In this case the difference is a multiple of n and as you see the difference is still a sum of some integers subset from 1 to n
What is subset?
If every element of set A is also an element of set B, then set B is a superset of set A and set A is a subset of set B. A and B could be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of another.
Consider the set{a1,a1+a2,a1+a2+a3,...,a1+a2+...+an}You have a set of n elements .If all remainders in dividing by n, are different, one of the remainders is 0 and we are done .Otherwise two remainders are the same.
In this case the difference is a multiple of n and as you see the difference is still a sum of some integers from 1 to n However I think it would be natural to consider the set{0,a1,a1+a2,a1+a2+a3,…,a1+a2+⋯+an}of n+1 elements, so that there is only one case instead of two.
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A landscaper uses boot length to estimate distances. The length of the boot is about 32 cm long. If the landscaper makes a garden that has a width of 3.5 m, approximately how many boot lengths is the width of the garden?
A. 1 boot length
B. 9 boot lengths
C. 11 boot lengths
D. 36 boot lengths
Answer:
I honestly hv iyiu u ughu ugvjug uyvbuyg uugbjug niyhnig mhyij. umnninji. oh jiuh
For each graph describe the domain and range using interval notation. Determine if the graph is a function. Also list increasing,decreasing, or constant intervals
The interval notation, which describes a set of numbers by using values enclosed in brackets, can be used to express the domain and range. When writing intervals, we place a square bracket around the endpoint when it is part of the set and a parenthesis around it if it is not or if the interval is unbound.
What the Finding the Domain of a Function Defined by an Equation?Our introduction to the ideas of domain and range was in Functions and Function Notation. Identifying the domains and ranges for particular functions will be practiced in this session. Be aware that while choosing domains and ranges, we must take into account what is realistically feasible or significant, such as the number of tickets sold and the year in the previous horror movie example. Additionally, we must think about what is allowed mathematically. As an illustration, if the domain and range are real numbers, we cannot include any input value that causes us to take the even root of a negative number. Alternatively, in a function denoted by a formula, we are not allowed to include any input value whose domain would cause us to divide by 0.The interval notation, which describes a set of numbers by using values enclosed in brackets, can be used to express the domain and range. When notating intervals, we use square brackets to denote inclusion of the endpoint in the set and parentheses to denote exclusion of the endpoint or unbounded intervals. The interval that is more than 0 and less than or equal to 100, for instance, must be expressed as [0,100] if someone has $100 to spend.To Learn more About domain and range refer To:
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i need help with the following question below
Answer:
see below
Step-by-step explanation:
b = √3
then move t to the end you'll see
m= -0.4√13
write an expression for the apparent nth term an of the sequence. (assume that n begins with 1.) 3, 10, 29, 66, 127,
the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.
the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.
an = 3*2^(n-1) + 1
The sequence appears to follow a pattern of 3*2^n + 1
Therefore, the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1. (Note that n begins with 1, so we subtract 1 from n.)
The nth term an of the sequence 3, 10, 29, 66, 127, can be expressed as 3*2^(n-1) + 1. This follows a pattern of multiplying the previous term by 2 and then adding 1. For example, the second term 10 is 3*2^1 + 1, and the third term is 3*2^2 + 1. This pattern continues for each term in the sequence, which begins at n=1. Therefore, the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.
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Finding the zeros of a polynomial
To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.
What is a polynomial?
A polynomial is a mathematical expression that is a sum of powers in one or more variables (indeterminates) with non-negative integer exponents and real or complex coefficients. The degree of a polynomial is the highest power of the variable. For example, the polynomial 3x^2 + 2x - 1 is a polynomial of degree 2, and the polynomial 5 is a polynomial of degree 0.
To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.
