we have
4P2
the formula is equal to
n!/(n-r)!
n=4
r=2
substitute
4!/(4-2)!
4!/2!=(4*3*2!)/2!
simplify
4*3=12
answer is 123. Which of the following equations is equivalent to the equation shown below? x^2 + 4x + 15 = 0
We need to expand the answer choices and see which one matches the equation
[tex]x^2+4x+15=0[/tex]Remember the algebraic rules:
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]Now, if we expand choice D, we should get this. Let's expand:
[tex]\begin{gathered} (x+2)^2=-11 \\ x^2+2(1)(2)+(2)^2=-11 \\ x^2+4x+4=-11 \\ x^2+4x+4+11=0 \\ x^2+4x+15=0 \end{gathered}[/tex]Please help with math problem FAST
The percent error in his calculation is 13.04%
How to find percent error?He calculated the object will take 2.3 seconds to fall on the ground.
It takes 2.5 seconds for the object to fall.
Therefore, the percent error can be calculated as follows:
percent error = | theoretical value - experimental value | / theoretical value × 100
Therefore,
percent error = |2.3 - 2.5| / 2.3 × 100
percent error = 0.3 / 2.3 × 100
percent error = 0.3 × 100 / 2.3
percent error = 30 / 2.3
percent error = 13.0434782609
Therefore,
percent error = 13.04 %
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Can someone help to solve question 18 from the picture below.
lim x → 0 (2/x - 2/|x|) does not exist.
We need to find lim x → 0 (2/x - 2/|x|)
lim x → 0 (2/x - 2/|x|) = lim x → 0 (2|x| - 2x / x |x|)
Consider the left hand limit.
lim x → 0^- [(2|x| - 2x) / x |x|]
As the x values approach 0 from the left, the function values decrease without bound.
i.e., the function approaches -∞
Consider the right hand limit.
lim x → 0^+ [(2|x| - 2x) / x |x|]
Consider a table to see the behavior of the function as x approaches 0 from the right.
x f(x)
0.1 0
0.01 0
0.01 0
As the x values approach 0 from right, the function values approach 0.
Thus, the limit of [(2|x| - 2x) / x |x|] as x approaches 0 from the right is 0.
Since the left sided and right sided limits are not equal, the limit does not exist.
Therefore, lim x → 0 (2/x - 2/|x|) does not exist.
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write -6/11×3/4 in lowest terms.-6/136/139/22-9/22
In order to multiply two fractions we just multiply each side of the fraction:
Then, in this case:
[tex]-\frac{6}{11}\cdot\frac{3}{4}=\frac{-6\cdot3}{11\cdot4}=\frac{-18}{44}[/tex]Since 18 and 44 are pair numbers, but can be divided by 2, then we divide both:
[tex]-\frac{18}{44}=-\frac{9}{22}[/tex]Answer: D -9/22you have 20oz of egg noodles. You need 5oz to make one of chicken noodle soup how many service can you make
Okay. You have 20 oz of egg noodles.
You need 5 oz to make one of chicken noodle soup,
Then I can make 20 / 5 = 4 services
For 4.5 lb,
I6 ounces = 1 pound.
4. 5 x 16 ounces = 4.5 lb= 72 ounces
Then, we have 8 oz per serving.
Then we can have 72/8 = 9 services.
4.5 x 16 / 8 = 72/8 =9 servings
Okay. 2 tbsp = 1 serving
18 tbsp = (18 x 1) / 2 = 9 servings
60 POINTS
Three points determine △ABC. The distance between A and B is 16.2 feet. The distance between B and C is 12.9 feet. What is the range for the distance between A and C? The range of the distance from A to C is greater than___feet and less than___feet.
The range of the distance from A to C is greater than 3.3 feet and less than 29.1 feet.
How to determine the range of distance?The given parameters are
AB = 16.2 feet
BC = 12.9 feet
To determine the range of the third length, we use the triangle inequality theorem
Using this theorem, we have the following inequalities
AB + BC > AC
AB + AC > BC
BC + AC > AB
So, we have
16.2 + 12.9 > AC
16.2 + AC > 12.9
12.9 + AC > 16.2
Solve for AC in the above inequalities
29.1 > AC
AC > -3.3
AC > 3.3
Remove the negative value
29.1 > AC
AC > 3.3
Rewrite as
AC > 29.1
AC > 3.3
This means that the values of AC are between 3.3 and 29.1 feet
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A group of hikers tracked how long it took to hike a 15-mile trail. They hiked 3.5 miles in 2 hours, 8.75 miles in 5 hours, and 12.25 miles in 7 hours.
