Answer:
y = g(x) = 1 + x
Now, the range of a function is the set of the possible values of y.
In this function, a linear function, y can be any real number, so the range of this function is { y ∈ ℝ )
y = h(x) = x^2 + 2*x
This is a quadratic function, as the leading coefficient is positive, we know that the arms of the function go up.
For a quadratic function y = a*x^2 + b*x + c
The minimum is at:
x = -b/2a.
In this case, b = 2 and 1 = 1
the minimum is at:
x = -2/2 = -1
The minimum is:
y = h(-1) = 1^2 +2*(-1) = -1
Then the range of this function is
{y ∈ ℝ ≥ -1 )
The composite functions are:
g∘h = g(h(x)) = 1 + x^2 + 2*x
The minimum is still at x = -1
g∘h(-1) = 1 + -1^2 + 2*-1 = 0
Then the range of this function is:
{y ∈ ℝ ≥ 0 )
The other composition is:
h∘g = h(g(x)) = (1 + x)^2 + 2*(1 + x) = 1 + 2*x + x^2 + 2 + 2*x
h∘g = x^2 + 4*x + 3
Here the minimum is at:
x = -4/2*1 = -2
h∘g(-2) = (-2)^2 + 4*-2 + 3 = 4 - 8 + 3 = -1
The range is:
{y ∈ ℝ ≥ -1 )
Please answer it now in two minutes
Answer:
3/4
Step-by-step explanation:
Rise over run.
Go up 3 units and 4 units to the right to find the next point
Answer:
Using points ( 8 , 9 ) and ( 4 , 6)
Slope = 6-9/4-8
= -3/-4
= 3/4
Hope this helps
Draw the reflected image of ABCD over line l.
Answer: The second image, the second image where b' is right above b is the correct answer for this, hope this helped!
<!> Brainliest is appreciated! <!>
Step-by-step explanation:
Answer
i woukldnt know
Step-by-step explanation:
ahahahahahahahahahahahahhahahahahaha
What is the sum of the measures of the interior angles of this heptagon? A 7-sided figure. 720 degrees 900 degrees 1,080 degrees 1,260 degrees
Answer:
900°
Step-by-step explanation:
interior angles of a polygon = (n−2)×180°, where n is number of sides
for heptagon it is: (7-2)×180°= 900°
AWARDING BRAINLIEST!
What is the first step to solve for x? -4= x+3/2
A: Subtract 2 to both sides
B: multiply 3 to both sides
C: subtract 3 to both sides
D: multiply 2 both sides
Question 2:
If x-5/7=1 then which answer shows the correct steps to solve x?
(Answers listed in photo)
A
B
C
D
Answer:
1. Is (A) Subtract 2 to both sides
2. Is (C)
Step-by-step explanation:
The University of Arkansas recently reported that 43% of college students aged 18-24 would spend their spring break relaxing at home. A sample of 165 college students is selected.
a. Calculate the appropriate standard error calculation for the data.
b. What is probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home?
Answer:
a. 0.0385
b. 3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.43, n = 165[/tex]
a. Calculate the appropriate standard error calculation for the data.
[tex]s = \sqrt{\frac{0.43*0.57}{165}} = 0.0385[/tex]
b. What is probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home?
This is 1 subtracted by the pvalue of Z when X = 0.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.43}{0.0385}[/tex]
[tex]Z = 1.82[/tex]
[tex]Z = 1.82[/tex] has a pvalue of 0.9656
1 - 0.9656 = 0.0344
3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home
Please need help also brinly staff this is homework not a quizz ok
Answer:
Graph A
Step-by-step explanation:
Lori is riding in a circular track in which Teri is standing at the center. With the passage of time, there would be no effect on the distance between Lori and Teri. The distance will remain the same because Teri is not moving. She is standing still. So consider her the center of a circle whose circumference is Lori riding bicycle while the radius at any point will be equal.
two positive intergers have a product of 50 one interger is twice the other . what are the intergers
Answer:
10 and 5.
