The completion of the equation to find w, the number of weeks until Ashely and Tanner have the same amount in their savings accounts is 25w + 450 = 40w + 200.
What is an equation?An equation is a mathematical statement claiming that two or more mathematical expressions are equivalent or equal.
Equations are depicted with the equation symbol (=) to show equality of the expressions.
Ashely Tanner
Savings $450 $200
Planned weekly deposits $25 $40
Let the number of weeks to save equal amounts = w
Equations:Ashely's total savings in w weeks = 25w + 450 ... Equation 1
Tanner's total savings in w weeks = 40w + 200 ... Equation 2
For the two friends to have an equal amount, Equation 1 must equal Equation 2:
25w + 450 = 40w + 200
-15w = -250
w = 16.67
Thus, for Ashely's and Tanner's savings to become equal in amount, it would take 16.67 weeks.
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The given pie-chart represents the division of sports played by students during summer camp.
If the total number of students took part in the summer camp was 300
, then how many students played cricket more than basketball?
17 students played cricket more than basketball.
What is a Pie Chart?A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.
Pie chart showing the preference of the students is given below.
Total number of students = 300
We know that total degree of the circle = 360°
Students who played cricket = 90°
Number of students who played cricket will be (90° / 360°)th of 300.
Number of students who played cricket = (90° / 360°) × 300
= 75
Students who played basketball = 70°
Number of students who played basketball = (70° / 360°) × 300
= 58.33 ≈ 58
Students played cricket - Students played basketball = 75 - 58 = 17
Hence there are 17 students more in cricket than that in basketball.
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Select the correct answer from each drop-down menu.
In a sequence described by a function, the notation f(2) = 4 means that the
term of the sequence has a value of
. Sequences can be described as functions because
.
The function that describes the sequence maps each index or position to its corresponding value.
What does "sequence" signify in functional analysis?A sequence space is a vector space that contains endless sequences of real or complex numbers. It is used in functional analysis and related mathematical fields. It is, in essence, a function space whose constituents are functions from the natural numbers to the field K of real or complex numbers.
The notation f(2) = 4 indicates that a term in a sequence defined by a function has a value of 4 when the term's index or position is 2.
Because sequences are a collection of ordered pairs with the first element being the index or position of the term and the second being the term's value, they can be characterised as functions. The function that represents the series maps each index or location to its associated value, and these ordered pairs can be seen as points on a coordinate plane.
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Lacey pays $15 for each hour of golf lessons and $10 for equipment rental. If the lesson is more than 3 hours long, she only pays $5 for equipment rental. Is the total cost of Lacey’s lesson a function of the number of hours scheduled? Use a table to help explain your answer. Show your work.
Answer:
60
Step-by-step explanation:
15x3=45
5x3=15
15+45=60
Frank is going to plant b vegetable seeds in one garden and 5b + 6 vegetable seeds in another . How many seeds is frank going to plant ?
The total number of seeds Frank is going to plant is 6b + 6 seeds.
How many seeds is frank going to plant ?From the question, we have the following parameters that can be used in our computation:
Graden 1 = b
Graden 2 = 5b + 6
Frank is going to plant b seeds in one garden and 5b + 6 seeds in another garden.
The total number of seeds Frank is going to plant is:
b + (5b + 6) = 6b + 6
So Frank is going to plant 6b + 6 seeds.
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Last night, the Dallas Mavs made 12 free throws. If
their free throw percentage is 75%, how many free
throws were attempted?
Help me pleaseeeeeeeee
Answer:
61
Step-by-step explanation:
√(2+3)^2+(2+4)^2
=√5^2+6^2
=√25+36
=√61
So the number is 61
I need help with these questions ?!
Answer:
Step-by-step explanation:
kiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiilllllllllllllllllllllllll
Answer:
The first one is 3/5 & The second one is 3/8 & The the third one is 1/8
Step-by-step explanation:
Hope this helps :)
PLEASE HELP!! MATH PROBLEM!!
please answer and explain
The polygon in the diagram is a square with center P. The length from the center to the vertex is 6sqrt(2) in. Find the area of the square to the nearest tenth of an inch.
A) 24.0 in^2
B) 72.0 in^2
C) 36.0 in^2
D) 144.0 in^2
there exist two complex numbers $c$, say $c 1$ and $c 2$, so that $3 2i$, $6 i$, and $c$ form the vertices of an equilateral triangle. find the product $c 1 c 2$ in rectangular form.
(200 - 100√2) / 16 is the rectangular form of the product c1*c2 for an equilateral triangle's vertices.
What is triangle?A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.