Determine if the relationship between the hikers' distance and time is proportional.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.75 miles per hour.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 0.6 miles per hour.
No, it is not proportional because 3.5 miles in 2 hours is not equivalent to 8.75 miles in 5 hours.
No, it is not proportional because 8.75 miles in 5 hours is not equivalent to 12.25 miles in 7 hours.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.75 miles per hour.
What are Ratio and Proportion?
When comparing two items of the same kind, a ratio is utilized. For two numbers, a and b, the ratio formula is written as a: b or a/b. Two or more ratios are deemed to be in proportion if they are all equal.
A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios.
A ratio is a comparison between two amounts that is calculated by dividing one amount by the other.
The equivalence of two ratios is referred to as proportion. There is never a difference between two comparable ratios. The ratio symbol (::) is used to express proportions, which aid in solving problems involving ambiguous quantities.
Given that,
15-mile trail covered as hiked 3.5 miles in 2 hours, 8.75 miles in 5 hours, and 12.25 miles in 7 hours.
determining the ratio for given data,
3.5/2→1.75
8.75/5→1.75
12.25/7→1.75
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.75 miles per hour.
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In the Kite ABCD, AB = 52‾√52 mm AP= 5 mm, PD = 7 mm, find the area to the nearest mm2.
Step 1
the area of a kite is given by:
The area of a kite is half the product of the lengths of its diagonals
[tex]Area=x*y[/tex]Step 1
given the rigth triangle
so, we can find the x and y values
hence
a)x
[tex]\begin{gathered} \frac{x}{2}=\text{ 5} \\ to\text{ solve for x, multiply both sides by 2} \\ \frac{x}{2}*2=5*2 \\ x=10 \end{gathered}[/tex]b) y
[tex]\begin{gathered} \frac{y}{2}=7 \\ to\text{ solve for y, multiply both sides by 2} \\ \frac{y}{2}*2=7*2 \\ y=14 \end{gathered}[/tex]so
x=10
y=14
Step 2
finally, replace in the formula to find the area
[tex]\begin{gathered} Area=xy \\ area=10\text{ mm *14 mm} \\ area=140\text{ mm}^2 \end{gathered}[/tex]therefore, the answer is
[tex]\begin{equation*} 140\text{ mm}^2 \end{equation*}[/tex]I hope this helps you
divide 80 into two parts so that the greater part is 4 times the smaller
only answer this when u know the answer pls bcz this is important
Answer:16 and 64
Step-by-step explanation: 4x+x=80 5x=80 x=16 16*4=64
16 and 64
Express 2cm as a percentage of 5cm
Answer:
40%
Step-by-step explanation:
2cm out of 5cm
2/5*100
=40%
Given the image below, identify the value of x. 9 2x - 19 M
You have the the length of segment NK is 23.
Furthermore, you have that segment NK is the sum of the following segments:
NK = NM + ML + LK
Each of the previous segments are given by the following algebraic expressions:
NM = x - 6
ML = 9
LK = 2x - 19
You sum the previous expression, by taking into account that the result is 23. Then you solve for x, just as follow:
NM + ML + LK = NK
(x - 6) + (9) + (2x - 19) = 23 eliminate parenthesis
x - 6 + 9 + 2x - 19 = 23 simplify similar terms
x + 2x - 6 - 19 + 9 = 23
3x - 16 = 23 add 16 both sides
3x = 23 + 16
3x = 39 divide by 3 both sides
x = 39/3
x = 13
Hence, the solution for x is x = 13
In a basketball game, the home team was down by
1 points at the end of the game. They only scored 3 points for every 4
points the visiting team scored. What was the final score of the game?
The final score of the visiting team is 4 points and the home team's points is 3 points.
The home team only scores 3 points for every 4 points the visiting team scored in the basketball game.
By the end of the game, the home team was down by 1 point.
