Let's begin by listing out the information given to us:
[tex]18x+12y-30[/tex]Factoring means we will use the common factor of the elements to break down the expression into a simpler form:
[tex]6(3x+2y-5)[/tex]Define table represents grouped frequency distribution of the number of hours found computer per week for49 students. What is the value of the upper class limit of the fifth class
Sample unit: students
Sample size: 49
Variable: number of hours spent on the computer per week
There are 5 classes. The 5th class (the last one) of the table is:
14.0 - 17.4
Its upper-class limit of the 5th class is 17.4 hours
Find the common ratio of the geometric sequence 19, -76,304, ...
Help me please what is the probability of all the letters?
Given:
• Number of male who survived = 338
,• Number if female sho survived = 316
,• Number f children who survived = 57
,• Number of male who died = 1352
,• Number of female who died = 109
,• Number of children who died = 52
,• Total number of people = 2224
Let's solve for the following:
(a). Probability of the passenger that survived:
[tex]P(\text{survived)}=\frac{nu\text{mber who survived}}{total\text{ number if people }}=\frac{711}{2224}=0.320[/tex](b). Probability of the female.
We have:
[tex]P(\text{female)}=\frac{\text{ number of females}}{total\text{ number }}=\frac{425}{2224}=0.191[/tex](c). Probability the passenger was female or a child/
[tex]P(\text{female or child)}=\frac{425}{2224}+\frac{109}{2224}=\frac{425+109}{2224}=0.240[/tex](d). Probability that the passenger is female and survived:
[tex]P(femaleandsurvived)=\frac{316}{2224}=0.142[/tex](e). Probability the passenger is female and a child:
[tex]P(\text{female and child)=}\frac{425}{2224}\times\frac{109}{2224}=0.009[/tex](f). Probability the passenger is male or died.
[tex]P(male\text{ or died) = P(male) + }P(died)-P(male\text{ and died)}[/tex]Thus, we have:
[tex]P(\text{male or died)}=\frac{1690}{2224}+\frac{1513}{2224}-\frac{1352}{2224}=0.832[/tex](g). If a female passenger is selected, what is the probability that she survived.
[tex]P(\text{survived}|\text{female)}=\frac{316}{425}=0.744[/tex](h). If a child is slelected at random, what is the probability the child died.
[tex]P(died|\text{ child)=}\frac{52}{109}=0.477[/tex](i). What is the probability the passenger is survived given that the passenger is male.
[tex]=\frac{338}{1690}=0.2[/tex]ANSWER:
• (a). 0.320
,• (b). 0.191
,• (c). 0.240
,• (d). 0.142
,• (e). 0.009
,• (f). 0.832
,• (g) 0.744
,• (h). 0.477
,• (i) 0.2
Give the sample space describing all the outcomes. Then give all of the out comes for the event that the number 3 chosen. Use the format H1 to mean that the coin toss is heads and the number chosen is 1. If there is more than one element in the set separate them with commas
The sample space is composed of all the possible outcomes i.e. of all the possible combinations between the result of tossing the coin and picking the card. There are two possible outcomes for the coin and four for the cards so there will be 8 different combinations in the saple space. These are:
[tex]H1,H2,H3,H4,T1,T2,T3,T4[/tex]Then we must show all the outcomes where the card with the 3 is picked. This set is composed of all the elements with a 3 in the list above. There are two:
[tex]H3,T3[/tex]AnswersThen the answers are:
Sample space: {H1,H2,H3,H4,T1,T2,T3,T4}
Event that the number chosen is 3: {H3,T3}
Knowledge CheckUse the distributive property to remove the parentheses.--7(-5w+x-3)X 5
The distributive property states that:
[tex]k\cdot\left(a+b+c\right?=k\cdot a+k\cdot b+k\cdot c.[/tex]In this problem, we have the expression:
[tex]-7\cdot(-5w+x-3)=(-7)\cdot(-5w+x-3).[/tex]Comparing this expression with the general expression of the distributive property, we identify:
• k = (-7),
,• a = -5w,
,• b = x,
,• c = -3.
Using the general expression for the distributive property with these values, we have:
[tex]\left(-7\right)\cdot(-5w)+\left(-7\right)\cdot x+\left(-7\right)\cdot(-3).[/tex]Simplifying the last expression, we get:
[tex]35w-7x+21.[/tex]AnswerApplying the distributive property to eliminate the parenthesis we get:
[tex]35w-7x+21[/tex]anumeha mows lawns she charges an initial fee and constant fee for each hour of work
Given the function:
[tex]F(t)=6+12t[/tex]Where F represents Anumeha's fees (in dollars) for working t hours. The initial fee can be calculated for t = 0:
[tex]F(0)=6+12\cdot0=6[/tex]So the constant fee is $6. Now, we need to calculate how much does she charges each hour. We can calculate the values at t = 1, t = 2, and t = 3:
[tex]\begin{gathered} F(1)=6+12\cdot1=18 \\ F(2)=6+12\cdot2=30 \\ F(3)=6+12\cdot3=42 \end{gathered}[/tex]As we can see, there is a constant increment of $12 for each hour. Then, Anumeha charges $12 for each hour of work.
there are 5 adult cats, 6 middle aged cats, and ___ kittens, if there are 19 animals in total, how many kittens are there, solve for the blank.
ANSWER
There are 8 kittens
EXPLANATION
If the sum of the number of adult cats, middle aged cats and kittens is 19:
[tex]\begin{gathered} \text{adult}+\text{middle aged+kittens=19} \\ 5+6+\text{kittens}=19 \\ \text{kittens}=19-5-6 \\ \text{kittens}=8 \end{gathered}[/tex]Calculate the determinant of this 2x2 matrix. Provide the numerical answer. |2 -1 | |4 -5|
Given the matrix
[tex]\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {}{}\end{bmatrix}[/tex]its determinant is computed as follows:
ad - cb
In this case, the matrix is
[tex]\begin{bmatrix}{2} & {-1} & \\ {4} & -5 & {}\end{bmatrix}[/tex]and its determinant is
2(-5) - 4(-1) = -10 - (-4) = -10 + 4 = -6
The following table shows a company's annual income over a 6-year period. The equation y=60000(1.2)x describes the curve of best fit for the company's annual income (y). Let x represent the number of years since 2001.
Given that the annual income of a company over a 6-year period is described by the equation:
[tex]\begin{gathered} y=60000(1.2)^x \\ \text{where} \\ x\text{ is the number of years since 2001} \end{gathered}[/tex]The annual income at the end of each year since 2001 is as shown in the table below:
Required: To evaluate the company's approximate annual income in 2009.
Solution:
Given the annual income described as
[tex]y=60000(1.2)^x[/tex]The number of years between 2001 and 2009 is evaluated as
[tex]x\text{ = 2009 -2001 = 8 years}[/tex]thus, it's been 8 years since 2001.
The annual income in 2009 is thus evaluated by substituting 8 for the value of x in the annual income function.
This gives
[tex]\begin{gathered} y=60000(1.2)^x \\ x\text{ = 8} \\ \text{thus,} \\ y\text{ = 60000}\times(1.2)^8 \\ =\text{ 60000}\times4.29981696 \\ y=\text{ }257989.0176 \\ \Rightarrow y\approx258000 \end{gathered}[/tex]Hence, the company's approximate annual income in the year 2009 will be $ 258000.
The third option is the correct answer.
[tex]f(x) = (x - 2) ^{2}(x + 3)(x + 1)^{2} [/tex]the multiplicity of the root x=2 is...?
The solution of the factor with power 2 in the function f(x) can be found as:
(x-2)=0
x=2.
So, the root is x=2.
The multiplicity is the power of the factor (x-2) with its root given as x=2.
So, the multiplicity of the root x=2 is 2.
-6 subtracted from a number equals -12.What is the number?
Answer:
The number is -18
Explanation:
-6 subtracted from a number equals -12.
We want to find the value of the number
Let the number be x
We can write the statement mathematically as:
[tex]x-(-6)=-12[/tex]Solving this equation, the value of x is the number we are required to find.
[tex]\begin{gathered} x+6=-12 \\ \text{Subtract 6 from both sides} \\ x+6-6=-12-6 \\ x=-18 \end{gathered}[/tex]The said number is -18
The change in the value of a stock is represented by the rational number -5.90 describe in words what this means
The change in the value of a stock which is represented by the rational number -5.90 means that the stock decreased by 5.90 units.
