power 121.three consecutive prime numbers, each less than $100$, have a sum that is a multiple of $5$. what is the greatest possible sum?
Answers
The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.
We have,
To find the three consecutive prime numbers with a sum that is a multiple of 5 and each less than 100, start by listing the prime numbers less than 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Check each combination:
(2, 3, 5): Sum = 2 + 3 + 5 = 10 (which is a multiple of 5)
(3, 5, 7): Sum = 3 + 5 + 7 = 15 (which is a multiple of 5)
(5, 7, 11): Sum = 5 + 7 + 11 = 23 (not a multiple of 5)
(7, 11, 13): Sum = 7 + 11 + 13 = 31 (not a multiple of 5)
(11, 13, 17): Sum = 11 + 13 + 17 = 41 (not a multiple of 5)
(13, 17, 19): Sum = 13 + 17 + 19 = 49 (which is not a multiple of 5)
(17, 19, 23): Sum = 17 + 19 + 23 = 59 (not a multiple of 5)
(19, 23, 29): Sum = 19 + 23 + 29 = 71 (not a multiple of 5)
(23, 29, 31): Sum = 23 + 29 + 31 = 83 (not a multiple of 5)
(29, 31, 37): Sum = 29 + 31 + 37 = 97 (not a multiple of 5)
(31, 37, 41): Sum = 31 + 37 + 41 = 109 (which is not a multiple of 5)
(37, 41, 43): Sum = 37 + 41 + 43 = 121 (which is not a multiple of 5)
(41, 43, 47): Sum = 41 + 43 + 47 = 131 (not a multiple of 5)
(43, 47, 53): Sum = 43 + 47 + 53 = 143 (which is not a multiple of 5)
(47, 53, 59): Sum = 47 + 53 + 59 = 159 (which is not a multiple of 5)
(53, 59, 61): Sum = 53 + 59 + 61 = 173 (not a multiple of 5)
(59, 61, 67): Sum = 59 + 61 + 67 = 187 (not a multiple of 5)
(61, 67, 71): Sum = 61 + 67 + 71 = 199 (not a multiple of 5)
(67, 71, 73): Sum = 67 + 71 + 73 = 211 (not a multiple of 5)
(71, 73, 79): Sum = 71 + 73 + 79 = 223 (not a multiple of 5)
(73, 79, 83): Sum = 73 + 79 + 83 = 235 (which is a multiple of 5)
(79, 83, 89): Sum = 79 + 83 + 89 = 251 (not a multiple of 5)
(83, 89, 97): Sum = 83 + 89 + 97 = 269 (not a multiple of 5)
Thus,
The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.
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Related Questions
Simplify the expression:
4 + 4f2 + 6f - 6f
Answers
Answer:
4f^2 +4
Step-by-step explanation:
4 + 4f^2 + 6f - 6f
Combine like terms
4f^2 +4
3/20 of a number is what percentage
Answers
Answer:
The answer is 15%
Step-by-step explanation:
Hope that helps.
which properties can be used to solve 7y-15=-29? select all that apply.
a. identity property of multiplication
b. addition property of equality
c. distributive property
d. inverse property of multiplication
e. commutative property of addition
Answers
Answer:
e d and b
Step-by-step explanation:
just trust me
Graph the following features: Y intercept = -3 Slope = 4/5
Answers
The equation of line where the y intercept is -3 and slope is 4/5 is
y = ( 4/5 )x - 3
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the equation A is y = mx + b
The y intercept of the line b = -3
The value of b = -3
The slope of the line m = 4/5
The value of m = 4/5
Now , substituting the values in the equation of line , we get
y = mx + b
y = ( 4/5 )x + ( -3 )
y = ( 4/5 )x - 3
The graph of the equation y = ( 4/5 )x - 3 is given below
Therefore, the value of the equation of line A is y = ( 4/5 )x - 3
Hence , The equation of line where the y intercept is -3 and slope is 4/5 is
y = ( 4/5 )x - 3
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Which function has zeros at x = -2 and x = 5?
O f(x) = x2 + 2x - 10
• f(x) = x2 - 2x - 10
O f(x) = X2 + 3x - 10
® f(x) = x2 - 3x - 10
Answers
Answer:
f(x)=x²-3x-10
Step-by-step explanation:
\(f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5\)
therefore the zeros of the equation are x₁=-2,x₂=5
Find the value of k in the diagram below.
Give your answer in degrees (°).
174°
k
k
Not drawn accurately
Answers
The measure of angle k from the given figure is 58 degree.
From the given figure, we have angle of sector = 174°.