Let's say the visiting team scored 4 points and the home team scored 3 points. Hence, the home team is down by 1 point.
Now, if the visiting team scored again.
Then the score of visiting team: 8 points and the home team: 6 points.
Hence, the home team is down by 2 points.
As we go along, the point difference between the home team and the visiting team will only increase.
Therefore, the final score of the team will be:
Visiting team = 4 points
Home team = 3 points
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For which of the following intervals does the function (in the image section) have a removable discontinuity?A. [−2.5,−1.5] B. [−1.5,−0.5] C. [−0.5,0.5] D. [0.5,1.5] E. [1.5,2.5]
Given the function below,
[tex]f(x)=\frac{x+2}{x^4-2x^3-x^2+2x}[/tex]Let us now factorize the denominator
[tex]x^4-2x^3-x^2+2x[/tex]First of all, let us factorize x out from the denominator.
[tex]\begin{gathered} x(\frac{x^4}{x}-\frac{2x^3}{x}-\frac{x^2}{x}+\frac{2x}{x}) \\ x(x^3-2x^2-x+2) \end{gathered}[/tex]Therefore, x is a factor of the denominator.
Let us now factorize the remainder
[tex]x^3-2x^2-x+2[/tex]Let us substitute x = 1 into the function to confirm if it is a factor.
[tex]\begin{gathered} x=1 \\ 1^3-2(1)^2-(1)+2 \\ 1-2-1+2=1+2-1-2=3-3=0 \end{gathered}[/tex]Therefore, (x - 1) is a factor.
Let us now divide the function by (x - 1)
[tex]\frac{x^3-2x^2-x+2}{x-1}=\frac{\left(x-2\right)\left(x+1\right)\left(x-1\right)}{x-1}=(x-2)(x+1)[/tex]Hence, the factors of the denominator are,
[tex]x(x-1)(x+1)(x-2)[/tex]Therefore,
[tex]f(x)=\frac{x+2}{x(x-1)(x+1)(x-2)}[/tex]Now, looking at both the numerator and the denominator, we can observe that there is no common factor between the numerator and the denominator.
Hence, there is no removable discontinuity.
What is the range of the following relation?{(-3, 3), (1, 1), (0, -2), (1, -4), (5, -1)}
What is the range of the following relation?
{(-3, 3), (1, 1), (0, -2), (1, -4), (5, -1)}
The range is
[tex]\lbrace3,1,-2,-4,-1\rbrace[/tex]what type of equation will best fit the data below
A quadratic equation
Here, we want to get the type of equation that will fit the given plot
From what we have, the tracing of a line in the direction of the plotted lines will give us a parabola
The parabola represents the plot of a quadratic equation
Hence, the data will be best fit by a quadratic equation
Gravel is being dumped from a conveyor belt at a rate of 40 ft/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast (in ft/min) is the height of the pile increasing when the pile is 5 ft high?
(Round your answer to two decimal places.)
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm/s) when the diameter is 40 mm? (Round your answer to two decimal places.)
The formula Wh = Rs + Q, where Q stands for total energy losses experienced upon impact, can be used to represent any of the five fundamental types of dynamic pile drive formulas now in use.
Calculate dynamic pile ?
Fixed Formula
Maximum load a pile or set of piles (group pile) can support (Qu)
Depending on the soil's properties
Qu=Qp+Qs
Maximum failure load
Qp is the pile's point resistance.
Qs is the shaft resistance caused by rubbing between the pile and the dirt.
Load (Q) (Q)
Qp
QsQs.
Given diameter
height = h = ft(say)
radius = r =h/2
volume =v =1/3πr²h =1/3π(h/2)²h
=1/3π(h²/4)(h)
=1/12πh³
dv/dt = 1/12π(3h²dh/dt)
dv/dt = π/4 h² dh/dt
here dv/df =40ft³ and h =5ft
40 = π/4 (5² dh/dl
=40*4/100π
= 160/100π
=8/5π
So, the height is increasing at the rate of (8/5π) ft/min.
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4 x 107 is
?
times as much as 4 x 10³.
Answer:
The answer is 10^4
Step-by-step explanation:
This is because 4 x 10^7 is 40,000,000
And 4 x 10^3 is 4,000
If you divide 40,000,000 by 4,000 you get
10,000
That answer is equivalent to 10^4.
