Answers
a + b + c = 17
First is 2 greater than two times the third:
a = 2c + 2
Sum of second and third is 9:
b + c = 9
First find the variables in terms of their relationship with other variables. We have variable a because we know that a = 2c + 2. We also know variable b because we have that b + c = 9, so b = 9 - c. We also know variable c because we have that b + c = 9, so c = 9 - b.
Now plug in the equations instead of their variables into the first equation so at the end we would only have one variable, which is easy to figure out.
First get rid of a by putting (2c + 2) instead of it. So the equation would be:
(2c + 2) + b + c = 17.
Then get rid of b by putting (9 - c) instead of it. So the equation would now be:
(2c + 2) + (9 - c) + c = 17.
To simplify this and figure out c, combine like terms so the equation would be:
2c + 11 = 17
Then get c by itself by subtracting 11 from both sides and then dividing both sides by 2 so the equation would be:
c = 3
Once you have c, you can figure out the other numbers by plugging it in:
for example, because a = 2c + 2, just plug in 3 for c to get a = 2(3) + 2, which is 6 + 2, which is 8, so a = 8.
also, because b = 9 - c, just plug in 3 for c to get b = 9 - 3, which is 6, so b = 6.
And since 8 + 6 + 3 = 17, and 8 is 2 greater than 2 x 3, and 6 + 3 = 9, those are the three numbers.
Related Questions
a jar contains 10 red marbles numbered 1 to 10 and 12 blue marbles numbered 1 to 12. a marble is drawn at random from the jar. find the probability of the given event. write your answers as reduced fractions.
Answers
The probability of drawing a red marble from the jar is 5/11 and the probability of drawing a blue marble from the jar is 6/11.
There are 22 marbles in the jar in total, 10 of which are red and 12 of which are blue. To find the probability of drawing a red marble, we can use the formula for probability:
Probability = Number of favorable outcomes / Total number of outcomes
In this case, the number of favorable outcomes is 10 (the number of red marbles), and the total number of outcomes is 22 (the total number of marbles in the jar). Plugging these values into the formula, we get:
Probability of drawing a red marble = 10/22
This fraction can be reduced to 5/11 by dividing both the numerator and denominator by 2. So, the probability of drawing a red marble from the jar is 5/11.
To find the probability of drawing a blue marble, we can use the same formula:
Probability = Number of favorable outcomes / Total number of outcomes
In this case, the number of favorable outcomes is 12 (the number of blue marbles), and the total number of outcomes is 22 (the total number of marbles in the jar). Plugging these values into the formula, we get:
Probability of drawing a blue marble = 12/22
This fraction can also be reduced to 6/11 by dividing both the numerator and denominator by 2. So, the probability of drawing a blue marble from the jar is 6/11.
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How would I solve this? I need steps..
Answers
Option 2 and option 4 are the respective answers.
what is a discriminant of a quadratic equation?The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
Given here -3x²+6x+2 = 0
therefore the discriminant is (6)² - ( -3×4×2) = 60
Thus the parabola formed by the curve would intersect the x-axis twice
Now for the second part of the answer, the equation is given as
3(2x-1) (x-4) = 3( 2x² - 9x + 4)
=6x² - 27x + 12
Applying the direct formula for root we get x = 27 + √(27² − 4×6×12)/12
Hence, option 2 is the correct answer for part 1, and option 4 is the correct answer for the latter question.
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Which equation represents twenty-nine is one-third of the number n?
Answers
Answer:
29=n/3
Step-by-step explanation:
Answer:
29 = n/3
Step-by-step explanation:
[tex]29 = \frac{1}{3} of \: n \\ 29 = \frac{1}{3} \times n \\ 29 = \frac{n}{3} [/tex]
3. What is wealth?
[A] A person's ability to consume.
[B] A person's ability to borrow money.
[C] A person's liabilities.
[D] A person's ability to give away assets.
[E] None of these
Answers
A shape has 7 non-congruent sides. If 6 of the exterior angles measure 310
degrees, and the remaining angle measures (6x + 2) degrees, what is the value
of x ?
Answers
The last remaining non - congruent side measure = 48°
what is non- congruent sides?Non congruent means "not congruent," i.e., not the same shape, and the sides. Congruent shapes are those that are copies of one another that have been rotated, reflected, and translated.
given
the sum of 6 exterior angles = 310°
remaining angle = ([tex]6x+2[/tex])
All sides of exterior angles sum= 360°
so , remaining angle + sum of all exterior angles=360°
[tex](6x+2)[/tex] + 310° = 360°
[tex](6x+2)[/tex] = 360° - 310C
[tex](6x+2)[/tex] = 50°
[tex]x[/tex] = 48°
The last remaining non - congruent side measure = 48°
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what is the slope of the line (5,-9) and (5,2)?
Answers
Answer:
The slope of a line is a measure of its steepness or incline. It is calculated by dividing the difference in the y-coordinates of two points on the line by the difference in their x-coordinates. In the case of the line (5,-9) and (5,2), the difference in the y-coordinates is -9 - 2 = -11 and the difference in the x-coordinates is 5 - 5 = 0. Since division by 0 is undefined, the slope of the line (5,-9) and (5,2) is undefined.
In general, when the x-coordinates of two points on a line are the same, the line is vertical and has no slope. This means that the line (5,-9) and (5,2) is a vertical line and has no slope.
The slope of a line is calculated as the rise over the run, which is the difference in the y-coordinates divided by the difference in the x-coordinates. In this case, the line has the same x-coordinate for both points, so the rise and run are both zero, and the slope is undefined.
when the spring is stretched and the distance from point a to point b is 5.3 feet, what is the value of θ to the nearest tenth of a degree?
a. 60.0
b. 35.2
c. 45.1
d. 55.5
Answers
When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13 degrees
The distance between point a to point b = 5.3 feet
The length of the top side = 3 feet
Therefore, it will form a right triangle
Here we have to use trigonometric function
Here adjacent side and the hypotenuse of the triangle is given
The trigonometric function that suitable for the given conditions is
cos θ = Adjacent side / Hypotenuse
Substitute the values in the equation
cos θ = 3 / 5
θ = cos^-1(3 / 5)
θ = cos^-1(0.6)
θ = 53.13 degrees
Therefore, the value of θ is 53.13 degrees
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Geometry: 6.7_Law of Cosines: 15 POINTS
Answers
The measure of side a is 4.1 unit.
What is law of cosine?Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
c² = a² + b² - 2ab cos C
(c is opposite side to angle A)
In the given triangle ABC, we have sides BC = a, AB = b and AC = c
Now we know as per cosine rule for all three sides of the triangle.
c² = a² + b² - 2ab cosC
Where; b = 9 and c = 7 degrees
Angle A = 35 degrees
Plugging these values into the equation, we have;
a² = c² + b² - 2cb cos A
a² = 9² + 7² - 2(9)(7) cos (35)
a² = 81 + 49 - 126 x (-0.9036)
a = 4.1
Therefore, the side a is 4.1 unit.
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because of different units being used for various data series, which fit statistic can be used across different series that are in fact measured in different units?
Answers
The fit statistic that can be used across different series that are in fact measured in different units is; MAPE
What statistic can be used?There are different statistics models in this regards such as;
Mean Absolute Error (MAE)
Mean Absolute Scaled Error (MASE)
Accuracy Percent (Accuracy %)
Mean Squared Error (MSE)
Root Mean Squared Error (RMSE)
Mean Absolute Percent Error (MAPE)
Now, we are told that we need the fit statistic that can be used across different series that are in fact measured in different units.
The correct one will be Mean Absolute Percent Error (MAPE) because the average absolute percent difference between the values that are fitted by the model and the observed data values.
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use the side-by-side boxplots shown to complete parts (a) through (e).
Answers
(a) The median of variable x is 70.
(b) The third quarterly of variable y is 94.
(c) Variable y has more dispersion.
(d) Shape of variable x is Symmetric.
(e) The shape of y variable is Skewed left.
a) The median of the variable x, which sits in the middle of the provided box plot, is 70 (roughly).
b) Variable Y's third quarterly value is 94. (approximately).
c) Because Q1 is farther away from the median than Q2, variable y has a higher inter quarterly range than variable x.
d) The shape of the variable x is symmetrical because both the left and right whiskers are roughly the same length and the median is located in the center of the box.
e) The left whisker of the y variable is longer than the right whisker, and the median is located outside the box's center.
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The complete question is given below:
What is the length of rs? 16 units 18 units 25 units 46 units
Answers
Answer:
Step-by-step explanation:
Answer: 25 units
Step-by-step explanation:
True
False
ܘ ܗ
10
15-
f(x)
0
3
Answers
The range of the given function in the figure is R - {0, 1, 2, 3}.
What is the range of a function?The range of a function is represented by the set of output values for the given input values.A range for a function depends on the domain of the function. Where the domain is nothing but the set of input values to the function.If a function is given by y = f(x), then the range is given by R = {y: x ∈ D of f}D - the domain of the function; R - the range of the functionCalculation:The given mapping shows a function f(x).
There are 4 inputs to the function and 5 outputs.
So, the domain set for the given function is written as D = {0, 5, 10, 15}
And the range set for the given function is written as R = {0, 1, 2, 3}
(Since the 5th output is repeating, in the range it is considered only once).
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Which of the following is not a type of matrix?
A. square matrix
B. scalar matrix
C. trace matrix
D. term matrix
Answers
Term matrix is not a type of matrix among the given options.
A matrix is a rectangular array of numbers or other mathematical objects for which operations such as addition and multiplication are defined.
There are several types of matrices, including:
1. Square Matrix: A square matrix is a matrix in which the number of rows is equal to the number of columns.
2. Scalar Matrix: A scalar matrix is a type of matrix in which all the elements are equal to a single number (the scalar).
3. Trace Matrix: A trace matrix is a type of matrix in which the trace (sum of the diagonal elements) is a scalar multiple of the identity matrix.
4. Identity Matrix: An identity matrix is a type of matrix in which all the elements on the main diagonal are 1s and all other elements are 0s.
5. Symmetric Matrix: A symmetric matrix is a type of matrix in which the elements above and below the main diagonal are equal.
6. Diagonal Matrix: A diagonal matrix is a type of matrix in which all the elements outside the main diagonal are 0s.
7. Triangular Matrix: A triangular matrix is a type of matrix in which all the elements above or below a specific diagonal are 0s.
8. Orthogonal Matrix: An orthogonal matrix is a type of matrix in which the product of two matrices is the identity matrix.
9. Singular Matrix: A singular matrix is a type of matrix in which the determinant is 0.
10. Inverse Matrix: An inverse matrix is a type of matrix in which the product of the matrix and its inverse is the identity matrix.
Therefore, the answer is D. Term Matrix, as it is not a type of matrix.
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Option D is Answer. Compared with the given matrix, The Term matrix is not a type of matrix.
Term Matrix: It defines a document-term matrix as simply a matrix describing the frequencies of all terms occurring in the collection of text documents.
square matrix: A matrix which is having the same number of rows and columns. It is also called an n*n matrix.
Example:
[tex]\left[\begin{array}{ccc}1&2\\4&5\\\end{array}\right][/tex]
Scalar matrix: It is a type of square matrix, whose diagonal elements are equal and off-diagonal elements are zero. It is basically a multiple of the square identity matrix.
Example:
[tex]3I=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] =\left[\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right][/tex]
Where I define the Identity matrix.
In a square matrix, the sum of elements of the principal diagonal is called the ‘trace of a matrix’. We denote the trace of the matrix A by ‘tr A’.
Example: If A =
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
, then tr A = 1 + 5 + 9 = 15.
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-(12/5a-7x+31/6b)-3x+3a b
Simplify
Answers
Answer:
3ab-12a/5-31b/6+4x
Step-by-step explanation:
Select the correct answer from each drop-down menu.
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
The center of the circle is at the point
O and its radius is
units. The equation of this circle in standard form is
Answers
The equation of this circle in standard form is x² + y² - 8x - 16y + 73.75 = 0
How to determine the equation of this circle in standard formFrom the question, we have the following parameters that can be used in our computation:
Endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5)
These endpoints represent endpoints of the diameter
So, we have the diameter to be
diameter = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the known values in the above equation, so, we have the following representation
diameter = √[(4 - 4)² + (5.5 - 10.5)²]
Evaluate
diameter = 5
So, we have
radius, r = 5/2
The midpoint is
(a, b)= 1/2[(4 + 4, 5.5 + 10.5)]
So, we have
(a, b)= (4, 8)
The circle equation is calculated as
(x - a)² +(y - b)² = r²
Substitute the known values in the above equation, so, we have the following representation
(x - 4)² +(y - 8)² = 2.5²
This gives
x² - 8x + 16 + y² - 16y + 64 = 6.25
Evaluate the like terms
x² + y² - 8x - 16y + 73.75 = 0
Hence, the equation is x² + y² - 8x - 16y + 73.75 = 0
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Which numbers make a true statement when placed in the box? 11.436>
A:11.422
B:11.484
C:11.621
D:11.286
Answers
Answer:
A and D
Step-by-step explanation:
> means larger than. 11.436 is larger than 11.422 and 11.286, but not 11.484 or 11.621.
Rita has $1,000 in a savings account. The interest rate is 5% per year and is not compounded. How much interest will she earn in 1 year? Use the formula i = p x r x t, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
The interest earned is $50
What is simple interest?Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments. Simple Interest=P×r×t
where:
P=Principal
r= interest rate per annum
t=Number of years
Given here, P = $1000 , r = 5% t=1
thus using the formula we get SI = 1000×5/100×1
= $50
Hence, the interest earned is equal to $50
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For a fundraiser, a group plans to sell x granola bars at $1.25 each and y bottles of water at $0.50 each. the group wants the revenue from the fundraiser to be at least $150. select the inequality that models the situation.
Answers
Answer:
[tex]1.25x + .50y \geqslant 150[/tex]
Mary' peed i inverely related to her drive home. Mary drive home from work in 40 minute driving 55mph. If Mary need yo get home 15 minute earlier, how fat doe he need to drive
Answers
To determine Mary's required speed, we need to first understand the relationship between speed and time.
If Mary's speed is inversely related to her drive home, then this means that as her speed increases, her drive time decreases, and vice versa. In other words, the drive time is inversely proportional to the speed. We can represent this relationship using the equation t = k/s, where t is the drive time, s is the speed, and k is a constant. If we plug in the given values, we get t = 40 minutes = k/55 mph.
Now, if Mary wants to arrive home 15 minutes earlier, we can set the desired drive time equal to 25 minutes (40 minutes - 15 minutes) and solve for the required speed. Substituting this value into the equation above, we get s = k/(25 minutes) = (55 mph)/(25 minutes) = 2.2 mph.
Therefore, Mary needs to drive at a speed of 2.2 mph in order to arrive home 15 minutes earlier. Note that this answer is not realistic, as it is much lower than the speed limit on most roads. This suggests that it may not be possible for Mary to arrive home 15 minutes earlier without breaking the law or increasing her risk of an accident.
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Complete Question:
Mary's speed is inversely related to her drive home. Mary drives home from work in 40 minutes driving 55mph. If Mary needs to get home 15 minutes earlier, how fast dose she need to drive?
A radioactive isotope has a half life of 1 month. It begins with 500 grams. After 8 months, how many grams would it have. Round to the nearest two decimal places.
Answers
Answer:
t1/2=1m => 30days
A0=500g =0.5kg
t=8m = 240days
A=?
λ=ln2÷t1/2
λ=0.6931÷30
λ=0.0231033333
A=A0×e^-λ×t
A=0.5×e^-0.0231033333×240
A=1.953125grams
What's the equation in y=mx+ b form?
Answers
Answer:
y= 2x +4 is the equation
when choosing the play of the mat that you will use for an image, what are you choosing? a. the thickness of the mat b. the color of the mat c. the size of the mat d. the texture of the mat
Answers
When selecting the ply of the mat which we will use for an image, what we choose is the thickness of the mat. The correct answer is option A.
How to choose the right mat?The width of our mat really influences how our art is showed. A perfect rule of thumb is to select a mat which is at least 1 inch wider than our moulding. Many mats are 2-4 inches wide; usually, larger artwork can use a wider mat, and smaller artwork should be paired with a narrower mat.
Mats available in 4 ply (0.040 to 0.052″) and 8 ply (0.125″); but it does not mean all ply are the same. For instance, there are 0.052″ 4 ply and 0.040″ 4 ply. Double or triple 4 ply mats are possible also to be used in area of 8 ply mats to produce a similar effect.
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a researcher at a major hospital wishes to estimate the proportion of the adult population of the united states that has high blood pressure. how large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 5%?
Answers
For the sample to be 99% confident and sample proportion to not differ more than 5% the sample size is 664 .
The term Sample Size is defined as number of observations that is used for determining estimations of a given population .
it is given that , sample proportion should not differ by 5% ,
that means , the Margin of Error (ME) = 0.05 .
Since , the prior information is unknown
we assume the sample proportion(p) = 0.05 .
and level of significance (α) ⇒ 0.01 ;
By using the z table ,critical value for 99% confidence interval is = 2.576
The sample size(n) can be calculated by the formula ,
n = p(1 - p)[(critical value)/ME]² ;
substituting the values of p , critical value and ME in the above equation ,
we get ;
n = 0.05×(1 - 0.05)×[2.576/0.05]²
n = 0.25 × 2654.3104
n = 663.5776
n ≈ 664
Therefore , the required sample size is 664 .
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The fraction 5/6 * i is equivalent to what percent ? Round your percent to the nearest tenth. 5/6 is approximately 96
Answers
It is approximately equal to 83.3%
What are percentages?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”
Given here, 5/6 thus in percentage terms it will be = 5/6 × 100
= 83.3%
Hence the answer is 83.3%
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ts.
11. Given the financial transaction: "Having bought
a pair of shoes worth $85 and used them for a
month". Which of the following statements is
NOT TRUE?
[A] Your cash balance decreases.
[B] You are increasing your liability.
[C] Your wealth decreases.
[D] You are incurring an expense.
[E] You are acquiring (non-cash) asset.
Answers
The correct answer is [B] You are increasing your liability.
When you buy a pair of shoes for $85, your cash balance decreases by $85, which means that your wealth also decreases by $85. This is represented by [A] and [C].
[D] You are incurring an expense is also true, because you are spending money on the shoes.
[E] You are acquiring (non-cash) asset is also true, because you are obtaining an asset (the shoes) that you can use or sell in the future.
[B] You are increasing your liability is not true, because a liability is a debt or an obligation that you owe to someone else. In this case, you are not taking on any debt or obligation by buying the shoes, so your liability does not increase.
A city has a 5% sales tax. What is the constant of proportionality?
Answers
Answer: 0.05
Step-by-step explanation:
The equation is k = y/x, which is a constant change rate
Take 5 divided by 100 = 0.05
5% = 0.05
So the constant of proportionality is 0.05
6.0 percent of a population are infected with a certain disease. there is a test for the disease, however the test is not completely accurate. 90.0 percent of those who have the disease test positive. however 3.1 percent of those who do not have the disease also test positive (false positives). a person is randomly selected and tested for the disease. what is the probability that the person has the disease given that the test result is positive?
Answers
Probability of the person has the diseases and the test result is positive = 1/90 = 0.011
What is probability?Probability refers to the possibility of occurring a certain event. It is expressed by the ratio of the number of favorable outcome to the total possible outcome.
How can we calculate probability?Given, percentage of people who have disease and test result positive =90
percentage of people who has not disease but test result positive =3.1
Suppose 6.0 percent of population are infected
Now, probability of a randomly selected person who has diseases and test positive
= 1/90
= 0.011
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The function f(x) = 5one-fifth is reflected over the y-axis. which equations represent the reflected function? select two options.
Answers
The correct option D. f(x) = 5(5)ˣ and E. f(x) = 5(1/5)⁻ˣ, for the reflected function over the y-axis.
Explain the term reflected over the y-axis?The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be an additive inverse.We are aware of:
f(x) = 5(1/5)ˣ
Positive x-values and negative x-values are switched by a reflection over the y-axis, which also swaps the values of x and x.
Therefore:
f(ax) = f(x)
The following will be the value of the supplied function's y-axis reflection:
(Remember to swap out positive and negative x-values.)
f(x) = 5(1/5)⁻ˣ
A comparable form will be:
f(x) = 5(1/5)⁻ˣ
f(x) = 5(1/5)⁽⁻¹⁾⁽ˣ⁾
f(x) = 5[(1/5)⁻¹]ˣ
f(x) = 5(5)ˣ
Therefore
The following equations depict the reflected function:
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The complete question is-
The function f(x) = 5(1/5)ˣ h is reflected over the y-axis. Which equations represent the reflected function? Select two options.
A. f(x) = One-fifth
B. f(x) = One-fifth.One-fifth.One-fifth
C. f(x) = 5One-fifth
D. f(x) = 5(5)ˣ
E. f(x) = 5(1/5)⁻ˣ
PLLEAASSEEE HELPP MEEEE DONT ANSWER IF U NOT GOING TO HELP PLS
Answers
On solving the provided question by slope intercept form, equation formed id=s 3x + 4y - 14= 0 .
What is Slope Intercept Form?One of the most popular ways to express a line's equation is in the slope intercept form of a straight line. Given the slope of the straight line and the y-intercept, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). A line's equation is the equation that each point on the line fulfills. There are several ways to solve the equation for a straight line given as, - Slope-intercept form, Point slope form Two-point form and Intercept the form
slope = -3/4
points ( -2,5 )
equation,
(y - y1) = m(x - x1)
( y - 5) = -3/4(x+2)
4y - 20 = -3x - -6
3x + 4y - 14= 0
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A table of values of a linear function is shown below. Find the output when the input is n Type your answer in the space provided.
Input 1 2 3 4 n
Output -7 -9 -11 -13
Answers
Output of n= -15