You can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.
How you can create a histogram?Determine the range of the data: 0.6 to 4.7.
Divide the range by the number of classes (5) to find the class width: (4.7 - 0.6) / 5 = 0.76.
Determine the lower limits of each class by starting at the minimum value (0.6) and adding the class width repeatedly: 0.6, 1.36, 2.12, 2.88, 3.64, 4.4.
Count the number of data values that fall into each class and record it in a table.
Draw a bar for each class using the lower limit of the class as the x-axis value and the height of the bar equal to the number of data values in the class.
After creating the histogram, you can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.
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Can someone help me with 11 and 12 plss
Answer:
Q11: x = 3
Q12: x = -4
Step-by-step explanation:
Q11
We have the equation as
[tex]\:64^{2x\:+\:4}=16^{5x}[/tex]
Convert the bases in terms of the common base 4
64 = 16 x 4 = 4 x 4 x 4 = 4³
16 = 4 x 4 = 4²
Therefore the original equation becomes:
[tex]\mbox {\large 4^{3\left(2x+4\right)}=4^{2\cdot \:5x}}[/tex]
Since the bases are the same in this equation, the exponents must also be the same
Equation the two exponents we get
3(2x + 4) = 2·5x
==> 6x + 12 = 10x
Move 12 to the right side
6x = -12 + 10x
Move 10x to the left:
6x - 10x = -12
-4x = -12
x = -12/-4 = 3
Answer to Q11
-------------------------------------------------------------
Q12
We can solve this in a similar manner to Q12
27 = 3 x 3 x = 3³
9 = 3 x 3 = 3²
Plugging these in we get
[tex]\mbox {\large 27^x = 3^{3(x)} = 3^{3x}}[/tex]
[tex]\mbox {\large 9^ {(x - 2)} = 3^{2(x-2)} = 3^{2x -4} }\\\\[/tex]
Thus we get
[tex]\mbox {\large 3^{3x} = 3^{2x -4} }\\\\[/tex]
Equating the exponents we get
[tex]3x = 2x - 4\\\\3x - 2x = -4\\\\x = -4[/tex]
ANSWER to 12
Example
The product of 4 and (3 + x) is equal to 36. What is the value of x?
The equation 4(3 + x) = 36 models this statement.
Think: 4 times what number is 36?
Since 4.9 equals 36, that means (3 + x) equals 9.
Since 3 + x = 9, and 3 + 6 = 9, that means x equals 6.
The sum of twice a number, n, and 14 is 30. Write an equation that models this
statement. Then explain how you might use reasoning to find the value of n.
The equation that models the statement is: 2n + 14 = 30 and the solution is x = 8
How to determine the equation and the solutionFrom the question, we have the following parameters that can be used in our computation:
The sum of twice a number, n, and 14 is 30.
When represented as an equation, we have
2n + 14 = 30
Subtract 14 from both sides
2n = 16
So, we have
n = 8
Hence, the value of n is 8
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What is the geometric mean of 16 and 27
Answer:
The answer is 12
Step-by-step explanation:
a patent is the exclusive right to a product for a period of enter your response here years from the date the patent is filed with the government. (enter your response as an integer.)
A patent is a form of intellectual property that gives an individual or organization the exclusive right to manufacture, use, and/or sell an invention for a set period of time.
The length of a patent varies by country, but generally lasts for 20 years from the date the patent is filed with the government. This period can be extended in certain cases if the patent office grants a patent term extension.
The formula for calculating the length of a patent is: Length of Patent = Initial 20 Year Period + Extension. The initial 20 year period starts from the filing date of the patent application and is the same for all countries. However, the length of the extension varies depending on the country and the circumstances of the patent. For example, some countries may offer a 5-year extension, while others may offer a 10-year extension.
The length of a patent must be carefully calculated so that the patent owner can maximize the benefits of the patent. By calculating the patent length and extension, the patent owner can ensure that they are able to take advantage of their exclusive right to the invention for the maximum amount of time possible.
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Please show your work.
Point (2, 1) is not the solution of the inequality y ≥ (1/2)x + 3.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
y ≥ (1/2)x + 3
Check whether point (2, 1) is the solution or not. Then we have
1 ≥ (1/2)(2) + 3
1 ≥ 1 + 3
Point (2, 1) is not the solution of the inequality y ≥ (1/2)x + 3.
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Jimmy bought a brand new Ford Mustang for $32,000. He decided to sell the Mustang after one year in order to
purchase the newer model. The car has an average depreciation of about 24% after one year. About how much is the
Mustang worth after one year?
The Mustang is worth $24,320 after one year.
Compound interest is computed on the principal as well as the interest accumulated over the preceding period. It differs from simple interest in that interest is not added to the principal when computing interest for the next month.
Compound annual growth rate (CAGR) is the average yearly growth rate of an investment over a time period greater than one year. It is one of the most reliable methods for calculating and determining returns for individual assets, investment portfolios, and anything else whose value might grow or decline over time.
The formula to calculate the value of the Mustang after one year is:
value_after_one_year = value_initial * (1 - 0.24)
Plugging in the given values:
value_after_one_year = $32,000 * (1 - 0.24)
= $32,000 * 0.76
= $24,320
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Barium metal was quantitatively precipitated from a 1.52 g sample of BaCl2∙2H2O. The mass of the barium that was collected was 0.844 g. Calculate the experimental mass percent of barium in the sample.
The experimental mass percent of barium in the sample is 55.526.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that the Barium metal was quantitatively precipitated from a 1.52 g sample of BaCl₂∙2H₂O.
The mass of the barium that was collected was 0.844 g.
We need to find the experimental mass percent of barium in the sample.
Let x/100 is the percentage of Barium.
x/100×1.52=0.844
0.0152x=0.844
x=55.526
Hence, the experimental mass percent of barium in the sample is 55.526.
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A boat heading out to sea starts out at Point A, at a horizontal distance of 853 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 7 ∘ ∘ . At some later time, the crew measures the angle of elevation from point � B to be 4 ∘ ∘ . Find the distance from point � A to point � B. Round your answer to the nearest foot if necessary.
The distance from A to B is 355.42 feet.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
From the figure,
Tan 4 = PQ/853
PQ = tan 4 x 853
PQ = 0.07 x 853 _____(1)
Tan 7 = PQ/(853 - x)
PQ = tan 7 x (853 - x)
PQ = 0.12 x (853 - x) ______(2)
Now,
From (1) and (2) we get,
0.07 x 853 = 0.12 x (853 - x)
59.71 = 102.36 - 0.12x
0.12x = 102.36 - 59.71
0.12x = 42.65
x = 355.42 feet
Thus,
A to B distance is 355.42 feet.
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How do I solve this to find the point on a graph?
Answer:
Step-by-step explanation: This equation only contains enough information to define a line in a Koordinates system as far as i can tell. One point on this line would be y=3 and x=0 another one y=0 and x=15:4
i think xD
A limousine service has 15 cars available for rides: 8 are Lincoln Town Cars and the remainder are Cadillac models. Suppose an event organizer requests five limousines from this company. How many different collections C of five limousines are possible?
If A limousine service has 15 cars available for rides: then the number of different collections C of 5 limousines are possible is 3003 .
To find the number of different collections C of five limousines, we can use combinations. A combination is a way to choose a subset of items from a larger set, without regard to order.
Let the number of Cadillac models n.
Then, 15 - 8 = 7 cars are Cadillacs. So, n = 7.
The number of different collections of 5 limousines from the 15 cars is given by the number of combinations of 5 items taken from a set of 15 items:
⇒ ¹⁵C₅ = 15!/(5!×(15 - 5)!) = 15!/(5!×10!) = 3003.
Therefore , there are 3003 different collections C of five limousines that the event organizer can choose from the limousine service's fleet of 15 cars.
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You are going to factor the polynomial x^2−17x+16x, you find the product of (a)(c)and the sum of (b.) Which two factors would you choose to factor your polynomial?
Answer:
Below
Step-by-step explanation:
I believe your equation is incorrect ( perhaps a typo)
probably it is x^2 - 17x +16
then you could choose factors 16 and 1
to get this (x-1)(x-16)
William needs to translate ALMN by the rule (x, y) -> (x - 4, y + 7) Which of the following graphs represents that translation?
The sum of angles is 360 degrees is the required graph which represents the translation.
What is triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
Given,
x , y and z are exterior angles of triangle ABC.
So,
By angle sum property of triangle
Angles of
1 + 2 + 3 = 180
1 + z = 180
3 + y = 180
2 + x = 180
z + 180 = 1
y + 180 = 3
x + 180 = 2
So,
by substituting we get ,
180 - z + 180 - y + 180 - x = 180
x + y + z = 180 +180 + 180 - 180
x+ y +z = 360
Therefore, The sum of angles is 360 degrees is the required graph which represents the translation.
