The number of all possible combinations of 3 letters can be made from the word 'oranges' = 35
The probability that the three letters will be consonants = 0.114
In this question, we have been given a word 'oranges'
We need to find the number of ways in which the letters of orange can be arranged.
Also, we need to find the probability that these three letters will all be consonants.
The number of letters in the word oranges = 7
So, n = 7
We need combinations of 3 letters.
so, r = 3
The number of all possible combinations of 3 letters would be,
^7C_3 = 7! / (7 - 3)! (3!)
^7C_3 = 35
The number of combinations of 3 letters = 35
We can observe that the consonants in the word 'oranges' are:
r, n, g, s
The number of consonants = 4
The combinations of 3 consonants would be,
^4C_3 = 4! / (4 - 3)! 3!
^4C_3 = 4
The required probability would be,
p = ^4C_3 / ^7C_3
p = 4 / 35
p = 0.114
Therefore, the number of all possible combinations of 3 letters can be made from the word 'oranges' = 35
the probability that the three letters will be consonants = 0.114
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The senior class plans a school trip to Washington DC. Students should bring money for meals and
souvenirs. They are told to bring at least $60 but no more than $135. Write a compound inequality that
represents the amounts of money a student can bring.
Answer:
$65 ≤ x ≤ $135
Step-by-step explanation:
Now, one should know the meaning of compound inequality. A compound inequality is an inequality that simply combines the two simple inequalities.
Now, in an inequality, three relations are performed, equal to, less than, and greater than. You can combine 'equal to' with 'less than' or 'greater than' according to the situation given.
Notice that in the given sign
≤
the value on the left side of the pointed side will be small or lesser than the value on the right side. Also notify that if inverted, like this ≥
The value of the left side will be greater. This means the value at the pointed side will always be smaller. The lower bar is a sign of equal to
if this is written
x ≤ 3
It means that x can be equal to three or any value less than 3 means 2,1,0,-1, etc.
Now in the question given, it is stated that money should be not less than $65 means it can either be $65 or more but not less than it. Let's assume 'x' as the amount required,
So one inequality is
$65 ≤ x
The second condition which is amount should be no more than $135, means it can be $135 or less, so inequality is
x ≤ $135
Remember that we use AND in the answer because both statements of inequality need to be fulfilled or satisfied.
(04.01 LC)
Simplify quantity x squared plus 5 x plus 6 end quantity over quantity x plus 2
x2 + 1
x2 − 1
x + 3
x − 3
Question 4(Multiple Choice Worth 5 points)
(04.03 MC)
What are the vertical asymptotes of the function f(x) = the quantity of 2x plus 8, all over x squared plus 5x plus 6?
x = −3 and x = −2
x = −3 and x = 2
x = 1 and x = −2
x = 1 and x = 2
Question 5(Multiple Choice Worth 5 points)
(04.02 LC)
Identify the restrictions on the domain of f(x) = quantity x minus 3 over quantity x plus 5.
x ≠ 5
x ≠ −5
x ≠ 3
x ≠ −3
Question 6(Multiple Choice Worth 5 points)
(04.02 LC)
What are the discontinuity and zero of the function f(x) = quantity x squared plus 6 x plus 8 end quantity over quantity x plus 4?
Discontinuity at (4, 6), zero at (−2, 0)
Discontinuity at (4, 6), zero at (2, 0)
Discontinuity at (−4, −2), zero at (−2, 0)
Discontinuity at (−4, −2), zero at (2, 0)
Question 7 (Essay Worth 10 points)
(04.02 MC)
Show all work to identify the asymptotes and zero of the function f of x equals 3 x over quantity x squared minus 9.
Add Audio Add Video
Question 8 (Essay Worth 10 points)
(04.04 MC)
The aquarium has 6 fewer yellow fish than green fish. 40 percent of the fish are yellow. How many green fish are in the aquarium? Show your work.
