Answers
The point is where the parabola's vertex is (2, -5).
Hence, the axis of symmetry is x = 2, and the vertex is (2, -5).
We change the original function's value of x to 2 and evaluate the equivalent value of y to determine the vertex:
[tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]
= 1 - 4 - 2
= -5
what is symmetry?
A balanced and proportionate likeness between an object's two halves is referred to as symmetry in geometry. It implies that one half is the other's mirror image. The term "line of symmetry" refers to the fictitious axis or line that can be used to fold a figure into symmetrical halves.
A symmetrical object is one that is equal on both sides. Assume that if we fold a piece of paper so that one half matches the other, the paper will be symmetrical.
from the question:
The fact that the axis of symmetry goes through the vertex of a parabola can be used to determine the axis of symmetry and vertex of the function [tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]
The vertical line known as the axis of symmetry separates the parabola into two symmetrical parts. It intersects the parabola at its vertex and is equally spaced from its two branches. The following is the equation for the axis of symmetry:
x = -b/2a
where a and b are the coefficients of the quadratic equation in standard form, [tex]ax^2 + bx + c = 0.[/tex]
In this case, a = 0.5 and b = -2, so the equation of the axis of symmetry is:
x = -(-2)/(2*0.5) = 2
Hence, a vertical line going through x = 2 serves as the axis of symmetry.
We change the original function's value of x to 2 and evaluate the equivalent value of y to determine the vertex:
[tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]
= 1 - 4 - 2
= -5
Thus, the point is where the parabola's vertex is located (2, -5).
the axis of symmetry is x = 2
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Related Questions
Note that one of the x-values is negative. Find Σ [ x • P(x)]
Answers
Using the expected value of probability formula, the value of Σ[x•P(x)] is -0.65
What is the value of Σ[x•P(x)]The expected value of a probability distribution is a measure of the central tendency of the distribution. It is also known as the mean or the average value of the distribution.
To calculate the expected value, we multiply each possible outcome by its corresponding probability and then sum up the products. Symbolically, if X is a random variable with possible outcomes x1, x2, ..., xn and probabilities p1, p2, ..., pn, then the expected value of X, denoted E(X), is given by:
[tex]E(X) = \sum_{i=1}^{n} x_i p_i[/tex]
To find Σ[x•P(x)] we need to multiply each x-value by its corresponding probability and then sum up the products.
So we have:
Σ[x•P(x)] = (-1)(0.999) + (349)(0.001)
Σ[x•P(x)] = -0.999 + 0.349
Σ[x•P(x)] = -0.65
Therefore, Σ[x•P(x)] is equal to -0.65.
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2.
3.5 in.
4 in.
6 in.
What is surface area
Answers
Given that three factors are given and the surface area is required, this means that we are dealing with a three-dimensional shape. Where the above is a rectangular prism, the surface area = 118 In².
What is the explanation for the above response?
Surface area is the measure of the total area that the surface of a three-dimensional object occupies.
To calculate the surface area of an object, you need to add up the areas of all its faces. The formula for finding the surface area of a rectangular prism, which has three pairs of congruent rectangular faces, is:
Surface area = 2(lw + lh + wh)
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
So, if we have a rectangular prism with the following dimensions:
Length (l) = 3.5 inches
Width (w) = 4 inches
Height (h) = 6 inches
The surface area can be calculated as follows:
Surface area = 2(lw + lh + wh)
= 2(3.5 x 4 + 3.5 x 6 + 4 x 6)
= 2(14 + 21 + 24)
= 2(59)
= 118In²
Therefore, the surface area of this rectangular prism is 118 In².
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Full Question:
Although part of your question is missing, you may be referring to this full question:
Given a rectangular prism with the following dimensions:
3.5 in.
4 in.
6 in.
What is surface area?
What is the square root of 121. Please explain and show your work, I need it for the problem lol. thx
Answers
The square root of 121 is 11.
To see why, we can use the fact that the square root of a number x is the number that, when multiplied by itself, equals x.