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Part of a train timetable is shown.
Preston
Nuneaton
07 29
08 52
Milton Keynes 09 28
08 40
10 28
11 11
1221
1354
14 24
a) Llyr catches the 08 40 train from
Preston. He arrives in
Nuneaton 6 minutes late.
What time does he arrive in
Nuneaton?
1034
b) How long is Llyr's journey from
Preston to Nuneaton?
Give your answer in minutes.
c) Kathy catches the 07 29 train from Preston.
She arrives in Nuneaton on time.
She attends a job interview.
She gets back to Nuneaton station 1 hour and 50 minutes later.
Is she back in time to catch the 10 28 train to Milton Keynes?
You must show your working.
minute
The time that Llyr arrives at Nuneaton, given that it is 6 minutes late, is 10 34.
Llyr's journey from Preston to Nuneaton took 114 minutes.
Kathy would not catch the 10 28 train to Milton Keynes.
How to find the time ?Llyr is meant to arrive in Nuneaton at 10 28 but arrived 6 minutes later which is:
= 10 28 + 6
= 10 34
The time that the trip took is therefore:
= Arrival at Nuneaton - Departure at Llyr
= 10 34 - 08 40
= 1 hour 54 minutes
= 114 minutes
The time that Kathy would get back to the station is:
= Arrival time at Nuneaton + 1 hour 50 minutes
= 08 52 + 1 hour 50
= 10 42
This is too late for the 10 28 train to Milton Keynes.
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Find the area of the region bounded by the parabola y = 5x2, the tangent line to this parabola at (1, 5), and the x-axis.
The area of the region bounded by the parabola is [tex]\frac {5}{12} $[/tex].
Area of the region bounded by y=f(x) and x axis between x=a and x=b is given by [tex]$\int_a^b f(x) d x$[/tex]. The coordinates of all the points mentioned are first calculated and then finally the area of required region OAC is calculated.
The area of the region bounded by the parabola y=[tex]5x^{2}[/tex].
The area that needs to be calculated is the area enclosed by OAC as shown in figure.
From the figure, it is clear that
Area of region OAC=area of region OAB-area of region ABC......(1) let us first calculate the equation of the tangent at(1,5).
⇒[tex]$\frac{d y}{d x}=10 x \Rightarrow \frac{d y}{d x}(1,5)=10$$[/tex]
Equation of tangent is y-5=10(x-1).
This tangent intercepts x axis at [tex]$x=\frac{-5}{10}+1=\frac{1}{2}$[/tex] (Putting y=0 in equation of tangent)
Hence, coordinates of C is (0.5,0) and B is (1,0).
⇒BC=OB−OC⇒BC=1−0.5=0.5
The area of region ABC is [tex]$\frac{1}{2} * B C * A B=\frac{1}{2} * 0.5 * 5=\frac{5}{4}$[/tex]
Now area of region OAB is given by [tex]$\int_0^1 5 x^2 d x \Rightarrow\left[\frac{5}{3} x^3\right]_0^1=\frac{5}{3}$[/tex]
Area of region OAB is thus [tex]$\frac{5}{3}$[/tex]
Now using equation (1) area of region OAC [tex]=\frac{5}{3}-\frac{5}{4}=\frac{5}{12}$[/tex]
The area of region OAC is [tex]\frac {5}{12} $[/tex].
Therefore, the area of the region is [tex]\frac {5}{12} $[/tex].
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what is the volume of a cell in cm^3 with an edge length of 10 angstroms?
The Volume of the cell with an edge length of 10 Angstroms is 1×10⁻²¹cm³.
The volume of a cube with edge length of "L" is calculated as "L³" .
In order to find the volume of a cube with edge length = 10 angstroms (A) , we first need to convert the units to cm.
we know that 1 Angstrom = 1×10⁻⁸ cm,
So, 10 angstroms = 10×10⁻⁸ cm ;
The volume of a cell with an edge length of 10 Angstroms can be calculated as follows:
The volume of the cube in cm³ is = (10×10⁻⁸ cm)³
⇒ 10³×10⁻²⁴ cm³
⇒ 1×10⁻²¹ cm³ .
Therefore , the volume of the cell is 1×10⁻²¹ cm³ .