For example, to find the zeroes of the polynomial 3x^2 + 2x - 1, we set the polynomial equal to zero:
3x^2 + 2x - 1 = 0
Then we can factor the polynomial or use the quadratic formula to find the solutions:
x = (-2 +/- sqrt(2^2 - 43(-1)) ) / (2*3) = (-2 +/- sqrt(4 + 12))/6 = (-2 +/- sqrt(16))/6 = (-1 +/- sqrt(4))/3 = (-1 +/- 2i)/3
The zeroes of the polynomial 3x^2 + 2x - 1 are x = (-1 + 2i)/3 and x = (-1 - 2i)/3, which are complex numbers.
Hence, To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.
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Which linear equation shows a proportional relationship?
y equals two thirds times x
y equals negative 3 times x minus one seventh
y equals three fourths times x minus 5
y equals 3 times x plus 7
Answer: y/x = k, where k is the constant of proportionality.
Step-by-step explanation:
The proportional connection is represented by the linear equation y equals two-thirds times x.
A proportionate connection is a two-variable relationship in which one variable is a constant multiple of the other. In other words, if y is proportional to x directly, then y = kx for some constant k. This can alternatively be written as y/x = k, where k is the proportionality constant.
The proportionate connection is represented by the linear equation y = 2/3x.
It demonstrates a direct connection since the coefficient of x (2/3) is constant and there is no constant term (y-intercept) to break the proportionality.
The other equations do not have a proportionate connection because they feature a variable coefficient or a constant term.
Answer:
y/x = k, where k is the constant of proportionality.
Step-by-step explanation:
Determine the angle between the diagonal of a cube and its edge, as shown in the figure. (Round your answer to one decimal place.)
the angle between the diagonal of a cube and its edge is equal to 35.2 degrees.
Let us consider a cube with side length = a.
Length of diagonal of cube on one of its faces = a√2
Length of diagonal of cube = a√3
To find the angle between the, use law of cosines.
The law of cosines is given by.
⇒ [tex]c^2=a^2+b^2-2abcosC[/tex]
Where c = length of side c, b = length of side b, a = length of side a
C = angle opposite to c
⇒ [tex]c^2=(a\sqrt{2})^2+(a\sqrt{3})^2-2a\sqrt{2}a\sqrt{3}[/tex]
On simplification,
[tex]cosC=\frac{2a^2}{a^2\sqrt{2}\sqrt{3}} \\cosC=\sqrt\frac{2}{3} \\[/tex]
C=35.2 degree
Therefore, the angle between the diagonals is 35.2°
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Find the values of x and y in each parallelogram
The value of x and y of the first parallelogram is x = 7 and y = 9
The value of x and y of the second parallelogram is x = 3 and y = 6
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
a)
Let the first parallelogram be ABCD
Now , the opposite sides are parallel and opposite sides are congruent
So , The measure of AB = measure of CD
And , the measure of AD = measure of BC
Substituting the values in the equation , we get
3x - 5 = 2x + 2 be equation (1)
On simplifying the equation , we get
Subtracting 2x on both sides of the equation , we get
x - 5 = 2
Adding 5 on both sides of the equation , we get
x = 7
Now , 2y - 6 = y + 3 be equation (2)
On simplifying the equation , we get
Subtracting y on both sides of the equation , we get
y - 6 = 3
Adding 6 on both sides of the equation , we get
y = 9
Therefore , the value of x and y of the parallelogram is 7 and 9 respectively
b)
Let the second parallelogram be ABCD
Now , the the diagonals of a parallelogram bisect each other
Let O be the point of intersection of diagonals
So , The measure of AO = measure of CO
And , the measure of DO = measure of BO
Substituting the values in the equation , we get
2x + 5 = 11 be equation (1)
On simplifying the equation , we get
Subtracting 5 on both sides of the equation , we get
2x = 6
Divide by 2 on both sides of the equation , we get
x = 3
Now , y + 4 = 2x + 4 be equation (2)
On simplifying the equation , we get
Substitute the value of x = 3 in the equation , we get
y + 4 = 2 ( 3 ) + 4
y + 4 = 10
Subtracting 4 on both sides of the equation , we get
y = 6
Therefore , the value of x and y of the parallelogram is 3 and 6 respectively
Hence , the measures of parallelogram is solved
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Howww did you fine the answer???
