Answer:
215.6 m²
Step-by-step explanation:
The area (A) of the polygon is
A = [tex]\frac{1}{2}[/tex] × perimeter × apothem
perimeter = 7 × 7.7 = 53.9 m, so
A = 0.5 × 53.9 × 8 = 215.6
The area of regular polygon with 7 sides is 215.6 m².
What is Polygon?Polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.
Here, the area (A) of the polygon is
A = 1/2 × perimeter × apothem
perimeter = length X width
= 7 × 7.7
= 53.9 m,
so, A = 0.5 × 53.9 × 8
= 215.6 m²
Thus, the area of regular polygon with 7 sides is 215.6 m².
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The value of an explanatory variable is 18, while the corresponding value of the response variable is 8. What would be the coordinates of this data point when plotted on a scatterplot?
A. (26, 8)
B. (8, 26)
C. (8, 18)
D. (18, 8)
D.(18.8) is the answer because the explanatory variable is the x-axis while the response variable is the y-axis.
Answer: The correct option is (D) (18, 8).
Step-by-step explanation: Given that the value of an explanatory variable is 18, while the corresponding value of the response variable is 8.
We are to find the co-ordinates of this data plot when plotted on a scatter plot.
Let y = f(x) be a function, where x is the independent variable and y is the dependent variable.
On a scatter plot, we plot any point satisfying this function as (x, y).
Explanatory variable = independent variable, x = 18
and
Response variable = dependent variable, y= 8
Therefore, the required coordinates of this data point when plotted on a scatter plot are (18, 8)
Option (D) is CORRECT.
Find the value of x to the nearest tenth
Check the picture below.
make sure your calculator is in Degree mode.
Answer:
The opposite side x is 7
Step-by-step explanation:
Step one
From the given expression in the picture
We can estimate x by applying the
SOH CAH TOA rule on the triangle
Since we have one side and one angle given
step two
From the given picture we have
We have θ and adjacent side given
Hence we need to apply
tan θ= opposite/adjacent =
Tan 35°=x/10
Step three
From 4 figure table or calculator
tan 35° is 0.7
0.7=x/10
x=0.7*10
x= 7
Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on. He continues to double his savings each day. Find the amount that he will save on the fifteenth day.
$16,384
$29
$32,768
$8192
ANSWER
$16,384
EXPLANATION
From the question we have that,
Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on.
This forms a geometric sequence,
[tex]1,2,4,...[/tex]
The first term of this sequence is
[tex]a = 1[/tex]
The common ratio is
[tex]r = \frac{2}{1} = \frac{4}{2} = 2[/tex]
The general term of a geometric sequence is given by the formula:
[tex]f(n) = a {r}^{n - 1} [/tex]
To find the 15th term, we plug in a=1, r=2 and n=15.
[tex]f(15) = 1 {(2)}^{15 - 1} [/tex]
[tex]f(15) = {2}^{14} [/tex]
[tex]f(15) = 16384[/tex]
The amount he will save on the 15th day is $16,384
Mary’s parents gave her $60 as pocket money to meet her daily expenses. She spent $20 on clothes and $10 on food. She wishes to buy some books, also. If each book costs $3 each, solve the inequality to find how many books she can buy. Question 5 options: at the most 10 at least 10 10 at the most 5
Answer: The correct option is
(A) at the most 10.
Step-by-step explanation: Given that Mary’s parents gave her $60 as pocket money to meet her daily expenses. She spent $20 on clothes and $10 on food.
Also, she wishes to buy some books and each book costs $3.
We are to solve the inequality to find the number of number of books that she can buy.
Let the number of books that Mary can buy be n.
Then, according to the given information, we have
[tex]20+10+n\times3\leq 60\\\\\Rightarrow 30+3n\leq 60\\\\\Rightarrow 3n\leq 60-30\\\\\Rightarrow 3n\leq 30\\\\\Rightarrow n\leq \dfrac{30}{3}\\\\\Rightarrow n\leq 10.[/tex]
Thus, Mary can buy at most 10 books.
Option (A) is CORRECT.
