Answer:
40 ft
Step-by-step explanation:
Given that the angle of elevation is 64.6°, this means that the angle of depression from the top of the flagpole is 180 - 90 - 64.6, which is 25.4°
We can solve by using the sine rule, or the cosine rule.
Using the sine, we have
Sinθ = OPP/HYP, we're going to use the angle of depression, and thus
Sin 25.4° = 19/x, on rearranging, we have
x = 19/ sin 25.4°
x = 19/0.4289
x = 44.30 ft.
Now, we use Pythagoras theorem to get the height of the flagpole.
44.3² = 19² + y²
y² = 44.3² - 19²
y² = 1962.49 - 361
y² = 1601.49
y = √1601.49
y = 40 ft
The distance between Dallas and Houston is 136 kilomenters. There are approximately 8 kilometers in 5
miles. What is the measurement that is closest to the number of miles between these two?
had a bag of 28 marbles 1/4 the marbles were red and 3/7 were yellow, how many marbles were neither red nor yellow?
Answer:
The answer is 9
Step-by-step explanation:
The number marbles were neither red nor yellow is 9.
Given that, a bag of 28 marbles 1/4 the marbles were red and 3/7 were yellow.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, the number of red marbles = 1/4 × 28
= 7
The number of yellow marbles = 3/7 × 28
= 12
Total number of red and yellow marbles = 7+12 = 19
Neither red nor yellow = 28-19=9
Therefore, the number marbles were neither red nor yellow is 9.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ2
Which product is modeled by the number line below?
O (-3/4)
O (-24)
O (214)
O (3)(4)
Answer:
D
Step-by-step explanation:
there are 4 jumps. and 3 numbers between the jumps
help pls i’ll give brainlest if it’s correct .
Answer:
Pb (Lead)
General Concepts:
The number of protons in the nucleus of an element determines where it is on the Periodic Table and what element it is.
Step-by-step explanation:
Given: 82 Protons
Looking at the Periodic Table, the element that has 82 protons is Lead (Pb).
A normally distributed population has a mean of 500 and a standard deviation of 60. Determine the probability that a random sample of size 25 selected from the population will have a sample mean greater than or equal to 515.
Answer:
The value is [tex]P(\= X \ge 515 ) = 0.8944[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 500[/tex]
The standard deviation is [tex]\sigma = 60[/tex]
The sample size is n = 25
Generally the standard error of mean is mathematically represented as
[tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma _{\= x } = \frac{60}{\sqrt{25} }[/tex]
=> [tex]\sigma _{\= x } = 12[/tex]
Generally the probability that a random sample of size 25 selected from the population will have a sample mean greater than or equal to 515 is mathematically represented as
[tex]P(\= X \ge 515 ) = 1 - P(\= X < 515)[/tex]
Here [tex]P(\= X < 515) = P(\frac{\= x - \mu }{\sigma_{\= x }} < \frac{515 - 500}{12} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(\= X < 515) = P(Z < 1.25 )[/tex]
From the z table the probability of (Z < 1.25 )
[tex]P(Z < 1.25 ) = 0.10565[/tex]
So
[tex]P(\= X < 515) = 0.10565[/tex]
So
[tex]P(\= X \ge 515 ) = 1 - 0.10565[/tex]
=> [tex]P(\= X \ge 515 ) = 0.8944[/tex]
The proportion of brown M&M’s in a milk chocolate packet is approximately 14% (Madison, 2013). Suppose a package of M&M’s typically contains 52 M&M’s. a.) State the random variable. b.) Find the mean. c.) Find the variance. d.) Find the standard deviation.
Answer: a) Let x be a random variable that represents the number of brown M&M’s in a milk chocolate packet.
b) Mean =7.28
c) Variance = 6.2608
d) Standard deviation = 2.5022
Step-by-step explanation:
Given : The proportion of brown M&M’s in a milk chocolate packet is approximately : p=14% =0.14
We have outcomes for every randomly selection : 1) its in a milk chocolate packet 2) its not.
a) Let x be a random variable that represents the number of brown M&M’s in a milk chocolate packet.
So x follows binomial distribution.
b) Sample size : n=52 (given)
Mean [tex]= np = (0.14)(52) =7.28[/tex]
c) Variance = [tex]n p (1-p)= 52 (0.14)(1-0.14) =7.28(0.86)=6.2608[/tex]
d) Standard deviation =[tex]\sqrt{Variance}=\sqrt{6.2608}\approx2.5022[/tex]
if a single pane of glass obliterates 3% of the light passing through it, then the percent p of light that passes through n successive panes is given approximately by function p(n)-100(0.97)^x. what percent of light will pass through 25 panes
Answer:
46.7
Step-by-step explanation:
3% of light is obliterated from this pane of glass
1-0.03
= 97% = 0.97
The function has been given as
P(n) = 100(0.97)^x
Let's take our x to be 25 just as the question says
P(n) = 100(0.97)²⁵
P(25) = 46.697
This is approximately equal to 46.7
Therefore the percentage of light that would pass through 25 panes is 46.7
Mark charges a one-time fee of $12 for travel and then $7.50 per hour for labor. How
many hours will he need to work to make $42?