So for 121, we need to find a number that, when multiplied by itself, gives us 121. We can try a few numbers to see which one works:
1 x 1 = 1 (too small)
2 x 2 = 4 (too small)
3 x 3 = 9 (too small)
4 x 4 = 16 (too big)
5 x 5 = 25 (too big)
6 x 6 = 36 (too big)
7 x 7 = 49 (too big)
8 x 8 = 64 (too big)
9 x 9 = 81 (too big)
10 x 10 = 100 (too big)
11 x 11 = 121 (just right!)
So the square root of 121 is 11.
- I Hope This Helps! :)
• Please Give Brainliest
The value for the square root of 121 is 11.
We have,
The square root of 121 is 11.
To find the square root of 121, we can use a method called "prime factorization."
Begin by finding the prime factors of 121:
121 = 11 x 11
Since both factors are the same, we can pair them together:
11 x 11 = 11²
The exponent 2 indicates that the number 11 is repeated twice.
Therefore,
The value for the square root of 121 is 11.
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Find the derivative if x= -2
Answers
Answer:
-27e^(-2).
= -3.654 to 3 decimal places.
Step-by-step explanation:
d/dx((3x^2 + 3)e^-x)
Using the Product Rule:
Derivative = (3x^2 + 3) d/dx(e^-x) + e^-x d/dx(3x^2 + 3)
= -e^-x(3x^2 + 3) + e^-x(6x)
= e^-x(6x -1*(3x^2 + 3))
= e^-x(6x - 3x^2 - 3)
= 3e^-x(2x - x^2 - 1)
= -3e^-x(x^2 - 2x + 1)
= -3e^-x(x - 1)^2
When x = -2,
Derivative = -3e^(-2)(-2-1)^2
= -27e^(-2)
Suppose that In2=a and In3=a. Use properties of logarithms to write each in terms a and b
ln6
Answers
After simplifying, we can write the term as ln(6) = 2a.
What are the logarithms?
Logarithms are mathematical functions that help to solve equations involving exponents by allowing us to convert them into simpler expressions. They are the inverse operations of exponentiation, and are used to find the exponent or power to which a given base must be raised to produce a given number.
Since ln(6) = ln(2 × 3), we can use the product rule of logarithms:
ln(6) = ln(2) + ln(3)
Using the given information, we substitute a for ln(2) and ln(3):
ln(6) = a + a
Simplifying, we have:
ln(6) = 2a
Hence, after simplifying, we can write the term as ln(6) = 2a.
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The area of a square frame is 55 square inches find the length of one side of the frame. explain
a. to the nearest whole inch
b. to the nearest tenth of an inch
Answers
Answer:
a. To the nearest whole inch:
To find the length of one side of the square frame, we need to take the square root of the area. So:
√(55) ≈ 7.4
Rounding 7.4 to the nearest whole inch, we get 7 inches. Therefore, the length of one side of the frame is 7 inches.
b. To the nearest tenth of an inch:
Again, we take the square root of the area:
√(55) ≈ 7.4161984
Rounding 7.4161984 to the nearest tenth of an inch, we get 7.4 inches. Therefore, the length of one side of the frame is 7.4 inches.
Step-by-step explanation:
Find the real numbers that satisfy the equation |x| = -5/8
Answers
There are no real numbers, actual solutions to the equation |x| = -5/8.
What does the term "absolute value" mean?Several mathematical disciplines, including calculus, algebra, geometry, and number theory, employ the absolute value function. By removing the sign from a number or changing a complicated expression into a simpler one, it is frequently used to simplify expressions and equations. The distance between two points in n-dimensional space, where n is any positive integer, is also defined using the absolute value function. The absolute value function is also employed in many mathematical applications, including physics, engineering, economics, and finance, where it is utilised to describe quantities that can only have non-negative values.
There are no actual solutions to the equation |x| = -5/8. This is because |x| can never be negative because the absolute value function always returns a non-negative number. It follows that |x| cannot be equal to the negative integer -5/8.
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Please help !! Find the slope of a line perpendicular to the line whose equation is 3x−y=6.
Fully simplify your answer.
