Answer:
(c) 8!/(6!·2!)
Step-by-step explanation:
You want to know how to compute the number of possible ways 2 different pizzas can be chosen from a menu of 8.
8 Choose 2The formula for computing the number of combinations of n things taken k at a time is ...
nCk = n!/(k!(n -k)!)
For 8 specialty pizzas chosen 2 at a time, this is ...
8C2 = 8!/(2!·6!)
The appropriate answer choice is ...
possibilities = 8!/(6!·2!)
__
Additional comment
That is (8·7)/(2·1) = 28 possibilities, assuming choice of different pizzas.
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See question in screenshot below:
The equations after the transformations are given as follows:
a) Shifted 7 units up: [tex]y = 3^x + 7[/tex].
b) Shifted 6 units left: [tex]y = 3^{x + 6}[/tex]
c) Reflected over the x-axis and over the y-axis: [tex]y = -3^{-x}[/tex].
What are the rules for a translation?There are four cases for the translation of an image, and their rules are listed as follows:
Shift left a units: f(x + a).Shift right a units: f(x - a).Shift up a units: f(x) + a.Shift down a units: f(x) - a.In this problem, the function is:
y = 3^x.
For a shift of 7 units up, we have that:
y = f(x) + 7 = 3^x + 7.
For a shift of 6 units left, we have that:
y = f(x + 6) = 3^(x + 6).
What are the reflection rules?The rules for reflections over the axes are given as follows:
Reflection over the x-axis: y = -f(x).Reflection over the y-axis: y = f(-x).Hence, for a reflection over both axes, the rule is:
y = -f(-x).
Considering the function in this problem, the rule is:
[tex]y = -3^{-x}[/tex]
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What is the length of the segment below?
Answer:
5
Step-by-step explanation:
Length is a positive number. Count the spaces from -2 to -7
Please help it’s due today!!!
Answer:
(a.): m∠ ACB = 40°; (b.): m ∠CBA = 25°; (c.): m ∠CAB = 115°
Step-by-step explanation:
Because Lines AB and DE are parallel, we can use the angle relationships to find the angles.
(For context of the problem, we can label the 40° angle as ∠C and the 155° as ∠B)
(a.) Angles C and ACB are vertical angles, which means they're congruent. Thus m ∠ACB = 40°.
(b.) AB is a straight line and angles B and CBA are supplementary angles. This means their total sum is 180°. We need to subtract angle B from 180 to find m ∠CBA:
[tex]180-155=CBA\\25=CBA[/tex]
(c.) We know that the sum of all the angles is 180°. Thus, we can subtract the sum of angles CBA and CBA from 180 to find the m ∠CAB:
[tex]180-(40+25)=CAB\\180-65=CAB\\115=CAB[/tex]
A bank receives an average of 7 bad checks a day, What is the probability that over a four day period, the bank will receive 39 bad checks? Step 2 of 2: Compute the probability, Round your answer to four decimatplaces, if necessary.
Answer:
39 bad checks because due to the math, 7 bad checks are received in a day
how do i find the x????
The side x is 6 cm when the triangle inside the parallelogram.
Given that,
In the picture we have triangle inside the parallelogram.
We have to find x side.
The parallelogram is ABCD.
Taking E as a midpoint of the AD.
The triangle is CDE.
The side CD is 6cm and ∠E is 90°.
The side ED is x cm.
Taking the trigonometric ratios that is
SinE= Opposite side/ hypothesis
Sin90° = 6cm /x cm
1= 6cm /x cm
x=6cm
Therefore, The side x is 6 cm when the triangle inside the parallelogram.
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What is the difference when (2x^2-2x-6) is subtracted from (7x^2+3x-5)?
Using the subtraction operation, the difference between 7x² + 3x - 5 and 2x² - 2x - 6 is 5x² + x + 1.
What is the difference?Mathematically, the difference is the result of a subtraction operation.
The difference is the product that results when the subtrahend is deducted from the minuend.
A subtraction operation is one of the basic mathematical operations, including addition, division, and multiplication.
7x² + 3x - 5
- 2x² - 2x - 6
= 5x² + x + 1
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Find the arc length of the curve y = ln(cos x) from x = 0 to x = π/4.
The arc length of the curve [tex]y = ln(cos x)[/tex] from [tex]x = 0[/tex] to [tex]x = \pi /4[/tex] is [tex]\ln\left|\sqrt{2} + 1\right|[/tex]
To find the arc length of the curve[tex]y = ln(cos x)[/tex] from[tex]x = 0[/tex]to [tex]x = \pi /4[/tex], we will use the arc length formula for a curve given by y = f(x):
[tex]\text{Arc length} (L) = \int_a^b \sqrt{1 + \left[ f'(x) \right]^2} \, dx[/tex]
Where:
- a and b are the limits of integration (starting and ending points of the curve).
