If you need to solve for x:
P= 1.5x -30,000
Add 30000 to both sides:
P + 30000 = 1.5x - 30000 + 30000
P + 30000 = 1.5x
Divide both sides by 1.5
P/1.5 + 20000 = x
How many different committees can be formed from 11 teachers and 46 students if the committee consists of 2 teachers and 4 students?The committee of 6 members can be selected in different ways.Help me solve thisView an example Get more help.D
Solution
Number teachers = 11
Number of students = 46
Then we want to form a committee of 2 teachers and 4 students
[tex]^{11}C_2\times^{46}C_4=55\times163185=8975175[/tex]433Plot and connect the points A (3,-3), B (-3, -2), C (-5, 1), D (-5, 4), E (-4,6), F (-2, 6), G (3, 2), and find the length of EF.OA 5 unitsOB.2 unitsO C. 3 unitsOD. 4 unitsResetSubmit
To find the length of EF we will use the formula for finding the distance between two points.
[tex]E(-4,\text{ 6) and F(-2, 6)}[/tex]From the points E and F:
[tex]undefined[/tex]Given the frequency table below, what is the relative frequency of the data value 7?
Relative frequency of data 7 = 3/20
Explanation:Relative frequency = number of times an item occurs/total number
The data 7 occurs 3 times
The total frequency for all the data = 7 + 6 + 4 + 3 = 20
Relative frequency of data 7 = frequency of 7/The total frequency for all the data
Relative frequency of data 7 = 3/20
Juanita was asked to create a scale drawing of her bedroom. Using the dimensions and scale shown, determine the actual area of her room.
Here, we want to get the actual area of the room
The shape is rectangular and the area of the shape is simply the product of the dimensions of its sides
Now, what we have to do here is to have the actual dimensions
That means we will multiply each of the dimensions in inch by 5 to get the dimensions in ft
Mathematically, we have this as;
[tex]\begin{gathered} 2.2\text{ in }\times\text{ 5 = 11 ft} \\ 4.3\text{ in }\times\text{ 5 = 21.5 ft} \end{gathered}[/tex]The actual area is thus the product of the actual dimensions above
We have the actual area as;
[tex]11\text{ ft }\times21.5ft=236.5ft^2[/tex]If x is a binomial random variable, compute p(x) for each of the cases below.a. n = 4,-1, p=0.6b.n=6,x=3,q=0,3d.n=4, X = 2, p=0.7e.n=6, x3, 0.7c. n 3, x0, p=0.8fin= 3,1.-0,9a. p(x) = (Round to four decimal places as needed.)27Enter your answer in the answer box and then click Check Answer,Help Me Solve ThieView anyamanlaGot Mora Hain
SOLUTION:
Step 1 :
If x is a binomial random variable, compute p( x ) for the following:
a) n = 4, x = 1 , p = 0.6
Step 2:
[tex]\begin{gathered} U\sin g\text{ the binomial random variable, we have that:} \\ p^{}(x)=^nC_{x_{}}(p)^x(q)^{n\text{ - x}} \\ p\text{ + q = 1} \\ 0.6\text{ + q = 1} \\ \text{q = 1 - 0. 6} \\ q\text{ = 0. 4} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} p^{}(1)=^4C_1(0.6)^1(0.4)^{4-\text{ 1}}_{^{}^{}} \\ =4X0.6X(0.4)^3 \\ =\text{ 4 X }0.6\text{ X 0. 0064} \\ p(\text{ 1 ) = 0.1536 ( 4 decimal places)} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]p\text{ ( 1 ) = 0. 1536 ( 4 decimal places)}[/tex]I need help with this now. She said that we were supposed to solve for the area of the composite structures inside the structures.
We can decompose the figure in structures such that we can calculate the area of each structure.
Then, we have 3 rectangles, two triangles and a semicircle. The semicircle has diameter equals to
[tex]\begin{gathered} d=43ft-10ft-9ft=24ft \\ \end{gathered}[/tex]Then, the radius is equal to r=12ft.
We divide the figure in 6 different structures:
Structures I and V are triangles, so their area is
[tex]\frac{b\times h}{2}[/tex]Structures II, III and IV are rectangles, so their area is
[tex]a\times b\text{.}[/tex]Structure VI is a semicircle, so the area is
[tex]\frac{\pi r^2}{2}\text{.}[/tex]All the areas are in squared feet.
Structure I (b=10, h=48-37=11)
[tex]\frac{10\times11}{2}=55[/tex]Structure II (a=37, b-10)
[tex]37\times10=370[/tex]Structure III (a=38-12=26, b=43-10-9=24)
[tex]26\times24=624[/tex]Structure IV (a=32, b=9)
[tex]32\times9=288[/tex]Structure V (b=9, h=40-32=8)
[tex]\frac{9\times8}{2}=36[/tex]Structure VI (r=12)
[tex]\frac{(3.14)(12)^2}{2}=226.08[/tex]Then, we can obtain the total area adding all the area of the structures.
[tex]55+370+624+288+36+226.08=1599.08[/tex]So, the total area is 1599.08 squared feet.
A restaurant added a new outdoor section that was 5ft wide 9ft long. What is the area of the new outdoor section?
Given:
a.) A restaurant added a new outdoor section that was 5 ft wide 9 ft long.
Based on the given, Length and Width, presuming it's rectangular in shape, let's now determine the area:
[tex]\text{ Area = Length x Width}[/tex][tex]=\text{ 9 x 5}[/tex][tex]\text{Area = 45 ft}^2[/tex]Therefore, the area of the new outdoor section is 45 ft.²
what is the sum of rocks between Pablo and Javier?
Answer:
4r-5
Explanation:
Maria collected r rocks.
Javier collected twice as many rocks as Maria = 2r
Pablo collected 5 less than Javier = 2r - 5
Therefore, the sum of rocks between Pablo and Javier
[tex]\begin{gathered} =2r+2r-5 \\ =4r-5 \end{gathered}[/tex]For reference:
i need help with a non graded 10 question prep test
Given data:
The given triangles is shown.
The expression for the ratio of adjacent side is,
[tex]\frac{3}{6}=\frac{1}{2}[/tex]Thus, the scale factor is 1/2, so the second option is correct.
Find the distance between (-6, 1) and (2, 2). Round to thenearest hundredth.
The given points are (-6, 1) and (2, 2).
To find the distance between these points, we need to use the following formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Replacing the given points, we have
[tex]d=\sqrt{(2-(-6))^2+(2-1)^2}=\sqrt{(8)^2+(1)^2}=\sqrt{64+1}=\sqrt{65}[/tex]Which is approximately 8.06.
Therefore, the distance between these two points is 8.06 units, approximately.Follow the instructions below.5Write a: a without exponents.D+ロロ5a. a=0хx5Fill in the blank.5wa = a
1. Without exponents:
[tex]a\cdot a^5=a\cdot a\cdot a\cdot a\cdot a\cdot a[/tex]2.
[tex]\begin{gathered} a\cdot a^5=a^1\cdot a^5 \\ =a^{1+5}=a^6 \end{gathered}[/tex]Damon deposits $2,240 into a savings account that earns 3½% interest compounded quarterly. What is his new balance after 6 months?
Given:
Principal, P = $2,240
Interest rate, r = 3½% = 3.5% = 0.035
Time, t = 6 months = 6/12 months a year = 0.5 years
Yearly deposits, n = 4 (quaterly)
Use the compound interest formula below:
[tex]A\text{ = P(}1\text{ + }\frac{r}{n})^{nt}[/tex]Therefore, we have:
[tex]A\text{ = 2240(1 + }\frac{0.035}{4})^{4\cdot0.5}[/tex]Solving further,
[tex]A\text{ = 2240 (1 + }0.1757)[/tex][tex]\begin{gathered} A\text{ = 2240( 1.01757)} \\ \text{ = }2279.3715 \end{gathered}[/tex]Therefore his new balance after 6 months is $2279.37
ANSWER:
$2,279.37
BEUse substitution to solve.f2x2 = 5 + y4y = -20 + 8x2Solve the first equation for y and substitute it into the second equation. The resulting equati4y = 16x2 - 608x2 - 20 = -20 + 8x22x2 = 5 + 2x2 - 5
Given that:
[tex]\begin{gathered} 2x^2=5+y \\ 4y=-20+8x^2 \end{gathered}[/tex]From the first equation,
[tex]y=5-2x^2[/tex]Substitute the obtained value of y into the second equation.
