3x + y = 9
Y= 3x +6
How to solve in systems of elimination ?
Answers
We have:
3x + y = 9
y = 3x + 6
3x + y = 9 ⇔
⇔ 3x + (3x + 6) = 9 ⇔
⇔ 3x + 3x + 6 = 9 ⇔
⇔ 6x + 6 = 9 ⇔
⇔ 6x = 9 - 6 ⇔
⇔ 6x = 3 ⇔
⇔ x = 3/6 ⇔
⇔ x = 1/2 = 0,5
y = 3x + 6 ⇔
⇔ y = 3 × 0,5 + 6 ⇔
⇔ y = 1,5 + 6 ⇔
⇔ y = 7,5
Related Questions
Given: sin(18m-12)=cos(7m+2), find the value of m.
Answers
Answer:
m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z
or m = 2/3 - (π n_2)/18 for n_2 element Z
Step-by-step explanation:
Solve for m:
-cos(7 m + 2) sin(12 - 18 m) = 0
Multiply both sides by -1:
cos(7 m + 2) sin(12 - 18 m) = 0
Split into two equations:
cos(7 m + 2) = 0 or sin(12 - 18 m) = 0
Take the inverse cosine of both sides:
7 m + 2 = π n_1 + π/2 for n_1 element Z
or sin(12 - 18 m) = 0
Subtract 2 from both sides:
7 m = -2 + π/2 + π n_1 for n_1 element Z
or sin(12 - 18 m) = 0
Divide both sides by 7:
m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z
or sin(12 - 18 m) = 0
Take the inverse sine of both sides:
m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z
or 12 - 18 m = π n_2 for n_2 element Z
Subtract 12 from both sides:
m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z
or -18 m = π n_2 - 12 for n_2 element Z
Divide both sides by -18:
Answer: m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z
or m = 2/3 - (π n_2)/18 for n_2 element Z
consider this equation.
1/2x^4 - 4x + 1 = 3/x-1 + 2
approximate the solution to the equation using three iterations of successive approximation. use the graph as a starting point.
a. x≈ 17/8
b. x≈ 35/16
c. x≈ 33/16
d. x≈ 19/8
Answers
The solution to the equation using three iterations of successive approximation is x≈35/16.
What is graph?
A graph is a structure that resembles a set of objects where some pairings of the objects are conceptually "connected" in discrete mathematics, more specifically in graph theory. Each connection between two adjacent vertices is referred to as an edge, and the items are symbolised by vertices, which are mathematical abstractions.
From the graph we get that at x=2.23 both graphs intersect each other.
17/8=2.125
35/16=2.1875
33/16=2.0625
19/8=2.375
35/16 is the nearest value to 2.23
Hence the correct answer is b, x≈ 35/16
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2. Suppose a 3×3 matrix A has eigenvalues 0,3,5∈R with corresponding independent eigenvectors u,v,w∈R3. (a) (5 points) Give a basis for the nullspace of A. (b) (5 points) Give a basis for the column space of A. (c) (5 points) Find a particular solution to Ax=v+w. (d) (5 points) Find all solutions to Ax=v+w.
Answers
After considering the given data we conclude that
a) basis for the nullspace of A is the trivial subspace, and there is no basis for the nullspace of A,
b) basis for the column space of A is is {u, v, w}
c) particular solution to \(Ax=v+w is x = pu + rw + (5/3)(h + (5/3)i)u + hv + iw\), where p, r, h, and i are constants,
d) solutions to Ax=v+w is \(x = au + (b - 3a)/3 v + (c - 5a)/5 w + pu + rw + (5/3)(h + (5/3)i)u + hv + iw\), where a, b, c, p, r, h, and i are constants.
To evaluate the basis for the nullspace of a 3x3 matrix A with given eigenvalues and eigenvectors, and to evaluate a particular solution and all solutions to a linear system, we can apply the following steps:
(a) To evaluate a basis for the nullspace of A:
Since A has eigenvalue 0, the nullspace of A is nontrivial.
Let us consider x be a vector in the nullspace of A. Then, Ax = 0.
Since u, v, and w are independent eigenvectors of A, any linear combination of them is also an eigenvector of A.
Then, we can express x as a linear combination of u, v, and w: \(x = au + bv + cw\), where a, b, and c are constants.
Staging this expression for x into the equation Ax = 0, we get \(a(0)u + b(3)v + c(5)w = 0.\)
Since u, v, and w are independent, we can conclude that a = b = c = 0.
Finally , the nullspace of A is the trivial subspace, and there is no basis for the nullspace of A.
(b) To evaluate a basis for the column space of A:
Since A is a 3x3 matrix, the column space of A is a subspace of R^3.
Since A has three linearly independent eigenvectors, the column space of A is spanned by these eigenvectors.
Then, a basis for the column space of A is {u, v, w}.
(c) To evaluate a particular solution to \(Ax = v + w\):
Since A has eigenvalue 3 with corresponding eigenvector v, we can express v as a linear combination of u and v: v = pu + qv, where p and q are constants.
Similarly, since A has eigenvalue 5 with corresponding eigenvector w, we can express w as a linear combination of u and w: \(w = ru + sw\), where r and s are constants.
Staging these expressions for v and w into the equation \(Ax = v + w\), we get \(A(x - pu - rw) = qv + sw\).
Since qv + sw is a linear combination of the eigenvectors of A, it is an eigenvector of A with eigenvalue 3q + 5s.
Then, we can choose x - pu - rw to be an eigenvector of A with eigenvalue 3q + 5s.
Let \(x - pu - rw = tu + hv + iw\), where t, h, and i are constants.
Staging this expression for x into the equation \(Ax = v + w\), we get \((3h + 5i)w = qv + sw.\)
Since v and w are independent, we can conclude that q = 0 and \(s = (3h + 5i)/5.\)
Finally , a particular solution to \(Ax = v + w is x = pu + rw + (5/3)(h + (5/3)i)u + hv + iw\), where p, r, h, and i are constants.
(d) To evaluate all solutions to Ax = v + w:
Since A has eigenvalues 0, 3, and 5, we can express any vector b in R^3 as a linear combination of the eigenvectors of A: \(b = xu + yv + zw\), where x, y, and z are constants.
Staging this expression for b into the equation \(Ax = v + w\), we get \(Ax = xu + 3yv + 5zw.\)
Since u, v, and w are eigenvectors of A, we can express x, y, and z in terms of a, b, and c, where a, b, and c are constants: x = a, y = (b - 3a)/3, and z = (c - 5a)/5.
Hence, the general solution to Ax = v + w is \(x = au + (b - 3a)/3 v + (c - 5a)/5 w + pu + rw + (5/3)(h + (5/3)i)u + hv + iw\), where a, b, c, p, r, h, and i are constants
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4s4 17s2 14s 2 = (2s3 3s2-4s 1)(x)
Answers
The required difference of the polynomial functions is -9s^2 + 4s - 2
Given the following difference of polynomial expressed as:
(–6s2 + 12s – 8) – (3s2 + 8s – 6)
We are to find the difference
(–6s2 + 12s – 8) – (3s2 + 8s – 6)
Expand
–6s^2 + 12s – 8 - 3s^2 - 8s + 6
Collect the like terms
–6s^2- 3s^2 + 12s - 8s - 8 + 6
-9s^2 + 4s - 2
Hence the required difference of the polynomial functions is -9s^2 + 4s - 2
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complete question
Find each difference.
(–6s2 + 12s – 8) – (3s2 + 8s – 6) =
–9s2 + 4s – 14
–9s2 + 4s – 2
–9s2 + 20s – 14
–9s2 + 20s – 2
if ab is parallel to cd and slop of ab is -3 what is the slope of cd
Answers
Answer:
-3
Step-by-step explanation:
Parallel lines share the same slope. Therefore, the slope of cd is -3.
1. (x + 2)(2x + 3) =
???? Help lol
Answers
Answer:
\(2x^2+7x+6\)
Step-by-step explanation:
Use the FOIL method to multiply these two expressions:
\((x+2)(2x+3)\\x(2x)+2(2x)+3(x)+2(3)\\2x^2+4x+3x+6\\2x^2+7x+6\)
What do you call the formula y =Mx+b
Answers
Answer:The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis
Step-by-step explanation:
suppose a population grows according to the logistic equation but is subject to a constant per capita harvest rate of h. if n(t) is the population size at time t, the population dynamics are dn dt
Answers
The equation \(\frac{{dN}}{{dt}} = rN(1 - \frac{{N}}{{K}}) - h\), where \(N(t)\) is the population size at time \(t\), \(r\) is the intrinsic growth rate, \(K\) is the carrying capacity, and \(h\) is the constant per capita harvest rate.
The logistic equation is a mathematical model that describes population growth with limited resources. It takes into account the intrinsic growth rate (\(r\)) and the carrying capacity (\(K\)), which represents the maximum population size that the environment can support. However, in this scenario, the population is also subject to a constant per capita harvest rate (\(h\)). This means that a certain number of individuals are harvested or removed from the population at a constant rate per individual.
To incorporate the harvest rate into the logistic equation, we subtract the harvest rate (\(h\)) from the growth term. The growth term \(rN(1 - \frac{{N}}{{K}})\) represents the intrinsic growth of the population, where \(rN\) represents the potential growth rate without any limitations, and \((1 - \frac{{N}}{{K}})\) represents the factor that slows down the growth as the population approaches the carrying capacity.
By subtracting the harvest rate (\(h\)), we account for the individuals that are removed from the population due to harvesting. The harvest rate is constant per capita, meaning that it applies to each individual in the population regardless of its size. Therefore, the total harvest is proportional to the population size (\(N\)).
The resulting equation \(\frac{{dN}}{{dt}} = rN(1 - \frac{{N}}{{K}}) - h\) describes the population dynamics under the influence of both intrinsic growth, limited resources (carrying capacity), and the constant per capita harvest rate.
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Ha mush and Harry work as plumbers Harry earns a dollar more than more than 5/4 the amount gaming earns per hour the amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour how much does each of them earn per hour
Answers
Answer:
Hamish's earning = $20
Harry's earning = $26
Step-by-step explanation:
Given the following :
Let Harry's earning per hour = x
Let Hamish earning per hour = y
Harry earns a dollar more than more than 5/4 the amount hamish earns per hour;
Therefore,
x = 5/4y + 1
x - 5/4y = 1 - - - - (1)
the amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour
x = 7/5y - 2 - - - - (2)
Substituting (2) into (1)
7/5y - 2 - 5/4y = 1
7/5y - 5/4y = 1 + 2
7/5y - 5/4y = 3
Taking the L. C. M
(28y - 25y) / 20 = 3
28y - 25y = 60
3y = 60
y = 20
Substitute y = 20 into (1)
x - 5/4(20) = 1
x - 100/4 = 1
x - 25 = 1
x = 1 + 25
x = 26
y = Hamish's earning = $20
x = Harry's earning = $26
4t+5su+7st how many terms are in this expression ?
Answers
Answer:
Step-by-step explanation:
Term is the product of its factors.
Terms:
4t
5su
7st
So, there are 3 terms in this expression.
which interval is considered too dissonant when constructing a polychord voicing that has tonic or subdominant function?
Answers
The interval is considered too dissonant is, major and minor seconds, sevenths, and ninths are dissonant when constructing a polychord voicing that has tonic or subdominant function.
Composer/theorist Vincent Persichetti, in his book Twentieth-Century Harmony, classifies major \(2nd's\), minor \(7th's\), and major \(9th's\) as "soft dissonances," whereas minor \(2nd's\), major \(7th's\), and minor \(9th's\) are "sharp dissonances."
Dissonance is a combination of notes that sound unpleasant or harsh. Dissonant interval examples are major and minor seconds, tritone, and major and minor sevenths. The consonant intervals are considered the perfect unison, octave, fifth, fourth and major and minor third and sixth, and their compound forms.
The intervals that are considered to be dissonant are the minor second, the major second, the minor seventh, the major seventh, and particularly the tritone, which is the interval in between the perfect fourth and perfect fifth.
Dissonance is a combination of notes that sound unpleasant or harsh. Dissonant interval examples are major and minor seconds, tritone, and major and minor sevenths. The consonant intervals are considered the perfect unison, octave, fifth, fourth and major and minor third and sixth, and their compound forms.
Therefore,
The interval is considered too dissonant is, major and minor seconds, sevenths, and ninths are dissonant when constructing a polychord voicing that has tonic or subdominant function.