Here,
An equilateral triangle is a triangle with three equal sides. If 3-2i, 6-i, and c form the vertices of an equilateral triangle, then the distance between 3-2i and 6-i is equal to the distance between 3-2i and c.
The distance between two complex numbers a + bi and c + di can be found using the formula:
√((c - a)² + (d - b)²)
So, the distance between 3-2i and 6-i is:
√((6 - 3)² + (-1 - (-2))²) = √((3)² + (1)²) = √(9 + 1) = √10
And the distance between 3-2i and c is:
√((c - 3)² + (c - (-2))²) = √((c - 3)² + (c + 2)²)
Since these distances must be equal, we have:
√((c - 3)² + (c + 2)²) = √10
Squaring both sides:
(c - 3)² + (c + 2)² = 10
Expanding both sides:
c² - 6c + 9 + c² + 4c + 4 = 10
Combining like terms:
2c² + 10c + 5 = 10
Subtracting 10 from both sides:
2c² + 10c - 5 = 0
This is a quadratic equation, which can be solved using the quadratic formula:
c = (-b ± √(b² - 4ac)) / 2a
Where a = 2, b = 10, and c = -5. Plugging these values into the formula:
c = (-10 ± √(10² - 4 * 2 * -5)) / 2 * 2
c = (-10 ± √(100 + 40)) / 4
c = (-10 ± √(140)) / 4
c = (-10 ± 10√2) / 4
So there are two complex solutions, c1 = (-10 + 10√2) / 4 and c2 = (-10 - 10√2) / 4.
The product of these two solutions is:
c1 * c2 = ((-10 + 10√2) / 4) * ((-10 - 10√2) / 4)
= (100 - 100√2 + 100) / 16
= (200 - 100√2) / 16
(200 - 100√2) / 16 is the answer in rectangular form for the product c1*c2 for the vertices of an equilateral triangle.
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A tree casts a shadow that is 180 feet long. At the same time, a person standing
nearby who is 5 feet 10 inches tall casts a shadow that is 60 inches long. How tall
is the tree?
Answer: 154.28 feet
Step-by-step explanation:
What is an angle that is adjacent to ∠CED?
The angle that is adjacent to the angle CED is the angle DEA.
What are adjacent angles?When two angles have a similar vertex and side, they are referred to as neighbouring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end. When adjacent angles have a same vertex and side, they can be a complimentary angle or supplemental angle.
An adjacent angle is complementary to another if the total of its adjacent angles is 90 degrees.
When the total of two adjacent angles is 180 degrees, they are supplementary to one another.
Two angles are said to be adjacent angles when they share a common vertex.
In the given figure the angle that shares the common vertex to angle CED is angle DEA.
Hence, the angle that is adjacent to the angle CED is the angle DEA.
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Suppose that you have at your disposal a software package that solves a square nonsingular system of equations Cx=d. Assume that the package either finds the unique solution of Cx=d or terminates with an error message if C is singular. Given an m×n matrix A of rank n and an m -vector b, briefly describe in words how you would use the package to find whether or not the equations Ax=b are compatible, and if they are, compute a solution x. Comment briefly on the uniqueness of a solution if one exists.
The equations Ax = b are not compatible.
What do you mean by equation?It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.
An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.
To determine whether the equations Ax = b are compatible and to compute a solution x, you would first form the augmented matrix [A|b]. Then, you would perform row operations on [A|b] to reduce it to an upper triangular matrix [C|d]. Finally, you would use the software package to solve the square system of equations Cx = d.
If the software terminates with an error message, it means that C is singular, and the equations Ax = b are not compatible. If the software finds the unique solution of Cx = d, it means that the equations Ax = b are compatible and that the solution x is unique. However, it is important to note that the uniqueness of the solution depends on the rank of A being equal to n. If the rank of A is less than n, the equations are not compatible, and if the rank of A is greater than n, the equations have infinitely many solutions.
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The scale of the map is missing. The actual distance from Granada Hills to Malibu is 54 miles, and it is 9 inches on the map. What is the scale of the map?
To find the average speed of an object, we find the change in distance divided by the time over which that change occurs. For the instantaneous speed, we must make the time interval very _______, so that the speed does not change appreciably.
To find the instantaneous speed of an object, we must make the time interval very small, so that the speed does not change appreciably.
How to find the speed?
Speed is a scalar quantity which tells how fast an object is moving, regardless of its direction.
To find the instantaneous speed of an object, we must make the time interval very short, so that the speed does not change appreciably. The formula for the instantaneous speed of an object is given by the limit as time approaches zero of the change in distance divided by the time over which that change occurs. The formula for average speed is simply the total distance traveled divided by the total time elapsed.
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Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.
