Answer:
A.
Step-by-step explanation:
We are given the two points (2,7) and (4,-1). In order to determine the linear equation, we need to find the slope and the y-intercept. First, find the slope m. Let (2,7) be x1 and y1, and let (4,-1) be x2 and y2:
[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{-1-7}{4-2}=-8/2=-4[/tex]
Thus, the slope is -4.
Now, to find the y-intercept, we can use the point-slope form. Recall that the point slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
Where (x1, y1) is a coordinate pair and m is the slope.
Use either of the two coordinate pair. I'm going to use (2,7). Substitute them for x1 and y1, respectively:
[tex]y-(7)=-4(x-(2))\\y-7=-4x+8\\y=-4x+15[/tex]
This is also slope-intercept form. The answer is A.
Answer:
A. y=-4x+15
Step-by-step explanation:
First, you want to find the slope by using the formula
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The first step is to put in the right numbers,
[tex]\frac{-1-7}{4-2}[/tex]
Then, subtract the numbers accordingly
[tex]\frac{-8}{2}[/tex]
Then simplify
[tex]\frac{-4}{1}[/tex] or -4
The next step is finding the y-intercept, you can do this by drawing it out or using the formula (i will be using the point (2,7) where y is 7 and x is 2)
y=-4x+b Plug in the values
7=-4(2)+b Multiply
7=-8+b add 8 to both sides to isolate the variable
15=b
so y=-4x+15
Hope this helps, if you have any questions, feel free to ask.
Have a good day! :)
Instructions: Find the measure of the indicated angle to the
nearest degree
Answer:
? = 33
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan ? = opp / adj
tan ? = 13/20
Take the inverse tan of each side
tan ^-1 tan ? = tan ^-1 ( 13/20)
? = 33.02386756
To the nearest degree
? = 33
Answer:
33.
Step-by-step explanation:
inverse tan (13/20) = 33.023867579302
This graph shows how the length of a time kayak is rented is related to the rental cost. What is the rate of change shown in the graph?
Answer:
A.
Step-by-step explanation:
pls help me for question no.4
Answer:
Area of the composite figure = 75.25 cm²
Step-by-step explanation:
Question (4). Given figure is a composite figure having,
(1). Right triangle STU
(2). A kite PSUV
(3). A trapezoid PQRS
Now we will calculate the area of each figure.
(1). Area of the right triangle = [tex]\frac{1}{2}(\text{ST})(\text{TU})[/tex]
= [tex]\frac{1}{2}(3.5)(3)[/tex]
= 5.25 cm²
(2). Area of the kite PSUV = [tex]\frac{1}{2}(\text{Diagonal 1})(\text{Diagonal 2})[/tex]
= [tex]\frac{1}{2}(\text{PU})(\text{SV})[/tex]
= [tex]\frac{1}{2}(\text{TS+RQ})(\text{SV})[/tex]
= [tex]\frac{1}{2}(3.5+7)(6)[/tex] [Since SV = 2 × 3 = 6 cm]
= [tex]3\times 10.5[/tex]
= 31.5 cm²
(3). Area of the trapezium = [tex]\frac{1}{2}(b_1+b_2)(h)[/tex] [Where [tex]b_1[/tex] and [tex]b_2[/tex] are the bases and h is the distance between the bases]
= [tex]\frac{1}{2}[(7-3)+7](7)[/tex]
= [tex]\frac{77}{2}[/tex]
= 38.5 cm²
Total area of the given figure = 5.25 + 31.5 + 38.5
= 75.25 cm²
An online seed supplier packages a seed mix that costs the company $20.70 per pound. The mix includes poppy seeds costing $24.00 per pound and clover seeds costing $13.00 per pound. If a worker is going to prepare some of this mix and has already measured out 26 pounds of poppy seeds, what quantity of clover seeds should he add?
