State and prove the converse of the pythagorean theorem using a two-column proof
Answer:
Step-by-step explanation:
I'm from the UK and I'm not familiar with a two column proof, but the following proves the converse.
Draw 2 right angled triangles with the 2 legs = a and b in each case and the longest side = c in one triangle and f in the other.
By Pythagoras a^2 + b^2 = c^2 (Given)
Also in the other triangle a^2 + b^2 = f^2, if it is right-angled.
Therefore a^2 = f^2 and a = f.
So the 2 triangles are congruent by SSS.
So m < C in one triangle = m < F ( the angles opposite the hypotenuse)
Therefore the second triangle is right angled .
This completes the proof.
30 is what percent of 44?
Answer:
68.18
Step-by-step explanation:
→ Set up an equation
[tex]\frac{44x}{100} =30[/tex]
→ Times both sides by 100
44x = 3000
→ Divide both sides by 44
68.18
The bell tower of the cathedral in Pisa, Italy, leans 5.6° from the vertical. A tourist stands 107 m from its base, with the tower leaning directly toward her. She measures the angle of elevation to the top of the tower to be 28.6°. Find the length of the tower to the nearest meter. m
Answer:
[tex]l=56m[/tex]
Step-by-step explanation:
From the question we are told that:
Angle from vertical [tex]\theta =5.6[/tex]
Horizontal Distance [tex]d=107m[/tex]
Angle of elevation [tex]\gamma=28.6[/tex]
Generally the Trigonometric equation for exterior angles is mathematically given by
[tex]Exterior\ angles=\sum of\ two\ interior\ angles[/tex]
Where
[tex]Exterior angles=90 \textdegree +5.6 \textdegree[/tex]
Therefore
[tex]90 \textdegree +\theta \textdegree=\omega+\gamma[/tex]
[tex]90 \textdegree +5.6 \textdegree=\omega+28.6 \textdegree[/tex]
[tex]\omega=67 \textdegree[/tex]
Generally the equation for The Sine rule is mathematically given by
[tex]\frac{sin \omega }{d}=\frac{sin \gamma}{l}[/tex]
[tex]l=\frac{107 sin 28.6}{sin 67 \textdegree }[/tex]
[tex]l=56m[/tex]
Please explain the answer
Answer:
3.5
Step-by-step explanation:
in order to find the maximum, we are basically solving to find the vertex of the graph. to find the vertex use :
-b/2a
the 'b' is 112
the 'a' is -16
so :
-112/-32 = 3.5
the answer is B, 3.5
The stemplot below represents the number of bite-size snacks grabbed by 37 students in an activity for a statistics class.
A stemplot titled Number of snacks has values 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 21, 22, 23, 25, 25, 28, 32, 38, 42, 45.
Which of the following statements best describes the distribution?
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 15 to 45. There are no outliers.
The distribution of the number of snacks grabbed is symmetric with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
The distribution of the number of snacks grabbed is skewed left with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
Answer:
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
Step-by-step explanation:
First, we can see if the graph is symmetric. A symmetric graph is even on both sides of the center. As there are a lot more students that grabbed a small number of snacks, and the data is not even around the center (which is somewhere around 20 or 30 snacks). This means that the graph is not symmetric, making the second answer incorrect.
Next, we can check if the graph is skewed right or left. If the left of the graph represents a smaller amount of snacks and the right of it represents a higher number of snacks, we can see that most of the data is on the left of the graph. There are a few values to the right, but the overwhelming amount of data is on the left, making the distribution skewed to the right. This keeps the first and last answers possible
Moreover, we can find the center of the distribution. This is generally equal to the median, which is 18, so the center is around 18
After that, we can see what the values vary from. The lowest tens value is 1, and the lowest ones value in that is 2, making the lowest value 12. Similarly, the highest tens value is 4, and the highest ones value there is 5, making the range 12 to 45. This leaves the last answer, but we can check the outliers to make sure.
With the data, we can calculate the first quartile to be 15, the third quartile to be 21.5, and the interquartile range to be 21.5-15 = 6.75 . If a number is less than Q₁ - 1.5 * IQR or greater than Q₃ + 1.5 * IQR, it is a potential outlier. Applying that here, the lower bound for non-outliers is 15 - 6.5 * 1.5 = 5.25, and the upper bound if 21 + 6.5 * 1.5 = 30.75. No values are less than 5.25, but there are four values greater than 30.75 in 32, 38, 42, and 45. There are possible outliers at 38, 42, and 45, matching up with the last answer.
Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find these probabilities. a. The student makes more than $15,000. b. The student makes between $13,000 and $14,000.
Answer:
a) 0.0749 = 7.49% probability that the student makes more than $15,000.
b) 0.227 = 22.7% probability that the student makes between $13,000 and $14,000.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Full-time Ph.D. students receive an average of $12,837 per year.
This means that [tex]\mu = 12837[/tex]
Standard deviation of $1500
This means that [tex]\sigma = 1500[/tex]
a. The student makes more than $15,000.
This is 1 subtracted by the p-value of Z when X = 15000.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15000 - 12837}{1500}[/tex]
[tex]Z = 1.44[/tex]
[tex]Z = 1.44[/tex] has a p-value of 0.9251.
1 - 0.9251 = 0.0749
0.0749 = 7.49% probability that the student makes more than $15,000.
b. The student makes between $13,000 and $14,000.
This is the p-value of Z when X = 14000 subtracted by the p-value of Z when X = 13000.
X = 14000
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14000 - 12837}{1500}[/tex]
[tex]Z = 0.775[/tex]
[tex]Z = 0.775[/tex] has a p-value of 0.7708.
X = 13000
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13000 - 12837}{1500}[/tex]
[tex]Z = 0.11[/tex]
[tex]Z = 0.11[/tex] has a p-value of 0.5438.
0.7708 - 0.5438 = 0.227
0.227 = 22.7% probability that the student makes between $13,000 and $14,000.
7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000
What is z score?
Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / standard deviation
Given that:
Mean = $12837, standard deviation = $1500
a) For >15000:
z = (15000 - 12837)/1500 = 1.44
P(z > 1.44) = 1 - P(z < 1.44) = 1 - 0.9251 = 0.0749
b) For >13000:
z = (13000 - 12837)/1500 = 0.11
For <14000:
z = (14000 - 12837)/1500 = 0.78
P(0.11 < z < 0.78) = P(z < 0.78) - P(z < 0.11) = 0.7823 - 0.5438 = 0.2385
7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000
Find out more on z score at: https://brainly.com/question/25638875
Kara ate 2 7/9 of the raisins she packed. Which box shows the decimal equivalent of the amount of raisins she ate? Box A: 2.777 etc Box B: 2.79 Box C: 2.999 etc.
Answer: Box A, 2.777
=======================================================
Explanation:
When using a calculator or long division, you should find that
7/9 = 0.7777...
where the 7s go on forever
So we can say that 7/9 = 0.777 approximately. You could argue that the last '7' would round up to an '8' and we could say 7/9 = 0.778; however, I'll stick to the first value so that it matches with the answer.
Since 7/9 = 0.777, this means 2 & 7/9 = 2 + 7/9 = 2 + 0.777 = 2.777 which is box A.
Answer:
A
Step-by-step explanation:
From the figure, the cylinder glass has a height of 6 inches and a radius of the mouth of the glass 1.25 inches. Find the length of SK in inches.
Answer:
D. 6.5
Step-by-step explanation:
The diameter of the cylinder is 1.25 x 2 = 2.5
SK = √1.25² + 6² = √42.25 = 6.5
The lengths of pregnancies in a small rural village are normally distributed with a mean of 264.1 days and a standard deviation of 12.9 days. In what range would you expect to find the middle 95% of most pregnancies
Answer:
The range of the 95% data (X) = 238.3 days < X < 289.9 days
Step-by-step explanation:
Given;
mean of the normal distribution, m = 264.1 days
standard deviation, d = 12.9 days
between two standard deviation below and above the mean is 96% of all the data.
two standard deviation below the mean = m - 2d
= 264.1 - 2(12.9)
= 238.3 days
two standard deviation above the mean = m + 2d
= 264.1 + 2(12.9)
= 289.9 days
The middle of the 95% of most pregnancies would be found in the following range;
238.3 days < X < 289.9 days
Zoe earns 22.50 per hour plus 3% commission on sales. last week she worked 34 hours and made sales totalling 15280. Calculate her pay for the week.
Answer: $1,223.40.
Step-by-step explanation:
Since she earns $22.5 per hour, for 34 hours, she would earn:
$22.5 × 34 = $765
She earn 3% of her sales, therefore find 3% of $15,280:
$15280(3%) = $15280(0.03) = $458.4
Add them together:
$765 + $458.4 = $1223.4
9514 1404 393
Answer:
$1,223.40
Step-by-step explanation:
Zoe's total pay is the sum of the products of hours and hourly rate, and sales and commission rate.