Step-by-step explanation:
Let the integers be x and y.
xy = 50
x = 2y
Put x as 2y in the first equation.
(2y)y = 50
2y² = 50
y² = 50/2
y² = 25
y = √25
y = 5
Put y as 5 in the second equation.
x = 2(5)
x = 10
Find the mode of 1, 4, 24, 14, 98, 37
Answer:
There is no mode
Step-by-step explanation:
Mode is the most occurring no. and there's no number which is the most occurring.
Answer:
No mode
Step-by-step explanation:
In a set of numbers, mode is the most repeated number.
1, 4, 24, 14, 98, 37
There are no repeated numbers in this set.
The Ship It Anywhere Company bought a truck for $245,000. According to the company’s accounting department, the truck will depreciate $32,500 per year. 1. Find a linear function V(t) of the form V(t) = mt + b that models the value of the truck. V is the value of the truck and t is the number of years after the truck was bought. a. What is the slope of the function? Interpret what the slope means. b. What is the V intercept? Interpret what the V intercept means. c. Give the formula for the function. 2. Usethefunctiontofindthetintercept.Interpretwhatthetinterceptmeans. 3. Graphthefunction. 4. What is the domain and range of V(t)? 5. Find V(8) and explain what it means. Does your answer make sense? 6. When will the truck have a value of $128,000? 7. When will the truck have a value between $62,000 and $140,000?
Answer:
1. [tex]V(t) = -32500t + 245000[/tex]
a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.
b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).
c. The formula is: [tex]V(t) = -32500t + 245000[/tex]
2. t-intercept: [tex]t = 7.5385[/tex]
The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.
3. Graph in the image attached.
4. The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].
5. [tex]V(8) = -15000[/tex]
It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.
6. After 3.6 years.
7. Between 3.23 years and 5.63 years.
Step-by-step explanation:
1.
The inicial value is 245,000, and each year the value decreases 32,500, so we can write the equation:
[tex]V(t) = -32500t + 245000[/tex]
a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.
b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).
c. The formula is: [tex]V(t) = -32500t + 245000[/tex]
2.
To find the t-intercept we just need to use V(t) = 0 and then find the value of t:
[tex]0 = -32500t + 245000[/tex]
[tex]32500t = 245000[/tex]
[tex]t = 7.5385[/tex]
The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.
3.
The graph of the function is in the image attached.
4.
The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].
5.
[tex]V(8) = -32500*8 + 245000 = -15000[/tex]
It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.
6.
[tex]128000 = -32500t + 245000[/tex]
[tex]32500t = 117000[/tex]
[tex]t = 3.6[/tex]
After 3.6 years.
7.
[tex]62000 = -32500t + 245000[/tex]
[tex]32500t = 183000[/tex]
[tex]t = 5.6308[/tex]
[tex]140000 = -32500t + 245000[/tex]
[tex]32500t = 105000[/tex]
[tex]t = 3.2308[/tex]
Between 3.23 years and 5.63 years.
Find the equation of a line that contains the points (5,0) and (-1,-6). Write the equation in slope-intercept form
Answer:
The equation in slope-intercept form is y = x-5
Step-by-step explanation:
Answer:
y = x-5
Step-by-step explanation:
Another one! (ikr how am I so rich in points?) Median of: 2, 81, 29, 18, x The average is 26.8. Solve for x!
Answer:
18
Step-by-step explanation:
The average is found by adding all the numbers and dividing by 5
(2+ 81+ 29+ 18+ x)/5 = 26.8
Multiply each side by 5
(2+ 81+ 29+ 18+ x) = 134
x+130 =134
Subtract 130 from each side
x = 4
Now we want the median
List the numbers in order from smallest to largest
2,4,18,29 ,81
The median is the middle
Answer:
x = 4, Median = 18
Step-by-step explanation:
Since the Average/Mean is 26.8
So,
Mean = [tex]\frac{Sum Of Observations}{Total No.OfObservations}[/tex]
26.8 = [tex]\frac{2+81+29+18+x}{5}[/tex]
=> 26.8*5 = 130 + x
=> 134 = 130 + x
Subtracting 130 to both sides
=> x = 134-130
=> x = 4
Now, The data becomes:
=> 2,81,29,18,4
In ascending order:
=> 2,4,18,29,81
Finding Median (The middlemost no.)
