As per my explanation to (b) above, the largest number of primes that could factor such a number is 4.
Note that 2,3,5 and 7 are the smallest primes, then use the reasoning from
(b) above. we are looking for four exponents, that, when 1 is added to each and all are multiplied together, would equal 20.
But no such integers k, l, m, and n exist such that (k + 1)(l + 1)(m + 1) (n + 1) = 20 where k, l,m, and n ≥ 1 so this number, whatever it is, can't have 4 prime factors
Let's drop 7 out of the mix and suppose it has just 3 prime factors 2, 3, and 5 again we are looking for three exponents, that, when 1 is added to each and all are multiplied together, would equal 20. Put another way, we are looking for k, l and m ≥ 1 such that (k + 1)(l + 1)(m + 1) = 20
Note that the only possibility here is when we have 2 *2 *5 = 20 and the smallest possible product would be 2^(4 )* 3^(1) * 5^(1) = 2^4 * 3 * 5 = 240
Now......the only remaining possibility is that this number is composed of the two smallest primes, 2 and 3, and we are looking for some k and l ≥ 1 such that (k + 1)(l + 1) = 20 clearly, the only possibilities are when k = 4 and l = 5, or vice-versa
So this number would factor as either 2^3 * 3^4 = 648 or 2^4 * 3^3 = 432 and both are > 240.
Learn more about positive integers at
https://brainly.com/question/1367050
#SPJ4
Todd is attempting to predict how much money his furniture company will make based on the amount raw materials the company currently has at its disposal. The average profit from the sale of 1 piece of furniture can be expressed 2x-2 as and the average number of pieces of furniture that can be made using the current supply of raw materials can be expressed as 2x-2. What polynomial function can Todd use to calculate the average profit
Answer:
[tex]4x^{2} -8x+4[/tex]
Step-by-step explanation:
The average profit expression is for 1 piece of furniture
The amount of furniture is another expression
So we have to multiply both expressions to get the total profit.
(2x-2) (2x-2) = 4x^2 - 4x - 4x + 4
= 4x^2 - 8x + 4
Please help I’ve tried to answer this 3 times and I keep getting it wrong
Answer:
[tex] \boxed{\bf A. \: x - 2}[/tex]
Step-by-step explanation:
[tex] \sf ( x + 1)^2-9/ x + 4 [/tex]
First, we need to factor the expressions that are not already factored.
[tex] \sf ( x - 2) ( x + 4) / x + 4 [/tex]Now, let's Cancel out x+4 in both numerator and denominator.
[tex] \sf x - 2 [/tex]----------------------------
Solve the following equation:
(d - 3) tan 37°
17
Give your answer to 1 d.p.
-
Answer: 25.6
Step-by-step explanation:
[tex](d-3) \tan 37^{\circ}=17\\\\d-7=\frac{17}{\tan 37^{\circ}}\\\\d=\frac{17}{\tan 37^{\circ}}+3 \approx \boxed{25.6}[/tex]
(2, -7) and (4, -13)
Answer:
-14 or (6,20)
Which statements accurately describe the function f(x) = 3(18)"? Select three options.
The domain is all real numbers.
The range is y> 3.
The initial value is 3.
The initial value is 9.
The simplified base is 3√2.
The initial value of the function f(x) = 3(18)ˣ is 3. The domain of the function is all real numbers and the range is y > 0
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the function f(x) = 3(18)ˣ, hence:
The initial value of the function f(x) = 3(18)ˣ is 3. The domain of the function is all real numbers and the range is y > 0
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
Help fast. i really need help fast
Answer: 80 miles
Step-by-step explanation:
- 400/5 = 80
- so 80 is 1/5 of 400
hope this helps :)
Answer:
80 miles
Step-by-step explanation:
The whole journey is 400 miles, so we say that he traveled x miles, where x equals 400.
if we multiple 1/5 by x miles, then we will get how much he travels
1/5*x = 1/5*(400), since x = 400, so you can replace x with 400
1/5*x=1/5*400=400/5=80 miles
what is the slope of the line shown below
Answer:
A. -3
Step-by-step explanation:
Use slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
Use the points given, (-1, 6) and (2,-3)
[tex]\frac{-3-6}{2+1}=\frac{-9}{3}[/tex]
Simplify the answer.
[tex]\frac{-9}{3}=-3[/tex]
The slope of the line is -3.
Hope this helps!