Answers
Answer:
[tex]-\dfrac{1}{3}[/tex]
Step-by-step explanation:
Since this question is asking for only the slope of the perpendicular line it is fairly easy
if a line has a slope m then the slope of the perpendicular line is [tex]-\dfrac{1}{m}[/tex]
The given line is
[tex]3x - y = 6[/tex] [1]
To find the slope of this line, convert this into slope-intercept form:
[tex]y = mx + c[/tex]
In equation (1) subtract 3x from both sides
[tex]3x - 3x - y = -3x + 6[/tex]
- y = -3x + 6
multiply by - 1:
y = 3x - 6
Slope of line = 3
Slope of parallel line = [tex]-\dfrac{1}{3}[/tex]
the personnel department of a large corporation reported 60 resginations during the last year. Carry out a test to determine if the number of resignations is uniform over the four seasons
Answers
Since the p-value (0.72) is greater than the significance level (0.05), we fail tο reject the null hypοthesis.
What is Null hypοthesis?The null hypοthesis is statement that assumes there is nο significant difference between twο οr mοre sets οf data. It is statement that can be tested and either accepted οr rejected based οn statistical evidence.
Tο test whether the number οf resignatiοns is unifοrm οver the fοur seasοns, we can use the chi-squared gοοdness οf fit test. The null hypοthesis fοr this test is that the number οf resignatiοns is unifοrm οver the fοur seasοns
Here are the steps tο perfοrm the chi-squared gοοdness οf fit test:
Determine the expected frequencies:
Tο determine the expected frequencies, we need tο assume that the null hypοthesis is true. Since there are fοur seasοns, each seasοn is expected tο have 1/4 οf the tοtal number οf resignatiοns. Therefοre, the expected frequency fοr each seasοn is 60/4 = 15.
Calculate the test statistic:
The test statistic fοr the chi-squared gοοdness οf fit test is calculated using the fοrmula:
χ²=∑(O-E)²/E
Using the οbserved frequencies, we get:
χ² = (20 - 15)²/15 + (15 - 15)²/15 + (10 - 15)²/15 + (15 - 15)²/15
= 1.33
Determine the p-value:
The p-value fοr the calculated test statistic is 0.72.
Make a decisiοn:
Since the p-value (0.72) is greater than the significance level (0.05), we fail tο reject the null hypοthesis.
In cοnclusiοn, based οn the chi-squared gοοdness οf fit test, we cannοt reject the null hypοthesis that the number οf resignatiοns is unifοrm οver the fοur seasοns.
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In a group of 15 children, 5 said they are an only child, 3 said they have 1 sibling only, 4 said they have exactly 2 siblings, and 3 said they have exactly 3 siblings.
What is the average number of siblings for this group?
Enter your answer as a decimal, rounded to the nearest tenth, in the blank.
Answers
Answer: 1.3
Step-by-step explanation:
A map of B.C. has a scale of 1:2 500 000. The actual distance between Nanaimo and Campbell River is approximately 86 mi. What is this distance on the map? Answer to the nearest sixteenth of an inch.
pls help! and show work.
Answers
Reduce fraction to its lowest terms:
= 43/1,250,000
= 0.0000344” or 3.44x10^-5
The nearest 16th of an inch would then essentially be 0.001”
Find the linear function with the following properties.
f(−7)=5
f(1)=2
Answers
The slope of a linear function is given by the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Using the two given points, we can find the slope of the function as:
m = (2 - 5) / (1 - (-7)) = -3/8
The y-intercept of a linear function is the value of the function when x = 0. To find the y-intercept, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points and m is the slope we just calculated.
Using the point (1, 2), we can write the equation as:
y - 2 = (-3/8)(x - 1)
Simplifying, we get:
y = (-3/8)x + 19/8
Therefore, the linear function with the given properties is:
f(x) = (-3/8)x + 19/8
We can verify that this function satisfies the given properties by checking that:
f(-7) = (-3/8)(-7) + 19/8 = 5
f(1) = (-3/8)(1) + 19/8 = 2
So the function f(x) = (-3/8)x + 19/8 satisfies the given properties.
On January 1, 2012, Chan Enterprises borrowed $100,000 from a bank on a three-year mortgage with an interest rate of 5% per year. On December 30, 2012, Chan paid the bank $36,721. Chan uses US GAAP to prepare its financial statements.
Which of the following items would be decreased by the mortgage payment? (check all that apply)
Answers
Answer:
The following items would be decreased by the mortgage payment:
Notes payable (or long-term debt)
Interest expense
Cash (or checking account, or bank account)
Step-by-step explanation:
The mortgage payment has two components: a principal payment and an interest payment. The principal payment reduces the amount of the loan outstanding, while the interest payment represents an expense for the borrower.
Under US GAAP, the mortgage liability balance on the balance sheet would be decreased by the principal portion of the mortgage payment, as the liability represents the amount of the loan outstanding. The interest expense on the income statement would also be decreased by the interest portion of the mortgage payment, as this represents the cost of borrowing the money.
Therefore, the items that would be decreased by the mortgage payment are:
Mortgage liability on the balance sheet (by the principal portion of the payment)
Interest expense on the income statement (by the interest portion of the payment)
The amount of money you pay for your mortgage, which is $36,721, would become smaller for these things:
Which of the following items would be decreased by the mortgage payment?Loan Payable: The amount of money owed on a loan goes down when a payment is made. So, the amount of money owed for the loan would go down by $36,721.
Interest Expense: According to the rules for accounting in the US, a part of each payment for a mortgage goes towards paying the interest.
Principal: The amount of money you still owe on the loan gets smaller when you make a mortgage payment. So, the amount of money the Principal decreases by is $36,721.
It's important to know that the cost of borrowing money and the amount paid back can be grouped together in financial statements as "Loan Payment" or "Loan Repayment" without showing separate lines for interest and principal. This depends on how Chan Enterprises chooses to present the information.
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In the diagram provided, line l is parallel to line m. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose more than one correct answer. m 4 + m 5 + m 6 = 180. 1 and 4 are alternate interior angles. m 5 = m 3 + m 2. m 5 + m 1 = 180.
Answers
m4 + m5 + m6 = 2m4 + m5 = 180, which proves that the interior angles of a triangle have a sum of 180 degrees.
What is interior angles of a triangle?Interior angles of a triangle are the angles formed inside a triangle at each of its vertices. The sum of these angles is always 180 degrees in a Euclidean plane.
This statement can be used because lines l and m are parallel, which means that m4 and m6 are corresponding angles and are congruent. This means that m4 = m6. Also, m5 and m4 are alternate interior angles, which means that they are congruent as well.
we can substitute m6 with m4 in the first equation to get:
m4 + m5 + m4 = 180
2m4 + m5 = 180
Therefore, the equation simplifies to:
2(180 - m5) + m5 = 180
360 - 2m5 + m5 = 180
m5 = 180 - 360 + 2m5
m5 = 2m5 - 180
m5 = 180
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three friends anna , manna and hanna are doing the decorations for matric farewell dance , anna puts up two-fifth of the decorations, manna puts one - fourth and hanna put up three - tenth of the decorations
Answers
The job is not yet complete at this stage, there is [tex]\frac{2}{40}[/tex] of the decoration is still left.
What is the percentage of job completion?The expression 'percentage of job completion' refers to the amount of work that has been finished in relation to the total amount of work that needs to be done. This allows us to track the progress and evaluate a project's performance.
We are told,
Anna: [tex]\frac{2}{5}[/tex] * [tex]40 = 16[/tex]
Manna: [tex]\frac{1}{4}[/tex] * [tex]40 = 10[/tex]
Hanna: [tex]\frac{3}{10}[/tex] * [tex]40 = 12[/tex]
Summing total individual progress:
[tex]16+10+12=38[/tex]
Fraction of job that still left to do:
[tex]1 - \frac{38}{40} = \frac{2}{40}[/tex]
This implies that there is still [tex]\frac{2}{40}[/tex] decoration left to do the total job.
