The number of ways Jose can arrange his family members into a row of 5 seats if Jose must sit in the first seat is 840.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
The number of ways Jose can make his family sit is,
Number of ways = number of ways people can sit on the first sit × number of ways people can sit on the second sit × number of ways people can sit on the third sit × number of ways people can sit on the fourth sit × number of ways people can sit on the fifth sit
Since Jose wants to sit on the first seat there are only options for the first seat, therefore,
Number of ways = 1 × 7 × 6 × 5 × 4 = 840
Hence, the number of ways Jose can arrange his family members into a row of 5 seats if Jose must sit in the first seat is 840.
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3
O Find the perimeter of the following shape, given its curves are made from parts of circles.
Give your answers in terms of π.
4cm
4cm
4cm
The diagram is not drawn to scale.
Answer:
12pi cm
Step-by-step explanation:
The Perimeter of the full shape is the sum of the lengths of the edges of the parts. For convenience in referencing them, we'll call the large curve "[tex]curve_{big}[/tex]" and the three smaller curves "[tex]curve_1[/tex]" "[tex]curve_2[/tex]" "[tex]curve_3[/tex]" in order from left to right.
Thus, the Perimeter of the full shape can be written as an equation:
[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex]Since all of those edge lengths are curves, and the question states that all of the curves are made from parts of circles, then we need to know how to find the length of the edge of a circle.
Parts of a circle
Since values in the diagram are diameters, use the formula for the Perimeter of a circle [tex]P=\pi d[/tex] (where d is the diameter).
Let's call the diameters of each of our curves "[tex]d_{big}[/tex]" "[tex]d_1[/tex]" "[tex]d_2[/tex]" "[tex]d_3[/tex]", with the subscripts denoting which curve we're referring to.
Note that for each curve, the curve only represents half of a circle. So, to find the length of each curve, we'll need half of the full perimeter of each circle.
So for instance: [tex]Length(curve_{big})=\frac{1}{2} \pi d_{big}[/tex]
Substituting back into the main equation above:
[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex][tex]P_{overall}=\frac{1}{2} \pi d_{big} + \frac{1}{2} \pi d_{1} + \frac{1}{2} \pi d_{2} + \frac{1}{2} \pi d_{3}[/tex]
Note that all terms have common factors of "one-half" and "pi" in them. These can be factored out:
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]
The diameter for the large Curve, is the sum of the three small diameters, so [tex]d_{big}=12cm[/tex], and [tex]d_{1}=d_{2}=d_{3}=4cm[/tex]
Substituting and simplifying (in terms of pi):
[tex]P_{overall}=\frac{1}{2} \pi ( (12cm) + (4cm) + (4cm) + (4cm) )\\P_{overall}=\frac{1}{2} \pi ( 24cm)\\P_{overall}=12 \pi cm[/tex]
Additional Understanding
Interesting for this problem, since the diameters of the 3 small curves formed the diameter of the large curve [tex]d_{1} + d_{2} + d_{3} =d_{big}[/tex], one could make a different substitution into one of our formulas above:
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + (d_{big}))[/tex]
[tex]P_{overall}=\frac{1}{2} \pi (2d_{big})[/tex]
[tex]P_{overall}=\pi d_{big}[/tex]
Notice that [tex]\pi d_{big}[/tex] is just the full perimeter of a circle with the big diameter.
So, if one imagined starting with a full circle with the big diameter, even though the bottom half of the circle was turned into a bunch of smaller half circles, since they were in a line along the diameter of the large circle, the full perimeter of the new shape didn't change.
The number of smaller circles doesn't need to be 3 either... as long as it goes the full distance across, right along the diameter.
Which information could he have used to determine this?
O GLH = ILM
O m KLM = 5m ILMO
O m GLI = 2m GLH
O m GLI = 1/2m GLH + 1/2m HLI
Answer:
m∠GLI = 2m∠GLH
Step-by-step explanation:
Angle GLI (red) is made of angles GLH (purple) and HLI (green).
m∠GLI = m∠GLH + m∠HLI
First option: ∠GLH ≅ ∠ILM (Angle GLH is congruent to angle ILM.)
This doesn't tell us anything about the relationship between angles GLI, GLH and HLI. So it can't be used.
Second option: m∠KLM = 5m∠ILM (Measure of angle KLM is 5 times the measure of angle ILM.)
This also cannot be used, because it doesn't include angles GLI, GLH or HLI.
Third option: m∠GLI = 2m∠GLH (Measure of angle GLI is two times the measure of angle GLH.)
Now this option is more interesting. It includes two angles of three that we are interested in.
If angle GLI is two times angle GLH, then that means that angle GLH is congruent to angle HLI!
Let's prove this with equations.
