Answer: y= -2/3 + 8/3
Step-by-step explanation:
-2/3 is the slope so you just need the y-intercept to write the equation in general form or slope intercept form
4= -2/3(-2) +b
4 = 4/3 + b
-4/3 -4/3
b= 8/3
general form is y= -2/3 + 8/3
How many solutions does the system have? y = -2x-4 \\\\ y = 3x+3
Answer:
The system has one solution.
Step-by-step explanation:
We have two equations:
y = -2x - 4
y = 3x + 3
Equalling them:
y = y
-2x - 4 = 3x + 3
5x = -7
[tex]x = -\frac{7}{5}[/tex]
And
[tex]y = 3x + 3 = 3(-\frac{7}{5}) + 3 = \frac{-21}{5} + 3 = \frac{-21}{5} + \frac{15}{5} = -\frac{6}{5}[/tex]
Replacing in the other equation we should get the same result.
[tex]y = -2x - 4 = -2(-\frac{7}{5}) - 4 = \frac{14}[5} - 4 = \frac{14}{4} - \frac{20}{5} = -\frac{6}{5}[/tex]
So the system has one solution.
This Question: 4 pts
1 of 11 (0 complete)
Music Preferences
Students at a high school were polled to determine the type of music they preferred. There were 1960 students who
completed the poll. Their responses are represented in the circle graph.
Rap 916
Alternative 46
Rock and Roll 279
Country 183
Jazz 32
Other 89
About What % of the students who completed the poll preferred rock and roll music.
(Round to one decimal place as needed.)
Answer:
The percentage of the students who completed the poll preferred rock and roll music.
P(RR) = 0.1423 = 14.23 %
Step-by-step explanation:
Explanation:-
Given total number of students n(S) = 1960
Given the Students at a high school were polled to determine the type of music they preferred.
Rap 916
Alternative 46
Rock and Roll 279
Country 183
Jazz 32
Other 89
Let ' RR' be the event of Rock and Roll preferred music
given Rock and Roll = 279
n( RR) = 279
The percentage of the students who completed the poll preferred rock and roll music.
[tex]P(RR) = \frac{n(RR)}{n(s)} = \frac{279}{1960}[/tex]
P(RR) = 0.1423 = 14.23 %
Which equation has a k-value of -12? y=−12x y=12+12x y=x−12 y=12x+1
Answer:
y = -12x
Step-by-step explanation:
We assume you're concerned with the form ...
y = kx
Putting -12 for k gives ...
y = -12x . . . . . the first choice
_____
Additional comment
The answer will depend somewhat on the context of the question. If you're studying proportions, then "k" is the constant of proportionality as shown above.
If you're studying function translations, then "k" is the vertical translation, as in ...
y = m(x -h) +k
In this case, the equation y = x -12 will have a "k" value of -12.
What value of x makes 3(x + 4) = 3x + 4 true?
Well lets see.
[tex]3(x+4)=3x+4\implies 12 = 4\implies x\notin\mathbb{C}[/tex].
There are no such x-es that satisfy the equation.
Find the median of the data in the dot plot below.
The value of the median is 25 from the dot plot because the middle value is 25 on the dot plot,
What is the median?A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.
We have a dot plot shown in the picture.
As we can see in the dot plot there are a total of 9 dots.
4 dots left side and 4 dots right side.
One dot is left which is pointing to the value 25 at the number line.
Thus, the value of the median is 25 from the dot plot because the middle value is 25 on the dot plot,
Learn more about the median here:
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what is the value of this expression plssssss 8z-3 when z =7
Answer:
53
Step-by-step explanation:
8•7 is 56
56 - 3 is 53
Answer:
53
Step-by-step explanation:
z = 7
8z is the same as saying 8×z
8×7-3 (do multiplication first)
56-3 = 53
What is the next pattern ?
Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college $26,000. Assuming the college wishes to offer a total of seven sections, accommodate 220 students, and bring in $292,000 in revenues, how many sections of each course should it offer?
Finite Math section(s)
Applied Calculus section(s)
Computer Methods section(s)
Answer:
meh
Step-by-step explanation:
In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.9 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 65 inches. The probability that the study participant selected at random is less than 65 inches tall is nothing. (Round to four decimal places as needed.)
Answer:
The probability that a study participant has a height that is less than 65 inches is 0.1103.
