/3 as a mixed number?
3 and 2/3 as a mixed number will be 11/3.
Define integers.Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold Z.
What is a mixed number?A mixed number is a combination of a whole number and a fraction. It represents a number that is greater than zero but less than the next whole number. A mixed number is written with the whole number followed by a space and then the fraction.
[tex]=3+2/3[/tex]
[tex]=(3*3+2)/3[/tex]
[tex]=(9+2)/3[/tex]
[tex]=11/3[/tex]
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Find the measure of MN
In the given the diagram of a circle, the measure of angle MON is 60°.
What is a circle?A circle is a two-dimensional shape created by a collection of points that are spaced uniformly or uniformly apart from a fixed point (centre) on the plane. The radius of a circle is the fixed distance between each point and the fixed point, which together make up the circle's origin or centre.
All angles add upto 360°
100 + 140 + ∠MOP = 360
∠MOP = 120°
Draw an imaginary straight line extending MO, making MOM'
∠QOM' = 180 - 140
= 40 = ∠MOQ' (vertically opposite)
Draw an imaginary straight line extending NO, making NON'
Draw an imaginary straight line extending PO, making POP'
P'OQ = 180 - 100
= 80 = ∠Q'OP (vertically opposite)
Draw an imaginary straight line extending QO, making QOQ'
P'OM = 60° = M'OP (vertically opposite)
Now, ∠N'OQ = 180 - 60 - 2(40)
= 20°
Then, ∠P'ON' = 80 - 20
= 60
And ∠MON = 40 + 20
= 60°
Hence, In the given the diagram of a circle, the measure of angle MON is 60°.
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Find the unit rate of the constant of proportionality for the following: $9.80 for 5 pounds.
Showing your work would be appreciated, so if you could, that’d be great. But it’s not needed, if you don’t want to. :)
Thank you in advance to anyone who answers!
The unit rate of constant means that for every 1 pound, the output is 1.96 dollar.
What is proportionality?Proportionality is a relationship between two variables in which their ratio is always equal to a constant value. In mathematical terms, it can be expressed as y = kx, where y and x are the two variables, and k is the constant of proportionality.
What is rate?A rate is a measure of how one quantity changes in relation to another quantity. It is usually expressed as a ratio and has units of measurement, such as miles per hour, dollars per pound, etc. A unit rate is a rate in which the second quantity is one unit of measurement.
The unit rate of the constant of proportionality is found by dividing the change in y (output) by the change in x (input).
In this case:
$9.8/5$ = $1.96$, so the unit rate of the constant of proportionality is 1.96 pounds/dollar.
It means that for every 1 pound, the output is 1.96 dollar.
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is y = x proportional
Answer:
yes
Step-by-step explanation:
Erin has 4 cards, one with the letter A, one with the letter B, one with the letter C, and one with the letter D. She places the cards in a row in random order. What is the probability that either the words BAD or CAB will appear as part of the row? Enter your answer as a percent, to the nearest tenth of a percent, like this: 42.5%
The probability that either the words BAD or CAB will appear as part of the row is 16.7%
How to determine the probability that either the words BAD or CAB?We have 4 places where we can put the cards.
Let's count the number of possible outcomes for each place.
In the first place, we can put one of 4 cards.
In the second place, we can put one of 3 cards (because one card was taken in the first place).
In the third place, we can put one of 2 cards
In the last place, we can put one of one cards.
The total number of different combinations is the product between the number of options for each place, then we have:
4×3×2×1 = 24
Now we need to count the number of combinations such that the words BAD or CAB appear. We have:
BADC
CBAD
CABD
DCAB
That is 4 out of 24.
Thus, the probability that either the words BAD or CAB will appear as part of the row will be:
P(BAD or CAB) = 4/24 = 16.7%
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The probability is 16.7%
Which of the following is the graph of y=-4 square root x
Answer:
It would look like that I think
Step-by-step explanation:
Help me on this question.
The value of y from the equation is y = 5
The measure of RS = 38
The measure of ST = 18
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , on the number line , the measures of the sides are
The measure of RS = 7y + 3 be equation (1)
The measure of ST = 2y + 8 be equation (2)
The measure of RT = 56
Now , from the line segment ,
RT = RS + ST be equation (3)
Substituting the values in the equation , we get
7y + 3 + 2y + 8 = 56
On simplifying the equation , we get
9y + 11 = 56
Subtracting 11 on both sides of the equation , we get
9y = 45
Divide by 9 on both sides of the equation , we get
y = 5
Substitute the value of y in equations (1) and equation (2) , we get
The measure of RS = 7 ( 5 ) + 3 = 38
The measure of ST = 2 ( 5 ) + 8 = 18
Hence , the equations are solved and the value of y = 5
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