Answer:
Following are the solution to the given question:
Step-by-step explanation:
In question 1:
[tex]\to \frac{x^2+5x+6}{x+2}\\\\\to \frac{x^2+(3+2)x+6}{x+2}\\\\\to \frac{x^2+3x+2x+6}{x+2}\\\\\to \frac{x(x+3)+2(x+3)}{x+2}\\\\\to \frac{(x+3) (x+2)}{x+2}\\\\\to (x+3)[/tex]
In question 2:
[tex]\to \frac{2x+8}{x^2+5x+6}\\\\[/tex]
[tex]\to x^2+5x+6=0\\\\\to (x+3)(x+2)=0\\\\\to x+3 =0 \ \ \ \ \ \ x+2 =0\\\\\to x = -3 \ \ \ \ \ \ x=-2 \\\\[/tex]
In question 3:
[tex]\to f(x) = \frac{x-3}{x+5}\\\\\to f(x) \neq 0\\\\when\\\to x+5=0\\\\\to x=-4 \ excluded \ value \\\\\to x \neq 5[/tex]
In question 4:
[tex]\to f(x) = \frac{x^2+6x+8}{(x+4)}\\\\\to f(x) = \frac{x^2+(4+2)x+8}{(x+4)}[/tex]
[tex]\to f(x) = \frac{x^2+4x+2x+8}{(x+4)}\\\\\to f(x) = \frac{x(x+4)+2(x+4)}{(x+4)}\\\\\to f(x) = \frac{(x+4)(x+2)}{(x+4)}\\\\\to f(x) = x= -4 and -2[/tex]
In question 5:
[tex]\to f(x) =\frac{3x}{x^2-9} \\\\ \to f(x) =\frac{3x}{x^2-3^2} \\\\ \to f(x) =\frac{3x}{(x+3)(x-3)}[/tex]
In question 6:
total number of fish = x
yellow fish [tex]= \frac{40}{100}=0.4X[/tex]
green fish [tex]= \frac{60}{100}) =0.6X[/tex]
It is now the case that the yellow fish number is 6 less than the green fish number.
[tex]\therefore \\\\\to 0.6x-0.4x = 6 \\\\\to 0.2x = 6\\\\\to x= \frac{6}{0.2} \\\\\to x=30[/tex]
green fish [tex]= 0.6 \times 30=18[/tex]
CAN SOMEONE ASP HELP ME
Answer:
152 sq. ft
Step-by-step explanation:
Area of rectangle:
L × W = A16 × 8 = A16 × 8 = 128 sq. ftArea of triangle:
B = 16 - 12B = 4B × H = A4 × 6 = A4 × 6 = 24 sq. ftCombine the areas:
128 sq. ft + 24 sq. ft = 152 sq. ftI hope this helps!
beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. if beth places the swings at point d, how could she prove that point d is equidistant from the jungle gym and monkey bars? if segment dc bisects segment ab, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. if segment dc bisects segment ab, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if segment ad bisects segment ab, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. if segment ad bisects segment ab, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent.
Answer:
Step-by-step segment dc bisects segment ab, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. if segment dc bisects segment ab, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if segment ad bisects segment ab, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from:
A company is manufacturing computer monitors that are 22 inches wide, 22 inches across, and 2 inches thick. If the average cost to produce a computer monitor is $0.43 per cubic inch, then about how much would it cost the company to make 10 computer monitors?
Answer:
$4162.4
Step-by-step explanation:
As per the question statement,
The computer monitors are in cuboid structure.
Width of computer monitors = 22 inches
Length of computer monitors = 22 inches
Thickness of computer monitors = 2 inches
Average cost of production per cubic inch = $0.43
To find:
Cost to the company to make 10 monitors.
Solution:
Volume of a cuboid is given as following:
[tex]Volume = Length \times Width \times Height[/tex]
Volume of one computer monitor as per the given dimensions = [tex]22\times 22 \times 2[/tex] = 968 cubic inches
Volume of 10 such monitors = 968 [tex]\times[/tex] 10 = 9680 cubic inches
Cost of manufacturing of 1 cubic inch = $0.43
Cost of manufacturing of 9680 cubic inch = $0.43 [tex]\times[/tex] 9680 = $4162.4
A math test has 12 multiplication problems and 24 division problems.
What is the ratio value of multiplication problems to division problems?
Type your answer as a fraction in simplest form.
Answer:
The answer would be 2/3
Step-by-step explanation:
There are 36 total problems and 24 division problems.
So take 24 over 36 and simplify and you get 2/3
Victoria created the scatterplot below based on the data in the table for the ages and heights of some teachers in her school. Teacher Age vs. Height Teacher Age Height (in.) 1 36 62 2 28 70 3 50 60 4 44 72 5 58 68 6 24 65 A graph titled Teacher Age versus height has age on the x-axis and height (inches) on the y-axis. Points are at (22, 66), (28, 70), (35, 62), (42, 72), (60, 50) and (59, 69). She wants to see if a teacher’s height depends on his or her age. What did she do wrong when she created the scatterplot? She mixed up the independent and dependent variables. She labeled the x-axis of the scatterplot “Age” when she should have labeled it “Teacher.” She plotted the point (36, 62) when she shouldn’t have. She mixed up the x- and y-coordinates of the point representing teacher 3.
Answer:
a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I took the test and got 100%.
HELPPPPPP PLEASEEEEE !!!!!
Answer:
m∠DBC is 43°
Step-by-step explanation:
Let us solve the question
∵ D is in the interior of ∠ABC
→ That means D divides ∠ABC into two angles ABD and DBC
∴ m∠ABD + m∠DBC = m∠ABC
∵ m∠ABD = (3x + 5)°
∵ m∠DBC = (5x - 7)°
∵ m∠ABC = 78°
→ Substitute them in the equation above
∴ 3x + 5 + 5x - 7 = 78
→ Add the like terms in the left side
∵ (3x + 5x) + (5 + -7) = 78
∴ 8x + -2 = 78
∴ 8x - 2 = 78
→ Add 2 to both sides
∴ 8x -2 + 2 = 78 + 2
∴ 8x = 80
→ Divide both sides by 8
∴ x = 10
→ To find m∠DBC, substitute x by 10 in its measure
∵ m∠DBC = 5(10) - 7
∴ m∠DBC = 50 - 7
∴ m∠DBC = 43°
Leon says that when any number between 1 and 9 is multiplied by 0 , the product always has a 0 or 5 in the ones place. Is this reasonable? explain
Answer:
No
Step-by-step explanation:
Any number multiplied by 0 is 0
4 × 0 = 0 , n × 0 = 0
Please help me with 5
Answer:
Fourth chice, 3/5
Step-by-step explanation:
Add all the numbers together, 12 + 3 + 5 = 20
There's 12 green cubes out of the 20 cubes so it's 12/20 which is 3/5
Choosing an Inequality Last week, Jason ran 26.1 miles. He wants to run further this week. He plans to run 2.4 miles to the park, four times around the park, and 2.4 miles back from the park. To represent that inequality, he wrote: 2.4 + 4p + 2.4 26.1 Which inequality symbol should he use? Why?
Answer:
> or ≥
Step-by-step explanation:
Distance ran last week = 26.1 miles
Since he wants to further on the total miles covered last week, then what is required is that total miles covered this week is greater than the total distance covered last week.
2.4 miles to the park ; 4 times around the park and 2.4 miles back from the park :
His coverage this week is should be represented by the Inequality :
2.4 + 4p + 2.4 > 26.1 ; which denotes that total coverage this week (2.4 + 4p + 2.4) is greater or more than last week's coverage of 26.1 miles
Answer:
He should use the greater than symbol, >. He would not beat his distance if he only ran 26.1 miles, so the greater than or equal to symbol would not be correct.
Step-by-step explanation:
that's the sample response on edge
What is the yyy-intercept of y=5x-1y=5x−1y, equals, 5, x, minus, 1?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
(-1,0)(−1,0)left parenthesis, minus, 1, comma, 0, right parenthesis
(Choice B)
B
(0,-1)(0,−1)left parenthesis, 0, comma, minus, 1, right parenthesis
(Choice C)
C
(5,0)(5,0)left parenthesis, 5, comma, 0, right parenthesis
(Choice D)
D
(0,5)(0,5)
Answer:
B.(0,-1)
Step-by-step explanation:
Answer:
B.(0,-1)
Step-by-step explanation:
i just got it right
A builder has metal rods that are each 3.73 centimeters long. If he puts 8 of them in a line, how long will the line be?
can someone help? exams are tomorrow and i have no clue how to do this problem?
For each ordered pair determine whether it is a solution to the system of equations 2x-7y=8 -3x+2y=5
Answers:
(-3,-2)
(4,0)
(5,4)
(-7,-8)
Answer:
The solution of this system of linear equations is [tex](x,y) = (-3,-2)[/tex].
Step-by-step explanation:
Let be the following system of linear equations:
[tex]2\cdot x - 7\cdot y = 8[/tex] (1)
[tex]-3\cdot x + 2\cdot y = 5[/tex] (2)
From (1) we clear [tex]y[/tex]:
[tex]2\cdot x -8 = 7\cdot y[/tex]
[tex]y = \frac{2\cdot x - 8}{7}[/tex]
And we apply this variable in (2):
[tex]-3\cdot x+2\cdot \left(\frac{2\cdot x -8}{7} \right)= 5[/tex]
[tex]-3\cdot x +\frac{4}{7} \cdot x -\frac{16}{7} = 5[/tex]
[tex]-\frac{17}{7}\cdot x = \frac{51}{7}[/tex]
[tex]x = -\frac{51}{17}[/tex]
[tex]x = -3[/tex]
And the value of [tex]y[/tex] is:
[tex]y = \frac{2\cdot (-3)-8}{7}[/tex]
[tex]y = -\frac{14}{7}[/tex]
[tex]y = -2[/tex]
The solution of this system of linear equations is [tex](x,y) = (-3,-2)[/tex].
Help please. Thanks!!!!!
Answer:
slope: 20/3 parallel
Step-by-step explanation:
y1-y2/x1-x2 gives you slope(30--10/12-6). Plot the points, create line segments, you'll find that they are parallel.
Answer:
1. 6[tex]\frac{2}{3}[/tex]
2. Parallel
Step-by-step explanation:
To find the slope, you need to find the [tex]\frac{rise}{run}[/tex] between two points.