=> 18
Divide:
10mm2-30m
5mn
O 2mºn - 6
O2mn3 - 6mn?
O2mn – 30mn
O 5m4n - 25
Solve for x Write both solutions, seperated by a comma 4x^2+5x+1=0
Answer:
-1/4 , -1
Step-by-step explanation:
I solved it using Factorization method and Quadratic Equation .
Factorization Method
[tex]4x^2+5x+1=0\\Write +5x- as- a -difference(write+5x-using- two- numbers -in-which-their-sum-is ; 5-and-their-product-is ; 4)\\4x^{2} +4x+1x+1=0\\Factorize-out-common-terms\\4x(x+1)+1(x+1)=0\\Factor-out-(x+1)\\(4x+1)(x+1)=0\\4x+1 =0 \\x+1=0\\4x=0-1\\x =0-1\\4x =-1\\x =-1\\4x=-\frac{1}{4} \\\\Answer = -1/4 , -1[/tex]
Quadratic Equation
[tex]4x^2+5x+1=0\\a = 4\\b =5\\c = 1\\\\x =\frac{-b\±\sqrt{b^2 -4ac} }{2a} \\\\x = \frac{-(5)\±\sqrt{(5)^2-4(4)(1)} }{2(4)} \\\\x = \frac{-5\±\sqrt{25-16} }{8} \\\\x = \frac{-5\±\sqrt{9} }{8} \\\\x = \frac{-5\±3}{8} \\\\x =\frac{-5+3}{8} \\\\x = \frac{-5-3}{8} \\\\x = \frac{-2}{8} \\\\x = \frac{-8}{8} \\\\x = -\frac{1}{4} \\x=-1[/tex]
The high temperatures (in degrees Fahrenheit) of a random sample of 6 small towns are: 99 97.5 97.9 99.4 97 97.7 Assume high temperatures are normally distributed. Based on this data, find the 95% confidence interval of the mean high temperature of towns. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place).
Assume that you earned an 87 on Exam 1 in this course. The class had an average of 78 (s=8.69). How many people earned a score below your score? (in percentage)
Answer:
85%
Step-by-step explanation:
Given data
Exam score earned by student = 87
class average = 78
s = 8.69
Calculate the percentage of people that earned a score below your score
P ( z < 1.04 ) = 0.8508 = 85%
Note : Z ( z score ) = (exam score - class average) / s
= (87 - 78) / 8.69 = 1.04
I need help plz someone help me solved this problem I need help ASAP! I will mark you as brainiest!
Step-by-step explanation:
y = [tex]{\log_b x}[/tex]
if x =4 then y = [tex]{\log_b 4}[/tex] =-1 --> [tex]b^{-1}[/tex] =4 --> b= 1/4
Answer:
b = 1/4
Step-by-step explanation:
It has to be a log because for x=0, b⁰ should be 1 for every b and that is not the case here.
Remember that [tex]y = \log_bx[/tex] means that [tex]b^y=x[/tex].
Since the point (4,-1) seems to be on the line, we can solve:
b⁻¹ = 4
so b = 1/4
finding the missing angles 35° and 145°
Answer:
145°Step-by-step explanation:
There are two ways to find the value of X
[tex]x + 35 = 180[/tex] ( sum of co-interior angles)
Move constant to R.H.S and change its sign
[tex]x = 180 - 35[/tex]
Calculate the difference
[tex]x = 145[/tex]°
You can use another way too.
[tex]x = 145[/tex]° ( being vertically opposite angles)
Vertically opposite angles are always equal.
Hope this helps...
Best regards!!