An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
Here, k+k+k=174° (Angle in equal sectors)
3k=174°
k=174°/3
k=58°
Therefore, the measure of angle k from the given figure is 58 degree.
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If you’re super bored and not dry click here!
Answers
Answer:
........
Step-by-step explanation:
A parking garage charges a 3.50$ base fee plus an hourly rate of 7.00$. If you have at most 21.50$ to pay for parking, how long can you park?
Answers
Answer:
You get a total of two hours of parking.
Step-by-step explanation:
First, you subtract the base fee of $3.50, which gives you $18.00. Then you subtract as many sevens there are in 18, which is two. And then your answer is shown, as two. Hope this helps!
please answer asap!!
The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12).
The equation of the parabola is y= (blank)x^2 + (blank)x + (blank)
Answers
Answer:
-5
Step-by-step explanation:
how to find the state of degrees in 8x+3?
Answers
8x+3
The degree of first term = 8x = 1 (bcz the power of x is 1 )
The degree of second term =3=1 (bcz its power is also 1 )
Hence the degree of the given term is = 1 bcz the highest power is 1.
Hope this helps !
Please mark it as the brainliest <3
1) How many words consisting of 4 letters can be formed from the letters in the word CHAIR if
i) there is no restriction
ii) the word contains the letter H in the first place
Answers
We are given the word "CHAIR" and need to determine the number of four-letter words that can be formed using its letters. In the first scenario, where there are no restrictions, we consider all possible combinations of the four letters.
In the second scenario, where the word must contain the letter "H" in the first position, we fix the first letter as "H" and consider the remaining three positions for the remaining letters.
i) To find the number of four-letter words that can be formed without any restrictions, we consider all the letters in the word "CHAIR". Since we are selecting four letters, we have 5 choices for each position. Therefore, the total number of words is calculated by multiplying the number of choices at each position: 5 * 5 * 5 * 5 = 625 words.
ii) In this scenario, we fix the first letter as "H" and consider the remaining three positions. For the second position, we have 4 choices, as we cannot choose "H" again. For the third position, we have 4 choices since "H" is fixed, and for the fourth position, we also have 4 choices. Therefore, the total number of words is obtained by multiplying the number of choices at each position: 1 * 4 * 4 * 4 = 64 words.
Hence, the number of four-letter words that can be formed from the letters in the word "CHAIR" is 625 words without any restrictions, and 64 words if the word must contain the letter "H" in the first position.
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Justine answered 28 questions correctly on a 50−question test. Drag and drop the amount she answered correctly into the boxes to show the amount as a fraction in simplest form, decimal, and percent.
Answers
Answer:
14/25
0.56
56%
Step-by-step explanation:
1. Turn it into a fraction (28/50)
2. Divided the numerator (28) and the denominator (50) by the greatest common factor (2), which makes the answer: 14/25
3. Divide the numerator (14) by the denominator (25) to get the decimal (14÷25=0.56)
4. Multiply the decimal (0.56) by 100 to get the percentage (0.56×100=56%)
Rewrite one eighth times x cubed times y plus seven eighths times x times y squared using a common factor.
Answers
Equation y (1/8 x3 + 7) is rewritten by using a common factor. A literal equation is regarded as having at least two variables.
Given that,
Use a common factor to rewrite one eighth times x cubed times y plus seven eighths times x times y squared.
This is how the equation can be rewritten:
The first equation is written as 1/8 x3y + 7/8 xy2.
It is possible to rewrite the equation 1/8 xy(x2 + y) using the common factor.
Equation two:
1/4x.y.4x2 + 28y
1/4 .4 x³ .y + 28y
x3.y + 28y equation to be solved
Using the formula
y = (x3 + 28).
Third claim:
1/4. x. y. x2 + 7y
Fix the problem.
1/4 . x³ .y + 7y
Write y = (1/4x3 + 7) in a new way.
Fourth assertion:
1/8 x3y2.y + 7 x 1/8 x3y3 + 7 x
After removing the common element x(1/8 x2y3+ 7), rewrite the equation.
Fifth Declaration
1/8 x. y. x² + 7y
1/8 x³. y + 7y
Equation y (1/8 x3 + 7) is rewritten.
Thus, a literal equation is one that contains at least two variables. Solve for one variable in terms of the other variable to rephrase a literal equation.
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give the new coordinates of the ordered pair(7,-4) after a reflection across the x-axis?
Answers
Answer:
(7,4)
Step-by-step explanation:
Reflection across x-axis is making the y value the opposite of what it was prior. (x, y)→(x,-y)
That is the formula.