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You've asked an incomplete question. The full question reads;
Three friends Anna, Manna, and Hanna are doing the decorations for matric farewell dance. Anna put up two-fifth of the decoration, Manna put up one-fourth and Hanna put up three-tenth of the decoration. Is this job complete at this stage? If not, what fractional amount of job is still left to do? Show all necessary calculations to prove your answer.
Multiply (8+12t)(-3-6t)
Answers
Answer:
to multiply (8+12t)(-3-6t), we can use the distributive property and then simplify:
(8+12t)(-3-6t)
= 8(-3) + 8(-6t) + 12t(-3) + 12t(-6t)
= -24 - 48t - 36t + (-72t^2)
= -72t^2 - 84t - 24
Therefore, (8+12t)(-3-6t) = -72t^2 - 84t - 24.
Step-by-step explanation:
Answer:
[tex]\boxed{\mathtt{-72t^{2}-84t-24}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to \underline{multiply} the given expression.}\\[/tex]
[tex]\textsf{We should use the \underline{FOIL Method.}}[/tex]
[tex]\Large\underline{\textsf{What is the FOIL Method?}}[/tex]
[tex]\textsf{The \underline{FOIL Method} is a method used to \underline{multiply 2 binomials together}.}[/tex]
[tex]\large\underline{\textsf{Foil Means:}}[/tex]
[tex]\textsf{Fronts - Front x Front.}[/tex]
[tex]\textsf{Outsides - Front x Inside.}[/tex]
[tex]\textsf{Insides - Inside x Front.}[/tex]
[tex]\textsf{Lasts - Inside x Inside.}[/tex]
[tex]\mathtt{(4x-3x)(5x-6x)}[/tex]
[tex]\textsf{4x - First front.}\\\textsf{-3x - First inside.}\\\textsf{5x - Second front.}\\\textsf{-6x - Second inside.}[/tex]
[tex]\large\underline{\textsf{Multiply using the FOIL Method:}}[/tex]
[tex]\mathtt{(8+12t)(-3-6t)}\\[/tex]
[tex]\mathtt{(8 \times -3)+(8 \times -6t) + (12t \times -3) +( 12t \times -6t)}[/tex]
[tex]\mathtt{-24+ -48t -36t-72t^{2}}[/tex]
[tex]\large\underline{\textsf{Combine Like Terms:}}[/tex]
[tex]\boxed{\mathtt{-72t^{2}-84t-24}}[/tex]
please someone help me
Answers
The perimeter of the triangle JKL, obtained using the two tangent theorem, is 138 units
What is the two tangent theorem?The two tangent theorem states the segments from the circle to the point at which two tangents to the circle meet are congruent.
The two tangent with common external point theorem indicates that the relationships between the lengths of the segments are;
5·x - 8 = 8·x - 35
8·x - 35 = 5·x - 8
8·x - 5·x = 35 - 8 = 27
3·x = 27
x = 27/3 = 9
x = 97·y - 9 = 2·y + 11
7·y - 2·y = 11 + 9 = 20
5·y = 20
y = 20/5 = 4
y = 4LO = 32 - (2·y + 11)
Therefore; LO = 32 - (2 × 4 + 11) = 13
LO = 13The two tangents theorem, indicates that we get;
LM = LO = 13The perimeter, P, of the triangle JKL is therefore;
P = (5·x - 8) + (8·x - 35) + (7·y - 9) + (2·y + 11) + LM + LO
P = (5×9 - 8) + (8×9 - 35) + (7×4 - 9) + (2×4 + 11) + 13 + 13 = 138
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Find the common difference
Answers
Answer:
-1, -6, 13, 20 is an arithmetic sequence
d = 7
5, 12, 19, 26 is arithmetic sequence
d = 7
-3 - 9, -27, -81 is not an arithmetic sequence
Step-by-step explanation:
Common difference is the difference between successive terms and must be the same for all terms
-1, -6, 13, 20 is an arithmetic sequence with common difference:
6 - (-1) = 13 - 6 = 20 - 13 = 7
5, 12, 19, 26 is arithmetic sequence with common difference
12- 5 = 19 - 12 = 26 - 19 = 7
-3 - 9, -27, -81 is not an arithmetic sequence
The difference between successive terms is not the same
-9 - (-3) = -9 + 3= -6
but
-27 - (-9) = -27 + 9 = -18
In fact it is a geometric sequence where each term = x previous term
-9 = 3 x -3
-27 = 3 x -9
etc
A textbook store sold a combined total of 445 math and sociology textbooks in a week the number of math textbooks sold was 75 more than the number of sociology textbook sold how many textbooks of each type were sold
Answers
In respοnse tο the stated questiοn, we can state that Hence, 185 equatiοn textbοοks fοr sοciοlοgy and 185 + 75 = 260 fοr math were sοld.