If not, I am sorry.
five times Linda’s age is 85
Geometry question I’m confused with this help
Answer: ∠PQR = 130°
Step-by-step explanation:
The word bisects means that angle PQS and SQR are equal to each other.
3x + 5 = 2x + 25
3x = 20
x = 20
Now, we will plug this value back in and solve for angle PQR. There are three ways we could do this.
[1]
(3x + 5) + (2x + 25)
(3(20) + 5) + (2(20) + 25)
(60 + 5) + (40 + 25)
(65) + (65)
130 degrees
[2]
(3x + 5) * 2
(3(20) + 5) * 2
(65) * 2
130 degrees
[3]
(2x + 25) * 2
(2(20) + 25) * 2
(65) * 2
130 degrees
How many liters are in 21 cups
Answer:
4.968
Step-by-step explanation:
bc yes
How many 50c make up $200
Answer:
40. 50c goes into 200 40 times
What function does this graph represent? f(x) 6 -4 -2 = 6- 4 2- A -6 lo 2 OA. f(x) = -3(x - 2)² + 4 OB. f(x) 3(x + 2)² + 4 Oc. f(x) = 3(x - 2)² + 4 OD. f(x) = -3(x + 2)² + 4
This graph represents Option D = [tex]-3(x+2)^{2} + 4[/tex]
As the given figure is a parabola, it will have quadratic equation because the general equation of parabola corresponds to [tex]x^{2} = 4ay[/tex] which has highest power of the variable equals to 2, thus its a quadratic equation.
The maximum value of a quadratic equation [tex]ax^{2} + b x +c[/tex] is at points
[tex](-b/2a, c-\frac{b^{2} }{4a} )[/tex]
By looking at the graph we can observe the point at which the graph has achieved maxima is (-2,4).
∴ ([tex]-b/2a = -2[/tex] , [tex]c-\frac{b^{2} }{4a} = 4[/tex]
The coefficient of [tex]x^2[/tex] should be negative the graph opens downwards.
∴ Option B and C are eliminated.
On putting x = -2 only option D yields 4.
Thus this graph represents Option D = [tex]-3(x+2)^{2} + 4[/tex]
Learn more about quadratic equation here :
https://brainly.com/question/17177510
#SPJ1
Jackson has a gift card for $120 to use at a department store. he wants to purchase 2 shirts and 3 pairs of pants with his gift card. if x represents the cost of the shirts and y represents the cost of the pants, what are the domain and range of this relationship?
0 ≤ x ≤ 60
The range of this relationship can be defined as,0 ≤ y ≤ 40
Definition of Domain and Range
The set of all the possible input values for which the provided function is defined is termed as the domain of that function.
The set of all the possible values that a given function can generate as an output is termed as the range of that function.
Forming the Relation
It is given that,
Jackson wants to purchase 2 shirts and 3 pairs of pants with his gift cardx represents the cost of the shirts and y represents the cost of the pantsThe limit of the gift card = $120Thus, the relation formed is given by,
[tex]2x + 3y \leq 120[/tex]
Domain and Range of the Given Relation
We have,
[tex]2x + 3y \leq 120[/tex]
⇒ [tex]2x \leq 120[/tex]
⇒ [tex]x\leq60[/tex]
Thus, the domain is given by,
⇒ [tex]0\leq x\leq 60[/tex]
Similarly,
[tex]3y\leq 120[/tex]
⇒ [tex]y\leq 40[/tex]
Thus, the range is given by,
⇒ [tex]0\leq y\leq 40[/tex]
Learn more about domain and range here:
https://brainly.com/question/1632425
#SPJ4
The perimeter of a square field is 336 yards. How long is each side?
Question:
The perimeter of a square field is 336 yd. How long is each side?
Answer:
1,344 yd
The actual half-life of amoxicillin is about 62 minutes. Recall that half-life is the amount of time it takes for a substance to decay to half of its original amount. How long after Haidar gives Aldi his last dose of medication will it take before the amount of medication in Aldi's bloodstream is effectively 0? Describe how you determined your solving method.
Using an exponential function, it would take 824 minutes before the amount of medication in Aldi's bloodstream is effectively 0.