So this is why the answer is 10^4
Six months ago, Guillermo purchased a coffee truck as a business. To determine how his coffee
truck is doing, he plotted the net profits over each of the past six months on the scatter plot below.
Guillermo's business partner told him that the data Guillermo plotted is misleading. What is the
BEST reason why the data is misleading?
The data is misleading because the scatter plot starts at $532, so a small increase in profits looks very large.
The data is misleading because Guillermo should expect to make more profits than $500-$600 per month.
The data is misleading because the profits of a new company should not show a decrease between months 2
and 3
The data is misleading because the scatter plot only shows the first six months of profits, and it does not show
projected profits over the next six months.
In just one month, this coffee truck spent over $11,000. This month's margins were extraordinarily good, and the overhead was less than $2,000 as a result. Although not every month exceeds $10,000, I've had quite a few.
I make between $6,000 and $9,000 a month on the coffee van on average working 30 to 40 hours a week.
Because so much can depend on the revenue from coffee cater or other events, there is a wide variety.
Three significant occasions significantly increased our income.
What is the first successful coffee truck event?The first was a contract for hot chocolate I had gotten the year before. During the holidays, a nearby church gave hot coffee to its attendees during one of its services. three distinct nights for the host. We had previously catered for one of their nights, but this year they ordered three times as much. At a cost of 0.97 cents apiece, we supplied 6,988 cups of hot chocolate. The price of each cup was 0.09 cents.
∴ 6 778.36 cents per cup× 6,988 cups.
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the inequality is 0.6x>6000
The graph of the solution is open circle at 10,000; arrow right
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a 9 and an 8
The probability to being a 9 and an 8 from a standard 52 - card deck
will be;
⇒ 2 / 13
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
The total number of cards = 52
Number of a 9 dealt = 4
Number of a 8 dealt = 4
Now,
Total number of cards = 52
And, Number of dealt a 9 and an 8 card = 4 + 4
= 8
Since, Probability = Number of dealt a 9 or 8 / Total number of cards
Thus, The probability of being dealt a 9 and an 8 will be;
= 8 / 52
= 2 / 13
Therefore, The probability to being a 9 and an 8 from a standard 52 - card deck will be;
⇒ 2 / 13
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Hi, can you help me to solve this exercise, please!!
Based on the statement, we can deduce that cot(θ) must be negative as θ is in the fourth quadrant.
We have to find the ratio between the adjacent leg and the opposite leg knowing that the ratio between the hypotenuse and the opposite leg is -(√638)/22.
Using the pythagorean theorem for this purpose, we have:
[tex]\begin{gathered} (\sqrt[]{638})^2=22^2+a^2\text{ (Given that the sum of the squares of the legs must be equal to the square of } \\ \text{ the hypotenuse)} \end{gathered}[/tex][tex]\begin{gathered} 638=484+a^2\text{ (Raising the numbers to the power of 2)} \\ 154=a^2(\text{ Subtracting 484 from both sides of the equation)} \\ \sqrt[]{154}=a\text{ (Taking the square root of both sides)} \end{gathered}[/tex][tex]\begin{gathered} \text{ The ratio between the adjacent leg and the opposite leg would be: } \\ \frac{\sqrt[]{154}}{22} \end{gathered}[/tex]Given that cot(θ) must be negative the answer would be:
[tex]\cot \mleft(\theta\mright)=-\frac{\sqrt[]{154}}{22}[/tex]please please please don't do a lot of explaining I'm in a rush
15 + 1.50 h = monthly cost
number 7 please Find the value of y if B is between A and C, AB= 2y, BC= 6y, and AC = 48
Find the value of y if B is between A and C, AB= 2y, BC= 6y, and AC = 48
I'll draw to help you understand:
AB = 2y and BC = 6y, so AB+BC = AC
Also: 2y+6y = 48
8y = 48
y = 48/8
y = 6
Answer: Letter C
solve each system of the equation by elimination method.3x-4y=1x-7y=23
Solve the system by elimination. This way:
Now, use the value of y to find the value of x.
[tex]\begin{gathered} 3x-4y=1 \\ 3x-4(-4)=1 \\ 3x+16=1 \\ 3x=-15 \\ x=-\frac{15}{3} \\ x=-5 \end{gathered}[/tex]The solution of the system is x=-5 and y=-4.
