What is 73 divided by 6
Answer:
12,1666666667
Step-by-step explanation:
Write an inequality for the word problem and answer the question about the inequality. Eric has an equal number of dimes and quarters that total less than 4 dollars. Could he have 12 dimes
Write an inequality for the word problem and answer the question about the inequality. Eric has an equal number of dimes and quarters that total less than 4 dollars. Could he have 12 dimes
Let
x -----> number of dimes coin
y -----> number of quarters coin
we have that
x=y ------> equation 1
and
0.10x+0.25y < 4 ------> inequality 1
substitute equation 1 in inequality 1
0.10x+0.25x < 4
solve for x
0.35x<4
x < 11.4
For 12 dimes
the value of x=12 not satisfy the inequality
that means
He couldn't have 12 dimes
Consider 4 consecutive odd integers. What is the sum of the 2nd and the 4th numbers if the first number is n?1. 2n+82.4n+123. n+64. 3n+6
4 consecutive odd integers
the next consecutive odd number is only 2 more than the first number so: n+2
n = first number
n + 2 = second number
n + 4 = third number
n + 6 = fourth number
the sum of the 2nd and the 4th numbers is:
n + 2 + n + 6 = n + n + 2 + 6 = 2n +8
2n + 8
Hence, option 1 is the correct answer
Find the sum of the interior angles of the shape. Use the remaining angles to solve for x. Polygons Help91°120°899Sum of interior angles =degreesX =degrees
Solution
For this case we have 4 sides
Then the sum of the interior angles is givne by
[tex]180(n-2)=180(4-2)=180\cdot2=360\text{ }[/tex]Sum of interior angles is 360º
And if we solve for x we can do this:
360-91-120-89= 60
x= 60 º
James received 60 texts yesterday. Of those texts 3/5 were from his friend Chris. Of the texts from Chris 1/3 referenced football. How many texts did James receive about football?
Out of the 60 texts that James recieved,
[tex]60\cdot\frac{3}{5}\cdot\frac{1}{3}=12[/tex]12 were about football.
Determine the slope of the line represented by the equation: y=3/10x+6
The slope intercept form is given by the equation
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Given:
[tex]y=\frac{3}{10}x+6[/tex]Based on the given, it is already in the slope intercept form, and by inspection, we can determine the slope of the line is equal to 3/10.
Write and equation of a line that passes through the point (5, -9) and is perpendicular to the line 2x + 11y = 22
The general equation of the line in slope - intercept form is :
[tex]y=m\cdot x+b[/tex]Where m is the slope and b is y - intercept
Given the line : 2x + 11y = 22
We need to write it in slope - intercept form to find the slope of it
so,
[tex]\begin{gathered} 2x+11y=22 \\ 11y=-2x+22 \\ y=-\frac{2}{11}x+2 \end{gathered}[/tex]So, the slope of the given line = -2/11
The required line is perpendicular to the given line
So, the product of the slope of the two lines = -1
So, if the slope of the given line is m , the slope of the required line will be = -1/m
So, the slope of the required line = 11/2
The equation of the required line will be :
[tex]y=\frac{11}{2}x+b[/tex]Using the given point ( 5 , -9 ) to find the value of b
So, when x = 5 , y = -9
[tex]\begin{gathered} -9=\frac{11}{2}\cdot5+b \\ -9=\frac{55}{2}+b \\ b=-9-\frac{55}{2}=-\frac{73}{2} \end{gathered}[/tex]so, the equation of the line is :
[tex]y=\frac{11}{2}x-\frac{73}{2}[/tex]And the standard form will be :
[tex]\begin{gathered} 2y=11x-73 \\ \\ 11x-2y=73 \end{gathered}[/tex]
2. Yan also has three times as many apples as Xavier. Write a second expression for how many apples Yanhas.
For this case, let be "x" the number of apples Xavier has and "y" the number of apples Yan has.
According to the information given in the exercise, you know that Yan has three times as many apples as Xavier. In other words, to find the number of apples Yan has, you need to multiply the number of apples Xavier has by 3.