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Exercise 0.2.1: Check that the y given is really a solution to the equation. Next, take the second order differential equation dy for some constantk > 0. The general solution for this equation is yx) Ci cos(kx) + C2 sin(kx). Note that because we have a second order differential equation, we have two constants in our general solution Exercise 0.2.2: Check that the y given is really a solution to the equation And finally, take the second order differential equation dy dx Py for some constantk > 0. The general solution for this equation is yx) CieCe* or yx = D1 cosh(kx) + D2 sinh(kx)
y = C1e^(kx) is a valid solution to the equation.
To check that the given y is a solution to the equation, we must first substitute the given y into the given equation. We can do this by substituting the constants C1, C2, and k into the equation. We then move each side of the equation to the same side and simplify. This will result in an equation of 0 = 0, which confirms that the given y is a solution to the equation. In this case, the general solution to the second order differential equation dy dx + ky is yx) C1 cos(kx) + C2 sin(kx) or yx = D1 cosh(kx) + D2 sinh(kx). As such, the given y is a solution to the equation.
For the given equation, dy/dx = Py, with a constant k > 0, the given solution is y = C1e^(kx) or y = D1 cosh(kx) + D2 sinh(kx). To check that this is a valid solution, we can substitute the given solution into the equation and calculate dy/dx. If the result is equal to Py, then we can be sure that the given solution is a valid solution to the equation. For example, if we take the first solution y = C1e^(kx), then we can calculate dy/dx as dy/dx = C1ke^(kx) which is equal to Py = kC1e^(kx). We can see that the two sides are equal, so we can confirm that y = C1e^(kx) is a valid solution to the equation.
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ind the work required to project a 4 oz object initially at rest to 170 ft/sec.
In other to get the height of the object after 4 seconds is to substitute 4 into the equation is h= 260 for the given velocity
given the equation:
h = -16t^2 + 129t
we are to find the height of the object after 4 seconds
in other to get the height of the object after 4 seconds is to substitute 4 into the equation.
that means we replace t by 4 in the equation
so,
h = - 16t^2 + 129t
substituting 4 into the equation
h = -16(4)^2 + 129(4)
h = - 16(16) + 516
h = -256 + 516
h =260
complete question
If an object is projected upward with an initial velocity of 129 ft per sec, its height h after t seconds is h = - 1662 + 129t. Find the heightof the object after 4 seconds.The height of the object after 4 seconds is(Simplify your answer.)ft.
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he total number of scarves knitted varies directly with the number of days. Four scarves require 6 days to knit.
Write a direct variation equation to represent this relationship. Express the constant of variation as a decimal.
Answer:
s = 1.5d
where s = number of scarves knitted
d = number of days required to knit s scarves
Step-by-step explanation:
Let s represent the number of scarves knitted in 4 days
The direct variation relationship is s = kd where k = constant of proportionality
So k = s/d
For s = 6, d = 4
So k = 6/4 = 1.5
So the direct variation equation is s = 1.5d
What is an example of categorical data?
Examples of categorical variables are race, sex, age group, and educational level.
What is of categorical data?Categorical data is a body of knowledge that is organised into categories. For example, if a company or government is attempting to collect personnel biodata, the resulting information is referred to as category.Examples of categorical data include gender, political party (republican, democrat, or other), and hair colour (red, blonde, or black) (male, female, or other). Because neither of these can be compared to the other, they are categorical in nature.Binary, nominal, and ordinal variables are the three different categories of category variables.A trait that cannot be quantified is referred to as a categorical variable, often known as a qualitative variable. Nominal or ordinal categorical variables are also acceptable.To learn more about categorical data refers to:
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A survey of all being on planet Hopt found that 10% preferred quect juice to all other juices. If 2 preferred quect juice, how many beings were surveyed altogether
Answer:
the answer is 20
Step-by-step explanation:
formulate the given
2/10%
rewrite the fraction
2/0.1 (then multiply both the numerator and denominator with the same integer)
= 20/1 (then simplify)
= 20
FA: 20
Answer:
Step-by-step explanation:
20 years from now Shrisha age will be three times her present age what is shirsha present age
20×3=60
the present age of shirsha
Answer:
Let Shrisha's present age be x
According to question ,
After 20 years ,
Shrisha's age will be 3 times her present age.
