The mathematical expression is 20÷n and the value of the expression at n=5 is 4.
We are given a phrase and we have to convert it into a mathematical expression. The phrase is given below :
P = "the quotient of twenty and a number"
An expression or mathematical expression is a finite collection of symbols that are well-formed according to context-dependent norms. In mathematics, an expression is a statement that involves at least two distinct numbers (known or unknown) and at least one operation. The mathematical expression equivalent to the above phrase is 20/n.
We now need to evaluate the mathematical expression for n = 5.
20/5 = 4
The value is 4.
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Find the mean of 86, 78, 94, 94, 98.Find the median of 86, 78, 94, 94, 98.Identify the mode of 86, 78, 94, 94, 98.
Mean:
We are asked to find the mean of the following data set.
86, 78, 94, 94, 98
The mean is given by
[tex]mean=\frac{sum}{n}[/tex]Where n is the total number of values in the data set.
[tex]mean=\frac{sum}{n}=\frac{86+78+94+94+98}{5}=\frac{450}{5}=90[/tex]The mean of the data set is 90.
Median:
To find the median, first, arrange the values in ascending order (least to greatest).
78, 86, 94, 94, 98
The median value is the most middle value in the data set.
[tex]median=(\frac{n+1}{2})^{th}=(\frac{5+1}{2})^{th}=(\frac{6}{2})^{th}=3^{rd}\;value[/tex]The 3rd value in the data set is 94.
Therefore, the median of the data set is 94.
Mode:
The mode is the most repeated value in the data set.
86, 78, 94, 94, 98
As you can see, the value 94 is the most repeated value (two times) in the data set.
Therefore, the mode of the data set is 94.
Consider the equations 3(−2)(+3)=0 and (2−4)(3+9)=0.Do they have the same solutions? Justify your answer.
First equation
3(x−2)(x+3)=0
3 is multiplying on the left, then it will divide on the right.
(x−2)(x+3) = 0/3
(x−2)(x+3) = 0
The solutions are:
x - 2 = 0 or x + 3 = 0
that is, x = 2 and x = -3
Second equation
(2x−4)(3x+9) = 0
The solutions are:
2x − 4 = 0
x = 4/2
x = 2
or 3x+9 = 0
x = -9/3
x = -3
Then, they have the same solutions.
A regular quadrilateral and a regular triangle have the same perimeter. The side length of one of the sides of the quadrilateral is 48. What is the length of a side of the triangle?
The length of a side of the triangle is 16.
Which is a Regular Polygon?A polygon is classified as regular when all sides and angles are equal. Therefore, a regular quadrilateral presents all the four sides and the four angles equal. You can use the same conclusion for a regular triangle, but for a triangle the three sides and the three angles are equal.
The question gives:
The perimeter for the regular quadrilateral = 48. Because of this, it is important that you know the definition for perimeter = sum of the sides of a geometric figure.As the triangle was classified as regular, all its sides (x) are equal. Then,
x+x+x=48
3x=48
x=48/3
x=16
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Find the missing number so that the equation has no solutions.
?missing number? x+18=5x–12
Answer:
x=1.5
Step-by-step explanation:
Simplifying
5x + 12 + -1x = 18
Reorder the terms:
12 + 5x + -1x = 18
Combine like terms: 5x + -1x = 4x
12 + 4x = 18
Solving
12 + 4x = 18
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + 4x = 18 + -12
Combine like terms: 12 + -12 = 0
0 + 4x = 18 + -12
4x = 18 + -12
Combine like terms: 18 + -12 = 6
4x = 6
Divide each side by '4'.
x = 1.5
Simplifying
x = 1.5
Answer:
Firstly: collect like terms
Secondly: simplify
Lastly: divide the number you got from the one without the letter x by the number you got with the letter x
enter an equation in standard form.slope=-7/2and (4, -14) is on the line.