- f'(x) is the derivative of the function y = f(x).
First, we find the derivative of y = ln(cos x):
[tex]y = \ln(\cos x)\\y' = \dfrac{d}{dx}[\ln(\cos x)][/tex]
To find the derivative of ln(cos x), we use the chain rule:
[tex]y' &= \frac{1}{\cos{x}} \cdot (-\sin{x}) \\&= \frac{-\sin{x}}{\cos{x}}[/tex]
Now, we can find the arc length from x = 0 to x = π/4:
[tex]\text{Arc length } (L) = \int_0^{\frac{\pi}{4}} \sqrt{1 + \left( \frac{-\sin x}{\cos x} \right)^2} \, dx\text{Arc length } (L) = \int_0^{\frac{\pi}{4}} \sqrt{1 + \frac{\sin^2 x}{\cos^2 x}} \, dx\text{Arc length } (L) = \int_0^{\frac{\pi}{4}} \sqrt{\frac{\cos^2 x}{\cos^2 x} + \frac{\sin^2 x}{\cos^2 x}} \, dx\text{Arc length } (L) = \int_0^{\frac{\pi}{4}} \sqrt{\frac{\cos^2 x + \sin^2 x}{\cos^2 x}} \, dx[/tex]
Remember that [tex]cos^2 x + sin^2 x = 1[/tex], so the expression becomes:
[tex]\text{Arc length (L)} = \int_0^{\frac{\pi}{4}} \sqrt{\frac{1}{\cos^2 x}} \, dx[/tex]
Now, simplify the expression inside the square root:
[tex]\text{Arc length (L)} = \int_0^{\frac{\pi}{4}} \sqrt{\frac{1}{\cos x}} \, dx[/tex]
Integrate with respect to x:
[tex]\text{Arc length (L)} = \int_0^{\frac{\pi}{4}} \sqrt{Sec x} \, dx[/tex]
Now, evaluate the integral:
[tex]\text{Arc length} (L) = \ln\left| \sec x + \tan x \right| ~\text{from}~ 0 ~\text{to}~ \frac{\pi}{4}\text{Arc length} (L) = \ln\left| \sec \left( \frac{\pi}{4} \right) + \tan \left( \frac{\pi}{4} \right) \right| - \ln\left| \sec (0) + \tan (0) \right|[/tex]
[tex]\sec\left(\frac{\pi}{4}\right) = \sqrt{2}, \quad \tan\left(\frac{\pi}{4}\right) = 1\\\sec(0) = 1, \quad \tan(0) = 0\\\text{Arc length} (L) = \ln|\sqrt{2} + 1| - \ln|1 + 0|\\\text{Arc length} (L) = \ln|\sqrt{2} + 1|[/tex]
Using the property of natural logarithms, ln(a) - ln(b) = ln(a/b), we get:
[tex]\text{Arc length (L)} = \ln\left|\sqrt{2} + 1\right| - \ln\left|1\right|\\\text{Arc length (L)} = \ln\left|\sqrt{2} + 1\right|[/tex]
The arc length of the curve [tex]y = ln(cos x)[/tex] from [tex]x = 0[/tex] to [tex]x = \pi /4[/tex] is [tex]\ln\left|\sqrt{2} + 1\right|[/tex]
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Arturo has a coin collection. He keeps 11 of the coins in his box, which is 2% of the collection. How many total coins are in his collection?Multiply/scale up to solve.
Answer:
550 coins
Step-by-step explanation:
2% = 2/100 = 0.02
11/0.02 = 550
The collection consists of 550 coins
Hope this helps
Factor the expression using GCF. 12 + 21
Factor the expression using GCF. 16x - 36
The factors of (12+21) and (16x-36) using GCF are 3(4+7) and 4(4x-9) respectively.
According to the question,
We have the following two expressions:
(12+21) and (16x-36)
Now, in order to find the factors of given expressions using GCF, first we should know what is GCF.
GCF stands for Greatest Common Factor which means that the highest number which can divide all the terms of an expression.
So, we have:
12+21
3 can divide both 12 and 21:
3(4+7)
For second expression:
16x-36
4 can divide both the terms:
4(4x-9)
Hence, the factors of (12+21) and (16x-36) using GCF are 3(4+7) and 4(4x-9) respectively.
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which expression is equivalent to 4 to the power of 8 over 4 to the power of 2
Answer:
4,096
Step-by-step explanation:
=4^8 / 4^2
=4^6
=4,096
Danielle is engineering a new brand of shoes. For x shoes sold,
in thousands, a profit of p(x) = -3x4 + 4x³ - 2x² + 5x + 10
dollars, in ten thousands, will be earned.
How much will be earned in profit for selling 1,000 shoes?
What do the x- and y-intercepts of the graph mean in this context? Do those values make sense?
a. For selling 1000 shoes, profit earned will be $140,000
Given,
Danielle is engineering a new brand of shoes. For x shoes sold,
in thousands, a profit of p(x) = -3x4 + 4x³ - 2x² + 5x + 10 dollars, in ten thousands, will be earned.
we are asked to determine the profit for selling 1000 shoes = ?
when sold 1000 shoes
X = 1 (in thousands)
substitute X=1 into p(x) = -3x⁴+4x³-2x²+5x+10
thus p(1) = -3×1⁴ + 4×1³ - 2×1² + 5×1 + 10
= -3+4-2+5+10
= 14 (in ten thousand)
so the profit is 14×10000 = 140,000
b. X intercepts means that when he sold X shoes, the profit p(x) equals zero, but the value doesn't make sense, because as long as he sold shoes, the profit would not be zero.
y intercepts means that when he sold zero shoes, the profit he earns,
calculate p(0)=10, the profit is greater than zero , it doesn't make sense, because if he sold zero shoes, there would not be income and profit.
Hence we get the required answers.
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Ill mark brainliest just answer right
Answer:
90
Step-by-step explanation:
14/20 = 0.7
28/40 = 0.7
63/90 = 0.7
Hope this helps.
Answer:
Step-by-step explanation:
The answer is D. 90 because the other numbers
14/20=.7
28/40=.7
63/90=.7
therefore, it would be 90.
PLEASE HELP
Calculate the area, in cm², of the rectangle
below.
Give your answer as an integer or as a surd
in its simplest form.
5√27 cm
area = ? cm²
2√3 cm
Answer:5/25 0.18
and then .66 for 2/3 them multiply both of those numbers
Step-by-step explanation:.467
The area of the rectangle that has a width of 2√3 cm and a length of 5√27 cm is calculated as: 90 cm².
What is the Area of a Rectangle?The area of a rectangle is calculated by multiplying the length and the width of the rectangle. It is given by the formula: Area = length × width.
Therefore, we are given the following dimensions:
length of rectangle = 5√27 cm
width of rectangle = 2√3 cm
Substitute the values into the area formula:
Area of rectangle = 5√27 * 2√3
= 5*3√3 * 2√3
= 15√3 * 2√3
Area of rectangle = 90 cm²
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Jason's water bottle has 20 ounces of water, and he is drinking ata rate of 1 ouncer per
second. Pedro's water bottle contains 65 bunces of water, and he is drinking at a rate of
2.5 ouncers per second. At how many seconds, s, will the two bottles have the same
amount of water if Jason and Pedro start drinking from each of their bottles at the same
time?
After 31 seconds, the bottle of Jason and Pedro will have the same amount of water.
According to the question,
We have the following information:
Jason's water bottle has 20 ounces of water, and he is drinking at the rate of 1 ouncer per second. Pedro's water bottle contains 65 ounces of water, and he is drinking at a rate of 2.5 ounces per second.
So, the water is decreasing at the constant rate. So, there will arithmetic progression where d is the rate.
Formula used to find nth term of an A.P:
an = a+(n-1)d where a is the first term
For Jason:
an = 20+(n-1)-1
an = 20-n+1
an = 21-n
For Pedro:
an = 65+(n-1)-2.5
an = 65-2.5n+2.5
an = 67.5-2.5n
Now, we have the following expression for equal amount of water:
21-n = 67.5-2.5n
21-67.5 = -2.5n+n
-46.5 = -1.5n
n = 46.5/1.5
n = 31
Hence, after 31 seconds, the bottle of Jason and Pedro will have the same amount of water.
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Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The equation which is quadratic in form is, [tex]6(2x+4)^2 = (2x+4)+2[/tex].
What is quadratic equation?
The polynomial equations of degree two in one variable of type
f(x) = ax^2 + bx + c = 0 and with a, b, c ∈ R and a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).
Consider the given equations,
[tex]x^4-6x^2-27=0\\3x^4=2x^2\\2(x+5)^4+2x^2+5=0\\6(2x+4)^2=(2x+4)+2\\6x^4=-x^2+5\\8x^4+2x^2-4x=0[/tex]
The first, second, third, fifth and sixth equation are all having 4th degree.
So, by the definition of quadratic equation, these equations are not a quadratic.