[tex]\frac{rise}{run}[/tex] = [tex]\frac{30-(-10)}{12-6}[/tex]
= [tex]\frac{40}{6}[/tex]
= 6[tex]\frac{2}{3}[/tex]
If a graph has more than a point on the y-axis even though the x-axis remains the same, it means that it is a vertical line. Since Graph 1 has (-1) on the x-axis but there are two points on the y-axis, 4 & (-9), it is a vertical graph. Since Graph 2 has (11) on the x-axis but there are two points on the y-axis, (-2) & 6, it is also a vertical graph. Thus, both graphs are parallel.
please help asapp!!!?!!?!?!?
Step-by-step explanation:
the sum of interior angles in a triangle is 180°
so
2x+2+12x-8+6x+6=180
20x=180
x=180/20=9
so
m<A =6x+6=6*9+6=54+6=60
m<M=12x-8=12*9-8=100
m<N=2x+2=2*9+2=18+2=20
MAN is an obtuse triangle
because of 100° angle
question 4
isosceles
help if you can please !!
Answer:
i think 160 or somewhere close to that
Step-by-step explanation:
Answer:
the answer is 120ft
Step-by-step explanation:
all you need to do is length times width so 15×8 and you'd get 120 don't forget the ft hope this helps you.
The sum of three consecutive numbers is 36. What are the numbers?
Answer:
11, 12, and 13
Step-by-step explanation:
Answer:
Step-by-step explanation:
11, 12, and 13
x - 9 = 0.7*x + 0.6*x
Answer:
x = -30
Step-by-step explanation:
[tex]0.7x+0.6x=1x-9\\=>1.3x=1x-9\\=>1.3x-1x=9\\=>0.3x=-9\\=>\frac{3}{10}x =-9\\=>x=\frac{-9*10}{3} =-30[/tex]
What is the simplified value of
(a-3-2(a - 3)(a + 3) + (a + 3)??
someone plzzz help me real fast on this its due in 10 mins plz helpppppppppppppppp
Answer:
first one = greater than or equal to 1 and less than 10
Step-by-step explanation:
it's a method of writing numbers as the product of two factors where the first factor is a number whose absolute value is greater than or equal to 1 but less than 10 while the second factor is a power of 10
Subtract 25¢ from $7.42. Include the dollar sign and no spaces in your answer.
Answer:
$7.17
Step-by-step explanation: hope it helped
I need a step by step to solving this problem 4|3x + 4 = 4x + 8
The solution to the equation given as 4(3x + 4) = 4x + 8 is x =-1
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution to the equation?The equation is given as
4(3x + 4) = 4x + 8
Open the bracket in the above equation
So, we have
12x + 16 = 4x + 8
Collect the like terms in the above equation
12x - 4x = 8 - 16
Evaluate the like terms in the above equation
8x = -8
Divide both sides by 8 in the above equation
x =-1
Hence, the solution to the equation given as 4(3x + 4) = 4x + 8 is x =-1
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Y = 9x^2 - 81
Solve by following quadratic function by utilizing the square root method
The angle measures of triangle ABC are given:
The measure of angle A is (2x−10)°.
The measure of angle B is 70°.
The measure of angle C is (4x)°.
What is the value of x?
Enter your answer in the box.
x =
Answer:
x=20
Step-by-step explanation:
By the Triangle Sum Theorem, the angles of a triangle add up to 180. So we can set up the equation like this:
2x-10+70+4x=180
Combine Like terms
6x+60=180
Subtract 60 from both sides
6x=120
Divide by 6 to isolate the variable
x=20
Answer:x= 20
Step-by-step explanation:
As the equation of three angles of a triangle is 180°,
Then, 2x-10+70+4x=180
6x=120
So,x= 20
what is the value of the expression PLS? HURRY I give 17 points and brainliest
Answer: -77[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
Please help its math...I will give brainliest!
For a holiday sale, all items at Marty’s Electronics are discounted by 25%. Paula bought a laptop that had an original list price of $1,700. If 8% tax was applied to the sale after the discount was taken off, how much did Paula pay for her new computer? SHOW YOUR WORK! Thank you
Answer:
$1,377
Step-by-step explanation:
the way that I did it-
100-25=75
1700x0.75=1275
8%=0.08, just add a 1 to the sales tax whenever you are calculating that.
1275x1.08=1377
therefore it is $1,377
brainliest would be appreciated :)
stephanie and amanda each improved their yards by planting hostas and shrubs. they bought their supplies from the same store. stephanie spent $141 on 13 hostas and 10 shrubs. amanda spent $87 on 11 and 2 shrubs. what is the cost of one hosta and the cost of one shrub?
where are the answer choices
Find the perimeter of the
polygon if ZB = D.
A
5 cm
B
6 cm
D
7 cm
P = [?] cm
What is the perimeter?
Answer: 48
Step-by-step explanation:
yes