Answer:
22
Step-by-step explanation:
Since the mean of the set is 11, the sum of the integers in the set must be 11 * 5 = 55. The median must be the 3rd integer, therefore the 3rd integer is 9. Since 9 > 7 and there are only 2 integers less than the median, the 1st and 2nd integers must be 7 and 7 because 7 is the mode. This leaves the last two integers to have a sum of 55 - (9 + 7 + 7) = 32. In order for the last integer (the greatest one) to have the largest value, the fourth integer must be as small as possible. Therefore, the fourth integer is 10 (it can't be 9 because 7 is the only mode) which makes the answer 32 - 10 = 22.
PLEASE HELP ME with this question! I really need help...
Answer:
One of the other perpendicular bisectors must pass through point B
Step-by-step explanation:
Let's look at the choices:
— incenter equidistant from B and C.
The incenter is on the perpendicular bisector of BC. Every point on that line is equidistant from B and C. This statement is True.
__
— angles B and C are congruent.
As we said above, A (on the perpendicular bisector of BC) is equidistant from B and C. That makes the triangle isosceles. The congruent angles are B and C, opposite congruent sides AC and AB. This statement is True.
__
— the perpendicular bisector of BC passes through the incenter.
The incenter is the point of concurrence of the angle bisectors. Since the perpendicular bisector of BC goes through the a.pex of triangle ABC at A, it is the angle bisector there. Hence the incenter lies on that line. The statement is True.
__
— B lies on one of the other perpendicular bisectors.
This will be true if the triangle is equilateral. Nothing in the problem statement indicates this is the case. The statement is False.
In the next three questions, complete the proof of Theorem 31 (Opposite angles of a parallelogram are congruent.) by selecting the best reason or statement.
Answer:
see attached figure
Step-by-step explanation:
table completed. See figure
answer choice D) The graph crosses the y-axis at (0,5), increasing from x=-10 to x=2 and decreasing from x=2 to x=10
Answer:
(A) see the attachments
Step-by-step explanation:
The graph is constant from x=2 to x=10. This eliminates all descriptions except A, which is the correct one.
The table below lists some of the characteristics of the houses on Katrina’s street. Characteristics of Homes For Sale on Katrina’s Street Bedrooms Acres of land Sale price Appraised value Property tax 2 0.17 $230,000 $200,000 $1,220 2 0.20 $210,000 $220,000 $1,232 3 0.20 $275,000 $250,000 $1,400 4 0.24 $275,000 $275,000 $1,540 4 0.52 $360,000 $310,000 $1,736 4 0.75 $350,000 $320,000 $1,792 5 1.23 $375,000 $350,000 $1,960 Which relationship describes a function?
HERE YOU GO!!!!!!!!!!
Answer:
D
Step-by-step im not Shure but I think its D
Beth says that the graph of g(x)=x-5+1 is a
Translation of 5 units to the left and 1 unit up of
F(x)=x
She continues to explain that the point (0,0) on the square root function would be translated to the point (-5,1) on the graph of g(x) is Beths description of the transformation correct? Explain
Answer: No.
Step-by-step explanation:
The graph of g(x) = x - 5 + 1 is a Translation of 5 units to the right not to the left and 1 unit up of F(x) = x
the point (0,0) on the square root function would be translated at the same value which will be to the point (5,1) on the graph of g(x)
Beths description of the transformation is therefore incorrect.
Answer:
No, Beth is not correct. The function g(x) has an h value of 5 and a k value of 1. This would be a horizontal translation of the square root function of 5 units to the right, rather than the left. Beth was correct about the vertical translation of the square root function of 1 unit up. The point (0, 0) from the square root function would be translated to the point (5, 1) on the graph of g(x).
Step-by-step explanation:
This came right from Edg
Sara needs to pack 108 stalks of roses, 81 stalks of lilies, and 54 stalks of orchids into identical baskets so that each type of flower is equally distributed among the baskets. Find the largest number of the basket that can be packed
Answer:
54
Step-by-step explanation:
There are 108 roses, 81 lilies and 54 orchids.
