Which of the following is FALSE? The diagonals of a parallelogram bisect each other. The diagonals of a rhombus bisect each other. The diagonals of a square bisect each other. The diagonals of a kite bisect each other
Answers
Answer:
The diagonals of a kite bisect each other
Step-by-step explanation:
Let analyse all possible answer:
a. The diagonals of a parallelogram bisect each other
True, it is one of the properties of a parallelogram
b. The diagonals of a rhombus bisect each other
True, In any rhombus, the diagonals (lines linking opposite corners) bisect each other at right angles (90°). That is, each diagonal cuts the other into two equal parts, and the angle where they cross is always 90 degrees.
c. The diagonals of a square bisect each other.
True, it is one of the properties of a square
d. The diagonals of a kite bisect each other
Wrong, because we do not know what shape of the kite is, it can have a really strange shape that we can not identify where the diagonals are as you can see in the attached photo.
Related Questions
A chi-square test involves a comparison between what is observed and what would be expected by _______.
Answers
A survey asked 30 people what their favorite genre of television broadcasting was, and the results were tabulated above. Find the probability that a person chosen at random was female, given that they like comedy. Round the answer to the nearest hundredth.
Answers
The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .
First, let's find the total number of females who like comedy. In the Venn diagram, there are 8 females who like comedy. There are also 7 males who like comedy. So, there are 15 people who like comedy in total.
Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.
Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."
P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)
P(A|B) = 8 / 15
To express this as a percentage, multiply by 100:
P(A|B) * 100 ≈ 0.5333
Rounded to the nearest hundredth, the probability is 0.53 or 53%.
The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .
First, let's find the total number of females who like comedy. In the Venn diagram, there are 8 females who like comedy. There are also 7 males who like comedy. So, there are 15 people who like comedy in total.
Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.
Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."
P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)
P(A|B) = 8 / 15
To express this as a percentage, multiply by 100:
P(A|B) * 100 ≈ 0.5333
Rounded to the nearest hundredth, the probability is 0.53 or 53%.
The area of a certain rectangle is 288 yd2. the perimeter is 68 yd. what are the dimensions of the rectangle?
Answers
P = 68
68 = 2(L + W)
68/2 = L + W
34 = L + W
34 - L = W
A = L * W
A = 288
W = 34 - L
288 = L(34 - L)
288 = 34L - L^2
L^2 - 34L + 288 = 0
(L - 16)(L - 18)
L - 16 = 0
L = 16
L - 18 = 0
L = 18
not exactly sure which (length or width) , but one is 16 yds and one is 18 yds
The dimensions of the rectangle are a length of 16 yds and a width of 18 yds.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
Given that the perimeter is 68 yd
We know that the perimeter of a rectangle is:
P = 2(L + W)
∴ P = 68
68 = 2(L + W)
68/2 = L + W
34 = L + W
34 - L = W ....(i)
The area of a rectangle is:
A = L × W ....(ii)
∴ A = 288
Substitute the value W = 34 - L in equation (ii), and solve for L
288 = L(34 - L)
288 = 34L - L²
L² - 34L + 288 = 0
(L - 16)(L - 18)
L - 16 = 0 and L - 18 = 0
L = 16 and L = 18
Take L = 16 and substitute the value in the equation (i)
So, W = 34 - 16 = 18
Therefore, the rectangle's length is 16 yds and its width is 18 yds.
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Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $100. Show your work.
Answers
Profit = Revenue - (Fixed Cost + Variable Cost)
You should note that the limit for profit is at least $100. So that means it can be more than $100 but can't be less than. Therefore, the symbol to be used is greater than or equal to, symbolized by ≥. Then the equation is
12x - (20 + 8x) ≥ 100, where x represents the minimum number of t-shirts to reach a profit of at least $100. Solving the equation,
12x - 20 - 8x ≥ 100
12x - 8x ≥ 100 + 20
4x ≥ 120
x ≥30
Therefore, the club needs to sell at least 30 shirts.
Generally, how would one work out the surface area of a frustum?
Answers
see the formula in the picture
R is larger diameter, r is smaller diameter
The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle?