[tex]\therefore \: 20 + x = 3x \\ \longrightarrow \: 3x - x = 20 \\ \longrightarrow \: 2x = 20 \\ dividing \: both \: sides \: by \: 2 \\ \\ \longrightarrow \: \cancel \frac{2x}{2} = \cancel \frac{20}{2} \\ \\ \longrightarrow \:\boxed{ x = 10}[/tex]
hence , Shrisha's present age is 10 years.
hope helpful! :)
I thought of a 2 digit number. It' a multiple of 9 and the um of it digit i 1/5 of the number itelf. What i my Number?
The 2-digit number that is a multiple of 9 and the sum of it digits is 1/5 of the number itself is 45.
Howto find the 2-digit number?A 2-digit number can be written as:
a*10 + b
Where a and b are single digit numbers.
We know that the number is a multiple of 9, and we also know that:
a + b = (1/5)*(a*10 + b)
We can isolate one of the variables:
a + b = 2a + (1/5)b
b - (1/5)b = 2a - a
(4/5)b = a
So, now we need to find values of b such that:
a is also a whole number.
10a + b is a multiple of 9.
if b = 5 we will get:
(4/5)*5 = a
4 = a
Then the number is 45, which is 5*9, so it is a multiple of 9.
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Use the above graph to answer the following question. An increase in demand would result in a shift of (1 point) a line two to the left b line two to the right c line one to the left d line one to the right
An increase in demand would result in a shift of line two to the right (option b).
What is the effect of an increase in demand?The lines shown are known as demand and supply curves. The demand curve is a curve that shows the relationship between price and quantity demanded.
The demand curve has a negative slope. This means that the higher the price, the lower the quantity demanded. This is in line with the law of demand.
When there is a change in demand, the demand curve would shift either to the left or to the right. If demand increases, the demand curve would shift to the right.
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describe the end behavior of the graph of the function f(x)=−5(4)x−10 .
For the function f(x) = -5(4)x - 10, the end behaviour signifies that [x→∞,f(x)→-∞] and [x→-∞,f(x)→∞].
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The given function is f(x) = -5(4)x - 10
On solving the function it gives -
f(x) = -20x - 10
The graph for the function is plotted.
The end behavior of a function f(x) describes the behavior of the function as x approaches +∞ and as x approaches -∞.
Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is -20x, the degree is 1, i.e. odd, and the leading coefficient is -20, i.e. negative.
This means that function f(x) approaches ∞ as x approaches -∞, and f(x) approaches -∞, as x approaches ∞.
Therefore, the end behaviour is [x→∞,f(x)→-∞] and [x→-∞,f(x)→∞].
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For the purposes of a marketing research, a survey of 1000 women is conducted in a town. The results show that 52 % liked watching comedies, 45% liked watching fantasy movies and 60% liked watching romantic movies. In addition, 25% liked watching comedy and fantasy both, 28% liked watching romantic and fantasy both and 30% liked watching comedy and romantic movies both. 6% liked watching none of these movie genres. Find The number of women who like watching at least two of the given genres
The number of women who like watching at least two of the given genres 1640 women.
Let's call the number of women who liked watching comedies C, the number who liked watching fantasy movies F, and the number who liked watching romantic movies R.
From the information given, we know:
C = 1000 * 52% = 520 women liked watching comedies
F = 1000 * 45% = 450 women liked watching fantasy movies
R = 1000 * 60% = 600 women liked watching romantic movies
We also know that:
25% of women liked watching both comedies and fantasy, so 0.25 * 1000 = 250 women.
28% of women liked watching both romantic and fantasy, so 0.28 * 1000 = 280 women.
30% of women liked watching both comedies and romantic, so 0.30 * 1000 = 300 women.
However, these numbers overlap because some women like all three genres, so we have to subtract the number of women who like all three genres from our total. We don't know the number of women who like all three genres, but we can calculate it by adding up the number of women who liked two genres and subtracting from the total number of women:
Number of women who liked all three genres = (C + F + R - (C & F) - (C & R) - (F & R) + (C & F & R)) = (520 + 450 + 600 - 250 - 300 - 280 + (C & F & R))
Since 6% of women liked watching none of these movie genres, we can subtract this from our total:
C & F & R = 1000 - 6% * 1000 = 940 women
So the number of women who like watching at least two of the given genres = (520 + 450 + 600 - 250 - 300 - 280 + 940) = 1640 women.