How to determine the timeA decaying exponential function is given as;
[tex]A(t) = A(0)e^-kt[/tex]
Where A = initial value
k = decay constant
We have the half-life of amoxicillin as 62minutes, to determine k, we get
[tex]A(62) = 0. 5(0)[/tex]
[tex]A(62) = 0.5A(0)[/tex]
[tex]0. 5A(0) = A(0) e^{-62k}[/tex]
Solve the exponential function thus
[tex]e^{-62k} = 0. 5[/tex]
㏑ [tex]e^{-62k}[/tex] = ㏑ 0. 5
- 62k = ㏑ 0.5
Make k subject of formula
k = -㏑[tex]\frac{0. 5}{62}[/tex]
k = 0. 011179
The equation is given by
[tex]A(t) = A(0)e^-0.011179[/tex]
We have
[tex]0. 0001A(0) = A(0)e^-0.01179[/tex]
[tex]e^-0.011179t = 0. 0001[/tex]
㏑ [tex]e^-0.011179[/tex] = ㏑ 0.0001
[tex]-0.011179t = In 0.0001[/tex]
t = [tex]-\frac{In 0. 0001}{0. 011179}[/tex]
t = [tex]824[/tex]
Therefore, it would take 824 minutes before the amount of medication in Aldi's bloodstream is effectively 0.
Learn more about half-life here:
https://brainly.com/question/26148784
#SPJ1
The Surface Area of a square pyramid is 3600 ft2. The slant height is 80 feet and the base is 20 feet. At most how many 1 foot cubic blocks can be stuffed in the pyramid?
(*Some of the blocks might have to be cut up to fit into crevices*)
The number of 1 foot cubic blocks that can be stuffed in the pyramid are; 10,583 cubes
How to find the surface area of a Pyramid?The equation for the surface area of a square pyramid is;
Surface area = A + 1/2·p·s
where;
A = area of base
p = perimeter
s = slant height
The volume of the pyramid = (1/3) × A × h
Where:
A = Area of the base = 20 × 20 = 400 ft²
h = The height of the pyramid = √((slant height)² - ((base side length)/2)²)
h = √(80² - (20/2)²) = 30√7
The volume of the pyramid = 1/3*400*30·√7 = 4000·√7 ft³ = 10,583.005 ft³
If the cubes are flexible, then there are approximately 10,583 cubes
For rigid cubes we have;
Given that the height of the pyramid = 30·√7
The slope of the pyramid = (30/10)√7 = 3·√7
A increase in height of 1 foot gives a reduction in width of 2/(3√7)
The bottom can hold 400 cubes, Then next layer can hold;
19 × 19 = 361
If we continue to iterate, we will get a total of approximately 9915 rigid cubes in the pyramid.
Read more about Pyramid Surface Area at; https://brainly.com/question/22744289
#SPJ1
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O A is 3. The length of A A prime is 9.
Triangle ABC is dilated to create triangle A'B'C' using point O as the center of dilation.
What is the scale factor of the dilation?
One-third
3
4
One-fourth
The scale factor of the dilation shown in the image is: C. 4.
How to Find the Scale Factor of Dilation?Scale factor = New dimension/corresponding old dimension.
From the image given, we have:
Scale factor = OA'/OA
OA' = 3 + 9 = 12 units
OA = 3 units
Scale factor of dilation = 12 units/3 units
Scale factor of dilation = 4
Learn more about the scale factor on:
https://brainly.com/question/2826496
#SPJ1
C. 4
Next one is 6 if you have the option on edge
a circular field was fenced using 66 posts placed two metres apart what is the area of the field in square metres
Answer:
1386m cubic
Step-by-step explanation:
hope it helps.in case of any other question, you can count on me.good day.
The area of the circular field in square meters will be equal to, 1386 m².
What is the area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass a compact figure's surface. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.
As per the given information in the question,
Total number of posts = 66
Distance between two posts = 2 meters
Then, the circumference of the area will be,
= 66 × 2 = 132 meters
Now, let's find the radius of the circle,
C = 2πr
132 = 2 × 3.14 × r
r = 132/(2 × 3.14)
r = 21.01 m
Use the formula for the area of the circle:
A = πr²
A = 3.14 × (21.01)²
A = 441.420 × 3.14
A = 1386 m²
To know more about the area:
https://brainly.com/question/27683633
#SPJ2
In the following exercises, multiply the binomials. Use any method.
249. (6p + 5)(p + 1)
Answer:
Hence the expression [tex]$$(6p+5)(p+1)=6p^2+11p+5$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (6p+5)(p+1).We have to multiply the given expression.Multiply the (6p+5) by 1 , multiply the (6p+5) by p then add like terms.[tex]$$\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ \times & {} & p & + & 1 \\ \end{matrix}}[/tex]
_____________
[tex]{\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ 6{{p}^2} & + & 5p & {} & {} \\ \end{matrix}}{\begin{matrix}6{{p}^2} & + & 11p & + & 5 \\ \end{matrix}}}$$[/tex]
PLEASE I NEED THIS
SO MANY POINTS
The speed of Sali is 18.75 km/hr.
Given,
Total distance travelled by Jane and Sali =63 km.
The total time is taken by Jane=3.5 hours.
Sali started to cycle 4 minutes after Jane started to cycle [tex]=\frac{4}{60}=\frac{1}{15}[/tex] hours.
What is the formula to find speed?The formula to find speed is [tex]Speed=\frac{Distance}{Time} \ km/hr[/tex].
The speed of Jane[tex]=\frac{63}{3.5}=18 \ km/hr[/tex].
Let the speed of Sali be [tex]x \ km/hr[/tex].
Sali caught up with Jane when they had both cycled 30 km.
Thus, [tex]\frac{30}{18}-\frac{30}{x}=\frac{1}{15}[/tex]
[tex]\implies \ \frac{30x-540}{18x} =\frac{1}{15}[/tex]
[tex]\implies \ 15(30x-540)=18x[/tex]
[tex]\implies \ 5(30x-540)=6x[/tex]
[tex]\implies \ 150x-2700=6x[/tex]
[tex]\implies \ 144x=2700\implies \ x=18.75[/tex]
Therefore, the speed of Sali is 18.75 km/hr.
To learn more about the speed visit:
https://brainly.com/question/7359669.
#SPJ1
Given that
5,6,-2,4,8,1,1,1,1,1
• find the mean
mode
median
Answer:
mean: 2.6, mode: 1, median: 1
Step-by-step explanation:
The mean is essentially the average of the data set which can be defined as: [tex]\frac{\text{sum of data set}}{\text{amount of data in data set}}[/tex]. So adding all the values together you get: [tex]26[/tex]. and counting all the numbers in the data set you find the data set has 10 numbers. This gives you the equation: [tex]\frac{26}{10} = 2.6[/tex] which is the mean
To find the mode, you find which number occurs most frequently, this is of course 1, which can really be determined by just looking at the data set for a second. all the other numbers only occur once, while 1 is in the data set 5 times. So 5 is the mode
To find the median you sort the data, from min to max, and then find the middle number. Sorting the data set gives you. -2, 1, 1, 1, 1, 1, 4, 5, 6, 8. Since this data set has an even amount of numbers, there is not going to be an exact middle. If you go the "middle" which is the 5th and 6th number, you add these two numbers and divide the sum by 2. This gives you: (1+1)/2 = 1 So the median is 1
Use the drawing tool(s) to form the correct answer on the provided number line.
Evaluate the following expression when a = 5 and b = 1. Then, plot the resulting value on the provided number line.
12+[2-(4·a²)] ÷ 7+b
Answer:
1
Step-by-step explanation:
12+[2-(4 × a²)] ÷ 7+b
= 12+[2-(4 × 5²)] ÷ 7+ 1
= 12+[2-(4 × 25)] ÷ 7+ 1
= 12 + (2 - 100)÷ 7 + 1
= 12 - 98 ÷ 7 + 1
= 12 - 14 + 1
= 1
Answer:
-1
Step-by-step explanation:
PROBLABILITY!!!
(I added the picture needed)
1.Create a sample space and find the product of each combination. What is the probability that a person wins the game? Express your answer as a fraction in lowest terms and as a percent rounded to the nearest tenth.
(answer to this one is 9/28 and 32.1%)
2. You realize a short time into the carnival that you don’t have enough prizes to last the entire event. You call your teacher, and she suggests that you change the winning number so that a participant will win only 25% of the time. What number will that be? Support your answer.
3. Participants achieving a winning score of 36 or higher in four consecutive attempts will receive a large prize! What is the probability of this occurring?
4. After changing the game rules, participants and the crowd are disappointed when the first five games yield scores of 12, 18, 30, 28, and 24. What statement can you recommend the teacher posts to reassure everyone that the game is fair?
The probability that a person wins the game is 32.1%
How to illustrate the probability?Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.
Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:
= 24 + 4 = 28
The frequency table will be such that 28 or more has a relative frequency of 9. Therefore, the probability that a person wins the game will be:
= 9/28 = 32.1%
When you win 25% of the time, this illustrates that the number of products picked will be:
= 25% × 28
= 7 products.