[tex]\begin{gathered} 4(5-2x^2)=-20+8x^2 \\ 20-8x^2=-20+8x^2 \end{gathered}[/tex]So, it has infintely many solutions.
Solutions are of the form:
[tex](x,y)=(x,5-2x^2[/tex]where x is any real number.
The equation represents the proportional relationship between the money earned (p) and the number of hot dogs sold (h)P=2hWhat is the money in dollars earned for each hot dog sold.Please help!!!
Answer:
$2
Explanation:
Given the below equation;
[tex]P=2h[/tex]where P = money earned in dollars
h = number of hot dogs sold
From the question, we are asked to determine the money in dollars earned for each hot dog sold, i.e., find P when h = 1;
[tex]\begin{gathered} P=2(1) \\ P=2dollars \end{gathered}[/tex]Which of the following expressions are equivalent to 4 - (-5) + 0?Choose 3 answers:А 4 - (-5)B 4 + 5С 4 - (-5 + 0)D (4 – 5) + 0E 4 – (5 – 0)
ANSWER
A, B and C
EXPLANATION
To find the expression that is equivalent as the given one, we will first simplify it:
4 - (-5) + 0
4 + 5 + 0
=> 9
Note:
- * - = +
- * + = + * - = -
Now, we will do the same for the others:
A. 4 - (-5)
=> 4 + 5
=> 9
It is equivalent
B. 4 + 5
=> 9
It is equivalent
C. 4 - (-5 + 0)
=> 4 + 5 - 0
=> 9
It is equivalent
The question askes for three answers, so the answers are:
A, B and C
Can you please help me with this trig ratios problem?
The expression is given
[tex]\sin \theta=\frac{\sqrt[]{3}}{2}[/tex]To determine the value of angle in degree.
[tex]\theta=\sin ^{-1}(\frac{\sqrt[]{3}}{2})[/tex][tex]\theta=60^{\circ}[/tex]Hence the value of angle in degree is 60 degree.
Bobby traveled 29 mles to get to work. It took him 32 minutes to get to his destination What was his speed durng hs trip to work?
distance, D = 29miles
time, T = 32mins
[tex]\text{speed = }\frac{dis\tan ce}{time}[/tex]Therefore,
[tex]S=\frac{29}{32}=0.91miles\text{ per minutes}[/tex]What is the equation of a quadratic function y = f(x) with two irrational zeros, -√h and √h, where h is a rational number?
We want to write the equation of a quadratic function with two irrational zeros, -√h and √h where h is a rational number.
As the zeros are irrational, we know that what is inside the square roots must be negative. Thus, h is less than zero.
Now we will write the equation, by remembering the factor theorem. We can write the polynomial as:
[tex]f(x)=(x-x_1)(x-x_2)[/tex]Where x₁ and x₂ are the roots of the function, in this case, -√h and √h. This means that f can be written as:
[tex]\begin{gathered} f(x)=(x-(-\sqrt[]{h}))(x-\sqrt[]{h}) \\ =(x+\sqrt[]{h})(x-\sqrt[]{h}) \\ =x^2-(\sqrt[]{h})^2 \\ =x^2-h \end{gathered}[/tex]This means that the polynomial with the irrational zeros -√h and √h is f(x)=x²-h, where h is a negative rational.
²
For each ordered pair, determine whether it is a solution to the system of equations:7x - 4y = 8-2x+3y=7
Answer:
The solution to the system of equations is
(x, y) = (4, 5)
Explanation:
Given the pair of equations:
[tex]\begin{gathered} 7x-4y=8\ldots.\ldots..\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ -2x+3y=7\ldots\ldots\ldots\ldots\ldots.\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]To know the solution to the system, we solve the equations simultaneously.
From equation (1), making x the subject, we have:
[tex]x=\frac{8+4y}{7}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(3)[/tex]Substituting equation (3) in (2)
[tex]\begin{gathered} -2(\frac{8+4y}{7})+3y=7 \\ \\ \text{Multiply both sides by 7} \\ \\ -2(8+4y)+21y=49 \\ -16-8y+21y=49 \\ -16+13y=49 \\ \\ \text{Add 16 to both sides} \\ -16+13y+16=49+16 \\ 13y=65 \\ \\ \text{Divide both sides by 13} \\ y=\frac{65}{13}=5 \end{gathered}[/tex]The value of y is 5
Using y = 5 in equation (3)
[tex]\begin{gathered} x=\frac{8+4(5)}{7} \\ \\ =\frac{8+20}{7} \\ \\ =\frac{28}{7} \\ \\ =4 \end{gathered}[/tex]The value of x is 4
Solve the system of equations by elimination. 3x − y − z = 2 x + y + 2z = 4 2x − y + 3z = 9
Given:
The system of equations is,
[tex]\begin{gathered} 3x-y-z=2.\text{ . .. . . .(1)} \\ x+y+2z=4\text{ . . . .. . (2)} \\ 2x-y+3z=9\text{ . . . . . . .(3)} \end{gathered}[/tex]The objective is to solve the equations using the elimination method.
Explanation:
Consider the equations (1) and (2).
[tex]\begin{gathered} 3x-y-z=2 \\ \frac{x+y+2z=4}{4x+z=6} \\ \ldots\ldots\ldots.(4)\text{ } \end{gathered}[/tex]Now, consider the equations (2) and (3).
[tex]\begin{gathered} x+y+2z=4 \\ \frac{2x-y+3z=9}{3x+5z=13} \\ \ldots\ldots\text{ . . . .. (5)} \end{gathered}[/tex]On multiplying the equation (4) with (-5),
[tex]\begin{gathered} -5\lbrack4x+z=6\rbrack \\ -20x-5z=-30\text{ . . . . . .(6)} \end{gathered}[/tex]To find x :
On solving the equations (5) and (6),
[tex]\begin{gathered} 3x+5z=13 \\ \frac{-20x-5z=-30}{-17x=-17} \\ x=\frac{-17}{-17} \\ x=1 \end{gathered}[/tex]To find z :
Substitute the value of x in equation (6),
[tex]\begin{gathered} -20(1)-5z=-30 \\ -5z=-30+20 \\ -5z=-10 \\ z=\frac{-10}{-5} \\ z=2 \end{gathered}[/tex]To find y :
Now, substitute the values of x and z in equation (2).
[tex]\begin{gathered} x+y+2z=4 \\ 1+y+2(2)=4 \\ y=4-1-4 \\ y=-1 \end{gathered}[/tex]Hence, the value of x is 1, y is -1 and z is 2.
Make a table of values and then graph the function:Where is there an asymptote?
f(x) = (1.5)^x
Table
x y
-2 0.4
-1 0.6
0 0.1
1 1.5
2 2.25
Exponential functions have a horizontal asymptote. The equation of the asymptote is y = 0
Horizontal Asymptotes: y = 0
know that two of the side lengths of the triangle are 3 inches and 4 inches. We represent the third side length of the triangle with the variable x.
Answer:
x < 7
Explanation:
Given the following sides of a triangle
s1 = 3
s2 = 4
Reqquired
Third side x (hypotenuse)
Using the pythagoras theorem;
x^2 = s1^2 + s2^2
x^2 = 3^2 + 4^2
x^2 = 9+16
x^2 = 25
x = \sqrt{25}
x = 5
Since x is equal to 5, this means we can say that the values of x is less than 7 (x < 7) based on the option
6: Find the equation of a polynomial with given zeros:
The given zeros are - 5/4, - 2/3, 2
We would find the factors
For x = - 5/4,
4x = - 5
4x + 5 = 0
For x = - 2/3,
3x = - 2
3x + 2 = 0
For x = 2,
x - 2 = 0
We would multiply the factors. We have
(4x + 5)(3x + 2)(x - 2)
By applying the distributive proerty of multiplication, we vae
(4x + 5)(3x + 2) = 12x^2 + 8x + 15x + 10
(4x + 5)(3x + 2) = 12x^2 + 23x + 10
(x - 2)(12x^2 + 23x + 10) = 12x^3 + 23x^2 + 10x - 24x^2 - 46x - 20
(x - 2)(12x^2 + 23x + 10) = - 24x^2 = 12x^3 + 23x^2 - 24x^2 + 10x - 46x - 20
= 12x^3 - x^2 - 36x - 20
The first option is correct
A city currently has 130 streetlights. As part of a urban renewal program, the city council has decided to install 2 additional streetlights at the end of each week for the next 52 weeks.How many streetlights will the city have at the end of 40 weeks?
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.
Use the equation to identify the center and radius of the circle (X+3)^2+(y-7^2=11
To find the radius od the circle using (X+3)²+(y-7)²=11
(x-a)²+(y-b)²=r² is the equation for a circle in a Cartesian plane
the center is given by c= (a,b) so the center would be (-3,7)
and to find the r use
11 =r²
√11 = r
3.31 = r
What is the equation of the line shown in the graph, in standard form ? please help me as soon as possible.
First find two points and locate its coordinate
(-2, 0) and (-3, -2)
x₁=-2
y₁=0
x₂=-3
y₂=-2
substitute the values into the formula below
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex][tex]y-0=\frac{-2-0}{-3+2}(x+2)[/tex][tex]y=\frac{-2}{-1}(x+2)[/tex][tex]y=2(x+2)[/tex]y= 2x + 4
Re-arrange
2x - y = -4
3. A store has two square rugs on sale. Thearea of the smaller rug is 52 square feet. Thesides of the larger rug are 1.5 times the length ofthe sides of the smaller rug. Which of thefollowing is closest to the area of the larger rug?A. 65 sqftB. 78 sqftC. 117 sqft
Answer:
C. 117 sqft
Step-by-step explanation:
Square:
A square has side s.
It's are is given by:
A = s²
In this question:
A = s² = 52.
Larger rug:
Sides 1.5 times the smaller rug.
So
A = (1.5s)² = (1.5)²*s² = 2.25s²
Since s² = 52.
A = 2.25s² = 2.25*52 = 117
The answer is C. 117 sqft
1 How many students are cleaning 96 desks if each student cleans 4 desks? a) Write an equation using a symbol for the unknown. b) Find the answer to the question and show your reasoning.
Given data:
The numbers of desk clean by a students are 4.
(a)
The expression for the given statement is,
[tex]1\text{ s= 4 d}[/tex]Here, s is the student and d represents desk.
(b)
Multiply 24 on both sides.
[tex]\begin{gathered} 24(\text{ 1 s)=24(4 d)} \\ 24\text{ s =96 d} \end{gathered}[/tex]Thus, for cleaning 96 desks 24 students needed.
Ramona has a new job as à chef. She earns the sameamount per hour as she did in her old job, plus she got a$100 sign-on bonus. Line p represents Ramona's earnings inher old job. Line q represents her earnings in her new job.Write an equation for line p. What does the slope mean?How can you use the equation for line p to write anequation for line q?Amount
Using the graph of line p, we select two points in order to find the slope through the equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]if we select points (0,0) and (4,40),
[tex]\begin{gathered} m=\frac{40-0}{4-0} \\ m=\frac{40}{4} \\ m=10 \end{gathered}[/tex]then, since the line passes through the point (0,0) the equation for line p is
[tex]y=10x[/tex]The meaning of the slope is the amount she earns per hour she works.
Since she earns the same on both jobs per hour worked, it means the slope of the line is the same in both cases, however, she hets a $100 bonus, which means that the resulting equation for q is:
[tex]y=10x+100[/tex]Answer:
- The equation of line p is: y=10x
- The slope means she earns $10 for every hour she works
- Both lines have the same slope, but line q has the bonus, meaning the equation is: y=10x+100
the cost of a dozen carnations at the florist is 4 1/3 dollars. how much would it cost for 3 dozen?
1 dozen = 4 1/3 dls. = 13/3
3 dozen = (13/3)*12 = 52 dollars.