Since the increment of number of lights is constant we can model the number of lights with a linear equation; we know that the line with slope (or rate of change) m and y-intercept b is given by:
[tex]y=mx+b[/tex]In this case, the slope of the line will be 2 and the y-intercept is 130; hence the number of lights in any week is given by:
[tex]y=2x+130[/tex]Now that we have an expression we can plug the week we want to know to determine the number of lights, since we want to know the number of lights at the end of week 40 we have that x=40; then:
[tex]\begin{gathered} y=2(40)+130 \\ y=80+130 \\ y=210 \end{gathered}[/tex]Therefore, at the end of week forty there will be 210 lights.
Find the distinct four letter word that can be formed from the word Singapore
We can create a number of words from the given word "SINGAPORE".
Some of them are:
•SING- Make musical sounds with your voice, especially words set to music
•SIGN- to affix a signature to demonstrate acceptance, agreement, or responsibility
•PORE- a minute opening in a surface, especially an organism's skin or integument, through which gases, liquids, or microscopic particles can pass
•RING- a small circular band, usually made of precious metal and set with one or more gemstones, worn on a finger as an ornament or as a symbol of marriage, engagement, or authority.
•PAIR- a pair of things used together or considered as a unit
Solve the system with elimination.3x + y = 9x + 2y = 3
In order to solve by elimination, let's multiply the first equation by -2. This way, when we add the equations, the variable y will be canceled out:
[tex]\begin{cases}-6x-2y=-18 \\ x+2y={3}\end{cases}[/tex]Now, adding the equations, we have:
[tex]\begin{gathered} -6x-2y+x+2y=-18+3\\ \\ -5x=-15\\ \\ x=\frac{-15}{-5}\\ \\ x=3 \end{gathered}[/tex]Now, calculating the value of y, we have:
[tex]\begin{gathered} x+2y=3\\ \\ 3+2y=3\\ \\ 2y=0\\ \\ y=0 \end{gathered}[/tex]Therefore the solution is (3, 0).
Sarah is conducting a science experiment the directions tell her to mix 5 parts of substance B how many mililters of substance A should she use
Answer: She should use 25 millimeters of substance A
This is a case of ratio. Substance A and B are to be mixed in a given ratio such that as A increases, B would similarly increase, not by the same quantity but by the same ratio. That means every time you add 5 parts of A, you need to add 3 parts of B. In effect, if you add 5 parts of A ten times (5 * 10 = 50 parts) you will need to add 3 parts of B ten times also (3 * 10 = 30).
So the
y Quinn had 3 more than two times the number of marbles Rowan has. Together they have 77marbles How many marbles door each child have?
Explanation
Step 1
Let
convert words into math terms
Let
x= number of marbles Quinn has
y= number of marbles Rowan has
Quinn had 3 more than two times the number of marbles, in other words you have to add 3 to twice the number or marlbles
x=2y+3
Rowan has. Together they have 77
x+y=77
Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The amounts she spent in each category are pictured here.Food - 422Other - 633Rent - 528Fun - 317What percent of her total spending did she spend on Rent?Round your answer to the nearest whole percent
Kate organized her spending month in four categories:
Food - 422
Other - 633
Rent - 528
Fun - 317
The amount of the total spending is the sum of all the categories:
So 422+633+528+317 = 1900 total spending
If we want to know the percent that she spent on rent, use
Rent/total of spending
528/1900= 0.2778
Rounded to the nearest whole percent:
0.2778 = 27,78% = 28%
What is the formula for converting a quadratic formula to standard form?
we have that
the quadratic formula is of the form
Ax^2+Bx+C=0 ------> that is the standard form of the quadratic equation
A quadratic equation can be written in vertex form
so
y=a(x-h)^2+k
where
(h,k) is the vertex of the quadratic equation
a is the leading coefficient
To convert vertex form to the standard equation
step 1
y=a(x-h)^2+k
y=a(x^2-2hx+h^2)+k
y=ax^2-2ahx+ah^2+k
group terms
y=ax^2-2ahx+(ah^2+k)
equate to zero
ax^2-2ahx+(ah^2+k)=0
where
the coefficients A, B and C are
A=aB=-2ahC=ah^2+ktherefore
To convert a quadratic equation in vertex form to standard form, apply the formula above
Given that DE¯¯¯¯¯¯¯¯, DF¯¯¯¯¯¯¯¯, and EF¯¯¯¯¯¯¯¯ are midsegments of △ABC, and DE=3.2 feet, EF=4 feet, and DF=2.4 feet, what is the perimeter of △AB
Given: The triangle ABC is provided with DE = 3.2 feet, EF = 4 feet and DF = 2.4 feet.
