Answer:
y = 8 - 5x
Step-by-step explanation:
both equations shares the same gradient as they are parallel
from y= 9-5x, the gradient is -5
subst x = 0, y=8, and m= -5 into the y = mx + c to find the value of c
8 = (-5)(0) + c
c= 8
therefore the eqn is y = 8 - 5x
A linear track begins at 0 meters and has a total distance of 100 meters to the finish line. Juliet starts at the 100 meter mark while practicing for a race. After running 45 meters how far is she from the beginning of the track?
Answer:
It’s D, 55.
Step-by-step explanation:
After running 45 meters, Juliet runs 55 meters from the beginning of the track
Divide £2.28 btw eve and amelie in the ratio 9:5 give your answer to the nearest penny Eve gets ? And amelie gets ?
Answer:
Eve gets 1.47 and Amelie gets 0.81
Step-by-step explanation:
the ratio is 9 to 5 so we can say 9x + 5x=2.28
14x=2.28
x=0.16
so eve gets 9x = 9(2.28/14) = 1.47
and amelie gets 5x = 5(2.28/14) = 0.81
A spherical balloon is inflated with gas at a rate of 600 cubic centimeters per minute.
(a) Find the rates of change of the radius when r = 50 centimeters and r = 85 centimeters.
r = 50 ? cm/min
r = 85 ? cm/min
(b) Explain why the rate of change of the radius of the sphere is not constant even though dv/dt is constant.
A.) dr/dt as a function runs parallel to the volume function, which is not linear
B.) The rate of change of the radius is a linear relationship whose slope is dV/dt
C.) The rate of change of the radius is a cubic relationship.
D.) The volume only appears constant; it is actually a rational relationship.
E.) dr/dt depends on r2, not simply r.
What is the value of m squared minus 2 m n + n squared for m = negative 2 and n = 4?
-4-2×-2×64
-4+4×64
-4+256
=252
Answer: (36)
hope this helps you have a wonderful day
Step-by-step explanation:
In a large population, 64% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? Give your answer as a decimal to 4 places.
Answer:
0.9940
Step-by-step explanation:
P(at least 1) = 1 − P(zero)
P(at least 1) = 1 − (1 − 0.64)⁵
P(at least 1) = 1 − (0.36)⁵
P(at least 1) = 0.9940
The probability that at least one of them has been vaccinated is 0.9939.
What is binomial distribution?
The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure. It helps to check the probability of getting “x” successes in “n” independent trials of a binomial experiment.
For the given situation,
Number of people vaccinated = 64% = 0.64
The formula of binomial distribution is
[tex]P(x:n,p) = nC_{x} p^x (1-p)^{n-x}[/tex]
Here x is the number of successes, x ≤ 1
n is the number of trials, n = 5
p is the probability of a success on a single trial, p = 0.64 and
where, [tex]nC_{x}=\frac{n!}{x!(n-x)!}[/tex]
The probability is [tex]P(X \leq 1)=1-P(X=0)[/tex]
[tex]P(X=0)= 5C_{0} (0.64)^{0} (1-0.64)^{5-0}[/tex]
⇒ [tex]P(X=0)= 1(1) (0.36)^{5}[/tex]
⇒ [tex]P(X=0)= 0.0060[/tex]
Thus, [tex]P(X \leq 1)=1-P(X=0)\\[/tex]
⇒ [tex]P(X \leq 1)=1-0.0060[/tex]
⇒ [tex]P(X \leq 1)=0.9939[/tex]
Hence we can conclude that the probability that at least one of them has been vaccinated is 0.9939.
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A spherical gemstone just fits inside a plastic cube with edges 12cm. a) calculate the volume of gemstone, to the nearest cubic centimeter. b) how much empty space is there.