Explanation
Step 1
to find the equation use:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ P(x_1,y_1)\text{ is a point of the line} \\ \text{and m is the slope} \end{gathered}[/tex]Let
slope=-7/2
point= P(4,-14)
Step 2
replace,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-14)=-\frac{7}{2}(x-4)_{} \\ y+14=-\frac{7}{2}x+\frac{28}{2} \\ add\frac{\text{ 7}}{2}x\text{ in both sides} \\ y+14+\frac{7}{2}x=-\frac{7}{2}x+\frac{28}{2}+\frac{7}{2}x \\ y+14+\frac{7}{2}x=14 \\ \text{subtract 14 in both sides} \\ y+14+\frac{7}{2}x-14=14-14 \\ y+\frac{7}{2}x=0\Rightarrow s\tan dard\text{ form} \end{gathered}[/tex]I hope this helps you
-4b + 8c + 12 - 8b - 2c + 6What is the value of the expression when b = 2 and c =-3? Enter your answer on the grid.
ANSWER
-24
EXPLANATION
We have the expression and we want to find its value when b is 2 and c is -3.
To do that, we replace b in the expression with 2 and c with -3.
The expression is:
-4b + 8c + 12 - 8b - 2c + 6
So, we have:
-4(2) + 8(-3) + 12 - 8(2) - 2(-3) + 6
=> -8 - 24 + 12 - 16 + 6 + 6
=> -24
That is the answer.
1 kg= converts to how many grams
By definition:
• the "k" in the unit kg means 1000,
,• the "g" in the unit kg means g (grams).
So we have that:
[tex]1kg=1*(k)*(g)=1*1000*g=1000g.[/tex]Answer1 kg is equivalent to 1000 grams
PLEASE HELP ASAPPPP!!!
Create a scatter plot using the data below.
week 1: $27,188,270 week 2: $34,664,856 week 3: $38,086,246 week 4: $40,603,493 week 5: $42,272,097 week 6: $43,514,327 week 7: $44,665,033 week 8: $45,900,553 week 9: $46,861,913 week 10: $47,881,047. Be sure to label your x and y axis and use appropriate scales and consistent intervals for each axis.
A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events, scatter plots are crucial in statistics (called variables).
Explain about scatter plot?In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are used to plot data points on a horizontal and vertical axis. The values of the columns set on the X and Y axes determine the position of the marker that represents each row in the data table.
A scatter plot is a form of plot or mathematical diagram that uses Cartesian coordinates to display values for typically two variables for a collection of data. It is also known as a scatter graph, scatter chart, scatter gram, or scatter diagram.
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When Kiran moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 33 inches tall and Tree B was 15 inches tall. Each year thereafter, Tree A grew by 4 inches per year and Tree B grew by 7 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t,t, and determine the interval of time, t,t, when Tree A is taller than Tree B.
Equation are AA = 33+15tt and BB = 15+7tt. Tree A will remain taller than tree B till 2.25 years.
Size of Tree A in the beginning = 33 inches
Size of Tree B in the beginning = 15 inches
Increase in length of Tree A per year = 4 inches
Increase in length of Tree B per year = 7 inches
Let AA represent the height of Tree A tt years after being planted. Let BB represent the height of Tree B tt years after being planted.
Formulating the equation we get:
For tree A:
Height after tt years = Height in beginning + Increase each year*Number of years
AA = 33 + 15tt-----(1)
For tree B:
Height after tt years = Height in beginning + Increase each year*Number of years
BB = 15 + 7tt------(2)
Equating (1) and (2) we get:
33 + 15tt = 15 + 7tt
18 = -8tt
tt = 2.25 years
So, the trees will be of the same height in 2.25 years
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25% of Ms. Devine’s jeans are from Abercrombie. 50% of Mr. Faretta’s jeans are from Abercrombie. Ms. Devine has more Abercrombie jeans than Mr. Faretta. How is this possible?
If Ms. Devine has more total jeans than Mr. Faretta, then it is possible that Ms. Devine has more Abercrombie jeans than Mr. Faretta.
25 percent of Ms. Devine's jeans and 50 percent of Mr. Faretta's jeans are from Abercrombie.
Let's say the number of jeans Ms. Devine have is x and the number of jeans Mr. Faretta have y number of jeans.
Now, let x = 20 and y = 10
Then, the number of Abercrombie jeans Ms. Devine has will be:
25 % of 30 = ( 25/100 ) × 30 = 25/5 = 7.5
and; the number of Abercrombie jeans Mr. Faretta has will be:
50% of 10 = ( 50/100 ) × 10 = 5
Hence, to conclude if Ms. Devine has more jeans when compared to Mr. Faretta it is possible that Ms. Devine has more Abercrombie jeans than Mr. Faretta.