The problem is asking that every basket contain the same number for that type of flower.
So if I put one of each flower in each basket, I will get 54 baskets at the most.
Sounds correct to you?
The roots of x^2 + 5x + 3 = 0 are p and q, and the roots of x^2 + bx + c = 0are p^2 and q^2. Find b + c.
Answer:
[tex]\large \boxed{\sf \ \ \ b=-19, \ \ c=9, \ \ \ b+c=-10 }[/tex]
Step-by-step explanation:
Hello,
we can write
[tex]x^2+5x+3=(x-p)(x-q)=x^2-(p+q)x+pq[/tex]
it means that p+q = -5 and pq=3
And then we are looking for b and c so that
[tex]x^2+bx+c=(x-p^2)(x-q^2)=x^2-(p^2+q^2)x+p^2q^2[/tex]
So
[tex]b=-(p^2+q^2)=-[(p+q)^2-2pq]=-[(-5)^2-2*3]=-(25-6)=-19\\\\c=p^2q^2=3^2=9[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
b + c = -10
Step-by-step explanation:
Notice that according to he quadratic formula, the solutions to a quadratic equation of the form:
[tex]x^2+bx+c=0[/tex]
are:
[tex]x=\frac{-b+/-\sqrt{b^2-4\,c} }{2}[/tex]
and such solutions verify the following conditions:
a) the product of the solutions is:
[tex](\frac{-b+\sqrt{b^2-4c} }{2} )\,(\frac{-b-\sqrt{b^2-4c} }{2} )=\frac{b^2-(b^2-4c)}{4} =\frac{4\,c}{4} =c[/tex]
b) the addition of the solutions is:
[tex](\frac{-b+\sqrt{b^2-4c} }{2} )+(\frac{-b-\sqrt{b^2-4c} }{2} )=\frac{-b-b}{2} =\frac{-2\,b}{2} =-b[/tex]
Therefore, applying these to the first equation, we get that the solutions p and q must verify:
[tex]p\,*\,q=3\,\,\,\,and\,\,\,\,p\,+\,q=-\,5[/tex]
On the other hand, we know that the solutions of the equation
[tex]x^2+bx+c=0[/tex]
are [tex]p^2\,\,\, and \,\,\,q^2[/tex]
Then considering what we found in step a), the product of these two solutions should equal the constant term"c":
[tex]p^2\,*\,q^2= c\\(p\,*\,q)\,(p\,*\,q)=c\\3\,*\,3 = c\\9=c[/tex]
so we know the value of "c" in the second quadratic expression: c = 9
Now, according to what we found in step b), the addition of the two solutions for the second quadratic expression should equal the opposite of the coefficient in the linear term. That is:
[tex]p^2+q^2=-b[/tex]
So, we need to find what the addition of these two squares is in order to find "b". We consider then what the expression [tex](p+q)^2[/tex] renders, since we know that [tex](p+q)=-5[/tex]:
[tex](p+q)^2=p^2+2\,p\,q+q^2\\(-5)^2=p^2+q^2+2\,(p\,*\,q)\\25=p^2+q^2+2\,(3)\\p^2+q^2=25-6\\p^2+q^2=19[/tex]
This means that
[tex]-b=19\\\\b=-19[/tex]
Now, knowing b and c, we can find what b+c is:
[tex]b+c=-19+9=-10[/tex]
You have just timed a person doing a hair cut for the first time. It took 50 minutes. What unit improvement factor learning curve would you use if the person took 35 minutes on the second hair cut?
A. 35 percent
B. 50 percent
C. 70 percent
D. 75 percent
E. 80 percent
Answer: C. 70 percent
Step-by-step explanation:
Given, Time for the first unit = 50 minutes
Time for the second unit = 35 minutes
The unit improvement factor learning curve = (The time for the second unit) ÷ (time for the first unit) x 100.