Answer:
The quantity of clover seeds the worker will add is 11.14 pounds
Step-by-step explanation:
Let
x=Poppy seed
y=clover seed
24x+13y=20.70(x+y)
x=26 pounds
Substitute x=26 pounds into the equation
24x+13y=20.70(x+y)
24(26)+13y=20.70(26+y)
624+13y=538.2 +20.70y
Collect like terms
624-538.2=20.70y-13y
85.8=7.7y
Divide both sides by 7.7
y=85.8/7.7
=11.14 pounds
Therefore, the quantity of clover seeds the worker will add is 11.14 pounds
Answer:
A 11.14
Step-by-step explanation:
To solve this, add the total cost of the poppy seed ($24 × 26) to the cost of the clover seeds ($13x), then divide both by the total number of pounds the finished mixture will weigh.
A car bought for $20,000. Its value depreciates by 10% each year for 3 years. What is the car's worth after3 years?
Answer:
$14,580
Step-by-step explanation:
To start off, 10% of 20,000-one easy way to do this is to multiply 20,000 by 0.1, which is 10% in decimal form
-In doing that, you get 2,000
-Now the question says that the value is depreciated which means it goes down in value, so subtract 2,000 from 20,000 to 18,000
-the value of the car after one year is now $18,000
Now, let's move to the second year. This time find 10% of 18,000
-multiply 18,000 by 0.1 to get 1,800
-since the value is depreciating, or becoming less, we will subtract 1,800 from 18,000 to get 16,200
-the value of the car after two years is now $16,200
Finally, let's look at the value of the car after three years. Only this time, we will now find 10% of 16,200
-multiply 16,200 by 0.1 to get 1,620
-since value is being depreciated, or lessened, we will once again be subtracting. Subtract 1,620 from 16,200 to get 14,580
Therefore, the value of the car after three years is now $14,580.
One equation 0f a pair of dependent linear equations is -5x+7y=2.The second equation can be a)10x-14y=-4 b)-10x-14y+4=0 c)-10x+14y+4=0 d)10x+14y=-4
Answer:
a) 10x - 14y = -4
Step-by-step explanation:
Two equations linear dependent if you can write one as a multiple of the other. It means that the equation that is a linear dependent with -5x+7y=2 is:
10x - 14y = -4
Because it can be written as:
-2(-5x+7y) = -2(2)
So, this equation is equivalent to -5x + 7y = 2
Below, is the sample size, is the population proportion and is the sample proportion. Use the Central Limit Theorem and the TI-84 calculator to find the probability. Round the answer to at least four decimal places.
n=111
p=0.54
P (P > 0.60) =
Answer:
Binomial probability online calculator gives P([tex]\hat p[/tex]>0.60) =0.1054
Step-by-step explanation:
Given that n = 111
p = 0.54
To find P([tex]\hat p[/tex]>0.60)
We have;
P([tex]\hat p[/tex]>0.60) = [tex]P \left (\dfrac{0.6 - p}{\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}} > Z \right )[/tex]
P([tex]\hat p[/tex]>0.60) = [tex]P \left (\dfrac{0.6 - 0.54}{\sqrt{\dfrac{0.54(1-0.54)}{111}}} > Z \right )[/tex]
P([tex]\hat p[/tex]>0.60) = P(1.268 > Z) = 1 - 0.8962 = 0.1038
The above result was obtained from calculation
Binomial probability online calculator gives P([tex]\hat p[/tex]>0.60) =0.1054.
What is the name of the method for drawing a trend line for the data in a scatterplot in which an oval is drawn around all the points in the scatterplot except the outliers?
a.the oval method
b.the divide-center method
c.the area method
d.the regression calculator method
ty if you answer! :3
Answer:
c.the area method
Step-by-step explanation:
A scatterplot is a plotting of data that represents the relationship between the two variables that should be numerical in nature. The data points i.e to be shown in a horizontal and vertical axis represent that how much one variable affected by another variable.
In the area method, we plot a data and then draw a shape which can be in oval but it does not include the outliers but the other methods like oval method, divide center method, regression calculator includes the outliers
Therefore the option c is correct
Answer:
c.the area method
Step-by-step explanation:
c.the area method c.the area method c.the area method c.the area methodc.the area methodc.the area methodc.the area method c.the area method c.the area method c.the area method c.the area method c.the area method
A track coach is trying to improve the 50 -meter-dash times of the track team. He times each student and then implements a month-long training program. At the end of the program, he timed each of the students again. The box plots show the number of seconds it took the students to run the 50 -meter-dash before and after the program. Using the plots, how much did the median change?