Pay = (34 h)($22.50/h) +($15,280)(.03) = $765.00 +458.40
Pay = $1,223.40
Zoe's pay for the week is $1,223.40.
What Is The Pythagorean Theorem?. ^ Means to the power of...
Answer:
I wish I knew that answer
Step-by-step explanation:
Which of the following equations is modeled by the graph?
A)
a = 50t
B)
a = 5t
C)
a = 50 + t
D)
a = 10t
Answer:
a = 50t
Step-by-step explanation:
A function is rise over run, or y/x.
In this graph, the rise (y) is the account balance, while the run (x) is time. To solve for the slope, or the "equation modeled by the graph," we need to divide the rise by the run.
The graph is shown in terms of (a, t). If we look at the first point, (50,1), the rise is 50 and the run is 1. 50/1 is 50. Therefore, a = 50t, since a = 50 and t = 1.
To check, we can try another point, (100, 2). The rise is 100 and the run is 2. Divide these together and you still get 50. You are multiplying the "t" value by 50 to get the "a" value.
Therefore, it's a = 50t
5. Does the infinite geometric series S = 25 + 20 + 16 + ... converge or diverge? Explain.
9514 1404 393
Answer:
converges
Step-by-step explanation:
The common ratio is 20/25 = 16/20 = 4/5. The magnitude of this is less than 1, so the series converges.
I really need the help please and thank you
Asnwer: C
-------------------------------------
Find the quotient of 68.4 ÷ 18 = ________. Use an area model to help you solve. (this is on flvs by the way) answers:
3.3
3.5
3.8
3.9
Answer:
C
Step-by-step explanation:
3.8 is the answer
68.4÷18=3.8
I need help ASAP anyone?
Explanation:
Each vertical asymptote is due to a division by zero error.
For instance, the vertical asymptote x = 3 is from the factor (x-3) in the denominator. If we plugged x = 3 into (x-3), then it turns into 0 and we cannot have 0 in the denominator.
Similarly, the factor (x+3) leads to x = -3
So overall, we have (x-3)(x+3) in the denominator.
Write the ratio as a fraction in simplest form
4.5 hr to 4 hr
9514 1404 393
Answer:
9/8
Step-by-step explanation:
To clear the fraction in the ratio 4.5 to 4, you can multiply both numbers by 2. This gives you the reduced ratio 9 to 8. As a fraction, that is 9/8.
The area of a rectangle is 63 ft^2, and the length of the rectangle is 11 ft more than twice the width. Find the dimensions of the rectangle.
When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 4 kg, the acceleration of the object is 13 m/s^2. When the same force acts upon another object, its acceleration is 2 m/s^2. What is the mass of this object?
Answer:
26 kg
Step-by-step explanation:
varies inversely :
y = k/x
acceleration = k/mass
13 = k/4
k= 52
---------------------
2 = k/mass
2 = 52/mass
mass = 26 kg
Adam sleeps for nine hours each night, five nights a week, and 11 hours for two nights a week.
Which is closest to the percentage of the whole week that Adam spends sleeping?
A) 25%
B) 30%
C) 33%
D) 40%
E) 50%
Answer:
E
Step-by-step explanation:
The percentage of the whole week that Adam spends in sleeping is 33%.
What is percentage?
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
How to find percentage of a number?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
According to the give question.
Adams sleeps for nine hours each night, five nights a week.
⇒ Number of hours he sleep for five nights = 5 × 9 = 45 hours
Also, 11 hours for two nights a week.
So, the total number of hours Adam sleeps in a week = 45 + 11 = 56 hours
And, total number of hours in a week = 24 × 7 = 168
Therefore,
The percentage of the whole week that Adam spends in sleeping
= (total number of hours Adam sleep in a week/Total numbers of hour in a week) × 100
[tex]=\frac{56}{168}[/tex] × 100
= 33.33%
= 33%
Hence, the percentage of the whole week that Adam spends in sleeping is 33%.
Find out more information about percentage here:
https://brainly.com/question/24159063
#SPJ2
Which statement is true about the value of Start Absolute Value negative 5 End Absolute Value?
Statements? At least look for one that says it is equivalent to positive 5.