(Pls mark me brainiest if it's correct :)
in a board of directors composed of people, how many ways can one chief executive officer, one director, and one treasurer be selected?
Answers
A chairman and vice chairman are to be selected from a committee of eight people in such a way that no one treasurer individual can hold more than one position. The permutation of 8 different objects, chosen two at a time, results in the number of possible chairman selections in this situation.
\(^{8} P_{2} =\)\(8/8-2=8/6=8*7*6/6=8*7=56\)
Cash and liquidity management, risk management, and corporate finance are among the important basic responsibilities of a corporate treasurer. The division in charge of a nation's finances, economy, and revenue is known as the treasury. Although in certain nations the treasury answers to a Secretary of the Treasury or Chancellor of the Exchequer, the treasurer is often in charge of the department. After the Prime Minister and Deputy Prime Minister, the Treasurer is a senior minister in Australia and frequently the second or third most significant member of the cabinet. Additionally, each Australian state and autonomous territory has its own treasurer.
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a telephone pole is 24 feet tall
Answers
Answer:i honestly dont know just trying to get points
Step-by-step explanation:
AABC is dilated by a factor of 2 to produce AA'B'C!
What is A'B, the length of AB after the dilation? What is the measure of A'?
Answers
Answer:
D
Step-by-step explanation:
in this case, because it is being dilated by a factor of 2 this means that figure A´B´C´ will be double the size of its pre-image ABC.
each side will now be its double which means:
side A´C´= 10
side B´C´= 6
and side A´B´= 8
since the figure is only increasing its sides the angles of the right triangle remain the same.
<A= 37 degrees
The length of A'B' is, 8 units and the measure of angle A' is, 37 degree.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
ΔABC is dilated by a factor of 2 to produce ΔA'B'C'.
Now, When the triangle undergoes dilation, the length of its sides gets multiplied by 2 (dilation factor) but the angles remain the same ( since, the shape has to remain same).
Thus, The length of A'B' is,
= 4 x 2
= 8
And, the measure of angle A' is, 37 degree.
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Determine the average rate of change from 0 to 3.
Answers
Answer:
A
Step-by-step explanation:
The average rate of change of f(x) in the close interval [ a, b ] is
\(\frac{f(b)-f(a)}{b-a}\)
Here [ a, b ] = [ 0, 3 ]
From the graph
f(b) = f(3) = 4
f(a) = f(0) = - 3 , thus
average rate of change = \(\frac{4-(-3)}{3-0}\) = \(\frac{7}{3}\) → A
√xx − 2 = 7
a. 51
b. 27
c. 23
Answers
Answer: c=23
Step-by-step explanation: Honest guess
PLEASE HELP 100 points AND brainlieest
Answers
Answer:
first row: 3 and 9 Second row: 30
Step-by-step explanation:
it looks like you are just adding 6 as you go up. random guess so prob wrong. sorry.
Answer:
2, 8, 45
Step-by-step explanation:
based off the one completed part of the table I decided that it would make sense if the time was multiplied by 3 to get the distance. So to complete these I divided or multiplied by 3 to find what to put in each box.
- For the first box I did 6/3 and found 2
- For the second box 24/3 = 8
- For the last box 15 x 3 = 45
this isnt my best area so please let me know if I got anything wrong but I think this is correct. Hope this helps!!
if you take 3 apples from 10 apples how many apples do you have
Answers
Answer:
still 10 even tho you took 3
Step-by-step explanation:
What is the slope and y-intercept of the graph of the linear function shown on the grid?
A. Slope = -2 , y-intercept = 4
B. Slope = 3 , y-intercept = -2
C. Slope = 2 , y-intercept = -2
D. Slope = 2 , y-intercept = 4
Correct answer will get Brainliest!
Answers
Answer:
Step-by-step explanation:
Refer to the graph. As you 'leave' the first point towards the second, x increases by 3. This is the 'run.' At the same time, y increases by 6. This is the 'rise.'
Therefore the slope is m = rise/run = 6/3, or m = 2. The second point, (0, 4), is the y-intercept.
Find the value of each variable and the measure of each labeled angle 1-3
Answers
Answer:
1.) x = 30 ; 150° 2.) x = 30 ; 50° 3.) x = 40 ; 122°
Step-by-step explanation:
Each one of the problems revolves around vertical angles. Verticle angles are equal to each other.
1.)
5x = 3x + 60
2x = 60 (Subtracted 3x on both sides.)
x = 30 (Divided 2 on both sides.)
Know that we know the variable's value, time to find the angles.
5(30) = 3(30) + 60
150 = 150
This means the angles are 150°.
2.)
