Answers
P.S I did the math by using PEMDAS
Related Questions
Let be the set of permutations of whose first term is a prime. If we choose a permutation at random from , what is the probability that the third term is equal to
Answers
Answer:
[tex]Pr = \frac{1}{6}[/tex]
Step-by-step explanation:
Given
[tex]S = \{1,2,3,4,5\}[/tex]
[tex]n = 5[/tex]
Required
Probability the third term is 3
First, we calculate the possible set.
The first must be prime (i.e. 2, 3 and 5) --- 3 numbers
[tex]2nd \to 4\ numbers[/tex]
[tex]3rd \to 3\ numbers[/tex]
[tex]4th \to 2\ numbers[/tex]
[tex]5th \to 1\ number[/tex]
So, the number of set is:
[tex]S = 3 * 4 * 3 * 2 * 1[/tex]
[tex]S = 72[/tex]
Next, the number of sets if the third term must be 2
[tex]1st \to 2[/tex] i.e. 1 or 5
[tex]2nd \to 3\ numbers[/tex] ---- i.e. remove the already selected first term and the 3rd the compulsory third term
[tex]3rd \to 1\ number[/tex] i.e. the digit 2
[tex]4th \to 2\ numbers[/tex]
[tex]5th \to 1\ number[/tex]
So
[tex]r = 2 * 3 * 1 * 2 * 1[/tex]
[tex]r = 12[/tex]
So, the probability is:
[tex]Pr = \frac{r}{S}[/tex]
[tex]Pr = \frac{12}{72}[/tex]
[tex]Pr = \frac{1}{6}[/tex]
Find the sum of the series -11 - 3 + 5 + 13 + ... + 125 using the series formula.
Answers
Answer:
1026
Step-by-step explanation:
Common difference = d = 2nd term - first term
d = -3 - (-11) = -3 +11 = 8
First term = a = -11
First we need to find the number of terms in this series
[tex]a_{n} = 125\\\\a + (n- 1)d = a_{n}\\\\[/tex]
-11 + (n- 1) * 8 = 125
(n-1)*8 = 125 + 11
(n-1) * 8 = 136
n -1 = 136/8
n -1 = 17
n = 17+1
n = 18
[tex]S_{n} =\frac{n}{2}(a+a_{n})\\\\S_{18} =\frac{18}{2}(-11+125)\\\\[/tex]
= 9 * 114
= 1026
What is the exact value of tan (9 pi)/12
Answers
Answer:
tan(9pi/12) = 0.041146549
Step-by-step explanation:
Find the measure of the indicated angle
Answers
Answer:
yes
Step-by-step explanation:
Step-by-step explanation:
Hey there! I’m not fully sure because I don’t do geometry shapes of finding x angles but this is how I got x.
The left and bottom bases are the same. Let’s say that A will be the top point of the triangle b will be the bottom left corner angle and c would be in the bottom right corner. We can already see that ∠AB = ∠BC. Because we can see that one line between them. so that means 52* = A angle because of the side length
52 + 52 = 104
180 = total
104 = among angles (we know)
180 - 104 = 76
x = 76
Pick the correct graph and equation pleasee!
Answers
Given:
Amount of flour in a bin = 30 cups
Flour required for each signature cake = [tex]1\dfrac{1}{2}[/tex] cups
To find:
The correct equation and graph for the given situation.
Solution:
Let F be the amount of flour in the bin and c be the number of signature cakes.
Flour required for each signature cake = [tex]1\dfrac{1}{2}[/tex] cups
Flour required for each signature cake = [tex]1.5[/tex] cups
Flour required for c signature cakes = [tex]1.5c[/tex] cups
Amount of flour in a bin is 30 cups and it is reduced by 1.5c cups. So, the amount of flour in the bin is:
[tex]F=30-1.5c[/tex]
At [tex]c=0[/tex], we get
[tex]F=30-1.5(0)[/tex]
[tex]F=30[/tex]
At [tex]F=0[/tex], we get
[tex]0=30-1.5c[/tex]
[tex]1.5c=30[/tex]
[tex]c=\dfrac{30}{1.5}[/tex]
[tex]c=20[/tex]
Therefore, the required equation is [tex]F=30-1.5c[/tex] and the 4th graph is correct.
