Because the lines have different slopes, we conclude that there is only one intercept, and thus, the system of linear equations has only one solution.
How many solutions does the system of equations has?Remember that a system of equations has as many solutions as intercepts are when we graph both equations in the same coordinate axis.
Now, in this case, we have a system of linear equations:
y = m1*x + b
y = m2*x + b
Remember that linear equations are parallel only if the two lines have the same slope, in this case, we know that m1 ≠ m2, so the slopes are different.
Then the lines are not parallel, which means that intersect only one time, so we conclude that the system of equations has one solution.
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What is the inverse of function f?
f(x)=10/9x+11
Helen needs 6 pints of water to make lemonade. How many gallons does she need?
f(x) = 4x³ + 6x² – 3x − 4
g(x) = 4x - 3
Find (f - g)(x).
Solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1
What are algebraic equations?Algebraic equations are defined as mathematical statements in which two algebraic expressions are set equal to each other. An algebraic expression usually consists of variables, coefficients and constants. Algebraic equations can be of many types, such as monomial algebraic equations, binomial algebraic equations, quadratic algebraic equations, polynomial equations.
Given in the question that the value of f(x) is equal to 4x³+6x²-3x-4
and the value of g(x) is equal to 4x-3.
Subtracting g(x) from f(x) we get,
(f-g)(x)= 4x³+6x²-3x-4-4x+3
4x³+6x²-7x-1
Therefore, solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1.
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find the confidence interval specified. assume that the population is normally distributed. a sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. their mean score is 76.2 and their standard deviation is 21.4. construct the 95% confidence interval for the mean score of all such subjects.
The 95% confidence interval for the mean score of all such subjects. will be ( 67. 7 , 84.7) using mean.
What is mean?
Mathematicians, particularly statisticians, use a variety of means. Every mean serves to condense a certain set of facts, frequently to help grasp the general significance of a particular data set.
sample mean = x' = 76.2
sample S = 21.4
sample size n = 27
Confidence level = a = 0.95
α=1-a=0.05
95% confidence interval for the mean score of all such subjects is
(x'-E , x'+E)
E = [tex]\frac{tc*s}{\sqrt{n}}[/tex]
E = [tex]\frac{2.056*21.4}{\sqrt{27}}[/tex]} = 8.466
95% confidence interval for the mean score of all such subjects is
(x'-E , x'+E)
=(76.2-8.466 , 76.2+8.466)
=(67.734 , 84.666)
= ( 67. 7 , 84.7)
Hence The answer will be ( 67. 7 , 84.7).
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Solve for x: -4x - 4 = -4(x + 2)
Oo
O-4
O All real numbers
O No solution
4 root symbol 84 x 10 to the power of 4
The simplified value for 4 √84 x [tex]10^4[/tex] is 800 √21.
What is exponents?The exponent of a number shows how many times the number is multiplied by itself.
For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power." In general, xn means that x is multiplied by itself for n times.
Given:
4 √84 x [tex]10^4[/tex]
Now, first factorize 84 into prime factor
84 = 2 x 2 x 3 x 7
The, we can write it as
4 √84 x [tex]10^4[/tex]
=4 x √(2 x 2 x 3 x 7 x (10²)²)
= 4 x 2 x 10² √( 3 x 7)
= 8 x 10² √21
=800 √21
Hence, the simplified value is 800 √21.
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Use distributive property to multiply the 3 in the expression 3(x−5)=12
Answer:
x = 9
Step-by-step explanation:
3(x - 5) = 12 ← distribute the parenthesis on the left by 3
3x - 15 = 12 ( add 15 to both sides )
3x = 27 ( divide both sides by 3 )
x = 9
the following data were obtained for days required to reach 230 lb and backfat thickness of a sample of 10 pigs: pig no. days to 230 lb, days backfat thickness, in 1 164 1.0 2 180 1.1 3 158 1.2 4 160 1.4 5 198 1.2 6 172 1.3 7 186 1.1 8 178 1.3 9 178 1.4 10 186 1.0 calculate the covariance between days to 230 lb and backfat thickness.
The covariance value between two variables says, days to 230 lbs and backfat thickness, is 0.48..
The covariance value between any two variables is used to determine whether the variables are changing in the same direction. It relates the two variables if they are from different data sets.
Let X and Y be two data sets with different values. Then the covariance between X and Y is given by
Cov ( X,Y) = ∑ ( X ᵢ– u) ( Yⱼ-v ) /n
Where are Xᵢ's elements in the X data set
Yⱼ→ elements of the Y set
μ → mean of X data set
ν→ mean of Y set
n→ total number of observations
As we have given two sets of data, let days to 230 lbs and backfat thickness be sets X and Y, respectively.
Now, we shall calculate the mean value for X and Y sets.
Mean of X set = (164+158+180 + +160+198+172+186+178+178+186)/10= 176
The mean of Y set =
(1.0+ 1.1+ 1.2+ 1.4+1.2+1.3++1.1+1.3+1.4+1.0)/10 = 1.2
Xᵢ– μ - 12 -18 4 -16 22 -4 10 2 2 10
Yⱼ– ν -.2 - .1 0 .2 0 .1 -.1 .1 .2 -.2
(Xᵢ - μ)(Yⱼ- ν) 2.4 1.8 0 - 3.2. 0 0.4 1 4.4 -2
∑ (Xᵢ - μ ) ( Yⱼ - ν) = 4.8
put all the values of variables in above formula we get,. Cov( X, Y) = 4.8 / 10 = 0.48 ..
So, the Covariance between the days of 230lb and backfat thickness is 0.48 ..
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tv sets: according to the nielsen company, the mean number of tv sets in a u.s. household in 2013 was 2.24 assume the standard deviation is 1.3. a sample of 80 households is drawn.
The probability of a random sample of 80 households having a sample means a number of at least 2.55 televisions per household is 0.48173.
Given: Mean(μ) = 2.24, Standard deviation(σ) = 1.38, Sample size(n) = 1.28 and a random variable for X = 2.55
The formula to calculate the z-score from the mean. The standard deviation is:
z = (X - μ) / ( σ / √(n)) where,
z = z-score,
X = random variable,
μ = mean,
σ = standard deviation, and
n = sample size
Let's solve the given question:
We have,
Mean(μ) = 2.24,
Standard deviation(σ) = 1.38,
Sample size(n) = 80, and
a random variable for X = 2.55
As it is given sample means at least 2.55 so we have to find the Z(x ≥ 2.55).
Therefore, Z(x ≥ 2.55) = (2.55 - μ) / ( σ / √(n))
Substituting all values we get:
Z(x ≥ 2.55) = (2.55 - 2.24) / ( 1.38 / √(80))
Z(x ≥ 2.55) = 0.01 / 0.21819
Z(x ≥ 2.55) = 0.48173
Hence the probability of a random sample of 40 households having a sample means a number of at least 2.55 televisions per household is 0.48173.
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What percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water? (1 point)
69%
30%
1%
71%
The percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water is 69%. Therefore, option A is the correct answer.
We need to find the percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Over 69 percent of the fresh water on Earth is found in icecaps and glaciers, and just over 30 percent is found in ground water. Only about 0.3 percent of our fresh water is found in the surface water of lakes, rivers, and swamps.
The percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water is 69%. Therefore, option A is the correct answer.
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Simplify: 12a+7x-3a-2x
Answer:
9a+5x
Step-by-step explanation:
9a+5x
all you need to do here is to collect like terms.
so first ignoring the X's, 12a minus 3a is 9a.
then 7x-2x=5x
then you put these together to give you 9a+5x
Answer:
9a+5x
Step-by-step explanation:
you just have to collect like terms and then you will be able to find your answer!
AB=AD and BC=DC What is y equal to? Please show your work of how you got the answer.
The measure of the angle y is 49 degrees if AB=AD and BC=DC; the answer is 49 degrees.
What is quadrilateral?It is defined as a four-sided polygon in geometry having four edges and four corners. The kite is quadrilateral, having two pairs of congruent sides and it has one pair of opposite congruent angles.
The kite is given in the picture.
AB = AD
BC = DC
∠DBC + ∠CBD + ∠C = 180
From the property of kite: ∠DBC = ∠CBD
y + y + 82 = 180
y = 98/2
y = 49 degrees
Thus, the measure of the angle y is 49 degrees if AB=AD and BC=DC; the answer is 49 degrees.
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Please answer this with an explanation:
Answer:
-2
Step-by-step explanation:
PT = TQ
3x + 4 = 5x - 8
-3x -3x
4 = 2x - 8
-8 -8
-4 = 2x
÷2 ÷2
x= -2
sooo
3 times -2 +4 = -2
A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7.50, and tickets for children cost $3.50. How many of each type of ticket were purchased?
There are 23 tickets which are purchased for children and 9 tickets are purchased for adults which cost total $148.
It is given in the question that 32 tickets are purchased by group which cost total $148.
Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x
Now cost of one ticket for adult = $7.50
Total amount spent on adult tickets = 7.50 × (32-x)
Similarly, cost of one ticket for child= $3.50
Total amount spent on children tickets = 3.50 × x =3.5x
Total amount spent by group on tickets = $148
⇒ 7.5 × (32-x) + 3.5x = 148
⇒ 240 - 7.5x + 3.5x = 148
⇒ 7.5x - 3.5x = 240 - 148
⇒ 4x = 92
⇒ x = 23
Children = 23
Adults = 32-x = 32-23 = 9
Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.
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A Construction worker needs to pour a rectangular slab 29 feet long 16 feet wide and 6 inches thick how many cubic yards of concrete does the worker need
We have a rectangular slab.
The volume of concrete is equal to the volume of this rectangular prism.
The volume of this prism is equal to the product of its length, width and thickness.
Then, we can write:
[tex]\begin{gathered} V=L\cdot W\cdot t \\ V=29ft\cdot16ft\cdot6in \\ V=29ft\cdot16ft\cdot(6in\cdot\frac{1ft}{12in}) \\ V=29\cdot16\cdot\frac{6}{12}ft^3 \\ V=232ft^3 \end{gathered}[/tex]We convert the thickness from inches to feet by multiplying it by a unit ratio 1 ft / 12 inches, which has a value of 1, as 1 ft = 12 inches, but let us change the units from inches to feet.
When we have all the measures in feet we can have the volume in cubic feet.
Answer: 232 cubic feet.
Suppose a sample of 1762 floppy disk is drawn. Of these disks, 70 were defective. Using the data estimate the proportion of disks which are defective. Enter your answer as a fraction or decimal number rounded to three decimal places.
In order to find the proportion of disks that are defective, we can divide the number of defective disks by the total number of disks in the sample:
[tex]p=\frac{70}{1762}=\frac{35}{881}[/tex]Therefore the proportion is 35/881.
Can anyone help me with this?
the population of a town increased by 2.59% per year from the beginning of 2000 to the beginning of 2010. the town's population at the beginning of 2000 was 74,500.
the town's population at the beginning of 2000 was 74,500.Then the population in 2010 will be 96206.97
In 2000, the population of a town = 74500
Every year, it increase by 2.59%
To find the equation P(t) which represents the population of this town t years from 2000 to 2010.
Formula
If a be the original population of a town and it increases by r% every year, after t year the population will be
A = P ( 1+r/100)^t
Now,
Taking, P =74500, r = 2.59% we get,
A = 74500( 1+0.0259)^10
A= 74500(1.0259)^10
A= 96206.97
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The equation of line c is y=–
7x+10. Line d is perpendicular to line c and passes through (7,4). What is the equation of line d?
PLEASE HELP!!!!!!!!!!!
Answer:
domain -2<x<2
range -2<y<2
not a function
Imagine you went to the store and bought a video game for $12.98. This item is taxable at 6% tax and the total tax is $0.78. What is the total amount due?
The total amount due will be equal to $6.24.
This question can be solved by converting the situation into form of an equation. An equation may be defined as an expression which consists of numbers, variables related to each other by arithmetic expressions. The solution of equation often referred to as the variables for which the equation must be solved, are the values of the unknowable variables that satisfy the equality. The cost of video game is given as $12.98, and tax is equal to $0.78, and he paid an amount of $20. let the change left be x.
Total amount = cost of game + tax + change
$20 = $12.98 + $0.78 + x
$20 = $13.76 + x
=> x = $20 - $13.76
=> x = $6.24 which is the due amount.
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Complete Question:
Imagine you went to the store and bought a video game for $12.98. This item is taxable at 6% tax and the total tax is $0.78. What is the total amount due? Next, you decide to pay with a $20.00 bill. How much change will you receive after paying for your video game?