Choose the TWO factored binominals for the expression: x2+6x – 27 Question 6 options: A) (x - 3) B) (x - 9) C) (x + 6) D) (x + 9) E) (x + 3)
Answer:
A) x-3 and D) x+9
Step-by-step explanation:
x^2 + 6x - 27
You need to find two numbers that multiply to -27 and add up to 6
Those two numbers are -3 and 9, because 9 * -3 = -27 and 9+ -3 = 6
So you add those to x and those are your two factored binomials
(x-3) and (x+9)
The first figure of the Sierpinski triangle has one shaded triangle. The second figure of the Sierpinski triangle has three shaded triangles. The third figure of the Sierpinski triangle has nine shaded triangles. Which summation represents the total number of shaded triangles in the first 15 figures?
Answer:
[tex]\texttt{The summation form} = \sum\limits_{n=1}^{15} 3^{(n-1)}=7,174,453[/tex]
Step-by-step explanation:
We can find the total number of shaded triangles in the first 15 figures by first finding the pattern between the first, second, and the third triangles.
1st triangle (T₁) has 1 shaded triangle2nd triangle (T₂) has 3 shaded triangles3rd triangle (T₃) has 9 shaded trianglesWe can see that the number of shaded triangles of T₂ is 3 times more compared to T₁. Also, the number of shaded triangles of T₃ is 3 times more compared to T₂. Then we can conclude that the numbers of shaded triangles form a geometric sequence with:
1st term (U₁) = 1 (the number of T₁'s shaded triangle)ratio (r) = 3 (the number is 3 times more than the previous number)For the summation form, we can find each term using the geometric sequence formula:
[tex]\boxed{U_n=U_1\cdot r^{(n-1)}}[/tex]
[tex]U_n=1\cdot 3^{(n-1)}[/tex]
[tex]U_n=3^{(n-1)}[/tex]
Then, the summation form for the 1st 15 term =
[tex]\displaystyle\sum\limits_{n=1}^{15} 3^{(n-1)}[/tex]
We can also find the summation by using the geometric series formula:
[tex]\boxed{S_n=\frac{U_1(r^n-1)}{r-1} ,\ \texttt{for r > 1}}[/tex]
Then, for S₁₅:
[tex]\begin{aligned}S_{15}&=\frac{U_1(r^{15}-1)}{r-1}\\\\&=\frac{1(3^{15}-1)}{3-1} \\\\&=\bf 7,174,453\end{aligned}[/tex]
Noa was paid a 25 percent commission for selling a used car If she was paid $1,631.24, what was the selling price of the car?
Answer:
$6,524.96
Step-by-step explanation:
Take the commission total which is $1631.24 divide it by 25% or .25.
$1,631.24 ÷ .25=$6,524.96 cost of the used car
Check your answer by taking your answer and multiple it by 25%.
$6,524.96 (cost of the car) × .25 =$1,631.24 commission
Answer:
$6,524.96
Step-by-step explanation:
Step One: Because the amount she is paid is the 25% commission, multiply the 1,631.24 by 4 ( 4 because she is paid 1 out of 4 parts of the total selling price)
Step Two: the answer is 6,524.96
HELP PLZZZZ! thank you
1. Same length.
2.vertically opposite angle.
3.BAC =BDE
4.AC = DE
Hope this helps you ___!!❤
Please help me answer this
Answer:
C
Step-by-step explanation:
As with most problems of this type, you need to draw an actual line that has approximately the same number of data points on each side of it. If you'll do that you'll see that this line crosses the y-axis at approx. y = 4. Only Answer C has that y-intercept.
The second side of a triangular deck is 6 feet longer than the shortest side and a third side that is 6 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 56 feet, what are the lengths of the three sides?
Answer:
14 ft20 ft22 ftStep-by-step explanation:
Let s represent the length of the shortest side. Then the other two sides are ...
s +62s -6The perimeter is the sum of the lengths of the three sides, so is ...