10 y is directly proportional to the cube of x. Given that y = 1512 when x = 6, find the equation for the y in terms of x.
Answers
Answer:
[tex]{ \tt{y \: \alpha \: {x}^{3} }} \\ { \tt{y = k {x}^{3} }} \\ { \bf{k \: is \: a \: proportionality \: constant}} \\ { \tt{1512 = (k \times {6}^{3}) }} \\ { \tt{k = 7}} \\ { \boxed{ \bf{y = 7 {x}^{3} }}}[/tex]
Here are the first five terms of a sequence. 4, 11, 22, 37, 56 Find an expression, in terms of , for the th term of this sequence.
Answers
Answer:
[tex] a_n = 2n^2 + n + 1 [/tex]
Step-by-step explanation:
4, 11, 22, 37, 56
11 - 4 = 7
22 - 11 = 11
37 - 22 = 15
56 - 37 = 19
After the first difference, 11 - 4 = 7, each difference is 4 more than the previous difference.
Difference of differences:
11 - 7 = 4
15 - 11 = 4
19 - 15 = 4
Since we need the difference of differences to find a constant, this must be a second degree function.
[tex] a_1 = 4 = 2^2 + 1(0)[/tex]
[tex] a_2 = 11 = 3^2 + 2 = 3^2 + 2(1) [/tex]
[tex] a_3 = 22 = 4^2 + 6 = 4^2 + 3(2) [/tex]
[tex] a_4 = 37 = 5^2 + 12 = 5^2 + 4(3) [/tex]
[tex]a_5 = 56 = 6^2 + 20 = 6^2 + 5(4)[/tex]
[tex] a_n = (n + 1)^2 + (n)(n - 1) [/tex]
[tex] a_n = (n + 1)^2 + (n)(n - 1) [/tex]
[tex] a_n = n^2 + 2n + 1 + n^2 - n [/tex]
[tex] a_n = 2n^2 + n + 1 [/tex]
Is the product of two prime numbers a prime number or a composite
number?
Answers
Step-by-step explanation:
No, the product of two (or more) prime numbers cannot result in another prime number. By definition, a prime number is a number that is divisible by 1 or itself - the act of multiplying two or more primes together will always yield a number divisible by 1, itself and the prime numbers multiplied together to achieve it.
Answer:
a composite one
Step-by-step explanation:
Why?
It is easy-peasy.
First, it is impossible to have a prime number. Because primes are only divisible by 1 and themselves.
For example, 3 is a prime. 7 is a prime. Multiply them and get 21.
I hope it helped:)
Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit but the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.
Answers
Answer:
there are 2 apples in the basket
there are 10 banana in the basket
Step-by-step explanation:
According to the Question,
We have, Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit.let x for apple And y for banana So, x+y=12---Equation 1
And, the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.Thus, 5x+7y=80 ----Equation 2
Now, (Equation 1) × 5 Subtract with (Equation 2) We get,
2y = 20 ⇒ y=10 (there are 10 banana in basket)
Put value of y=10 in Equation 2 we get5x+70=80 ⇔ x=2(there are 2 apples in basket)
Find x
Help me please
Answers
Answer:
19
Step-by-step explanation:
What is the volume of the rectangular prism below? ⊕
Answers
Answer:
32cm³ is the volume of the given rectangle.
Step-by-step explanation:
volume of rectangle=l×w×h
2×4×432cm³hope it helps
stay safe healthy and happy..Answer:
bro i go to your school
lol
Step-by-step explanation:
A school received 12 boxes of notebooks. Each box had 36 notebooks. How many total notebooks did the school receive?
Answers
Answer:
12x36
Step-by-step explanation:
Answer:
36*12 = 432
Step-by-step explanation:
Find the inverse of the function y = x2 – 12
Answers
Answer: [tex]y=\sqrt{x+12}[/tex]
Step-by-step explanation:
I hope you mean y = x² - 12 and not y = 2x - 12.
You switch the y and x variables:
x = y² - 12
And solve for y:
x + 12 = y²
[tex]y=\sqrt{x+12}[/tex]
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Answers
Answer:
The points lie INSIDE THE CIRCLE
hope it helps
have a nice day
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle .
Instructions: Find the missing angle in the image below. Do not include spaces in your answers
Answers
Answer:
15
Step-by-step explanation:
to find angle C, you subtract 50 from 180 which is 130. that means then you add 35 and 130 together which is 165. then subtract 180-165 which is 15.
