Given:
Prime numbers can be expressed as a sum and difference of 2 prime numbers.
To find:
The prime numbers that can be expressed as a sum and difference of 2 prime numbers.
Solution:
Prime numbers are the positive integers which are greater than 1, divisible by only 1 and itself.
Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19,... .
Only 2 is the even prime number.
The sum and difference of two odd integers is always an even number. So, we need to take one even prime number and one odd prime number to add and subtract the numbers to get a prime number.
[tex]2+3=5[/tex]
[tex]7-2=5[/tex]
Therefore, 5 is the only prime number that can be expressed as a sum and difference of 2 prime numbers.
What is the value of the power? Negative StartFraction 9 Over 12 EndFraction Negative StartFraction 27 Over 64 EndFraction StartFraction 9 Over 12 EndFraction StartFraction 27 Over 64 EndFraction
Answer:
[tex](\frac{-3}{4})^3 = -\frac{27}{64}[/tex]
Step-by-step explanation:
Given
[tex](\frac{-3}{4})^3[/tex]
Required
Evaluate
The expression can be represented as:
[tex](\frac{-3}{4})^3 = (\frac{-3}{4})*(\frac{-3}{4})*(\frac{-3}{4})[/tex]
So, we have:
[tex](\frac{-3}{4})^3 = \frac{-3*-3*-3}{4*4*4}[/tex]
[tex](\frac{-3}{4})^3 = \frac{-27}{64}[/tex]
Rewrite as:
[tex](\frac{-3}{4})^3 = -\frac{27}{64}[/tex]
Answer:
B -27/64
Step-by-step explanation:
can you please help me with number 4 please?
A committee that consists of five members are to be chosen from 6 boys and 5 girls. Find the number of different committees that can be formed if only two boys are selected
Answer:
150 different committees can be formed
Step-by-step explanation:
We have 6 boys and 5 girls and we want to select 5 members
Out of these 5 members, two boys are selected
Since two boys are selected, we are left with three girls
So, out of 6 boys, we select 2 boys and out of 5 girls, we select 3 girls
Mathematically, we know that the number of ways in which we can select r items from a total n follows the combinatorial formula;
nCr = n!/(n-r)!r!
With this, we have;
6C2 * 5C3
= (6!/(6-2)!2!) * (5!/(5-3)!3!) = 150 different committees can be formed
Katie approximated the volume and the surface area for a ball she was using for some exercises by assuming the ball is a sphere. She was surprised when the numerical value of the volume in cubic inches was the same as the numerical value of the surface area in square inches. What is the radius of the ball?
Answer:
3
Step-by-step explanation:
Volume of sphere:
4/3 * pi * r^3
Surface Area of Sphere:
4 * pi * r^2
So if V = SA
4/3 * pi * r^3 = 4 * pi * r^2
4/3 * pi * r^3 = 4 * pi * r^2
1/3 * r^3 = r^2
1/3 * r = 1
r = 3
Volume is a three-dimensional scalar quantity. The radius of the ball is equal to 3 units.
What is volume?
A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the sphere is given by the formula,
V = (4/3)πR³
The surface area of the sphere is given by the formula,
Surface area = 4πR²
Also, it is mentioned that the numerical value of the volume in cubic inches was the same as the numerical value of the surface area in square inches. Therefore,
(4/3)πR³ = 4πR²
R³/3 = R²
R = 3
Hence, the radius of the ball is equal to 3 units.
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The expression 2(a+b)-8.1 for certain values of a and b.find the value of the following expressions for the same values of a and b: 3(a+b)
Note: Consider the given equation is [tex]2(a+b)=8.1[/tex] instated of [tex]2(a+b)-8.1[/tex].
Given:
The expression [tex]2(a+b)=8.1[/tex] for certain values of a and b.
To find:
The value of [tex]3(a+b)[/tex] for the same value of a and b.
Solution:
We have,
[tex]2(a+b)=8.1[/tex]
Divide both sides by 2.
[tex](a+b)=\dfrac{8.1}{2}[/tex]
[tex](a+b)=4.05[/tex]
Multiply both sides by 3.
[tex]3(a+b)=3\times 4.05[/tex]
[tex]3(a+b)=12.15[/tex]
Therefore, the value of [tex]3(a+b)[/tex] is 12.15.
Cayden has several screws on a scale, and the scale reads 80.955 cayden add 1 more screw and the scale reads 84.81
Answer:
-3.855
Step-by-step explanation:
Not sure if you need the weight of each screw! but you just subtract 80.955-84.81
Answer:
1
Step-by-step explanation:
itnisbbsndnfnfnfnnfnfnfncjcjccjcj
Ming drew the model below to represent the equation 24+12=_x(8+4) What is the missing value in Ming's equation?
Given:
The equation is:
[tex]24+12=\_\_\times (8+4)[/tex]
To find:
The missing value.
Solution:
We have,
[tex]24+12=\_\_\times (8+4)[/tex] ...(i)
Taking left hand side, we get
[tex]24+12=3\times 8+3\times 4[/tex]
Taking 3 common, we get
[tex]24+12=3\times (8+4)[/tex] ...(ii)
On comparing (i) and (ii), we get
Missing value = 3
Therefore, the missing value in the given equation is 3.
What is the value of Z?
Answer:
137
Step-by-step explanation:
Since angle Z and the angle of 43° are supplementary, the sum of them must equal 180. Therefore,
∠Z + 43 =180
∠Z = 137°
Answer:
137 degrees
Step-by-step explanation:
First thing, we know y is 43 because 43 degrees and y are vertical angles meaning they are congruent. (This is just a small part doesn't really do much though.)
Straight lines add up to 180 so simply just subtract 43 from 180.
180 - 43 = 137.
Therefore,
z = 137 degrees
A marketing researcher interviews a large number of respondents and asks them a set of questions that are listed in a questionnaire. The respondents are required to select a response from a given set of options. In this case, the researcher is _____.
Answer: conducting quantitative research
Step-by-step explanation:
Quantitative research refers to the collection and the analysis of numerical data. Quantitative research can be used in making predictions, and testing casual relationships.
Quantitative research methods emphasize the numerical analysis of data which can be collected through questionnaires, polls, surveys etc.
60
What is the value of x in the equation x - y = 30, when y= 15?
O. 4
O. 8
O. 80
O. 200
Answer:
Step-by-step explanation:
x - y = 30
Substitute 15 for y.
x - (15) = 30
Add 15 to both sides.
x = 45
what is the average cost of 7 articles if 3 of them cost 30k each and the rest cost 12.5k each
[tex] {\bold{\red{\huge{\mathbb{QUESTION}}}}} [/tex]
what is the average cost of 7 articles if 3 of them cost 30k each and the rest cost 12.5k each
[tex]\bold{ \red{\star{\blue{GIVEN }}}}[/tex]
TOTAL NUMBER OF ARTICLE= 7
ARTICLES FOR 30K = 3
ARTICLES FOR 12.5K = 7-3= 4
[tex]\bold{\blue{\star{\red{TO \: \: FIND}}}}[/tex]
Average cost of 7 articles
[tex] \bold{ \green{ \star{ \orange{FORMULA \: USED}}}}[/tex]
[tex] \red{AVERAGE = \frac{TOTAL \: COST}{ NUMBER \: OF\: ARTICLES }}[/tex]
[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]
[tex]Average \: cost \: of \: 7 \: articles - > \\ \frac{(3 \times 30k) + (12 .5k \times 4)}{7} \\ \frac{90k + 50k}{7} \\ \frac{140k}{7} \\ \blue {Average \: cost \: of \: 7 \: articles - >} \\ 20k[/tex]
ANSWER THIS PLEASE !!
Answer:
B. point B
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
B(-1, -3)
y = 3x
When x = -1,
y = 3(-1) = -3
Answer: B.
For each calculation choose the correct answer written in standard form.
a) (7 * 10°) ~ (3 x 10?)
A
B
21 x 100 21 x 10
С
2.1 x 10"
D
2.1 x 10
b) (2 x 10°) = (4 x 102)
A
2 x 10
B
5 x 10
с
0.5 x 10
D
2 x 10
Answer:
Both the answers will be B
PLS HELP ASAP IS THIS TRUE OR FALSE?