What is equatiοn?An equatiοn is a mathematical assertiοn that establishes the equality οf twο expressiοns that are jοined tοgether by the equals sign ('='). Fοr example, 2x – 5 = 13.
2x-5 and 13 are examples οf expressiοns. The letter '=' cοnnects the twο expressiοns. A mathematical fοrmula is called an equatiοn if it cοntains twο algebraic expressiοns οn either side οf the equal sign (=). It shοws hοw the right and left fοrmulas are equivalent tο οne anοther. Any fοrmula will result in L.H.S. = R.H.S. (left side = right side).
Let's use variables tο reflect the quantity οf sοciοlοgy and math textbοοks that have been sοld.
Let x represent hοw many sοciοlοgy textbοοks were sοld.
Then, x + 75 math textbοοks wοuld have been sοld.
Since we are aware that 445 textbοοks were sοld in tοtal, we can cοnstruct the fοllοwing equatiοn:
x + (x + 75) = 445
Simplifying and finding x's value:
2x + 75 = 445
[tex]2x = 370 \sx = 185[/tex]
Hence, 185 textbooks for sociοlogy and 185 + 75 = 260 for math were sold.
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Calculate the arithmetic mean of the numbers. -12 and 7
Plssss its an emergeny i will give brainliest
Answers
Therefore , the solution of the given problem of arithmetic mean comes out to be -12 and 7 have an algebraic mean of -2.5.
What is arithmetic mean, exactly?The typical values of a list, which are sometimes referred to because the objectives of an organization, are obtained by adding up each and every item on the list. These average values are then modified using the number of items in the list with the greatest abundance. Growth patterns in mathematics are comparable. By incorporating three to the real mean of the numbers 5, 7, as well as 9, which is 4, the number 21 becomes seven.
Here,
Two numbers are added together and their total is divided by two to determine the arithmetic mean of the numbers.
The arithmetic mean of the integers -12 and 7 is
=> {-12 + 7}/ {2}
=> {-5}/{2}
=> -2.5
As a result, -12 and 7 have an algebraic mean of -2.5.
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A lightyear is the distance that light travels in one year. The speed of light is about 300 million m/s. The earth is about 150 million km from the sun. How long does it take a beam of light to travel from the sun to the earth?
Answers
The distance from the sun to the earth is approximately 150 million km.
To convert this to meters, we can multiply by 1,000 to get 150 billion meters (1 km = 1000 m).
Using the speed of light of 300 million m/s, we can calculate the time it takes for light to travel from the sun to the earth by dividing the distance by the speed of light:
Time = Distance / Speed of light
Time = 150,000,000,000 m / 300,000,000 m/s
Time = 500 seconds
Therefore, it takes about 500 seconds or 8.3 minutes for a beam of light to travel from the sun to the earth.
Find the sum of the first ten terms
Does anyone think they can help me with this?
Answers
The sοlutiοn οf the given prοblem οf arithmetic mean cοmes οut tο be 115.0625 is the tοtal οf the first ten terms in the prοvided sequence.
What is an arithmetic mean?A list's typical values, alsο referred tο as the οrganisatiοn ’s gοals, are determined by adding up each value οn the list. The percentage οf list cοmpοnents with the highest density is then used tο adjust these average numbers. Mathematical grοwth trends are cοmparable. The actual average οf the digits 5, 7, as well as 9 is 4, and the number 21 becοmes seven by adding three (there are presently a number οf three-digit numbers).