Consider, the fourth equation,
[tex]6(2x+4)^2=(2x+4)+2\\[/tex]
Simplifying this, we get
[tex]6(4x^2 + 16x + 16 = 2x + 6\\24x^2 + 96x + 96 = 2x + 6\\24x^2 + 96x - 2x + 96 - 6 = 0\\24x^2 + 94x + 90 = 0[/tex]
This equation having degree 2.
Therefore the equation [tex]6(2x+4)^2 = (2x+4)+2[/tex] is a quadratic equation.
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This question has two parts. Use the information to answer Part A and Part B.
Three sides of a quadrilateral are equal lengths. The length of the fourth side is 5 inches.
The perimeter of the quadrilateral is 26 inches.
Answer:
7 cm
Step-by-step explanation:
assuming you require the length of the 3 equal sides.
let one of the equal sides be x then perimeter is
P = 3x + 5
given P = 26 , then
3x + 5 = 26 ( subtract 5 from both sides )
3x = 21 ( divide both sides by 3 )
x = 7
the 3 equal sides are 7 cm each in length
Billy's sister Elly is 21 years younger than Aunt Polly.
How old is Elly?
Which rule explains why these triangles are
congruent?
U
T
V
W
AAS
ASA
SAS
SSS
These triangles
cannot be proven
congruent.
These triangles can be proven congruent by using ASA RULE.
What is congruent triangles and its rules ?
When two triangles are congruent, their three sides and their three angles match precisely.
If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.
ASA rule stands for Angle-Side-Angle rule which means two angles and a side of both triangles are equal.
Main Body:
In ΔTUV and ΔTWV
VT =VT ----(1)
∠VTU=∠TVW -----(2)
As TUVW is a parallelogram
so, ∠T = ∠U
hence, ∠TVU =∠VTW ----(3)
taking equation 1, 2,3
therefore, ΔTUV ≅ ΔTWV by ASA rule which means by Angle- Side- Angle rule.
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Cameron tracks the number of people who read his blog. In weeks 1, 2, 3, 4, and 5 the blog had 12, 60, 300, 1500, and 7500 visitors, respectively.
f(x)=
The function f(x) = 12×[tex]5^{x-1}[/tex], x = week number
Given data,
week 1 = 12 visitors
week 2 = 60 visitors
week 3 = 300 visitors
week 4 = 1500 visitors
week 5 = 7500 visitors
The function can be given by :
f(x) = 12×[tex]5^{x-1}[/tex], x = week number
f(1) = 12×[tex]5^{0}[/tex] = 12
f(2) = 12×[tex]5^{1}[/tex] = 60
f(3) = 12×[tex]5^{2}[/tex] = 300
f(4) = 12×[tex]5^{3}[/tex] = 1500
f(5) = 12×[tex]5^{4}[/tex] = 7500
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A farmer with 350 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? What are the dimensions of the enclosed area?
The width, labeled x in the figure, is ____
(Type an integer or decimal rounded to the nearest tenth as needed.)
The length, labeled 350-2 x in the figure, is ____
(Type an integer or decimal rounded to the nearest tenth as needed.)
The largest area that can be enclosed is _______
(Type an integer or decimal rounded to the nearest tenth as needed.)
The solution to the questions are:
The width, labelled x in the figure is 87.5 metersThe length, labelled 350-2 x in the figure, is 175 metersThe largest area that can be enclosed is 15312.5 square metersHow to determine the width and the length of the rectangle?From the question, we have the following parameters that can be used in our computation:
Length = 350 - 2x
Width = x
The area of a rectangle is the product of its dimensions
So, we have
Area = Length x Width
Substitute the known values in the above equation, so, we have the following representation
A = (350 - 2x) * x
Evaluate
A = 350x - 2x²
Differentiate and set to 0
350 - 4x = 0
So, we have
4x = 350
Divide by 4
x = 87.5
Recall that
Length = 350 - 2x
So, we have
Length = 350 - 2 x 87.5
Evaluate
Length = 175
The area is then calculated as
Area = Length x Width
So, we have
Area = 175 x 87.5
Evaluate
Area = 15312.5 square meters
Hence, the area is 15312.5 square meters
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Which correctly identifies ways that earthquakes and tsunamis can cause destruction? (1 point)
earthquakes: erosion of beaches
tsunamis: move blocks of land up or down
earthquakes: open up large cracks in Earth's crust
tsunamis: erosion of beaches
earthquakes: landslides
tsunamis: move blocks of land up or down
earthquakes: landslides
tsunamis: open up large cracks in Earth's crust
The answer is earthquakes: open up large cracks in Earth’s crust tsunamis: erosion of beaches.
What is tsunamis?