To find: The perimeter of the triangle ABC.
Explanation:
The triangle ABC is given where DE , EF and DF are the midsegments of the triangle ABC.
If DE is the midsegment then using midsegment theorem we have
[tex]\begin{gathered} DE=\frac{1}{2}BC \\ BC=2DE \\ BC=2\times3.2 \\ BC=6.4 \\ \end{gathered}[/tex]Since, EF is the midsegment then using midsegment theorem we have
[tex]\begin{gathered} EF=\frac{1}{2}AB \\ AB=2EF \\ AB=2\times4 \\ AB=8 \end{gathered}[/tex]Since, DF is the midsegment then using midsegment theorem we have
[tex]\begin{gathered} DF=\frac{1}{2}AC \\ AC=2DF \\ AC=2\times2.4 \\ AC=4.8 \end{gathered}[/tex]We have the sides of the triangle as AB = 8 feet, BC = 6.4 feet and AC = 4.8 feet.
The perimeter of the triangle ABC will be :
P = AB+BC+AC
=8+6.4+4.8
=19.2
Therefore, the perimeter of the triangle is P = 19.2 feet
Final Answer: The perimeter is P = 19.2 feet.
At $450 per person, an airline anticipates selling 300 tickets for a particular flight. At $500 p person, the airline anticipates selling 150 tickets for the same flight. Assume a linear relation between the cost per ticket C and the number of tickets, x sold. Whi the following equations can be used to model the given information?C=-(2)/(3)x+555C=-(2)/(3)x+550C=-(1)/(3)x+555C=-(1)/(3)x+550
1) We can begin by writing C as a function of x and find the slope between two points (300,450) and (150,500)
[tex]\begin{gathered} C=mx+b \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{500-450}{150-300}=\frac{50}{-150}=-\frac{1}{3} \end{gathered}[/tex]2) Now that we know the slope, we need to find the linear coefficient (y-intercept), using one of those ordered pairs: (150,500)
[tex]\begin{gathered} 500=-\frac{1}{3}(150)+b \\ -\frac{1}{3}\left(150\right)+b=500 \\ -50+b=500 \\ b=550 \end{gathered}[/tex]So the function is:
[tex]C=-\frac{1}{3}x+550[/tex]Need help with question 7 section a b and c please
We have the function h(n) = 4x+3
h(n) = 15
4x+3 = 15
4x = 12
x= 3
And f(x) = 2(4)^x
f(3) = 2(4)³
f(3) = 2*64
f(3)= 128
The polynomial P(x) = 5x^3 + 2x^2 - 4x has ____ local maxima and minima
Answer:
The local maximum is (-0.667, 2.074) and the local minimum is (0.4, -0.96).
Explanation:
The graph for the function P(x) = 5x^3 + 2x^2 - 4x is
Then, the local minima and maxima are the points where the graph has a minimum or maximum in a given interval.
In this case, it has a local maximum at x = -0.667 and a local minimum at x = 0.4
Therefore, the local maximum is (-0.667, 2.074) and the local minimum is (0.4, -0.96).
Given the table values, Determine the base for the expoent function
To determine the value of the exponential function:
[tex]y=a^x[/tex]we use the first values from the table and plug them in the expression for the function:
[tex]\begin{gathered} \frac{1}{81}=a^{-\frac{1}{2}} \\ \frac{1}{a^2}=\frac{1}{81} \\ a^2=81 \\ a=\sqrt[]{81} \\ a=9 \end{gathered}[/tex]Therefore the base of the exponent function is 9
In nursing one procedure for determining the dosage for a child ischild dosageage of child in yearsage of child+12- adult dosageIf the adult dosage of a drug is 328 ml., how much should a 10-year old child receive? Round your answer to the nearest hundredth.