The measure of the angle ∠BAC of the triangle ABC will be 15°.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In triangle ABC, the angle B is 35° and the exterior angle C is 50°.
The measure of the angle ∠BAC of the triangle ABC will be,
We know that the sum of any two interior angle of the triangle is equal to the third exterior angle of the triangle.
The sum of the angles ∠BAC and ∠ABC is equal to angle ∠BCF. Then the equation will be
∠BAC + ∠ABC = ∠BCF
∠BAC + 35° = 50°
∠BAC = 50° – 35°
∠BAC = 15°
Thus, the measure of the angle ∠BAC will be 15°.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ5
−3x−6+(−1)
need answer pls
Answers
Step-by-step explanation:
−3x−6+(−1)
-3x-7
Hope it helps youAnswer:
−3 −7
Step-by-step explanation:
-3x-6-1
-3x-7
lic/activity/6000001/assessment
1 Pretest: Unit 6
Question 1 of 21
What is the domain of the exponential function shown below?
Rx) = 5.3x
Answers
Given:
The exponential function is:
[tex]R(x)=(5.3)^x[/tex]
To find:
The domain of the given exponential function.
Solution:
We know that the general form of an exponential function is:
[tex]f(x)=ab^x[/tex]
Where, a is the initial value and b is growth/decay factor.
This function is defined for all real values of x, so the domain of these type of functions is the set of all real number.
We have,
[tex]R(x)=(5.3)^x[/tex]
Here, a is 1 and b is 5.3. This function is defined for all real values of x
Therefore, the domain of these type of functions is the set of all real number or it can be written as [tex](-\infty,\infty)[/tex].
simplify 3[(15-3)^2 + 4]
Answers
Answer:
444
Step-by-step explanation:
3 [ ( 15 - 3 )^2 + 4 ]
= 3 [ ( 15 - 3 )^2 + 4 ]
= 3 [ ( 12 )^2 + 4 ]
= 3 [ 144 + 4 ]
= 3 [ 148 ]
= 444
Step-by-step explanation:
3(15-3)²+4
3(12)²+4
3×144+4
432+4
436 Answer
1) Give 5 examples of a difference of two perfect squares
2) Give the factors of your examples
3) What do you call the factors of a difference of two perfect squares?
please help me
Answers
ᴀɴsᴡᴇʀ:
1.Example, x²-25 can be factored as (x+5)(x-5).
2.This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).
3.When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5).
ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs!
☞︎︎︎ᴄᴀʀʀʏ ᴏɴ ʟᴇᴀʀɴɪɴɢ☜︎︎︎
please help me it’s urgent
Answers
Answer:
600g of Flour
Step-by-step explanation:
According to the question every 15 biscuits is 50g it need 50g of sugar and flour is 3 times the amount it needs for 15 biscuits so 50*3=150 now we know 15 biscuits need 150g of flour so 30 requires 300 and 300g +300g is equal to 600g of flour.
Answer:
600 g of flour.
Step-by-step explanation:
If Deon needs 50 g of sugar to make 15 biscuits, and she is going to make 60 biscuits, then she will need 200 g of sugar, since 60/15 is 4.
If the amount of flour she needs is equal to the amount of sugar multiplied by three, or 3x, if x is the amount of sugar, then she will need 200 x 3 g of flour.
Therefore, she will need 600 g of flour.
what is the answer of this questoin 2c-3b+6+7b-2b+11?
Answers
Answer:
[tex]2c+2b+17[/tex]
Step-by-step explanation:
-----------------------
Given:
[tex]2c-3b+6+7b-2b+11[/tex]
---------->>>>
Collect like terms.
[tex]2c+(-3b+7b-2b)+(6+11)[/tex]
---------->>>>
Simplify
[tex]2c+2b+17[/tex]
------------------------
Hope this is helpful.
