Which statements are true about the lines of symmetry of a regular pentagon? Select three options
Complete question is;
Which statements are true about the lines of symmetry of a regular pentagon? Check all that apply.
A) Every line connects two vertices.
B) Every line connects the midpoints of 2 sides.
C) Every line bisects a vertex angle.
D) Every line bisects a side.
E) Every line is perpendicular to a side.
Answer:
C: Every line bisects a vertex angle.
D: Every line bisects a side.
E: Every line is perpendicular to a side.
Step-by-step explanation:
A shape will have a line of symmetry when after the perpendicular line is drawn through from one vertex to the centre of one side, it can be folded and the folded part will sit perfectly on top in such a way that all the edges match.
Now, a pentagon has 5 sides and by implication from the explanation of line of symmetry above, it has 5 lines of symmetry.
Attached below is an image showing the 5 lines of symmetry of a pentagon.
From the attached image, we can see that the lines of symmetry bisects a vertex angle, it bisects a side and is perpendicular to a side.
Thus correct answer is Options C, D & E
Answer:
C, D, EStep-by-step explanation:
how do you solve -5x - 6 =1
Someone please help with this !
Answer:
Step-by-step explanation:
Select the expressions that are equivalent to -5.
1) -5 x 1
2) 5 x -1 x -1 x -1
3) -3 x -5/3
4) -5 x -1
5) -25/5 divided by 5/5
Answer:
1, 2, and 5 :)
Step-by-step explanation:
3: negative times a negative is a positive
4: negative times negative is a positive
hope this helps !! <3
If 900x2= 1800 then what does 1800x400-40+3000000=? please help
Answer:
720,000-3,000,040= -2279960 or positive if you minus the other way
Answer:
-2279960
Step-by-step explanation:
A new version of the Medical College Admissions Test (MCAT) was introduced in spring 2015 and is intended to shift the focus from what applicants know to how well they can use what they know. One result of the change is that the scale on which the exam is graded was modified, with the total score of the four sections on the test ranging from 472 to 528. In spring 2015, the mean score was 500.0 with a standard deviation of 10.6.
1) Assuming that the MCAT scores are normally distributed, use Table to find the median and the first and third quartiles of the MCAT scores.
A) Find the median of the MCAT scores.
B) Find the first quartile of the MCAT scores.
C) Find the third quartile of the MCAT scores.
D) Find the interquartile range of the MCAT scores.
2) Which interval contains the central 80% of the MCAT scores?
a. 486.432 to 513.568.
b. 472 to 528.
c. 491.096 to 508.904.
d. 480 to 520.
Answer:
Kindly check explanation
Step-by-step explanation:
Assume a normal distribution with:
Mean (m) = 500
Standard deviation (sd) = 10.6
A) The median of the MCAT scores :
For a normal distribution, the Median = mean = 50% = 0.5
Zscore at 0.5 = - 0.0
-0.0 = (x - m) / sd
-0.0 = (x - 500) / 10.6
0 = x - 500
x = 500
B) the first quartile (Q1) score = 25% = 0.25
Using :
Zscore at 25% = 0.25 = -0.675
Zscore = (X - m) / sd
-0.675 = (X - 500) / 10.6
-7.155 = x - 500
x = - 7.155 + 500
X = 492.845
C.) the third quartile (Q3) score = 75% = 0.75
Using :
Zscore at 75% = 0.25 = 0.675
Zscore = (X - m) / sd
0.675 = (X - 500) / 10.6
7.155 = x - 500
x = 7.155 + 500
X = 507.155
D.) The interquartile range :
Q3 - Q1
= 507.155 - 492. 845
= 14.31
2.) Interval which contains 80% of MCAT Scores:
Zscore of the (100-80)% / 2 at the extremes ; = 20%/2 = 0.1 ; 0.1 = - 1.28
Interval:
(-1.28 * sd) + mean and (1.28 * sd) + mean
(- 1.28 * 10.6) + 500 and (1.28 * 10.6) + 500
-13.568 + 500 and 13.568 + 500
486.432 and 513.568
Leah bought 3/4 pound of trail mix to make snack bags . She put 1/8 pound of trail mix into each snack bag. Which expression can be used to find how many snacks Leah made
Answer:
3/4 ÷ 1/8 = 6
Step-by-step explanation:
first you would have to figure out how to make them even factors.
6/8 ÷ 1/8
Then you would divide, and get 6.
Which expression is equivalent to -11 - (-7)?
