Answers
Answer:
16
Step-by-step explanation:
The right triangle shown is a 30:60:90 triangle.
30:60:90 right triangles have a 1:sqrt(3):2 ratio between their sides.
Since the side opposite from the 30 degree is 8, and x is opposite from the 90 degree angle, 8 and x have a 1:2 ratio, or 8:16.
Related Questions
What is the equation of the line that passes through (5, -2) and (-3, 4)?
Answers
Answer:
y = (-3/4)x + 7/4
Step-by-step explanation:
Step 1: Define general form of equation of line
An equation of a straight line on two-dimensional plane could be represented in form of: y = Mx + b, with M is slope and b is y-intercept
Step 2: Set up the system to solve for parameters of equation of line
(solve for M and b)
That equation passes 2 points, which are represented in form of (x, y), (5, -2) and (-3, 4).
Substitute these values of x and y into the original equation in step 1:
-2 = 5M + b
4 = -3M + b
Step 3: Solve the system of equations in step 2 for M and b
Subtract 1st equation from 2nd equation:
6 = -8M
=> M = -6/8 = -3/4
Substitute M back into 1st equation:
=> -2 = 5*(-3/4) + b
=> b = -2 + 15/4
=> b = 7/4
=> The equation of the line that passes through (5, -2) and (-3, 4):
y = (-3/4)x + 7/4
Hope this helps!
:)
Answer:
Y= -4/3(x-7/2)
Step-by-step explanation:
So first calculate the difference between them,
changes by 8 x units, and -6 y units.
Then substitute them into y/x to find gradient
-6/8 = -4/3
so now we have a part of the equation:
Y= -4/3(x-a)
substitute Y= -2 and x=5 (from (5,-2))
-2= -4/3(5-a)
-2= -20/3+4a/3
Multiply by 3 on both sides
-6= -20+4a
add 20 on both sides
14=4a
a=7/2
use this as the value of a
Y= -4/3(x-7/2)
Please everyone help me!
Answers
Answer:g=0 is not the solution
Step-byd-step explanation:
-1 1/2 is a negative number and 0 is not negative
Answer:
g=0
Step-by-step explanation:
happy to help ya :)
A recent survey found that 86% of employees plan to devote at least some work time to follow games during the NCAA Men's Basketball Tournament. A random sample of 100 employees was selected. What is the probability that less than 80% of this sample will devote work time to follow games?
Answers
Answer:
4.18% probability that less than 80% of this sample will devote work time to follow games
Step-by-step explanation:
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
[tex]p = 0.86, n = 100[/tex]
So
[tex]\mu = 0.86, s = \sqrt{\frac{0.86*0.14}{100}} = 0.0347[/tex]
What is the probability that less than 80% of this sample will devote work time to follow games?
This is the pvalue of Z when X = 0.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8 - 0.86}{0.0347}[/tex]
[tex]Z = -1.73[/tex]
[tex]Z = -1.73[/tex] has a pvalue of 0.0418
4.18% probability that less than 80% of this sample will devote work time to follow games
B
ABC is a right-angled triangle.
AC = 16 cm
Angle C = 90°
А.
size of angle B : size of angle A = 3:2
С
16 cm
Work out the length of AB.
Give your answer correct to 3 significant figures.
Answers
Answer:
19.8 cm
Step-by-step explanation:
Angle B is the complement of angle A, so we have this relation for the angles:
B/A = 3/2 = (90°-A)/A
2(90° -A) = 3A . . . . . cross multiply
180° = 5A . . . . . . . . . eliminate parentheses, add 2A
36° = A . . . . . . . . . . . divide by 5
The relations expressed by the mnemonic SOH CAH TOA remind you that ...
Cos = Adjacent/Hypotenuse
cos(A) = AC/AB
AB = AC/cos(A) = (16 cm)/cos(36°)
AB ≈ 19.8 cm
The first digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9 because we do not write numbers such as 15 as 015. While it is reasonable to think that for most real-life data each digit occurs with equal frequency so that each digit 1, 2, ..., 9 has probability 1/9 of being the first digit, this is not true. It is a surprising phenomenon that in many naturally occurring numbers and web-based data the first digit has a probability distribution known as Benford's law.
Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way.
Specifically, for d = 1, 2, 3, 4, 5, 6, 7, 8, 9, Benford's law states P(first digit is d) = log_10(1+(1/d)) . The distribution of the first digit according to Benford's law, calculated to 3 decimal places, is shown in the table below.
