Answer: [tex]\frac{4}{7}[/tex]
Step-by-step explanation:
P(a) or P(b) = P(a) + P(b)
This means that the probability of a or b is the same of the probability of a plus b
So let's see the probability of a, selecting a professor
[tex]\frac{12}{12+6+9+8} \\\\\frac{12}{35}[/tex]
We won't simplify just yet so that addition will be easier later
Now let's see the probability of selecting b, an instructor
[tex]\frac{8}{12+6+9+8} \\\\\frac{8}{35}[/tex]
Now add the 2 probabilities together
[tex]\frac{12}{35} +\frac{8}{35} =\frac{20}{35}[/tex]
Simplify.
[tex]\frac{20}{35} =\frac{4}{7}[/tex]
Simplify the inequality-1 + 6(-1 -3x) > -39 - 2x.
Answer:
2 > x or x < 2
Step-by-step explanation:
-1 + 6(-1 - 3x) > -39 - 2x
-1 - 6 - 18x > -39 - 2x
-7 - 18x > -39 - 2x
32 > 16x
2 > x or x < 2
the reason that x < 2 is because of the negative sign. I solved it so that x stays positive but if you solve the equation with x on the other side like -16x > -32 then when you divide by -16 it changes to x < 2
PLEASE RATE!!! I hope this helps!!
(I have verified my answer on an online calculator)
Need Help Asap!!
[tex] \: \: \: \: [/tex]
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's check I the given pairs of triangles are congruent or not ~
problem 1[tex]\qquad \sf \dashrightarrow \:ABC \cong FED[/tex]
These triangles are congruent by SSS congruency, as it's three sides are equal.
・ ．━━━━━━━†━━━━━━━━━．・
problem 2[tex]\qquad \sf \dashrightarrow \:LMN \not \cong PQO[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
These triangles are not congruent because they don't fulfill any congruency criteria.
problem 3[tex]\qquad \sf \dashrightarrow \: XVW \cong YZA [/tex]
These triangles are congruent by AAS congruency criteria, since two angles and one of the side is common.
・ ．━━━━━━━†━━━━━━━━━．・
problem 4[tex]\qquad \sf \dashrightarrow \: GHI \not \cong IJG [/tex]
These triangles are not congruent because they don't fulfill any criteria.
・ ．━━━━━━━†━━━━━━━━━．・
problem 5[tex]\qquad \sf \dashrightarrow \: PQR\cong QPO[/tex]
These triangles are congruent by SSS congruency, as it's two sides are equal and one side is common.
・ ．━━━━━━━†━━━━━━━━━．・
problem 6[tex]\qquad \sf \dashrightarrow \: JIK \cong HIG [/tex]
These triangles are congruent by SAS congruency, since two sides and Angle between them are equal.
・ ．━━━━━━━†━━━━━━━━━．・
Problem 7These given triangles are congruent by SSS congruency, because they have two equal sides and one common side in there.
・ ．━━━━━━━†━━━━━━━━━．・
problem 8[tex]\qquad \sf \dashrightarrow \: BCD \cong FED [/tex]
These triangles are congruent by ASA congruency, because they have one pair equal angles, one pair of vertical opposite angles (they are equal) and a side between them equal.
・ ．━━━━━━━†━━━━━━━━━．・
problem 9[tex]\qquad \sf \dashrightarrow \: LKM \cong LNM [/tex]
These given triangles are congruent by SSS congruency, because they have two equal sides and one common side in there.
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
The sum of 3 times a number and 7 equals 4.
Answer: x = -1
Step-by-step explanation:
The problem is asking you the sum (+) of 3 times of a unknown number (let the unknown number be x) and 7, as in 3x + 7
According to the problem this expression is equal to 4,
3x + 7 = 4
1. Subtract 7 from both sides
3x = -3
2. Divide 3 on both sides
x = -1
Your final answer would be negative 1
Use the quadratic formula to solve the equation: y = x2 - 3x - 1
Group of answer choices
x = 5.6 and -1.3
x = 3.3 and -.3
x = -5.4 and -.4
x = 6.3 and 3.2
Answer:
3.3 and -0.3
Step-by-step explanation:
Using the quadratic formula plug in the a, b, and c values in this equation into the formula and you get 3.3 as a result. Not sure where the 0.3 part came from since it is not the opposite equation, but 3.3 is for sure correct. Work is linked below.