Suppose that the functions p and q are defined as follows in the attachment
1) In this question, we need to write out two composite functions.
2) So let's start with the following composite functions and then evaluate them for x=-5:
[tex]\begin{gathered} (q\circ p)(x)=\mleft(x-2\mright)^2+1 \\ (p\circ q)(x)=-(x^2+1)+2=-x^2-1+2=-x^2+1 \end{gathered}[/tex]2.2) Now, we can evaluate those two composite functions for x=-5
[tex]\begin{gathered} (q\circ p)(x)=\mleft(x-2\mright)^2+1 \\ (q\circ p)(-5)=\mleft(\mleft(-5\mright)-2\mright)^2+1=50 \\ \\ (p\circ q)(x)=-(x^2+1)+2 \\ (p\circ q)(-5)=-((-5)^2+1)+2=-(26)+2=-24 \end{gathered}[/tex]3) Hence, the answers are:
[tex]\begin{gathered} (q\circ p)(-5)=50 \\ (p\circ q)(-5)=-24 \end{gathered}[/tex]A car rental company charges $15 per day and $0.55 per kilometer to rent a car. What is the total bill if a car is rented for 4 days and is driven 146 kilometers?
What is the answer to this please need answers asap
SOLUTION:
Case: Geometry: Sum of angles in a triangle
Given: Three angles in a triangle in algebraic format
Required: To find angle K by first solving the resulting algeba
Method: Use sum of angles in a triangle to find x, then plug the value of x to get angle K.
Finding the value of x using sum of angles in a triangle
[tex]\begin{gathered} \measuredangle J\text{ + }\measuredangle K+\text{ }\measuredangle L\text{ = 180}\degree\text{ (Sum of angles in a triangle)} \\ (6x-11)\text{ + (8x-29) + (3x -1) =180}\degree \\ \text{Collecting like terms} \\ 6x+\text{ 8x+3x -11}\degree\text{-29}\degree\text{-1}\degree=\text{ 180}\degree \\ 17x\text{ -41}\degree=180\degree\text{ } \\ 17x=\text{ 180}\degree+41\degree \\ 17x=\text{ 221}\degree \\ \text{Dividing both sides by 17} \\ x=\text{ 13}\degree \end{gathered}[/tex]Finding the angles K
[tex]\begin{gathered} \measuredangle K=\text{ 8x -29}\degree \\ \measuredangle K=\text{ 8(13) -29}\degree \\ \measuredangle K=\text{ 104}\degree\text{ -29}\degree \\ \measuredangle K=75\degree \end{gathered}[/tex]Final answer:
The value of angle K is 75 degrees
Match each letter in the image with the correct description.Question 1Not yetansweredAPoints out of1.00Flag question- 5GBandChoose..g for27)Quadrant5cions,Quadrant IVE10/4)Quadrant IIDourseOrigin-5Y-AxisX-Axis
we have that
y-axis ------> point A
x-axis ------> point C
origin -----> point E
I quadrant ------> point B
II quadrant -----> point G
III quadrant ----> point F
IV quadrant ----> point D
Alison is preparing for a math contest. Each day, she works on multiplication problems for 10 minutes anddivision problems for 50 minutes.How many minutes does Alison practice multiplication and division problems in 20 days?Alison practices multiplication and division problems forminutes in 20 days.W
Each day she works on multiplication problems for 10 minutes and division for 50 minutes. In a day she studies a total of 60 minutes
For 20 days that means she will spend the following minutes studying
[tex]20\times60=1200\text{ minutes}[/tex]For multilication she will spend the following minutes studying
[tex]10\times20=200\text{ minutes}[/tex]For division she will spend the following minutes studying
[tex]50\times20=1000\text{ minutes}[/tex]Determine the sine and cosine ratios for an angle that measures pi/2
We need to determine the values of the functions sine and cosine for the angle π/2.
One way of finding those values is by observing the following unit circle:
Then, for the angle π/2, we have:
[tex]\begin{gathered} \sin\left(\frac{\pi}{2}\right)=1 \\ \\ \cos\left(\frac{\pi}{2}\right)=0 \end{gathered}[/tex]can you help me please