Find the dot product of m=−4i−j and n=5j.
1. Consider the graph of the function y = sin x + cos x. Describe its overall shape.
Is it periodic?
How do you know?
2. Using a graphing calculator or other graphing device, estimate the x- and y-values of the maximum point for the graph (the first such point where x > 0). It may be helpful to express the x-value as a multiple of π.
3. Now consider other graphs of the form y = A sin x + B cos x for various values of A and B.
Sketch the graph when A = 2 and B = 1, and, find the x - and y-values for the maximum point. (Remember to express the x-value as a multiple of π, if possible.)
Has it moved?
4. Repeat and sketch the graph for A = 1, B = 2.
Is there any relationship to what you found in part (2)?
5. Explain what you have discovered from completing this activity using details and examples.
It is revealed through completing the task that the graph of y = sin x + cos x is periodic, having a maximum point at x 0.94 and y 2.24. We've also noted that changing the values of A and B causes the graph to move to the left, with the highest point at x 0.44 and y 2.84. This demonstrates that the ratio of A and B determines the greatest point of the graph.
What does this activity shows?This activity has demonstrated the effect of changing the coefficients of sine and cosine functions when combined. For example, when A and B are both 1, the graph of y = sin x + cos x creates a wave-like shape with a maximum point at (π/2, 2). When A is increased to 2 and B is kept at 1, the maximum point moves to the right and increases in y-value to (2π/3, 3). When B is increased to 2 and A is kept at 1, the maximum point moves to the left and increases in y-value to (π/3, 3). This shows that when the coefficient of the sine term is increased, the maximum point moves to the right, and when the coefficient of the cosine term is increased, the maximum point moves to the left. This also shows that the maximum point of the graph y = A sin x + B cos x increases in y-value as A and B increase.
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How many different committees can be formed from 11 teachers and 50 students if the committee consists of 2 teachers and 2 students?
Answer:
5 committees can be formed
Step-by-step explanation:
number of teachers=11
number of students=50
number of teachers in a committee=2
number of students in a committee=2
Draw a triangle with a side length of 1 1/4 inches and a side length of 1 3/4 inches that meet at a 50 degree angle.
The triangle with the side lengths and the angle is drawn by the image given at the end of the answer.
The area of the triangle is given as follows:
1.68 inches squared.
How to obtain the area of a triangle?The area of a triangle, given two side lengths a and b, and the angle θ between them, is given as follows:
A = ab x sin(θ).
The parameters for this problem are given as follows:
a = 1.25, as 1/4 = 0.25.b = 1.75, as 3/4 = 0.75.The angle is of 50º, hence the area is given as follows:
A = 1.25 x 1.75 x sin(50º)
A = 1.68 inches squared.
Missing InformationThe problem asks for the area of the triangle.
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g as a generalization of the two-dimensional transformation above, what property must the linear transformation a satisfy if the pdfs for x and y, where y
The linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1. In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property.
In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property. To determine this property, we can look at the two-dimensional transformation above, where y = ax + b. In order for the PDFs of x and y to be the same, the linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1. The linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1.In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property.
The complete question is : g as a generalization of the two-dimensional transformation above, what property must the linear transformation a satisfy if the pdfs for x and y, where y = ax + b, are to be the same?
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For every m ≥ 2, let Q(m) be the least positive integer with the following property: For every n ≥ Q(m), there is always a perfect cube k^3 in the range n < k^3 ≤ m.n Find the remainder when Σ 2017 m=2 Q(m) is divided by 1000.
The remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000 is 448.
448
Q(m) is the least positive integer such that for every n ≥ Q(m), there is a perfect cube k^3 in the range n < k^3 ≤ m.
For example, Q(2) = 1 since 1^3 is in the range 1 < 1^3 ≤ 2.
Similarly, Q(3) = 2 since 2^3 is in the range 2 < 2^3 ≤ 3, and Q(4) = 3 since 3^3 is in the range 3 < 3^3 ≤ 4.
We are asked to find the remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000.
To do this, we can calculate the sum of the first 2017 terms of the sequence.
Q(2) + Q(3) + Q(4) + ... + Q(2017) = 448
Since 448 is divisible by 1000, the remainder when the sum is divided by 1000 is 0.
The remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000 is 448.
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8. A vase contains four white roses and one red rose. You randomly select two roses to take home. Use a sample space to determine whether randomly selecting a white rose first and randomly selecting a white rose second are independent events.
Choosing a white rose at random first and then again at a later time are separate actions. based on the information provided White roses in a vase total four.
What is the sample space for this random experiment?All potential results are gathered in a random experiment's sample space. A portion of the sample space is made up of an event connected to a random experiment. A value between 0 and 1 represents the chance of any result. All possible outcomes have a cumulative probability of 1.
A random experiment's sample space, or S, is referred to as the collection of all potential results. The results, often referred to as sample points, in a random experiment are exclusive (i.e., they cannot occur simultaneously). Sample space is the collection of all outcomes that can be found in a random experiment. The S sign stands in for it. the sample space is (S) = (HH), (HT), for two coin tosses, for instance (TT) .
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please i need HELPPP
Answer:
vertex point is (4,-6)
and it opens upwards as the coefficient of x is positive.
I assume B is the correct answer, good luck!
Each day, Millie reads 225 pages of a book while her brother Lee reads 155 pages. Which expression can be used to find p, the total number of pages Millie and Lee read each day?
A. 72-48=r
B. 48+r=72
C.72-r=48
D.72+48=r
The expression for the total number of pages Millie and Lee read each day is 225 + 155.
How to determine the total number of pages Millie and Lee read each day?From the question, we have the following parameters that can be used in our computation:
Mille = 225 pages
Lee = 155 pages
The expression to find the total number of pages Millie and Lee read each day is given by the sum of the individual pages
i.e. p = 225 + 155
So, the expression to find p is p = 225 + 155.
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Can you help me with this question its times
The length of side LN is equal to 44 units. (Correct choice: A)
How to determine a missing length in a system of two similar trianglesTwo triangles are similar when these triangles have congruent angles but non-congruent though proportional sides. Triangles LMN and NUV are similar. Therefore, we can determine the length of side LN of geometrical system by means of following relationship:
NV / LN = NU / MN
LN = NV × MN / NU
If we know that NV = 11, MN = 32 and NU = 8, then the length of side LN is:
LN = 11 × (32 / 8)
LN = 11 × 4
LN = 44
The side LN has a length of 44 units.
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5+w=8 simplified in to simplest form
[tex] \large \frak{ \green 5 + \red{w }= \green 8}[/tex]
[tex] \: [/tex]
[tex] \ \: \large \frak{ \red{w }= \green 8 { -} \green5}[/tex]
[tex] \: [/tex]
[tex] \underline{ \boxed{ \large \frak{ \: \red{w }= \green 3 \: }}}[/tex]
[tex] \: [/tex]
hope it helps!
The sum of ages of Akua and Yeboah is 23 years. Akua is 3 years older than Yeboah. Find: 1. The age of Yeboah. 2. The products of their ages.
Answer:
Step-by-step explanation:
we first have to remove the 3 years as it is the difference
then when we divide it we get the age of yeboah=10
as akua is 3 years older we add the3 to the 10= 13
the product is = 10×13=130
Nick selects a simple random sample of 25 seniors at his large school and finds that 20 of them eat a healthy breakfast. He wants to construct a confidence interval for p = the proportion of all seniors at this school who eat a healthy breakfast, but he realizes he hasn't met all the conditions for constructing the interval. Which condition for this procedure has he failed to meet?
n ≥ 30
n p hat greater-than-or-equal-to 10
n (1 minus p hat) greater-than-or-equal-to 10
The sample size must be less than 10% of the population size.
Nick has failed to meet the condition that n p hat greater-than-or-equal-to 10 and n (1 minus p hat) greater-than-or-equal-to 10.
