Reading and similar triangles
In the diagram below of MADE, B is a point on AE and C
is a point on AD such that BC is parallel to ED. AC = x - 5,
AB = 15, BE = 40,, and AD = 2x + 3. Find the value of x
and the length of CD
A
Answers
Answer:
x = 12.8CD = 20.8Step-by-step explanation:
The parallel lines create similar triangles, so corresponding sides are proportional.
AC/AD = AB/AE
(x -5)/(2x +3) = 15/(15+40)
Cross-multiplying gives ...
55(x -5) = 15(2x +3)
55x -275 = 30x +45 . . . . eliminate parentheses
25x = 320 . . . . . . . . . . . . add 275-30x
x = 12.8 . . . . . . . . . . . . . . .divide by 25
__
CD = AD -AC = (2x +3) -(x -5) = x +8 = 12.8 +8
CD = 20.8
Related Questions
multiply -x^2(x^2+5x-8)
Answers
Answer:
[tex]-x^4-5x^3+8x^2[/tex]
Step-by-step explanation:
[tex]\left(-x^2\right)x^2+\left(-x^2\right)\cdot \:5x+\left(-x^2\right)\left(-8\right)\\-x^2x^2-5x^2x+8x^2\\-x^4-5x^3+8x^2[/tex]
Answer: −x4−5x3+8x2
Step-by-step explanation:
Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random sample and use a 5 % significance level. Test H0 : p = 0.5 vs Ha : p > 0.5 using the sample results p= 0.64 with n = 75. Round your answer for the test statistic to two decimal places, and your answer for the p-value to three decimal places.
Answers
Answer:
[tex]z=\frac{0.64 -0.5}{\sqrt{\frac{0.5(1-0.5)}{75}}}=2.43[/tex]
Now we can calculate the p value with the following probability:
[tex]p_v =P(z>2.43)=0.0075 \approx 0.008[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5
Step-by-step explanation:
Data given and notation
n=75 represent the random sample taken
[tex]\hat p=0.64[/tex] estimated proportion of interest
[tex]p_o=0.5[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the true proportion is higher than 0.5:
Null hypothesis:[tex]p =0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.64 -0.5}{\sqrt{\frac{0.5(1-0.5)}{75}}}=2.43[/tex]
Now we can calculate the p value with the following probability:
[tex]p_v =P(z>2.43)=0.0075 \approx 0.008[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5
Testing the hypothesis, it is found that:
The test statistic is z = 2.42.The p-value is of 0.008.Since the p-value of the test is 0.008 < 0.05, there is significant evidence to conclude that the proportion is greater than 0.5.The null hypothesis is:
[tex]H_0: p = 0.5[/tex]
The alternative hypothesis is:
[tex]H_0: p > 0.5[/tex].
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are: [tex]\overline{p} = 0.64, p = 0.5, n = 75[/tex].
The value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.64 - 0.5}{\sqrt{\frac{0.5(0.5)}{75}}}[/tex]
[tex]z = 2.42[/tex]
The p-value is the probability of finding a sample proportion above 0.64, which is 1 subtracted by the p-value of z = 2.42.
Looking at the z-table, z = 2.42 has a p-value of 0.992.
1 - 0.992 = 0.008, hence, the p-value is of 0.008.
Since the p-value of the test is 0.008 < 0.05, there is significant evidence to conclude that the proportion is greater than 0.5.
A similar problem is given at https://brainly.com/question/15350925
In the right hexagonal pyramid below. The hexagonal base is regular and has sides that are 8 units long. The altitude of the pyramid is 18 units. Determine the volume of the pyramid to the nearest cubic unit.
Answers
Answer:
The volume is 997.62 cubic units..
Step-by-step explanation:
We are given the following details:
The pyramid has a regular hexagonal base i.e. each side of hexagon is equal.
Side of hexagonal base, a = 8 units
Altitude of pyramid, h = 18 units
We have to find the volume of pyramid.
Formula:
[tex]V = \dfrac{1}{3} \times B \times h[/tex]
Where, B is the area of base of pyramid.
h is the height/altitude of pyramid
To calculate B:
Here, base is a hexagon with side 8 units.
[tex]\text{Area of hexagon, B }= 6 \times \dfrac{\sqrt{3}}{4}a^{2}[/tex]
Here, a = 8 units
[tex]\Rightarrow B = 6 \times \dfrac{\sqrt{3}}{4}\times 8^{2}\\\Rightarrow B = 166.27\text{ square units}[/tex]
Putting values of B and h in Formula of volume:
[tex]\Rightarrow V = \dfrac{1}{3} \times 166.27 \times 18\\\Rightarrow V = \dfrac{2992.89}{3} = 997.62\text{ cubic units}[/tex]
Hence, the volume is 997.62 cubic units.