Answer:
a) (V) = 904.78 of a sphere = 288pi diameter = 12
(V) = 1728cm^3 of a cube = face diagonal = 16.9cm
b) Difference Volume = 1728-904.78 = 823.22cm^3
Step-by-step explanation:
To find volume of an inscribed sphere within a square cube
We use 4 π/3 * r^3 for the equation
As Radius = 6 = 6cm this is the only thing plugged into the equation to create a division first then a multiplication square of radius and then a multiplication. 4pi /3 * 6^3
r^3 = 216
4pi/3 = 4.18
4.18 * 216 = 904.78
This means the answer is 288 pi cm^3.
Answer:
volume of gemstone = 905 cm^3
volume of empty space = 823 cm^3
Step-by-step explanation:
volume of cube = s^3, where s = length of edge
volume of sphere = (4/3)(pi)r^3, where r = radius of sphere
The cube has a 12-cm edge. The sphere fits tightly inside the cube, so the diameter, d, of the sphere is 12 cm. The radius is half the diameter, so radius = r = diameter/2 = 12 cm/2 = 6 cm.
a)
volume of sphere = (4/3)(pi)r^3
volume of sphere = (4/3)(3.14159)(6 cm)^3
volume of sphere = 905 cm^3
b)
The empty space is the difference between the volume of the cube and the volume of the sphere.
volume of cube = s^3
volume of cube = (12 cm)^3
volume of cube = 1728 cm^3
empty space = volume of cube - volume of sphere
empty space = 1728 cm^3 - 905 cm^3
empty space = 823 cm^3
1960 were polled. 279 of them preferred Rock and Roll. What is the % of these students?
Answer:
14.2% students
Step-by-step explanation:
279 / 1960 = 0.142
0.142 x 100% = 14.2 %
Explain how to find the range of a data set. Choose the correct answer below. A. The range is found by subtracting the first data entry from the last data entry. B. The range is found by adding the first and last data entries. C. The range is found by subtracting the minimum data entry from the maximum data entry. D. The range is found by adding the minimum and maximum data entries.
Answer:
C
Step-by-step explanation:
The range of a data set is the difference between the biggest and smallest values, so to find it, you just subtract the minimum from the maximum.
Please answer this correctly
4yd^2
2yd^2
6yd^2
Step-by-step explanation:
Rule: height x base/2
The area of the big triangle=2 x 4/2 = 4 yd^2
The area of the small one= 2 x2/2 =2yd^2
The total area of the trapezoid is the sum of these areas= 2+4=6yd^2
PLEASE ANSWER THIS!
In the diagram, PQRS, JQK and LRK are straight lines
Р
Question 1
Question 2
Question 3
J-
2yQ
Question 4
O
x
K
Question 5
Question 6
Question 7
Question 8
Question 9
M
33°
DO
R
L
2x/
Question 10
S
What is the size of the angle JKL?
Question 11
Question 12
Question 13
Question 14
A Question 15
Question 16
Question 17
Question 18
Question 19
37°
38°
36°
34°
35°
Answer:
38°
Step-by-step explanation:
The sum of angles that make a line is 180°; the sum of angles in a triangle is 180°. So, we have the following relations:
2x +y +A = 180
2y +x + B = 180
A +B +33 = 180
Adding the first two equations and subtracting the third, we get ...
(2x +y +A) +(2y +x +B) -(A +B +33) = 180 +180 -180
3x +3y -33 = 180
x + y - 11 = 60
x + y = 71
__
We know vertical angles are congruent, so in triangle QRK, we have ...
2y +2x +∠K = 180
∠K = 180 -2x -2y = 180 -2(x +y) = 180 -2(71)
∠JKL = 38°
Answer:
38 degrees
Step-by-step explanation:
simplify 2(f^4)^2/8f^12
Answer:
Step-by-step explanation:
2(f^4)^2/8(f^12)
2/8= 1/4
f^16/f^12
f^(16-12)= f^4
f^4/4 is the solution
A random sample of 1,000 StatCrunchU students contains 598 female and 402 males. We analyze responses to the question, "What is the total amount (in dollars) of your student loans to date?" Two sample T confidence interval: μ 1: Mean of Loans where Gender="Female" μ 2: Mean of Loans where Gender="Male" μ 1 − μ 2: Difference between two means (without pooled variances) 95% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit μ 1 − μ 2 516.74334 368.41116 907.34739 -206.29374 1239.7804 What can we conclude from the 95% confidence interval? Check all that apply. Group of answer choices
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
Here, we have,
From the provided 95% confidence interval, we can make the following conclusions:
The point estimate of the difference between the mean student loans for females and males is 516.74334 dollars.
The standard error of the difference between the means is 368.41116 dollars.
The degrees of freedom (DF) associated with the confidence interval is 907.34739.
The lower limit of the confidence interval is -206.29374 dollars.
The upper limit of the confidence interval is 1239.7804 dollars.
The confidence interval does not contain zero.
Since zero is not within the interval, we can conclude that the difference between the mean student loans for females and males is statistically significant at the 95% confidence level.
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
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The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Based on the 95% confidence interval provided for the difference in means between the loans of female and male StatCrunchU students, we can draw the following conclusions:
The sample difference in means is 516.74334.
The standard error of the difference is 368.41116.
The degrees of freedom (DF) for the analysis is 907.34739.
The lower limit of the confidence interval is -206.29374.
The upper limit of the confidence interval is 1239.7804.
Therefore, we can conclude the following:
The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Note: Since the confidence interval includes both positive and negative values, we cannot conclude with certainty whether there is a significant difference or not in the mean student loans between females and males. The confidence interval suggests that the difference could be positive, negative, or even zero.
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Help asap giving branlist!!
Answer: Thr amount spent to manufacture each radio.
Step-by-step explanation: I put two and two together...lol...plz brainlest.
Answer:
The amount spent to manufacture each radio.
Step-by-step explanation:
125 is the start up cost and each radio costs 5.25 to make.
Which of the following rational numbers is greater than 5/17 but less than 6/17.
Answer:
[tex]\frac{51}{170},\ \frac{52}{170},\frac{53}{170},...................\ \frac{59}{170}[/tex]
Step-by-step explanation:
As mention in the question number is
[tex]\frac{5}{17}\ < \frac{6}{17} \\multiply\ both\ side\ by\ 10\ in\ numerator\ and\ denominator\ we\ get \\\frac{50}{170} <\frac{60 }{170}\\[/tex]
Therefore the number is :
[tex]\frac{51}{170},\ \frac{52}{170},\frac{53}{170},...................\ \frac{59}{170}[/tex]
Some scientists believe there is a limit to how long humans can live. One supporting argument is that during the past century, life expectancy from age 65 has increased more slowly than life expectancy from birth, so eventually these two will be equal, at which point, according to these scientists, life expectancy should increase no further. In 1900, life expectancy at birth was 45 years, and life expectancy at age 65 was 75 yr. In 2010, these figures had risen to 78.7 and 84.5, respectively. In both cases, the increase in life expectancy has been linear. Using these assumptions and the data given, find the maximum life expectancy for humans.
Answer:
The maximum life expectancy for humans is approximately 87 years.
Step-by-step explanation:
We have to calculate the point in which both linear functions (Life expectancy from birth and Life expectancy from age 65) intersect, as this is the point in which is estimated to be the maximum life expectancy for humans.
NOTE: to simplify we will consider t=0 to the year 1900, so year 2010 becames t=(2010-1900)=110.