Giant waves that are brought on by ocean floor movement are known as tsunamis. Landslides, underwater volcanic eruptions, earthquakes, and even meteorite collisions can cause the ocean floor to tremble. These are often referred to as seismic sea waves, albeit they are sometimes misidentified as tidal waves. A tsunami is a set of waves that are caused by a disturbance in the ocean or another body of water, such as an earthquake, landslide, volcanic eruption, or meteorite strike.
The water above shifts up or down as a result of undersea earthquakes, which often take place along tectonic plate borders. Earth’s crust tsunamis: erosion of beaches.
Hence, earthquakes: open up large cracks in the Earth’s crust tsunamis: and erosion of beaches.
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How can you write the prime factorization and find the greatest common factor and the least common multiple of two numbers?
You can the greatest common factor and least common multiple of two numbers by prime factorization by finding common prime numbers and the prime numbers that account for both numbers respectively
How to write the prime factorization and find the GCF and LCM of two numbers?
A prime number has two factors, 1 and itself e.g. 2, 3, 5, 7, 11, etc.
When a number is written as a product of its prime factors, we have the prime factorization of the number e.g 8 = 2×2×2
By writing the prime factorization of two numbers we can find the greatest common factor(GCF) and least common multiple (LCM) of the numbers. For example 8 and 24:
The prime factorization of 8 and 24 is:
8 = 2×2×2
24 = 2×2×2×3
The greatest common factor of the two numbers is 2×2×2 = 8 because 2×2×2 appears in the prime factorization of both numbers
The least common multiple of the two numbers is 2×2×2×3 = 24 because all the elements of the prime factorization of both numbers must be accounted for
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Write ln8t‾‾√ in expanded form. Note: When entering natural log in your answer, enter lowercase LN as “ln”. There is no “natural log” button on the Alta keyboard.
Answer:
Step-by-step explanation:
blake is ordering 6 bags of cat food. Each bag has a mass of 7.5. to know shipping costs. blake needs to know the total of weight in lbs. what is the weight of cat food in lbs?
Recall that whenever suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing 4 red, 3 green, 2 white, and 1 purple. She grabs five of them, Find the probability of having at least one white one.
The probability of having at least one white marble, using the hypergeometric distribution, is of:
0.7778 = 77.78%.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are listed as follows:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem, the values of these parameters are listed as follows:
N = 4 + 3 + 2 + 1 = 10.k = 2, as there are 2 white balls.n = 5, as five balls will be taken.The probability of having at least one white one is:
P(X > 0) = 1 - P(X = 0).
In which:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,10,5,2) = \frac{C_{2,0}C_{8,5}}{C_{10,5}} = 0.2222[/tex]
Then:
P(X > 0) = 1 - 0.2222 = 0.7778 = 77.78%.
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help me out thanks so much
Answer:
D: 1+2x6
Step-by-step explanation:
5+2^3
5+8
13
1+2x6
1+12
13
D is the only option equal to 13
Hopes this helps please mark brainliest
4. Which one of these is not a type of triangle?
a. Equilateral
b. Scalene
c. Isosceles
d. None of these.
Answer: D.
Step-by-step explanation:
Equilateral, scalene, and isosceles are all valid types of triangles.
solve linear equation
u+6y=32
u+3y=17
Answer:
Step-by-step explanation:
u=31/3
y=-11/9
Wilma goes to a college that is 106 miles away. Wilma drives a Honda Civic and gets 35 mpg. If Wilma plans on making 8 round trips to and from her college this year, how much will she spend on gas over the course of the year? (Assume that gas remains constant at $3.59/gal).
Answer: $173.96
Step-by-step explanation: If I'm not mistaken first you have to take 106 and multiply it by 2 to count for the round trips so that makes 212 miles for one trip, then you have to multiple by 8 to figure out how many miles in total which equals 1696, then you divide by the 35 to figure out how many gallons she use, which is 48.457(rounded) then you multiple that by the rate of gas which is 3.59 which means she spent 173.96(rounded to the nearest tenth)
F(x) = 2x4 + 3x³+4x²+5x+ 6 using remainder theorem
The factorized form of the given polynomial is F(x) = 2x^4 + 3x³ + 4x² + 5x + 6.
We are given a polynomial. The highest degree of the polynomial is four. The polynomial is a biquadratic equation. We will try to find a solution by hit and trial method. We will use the positive and negative of the factors of the constant term. The factors of 6 are 1, 2, 3, and 6. One by one, we will substitute -1, 1, -2, 2, -3, 3, -6, and 6 in the polynomial equation and check if the equation becomes zero. We see that none of these numbers make the equation zero. So, the equation cannot be factorized.
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