Help please. Will put brainliest
Answers
Answer:
ok
Step-by-step explanation:
For two years, two samples of fish were taken from a pond. Each year, the second sample was taken six months after the first sample.
Table:2 tables. A 3-column table with 4 rows. Column 1 is labeled Year 1 with entries trout, catfish, bass, all fish. Column 2 is labeled Sample 1 with entries 3, 9, 8, 20. Column 3 is labeled Sample 2 with entries 5, 9, 6, 20. The second table is a 3-column table with 4 rows. Column 1 is labeled Year 1 with entries trout, catfish, bass, all fish. Column 2 is labeled Sample 1 with entries 8, 10, 2, 20. Column 3 is labeled Sample 2 with entries 10, 9, 1, 20.
Question:Make an inference about which fish increased its predicted average population from Year 1 to Year 2.
A.All three types of fish increased their predicted average population.
B.Trout increased its predicted average population.
C.Bass increased its predicted average population.
D.None of the fish increased their predicted average population.
Answers
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Trout increased its predicted average population.
Dan drives 140 miles on Monday and 125 km on Tuesday. How many km did he drive in total?
Answers
Answer:
365.308 km
Explanation:
If you convert 140 miles into kilometers you get 225.308 km. Then you just have to add 140 and 225.308 together to get your answer. Hope this helped.
What’s the correct answer for this?
Answers
Answer:
[tex]\mathrm{Circle\:with\:center\:at}\:\left(13,\:1\right)\:\mathrm{and\:radius}\:r=2[/tex]
Step-by-step explanation:
[tex]\left(x-13\right)^2+\left(y-1\right)^2=4\\Circle\:Equation\\\left(x-a\right)^2+\left(y-b\right)^2=r^2\:\:\mathrm{is\:the\:circle\:equation\:with\:a\:radius\:r,\:centered\:at}\:\left(a,\:b\right)\\\mathrm{Rewrite}\:\left(x-13\right)^2+\left(y-1\right)^2=4\:\mathrm{in\:the\:form\:of\:the\:standard\:circle\:equation}\\\left(x-13\right)^2+\left(y-1\right)^2=2^2\\Therefore\:the\:circle\:properties\:are:\\\left(a,\:b\right)=\left(13,\:1\right),\:r=2[/tex]
a cylinder has a volume of (x+5) (x^2+10x+25)pi and a diameter of 2x+10. Find the height. PLEASE HELP
Answers
Answer:
Height = (x² + 10x + 25)
Step-by-step explanation:
We are given;
volume of cylinder; v = (x+5)•(x² + 10x + 25)π
Diameter = 2x + 10
So radius;r = diameter/2 = (2x + 10)/2 = x + 5
Now,formula for volume of cylinder is;
V = πr²h
Where r is radius and h is height
Plugging in the relevant values, we have;
(x+5)•(x² + 10x + 25)π = π(x + 5)*h
Dividing both sides by π(x + 5) gives us;
h = (x² + 10x + 25)
What is the midpoint of the segment shown below? (-2,4) (6,-4)
Answers
Answer:
(2,0)
Step-by-step explanation:
To find the midpoints of two points in the format (x,y), we find the mean for the values of x and y.