Answer:
-5
Step-by-step explanation:
Given the two box plots showing the number of seconds the students completes the 50-meter-dash race before and after the program, we are to determine the difference between the median value of seconds before and after the program.
Median in a box plot is represented by the vertical line that divides the rectangular box in a box plot.
Thus, the median before the program = 15 seconds
The Median after the program = 10 seconds
The median change = 10 - 15 = -5 seconds.
This means, after the program, most of the students now finish the 50-meter-dash faster, about 5 seconds less the former seconds used before the program.
Answer:
-5
Step-by-step explanation:
i did it on Imagine Math and i got it correct!
Please Help! Two lines, A and B, are represented by the following equations: Line A: y = x − 1 Line B: y = −3x + 11 Which of the following options shows the solution to the system of equations and explains why? (3, 2), because the point does not lie on any axis (3, 2), because one of the lines passes through this point (3, 2), because the point lies between the two axes (3, 2), because both lines pass through this point
Answer:
The last choice (3,2), because both lines pass through this point.
Step-by-step explanation:
For a point to be a solution to a system of linear equations, both equation's lines have to pass through that same point.
Answer: (3, 2), because both lines pass through this point
Step-by-stepexplanation:
This can be solved by substitution. The graph will show the same result.
What is the length of AC?
Please help me ASAP!!!
Answer:
a
Step-by-step explanation:
Factorize: 14x^6-45x^3y^3-14y^6
Answer:
(7x^3+2y^3)(2x^3−7y^3)
9 is subtracted from 3 times the sum of 4 and 2
Answer:
9
Step-by-step explanation:
3 times the sum of 4 and 2 = 3*(4+2)
= 3 * 6
= 18
18 - 9 = 9
John wants to nail a thumbtack on his circular board, pictured below. If the thumbtack is equally likely to be placed anywhere on the board, what is the probability that the thumbtack will be placed on the inner circle? Use 3.14 for pi , and round your answer to the nearest whole percent. A. 51% B. 55% C. 57% D. 60%
Answer: A. 51%
Step-by-step explanation:
Area of circle = [tex]\pi r^2[/tex] , where r = radius of the circle.
In the figure below, we have the complete question.
According to that,
Radius of outer circle = 7ft
Radius of inner circle = 5ft
The probability that the thumbtack will be placed on the inner circle
[tex]=\dfrac{\text{Area of inner circle}}{\text{Area of outer circle}}\\\\=\dfrac{\pi (5)^2}{\pi (7)^2}\\\\=\dfrac{25}{49}[/tex][π is canceled from numerator and denominator
in percent, [tex]\dfrac{25}{49}\times100=51.0204081633\%\approx51\%[/tex]
So, the probability that the thumbtack will be placed on the inner circle = 51%
Hence, the correct option is A. 51%.
Which of the following is not a congruence theorem or postulate A. SSA B. SAS C. AAS D. SSS
Answer:ITS A
Step-by-step explanation:
SAS: side angle side
SSA: is not a congruence theorem
AAS:angle angle side
SSS:side side side
Answer:
The answer is A.
Step-by-step explanation:
Just took the test
Kate opens a savings account with a deposit of $1250. After 2 years, she has
receives $112.50 in interest. What is the annual interest rate?
Answer:
4.5%
Step-by-step explanation:
Simple interest:
I = Prt
112.5 = 1250(r)(2)
1250r = 56.25
r = 0.045 = 4.5%
Answer: 4.5%
The table below shows data from a survey about the amount of time students spend doing homework each week. The students were in either college or high school:
High Low Q1 Q3 IQR Median Mean σ
College 20 6 8 18 10 14 13.3 5.2
High School 20 3 5.5 16 10.5 11 11 5.4
Which of the choices below best describes how to measure the spread of these data?
(Hint: Use the minimum and maximum values to check for outliers.)