Answer:
x = 145°
Step-by-step explanation:
Vertically opposite, also interior angles always add up to 180° so if you want to double check this, do 145° + 35° you should get 180°
I hope this helped you :)
use substitution {y-4x=-7 5x+y=-6
Answer:
First, you put the answer in slope intercept form,y=-7+4x. You substiuite which is going to be y-4x+4x=-7+4x. You simplify to y=-7+4x. You plug that into the other equation and solve. It turns out to be y= -59/9, and x=1/9. Hope this helps!
Answer:
y - 4x = -7 ...... 1
5x+y=-6 ......... 2
Make y the subject in equation 1
Thus
y = - 7 + 4x
Substitute this into Equation 2
We get
5x - 7 + 4x = - 6
9x = -6 + 7
9x = 1
x = 1/9
Substitute x = 1/9 into equation 1
y = -7 + 4x
y = - 7 + 4(1/9)
y = -7 + 4/9
y = - 59/9
x = 1/9 , y = -59/9
Hope this helps
what is 1 1/5 subtracted by 3 1/10
whoever gets it right I will choose as the brainliest
Answer:
6/5÷31/10=12/31
Step-by-step explanation:
6/5÷31/10=?Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
6/5×10/31=?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
6×10 5×31=60/155
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 60 and 155 using
GCF(60,155) = 5
60÷51 55÷5=12/31
Therefore:
65÷3110=12/31
3) The fastest train on Earth, the TGV from France, can travel at faster speeds than trains in the
United States. During a speed test, the train traveled 8.0 x 10^2 miles in 2.5 hours. Compute the
speed of the train. (Try solving this problem using scientific notation.)
Answer:
[tex]3.2*10^2=320[/tex] mph
Step-by-step explanation:
hello,
it travels [tex]8.0*10^2[/tex] miles in 2.5 hours
So in 1 hours it travels
[tex]\dfrac{8.0*10^2}{2.5}=3.2*10^2[/tex]
miles
hope this helps
A tennis lesson lasts from 9:00 a.m. to 10:00 a.m., and should include an 8-min break with equal time before and after the break. At what time should the break start?
Answer:
8:26 AM
Step-by-step explanation:
9:00 a.m. to 10:00 a.m constitute one hour
1 hour = 60 minutes
as we have to distribute time within 1 hour only, it is better to take it in minutes as we have to divide it into three parts.
Given break duration = 8 minutes
let time before break and after break be x minutes.
Thus,
Time before break + interval duration+Time after break = 60 minutes
x + 8 + x = 60
=> 2x = 60-8 = 52
=> x = 52/2 = 26
Thus, first lesson should end at 26 minutes
so time will be 8 Am + 26 minutes = 8:26 AM
Thus, break will start at 8:26 AM.
Two angle are supplementary if their sum is 180. The large angle measure five degrees more than four times the measure of a smaller angle. If x represents the measure of the smaller angle and this two are supplementary, find the measure of each angle
Answer:
35 degrees
Step-by-step explanation:
4x + 5 (the measure of the large angle) + x (the measure of the supplementary angle) = 180. Therefore x = 35
Answer:
35,145
Step-by-step explanation:
angle 1+angle 2=180 degrees
x=angle 1
x+4x+5=180
4x+5 is angle 2 (larger angle) bc it is 5 more than 4 time the measure of the smaller angle
now we solve
x+4x+5=180
5x+5=180
5x=175
x=35
the smaller angle is 35 degrees
4x+5=bigger angle
4(35)+5=
140+5=
145=bigger angle
given circleR, how is it known that QS = YT
(idk the answer it was a guess)
Answer:
The diameters acts as diagonals
Step-by-step explanation:
QTSY is known to be a rectangle inscribed successfully inside a circle.
Now one of the properties of a rectangle is that it's diagonal divide it's shape into two equal parts and that it's has two equal diagonals.
In this case, the diagonals are QS and YT.
Another thing to observe it's that the diagonals of the rectangle pass through the center of the circle R and touching the circumference at both ends making the both diagonals a diameter as well.
So to prove that QS=YT
they are both diagonals that are diameters and they are equal because diameters of a circle are always equal while diagonals of a rectangle are also always equal.
