Answers
[tex]\huge\begin{array}{ccc}BT=21\\DC=10.2\end{array}[/tex]
If BT is the midsegment of ΔMAH and DC is the midsegment of ΔBTH, then MA, BT and DC are parallel.
Therefore the segments form the proportion:
[tex]\dfrac{HM}{MA}=\dfrac{HB}{BT}=\dfrac{HD}{DC}[/tex]
BT is the midsegment of ΔMAH, therefore
[tex]HB=\dfrac{1}{2}HM[/tex]
DC is the midsegment of ΔBTH, therefore
[tex]HD=\dfrac{1}{2}HB=\dfrac{1}{2}\cdot\dfrac{1}{2}HM=\dfrac{1}{4}HM[/tex]
Substitute:[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{2}HM}{BT}[/tex]
cross multiply
[tex]HM\cdot BT=42\cdot\dfrac{1}{2}HM[/tex]
divide both sides by HM
[tex]\boxed{BT=21}[/tex]
[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{4}HM}{DC}[/tex]
cross multiply
[tex]HM\cdot DC=42\cdot\dfrac{1}{4}HM[/tex]
divide both sides by HM
[tex]\boxed{DC=10.5}[/tex]
Related Questions
Simplify the following expressions by adding the like terms: 3a² - 2a - 7 + 3a + 4 - 2a² + 9a x² + 6xy + 5y² - 6xy + 2y² 1 2
Answers
Hope that helps
The football team played 10 games and won 7 games. What was its winning percentage?
Answers
Answer: 70%
Step-by-step explanation:
Percentage is always out of 100. And 10x10 =100 so you do the same to 7 multiply it by ten then your answer is 70 which is 70%.
Determine the total number of Fish food cubes that will fill the shipping box
Answers
I hate to leave you without an answer, but there isn't enough information to be able to answer your problem.
the physical examination records of the freshmen class of 1935 at university of toronto were examined in 1980 to see whether the freshman's record of bmi at the time of admission to the university were related to their chance of developing coronary heart disease in 1980. this is an example of:
Answers
A prospective research of men and women looked at body mass index, waist circumference, and the risk of coronary heart disease.
What is body mass index?Body Mass Index (BMI) is calculated by dividing a person's weight in kilograms (or pounds) by their height in meters squared (or feet). High body fatness may be indicated by a high BMI.BMI does not make a body fat or health diagnosis for a person, but it does screen for weight categories that may cause health issues.Calculate Adult BMI Using This WidgetBy including this widget on your website, anyone can determine their BMI. For the majority of persons, BMI is an accurate indication of body fatness. It is used to check for weight ranges that could cause health issues. The BMI and accompanying weight category are provided by this calculator. Adults who are at least 20 years old should use this calculator.Child and Teen BMI Calculator Widget from the CDCInclude this widget on your webpage. The CDC BMI-for-age growth chart is used to calculate BMI and the related BMI-for-age percentile. From the age of two to nineteen, kids and teenagers can use this calculator.For Schools: The Children's BMI ToolThis spreadsheet can be used by educators, daycare operators, and other experts to calculate BMI forLearn more about bmi here:
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we are exploring the following model for fireflies flashing: a firefly flips a biological equivalent of a coin every second. if it comes up heads (probability of 0.1) it lights up for that second; otherwise it does not. for a given firefly, what is the average number of flashes over a minute? what is the spread (standard deviation) of that number? if we have 1000 fireflies in our field of view, what is the expected number of flashes we will see in 10 seconds? if each flash is .1 lumens and we want 40 lumens at least 70% of the time, how many fireflies do we need? we are monitoring 100 fireflies and determine that the number of flashes per minute per firefly is about 7. is this consistent with our model?
Answers
Given,
The probability of head ups of a firefly = 0.1 = 10%
The average flashes per minute = 10% of 60 seconds = 6 flashes.The average flashes per minute is 6.
If there is 1000 fire flies, number of flashes in 10 seconds.1 firefly 6 flashes per minute = 0.1 flash per second
Then,
1000 × 0.1 = 100 flashes per second
100 × 10 = 1000 flashes per 10 seconds
There will be 1000 flashes per 10 seconds.
How many fireflies are required if each flash produces.1 lumens, and we aim for 40 lumens at least 70% of the time?Each flash = 0.1 lumen
40 lumens = 4 flash
70/100 = 0.7
0.7 x 4 = 2.8 = 3 fireflies.
There is 3 fireflies required to produce 40 lumens
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PLEASE HELP 69 POINTS
Triangle A has vertices (−2, 1), (1, 1), and (1, 0).
Which triangle is similar to triangle A?
Responses
Triangle Y with vertices (−4, 3), (2, 3), and (2, 2)
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)
Triangle X with vertices (−2, 2), (1, 2), and (1, 0)
Triangle Z with vertices (−4, −1), (2, −1), and (2, −2)
Answers
The triangle with vertices (−2, 1), (1, 1), and (1, 0) is similar to
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions.
Examining the vertices shows that; Triangle W with vertices (−4, 2), (2, 2), and (2, 0) is in proportion to the given vertices (−2, 1), (1, 1), and (1, 0)
The difference is a scale factor of 2
(−2, 1) * 2 = (−4, 2)
(1, 1) * 2 = (2, 2)
(1, 0) * 2 = (2, 0)
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How do I find the measure of the triangles? Help.
Answers
Answer:
Step-by-step explanation: I am guessing that it is 180
If 2,000 mL can fit in a certain glass jar, how many liters can fit in 4.5 of these jars?
Answers
Answer: 9,000 mL
Step-by-step explanation:
If you multiply 2,000 by 4, you would get 8,000 & if you multiply .5 by 2,000, you get 1,000. If you add both the totals, you would end up with a final answer of 9,000 mL.
Pls help, due tomorrow!!!!!
Answers
Answer:
try -1 it's easier to get the question answered so it can be turned in
pls help! Last year, 180 new houses were built in a neighborhood. So far this year, 5/6 of them have been sold. How many new houses have been sold this year? Write your answer in simplest form.
Answers
Answer:
150 Houses
Step-by-step explanation:
180/6=30. Every 1/6 is 30 houses. Therefore you multiply 30x5 to get 150. 150 is 5/6 of the houses sold.
the width of bolts of fabric is normally distributed with mean 951 mm (millimeters) and standard deviation 10 mm. (a) what is the probability that a randomly chosen bolt has a width between 942 and 959 mm? (round your answer to four decimal places.) (b)
Answers
The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.
Define probability.The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.
Given,
The width of bolts of fabric is normally distributed with mean 951 mm (millimeters) and standard deviation 10 mm.
Z = X - 951/10 ≈ N(0.1)
P(942 ≤ X ≤ 959)
P(942 - 951/10 ≤ X - 951/10 ≤ 959- 951/10)
P( -0.9 ≤ Z ≤ 0.8)
P(Z ≤ 0.8) - P(Z ≤ -0.9)
∅(0.8) - (1 - ∅(0.9))
∅(0.8) + ∅(0.9) - 1
0.788 + 0.859 - 1
0.647
The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.
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Carrie visited two different pet adoption centers. At the first adoption center, the ratio of dogs to birds was 4:24. The ratio of dogs to birds at the second adoption center was equivalent.
Which is the ratio of dogs to birds at the second adoption center?
Answers
The ratio of dogs to birds at the second adoption center that are equivalent is 2:12.
What is a ratio?Ratio demonstrates how many times one number can fit into another number. They contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
At the first adoption center, the ratio of dogs to birds was 4:24. The ratio will be:
= 4 / 24
= 1/6
= 1:6
Since the ratio of dogs to birds at the second adoption center is equivalent, this can be 2 to 12. This will be:
= 2/12.
= 1/6
= 1:6
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The points P, Q, R and S all lie on the same line segment, in that order, such that the ratio of PQ:QR:RSPQ:QR:RS is equal to 1:3:1.1:3:1. If PS=35,PS=35, find PR.PR.
Answers
The distance of PR is 21
Given,
The points P, Q, R and S all lie on the same line segment.
The ratios;
PQ:QR:RS = 1:3:1.
Distance of PS = 35
We have to find the distance of PR.
A line segment is a piece of a straight line that has all of the points on the line contained within and is bounded by two distinct endpoints. A line segment's length is determined by the Euclidean distance that separates its two ends.
Here,
PQ : QR : RS = 1 : 3 : 1.
Now let PQ = x, QR = 3x and RS = x.