A.3
B.4
C.5
D.6
Answer:
$42
Step-by-step explanation:
D
A boy is twirling a model airplane on a string 4 feet long. If he twirls the plane at 0.5 revolutions per minute, how far does the plane travel in 4 minutes
Answer:
Airplane covers a distance of approximately 50.265 feet in 4 minutes.
Step-by-step explanation:
From Rotation Physics we know that angular speed is the number of revolutions done by a particle at a given time. If the boy is twirling a model airplane at constant speed, then we calculate such variable as follows:
[tex]\dot n = \frac{n}{t}[/tex] (Eq. 1)
Where:
[tex]\dot n[/tex] - Angular speed, measured in revolutions per minute.
[tex]n[/tex] - Number of revolutions done by airplane, measured in revolutions.
[tex]t[/tex] - Time, measured in minutes.
Now we clear the number of revolutions done by airplane within expression:
[tex]n = \dot n \cdot t[/tex]
If we know that [tex]\dot n = 0.5\,\frac{rev}{min}[/tex] and [tex]t = 4\,min[/tex], then we get that number of revolutions is:
[tex]n = \left(0.5\,\frac{rev}{min} \right)\cdot (4\,min)[/tex]
[tex]n = 2\,rev[/tex]
The airplane made two revolutions in four minutes.
Now, the distance covered by the airplane ([tex]s[/tex]), measured in feet, is calculated by means of the equation below:
[tex]s = 2\pi\cdot l\cdot n[/tex]
Where:
[tex]l[/tex] - Length of the string, measured in meters.
[tex]n[/tex] - Number of revolutions done by airplane, measured in revolutions (dimensionless).
If we get that [tex]n = 2\,rev[/tex] and [tex]l = 4\,ft[/tex], then the distance covered by the airplane in 4 minutes is:
[tex]s = 2\pi\cdot (4\,ft)\cdot (2\,rev)[/tex]
[tex]s \approx 50.265\,ft[/tex]
Airplane covers a distance of approximately 50.265 feet in 4 minutes.
In order to qualify for Glamazon's free shipping, Wendy
must purchase at least $50 worth of cosmetics. So far
she has 4 eye shadows which cost $8.00 a piece in her
basket. How many lip glosses can she get to qualify for
free shipping, if lip glosses are $10 each?
Answer:
2 lip glosses
explanation
4x8= 32
50-32=18
2 lipglosses would be $20
32+20=52
52>50 meaning she qualifies for free shipping
4 eye shadows -- 8 x 4 = $32
lip glosses $10 -- 32 + 10 + 10 = $52
to qualify for free shipping, wendy needs to buy 2 lip glosses.
need help on my homework please
Answer:
32
Step-by-step explanation:
[tex] \frac{8(8)}{2} = 32[/tex]
i think this is the answer
Answer:
32
Step-by-step explanation:
8 x 8 = 64
64/2 = 32
Hope this helps!
A quality control inspector has drawn a sample of 15 light bulbs from a recent production lot. Suppose that 60% of the bulbs in the lot are defective. What is the expected value of the number of defective bulbs in the sample
Answer:
9
Step-by-step explanation:
Expected number of defective is given as :
N x P = np
Where = number of the sample drawn from the production lot
P= percentage of bulbs In The lot which are defective
N = 15
P = 60% = 0.60
So when we do the multiplication,
We have:
NP = 15x0.60
= 9
So in conclusion the expected value of defective bulbs in the sample is 9.
Please help, please please!
4) Two-thirds of a number subtracted by five is thirty.
Answer:
x=52.5
Step-by-step explanation:
2/3x-5=30
2/3x=35
x=52.5
Estimating Sample Size: You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p ∗ = 54 % . You would like to be 90% confident that your esimate is within 1.5% of the true population proportion. How large of a sample size is required? (please do not do any intermediate rounding)
Answer:
The value is [tex]n = 2887[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.54[/tex]
The margin of error is [tex]E = 1.5 \% = 0.015[/tex]
From the question we are told the confidence level is 90% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } }{E} ]^2 * p(1-p)[/tex]
=> [tex]n = [\frac{1.645 }{0.015} ]^2 * 0.54(1-0.54)[/tex]
=> [tex]n = 2887[/tex]
This table gives a few (x,y) pairs of a line in the coordinates plane
What is x look at photo
Answer: it’s -32,0! - 10 on the left and -7 on the right because of you start at -12,14 you get the y value to 0 and increase by 10 since it is shown to be a increase in each x and y value
Step-by-step explanation:
A middle school sold 673 student tickets and staff tickets for the end of year carnival.