Given:
[tex]child\text{ dosage=}\frac{age\text{ of child in year }}{\text{age of child}+12}\times adult\text{ dosage}[/tex]To determine: Child dosage given that
[tex]\begin{gathered} \text{age of chld = 10,} \\ \text{adult dosage = 328ml} \end{gathered}[/tex]Solution:
In other to determine the child dosage, we would substitute the age of the child given and the adult dosage into the formula
[tex]\begin{gathered} child\text{ dosage=}\frac{age\text{ of child in year }}{\text{age of child}+12}\times adult\text{ dosage} \\ child\text{ dosage=}\frac{10}{10+12}\times328ml \\ child\text{ dosage=}\frac{10}{22}\times328ml \end{gathered}[/tex][tex]\begin{gathered} child\text{ dosage=}\frac{3280ml}{22} \\ child\text{ dosage=}149.090909ml \\ child\text{ dosage=}149.09ml(\text{nearest hundredth)} \end{gathered}[/tex]Hence, a 10-year old child would receive to the nearest hundredth 149.09 ml
Which fractional comparison below is NOT true? A. 2/3 = 6/9 B. 4/5 > 8/16 C. 2/5 < 5/10 D. 1/2 > 3/4
We can evaluate expression one by one,
1
[tex]\begin{gathered} \frac{2}{3}=\frac{6}{9} \\ \frac{6}{9}\rightarrow\frac{3\times2}{3\times3}=\frac{2}{3} \end{gathered}[/tex]This is true.
2.
[tex]\begin{gathered} \frac{4}{5}>\frac{8}{16} \\ \frac{8}{16}=\frac{1}{2}=0.5 \\ \frac{4}{5}=0.8 \\ \text{0}.8>0.5 \end{gathered}[/tex]This is true.
3.
[tex]\begin{gathered} \frac{2}{5}<\frac{5}{10} \\ \frac{5}{10}=\frac{5}{5\times2}=\frac{1}{2}=0.5 \\ \frac{2}{5}=0.4 \\ \text{0}.4<0.5 \end{gathered}[/tex]This is true.
4.
[tex]\begin{gathered} \frac{1}{2}>\frac{3}{4} \\ \frac{1}{2}=0.5 \\ \frac{3}{4}=0.75 \\ \end{gathered}[/tex]This is not true.
Thus, the correct option is D
Given that GEO - FUN, Snd UF12 ft17 ftE15 ftUFEft
Since this is a congruent triangle problem, The side UF is equal to side GE
so UF is 12
The definition of congruent triangles is "Two triangles are congruent if they have the same shape and the same size"
1512 trSrc) Me 19h 15) r + 1 + 1 + or > 3(r - 4) - (1) N *中24GA BX1Z -xt 2+M-LA2%2-22 tryx2X-8 2 S > > - 17) 2(1 - 4r) < -2(r+ 3) - 4 셈 18) -61 + 0 + 2 +
we have the inequality
x+1+1+6x > 3(x-4)-(x-4)
7x+2 > 2(x-4)
7x+2 > 2x-8
7x-2x > -8-2
5x > -10
x > -2
in a number line the solution is the interval (-2, infinite)
a shaded area at right of x=-2
see the attached figure
COLOR THEME O ZOOM 11. Larry purchased 0.4 pounds of jellybeans for his niece. If the jellybeans cost 70¢ per pound, which model represents how to determine the amount Larry paid for the jellybeans? < PREVIOUS 7 8 9
We know that
• He purchases 0.4 pounds of jelly beans.
,• Each pound costs 70 cents.
To determine the amount of money Larry paid, we can use the following proportion.
[tex]\frac{0.70}{1}=\frac{x}{0.4}[/tex]Then, we solve for x.
[tex]x=0.70\cdot0.4=0.28[/tex]Larry paid 28 cents for 0.4 pounds of jelly beans for his niece.Jeff is a popcorn vendor at the Linc. He is paid $50.00 for a game, plus $1.50 for each box of popcorn sold (X). If at the end of the night, he has made $182.00, how many boxed os popcorn did he sell?
Determine if the two triangles shown are similar if so right similarities statement
Let us compare the ratios of the lengths to see if there is a relationship
[tex]\begin{gathered} \frac{14}{49}=\frac{2}{7} \\ \text{also} \\ \frac{8}{28}=\frac{2}{7} \end{gathered}[/tex]From the comparison, we can see that
[tex]\frac{14}{49}=\frac{8}{28}[/tex]Then it followed that
[tex]\frac{VM}{MU}=\frac{ML}{MT}=\frac{VL}{UT}[/tex]Since the ratios of the sides of the two triangles are equals to each other, it is definite that the two triangles are similar.
Hence, triangle VLM is congruent of similar to triangle UTM
If M is between G and T, MG = 5x+3, MT = 2x-1, and GT = 37then x = MG =MT =
We have:
Then:
[tex]\begin{gathered} MG+MT=GT \\ 5x+3+2x-1=37 \end{gathered}[/tex]And solve for x:
[tex]\begin{gathered} 7x+2=37 \\ 7x+2-2=37-2 \\ 7x=35 \\ \frac{7x}{7}=\frac{35}{7} \\ x=5 \end{gathered}[/tex]Therefore, for MG and MT:
[tex]\begin{gathered} MG=5(5)+3=25+3=28 \\ MT=2(5)-1=10-1=9 \end{gathered}[/tex]Answer:
x = 5
MG = 28
MT = 9
Write the trigonometric form of the complex number. (Let 0 ≤ < 2.)
Find: the graph of -7i
Explanation:
Final answer: option d is correct option.
the bottom part of the question is what i’m stuck on
hello!
First, let's write the possibilities of each thing:
2 body styles (2 or 4 doors)
3 interior (deluxe, luxury, or special edition)
2 drive trains (front-wheel or four-wheel)
Now, let's write the possibility chosen by the exercise:
4 door, special edition, and four-wheel drive model.
we must calculate the probability of each of these choices happening, and then multiply them up:
Now that we know the possibilities of each one of the choices, we have to multiply it.
The fuel efficiency ( in miles per gallon) of a car going at a speed of x miles per hour is given by the polynomial - 1/150x^2 + 1/3x. Find the fuel efficiency when x= 30 mph
Given:
The expression of fuel is given as,
[tex]f(x)=\frac{1}{150}x^2+\frac{1}{3}x\text{ . . . . . (1)}[/tex]The objective is to find the efficiency when x = 30mph.
Explanation:
To obtain the efficiency, substitute x=30 in equation (1).
[tex]f(30)=\frac{1}{150}(30)^2+\frac{1}{3}\times30[/tex]On further solving the above equation,
[tex]\begin{gathered} f(30)=\frac{900}{150}+10 \\ =6+10 \\ =16 \end{gathered}[/tex]Hence, the fu
15 people fit comfortably in a 5 feet by 5 feet area. use this value to estimate the size of a crowd that is standing 7 feet deep on both side of the street along a 2 mile section
98560 people
Explanations:From the given question, we have the following information
The number of people that can fit comfortably in a 5 feet by 5 feet area = 15people
Area = 5ft * 5ft
Area = 25 square feet
The ratio of the number of people per unit area is expressed as:
[tex]\begin{gathered} k=\frac{15}{5\times5} \\ k=\frac{15}{25} \end{gathered}[/tex]Determine the area occupied by the crowd.
[tex]\begin{gathered} Area=7feet×2mile×2 \\ Area=7ft\times10,560ft\times2\text{ \lparen1mile = 5280ft\rparen} \\ Area=147840ft^2 \end{gathered}[/tex]Determine the required size of the crowd
[tex]\begin{gathered} Size\text{ of crowd}=\frac{15}{25}\times147,840 \\ Size\text{ of crowd}=\frac{2}{3}\times147,840 \\ Size\text{ of crowd}=98560peoples \end{gathered}[/tex]Hence the size of a crowd that is standing 7 feet deep on both side of the street along a 2 mile section is 98560 people.
