Answer:
5
Step-by-step explanation:
The 5 terms in the expression are ...
6y
3
y
4y
5
__
If like terms were combined, the expression could be reduced to one with 2 terms:
11y +8
Answer:
5 terms
Step-by-step explanation:
In an expression, a term can be a number, a variable, or a number and variable multiplied together. Terms are separated by addition or subtraction.
In the expression:
6y+3+y+4y+5
There are 5 terms. The 5 terms are:
1. 6y
2. 3
3. y
4. 4y
5. 5
We can simplify this expression by combining like terms. We can add the constants (just numbers) and the terms with variables being multiplied by numbers.
6y+3+y+4y+5
(6y+y+4y)+(3+5)
11y+(3+5)
11y+8
Can you draw the reflection Across the y-axis of the attached image.
Answer:
see graph
Step-by-step explanation:
A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.
An HR manager would like to test the hypothesis that the proportion of agenda-less meetings is more than 45%. Based on the information below, choose the correct conclusion for this hypothesis test. To test this, he randomly selected minutes from 100 past meeting, and found that 65 of them had no agenda. The following is the setup for this hypothesis test: H0:p=0.45 Ha:p>0.45 The p-value for this hypothesis test is 0.025. At the 5% significance level, should he reject or fail to reject the null hypothesis? Select the correct answer below: Reject the null hypothesis because 0.45>0.05. Fail to reject the null hypothesis because 0.45>0.05. Reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05. Fail to reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05.
Answer: Reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05.
Step-by-step explanation: Trust me
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k. A) 2 B) 3 C) 4 D) 5 IF YOU ANSWER IN 5 MINUTES I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!
Ans k = 4
Step-by-step explanation:
Here g(x) =[tex]\frac{-1}{3}x + 1[/tex] and
f(x) = [tex]\frac{-1}{3} x -3[/tex]
Now, g(x) = f(x) + k
or, [tex]\frac{-1}{3}x + 1[/tex] = [tex]\frac{-1}{3} x -3 + k[/tex]
or, 1 + 3 = k
So, k = 4 Answer.
the perimeter of a square flower bed is 100 feet. what is the area of the flower bed in sqaure feet
Answer:
A =625 ft^2
Step-by-step explanation:
The perimeter of a square is
P = 4s where s is the side length
100 =4s
Divide each side by 4
100/4 = 4s/4
25 = s
A = s^2 for a square
A = 25^2
A =625
solve the rational equation 5/x = 4x+1/x^2
Answer:
x = 1
Step-by-step explanation:
Set up the rational expression with the same denominator over the entire equation.
Since the expression on each side of the equation has the same denominator, the numerators must be equal
5x =4x+1
Move all terms containing x to the left side of the equation.
Hope this can help you
What is the value of y iin this equation? 4(y-3) =48
Answer:
y = 15Step-by-step explanation:
Question:
4(y - 3) = 48
1. Distribute
4y - 12 = 48
2. Simplify Like terms
4y - 12 = 48
+ 12 + 12
4y = 60
3. Solve
4y = 60
/4 /4
y = 15
4. Check:
4(y - 3) = 48
4((15) - 3) = 48
4(12) = 48
48 = 48 Correct!
Hope this helped,
Kavitha
Answer:
[tex]y=15\\[/tex]
Step 1:
To find y, we first have to multiply [tex]4(y-3)[/tex]. When we do that (4 * y, 4 * - 3), we get [tex]4y-12[/tex].
Step 2:
Our equation looks like this now:
[tex]4y-12=48[/tex]
To solve this equation, we have to add 12 on both sides so we can cancel out the -12 on the left side of the equation.
[tex]4y-12(+12)=48(+12)[/tex]
[tex]4y=60[/tex]
Now, we can divide 4 on both sides to get y by itself.
[tex]4y/4\\60/4[/tex]
[tex]y=15[/tex]
In the diagram of RST, which term describes point U?
A.
Circumcenter
B.
Centroid
C.
