hello
tp solve this question, let's get the data out
we have a total of 6000 students. 1/4 of the students are seniors, let's find the numbers of seniors in the school
the number of senior students are
[tex]\frac{1}{4}\times6000=1500[/tex]we have 1500 seniors in the school.
we can find the seniors in support of a debate team by multiplying 2/3 by 1500
[tex]\frac{2}{3}\times1500=1000[/tex]now we know that 1000 students are in support of the debate team. let's subtract the numbers of students in support of debate team from numbers of seniors in the schoolto giveus the numbers of seniors that are not in support of debate team.
[tex]1500-1000=500[/tex]500 seniors from the school are not in support of a debate team.
Also note that 1/5 of the remaining students are not in support of the debate team.
which would be
[tex]\begin{gathered} 6000-1500=4500 \\ \frac{1}{5}\times4500=900 \end{gathered}[/tex]now, we can add the numbers of seniors that are not in support of a debate team plus number of remaining students not in support of a debate team
[tex]500+900=1400[/tex]from the calculationabove, a total of 1400 students are not in support of the idea
the fraction 1-2 equals?
The given fraction is 1/2.
IF we divide, we have
[tex]\frac{1}{2}=0.5[/tex]Therefore, the answer is 0.5.In 2000, there were 750 cell phone subscribers in a small town. The number of subscribers increased by 80% per year after 2000. How many cell phone subscribers were in 2010? Round off the answer to the nearest whole number.
This is an exponential growth. We would apply the exponential growth formula which is expressed as
y = a(1 + r)^t
Where
a represents the imitial number of subscribers
r represents the growth rate
t represents the number of years
y represents the number of subscribers after t years
From the information given,
a = 750
r = 80/100 = 0.8
t = 9 (number of years between 2000 and 2010)
Thus,
y = 750(1 + 0.8)^9
y = 750(1.8)^9
y = 148769.48
Rounding to the nearest whole number, the number of cell phone subscribers in 2010 is
148769
Find the time. Round to the nearest day given the following:Principal: $74,000Rate: 9.5%Interest: $2343.33
Explanation
Simple Interest is calculated using the following formula:
[tex]I=\text{PRT}[/tex]where P is the principal ( initial amount)
R is the rate ( in decimal)
T is the time ( in years)
so
Step 1
Let
[tex]\begin{gathered} P=74000 \\ \text{rate}=\text{ 9.5\% =9.5/100= 0.095} \\ T=t\text{ ( unknown)} \\ \text{Interest}=\text{ 2343.33} \end{gathered}[/tex]now, replace
[tex]\begin{gathered} I=\text{PRT} \\ 2343.33=74000\cdot0.095\cdot t \\ 2343.33=7030t \\ \text{divide both sides by 7030} \\ \frac{2343.33}{7030}=\frac{7030t}{7030} \\ 0.3333=t\text{ } \end{gathered}[/tex]so, the time is 0.333 years
Step 2
convert 0.333 years into days
[tex]1\text{ year }\Rightarrow365\text{ days}[/tex]so
[tex]\begin{gathered} 0.333years(\frac{365}{1\text{ year}})=121.66 \\ \text{rounded} \\ 122\text{ days} \end{gathered}[/tex]therefore, the answer is
122 days
Carl is sewing a quilt. The number of yards of green fabric in the quilt is proportional to the number of yards of bluefabric in the quilt. This equation represents the proportional relationship between the number of yards of greenfabric, g, and yards of blue fabric, b, in the quilt.6 2/3 b = 5 1/3 gEnter the number of yards of green fabric used for 1 yard of blue fabric
Answer:
1 1/4 yards of green fabric.
Explanation:
The equation representing the proportional relationship between the number of yards of green fabric, g, and yards of blue fabric, b, in the quilt is:
[tex]6\frac{2}{3}b=5\frac{1}{3}g[/tex]If 1 yard of blue fabric is used: b=1
[tex]\begin{gathered} 6\frac{2}{3}\times1=5\frac{1}{3}g \\ \frac{20}{3}=\frac{16}{3}g \\ \text{ Multiply both sides by }\frac{3}{16} \\ \frac{3}{16}\times\frac{20}{3}=\frac{16}{3}\times\frac{3}{16}g \\ g=\frac{20}{16} \\ g=1\frac{1}{4}\text{ yards} \end{gathered}[/tex]If 1 yard of blue fabric is used, then 1 1/4 yards of green fabric will be used.