1) m∠GLI = m∠GLH + m∠HLI (from picture)
2) m∠GLI = 2m∠GLH (from third option)
Substitute m∠GLI in first equation with m∠GLI in second.
m∠GLI = m∠GLH + m∠HLI
2m∠GLH = m∠GLH + m∠HLI
m∠GLH = m∠HLI
So this proves that the angles GLH and HLI have the same measure, therefore ray LH is bisector of GLI.
Fourth option: m∠GLI = 1/2m∠GLH + 1/2m∠HLI
There are all angles we are interested in, but there is a mistake. We can see in the picture that angle GLI is made of angle GLH and HLI and not of half of them. This just is not true. The correct equation would be m∠GLI = m∠GLH + m∠HLI.
Please someone help me with steps!
Answer:
96
Step-by-step explanation:
The formula for average = [tex]\frac{Sum \hspace{0.15cm} of\hspace{0.15cm} Items}{No.\hspace{0.15cm} of \hspace{0.15cm} Items}[/tex]
After taking 3 tests, the average is 88.
∴ 88 = Sum of Items / 3
Sum of Items = 88 x 3
= 264
This means Lenny's total score after 3 tests is 264.
We now have to calculate how many marks needs to be added to 264 so that after four tests, the average is 90.
Now the number of items (tests) = 4, and average = 90.
Let the marks required in 4th test = [tex]x[/tex]
∴ [tex]\frac{264 + x}{4} = 90[/tex]
264 + [tex]x[/tex] = 360
[tex]x[/tex] = 360 - 264
= 96
easy:
Clara buy: 300 apples, 74 potato, 15 eggs e 2 phone.
how many things did he buy in all?
Hard:
There are 92 boys in a school, the girl 100.How many more girl are there than boys?
Answer:
easy = 391 items
hard = there are 8 more girls than there are boys
The driving distance from Seattle to Portland is 175 miles. Your car gets 25 miles per gallon. If gasoline is $2.80 per gallon, how much will the round trip from Seattle to Portland and back cost in dollars?
Answer:
$980
Step-by-step explanation:
Given the cost of gasoline = $2.80/mile
Total Distance = 175miles x 2 (Back and forth)
= 350 miles
Total Cost = Cost of gasoline x Total Distance =
= $2.80 x 350
= $980
The total cost of the trip from Seattle to Portland and back cost in dollars will be;
⇒ $250
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The driving distance from Seattle to Portland is 175 miles.
Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.
Now,
Since, The driving distance from Seattle to Portland is 175 miles.
Hence, The total distance from Seattle to Portland and back = 175 + 175
= 350 miles
And, Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.
Hence, The cost of gallon = 350/25 x $2.50
= 100 x $2.50
= $250
Thus, The total cost of the trip from Seattle to Portland and back cost in dollars will be;
⇒ $250
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Philip ran out of time while taking a multiple-choice test and plans to guess the last 4 questions. Each question has 5 possible choices, one of which is correct. Let X=X=X, equal the number of answers Philip correctly guesses in the last 444 questions. Assume that the results of his guesses are independent.
What is the probability that he answers exactly 1 question correctly in the last 4 questions?
Using the binomial distribution, it is found that there is a 0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.Considering that there are 4 questions, and each has 5 choices, the parameters are given as follows:
n = 4, p = 1/5 = 0.2.
The probability that he answers exactly 1 question correctly in the last 4 questions is P(X = 1), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.2)^{1}.(0.8)^{3} = 0.4096[/tex]
0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
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Which is the graph of 2x - 4y > 6?
-4 -2
2
-2
2
RUTA
4-2
414
2
O
W
4 -4-2
414
2
-2
O
2
RY
4
-2
2
211
Answer:
(d) see attached
Step-by-step explanation:
There are a couple of quick checks you can do to identify the correct graph.
__
shading and line styleFind a variable with a positive coefficient, and write that in the given relation to the inequality symbol:
x >
This tells you ...
shading is to the right of the line (where x-values are greater)the line is dashed (the = case is not included)location of the lineThe x-coefficient is a factor of the constant, so the x-intercept of the boundary line is easily found. Set y=0, and you have ...
2x = 6
x = 3
The boundary line you're looking for has an x-intercept at x=3.
__
The correct graph is shown in the attachment.
Solve the equation -8 = -3 - 6 cube root x^2
a. 0.76, -0.76
b. 4.98
c. 3.87
d. 1.53, -1.53
Answer:
0.76
Step-by-step explanation:
-8+3=-6x^(2/3)
-5=-6 x^(2/3)
-5/-6=x^(2/3)
(2/3)√{5/6}=x
0.76=x
x=0.76
Q5
The following are data from an independent measures experiment comparing
two treatment conditions:
Treatment 1
n=8
M = 8
SS=104
Treatment
n=8
M = 14
SS = 120
a. Do these data indicate a significant difference between the two
treatments?
b. Compute r2 and interpret the size of the treatment effect.