Step-by-step explanation:
We are given that the heights in the 20-29 age group were normally distributed, with a mean of 69.9 inches and a standard deviation of 4.0 inches.
A study participant is randomly selected.
Let X = heights in the 20-29 age group.
So, X ~ Normal([tex](\mu=69.9,\sigma^{2} =4.0^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean height = 69.9 inches
[tex]\sigma[/tex] = standard deviation = 4.0 inches
Now, the probability that a study participant has a height that is less than 65 inches is given by = P(X < 65 inches)
P(X < 65 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{65-69.9}{4}[/tex] ) = P(Z < -1.225) = P(Z [tex]\leq[/tex] 1.225)
= 1 - 0.8897 = 0.1103
The above probability is calculated by looking at the value of x = 1.225 in the z table which lies between x = 1.22 and x = 1.23 which has an area of 0.88877 and 0.89065 respectively.
Alguien me puede ayudar con en esto por favor !!!
Answer:
y=cosx
Step-by-step explanation:
cosx has a domain of all real numbers
Find x in this 45°-45°-90° triangle.
145972
x
X=
4.572
9
18
PLEASE HELP Last year Lenny had an annual earned income of $58,475. He also had passive income of $1,255, and capital gains of $2,350. What was Lenny’s total gross income for the year?
a.
$58,475
b.
$59,730
c.
$60,985
d.
$62,080
Please select the best answer from the choices provided
A
B
C
D
Answer:
D
Step-by-step explanation:
The total mass of the Sun is about 2×10^30 kg, of which about 76 % was hydrogen when the Sun formed. However, only about 12 % of this hydrogen ever becomes available for fusion in the core. The rest remains in layers of the Sun where the temperature is too low for fusion.
Part A
Use the given data to calculate the total mass of hydrogen available for fusion over the lifetime of the Sun.
Express your answer using two significant figures.
Part B
The Sun fuses about 600 billion kilograms of hydrogen each second. Based on your result from part A, calculate how long the Sun’s initial supply of hydrogen can last. Give your answer in both seconds and years.
Express your answer using two significant figures.
Part D
Given that our solar system is now about 4.6 billion years old, when will we need to worry about the Sun running out of hydrogen for fusion?
Express your answer using two significant figures.
Answer:
A. 1.8 ×[tex]10^{30}[/tex] Kg
B i. 3.0 × [tex]10^{17}[/tex] seconds
ii. 9.6 × [tex]10^{9}[/tex] years
C. After 9.2 × [tex]10^{9}[/tex] (9.2 billion) years
Step-by-step explanation:
Given that the mass of the Sun = 2× [tex]10^{30}[/tex] Kg.
Mass of hydrogen when Sun was formed = 76% of 2× [tex]10^{30}[/tex] Kg
= [tex]\frac{76}{100}[/tex] ×2× [tex]10^{30}[/tex] Kg
= 1.52 × [tex]10^{30}[/tex] Kg
Mass of hydrogen available for fusion = 12% of 1.52 × [tex]10^{30}[/tex] Kg
= [tex]\frac{12}{100}[/tex] × 1.52 × [tex]10^{30}[/tex] Kg
= 1.824 ×[tex]10^{30}[/tex] Kg
A. Total mass of hydrogen available for fusion over the lifetime of the sun is 1.8 ×[tex]10^{30}[/tex] Kg.
B. Given that the Sun fuses 6 × [tex]10^{11}[/tex] Kg of hydrogen each second.
i. The Sun's initial hydrogen would last;
[tex]\frac{1.8*10^{30} }{6*10^{11} }[/tex]
= 3.04 × [tex]10^{17}[/tex] seconds
The Sun's hydrogen would last 3.0 × [tex]10^{17}[/tex] seconds
ii. Since there are 31536000 seconds in a year, then;
The Sun's initial hydrogen would last;
[tex]\frac{3.04*10^{17} }{31536000}[/tex]
= 9.640 × [tex]10^{9}[/tex] years
The Sun's hydrogen would last 9.6 × [tex]10^{9}[/tex] years.