(a) y=Ï€x
(b) y=xπ
(c) y=x2(2−x3)
(d) y=tant−cost
(e) y=s1+s
(f) y=x3−1√1+x√3
(a) f(x) = [tex]log_2(x)[/tex] is a logarithmic function
(b) g(x) = ∜x is a root function
(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function
(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2
(e) v(t) = [tex]5^t[/tex]is an exponential function
(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is a trigonometric function.
(a) f(x) = [tex]log_2(x)[/tex] is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.
(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.
(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.
(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.
(e) v(t) = [tex]5^t[/tex] is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.
(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.
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The complete question is -
Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.
(a) f(x) = [tex]log_2(x)[/tex]
(b) g(x) = ∜x
(c) h(x) = [tex]2x^3/(1 - x^2)[/tex]
(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex]
(e) v(t) = [tex]5^t[/tex]
(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex]
What does 100 liters equal to 1
Answer:
100 liters is equal to 100,000 milliliters.
Step-by-step explanation:
3. Mr. Jackson could think about his experiment a little differently. How many times should he expect to roll a 4 if he rolls his number cube 30 times? This is called the mean, or expected value. You can find it if you know the number of trials and the probability of success for an individual trial. Use the formula μx = np to find the expected value.
The probability of having a 4 in a 30 roll is 5 times
What is the probability distribution
The expected value, μ, of rolling a 4 on a fair number cube (with faces numbered 1 to 6) can be found by using the formula μ = np, where n is the number of trials (30 in this case) and p is the probability of success for an individual trial (rolling a 4).
The probability of rolling a 4 on a fair number cube is 1/6. Therefore, the expected value of rolling a 4 30 times can be calculated as follows:
μ = 30 * (1/6) = 5
So, Mr. Jackson can expect to roll a 4 approximately 5 times in 30 rolls of his number cube.
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A newly hired lawyer receives a $15,000 signing bonus from a law firm and invests the money in a savings account at 4.75% interest. After 42 months, the lawyer checks the account balance. Part A: Calculate the interest earned, to the nearest dollar, if the interest is compounded quarterly. Show all work. (2 points) Part B: Calculate the interest earned, to the nearest dollar, if the interest is compounded continuously. Show all work. (2 points) Part C: Using the values from Part A and Part B, compare the interest earned for each account by finding the difference in the amount of interest earned. (1 point)
The amount when compounded quaterly and compounded continuously will be $16,979.44 and $17,713.02. And the difference is $733.58
What is continuous compounding?Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.
The equation is given as,
[tex]\rm P=P_o \times e^{rt}[/tex]
The initital amount is $15,000 and the interest rate is 4.75% annually.
A. If the interest is compounded quarterly. Then the amount is given as,
[tex]\rm A = \$15,000 \times \left (1 + \dfrac{0.0475}{4} \right)^{42/4}[/tex]
A = $15,000 x 1.1319
A = $16,979.44
B. if the interest is compounded continuously. Then the amount is given as,
[tex]\rm A = \$ 15,000 \times e^{0.0475 \times (42 / 12)}[/tex]
A = $15,000 x 1.1808
A = $17,713.02
C. The difference in the amount of interest earned is given as,
Differenece = $17,713.02 - $16,979.44
Differenece = $733.58
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Nanuk has a savings account which gathers compound interest each year.
He opened the account with a deposit of
£2000.
After 4 years there is £2545.10 in the
account.
Work out the annual interest rate of the
savings account.
Give your answer as a percentage to 1
dp
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2545.10\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]2545.10 = 2000\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4} \implies \cfrac{2545.10}{2000}=\left( 1+\cfrac{r}{100} \right)^4 \\\\\\ \cfrac{2545.10}{2000}=\left( \cfrac{100+r}{100} \right)^4\implies \sqrt[4]{\cfrac{2545.10}{2000}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[4]{\cfrac{2545.10}{2000}}=100+r\implies 100\sqrt[4]{\cfrac{2545.10}{2000}}-100=r\implies \boxed{6.2\approx r}[/tex]
I don’t think 53/63 is in lowest terms haha so help is def needed
Answer:
53/63
Step-by-step explanation:
It is already in simplest form
Try adding up the first few odd numbers and see if the numbers you get satisfy some sort of pattern. Once you find the pattern, express it as a formula. Give a geometric verification that your formula is correct.
The required sum of the first n odd numbers is equal to n².
How we take numbers to make pattern?The first few odd numbers are 1, 3, 5, 7, 9, 11, and so on. When we add up the first few of these numbers, we get the following sums:
1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
We can see that the nth odd number is equal to 2n - 1. And the sum of the first n odd numbers is equal to n². This can be verified geometrically by considering a square with sides of length n.