The average score on a stats midterm was 73 points with a standard deviation of 7 points. Gregory s-score was -2. How many points did he score?
scoressolution
average = 73
SD = 7
then
[tex]-2=\frac{n-73}{7}[/tex]where n = number of points, so:
[tex]\begin{gathered} -2\cdot7=\frac{n-73}{7}\cdot7 \\ -14=n-73 \\ -14+73=n-73+73 \\ n=59 \end{gathered}[/tex]answer: 59 points he scores
Haley practiced her free throws at the basket ball court and shot 25 times. She made 11 of her shots. What percent of her shots did she NOT make?
WE know that
• She threw 25 times.
,• She made 11 of them.
To know the percentage number that 11 presents, we just have to divide
[tex]\frac{11}{25}=0.44[/tex]Then, we multiply by 100 to express it in percentage
[tex]\text{0}.44\cdot100=44[/tex]Therefore, Haley made 44% of the shots.5. The table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their car.Red CarNot Red CarTotalSpeeding Ticket162541No Speeding Ticket215279494Total231304535If one person is randomly selected from the group, what is the probability that this person does not drive a red car or did not get a speeding ticket?
The total number of persons = 535
The number of persons that does not drive a red car is 304
The number of persons that didn't get a speeding ticket is 494
The number of persons that don't drive a red car and didn't get a speeding ticket is 279
Therefore, the probability that a person selected at random does not drive a red car and did not get a speeding ticket is
(number of persons not driving a red car + number of persons without speeding ticket - number of persons in both cases)/total number of persons
Thus, we have
(304 + 494 - 279)/535
= 0.97
The probability is 0.97
1/6 of loop around the circle would be a rotation of how many degrees (q)? A=6B=60C=30D=36
Note that a whole circle measures 360 degrees.
1/6 of it will be :
[tex]\frac{1}{6}\times360^{\circ}=60^{\circ}[/tex]The answer is B. 60
Some of the first n terms of the geometric sequence
1) We have to find the sum of the first four terms of the geometric sequence:
[tex]3+3(\frac{1}{4})+3(\frac{1}{4})^2+3(\frac{1}{3})^3+3(\frac{1}{4})^4[/tex]In this case, we can take out the factor 3 and we have a common ratio r = 1/4. We have to add the first 5 terms.
Then, the sum can be expressed as:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]For this problem, r1 = 3, r = 1/4 and n = 5:
[tex]\begin{gathered} S_5=\frac{3(1-(\frac{1}{4})^5)}{1-\frac{1}{4}} \\ S_5=\frac{3(1-\frac{1}{1024}_)}{\frac{3}{4}} \\ S_5=\frac{3(\frac{1024-1}{1024})}{\frac{3}{4}} \\ S_5=\frac{4}{3}\cdot3\cdot\frac{1023}{1024} \\ S_5=\frac{1023}{256} \end{gathered}[/tex]2) We have this sum already solved but we can check it as:
[tex]\begin{gathered} S=\sum_{i\mathop{=}1}^7(-3)^i \\ S=(-3)+(-3)^2+(-3)^3+(-3)^4+(-3)^5+(-3)^6+(-3)^7 \\ S=-3+9-27+81-243+729-2187 \\ S=-1641 \end{gathered}[/tex]Answer:
1) 1023/256
2) -1641
What is the solution to the equation below? Round your answer to two decimal places.3x = 9.2A.x = 2.02B.x = 2.22C.x = 0.50D.x = 0.96
A)2.02
ExplanationStep 1
given
[tex]3^x=9.2[/tex]a) write the rigth side of the equation as a fraction
[tex]9.2=\frac{92}{10}=\frac{46}{5}[/tex]hence
[tex]3^x=\frac{46}{5}[/tex]b) take the logarithms in both sides
[tex]\begin{gathered} 3^x=\frac{46}{5} \\ \ln3^x=ln\frac{46}{5} \\ apply\text{ the property} \\ x=log_3(\frac{46}{5}) \\ x=2.02 \end{gathered}[/tex]so, the answer is
A)2.02
supposed relationship between X and Y is proportional when X is 29 and Y is 276.5. find the constant of proportionality of y 2x use the constant of proportionality to find X when Y is 400 + 8.5 explain how you can tell a relationship that is proportional from a relationship that is not proportional
Proportional relationships follow the next equation.
y = kx
where y and x are the variables, and k is a constant
when x is 29 and Y is 276.5.