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2=From Sonnet XIX, by John Milton That murmur, soon replies, "God doth not need Either man’s work or his own gifts; who best Bear his mild yoke, they serve him best. His state Is kingly. Thousands at his bidding speed And post o’er land and ocean without rest: They also serve who only stand and wait. "
The mood of this sestet in Sonnet XIX by John Milton is hopeful.
This quote is from John Milton's Sonnet XIX and speaks about the idea that serving God does not necessarily mean doing physical work for him, but rather bearing his "mild yoke" with devotion.
The line "They also serve who only stand and wait" suggests that waiting for God's will with patience and humility is a form of service in itself. This sonnet explains how a devotee must be. The state of God is described as "kingly" and those who serve him well are said to speed at his bidding, without rest.
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The question for the answer is
That murmur, soon replies, “God doth not need
Either man’s work or his own gifts; who best
Bear his mild yoke, they serve him best. His state
Is kingly. Thousands at his bidding speed
And post o’er land and ocean without rest:
They also serve who only stand and wait.”
What is the mood of this sestet in Sonnet XIX by John Milton?
grim
hopeful
detached
somber
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A certain cylinder and square prism have equal lateral surface area. Given the height of the cylinder is equal to the height of the prism, what is the ratio of the volume of the cylinder to the volume of the prism?
The ratio of the volume of the cylinder to the volume of the prism is 4/π.
The volume of a cylinder is the number of unit cubes (cubes of unit length) that can be fit into it. It is the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it. The volume of a cylinder is measured in cubic units such as cm3, m3, in3, etc.
The volume of a square prism is referred to as the amount of space occupied by a 3-dimensional prism that has two congruent square bases and four rectangular faces are known as the volume of square prism. It is measured in cubic units. The volume of a prism is the product of the cross-sectional area and its length. The cross-sectional area is also known as the base area of the square prism.
We are given that a certain cylinder and square prism have equal lateral surface area.
Lateral surface area of cylinder = 2πrh
Lateral surface area of square prism = 4sH
So, 2πrh = 4sH
Also, the height of the cylinder is equal to the height of the prism.
So, h=H
Put in above equation:
2πrh = 4sh
⇒ πr = 2s
⇒ r/s = 2/π
The ratio of the volume of the cylinder to the volume of the prism
⇒ Volume of cylinder/ Volume of prism
⇒ πr²h/s²h
⇒ π(r/s)²
⇒ π(2/π)² ---- (From above)
⇒ 4/π
Thus, the ratio of the volume of the cylinder to the volume of the prism is 4/π.
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solve the system
6x+2y=-4
x-2y=4
Answer:
x = 0
y = -2
Step-by-step explanation:
1. 6x+2y = -4
2. x - 2y = 4
in our second equation lets isolate x
x = 2y + 4
now lets plug this into our first equation
6(2y+4) + 2y = -4
12y + 24 + 2y =-4
14y +24 = -4
14y = -28
y = -2
lets plug in y into the second equation to find x
x = 2(-2)+4
x = -4+4
x = 0
What postulate, if any, can be used to prove the triangles are congruent?
Answer: The correct option is, (B) SAS.
Step-by-step explanation: The SAS Postulate says that triangles are congruent if any pair of corresponding sides and their included angle are congruent.
there are different books to arrange on a shelf: 3 blue, 3 greens, and 2 red. a) in how many ways can the books be arranged on a shelf? enter the answer without commas. b) if books of the same color are to be grouped together, how many arrangements are possible? enter the answer without commas.
To calculate the number of ways to arrange the books on a shelf, we can use the formula for permutations.
The formula for permutations is [tex]\frac{n!}{(n-r)!}[/tex]
where: n is the total number of items
r is the number of items being selected.
a. In this case, there are 8 books total (3 blue + 3 green + 2 red), and we are arranging all of them.
so n= 8 and r = 8, the number of arrangements is
[tex]\frac{8!}{(8-8)!}[/tex] = 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
So the answer to (a) is 40320.
b. To calculate the number of arrangements if the books of the same color are grouped, we can consider each group as one item.
There are 3 groups (blue, green, red), and we are arranging those
so n = 8 and r = 3.
Hence, the number of arrangements is
[tex]\frac{8!}{(8-3)!}[/tex] = [tex]\frac{8!}{5!}[/tex] = [tex]\frac{8x7x6x5x4x3x2x1}{5x4x3x2x1}[/tex] = 336
So the answer to (b) is 336.
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