The amount of money he must put in the account is $16666.66
What is meant by interest rate?A portion of the total loan amount that the borrower is required to pay the lender as interest over a predetermined timeframe.
This year, the Bank of Canada quickly increased its policy rate, taking it from 0.25% in March 2022 to 4.25% in December 2022, and in the process, driving up mortgage and prime rates. An interest rate is the portion of a loan, deposit, or borrowing that must be paid in interest each period. The total amount of interest charged depends on the amount lent or borrowed, the interest rate, the frequency of compounding, and the length of time it was lent, deposited, or borrowed.
Given,
r=4%
T=5 years
Total amount=SI+P
=20000
SI+P=20000
SI=20000-P
SI=PTR/100
20000-P=(P×5×4)/100
2000000-100P=20P
120P=2000000
P=16666.66
Therefore, The amount of money he must put in the account is $16666.66.
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What is the equation of the circle shown on the graph
The equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.
What is an equation of a circle?
A circle can be characterized by its centre's location and its radius's length.
Let the center of the considered circle be at the (h, k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
The center of the circle is at (-2, 1) and the radius of the circle is 2 units. Then the equation of the circle will be
(x - (-2))² + (y - 1)² = 2²
(x + 2)² + (y - 1)² = 2²
(x + 2)² + (y - 1)² = 4
Hence, the equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.
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Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 6 inches. If a random sample of fifteen 18-year-old men is selected, what is the probability that the mean height x is between 68 and 70 inches? (Round your answer to four decimal places.)
The probability that the mean height x is between 68 and 70 inches is found as 37.28%.
What is meant by the term z score?The z-score effectively represents the standardized distance in units of "number standard deviations" between the raw score (procured from a population assuming a normal distribution) as well as the population mean.The z-score is written as follows:
z = (x - μ)/σ
In which,
x = between 68 and 70 inches.
μ = mean 69 inches
σ = standard deviation 6 inches
Put the values in the formula,
Probability that the mean height x is between 68 and 70 inches
P(68 < x < 70) = (68 - 69 / 6) < z < (70 - 69 / 6)
P(68 < x < 70) = (-0.16) < z < (0.16)
P(68 < x < 70) = 0.4364 - 0.0636
P(68 < x < 70) = 0.3728
P(68 < x < 70) = 37.28%
Thus, the probability that the mean height x is between 68 and 70 inches is found as 37.28%.
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A researcher needs to assign 10 subjects, numbered 0 to
9, to one of two treatment groups: A and B. Use the table
of random digits, starting with the first row and first
column, to carry out the random assignment.
Table of Random Digits
1 07581 34728 65182 58648 53252 83952
2 23290 98227 30144 83191 12167 90414
3 79486 99776 71793 95330 58256 71156
4 46354 09077 98202 03946 07455 39303
5 00472 20787 54571 73719 04368 41032
Select the correct random assignment using the table.
A: 0, 7, 5, 8, 1
A: 0, 2, 4, 6, 8
B: 3, 4, 7, 2, 8
B: 1, 3, 5, 7, 9
B: 2, 9, 1, 7, 4
OA: 0, 3, 6, 5, 8
A: 0, 7, 5, 8, 1
B: 3, 4, 2, 6, 9
In response to the question, we may say that As a result, the right answer expression is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To carry out the random assignment, we may utilise the following table of random digits:
Allocate the first ten topics to the table's rows, beginning with 0 and ending with 9.
Read the numerals from left to right, top to bottom, until 5 participants have been allocated to treatment A and 5 subjects have been assigned to treatment B.
We can get the following random assignment using this method:
A: 0, 3, 6, 5, 8 \sB: 1, 7, 4, 2, 9
As a result, the right answer is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.
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Answer:
A: 0, 7, 5, 8, 1 B: 3, 4, 2, 6, 9
Step-by-step explanation:
THE ANSWER IS D
7. Multiply the
polynomials.
(2x³ + 4x² − 5x)(x³ + 2x - 1)
2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).
Define multiplication.Multiplication in elementary algebra is the process of figuring out what happens when a number is multiplied by itself. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication.