56 ft = s + (s+6) + (2s-6) = 4s . . . . collect terms
14 ft = s . . . . . . . divide by the coefficient of s
The shortest side is 14 ft; the second side is 20 ft; the third side is 22 ft.
Final answer:
Using the given information about the sides of the triangular deck and its perimeter, we set up an equation to solve for the shortest side and then used that to find the lengths of the other two sides. The three sides of the triangular deck are 14 feet, 20 feet, and 22 feet.
Explanation:
To solve the problem, we need to set up an equation based on the given information. Let's define the shortest side of the triangle as x feet. According to the problem, the second side is x + 6 feet, and the third side is 2x - 6 feet. The perimeter of the triangle is the sum of the lengths of all three sides, which is given as 56 feet.
We can set up the following equation:
x + (x + 6) + (2x - 6) = 56
Combining like terms, we get:
4x = 56
Divide both sides by 4:
x = 14
Now we can find the lengths of the sides:
The shortest side: 14 feet
The second side: 14 + 6 = 20 feet
The third side: 2(14) - 6 = 22 feet
A vintage guitar is being auctioned. The graph below traces the prices quoted by bidders at different time intervals, measured in minutes, since the auction began.
Which statement is true about the graph?
A. The average rate of change is greater for interval D than for interval E because the line is increasing more quickly at interval D than at interval E.
B. The average rate of change is greater for interval C than for interval B because the line is increasing more slowly at interval C than at interval B.
C. The average rate of change is greater for interval A than for interval B because the line is increasing more slowly at interval A than at interval B.
D. The average rate of change is greater for interval D than for interval C because the line is increasing more quickly at interval D than at interval C.
Answer:
d. :)
Step-by-step explanation:
Answer:
D. The average rate of change is greater for interval D than for interval C because the line is increasing more quickly at interval D than at interval C.
Step-by-step explanation:
The difference between C and D interval is the lowest.
This means that line is increasing more quickly at interval D as compared to others.
Therefore, option D is the right answer.
The center pole used to hold up a circus tent is supported by a guy wire 53 feet long. The guy wire is anchored to the ground 45 feet from the base of the pole. What is the height, h, of the center pole? Round your answer to the nearest foot if necessary.
A. h = 31 feet
B. h = 70 feet
C. h = 784 feet
D. h = 28 feet
Answer:
D. 28 feet
Step-by-step explanation:
a²+b²=c²
45²+b²=53²
2025+b²=2809
b²=784
[tex]\sqrt{784}[/tex]=[tex]\sqrt{b}[/tex]
b=28
Answer:
D. 28 feet
Step-by-step explanation:
The Sudsy car wash loses $40 on rainy days and gains $150 on sunny days. If the probability of rain is 15%, what its he expected value of the net profit?
-40*.15 + 150*(1-.15)= 121.50
Given the probabilities of sunny and rainy days and the respective profits, the Sudsy car wash's expected net profit per day, considering the rain probability, is $121.5.
Explanation:The subject of the question is about Expected Value, a concept in Probability Theory. Considering the Sudsy car wash's situation, we know that it loses $40 on rainy days and gains $150 on sunny days. The probability of having a rainy day is given as 15%, which means the probability of having a sunny day is 85% (100% - 15%).
The expected value of the net profit can be calculated by the formula for Expected Value: E[X] = ∑[x*P(X=x)]. In the context of this problem, we can write out the expected value E[N] of the net profit N as E[N] = (-$40 * 0.15) + ($150 * 0.85) = -$6 + $127.5 = $121.5. So, it is expected that the Sudsy car wash will have a net profit of $121.5 per day, on average.
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Please help me with this
Answer:
7, 5
Step-by-step explanation:
_________________________________________________
Answer:
7 and 5
Step-by-step explanation:
So we can start with 1 and 4. We can see they added 3 to 1. Ok, that's the first part.
Then, they took 4 and subtracted 2. We can see they subtracted 2. Ok, that's the second part.
We can see they keep doing this:
Add 3, subtract 2. Add 3, subtract 2. and so on, until we get to 4. They just subtracted 2, so we can add 3. So, our first unknown number would be 7. We can then subtract 2, making the second unknown number 5.