Then, knowing the above, you can write the following equation:
[tex]y=3x[/tex]Therefore, you can determine that an expression that represents how many apples Yan has, is the one shown below:
[tex]3x[/tex]Go5. Given functions f(x) = 9x – 2, g(x) = 5 – 3x/2, and h(x) = 4x – 7/4(a) Find g(-8).(b) Find the value of x that makes g(x) = -7.(c) Find the value of x that makes f(x) = g(x).(d) Find the value of x that makes f(x) = h(x)(e) Find the x-intercept of h(x).
Answer
a) g(-8) = 17
b) When g(x) = -7, x = 8
c) When f(x) = g(x), x = (2/3)
d) When f(x) = h(x), x = (1/20)
e) x-intercept of h(x) = (7/16)
Explanation
f(x) = 9x - 2
g(x) = 5 - 3x/2
h(x) = 4x - 7/4
(a) Find g(-8).
g(x) = 5 - 3x/2
g(-8) means the value of g(x) when x = -8
g(-8) = 5 - [3×-8/2]
= 5 - (-12)
= 5 + 12
= 17
(b) Find the value of x that makes g(x) = -7.
g(x) = 5 - 3x/2
When g(x) = -7,
5 - 3x/2 = -7
5 - (3x/2) - 5 = -7 - 5
-(3x/2) = -12
[tex]\begin{gathered} \frac{-3x}{2}=-12 \\ \text{Cross multiply} \\ -3x\text{ = 2}\times-12 \\ -3x\text{ = -24} \\ \text{divide both sides by -3} \\ \frac{-3x}{-3}=\frac{-24}{-3} \\ x\text{ = 8} \end{gathered}[/tex](c) Find the value of x that makes f(x) = g(x).
f(x) = 9x - 2
g(x) = 5 - 3x/2
When f(x) = g(x)
9x - 2 = 5 - (3x/2)
9x + (3x/2) = 5 + 2
(21x/2) = 7
[tex]\begin{gathered} \frac{21x}{2}=7 \\ \text{Cross multiply} \\ 21x\text{ = 2}\times7 \\ 21x=14 \\ \text{Divide both sides by 21} \\ \frac{21x}{21}=\frac{14}{21} \\ x=\frac{14}{21}=\frac{2}{3} \end{gathered}[/tex](d) Find the value of x that makes f(x) = h(x)
f(x) = 9x - 2
h(x) = 4x - 7/4
When f(x) = h(x)
9x - 2 = 4x - (7/4)
9x - 4x = 2 - (7/4)
5x = (1/4)
[tex]\begin{gathered} 5x=\frac{1}{4} \\ \text{Divide both sides by 5} \\ \frac{5x}{5}=\frac{1}{4\times5} \\ x\text{ =}\frac{1}{20} \end{gathered}[/tex](e) Find the x-intercept of h(x).
h(x) = 4x - 7/4
The x-intercept is the value of x when h(x) = 0
When h(x) = 0
4x - (7/4) = 0
4x = (7/4)
[tex]\begin{gathered} 4x=\frac{7}{4} \\ \text{Divide both sides by 4} \\ \frac{4x}{4}=\frac{7}{4\times4} \\ x=\frac{7}{16} \end{gathered}[/tex]Hope this Helps!!!