Benford's law
First Digit X 1 2 3 4 5 6 7 8 9
Probability .301 .176 .125 .097 .079 .067 .058 .051 .046
Benford's Law and the Equally Likely Model benford equally likely
The law is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881. A surprising variety of data from the natural sciences, social affairs, and business obeys Benford's law.
This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature).
Numbers that are assigned, such as social security numbers and zip codes, or data with a fixed maximum, such as deductible contributions to individual retirement accounts, or randomly generated numbers, do not follow Benford's law.
The figure below shows how the distribution of the first digit of various naturally occurring and web-based data compares with Benford's law.
benford natural data web data
Figure information. Earthquakes: depth in km of 248,915 quakes, 1989-2009; source National Earthquake Information Center, United States Geological Survey. Minnesota lakes: size in acres of approx. 1100 lakes; source Wikipedia. Births: number of births in each county of the United States (approximately 3200), 2010; source: US Census Bureau. Diggs: total number of diggs for each of the top 1000 diggers at digg.com; source: socialblade.com.
Question 1:
(1a). What is the expected value of the first digit when the first digit follows Benford's law?
expected value (Use 3 decimal places).
(1b). What is the expected value of the first digit when the possible first digits are equally likely?
expected value (Use 3 decimal places).
(1c). What is the standard deviation of the first digit when the first digit follows Benford's Law?
Answers
Answer:
0.699
Step-by-step explanation:
got it on khan academy, should get brainliest thanks
if r is the radius of a circle and d is its diameter which of the following is an equivalent formula for the circumference c = 2 pie r
a C = pie d2
b C = pie rd
c C = pie d
d C = 2 pie d
Answers
Answer:
C
Step-by-step explanation:
C=2pier or pied
Answer:
a. C = 2πr
c. C= πd
both are correct
A certain city's population is 120,000 and decreases 1.4% per year for 15 years.
Is this exponential growth or decay? Growth
What is the rate of growth or decay?
What was the initial amount? 120000
What is the function?
What is the population after 10 years? Round to the nearest whole number.
Answers
Answer:
Decay Problem.Decay rate, r = 0.014Initial Amount =120,000[tex]P(t)=120000(0.986)^t[/tex]P(10)=104,220Step-by-step explanation:
The exponential function for growth/decay is given as:
[tex]P(t)=P_0(1 \pm r)^t, where:\\P_0$ is the Initial Population\\r is the growth/decay rate\\t is time[/tex]
In this problem:
The city's initial population is 120,000 and it decreases by 1.4% per year.
Since the population decreases, it is a Decay Problem.Decay rate, r=1.4% =0.014Initial Amount =120,000Therefore, the function is:
[tex]P(t)=120000(1 - 0.014)^t\\P(t)=120000(0.986)^t[/tex]
When t=10 years
[tex]P(10)=120000(0.986)^10\\=104219.8\\\approx 104220 $ (to the nearest whole number)[/tex]
If \\(z_1=3+2i\\) and \\(z_2=4+3i\\) and are complex numbers, find \\(z_1z_2\\)
Answers
[tex]z_1z_2=(3+2i)(4+3i)=3\cdot4+2i\cdot4+3\cdot3i+2i\cdot3i[/tex]
[tex]z_1z_2=12+8i+9i+6i^2[/tex]
[tex]i^2=-1[/tex], so
[tex]z_1z_2=12+8i+9i-6=\boxed{6+17i}[/tex]
can someone please help meee!???
Answers
What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve
Answers
Answer:
[tex]x=1\\x=-1[/tex]
Step-by-step explanation:
[tex]9x^{4} -2x^{2} -7=0\\y=x^{2} \\9y^{2} -2y-7=0\\y=\frac{2\pm\sqrt{(-2)^{2} -4*9(-7)} }{2*9} =\frac{2\pm\sqrt{4+252} }{18} =\frac{2\pm\sqrt{256} }{18}[/tex]
[tex]\sqrt{256} =16[/tex]
[tex]y=\frac{2+16}{18} =\frac{18}{18} =1 \\or \\y=\frac{2-16}{18} =-\frac{14}{18} =-\frac{7}{9}[/tex]
[tex]x^{2} = 1 \\or \\x^{2} =-\frac{7}{9}[/tex]
[tex]x=\pm 1[/tex]
[tex]x^{2} =-\frac{7}{9}[/tex] has no solution since fot all [tex]x[/tex] on the real line, [tex]x^{2} \geq 0[/tex] and [tex]-\frac{7}{9} < 0.[/tex]
Question 1 of 20 :
Select the best answer for the question.