The linear function for Life expectancy from birth can be calculated as:
[tex]t=0\rightarrow y=45\\\\t=110\rightarrow y=78.7\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{78.7-45}{110-0}=\dfrac{33.7}{110}=0.3064\\\\\\y=0.3064t+45[/tex]
The linear function for Life expectancy from age 65 can be calculated as:
[tex]t=0\rightarrow y=75\\\\t=110\rightarrow y=84.5\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{84.5-75}{110-0}=\dfrac{9.5}{110}=0.0864\\\\\\y=0.0864t+75[/tex]
Then, the time t where both functions intersect is:
[tex]0.3064t+45=0.0864t+75\\\\(0.3064-0.0864)t=75-45\\\\0.22t=30\\\\t=30/0.22\\\\t=136.36[/tex]
The time t=136.36 corresponds to the year 1900+136.36=2036.36.
Now, we can calculate with any of both functions the maximum life expectancy:
[tex]y=0.0864(136.36)+75\\\\y=11.78+75\\\\y=86.78\approx87[/tex]
The maximum life expectancy for humans is approximately 87 years.
1/2x+4=2/3x+1, solve for x
Answer:
x=18
Step-by-step explanation:
Step 1: Subtract 2/3x from both sides.
1/2x+4=2/3x+1
-2/3x -2/3x
= -1/6x+4=1
Step 2: Subtract 4 from both sides.
-1/6x+4=1
-4 -4
= -1/6x=-3
Step 3: Multiply both sides by 6/(-1).
-1/6x=-3
*6/(-1) * 6/(-1)
x=18
find the slope of the line through points 8,2 and -1,-4
Answer:
2/3
Step-by-step explanation:
We can find the slope by using the slope formula
m= (y2-y1)/(x2-x1)
= (-4-2)/(-1-8)
= -6/ -9
= 2/3
The average score Josie had in 6 subjects is 72 and her average score after 2 additional subjects were added is 74.25. If she scored 80 in the 7th subject, what was her score in the 8th subject correct to the nearest whole number?
Answer:82
Step-by-step explanation:
a+b+c+d+e+f/6=72
a+b+c+d+e+f=6*72
a+b+c+d+e+f=432
a+b+c+d+e+f+g+h/8=74.25
a+b+c+d+e+f+g+h=594
g=80
h=?
432+80+h=594
512+h=594
h=82
hope it helps brainleast plz...
simplify 8-(3a+8)=
havent done these in a while so...
Answer:
3
Step-by-step explanation:
8-(3a+8)
8-(11a)
8-11a
a=11-8
a=3
Answer:
0
Step-by-step explanation:
8-(3a+8)=0
8-3a-8=0
-3a=0
a=0
What is simplified form of the fifth square root of x times the fifth square root of x times the fifth square root of x times the fifth square root of x
Answer: This was a bit hard to understand, x times the 5th root of x
Step-by-step explanation:
When you multiply square roots of the same root and inside value, they essentially get rid of the square roots. So the first two terms boil down to just x. Then multiply x by the 5th root of x to get:
[tex]x\sqrt[5]{x}[/tex]
Answer:
[tex]x[/tex]
Step-by-step explanation:
Apply exponent rules.
[tex]\sqrt{x} =x^\frac{1}{2}\\\:a^b\times \:a^c=a^{b+c}[/tex]
[tex]\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x}[/tex]
[tex]x^{\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}[/tex]
[tex]x^1[/tex]
A store has 80 modems in its inventory, 30 coming from Source A and the remainder from Source B. Of the modems from Source A, 20% are defective. Of the modems from Source B, 8% are defective. Calculate the probability that exactly two out of a sample of five modems selected without replacement from the store’s inventory are defective.
Answer:
0.102
Step-by-step explanation:
The number of defective modems in the inventory is 20% * 30 + 8% * 0.50 =10 (out of 80)
Note that the number of defectives in the inventory is fixed i.e. we are told that there is 1/8 probability that a modem in the inventory is defective, but rather that exactly 1/8 of all modems are defective.
The probability that exactly two modems in a random sample of five are defective is :
(10↓2)(70↓3) / (80↓5) = 0.102
Which line is perpendicular to the line Y= -1/3x -2 and passes through the point (1,4)
Answer:
work is shown and pictured
The sum of three consecutive odd numbers is 315 what are the numbers?