multiply or divide as indicated. be sure to reduce all answers to lowest terms. ( the numerator and denominator of the answer should not have any factors in common)
we have the expression
[tex]\frac{3a^2+3a}{a^2-36}\cdot\frac{a^2-6a}{12a}[/tex]Simplify
we have that
a^2-36=(a+6)(a-6)
3a^2+3a=3a(a+1)
a^2-6a=a(a-6)
substitute in the given expression
[tex]\frac{3a(a+1)}{(a+6)(a-6)}\cdot\frac{a(a-6)}{12a}[/tex]Simplify
[tex]\frac{(a+1)}{(a+6)}\cdot\frac{a}{4}[/tex]therefore
the answer is
[tex]\frac{(a^2+a)}{(4a+24)}[/tex]Two number cubes are rolled what is the probability that the sum of the numbers rolled is either a 1 and a 4 in either order
The first thing we have to know is that a cube with numbers is a dice that has 6 faces and that its numbers go from 1 to 6, so the probability that the sum of both dice gives 1 is zero, since the minimum that we are going to give is 2
[tex]P(sum=1)=0[/tex]Now for the sum of both dice of 4 we have the following combinations
• 1 and 3
,• 3 and 1
,• 2 and 2
We have 3 combinatorics that we have to get the probability of each of the combinations in order to find our final probability
[tex]\begin{gathered} P(1|3)=P(1)P(3)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \\ P(3|1)=P(3)P(1)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \\ P(2|2)=P(2)P(2)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \end{gathered}[/tex]The probability that the sum of 4 would be the sum of the probabilities of the combinatorcs
[tex]\begin{gathered} P(sum=4)=P(1|3)+P(3|1)+P(2|2) \\ P(sum=4)=\frac{1}{36}+\frac{1}{36}+\frac{1}{36} \\ P(sum=4)=\frac{3}{36} \\ P(sum=4)=\frac{1}{12} \end{gathered}[/tex]What is the probability of getting a 1 and a 4 in either order?The probability of getting any number on a die will be 1/6 if we can get a 1 or a 4 then our population will be 2/6
[tex]\begin{gathered} P(1|4)=\frac{2}{6} \\ P(4|1)=\frac{2}{6} \\ P(1\&4)=\frac{2}{6}\cdot\frac{2}{6} \\ P(1\&4)=\frac{4}{36} \\ P(1\&4)=\frac{1}{9} \end{gathered}[/tex]Students and adults purchased tickets for a recent school play. All tickets were sold atthe ticket booth (discounts of any type) were not allowed.Student tickets cost $8 each, and adult tickets cost $10 each. A total of $1,760 wascollected. 200 tickets were sold.a. Write a system of equations that can model the number of student and adulttickets sold at the ticket booth for the play.
Given:
Cost of students tickets is, c (s) = $8.
Cost of adult tickets is, c (a) = $10.
Total cost collected for by selling the tickets is, c (t) = $1,760.
Number of tickets sold is, n = 200.
The objective is to find the system of equations that can model the number of students and adults tickets sold at the booth.
Consider the number of students as x and number of adults as y.
Then, the equation of total numner of students will be,
[tex]\begin{gathered} \text{Number of students+Number of adults=n} \\ x+y=200\ldots\ldots\ldots..(1) \end{gathered}[/tex]Now, the cost equation can be calculated as,
[tex]\begin{gathered} c(s)\cdot x+c(a)\cdot y=c(t) \\ 8x+10y=1760\ldots\ldots..\ldots..(2) \end{gathered}[/tex]Hence, the system of equations that can model the number of students and adults tickets are x + y = 200 and 8x + 10y = 1760,
Point O is the center of this circle. What is m
The value of the angle ∠CAB subtended at the circumference of the circle is 48° .
It is given that the center of the circle is at O.
∠AOB = 96° .
We know that the angle subtended by an arc at the center is twice that subtended at the circumference.
Therefore ∠CAB = 1/2 of ∠AOB
or, ∠CAB = 1/2 × 96°
or, ∠CAB = 48°
An arc is any segment of a circle's circumference. The angle formed by the two line segments joining a point to an arc's endpoints at any given position is known as the arc's angle.
The circle in the following illustration features an arc that subtends an angle at both the center O and a point on the circumference AB is a chord.
The angle of an arc at the center of a circle is twice as large as its angle elsewhere on the circle's edge.
Therefore the value of ∠CAB is 48° .
To learn more about circle visit:
https://brainly.com/question/190113
#SPJ1
The number of calories burnes by a 90-pound cyclist is proportional to the numer of hours the cyclist rides. the equation to represent this relationship is Y=225×. What is the constant of proportionality?
Answer
Constant of proportionality = 225
Explanation
If y varies directly as x, this can be written as
y ∝ x
Introducing the constant of variation, k, we have
y ∝ x
y = kx
So, for this question,
y = 225x
Constant of proportionality = 225
Hope this Helps!!!
Find mZCEF if mZCEF= 2x + 30,mZDEC = x + 102, and mZDEF = 132°DEFA) 30°C) 410B) 29°D) 320
1) Gathering the data
m∠CEF=2x +30
m∠DEC=x+102
m∠DEF=132
2) From the picture we infer that
m∠DEF = m∠CEF+m∠DEC
132 = m∠CEF +x +102
132-x-102=m∠CEF
m∠CEF=30
An animal shelter provides a bowl with 1.35 liters of water for 6 cats.About how much water will be left after the cats drink their average daily amount of water?Water ConsumptionAverage Amount(Liters per day)AnimalCanada Goose0.24Cat0.15Mink0.10Opossum0.30Bald Eagle0.16liter(s) of water will be left after the cats drink their average daily amount of water.
Data
1.35 litres of water
6 cats
0.15 litres per day
Procedure
Amount of water taken by the 6 cats
[tex]0.15\cdot6=0.9[/tex]Left
[tex]1.35-0.9[/tex]0.45 litres of water will be left
findvthe volume of the cylinder below to the nearest cubic foot.
Answer: The volume of the cylinder is 164.9 cubic foot
Given data
The diameter of the cylinder = 5ft
Height of the cylinder = 8.4 ft
Radius = diameter / 2
radius = 5/2
Radius = 2.5 ft
[tex]\begin{gathered} \text{Volume = }\pi\cdot r^2\cdot\text{ h} \\ \text{Volume = 3.14 }\cdot2.5^2\cdot\text{ 8.4} \\ \text{Volume = 3.14 x }6.25\text{ x 8.4 } \\ \text{Volume = }164.85ft^3 \\ Tothenearesttenth164.9ft^3 \end{gathered}[/tex]The answer is 164.9 cubic foot
I need help finding the answer and to show work
6) 4r + 8 + 5 = -15 - 3r
4r + 3r = -15 -8 - 5
7r = -28
r = -28/7
r = -4
8) 3n - 15 = 7n + n
-15 = 7n + n - 3n
-15 = 5n
n = -15/5
n = -3
f(x) = 4x - 3g(x) = x^3 + 2xFind (f-g)(4)
Given:
Two functions are given as below
[tex]\begin{gathered} f(x)=4x-3 \\ g(x)=x^3+2x \end{gathered}[/tex]Find:
we have to find the value of (f - g)(4).
Explanation:
we will find the value of (f - g)(4) as following
[tex]\begin{gathered} (f-g)(x)=f(x)-g(x)=4x-3-(x^3+2x)=2x-x^3-3 \\ (f-g)(4)=2(4)-(4)^3-3=8-64-3=-59 \\ (f-g)(4)=-59 \end{gathered}[/tex]Therefore, the value of (f - g)(4) = -59
. Noah may choose between two accounts in which to invest $4000. Account A offers 2.2% annual interest
compounded monthly. Account B offers continuous compound interest. Noah plans to leave his investment
untouched (no further deposits and no withdrawals) for 15 years.
(a) Which account will yield the greater balance at the end of 15 years?
(b) How much more money does Noah earn by choosing this more profitable account?
Answer:
Using the compound amount formula, account B will yield the greater balance at the end of 15 years and Noah earn $4 more money by choosing this more profitable account.
In the given question,
Noah may choose between two accounts in which to invest $4000.
Principal Amount(P) = $4000
Account A offers 2.2% annual interest compounded monthly.
Rate(r) = 2.2% = 0.022
In a year have twelve month so n=12
Account B offers continuous compound interest.
Noah plans to leave his investment untouched for 15 years.
Time(t) = 15
Formula for amount after t years = P(1+ r/n)^nt
Amount after 15 years = 4000(1+ 0.022/12)^12*15
Simplifying
Amount after 15 years = 4000(1+0.00183)^180
Amount after 15 years = 4000(1.00183)^180
Amount after 15 years = 4000*1.39
Amount after 15 years = $5560
Account B offers compounded continuously.
So formula used = Pe^(rt)
Amount after 15 years = 4000*e^(0.022*15)
Amount after 15 years = 4000*e^(0.33)
Amount after 15 years = 4000*1.391
Amount after 15 years = $5564
(a) We have to find which account will yield the greater balance at the end of 15 years.
As we can see in Account A amount after 15 years is $5550 and in Account B amount after 15 years is $5564.
So account B will yield the greater balance at the end of 15 years.
(b) We have to find how much more money does Noah earn by choosing this more profitable account.
Noah earn money more by profitable account=Account B amount-Account A amount
Noah earn money more by profitable account=$5564-$5560
Noah earn money more by profitable account=$4
To learn more about compound amount formula link is here
brainly.com/question/28710847
#SPJ1
At East Zone University (Ezu) thereare 564 students taking College Algebra or English Comp . 454 are taking college Algebra ,148 are taking English Comp and 38 are taking both College Algebra and English Comp . How many are taking Algebra but Not English Comp?
Step 1: Write the information given in a set notation.
[tex]\begin{gathered} n(U)=564,U\Rightarrow\mleft\lbrace The\text{ entire students}\mright\rbrace \\ E\Rightarrow\mleft\lbrace e\text{nglish comp.}\mright\rbrace \\ C\Rightarrow\mleft\lbrace\text{college algebra}\mright\rbrace \\ \end{gathered}[/tex]Step 2: State the number of students that partake in each subject.
[tex]\begin{gathered} n(C\cap E)=38 \\ n(C\cap E^{\prime})=454-38=416 \\ n(E\cap C^{\prime})=148-38=110 \\ n(C\cup E)^{\prime}=x \end{gathered}[/tex]Step 3: Draw a Venn diagram showing the information above
Step 4: To find the number of students that College Algebra but not English comp., we will check for the number of students that take only College Algebra. This is shown below
[tex]n(C\cap E^{\prime})=416[/tex]Hence, the number of students that are taking Algebra but Not English Comp is 416
A science fair poster is a rectangle 36 inches long and 24 inches wide what is the area of the poster in square feet with sure to include the correct unit in your answer
Okay, here we have this:
Considering the provided information, we are going to calculate the area of the rectangle ins square inches and after we are going to convert it to square feet, so we obtain the following:
Area of the rectangle=36 inches * 24 inches = 864 square inches
Now, let's convert it to square feet, then we have:
[tex]\begin{gathered} 864in^2\cdot\frac{1ft^2}{144in^2} \\ =6ft^2 \end{gathered}[/tex]Finally we obtain that the area in square feet of the rectangle is 6 square feet.
The question is in the picture. Using the answer choice word bank, fill in the proportion to find the volume of the larger figure.
It is given that two similar solids have surface areas of 48 m² and 147 m², and the smaller solid has a volume of 34 m³.
It is required to find the volume of the larger solid.
Recall that the if the scale factor of similar solids is a/b, then the ratio of their areas is the square of the scale factor:
[tex]\frac{\text{ Area of smaller solid}}{\text{ Area of larger solid}}=\frac{a^2}{b^2}[/tex]Substitute the given areas into the equation:
[tex]\frac{48}{147}=\frac{a^2}{b^2}[/tex]Find the scale factor a/b:
[tex]\begin{gathered} \text{ Swap the sides of the equation:} \\ \Rightarrow\frac{a^2}{b^2}=\frac{48}{147} \\ \text{ Reduce the fraction on the right with }3: \\ \Rightarrow\frac{a^2}{b^2}=\frac{16}{49} \\ \text{ Take the square root of both sides:} \\ \Rightarrow\frac{a}{b}=\frac{4}{7} \end{gathered}[/tex]Recall that if the scale factor of two similar solids is a/b, then the ratio of their volumes is the cube of the scale factor:
[tex]\frac{\text{ Volume of smaller solid}}{\text{ Volume of larger solid}}=\left(\frac{a}{b}\right)^3[/tex]Let the volume of the larger solid be V and substitute the given value for the volume of the smaller solid:
[tex]\frac{34}{V}=\left(\frac{a}{b}\right)^3[/tex]Substitute a/b=4/7 into the proportion:
[tex]\begin{gathered} \frac{34}{V}=\left(\frac{4}{7}\right)^3 \\ \\ \Rightarrow\frac{34}{V}=\frac{4^3}{7^3} \\ \\ \Rightarrow\frac{34}{V}=\frac{64}{343} \end{gathered}[/tex]Find the value of V in the resulting proportion:
[tex]\begin{gathered} \text{ Cross multiply:} \\ 64V=343\cdot34 \\ \text{ Divide both sides by }64: \\ \Rightarrow\frac{64V}{64}=\frac{343\cdot34}{64} \\ \Rightarrow V\approx182.22\text{ m}^3 \end{gathered}[/tex]Answers:
The required proportion is 34/V =64/343.