Therefore,
PQ + PR + RS = PS.
x + 3x + x = 35
5x = 35
x = 7
Therefore,
PR = 3x
PR = 3 × 7
PR = 21
The distance of PR is 21
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What is the slope of the secant line that intersects the graph of f(x) = √4x+1 at x = = 0 and x = 6?
=
Answers
every week roger pays for a movie ticket and a soda out of his allowance. last week, roger's allowance was aa dollars. the cost of his movie ticket was 20\ % of the difference between aa and the cost of his soda, while the cost of his soda was 5\%5% of the difference between aa and the cost of his movie ticket. to the nearest whole percent, what fraction of aa did roger pay for his movie ticket and soda?
Answers
Answer:
23%
Step-by-step explanation:
We can create two equations:
\[m = \frac{1}{5}(A - s)\]\[s = \frac{1}{20}(A - m)\]
Substituting we get:
\[m = \frac{1}{5}(A - \frac{1}{20}(A - m))\]which yields:
\[m = \frac{19}{99}A\]
Now we can find s and we get:
\[s = \frac{4}{99}A\]
Since we want to find what fraction of $A$ did Roger pay for his movie ticket and soda, we add $m$ and $s$ to get:
\[\frac{19}{99}A + \frac{4}{99}A \implies \boxed{\text{(D)}\ 23\%}\]
plss need help with this
Answers
Answer:
The solution is (-2, 4).
Explain+how+you+csn+use+similar+triangles+to+find+a+missing+measurement.++Write+a(n)+that+uses+the+missing+measurement+because+the+++are++
Answers
You can use similar triangles to find missing measures according to proportional relationships.
What are similar triangles?Similar triangles are two triangles that share these two features listed as follows:
Same angle measures.Proportional side lengths.The second feature, the proportional side lengths, is what is used to find the missing measures, as proportional relationships are built according to them.
When two triangles are similar, the equivalent side lengths have to be identified for the two triangles, and those are the sides that have the same angle measures.
Then, for the two triangles, the equivalent sides will have proportional lengths, and then these equations will involve a missing length. Then cross multiplication is applied and the equation can be solved for the missing length.
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3 is divided by the difference of 4 and a number
Answers
Answer:
[tex] \frac{3}{4 - x} [/tex]
find the volume of the frustum by calculating the radius
Answers
The value of 'r' is 15 cm. Then the volume of the frustum will be 2625 cm³.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
By the similar triangle, then the value of r is calculated as,
r/30 = 20/40
r = 15 cm
Then the volume of the frustum is calculated as,
V = 1/3 × (30/2)² × 40 - 1/3 × (15/2)² × 20
V = 1/3 × [9000 - 1125]
V = 1/3 × 7875
V = 2625 cm³
The value of 'r' is 15 cm. Then the volume of the frustum will be 2625 cm³.
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Find the nth term : 6, 12, 22, 36…
Answers
The nth term of the given sequence is 6n
The given sequence is 6, 12, 22, 36,....
The formula to find the nth term is
T(n) = a + (n-1)d ... (1)
Where n is the number of terms
a is first term
d is common difference
Here
n = n. a = 6,
d = 12 - 6 = 6
Substitute the values in equation (1)
T(n) = 6 + (n-1)6
⇒ T(n) = 6 + 6n - 6
⇒ T(n) = 6n
Hence the nth term of the given sequence is 6n
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What is an equation of the line that passes through the points (-4, 5)(−4,5) and (-4, -2)(−4,−2)?
Answers
Answer:
∅
Step-by-step explanation:
set up your equation which will be [tex]\frac{-2-5}{-4+4}[/tex] which is undefined because denominator cannot be 0
write a function that will standardize a multivariate normal sample for arbitrary n and d. that is, transform the sample so that the sample mean vector is zero and sample covariance is the identity matrix. to check your results, generate multivariate normal samples and print the sample mean vector and covariance matrix before and after standardization.
Answers
The function that will standardize a multivariate normal sample is
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
According to a multivariate normal distribution with mean vector m and variance-covariance matrix M, then this random vector, X , will have the joint density function as shown:
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
where, |M| denotes the determinant of the variance-covariance matrix M and M^(-1) is just the inverse of the variance-covariance matrix M.
Hence, the function that will standardize a multivariate normal sample is
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
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Write 10x - 5y = -30 in slopeintercept form.
y =
X +
Answers
Answer:
[tex]y=2x+6[/tex]
Step-by-step explanation:
Slope-intercept form is [tex]y=mx+b[/tex].