So, The unit improvement factor learning curve = 35÷ 50 × 100 = 70 percent.
Hence, the correct option is "C. 70 percent".
The step function g(x) is defined as shown. g(x) = StartLayout Enlarged left-brace 1st row 1st column negative 3, 2nd column x less-than-or-equal-to 0 2nd row 1st column 2, 2nd column 0 less-than x less-than-or-equal-to 4 3rd row 1st column 5, 2nd column 4 less-than x less-than-or-equal-to 10 EndLayout
Answer:
{–3, 2, 5}
Step-by-step explanation:
The range refers to the values for the axis i.e to be dependent when there is a defined function
And the range is the combination of the integer i.e to be compounded by these three values
Data provided in the question
-3 , x ≤ 0
2, 0 < x ≤ 4
5, 4 < x ≤ 10
Based on the above information, the range of g(x) is {-3,2,5}
Hence, the correct option is c.
Answer:
C
Step-by-step explanation:
Find the missing side. Round your answer to the nearest tenth.
Answer:
44.8
Step-by-step explanation:
cos α = adjacent leg/hypotenuse
cos 48° = 30/x
x = 30/(cos 48°) = 44.8
what are the x intercepts of the graph of the function below y=x^2-2x-15
Answer:
(5, 0) and (-3, 0)
Step-by-step explanation:
To find the x-intercepts, let's set y = 0.
0 = x² - 2x - 15
0 = (x - 5)(x + 3) -- To factor x² - 2x - 15, we need to find 2 numbers with a sum of -2 and product of -15; these numbers are -5 and 3.
x - 5 = 0 or x + 3 = 0 -- Use ZPP (Zero Product Property)
x = 5, x = -3
Answer:
x = -3 and x = 5.
Step-by-step explanation:
y = x^2 - 2x - 15
y = (x - 5)(x + 3)
The x-intercepts occur when y = 0. In this case, it's when either (x - 5) = 0, or (x + 3) = 0.
x - 5 = 0
x = 5
x + 3 = 0
x = -3
Hope this helps!
Given a normal population which has a mean of 110 and a standard deviation of 5, find the probability that a random sample of 49 has a mean between 109 and 112. Report your answer to four decimal places.
Answer:
0.9168
Step-by-step explanation:
From the data given:
Mean = 110
standard deviation = 5
Let consider a random sample n =49 which have a mean between 109 and 112.
The test statistics can be computed as:
[tex]Z_1 = \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z_1 = \dfrac{109- 110}{\dfrac{5}{\sqrt{49}}}[/tex]
[tex]Z_1= \dfrac{-1}{\dfrac{5}{7}}[/tex]
[tex]Z_1[/tex] = -1.4
[tex]Z_2= \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z_2 = \dfrac{112- 110}{\dfrac{5}{\sqrt{49}}}[/tex]
[tex]Z_2 = \dfrac{2}{\dfrac{5}{7}}[/tex]
[tex]Z_2 =2.8[/tex]
Thus; P(109 < [tex]\overline x[/tex] < 112) = P( - 1.4 < Z < 2.8)
= P(Z < 2.8) - P( Z < -1.4)
= 0.9974 - 0.0806
= 0.9168
HELPPPPPPPPPPPPPPPPPPPPPPP
Answer:
1) A'(8, -10)
B'(10, -8)
C'(2, -4)
2) A''(8, -4)
B''(10, -6)
C''(10, -10)
Step-by-step explanation:
1) For reflection across the line y = -1, given that the lowest point is of ABC which is point C with coordinates (2, 2), we have;
The vertical distance from the point C to the line y = -1 is 3 units down, therefore, the coordinate of the reflection of C will be 3 units below the line y = -1 at C'(2, -4)
The coordinates of the point A(8, 8) will be A'(8, -10)
The coordinate of the point B(10, 6) will be B'(10, -8)
2) Given that we have A'(8, -10), B'(10, -8), and C'(2, -4), we have reflection over y = -7, we have;
The coordinates of the point A'(8, -10) will be A''(8, -4)
The coordinate of the point B'(10, -8) will be B''(10, -6)
The coordinate of the point C'(2, -4)will be C''(10, -10)
Which gives, a total translation of -12 units down as follows;
A''(8, -4) - A(8, 8) = (0, -12)
B(10, 6) - B''(10, -6) = (0, -12)
C(2, 2) - C''(10, -10) = (0, -12).