In this question:
(-2,4) and (6,-4)
Mean for the values of x:
(-2 + 6)/2 = 2
Mean for the values of y:
(4-4)/2 = 0
Midpoint:
(2,0)
1 pts
Question 5
The size of gasoline tanks in cars is normally distributed with a mean size of 24.8 gallons and a standard
deviation of 6.2 gallons. What percent of tanks are less than 31 gallons. Round answer to the nearest
percent
84%
71%
16%
20%
Answers
Answer:
[tex]P(X<31)=P(\frac{X-\mu}{\sigma}<\frac{31-\mu}{\sigma})=P(Z<\frac{31-24.8}{6.2})=P(z<1)[/tex]
And we can find this probability using the normal standard distribution or excel and we got:
[tex]P(z<1)= 0.84[/tex]
And if we convert this into % we got 84% so then the best solution would be:
84%
Step-by-step explanation:
Let X the random variable that represent the size of gasoline tanks of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(24.8,6.2)[/tex]
Where [tex]\mu=24.8[/tex] and [tex]\sigma=6.2[/tex]
We are interested on this probability
[tex]P(X<31)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the last formula we got:
[tex]P(X<31)=P(\frac{X-\mu}{\sigma}<\frac{31-\mu}{\sigma})=P(Z<\frac{31-24.8}{6.2})=P(z<1)[/tex]
And we can find this probability using the normal standard distribution or excel and we got:
[tex]P(z<1)= 0.84[/tex]
And if we convert this into % we got 84% so then the best solution would be:
84%
Solve this equation: -72 + 12 - 2.x = 23 + 13.2
Answers
Answer:
x =-48.1
Step-by-step explanation:
-72 + 12 - 2.x = 23 + 13.2
Combine like terms
-60 -2x = 36.2
Add 60 to each side
-2x -60+60 = 36.2+60
-2x = 96.2
divide by -2
-2x/-2 = 96.2/-2
x =-48.1
Answer:
[tex] = - 48.1[/tex]
Step-by-step explanation:
[tex] - 72 + 12 - 2x = 23 + 13.2 \\ - 2x = + 72 - 12 + 23 + 13.2 \\ - 2x = 96.2 \\ \frac{ - 2x}{ - 2} = \frac{96.2}{ - 2} \\ x = - 48.1[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Rewrite the equation by completing the square x^2+2x-3=0
Answers
Answer:
( x+1)^2 = 4
Step-by-step explanation:
x^2+2x-3=0
Add 3 to each side
x^2 +2x = 3
Take the coefficient of x
2
Divide by 2
2/2 =1
Square it
1^2 =1
Add to each side
x^2 +2x = 3
x^2 + 2x+1 = 3+1
( x+1)^2 = 4
Take the square root of each side
x+1 = ±2
Subtract 1 from each side
x+1-1 = -1 ±2
x = -1+2 x = -1-2
x =1 x = -3
6th grade math help :D....
Answers
The unit price of the first one which is a is 8 cents an ounce. The second one is 9 cents an ounce.
What you do is you take your price and divide it by the ounces.
Question one's answer is 0.08
Question two's answer is 0.09
A wage sheet of a small business shows one employee’s details. The employee is paid $40 an hour for overtime hours where they work more than their usual 26 hours.
Answers
Answer: whats the question tho
Step-by-step explanation:
Answer:whats the question
Step-by-step explanation:
13s = 611 solve for s
Answers
Answer:
s=47
Step-by-step explanation:
s=[tex]\frac{611}{13}[/tex]
s=47
10)
For which value of x is the equation 2(1 + x) = x + 3 true?
A) 1
B) 2
03
D)
4
Answers
Answer:
A) 1
Step-by-step explanation:
2(1+x)= x+3
2(1+1)= 1+3
2×2= 4
4=4
Hence proven
Answer:
A. 1
Step-by-step explanation:
2(1 + x) = x + 3
2 + 2x = x + 3
2x - x = 3 - 2
x = 1
Holly drew the parallelogram below to represent the design of her new garden. A parallelogram with base b and height h. She found that the area of the garden will be 127 and one-half square feet by using the equation Area = b h. If the height, h, of the parallelogram-shaped garden is 8 and one-half feet, what is the base, b, in feet? 1.5 7.5 15 75
Answers
Answer: i just took the quiz it is 15
Step-by-step explanation:
Answer:
The answer is 15
Step-by-step explanation:
She found that the area of the garden will be 127 and one-half square feet by using the equation Area = b h. If the height, h, of the parallelogram-shaped garden is 8 and one-half feet, what is the base, b, in feet? Hmm so it says that base times height equals 127 and one half square feet and the height is 8 and one half feet so you guessed it you have to divided 127 and one half square feet by 8 and one half feet which is 15.
Hope this helped for you understanding how to do this problem have a great day!
What’s the correct answer for this?
Answers
Answer:
centre = (2, - 5) and radius = 4
Step-by-step explanation:
The centre is positioned at (2, - 5 )
The distance from the centre to the circumference, the radius, is 4
a bus drives 66km/h at an average of 24 km/h how long does the journey take?
Answers
Answer:
2 hours and 45 minutes
Step-by-step explanation:
speed=distance/time
given speed=24kmph
distance=66km
time=distance/speed
66/24
What does this mean?
Answers
Answer:
The correct answer is A
Using the numbers shown each line on the graph represents 0.1
R is 2 lines above 33.0, so R would be 33.2
The answer is A.
Which is the equation of a hyperbola centered at the origin with focus 0,4) and vertex (0, square root of 12 )?