C. Given that our solar system is now about 4.6 × [tex]10^{9}[/tex] years, then;
[tex]\frac{9.6*10^{9} }{4.6*10^{9} }[/tex]
= 2.09
So that; 2 × 4.6 × [tex]10^{9}[/tex] = 9.2 × [tex]10^{9}[/tex] years
Therefore, we need to worry about the Sun running out of hydrogen for fusion after 9.2 × [tex]10^{9}[/tex] years.
Part(A): The total mass of hydrogen available 9.6 billion years.
Part(B): The total time is 5.10 billion years.
Part(D): The hydrogen will last [tex]5.04\times 10^9 \ years[/tex]
Mass of the sun:Our sun is the largest object in our solar system. The mass of the sun is approximately [tex]1.988\times 1030[/tex] kilograms
Part(A):
Given that,
The total mass of the Sun =[tex]2\times10^{30} kg[/tex]
Mass of hydrogen in Sun = [tex]2\times10^{30} \times0.76\ kg[/tex]
The mass of hydrogen ever available for fusion is,
[tex]2\times10^{30} \times 0.76 \times 0.12 kg = 1.824\times 10^{29}[/tex]
Mass of hydrogen fuses each second = 600 billion kg/second.
Time hydrogen will last in seconds=[tex]1.824\times 10^{29}seconds.[/tex]
[tex]= 0.00304\times 10^{29 }= 3.04\times 10^{17}.[/tex]
Time hydrogen will last in seconds =[tex]1 year = 31,536,000 seconds.[/tex]
[tex]31,536,000 x = 3.04\times 10^{17} = 9.6 \ billion \ years.[/tex]
(B) Present age of sun = [tex]9.6-4.5 \ billion \ years[/tex]
The time when we need to worry about Sun running out of hydrogen for fusion = 5.10 billion years.
(D) The solar system is 4.6 billion years old that is [tex]4.6\times 10^9\ years[/tex]
And in part (B) we have calculated that hydrogen will last [tex]9.64\times 10^9[/tex] then,
[tex]9.64\times 10^9-4.6\times 10^9=5.04\times 10^9[/tex]
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A boy is playing a ball in a garden surrounded by a wall 2.5 m high and kicks the ball vertically up from a height of 0.4 m with a speed of 14 m/s. For how long is the ball above
the height of the wall.
Answer:
2.54 seconds
Step-by-step explanation:
We can use the following equation to model the vertical position of the ball:
S = So + Vo*t + a*t^2/2
Where S is the final position, So is the inicial position, Vo is the inicial speed, a is the acceleration and t is the time.
Then, using S = 2.5, So = 0.4, Vo = 14 and a = -9.8 m/s2, we have that:
2.5 = 0.4 + 14*t - 4.9t^2
4.9t^2 - 14t + 2.1 = 0
Solving this quadratic equation, we have that t1 = 2.6983 s and t2 = 0.1588 s.
Between these times, the ball will be higher than 2.5 m, so the amount of time the ball will be higher than 2.5 m is:
t1 - t2 = 2.6983 - 0.1588 = 2.54 seconds
A multiple-choice standard test contains total of 25 questions, each with four answers. Assume that a student just guesses on each question and all questions are answered independently. (a) What is the probability that the student answers more than 20 questions correctly
Answer:
[tex]P(x>20)=9.67*10^{-10}[/tex]
Step-by-step explanation:
If we call x the number of correct answers, we can said that P(x) follows a Binomial distribution, because we have 25 questions that are identical and independent events with a probability of 1/4 to success and a probability of 3/4 to fail.
So, the probability can be calculated as:
[tex]P(x)=nCx*p^{x}*q^{n-x}=25Cx*0.25^{x}*0.75^{25-x}[/tex]
Where n is 25 questions, p is the probability to success or 0.25 and q is the probability to fail or 0.75.
Additionally, [tex]25Cx=\frac{25!}{x!(25-x)!}[/tex]
So, the probability that the student answers more than 20 questions correctly is equal to:
[tex]P(x>20)=P(21)+P(22)+P(23)+P(24)+P(25)[/tex]
Where, for example, P(21) is equal to:
[tex]P(21)=25C21*0.25^{21}*0.75^{25-21}=9.1*10^{-10}[/tex]
Finally, P(x>20) is equal to:
[tex]P(x>20)=9.67*10^{-10}[/tex]
What is the simplest form of this expression?
4(y + 2) - 2
Answer & Step-by-step explanation:
4(y + 2) - 2
Distribute 4 to (y + 2)
4y + 8 - 2
Combine like terms
4y + 6
So, your answer in the simplest form is 4y + 6
123 grams is rounded to nearest whole. Write down the minimum possible mass it could have been.
Answer:
The nearest whole is 122.99 repeated
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
First finding height using Pythagoras theorem
(H)²=(B)²+(P)²
8.2²=5.4²+P²
P² = 67.24 - 29.16
P² = 38.08
P = 6.2
Now
Volume of cone = (1/3)πr²h
= (1/3)(3.14)(5.4)²(6.2)
= (1/3)(567.9)
= 189.2 cm³
Which point is coplanar with B , C , H ?
Answer:
G
Step-by-step explanation:
Point G is coplanar with points B, C, H.
the length of a ruler is 170cm,if the ruler broke into four equal parts.what will be the sum of the length of three parts
Answer:
Step-by-step explanation:Srry it's bit rough...
You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h = 130 and a square base with side s = 870
To impress your Egyptian subjects, find the volume of the pyramid.
Answer:
32799000 cubic units
Step-by-step Explanation:
Height if the Pyramid=130 Units
Side Length of square base=870 Units
Volume of a Pyramid=[tex]\frac{1}{3}[/tex]* Base Area*Height
Since the base is a square,
Area of a Square of side length s[tex]=s^2[/tex]
Therefore:
Volume[tex]=\frac{1}{3}*870^2*130[/tex]
=32799000 cubic units
The volume of your pyramid is 32799000 cubic units.
Answer:
V = 3.28x10⁷
Step-by-step explanation:
The volume of a pyramid is given by:
[tex] V = \frac{1}{3}bh [/tex]
Where:
b: is the base of the pyramid
h: is the height of the pyramid = 130
The base of the square base of the pyramid is given by:
[tex] b = s^{2} [/tex]
Where:
s: is the side of the square base = 870
Thus, the base of the square base of the pyramid is:
[tex] b = s^{2} = (870)^{2} = 7.56 \cdot 10^{5} [/tex]
Now, the volume of a pyramid is:
[tex] V = \frac{1}{3}bh = \frac{1}{3}(7.56 \cdot 10^{5})*130 = 3.28 \cdot 10^{7} [/tex]
Therefore, the volume of the pyramid is 3.28x10⁷.
I hope it helps you!
Which triangle congruence postulate can be used to prove that FEH=HGF?
SAS
HL
ASA
SSS
Answer:
Option (2).
Step-by-step explanation:
From the figure attached,
EFGH is a quadrilateral and FH is line which divides the quadrilateral into two right triangles, ΔFEH and ΔHGF.
In ΔFEH and ΔHGF,
Sides EH ≅ FG [Given]
FH ≅ FH [reflexive property]
ΔFEH ≅ ΔHGF [HL (Hypotenuse - length) postulate of congruence]
Option (2) will be the answer.
85% of z is 106,250. What is z?
Answer:
z=12500
Step-by-step explanation:
Of means multiply and is means equals
85% *z = 106250
Change to decimal form
.85z = 106250
Divide each side by .85
.85z/.85 = 106250 /.85
z=12500
A recent graduate school study of a random sample of 250 US manufacturing companies determined the average financial report preparation time was 68.04 days with a standard deviation of 35.74 days. Calculate to three decimal places the 95 percent confidence interval for the mean report prep time for all US manufacturing companies. [63.001, 72.008] [63.957, 75.568] [63.505, 72.414] [61.612, 74.468] [63.612, 72.468]
Answer:
[tex]68.04-1.959\frac{35.74}{\sqrt{250}}=63.618[/tex]
[tex]68.04+1.959\frac{35.74}{\sqrt{250}}=72.461[/tex]
And the best option for this case would be
Step-by-step explanation:
Information given
[tex]\bar X=68.04[/tex] represent the sample mean
[tex]\mu[/tex] population mean
s=35.74 represent the sample standard deviation
n=250 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=250-1=249[/tex]
The Confidence level is 0.95 or 95%, and the significance [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this case woud be [tex]t_{\alpha/2}=1.956[/tex]
And replacing we got:
[tex]68.04-1.959\frac{35.74}{\sqrt{250}}=63.618[/tex]
[tex]68.04+1.959\frac{35.74}{\sqrt{250}}=72.461[/tex]
And the best option for this case would be
The accompanying data are the times to failure (in millions per cycle) of high-speed turbine engine bearings made out of two different compounds. These were taken from "Analysis of Single Classification Experiments Based on Censored Samples from the Two-parameter Weibull Distribution" by J.I. McCool (The Journal of Statistical Planning and Inference, 1979) Compound 1 3.03 5.53 5.60 9.30 9.92 12.51 12.95 15.21 16.04 16.84 Compound 2 3.19 4.26 4.47 4.53 4.67 4.69 5.78 6.79 9.37 12.75 (a) Find the 0.84 quantile of the Compound 1 failure times (b) Give the coordinates of the two lower-left points that would appear on a normal plot of the compound 1 data (c) Make back-to-back stem-and-leaf plots for comparing the life length properties of bearings made from Compounds 1 and 2 (d) Make (to scale) side-by-side boxplots for comparing the life lengths for the two compounds. Mark numbers on the plots indicating the locations of their main features (e) Compute the sample means and standard deviations of the two sets of lifetimes (f) Describe what your answers to parts (c), (d), and (e) above indicate about the life lengths of these turbine bearings.
