Answer:
y = 39
Step-by-step explanation:
|y−43|−|y−35| =0
add |y−35| to each side
|y−43|= |y−35|
This tells us that y must be between 35 and 43
That means |y−35| is positive so we can remove the absolute value signs
|y−43| is negative so we negate each term ( or multiply by -1)
-y+43 = y - 35
Add y to each side
y-y+43 = y+y-35
43 = 2y -35
Add 35 to each side
43+35 = 2y
78 = 2y
Divide by 2
78/2 = 2y/2
39 = y
Answer:
Step-by-step explanation:
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
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
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?
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
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).
multiples of 7 (-7,-4,2,14,21,34,42)ñ
Answer:
(-7,14,21,42)
Step-by-step explanation:
(-7,-4,2,14,21,34,42)
-7 = 7*-1 yes
14 = 7*2 yes
21 = 7 *3 yes
42 = 7*6 yes
Answer:
[tex]\huge\boxed{(-7,14,21,42)}[/tex]
Step-by-step explanation:
Let's check which multiples are of 7:
-7 => 7 × -1 [A multiple of 7]
-4 => Not a multiple of 7
2 => Not a multiple of 7
14 => 2 × 7 [A multiple of 7]
21 => 3 × 7 [A multiple of 7]
34 => Not a multiple of 7 [Doesn't come in the table of 7]
42 => 6 × 7 [A multiple of 7]
So, the multiples of 7 are:
(-7,14,21,42)
Please help asapppppp
Answer:
Step-by-step explanation:
(500 x 4) + (50 x 4) + (4 x 2)
2000 + 200 + 8
2208 is the solution
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
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
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.
~
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 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]
Andy currently has a balance of $4,585.92 in an account he has held for 21 years. He opened the account with an initial deposit of $3,278. What is the simple interest rate on the account? (2 points)
a.1.9%
b.1.4%
c.4.8%
d.6.7%
The closest answer I got was D. Add 4,585.92+3,278, because he initial deposited the money into the bank.
Angles R and S are supplementary angles. which is the measure of R?
Answer:
R = 15°Step-by-step explanation:
Since angles R and S are supplementary angles it means that the sum of their angles add up to 180°
To find R we must first find x
To find x , add angles R and S and equate them to 180
That's
R + S = 180
80 - x + 3x - 30 = 180
2x + 50 = 180
2x = 180 - 50
2x = 130
Divide both sides by 2
x = 65°
From the question
R = 80 - x
But x = 65°
Substitute the value of x into the expression
That's
R = 80 - 65
We have the final answer as
R = 15°Hope this helps you
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
Use the round trip airfare table to determine the percentile rank of $1,133
Answer:
R= $1,133/100(7+1)
=234.86 RS.
Step-by-step explanation:
percentile rank is the percentage of scores that shall be equal to or less than a given value. The percentage falls within the range of 0 to 100. To find out the percentile rank, we used the formula:
R= P/100(N+1). Where R is the percentile rank, p is a percentile and N number of items.
Let for round trip airfare; the percentile is $1,133. And the number of days for the trip is 7.put these values in the formula, we have
R= $1,133/100(7+1)
=234.86 RS.
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
State all possible names for the figure part 3
Answer:
quadrilateral,parallelogram
Step-by-step explanation:
A quadrilateral is a four-sided polygon.
A parallelogram is a quadrilateral with two sets of parallel sides, much like a rectangle, but with no right angles.
What are the full steps to 7x(x-2)+5(x-3)=-5
Answer:
[tex]x = -\frac{5}{7}, 2[/tex]
Step-by-step explanation:
To solve this equation, we need to simplify it down first. To do this, we must apply the distributive property to each term.
[tex]7x(x-2) + 5(x-3) = -5\\\\(7x^2 - 14x) + (5x - 15) = -5[/tex]
Now we can combine like terms.
[tex]7x^2 - 9x - 15 = -5[/tex]
Add 5 to both sides:
[tex]7x^2 -9x - 10 = 0[/tex]
We can see that this is a quadratic equation, in the form [tex]ax^2 + bx + c[/tex]. To solve for x, we must use the Quadratic Formula, which is [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex], where a is 7, b is -9, and c is -10.
Substitute inside the equation:
[tex]\frac{-(-9)\pm\sqrt{-9^2-4\cdot7\cdot-10}}{2\cdot7}\\\\\frac{9\pm\sqrt{81+280}}{14}\\\\\frac{9\pm19}{14}\\\\(9+ 19)\div14 = 2\\\\(9 - 19)\div14 = -\frac{5}{7}[/tex]
Hope this helped!
Answer:
Brianliest!
Step-by-step explanation:
simplify
7x^2-14x+5x-15 = -5
7x^2 - 9x - 10
x= 1
x = -0.7142857143
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:
What is the distance between the coordinates (5, 5) and (7, 2)? Round your
answer to the nearest tenth.
Answer: 3.6
Step-by-step explanation:
To find the distance, find the difference in the x and y coordinates then square them to add them and find the square root of that number you get after you added it.
x coordinate: 5 - 7 = -2
y coordinate: 5-2 = 3
2^2 + 3^2 = c^2 where c is the length
4 + 9 = c^2
13 =c^2
c = [tex]\sqrt{13}[/tex]
c= 3.605 rounded to the nearest tenth is 3.6
What is a unit rate
[tex]{Option: A}[/tex]
What is a unit rate?
=> A rate that has a 1 as its denominator.
______________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
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
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
What are the x-intercepts of the graphed function?
O (-3,0) and (0, 1.5)
O (-3,0) and (1,0)
0 (-1,2) and (1,0)
O (0, 1.5) and (1,0)
Answer:
(-3,0) and (1,0)
Step-by-step explanation:
The x-intercepts of the function that is graphed above are the points where the line of the graph intercepts or crosses the y-axis. At that point, y is always 0.
Thus, the line of the graph intercepts the x-axis at x = -3, when y = 0 (-3, 0), and also at x = 1, when y = 0 (1, 0).
Therefore, the x-intercepts of the graphed function are (-3,0) and (1,0).
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
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:
Write an inequality that represents "nine less than three times a number is greater than forty"?
Answer:
Three times a number is 3n. Nine less than that is 3n-9. This is NOT the same thing: 9-3n. Subtraction is not commutative. If n was 1, for example, 3(1)-9=-6. Looking at the other expression, 9-3(1)=6. 6 and -6 are definitely not the same number. So be careful how you set up your expression. Our inequality then would be
Step-by-step explanation: