What is 1/3 of the sum of 45 and a number is 16 Translated to algebraic equation
Answers
the statement given 1/3 of the sum of 45 and a number is 16
\(\frac{1}{3}(45+x)=16\)In order to find the value of x, w
Related Questions
College students were given three choices of pizza toppings and asked to choose one favorite Results are shown in the table toppings Sremam 15 24 28 28 15 1 11 23 28 cheese meat 23 15 veggie Estimate the probability that a randomly selected student who is a junior or senior prefers veggie. Round the answer to the nearest thousandth
A. 371
B. 220
C. 395
D. 662
Answers
Answer:
B. 0.220
Step-by-step explanation:
The table is presented properly below:
\(\left|\begin{array}{c|cccc|c}$toppings&$Freshman&$Sophomore&$Junior&$Senior&$Total\\---&---&---&---&---&---\\$Cheese&11&15&24&28&78\\$Meat&23&28&15&11&77\\$Veggie&15&11&23&28&77\\---&---&---&---&---&---\\$Total&&&&&232\end{array}\right|\)
Number of junior students who prefers veggies =23
Number of senior students who prefers veggies =28
Total =23+28=51
Therefore, the probability that a randomly selected student who is a junior or senior prefers veggie
=51/232
=0.220 (to the nearest thousandth)
The correct option is B.
Use the fundamental theorem of algebra to determine the number of roots for each polynomial function
shown.
f(x) = (x2+6)2
Answers
Answer:
4 roots.
Step-by-step explanation:
The number of roots is equal to the degree of the function
For example
f(x) = x^2 has 2 roots because the highest exponent is 2.
f(x) = x^3 + 2x - 1 has 3 roots , because the function is of degree 3.
(x^2+ 6)^2 = x^4 + 12x^2 + 36 so because of the x^4 it is of degree 4 and has 4 roots.
Chris saved x dollars and spent half of his savings buying video games. After earning an additional $10 cutting grass, he had $32. If the equation one half times x plus 10 equals 32 represents the scenario, how much did he start with in his savings? $11 $21 $44 $84
Answers
The amount Chris started with in his savings is $44. option C
EquationAmount Chris saved = $xAmount spent on video games = 1/2xAdditional amount earned = $10Total = $321/2x + 10 = 32
subtract 10 from both sides1/2x = 32 - 10
1/2x = 22
divide both sides by 1/2x = 22 ÷ 1/2
x = 22 × 2/1
x = $44
Therefore, the amount Chris started with in his savings is $44. option C
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Answer:
Step-by-step explanation:
Graph the solution of the linear inequality and answer the questions below
Answers
The first step we need to take is to determine two points on the boundary line. To do that we will find the point for which x is 0 and the point for which y is 0. This is done below:
\(\begin{gathered} -2y=6\cdot0-18 \\ -2y=-18 \\ y=9 \end{gathered}\)The first point is (0,9).
\(\begin{gathered} -2\cdot0=6\cdot x-18 \\ -6\cdot x=-18 \\ x=\frac{-18}{-6}=3 \end{gathered}\)The second point is (3,0).
Since the signal is " less or equal", the line must be solid.
The two points are (0,9) and (3,0).
The region above the boundary line should be shaded.
In Problem, p is in dollars and q is the number of units.
(a) Find the elasticity of the demand function
p2 + 2p + q = 49 at p = 6.
(b) How will a price increase affect total revenue?
Answers
Answer:
-14
Explanation:
Elasticity of demand is the degree of change in demand after a change I'm price, basically demand's sensitivity to price change.
Formula for calculating price elasticity is: change in price/change in quantity =dq/dp
Since we are given p²+2p+q=49 and not initial and current amount of price and quantity, we differentiate to find demand elasticity, thus:
2p+2+dq/dp=0
dq/dp=-2p-2
Given p =6, we substitute:
dq/dp=-2×6-2
dq/dp=-12-2
dq/dp=-14
With a demand elasticity of -14 there is an inverse relationship between price and demand. While price increases, demand falls.
What is the solution to the system of equations?
6x-2y=-14
4x-3y=-31
A:(2,1)
B:(-6,11)
C:(2,13)
D:(-2,1)
Answers
The solution to the system of equations is 6x – 2y = -14 with x = -4 and y = -5
How to get perfect solution?4x – 3y = -31
To find x or method, you must first make one of the words the same so that they may cancel out.
To determine the x terms, we will make the y terms the same in this example.
To do so, multiply the first equation by three, yielding:
18x – 6y = - 42
And multiply the second equation by two to get:
8x – 6y = - 62
Now that we have the y terms, you may cancel them out.
You now have the following two equations:
18x = -42
8x = -62
The next step is to combine them, since the preceding – and – form a +.
This implies that you are left with one equation
26x = -104
Now divide by 26 on each side to get:
x = -4
As you have x, you substitute it into one of the ORIGINAL equations.
6x – 2y = -14
Substitute x in:
6(-4) – 2y = -14
-24 – 2y = -14
Add 24 on each side to get:
-2y = 10
y = -5
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F(x)=2cos^2(x)-3x+4 sketch the graph of the function f(x) for the values of x between 0 and 2
Answers
To sketch the graph of the function f(x) = 2cos^2(x) - 3x + 4 for the values of x between 0 and 2, we can follow these steps:
1. Determine key points: Find the critical points and important features of the function within the given range. This includes the x-intercepts, local maxima, and minima.
2. Plot the x-intercepts: To find the x-intercepts, set f(x) = 0 and solve for x. In this case, cos^2(x) = (0 + 3x - 4)/2. Find the values of x where this equation holds true.
3. Identify local maxima and minima: Use calculus or other methods to find the local maximum and minimum points of the function within the given range.
4. Sketch the graph: Once you have the key points, plot them on a graph and connect them smoothly. Pay attention to the shape and behavior of the function.
Since the process of sketching a graph is best done visually, I'm unable to provide an image here. However, by following the steps outlined above, you can plot the graph of f(x) within the range of x between 0 and 2. Remember to label the axes and indicate any important points you have found.
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An artist sells her sculptures for $250. Each piece costs her $150 to make, and she spends $11000 per year for her studio and other fixed costs. How many sculptures must she sell if she wants to make $10000 in profit
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l don't know if you know it tell please
(6.2 x 10²) x (3.5 x 10³)
Answers
Answer:
\(21.7 x 10^5\)
Step-by-step explanation:
(6.2 x 10²) x (3.5 x 10³)
First, multiply the coefficients: 6.2 x 3.5 = 21.7.
Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.
Therefore, the result is 21.7 x 10^5.
Answer:
3286000
Step-by-step explanation:
find the difference between 8n and (3n_6)
Answers
(
2
x
4
+
5
x
3
+
8
x
+
24
)
÷
(
x
+
2
)
Answers
Answer:
47 + 8x
x + 2
_________________________
Excluded values answer:
x = -2
Step-by-step explanation:
Please help I will mark brainliest
Answers
Answer: the graph is incorrect
Step-by-step explanation:
The graph should be headed towards the left (the negative x side) because x is negative
Answer:
The graph is not correct, because it is a positive graph. It answers the equation y= x, and Franco said it was y= -x. His line would be negative, and this graph is positive.
Step-by-step explanation:
Drag and drop the answers into the boxes to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A sequence of transformations that maps △DEF to △D′E′F′is a Response area followed by a Response area.
The two right triangles are on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 with an increment of 1. The vertical y-axis ranges from negative 5 to 5 with an increment of 1. A dashed triangle has vertex F prime at begin ordered pair 0 comma 1 end ordered pair, vertex D prime at begin ordered pair 1 comma 1 end ordered pair and vertex E prime at begin ordered pair 1 comma 4 end ordered pair. A solid triangle has vertex F at begin ordered pair negative 1 comma negative 1 end ordered pair, vertex D at begin ordered pair negative 2 comma negative 1 end ordered pair and vertex E at begin ordered pair negative 2 comma negative 4 end ordered pair.
Answers
A sequence of transformations that maps △ABC to △A′B′C′ is a rotation of 90° counterclockwise about the origin followed by a translation 2 units right.
Transformations are changes done in the shapes on a coordinate plane by rotation, reflection, or translation
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A sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.
What is the sequence of transformations?The sequence of vertices ABC(DEF in this question) is clockwise, as is the sequence of A'B'C'(D'E'F in this question). Thus, an even number of reflections is involved, if any reflections are involved. The offered choices do not include suitable reflections.
The orientation of AB(DE) is toward the right. The orientation of A'B'(D'E') is up, so there must be a rotation of 90° CCW. Rotation of 90° CCW about the origin will leave the figure in a position that is 2 units left of where it is shown. The rotation must be followed by a translation 2 units to the right.
Thus, we conclude that a sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.
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What is the y intercept of the equation-16x^2+64x+80?
Answers
Answer:
(0, 80)
Step-by-step explanation:
The y-intercept is the value of the function when x=0. For a polynomial in x, setting x=0 effectively eliminates all of the variable terms, leaving only the constant term.
__
The y-intercept is the constant: 80. The coordinates of the y-intercept point reflect the fact that x=0 there: (0, 80).
Find the area of the shape shown.
Answers
Answer:
well area is the space inside of a shape. so you would multiply 2 by 4 because there are 4 sides.
Step-by-step explanation:
Answer: area is 10
Step-by-step explanation:
add top and bottom base
8+2=10
then divide by 2
10/2 = 5
then times 5 by 2
5*2=10
8+2/2 * 2 = 10
10 = area
Based on experience, the probability that an incoming email is spam (an undesired message of solicitation) is 38%. If three emails are in my inbox, what is the probability that:A. All three messages are spam.B. At least one of the three messages are spam.C. None of the three messages are spam.
Answers
Answer:
0.0549
0.7617
0.2383
Step-by-step explanation:
Given that:
Probability that incoming email is spam ;
P(spam) = 0.38
If three emails are in my inbox, what is the probability that:
A. All three messages are spam.
P(1st message being spam) * p(second message being spam) * p(3rd message being spam)
= (0.38) * (0.38) * (0.38)
= 0.054872
= 0.0549
B. At least one of the three messages are spam.
1 - p(none of the 3 messages are spam)
P(none of the 3 messages are spam)
P(not spam) = 1 - p(spam) = 1 - 0.38 = 0.62
1 - [P(not spam) * p(not spam) * p(not spam)]
1 - (0.62 * 0.62 * 0.62)
= 1 - 0.238328
= 0.761672
= 0.7617
C. None of the three messages are spam.
P(not spam) = 1 - p(spam) = 1 - 0.38 = 0.62
P(not spam) * p(not spam) * p(not spam)
(0.62 * 0.62 * 0.62)
= 0.238328
= 0.2383
Susan says 'the bigger radius is the bigger diameter' is she correct why
Answers
Answer:
yes this is correct because radius is double of diameter or radius is half of diameter.
Santos takes the train into the city five days a week for work. For one work week, he kept track of how many minutes long each train ride was: 48, 51, 48, 48, 50
Calculate the mean, median, range, and midrange of the train ride times for the week.
Answers
The mean, median and range of the given data are respectively; 49, 48 and 3.
How to calculate mean, median and range?Formula for mean is;
Mean = Total sum/sample size
Total sum = 48 + 51 + 48 + 48 + 50
Total sum = 245
Sample size = 5
Mean = 245/5
Mean = 49
To get the median, we arrange in ascending order and pick the mid term.
48, 48, 48, 50, 51
Median is mid term which is 48.
Range is difference between highest and lowest term.
Range = 51 - 48
Range = 3
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6. Rewrite y = √√4x+16 +5 to make it easy to graph using a translation. Describe the graph.
Answers
Answer:
~
Step-by-step explanation:
To make it easier to graph using a translation, we can rewrite the given equation as:
y - 5 = √√4x + 16
This is obtained by subtracting 5 from both sides of the equation.
The graph of the original equation y = √√4x+16 +5 can be obtained by taking the graph of y = √√4x + 16 and shifting it upwards by 5 units. The graph of y = √√4x + 16 is a square root function that has a vertical stretch of 2, a horizontal compression of 4, and a vertical translation of 16 units upwards. So the graph of the given equation y = √√4x+16 +5 will be the same as the graph of y = √√4x + 16, but shifted upwards by 5 units.
a girl is three years older than his brother. the product of their ages is 54, find their ages
Answers
Answer:
The sister is 25.5. The brother is 28.5.