The sum of the first n odd numbers can be thought of as the sum of the diagonal elements of the square, which forms a square of length n.
Thus, the sum of the first n odd numbers is equal to n².
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Question 19). TPRS is a parallelogram. Identify m∠R.
Solve what is in the attatchment!!
the measurement of the ∠R will be 101 degrees.
What is a parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.
Given TPRS is a parallelogram. in that ∠T = (4x +1) and ∠S = (3x +4)°
Since in a parallelogram, opposite angles are equal Thus,
∠P = ∠S = 3x + 4
∠R = ∠T = 4x +1
Since we know the sum of all angles of a quadrilateral is 360°
3x +4 + 4x +1 + 3x +4 + 4x +1 = 360
14x + 10 = 360
14x = 350
x = 350/14
x = 25
Thus,
∠R = 4x +1
∠R = 4 *25 + 1
∠R = 101°
therefore, the measurement of the ∠R will be 101 degrees.
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The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 38 liters, and standard deviation of 4.3 liters.
A) What is the probability that daily production is between 28 and 45.9 liters? Do not round until you get your your final answer.
The probability that daily production is between 28 and 45.9 liters is 0.024.
What is standard deviation?Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.
Given that, x₁=28, x₂=45.9, μ=38 and σ =4.3
We know that, Z=(x-μ)/σ
Z=standard score, x=observed value, μ=mean of the sample and σ=standard deviation of the sample
z =(38-28)/4.3= 2.32 and probability on the z-table is 0.9896
z = (38-45.9)/4.3 = -1.83 and probability on the z-table is 0.9656,
Now, P(2.32<z<-1.83) = 0.9896-0.9656
= 0.024
Therefore, the probability that daily production is between 28 and 45.9 liters is 0.024.
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If x= 45, then √x is between
4 and 5
44 and 46
22 and 23
6 and 7
y= -3x+7 = what number is for solving y?
Answer:
y=-3x+7
its the same thing
Step-by-step explanation:
The local zoo nurses 15 species of cats. Last week, several species of cats were moved to other zoos due to lack of funding. The zoo now nurses only 7
species.
Let x represent the number of cats.
Which equation models the scenario?
x 7 = 15
x + 7 = 15
15 + x = 7
15-x = 7
The equation 15 - x = 7 models the scenario because it represents the decrease in the number of cats that the zoo now nurses. It can be read as "15 (the number of cats originally) minus x (the number of cats moved) equals 7 (the number of cats the zoo now nurses)".
FIND MULTIPLICITY AND ZEROS OF THE GRAPH!
Calculate the expectation value of and for a particle in the state n = 5 moving in a one dimensional box of length 2.50 × 10−10. Is =2. Explain
The expectation values are <x> = 1.25 x 10⁻¹⁰ , <x²> = 2.07 x 10⁻²⁰
What is average?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
We need to find expectation value of <x> and < x²>
average value for <x> is given by a/2 where a = length of box
hence <x> = ( (2.5 x 10⁻¹⁰) /2) = 1.25 x 10⁻¹⁰
hence <x²> = (1.25 x 10⁻¹⁰)² = 1.56 x 10⁻²⁰
<x²> = ( a/2 x 3.14 x n)² x ( 4 x 3.14² x n² /3 -2)
hence <x²> = ( 2.5 x 10⁻¹⁰ / 2 x 3.14 x 5)² x ( 4 x 3.14² x 5² /3 -2)
<x²> = 2.07 x 10⁻²⁰
<x²> is not equal to <x>²
The expectation values are <x> = 1.25 x 10⁻¹⁰, <x²> = 2.07 x 10⁻²⁰
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Please help I will give brainliest and 5 stars!!
A. The properties of parallelogram involving slope is the slope of opposite sides of parallelogram are equal as the lines are parallel. Hence, the vertices ABCD form a parallelogram.
What is a parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.
A. The properties of parallelogram involving slope is the slope of opposite sides of parallelogram are equal as the lines are parallel.
B. The opposite sides of the parallelogram are parallel and equal, and their slopes are equal.
C. The given vertices of a parallelogram are:
A(-2, 0), B(0, 9), C(2, 0) and D(0, -9).
Calculate the slope of segment AB and CD.
The slope is given as:
m = (y2 - y1) / (x2 - x1)
For AB:
m = (9 - 0) / (0 + 2) = 9/2
For CD:
m = (-9 - 0) / (0 - 2) = 9/2
Since the slopes of the segments AB and CD are equal the two lines are parallel to each other. Hence, the vertices ABCD form a parallelogram.
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