Answer:
y = - (1/2) x + 1
Step-by-step explanation:
The given equation of the line is:
2 x - y - 7 = 0
solving for y gives:
2 x - 7 = y
so y = 2 x - 7
where the slope is "2", which is fundamental to know in order to construct a perpendicular line to it by using the "opposite of the reciprocal" of the given slope.
So in our case, the slope of the perpendicular line must be: "- 1 / 2" (negative one half).
now we can build the equation of the new line, using this slope and requesting the point (4, -1) to be in it:
y = - (1/2) x + b
-1 = - (1/2) (4) + b
-1 = - 2 + b
solve for b:
b = 2 - 1 = 1
Then the equation of the perpendicular line is:
y = - (1/2) x + 1
y= -1/2 x+1
Step-by-step explanation:
2x-y-7=0
2x-7=y
y=2x-7
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?
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
maurice has 20 strips of leather that are each 4 1/2 feet long. maurice wants to punch holes in each strip of leather that are 3/8 of a foot apart. maurice will use the expression shown to determine the number of hles to punch in each strip of leather.
4 1/2 ÷3/8
which expression will also give the number of holes that maurice will punch into each strip of leather?
2/9 ÷8/3
2/9÷3\8
9/2 . 8/3
9/2 . 3/8
Answer:
A
Step-by-step explanation:
Answer:
9/2 . 8/3
Step-by-step explanation: Both equations equal 12
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
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]
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
What is the slope of the line given by the equation below?
y+ 2 = -3(x-5)
O A. 2
O B.-3
O c.3
O D.-5
Answer:
B. -3
Step-by-step explanation:
y + 2 = -3(x - 5)
y + 2 = -3x - 15
y = -3x - 15 - 2
y = -3x - 17
y = mx + b
m = -3
can i get brainliest please?
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 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.
I Need help
Which of the following responsibilities are held by federal government. choose all that apply
1. protecting national parks
2.administering healthcare
3.providing social security
4.managing intercity traffic
5.creating garbage collection services
6.chartering city governments into existence
there are two answers
Answer:
I thinks it's 2 an 3 sorry if I'm wrong btw have a nice day
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:
Help out please ASAP!
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
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]
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]
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
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!
Which of the following pairs of functions are inverses of each other?
Answer: A
Step-by-step explanation: just took the test
Leanna has a rectangular piece of fabric. The fabric is 24 inches wide and 40 inches long. Leanna folds the piece of fabric along its diagonal to form a triangular scarf.
What is the area, in square inches, of the triangular scarf?
Given:
Length of a rectangular piece of fabric, l = 24 inches
Width, w = 40 inches
Leanna folds the piece of fabric along its diagonal to form a triangular scarf.
To find:
The area of the triangular scarf.
Solution:
Area of the rectangular piece of fabric is
[tex]Area=length\times width[/tex]
[tex]Area=24\times 40[/tex]
[tex]Area=960[/tex]
Area of rectangular piece of fabric is 96 sq. inches.
We know that diagonal of a rectangle divides the rectangle in two equal parts.
Leanna folds the piece of fabric along its diagonal to form a triangular scarf. So, area of triangular scarf is half of area of rectangular piece of fabric.
[tex]\text{Area of triangular scarf}=\dfrac{1}{2}\times 960[/tex]
[tex]\text{Area of triangular scarf}=480[/tex]
Therefore, the area of triangular scarf is 480 sq. inches.
What is an equation to 3,
509
Answer:
3000+509
Step-by-step explanation:
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:
PLEASE SOMEONE HELP QUICK I WILL GIVE BRAINLIEST
Answer:
134 deg
Step-by-step explanation:
x + 46 = 180
v + 46 = 180
Solve
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
Suppose that, on average, 1 person in 1000 makes a numerical error in preparing his or her income tax return. If 10,000 returns are selected at random and examined, find the probability that 6, 7, or 8 of them contain an error.
Answer:
0.2657
Step-by-step explanation:
Given that:
Probability of Error (p) = 1/ 1000 = 0.001
Number of trials (n) = 10000
μ = (n * p) = 10000 * 0.001 = 10
Using the binomial distribution :
P(x, μ) = e^-μ (μ^x) / x!
for x = 6
P(6, 10) = e^-10 (10^6) / 6!
P(6, 10) = 0.0000453999 (1388.8888) = 0.06305541263112
for x = 7
P(7, 10) = e^-10 (10^7) / 7!
P(7, 10) = 0.0000453999 (1984.1269) = 0.09007916284731
for x = 8
P(8, 10) = e^-10 (10^8) / 8!
P(8, 10) = 0.0000453999 (2480.1587) = 0.11259895696413
P(6) + P(7) + P(8)
0.06305541263112 + 0.09007916284731+ 0.11259895696413
= 0.26573353244256
= 0.2657
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]
Solve: 2x – 1125
Yeeeeeeeeeeeeeeeeeeeeer
Answer:
2(x - 562.5)
Factor out the 2
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
-4x - 2y - z = 15
12x + 6y + 3z = 45
2x + 5y + 72 = -29
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!
Need help with 24 I’ve been stuck on it for a minute now idk