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A helicopter hovers 1075 feet above a small island. The figure shows that the angle of depression from the helicopter to point P on the coast is 35". How far off the coast, to the nearest
foot, is the island?
The situation forms a right angle triangle. The distance form the coast to the helicopter is 1535.25910 ft.
What is meant by Right angle triangles?Right angle triangles exists triangle that contains one of its angles as 90 degrees. The height of the helicopter exists the opposite side of the triangle formed.
How far off the coast to the helicopter is the adjacent side.
The situation forms a right angle triangle.
Therefore, tan 35° = opposite / adjacent
tan 35° = 1075 / a
Multiply both sides by a,
tan (35°) a = (1075 / a) a
Simplifying the above equation, we get
[tex]$\tan \left(35^{\circ}\right) a=1075$$[/tex]
Divide both sides by [tex]$\tan \left(35^{\circ}\right)$[/tex]
tan (35°) a / tan (35°) = 1075 / tan (35°)
Simplifying the above equation, we get
a = 1075 / tan (35°)
singularity points: a = 0
Combine undefined points with solutions:
a = 1075 / tan (35°)
a = 1535.25910 ft
Therefore, the distance form the coast to the helicopter exists 1535.25910 ft.
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What is the equation of the line that is parallel to y=-3x+4 and that passes through (-2,-2)?
0--1-1
Please help me solve the problem on the picture
Answer:
5/6
Step-by-step explanation:
Well......I don't know how to tell you how to solve it....it just is .
Using the graph, determine the value of the slope. y What is the slope? 2. e about the graph? -3 -2 Y 2 0 -2 3 no slope 4
What is a slope?
It shows how inclinated is a line. It goes from zero, 0 (no inclination - horizontal line), no infinity (total inclination - vertical line).
It can also be representated by negative numbers
Since the line of the graph is horizontal, we can say its slope, m, is given by zero : m = 0Arrange the equations in the correct sequence to rewrite the formula for displacement, ,
D=VT-1/2at^2
to find a. In the formula, d is displacement, v is final velocity, a is acceleration, and t is time.
The solution of the equation for a is a = 2(vt - d)/t²
What is subject of formula?Subject of formula involves isolating a variable in an equation different from the initial isolated variable
How to determine the equation for a?The equation is given as
d = vt - 1/2at²
From the question, we have
d is displacementv is final velocitya is accelerationt is time.Subtract vt from both sides of the equation
d - vt = - 1/2at²
Multiply both sides by -2
at² = 2(vt - d)
Divide both sides by t²
So, we have the following equation
a = 2(vt - d)/t²
Hence, the solution is a = 2(vt - d)/t²
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mrs.bells daughter has 3.5 baskets of towels that need to be folded.if she gets 1.5 baskets folded per hour,how many hours will it take her daughter to fold all of the towels
mrs.bells daughter has 3.5 baskets of towels that need to be folded.if she gets 1.5 baskets folded per hour,how many hours will it take her daughter to fold all of the towels
we know that
The unit rate is 1.5 baskets per hour
To find out the number of hours , divide the total baskets by the unit rate
so
3.5/1.5=2.33 hours
2.33 hours=2 1/3 hours or 2 hours 20 minutes
therefore
the answer is
2 1/3 hours or 2 hours 20 minutesPlease help with the problem
Solve for n1/2(12n- 4) =14-10n
1/2(12n- 4) =14-10n
First, apply the distributive property to solve the parenthesis
1/2 (12n)+1/2 (-4) = 14-10n
6n-2 =14-10n
Combine like terms
6n+10n = 14+2
16n=16
Divide both sides of the equation by 16
16n/16 =16/16
n= 1
When moving from Chicago to Milwaukee, your salary went from $65,000 per year to $55,000 per year. By what percent does your salary decrease? Round your answer to the nearest tenth of a percent (one decimal place).