Find the circumference. Use 3.14. r = 4 cm C = [?] cm
Answer:
24.12
Explanation --
Circumference = Pi x D (d --> diameter)
Diameter = 2r (r --> radius)
4+4 (4[2]) = 8
3.14 times 8 (8 is the diameter we just found out, while 3.14 is pi) -->
25.12
Hope this helps!!
Answer: c=πd
we need 'd'
hence,
d=2r
d=2(4cm)
d=8cm
now,
c=3.14×8cm
c=25.12cm
The 90% confidence interval for the mean one-way commuting time in New York City is
5.22 < < 5.98 minutes. Construct a 95% confidence interval based on the same data.
Which interval provides more information?
Answer:
95% provides more information
Step-by-step explanation:
The confidence interval is obtained by using the relation :
Xbar ± Zcritical * σ/√n
(Xbar - (Zcritical * σ/√n)) = 5.22 - - - (1)
(Xbar + (Zcritical * σ/√n)) = 5.98 - - (2)
Adding (1) and (2)
2xbar = 5.22 + 5.98
2xbar = 11.2
xbar = 11.2 / 2 = 5.6
Margin of Error :
Xbar - lower C.I = Zcritical * σ/√n
Zcritical at 90% = 1.645
5.6 - 5.22 = 1.645 * (σ/√n)
0.38 = 1.645 * (σ/√n)
(σ/√n) = 0.38 / 1.645 = 0.231
Therefore, using the se parameters to construct at 95%
Zcritical at 95% = 1.96
Margin of Error = Zcritical * σ/√n
Margin of Error = 1.96 * 0.231 = 0.45276
C.I = xbar ± margin of error
C. I = 5.6 ± 0.45276
C.I = (5.6 - 0.45276) ; (5.6 + 0.45276)
C. I = (5.147 ; 6.053)
Hence, 95% confidence interval provides more information as it is wider.
Adam runs 13 miles in 143 minutes. How many minutes does it take him to run one mile? Adam runs at a rate of minutes per mile.
Answer:
Adam runs at a rate of 11 minutes per mile.
Step-by-step explanation:
Take 143 minutes and divide by 13 miles and you will get the answer of 11 minutes.
PLEASE MARK ME BRAINEIST.
Answer:
it would take him 11 minuets to run a mile
Step-by-step
143 divided by 13 is 11 which means each mile takes 11
you can also check the answer by multiplying 13 times 11 which is 143
Help me please, is it d?
Answer:
Yes D is the correct answer :)
Answer:
Yes, D
Step-by-step explanation:
Which expressions are equivalent to -6(b+2)+8
Choose all answers that apply:
A. -6b+2+8
B. -6b-4
C. None of the above
Answer:
B. -6b-4
Step-by-step explanation:
-6(b+2)+8
Distribute
-6b-12+8
Combine like terms
-6b-4
A veterinarian is visited by many pets and their owners each day. Before the doctor attends to each pet, an assistant records information including the type, age, weight, and height of each pet. What are the individuals in the data set?
[What are the individuals in the data set?]
pets
types
weights
heights
I think it's pets, just posting so it helps other people with it. Someone make sure in the answers though.
Answer:
pets bcos a vetenarian is a doctor for animals and tha question also says their owners.
If it takes sally 45 minutes to walk 1 mile how long will it take sally to walk 1,954 miles?
Answer:
87,930 Minutes
Step-by-step explanation:
Let us use unit rates for this question. Let's first draw a table.
Minutes Mile
45 1
This table represents the relation of Sally walking 1 mile in 45 minutes. Let's put the other data we know of in the table.
Minutes Mile
45 1
1954
To find the number of minutes, we must know that if 1 mile takes 45 minutes, we must multiply the number of minutes, which is 45, by 1954 to get the result desired. Let us do that.
1954*45 = 87,930
Minutes Miles
45 1
87,930 1954
Therefore it will take Sally 87,930 minutes to walk 1,954 Miles.
I Hope This Helps!
Please Mark Brainliest!
If a drug has a concentration of 8.22 mg per 3.039 mL, how many mL are needed to give 7.469 gram of the drug? Round to 1 decimal.
Answer:
2.8 litres
Step-by-step explanation:
8.22 mg per 3.039 mL
2.704 mg per 1 mL
7.469 gram = 7469 milligrams
7469 milligrams per 2,761.34927mL
= 2.761 litres = 2.8 litres
write 11.4 in standard form
[tex]11.4[/tex]
[tex] \to \: 1.14 \times {10}^{1} [/tex]