3x - 40 = x + 20
2x - 40 = 20
2x = 60
x = 30
3(30) - 40 = (30) + 20
90 - 40 = 50
50 = 50
This means the angles are 50°.
3.)
5x - 78 = 3x + 2
2x - 78 = 2
2x = 80
x = 40
5(40) - 78 = 3(40) + 2
122 = 122
This means the angles are 122°.
The value of x is 30° and the unknown angle is 150°.
We need to find the unknown angles from the given figure.
What are vertically opposite angles?The vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
From figure 1:
(5x)°=(3x+60)°
⇒5x-3x=60
⇒2x=60
⇒x=30
So, (5x)°=(3x+60)°=150°
From figure 2:
(3x-40)°=(x+20)°
⇒3x-x=60
⇒2x=60
⇒x=30
So, (3x-40)°=(x+20)°=50°
From figure 3:
(3x+2)°=(5x-78)°
⇒5x-3x=78+2
⇒2x=80
⇒x=40
So, (3x+2)°=(5x-78)°=122°
Therefore, the value of x is 30° and the unknown angle is 150°.
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PLSSS HELP IF YOU TURLY KNOW THISS
Answers
The negative integer meet on integer hill .The result of -6+(-7) is -13
What is meant by negative integer ?Any integer with a value below zero is referred to as a negative integer. Examples for each operation will help you understand the rules for adding, subtracting, multiplying, and dividing negative numbers.
On the number line, a negative integer is an integer that is to the left of zero.
All positive counting numbers, zero, and all negative counting numbers that count from negative infinity to positive infinity are included in the category of integers.
Real integers that are less than zero are the negative integers. For instance, 147 and 4 are both negative numbers, but 10 and 0.4181554 are not (the former is a negative number but not an integer, the latter is a positive integer)
Given,
-6+(-7) by simplifying we got
=-13
Therefore The negative integer meet on integer hill .The result of -6+(-7) is -13
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A) These polygons are similar. Determine the values of x° and y°.
Answers
Y= 64
They’re similar which means they’re enlarged so therefore the angles are unaffected
If f(x) = 6x – 1 and g (x) = StartFraction x + 1 Over 6 EndFraction, which expressions can be used to verify g(x) is the inverse of f(x)? Check all that apply.
Answers
Answer:
B and C
Step-by-step explanation:
Answer: B and C
Step-by-step explanation:
LA DISTANCIA ENTRE LA TIERRA YLA LUNA ES DE 384 392 KM. LOS AUSTRONAUTAS DE LA APOLO XL SALIERON EL 16 DE JULIO DE 1969 DESDE EL CENTRO ESPACIAL KENNEDY Y ALCANZARON LA ORBITA LUNAR EL 16 DE JULIO DE 1969.SUPONIENDO QUE CADA DIA RECORRIERON LA MISMA CANTIDAD DE KILOMETROS.¿CUANTOS KILOMETROS RECORRIERON POR DIA.
Answers
Complete question :
la distancia entre la tierra y la luna es de 384 392 km. Los astronautas de la Apolo XL salieron el 16 de julio de 1969 desde el Centro Espacial Kennedy y al alcanzaron la orbita el 19 de julio de 1969. Suponiendo que cada dia recorrieron la misma cantidad de kilometros cuantos kilometros recorrieron por dia
Responder:
128130,66 kilometros
Explicación paso a paso:
Dado que:
Distancia entre la tierra y la luna = 384,392 km
Tiempo empleado = (19 de julio - 16 de julio) mismo año = 3 días
Velocidad = distancia / tiempo
El tiempo empleado es (3 * 24) = 72 horas
Por lo tanto,
velocidad = 384,392 / 72
= 5338,7777 kilómetros por hora
Dado que se supone que la distancia recorrida diariamente es la misma m:
El número de kilómetros recorridos por día:
5338,7777 kilómetros por hora * 24
= 128130,66 kilometros
the following statements is are true regarding the figure above
Answers
Answer:
a and b
Step-by-step explanation:
it is a point and a point is a zero demensional object.
John has a few shoes. mike has 10 shoes more than john. james has 8 less than john. mike has two times of james, how many shoes does john have
Answers
Step-by-step explanation:
M=2G
M=J+10
G=J-8
2G=J+10
G=J-8
2(J-8)=J+10
2J-16=J+10
J=26
my✋nameisnot❌fiveweeniesiamshoto❄fromUAandIwanna✨beahero
Answers
Answer:
23
Step-by-step explanation:
12+24=36
36-13=23
He gave 23 away.
Answer:
Is that a prolem and only real ones get the refance lol
Step-by-step explanation: