Answer:
y=-5/2x-1
Step-by-step explanation:
first find the gradient whereas since the two lines are parallel they hav the same gradient. y=mx+c whereas m is the gradient. 5x+2y=12
2y=-5x+12
y=-5/2x+12(so the gradient is -5/2x..... gradient=-5/2
y-4=-5/2
x+2
y-4=-5/2(x+2)
y-4=-5/2x-5
y=-5/2x-5+4
y=-5/2x-1
The equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4) is y = -5/2 x - 1.
What is the Equation of line in Slope Intercept form?Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.
Given that the equation of the line is,
5x + 2y = 12
2y = -5x + 12
y = -5/2 x + 6
This is in the slope intercept form, where the slope = -5/2.
Slopes of two parallel lines are equal.
So any line parallel to the given line will be of the form y = -5/2 x + c
Given line passes through (-2, 4).
Substituting (-2, 4) in y = -5/2 x + c, we get,
(-5/2) (-2) + c = 4
c = -1
So the equation is, y = -5/2 x - 1
Hence the required equation is y = -5/2 x - 1.
Learn more about Slope Intercept form here :
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What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
The cottage inside the pen is a shape of a cylinder.
Answer:
Cylinder
As u can see the shape it's like a cylinder
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
A new post-surgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven others (the controls) receive the standard treatment. The recovery times, in days, are given below.
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
Required:
Find a 98% confidence interval for the difference in the mean recovery times between treatment and control.
Answer:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
Step-by-step explanation:
For this case we have the following info given:
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
We can find the sample mean and deviations with the the following formulas:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s =\sqrt{\frac{\sum_{i=1}^n (X_i- \bar X)^2}{n-1}}[/tex]
And repaplacing we got:
[tex] \bar X_T = 17.714[/tex] the sample mean for treatment
[tex] \bar X_C = 28.714[/tex] the sample mean for treatment
[tex] s_T= 4.461[/tex] the sample deviation for treatment
[tex] s_C= 7.387[/tex] the sample deviation for control
[tex]n_T= n_C= 7[/tex] the sample size for each sample
The degrees of freedom are given by:
[tex] df= 7+7-2= 12[/tex]
The confidence interval for the difference of means is given by:
[tex] (\bar X_T -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_T}{n_T} +\frac{s^2_C}{n_C}}[/tex]
The confidence is 98% so then the significance is [tex]\alpha=0.02[/tex] and [tex] \alpha/2 =0.01[/tex]. Then the critical value would be:
[tex] t_{\alpha/2}=2.681[/tex]
And replacing we got:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
A shopkeeper buys 1 dozen of pens at Rs 15 each and sells them at Rs 18
ch. Find his profit and profit percent.
Answer:
20%
Step-by-step explanation:
Cost price (C. P.) of each pen = ₹ 15
Selling price (S. P.) of each pen = ₹ 18
Profit = S. P. - C. P. = 18 - 15 = ₹3
[tex]profit \: percent \\ \\ = \frac{profit}{c.p.} \times 100 \\ \\ = \frac{3}{15} \times 100 \\ \\ = \frac{3}{3} \times 20 \\ \\ = 20\%[/tex]
if log3(x+1) - log3x=2, then x = ?
Answer:
x= 1/8
Step-by-step explanation:
I’ll give the bralyist to the first correct answer
Let f be defined as shown.
What is f1 (-7)?
Answer:
The answer is 2
From the function when the input is 2 the output is -7. The inverse reverses the order so the input will be -7 and the output will be 2.
Angle EFB is 108º
a)Find the size of angle x.
b) which one of these justifies your answer?
A-corresponding angles
B- Alternate angles
C- vertically opposite angles
Answer:
c of what im sure about
Step-by-step explanation:
3. What would you expect the relationship between the length of a baby at birth and
the month in which the baby was born to be?
A positive correlation
B negative correlation
C no correlation
Express the following ratio in its simplest form.
4:12
Answer:
3:12
Step-by-step explanation:
Answer:
1:3
Step-by-step explanation:
Think 4:12 as a fraction for a moment, it would be 4/12. Now completely simplify 4/12, you get 1/3. Now put 1/3 as a ratio, it would be 1:3.
Please mark BRAINLIEST, thanks!
What is true about the number 3.872? Check all that apply.
The 8 is in the tens place.
The 7 is in the hundredths place.
The 3 is in the ones place.
This number is read as "three and eight seventy-two hundredths."
3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001).
Answer:
The 7 is in the hundredths place.
The 3 is in the ones place.
3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001).
Step-by-step explanation:
Given the number 3.872, to check all the given options that are true apply to the number, let's take a look at each position occupied by each digit. In order words, let's consider their place value.
Thus,
The 3 is in the ones place and as such has a value of 3.
8 is in the tenths place having a place value of 0.8 (⁸/10)
7 is in the hundredths place having a place value of 0.07 (⁷/100)
2 is in the thousandths place having a place value of 0.002 (²/1000)
Going by these, the following statements are true :
"The 7 is in the hundredths place."
"The 3 is in the ones place."
"3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001)."
The number is pronounced as three and eight hundred seventy-two thousandths rather than the option given.
Therefore, only 3 if the options are correct
Answer: The 7 is in the hundredths place.
The 3 is in the ones place.
3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001).
Step-by-step explanation:
In the question, 3 is in the ones place. The first number after the decimal point is the tenths. In the question, the place value of 8 is 8 tenths; 7 is in the hundredths place.
3.872 = (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001)
= 3 + 0.8 + 0.07 + 0.002
= 3.872
The number is pronounced as three and eight hundred seventy-two thousandths
What is an equivalent function to f(x)=(x-2)^3
Answer:
x^3-6x^2-4x-8
Step-by-step explanation:
First you would multiply (x-2) by itself (x-2) to get
x^2-2x-2x+4
then you would combine like terms
x^2-4x+4
Then you would multiply that by x-2
(x^2-4x+4)(x-2)
x^3-2x^2-4x^2-8x+4x-8
then you combine like terms
x^3-6x^2-4x-8
A designer makes a model of a patio using 1/2 inch square tiles each 1/2 inch square tiles = 4 square feet what area is represented by the 8 x 6 model
Answer:
[tex]192ft^2[/tex]
Step-by-step explanation:
The model of a patio was made by
using 1/2 inch square title=4 square feet.
area represented by the 8 *6 model can be calculated as follows;
FIRSTLY, the number of tiles in the 8 *6 model can be calculated by multiplying it i.e
8 *6 model =[tex]48 tiles[/tex]
Hence there are 48 tiles in 8 *6 model
It was given that 1/2 inch square title=4
square feet.
So to calculate the total Area occupied by the 48 tiles
[tex]Area=1/2×48[/tex]
[tex]Area=24inches^2[/tex]
If [tex]1/2inches^2=4ft^2[/tex] ( from the question)
Let X represent [tex]24inches^2[/tex]
Then, [tex]24inches^2=Xft^2[/tex]
Cross multiply
[tex]4×24=X×1/2
X=4×24×2
X=[tex]192ft^2[/tex]
[tex]24inches^2=[tex]192ft^2[/tex]
Therefore, the area represented by the 8 *6 model is [tex]192ft^2[/tex]
if a propane tank has the shape of a cylindrical tank with a height of 4.2m and a radius of 1.3m how many cubic metres of propane is in the tank if it's only 50% full
Answer:
11.1 cm³
Step-by-step explanation:
V=πr²h / 2 (for half full)
V = (3.14)(1.3)²(4.2)/2
V = 11.1 cm³
A, B, and C are collinear points C is the midpoint of AB AC = 5x - 6 CB = 2x Find AB
Answer:
AB = 8
Step-by-step explanation:
Since C is the midpoint, ...
AC = CB
5x -6 = 2x
3x = 6 . . . . . . . add 6-2x
x = 2
Then the length of AB is ...
AB = 2(CB) = 2(2x) = 4(2)
AB = 8
Mitch opened a retirement account that has an annual yield of 4.2% compounding annually. He is planning on retiring in 13 years. How much must he deposit into that account each year so that he can have a total of $1,000,000 by the time he retires?
Answer:
P = 4878
Step-by-step explanation:
So we'll use the formula
A = p(1+r/n)^ (nt)
A = 1000000
P is the unknown
R = 4.2
N = 13
T = 13
1000000= p ( 1+ 0.42/13)^ 169
1000000 = p (1.032)^169
1000000= p 205
P = 4878
PLEASE HELP!!!!!
This is edge!
A b c d
Will mark brainliest!!!!
Answer:
D. [tex] \frac{7}{12} \: of \: a \: pound[/tex]
Step-by-step explanation:
[tex]total \: candies = 2 \frac{1}{4} + \frac{2}{3} \\ \\ = \frac{9}{4} +\frac{2}{3} \\ \\ = \frac{9 \times 3 + 2 \times 4}{3 \times 4} \\ \\ = \frac{27 + 8}{12} \\ \\ = \frac{35}{12} \\ \\ share \: of \: brother = \frac{1}{5} \times \frac{35}{12} \\ \\ = \frac{7}{12} \: of \: a \: pound[/tex]
Answer:
[tex]\fbox{\begin{minipage}{10em}Option D is correct\end{minipage}}[/tex]
Step-by-step explanation:
Step 1: Let's find the total amount of candy that Loret and her sister have:
Loret has [tex]2\frac{1}{4}[/tex] pound of candy
Loret's sister has [tex]\frac{2}{3}[/tex] pound of candy
=> Total amount: [tex]A =2\frac{1}{4} + \frac{2}{3} = \frac{9}{4} + \frac{2}{3} = \frac{27}{12} + \frac{8}{12} = \frac{35}{12}[/tex] pound of candy
Step 2: Let's find the amount of candy Loret's brother could get:
If Loret's brother did the chores, he can get [tex]\frac{1}{5}[/tex] total amount of candy that Loret and her sister have.
=> The amount Loret's brother can get:
[tex]B = A*\frac{1}{5} = \frac{35}{12} * \frac{1}{5} = \frac{7}{12}[/tex] pound of candy
=> Option D is correct
Hope this helps!
:)
A motorboat can maintain a constant speed of 13 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 63 minutes; the return trip takes 15 minutes. What is the speed of the current?
Answer:
8 mph
Step-by-step explanation:
The speed in each direction is the speed of the boat with the speed of the current appropriately added. If x is the speed of the current, the upstream speed is 13-x; the downstream speed is 13+x.
The ratio of times is inversely proportional to the ratio of speeds, so we ahve ...
15/63 = 5/21 = (13-x)/(13+x)
5(13 +x) = 21(13 -x) . . . . . . . cross multiply
26x = 13(21 -5) = 13·16
x = 13·16/26 = 16/2 = 8
The speed of the current is 8 miles per hour.
Please answer this correctly
Answer:
169.5 yd²
Step-by-step explanation:
See attachment.
In situations like this, ALWAYS (!) make as sketch.
Divide the areas by adding dotted lines on sensible places, and write in the missing numbers for the correct distances.
The only possible difficult one is the triangle, which is the half of a rectangle. So you are dealing with a series of areas of rectangles. That is really easy if you understand what you are doing.
Total area =
area 1 + area 2 + area 3 + area 4
10*4 + 4*7 + 3*13 + (0.5 * 7*17)
40 + 28 + 42 + 59.5
Total area = 169.5 yd²
Mr. Hobbs took out a loan of $12,000 for 4 years at a simple annual
interest rate of 7%. How much interest did he pay?
Answer:
Step-by-step explanation:
I= P*r*t
I = 12000* 7% *4
Total interest paid was $3360.
Answer: $3,360
Step-by-step explanation:
3. Set up an equation and use it to solve for x.
51°
(5x + 1)
Answer:
51 = 5x+1
x = 10
Step-by-step explanation:
The angles are vertical angles which means they are equal
51 = 5x+1
Subtract 1 from each side
51-1 = 5x+1-1
50 = 5x
Divide each side by 5
50/5 = 5x/5
10 =x
Answer:
10
Step-by-step explanation:
51 = 5x + 1
5x = 51 - 1
5x = 50
x = 10
Hope this helps!
For a particular disease, the probability of having the disease in a particular population is 0.04. If someone from the population has the disease, the probability that she/he tests positive of this disease is 0.95. If this person does not have the disease, the probability that she/he tests positive is 0.01. What is the probability that a randomly selected person from the population has a positive test result
Answer:
4.76% probability that a randomly selected person from the population has a positive test result
Step-by-step explanation:
We have these following probabilities:
4% probability of having the disease.
If a person has a disease, 95% probability of a positive test.
100-4 = 96% probability a person does not have the disease.
If a person does not have the disease, 1% probability of a positive test.
What is the probability that a randomly selected person from the population has a positive test result
95% of 4% and 1% of 96%. So
p = 0.95*0.04 + 0.01*0.96 = 0.0476
4.76% probability that a randomly selected person from the population has a positive test result
1/216^-2/3 + 1/256^-3/4 + 1/243^-1/5
Answer:
103
Step-by-step explanation:
[tex]\dfrac{1}{216}^{-2/3}+\dfrac{1}{256}^{-3/4}+\dfrac{1}{243}^{-1/5}= \\\\\\\sqrt[3]{216^2}+\sqrt[4]{256^3}+\sqrt[5]{243}=\\\\\\6^2+4^3+3=\\\\\\36+64+3=\\\\\\103[/tex]
Hope this helps!
The aspect ratio of a rectangular shape is it's length divided by it's width (L/W). If the aspect ratio of a chalkboard is 4:3 and the width is 5 in, what is the length of the chalkboard? A. 6.67 in B. 9.33 in C. 12 in D. 14 in
Answer:
A. 6.67 in
Step-by-step explanation:
length/width = 4/3 = x/5
Multiply by 5:
5(4/3) = x = 20/3 = 6 2/3
The length of the chalkboard is 6.67 inches.
a cone has the diameter of 3 inches. the cone holds 12 cubic inches of water. to the nearest inch, what is the height of the cone?
Answer:
The height is about 5 inches.
Step-by-step explanation:
The volume for a cone is [tex]\frac{1}{3}[/tex] × π × r² × h
The radius of the cone is 1.5
12= [tex]\frac{1}{3}[/tex] × π × 1.5² × h
12= [tex]\frac{1}{3}[/tex] × π × 2.25 × h
12=0.75×π×h
Divide both sides by 0.75
16=π×h
Divide both sides by π
5≈h
The height is about 5 inches.
what are 80 percent of 500
Answer: 400
Step-by-step explanation:
500 x 0.80 = 400
Answer:
400
Step-by-step explanation:
Of means multiply
80% * 500
Change to fraction form
80/100 * 500
Rewriting to reduce
80 * 500/100
80 * 5
400
Which of the following expressions represents "the sum of n and the sum of 8 and 6"? n(8 + 6) n + (8 + 6) (n + 6)8
what is 3 43/ 100 as a decimal number.
Answer:
3.43
Step-by-step explanation:
3 is the whole number and 43 out of 100 is a standard fraction that can simply be stated as 0.43. Hope this helps!
Answer:
3.43
Step-by-step explanation:
Used calculator.
Please answer this correctly
Answer:
Pennies: 20%
Nickels: 36%
Dimes: 18%
Quarters: 21%
Step-by-step explanation:
Pennies: [tex]\frac{125}{125+180+90+105} =\frac{125}{500} =\frac{25}{100}[/tex] or 20%
Nickels: [tex]\frac{180}{125+180+90+105} =\frac{180}{500} =\frac{36}{100}[/tex] or 36%
Dimes: [tex]\frac{90}{125+180+90+105} =\frac{90}{500} =\frac{18}{100}[/tex] or 18%
Quarters: [tex]\frac{105}{125+180+90+105} =\frac{105}{500} =\frac{21}{100}[/tex] or 21%
According to exit polls, the voting "gender gap" was 22 points in the 2016 House of Representatives election; that is, women voted for Democrats by 10 percentage points, and men voted for Republicans by 12 percentage points. Political scientists are curious to see if this gap holds- or increases- in 2018, but statisticians might be more interested in the processes behind exit polling and the rellabllity of thelr results.
When conducting exit polls, pollsters will randomly select a certain number of precincts, then attempt to get all the voters leaving the polling place to participate in their poll. If they can't get all voters, they will instead attempt to get every nth voter to participate. Many polling companies believe that Democrats are more likely to agree to an exit poll than Republicans or Independents.
Of course, not everyone votes in the morning/mid-afternoon of the election. To get an idea of the preferences of people who voted in the precinct before election day, typically by absentee ballots, companies will attempt a random telephone survey of those voters. Exit polls often wrap up and leave the field before voting stations close, so people voting in the last couple hours of the day may also be missed
(a) What type of sampling methods are used in selecting people for exit polls?
a. Simple Random Sampling
b. Cluster Sampling
c. Stratified Sampling
d. Convenience Sampling
e. Systematic Sampling
(b) Why do the polllng companles randomly select the preclncts to vislt?
a. Randomly selecting precincts to assign pollsters ensures that the companies can conclude a cause and effect relationship between the voters' beliefs and their voting pattern
b. There are too many precincts to manually select, so they are forced to randomly select them
c. Randomly selecting precincts increases the likelihood that the people polled represent the population well.
Answer:
A) cluster sampling ( b ) and systematic sampling ( e )
B ) Randomly selecting precincts increases the likelihood that the people polled represent the population well. ( c )
Step-by-step explanation:
Cluster sampling is a type of sampling plan used when there is an internally heterogeneous groups can be found inside a population that is supposed to be mutually homogeneous . while systematic sampling is a type of probability sampling that involves the selection of samples from a larger population at random but using a specific interval. to get the systematic sample the larger population is divided by the sample size.
from the information available in the report it is very evident that not all voters can be captured at once hence cluster sampling and systematic sampling would be employed .
B) the company will randomly select precinct to increase the likelihood of the sample size representing the entire population very well
Nadeen is at an arcade. She started with 18 tokens. Each game costs 3 tokens. So far, Nadeen has played 2
games.
Answer:
see below
Step-by-step explanation:
I think you are asking how many tokens she has left. She has 18 - 3 * 2 = 18 - 6 = 12 tokens left. She can play 12/3 = 4 more games.