A. 11 + 7
B. -11 -7
C. 11 - 7
D. -11 + 7
Answer:
D. -11+7
Step-by-step explanation:
1) . -11 - (-7)
2). -11+7
If you are multiplying 2 negatives it becomes positive so - (-7) equals to +7
Answer:
11+7
Step-by-step explanation:
Step 2: Testing Jerome's brother's approach I Jerome's brother told him to add one cup of water for every one cup of drink mix hel added to keep the ratio of water to drink mix the same and still increase the total amount of energy drink. a) Complete the table below. (2 points) Original Ratio +1 +2 6 7 3 Drink mix (cups) 12 10 Water (cups)
Answer: the brother in incorrect
Step-by-step explanation:
No his brother is incorrect because the ratio would go from 8:3 to 4:9
I know this answer is correct because I did this question on edgenuity and it was correct.
Answer:
No his brother is incorrect because the ratio would go from 8:3 to 4:9
Step-by-step explanation:
Polygon V has an area of 1 square unit. Jun-seo drew a scaled version of Polygon V using a scale factor of 7 and labeled it Polygon W.
Answer:
49
Step-by-step explanation:
Answer:
it is 49 for sure
Step-by-step explanation:
it worked for me on khan
The average of five numbers is 115. If four of the numbers are 116, 132, 145, and 106,
what is the fifth number?
Pls help fast
Answer:
Step-by-step explanation:
average of 5 numbers=115
total of 5 numbers=115×5=575
total of 4 numbers=116+132+145+106=499
fifth number=575-499=76
A fair coin is tossed three times. A player wins $1 if the first toss is a head, but loses $1 if the first toss is a tail. Similarly, the player wins $2 if the second toss is a head, but loses $2 if the second toss is a tail, and wins or loses $3 according to the result of the third toss. Let the random variable X be the total winnings after the three tosses (possibly a negative value if losses are incurred). (a) Construct the probability mass function. (b) Construct the cumulative distribution function. (c) What is the most likely value of the random variable X?
Answer:
Step-by-step explanation:
First lets construct the outcome tree based on the winning situation in the question;
the coin was toasted 3 times
so
FIRST SECOND THIRD TOTAL
toss winning toss winning toss winning winning
H 1 H 2 H 3 6
H 1 H 2 T -3 0
H 1 T -2 H 3 2
H 1 T -2 T -3 -4
T -1 H 2 H 3 4
T -1 T 2 H -3 -2
T -1 T -2 H 3 0
T -1 T -2 H -3 -6
NOW
a) the probability mass function is;
Xi -6 -4 -2 0 2 4 6
Pi 1/8 1/8 1/8 2/8 1/8 1/8 1/8
b) the cumulative distribution function
Xi -6 -4 -2 0 2 4 6
Pi 1/8 1/8 1/8 2/8 1/8 1/8 1/8
F(Xi) 1/8 2/8 3/8 5/8 6/8 7/8 8/8
c) most likely value of the random variable X
The most likely value of the random variable X is 0
from the probability mass function in (a), the probability the random variable is highest at 2/8, te Xi value above 2/8 is 0
therefore the most likely value of the random variable X is 0
What are the roots of 4x2 + 35x − 9 = 0?
Answer:
Solution given:
4x²+35x-9=0
comparing above equation with ax²+bx+c.
we get
a=4
b=35
c=-9
we have
x=[tex] \frac{ - b±\sqrt{b²-4ac}}{2a} [/tex]
x=[tex] \frac{ - 35±\sqrt{35²-4*4*-9}}{2*4} [/tex]
x=[tex] \frac{ - 35±\sqrt{1369}}{2*4} [/tex]
x=[tex] \frac{ - 35±37}{8} [/tex]
taking positive;
x=[tex] \frac{ - 35+37}{8} [/tex]
x=[tex] \frac{1}{4} [/tex]
taking negative
x=x=[tex] \frac{ - 35-37}{8} [/tex]
x=-9
Therefore:the roots of 4x²+ 35x − 9 = 0 is [tex] \frac{1}{4} [/tex] or-9.
Write an integer to represent a 6 yard loss in football.
Answer:
-6
Step-by-step explanation:
Divide (x3 + 3x2 + 16x + 48) by (x + 3)
A) x - 16
B) x + 16
C) x2 - 16
D) x2 + 16
Divide (x2 + x - 6) by (x + 3).
A) x - 2
B) x + 3
C) x - 3
D) x + 2
please explaine how you got it thank you so much.
Answer:
D) x² + 16
A) x − 2
Step-by-step explanation:
(x³ + 3x² + 16x + 48) / (x + 3)
Use grouping:
(x² (x + 3) + 16 (x + 3)) / (x + 3)
Divide:
x² + 16
(x² + x − 6) / (x + 3)
Factor:
(x + 3) (x − 2) / (x + 3)
Divide:
x − 2
A company produces two types of computers; desktops and laptops. They will make a profit of $248 on each desktop and $259 on each laptop. Each desktop computer takes 10 hours of assembly time and 2 hours of quality control time. Each laptop computer takes 6 hours of assembly time and 7 hours of quality control time. The company has a maximum of 2,800 assembly hours and 1,000 quality control hours per week. In your answer, let x be the number of desktops to produce, and let y be the number of laptops to produce. Write the linear programming problem which must be solved to determine how many of each kind of computer should be made in order to maximize profit.