What would be the formula for this?
Answer:
ba/2+bd/2+cd, in this case the area is 46
Step-by-step explanation:
The formula for this would simply be the area of the trapazoid plus the area of the rectangle.
The area of a trapazoid(in this case) is b(a+d)/2
The area of the rectangle is cd
Adding these you get ba/2+bd/2+cd
In this case the area is 46
Find the missing endpoint given one endpoint and the midpoint of a line segment. The midpoint of line segment AB is (2,-5) If the coordinates of a point A are (4,4), what are the coordinates of B
Answer:
(0, -14)
Step-by-step explanation:
Midpoint formula: [tex](x_m, y_m) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]
Substitute known value: [tex](2, -5) = (\frac{4 + x_2}{2} ,\frac{4+y_2}{2} )[/tex]Find [tex]x_2[/tex] : [tex]2 = \frac{4+x_2}{2}[/tex] >> [tex]4 = 4 +x_2[/tex] >> [tex]0 = x_2[/tex] Find [tex]y_2[/tex] : [tex]-5 = \frac{4+y_2}{2}[/tex] >> [tex]-10 = 4 + y_2[/tex] >> [tex]-14 = y_2[/tex]- - Use the Quadratic Formula to solve the equation x2 – 2x = -9.
Solve the quadratic equation by using either a numeric or a graphic approach. x squared + 2 x minus 3 = 0 a. x = -1.1 or x = -2 c. x = 2 or x = -5 b. x = 2.3 or x = -0.82 d. x = 1 or x = -3
[tex]x^2+2x-3=0\\\\\implies x^2 +3x -x -3 =0\\\\\implies x(x+3) -(x+3)=0\\\\\implies (x-1)(x+3)=0\\\\\implies x =1 ~ \text{or}~ x = -3[/tex]
A flower shop has 426 flowers. This week they sell 285 flowers.
At the end of the week, the shop gets a delivery of 310 more flowers.
How many flowers does the flower shop have now?
A.
401
B.
429
C.
451
D.
461
Answer:
C. 451
Step-by-step explanation:
426 - 285 = 141
141 + 310 = 451
Rewrite the expression 2 square root X•4x^-5/2 in the form k•x^n
Answer:
(4x)
2
=16×x
2
Step-by-step explanation:
hope it's help
enter order pairs for
y = 2x + 7
y= 3x – 3
Answer:
(10, 27)
Step-by-step explanation:
We have to solve the given set of equations :
y = 2x + 7y = 3x - 3As both equations are equal to y, equate the RHS of both of the equations.
2x + 7 = 3x - 3x = 10The x-coordinate is 10y = 3(10) - 3 = 27The y-coordinate is 27
Writing an ordered pair
The standard form of an ordered pair is given by (x, y) where x and y are x and y coordinates respectivelyTherefore, the answer is :⇒ (10, 27)Answer:
[tex]\displaystyle [10, 27][/tex]
Step-by-step explanation:
Set each equation equivalent to each other:
[tex]\displaystyle 3x - 3 = 2x + 7 \\ \\ \frac{-10}{-1} = \frac{-x}{-1} \\ \\ \boxed{10 = x, 27 = y}[/tex]
I am joyous to assist you at any time.
Jack had m math problems to complete during his vacation. He solved the same number of problems everyday and finished them all in 5 days. (a) how many problems did jack solve per day? (b) suppose jack was solving 15 problems per day. (c) How many problems were assigned for homework
Jack's problems illustrates algebraic expressions
He solved m/5 problems everyday.75 questions were assigned in totalNumber of problems solved per dayThe given parameters are:
Problems = mNumber of days = 5The number of questions solved per day is calculated as:
Daily = Days/Problems
So, we have:
Daily = m/5
Number of problems in the assignmentWe have:
Daily = m/5
He solved 15 daily.