The tickets for the carnival were $2.50 for students and $4.00 for staff. The school made
$1,924.00 from student and staff ticket sales. Which equation will help to determine the
number of student tickets (s) and the number of staff tickets (1) sold?
OA
45 + 2.5f = 673
OB. suf = 1,924
• C. 2.5s + 4f = 673 + 1,924
OD. 2.5s + 4f = 1,924
|3x+1|-1=8Please help me
Answer:
Your answer is: x = 8/3 , -10/3
Solve for x by simplifying both sides of the equation, then isolating the variable.
Step-by-step explanation:
Hope this helped : )
Using the constant if proportionality, write an equation that represents this proportional relationship. Let x be the number of kilograms, and let y be the number of inches.
Answer:
the question 55 and 66
Step-by-step explanation:
Answer:
x: weight in kilograms
y: distance stretched in inches
proportionality constant: k = 1/3
Step-by-step explanation:
A Store makes a profit of 18 on a blanket after a markup of 30% what was the selling price
Answer:
78
Step-by-step explanation:
% profit= profit/CP ×100/1
Profit= selling price (S.P) - cost price(C.P)
%profit= 30
profit= 18
% profit= profit / CP×100/1
30= 18/CP ×100/1
30 = 1800 /CP
CP= 1800/30
CP =60
Recall that:
Profit= SP- CP
SP= Profit +CP
= 18+60
=78
Need help with 24 I’ve been stuck on it for a minute now idk
Solve: 2x – 1125
Yeeeeeeeeeeeeeeeeeeeeer
Answer:
2(x - 562.5)
Factor out the 2
-4x - 2y - z = 15
12x + 6y + 3z = 45
2x + 5y + 72 = -29
can yall tell me my GPA pl i dont know how to calculate it
Answer:your GPA is 3.914
Step-by-step explanation:your making me realized how stupid i am with those grades T-T
A lighthouse is located on an island 7 miles from the closest point on a straight shoreline. If the lighthouse light rotates clockwise at a constant rate of 8 revolutions per minute, how fast does the beam of light move across the shore when it is 3 miles from the point on the shore closest to the island
Answer:
[tex]\dfrac{800 \pi}{7} \ miles/min[/tex]
Step-by-step explanation:
From the given information:
We learned that the light rotates 8 revolutions per minute.
Therefore;
[tex]\dfrac{d \theta}{d t}= \dfrac{8 * 2 \pi}{1 \ min}[/tex]
[tex]\dfrac{d \theta}{d t}= 16\pi \ rads/min\\[/tex]
From the trigonometry formula, the tanget of the lighthouse in relation to the closest point on a straight shoreline can be expressed as:
[tex]tan \theta = \dfrac{x}{7}[/tex]
By differentiation with respect to t; we have:
[tex]\dfrac{d(tan \theta)}{dt} = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
[tex]\dfrac{d(tan \theta)}{d \theta}* \dfrac{d \theta}{dt} = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
By applying the chain rule:
[tex]sec^2 * \dfrac{d \theta }{d t} = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
[tex](1 + tan ^2 \theta) \dfrac{d \theta }{dt} = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
When x = 3 ; we have [tex]tan \theta = \dfrac{1}{7}[/tex]
[tex]\bigg (1 + \dfrac{1}{49} \bigg ) \dfrac{d \theta }{dt} = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
Also;
[tex]\dfrac{d \theta}{d t}= 16\pi \ rads/min\\[/tex]
[tex]\bigg (1 + \dfrac{1}{49} \bigg ) 16 \pi = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
[tex]\bigg ( \dfrac{50}{7} \bigg ) 16 \pi = \dfrac{dx}{dt}[/tex]
[tex]\dfrac{dx}{dt} = \dfrac{800 \pi}{7} \ miles/min[/tex]
what is the solution of
Answer:A
Step-by-step explanation:
Answer: D (12)
Step-by-step explanation: I put both equations into desmos and the coordinates are (12,23) and x=12. It's not 6!
f(x) =-7x -5
When the input is -5 , the output is __
Jamie saw an advertisement for a 6 ounce tube of toothpaste that cost $.90 how much should a 4 ounce tube cost?
Answer:
it will be $.60
Step-by-step explanation:
divide 90 by 6 and get 15. multiply 4 by 15 and get 60!
4 ounces would be 0.60 cents
Point P is in the interior of ∠NOQ. If m∠NOP = 37 and m∠NOQ = 123, what is m∠POQ?
Answer:
86
Step-by-step explanation:
angle NOP and angle POQ add up to create angle NOQ which equals 123 degrees. We just have to subtract 123-37 (NOP) to find the measure of angle POQ which equals 86 degrees
Answer:
The measure of angle ABD is 86 degrees.
Step-by-step explanation:
Which of the following pairs of functions are inverses of each other?
Answer: A
Step-by-step explanation: just took the test