1. Divide7/15 by 3/5
OA%
O B./25
O c. 75/21
O D.21/75
Answers
Answer:
7/9
Step-by-step explanation:
7/15 ÷ 3/5
Copy dot flip
7/15 * 5/3
7/3 * 5/15
7/3 * 1/3
7/9
2/5 of the members of a school band are 6th graders. What percent of
the students in the band are non-sixth graders?
Answers
Answer:
60%
Step-by-step explanation:
3/5 is 60%
Answer:
60%
Step-by-step explanation:
5/5 minus 2/5 is 3/5
5 divided by 3 is .6
in order to find out the percent move the decimal over to the right
Convert 88 ounces to pounds.
A.0.18 pounds
B.5.5 pounds
C.1408 pounds
Answers
Answer: it is b because 2.5 lbs = 40 oz. then i know that 40 is half of 80 then there is not way it is the 1000 pound choice
Step-by-step explanation:
In the circle above, P is the center,What is the value, in degrees, of θ?
Answers
Answer:
45°
Step-by-step explanation:
There is a propiety that says "The measure of the inscribed angle is half that of the arc that the two sides cut out of the circle."
So the central angle is 90, the inscribed angle will be 90/2=45°
When Ryan was born, he weighed 7 pounds.At 6 months, he weighed 11.2 pounds. Amanda weighed 6 pounds when she was born, and 12.9 pounds at 6 months. Which baby had a greater percent increase in weight? Explain
Answers
Answer:
✅Amanda had a greater percent increase in weight.
Step-by-step explanation:
The percent change in Ryan’s weight was 42/7 or 60%. The percent change in Amanda’s weight was 6.9/6, or 115%. Amanda had a greater percent increase in weight.
IamSugarBee
Answer:
The percent change in Ryan’s weight was 4.2/7, or 60%. The percent change in Amanda’s weight was 6.9/6 , or 115%. Amanda had a greater percent increase in weight.
Step-by-step explanation:
its the sample answer i just did it
The m∠ABC = (10x-5)°and m∠CBD=35°. If the angles are supplementary, find the value of x.
Answers
Answer:
15
Step-by-step explanation:
Supplementary angles completes each other to 180°
if the teo angles are supplementary here the the sum of 10x - 5 + 35 should be 180°
10x - 5 + 35 = 180
10x + 30 = 180
10x = 150
x = 15
A 12cmx2cm rectangle sits inside a circle with a radius of 8cm. What isnthe area of the shaded region of the circle
Answers
Answer:
The answer would 177.06 centimeters
A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby casts a shadow that measures 24 feet. How tall is the building?
(Hint: Draw a picture and Set up a proportion)
Answers
The building height is 32 feet.
Let us consider that building height is x feet.
From attached diagram shown below,
Two triangles are formed.
Apply law of similarity of triangles.
Corresponding sides are in equal proportion.
[tex]\frac{x}{24}=\frac{12}{9} \\\\9x=12*24\\\\x=\frac{12*24}{9}=32 feet[/tex]
Learn more:
https://brainly.com/question/14285697
Which of the following is the slope of the line that passes through the points (-3,5) and (-3,-2)
Answers
Answer:
undefined.
Step-by-step explanation:
-2-5/-3-(-3)
-7/0
Undefined
Simplify
20x over 70x
Answers
Answer:
The answer is 2/7.
Step-by-step explanation:
You have to cut out the common terms :
[tex] \frac{20x}{70x} [/tex]
[tex] \frac{20}{70} [/tex]
[tex] \frac{2}{7} [/tex]
hope that helps!!
Can anyone help me with my homework ?
2x+3y=20
7x+2y=53
Answers
Answer:
x=7, y=2
Step-by-step explanation:
Solve2x+3y=20for x:
2x+3y=20
2x+3y+−3y=20+−3y
2x=−3y+20
2x/2=-3y+20/2
x= -3/2 y
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.19degreesF and a standard deviation of 0.61degreesF. Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.36degreesF and 100.02degreesF? b. What is the approximate percentage of healthy adults with body temperatures between 96.97degreesF and 99.41degreesF?
Answers
Answer:
a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.
b) [tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]
[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]
And within 2 deviations from the mean we have 95% of the values.