So, the equation becomes
m/5 = 15
Multiply both sides by 15
m = 75
Hence, 75 questions were assigned in total
Read more about expressions at:
https://brainly.com/question/723406
A wire is first bent into the shape of a triangle. Each side of the triangle is 16 long. Then the wire is unbent and reshaped into a rectangle. If the length of the rectangle is 15 in, what is its width?
Answer:
the width is 9in
Step-by-step explanation:
perimeter of triangle =3×16 = 48
let w= width of rectangle
perimeter of triangle = perimeter of rectangle
48= 2(15 +w)
24= 15 + w
w= 9
100 students went on a field trip. Six busses were filled and 10 students traveled in
cars with their parents. How many students were on each bus?
Answer:
15 students in each bus.
Step-by-step explanation:
Subtract 10 from 100 and you get 90 then divide 90 by 6 and that gives you how many students in each bus
What is the value of x in the equation –2.4x = 8.4?
Answer:
x = -3.5
Step-by-step explanation:
−2.4x=8.4
Divide both sides by −2.4.
x= 8.4/-2.4
Expand 8.4/-2.4 by multiplying both numerator and the denominator by 10.
x= 84/-24
Reduce the fraction 84/-24 to lowest terms by extracting and canceling out 12.
x= −7/2
-7/2 = -3.5
Answer:
-3.5
Step-by-step explanation:
Hello there?
given such a question,
You have to carry out division on of both RHS and LHS.
Take -2.4 and divide through -2.4{LHS} and 8.4{RHS}.
You are then remained with 1(x) in LHS and -3.5 in RHS
-2.4x /(-2.4)= {8.4}/(-2.4)
= -3.5
I hope this helps. Have a nice studies
dado el polinomio de variable "x", identicamente nulo (3n-9)x^5+(m-2)^3+(p+7)=0
entonces halla el valor de
El valor de "n" es
El valor de "m" es:
El valor de (n + m + p) es:
The value of n is 3, value of m is 2 and the value de m + n + p is -2.
How to identify a null polynomialIn this question we must analyze a null polynomial and determine three unknown variables. A null polynomial is those whose coefficients are equal to zero.
Therefore, we must resolve the following system of linear equations:
3 · n - 9 = 0 (1)
m - 2 = 0 (2)
p + 7 = 0 (3)
The solution of this system of linear equations is: n = 3, m = 2, p = -7. The value of n is 3, value of m is 2 and the value de m + n + p is -2. [tex]\blacksquare[/tex]
To learn further on polynomial, we kindly invite to check this verified question: https://brainly.com/question/23542646
Help picture below problem 8
Solution :-
Here, we have been given that lines f and g are parallel. Thus, the angle measuring 135° and ∠2 are vertically opposite angles.
And we know that vertically opposite angles measure same. Thus,
∠2 = 135°
Hope that helps ~~~
Find the fraction suitable for the blank. Show the method how you found.
Answer:
3/5Step-by-step explanation:
Let the blank is x, solve the equation for x:
(4 1/2 - x) × 1 3/13 = 4 4/5(9/2 - x) × 16/13 = 24/59/2 - x = 24/5 × 13/169/2 - x = 39/10x = 9/2 - 39/10x = 45/10 - 39/10x = 6/10x = 3/5Let that be x
(9/2-x)×16/13=24/5(9-2x)/2=24/5×16/13(9-2x)/2=39/1090-20x=7820x=12x=12/20x=6/10x=3/5Help help help help math
Answer:
It's 77, the absolute value bars will just make the number positive
Step-by-step explanation:
The area of a square slice of cheese is 25 square inches. The perimeter of the slice of cheese is
Choose...
inches.
Answer:
As Per Provided Information
Area of given square slice of cheese is 25 square inches .
We have been asked to determine the perimeter of the slice of cheese .
First we will find the side of square slice of cheese .
Let us assume the side of square slice of cheese be s .
