MatemáticasJavier pagó $92 por 5 libretas y 3 lápices. Laura compró 2 libretas y 6 lápices, y pagó $56, ¿cuál es el
precio de cada libreta y de cada lápiz?
A) $11 por una libreta y $5 por un lápiz.
B)
$13 por una libreta y $9 por un lápiz.
C)
$16 por una libreta y $4 por un lápiz.
D) $10 por una libreta y $6 por un lápiz.
Answers
If Javier paid $92 for 5 notebooks and 3 pencils and Laura paid $56 for 2 notebooks and 6 pencils, then the price of each notebook is $16 and that of each pencil is $4, calculated using linear equations.
As per question statement, Javier paid $92 for 5 notebooks and 3 pencils while Laura paid $56 for 2 notebooks and 6 pencils.
We are required to calculate the price of each notebook and each pencil.
To solve this question, let us assume that the price of each notebook is "x" and that of each pencil is "y". Now, we will form two linear equations, each with the two assumed variables, based on the conditions mentioned in the question statement, and solving the equations, we will obtain our desired answer.
Since Javier bought 5 notebooks and 3 pencils for $92 and the price of each notebook is assumed to be "x" and that of each pencil is assumed to be "y", we can write that
\([(5x+3y)=92]...(1)\\or,5x = 92-3y\\or,x=\frac{(92-3y)}{5}...(2)\)
And in Laura's case, she bought 2 notebooks and 6 pencils for $56, i.e.,
\([(2x+6y)=56]...(3)\\or, 2(x+3y)=56\\or, (x+3y)=\frac{56}{2}\\ or,(x+3y)=28\\or,x=(28-3y)...(4)\)
Now, equating (2) and (4), we get,
\(x=\frac{(92-3y)}{5}=(28-3y)\\ or, \frac{(92-3y)}{5}=(28-3y)\\ or, (92-3y)=5(28-3y)\\or, 92-3y=140-15y\\or,(15y-3y)=140-92\\or,12y=48\\or,y=\frac{48}{12}=4\)i.e., Price of each pencil is $4.
Now, using (y = 4) in the equation (4), we get,
\(x=[28-(3*4)]\\or,x=(28-12)\\or,x=16\)i.e., Price of each notebook is $16.
Hence, the correct answer is
option(C) $16 for a notebook and $4 for a pencil.
linear equations: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line and hence comes the name "Linear". Here, each term has an exponent of 1 and is often denoted as (y = mx + c) where, 'm' is the slope and 'b' is the y-intercept. Occasionally, it is also called as a "linear equation of two variables," where y and x are the variables.Variable: n Mathematics, a variable is a symbol or a representative of a value, which is unknown.To learn more about Linear Equations, click on the link below.
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Related Questions
a data set has its first and third quartiles as 9 and 17 respectively. Which of the following data points would be considered an outlier for the data set
A. 27
B. 17
C. 3
D. 41
In which of these cases should the mean be used?
A. When the data is left-skewed
B. When the data is symmetric
C. When the data is right-skewed
D. When the data has extreme values
Answers
To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).
We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:
IQR = Q3 - Q1 = 17 - 9 = 8
To identify outliers, we can use the following rule:
- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.
Using this rule, we can evaluate each data point:
A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.
B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).
C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.
D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.
Therefore, the outliers in the data set are A (27) and D (41).
As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.
Therefore, the correct option would be B. When the data is symmetric.
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Write the first four multiples of each number.
1. 3
2. 4
3. 8
4. 15
Answers
Answer:
3, 6, 9, 12
4, 8, 12, 16
8, 16, 24, 32
15, 30, 45, 60
Step-by-step explanation:
multiply each number by itself
The students at a certain high school have an elective period, where each student chooses an elective from among four options. The following table shows the number of students who selected each elective for the 1,500 students at the high school.
Answers
If each student can only choose one elective, picking both is impossible, making the probability 0.
There is no chance of picking a single kid for music and art electives (0).
Information disclosed:
A high school's students are participating in electives.
Since each student is only allowed to choose one elective course from the options provided, they can either choose music or art as their elective.
Therefore, it is impossible to choose a student who has chosen to study art and music.
As a result, there is no chance of picking a student for whom both music and art are electives (0).
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observations 1 2 3 4 5 6 num. of defects 10 18 13 15 9 12the number of runs above and below the sample median is:
Answers
The median element of a dataset is the middle element of the dataset.
There are 3 runs above and below the sample median
What is the median of a data set ?
The median of a data set is the value that falls in the middle, indicating that 50% of the data points have values that are lower or equal to the median and 50% of the data points have values that are higher or equal to the median. When working with a small data collection, you must first count the number of data points (n) and organize them in ascending order.
The information is given as:
Observations 1 2 3 4 5 6
Defects 10 18 13 15 9 12
In ascending order, the information is represented as:
Defects 9 10 12 13 15 18
Observations 5 1 6 3 4 2
The total number of observations is:
n=5+1+6+3+4+2 = 21
The median element is calculated as:
Median = (n+1)/2 th
Substitute 21 for n
Median = (21+1)/2 th
Median = 11th
The 11th element is 12.
So, the median is:
median = 12
Considering the given information;
Observations 1 2 3 4 5 6
Defects 10 18 13 15 9 12
The defects greater than the median (i.e. 12) are above (A) the median, while the defects less than the median are below (B)
So, we have:
Observations 1 2 3 4 5 6
Defects 10 18 13 15 9 12
Status B A A A B -
Next, we take a count of the number of times the status changes, i.e. from B to A, from A to B, from A or B to -
The count is 3.
Hence, there are 3 runs above and below the sample median
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According to the video above, the geometric object called a(n) ___ has the characteristics that it has one endpoint and extends in away from that endpoint without end.
Answers
They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.
According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.
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Write a story that could represent this math problem. 70 points
Answers
Answer:
2/3+2/3+2/3+2/3+2/3
Step-by-step explanation:
Write four different expressions for the perimeter of a square whose sides are all s 2 2 units long.
Answers
Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both.
What are expressions in maths?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You may think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.For a square whose side are 2 units long is :
= 2 + 2 x 2 + 2
= ( 2 + 2 ) x 2
= 2 x 4
= 2 x 3 + 2 = 8
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Find the 8th partial sum of the sequence an=24(–1)n. (picture included)
Answers
The sequence's eighth partial total, then, is zero.
A sequence, is it a math?A series is a collection of things that is in order in mathematics. (or events). Similar to a group, it has individuals. (also called elements, or terms). The total length of the series is the number in ordered components (possibly endless).
The sequence is: 24, -24, 24, -24, ...
To find the 8th partial sum, we need to add the first 8 terms of the sequence.
S8 = 24 + (-24) + 24 + (-24) + 24 + (-24) + 24 + (-24)
Simplifying this expression, we see that every pair of adjacent terms cancels each other out, leaving us with:
S8 = 0 + 0 + 0 + 0
Therefore, the 8th partial sum of the sequence is 0.
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Isoke is solving the quadratic equation by completing the square. 10x2 40x-13=0 10x2 40x=13 a(x2 4x)=13
Answers
The value of a is 10 by solving the quadratic equation by completing the square method.
In this question,
Completing the square is a method in algebra that is used to write a quadratic expression in a way such that it contains the perfect square. It is a method that is used for converting a quadratic expression of the form ax^2 + bx + c to the vertex form a(x - h)^2 + k.
The quadratic equation is
10x^2 + 40x - 13 = 0
Solving the quadratic equation by completing the square as
Step 1:
10x^2 + 40x = 13
Step 2:
10(x^2 + 4x) = 13
Thus on comparing the step 2 with the equation a(x^2 + 4x) = 13, the value of a is 10.
Hence we can conclude that the value of a is 10 by solving the quadratic equation by completing the square method.
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Of 100 random students surveyed, 42 own a dog, 34 own a cat, 15 own a dog and a cat, and 9 own neither a dog nor a cat. Based upon the results, how many of the next 20 students surveyed would you expect to own a dog and a cat?
Answers
In the next 20 students surveyed, you would expect 5 to own a dog and a cat
How many of the next 20 students surveyed would you expect to own a dog and a cat?From the question, we have the following parameters that can be used in our computation:
Dog = 42
Cat = 34
Dog and cat = 15
Neither = 9
This means that
P(Dog and cat) = 15/100
When evaluated, we have
P(Dog and cat) = 5/20
So, when the next 20 students surveyed, we have
Dog and cat = 5/20 * 20
Evaluate
Dog and cat = 5
Hence, the number of dogs and cats is 5
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a cylinder has a height of 18 meters and a radius of 18 meters what is the volume
Answers
Answer:
18321.77m^3
Step-by-step explanation:
V=πr2h=π·182·18≈18321.76836m³
Answer:
18,329.14 (2 DP)
Using 22/7 for pi
V = πr²h = π × 18² × 18 ≈ 18,329.14
What is the length for both questions???
Answers
Answer:
1). 5.2 cm
2). 8.3 cm
step by step explanation
Answer:
5.4 and 8.6
Step-by-step explanation:
This is the right answer
Test the exactness of ODE, if not, use an integrating factor to make exact and then find general solution: (2xy-2y^2 e^3x)dx + (x^2 - 2 ye^2x)dy = 0.
Answers
It is requred to test the exactness of the given ODE and then find its general solution. Then, if the given ODE is not exact, an integrating factor must be used to make it exact.
This given ODE is:(2xy - 2y²e^(3x))dx + (x² - 2ye^(2x))dy = 0.To verify the exactness of the given ODE, we determine whether or not ∂Q/∂x = ∂P/∂y, where P and Q are the coefficients of dx and dy respectively, as follows: P = 2xy - 2y²e^(3x) and Q = x² - 2ye^(2x).Then, we have ∂P/∂y = 2x - 4ye^(3x) and ∂Q/∂x = 2x - 4ye^(2x).Thus, since ∂Q/∂x = ∂P/∂y, the given ODE is exact.To solve the given ODE, we have to find a function F(x,y) that satisfies the equation Mdx + Ndy = 0, where M and N are the coefficients of dx and dy respectively. This is accomplished by integrating both P and Q with respect to their respective variables. We have:∫Pdx = ∫(2xy - 2y²e^(3x))dx = x²y - y²e^(3x) + g(y), where g(y) is a function of y. We differentiate both sides of this equation with respect to y, set it equal to Q, and then solve for g(y). We have:(d/dy)(x²y - y²e^(3x) + g(y)) = x² - 2ye^(2x)Thus, g'(y) = 0 and g(y) = C, where C is a constant.Substituting the value of g(y) in the equation above, we get:x²y - y²e^(3x) + C = 0, as the general solution.The given ODE is exact, so we can solve it by finding a function that satisfies the equation Mdx + Ndy = 0. After integrating both P and Q with respect to their respective variables, we find that the general solution of the given ODE is x²y - y²e^(3x) + C = 0.
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The parent function of graph C below is:
A) y=b^x
B) y=|x|
C) y=sqrtx
D) y=x^3
Answers
Answer: Well, it’s obviously not the first one. But if you could scroll down, so I could see the other graphs, that would be amazing. It would also help me answer the question!
Step-by-step explanation:
What is the volume of a cone if the diameter is 5 and the height is 13?
Answers
Answer:
volume = 85.095cm³
Step-by-step explanation:
Volume of cone is ¹/³ πr ²h
volume = ¹/³ x 3.142 x (2.5)² x 13
volume = 85.095cm³
Answer: D.
Step-by-step explanation:
V(cone)=(1/3)\(\pi r^{2} h\) they gave diameter=5 but radius is half of that
r=2.5 h=13
V(cone)=\((1/3)\pi (2.5)^{2} 13\) to get an answer like the choices. multiply everything in calculator except pi
so
V(cone)=27.083\(\pi\)
=
Finding a final amount in a word problem on exponential growt...
A principal of $4000 is invested at 5.25% interest, compounded annually. How much will the investment be worth after 11 years?
Use the calculator provided and round your answer to the nearest dollar.
$
X
5 ?
Answers
Solve: 25.8 - 14 / 2 = ?
Round your answer to the nearest
one decimal place.
Answers
The result of the equation 25.8 - 14 / 2, rounded to the nearest one decimal place, is 18.8.
To solve the equation 25.8 - 14 / 2, we need to perform the division first, and then subtract the result from 25.8.
Division: 14 divided by 2 equals 7.
Subtraction: 25.8 minus 7 equals 18.8.
Rounding to one decimal place: The answer, 18.8, rounded to the nearest one decimal place, remains as 18.8.
Therefore, the result of the equation 25.8 - 14 / 2, rounded to the nearest one decimal place, is 18.8.
Following the order of operations (PEMDAS/BODMAS), we prioritize the division operation before subtraction. Thus, we divide 14 by 2, resulting in 7. Then, we subtract 7 from 25.8 to obtain 18.8. Since no rounding is necessary for 18.8 when rounded to one decimal place, the answer remains as 18.8.
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What is another word for change in y
Answers
When finding the slope of real-world situations, it is often referred to as rate of change. change in y Rate of change = change in x change in height change in time The average rate of change or a rider between 0 and 5 seconds is —24 ft/s. magnitude relation. Another synonym is "velocity".
Hope this helps
If a significant result is yielded by a repeated-measures analysis of variance, _____ would be used to determine which levels of the independent variable significantly differ from each other.
Answers
If a significant result is yielded by a repeated-measures analysis of variance, post - hoc tests would be used to determine which levels of the independent variable significantly differ from each other.
What is the purpose of a post hoc test?
When an analysis of variance (ANOVA) F test indicates that there are significant differences between three or more group means, post hoc (Latin for "after this") tests are employed to identify the precise discrepancies.
When an experiment's findings show that the dependent variable has a substantial effect size You can infer it from this, right?
In a between-subjects design, the independent variable has two levels. When the outcome of an experiment reveals a big effect size for the dependent variable, the degree of difference between groups reveals a practically significant conclusion.Learn more about independent variable
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a card is chosen at random from a deck of 52 playing cards. what is the probability that the card chosen is a hearts or a king?
Answers
Answer:
16/52
8/26
4/13
As 13 cards are one suit or are hearts, and in that suit, there is one king, I just add 3 more cards for the other king cards as well and you get 16/52
Step-by-step explanation:
Please please please!!! Help!! I got 10 more minutes
Answers
The region invthe first quadrant bounded by the graph of y = secx, x =π/4, and the axis is rotated about the x-axis what is the volume of the solar gnerated
Answers
V = 2π [x * ln|sec(x) + tan(x)| - ∫ln|sec(x) + tan(x)| dx]. The remaining integral on the right side can be evaluated using standard integral tables or computer software.
To find the volume of the solid generated by rotating the region in the first quadrant bounded by the graph of y = sec(x), the x-axis, and the vertical line x = π/4 about the x-axis, we can use the method of cylindrical shells.
First, let's visualize the region in the first quadrant. The graph of y = sec(x) is a curve that starts at x = 0, approaches π/4, and extends indefinitely. Since sec(x) is positive in the first quadrant, the region lies above the x-axis.
To find the volume, we divide the region into infinitesimally thin vertical strips and consider each strip as a cylindrical shell. The height of each shell is given by the difference in y-values between the function and the x-axis, which is sec(x). The radius of each shell is the x-coordinate of the strip.
Let's integrate the volume of each cylindrical shell over the interval [0, π/4]:
V = ∫[0,π/4] 2πx * sec(x) dx
Using the properties of integration, we can rewrite sec(x) as 1/cos(x) and simplify the integral:
V = 2π ∫[0,π/4] x * (1/cos(x)) dx
To evaluate this integral, we can use integration by parts. Let's set u = x and dv = (1/cos(x)) dx. Then du = dx and v = ∫(1/cos(x)) dx = ln|sec(x) + tan(x)|.
After evaluating the integral and applying the limits of integration, we can find the volume V of the solid generated by rotating the region about the x-axis.
It's important to note that the integral may not have a closed-form solution and may need to be approximated numerically.
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Pls, help...
Find the equation of the line.
Use exact numbers
y=__x+__
Answers
\(m = \frac{5 - 4}{0 - 3} = \frac{ - 1}{3} \)
\(b = 5 \: \: \: \: (y \: intercept)\)
\(y = \frac{ - 1}{3} x + 5\)
Which transformations can be used to create frieze patterns?
Answers
Every frieze pattern can be mapped onto itself by a translation. Some also can be mapped onto themselves by other transformations, such as reflections. Decide whether each frieze pattern can be mapped onto itself by a reflection in a horizontal line, a vertical line, or both.
f(x) = -x² +9
Find f(-5)
Answers
Answer:
f(-5) = -16
Step-by-step explanation:
f(-5) = - \((-5)^{2}\) + 9
-(25) + 9
-25+9
-16
can someone answer page 3 question 3, page 5 question 3, all of page 6
Answers
The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7
What is trigonometrical ratios?Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle. There are three common trigonometric ratios: sine, cosine, and tangent
For page 3 question 3,
a) <A + <B = 90 since <C = right angle
b) SinA = BC/AB and CosB = BC/AB
The ratio of the two angles BC/AB ÷ BC/AB = 1
I notice that the ratio of sinA and cosB gives 1
b) The ratio of CosA and SinB will give
BC/AB ÷ BC/AB
= BC/AB * AB/BC = 1
For page 5 number 3
Tan28 = g/i
g/12.2 = tan28
cross multiplying to have
g = 12.2*tan28
g = 12.2 * 0.5317
g = 6.5
b) the angle I is given as 90-28 degrees
<I = 62 degrees
To find the side h we use the Pythagoras theorem
h² = (12.2)² + (6.5)²
h² = 148.84 +42.25
h²= 191.09
h=√191.09
h= 13.8
For page 6
1) Sin42 = x/18
x=18*sin42
x = 18*0.6691
x = 12.0
2) cos28 = 6/x
xcos28 = 6
x = 6/cos28
x [= 6/0.8829
x = 6.8
3) Tan63 = x/34
x = 34*tan63
x= 34*1.9526
x = 66.4
4) Sin50 123/x
xsin50 = 123
x = 123/sin50
x = 123/0.7660
x =160.6
5) Sin57 = P/8
Pole = 8sin57
the pole = 8*0.8387
The pole = 6.7
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which of the following statements is true
about rays
Answers
The true statement about ray is that B. They are one-dimensional objects
What is a ray?They are one-dimensional entities. This also applies to line segments and lines. When it comes to determining a location on a one-dimensional object, there is only one component to consider.They are one-dimensional entities.
This also applies to line segments and lines. When it comes to determining a location on a one-dimensional object, there is only one component to consider.
A number line, for example, is one-dimensional because we only need one number to determine where we are. A ray is essentially a half-line, or a line is the combination of two rays glued together. A ray will always point in one direction, whereas a line will point in two opposite directions.
A ray is a a half-line, or a line is the combination of two rays glued together. Therefore based on the information the correct option is B.
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Complete question
Which of the following statements is true about rays?
OA. They are zero-dimensional objects
B. They are one-dimensional objects,
OC. They are three-dimensional objects
OD. They are two-dimensional objects
1/2 gallon in 5 hours how many gallons per hour
Answers
A quadrilateral has no right angles, and two pair of congruent, parallel sides. What is the figure
Answers
Answer:
rhombus, or a parallelogram
Step-by-step explanation:
2.13 A weird density curve A line segment can be considered a density "curve" as shown
in Exercise 2.1A bekline graph can abe b ended a demiry curve. Figure 2.10
shows such a demity curve.
Figure 2.10 An unusual broken-line" density curve, for Exercise 2.13
0.2
0.4
0.5
0.3
(a) Verify that the graph in Figure 2.10 is a valid density curve.
For each of the following, use areas under this density curve to find the proportion of
observations within the given interval
(b) 0.6 ≤ x ≤0.8
(c) 0≤x≤ 0.4
(d) 0≤x≤02
(e) The median of this density curve is a point between X=0.2 and X=0.4. Explain why.
Answers
Regarding the piecewise curve and probabilities, we have that:
a) The figure is a value density curve because the area under the figure is of 1.
b) The probability is: P(0.6 ≤ X ≤ 0.8) = 0.2.
c) The probability is: P(0 ≤ X ≤ 0.4) = 0.6.
d) The probability is: P(0 ≤ X ≤ 0.2) = 0.3.
e) The median is the value of a for which P(0 ≤ X ≤ a) = 0.5, P(0 ≤ X ≤ 0.2) = 0.3 and P(0 ≤ X ≤ 0.4) = 0.6, hence the median of this density curve is a point between X=0.2 and X=0.4.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
For this problem, to the left of x = 0.4, we have a linear curve with:
An intercept of 2.Slope of -2.5, as when x increases by 0.4, y decays by 1.Then, considering the constant:
y = -2.5x + 2, x ≤ 0.4.y = 1, 0.4 < x ≤ 0.8.To represent a distribution, it's area over the entire interval has to be of 1. The area is composed by.
A rectangle of dimensions 1 and 0.8.A right triangle with dimensions 1 and 0.4.Hence the total area is:
A = 0.8 x 1 + 0.5 x 0.4 x 1 = 1.
Hence:
The figure is a value density curve because the area under the figure is of 1.
For itens b to d, the probabilities are also given by areas, hence:
0.6 ≤ X ≤ 0.8 = 1 x 0.2 = 0.2.0 ≤ X ≤ 0.4 = 1 x 0.4 + 0.5 x 0.4 x 1 = 0.6.0 ≤ X ≤ 0.2 = 1 x 0.2 + 0.5 x 0.2 x 1 = 0.3.For item e, we have that:
The median is the value of a for which P(0 ≤ X ≤ a) = 0.5, P(0 ≤ X ≤ 0.2) = 0.3 and P(0 ≤ X ≤ 0.4) = 0.6, hence the median of this density curve is a point between X=0.2 and X=0.4.
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