Given
Polynomial
(2x³ + 4x² − 5x)(x³ + 2x - 1)
Multiplying by distributive method,
2x³(x³ + 2x - 1) + 4x²(x³ + 2x - 1) - 5x(x³ + 2x -1)
2x⁶ + 4x⁴ - 2x³ + 4x⁵ + 2x³ - 4x² - 5x⁴ + 10x² - 5x
Adding polynomials with same powers
2x⁶ + 4x⁵ + 4x⁴ - 5x⁴ - 2x³ + 2x³ - 4x² + 10x² - 5x
2x⁶ + 4x⁵ - x⁴ + 6x² - 5x
2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).
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The population of Kingsfield grew from 7,500 to 9,000
in one year. During the same time the population of
Queensville dropped from 32,000 to 25,600. Let the
original populations represent year 1. If these percentage
rates of decline and growth continue, during what year will
Kingsfield have a larger population than Queensville?
The time that it will take for Kingsfield to have a larger population than Queensville is given as follows:
3.58 years.
How to model the populations?The rates of decline and growth are constant, meaning that the populations for each town are modeled by exponential functions.
The rates for each town are given as follows:
Kingsfield: 9000/7500 = 1.2.Queensville: 25600/32000 = 0.8.Considering the initial population, the exponential functions for the population of each town after t years are given as follows:
Kingsfield: y = 7500(1.2)^t.Queensville: y = 32000(0.8)^t.Kingsfield will have a larger population than Queensville when:
[tex]7500(1.2)^t > 32000(0.8)^t[/tex]
Hence:
[tex]\left(\frac{1.2}{0.8}\right)^t > \frac{32000}{7500}[/tex]
(1.5)^t > 4.27
tlog(1.5) > log(4.27)
t > log(4.27)/log(1.5)
t > 3.58 years.
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Consider the function f (same as in the previous problem) defined on the interval [0, 4) as follows, F(x) = { 2/2 x. x € [0,2]. 2, x € [2, 4]Find the coefficients Cn of the eigenfunction expansion of function ff(x) = Σ[infinity], n=1 cnyn(x), where y... for n = 1,2,3,... are the unit eigenfunctions of the Regular Sturm-Liouville system - y^n = ꟾλy, y’(O) = 0, y(4) = 0Note: Label your eigenfunctions so the eigenfunction for the lowest eigenvalue corresponds ton = 1. Therefore, use 2n – 1 instead of 2n +1.C= ___
Coefficient Cn is determined by Cn = 1/2 ∫[0,2] (x+2)yn(x) dx
To find the coefficients Cn of the eigenfunction expansion of a function f(x), f(x) must be expanded with the eigenfunction yn(x). The expansion of f(x) with respect to the eigenfunction yn(x) is given by
f(x) = Σ[∞], n=1 cnyn(x)
To find the coefficient cn, we need to compute the dot product of f(x) and yn(x).
cn = (f,yn) = ∫[0,4]f(x)yn(x)dx
Since the eigenfunctions yn(x) are orthonormal, the scalar product is given by
cn = ∫[0,4]f(x)yn(x)dx = ∫[0,2]f(x)yn(x)dx + ∫[2,4]f(x)yn(x)dx
Since f(x) = 2/2 x for x in [0,2] and f(x) = 2 for x in [2,4], compute the coefficient cn as I can do it.
cn = ∫[0,2](2/2x)yn(x)dx + ∫[2,4](2)yn(x)dx
= ∫[0,2]xyn(x)dx + ∫[2,4]2yn(x)dx
= 1/2 ∫[0,2] (xyn(x) + 2yn(x)) dx
= 1/2 ∫[0,2] (x+2)yn(x) dx
Therefore, the coefficient Cn is given by
Cn = 1/2 ∫[0,2] (x+2)yn(x) dx
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Find x to the nearest tenth.
After using trigonometric function the value of to the nearest tenth digit is 11.11
What is Trigonometric function ?
Trigonometric functions are mathematical functions that are used to describe relationships between certain angles and lengths in a triangle. They are based on the ratios of the sides of a right triangle and are used in a variety of applications including surveying, navigation, engineering, and physics. Trigonometric functions are commonly referred to as sine, cosine, tangent, cotangent, secant, and cosecant. Each of these functions can be used to calculate the angle of a triangle, the length of the sides, or the area of the triangle.
Function of Sine
The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function.
Sin a =Opp/Hypot = CB/CA
Cos Function
The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length.
Adjacent/Hypotenuse = AB/CA is the cosine of.
Functional Tan
The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It should be noted that the ratio of sine and cosine to the tan may also be used to express the tan.