Identify the slope and y-intercept of equation 5x-3y=9
To identify the slope and y-intercept, we will take the given equation to its slope-intercept form:
[tex]y=mx+b,[/tex]where m is the slope and b is the y-intercept.
To take the equation to its slope-intercept form, we add 3y to the given equation:
[tex]\begin{gathered} 5x-3y+3y=9+3y, \\ 5x=9+3y\text{.} \end{gathered}[/tex]Now, we subtract 9, and get:
[tex]5x-9=3y\text{.}[/tex]Finally, dividing by 3, we get:
[tex]y=\frac{5}{3}x-3.[/tex]Therefore, the slope and y-intercept are:
[tex]\frac{5}{3},\text{ and -3 }[/tex]correspondingly.
Answer:
Slope:
[tex]\frac{5}{3}\text{.}[/tex]Y-intercept:
[tex]-3.[/tex]Is this continous or discrete?Fees for Overdue Books
The following graph is given, representing the fees due for Overdue books:
find the first term when the 31st 32nd and 33rd are 1.40, 1.55, and 1.70
jadeymae06, this is the solution:
This is an arithmetic sequence, where d (common difference) = 0.15
(1.70 - 1.55) or (1.55 - 1.40)
•
,• a + 30d = 1.40
,• a + 30(0.15) = 1.4
,• a + 4.5 = 1.4
,• a = 1.4 - 4.5
,• a = -3.1
Jade, the first term is -3.1
Solve for x and then give the m
x = 38
Step-by-step explanation:
(x + 6) + (3x - 16) + x = sum of angles in a triangle
(x + 6) + (3x - 16) + x = 180
(x + 3x + x ) + (6 - 16) = 180
5x +(-10) = 180
5x - 10 = 180
5x = 180 + 10
5x = 190
5x/5 = 190/5
x = 38
Answer:
x = 38 and m∠M = 98
Step-by-step explanation:
Angles in any triangle will always add up to 180 :
So angle O + Angle N + Angle M = 180
(x+6)+(3x-16)+(x) = 180
Simplify:
5x-10 = 180
Add 10 to both sides :
5x = 190
Divide both sides by 5 :
x = 38
Angle M will therefore
= 3(38) - 16
= 114 - 16
= 98
Hope this helped and have a good day
Rewrite the function by completing the square.
g(x)=x^2 − x − 6
g(x)= _ ( x + _ )^2 + _
The completed square function is (x - 1/2)² = 25/4
Square function:
A square function is a 2nd degree equation, meaning it has an x². The graph of every square function is a parabola.
Given,
Here we have the function g(x) = x² - x - 6
Now, we need to convert this into the complete square function.
In order to solve this we have to do the following:
Add 6 to both sides of the equation,
x² - x = 6
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b.
(b/2)² = (-1/2)²
Add the term to each side of the equation.
x² - x + (-1/2)² = 6 + (-1/2)²
When we simplify the equation, then we get,
x² - x + 1/4 = 25/4
Factor the perfect trinomial square into,
(x - 1/2)² = 25/4
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How many different choices of shirts does the store sell
Answer:
11
Explanation:
From the probability tree:
• There are 3 choices of small shirts.
,• There are 3 choices of medium shirts.
,• There are 3 choices of large shirts.
,• There are 2 choices of X-Large shirts.
Therefore, the number of different choices of shirts the store sells:
[tex]\begin{gathered} =3+3+3+2 \\ =11 \end{gathered}[/tex]There are 11 choices of shirts.
A tornado siren begins blaring from the center of town 9.5 seconds after a tornado was spotted. The siren is located 490 meters north of a school. If the siren’s sound wave travels at a constant velocity of 350 meters per second south, how long will it take the sound wave to travel from the siren to the school?
