Answer:
2
Step-by-step explanation:
The gradient of the straight line is equal to (y2-y1)/(x2-x1), where
(x1,y1) and (x2,y2) coordinates of the points A and B which belong to the line.
So y2=2 ,x2=1-2p , y1=2+4p, x1=1
k=(2-(2+4p))/((1-2p)-1)= (2-2-4p)/(1-2p-1)= (-4p)/(-2p)=2
The gradient of the straight line joining (1, 2+4p) to (1-2p, 2) is 2 and this can be determined by using the two-point slope formula.
Given :
Points -- (1,2+4p) and (1-2p,2)
The following steps can be used in order to determine the gradient of the straight line joining (1, 2+4p) to (1-2p, 2):
Step 1 - According to the given data, the points on the straight line are (1, 2+4p) to (1-2p, 2).
Step 2 - The two-point slope formula can be used in order to determine the gradient of the straight line joining (1, 2+4p) to (1-2p, 2).
Step 3 - The two-point slope formula is given below:
[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
Step 4 - Substitute the values of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the above expression.
[tex]\rm m = \dfrac{2-(2+4p)}{1-2p-1}[/tex]
Step 5 - Simplify the above expression.
[tex]\rm m = \dfrac{-4p}{-2p}[/tex]
m = 2
For more information, refer to the link given below:
https://brainly.com/question/3605446
f(x) = -x² – 3 x + 3
Find f(7)
the answer is -67 because you use the given function to set up and simplify f(7).
PLEASE HELP ME!!! Which expression is equivelent to 4(9+7) A. 36 + 7 B. 13 + 11 C. 36 + 28 D. 13 + 7
Answer:C
Step-by-step explanation:
9+7=16
16 times 4 = 64
36+28=64
A dilation by a factor of 7/8 maps triangle ABC to triangle XYZ. Segment BC has a length of 4 cm.
What is the length of segment YZ?
3.5 cm
7.8 cm
4.5 cm
0.5 cm
HELP ASAPPPPP
The last digit of the heights of 39 statistics students were obtained as part of an experiment conducted for a class. Use the frequency distribution below to construct a histogram. Choose the correct histogram below. Answer
Answer: 32
Step-by-step explanation:
A rectangle has_______sides that are straight lines, ______ and _____ opposite sides, and angles of _____. I need help
Answer:
A rectangle has_four_sides that are straight lines, _parallel_ and _equal_ opposite sides, and angles of [tex]90^o[/tex]_.
Step-by-step explanation:
if you have driven 225 miles in 3 hours, then how long would it take you to drive 300 miles?
Answer:How many miles can a car be driven in 3 hours at 50 miles per hour? Under normal circumstances and the generally assumed conditions, the answer is of course (3 hours) * (50 miles / hour) = 150 miles.
3.5 hours
It will take you 3.5 hours to go 280 miles at 80 miles an hour.It travels at constant speed for the remaining time. Let x be the time traveled at the unknown constant speed. The total itme for the trip was 6 hours so: 6 = time traveled at 50 mph + time traveled at 60 mph + time traveled at x mph.
Step-by-step explanation:So you drive 25 miles / hour. then 25 miles/ 1 hour = 225 miles / nb of hours.2 minutes
However, traveling at 30 MPH for 1 mile (1 lap) takes 2 minutes, which means that your average will never be 60MPH.approximately 0.6818 miles per hour.
Which of these fractions are greater than 11/20 ?
a. 3/4
b. 3/10
c. 4/5
d. 1/2
Answer:
A.
Step-by-step explanation:
All you have to do is convert all those fractions to 20.
So 3/4 will be 15/20, 3/10 would be 6/20, 4/5 would be 16/20 and 1/2 would be 10/20. It could be a or b. Does it say select all possible answers?
please help me in this question!
Answer:
n = 5
Step-by-step explanation:
All of the other choices are true except for n = 5, which is a counterexample. [tex]4^{5}[/tex] = 1024, which is greater than the other side as the other side is:
and [tex]4^{2}[/tex] = 16, 16 + 250 = 266
1024 < 266 is definitely false.
Therefore, the counterexample is n = 5.
Margaret is going to paint a wall that 'is 8 feet high and 15 feet long. How many square feet will she be covering with paint?
Answer:
120
Step-by-step explanation:
you would do length times width equals area. First you would multiply 8 by 15 which would give you 120 square feet. So Maragaret would be covering 120 square feet with paint
f(x) = 5(x+4) − 6, solve for the inverse function when x = 19
Answer:
-1
Step-by-step explanation:
First find the inverse function. Rewrite the given function as
y = 5(x + 4) - 6 = 5x + 20 - 6 = 5x + 14
Second, interchange x and y:
x = 5y + 14
Third, solve this result for y:
5y = 14 - x, or y = (1/5)(14 - x)
This last result is the inverse function of the given f(x).
The value of this inverse at x = 19 is (1/5)(14 - 19) = (1/5)(-5) = -1
Julio is paid 1.1 times his normal hourly rate for each hour he works over 30 hours in a week. Last week he worked 45 hours and eamed $520.80. Enter and solve an equation to find Julio's normal hourly rate, r. Complete the explanation how you know that your answer is reasonable. The earnings equation is $520.80 = Julio's hourly rate is $ per hour. This is reasonable because working 45 hours at a rate of $11 per hour is 45 - 11 = 45(10+1)=450 + 45 = |, and $ is dose to $520.80.
PLEASE ANSWER ASAP!!
Julio's hourly rate is going to be $14.4 per hour
If m/_a is 155º, what is m/_c?
Pls help ASAP
Being able to open and close windows is not a primary technology skill. Please select the best answer from the choices provided
Answer: False
Step-by-step explanation:
Primary technology skills are simply the skills which are vital in order to attain success in online education. It should be noted that technical skills are knowledge and abilities that are related to information technology which are needed to do certain tasks.
It should be noted that online education is the form of education that is delivered and being administered through the internet.
For one to learn online, it should be noted that being able to open and close windows is a primary technology skill.
Therefore, the statement in the question is false.
Answer: F
I already did the test
Use the summation formulas to rewrite the expression without the summation notation. summation_k = 1^n 12k(k - 1) / n^3 Use the result to find the sums for n = 10, n= 100, n= 1000 n= 10,000.
Answer:
[tex]Sum=4*[\frac{n^2-1}{n^2}][/tex]
For n=10:
Sum=3.96
For n=100:
Sum=3.9996
For n=1000:
Sum=3.999996
For n= 10000:
Sum=3.99999996
Step-by-step explanation:
Formula:
[tex]\sum_{k=1}^n \frac{12k(k-1)}{n^3}[/tex]
Rearranging the above formula:
[tex]\sum_{k=1}^n \frac{12}{n^3}*k(k-1)\\\sum_{k=1}^n \frac{12}{n^3}*(k^2-k)[/tex] Eq (1)
According to summation formula:
[tex]\sum_{k=1}^n\ k= \frac{n(n+1)}{2}\\ \sum_{k=1}^n\ k^2= \frac{n(n+1)(2n+1)}{6}\\[/tex]
Putt these in Eq (1), and we will get:
[tex]=\frac{12}{n^3}[\frac{n(n+1)(2n+1)}{6}-\frac{n(n+1)}{2}]\\Taking\ n\ as\ common\\=n*\frac{12}{n^3}[\frac{(n+1)(2n+1)}{6}-\frac{(n+1)}{2}] \\=\frac{12}{n^2}*[\frac{(n+1)(2n+1)}{6}]-\frac{12}{n^2}*[\frac{(n+1)}{2}] \\=\frac{2*(n+1)(2n+1)}{n^2}-\frac{6(n+1)}{n^2}\\[/tex]
Taking [tex]2(n+1)[/tex] as common:
[tex]=2(n+1)*\frac{2n+1-3}{n^2} \\=(2n+2)*\frac{2n-2}{n^2}\\=\frac{4n^2-4}{n^2}[/tex]
After more simplifying,
[tex]Sum=4*[\frac{n^2-1}{n^2}][/tex]
Now ,for n=10:
[tex]Sum=4[\frac{(10^{2})-1}{10^{2}}]\\Sum=3.96[/tex]
For n=100:
[tex]Sum=4[\frac{(100^{2})-1}{100^{2}}]\\Sum=3.9996[/tex]
For n=1000
[tex]Sum=4[\frac{(1000^{2})-1}{1000^{2}}]\\Sum=3.999996[/tex]
For n=10000:
[tex]Sum=4[\frac{(10000^{2})-1}{10000^{2}}]\\Sum=3.99999996[/tex]
The within-subjects F is the non-independent groups equivalent of the one-way ANOVA. True or False?