Answer:
Search Results
Featured snippet from the web
Which means that the first number is 104, the second number is 104 + 1 and the third number is 104 + 2. Therefore, three consecutive integers that add up to 315 are 104, 105, and 106.
Step-by-step explanation:
Help asap giving branlist!!
Answer:
option 3
Step-by-step explanation:
x = 2 is a vertical line with an x-intercept of (2, 0) so the answer is Option 3.
Answer:
Option 3
Step-by-step explanation:
The value of x will always be 2. Y can be anything it wants to be and x will still be 2 no matter what, You could pick multiple points on the line for each graph, and only Option 3 will have x always being 2.
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 258.7 and a standard deviation of 63.5. (All units are 1000 cells/muL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 68.2 and 449.2? b. What is the approximate percentage of women with platelet counts between 195.2 and 322.2?
Answer:
a) [tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]
And from the empirical rule we know that this probability is 0.997 or 99.7%
b)[tex] P(195.2 <X<322.2)[/tex]
Using the z score we have:
[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]
[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]
And within one deviation from the mean we have 68% of the values
Step-by-step explanation:
For this case we defien the random variable of interest X as "blood platelet counts" and we know the following parameters:
[tex] \mu = 258.7, \sigma =63.5[/tex]
Part a
We can use the z score formula given by:
[tex] z =\frac{\bar X -\mu}{\sigma}[/tex]
And we want this probability:
[tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]
And from the empirical rule we know that this probability is 0.997 or 99.7%
Part b
For this case we want this probability:
[tex] P(195.2 <X<322.2)[/tex]
Using the z score we have:
[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]
[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]
And within one deviation from the mean we have 68% of the values
Find the area of the smaller sector.
Round to the nearest tenth.
Help needed fast
Answer:
About 22.2 square feet
Step-by-step explanation:
First, you need to find the area of the full circle. The area of a circle is \pi r^2, which in this case is:
[tex]\pi r^2 = \pi \cdot 7.13^2\approx 159.628[/tex]
Now, since the sector is only 50 out of the total 360 degrees in a circle, you need to multiply this value by 50/360, which yields and area of about 22.2 square feet. Hope this helps!
Which equation can be used to find mMN
Answer:
Its depending on the angle
A 2-pack of scented candles costs $0.95. What is the unit price, rounded to the nearest cent?i mark the 1st answer brainliest
Step-by-step explanation:
Cost of 2 pack = 0.95
Cost of 1 pack = 0.95 ÷ 2 = 0.475
Unit price = 0.475
Arun’s restaurant bill is $58, and he wants to leave the waiter an 18 percent tip. What will Arun’s total bill be? $10.44 $47.56 $68.44 $76.00
Answer:
The Answer is 68.44. I wish it helpsAnswer:
68.44$
Step-by-step explanation:
x=18*58/100=10.44 $(the tip)
58+10.44=68.44 ( the bill )
The lengths of text messages are normally distributed with a population standard deviation of 6 characters and an unknown population mean. If a random sample of 21 text messages is taken and results in a sample mean of 30 characters, find a 80% confidence interval for the population mean. Round your answers to two decimal places. z0.10 z0.05 z0.04 z0.025 z0.01 z0.005 1.282 1.645 1.751 1.960 2.326 2.576
Answer:
The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.
Step-by-step explanation:
We have the standard deviation for the population, so we can use the normal distribution. If we had the standard deviation for the sample, we would have to use the t-distribution.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.8}{2} = 0.1[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.5 = 0.9[/tex], so [tex]z = 1.282[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.282*\frac{6}{\sqrt{21}} = 1.68[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 30 - 1.68 = 28.32 characters.
The upper end of the interval is the sample mean added to M. So it is 30 + 1.68 = 31.68 characters.
The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.