Answer:
248x+259y>=P (objective function)constraints10x+6y<=2800------12x+7y<=1000-------2To maximize profit(P>=$79,905)the company needs to produce 35 desktop computers and 275 laptops computersStep-by-step explanation:
let x be the number of desktops to produce, and
let y be the number of laptops to produce.
let the profit be p
maximize P (objective function)
248x+259y>=P
The products are subject to the constraints (that is, the restrictions)
1. Assembly hours
assembly time 10 hours and 6 hours for desktop and laptop respectively
maximum assembly hours is 2800
10x+6y<=2800------1
2. Quality control time
Quality control time 2 hours and 7 hours for desktop and laptop respectively
maximum assembly hours is 1000
2x+7y<=1000-------2
we can now solve equation 1 and 2 to get the values of x and y
10x+6y<=2800------1
2x+7y<=1000-------2
multiply equation 2 by 5 we have
10x+6y<=2800------1
10x+14y<5000-----3
subtract equation 3 from 1 we have
0x-8y<=-2200
8y<=2200
divide both sides by 8
y<=275
substitute y=275 in equation 1 we have
10x+6y<=2800------1
10x+6(275)<=2800------1
10x+1650<=2800
10x<=2800-1650
10x<=350
divide both sides by 10 we have
x<=35
we proceed by substituting x=35 and y=275 in the objective function we have
248x+259y>=P
248(35)+259(275)>=P
8680+71225>=P
P>=$79,905
To save for retirement, you decide to deposit $1,000 into an IRA at the end of each year for the next 30 years. If this savings annuity has an interest rate of 10% per year compounded annually, then how much interest will you earn over the course of the 30 years?
Answer:
134494
Step-by-step explanation:
Answer: 134,494
Step-by-step explanation: d=$1,000, the yearly deposit.
r=0.10, or a 10% annual rate.
k=1, since we’re doing yearly deposits and we’ll compound yearly.
N=30, we want the amount after 30 years.
Putting this into the annuity formula:
PN=d⋅((1+rk)N⋅k−1)rkP30=1,000⋅((1+0.101)30⋅1−1)(0.101)P30=1,000⋅((1.1)30−1)(0.10)P30=1,000⋅(17.4494−1)(0.10)P30=1,000⋅(16.4494)(0.10)=$164,494.
The account will grow to $164,494 after 30 years.
Notice that you deposited into the account a total of $30,000 ($1,000 a year for 30 years). The difference between what you end up with and how much you put in is the interest earned. In this case it is $164,494–$30,000=$134,494.
N
h(x) =
x +3
Find the inverse of the function
Answer:
The inverse is x-3
Step-by-step explanation:
h(x) = x +3
y = x+3
Exchange x and y
x = y+3
Solve for y
Subtract 3 from each side
x-3 = y+3-3
x-3 = y
The inverse is x-3
City lake waterpark has many attractions one of which is super slide
Answer:
6444444445555555555555555555555
Steven's family needs a new microwave. There is one on sale that measures 20 inches by 14 inches by 11 inches. What is the volume of the microwave?
Answer:
3,080 in³
Step-by-step explanation:
To find the volume you use the formula
Length*Width*Height= Volume
So,
14*11*20 = 3080
and you unit will be cubed because volume is cubed!
I need help you don't have to explain the answer I just need it, thank you!
Answer:
j = 38
Step-by-step explanation:
j/-2 + 7 = -12
first subtract 7 from both sides
j/-2 = -19
then multiply both sides by -2
j = 38
Help me asap pls I will Mark 1st answer brainiest!
On Monday 428 students are going on a trip to the zoo. If 47 students fit on each bus, how many buses are needed?
Answer:9 buses
Step-by-step explanation:
Is 44/37 a rational number
Answer:
no
Step-by-step explanation:
The ratio of boys to girls is 5:3 there are 80 more boys than girls how many girls are there
Answer: 120
Step-by-step explanation:
Ratio Quantity
Boys: 5 80 + x
Girls: 3 x
[tex]\dfrac{5}{3}=\dfrac{80+x}{x}\\\\\\5x=3(80+x)\\\\5x=240+3x\\\\2x=240\\\\x=120[/tex]
Alice, Bob, and Carmen are three recent graduates of the ASU Engineering program who are now gainfully employed. They tell you their salaries; from this data, you wish to determine whether the mean salary of recent graduates of the ASU Engineering program is above the national average. Match each of the following elements of this example with its correct name.