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How many pennies do you save on the twenty-third day?
Answers
Solution:
Given:
\(\begin{gathered} Day1=1penny \\ Day2=2pennies \\ Day3=4pennies \\ Day4=8pennies \end{gathered}\)An exponential function is of the form:
\(y=ab^x\)To get the exponential function for the relation;
\(\begin{gathered} For\text{ day 1:} \\ 1=ab^1.........................(1) \\ For\text{ day 2:} \\ 2=ab^2.........................(2) \\ For\text{ day 3:} \\ 4=ab^3 \\ \\ \\ \\ Hence,\text{ equation \lparen2\rparen divided by equation \lparen1\rparen;} \\ \frac{2}{1}=\frac{ab^2}{ab} \\ 2=b \\ b=2 \\ \\ Substituting\text{ b into equation \lparen1\rparen;} \\ ab=1 \\ a(2)=1 \\ 2a=1 \\ a=\frac{1}{2} \\ \\ \\ \\ Hence,\text{ the function is;} \\ y=\frac{1}{2}(2^x) \end{gathered}\)Part A:
Relating this to the parameters given:
The exponential function that models the problem is;
\(f(t)=\frac{1}{2}(2^t)\)Part B:
On the twenty-third day,
\(\begin{gathered} when\text{ }t=23,\text{ the pennies saved will be;} \\ \\ f(t)=\frac{1}{2}(2^{23}) \\ f(t)=\frac{2^{23}}{2} \\ f(t)=4,194,304\text{ pennies} \end{gathered}\)Therefore, he would have saved 4,194,304 pennies on the twenty-third day.
A snack mix recipe calls for 10 cups of cereal and 4 cups of pretzel sticks.
What is the constant of proportionality that relates the number of cups of cereal, y, to the number of cups of pretzel sticks, x?
Answers
The constant of proportionality that relates the number of cups of cereal, y, to the number of cups of pretzel sticks, x is y= 5/2x.
We have,
A snack mix recipe calls for 10 cups of cereal and 4 cups of pretzel sticks.
Using constant of proportionality
y = kx
where k is the constant
So, put y= 10 and x= 4 then
10 = k (4)
k = 10/4
k= 5/2
Thus, the constant of proportionality is 5/2.
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what is 3 and 1/6 as an improper fraction
Answers
Answer:
Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer
Find the area of this shape. (Note: the figure is NOT drawn to scale)
Answers
Answer:
The area of this shape is \(50cm^2\).
Step-by-step explanation:
To find the area of this figure, you only need to know the area of the rectangle and the area of the triangle. The area of the rectangle would be 5 * 6 = \(30cm^2\). Since the length of the rectangle plus the base of the triangle is equivalent to 14, that means the base of the triangle is equal to 14 - 6 = 8 cm. The formula for the area of a triangle is \(\frac{1}{2} bh\), the base you now know is 8 cm, and the height is 5 cm, which means the area of the triangle would be \(\frac{1}{2} *5*8\) = \(\frac{1}{2} * 40\) = \(20cm^2\). Add the area of the rectangle to the area of the triangle and you'll get the area of the entire shape, which is 30 + 20 = \(50cm^2\).
a workbook contains a list of houses and the months that they were sold in several cities in florida in june. you are interested in determining the average price of sold houses in ft. lauderdale. what function is best suited for this calculation? (1 point) maxifs averageifs sumif averageif
Answers
As per the statement the function which is best suited for this calculation is averageif.
What is averageifs?In Microsoft Office Excel, averageifs may be a function that helps to determine the average of cells that follow different criteria. Averageif is one among many functions under the "Statistic" category. the standards for averageifs can be words or a range of numbers which allows more diverse analysis compared to other average functions.While averaging the equation this option is very easy to implement. you need not recall any formula just go for the formulas option at tabs in excel there are many formulas such as SUMIF, MAXIFS ETC.To know more about averageifs visit:
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i need help with this
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
Answers
The measure used by the charity is: The IQR of 13 is the most accurate to use, since the data is skewed.