The relationship between distance, time and velocity is:
[tex]v=\frac{d}{t}[/tex]The question ask us for the time, we can solve for t:
[tex]v=\frac{d}{t}\Rightarrow t=\frac{d}{v}[/tex]To find the time that it will take the sound wave travelling at 350 m/s to reach the school at 490m is the distance divided the velocity:
[tex]\begin{gathered} t=\frac{490m}{350\frac{m}{s}} \\ \end{gathered}[/tex][tex]t=1.4s[/tex]The answer is 1.4s
How many soultions?x + 3 = 2x - 18A single solutionInfinite solutionsNo solution
The given equation is expressed as
x + 3 = 2x - 18
Subtracting x from both sides of the equation, it becomes
x - x + 3 = 2x - x - 18
3 = x - 18
Adding 18 to both sides of the equation, it becomes
3 + 18 = x - 18 + 18
21 = x
x = 21
Since there is only one value for x, the correct option is
a. A single solution
The parabola f (x) = (x - 2)2 + 1 is graphed in the xy-coordinate plane.8Part ASelect from the drop-down menus to correctly complete the sentence.The vertex of the parabola is 2 units(a)(b) Part BSelect from the drop-down menus to correctly complete the sentence.How does the function f (x+3) compare to f (x)?f (x + 3) has avshift 3 unitsV the origin and 1 unitv f(x).the origin.
We will have the following:
a) The vertex of the parabola is 2 units right of the origin and 1 unit up from the origin.
b) We will have that:
f(x+3) has vertex shift 3 units left of f(x).
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
combine like terms
(x+3)+(9+x)
Answer:
[tex]x^{2}[/tex]+12x+27
Step-by-step explanation:
First, you need to distribute. You multiply x by 9 and x, and then multiply 3 by 9 and x, which results in 9x + [tex]x^{2}[/tex] +27 +3x.
Second, you collect like terms. In this case, there is only one like term, which is x. The results of this should be [tex]x^{2}[/tex] + 27 + 11x.
Lastly, reorder the terms properly, and you're done!
Hope this helps.
How many possible values for y are there where y = Cos-lo? O A. O Ο. O B. Infinite O C. 1 O D. 2
Answer:
B. Infinite
Explanation:
Given that:
[tex]y=\cos ^{-1}(0)[/tex]This implies that:
[tex]\cos (y)=0[/tex]From the graph of f(x)=cos(x), we observe that:
[tex]\cos (x)=0\text{ for }x=\frac{\pi}{2}+k\pi\text{ for any }k\in\Z,\text{ }\Z\text{ being the set of integers}[/tex]Therefore, there are infinitely possible values of y.
The GCD of two numbers is 11 and their LMC is 220. One of the numbers is 55. find the other number.
If the GCD of two numbers is 11 and their LCM is 220 and one of the number is 55, then the second number is 44
The one number = 55
Consider the second number as x
GCD is the greatest common divisor
LCM is the least common multiple
The greatest common divisor of two numbers = 11
The least common multiple of two numbers = 220
We know
The product of two numbers= The product of GCD and LCM
55 × x = 11 × 220
55x = 2420
x = 44
Hence, If the GCD if two numbers is 11 and their LCM is 220 and one of the number is 55, then the second number is 44
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What is an example of a situation from your professional or personal life that requires you to compare, understand, and make decisions based on quantitative comparison? Be sure to describe the types of quantitative comparisons you had to make, what decisions you made, and why.
An example of situation involving quantitative variables is given by:
The gameplan of an NFL coach.
What are qualitative and quantitative variables?The variables are classified as follows:
Qualitative variables are variables that assumes labels or ranks, such as good/bad, yes/no and so on.Quantitative variables are variables that Assume numerical values.In the context of this problem, we want to use quantitative variables, that is, numbers.
Multiple examples of this are given by the gameplan of NFL coaches, as the following example:
How often to blitz? The coach has to analyze the opposing offense statistics against the blitz or against standard pressure. For example, Patrick Mahomes is known to be a blitz killer, hence a coach should visualize the statistics and conclude that he has a better chance of stopping Mahomes playing standard coverage than blitzing.
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Please give steps and explanations to how you get the correct answer I am confused
To find the area under a function in a given interval you need to find the definite integral of the function in that interval.
For the given function:
[tex]\begin{gathered} P=100(0.4)^t \\ \\ \int_0^8Pdt=\int_0^8100(0.4)^tdt \end{gathered}[/tex]Use the next properties to find the integral:
[tex]\begin{gathered} \int a\times f(x)dx=a\int f(x)dx \\ \\ \int a^xdx=\frac{a^x}{\ln(a)} \end{gathered}[/tex][tex]\int_0^8100(0.4)^tdt=100\int_0^80.4^tdt=100\times\frac{0.4^t}{\ln(0.4)}\lvert^8_0[/tex]Evaluate the result for the given interval:
[tex]\begin{gathered} (100\times\frac{0.4^8}{\ln(0.4)})-(100\times\frac{0.4^0}{\ln(0.4)}) \\ \\ =-0.07152-(-109.13566) \\ \\ =109.06 \end{gathered}[/tex]Then, the area under the given function in the interval (0,8) is 109.06CorrectBob's Golf Palace had a set of 10 golf clubs that were marked on sale for $840. This was a discount of 10% off the original selling price.Step 3 of 4: What was the store's percent of profit based on cost ($390)? Follow the problem-solving process and round your answer tothe nearest hundredth of a percent, if necessary.