Data:
Initial salary: $65,000
Salary after decrease: $55,000
To find the percentage of decrease you use the next formula:
[tex]D=\frac{O-N}{O}\cdot100[/tex]Where:
D is the percentage of decrease
O is the original value
N is the new value
Then, you have the next:
O=$65,000
N= $55,000
[tex]\begin{gathered} D=\frac{65000-55000}{65000}\cdot100 \\ \\ D=\frac{10000}{65000}\cdot100 \\ \\ D=0.1538\cdot100 \\ \\ D=15.38 \end{gathered}[/tex]Then, the percentage of decrease is 15.4% (round to the nearest tenth)which set of output values correctly completes the function table?
EXPLANATION
Applying the relationship output = input * 4 give us the appropiate y-value as shown as follows:
x y
-5 -5*4= -20
12 12*4 = 48
32 32*4 = 128
The answer is the second option.
At Community Hospital, the nursing staff is large enough so that 80% of the time a nurse canrespond to a room call within three minutes. Last night there were 25 room calls. Find theprobability that nurses responded to 21 of the calls within three minutes.
This situation can be modeled by the binomial distribution, because there are two outcomes: a nurse can respond or a nurse cannot respond. The probability, p, that a nurse can respond is 0.8 (or 80%), the probability, q, that a nurse cannot respond is 0.2 (= 1 - 0.8). In 25 trials, we need that in 21 of them a nurse can respond.
The binomial distribution formula is:
[tex]P=_nC^{}_xp^xq^{n-x}[/tex]where xCn means number of combinations, n is the number of trials, x is number of times for a specific outcome within n trials, p is the probability of succes, and q is the probability of failure.
Substituting with n = 25, x = 21, p = 0.8 and q = 0.2, we get:
[tex]\begin{gathered} P=_{25}C_{21}\cdot0.8^{21}\cdot0.2^4 \\ P=12650\cdot0.8^{21}\cdot0.2^4 \\ P=0.19 \end{gathered}[/tex]Find the nth term of this quadratic sequence
3, 11, 25, 45, …
Using the principle of mathematical induction, the [tex]n^{th }[/tex] term of the given quadratic sequence is found to be 3n² - n + 1.
What exactly is mathematical induction?Mathematical induction is a technique for proving the truth of a statement, theorem, or formula for each and every natural number n. This is generalized as the 'Principle of Mathematical Induction,' which we would use to prove any mathematical statement.Given sequence: 3, 11, 25, 45,...
The first term of the sequence is 3, the second term is 11, the third term is 25, and the fourth term is 45.
The difference between the first and second terms can be calculated as follows:
11-3 = 8
The difference between the second and third terms can be calculated as follows:
25-11 = 14
The difference between the third and fourth terms can be calculated as follows:
45-25 = 20
The sequence is expressed as follows:
3,3+8,11+11,25+20,...
The difference between consecutive terms expands by 6.
Use the principle of mathematical induction.
[tex]6(\frac{n(n+1)}{2})[/tex]
= 3n(n+1)
The sequence's nth term can be calculated as follows:
[tex]n^{th }[/tex] term = 3n(n+1) - 4n + 1
= 3n² - n + 1
Therefore, the [tex]n^{th }[/tex] term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.
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An equilateral triangle has an
area of 97.5 square meters. If the
height of the triangle is 13 meters,
find the perimeter of the triangle.
The perimeter of the equilateral triangle is 45 meters.
What is the perimeter?An equilateral triangle is a polygon that has three sides that are of equal length. The sum of angles in an equilateral triangle is 180 degrees. The perimeter of an equilateral triangle is the distance round the triangle. It can be determined by adding the length of the three sides of the triangle together.
The first step is to determine the side length of the triangle. The base can be determined from the area.
Area of a triangle = 1/2 x base x height
97.5 = 1/2 x 13 x b
b = (97.5 x 2) / 13
b = 15 meters
Perimeter = 15 x 3 = 45 meters
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Help please show your work please
Using Subtraction, At least 15 more people are required to register for the swimming class to held.
What does math subtraction mean?To remove anything from a set or a group of items in mathematics is to take that item away. The total number of elements in the group decreases or decreases when we subtract from it.
What different types of subtraction are there?There are actually three methods to understand subtraction: taking away. Part-whole. Comparison.