What is a histogram?In a graphic representation of data called a histogram, a set of continuous numerical data is distributed in a given way. Each rectangle's area is related to the frequency of data values occurring within a given interval or bin. It consists of a sequence of rectangles or bars. The y-axis displays the frequency or count of values that fall inside each interval, while the x-axis displays the range of values that are divided up into intervals or bins. Large data sets can be visually summarised using histograms, which can also be used to spot patterns and trends as well as outliers or unexpected numbers.
A measure of variability that is less susceptible to outliers than the range is the IQR (interquartile range). The data in this instance is skewed to the right, which means that a few large donations are pushing the range upward.
From the given data we see that the values are skewed. Thus, for the values IQR will be an appropriate way to represent the data and understand about the range in the upper and the lower bound.
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John spent 80% of his money and saved the rest. Peter spent 75% of his money and saved the rest. If they saved the same amount of money, what is the ratio of John’s money to Peter’s money? Express your answer in its simplest form.
Answers
The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.
Let's assume John has 'x' amount of money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'
So,
p = x - 80x/100 (equation 1)
q = y - 75y/100 (equation 2)
According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.
p = q
x- 80x/100 = y - 75y/100
x - 0.8x = y - 0.75y
0.2x = 0.25y
x = 0.25y/0.2
x/y = 0.25/0.2
x/y = 25/20
x/y = 5/4
Hence, the ratio of John's money to Peter's money is 5/4.
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find the number of units of natural gas that are to be produced to maximize the profit if….
Answers
We are asked to determine the maximum value of "x" for a profit function given the functions of revenue and cost. To do that let's remember that profit is defined as:
\(\text{Profit}=\text{revenue - cost}\)Let P(x) be the function of profit, then the difference between the functions of revenue and cost is the function of profit, therefore:
\(P(x)=R(x)-C(x)\)Replacing the functions we get:
\(P(x)=162x-2x^2-(x^2+114x+2)\)Now we apply the distributive property in the parenthesis:
\(P(x)=162x-2x^2-x^2-114x-2\)Adding like terms:
\(P(x)=48x-3x^2-2\)Now, to determine the maximum profit we will determine the derivative of the profit function with respect to "x":
\(\frac{dP}{dx}=\frac{d}{dx}(48x-3x^2-2)\)Now we distribute the derivative on the left side:
\(\frac{dP}{dx}=\frac{d}{dx}(48x)-\frac{d}{dx}(3x^2)-\frac{d}{dx}(2)\)Now we determine the derivative using each corresponding rule:
\(\frac{dP}{dx}=48-6x\)Now we set the result to zero:
\(48-6x=0\)Now we solve for "x" first by subtracting 48 from both sides:
\(-6x=-48\)Now we divide both sides by -6:
\(x=-\frac{48}{-6}=8\)Now, since the original function is a parabola that opens downwards, this point must be a maximum. To verify that we can determine the second derivative and we get:
\(\frac{d^2P}{dx^2}=\frac{d}{dx}(48-6x)=-6\)Since the second derivative is smaller than zero, the point is a maximum as hypothesized. Therefore, the maximum value of "x" is 8.
b. the determinant of a is the product of the pivots in any echelon form u of a, multiplied by .1/r , where r is the number of row interchanges made during row reduction from
Answers
The determinant of a matrix 'a' can be calculated by taking the product of the pivots in any echelon form 'u' of 'a', multiplied by 0.1 divided by the number of row interchanges made during row reduction.
To calculate the determinant of a matrix 'a', we can use row reduction to obtain an echelon form 'u' of 'a'. During the row reduction process, we perform elementary row operations such as row swaps (interchanges), scaling, and addition.
The echelon form 'u' is a triangular matrix with non-zero pivots (the leading non-zero entries in each row) along the main diagonal. The product of these pivots gives us the determinant of 'u'.
Now, each row interchange swaps the sign of the determinant. Therefore, to account for the effect of row interchanges, we multiply the determinant of 'u' by a factor of (-1) raised to the power of 'r', where 'r' is the number of row interchanges made.
Finally, to ensure consistency with the standard definition of the determinant, we divide the obtained product by 10 times 'r' (0.1/r).
In summary, to find the determinant of matrix 'a', we find the echelon form 'u', calculate the product of the pivots in 'u', and multiply it by 0.1 divided by the number of row interchanges made during row reduction. This formula incorporates the effects of row interchanges and provides an accurate determinant value.