Answers
Answer:
The equation of the hyperbola is:
[tex]\frac{x^{2}}{76} - \frac{y^{2}}{12} = 1[/tex]
Step-by-step explanation:
The equation of a hyperbola centered in the origin in standard form is:
[tex]\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} = 1[/tex]
The distance between both vertexes is equal to:
[tex]2\cdot b = \sqrt{(0-0)^{2}+(\sqrt{12}+\sqrt{12})^{2}}[/tex]
[tex]2\cdot b = 2\cdot \sqrt{12}[/tex]
[tex]b = \sqrt{12}[/tex]
Now, the distance between any of the vertexes and origin is:
[tex]c = \sqrt{(0-0)^{2}+[(4-(-4)]^{2}}[/tex]
[tex]c = 8[/tex]
The remaining parameter of the hyperbola is determined by the following Pythagorean expression:
[tex]c^{2} = a^{2} - b^{2}[/tex]
[tex]a = \sqrt{c^{2}+b^{2}}[/tex]
[tex]a = \sqrt{64+12}[/tex]
[tex]a = \sqrt{76}[/tex]
The equation of the hyperbola is:
[tex]\frac{x^{2}}{76} - \frac{y^{2}}{12} = 1[/tex]
Answer:
The equation of the hyperbola is:
x²/76 - y²/12 = 1
Step-by-step explanation:
The standard for of an equation of a hyperbola centered in the origin is given as:
x²/a² - y²/b² = 1
The distance between both vertexes is:
2b, where b = √12
The distance between any of the vertexes and origin is:
c = 8
But a² = b² + c² (Pythagoras rule)
c² = a² - b²
8² = a² - 12
a² = 64 + 12 = 76
a = √76
Therefore, the equation of the hyperbola is:
x²/76 - y²/12 = 1
Given the following expressions: which expression result in an irrational number?
Answers
Answer:
(1) II only
Step-by-step explanation:
[tex]\frac{1}{2} +\sqrt{2} \:is\: the\: only\: irrational\; number\: out\; of\: the\: given\: numbers.[/tex]
The distance between two cities on a map measures 3.75 inches.The scale on the map shows 2 inches is equal to 50 miles.How many miles apart are the two cities
Answers
Answer:93.75 miles
Step-by-step explanation:
Given
Distance between two cities is [tex]3.75\ inches[/tex]
and Map 2 shows 2 inches is equal to [tex]50\ miles[/tex]
So each inch is equal to [tex]25\ miles[/tex]
So [tex]3.75\ in.[/tex] measures
[tex]\Rightarrow =3.75\times 25=93.75\ miles[/tex]
So cities are [tex]93.75\ miles[/tex] apart
find the volume of the cylinder with a diameter of 12 inches and a height of 10
Answers
Answer:
360 pi in ^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
We know the diameter is 12 so the radius is 1/2 the diameter
r = d/2 = 12/2 = 6
V = pi (6)^2 * 10
V = pi (36)*10
V = 360 pi in ^3
We can approximate pi by 3.14
V =1130.4 in ^3
Or we can approximate pi by using the pi button
V =1130.973355 in ^3
If a bus traveled 175 miles in 5 hours, what was the average speed of the bus in miles per hour?
Answers
Answer: 35 miles per hour.
Step-by-step explanation:
Miles per hour is found by dividing miles driven by the time it took to drive said miles.
175 / 5 = 35 miles per hour.
Answer:
35 mph
Step-by-step explanation:
175/5=35
Fill in the missing numbers...
8, 18, 11, 15, 5, 4, 14, 9, 19, 1, 7, 17, 6, 16, ?, ?, ?, ?, ?
Answers
Answer:
10, 13, 3, 12, and 2
Step-by-step explanation:
Peter rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a multiple of 6.
Answers
Answer:
i think it might be 17%
Step-by-step explanation:
if you divide 100 by 10 u get 10 then divide 10 by 6 to get 1.6666666667 round that to one decimal place to get 1.7 then times it by 10 to get 17
Answer:
Answer is 1/6 (fraction answer)
2x + 3 = x -4 what is the solution to this equation
Answers
Step-by-step explanation:
2x + 3 = x-4
2x-x. = -4-3
x= -7
What is the similarity ratio of PQR to VXW?
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
I'll give brainliest if you can answer correctly before midnight!
Answers
The similarity ratio of PQR to VXW is represented as 4 / 1
What are similar triangles?Similar triangles have the same shape but there sizes may vary. In similar triangles, corresponding sides are always in the same ratio.
The corresponding angles are congruent.
Therefore, the similarity ratio can be found as follows:
PQ / VX = PR / VW = QR / XW
Therefore,
8 / 2 = 4 / 1 = 8 / 2
4 / 1 = 4 / 1 = 4 / 1
Therefore, he similarity ratio of PQR to VXW is 4 / 1
learn more on similar triangle here: https://brainly.com/question/12062060
#SPJ2
In the formula for the surface Area of a pyramid, whar do the letters of the formula mean?
Answers
Answer:
The formula for surface area of a pyramid is A=B*P*I
Step-by-step explanation:
Where B= Area of the base
P=Perimeter of the base
I=Slant height.