One angle of an isosceles triangle is 80º. What are the other two angles?
Answer:
80 and 20
Step-by-step explanation:
80+80+20=180
The floor of a rectangular swimming pool has an area of 350 sq.meters, and every point on the floor is of equal depth. If 4,200
cubic meters of water is poured into the pool, how deep will the water level be?
Answer: The depth is 12m
Step-by-step explanation:
The area is 350m^2
And the depth in each point of the base is at the same depth D.
Then we have a cuboid.
Now, the volume of a cuboid is equal to:
V= L*W*D
L = lenght, W = width and D = depth.
Such that L*W = area = 350m^2
then we have:
V = D*350m^2
Now we want V = 4200m^3
4200m^3 = D*350m^2
D = (4200/350) m = 12m
The depth is 12m
Help me to solve this problem ASAP please, also {} is incorrect.
Answer:
8/9
Step-by-step explanation:
2/3 + 1 / ( 2 2/5) - 1/x = 1/3 - 1 / ( 2 2/3)
Changing to improper fractions
2 2/5 = ((5*2+2) / 5 = 12/5
2 2/3 = ( 3*2+2) /3 = 8/3
2/3 + 1 / ( 12/5) - 1/x = 1/3 - 1 / ( 8/3)
1 over and improper fraction flips the improper fraction 1 / ( a/b) = b/a
2/3 + 5/12 - 1/x = 1/3 -3/8
Subtract 2/3 from each side
5/12 -1/x = 1/3 -2/3 -3/8
5/12 -1/x = -1/3 -3/8
Subtract 5/12 from each side
-1/x = -1/3 -3/8-5/12
Multiply each side by 24 to get rid of the fractions
-24/x = -24/3 -3*24/8 -5*24/12
-24/x = -8 -9 -10
-24/x = -27
Multiply each side by x
-24 = -27x
Divide by -27
-24/-27 =x
8/9 =x
!!geometry! Find the value of x if m∠P=18°
Answer:
x = 72
Step-by-step explanation:
If P is 18 degrees and Q is 90 degrees you just add them up and subtract it by 180.
The volume of a cone is 1540cm³. If its radius is 7cm, calculate the height of the cone. (Take pi = 22/7)
Answer:
[tex]h=30[/tex]
Step-by-step explanation:
Volume of a cone=1540[tex]cm^{3}[/tex], Radius=7cm.
The height of a cone=h
When we need to find the height of a cone, we can use the formula of the volume of a cone, which is [tex]\frac{1}{3} \pi r^{2} h[/tex] to find the height of a cone.
[tex]1540cm^{3} =\frac{1}{3}\pi r^{2} h[/tex]
Put the pi value=22/7 and the value of radius which is 7 cm into the formula.
[tex]1540cm^{3}=\frac{1}{3}*\frac{22}{7} 7^{2}h[/tex]
[tex]1540cm^{3} =\frac{154}{3}h[/tex]
Move [tex]\frac{154}{3}[/tex] to another side. 1540 divided by [tex]\frac{154}{3}[/tex] to calculate what is the value of h, h is the height of a cone. Like this.
[tex]\frac{1540cm^{3} }{\frac{154}{3} } =h[/tex]
[tex]30=h[/tex]
Rearrange the h.