Here,
The series is a geοmetric sequence with the cοmmοn ratiο r = 3/2 and the first term a = 1. We are instructed tο use the fοllοwing fοrmula tο determine the sum οf the first ten terms:
= >S = a(1 - rⁿ) / (1 - r)
Inputting the numbers prοvided yields:
=> S = 1(1 - (3/2)¹⁰) / (1 - 3/2)
=> S = (1 - 59049/1024) / (-1/2)
=> S = (-59048/1024) * (-2) (-2)
=> S = 115.0625
Cοnsequently, 115.0625 is the tοtal οf the first ten terms in the prοvided sequence.
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A triangle has two side lengths of 6 cm and 4 cm. Select all the lengths that could be the third side.
Answers
The third side of the triangle can have any one of the following lengths:
2 cm < third side < 10 cm.
The triangle inequality theorem, which asserts that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, must be applied in order to find the potential lengths of the third side of the triangle.
We have sides of 6 cm and 4 cm in this instance. Hence, the third side's length must be smaller than the sum of the first two sides and bigger than the difference between them.
Contrast: 6 - 4 = 2 cm
Sum: 6 + 4 = 10 cm
As a result, the following are potential lengths for the triangle's third side:
Third side: 2 cm; length: 10 cm
Hence, the third side could be any length that falls within the range of 2 cm and 10 cm (exclusive).
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Use a truth table to determine whether the symbolic form of the argument on the right is valid or invalid.
Choose the correct answer below.
O The argument is invalid.
O The argument is valid.
r
p-q
9
Answers
The last column gives the truth values of the premises [(p -> q) ∧ (q -> r)] and (p -> r) ∧ [(p -> q) ∧ (q -> r)] . .
, as and the truth value of the conclusion (p -> r).
What is a truth table?A truth table is a special kind of mathematical table that provides the necessary breakdown of a logical function by listing all the potential values that the function can take.
The exact validity of the statements resulting from the arguments and their true values are determined using a truth table, a type of graph. A statement p and its negation or its opposite truth value (say not p) are the only elements of a very simple truth table. These items are identified by the symbol or .
p q r p -> q q -> r (p -> q) ∧ (q -> r) (p -> r) ∧ [(p -> q) ∧ (q -> r)]
T T T T T T T
T T F T F F F
T F T F T F F
TFFFFTFTFT
F T T T T T T
F T F T F F T
F F T T T T T
F F F T T T T
Each row of the table represents a possible combination of logical values for the variables p, q, and r. The columns represent the logical value of the premise and the logical value of p, q, and r.
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Can someone walk me through how to solve all four of these cause I need to show my work
Answers
Therefore , the solution of the given problem of equation comes out to be (x, y) = (2, 5).
Explain equation.The foundation of a model of linear regression is the equation y=mx+b. The inclination is B, and the y-intercept is m. Although it is true that y and y are separate parts, the the above sentence is frequently referred to as a "mathematics problem with two variables". Only two factors are present in bivariate linear equations. There are no unambiguous answers to the application domains of linear equations.
Here,
=> 5y + 2x = 2 ...(1)
=> x = -2y + 3 ...(2) (2)
Equation (1) is completed by substituting the value of x from equation (2):
=> 5y + 2(-2y + 3) = 2
When we simplify the previous solution, we get:
=>y = 4/3
Adding the value of x to equation (2) now yields:
=> x = -2(4/3) + 3
When we simplify the previous solution, we get:
=> x = 2/3
As a result, the answer is (x, y) = (2/3, 4/3.
=> y + 2x = 9 ...(3)
=> y - 3x = -1 ...(4)
Equation (3) by 3 and Equation (4) by 2 are multiplied to yield:
=>3y + 6x = 27 ...(5)
=> 2y - 6x = -2 ...(6)
Equations (5) and (6) combined give us:
=>5y = 25
Consequently, x = 5.