Please answer this correctly
Answer:
1/6
Step-by-step explanation:
P(8) = number of 8's / total = 1/3
Then keeping the card so we have 7 and 9
P(7) = number of 7's / total = 1/2
P(8, keep, 7) = 1/3 * 1/2 = 1/6
En una inecuación, al multiplicar o dividir por un número negativo: *
Answer:
hyg
Step-by-step explanation:
Express this sum as a common fraction: $.\overline{8} + .\overline{2}$
Answer:
It just says overline
Step-by-step explanation:
Answer:
10/9
Step-by-step explanation:
Circles A, B, and C overlap. The overlap of circles B and C is labeled x. Which statements are true about x? Select three options. x ∈ B ⋃ C x ∈ B ∩ C x ∈ A ⋃ C x ∈ A ∩ C x ∈ A
Answer:
(A)x ∈ B ⋃ C
(B)x ∈ B ∩ C
(C)x ∈ A ⋃ C
Step-by-step explanation:
A diagram has been created and attached for more understanding.
If the overlap of circles B and C is labeled x.
Then: [tex]x \in (B \cap C)[/tex]
If x is contained in the intersection of B and C, it means that:
[tex]x \in B $ and x \in C.\\$Therefore:\\x \in B \cup C[/tex]
Finally:
[tex]x \in C $ and x \notin A\\$x will be in the union of A and C\\Therefore, x \in A \cup C[/tex]
The correct options are A, B and C.
Answer: A, B, C
just took it on edge
find the probability of being delt 5 clubs and 3 cards with one of each remaining suit in 8 card poker
Answer: 0.003757(approx).
Step-by-step explanation:
Total number of combinations of selecting r things out of n things is given by:-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Total cards in a deck = 52
Total number of ways of choosing 8 cards out of 52 = [tex]^{52}C_8[/tex]
Total number of ways to choose 5 clubs and 3 cards with one of each remaining suit = [tex]^{13}C_5\times^{13}C_1\times^{13}C_1\times^{13}C_1[/tex] [since 1 suit has 13 cards]
The required probability = [tex]=\dfrac{^{13}C_5\times^{13}C_1\times^{13}C_1\times^{13}C_1}{^{52}C_8}[/tex]
[tex]=\dfrac{\dfrac{13!}{5!8!}\times13\times13\times13}{\dfrac{52!}{8!44!}}\\\\=\dfrac{24167}{6431950}\\\\\approx0.003757[/tex]
Hence, the required probability is 0.003757 (approx).
What is the value of the expression below?
(7^1/2)^2
Answer:
7
Step-by-step explanation:
We can multiply the exponents so (7¹⁺²)² = 7⁽¹⁺² * ²⁾ = 7¹ = 7.
Answer:
7
Step-by-step explanation:
[tex](7^{\frac{1}{2}})^2 = (\sqrt{7})^2 = \sqrt{7} \times \sqrt{7} = \sqrt{7 \times 7} = \sqrt{49} = 7[/tex]
Solve the system of equations for the variables: 5x+2y=13 x+2y=9
Answer:
x = 1
y = 4
Step-by-step explanation:
5x + 2y = 13
x + 2y = 9
Add both equations.
6x + 4y = 22
Solve for x.
6x = 22 - 4y
x = 22/6 - 4/6y
Put x as 22/6 - 4/6y in the second equation and solve for y.
22/6 - 4/6y + 2y = 9
-4/6y + 2y = 9 - 22/6
4/3y = 16/3
y = 16/3 × 3/4
y = 48/12
y = 4
Put y as 4 in the first equation and solve for x.
5x + 2(4) = 13
5x + 8 = 13
5x = 13 - 8
5x = 5
x = 5/5
x = 1
Answer:
x = 1, y = 4
Step-by-step explanation:
5x+2y = 13
x+2y = 9
Subtracting both equations
=> 5x+2y-x-2y = 13-9
=> 4x = 4
=> x = 1
Now, Putting x = 1 in the first equation
=> 5(1)+2y = 13
=> 2y = 13-5
=> 2y = 8
=> y = 4