[tex]h=30[/tex]
I hope you will understand my solution and explanation. If you still cannot get the point, you can ask me anytime! Thank you!
Answer:
The height of the cone is h = 30 cm.
Step-by-step explanation:
The formula for a cone is:
[tex] \\ V = \frac{1}{3}*\pi*r^2*h[/tex]
We have (without using units) and using pi = 22/7:
[tex] \\ 1540 = \frac{1}{3}*\frac{22}{7}*(7)^2*h[/tex]
Which is equals to:
[tex] \\ 1540 = \frac{1}{3}*\frac{22}{7}*(7)*h[/tex]
[tex] \\ 1540 = \frac{1}{3}*22*7*h[/tex]
Well, we have to solve the equation for h:
[tex] \\ \frac{1540*3}{22*7} = h[/tex]
[tex] \\ 30 = h[/tex]
Therefore, the height of the cone is 30 cm.
Nora bought a car last year so that she could drive to work after school. She spent $250 last year for gas. This year she spent $295. Disregarding other factors, what is the inflation rate? 18% 19% 20% 21%
Answer:
here,
money spent in 1st year =$250
money spent in 2nd year=$295
total inflated amount=$295- $250
=$45
Then,
inflation rate= ($45/ $250)×100%
=18%
HELPPPPPPPPPPPPPPPPPPPPPP
Answer:
x= 24, y= 33°
Step-by-step explanation:
MJ is part of the diameter of the circle and there is right angle between the diameter and HK
As the diameter and HK are perpendicular, HM=MK and mHJ= mJK
So,
x= 24and
y= 66°/2= 33°Please help me!!!!!! I do not understand...
Answer:
the second one........the shape of the conic section os circle
what is 3x^3 - 11x^2 - 26x + 30 divided by x-5?
Answer:
Most likely the answer is
3x^2+4x-6
Answer:
3x^2+4x-6 is correct
Suppose that Mike invests $5000 into an account that pays 12% interest compounded
continuously. He wants to know how many years it will take for his investment to double and be worth
$10,000. Can Mike solve the following equation to find his answer? Why or why not?
2 = e 120. Solve the equation listed in the question above for t. First find the exact answer. Then
approximate your answer to three decimal places
Answer:
t = log(2)/0.12 years (exact value)
= 5.776 years (to three decimal places)
Step-by-step explanation:
The future value of an amount P at continuous interest rate i% for t years can be calculated using the continuous interest formula:
FV = Pe^((i)t)
where e is the Euler's constant = 2.7182818284....
We're given
10000 = 5000 e^((0.12)t)
simplify
2 = e^(0.12t) ........................ see below
[ please compare if this is the same as the one shown in the original question, the formula posted as "2 = e 120" does not look right, probably because of typographical difficulties, then answer if the equation given in the question can be used to solve the problem]
take (natural) log using the power property of logarithms
log(2) = 0.12t log(e)
using natural log, log(e) = 1
log(2) = 0.12t
simplify
t = log(2)/0.12 years (exact value)
To obtain the time (in years)
t = log(2)/0.12 = 0.6931/0.12 = 5.7762 years
Check using the rule of 72 (approximate)
72/12(%) = 6,
Since continuous interest accumulates interest faster, so 5.8 years sound reasonable.
A middle school took all of its 6th grade students on a field trip to see a play at a theatre that has 2000 seats. The students filled 65% of the seats in the theatre. How many 6th graders went on the trip?
Answer: 1,300 students went on the trip
Step-by-step explanation: So we know that 65% filled the seats so let's turn that into a fraction. [tex]\frac{65}{100}[/tex] . Now we know that there are 2,000 seats in total so let's put that into a fraction. [tex]\frac{x}{2,000}[/tex] The x represents the students that went on the trip.