Therefore, rearranging the given formula:
[tex]10x-5y=-30[/tex]
[tex]-5y=-10x-30[/tex]
[tex]\frac{-5y}{-5}=\frac{-10x}{-5}-\frac{30}{-5}[/tex]
[tex]y=2x-(-6)[/tex]
[tex]y=2x+6[/tex]
Answer: y=2x+6
Step-by-step explanation:
A slope-intercept form is y=mx+b
Hence,
[tex]10x-5y=-30\\\\10x-5y+5y=-30+5y\\\\10x=-30+5y\\\\10x+30=-30+5y+30\\\\10x+30=5y[/tex]
Divide both parts of the equation by 5:
2x+6=y
Thus, y=2x+6
A solon prices bottles of conditioner by the ounce. An 8-ounce bottle of Brand C cost $14. tHe cost of Brand S is represented by the equations y = 1.5x, where y is the total cost for a bottle with x ounces
Answers
Store´s B bottle cost less per ounce.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Store A
Cost of a 8-ounce bottle of water: $14
Store B
Cost of bottle: y= 1.5x
Cost per ounce (A)
=$14/ 8
= $1.75per ounce
Cost per ounce (B); $1.5 per ounce
So, $1.75 > $1.5
Hence, Store´s B bottle cost less per ounce.
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a wooden artifact from an ancient tomb contains 25 percent of the carbon-14 that is present in living trees. how long ago, to the nearest year, was the artifact made? (the half-life of carbon-14 is 5730 years.)
Answers
The artifact was created 11,460 years ago.
Given
that,25% of the carbon-14 found in living trees can be found in a wooden artifact from an ancient tomb and the half-life of carbon-14 is 5730 years Half Time [tex]t_{1/2}[/tex] = 5730 yearsln 2 / k = 5730k = 5730 / ln 2Let Po = 100P(t) =25 after t yearsP(t) = Po e^ -kt25 = 100 e ^ -(5730t / ln 2)5730t / ln 2 = ln 4
By applying
we get,t = 5730 * log⁴₂t = 11460 years Hence, the artifact was made 11,460 years ago.
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In a wildlife park they were 18 gray wolves after three years they were 27 gray wolves. What is the percent gain?
Answers
Answer: 66.66.....% (6 recurring) / 66.67%
Step-by-step explanation: To get the percent form of this, you'll need to turn this into a fraction, which would be 18/27, then you can simplify it to 2/3 and convert it to a percent which would be 66.66..... .
victoria deposited $5000 into a savings account that earns an annual simple interest rate of 0.3%. To the nearest tenth of a year, how long will it take for the account to reach $5500?
Answers
It will take 33.33 years for the account to reach $5500
What is simple interest?
Simple interest is defined as the direct crediting of cash flows related to an investment or deposit.
We know,
Victoria deposited into a savings account $5000
Annual simple interest rate of 0.3%.
Formula of Simple Interest
A = P(1 + rt)
5500 = 5000(1 + 0.003t)
5500 = 5000 + 15t
15t = 500
[tex]t = \frac{500}{15} = 33.33[/tex]
It will take 33.33 years for the account to reach $5500
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Isosceles and Equilateral Triangles !
Answers
Unit 4 congruent triangles
Answers
Answer: 9/3
Step-by-step explanation: the trriangles proportion is three and 9/3=3
the motel in the preceding example uses approximately600 bars of soap each day, and this tends to be fairly constant. lead time for soap delivery is normally distributed with a mean of six days and a standard deviation of two days. a service level of 90 percent is desired. the re-order point (rop) is:
Answers
The re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.
Define the term reorder point (ROP)?An exact level where the your stock has to be restocked is characterized as a reorder point (ROP). To put it another way, it advises you when to order so that you won't run out of supply.You'll need to be aware of the following factors in order to figure out the ROP for every item:Lead period: Days needed (in days) for the vendor to complete your orderSafeguard stock: The quantity of excess stock, if any, you maintain on hand to assist prevent stockoutsDaily usage: Average number of sales that particular item typically sees per day.ROP = (Daily usage x Lead period) + Safeguard stock
For the given question;
Lead time = 6 days
Safety stock = 2 days x 600 bars = 1200 bars
ROP = (600 x 6) + 1200 = 4800 bars.
Thus, the re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.
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