Step-by-step explanation:
For this case we know that the distribution of the temperatures have the following parameters:
[tex] \mu = 98.19, \sigma =0.61[/tex]
Part a
From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.
Part b
We can calculate the number of deviations from the mean with the z score with this formula:
[tex]z=\frac{X -\mu}{\sigma}[/tex]
And using this formula we got:
[tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]
[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]
And within 2 deviations from the mean we have 95% of the values.
no guess please explain
Answers
A payday loan store charges $40 for a one month loan of $600. What’s the annual interest rate equivalent to?
Answers
Answer:
80%
Step-by-step explanation:
rate=100×Interest/ principal × time
Interest= 40
principal= 600
time= 1 month=1/12
100%×$40×12/$600×1=80%
a circle with circumference 20 has an arc at 72 central angle. what is the length of the arc
Answers
Answer:
4 units
Step-by-step explanation:
[tex] \because \: l = \frac{ \theta}{360 \degree} \times c \\ \\ \therefore \: l = \frac{72 \degree}{360 \degree} \times 20 \\ \\ \therefore \: l = \frac{72 \degree}{18\degree} \\ \\ \therefore \: l = 4 \: units[/tex]
A machine produces 576 units in 18 hours at this rate how many will it produce in 28 hours
Answers
Answer: 896
Step-by-step explanation:
Let's use a rule of three here.
[tex]\frac{576}{x}=\frac{18}{28}[/tex]
Solve for x;
[tex]x=\frac{576*28}{18}[/tex]
[tex]x=896[/tex]
Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
The product of 8 and a number is 96. Find the number.
Write an equation for the given conditions.
Answers
Answer:
12
Step-by-step explanation:
8x=96
x=96/8
x=12
Answer:
12
Step-by-step explanation:
8x=96
96/8
x=12
so the the product of 8and 12=96
4. In the Department of Natural Sciences, 14 faculty members have a PhD, and 30 faculty
members do not have a PhD. In the Department, the number of female faculty who do not
have a PhD is 10 more than the number of females who have a PhD. If a third of the male
faculty in the Department have a PhD, then what is the number of female faculty in the
Answers
Answer:
8
Step-by-step explanation:
We can start by making the table below to show the given numbers (red) and to assign a variable (x) to the number we want to find: female PhDs.
By subtracting the female numbers from the totals, we can find the corresponding numbers of male PhDs and non-PhDs.
The number of male non-PhDs is twice the number of male PhDs, so we have ...
2(14 -x) = 20 -x
28 -2x = 20 -x . . . . eliminate parentheses
8 = x . . . . . . . . . . . .add 2x-20
The number of female faculty with PhDs is 8.
MY LAST 2 QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
1. Molly is trying to find a relationship between the largest angle and largest side of a triangle. She has drawn dozens of triangles, and measured their parts. She’s ready to make a conjecture. What kind of reasoning was Molly using? Explain how you know it’s that kind of reasoning.
11. Which step in the proof has a flaw?
Given AB=BC prove B is the midpoint of AC
IMAGE BELOW
A) Step 1
B) Step 3
C) No Flaw.
D) Step 2
Answers
Answer:
C.
Step-by-step explanation:
11. There is no flaw since step 1 is given, and there is the right reason for step 2.
1. Molly is using inductive reasoning because she is collecting the data to make a conjecture.
11. There is no flaw.
Gordon Miller's job shop has four work areas, A, B, C, and D. Distances in feet between centers of the work areas are: A B C D A − 5 9 7 B − − 6 8 C − − − 11 D − − − − Workpieces moved per week between work areas are: A B C D A − 900 900 500 B − − 500 200 C − − − 600 D − − − − It costs Gordon $22 to move 1 work piece 1 foot.What is the weekly total material handling cost of the layout?
Answers
Answer: $600,600
Step-by-step explanation:
Total handling cost :
Workpiece moved * cost * distance
Work area A :
-, (5 × 22 × 900), (9 × 22 × 900), (7 × 22 × 500)
-, 99000, 178200, 77000
Work area B:
-, -, (6 × 22 × 500), (8 × 22 × 200)
-, -, 66000, 35200
Work area C:
-, -, -, (11 × 22 × 600)
-,-,-, 145200
Work area D:
-, -, -, -
Total weekly handling cost :
(99000 + 178200 + 77000 + 66000 + 35200 + 145200)
= $600,600
Kindly check attached picture for more explanation