Tan a = Opposite/Adjacent = CB/BA
In terms of sine and cos, tan is also equivalent to:
Tan = cos a/sin a
Sin 46° = 8/x
x = 8/Sin 46°
x= 8/0.72
x=11.11
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The linear regression equation for the data set is...
Answer: C
Step-by-step explanation: Because
A line is graphed on the coordinate grid to the right.
Which equation describes the line?
A.y=x/2+1/3
B.y = x/3+1/2
C.y=x/2+15 1/2
D.y=x/3+15 1/2
The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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Let f:R→S be a surjective homomorphism of rings with identity.
(a) If R is a PID, prove that every ideal in S is principal.
(b) Show by example that S need not be an integral domain.
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient
Let f:R⇒S be a surjective homomorphism of rings with identity.
We have to find if R is a PID, prove that every ideal in S is principal.
We know that,
Let I be the ideal of S
Since f is sufficient homomorphism.
So, f⁻¹(I) is an ideal of R.
Since R is PID so ∈ r ∈ R such that
f⁻¹(I) = <r>
I = <f(r)>
Therefore,
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
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Find the vertex of the graph of f(x) = |0.25x − 0.75|. vertex ?
The vertex of the graph (3, 0)
What is Vertex of graph?
A vertex or node is the basic building block of a graph in discrete mathematics, and more precisely in graph theory. An undirected graph is made up of a set of vertices and a set of edges, whereas a directed graph is made up of a set of vertices and a set of arcs.
According to question
when f(x) = 0
that's the minimum point, the vertex, or the intersection of two lines, g(x) = 0.25x − 0.75 and h(x) = 0.75 - 0.25x
Therefore
find the intersection of Two line which are
⇒ y = x/4 - 3/4
⇒ 4y = x - 3 → First line
⇒ y = 3/4 - x/4
⇒ 4y = 3 - x → Second line
So x - 3 = 3 - x
2x = 6 ,
x = 3
And y = 0
hence the vertex of f(x) = (3, 0)
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Isosceles trapezoid ABCD is shown.
A
B
D
C
Which three statements are correct?
ZBAC ZCAD
ZACD ZACB
ZADC ZBCD
AD
AB
AC
BC
CD.
BD
ہے
From the given Isosceles trapezoid ABCD, the three correct statements are:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
What is Isosceles trapezoid?An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths.
Particularly in isosceles trapezoids, there are unique correlations. "Equal legs" is what the term "isosceles" denotes. Non-parallel sides on isosceles trapezoids have the same lengths. The "legs" are another name for these equal sides.
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. A triangle with two congruent sides is referred to as being isosceles, in other words.
Thus, three correct statements are -
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Given the ellipse with equation substitute the x-values from the table into the equation to obtain y-values, rounded to the nearest integer.
The value of y when X value is -1 would be = -5
What is substitution equation method?The substitution equation method is the method of solving equation whereby a value is being simplified and substituted into the second equation to obtain the next unknown value.
From the given equation:
(x-2)²/16 - (y-4)²/9 = 1
Take X = -1 and substitute X for -1 into the given equation,
(-1-2)²/16 - (y-4)²/9 = 1
9/16 - (y-4)²/9 = 1
(y-4)²/9 = 9/16- 1
(y-4)²/9 = -7/16
Cross multiply
(y -4)² = 9(-7)/16
y²+16 = -63/16
16(y²+16) = -63
16y²+256 = -63
16y² = -319
y² = -319/16
y² = -20
y= -√20
y = -4.5
y = -5
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PLEASE ANSWER QUICK!!
Consider the functions and f(x)=|x|-2 and g(x)=2f(x).
a. Complete the table.
b. Describe the graph of f. How does each point on the graph of f map to the corresponding point on g?
The function f(x) is an absolute function and the function g(x) will be twice the function f(x). The table is completed below.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
f(x) = |x| - 2 and g(x) = 2 f(x)
The function g(x) is rewritten as,
g(x) = 2 (|x| - 2)
g(x) = 2|x| - 4
The function f(x) is an absolute function and the function g(x) will be twice the function f(x).
x f(x) = |x| - 2 g(x) = 2f(x)
-2 0 0
-1 -1 -2
0 -2 -4
1 -1 -2
2 0 0
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Annette's Floral Shop has a charge account with Southern Flowers, a wholesaler where she
buys her floral supplies. This month, Annette has purchased 16 dozen roses at $30.96 per
dozen, 40 dozen chrysanthemums at $17.80 per dozen, and 20 dozen tulips at $21.10 per
dozen. In her state, Annette must pay a 6% sales tax on all orders. At the end of the month,
what is the balance on Annette's charge account?
Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.
What is Percentage ?The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
1 dozen of Rose costs = $30.96
1 dozen of chrysanthemums costs = $17.80
1 dozen of of tulips costs = $ 21.10
Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips
= 16 * 30.96 + 40 * 17.80 + 20 *21.10
= $1629.36
There is a 6% sales tax on all order = 6% of 1629.36 = $ 97.76
Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.
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Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.
What is Percentage ?
The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
Use the unitary approach.
by adjusting the fraction's denominator to 100.
It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
1 dozen of Rose costs = $30.96
1 dozen of chrysanthemums costs = $17.80
1 dozen of of tulips costs = $ 21.10
Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips
= 16 * 30.96 + 40 * 17.80 + 20 *21.10
= $1629.36
There is a 6% sales tax on all order = 6% of 1629.36 = $ 97.76
Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.
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given a binary-class classification problem in which the class labels are binary, the dimension of feature is d, and each attribute can take k different values. please provide the numbers of parameters to be estimated with and without the simplifying assumption. please explain your answer. briefly justify why the simplifying assumption is necessary.
For binary class classification, assumptions are necessary in a way:
Given that
From Boyer Naive classifier,
We evaluate (ai | vj) is given below
(ai | vj) = n(e) + m(p) / n + m
Here,
m = equivalent sample size
n(e) = number of training examples
for which v = vj and a = ai
n(i) = number of training example for which v = vj
P = a prior estimate for P(ai | vj)
Here, we calculate that
P(SUV | yes), P(Red | yes), P(Domestic | yes)
P(SUV | no), P(Red | no), P(Domestic | no)
We evaluating this value like
yes:
RED : SUV: DOMESTIC:
n = 5 n = 5 n = 5
n(c) = 3 n(c) = 1 n(c) = 2
P = 0.5 P = 0.5 P = 0.5
m = 3 m = 3 m = 3
Therefore, with the above calculation we can justify that the simplifying assumptions are necessary in a binary class classification.
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What is the image of (10,-6) after a dilation by a scale factor of 1/2 centered at the origin?
The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).
What is dilation?
A dilation is a function f from a metric space M into itself that, for any points x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is a positive real number. Such a dilatation is a resemblance of the space in Euclidean space.
Here, we have
Given
The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin.
We have to find the image after dilation.
The coordinates of an image (-10,-6), dilating the coordinate by 1/2 means reducing the image by multiplying each coordinate by the factor of 1/2.
Image = (1/2(-10), 1/2(-6))
Image = (-5,-3)
Hence, the image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).
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Calculate two-thirds of three-quaters of one half
Answer:
0.25
Step-by-step explanation:
Step 1: Convert all fractions to decimals
Two-thirds = 0.6666
Three-quarters = 0.75
One-half = 0.5
Step 2: Multiply all fractions
0.6666 * 0.75 * 0.5 = 0.25
Step 3: The answer is 0.25
Answer:
[tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
Three-quarters of one half:
[tex]\implies \dfrac{3}{4} \times \dfrac{1}{2}=\dfrac{3 \times 1}{4 \times 2}=\dfrac{3}{8}[/tex]
Two-thirds of "Three-quarters of one half":
[tex]\implies \dfrac{2}{3} \times \dfrac{3}{8}=\dfrac{2 \times 3}{3 \times 8}=\dfrac{6}{24}=\dfrac{6 \div 6}{24 \div 6}=\dfrac{1}{4}[/tex]
5. You use a line of best fit for a set of data to make a prediction about an unknown value. The
correlation coefficient for your data set is -0.993. How confident can you be that your
predicted value will be reasonably close to the actual value?
Answer: The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of -0.993 indicates a very strong negative relationship, which means that as one variable increases, the other variable decreases. This suggests that you can be quite confident that your predicted value will be reasonably close to the actual value.
Question 1
Two months ago, a car dealership sold 30 red cars and 120 cars that were not red. Last
month the car dealership sold a total of 200 cars. Tarik predicts that the dealership sold
45 red cars last month. Do you think this is a reasonable prediction? Explain.
Answer:
Yes this is a resendable prediction
Step-by-step explanation:
Express in a single log term
The simplified form of the given logarithmic expression as required in the task content bis Choice B; 2log8.