Both spreads are best described by the IQR.
Both spreads are best described by the standard deviation.
The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
The college spread is best described by the standard deviation. The high school spread is best described by the IQR.
Answer:
The correct option is;
Both spreads are best described by the standard deviation
Step-by-step explanation:
The given information are;
, College High School
High, 20 20
Low, 6 3
Q₁, 8 5.5
Q₃, 18 16
IQR, 10 10.5
Median, 14 11
Mean, 13.3 11
σ, 5.2 5.4
Checking for outliers, we have
College
Q₁ - 1.5×IQR gives 8 - 1.5×10 = -7
Q₃ + 1.5×IQR gives 18 + 1.5×10 = 33
For high school
Q₁ - 1.5×IQR gives 5.5 - 1.5×10.5 = -10.25
Q₃ + 1.5×IQR gives 16 + 1.5×10.5 = 31.75
Therefore, there are no outliers and the data is representative of the population
From the data, for the college students, it is observed that the difference between the mean, 13.3 and Q₁, 8, and between Q₃, 18 and the mean,13.3 is approximately the standard deviation, σ, 5.2
The difference between the low and the high is also approximately 3 standard deviations
Therefore the college spread is best described by the standard deviation
Similarly for the high school students, the IQR is approximately two standard deviations, the difference between the mean, 11 and Q₁, 5.5, and between Q₃, 16 and the mean,11 is approximately the standard deviation, σ, 5.4
Therefore the high school spread is also best described by the standard deviation.
Answer:
Both spreads are best described by the standard deviation
Step-by-step explanation:
Solve by factoring 25x^2+5x-12=0
Answer:
x = -4/5 and x = 3/5.
Step-by-step explanation:
The coefficient of x^2 is 25, which is 5 * 5. 5 * -3 = -15, and 5 * 4 = 20. 20 - 15 = 5.
So...
25x^2 + 5x - 12 = 0
(5x + 4)(5x - 3) = 0
5x + 4 = 0
5x = -4
x = -4/5
5x - 3 = 0
5x = 3
x = 3/5
So, x = -4/5 and x = 3/5.
Hope this helps!
which of the following is not a congruence theorem or postulate a) sas b) aas c) sss d) aa
Answer:
d)aa (AA is not congruence theorem, it is similarity postulate)
Step-by-step explanation:
Answer:
aa
Step-by-step explanation:
The direct distance from a starting point to a finish line is 20 miles. Unfortunately, you can't take the direct route. If you travel 16 miles west, how many miles south must you travel to reach the finish line? A. 12 B. 16 C. 4
Answer:
12
Step-by-step explanation:
If a polynomial function f(x) has roots -9 and 7 -i, which must be a factor of f(x)
Answer:
(x + 9) (x - 7)
Step-by-step explanation:
when we put x + 9 = 0 then x = -9 as it's the root of the fuction.
same thing here: x - 7 = 0 then x = 7
plz answer this question
Answer:
D is correct one
Step-by-step explanation:
The pattern consists of repeating 4 faces
1000 is fully divisible by 4
1000/4= 250The 1000th face ends the pattern of 4
The next, 1001th one is the very first face
Correct choice is D
In the table, describe the shape of the cross section formed when a particular plane passes through the cylinder.
triangle is the best answer
Answer:
Step-by-step explanation:
Use the explicit formula 8. = a + (n-1). d to find the 500th term of the
sequence below.
24, 31, 38, 45, 52, ...
A 3545
B. 3517
C. 3524
D. 3493
Answer:
The 500th term is 3,517
Step-by-step explanation:
Here in this question, we are given an explicit formula to calculate the 500th term of the sequence
The formula to use is ;
a + (n-1)d
where a refers to the first term which is 24 in this case, while d is the common difference which is the difference between success terms and that is 52-45 = 45-38 = 7 and finally n is 500
Now we make a substitution into the formula and we have
24 + (500-1)7
= 24 + (499)7
= 24 + 3493 = 3,517
Please help out show work ty!
Answer:
C
Step-by-step explanation:
This is because it has a constant rate of change.