Answer:
2c-2b+17 if using algebra
Step-by-step explanation:
firstly group like terms 2c+(-3b)+7b-2b+6+11
2c-2b+17
evaluate f(3) if (x) = -4x+5
Answers
Answer:
-7
Step-by-step explanation:
(05.05 HC)The four points (−2, 5), (−2, −1), (5, −1), and (3, 5) are the vertices of a polygon. What is the area, in square units, of this polygon? 27 units2 33 units2 36 units2 51 units2
Answers
Answer:
Area = 36 squ. unit
Step-by-step explanation:
According to the Question,
Given That, The four points (−2, 5), (−2, −1), (5, −1), and (3, 5) are the vertices of a polygon. (Please find diagram in attachment)by using these points a quadrilateral is formed with two opposite sides 7 and 5 and with height 6 (Refer in the diagram).
Therefore, the area of this polygon isArea = 1/2 * (sum of opposite side) * height
Area = 1/2 * (7+5) * 6
Area = 3*12
Area = 36 squ. unit
Answer:
36
Step-by-step explanation:
Describe fully the single transformation that maps triangle A onto triangle B
Answers
Answer:there’s needs to be an image
Step-by-step explanation:
Find the value of x.
Answers
Answer:
The value of x is 18°
Step-by-step explanation:
Sum of the angles are 180°
3x+126=180
3x=180-126
3x=54
x=18
Answered by GAUTHMATH
A plane flies from Los Angeles west to Paradise Isle and returns. During both flights there is a steady upper air wind from the west at 80 mph. If the trip west to Paradise Isle took 17 hours and the return trip to Los Angeles took 13 hours, what was the plane's average airspeed?
Answers
Answer: [tex]589.33\ mph[/tex]
Step-by-step explanation:
Given
Trip form Los Angeles west to Paradise Isle took 17 hours and return trip took 13 hours.
Wind from west is 80 mph
Distance traveled is same in both the cases. During the first Journey, wind causes an upstream and for second half, it creates a downstream.
Suppose the speed of plane is
[tex]\Rightarrow (v-80)17=(v+80)13\\\Rightarrow 17v-1360=13v+1040\\\Rightarrow 4v=2400\\\Rightarrow v=600\ mph[/tex]
Suppose the distance is x
[tex]\Rightarrow x=(600-80)\times 17\\\Rightarrow x=520\times 17\\\Rightarrow x=8840\ \text{miles}[/tex]
Average speed is
[tex]\Rightarrow v_{avg}=\dfrac{x+x}{17+13}\\\\\Rightarrow v_{avg}=\dfrac{2\times 8840}{30}\\\\\Rightarrow v_{avg}=589.33\ mph[/tex]
Answer:
The speed of plane is 600 mph.
Step-by-step explanation:
Let the distance is d.
Speed of wind , u = 80 mph
Time, t = 17 hours
time, t'= 13 hours
Let the speed of airplane is v.
distance = speed x time
d = (v + u) x 13= (v - u) x 17
(v + 80) x 13 = (v - 80) x 17
13 v + 1040 = 17 v - 1360
4 v = 2400
v = 600 mph
How can Preena share 11 identical apples among 30 of her classmates evenly so that no apple is sliced into more than 10 pieces?
Answers
Answer:
Step-by-step explanation:
you can divide 11/30 and get 0.37
0.37%/ 100*11 =
Multiply:
0.37*11 =
add the 100 to the product you multiplied and divide them together:
4.07/100=
your quotient:
0.0407
round by 2 decimals:
0.04
your final answer is :
0.04
Write the number in standard notation. 9.07 x 10−2
Answers
Answer:
Yeah, so that is right, just put it into a formula.
[tex]9.07*10x^{-2}[/tex]
Simplify: 4y2 + 5y + 2 + 8y2 + 4y + 5.
Answers
Answer:
12y² + 9y + 7
General Formulas and Concepts:
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
4y² + 5y + 2 + 8y² + 4y + 5
Step 2: Simplify
Combine like terms (y²): 12y² + 5y + 2 + 4y + 5Combine like terms (y): 12y² + 9y + 2 + 5Combine like terms: 12y² + 9y + 7Answer:
12y² + 9y + 7
Step-by-step explanation:
4y² + 5y + 2 + 8y² + 4y + 5
Simplify :-
4y² + 5y + 2 + 8y² + 4y + 5
arranging like terms4y² + 8y² + 5y + 4y + 2 + 5
Combine like terms12y² + 9y + 7
Someone please help me with this math problem? !!
Answers
Answer:
x = -1
Step-by-step explanation:
If you input -1 to both functions, you get 3.