In order for the Central Limit Theorem to be applied and for the sample proportion to be approximately normally distributed, the sample size must be at least 30. This means that the sample size must be large enough so that the sample proportion of healthy breakfast eaters (p hat) and the sample proportion of non-healthy breakfast eaters (1-p hat) are both greater than or equal to 10. In this case, since the sample proportion of healthy breakfast eaters is 20/25 = 0.8, the sample proportion of non-healthy breakfast eaters is 5/25 = 0.2. Since 5 is less than 10, this condition is not met, and Nick cannot construct a confidence interval for p.
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A rancher wants to enclose a rectangular field with 220 ft of fencing. One side is a river and will not require a fence. What is the maximum area that can be enclosed?
5329 Sq meters is the maximum area that can be enclosed.
What is a rectangle, exactly?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. It is also known as an equiangular quadrilateral for this reason.
The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
Perimeter of Rectangle: 2W + 2L
One L is the river so we have 3 sides
220m/3 = 73m
Area of Rectangle is WL
73 × 73 = 5329 Sq meters
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the inside of a flashlight surrounding the bulb is shaped like a parabola in which the base of the bulb represents the vertex and the top of the bulb represents the focus. which of the following standard equations represents the parabola in which the base of the bulb is at (1, 5) and top of the bulb is at (1, 1)? (x 1)2
The equation for the parabola is: (x - 1)^2 = 4(y - 5). The vertex of the parabola is located at (1, 5) and the focus is at (1, 1). The equation describes a parabola that opens upward, and is symmetrical about the y-axis.
The equation for the parabola is: (x - 1)^2 = 4(y - 5). This equation describes a parabola with its vertex located at (1, 5) and its focus at (1, 1). The parabola is symmetrical about the y-axis and opens upward. This means that the base of the bulb is at (1, 5) and the top of the bulb is at (1, 1). To get the equation for the parabola, we need to subtract the x-coordinate of the vertex from the x-coordinate of the focus, which gives us 1. We then square this number, giving us 1. We then subtract the y-coordinate of the vertex from the y-coordinate of the focus, giving us 4. We then multiply this number by the squared number from before, giving us 4. The final equation is then (x - 1)^2 = 4(y - 5).
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Marie earns £340 each week.She is given a 6.5% pay rise. How much does she earn each week after the pay rise?
Answer:
£362.1
Step-by-step explanation:
6.5% =
6.5 / 100 =
65 / 1000 = 0.065
£340 * 0.065 = £22.1 => £22.1 is the pay raise in terms of English pounds(£)
Now add the pay raise to the earnings per week to get the total earnings after the raise:
£22.1 + £340 =
£22.1 + £340.0 = £362.1
Si mi tía llega a la casa con cuatro donas de azúcar y estamos seis personas en la casa ¿ de cuánto nos tocaría ha cada uno en fracciones?
A coda ulna de las personas le Toccara ulna porcino de 2/3 de Dona
de canto no's Toccara ha coda uno eon fractions?Si mi tía ha legato a la casa y trae consigo 4 Donas de azúcar, pero no se ha percatado que la cantidad de personas en la casa es de 6 contándose, entonces decide repartir en partes iguales, para esta operation deems divider la candida de donnas entre la cantidad de personas
4 donnas / 6 personas = 2 /3 ester 2/3 es la porcino de coda uno es décor coda Dona se picara eon tress torsos y dos torsos para coda persona de 2/3
Respuesta:
para que alkanes les tocaria
a 4 personas la mated de una dona
(osea 2 donas las partes a la mated)
y a las okras 2 personas la Dona entera
Explication paso a paso:
esparto hiver aoudad:)
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An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in
x = 18.19 kgf/cm2 for the modified mortar (m = 42) and y = 16.87 kgf/cm2 for the unmodified mortar (n = 32). Let m1 and m2 be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal.
(a) Assuming that ?1 = 1.6 and ?2 = 1.3, testH0: m1 ? m2 = 0 versus Ha: m1 ? m2 > 0 at level 0.01.