5 x 1.5 = 7.5
6 x 1.5 = 9
7 x 1.5 = 10.5
You can find this image by dividing y by x and testing this rate of change on the other y values. Thus C is correct.
Please find out the answer and I will mark your answer as the brain test with a five-star rating and a thank you. But only if the answer will be proper and neat...
Answer:
Below
Step-by-step explanation:
Let x be that missing number
One third of it is x/3
One-ninth of it is x/9
Multiply x/3 and x/9
● (x/3)*(x/9) = (x^2/27)
● (x^2/27) = 108
Multiply both sides by 27
● (x^2/27)*27 = 108*27
● x^2 = 2916
● x = √(2,916) or x = -√(2,916)
● x = 54 or x = -54
So there are two possibilities 54 and -54.
a1/3×1/9=!08
if you multiply you should get 1/27a=108
in order to let a alone multiply both sides by 27
and now your a which is unknown will equal 2916.
11 POINTS! GEOMETRY!! Find the area of the composite function and explain how you broke the shape into pieces to find the area.
Answer:
370 mm²
Step-by-step explanation:
The area of this figure can be calculated by taking the whole figure as a full rectangle, and consider the part that is cut out from the middle of the shape as another rectangle.
Find the area of the cut-out part and subtract from the area of the full rectangular shape to get the area of the composite figure.
=>Area of full rectangular shape:
Length = 30 mm
Width = 15 mm
Area = L * B = 30*15 = 450 mm²
=>Area of the cut-out Rectangle part:
Length = 10 mm
Width = 8 mm
Area = 10*8 = 80 mm²
=>Area of composite figure = 450 mm² - 80 mm² = 370 mm²
The standard deviations of four data sets are shown in the table below. Which
of the data sets is the most spread out?
You are correct. The higher the standard deviation is, the more spread out the data set will be. Nice work.
Answer:
Hey there! The correct answer is A. Data set C.
---
What is standard deviation?Standard deviation is simply defined as the spread of a data set in relation to the mean of the data set. The standard deviation can be calculated with a formula as shown below.
[tex]\displaystyle \sigma = \sqrt{\frac{\Sigma(x_i-\mu)^2}{N}[/tex]
What does each variable stand for?Each variable has a significant meaning for this formula.
[tex]\sigma[/tex] - the standard deviation of the population[tex]\Sigma[/tex] - the summation of all values after the symbol[tex]x_i[/tex] - all data values in the set[tex]\mu[/tex] - the mean of the population[tex]N[/tex] - the number of data valuesWith this information, we can find the standard deviation of a data set.
What does standard deviation mean for a data set?Generally speaking, statisticians want a standard deviation that is on the lower end so that conclusions can be drawn about the data that was observed.
If a standard deviation is large, that means that most of the data is quite far from the mean and the data usually disproves a hypothesis. This is undesirable since the original hypothesis cannot be proven with this experiment.
When the standard deviation is quite low, this points to data that can be relied upon since it fulfills the initial requirement to prove the hypothesis.
Therefore, since the highest standard deviation correlates with the most spread out data, A. Data set C is the answer.
PLS HELP THE 1ST PERSON TO ANSWER THIS CORRECTLY AND EXPLAINS IT ILL MARK BRAILIEST. What is the solution to the equation 3.6m − 2.7 = −1.8m? m = 0.25 m = 0.5 m = 1.25 m = 1.5
Answer:
m=0.5
Step-by-step explanation:
Copy the equation.
3.6m-2.7=-1.8m
Subtract 3.6m from both sides.
-2.7=-5.4m
Divide by -5.4 on both sides.
0.5
Which of the following correlation coefficients would correspond to a strong linear relationship in a data set? a. 0 b. 7 c. 0.9 d. 0.4
The correlation coefficient r is always between -1 and 1, inclusive of both endpoints. We can write [tex]-1 \le r \le 1[/tex]
If r = 0, then we have no linear correlation at all. If r = 1, then we have perfect positive correlation. If r = -1, then we have perfect negative correlation.
We see that r = 0.9 is close to r = 1, so we have strong positive linear correlation going on here.