We are to find f(x) - g(x):
We will subtract the expressions of g(x) from f(x)
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ + 1 - (2x - 5)} \\ \end{gathered}[/tex]Expanding the parenthesis using distributive property:
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ + 1 - (2x) -(-5)} \\ mu\text{ltiplication of same signs gives positive sign} \\ m\text{ ultiplication of opposite signs give negative sign} \\ \\ f(x)-g(x)=x^2\text{ + 1 -2x + 5} \end{gathered}[/tex]collect like terms:
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ -2x + 5 }+\text{ 1} \\ f(x)-g(x)=x^2\text{ - 2x + 6} \end{gathered}[/tex]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]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
the top of the hill rises 67 feet above checkpoint 4, which is -211. What is the altitude of the top of the hill?
Answer:
-144 feet
Step-by-step explanation:
-211 plus the added 67 feet it is above equals an altitude of -144ft
he multiplication table below can be used to find equivalent ratios.
A multiplication table.
Which ratio is equivalent to the ratio 18:24?
15:20
20:15
30:36
36:30
Answer:
15:20
Step-by-step explanation:
18:24 can be written [tex]\frac{18}{24}[/tex] if I simplify this by dividing the top and bottom by 6, I get [tex]\frac{3}{4}[/tex]
I am looking for what other ration will reduce to [tex]\frac{3}{4}[/tex]
[tex]\frac{15}{20}[/tex] Divide the top and bottom by 5 and you will get [tex]\frac{3}{4}[/tex]
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.
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!
Which expression has a negative value
Answer:
bottom one
Step-by-step explanation:
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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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
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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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
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 average score for games played in the NFL is 22 and the standard deviation is 9.3 points. 41 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.
a. What is the distribution of ¯x x¯
? ¯xx¯ ~ N( , )
b. What is the distribution of ∑x ? ∑x ~ N ( , )
c. P( ¯x > 19.8214) =
d. Find the 60th percentile for the mean score for this sample size.
e. P(20.6214 < x¯< 23.2262) =
f. Q1 for the x¯distribution =
g. P( ∑x > 829.0774) =
For part c) and e), Is the assumption of normal necessary? NoYes
Using the normal distribution and the central limit theorem, it is found that:
a) The distribution is: x¯ ~ N(22, 1.45).
b) The distribution is: ∑x ~ N(902, 59.55).
c) P( ¯x > 19.8214) = 0.9332 = 93.32%.
d) The 60th percentile for the mean score for this sample size is of 22.37 points a game.
e) P(20.6214 < x¯< 23.2262) = 0.6312 = 63.12%.
f) Q1 for the x¯distribution = 21 points a game.
g) P( ∑x > 829.0774) = 0.8888 = 88.88%.
Assumption of normality is not necessary, as the sample sizes are greater than 30.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Also by the Central Limit Theorem, for the sum of n instances of a variable, the mean is of [tex]\n\mu[/tex] and the standard deviation is of [tex]\sigma\sqrt{n}[/tex].Finally, by the Central Limit Theorem, assumption of normality is only necessary when the sample size is less than 30.For a single game, the mean and the standard deviation of the number of points scored are given as follows:
[tex]\mu = 22, \sigma = 9.3[/tex]
For the average of 41 games, the standard error is:
[tex]s = \frac{9.3}{\sqrt{41}} = 1.45[/tex]
Hence the distribution is: x¯ ~ N(22, 1.45).
For the sum of the 41 games, the mean and the standard error are given as follows:
41 x 22 = 902.[tex]s = 9.3\sqrt{41} = 59.55[/tex].Hence the distribution is: ∑x ~ N(902, 59.55).
In item c, the probability is one subtracted by the p-value of Z when X = 19.8214, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (19.8214 - 22)/1.45
Z = -1.5
Z = -1.5 has a p-value of 0.0668.
1 - 0.0668 = 0.9332 = 93.32%.
The 60th percentile for the distribution is X when Z = 0.253, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
0.253 = (X - 22)/1.45
X - 22 = 0.253 x 1.45
X = 22.37.
For item e, the probability is the p-value of Z when X = 23.2262 subtracted by the p-value of Z when X = 20.6214, hence:
X = 23.2262:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (23.2262 - 22)/1.45
Z = 0.85
Z = 0.85 has a p-value of 0.8023.
X = 20.6214:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (20.6214 - 22)/1.45
Z = -0.95
Z = -0.95 has a p-value of 0.1711.
0.8023 - 0.1711 = 0.6312 = 63.12%.
The first quartile for the distribution is X when Z = -0.675, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
-0.675 = (X - 22)/1.45
X - 22 = -0.675 x 1.45
X = 21.
For item g, the probability is one subtracted by the p-value of Z when X = 829.0774, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (829.0774 - 902)/59.55
Z = -1.22
Z = -1.22 has a p-value of 0.1112.
1 - 0.1112 = 0.8888 = 88.88%.
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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 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.
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
[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.
Can someone please help me with this drag and drop? I would appreciate It a lot! Please explain :) I’ll give brainliest
Answer:
move B to true then everything is right ✅
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}
Find the common ratio of the geometric sequence 19, -76,304, ...
factor the trinomial6x² + 17x + 12
Answer: The factor of the above function is (2x + 3) (3x + 4)
We are given the below function
[tex]6x^2\text{ + 17x + 12}[/tex]This function can be factor using factorization method
The co-efficient of x^2 = 6
Multiply 6 by 12 to get the constant of the function
12 x 6 = 72
Next, find the factors of 72
Factors of 72 : 1 and 72, 2 and 36, 6 and 12, 9 and 8, 3 and 24
The only factor that will give us 17 when add and give us 72 when multiply is 8 and 9
The new equation becomes
[tex]\begin{gathered} 6x^2\text{ + 17x + 12} \\ 6x^2\text{ + 8x + 9x + 12} \\ \text{Factor out 2}x \\ 2x(3x\text{ + 4) + 3(3x + 4)} \\ (2x\text{ + 3) (3x + 4)} \end{gathered}[/tex]The factor of the above function is (2x + 3) (3x + 4)
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.
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]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.
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]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]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.
the Center is (2,0) the circle passes through the point (4.5,0) What is the Radius?
The radius of the circumference would be
x2 = 4.5
x1 = 2
r = x2 - x1
r = 4.5 - 2.0
r = 2.5
The radius would be 2.5