The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:
= 1/6⁴
= 1/1296
Learn more about probability on:
brainly.com/28021921
#SPJ1
If −1 is a zero of the polynomial p(x)=ax^3−x^2+x+4, find the value of a.
Answer:
a = 2
Step-by-step explanation:
given x = - 1 is a zero then f(- 1) = 0 , that is
a(- 1)³ - (- 1)² - 1 + 4 = 0
- a - 1 - 1 + 4 = 0
- a + 2 = 0 ( subtract 2 from both sides )
- a = - 2 ( multiply both sides by - 1 )
a = 2
X=
Help mea please thank u :)
The value of x is the length GH, which is determined as 6.
Value of xThe value of x is the length GH and can be calculated from Pythagoras theorem.
|OG|² = |OS|² + |SG|²
|OG|² = 9² + 12²
|OG|² = 225
|OG| = √225
|OG| = 15
x + H = |OG|
where;
H is radius of the circle = 9x + 9 = 15
x = 15 - 9
x = 6
Learn more about Pythagoras theorem here: https://brainly.com/question/343682
#SPJ1
what is something you do that can be set up as a two- step equation? how would you set that up as an equation to explain to someone else how it can be solved?
What you can do that can be set up as a two- step equation is to follow the form which is [tex]ax + b = c[/tex] and should be noted that a, b, c are real numbers.
Two- step equation can be solved by following these
Perform the Simplification by getting rid of all brackets and parenthesis. perform Addition or subtraction to isolate the variable.Simplify to determine the value of the variable.Perform verification through substituting of answers in the given equation.What is two- step equation?Two step equations serves as algebraic equations which can be solved in exactly two steps to get the final value of the variable .
Example of this is [tex]2x + 3 = 7.[/tex]
Learn more about two- step equation at:
https://brainly.com/question/2972832
determine intervals when the graph is concave up or concave down
The graph is concave has two curved part as follows;
The graph is concave up between;(0, 1), and (1, 0)The graph is concave down between; (0, 1), and (-a, 2)How can the direction of concavity be found?The direction the concave part of the graph faces is given as follows;
The graph is concave up when the concave part faces up
It is concave down when the concave part faces down
From the given diagram, we have;
The graph is concave up between;
(0, 1), and (1, 0)
The graph is concave down between; (0, 1), and (-a, 2)
Where a is in the range; 1 < a < 2
Learn more about graphs here:https://brainly.com/question/17136458
#SPJ1
Using the unique pythagorean triple 5 12 13 as a guide, what is the missing number from the triple x, 48, 52?
The missing number from the triplet x, 48, 52, using the triplet 5, 12, 13, is found to be 5.
The Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is always equal to the sum of the squares of the other two legs.
If the hypotenuse is taken as a, and the two legs are taken as b and c, then by the Pythagoras Theorem, we can write that:
a² = b² + c².
A Pythagoras triplet, is the combination of c, b, and a.
If all three sides of a right triangle are multiplied by the same quantity, we get another right triangle, where the sides of both make Pythagoras Triplet.
In the question, we are given a unique triplet: 5,12, 13, and are asked to find x in x, 48, 52.
We divide the second triplet by the first one, to get:
x/5, 48/12, 52/13,
or, x/5, 4, 4.
The ratio of the two triplets will always be a constant, thus
x/5 = 4,
or, x = 5*4 = 20.
Thus, the missing number from the triplet x, 48, 52, using the triplet 5, 12, 13, is found to be 5.
Learn more about the Pythagoras Theorem at
https://brainly.com/question/231802
#SPJ4
What term in the sequence is the value 107?
Answer:
17th term
Step-by-step explanation:
Substitute [tex]a_{n}[/tex] with the value 107
107=11+6(n-1)
96=6n-6
102=6n
n=17
17th term !!
Hope it helps!
What is the solution of √x+ 12 =
= x?
O x = -3
O x = 4
O x = -3 or x = 4
Ono solution
PLEASE HELP
Answer:
x₁ = 4
(x₂ = -3)
Step-by-step explanation:
√(x + 12) = x
x + 12 = x²
x² - x - 12 = 0
Δ = 49
x = (1 ±√Δ)/2
x₁ = 4
x₂ = -3
the right solution is 4 this can be seen by inserting the solutions found in the starting equation