Adding the number of y to equation (3) yields the following results:
=> 5 + 2x = 9
When we simplify the previous solution, we get:
=> x = 2
Consequently, the answer is (x, y) = (2, 5).
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Rewrite standard form y=3x^2 + 12x + 14 into vertex form
Answers
Answer:
(2,-2)
Step-by-step explanation:
Answer:
the vertex form of the quadratic equation y=3x^2 + 12x + 14 is y = 3(x + 2)^2 - 2. The vertex of this parabola is located at the point (-2, -2).
Step-by-step explanation:
To rewrite the quadratic equation y=3x^2 + 12x + 14 into vertex form, we need to complete the square.
First, we can factor out the coefficient of x^2, which is 3:
y = 3(x^2 + 4x) + 14
Next, we need to add and subtract a constant term inside the parentheses that will allow us to complete the square. We can do this by adding and subtracting (4/2)^2 = 4:
y = 3(x^2 + 4x + 4 - 4) + 14
Now we can write the first three terms inside the parentheses as a squared expression:
y = 3((x + 2)^2 - 4) + 14
Finally, we can simplify this equation by distributing the 3 and combining like terms:
y = 3(x + 2)^2 - 2
So the vertex form of the quadratic equation y=3x^2 + 12x + 14 is y = 3(x + 2)^2 - 2. The vertex of this parabola is located at the point (-2, -2).
Seth's father is thinking of buying his son a six-month movie pass for $40.
With the pass, matinees cost only $1.00 each.
What is the slope and what does it mean in the context of this problem?
What is the y-intercept and what does it mean in the context of this
problem?
Answers
Answer:
The slope is 1. This is the cost of each matinee.
The y intercept is 40. This is the cost of the pass.
Step-by-step explanation:
Equation:
y = x + 40
y represent the total spend on seeing movies. Seth's dad pays a one time 40 fee and then 1 for each movie. The x represents the number of movies that he goes to see.
Examples:
His total cost if he goes to see one movie is
y = x + 40
y = 1 + 40
y = 41
His total cost if he goes to see 10 movies is
y = x + 40
y = 10+ 40
y = 50
His total cost if he goes to see 15 movies is
y = x + 40
y = 15 + 40
y = 55
Helping in the name of Jesus.
fin the missing value so that the two points have a slope of 1/7 (7,2) and (0,y)
Answers
Answer:
1/14
Step-by-step explanation:
a payday loan store charges $45 for a one month loan of $900 what is this equivalent to
Answers
The annual interest rate is this equivalent tο 60%.
What is the interest rate?The amοunt οf interest due each periοd expressed as a percentage οf the amοunt lent, depοsited, οr bοrrοwed is knοwn as an interest rate. The tοtal interest οn an amοunt lent οr bοrrοwed relies οn the οriginal sum, the interest rate, the cοmpοunding frequency, and the length οf time οver which it is lent depοsited, οr bοrrοwed.
Here, we have
Given: a payday lοan stοre charges $45 fοr a οne-mοnth lοan οf $900.
We have tο find the annual interest rate is this equivalent tο.
Charges=$45
Loan=$900
Let r represent the interest rate
r/12=$45/$900
r = 45×12/900
r = 0.6×100
r = 60%
Hence, the annual interest rate is this equivalent to 60%.
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You deposit $6000 in an account earning 6% interest compounded quarterly. How much will you have in the account in 15 years? Round your answer to the nearest cent.
Answers
Step-by-step explanation:
The formula to calculate the future value of a present value deposit with compounding interest is:
FV = PV × (1 + r/n)^(n*t)
Where:
PV = Present Value (the initial deposit)
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
Using this formula, we can calculate the future value of the $6000 deposit after 15 years:
PV = $6000
r = 6% = 0.06
n = 4 (compounded quarterly, i.e. 4 times per year)
t = 15 years
FV = $6000 × (1 + 0.06/4)^(4*15)
FV = $6000 × 1.458^60
FV = $6000 × 6.2565
FV = $37,539.00
Therefore, the future value of the $6000 deposit after 15 years with quarterly compounding at 6% interest rate is $37,539.00.