Sophie opened a picture of a tree on her cell phone screen and zoomed in 2.5 times. The new scale of the photograph became 1:168. What would be the scale if Sophie zoomed the image in 4 times?
the hypotenuse of a right triangle is 10 inches. the length of the two legs are given by two consecutive even integers. find the length of the two legs. the lengths of the two legs are and inches. license points possible: 1
Answer:
6 and 8
Step-by-step explanation:
x = one integer
x+2 = other integer
Pythagorean Theorem:
x^2 + ( x+2)^2 = 10^2
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
x^2 + 2x -48 = 0 Use factoring ( or Quadratic Formula)
(x+8)(x-6) = 0 shows x = 6 the other integer is 8
Which symbol correctly compares these fractions? −4/5 −8/9
Answer:
-4/5 > -8/
-4/5 greater than -8/
Answer:
" > "
Step-by-step explanation:
-4/5=4x9 5×9
-4/5 = - 36/ 45
-8/9=8×5 9×5
-8/9 =-40/45
-36/ 45 > -40/45
-4/5 > -8/9
in this case - 4/5 is closer to 0
sam's bowling score is 5 less than twice the score of eva's. The sum of their scores is 235. Write and solve the equation to find the score of each student.
Which shows the expressions in the order they would appear on a number line from least to greatest? (5 points) a 17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3 b 3 to the power of 3, square root of 30, square root of 15, square root of 6, 17 over 9 c 3 to the power of 3, square root of 6, square root of 15, 17 over 9, square root of 30 d 17 over 9, square root of 30, square root of 15, 3 to the power of 3, square root of 6
An expression which shows the order the numbers would appear on a number line from least to greatest is: A. 17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.
In Mathematics, a number line typically increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
In order to arrange the given numbers in order from least to greatest, we would convert them into a decimal number as follows:
17/9 = 1.8889√6 = 2.4495√15 = 3.8730√30 = 5.47723³ = 9Read more on number line here: brainly.com/question/28032137
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2. Find the volume to the nearest cubic millimeter of the 3-D object in the diagram.
200 mm
300 mm
Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex. Then the height is 6 feet.
What is the volume of the square pyramid?Using the equation volume = base area height / 3, one may calculate the volume of a regular square pyramid. Keep in mind that the base area is equal to the base edge length squared.
A polygonal base and an apex come together to form a polyhedron known as a pyramid. Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex.
The volume of a square pyramid exists found by multiplying the area of the base by the height divided by 3.
32 = 4² × h/3
32 = 16 × h/3
Multiply both sides by 3
96 = 16 × h
Divide both sides by 16
H = 96/16
H = 6
Therefore, the height is 6 feet.
The complete question is:
Find the height of a square pyramid that has a volume of 32 cubic feet and a base length of 4 feet.
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Julie is using a 1/2
1
2
-cup measuring cup to fill a gallon jug with water. Julie will need Response area scoops of the 12
1
2
-cup measuring cup to completely fill the jug.
16 cups of water using 1/2 cup of measuring cup will fill a gallon of water.
Measuring of VolumeTo find the number of 1/2 cups that will fill a gallon, we simply need to know how many cups are in one gallon.
[tex]1cup = 0.0625 gallon[/tex]
This implies that
[tex]\frac{1}{2} cup = 0.03125 gallon[/tex]
Let's equate this and find how many cups are in one gallon.
[tex]\frac{1}{2} cup = 0.03125 gallon\\x cup = 1 gallon\\[/tex]
cross multiply both sides and make x the subject of formula
[tex]x = \frac{0.5}{0.03125}\\x = 16 cups[/tex]
The number of 1/2 cups that will fill 1 gallon will be 16 cups.
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10) 18p³ - 6p² +3p-1
Answer:
Evaluate
18p
3
−6p
2
+3p−1
Rewrite the expression
18p
3
+3p−6p
2
−1
Factor out 3p from the expression
3p(6p
2
+1)−6p
2
−1
Factor out −1 from the expression
3p(6p
2
+1)−(6p
2
+1)
Solution
(3p−1)(6p
2
+1)
Halp me with this 1 question Brainliest to correct answer
Answer:
A is correct.
[tex]g = \frac{p}{6} - 15[/tex]
Step-by-step explanation:
[tex]p = 6g + 90[/tex]
[tex]6g = p - 90[/tex]
[tex]g = \frac{p}{6} - 15[/tex]
So A is correct.