The solution to the inequality is (7/6, ∝) and (-∝, 7/6)
How to solve the inequality?The inequality expression is given as:
2−5|6x−4|<−13
Subtract 2 from both sides
|6x−4|<−15
Divide through by -5
|6x−4| > 3
Remove the inequality sign
6x - 4 > 3 or 6x - 4 < 3
Add 4 to both sides
6x > 7 or 6x < 7
Divide by 6
x > 7/6 or x < 7/6
In interval notation, we have:
(7/6, ∝) and (-∝, 7/6)
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Consider the equation y = 12 – 3x.
Which of the following is a graph of this equation?
Answer:
second graph
Step-by-step explanation:
looking at the y intercept. 12 is y int
Answer:
Second line
Step-by-step explanation:
our equation rearranged is y=-3x+12
meaning that y-intercept is 12, that is where the line cuts the y axis
we find that the second line cuts the y axis around that 12 therefore it is the most relevant line here
What is the quadratic regression equation that fits these data?
X
-4
-3
-2
-1
0
1
2
3
4
O A. ý = 0.82x2 + 0.78x+7.23
OB. 9=1642 +1.24x+8.08
O c. y = 2.13x² +0.13x+ 6.39
O D. = 16.76 1.02*
40
28
10
8
7
10
16
26
40
Using a calculator, the quadratic regression equation that fits the data is:
C. y = 2.13x² + 0.13x + 6.39
How to find the equation of regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, the points are:
(-4,40), (-3,28), (-2, 10), (-1, 8), (0,7), (1,10), (2,16), (3,26), (4,40).
Hence the equation is:
C. y = 2.13x² + 0.13x + 6.39
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Solve the system of equations. Type in all points of intersection for the two functions and round to the nearest tenth if necessary f(x)=sr5x+25-1 g(x)=x^2-2x-3
The solution to the system of equations are (-1.7, 3.1) and (4.1, 5.8)
How to solve the system of equation?The equations are given as:
[tex]f(x)=\sqrt{5x+25}-1[/tex]
[tex]g(x)=x^2-2x-3[/tex]
Next, we plot the graph of the equations (see attachment)
From the attached graph, we can see that both equations intersect at (-1.7, 3.1) and (4.1, 5.8)
Hence, the solution to the system of equations are (-1.7, 3.1) and (4.1, 5.8)
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The table shows the size of outdoor decks (x) in square feet, and the estimated dollar cost to construct them (y).
y
xy
100
600
10,000
60,000
144
850
20,736
122,400
225
1,300
50,625
292,500
324
1,900
104,976
615,600
400
2,300
160,000
920,000
Σχ=1,193 | Σy=6,950 | Ex?=346,337 | Σxy=2,010,500
Which regression equation correctly models the data?
X
xy=5.83x-1.04
y = 5.83x + 17
y = 5.71x + 29
y
= 5.71x + 27.6
Submitted
The regression equation of the table is y = 5.71x + 27.6
How to estimate the regression equation?From the table of values, we have the following parameters:
[tex]\sum x = 1193[/tex]
[tex]\sum y = 6950[/tex]
[tex]\sum x^2 = 346337[/tex]
[tex]\sum xy = 2010500[/tex]
Calculate A using
[tex]A = \frac{\sum y * \sum x^2 - \sum x * \sum xy}{n\sum x^2 - (\sum x)^2}[/tex]
This gives
[tex]A = \frac{6950 * 346337 - 1193 * 2010500}{5 * 346337 - (1193)^2}[/tex]
Evaluate
[tex]A = \frac{8515650}{308436}[/tex]
Divide
A = 27.6
Calculate B using
[tex]B = \frac{n\sum xy - \sum x * \sum y}{n\sum x^2 - (\sum x)^2}[/tex]
This gives
[tex]B = \frac{5 * 2010500 - 1193 * 6950}{5 * 346337 - (1193)^2}[/tex]
Evaluate
[tex]B = \frac{1761150}{308436}[/tex]
Divide
B = 5.71
The regression equation is represented as:
y = Bx + A
So, we have
y = 5.71x + 27.6
Hence, the regression equation of the table is y = 5.71x + 27.6
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Complete the table of inputs and outputs for the given function. F(x)= -5(x+7)
The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the function f(x) = -5(x + 7)
When x = -2; f(-2) = -5(-2 + 7) = -25
When x = -1; f(-1) = -5(-1 + 7) = -30
When x = 0; f(0) = -5(0 + 7) = -35
When x = 1; f(1) = -5(1 + 7) = -40
When x = 2; f(2) = -5(2 + 7) = -45
The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).
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Need help please with number 2!!!
Answer:
Step-by-step explanation:
Which expression is equivalent to (43) (
what is the following product?
(2√7 + 3√6) (5√5 +4√3)?
What is the approximate area of a circle with a radius of 10 in?
[tex]\huge\boxed{\textsf{A.}\ 78.5\ \text{in}^2}[/tex]
Correction to your question text: diameter, not radius.
The area of a circle is given by:
[tex]A=\pi r^2[/tex]
The radius is half of the diameter.
[tex]A=\pi\cdot\left(\dfrac{10}{2}\right)^2[/tex]
Substitute and solve.
[tex]\begin{aligned}A&=\pi\cdot\left(\frac{10}{2}\right)^2\\&=\pi\cdot5^2\\&=\pi\cdot25\\&\approx\boxed{78.5}\end{aligned}[/tex]
Find the value of y.
A. 4
B. 6
C. 10
D. 12
Answer:
y=12
Step-by-step explanation:
30,60,90 triangle
8*rad3=8rad3
8rad3/2=4rad3
4rad3*rad3=12
Firm X is a monopolist with marginal cost of $37/unit. If elasticity of demand is -9, use the markup formula to determine the price Firm X should charge to maximize profit.
Step-by-step explanation:
hggggggggggggggggggggg
If p = the price of a pair of basketball shoes, which algebraic expression
represents the phrase below?
4
the difference of the price of the shoes and 5 dollars
A. 5p
B. p+5
c. ff
D. p-5
Hello :
The difference of the price of the shoes and 5 dollars is p - 5.
Northlake High School has two lunch periods. Students can eat their lunch in
the cafeteria or on an outside patio. About 35% of students who have first
lunch eat outside. Compare this with the percentage of second-lunch
students who eat outside.
First lunch
Second lunch
Total
Select the true statement.
Eat outside
0.19
0.18
0.41
Eat inside
0.35
0.24
0.59
Total
0.54
0.46
1.0
Based on the given information on the first and second lunch students, the true statement is B. A greater percentage of second-lunch students (39%) eat outside.
which lunch students eat more outside?the percentage of second lunch students who eat their lunch outside is:
= Second lunch students who eat outside / Second lunch students
this gives:
= 0.18 / 0.46 x 100%
= 39%
options for this question include:
A. A smaller percentage of second-lunch students (24%) eat outside.
B. A greater percentage of second-lunch students (39%) eat outside.
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Select the correct answer. Suppose that 3 boys and 2 girls go to the theatre and occupy 5 seats in a row. In how many ways can they be seated if all 3 boys sit together?
Answer:
Possibly 3
Step-by-step explanation:
Lets say
g=girls
b=boys
1st option: gbbbg
2nd option: bbbgg
3rd option: ggbbb
Please answer all parts as I know the answers but need the work to go with them. Thus, I believe the above answers are correct. Thank you!
As the sample size n is less than 30 normal distribution is used.
The values of x are converted into z by using the formula z= x-u/ s and then the z values are found out from the table.
The limits are found by using the formula x±σz or x±sz where s= σ
As the sample size is 10 which is less than 30 the normal distribution is used.
The probability of x< 2.59 is 0.3446
The probability 2.60<X <2.63 is 0.9484
So lower and upper limits are 2.607 and 2.612
Part A
As the sample size is 10 which is less than 30 the normal distribution is used.
Part B
For given value of x= 2.59 z is obtained =0.4
x= 2.59
z= x-u/ s
z= 2.59-2.61/0.05
z= -0.02/0.05
z=- 0.4
P (X<2.59) = P(-0.4 <Z<0) = 0.5 -0.1554= 0.3446
The probability of x< 2.59 is 0.3446
Part C
For two given values of x= 2.60 and 2.63 z is obtained as =0.2 and 0.4
x1= 2.60
z1= x-u/ s
z= 2.60-2.61/0.05
z= -0.01/0.05
z=- 0.2
x2= 2.63
z2= x-u/ s
z= 2.63-2.61/0.05
z= 0.02/0.05
z= 0.4
P (2.60<X<2.63) = P(-0.2 <Z<0.4)
= P(-0.2 <Z<0)+ P(0 <Z<0.4)
=0.793 + 0.1554= 0.9484
The probability 2.60<X <2.63 is 0.9484
Part D"
p= 0.57
From the table z= 0.045
z= x-u/ s
zs= x-u
zs+u = x
x1= 0.045*0.05 +2.61= 2.61225
x2= 2.61- 0.00225= 2.60775
So lower and upper limits are 2.607 and 2.612
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Given the functions f and g below, find f(g(0)).
After calculation, the composite function f(g(0)) returns the value 2 as the response.
Given, the values of the functions are:
f(x) = √₋x₊1 and g(x) = ₋x₋3
we need to find f(g(0)) = ?
F of g of x is another name for a composite function. Normal representations include f(g(x)) or (f g)(x), which denote that x = g(x) should be used in place of f(x). While the function g (x) is referred to as an inner function, the function f (x) is referred to as an outer function.
It means that every instance of an x in the function f is replaced with the function g(x).
∵ g(x) = ₋x₋3 so we can substitute this in the following expression:
g(0) = -(0) ₋ 3
g(0) = ₋3
Now in place of g(0) we can write ₋3, hence the changed expression becomes:
f(g(0)) = f(₋3)
= √₋(₋3)₊1
= √4
∴ f(g(0)) = 2
Hence we get the calculated function value as 2.
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A man walks to a coffee shop which is 4 km from his house in 20 minutes. Again, he walks to another shop at the same rate, and the total distance covered by him is 10 km in 50 minutes. What is his speed between the coffee shop and the other shop?
a. 10 km/hr
b. 8 km/hr
c. 12 km/hr
d. 6 km/hr
Answer:
c. 12km/hr
Step-by-step explanation:
Speed = distance/time
Coffee shop: Divide distance traveled by time taken to get the speed in km/min, then convert minutes to hours, and finally simplify to calculate the speed in km/hr
4km/20min * 60min/1hr = 240km/20hr = 12km/1hr = 12km/hr
Other shop: Same task, in the question it already says he is traveling at the same rate so this is only useful to check your answer
10km/50min * 60min/1hr = 600km/50min = 12km/1hr = 12km/hr
Points out
1.00
P Flag
question.
Instructions: Given the preimage and image, find the dilation scale factor. Use the forward slash (i.e.
"/") for all fractions (e.g. -1/2 is the same as
-6 -5
Scale Factor:
5
J'
-3 -2 -1
P
KT
3
T
4
5 6
The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Dilation is the increase or decrease in size of a figure by a scale factor.
The scale factor of the image = K'T'/KT = 1/2 ÷ 1 = 1/2
The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2
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let A and B sets. when do we say set A is equal to set B
Answer:
We say sets A and B are equal, and write A = B if they have exactly the same elements.
Step-by-step explanation:
Answer:
When set A is equal to set B. It is denoted as A = B.
Have a nice day!
Susan begins counting backward from 1298 by 4's, saying one number every 5 seconds. At the same time, Jim begins counting forward from 171 by 3's, saying one number every 5
seconds. What number will they both say at the same time? (By the way I'm only in 6th grade so please explain well :)
Answer:
Step-by-step explanation:
In 2000, the total population of the U.S. was 281.4 million people. In 2010, it was 308.7 million people. What is the average rate of change in the total population over this time period?
2.73 million people per year
27.3 million people per year
13.6 million people per year
1.36 million people per year
Answer:
2.73 million people per year
Step-by-step explanation:
Turn sentences into coordinates/points:
In 2000, 281.4 million people
(x₁, y₁) = (2000, 281.4)In 2010, 308.7 million people
(x₂, y₂) = (2010, 308.7)Rate of population per year:
[tex]\sf \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf \dfrac{308.7-281.4}{2010-2000}[/tex]
[tex]\rightarrow \sf 2.73 \ million \ people[/tex]
Does anyone know how to do this please help
18 + 5 + 23=46
Step-by-step explanation:
Answer:
1238
Step-by-step explanation:
22, 66, 198, ...