Now Let's Solve
[tex] \boxed{\bf \:Area_{(Square)} = {Side}^{2}}[/tex]
Substituting the value and we obtain
[tex] \sf \longrightarrow \: 25 = {s}^{2} \\ \\ \\ \sf \longrightarrow \: \sqrt{25} = s \\ \\ \\ \sf \longrightarrow \: s \: = 5 \: inch[/tex]
So, the side of square slice cheese is 5 inch
Now let's calculate the Perimeter of cheese
[tex] \boxed{\bf \: Perimeter_{(Square)} = 4 \times side}[/tex]
Substituting the value we obtain
[tex] \longrightarrow \sf \: Perimeter_{(Square)} = 4 \times 5 \\ \\ \\ \longrightarrow \sf \: Perimeter_{(Square)} =20 \: inches[/tex]
Therefore,
Perimeter of square slice of cheese is 20 inches .pls help quick!!
10 points
Answer:
The angle B = 70°
Step-by-step explanation:
The sum of angles of a triangle is 180°
=> 40°+(2x-30)°+(x+20)° = 180°
=> 40°+2x°-30°+x°+20° = 180°
=> 30°+3x= 180°
=> 3x = 180°-30°
=> 3x = 150°
=> x = 150/3
=> x = 50°
So,the value of x = 50°
now , angle B = (2x-30) = (2×50 -30 ) = (100-30) = 70°
Find the value of the expression.
[tex]( (\frac{3}{5}) {}^{0} ) {}^{ - 2} = (1) {}^{ - 2} = \frac{1}{1 {}^{2} } = \frac{1}{1} = 1[/tex]
Help picture below problem 8
Answer:
Together they equal 180 l so you need to do 180-128 which equals 52. The answer is <D measures 52
Step-by-step explanation:
A right square pyramid has a volume of 12 cubic centimeters. If the height remains fixed but the sides of the base are multiplied by 3, what is the volume of the new pyramid?
A. 36 cm³
B. 48 cm³
C. 108 cm³
D. 72 cm³
Answer:
36 cm^3
Step-by-step explanation:
Because you need to multiply 12x3 giving you 36.
Answer:
its a
Step-by-step explanation:
i took the test
How can i find the answer to this question: simplify (7^5)^3
Answer:
Option D
Step-by-step explanation:
Given the following question:
[tex](7^5)^3[/tex]
To find the answer we simply have to apply the exponent rule and multiply the exponents.
[tex](7^5)^3[/tex]
[tex](a^b)^c=a^{bc}[/tex]
[tex]5\times3=15[/tex]
[tex]=7^{15}[/tex]
Your answer is "7^15" or option D.
Hope this helps.
Answer:
7^15
Step-by-step explanation:
We know that a^b^c = a^(b*c)
7^5^3
7^(5*3)
7^15
Describe how to find the sale price of an item that has been discounted 15%
solve this to get brainiest
Answer:
1 a. commutative property of multiplication
b. distributive property of multiplication
2 x=23\12
-x = -23\12
-23\12+23\12=0
thus -(-x)+x
Answer:
See below ↓
Step-by-step explanation:
1.
a) commutative propertyb) commutative property2.
Given : x = 23/12To verify = -(-x) = x⇒ -(-(23/12)) ⇒ -1 x -1 x 23/12⇒ 1 x 23/12⇒ 23/12⇒ VerifiedAlexandra deposited $1,000 in
a savings account
Her
savings account pays 3.5% simple
interest. How much interest will the
account earn in 5 years?
My answers are
A. 35.00
B. 145.00
C . 175.00
D . Not here
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (1000)(0.035)(5)\implies I=175[/tex]
The cone shaped roof has the height of 30ft and the radius of 15ft find it's lateral area and the surface area
Answer:
Lateral surface area of cone is 1580 feet²Surface area of cone is 2287 feet²[tex]\\[/tex]
Step-by-step explanation:
Given that Height of cone shaped roof is 30 ft and radius is 15 ft.