[tex]\frac{65}{100} = \frac{x}{2,000}[/tex] we have to cross multiply
65(2,000) = 100 (x)
130,000 = 100 (x)
130,000 ÷ 100
1,300 = x So now we know that 1,300 went to the trip students
Courtney constructed this figure using a compass with its width set equal to PR, the radius of the circle. She claims triangle PRS is equilateral because all three sides of the triangle are equal to PR. She also claims that applying the same argument to prove each triangle in the figure is equilateral proves that the inscribed hexagon is also equilateral. Which statement is true? A. Courtney's reasoning about triangle PRS is correct, but the hexagon is not equilateral. B. Courtney's reasoning about triangle PRS is correct, and the hexagon is equilateral. C. Courtney's reasoning about triangle PRS is incorrect, and the hexagon is not equilateral. D. Courtney's reasoning about triangle PRS is incorrect, but the hexagon is equilateral.
Answer:
B
Step-by-step explanation:
It helps if you have the figure included. However, since it is not, we can assume that she has gone around the circle with all six sides of the hexagon is set to PR.
That makes the hexagon with 6 equal sides. It also makes each triangle using one of the sides equal to PR. The radii are all equal. There are 6 triangles making up the hexagon.
Both statements she makes are true and that makes B the answer.
Given a graph for the transformation of f(x) in the format g(x) = f(kx), determine the k value.
ту
g(x)
f(x)
k= -4
k= -1/4
k= 1/4
k= 4
ASAP!!!!
Answer: C
1/4
Step-by-step explanation:
Given a graph for the transformation of f(x) in the format g(x) = f(kx),
This means that for every value of x, f(x) will take the value it would have had at kx, that is, the graph of f(x) is stretched by a factor of 1/k in the direction of positive x-direction.
Therefore, the value of k will be 1/4.
Answer:
k=4
Step-by-step explanation:
The level of water in a dam was decreasing by 20% each day. If the level of water was 1500cm,what was the level after two days?
Answer:900
Step-by-step explanation:
Answer:
960 cm.
Step-by-step explanation:
For the first day:
Subtract the primary level of water by the 20% of it. 20% of 1500 is:
[tex]0.2*1500=300[/tex] (Convert the percent to decimal)
Then subtract 1500 to 300. That would become 1200cm for the first day.
For the second day:
Subtract the level of water from the first day by 20% of it. 20% of 1200 is:
[tex]0.2*1200= 240[/tex]
Then subtract 1200 to 240. That would become 960 for the second day.
The level of the water after 2 days is 960 cm.
Factor the polynomial.
X2-13x+30
Answer:
[tex] \ \boxed{(x - 3)(x - 10)}[/tex]Step-by-step explanation:
[tex] {x}^{2} - 13x + 30[/tex]
Write -13x as a difference
[tex] {x}^{2} - 3x - 10x + 30[/tex]
Factor out x from the expression
[tex]x(x - 3) - 10x + 30[/tex]
Factor out -10 from the expression
[tex]x(x - 3) - 10(x - 3)[/tex]
Factor out x-3 from the expression
[tex](x - 3)(x - 10)[/tex]
Hope I helped!
Best regards!!
WILL MARK BRAINLIEST
PLEASE HELP x
Answer:
3. time = 6.4999 approximately 6.5 years
4. $2235.35
5. $ 3950
Step-by-step explanation:
4. amount of interest = final amount - principle= 7535.35 - 5300 = 2235.35
5. principle = final amount - interest earned = 4435.25 - 485.25 = 3950
can someone answer the underlined question? (number 9)
Answer:
Slope = -6/7
Step-by-step explanation:
You need to use the formula m = y2 - y1 ÷ x2 - x1
The formula means: slope = the y coordinate of point 2 subtract the y coordinate of point 1, divided by the x coordinate of point 2 subtract the x coordinate of point 1
So,
m = 2 - 5 ÷ 3/2 - (-2)
m = -3 ÷ 7/2
m = -6/7
Hope this helps :)