Answer:
Step-by-step explanation:
True
Andrew has a cell phone plan that provides 300 free minutes each month for a flat rate of $19. for any minutes over 200, andrew is charged $0.39 per minute. which of the following piece-wise functions represents charges based on andrews cell phone plan?
Answer:
f (x) = { 19 + 0.39(x - 300), x > 300
Step-by-step explanation:
Andrew has a cell phone plan that provides 300 free minutes each month for a flat rate of $19. For any minutes over 300, Andrew is charged $0.39 per minute. Let x be the number of minutes Andrew uses per month and f(x) be the charges based on Andrew's cell phone plan. If then If then first 300 minutes are free and each minute of next (x-300) minutes costs $0.39, therefore Hence, { 19 + 0.39(x - 300), x > 300
Hoped I helped
Write an inequality for the graph shown below.
Use x for your variable.
Answer:
x ≤ 3
Step-by-step explanation:
In the graph given, values of variable x is represented.
From the plot, we note that a small circle is at point 3 on the numberline. This small "o" is shaded, which indicates that the values of x includes 3.
The arrow which starts at 3 on the numberline, points towards our left. This means that the values of x are less than or equal to 3. No value of x is greater than 3.
Therefore, the following inequality can be written for the graph:
x ≤ 3
The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 12 supermarkets from Region 1 had mean sales of 79.8 with a standard deviation of 8.8. A random sample of 17 supermarkets from Region 2 had a mean sales of 85.2 with a standard deviation of 8.3. Does the test marketing reveal a difference in potential meal sales per market in Region 2? Use a signifiance level of a = 0.02 for the test. State the null and alternative hypotheses for the test and find the test statistic.
Answer:
The null hypothesis is [tex]H_o: \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_1 : \mu_1 \ne \mu_2[/tex]
The test statistics is [tex]t = -1.667[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 12[/tex]
The first sample mean is [tex]\= x_1 = 79.8[/tex]
The first standard deviation is [tex]\sigma _1 = 8.8[/tex]
The second sample size is [tex]n_2 = 17[/tex]
The second sample mean is [tex]\= x_2 = 85.2[/tex]
The second standard deviation is [tex]\sigma _2 = 8.3[/tex]
The null hypothesis is [tex]H_o: \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_1 : \mu_1 \ne \mu_2[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x_ 1 - \= x_2 }{ \sqrt{ \frac{\sigma_1^2 }{n_1 } +\frac{\sigma_2^2 }{n_2} } }[/tex]
=> [tex]t = \frac{ 79.8 - 85.2 }{ \sqrt{ \frac{8.8^2 }{12} +\frac{ 8.3^2 }{17} } }[/tex]
=> [tex]t = -1.667[/tex]
Interpret the coefficient of variation according to the context, determining the most homogeneous set
Answer:
2009 data set is most homogeneous
Step-by-step explanation:
As per coefficient of variation, which is around 5% for the year 2009 and around 20% for the year 2010 we can state that the data set for the year 2009 is most homogeneous
Homogeneous means similar, it can be observed on the graph as well that the data for the year 2009 is less variant
Hope it answers your question.
What is the probability of rolling a 2 and then a 4? Answer choices are in the form of a percentage, rounded to the nearest whole number.
Question:
Carl throws a single die twice in a row. For the first throw, Carl rolled a 2; for the second throw he rolled a 4. What is the probability of rolling a 2 and then a 4? Answer choices are in the form of a percentage, rounded to the nearest whole number. O 22% 36% O 3% O 33%
Answer:
The probability of rolling a 2 then 4 is 3%
Step-by-step explanation:
Given
A die rolled twice
Required
Probability of rolling a 2 then 4; i.e. P(2 n 4)
First, we need to list out the sample space
[tex]S = \{1,2,3,4,5,6\}[/tex]
[tex]n(S) = 6[/tex]
Next, is to calculate P(2)
[tex]P(2) = \frac{n(2)}{n(S)}[/tex]
[tex]P(2) = \frac{1}{6}[/tex]
Next, is to calculate P(4)
[tex]P(4) = \frac{n(4)}{n(S)}[/tex]
[tex]P(4) = \frac{1}{6}[/tex]
Next,is to calculate the required probability using the following formula
[tex]P(2\ n\ 4) = P(2) * P(4)[/tex]
[tex]P(2\ n\ 4) = \frac{1}{6} * \frac{1}{6}[/tex]
[tex]P(2\ n\ 4) = \frac{1}{36}[/tex]
[tex]P(2\ n\ 4) = 0.02777777777[/tex]
Convert to Percentage
[tex]P(2\ n\ 4) = 2.777777777\%[/tex]
Approximate
[tex]P(2\ n\ 4) = 3\%[/tex]
Hence, the probability of rolling a 2 then 4 is 3%
Answer:
3%
Step-by-step explanation:
An 14-meter-tall cylindrical tank with a 2-meter radius holds water and is half full. Find the work (in mega-joules) needed to pump all of the water to the top of the tank. (The mass density of water is 1000 kg/m3. Let g = 9.8 m/s2. Round your answer to two decimal places.)
Answer:
to two decimal places
= 6.04 mega joules
Step-by-step explanation:
The volume of the half tank
= πr²h
r= 2 m
h= 14/2= 7 m
Volume= 22/7 *2² *7
Volume= 88 m³
work (in mega-joules) needed to pump all of the water to the top of the tank
= Volume*mass density *acceleration*distance
= 88*1000*9.8*7
= 6036800 joules
In mega joules
= 6.036800 mega Joules
to two decimal places
= 6.04 mega joules
The work needed to pump all of the water to the top of the tank is 6.03 MJ
What is work?
Work is said to be done whenever a force move a body through a certain distance.
To calculate the work needed to pump the water to the tank, first we need to find the volume of the water in the tank half full.
Formula:
V = πr²h/2................ Equation 1Where:
V = Volume of half full water in the tankh = height of the tankr = radius of the base of the tankπ = pieFrom the question,
Given:
r = 2 mh = 14 mπ = 3.14Substitute these values into equation 1
V = 3.14(2²)(14)/2V = 87.92 m³.Finally, to get the work needed to pump all the water to the top of the tank, we use the formula below.
W = ρVhg/2................. Equation 2Where:
W = Work needed to pump all the water to the of the tankρ = Density of the tankh = height of the tankV = Volume of halfull water in the tankg = acceleration due to gravityFrom the question.
Given:
ρ = 1000 kg/m³h = 14g = 9.8 m/s²V = 87.92 m³Substitute these values into equation 2
W = 1000(14)(9.8)(87.92)/2W = 6031312 JW = 6.03 MJ.Hence, The work needed to pump all of the water to the top of the tank is 6.03 MJ.
Learn more about work here: https://brainly.com/question/8119756
Round each number to three significant figures.a. 3.14159 b. 6.12356c. 4.56787
Answer:
The round off values are- 3.14, 6.12, and 4.57 respectively.
Step-by-step explanation:
The given value to which we have to round off is a. 3.14159 b. 6.12356 c. 4.56787
In order to round off the number we must keep in mind that there should be three digits in total and we will increase the value by one if the right-hand side value is more than 5.
Thus round off figure of 3.14159 is 3.14.
The round off figure of 6.12356 is 6.12.
The round off figure of 4.56787 is 4.57.
If $10,000 is placed in an investment paying 4.8% yearly interest compounded annually, how long will it take for the account to double?
Answer:
15 years.
Step-by-step explanation:
We have the equation:
20000 = 10000(1 + 0.048)^t where t is the number of years.