*image below*
Answer:
true
Step-by-step explanation:
idek
Answer:
True
Step-by-step explanation:
If we say x-1=0
x=1
F(1)=(1)^3-7(1)^2+15(1)-9
=1-7+15-9
=-6-9+15
=0
So this proves that it's a factor by factor theorem
A factor must give 0 if it's substituted to the equation
Find the surface area of the pyramid
line I is parallel to line m.if the maesure of angle 6 is 75 what is the measure of angle 3
Answer:
105
Step-by-step explanation:
l is parallel m so angle 3+angle 6=180
use the substitution method to solve the system of equations
3x+2y=13
y=x-1
Answer:
[tex]x=3\\y=2[/tex]
Step-by-step explanation:
[tex]3x+2y=13\\y=x-1[/tex]
Solve for [tex]y=x-1[/tex] for y:
[tex]y=x-1[/tex]
Substitute [tex]x-1[/tex] for y in [tex]3x+2y=13[/tex]:
[tex]3x+2y=13[/tex]
[tex]3x+2(x-1)=13\\[/tex]
[tex]5x-2=13[/tex]
[tex]5x=13+2[/tex]
[tex]5x=15[/tex]
[tex]x=15/5[/tex]
[tex]x=3[/tex]
Substitute 3 for x in [tex]y=x-1[/tex]:
[tex]y=x-1[/tex]
[tex]y=(3)-1[/tex]
[tex]y=2[/tex]
[tex]x=3[/tex] and [tex]y=2[/tex]
hope this helps...
Which of the following expressions represents the distance between -3.9 and -4.7
Answer:
None of the above
Step-by-step explanation:
Distance is the difference between two positions. That is x1- x2 Since both numbers were negative, you would want the absolute value of one plus the other, because subtracting a negative results in a positive. For this example the distance would look more like this:
| -4.7 - ( -3.9 ) | = .8
How many solutions are there to the equation below? 9(x – 4) = 9x – 33
Answer:
no solution
Step-by-step explanation:
express 8cm as fraction of 2metres.
Answer:
4/200 is the answer
solve the following simultaneous equations using SUBTITUTION METHOD
m+3n=7 and 5m-n=3
To check:put value of m and n in both equations
Answer: n=2 and m=1
Step-by-step explanation:
m+3n=7 , 5m-n=3
m=7-3n => 5(7-3n)-n=3
=> 35-15n-n=3
=> -16n=-32
=> n=2
n=2 => 5m-2=3
=> m=1
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
10-
(7.2)
- 10
(0,0)
10
- 10 -
A. y 1x
B. y = 7x
C. y = 2x
D. y = -7x
E. y= ²x
F. y= -2x
Answer:
[tex]y = \frac{2}{7} x[/tex]
Step-by-step explanation:
The slope is
[tex]slope = \frac{rise}{run} = \frac{2}{7} [/tex]
The y-intercept is 0
The equation of line between the points is y = ( 2/7 )x
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 value of A is
Let the first point be P ( 7 , 2 )
Let the second point be Q ( 0 , 0 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 2/7 )
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 0 = ( 2/7 ) ( x - 0 )
y = ( 2/7 )x
Hence , the equation of line is y = ( 2/7 )x
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Simplify: 4y2 + 5y + 2 + 8y2 + 4y + 5.
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
Nachelle went to the store to buy some almonds. The price per pound of the almonds is $6.50 per pound and she has a coupon for $4.75 off the final amount. With the coupon, how much would Nachelle have to pay to buy 5 pounds of almonds? Also, write an expression for the cost to buy pp pounds of almonds, assuming at least one pound is purchased.
Step-by-step explanation:
hope this will help you mark me as brinalist friend please
The amount paid for the 5 pound of almond by Nachelle is $27.75.
What is meant by the term equation?In its most basic form, an equation is a numerical declaration that demonstrates that two formulas are equal. 3x + 25 = 14, for example, is an equation whereby a 3x + 25 and 14 are 2 expressions separated by a 'equal' sign.Let 'p' be the number of pounds of almonds purchased by Nachelle.