Given:
No. of people required to start the class = 24
no. of people registered = 9
Therefore no. of people required = 24 - 9
= 15 people
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4x + 7 = 23 S = {3, 4, 5, 6}
[tex]4x = 23- 7 \\ 4x = 16 \\ \frac{4x}{4} = \frac{16}{4} \\ x = 4[/tex]
I HOPE THIS IS WHAT YOU WANT SINCE YOU WERE NOT STRAIGHTFORWARD.
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Hello, I need help with task 3 which has 3question as it is part of one big question. Therefore 30 for a question for each. These questions are connected to previous ones so, I will send an image of the other two task
Task 3 (of 3)
Part 1: In this case the probabilitie that a person saw resould and receive the power pill is 0.65, so in order to have a trustable resould should be more than 95% to be certan. How ever I think that with a probabiliti of more that the 70% could wor. So in this case a probabilitie of 65% is not enogh to produce or dristribute.
Part 2: We can compare the resoulds of group A and group B and the resoulds of group C vs the resould in group D so we check if telling the subject affect anything.
So for group A and B are 0.15 and 0.175 so there is no significant difference and for C and the are 0.125 and 0.1 so there is again not significant effect.
Part 3: In this case maybe a better way to made the experiment is to take a bigger poblation, becuase each group has to low participants. if we have more particiants we can have better resoulds. Also we can calculate a standart deviation to be sure of the difference between the groups.
Suppose you place 20 pennies on the table in a row. Now replace every fourth coin with a nickel. Now replace every third coin with a dime.
Now replace every sixth coin with a quarter. What is the value of the 20 coins now on the table?
The value of the 20 coins now on the table is $1.35.
What is replacement?It is a group of components from which any one may be chosen to take the place of a certain variable or placeholder in a mathematical phrase or expression (such as an equation).
Given Data
You place 20 pennies on the table in a row. Now replace every fourth coin with a nickel. Now replace every third coin with a dime.
Now replace every sixth coin with a quarter.
You will receive 5 nickels if you exchange every fourth coin for one because
[tex]\frac{20}{4}[/tex]= 5.
You will then have 6 dimes if you substitute a dime for every third coin. Finally, you will receive three quarters for every sixth coin that contains a quarter.
However, there is some overlap when a nickel is replaced with a dime or a dime is replaced with a quarter, resulting in 3 quarters, 3 dimes, and 4 nickels, with the remaining pennies.
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Change the proper fraction below to a decimal.
31/200
31/200 converted from a proper fraction to a decimal is 0.155.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
We can convert this proper fraction 31/200 into a decimal by first eliminating the zeroes and moving a decimal point from right to left to as many places as zeroes.
∴ 31/200.
= 0.31/2.
Now, we know that 30/2 is 15 and 32/2 is 16.
So, 31/2 must be 15.5.
∴ 0.31/2.
= 0.155.
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Which of the following expressions are equivalent to 36x + 24y? Choose ALL that apply.
Notice how the coefficients of 'x' and 'y' are both divisible by 4, therefore:
[tex]36x+24y=4(9x+6y)[/tex]So, the equivalent expression of 36x+24y is 4(9x+6y)
Find the coordinates of the midpoint of a segment with the endpoints ( 22 , 4 ) and ( 15 , 7 ) .
The coordinates of the midpoint of a segment with two endpoints ( 22, 4 ) and ( 15, 7 ) is ( 37/2, 11/2 ).
The center of a line segment is known as the midpoint. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
Consider the two endpoints of the segments as:
A( 22, 4 ) and B( 15, 7 )
Let M( x, y ) be the midpoint of the line segment.
Then AM = MB = ( 1/2 )AB
Therefore, the points will also the halfway from the midpoint.
Therefore,
M( x, y ) = ( 1/2 )A + ( 1/2 )B
M( x, y ) = 1/2( 22, 4 ) + ( 1/2 )( 15, 7 )
M( x, y ) = ( 11, 2 ) + ( 15/2, 7/2 )
M( x, y ) = ( 11 + 15/2, 2 + 7/2 )
M( x, y ) = ( 37/2, 11/2 )
Therefore, the coordinate of the midpoint of the line segment is ( 37/2, 11/2 ).
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