Step-by-step explanation:
25.5 + 28.5 = 54.
The boy's age is 9.
The girl's age is 12.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Boy's age = x
Girl's age:
y = x + 3
Now,
x (x + 3) = 54
x² + 3x - 54 = 0
x² + (9 - 6) - 54 = 0
x² + 9x - 6x - 54 = 0
x(x + 9) - 6(x + 9) = 0
x - 6 = 0
x = 6
x + 9 = 0
x = -9 ( cannot be negative)
Now,
x = 9
Boy's age = 9
Girl's age = 9 + 3 = 12
Thus,
The boy's age and the girl's ages are 9 and 12.
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In a multiplicative model, if the seasonal factor is 1.15 for a particular season, then we expect that the time series in that season would be (other things being equal
Answers
Answer:
15% above the trend.
Step-by-step explanation:
A time series represented by Y comprises of dataset observed over a particular period of time. Time series is handy in determining the future of a particular business.
In a multiplicative model, if the seasonal factor is 1.15 for a particular season, then we expect that the time series in that season would be
Y = T × C × S × 1
where;
Seasonal S = 1.15
As such Y would increase by 15% above the trend if all other things are being equal.
WILL GIVE BRAINLIEST‼️‼️ If the mean of the following frequency distribution is 24; determine the value of p.
Answers
Step-by-step explanation:
Greetings !
Firstly, find the class-midpoints (X) to solve for the mean.
Thus, mid points of each classes are
\(5.15.25.35.45\)
Solve, for p using mean grouped data formula
\( \frac{5(3) + 15(4) + 25(p) + 35(3) + 45(2)}{3 + 4 + p + 3 + 2} = 24\)
multiply each values add them and solve for p.
\( \frac{15 + 60 + 25p + 105 + 90}{12 + p} = 24\)
make a cross multiplication
\(270 + 25p = 24(12 + p) \\ 270 + 25p = 288 + 24p\)
subtract 270 from both sides
\(270 + 25p - 270 = 288 + 24p - 270 \\ 25p = 24p + 18\)
subtract 24p from both sides
\(25p - 24p = 24p + 18 - 24p \\ p = 18\)
Also refer the attached image for further details
Hope it helps!
Wendy and Roger camped out at a state park, and then hiked back to their cars, which were
parked on opposite ends of the park. Wendy headed due north at 3 miles per hour, and Roger
hiked due south at 6 miles per hour. In how long were the two friends 2 miles apart?
If necessary, round your answer to the nearest minute.
Answers
In 30 minutes the two friends 2 miles apart.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, Wendy headed due north at 3 miles per hour, and Roger hiked due south at 6 miles per hour.
We know that, Time= Distance/Speed
Now, T₁= 2/3
T₂= 2/6 =1/3
T=T₁-T₂
T=2/3+1/3
T=1/3
T=0.33 hours
= 30 minutes
Therefore, in 30 minutes the two friends 2 miles apart.
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A box contains 2 red marbles, 5 green marbles and 8 blue marbles. Find the probability of the different events.
P ( 3 blue ) =
P (blue & green)
Answers
The value of the probability of the different events are,
The value of the probability P (3) is,
⇒ 1 / 5
And, The value of the probability P (blue & green) is,
⇒ 8/45
We have to given that;
A box contains 2 red marbles, 5 green marbles and 8 blue marbles.
Hence, Total marbles = 2 + 5 + 8 = 15
So, The value of the probability P (3) is,
⇒ 3 / 15
⇒ 1 / 5
And, The value of the probability P (blue & green) is,
⇒ 8/15 x 5/15
⇒ 8/15 x 1/3
⇒ 8 / 45
Thus, The value of the probability P (3) is,
⇒ 1 / 5
And, The value of the probability P (blue & green) is,
⇒ 8/45
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Graph the line with the given point and slope.