State the rejection region(s). (If the critical region is one-sided, enter NONE for the unused region. Round your answers to two decimal places.)
z ? z ? Compute the test statistic value. (Round your answer to two decimal places.)
z = State the conclusion in the problem context.
Reject H0. The data does not suggest that the difference in average tension bond strengths exceeds 0.
Fail to reject H0. The data does not suggest that the difference in average tension bond strengths exceeds from 0.
Fail to reject H0. The data suggests that the difference in average tension bond strengths exceeds 0.
Reject H0. The data suggests that the difference in average tension bond strengths exceeds 0.
the data suggests that the difference in average tension bond strengths is greater than 0. In other words, the polymer latex modified mortar has a higher tension bond strength than the unmodified mortar.
a) The rejection region for this one-tailed hypothesis test is z ? z > 2.33.
The test statistic value is z = 2.76.
Therefore, the conclusion is that we reject H0. The data suggests that the difference in average tension bond strengths is greater than 0.
For this one-tailed hypothesis test, we must reject the null hypothesis (H0: m1 - m2 = 0) if the test statistic is greater than 2.33. Our test statistic value is 2.76, which is greater than 2.33, so we reject H0. This indicates that the data suggests that the difference in average tension bond strengths is greater than 0. In other words, the polymer latex modified mortar has a higher tension bond strength than the unmodified mortar.
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What is the equation in slope intercept form?
2x−y=−21
The required equation in slope intercept form is equal to y = -2x - 21.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x and y represents the data points.m represents the slope of a line.c represents the y-intercept of a line.Based on the information provided about the line, it is represented by this equation;
2x - y = -21
Making y the subject of formula in the above equation, we have the following:
y = -2x - 21
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Premises: If a child is arrested for a minor crime, he or she is either charged with the crime or released with no charges. A child released with no chargers cannot be required by the court to seek counseling. Children are almost never charged with first time they are arrested. A child, Jonathan, was arrested for a first crime and is required by the court to seek coun Conclusion: Jonathan was not charged with the crime
Necessarily true
Probably, but not necessarily, true.
Indeterminable, cannot be determined.
Probably, but not necessarily, false/
Necessarily false.
The correct option is e. (Necessarily False) It required by the court to seek counselling
Because it is given as a fact that the child was "required by the court to seek counselling" ; and there is already P -> Q statement; where P : A child is released with no charges. and Q : Child is NOT required by the court to seek counseling. Taking the negation of this [tex]$\sim Q \Longrightarrow \sim P$[/tex]
[tex]$\sim P:$[/tex]Child is released with some charge.
If your child is arrested for a criminal offence and they are under 18, the police must tell you as soon as possible. The police should not interview your child until you are present, unless a delay would mean an immediate risk of harm to someone or serious loss of, or damage to, property.
Legal Counselling is the process by which a lawyer communicates advice to a client. I cannot emphasize anymore over the fact that it is the duty of an advocate to fearlessly uphold the interests of his client by all fair and honorable means without regard to any unpleasant consequences to himself or any other.
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Kerri keeps a bowl of change on her dresser. She only keeps dimes and quarters. She has five dollars in change in the bowl right now. If she has exactly 29 coins in the bowl, how many quarters does she have?
The number of quarters in the bowl is 14.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x+ 3 = 9 is an equation.
We have,
Dimes = x
Quarters = y
10 dimes = $1
1 dime = $0.1
4 quarters = $1
1 quarter = $0.25
Now,
0.1x + 0.25y = 5 _____(1)
x + y = 29 _____(2)
Solve for y from (1) and (2),
x = 29 - y
Substitute in (1) we get,
0.1 (29 - y) + 0.25y = 5
2.9 - 0.1y + 0.25y = 5
2.9 + 0.15y = 5
0.15y = 5 - 2.9
y = 2.1/0.15
y = 14
Thus,
There are 14 quarters in the bowl.
Learn more about equations here:
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