Whenever we use negative value to describe change, it means that the value of that particular entity that been decreased by that number.
On the contrary, If we are using positive value to describe change, it means that the value of that particular entity that been increased by that number.
For example:- The change in total money possessed by Daniel is $ 50 means there is an increase of $ 50 in the money with Daniel.
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Which expression has a negative value
Answer:
bottom one
Step-by-step explanation:
Evaluate: sin-¹(1)
A) 0
B) pi/3
C)pi/2
Answer:
The correct answer is C. Pi/2
Step-by-step explanation:
I got it wrong on edgen, and it told me the correct answer was C.
Suppose that $16,065 is invested at an interest rate of 6.6% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years?5 years? 10 years? c) What is the doubling time?
Okay, here we have this:
Considering the provided information we obtain the following:
a)
Replacing in the Compound Interest formula we obtain the following:
[tex]\begin{gathered} A(t)=Pe^{rt} \\ A(t)=16065e^{0.066t} \end{gathered}[/tex]b)
After 1 year (t=1):
[tex]\begin{gathered} A(1)=16065e^{0.066(1)} \\ A(1)\approx17,161.06 \end{gathered}[/tex]We obtain that after one year the balance is aproximately $17,161.06.
After 2 years (t=2):
[tex]\begin{gathered} A(2)=16065e^{0.066(2)} \\ A(2)=18331.90 \end{gathered}[/tex]We obtain that after two years the balance is aproximately $18,331.90
After 5 years (t=5):
[tex]\begin{gathered} A(5)=16065e^{0.066(5)} \\ A(5)=$22,345.90$ \end{gathered}[/tex]We obtain that after five years the balance is aproximately $22,345.90.
After 10 years (t=10):
[tex]\begin{gathered} A(10)=16065e^{0.066(10)} \\ A(10)=$31,082.44$ \end{gathered}[/tex]We obtain that after ten years the balance is aproximately $31,082.44.
c)
In this case the doubling time will be when she has double what she initially had, that is: $16,065*2=$32130, replacing in the formula:
[tex]32130=16065e^{0.066t}[/tex]Let's solve for t:
[tex]\begin{gathered} 32130=16065e^{0.066t} \\ 16065e^{\mleft\{0.066t\mright\}}=32130 \\ \frac{16065e^{0.066t}}{16065}=\frac{32130}{16065} \\ e^{\mleft\{0.066t\mright\}}=2 \\ 0.066t=\ln \mleft(2\mright) \\ t=\frac{\ln\left(2\right)}{0.066} \\ t\approx10.502years \end{gathered}[/tex]Finally we obtain that the doubling time is approximately 10.502 years or about 10 years 6 months.
The data shows the total number of employee medical leave days taken for on-the-job accidents in the first six months of the year: 12, 6, 15, 9, 28, 12. Use the data for the exercise. Find the standard deviation.
ANSWER:
The standard deviation is 7
STEP-BY-STEP EXPLANATION:
The standard deviation formula is as follows
[tex]\sigma=\sqrt[]{\frac{\sum^N_i(x_i-\mu)^2_{}}{N}}[/tex]The first thing is to calculate the average of the sample like this:
[tex]\begin{gathered} \mu=\frac{12+6+15+9+28+12}{6} \\ \mu=\frac{82}{6}=13.67 \end{gathered}[/tex]Replacing and calculate the standard deviation:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(12_{}-13.67)^2_{}+(6_{}-13.67)^2_{}+(15_{}-13.67)^2_{}+(9_{}-13.67)^2_{}+(28-13.67)^2_{}+(12_{}-13.67)^2_{}}{6}} \\ \sigma=\sqrt[]{\frac{293.33}{6}} \\ \sigma=6.99\cong7 \end{gathered}[/tex]The numerator of a certain fraction is five times the denominator. If nine is added to both the numerator and the denominator, the resulting fraction is equivalent to two. What was the original fraction (not written in lowest terms)?
Explanation
To solve the question,
Let
The numerator = x
The denominator = y
So that the original equation will be
[tex]\frac{x}{y}[/tex]Next, we are told that the numerator is five times the denominator.