Incenter
D.
Orthocenter
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is C, Incenter.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
In a triangle, the point at which all the angle bisectors of the triangle meet is known as the Incenter.
Since In ΔRST, all the angles are bisected by the angle bisector, and the point at which all the angle bisectors meet is represented by U. Thus, it can be concluded that the point U represents the incenter of the triangle.
Learn more about Triangle:
https://brainly.com/question/2773823
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Use an appropriate series to find Taylor series of the given function centered at the indicated value of a. Write your answer in summation notation.
sinx, a= 2π
Answer:
The Taylor series is [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x) = sin (x)[/tex]
This is centered at
[tex]a = 2 \pi[/tex]
Now the next step is to represent the function sin (x) in it Maclaurin series form which is
[tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]
=> [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Now since the function is centered at [tex]a = 2 \pi[/tex]
We have that
[tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]
This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]
[tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]
Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]
This because [tex]2 \pi[/tex] is a constant
Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is
[tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
please show on graph (with x and y coordinates) state where the function x^4-36x^2 is non-negative, increasing, concave up
Answer:
[tex] y'' =12x^2 -72=0[/tex]
And solving we got:
[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]
We can find the sings of the second derivate on the following intervals:
[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up
[tex]x=-\sqrt{6}, y =-180[/tex] inflection point
[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down
[tex]x=\sqrt{6}, y=-180[/tex] inflection point
[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up
Step-by-step explanation:
For this case we have the following function:
[tex] y= x^4 -36x^2[/tex]
We can find the first derivate and we got:
[tex] y' = 4x^3 -72x[/tex]
In order to find the concavity we can find the second derivate and we got:
[tex] y'' = 12x^2 -72[/tex]
We can set up this derivate equal to 0 and we got:
[tex] y'' =12x^2 -72=0[/tex]
And solving we got:
[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]
We can find the sings of the second derivate on the following intervals:
[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up
[tex]x=-\sqrt{6}, y =-180[/tex] inflection point
[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down
[tex]x=\sqrt{6}, y=-180[/tex] inflection point
[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up
PLLZZZZ help me find x you are AWSOME!! I need this ASAP
Answer:
27°
Step-by-step explanation:
D is 72° because it alternates with B, alternate angles are equal.
2x+72°+2x= 180° because it is a straight line.
4x+72°=180°
4x=108°
x=27°
The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time. When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year. By how much does the machine depreciate during the fifth year
Answer: The machine depreciates during the fifth year by $4000.
Step-by-step explanation:
Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.
When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.
Then, the machine depreciates A(x) during the fifth year as
[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]
Hence, the machine depreciates during the fifth year by $4000.
If y>0, which of these values of x is NOT in the domain of this equation? y=x2+7x
Answer:
[tex]\boxed{\sf \ \ \ [-7,0] \ \ \ }[/tex]
Step-by-step explanation:
Hello
[tex]y=x^2+7x=x(x+7) >0\\<=> x>0 \ and \ x+7 >0 \ \ or \ \ x<0 \ and \ x+7<0\\<=> x>0 \ \ or \ \ x<-7\\[/tex]
So values of x which is not in this domain is
[tex]-7\leq x\leq 0[/tex]
which is [-7,0]
hope this helps
Translate into a variable expression the product of p and the sum of p and 12
They're making me write something here so I can post the answer:
p(p + 12)
Which table represents the inverse of the function defined above?
Hello!
Answer:
Table B.
Step-by-step explanation:
An inverse of a function means that the x and y values are swapped in comparison to the original function. For example:
We can use points on the table:
[tex]f(x)[/tex] = (7, 21)
The inverse of this function would 7 as its y value, and 21 as its x value:
[tex]f^{-1} (x)[/tex] = (21, 7)
The only table shown that correctly shows this relationship is table B.