Answers
multiply 4 by the cos(45)
4 x cos(45) = 2sqrt(2) approximately 2.828cm
so depending how you are supposed to answer, either 2 sqrt(2) or approximately 2.83 cm
I am confused about this question in trigonometry:
Answers
use AE and CE to find the angle
AE = 20, CE = 6
so the angle FOR CAE = tan^-1(6/20) = 16.7 degrees
to Find DF
a^2 = b^2 +c^2-2abcos(A)
a^2 = 10^2 + 14^2 -2(14)(10)cos(16.7)
a^2 = 30
sqrt((30)=5.47 rounded to 5.5
EF =
a^2 = b^2 +c^2-2abcos(A)
a^2 = 20^2 + 14^2 -2(14)(20)cos(16.7)
a^2 = 64
sqrt(64)=8
Where does the normal line to the parabola, given below, at the given point, intersect the parabola a second time? illustrate with a sketch. (round the answers to three decimal places.) y = 4 x - 2 x^ 2 p = (2, 0)?
Answers
y' = 4 - 4x = 4-4(2) = -4
Thus, the slope of the normal line is 1/4 (negative reciprocal of -4). Its equation would be y = 1/4 x + b. To find b (y-intercept), substitute the coordinates of point (2,0):
0 = 1/4 (2) + b
b = -0.5
Therefore, the equation of the normal line is y = 1/4 x - 0.5. This is illustrated as the orange line in the picture.
It doesn't matter which of the two points on a line you choose to call (x1, y1) and which you choose to call (x2, y2) to calculate the slope of the line.
A. True
B. False
Answers
A. True
EXPLANATION
Let
[tex](x_1,y_1) = (1,2)[/tex]
and
[tex](x_2,y_2) = (2,3)[/tex]
be two points on the straight line.
Then the slope is given by
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
This implies that,
[tex]m = \frac{3 - 2}{2 - 1} = \frac{1}{1} = 1[/tex]
Let us now choose it the other way round,
[tex](x_1,y_1) = (2,3)[/tex]
[tex](x_2,y_2) = (1,2)[/tex]
Then the slope is,
[tex]m = \frac{2 - 3}{1 - 2} = \frac{ - 1}{ - 1} = 1[/tex]
We still had they same result. Hence it doesn't matter which one you choose to call
[tex](x_1,y_1)[/tex]
and which to call
[tex](x_2,y_2) [/tex]
Answer:
the answer is true
Step-by-step explanation:
it's what I got
A number is chosen at random from the integers between 11 and 99, inclusive. what is the probability that the number contains the digit 2?
Answers
The volumes of two similar figures 27mm^3 and 1331mm^3. If the surface area of the smaller figure is 18mm^2, what is the surface area of the larger figure
Answers
[tex]\bf \cfrac{small}{large}\qquad \cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\qquad thus\qquad \cfrac{\sqrt[3]{27}}{\sqrt[3]{1331}}=\cfrac{\sqrt{18}}{\sqrt{a}} \\\\\\ \cfrac{3}{11}=\sqrt{\cfrac{18}{a}}\implies \left( \cfrac{3}{11} \right)^2=\cfrac{18}{a}\implies \cfrac{3^2}{11^2}=\cfrac{18}{a}\implies a=\cfrac{11^2\cdot 18}{3^2}[/tex]
and surely, you know how much that is.
PLEASE HELP!!!! Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work.
x = _____ or _____
Answers
16x^2+24x+9=81+36x+4x^2 subtract the right side from both sides
12x^2-12x-72=0 now we can factor
12(x^2-x-6)=0
12(x^2+2x-3x-6)=0
12(x(x+2)-3(x+2)=0
12(x-3)(x+2)
So:
x= -2 or 3
Answer:
-3
Step-by-step explanation:
Suppose you toss a coin 100 times and get 76 heads and 24 tails. based on these results, what is the probability that the next flip results in a head?
Answers
The probability that the next flip results in a head is 50% or 0.5.
We have,
Total number of coins tossed = 100
Number of heads outcome = 76
Number of tails outcome = 24
Now,
The probability of getting heads in the tossing of coins 100 times.
= 76/100
= 0.76
= 76%
Now,
Generally for an unbiased coin.
The probability of getting a head in tossing a coin is 50%.
So,
Based on the results of the first 100 coin tosses, even if the probability of getting a head is 76% the probability that the next flip results in a head is still 50%.
Thus,
The probability that the next flip results in a head is 50% or 0.5.