A. Alice's, Bob's, and Carmen's salaries
B. Salaries of recent graduates of the ASU Engineering program
C. A number computed from the average of Alice's, Bob's, and Carmen's salaries that helps us decide whether to reject the null hypothesis
Complete Question
Generally the complete question is shown on the first uploaded image
Answer:
A. Alice's, Bob's, and Carmen's salaries Sample
B Salaries of recent graduates of the ASU Engineering program Population
C A number computed from the average of Alice's, Bob's, and Carmen's salaries that helps us decide whether to reject the null hypothesis
P-value
Step-by-step explanation:
Considering A
The salaries of Alice, Bob, and Carmen are Samples because they are selected from a larger population (i.e the salaries of recent graduates of the ASU Engineering program)
Considering B
The salaries of recent graduates of the ASU Engineering program is the population because it is the entire pooled of data from which the samples are selected from
Considering
A number computed from the average of Alice's, Bob's, and Carmen's salaries that helps us decide whether to reject the null hypothesis is the P-value because the P-value is computed from the sample and it is use to make decision whether to reject or fail to reject the null hypothesis
Please help. I need help with number 76.
Answer: [tex]12x^2+12xh+4h^2-2[/tex]
==================================================
Explanation:
First let's find the expression f(x+h). We replace every copy of x with x+h, expand, and simplify like so.
[tex]f(x) = 4x^3 - 2x\\\\f(x+h) = 4(x+h)^3 - 2(x+h)\\\\f(x+h) = 4(x+h)(x+h)^2 - 2(x+h)\\\\f(x+h) = 4(x+h)(x^2+2xh+h^2) - 2(x+h)\\\\f(x+h) = 4x(x^2+2xh+h^2)+4h(x^2+2xh+h^2) - 2(x+h)\\\\f(x+h) = 4x^3+8x^2h+4xh^2+4hx^2+8xh^2+4h^3 - 2x-2h\\\\f(x+h) = 4x^3+12x^2h+12xh^2+4h^3 - 2x-2h\\\\[/tex]
This may look ugly, but things will simplify a bit when we subtract off f(x)
Note how in f(x+h) we have the following terms
4x^3-2xWhich are the exact terms found in f(x) as well.
Why is this important? It helps us subtract and cancel. When we subtract off f(x), we cross off the 4x^3 and -2x terms in that f(x+h) equation above.
We'll be left with this
[tex]f(x+h)-f(x) = 12x^2h+12xh^2+4h^3-2h\\\\[/tex]
At this point, every term shown has at least one copy of 'h' as a factor.
This allows us to factor out h
[tex]f(x+h)-f(x) = h(12x^2+12xh+4h^2-2)\\\\[/tex]
Then we can divide both sides by h to get our final answer
[tex]\frac{f(x+h)-f(x)}{h} = \frac{h(12x^2+12xh+4h^2-2)}{h}\\\\\frac{f(x+h)-f(x)}{h} = 12x^2+12xh+4h^2-2\\\\[/tex]
----------------------------------------------------
Extra info:
h is nonzero to avoid dividing by zero. Though as h gets closer and closer to zero, terms with h in them will drop out since those terms will be very small. We'll be left with 12x^2-2. This is the derivative of f(x).
At 10:30am,a submarine was 43 feet below the ocean surface.By10:45am,it was 271 feet below the surface. How much did it descend in that 15 minutes?
Hi!
Your answer would be: 228ft below the ocean surface.
Reason being: when you subtract 43 from 271, you get 228.
Hope this helps!
If you need anymore help, please let me know!
Yours Truly,
~~~PicklePoppers~~~The jacks and balls have to be split among 6 people. Use the Distributive Property to pull the number 6 out of the expression you wrote in part a. Write the resulting expression below.
Answer: (24 + 60) = (6 × 4 + 6 × 10) = 6 × (4 + 10)
Write an equation of the line passing through the point (-7,-6) that is parallel to the line y=3x+2
========================================================
Explanation:
Parallel lines have equal slopes but different y intercepts.
The slope of y = 3x+2 is m = 3 (compare it to y = mx+b)
Any parallel line will also have slope m = 3
The parallel line goes through (x1,y1) = (-7, -6)
--------------------
Turn to point-slope form. Plug in the values mentioned and solve for y
y-y1 = m(x-x1)
y-(-6) = 3(x-(-7))
y+6 = 3(x+7)
y+6 = 3x+21
y = 3x+21-6
y = 3x+15
---------------------
Or you could use slope intercept form
y = mx+b
y = 3x+b
-6 = 3(-7)+b
-6 = -21+b
-6+21 = b
15 = b
b = 15
Since m = 3 and b = 15, we know the equation is y = 3x+15
Rewrite in simplest terms: (3x + 2) + (-10x – 3)
-7x-1
Step-by-step explanation:
this is extra words