Answer:
A 2kg block is moved a long a level floor by a horizontal force of 20N if the coefficient of sliding friction is 0.4
what is the acceleration of the blove
Item 2
A container holds 54.6 gallons of liquid. The container leaks 8.4 gallons per hour.
How many hours will it take for the container to empty?
Enter your answer as a decimal in the box.
Answer:
54.6 ÷ 8.4 = 6.5 hours
6 hours, 30 minutes:)
can someone help me
Answer:
See Pictures
Step-by-step explanation:
Determine the number of zeros of the polynomial function. f(x) = x^3 + 7x^2 + 2
Answer:
3
Step-by-step explanation:
The fundamental theorem of algebra tells you the number of zeros is equal to the degree of the polynomial.
__
applicationThe given degree-3 polynomial has 3 zeros.
__
Additional comment
Descarte's rule of signs tells you the absence of sign changes among the coefficients means that there are no positive real roots. Changing the sign of the one odd-degree term gives one sign change, so there is one negative real root. The other two zeros are complex.
one negative real zero, and two complex zeros
A graph confirms that the only real zero is negative and irrational, about -7.04.
What is the solution to this system of equations 5x+2y=29
X+4y=13
Answer:
(5, 2 )
Step-by-step explanation:
5x + 2y = 29 → (1)
x + 4y = 13 → (2)
multiplying (1) by - 2 and adding to (2) will eliminate y
- 10x - 4y = - 58 → (3)
add (2) and (3) term by term to eliminate y
- 9x + 0 = - 45
- 9x = - 45 ( divide both sides by - 9 )
x = 5
substitute x = 5 into either of the 2 equations and solve for y
substituting into (2)
5 + 4y = 13 ( subtract 5 from both sides )
4y = 8 ( divide both sides by 4 )
y = 2
solution is (5, 2 )
8 cm
6 cm
2 cm
Find the surface area of the rectangular prism.
Surface Area = [?]cm²
Answer:
152cm²
Step-by-step explanation:
math and stuff and things
A sample of 40 11th graders were asked to select a favorite pattern out of 6
choices. The following display shows what their favorite color patterns were.
The counts have been recorded in the accompanying table according to
pattern and the number of students who selected that pattern. What is the
missing value in the table?
NEN
OA. 12
OB. 10
O C. 11
D. 13
Color Pattern
Blue on gray
Green
Pink polka dots
Purple
Red and orange
stripes
Yellow
Frequency
6
7
8
7
3
The missing value in the table is 12 , Option A is the correct answer.
What is a Graph ?A graph is a mathematical representation of the data available , It makes the study of the data over a wide period easier.
It is given in the question that there are 40 students and the frequency they select for each pattern is mentioned as number , which can be seen in the image attached with the answer.
It has been asked to determine the missing value in the frequency table corresponding to the pink Polka dots
The other number in the frequency table is 4, 6 ,8 ,7, 3
Total students are 40
Therefore the value corresponding to the pink polka dot is given by
40 - ( 4+6+7+8 +3)
= 12
Therefore The missing value in the table is 12 , Option A is the correct answer.
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curved surface area of a cone = Trl, where r is the
radius and is the slant height.
The ice cream cone below is made from a piece of wafer.
Work out the area of wafer required to make the ice
cream cone.
Give your answer to 1 d.p.
2 cm
9 cm
The area of wafer required to make the ice cream cone 68.75 cm²
What is Area?The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.
Given:
r= 2cm, l=9 cm
Surface area,
=πr(l +r)
=3.14*2(9 + 2)
= 6.25*11
=68.75 cm²
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What is the value of x?
The value of x in the segment is 3
How to determine the value of x?Using the secant and segment theorem, we have:
x * (x + 21) = (x + 1) * (x + 1 + 14)
Evaluate the sum
x * (x + 21) = (x + 1) * (x + 15)
Expand
x^2 + 21x = x^2 + 15x + x + 15
Subtract x^2 from both sides
21x = 15x + x + 15
Evaluate the like terms
5x = 15
Divide both sides by 5
x = 3
Hence, the value of x is 3
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X^2=50 where x is a real number
The value of x in the given expression x² = 50 is 5√2
Data obtained from the questionx² = 50Value of x =?How to determine the value of xx² = 50
Thake the square root of both sides
x = √50
Recall
√50 = √(25 × 2) = 5√2
Thus,
x = √50
x = 5√2
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Consider the matrix [tex]A_{4x4}, det(A) = -2[/tex]
Show that the following is true or false:
[tex]det(adj(2A^{-1}) =-2^{9}[/tex]
We found a counterexample, so the statement is false.