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Can you check my work please!! And don't joke about it! Thanks
Answers
2. 44
3. 50
4. 86
5. 44
6. 50
7. 130
8. 50
9. 130
10. 50
11. 86
12. 94
13. 86
14. 94
Remember that the triangle's inner angles should equal 180 for angle 8 and that angles that form a straight line add to 180 as well.
If you would like an explanation for any of these, please comment down below.
A country population in 1991 was 231 million in 1999 it was 233 million . Estimate the population in 2003 using the exponential growth formula. Round you answer to the nearest million
Answers
233=231r^(1999-1991)
(233/231)^(1/8)=r
p(y)=231(233/231)^((y-1991)/8) so in 2003
p(2003)=231(233/231)^((2003-1991)/8)
p(2003)=231(233/231)^(1.5)
p(2003)=234
So 234 million (to the nearest million people)
Answer:
population in 2003 is 234 million.
Step-by-step explanation:
A country's population in 1991 was 231 million
In 1999 it was 233 million.
We have to calculate the population in 2003.
Since population growth is always represented by exponential function.
It is represented by [tex]P(t)=P_{0}e^{kt}[/tex]
Here t is time in years, k is the growth constant, and is initial population.
For year 1991 ⇒
233 = [tex]P_{0}e^{8k}[/tex] = 231 [tex]e^{8k}[/tex]
[tex]\frac{231}{233}= e^{8k}[/tex]
Taking ln on both the sides ⇒
[tex]ln(\frac{233}{231})=lne^{8k}[/tex]
ln 233 - ln 231 = 8k [since ln e = 1 ]
5.451 - 5.4424 = 8k
k = [tex]\frac{0.0086}{8}=0.001075[/tex]
For year 2003 ⇒
[tex]P(t)=P_{0}e^{kt}[/tex]
P (t) = 231 × [tex]e^{(0.001075)(12)}[/tex]
= 231 × [tex]e^{0.0129}[/tex]
= 231 × 1.0129
= 233.9 ≈ 234 million
Therefore, population in 2003 is 234 million.
Solve △ABC if B=120°, a=10, c=18
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write the square root of 23 in exponential form
Answers
so
[tex]\sqrt{23}=\sqrt[2]{23^1}=23^\frac{1}{2}[/tex]
parallel lines r and s are cut by two transversals, parallel lines t and u
Answers
i believe it is b
What is the vertex of the graph of y + 2x + 3 = –(x + 2)2 + 1?
Answers
[tex]y+2x+3=-(x+2)(x+2)+1[/tex] and
[tex]y+2x+3=- x^{2} -4x-4+1[/tex]
We are going to combine all the like terms now and get them all on one side of the equation:
[tex]- x^{2} -6x-6=y[/tex]
Now we are going to complete the square on the polynomial in order to find the vertex. Do this by first setting the equation equal to 0 and then moving the constant over to the other side of the equals sign, like this:
[tex]- x^{2} -6x=6[/tex] and now factor out the negative sign (cuz negative signs are a pain):
[tex]-( x^{2} +6x)=6[/tex]. To complete the square, you take half the linear term, square it, and add it in to both sides. Our linear term is 6x. Half of 6 is 3, and 3 squared is 9. That's easy to add in on the left side, but we cannot forget that fact that we factored out a negative 1, and that the negative 1 is still there and has to be taken into consideration when we "add" in a 9 to the other side. We actually multiply the negative 1 times the 9 and that's what's added in to the right:
[tex]-( x^{2} +6x+9)=6-9[/tex]
What you do when you complete the square is create a perfect square binomial on the left, which we have and which looks like this:
[tex]-(x+3) ^{2} = -3[/tex]
When we move the 3 back over to be with its mates (the 3 is the y coordinate for the vertex), we have the actual sign of the y coordinate. The number inside the parenthesis with the x is the x coordiante of the vertex in the form [tex](x-h) ^{2} [/tex]. So the vertex of your problem is (-3, 3). The negative outside the parenthesis just indicates to us that the parabola is an upside down one, like a mountain instead of a valley.
17. Evaluate. Show your work.
a. 6!
b. 6P5
c. 12C3
Answers
A researcher wishes to find out whether giving a student $1 million in cash will improve or ruin the student's grades in school. A high school class consists of the 8 students numbered in the following list. 0 Juanita 1 Tuan 2 Harry 3 Greta 4 William 5 Hiroshi 6 Betty 7 Jane Help the researcher by using the line from a table of random numbers (shown below) to assign 4 of these students to the treatment group. 39661 55832 02589 52612 25414 19879 60880 30641 55259 35324 Which students go in the treatment group?