Hope I helped, soz if I'm wrong ouo.
~Potato.
Copyright Potato 2019.
Brody and four of his friends purchased tickets to a movie. The total was $32. How much did each person spend on their ticket? Use the equation 5x = 32 to solve.
x = $6.00
x = $6.40
x = $27.00
x = $160.00
If f(x) = 2x – 1 and g(x) = – 2, find [g ◦ f](x).
Answer:
[tex][g\circ f](x)=-2[/tex]
Step-by-step explanation:
By the definition
[tex][g\circ f](x)=g(f(x))[/tex]
You are given
[tex]f(x)=2x-1\\ \\g(x)=-2[/tex]
So,
[tex][g\circ f](x)=g(f(x))=g(2x-1)=-2[/tex]
Assume that the probability of a driver getting into an accident is 7.6%, the average cost of an accident is $16,412.05, and the overhead cost for an e company per insured driver is $105. What should be this drivers insurance premium?
Answer:
1,352.32
Step-by-step explanation:
If you take 7.6 and multiply it to 16,412.05 (.076)(16,412.05), you get 1,247.32. You then add the overhead cost of 105 to get 1352.32. (Apex verified too)
The drivers insurance premium is:
$ 1352.3158
Step-by-step explanation:The probability of a driver getting into an accident is 7.6%.
The average cost of an accident is $16,412.05.
This means that the expected amount that will be paid to each of the driver by the company on accident will be: 0.076×16412.05
= $ 1247.3158
Also, the overhead cost for an e company per insured driver is $105.
This means that the insurance premium of driver is:
= 105+1247.3158
= $ 1352.3158
Which is the equation in slope-intercept form for the line that passes through (-1,5) and is parallel to 3x + 2y = 4?
A. y = 2/3x + 7/2
B. y = -2/3x + 7/2
C. y = 3/2x - 7/2
D. y = -3/2x + 7/2
Answer: -3/2x + 7/2
Step-by-step explanation:
for parallel lines; m₁ = m₂
the gradient of the given line is -3/2
2y= -3x + 4
y = -3/2x + 2
therefore the gradient of the parallel line is -3/2
hence the equation is y-y₁ = m(x-x₁)
y-5 = -3/2(x+1)
y - 5 =-3/2x - 3/2
y = -3/2x -3/2 + 5
y = -3/2x + 7/2
Please help............... :)
Answer:
False
Step-by-step explanation:
Let's list all the odd numbers less than 15.
13, 11, 9, 7, 5, 3, 1
Prime numbers are numbers that can only be multiplied by 1 and themselves. But, we can see, that 9 can be multiplied by 3 and 3, making it a not-prime number (sorry I don't remember the exact name for that, I'm blanking out).
The number 9 makes that statement false.
Hope I helped! ouo.
~Potato.
Copyright Potato 2019.
Answer:
False
Step-by-step explanation:
Consider the odd numbers less than 15
1, 3, 5, 7, 9, 11, 13
A prime number has only 2 factors, namely 1 and itself
9 has factors : 1, 3, 9 ← not Prime
The statement is therefore False
What is the slope of this graph?
Write your answer as a decimal (with one decimal place or as a simplified fraction
Answer:
slope = -0.5
Step-by-step explanation:
Answer:
slope = change in y / change in x
slope = 0 -3.5 / 7 -0
slope = -3.5 / 7
slope = -.5
Step-by-step explanation:
A company launches 4 new products.
The market price, in dollars, of the four products after a different number of years, x, is shown in the following table:
Product 1 | f(x)=3^x |$3 | $9| $27
Product 2 | g(x)= x^2+4| $5 | $8 | $13
Product 3 |h(x)=3x+8| $11| $14| $17
Product 4 | j(x) = x^3| $1 | $8 | $27
Based on the data table, for which product does the price eventually exceed the others?
A. product 1
B. Product 2
C. Product 3
D. Product 4
Answer:
A. product 1
Step-by-step explanation:
An exponential function (with a base larger than 1) will eventually exceed the value of any polynomial function. Product 1 has a price described by an exponential function, so its price will exceed all others. (One only need to compute the values for x=4 to see this.)
_____
The attachment extends the table and plots the functions up to the point where Product 1 exceeds the others.
how do you find the area of a compound figure
Answer: It's easy and simple!
Step-by-step explanation: Split it into rectangles and multiply the height and length. Than add it together and Then you have your answer.
Answer:
It depends on the figure.
Step-by-step explanation:
The compound figures we're generally concerned with are combinations of rectangles, triangles, circles or parts of circles, with or without cutouts of those shapes. The area is the sum of the areas of the component shapes, less the areas of any cutouts.
__
Consider the attached examples:
7) This is half a circle together with two triangles. Or, the two triangles can be considered to be a rectangle with a triangular cutout.
The area is the sum of the areas of the semicircle and the rectangle, less the area of the triangular cutout.
__
8) This can be considered as a square with a square cutout. The area is the difference between the area of the larger square and the area of the smaller one. Alternatively, one can find the area by finding the length of the centerline of the shaded area and multiplying that by the width of the shaded area.
__
9) The area of this figure can be considered to be the total of the area of the bottom rectangle and the top triangle. Alternatively, one can cut the figure into two trapezoids (with a vertical line) and sum their areas.
For a certain font, the scale factor is 1.414 and one of the scale sizes is 1.999. What is the next larger scale size ?
Sorry this is a little late, but I hope it'll still help someone in the near future.
The next larger scale size is 2.827
Hope this helps :)
Answer:
Next larger scale size = 2.827
Step-by-step explanation:
For a certain font scale factor is 1.414 and one of the scale size is 1.999.
so we have to find the next larger scale size.
Since scale factor will be defined as the ratio of larger scale size of the font and smaller font size.
[tex]\text{Scale factor}=\frac{\text{Larger font size}}{\text{smaller font size}}[/tex]
1.414 = [tex]\frac{\text{Larger font size}}{1.999}[/tex]
Larger font size = 1.414 × 1.999 = 2.8266 ≈ 2.827
Next larger scale size = 2.827
What decimal is represented by this expanded form?
2×10,000+7×1,000+4×100+9×1+3×1/10+8×1/1,000
Answer:
27,409.308
Step-by-step explanation:
Compute the given sum. If you're really stuck, your calculator can help you.
Please help me out with this
Answer:
10.4 cm
Step-by-step explanation:
The volume (V) of a pyramid is calculated using
V = [tex]\frac{1}{3}[/tex] area of base × height (h)
area of square base = 6² = 36, thus
[tex]\frac{1}{3}[/tex] × 36h = 120
12h = 120 ( divide both sides by 12 )
h = 10 cm
To find the slant height (s) consider the right triangle from the vertex to the midpoint of the base and from the midpoint of base to the side.
That is a right triangle with hypotenuse s and legs 10(h) and 3 (midpoint of the base )
Using Pythagoras' identity then
s² = 10² + 3² = 100 + 9 = 109
Take the square root of both sides
s = [tex]\sqrt{109}[/tex] ≈ 10.4 cm
One hundred football players were asked how many broken bones they have suffered. The probability distribution shows the probability of the number of bones broken by a football player.
What is the probability that a football player has suffered more than 3 broken bones?
Enter your answer, as a decimal, in the box.
Answer:
0.25
Step-by-step explanation:
The probability that a football player has suffered more than 3 broken bones is equal to the probability they suffered 4 or 5.
P(x>3) = P(4 or 5)
P(x>3) = P(4) + P(5)
P(x>3) = 0.10 + 0.15
P(x>3) = 0.25
Triangle DEF is congruent to D'EF' by the SSS theorem. Which single rigid transformation is required to map DEF onto D'EF'? dilation reflection rotation translation
Answer: rotation
Step-by-step explanation:
Rotation is required to map DEF onto D'EF'
What is Rotation?Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.
Rotation exists as the operation or act of turning or circling something.
Rotation exists in the circular movement of an object around an axis of rotation. A three-dimensional object may include an infinite numeral of rotation axes.
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Please please help me
Answer:
(a + b, c )
Step-by-step explanation:
Using the midpoint formula
given 2 points (x₁, y₁ ) and (x₂, y₂ ) then midpoint is
[ [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] ]
let (x₁, y₁ ) = P(0, 0) and (x₂, y₂ ) = R(2a+2b, 2c), then
midpoint = [ [tex]\frac{0+2a+2b}{2}[/tex], [tex]\frac{2c}{2}[/tex] ]
= [tex]\frac{2(a+b)}{2}[/tex], c ] = (a + b, c )
Use the addition-subtraction method to solve each of the following systems of equations.
1. 4x + 3y = 17 and 5x – 3y = 1
2. –5m + 6n = –8 and –5m + 8n = 6
3. 2x – 7y = –9 and 6x + 7y = 57
4. 5p – 4q = 3 and –5p – 4q = 13
5. 6c + d = 12 and c – d = 2
The best answer will receive Brainliest .
Answer:
1. x=2, y=3
2. n=7, m=-6.8
3. x=6, y=3
4. q=-2, p=-1
5. c=2, d=0
Step-by-step explanation:
4x + 3y = 17
5x – 3y = 1
first make it so either x or y can cancel out in both equations, then combine the equations, giving you 9x=18. solve for x, x=2. substitute 2 for x in either equation, 4(2) + 3y = 17. solve for y, 8+3y=17, 3y=9, y=3
–5m + 6n = –8
–5m + 8n = 6
first make it so either m or n can cancel out in both equations, multiply –5m + 6n = –8 by -1, 5m - 6n = 8, then combine the equations, giving you 2n=14. solve for n, n=7. substitute 7 for n in either equation, 5m - 6(7) = 8. solve for m, 5m - 42 = 8, 5m = -34, m = -6.8
2x – 7y = –9
6x + 7y = 57
first make it so either x or y can cancel out in both equations, then combine the equations, giving you 8x=48. solve for x, x=6. substitute 6 for x in either equation, 2(6) – 7y = –9. solve for y, 12 – 7y = –9, –7y = –21, y = 3
5p – 4q = 3
–5p – 4q = 13
first make it so either p or q can cancel out in both equations, then combine the equations, giving you -8q=16. solve for q, q=-2. substitute -2 for q in either equation, 5p – 4(-2) = 3. solve for p, 5p + 8 = 3, 5p = -5, p = -1
6c + d = 12
c – d = 2
first make it so either c or d can cancel out in both equations, then combine the equations, giving you 7c=14. solve for c, c=2. substitute 2 for c in either equation, 6(2) + d = 12. solve for d, 12 + d = 12, d = 0
[EDIT] question 2 is impossible.
12. (07.06 LC) A library building is in the shape of a rectangle. Its floor has a length of (3x + 5) meters and a width of (5x − 1) meters. The expression below represents the area of the floor of the building in square meters: (3x + 5)(5x − 1) Which of the following simplified expressions represents the area of the floor of the library building in square meters? (5 points) 28x − 5 15x2 − 5 15x2 + 28x − 5 15x2 + 22x − 5
ANSWER
[tex]15 {x}^{2} + 22x - 5[/tex]
EXPLANATION
It was given that, the length of the rectangular building is
[tex](3x + 5) \: meters[/tex]
and the width of the is
[tex](5x - 1) \: meters[/tex]
The area of a rectangular building is calculated using the formula for finding the area of a rectangle.
[tex]A = l \times w[/tex]
Since the dimensions are given in terms of x, the area is also a function of x,
[tex]A(x) = (3x +5 )(5x - 1)[/tex]
We expand to get,
[tex]A(x) = 3x(5x - 1) + 5(5x - 1)[/tex]
[tex]A(x) = 15 {x}^{2} - 3x + 25x - 5[/tex]
[tex]A(x) = 15 {x}^{2} + 22x - 5[/tex]
meters square
Answer:
D. 15x^2 + 22x -5
Step-by-step explanation:
I just took the test