To calculate the lateral surface area and Surface area of the cone we will use the formula given below:
[tex]\\[/tex]
[tex]\star \: { \underline { \boxed { \purple{ \pmb { \sf{Lateral \: surface \: Area _{(cone)} = \pi rl}}}}}}[/tex]
[tex]\\[/tex]
[tex]\star{\underline{ \boxed{ \purple{ \pmb { \sf{Surface \: area _{(cone)} = \pi rl + \pi {r}^{2} }}}}}}[/tex]
[tex]\\[/tex]
Finding the Slant height of the cone:
[tex]\dashrightarrow \: \:L = \sqrt{ {(r)}^{2} + {(h)}^{2} } \\ [/tex]
[tex] \dashrightarrow \: \: L = \sqrt{225 +900 } \\ [/tex]
[tex] \dashrightarrow \: \: L = \sqrt{1125 } \\ [/tex]
[tex]{ \dashrightarrow \: \: { \pink{ \boxed { \: L = 33.541 }}}}\\ [/tex]
Hence, Slant height of cone is 33.54 feet.Substituting values in above formula:
[tex]\dashrightarrow \: \: LSA = \pi rl \\ [/tex]
[tex]\dashrightarrow \: \: LSA = \dfrac{22}{7} \times 15 \times 33.54 \\ [/tex]
[tex]\dashrightarrow \: \: LSA = \dfrac{22 \times 15 \times 33054}{7} \\ [/tex]
[tex]\dashrightarrow \: \: LSA = \dfrac{11068.2}{7} \\ [/tex]
[tex]\dashrightarrow \: \:{ \boxed { \pmb{ \sf {\pink{ LSA \: \approx1580 \: {ft}^{2}}}} }} \\ [/tex]
[tex]\\[/tex]
Hence, Lateral surface area of cone is 1580 feet²
Now, Calculating surface area:
[tex]\dashrightarrow \: \:SA = \pi rl + \pi {r}^{2} \\ [/tex]
[tex]\dashrightarrow \: \:SA = \pi (15)(33.54) + \pi {(15)}^{2} \\ [/tex]
[tex]\dashrightarrow \: \:SA = \pi(503.1) + 22 5 \pi \\ [/tex]
[tex]\dashrightarrow \: \: SA = 728.1 \pi \\ [/tex]
[tex]\dashrightarrow \: \:SA = 728.1 \times 3.14 \\ [/tex]
[tex]\dashrightarrow \: \:{ \boxed{ \pmb{ \pink{ \sf{SA \approx2287 \: {ft}^{2} }}}}} [/tex]
[tex]\\[/tex]
Hence, surface area of cone is 2287 feet²How to write the slope intercept equation for points of (6,0) and (0,-5)?
Answer:
[tex]y=\frac{5}{6} x -5[/tex]
Step-by-step explanation:
Hi there!
We are given the points (6,0) and (0, -5), and we want to write the equation of the line containing those points in slope-intercept form
Slope-intercept form can be written as y=mx+b, where m is the slope and b is the y intercept
First, we need to find the slope of the line
The formula for the slope can be written as [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We have everything we need to find the slope, but let's label the points to avoid confusion
[tex]x_1=6\\y_1=0\\x_2=0\\y_2=-5[/tex]
Now substitute these values into the formula
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-5-0}{0-6}[/tex]
Subtract
m=[tex]\frac{-5}{-6}[/tex]
Simplify
m=[tex]\frac{5}{6}[/tex]
The slope of the line is 5/6
Let's plug this value into the formula for the equation of the line in slope-intercept form.
We substitute 5/6 for m in y=mx+b:
y=[tex]\frac{5}{6}x+b[/tex]
Now we need to find b
As stated before, b is the y intercept, which is the value where the line hits the y axis. The value of x at the y intercept is 0.
One of the points we were given is actually the y intercept; that point is (0, -5); notice how the value of x in this point is 0
The value of b is the value of y in this point, which is -5 in this case.
Substitute -5 as b in the formula.
[tex]y=\frac{5}{6} x -5[/tex]
Hope this helps!
See more on this subject here (n.b. the answer uses a different way of solving): https://brainly.com/question/20891204