Find the 8th term.
Answer:
The 8th term will be 48114.
Step-by-step explanation:
This series is an geometric series.
The formula for the nth term in an geometric series is [tex]ar^{n-1}[/tex], where a is the first term, r is the ratio (how much each term is multiplied by and n is the term you want to find.
In this question, the 8th term will be [tex]22\times3^7[/tex] = 48114
The student council members are selling tickets to a school performance. Tickets are $10 for adults, a, and $5 for students, s, and they expect that twice as many students as adults will attend. Their goal is to earn $1500 from ticket sales.
Answer:
How about 100 adults and 100 students?
Step-by-step explanation:
Could you respond?
Find the surface of the rectangular solid
Answer: 80.28 square feet
Step-by-step explanation:
[tex]2(6.1\cdot 3+3\cdot 2.4+2.4 \cdot 6.1)=80.28[/tex]
Whats the correct answer answer asap
The environmental threat in Japan and Korea that threatens food security is: B. soil erosion.
What is Soil Erosion?Soil erosion can be defined as the washing away of the top soil that supports plants growth and also contains vital nutrients for plants growth.
Crops are grown majorly on land. The disruption of soil nutrients by soil erosion poses a serious environmental threat to food security in both Japan and Korea. Therefore, the answer is: B. soil erosion.
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Dollar General sold garden hoses at a reduced price of $7.64 and took an end of the season markdown of $12.35. What was the original selling price of each hose? Use formula M=S-N = selling price-reduced price
The original selling price of the garden hoses is $19.99
How to find the original selling price?Using the given formula,
M = S - N
where
M = markdownS = original selling price,N = reduced priceHence,
M = $12.35.
N = $7.64
Therefore,
S = M + N
S = 12.35 + 7.64
S = $19.99
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Need help with number 9 and number 10
Answer:
9. 3 acute angles
10: a) Acute Isosceles
b) Acute Scalene
Step-by-step explanation:
9: Sum of Interior angle theorem: Sum of the interior angles of a Triangle = 180°
An Acute angle is a angle that is less than 90°
the sum of the two acute angles must be less than 180°
The base angles of an isosceles triangle are congruent.
So For example,
the base angles of the isosceles are ∠1 and ∠2
Lets make the three angle measure closer:
if ∠1 = 46° then ∠2 also have to be 46° and ∠3 = 88°
all three angle are less than 90° and two angles are congruent.
help me solve this need help asap
Answer:
(-5-5x)/(4x+3
Step-by-step explanation:
Replace x with y to get (-3y-5)/(4y+5). Solve for y to get (-5-5x)/(4x+3).
find the midpoint of the segment with endpoints at (-2,1) and (0,9) using (x1+x2,y1+y2)
Answer:
(-1, 5)
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Define the endpoints:
[tex]\textsf{let}\:(x_1,y_1)=(-2,1)[/tex][tex]\textsf{let}\:(x_2,y_2)=(0,9)[/tex]Substitute the defined points into the formula:
[tex]\begin{aligned}\implies \textsf{Midpoint} & =\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\\ & =\left(\dfrac{0+(-2)}{2},\dfrac{9+1}{2}\right)\\\\& =\left(\dfrac{-2}{2},\dfrac{10}{2}\right)\\\\& =\left(-1,5\right)\end{aligned}[/tex]
Therefore, the midpoint of the segment with endpoints (-2, 1) and (0, 9) is (-1, 5).
HELP PLSSS WILL GIVE BRAINLIEST PLSSSS
Houa works at an electronics store as a salesperson. Houa earns a 4% commission on the total dollar amount of all phone sales she makes, and earns a 5% commission on all computer sales. Houa had $600 more in computer sales than in phone sales and earned a total of $129 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Houa made and the dollar amount of computer sales she made. Define the variables that you use to write the system.
One of the two equations required in the system of equations needed to determine the dollar amount of phone and computer sales Houa made is y = x + 600.
How do we write the system of equations?Let x represents the dollar amount of phone sales Houa made, and y represents the dollar amount of computer sales she made.
Therefore, a system of equations that could be used to determine x and y can be written as follows:
y = x + 600 ........................................................... (1)
0.04x + 0.05y = 129 ......................................... (2)
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