Is the statement true?
Let's use the matrix:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
This is a 4x4 matrix with determinant equal to -2.
The inverse matrix is:
[tex]\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right][/tex]
If we multiply it by 2, we get:
[tex]\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right][/tex]
The adjoint of that is the original matrix, actually:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
Which we already know, has a determinant of -2.
So the statement is false, as we found a counterexample.
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Given 2 (x+3) - 4x = x
Prove = 2
Complete the proof. Provide reasons for 1-6 below.
step-by-step explanation:
#1: simplify both sides of the equation.
2(x+3)−4x=x
(2)(x)+(2)(3)+−4x=x
2x+6+−4x=x
(2x+−4x)+(6)=x
−2x+6=x
−2x+6=x
***
#2: subtract x from both sides.
−2x+6−x=x−x
−3x+6=0
***
#3: subtract 6 from both sides.
−3x+6−6=0−6
−3x=−6
***
step 4: divide both sides by -3.
−3x/-3 = -6/-3
solution x = 2
Bella wants to know how long her dog is. She measure its body and finds that it is 54 cm long. Then she measures the tail and find it is 34 cm long. How long is Bella's dog from body to tail?
Answer:
88 cm
Step-by-step explanation:
body to tail = length of body + length of tail
body to tail = 54 cm + 34 cm
body to tail = 88 cm
Instructions: Complete the following proof by dragging and dropping the
correct reason in the spaces below.
Statement
Complete the Proof
8x5= 2x + 1
6x5=1
6x = 6
x = 1
Reason
1
Someone help proofs aren’t my thing
The solution to the given linear equation is x=1
Solution to linear equationLinear equations are equations that has a leading degree of 1.
Given the linear equation as shown below;
8x - 5= 2x + 1
Subtract 2x from both sides
8x - 2x - 5 = 2x + 1-2x
6x - 5 = 1
Add 5 to both sides
6x - 5 + 5 = 5 + 1
6x = 6
Divide both sides by 6
6x/6 = 6/6
x = 1
Hence the solution to the given linear equation is x=1
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Which of the following is the graph of y= e^x + 1?
Answer + Step-by-step explanation:
y= e^x + 1
+ 1 will shift the graph up 1In the natural exponential function, eˣ = e power x, we employ e. In the eˣ function, the tangent line's slope to any point on the graph is equal to that point's y-coordinate. The sequence we employ to calculate the value of e is (1 + 1/n)Learn more about Natural Exponential Functions here: https://brainly.com/question/1979778
The formula M = 5/8 K gives the approximate distance in miles as a function of kilometers. Use the inverse to express 25 miles in kilometers.
2 ft
4.5 ft
6 ft
A) 38 cubic feet
B) 54 cubic feet
C)
66 cubic feet
D) 125 cubic feet
What is the volume?
Answer:
B
Step-by-step explanation:We know Volume = (a*b*c)
Answer:
B) 54 cubic feet
Step-by-step explanation:
Which function is represented by this graph? A line is graphed in an x y plane, where the x and the y axes range from negative 10 to 10 in increments of 2. The line falls through (negative 6, 10), (0, 4), (4, 0) to (7, negative 3), and then it rises through (10, 0). A. f(x) = |x + 7| − 3 B. f(x) = |x − 7| − 3 C. f(x) = |x + 3| − 7 D. f(x) = |x − 3| − 7
The line that represents the graph satisfying all condition is f(x) = |x − 7| − 3.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
As, the points are given.
We have to find which equation satisfies all the points.
f(x) = |x − 7| − 3
put x= -6
y= 13-3 = 10
Similarly by putting all the values the only condition that satisfies is
f(x) = |x − 7| − 3
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definition of Identity property, Association property and communicative property please answer!
Answer:
09
Step-by-step explanation:
07
Please solve these questions with an explanation
Answer:
Step-by-step explanation:
The line whose equation is y=4x+2 has a y-intercept with coordinates
Answer: 2xy
Step-by-step explanation: 2xy is the answer bra
What value represents the vertical translation from the graph of the parent function f(x)=x² to the graph of the function
g(x)=(x+5)2+3?
-5
-3
O
3
O5
The value is 3 which represents the vertical translation from the graph of the parent function f(x)=x² option third 3 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = x²
The above function is a parent function.
The translation: vertical translation from the graph of the parent function.
F(x) → f(x) + 3
F(x) = x² + 3
The above function will shift vertical up by 3 units.
Thus, the value is 3 which represents the vertical translation from the graph of the parent function f(x)=x² option third 3 is correct.
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