Find the given attachments
Salinas Corporation has net income of $15 million per year on net sales of $90 million per year. It currently has no long-term debt but is considering a debt issue of $20 million. The interest rate on the debt would be 7%. Salinas Corp. currently faces an effective tax rate of 40%. What would be the annual interest tax shield to Salinas Corp. if it goes through with the debt issuance?
Answer:
The annual interest tax shield to Salinas Corp would be of $560,000
Step-by-step explanation:
In order to calculate the annual interest tax shield to Salinas Corp if it goes through with the debt issuance we would have to calculate the following formula:
Annual Interest tax shield = Interest * tax
Interest = debt *rate of interest
Interest=$20 million * 0.07
Interest= $ 1.40 million
tax= 40%
Therefore, Annual Interest tax shield =$1.40 million * 0.40
Annual Interest tax shield = $560,000
The annual interest tax shield to Salinas Corp would be of $560,000
5 of 5
It is worked out that if 5 ladles full of soup are given to
each person,
140 people can be fed.
The customers have complained in the past that the
portions are too small.
The cook decides to give 7 ladles full of soup to each
person.
How many people can now be fed soup?
people
Answer:
Number of people that can be served 7 ladles = 100 people
Step-by-step explanation:
We are told that;
Initial number of ladles proposed per person = 5
Number of persons to be fed based on 5 ladles = 140 persons
Thus, amount of ladles based on that data is;
140 people x 5 ladle/1 person = 700 ladles full of soup
Now, since the cook decides to give 7 ladles full of soup to each person, the number of people that can be fed will now be;
700 ladles ÷ 7 ladles/person = 100 persons
Which of the following terminating decimals is equivalent to -1 3/4
Answer:
-1.75
Step-by-step explanation:
Write the number one and three quarter million in figures.
Answer 1750000
Step-by-step explanation:
The number "one and three-quarter million" can be written in figures as 1,750,000.
Given the number one and three quarter million.
"One" represents the digit 1.
"Three-quarter" means three-fourths or 3/4.
In decimal form, this fraction is 0.75.
"Million" signifies a value of 1,000,000.
To represent this number in figures, we combine these components:
We start with the digit 1, representing "one."
Then we append the value 750,000, which corresponds to "three-quarter million."
Combining these two parts, we have 1,750,000.
Therefore, "one and three-quarter million" can be written in figures as 1,750,000.
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From a sample with nequals24, the mean number of televisions per household is 4 with a standard deviation of 1 television. Using Chebychev's Theorem, determine at least how many of the households have between 2 and 6 televisions. At least nothing of the households have between 2 and 6 televisions.
Answer:
At least 18 of the households have between 2 and 6 televisions.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Mean = 4
Standard deviation = 1
Percentage of households that have between 2 and 6 televisions.
2 = 4 - 2*1
So 2 is two standard deviations below the mean
6 = 4 + 2*1
So 6 is two standard deviations above the mean
By Chebyshev's Theorem, at least 75% of the measures are within 2 standard deviations of the mean.
Out of 24
0.75*24 = 18
At least 18 of the households have between 2 and 6 televisions.