The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism? PLEASE COMMENT, I Can't SEE ANSWERS CAUSE OF A GLITCH
Answer:
x + 1 - ( 4 / x³ + 3x² + 8 )
Step-by-step explanation:
If the volume of this rectangular prism ⇒ ( x⁴ + 4x³ + 3x² + 8x + 4 ), and the base area ⇒ ( x³ + 3x² + 8 ), we can determine the height through division of each. The general volume formula is the base area [tex]*[/tex] the height, but some figures have exceptions as they are " portions " of others. In this case the formula is the base area [tex]*[/tex] height, and hence we can solve for the height by dividing the volume by the base area.
Height = ( x⁴ + 4x³ + 3x² + 8x + 4 ) / ( x³ + 3x² + 8 ) = [tex]\frac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}[/tex] = [tex]x+\frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex] = [tex]x+1+\frac{-4}{x^3+3x^2+8}[/tex] = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex] - and this is our solution.
Answer:
[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
Step-by-step explanation:
[tex]volume=base \: area \times height[/tex]
[tex]height=\frac{volume}{base \: area}[/tex]
[tex]\mathrm{Solve \: by \: long \: division.}[/tex]
[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]
[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]
[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
√9m^2n^2 + 2√m^2n^2 - 3mn
Answer:
I think it is
Step-by-step explanation:
Answer:
5n√2m^ - 3mn
Step-by-step explanation:
Create a circle such that its center is point a and b is a point on the circle
Step-by-step explanation:
The center of a circle is the point in the circle which is equidistant to all the edges of thr circle. The point a is the center, while point b is an arbitrary point in the circle. Find attachment for the diagram.
Answer:
i think that this question is wrong
Step-by-step explanation:
The first and last term of an AP are 1 and 121 respectively. If the sum of the series is 671,find a) the number of terms (n) in the AP b) the common
difference between them
Answer:
(a)11
(b)12
Step-by-step explanation:
The first term, a = 1
The last term, l=121
Sum of the series, [tex]S_n=671[/tex]
Given an arithmetic series where the first and last term is known, its sum is calculated using the formula:
[tex]S_n=\dfrac{n}{2}(a+l)[/tex]
Substituting the given values, we have:
[tex]671=\dfrac{n}{2}(1+121)\\671=\dfrac{n}{2} \times 122\\671=61n\\$Divide both sides by 61\\n=11[/tex]
(a)There are 11 terms in the arithmetic progression.
(b)We know that the 11th term is 121
The nth term of an arithmetic progression is derived using the formula:
[tex]a_n=a+(n-1)d[/tex]
[tex]a_{11}=121\\a=1\\n=11[/tex]
Therefore:
121=1+(11-1)d
121-1=10d
120=10d
d=12
The common difference between them is 12.
A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 95% confidence interval for the mean score, , of all students taking the test
Answer:
The 95% confidence interval for the mean score, , of all students taking the test is
[tex]28.37< L\ 30.63[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 59[/tex]
The mean score is [tex]\= x = 29.5[/tex]
The standard deviation [tex]\sigma = 5.2[/tex]
Generally the standard deviation of mean is mathematically represented as
[tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }[/tex]
[tex]\sigma _{\= x} = 0.677[/tex]
The degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
substituting values
[tex]df = 59 -1[/tex]
[tex]df = 58[/tex]
Given that the confidence interval is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 -95[/tex]
[tex]\alpha =[/tex]5%
[tex]\alpha = 0.05[/tex]
Now the critical value at this significance level and degree of freedom is
[tex]t_{df , \alpha } = t_{58, 0.05 } = 1.672[/tex]
Obtained from the critical value table
So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as
[tex]\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})[/tex]
substituting value
[tex](29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)[/tex]
[tex]28.37< L\ 30.63[/tex]
need some help thxx ;)
Answer:
DEA
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the trigonometric ratios with their values based on the triangle shown in the diagram.
Answer:
A-2, B-DNE*, C-3, D-DNE, E-4, F-1
---------------------
The first attachment shows the solutions to A and C.
The second attachment shows the solutions to E and F.
There are no real number solutions to systems B and D.