Let 'c' be the total cost paid.
The cost of per pound of the almonds is $6.50 per pound.
The amount of the coupon is $4.75.
Thus, the equation will be ;
c = 6.50p - 4.75 ......equation.
For number of pounds p = 5.
c = 6.50×5 - 4.75
c = $27.75
Thus, the amount paid for the 5 pound of almond by Nachelle is $27.75.
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A teacher asks students to determine the accuracy of this statement.
A reflection over the x-axis and then over the y-axis results in the same transformation as a 180degree rotation about the origin of the original figure.
Kwame’s explanation of the accuracy of the statement is shown below.
Step 1: Choose the vertices of a pre-image: (1, 2), (1, 4), (2, 3).
Step 2: Reflect the pre-image over the x-axis: (1, –2), (1, –4), (2, –3).
Step 3: Reflect the figure from step 2 over the y-axis: (–1, 2), (–1, 4), (–2, 3).
Step 4: Rotate the pre-image 180degree: (–1, –2), (–1, –4), (–2, –3).
Step 5: Compare the reflected figure to the rotated figure. The vertices are not located in the same place, therefore the statement made by the teacher is inaccurate.
Which best explains Kwame’s solution?
Kwame’s explanation and solution are incorrect. He reflected the image over the y-axis in step 2 and the x-axis in step 3, instead of the reverse.
Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
Kwame’s explanation and solution are incorrect. When reflecting over the x- and y-axes, he negated the incorrect coordinate in the ordered pair.
Kwame’s explanation and solution are incorrect. The coordinates of the rotated figure should be switched and negated, not just negated.
Answer:
B. Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
Step-by-step explanation:
I just did it, and thankfully, all was well! :) :) :)
Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation. Rotation, translation and reflection produce congruent images.
The vertices of the pre-image is (1, 2), (1, 4), (2, 3). It is reflected over the x axis to get (1, –2), (1, –4), (2, –3)It is then reflected over the y axis to get (-1, 2), (-1, 4), (-2, 3) instead of (-1, –2), (-1, –4), (-2, –3).Rotating the vertices 180 degrees gives (-1, –2), (-1, –4), (-2, –3).
Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
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Five number have amean of 12,when one number is removed, the mean becomes 11,what is the removed number
Answer:
The removed number is 16
Step-by-step explanation:
Five numbers have a mean of 12.
Now;
Mean = Σx/x
Thus; Σx = 12 × 5 = 60
Now,we are told that if one number is removed, the mean is 11.
Thus;
(60 - x)/4 = 11
60 - x = (11 × 4)
60 - x = 44
x = 60 - 44
x = 16
Thus,the removed number is 16
91.55
Which equation has the solutions -
5:27
3
1?
I
3x2 - 5x + 7 = 0
03x2 - 5x – 1 = 0
3x2 - 10x + 6 = 0
O 3x2 _ 10x + 1 = 0
Answer:
the answer is 3x2-10x+6=0
does this table represent a function? why or why not 2,1 3,4 4,4 5,2 5,5
What is the next term in the sequence below?
1, 2, 4, 8, 16, . . .
A. 24
B. 32
C. 34
D. 64
B
the number doubles by itself
1). What is the equation of the line that is perpendicular to y= -3x+1 that passes through the point (9,0)?
2). What is the equation of the line that is parallel to y= -3x+1 that passes through the point (9,0)?
Answer:
Step-by-step explanation:
1) Slope of the given line = -3
slope of the perpendicular line = 1/3
y - 0 = 1/3(x-9)
y = 1/3x - 3
2) slope of the parallel line = -3
y - 0 = -3(x-9)
y = -3x + 27
Answer:
1). y = 1/3x - 3 2).y = -3x + 27
Step-by-step explanation:
1). y = 1/3x + b
0 = 1/3(9) + b
0 = 3 + b
-3 = b
y = 1/3x - 3
2)/ y = -3x + b
0 = -3(9) + b
0 = -27 + b
27 = b
y = -3x + 27