Answers
Answer:
Greta, Betty, Tuan and Hiroshi
Step-by-step explanation:
Start from the beginning:
3 - Greta
Then, continue with the next numbers:
9 - skip (there is no student numbered with a 9)
6 - Betty
6 - skip (Betty is already chosen)
1 - Tuan
5 - Hiroshi
In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials? a. 0.0554
Answers
For two successes in seven binomial trials with a success probability of 0.06, use the binomial probability formula. Calculate (7 choose 2) * (0.06^2) * (0.94^5) to get the probability of 0.0554.
Explanation:To calculate the probability of two successes in seven trials with a success probability of 0.06, you can use the binomial probability formula, which is P(X = k) = (n choose k) * p^k * q^(n-k), where 'n' is the number of trials (7), 'k' is the number of successes (2), 'p' is the probability of success (0.06), and 'q' is the probability of failure (q = 1 - p = 0.94).
First, calculate the binomial coefficient using 'n choose k', which is (7 choose 2). Then, raise the probability of success to the power of the number of successes (0.06^2) and the probability of failure to the power of the number of failures (0.94^5). Lastly, multiply these values together to get the probability.
The calculation is as follows:
(7 choose 2) * (0.06^2) * (0.94^5) = 21 * 0.0036 * 0.7339 = 0.0554
What is the slope of the line shown below?
Answers
Answer:
correct option is B) 2
Step-by-step explanation:
Slope of line is calculated by formula :-
Suppose two points on line are [tex](x_1, y_1) and (x_2 ,y_2)[/tex] then slope 'm' is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
We can see two points on line of graph are :- (-1, -4) and (2,2)
then slope will be calculated as,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
since [tex]x_1 = -1, x_2 =2, y_1=-4\;and\; y_2=2[/tex]
now, put in formula
[tex]m=\frac{2-(-4)}{2-(-1)}[/tex]
[tex]m=\frac{2+4}{2+1}[/tex]
[tex]m=\frac{6}{3}[/tex]
[tex]m=2[/tex]
Hence, slope is 2 of the provided graph.
Therefore, correct option is B) 2
1 oz of walnuts were mixed with 4 oz of peanuts which cost $4/oz to make mixed nuts which cost $5/oz. what is the price per oz of walnuts
Answers
total cost of walnuts = 1oz * w
Total cost of peanuts = 4 oz * $4/oz = $16
Total cost of nuts = 5oz * $5 /oz = $25
=> 1oz*w + $16 = $25 => w = ($25 - $16) /1oz = $9/oz
Verfify:
1oz * $9/oz + 4oz * $4/oz = $9 + $16 = $25, which is equal to 5oz * $5/oz.
Answer: $9 per oz.
Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2
***PLEASE HELP**
Answers
[tex]a_{n+1}=-4a_{n+2}[/tex] and [tex]a_1=2[/tex]
For n = 0,
[tex]a_1=-4a_2 \\ \\ 2=-4a_2 \\ \\ \Rightarrow a_2=-\frac{1}{2}[/tex]
common ratio = [tex]\frac{a_2}{a_1}=\frac{-\frac{1}{2}}{2}=-\frac{1}{4}[/tex]
4th term = [tex]a_4=a_1r^{4-1}=2(-\frac{1}{4})^3=2(-\frac{1}{64})=-\frac{1}{32}[/tex]
Branliest and 30 points to who answers first
To make one dose chispa put 2 drops of a herbal remedy into a 30 ml bottle and adds spring water he has now used 54 drops of the 120 that the full bottle contained how many more times can chispa use his herbal remedy
Answers
What is the area for this problem?
Answers
C = 2* pi *r = 36 pi
r = 36pi/2pi = 18
We know that A= r^2 * pi
A = 18^2 * pi = 324 pi
the area would be 324PI square units
Has 320 yards of fencing to enclose a rectangular area. find the dimensions of the rectangle that maximize the enclosed area. what is the maximum area
Answers
The dimensions of the rectangle that maximize the enclosed area are L = 80 yards and W = 80 yards. The maximum area is A = 80 * 80 = 6400 square yards.
To find the dimensions of the rectangle that maximize the enclosed area using 320 yards of fencing, we'll use the concept of optimization. Let's solve it step by step:
Let's assume the length of the rectangle is L and the width is W.
Perimeter constraint:
The perimeter of the rectangle is given as 2L + 2W, which must equal 320 yards:
2L + 2W = 320
Simplify the perimeter equation:
Divide both sides by 2 to get:
L + W = 160
Express one variable in terms of the other:
Solve the equation for L:
L = 160 - W
Area equation:
The area of the rectangle is given by A = L * W.
Substitute the value of L from the previous step into the area equation:
A = (160 - W) * W
A = 160W - W^2
Maximize the area:
To find the maximum area, we need to maximize the function A = 160W - W^2. This is achieved when the derivative is zero.
Take the derivative of A with respect to W:
dA/dW = 160 - 2W
Set dA/dW = 0 and solve for W:
160 - 2W = 0
2W = 160
W = 80
Substitute the value of W back into the perimeter equation to find the corresponding value of L:
L = 160 - W = 160 - 80 = 80
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The optimization problem involves finding the dimensions of a rectangle to maximize its area using a fixed amount of fencing. The dimensions that maximize the area are both 80 yards, making the maximum area 6400 square yards.
Explanation:The subject of this question is Mathematics, specifically a problem about optimization in the field of Calculus. In the given problem, we wish to find a rectangular area that can be enclosed by 320 yards of fencing that maximizes the area.
Let's designate the rectangular area's width and length as x and y respectively. The problem can now be rephrased. With the total length of fencing equal to 320 yards, you can express this as 2x + 2y = 320. Simplifying this equation, we get x + y = 160, or y = 160 - x.
The area of a rectangle is computed as width times length, or in this case, x(160 - x). This is a quadratic function, and its maximum value happens at the vertex of the parabola defined by this function. For a quadratic in standard form like y = ax^2 + bx + c, the x-coordinate of the vertex is at -b/2a. In this case, the maximum area happens when x = 160/2 = 80.
Substituting this value back into the equation for the rectangle's dimensions gives y = 160 - 80 = 80. So, the dimensions that maximize the area for a rectangle with a parameter of 320 yards are both 80 yards. Therefore, the maximum area possible is 80*80 = 6400 square yards.
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Write the total population of india and china.estimate the total population by rounding off each population to nearest 100000
Answers
As of Thursday, August 17, 2017, based from the data of the latest United Nations estimates, the current population of China is 1,388,979,446.
China’s population is equivalent to 18.47% of the total world population.
18.47% of
the total world population is composed by China’s population.
China is ranked number 1 in the list of countries by population.
Rounding that number off to the nearest 100,000, it would be 1,388,980,000.
As of Thursday, August 17, 2017, based from the data of the latest United Nations estimates, the current population of India is 1,344,431,890.
17.86% of the total world population is composed by India’s population.
India is ranked number 2 in the list of countries by population.
Rounding that number off to the nearest 100,000, it would be 1,344,400,000.
A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function? graph of function t of x is a curve which joins the ordered pair 0, 1 and 1, 3 and 3, 27. Graph of function p of x is a curve which joins the ordered pair 0, 2 and 1, 3 and 3, 11 and 5, 27 and 6, 38
Answers
Quadratic equation: y = 2x²+5
Exponential equation: y = 2³ˣ
If you would test it quantitatively the rate of change, or the slope, between points is greater for exponential than quadratic equations. Because a slight increase in x, will cause an exponential rise, To you observe visually if the slope is greater if the curve is closer to a vertical line. From the picture, we can see that the blue curve has a greater slope. Therefore, the exponential function is t(x).
Final answer:
The function t(x) with ordered pairs (0, 1), (1, 3), and (3, 27) most likely represents the exponential function because it shows rapidly increasing growth rates, which is a defining feature of exponential behavior.
Explanation:
The function that most likely represents the exponential function is the one whose growth rate increases significantly for larger values of x. Examining the ordered pairs, the function t(x), which passes through the points (0, 1), (1, 3), and (3, 27), clearly demonstrates this behavior as the increase between the y-values gets dramatically larger as x increases.
This is a classic characteristic of exponential growth. In contrast, the function p(x) that passes through (0, 2), (1, 3), (3, 11), (5, 27), and (6, 38) shows a more consistent increase in y-values as x increases, indicative of a quadratic function.