The percent change is given by:
[tex]Percent_{\text{ }}change=\frac{New_{\text{ }}value-old_{\text{ }}value}{old_{\text{ }}value}\times100[/tex]The old value is $390
I need to find the equation of a circle I will include picture
Given,
The center of the circle is (6, -3).
The coordinates of the point, circle is passing through (6,6).
The general equation of the circle is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Here, x, y are the coordinates of the point.
h and k are the center of the circle.
r is the radius of the circle.
Substituting the value of h, k , x and y in the equation of circle then,
[tex]\begin{gathered} (6-6)^2+(6-(-3))^2=r^2 \\ 0+9^2=r^2 \\ r=9 \end{gathered}[/tex]So, the radius of the circle is 9.
Substituting the value of h, k and r in the general equation of circle.
[tex]\begin{gathered} (x-6)^2+(y-(-3))^2=9^2 \\ x^2+36-12x+y^2+9+6y=81 \\ x^2+y^2-12x+6y-36=0 \end{gathered}[/tex]Hence, the equation of circle is x^2+y^2-12x+6y-36=0
PLEASE help I'll send a picture in later.
Given
Table of names
Procedure
Names end with an E
Gabe
Steve
The probability would be independent and equal to:
[tex]\begin{gathered} \frac{2}{6}\cdot\frac{2}{6} \\ \frac{4}{36} \\ \\ \frac{1}{9} \end{gathered}[/tex]The probability would be 1/9
2+2=im in kendergardenin. pls help.
The addition is the operation that puts together two quantities of numbers. It is represented by the signal "+". To add the two numbers we can use a visualization method as shown below:
We have two sticks on the left and two sticks on the right, we need to add them both, this is the same as joining them together, the result is 4 sticks. The answer is 4.
Answer:
the answer is 11
duuuh
Step-by-step explanation:
I need help on this question
Answer:
Real zeros are: x = 0, x = 1 and x =2
***Your graph is incorrect. See mine for the correct graph***
Step-by-step explanation:
We have the polynomial
[tex]$\displaystyle \:x^{4}-3x^{3}+2x^{2}\:=\:0$[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x^2:\\\\[/tex]
[tex]=x^2\left(x^2-3x+2\right)[/tex]
[tex]\mathrm{Factor}\:x^2-3x+2:[/tex]
For an expression of the form ax² + bx + c we can find factors if we find two values u and v such uv = c and u + v =b and factor into (ax +ux)+ (vx+c)
We have here a = 1, b = -3 c = 2
==> u = -1, v = -2
[tex]\:x^2-3x+2 = (x-1)(x-2)[/tex]
So the original expression becomes
[tex]\:x^2-3x+2 = x^2\left(x-1\right)\left(x-2\right)[/tex]
To find the zeros, set this equal to 0 and solve for x
[tex]x^2\left(x-1\right)\left(x-2\right)=0[/tex]
We end up with 3 roots corresponding to the 0 values for each of the three terms
[tex]x^2 = 0 == > x = \pm 0 = 0\\\\[/tex]
[tex](x - 1) = 0 == > x = 1\\\\(x - 2) = 0 == > x = 2\\\[/tex]
Answer real zeros are: x = 0, x = 1 and x =2
**** Your graph is incorrect. Check mine. The zeros happen where the curve intersects the x axis and these are at x = 0, x = 1, x =2
Draw a figure to use for numbers 13 - 15. Points A. B. and C are collinear and Bis the midpoint of AC. 13. If AB = 3x - 8 and BC = x + 4, find the length of AB 14. If BC = 6x - 7 and AB = 5x + 1. find the length of AC 15. If AB = 8x + 11 and BC = 12x - 1. find the length of BCAnswer 13
13.