So that
[tex]x=5y[/tex]Again, we are told that If nine is added to both the numerator and the denominator, the resulting fraction is equivalent to two. so
[tex]\frac{x+9}{y+9}=2[/tex]Hence
we can substitute x =5y into the above
[tex]\begin{gathered} \frac{5y+9}{y+9}=2 \\ \\ cross\text{ multiplying} \end{gathered}[/tex][tex]\begin{gathered} 5y+9=2(y+9) \\ 5y+9=2y+18 \\ Taking\text{ like terms} \\ 5y-2y=18-9 \\ 3y=9 \\ \\ y=\frac{9}{3} \\ \\ y=3 \end{gathered}[/tex]Thus, the denominator is 3
The numerator will be
[tex]\begin{gathered} x=5y \\ x=5\times3 \\ x=15 \end{gathered}[/tex]The numerator is 15
Therefore, the fraction is
[tex]undefined[/tex]I need help with this question Write and expression that models the situation:Sarah has spent x dollars out of the 30 dollars she started with.
Okay, here we have this:
Considering that it says "spent", it represents an outflow of money, therefore we take it as negative, so we obtain:
Actual Situation: Initial money - money spent
Actual Situation: 30 - x
Find all solutions to the equationin the interval [O, 27). Enter thesolutions in increasing order.cos 2x = cos X[?]Tx = 0,2Remember: cos 20 = cos20 – sin20
SOLUTION
From
[tex]\begin{gathered} \cos 2x=\cos x \\ \cos ^2x-\sin ^2x=\cos x \\ \cos ^2x-(1-\cos ^2x)=\cos x \\ 2\cos ^2x-1=\cos x \\ 2\cos ^2x-\cos x-1=0 \\ \text{From the quadratic formula} \\ \cos x=\frac{1\pm\sqrt[]{1-(-8)}}{4} \\ \\ \cos x=\frac{1\pm3}{4} \\ \cos x=\text{ 1 or -}\frac{1}{2} \\ \text{Taking the cos}^{-1}of\text{ 1 and -}\frac{1}{2} \\ We\text{ have }\theta\text{ = 0, }\frac{2\pi}{3},\frac{4\pi}{3},\frac{8\pi}{3}\ldots\ldots\ldots2\pi \end{gathered}[/tex]So your answer is
[tex]0,\text{ }\frac{2\pi}{3},\text{ }\frac{4\pi}{3}[/tex]What is the answer to this equation?
Answer:
D 7.5
Step-by-step explanation:
n + n-3 + 2n-4 = perimeter ≥ 37
4n-7≥37
4n≥30
n≥7.5
I need these answers quickly. If I don't get them by midnight ill cry.
1) find the value of AC
2) find the measure of
1) The value of AC = 116
2) The measure of ∠BEF = 53°
What is Bisector?
When anything is divided into two equal or congruent portions, usually by a line, it is said to have been bisected in geometry. The line is then referred to as the bisector. Segment bisectors and angle bisectors are the sorts of bisectors that are most frequently taken into consideration.
Given,
BD is a perpendicular bisector
A is an angle bisector
BD is a perpendicular bisector then AD = DC
2n + 18 = 4n - 22
4n - 2n = 18 + 22
2n = 40
n = 40/2
n = 20
AD = 2(20) + 18
= 40 + 18
AD = 58
Now,
1) Length of AC
AC = 2AD
Here, AD = 58
AC = 2(58)
AC = 116
Hence, The value of AC is 116
2) A is an angle bisector
∠BAE = ∠DAE = 37°
∠DAE = 37°
Δ ADE is a right angle triangle
∠DEA = 90 - ∠DAE
= 90 - 37
= 53°
Since, ∠DEA = ∠BEF
∠BEF = 53°
Hence, The measure of ∠BEF = 53°
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Darell made a scale drawing of a shopping center. The parking lot is 4 centimeters wide in the drawing. The actual parking lot is 40 meters wide. What scale did Darell use?