What is the simplified form of the expression as a single log term?It follows from the task content that the simplified form of the logarithmic expression is to be determined as a single log term.
On this note, since the given expression is;
2log2 + 2log4
It follows from factorisation that we have;
2 ( log 2 + log 4 )
Therefore, the expression in the parentheses can be simplified as a single log term using the sum of logarithms law as follows;
= 2 ( log ( 2 × 4 ) )
= 2 log 8.
Ultimately, the answer choice which represents the simplified form of the expression as a single log term is; Choice B; 2 log 8.
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PLEASE ANSWERE ASAP
If BC = 16.7 ft, what is AY?
Answer:
Since YA=AX, XB=BZ, ZC=CY, it follows that A, B and C are the midpoints of the sides TX, XZ, ZY. AB, BC, AC are parallel to the sides and equal to their half. In fact, AB = YC=ZC. Therefore BC=AY.)
Good luck;)
Step-by-step explanation:
I need the answer
2x+3y+7x+4y
Answer:
The correct answer to this expression is 9x + 7y. To find this answer, you need to combine like terms. This means that you need to add together any terms that have the same variable and coefficient. In this case, the expression has two terms with the variable x and two terms with the variable y. The coefficients of the x terms are 2 and 7, and the coefficients of the y terms are 3 and 4. To combine these terms, you need to add the coefficients of the x terms together to get 9, and add the coefficients of the y terms together to get 7. Therefore, the combined expression is 9x + 7y.
if ride cast birr 50 to pick up and 10 birr per km how much you go with birr1350
The distance the ride will go for birr 1350 is 130 kilometres.
How to find the distance the ride can go base on the amount?The ride cost birr 50 to pick up and 10 birr per km. The distance you can go with birr 1350 can be calculated as follows;
Let's use equation to represent the total amount spent on the distance covered.
Therefore,
let
x = total distance travelled in kilometresy = total amount in birrHence,
y = 50 + 10x
Therefore,
where
y = 1350
y = 50 + 10x
1350 = 50 + 10x
1350 - 50 = 10x
1300 = 10x
divide both sides by 10
x = 1300 / 10
x = 130 km
Therefore, the ride will go 130 km.
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A recipe for a sports drink calls for 5/8 cup of powder for every 2 quarts of water. If Dionne uses 3 quarts of water, how many cups of powder are needed?
Answer: i think 15/8 but, im not sure
Step-by-step explanation:
The sum of an infinite geometric series with first term a and common ratio r < 1 is given by The sum of a given a/1-r infinite geometric series is 300, and the common
ratio is 0.1. What is the second term of this series?
The second term of the series will be 27.
What is a Geometric progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.
Sum to infinity = a/1-r
where s = 300
r = 0.1
a = 300 (1 - 0.1)
a = 300 (0.9)
a = 270
The second term of the progression will be = ar
Second term = 270 x 0.1
Second term = 27
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What is the greatest common factor of 18, 24, and 40?
2
3
4
8
Answer:
(a) 2
Step-by-step explanation:
You want the greatest common factor of 18, 24, 40.
FactorsThe prime factorization of these numbers is ...
18 = 2 · 3²24 = 2³ · 340 = 2³ · 5The only common factor is 2.
2 is the greatest common factor of 18, 24, and 40.
to specify that x1 must be at most 75% of the blend of x1 , x2 , and x3 , we must have a constraint of the form
The linear constraint form of the variables is X1 =< 0.75(X1 + X2 + X3)
The term linear refers the algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Here we have given that x1 must be at most 75% of the blend of x1 , x2 , and x3 ,
Abd here we must have to find the linear constraint of the form of the variables.
While we looking into the given question we have identified the three are three variables are given they are x1, x2 and x3.
And we have also given that x1 must be greater than 75% when we convert this into decimal then we get the value 0.75.
Here the term of blend refers the sum of the terms,
Then the linear constraint form of the variables is written as,
=> X1 =< 0.75 (X1 + X2 + X3)
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t=10-x identify to dependent and independent variable
Answer: t is the dependent variable and x the independent variable
Step-by-step explanation: t is the dependent variable it depends upon the values of x that we put in.
x is the independent variable as we can use whatever values we want for x it is not affected by t
Advanced Algebra - please help
Answer:
Below
Step-by-step explanation:
Only the middle three are tri -nomials ( three terms)
the third one reduces to (x+ 2)^2
Answer:
3
Step-by-step explanation:
(x+2)^2