The volume of the larger solid is about 182.22 m³.
A cylinder shaped above ground pool is 4.5 deep. If the diameter of the pool is 16 ft, determine the capacity of the swimming pool in cubic feet. Write your awnser in terms of pi
For this exercise you need to use the following formula for calculate the volume of a cylinder:
[tex]V=\pi r^2h[/tex]Where "r" is the radius and "h" is the height of the cylinder.
In this case you can identify that:
[tex]h=4.5ft[/tex]You know that the diameter of the pool is 16 feet. Since the radius is half the diameter:
[tex]\begin{gathered} r=\frac{16ft}{2} \\ \\ r=8ft \end{gathered}[/tex]Knowing the radius and the height of the pool, you can substitute them into the formula and then you have to evaluate, in order to find the capacity of the swimming pool in cubic feet:
[tex]\begin{gathered} V=\pi(8ft)^2(4.5ft) \\ V=288\pi\text{ }ft^3 \end{gathered}[/tex]The answer is:
[tex]288\pi\text{ }ft^3[/tex]6. 6.5 ounces →g7.45 miles → km8.2.3 miles → cmCovert #6#7#8
Answer:
6. 184.275 gr
7. 72 km
8. 368000 cm
Explanation:
To make these conversions, we need to know the following relationships:
1 ounce = 28.35 gr
1 mile = 1.6 km
1 km = 100000 cm
Then, we can convert each expression as follows:
6.5 oz x 28.35gr / 1 oz = 184.275 gr
45 mi x 1.6 km / 1 mi = 72 km
2.3 mi x 1.6 km/ 1 mi = 3.68 km x 100000 cm/ 1km = 368000 cm
Therefore, the answers are:
6. 184.275 gr
7. 72 km
8. 368000 cm
How can I draw a histogram to illustrate the information? How do I calculate the median age of the population?
We can see from the question that we have 8 class intervals, and they are all of the same lengths. We have the frequency for age in each interval.
We need to remember that a histogram is similar to a bar plot. However, it does not have any description on the x-axis. Instead, it will have the given class intervals.
In this case, we have that the class intervals do not overlap, and it is easier to graph the histogram as follows:
1. We need to graph the class intervals on the x-axis, and then we have to draw the frequencies for each interval on the y-axis.
During World War I, mortars were fired from trenches 3 feet below ground level. The mortars had a velocity of150 ft/sec. Determine how long it will take for the mortar shell to strike its target.• What is the initial height of the rocket? -3 ft.• What is the maximum height of the rocket? 348.56 ft• How long does it take the rocket to reach the maximum height ? 4.68750 sec.• How long does it take the rocket to hit the ground (ground level)? 9.35 sec.• How long does it take the rocket to hit a one hundred feet tall building that is in it's downward path?[ Select]• What is the equation that represents the path of the rocket? Select]
Will give brainliest if someone answers this problem correctly
The equation of the line in fully simplified slope intercept form is y = -5x + 8.
From the graph:
Take any two points:
suppose (1,3) and (2,-2)
slope m = y2 - y1 / x2 - x1
= -2 - 3 / 2 - 1
= -5/1
= -5
substitute m and (1,3) in y = mx + c
3 = -5*1 + c
3 = -5 + c
c = 3+5
c = 8
y = mx+c
y = -5x + 8.
Therefore the equation of the line in fully simplified slope intercept form is y = -5x + 8.
Learn more about the equation of line here:
https://brainly.com/question/21511618
#SPJ1
E:Given f(x) = log x and g(x) = -x + 1,which is the graph of (fog)(x)?-2-2COMPLETEThe domain of (fog)(x) isDONEX>0x < 0X > 1x <1
Given data:
The first function is f(x) = log x .
The second function is g(x) = -x + 1.
The expression for (fog)(x) is,
[tex]\begin{gathered} \mleft(fog\mright)\mleft(x\mright)=f(g(x)) \\ =f(-x+1) \\ =\log (-x+1) \end{gathered}[/tex]The domain of the above function is x<1.
What is numeral value of 3/4 + 5/8
The given expression is
[tex]\frac{3}{4}+\frac{5}{8}[/tex]We have to sum these fractions with the cross-rule. The image below shows this method.