The line through (-1,-2) with slope
6/5
Answers
The graph of the line passing through the points (-1,-2) with the slope 6/5 has been plotted
The line passing through the points = (-1,-2)
The slope of the line = 6/5
The slope of the line the change in y coordinates with respect to change in x coordinates of the line
We know
Point slope form \((y-y_{1})=m(x-x_{1})\)
Where m is the slope of the line
Substitute the values in the equation
(y-(-2))= 6/5(x-(-1))
y+2 = 6/5(x+1)
y+2 = (6/5)x+6/5
y = (6/5)x+(6/5)-2
y = (6/5)x+(-4/5)
Draw the graph
Hence, the graph of the line passing through the points (-1,-2) with the slope 6/5 has been plotted
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What is the solution to this equation?
7x-3(x-6)= 30
A. X= 3.
B. x = 12
C. X= 9
D. x=6
Answers
Answer:
A
Step-by-step explanation:
To solve the equation 7x-3(x-6)=30, we need to use the distributive property to simplify the left-hand side of the equation:
7x - 3(x-6) = 30
7x - 3x + 18 = 30
4x + 18 = 30
Next, we need to isolate the variable term on one side of the equation. To do this, we can subtract 18 from both sides:
4x + 18 - 18 = 30 - 18
4x = 12
Finally, we can solve for x by dividing both sides by 4:
4x/4 = 12/4
x = 3
Therefore, the solution to the equation 7x-3(x-6)=30 is x = 3. Answer A is correct.
Please look at the photo for the question. Thank you!
Answers
The function g(x) = x² + 4x has a: A. minimum.
The minimum value occur at x = -2.
The function's minimum value is -4.
How to determine the axis of symmetry and vertex of a quadratic function?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:
Axis of symmetry = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function g(x) = x² + 4x, we have:
a = 1, b = 4, and c = 0
Axis of symmetry, Xmax = -b/2a
Axis of symmetry, Xmax = -(4)/2(1)
Axis of symmetry, Xmax = -2
Next, we would determine vertex as follows;
g(x) = x² + 4x
g(-2) = -(-2)² + 4(-2)
g(-2) = -4.
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Which fraction is closest to 1/2
?
Answers
The fraction which is closest to 1/2 is, 3/8. So option B is correct
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
Given that,
A fraction number 1/2
In decimal form = 0.5
Closest fraction number = ?
Most closest number is that number from which we subtract the given number and the magnitude of result we get is very less,
Lets take, A fraction 1/6
In decimal form it can written as, 0.167
Difference 1 = 0.5 - 0.167
= 0.333
Similarly, For numbers 3/8, 3/4, -1/2
Difference 2 = 0.5 - 0.375 = 0.125
Difference 3 = 0.5 - 0.75 = -0.25
Difference 4 = 0.5 - (-0.5) = 1.0
It can be seen that,
Magnitude of difference in case of 3/8 is very less
Hence, the closest number is 3/8
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A ladder of length (2x+6) feet is positioned x feet from a wall. If the ladder reaches a height of (2x+4) feet along the wall. Find the longest leg.
A. 10ft
B. 24ft
C. 26ft
D. 13cm
Answers
Using the Pythagoras theorem, the longest leg has the length of 24 feet.
Given that,
A ladder of length (2x+6) feet is positioned x feet from a wall.
Height of the ladder = (2x + 6) feet
Distance of ladder from the wall = x feet
Height of the wall that the ladder is placed = (2x + 4) feet
These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.
Longest leg is (2x + 4) feet
Using the Pythagoras theorem,
(2x + 6)² = (2x + 4)² + x²
4x² + 24x + 36 = 4x² + 16x + 16 + x²
4x² + 24x + 36 = 5x² + 16x + 16
x² - 8x - 20 = 0
(x - 10) (x + 2) = 0
x = 10 or x = -2
x = 2 is not possible.
So x = 10
Longest leg = 2x + 4 = 20 + 4 = 24 feet
Hence the length of the longest leg is 24 feet.
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decide which of the following sets of points.
Answers
Answer:
Im pretty sure that the answer would be choice f.
Step-by-step explanation:
(a) {T, P, E}: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.
(b) {A, B, D, M}: Coplanar. These points lie on the same plane since they are contained within the drawing.
(c) {B, K, C}: Collinear. These points lie on the same line within the drawing.
(d) {A, K, E}: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.
(e) {M, K, T}: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.
(f) {A, Q, P, D}: Coplanar. These points lie on the same plane since they are contained within the drawing.
EM, P, B: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.
EM, P, B: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.
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