Answer:
1 cm to 10 m
Step-by-step explanation:
4 cm to 40 m = 1 cm to 10 m
I need help with a math assignment. i linked it below
Since Edson take t minutes in each exercise set
Since he does 6 push-ups sets
Then he will take time = 6 x t = 6t minutes
Since he does 3 pull-ups sets
Then he will take time = 3 x t = 3t minutes
Since he does 4 sit-ups sets
Then he will take time = 4 x t = 4t minutes
To find the total time add the 3 times above
Total time = 6t + 3t + 4t
Total time = 13t minutes
The time it takes Edison to exercise is 13t minutes
third time asking, please help.
In a triangle one angle is three times the smallest angle and the third angle is 45 more than twice the
smallest angle. Find the measure of all three angles. Hint: The angles of a triangle add up to 180°
Answer:
The 3 angles are 22.5, 67.5 and 90 degrees.
Step-by-step explanation:
Let the smallest angle be x degrees.
Then the other angles = 3x and 2x + 45.
x + 3x + 2x + 45 = 180
6x = 180 - 45
6x = 135
x = 135/6 = 22.5 degrees
3x = 67.5 degrees
2x+45 = 90 degrees.
number one name three collinear points number to name four coplanar Point number three name two sets of lines intersect number for name two points not contained in the plane
The points lying on a single line are called colinear points. So here,
KJD are colinear points as they are lying on a same line.
Points lying on the same plane are called coplanar points. So here, IJFE are coplanar points.
The two sets of line intesects are KD and CF, IG and FH.
The two points that are not in the plane are A and B.
Which inequality is represented by the graph?
Answer:
A. x > -1
Step-by-step explanation:
x > -1
-------------->
<----0------------->
-1
x < -1
<-------
<------0------------>
-1
x ≥ -1
---------->
<---------|---------->
-1
x ≤ -1
<----------
<---------|---------->
-1
< and > represent an open circle
≤ and ≥ represent a closed circle
I hope this helps!
The height of a diver above the water’s surface can be modeled by the function h(t)= –16t^2+ 8t + 48. How long does it take the diver to hit the water? Solve by factoring
Given the function:
[tex]h(t)=-16t^2+8t+48[/tex]Where h(t) is the height of the diver above the surface of the water and t is the time.
Let's find how long it takes the diver to hit the water.
When the diver hits the water, the height h(t) = 0.
Now substitute 0 for h(t) and solve for the time t.
We have:
[tex]0=-16t^2+8t+48[/tex]Rearrange the equation:
[tex]-16t^2+8t+48=0[/tex]Solve for t.
Let's factor the expression by the left.
Factor 8 out of all terms:
[tex]8(-2t^2+t+6)=0[/tex]Now, factor by grouping.
Rewrite the middle term as a sum of two terms whose product is the product of the first term and the last term:
[tex]\begin{gathered} 8(-2t^2+4t-3t+6)=0 \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} 8((-2t^2+4t)(-3t+6))=0 \\ \\ 8(2t(-t+2)+3(-t+2))=0 \\ \\ 8(2t+3)(-t+2)=0 \end{gathered}[/tex]Hence, we have the factors:
[tex]\begin{gathered} 2t+3=0 \\ -t+2=0 \end{gathered}[/tex]Solve each factor for t:
[tex]\begin{gathered} 2t+3=0 \\ \text{ Subtract 3 from both sides:} \\ 2t=-3 \\ \text{ Divide both sides by 2:} \\ \frac{2t}{2}=-\frac{3}{2} \\ t=-\frac{3}{2} \\ \\ \\ -t+2=0 \\ t=2 \end{gathered}[/tex]Hence, we have the solutions:
t = -3/2
t = 2
The time cannot be negative, so let's take the positive value.
Therefore, the will take 2 seconds for the diver to hit the water.
ANSWER:
2 seconds.
Rewrite the polynomial expression using the GCF: 4x^2+8x+24 ?What is the new polynomial expression
GCF of 4,8 and 24
is. = 4
Then new expression is
y = 4• (x^2 + 2x + 6)
Need to graph and then mark length of stay (in days) on the bottom of the graph. Need 4 points on graph and 4 number on bottom of graph
given the data
13,9,5,11,6,3,12,10,11,7,3,2,2,2,10,10,12,12,12,8,8
sort data
s= 2, 2, 2, 3, 3, 5, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13
then we have
2 ---- 3
3 ----- 2
5----- 1
6 ---- 1
7 -----1
8------2
9 ------1
10-----3
11-------2
12------4
13-------1