_____
In general, you can solve the linear equation for y, then substitute that into the quadratic. You can subtract the x-term on the left and complete the square to find the solutions.
A.
(3-x) +12 = x^2 +x
15 = x^2 + 2x
16 = x^2 +2x +1 = (x +1)^2 . . . . add the square of half the x-coefficient to complete the square; next take the square root
±4 -1 = x = {-5, 3) . . . . . identifies the second solution set for system A
__
B.
(x -1) -15 = x^2 +4x
-16 = x^2 +3x
-13.75 = x^2 +3x +2.25 = (x +1.5)^2
roots are complex: -1.5 ±i√13.75
__
C.
(1-2x) +5 = x^2 -3x
6 = x^2 -x
6.25 = x^2 -x + .25 = (x -.5)^2
±2.5 +.5 = x = {-2, 3} . . . . . identifies the third solution set for system C
__
remaining problems are done in a similar way.
_____
* DNE = does not exist. There is no matching solution set for the complex numbers that are the solutions to this.
---------------------
Hope this helps!
Brainliest would be great!
---------------------
With all care,
07x12!
A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is$31 . The total cost to rent 6 chairs and 5 tables is $59 . What is the cost to rent each chair and each table?
Answer:
The cost to rent each chair is $2.75 and the cost to rent each table is $8.50
Step-by-step explanation:
Let the:
Cost to rent a chair = x
Cost to rent a table = y
We would form an algebraic equation.
The total cost to rent 2 chairs and 3 tables is $31
2x + 3y = 31 ...... Equation 1
The total cost to rent 6 chairs and 5 tables is $59
6x + 5y = 59 ......... Equation 2
We solve the above equation above using elimination method
Multiply Equation 1 all through by the coefficient of x = 6 in Equation 2
Multiply Equation 2 all through by the coefficient of x = 2 in Equation 1
Hence, we have:
2x + 3y = 31 ...... Equation 1 × 6
6x + 5y = 59 ......... Equation 2 × 2
12x + 18y = 186........ Equation 3
12x + 10y = 118 .…...... Equation 4
Subtracting Equation 4 from Equation 3
= 8y = 68
y = 68/8
y = 8.5
Therefore, the cost to rent a table = $8.50
Substituting 8.5 for y in Equation 1 to get the value of x
2x + 3y = 31 ...... Equation 1
2x + 3(8.5) = 31
2x = 31 - 3(8.5)
2x = 31 - 25.5
2x = 5.5
x = 5.5/2
x = 2.75
The cost to rent a chair = $2.75
Therefore, the cost to rent each chair is $2.75 and the cost to rent each table is $8.50
Determine the measure of the unknown variables.
Answer:
75
Step-by-step explanation:
x = 75°
yes x = 75°(OPPOSITE ANGLES ARE EQUAL)
..
At noon a passenger train leaves the Dupont Railway station and travels due east for 2 hours. At 12:45 pm the same day a second passenger train leaves the same railway station and travels due west for 1 hour and 15 minutes at a speed 10 kilometers per hour slower than the first passenger train. At 2pm the two trains were 215 kilometers apart. How fast had each train been traveling
Answer:
The speed of the first train is 70 km/hr
The speed of the second train is 60 km/hr
Step-by-step explanation:
For the first train:
Travel time = 2 hours
The speed = ?
we designate the speed as V
For the second train:
The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)
speed = 10 km/hr slower than that of the first train, we can then say
the speed = V - 10
The total distance traveled by both trains in the opposite direction of one another is 215 km
we can put this problem into an equation involving the distance covered by the trains.
we know that distance = speed x time
the distance traveled by the first train will be
==> 2 hrs x V = 2V
the distance traveled by the second train will be
==> 1.25 hrs x (V - 10) = 1.25(V - 10)
Equating the above distances to the total distance between the trains, we'll have
2V + 1.25(V - 10) = 215
2V + 1.25V - 12.5 = 215
3.25V = 215 + 12.5
3.25V = 227.5
V = 227.5/3.25 = 70 km/hr this is the speed of the first train
Recall that the speed of the second train is 10 km/hr slower, therefore
speed of the second train = 70 - 10 = 60 km/hr
The speed of the trains are 70km/hr and 60km/hr respectively.