Given:
AB = 3x - 8, BC = x + 4
A, B and C are collinear
B is a midpoint of AC
Since B is the midpoint, we can write:
[tex]\text{length of AB = Length of BC}[/tex]Hence, we have:
[tex]3x\text{ - 8 = x + 4}[/tex]Solving for x:
[tex]\begin{gathered} \text{Collect like terms} \\ 3x\text{ -x = 4 + 8} \\ 2x\text{ = 12} \\ \text{Divide both sides by 2} \\ x\text{ = 6} \end{gathered}[/tex]Hence, the length of AB is:
[tex]\begin{gathered} =\text{ 3x - 8} \\ =\text{ 3}\times\text{ 6 -8} \\ =\text{ 18 -8} \\ =\text{ 10} \end{gathered}[/tex]Answer:
The length of AB is 10 unit
A scale drawing of a rectangular park is 4 inches wide and 8 inches long. The actual park is 320 yards long. What is the perimeter of the actual park, in square yards?
Given:
• Width of scale drawing = 4 inches
,• Length of scale drawing = 8 inches
,• Length of actual park = 320 yards
Let's find the perimeter of the actual park.
Let's first find the width of the actual park.
To find the width of the actual park, we have:
[tex]\begin{gathered} \text{ width of actual = }\frac{\text{ length of actual}}{\text{ length of scale}}*\text{ width of scale} \\ \\ \\ \text{ width of actual = }\frac{320}{8}*4 \\ \\ \text{ width of actual = 40 * 4 = 160 yards} \end{gathered}[/tex]The width of the actual park is 160 yards.
Now, to find the perimeter of the actual park, apply the formula do perimeter of a rectangle:
P = 2(L + W)
Where:
P is the perimeter
L is the length = 320 yards
W is the width = 160 yards
Thus, we have:
P = 2(320 + 160)
P = 2(480)
P = 960 yards
Therefore, the perimeter of the actual park is 960 yards.
ANSWER:
960 yards
Find the perimeter and area of the polygon with given vertices
Let's begin by listing out the information given to us:
[tex]\begin{gathered} A(-3,3),B(-3,-1),C(4,-1),D(4,3) \\ AB=3-(-1)=3+1=4_{} \\ BC=|-3-4|=|-7|=7 \\ CD=|-1-3|=|-4|=4 \\ AD=|-3-4|=|-7|=7 \\ \\ Perimeter=2(l+w)=2(7+4)_{}=2(11)=22 \\ Perimeter=22unit \\ \\ Area=lw=7\cdot4=28unit^2 \\ Area=28unit^2 \end{gathered}[/tex]Carlos is saving money to buy a new Nintendo Switch game. He has $25. After he receives his allowance (n), he will have $45. Which of the following equations models this situation?
ANSWER
25 + n = 45
EXPLANATION
We have that Carlos already has $25.
His allowance is n. After receiving it, he now has $45.
This means that if we add the amount he had and his allowance, we will have $45.
Therefore:
25 + n = 45
This equation models the situation accurately.
Convert €3.2 per kilogram to unit price dollars per pound
We get 1.45 dollars per pound when we convert 3.2 Euros per kilogram to dollar per pound.
According to the question,
We have the following information:
3.2 Euros per kilogram
We need to convert its units into dollars per pounds.
We know that 1 Euro is approximately equal to 1 US dollar and 1 kilogram of weight is equal to 2.205 pounds.
(Note that there are various conversions from Euro to dollars which have 1 Euro equal to 1.00755 and many other values. In this case, we have rounded it off to 1 to avoid any confusion.)
(We know that per means the unit given is in divide.)
So, we have:
(3.2*1)/(1*2.205)
3.2/2.205
1.45 dollar per pounds
Hence, the conversion to dollars per pounds is 1.45 dollar per ponds from Euros per kilogram.
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Find the first five terms in sequences with the following 3n+2
To determine the first five terms of the sequence we substitute n by 1, 2, 3, 4, and 5.
For n=1, we get:
[tex]3(1)+2=3+2=5.[/tex]For n=2, we get:
[tex]3(2)+2=6+2=8.[/tex]For n=3, we get:
[tex]3(3)+2=9+2=11.[/tex]For n=4, we get:
[tex]3(4)+2=12+2=14.[/tex]For n=5, we get:
[tex]3(5)+2=15+2=17.[/tex]Answer: The first five terms of the sequence are:
[tex]5,\text{ 8, 11, 14, 17.}[/tex]