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IQ test scores are standardized to produce a normaldistribution with a mean of 100 and a standarddeviation of 15. Find the proportion of the popula-tion in each of the following IQ categories.Gartea. Average or normal intelligence: IQ from 90 to 109
Answers
The mean, µ = 100
The standard deviation, σ = 15
At X = 90, the z-score is calculated below
\(\begin{gathered} z=\frac{X-\mu}{\sigma} \\ \\ z=\frac{90-100}{15} \\ \\ z=-\frac{10}{15} \\ \\ z=-0.67 \end{gathered}\)At X = 109
\(\begin{gathered} z=\frac{109-90}{15} \\ \\ z=\frac{19}{15} \\ \\ z=1.27 \end{gathered}\)P(90 < X < 109) = P(-0.67 < z < 1.27)
From the standard normal
P(-0.67
The proportion of the population with IQ from 90 to 109 = 0.64653 x 100% = 64.65%
Two landscaping companies made bids on the landscaping of a new apartment complex. Company A bid $595,000 for materials and plants and $204,000 for labor. Company B bid $660,000 for materials and plants and $136,000 for labor. How much lower was the bid made by Company B?
Answers
Answer:
$3,000
Step-by-step explanation:
Company A bid $595,000 for materials and plants and $204,000 for labor.
Total = $595,000 + $204,000 = $799,000Company B bid $660,000 for materials and plants and $136,000 for labor.
Total = $660,000 + $136,000 = $796,000The difference:
$799,000 - $796,000 = $3,000What is an equivalent expression to 2(4x+1)?
Answers
Answer:
8x+2
Step-by-step explanation:
Distribute the 2, the resulting expression will be equivalent
I hope this helps:)
Can you guys help me find the answer
Answers
:))))))))))))))
Answer:
Step-by-step explanation:
Start by looking at the face that is closest to the bottom left. It is a hexagon and it makes 1 face.
It is connected to a similar hexagon on the upper right by 6 tiles. So that adds 7 more faces.
The total is 2 hexagons + 6 rectangles = 8 faces.
If Jose can make 3 baskets in 20 seconds, what is the unit rate?
Answers
Jasper was testing H_0: \mu=36H
0
:μ=36H, start subscript, 0, end subscript, colon, mu, equals, 36 versus H_\text{a}: \mu\neq36H
a
:μ
=36H, start subscript, start text, a, end text, end subscript, colon, mu, does not equal, 36 with a sample of 161616 observations. His test statistic was t=2. 4t=2. 4t, equals, 2, point, 4. Assume that the conditions for inference were met. What is the approximate P-value for Jasper's test?
Answers
Answer:
0.02<P-value<0.04
Step-by-step explanation:
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An adult blue whale can eat about 40,000,000 krill a day. Write this number in scientific notation.
Answers
Answer:
4 x 10^7
Step-by-step explanation:
1 x 10^7 is 10 million, just multiply that 1 by 4 to get your answer
Answer:
4 x 10^7
Step-by-step explanation:
each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. find the range and domain of the relation.pls explain also i will reward brainliest!!!!!!!!!
Answers
By reading the graph, we can see that:
domain: [-2, 0) U {2}range: [0, 2)How to find the domain and range of the graphed relation?For a relation that maps inputs x into outputs y, we define the domain as the set of the values x, and the range as the set of the values y.
To identify the domain we need to look at the horizontal axis, we can see a closed dot at x = -2 and an open dot at x = 0, plus another closed dot at x = 2.
Then the domain is:
D: [-2, 0) U {2}
For the range, we just need to look at the vertical axis, the minimum is at y = 0, and the maximum is at y = 2 (but with an open dot, which means that this value does not belong to the range) Then the range is:
y : [0, 2)
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a jar containing only nickels an dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. What is the number of nickels and dimes in the jar?
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Answer:
31 nickels and 29 dimes
Step-by-step explanation:
If you were constructing a 99% confidence interval of the population mean based on a sample of n=30 where the standard deviation of the sample S=0.05, the critical value of t will be 2.7564 2.4922 2.7969
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The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.
A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.
The formula for calculating the confidence interval for the population mean is:
Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)
Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.
Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.
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