1.048 t = 20000/10000 = 2
Taking logs:
t ln 1.048 = ln 2
t = ln 2 / ln 1.048
t = 14.78
Un guardia forestal divisa, desde un punto de observación A, un incendio en la dirección N27° 10’ E. Otro guardia, que se encuentra en el punto de observación B, a 6 millas al este de A, ve el mismo fuego en la dirección N52° 40’ W. Calcula, al décimo de milla más cercano la distancia de cada uno de los puntos de observación al incendio
Answer:
la distancia del punto de observación A al incendio = 5.5 millas
la distancia del punto de observación B al incendio = 3.8 millas
Step-by-step explanation:
La expresión esquemática de la pregunta se puede ver en la imagen adjunta a continuación :
Del siguiente diagrama;
Usando la sine regla:
[tex]\dfrac{sin \ F}{f} = \dfrac{sin \ A }{a}[/tex]
[tex]\dfrac{sIn \ 79}{6} = \dfrac{sin \ 63}{a}[/tex]
a sin 79 = 6 sin 63
[tex]a =\dfrac{6 \times sin \ 63}{sin \ 79}[/tex]
[tex]a =\dfrac{6 \times 0.8910}{0.9816}[/tex]
a = 5.446 millas
la distancia del punto de observación A al incendio = 5.5 millas (a la décima más cercana)
[tex]\dfrac{sin \ F}{f} = \dfrac{sin \ B}{b}[/tex]
[tex]\dfrac{sin \ 79}{6} = \dfrac{sin \ 38}{b}[/tex]
b sin 79 = 6 sin 38
[tex]b = \dfrac{6 \times sin \ 38}{sin \ 79}[/tex]
[tex]b = \dfrac{6 \times0.6157 }{0.9816}[/tex]
b = 3.7635 millas
la distancia del punto de observación B al incendio = 3.8 millas (a la décima más cercana)
find sum of series: 1+2+3+...+n
Answer:
the sum of the this series is Sn = [n(n+1)] / 2
solve for x 30=5(x + 5)
Answer:
x = 1
Step-by-step explanation:
Given
30 = 5(x + 5) ← divide both sides by 5
6 = x + 5 ( subtract 5 from both sides )
1 = x
Answer:
Step-by-step explanation:
30 = 5(x + 5) ← divide both sides by 5
6 = x + 5 ( subtract 5 from both sides )
x=1
Calculate the perimeter of the segment of a circle of radius 8cm. If chord subtemds angle 98 degree at the center
Answer:
If radius = 8 cm and we needed perimeter of complete circle then
circumference (or perimeter) = 2*PI * 8 = 50.2654824574 cm
or 50.27 cm (rounded)
Step-by-step explanation:
The sum of 2 consecutive integers is 21 what’s the two numbers
Answer:
10 and 11
Step-by-step explanation:
Let the first integer be x.
Then the next one, since it's consecutive, must be (x+1).
The two equals 21. Thus:
[tex](x)+(x+1)=21[/tex]
Combine like terms:
[tex]2x+1=21[/tex]
Subtract 1 from both sides:
[tex]2x=20[/tex]
Divide both sides by 2:
[tex]x=10[/tex]
So, the first integer is 10.
And the second integer is 10+1=11.
Answer:
10 , 11
Step-by-step explanation:
The sum of two consecutive integers is 21.
Let the least of the integer be signified by the variable x.
Consecutive means "directly after", which means the other integer would be: x + 1
Set the equation:
(x) + (x + 1) = 21
Simplify. Combine like terms:
x + x + 1 = 21
(x + x) + 1 = 21
2x + 1 = 21
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 1 from both sides:
2x + 1 (-1) = 21 (-1)
2x = 21 - 1
2x = 20
Next, divide 2 from both sides:
(2x)/2 = (20)/2
x = 20/2
x = 10
Plug in 10 for x in the equation:
(x) + (x + 1) = 21
10 + (10 + 1) = 21
10 + 11 = 21
21 = 21 (True)
The two numbers are 10, 11.
~
Solve 3x – 1.1 = 0.7
Answer:
x = 0.6
Step-by-step explanation:
3x - 1.1 = 0.7
3x = 1.8
x = 0.6
Answer:
x = .6
Step-by-step explanation:
3x – 1.1 = 0.7
Add 1.1 to each side
3x – 1.1+1.1 = 0.7+1.1
3x = 1.8
Divide each side by 3
3x/3 = 1.8/3
x = .6
What is the slope of a line that passes through the points (-2,4) and (-6,12) Give your answer in lowest terms
Answer:
-2
Step-by-step explanation:
We can find the slope for two points
m = ( y2-y1)/(x2-x1)
= ( 12 - 4)/(-6- -2)
= 8/( -6+2)
= 8/-4
= -2