The distance of the first train will be represented by: = 2 × D = 2D
The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).
Based on the information given in the question, the equation to solve the question will be:
2D + 1.25(D - 10) = 215
Collect like terms
2D + 1.25D - 12.5 = 215
3.25D = 215 + 12.5
3.25D = 227.5
D = 227.5/3.25
D = 70km/hour
The speed of the second train will be:
= 70 - 10 = 60km per hour.
Read related link on:
https://brainly.com/question/24720712
Use the line of best fit to determine the x-value when the y- value is 190
Answer:
A. 9
Step-by-step explanation:
Well if you go to 190 on the y-axis and go all the way to the right you can see according to the line of best fit A. 9 should be the correct answer.
Thus,
A.9 is the correct answer.
Hope this helps :)
Answer:
A. 9
Step-by-step explanation:
A line of best fit is a line that goes through a scatter plot that will express the relationship between those points. So, if we look at 190 on the y-axis, we can approximate that on the line of best fit it would be closest to 9 on the x-axis.
Use Bayes' theorem to find the indicated probability 5.8% of a population is infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
a. 0.905
b. 0.585
c. 0.038
d. 0.475
Answer:
b. 0.585
Step-by-step explanation:
According to Bayes' theorem:
[tex]P(A|B)=\frac{P(B|A)*P(A)}{P(B)}[/tex]
Let A = Person is infected, and B = Person tested positive. Then:
P(B|A) = 93.9%
P(A) = 5.8%
P(B) = P(infected and positive) + P(not infected and positive)
[tex]P(B) = 0.058*0.939+(1-0.058)*0.041\\P(B)=0.09308[/tex]
Therefore, the probability that a person has the disease given that the test result is positive, P(A|B), is:
[tex]P(A|B)=\frac{0.939*0.058}{0.09308}\\P(A|B)=0.585[/tex]
The probability is 0.585.
WHY CAN'T ANYONE HELP ME? PLEASE What one is the standard form of the equation y = – 1/4 x – 2? A. x + 4y = 8 B. x + 4y = – 2 C. x + 4y = – 8 or D. –x + 4y = – 8
Answer:
C. x+4y=-8
Step-by-step explanation:
The standard form of an equation is Ax+Bx=C
y= -[tex]\frac{1}{4}[/tex]x-2
Multiply 4 by both sides
4y= -x-8
1+4y= -8
i
dont
get
this
help
rn
Answer:
6 first box. 12 second box. 21 third box. 10 fourth box. 4 fifth box.
Step-by-step explanation:
Look for common denominaters, that will show you what to multiply the equation by to get rid of fractions.
A distribution has a mean of 90 and a standard deviation of 15. Samples of size 25 are drawn randomly from the population. Find the probability that the sample mean is more than 85 g
Answer:
The probability is 0.04746
Step-by-step explanation:
Firstly, we calculate the z-score here
Mathematically;
z-score = x-mean/SD/√n
Where from the question;
x = 85, mean = 90 , SD = 15 and n = 25
Plugging these values into the equation, we have;
Z = (85-90)/15/√25 = -5/15/5 = -1.67
So the probability we want to calculate is ;
P(z > -1.67)
We use the standard normal distribution table for this;
P(z > -1.67) = 0.04746
4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced?
Answer:
The volumes of the cubes are 6³ = 216, 8³ = 512, 10³ = 1,000 and 12³ = 1,728 for a combined volume of 216 + 512 + 1,000 + 1,728 = 3456 which means that each side of the scale must have a combined volume of 3456 / 2 = 1728. This means that in order for the scale to be balanced we need to put the 12 cm cube on one side and the other 3 cubes on the other side.