Write an equation based on the following table

As a result, SI = $194.25 is calculated as the simple interest collected on the sum of $7400.

Simple interest is just the percentage that is added to the loaned or borrowed principal amount. Similar to this, you can also receive interest by depositing a specific sum in a bank. Several sectors, including banking, mortgages, vehicles, and other financial organisations, heavily rely on the idea of simple interest.

Given data:

Formula for calculation of  simple interest:

SI = PRT / 100

SI = 7400* 10.5*0.25 / 100

SI = 19425 / 100

SI = 194.25

As a result, SI = $194.25 is calculated as the simple interest collected on the sum of $7400.

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Complete question:

Find the simple interest for the sum of $7400 at  rate of interest of 10.5% for period of 1/4 years.

Answer:

I dont see a

Step-by-step explanation:

If the given equations are true, then the value of x + z is 6.

Simultaneous equations or systems of equations are two or more equations in algebra that must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.

Consider the equations are true,

4x + 2y + 8z = 30                                                                    ------------(1)

3x + 2y + 7z = 24                                                                    ------------(2)

Now,

By subtracting equation (2) from equation (1) we get:

eq(1) - eq(2)

4x + 2y + 8z - ( 3x + 2y + 7z ) = 30 -24

4x + 2y + 8z - 3x - 2y - 7z = 6

( 4x - 3x ) + ( 2y - 2y ) + ( 8z - 7z ) = 6

x + 0 + z = 6

x + z =6

Therefore, assuming the equations to be true the value of x + z is equal to 6.

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The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A.

The above statement is True.

Eigenvalue:

An eigenvalue is a special set of scalar values ​​associated with the most probable system of linear equations in a matrix equation. Eigenvectors are also called eigenvalues. It is a non-zero vector which can be modified by at most its scalar factor after applying a linear transformation.

According to the Question:

If the geometric multiple of the eigenvalues ​​is greater than or equal to 2, the linearly independent set of eigenvectors is no longer unique to the multiple as before. For example, for the diagonal matrix A=[3003], one could also choose the eigenvectors [11] and [1−1], or any pair of two linearly independent vectors.

Sometimes vectors are simply expanded to vector times matrix. If this happens, this vector is called the eigenvector of the matrix and the "stretch factor" is called the eigenvalue. Example: Given a square matrix A, λ is the eigenvalue of A, and the corresponding eigenvector x is

Ax = λx.

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The given power series is of the form:

∑ n=0[infinity]5(n+1) / 2^n(x - 3)^n

To find the center and radius of convergence, we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges.

Conversely, if the limit is greater than 1, the series diverges.

Let's apply the ratio test to the given series:

lim(n→∞) | [5(n+1) / 2^(n+1)] / [5(n+1) / 2^n] |

lim(n→∞) | 1/2 |

1/2 < 1

Since the limit is less than 1, the series converges. Therefore, the series has a center of convergence.

Now, let's determine the radius of convergence. The ratio test also provides us with the radius of convergence, which is the distance from the center to the nearest point where the series converges.

In this case, the ratio test gave us a ratio of 1/2, indicating that the terms of the series decrease by a factor of 1/2 as n increases.

The radius of convergence is the reciprocal of this ratio:

R = 1 / (1/2) = 2

So, the radius of convergence is 2.

To determine the interval of convergence, we consider the distance from the center (x = 3) to the nearest points where the series converges.

Since the radius of convergence is 2, the interval of convergence is centered at x = 3 with a radius of 2.

Therefore, the interval of convergence is (1, 5), which means the series converges for x values between 1 and 5 (exclusive) and diverges for x values outside this interval.

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The points X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below. From the obtained graph ∠XYZ is the obtuse angle.

The given coordinates are X(5,-3), Y(4,-1) and Z(6,-2).

We need to classify ∠XYZ whether it is right, acute, or obtuse.

A cartesian plane or coordinate plane can be defined as a plane formed by the intersection of two coordinate axes that are perpendicular to each other. The horizontal axis is called the x-axis and the vertical one is the y-axis. These axes intersect with each other at the origin whose location is given as (0, 0). Any point on the cartesian plane is represented in the form of (x, y). Here, x is the distance of the point from the y-axis and y is the distance from the x-axis.

Now, X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below:

The given points X(5,-3), Y(4,-1) and Z(6,-2) have positive x-coordinate and negative y-coordinate.

In the cartesian plane, the fourth quadrant positive x-coordinate and negative y-coordinate.

So, all points X(5,-3), Y(4,-1) and Z(6,-2) lie in the fourth quadrant.

From the graph, we can see that the two lines make an obtuse angle, which is more than 180° and less than 360°.

From the obtained graph ∠XYZ is the obtuse angle.

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Answer:

1st choice:  1/4(y - 10) = 2/3

Step-by-step explanation:

the "variable" is y

"is" means "=" (equals sign)

one fourth =  1/4

"difference of" means subtract

Answer:  1/4(y - 10) = 2/3

Answer:

DF = 13.3

KF = 7.2

Step-by-step explanation:

Because of the parallel sides, triangles DEF and LKF are similar by AA.

Then DE/KL = DF/LF = EF/KF.

25/15 = DF/8 = 12/KF

15DF = 8 * 25

DF = 13.3

25KF = 15 * 12

KF = 7.2

Answer: 9 quarters and 14 nickels

Step-by-step explanation:

9*25=225

14*5=70

225+70=295

The total number of nickels is 14 and the total number of quarters is 9 and this can be determined by forming the linear equation.

Given :

kate has $2.95 in quarters and nickels and the total number of coins is 23.

The following steps can be used in order to determine the total number of quarters and nickels Kat have:

Step 1 - Let the total number of quarters be 'x' and the total number of nickels be 'y'.

Step 2 - Remember one quarter is equal to $0.25 and one nickel is $0.05.

Step 3 - The total amount of money Kat has:

0.25x + 0.05y = 2.95  --- (1)

Step 4 - Total number of coins is given by:

x + y = 23

x = 23 - y    --- (2)

Step 5 - Substitute the value of 'x' in equation (1).

0.25(23 - y) + 0.05y = 2.95

5.75 - 0.25y + 0.05y = 2.95

2.8 = 0.20y

y = 14

Step 6 - Now, substitute the value of 'y' in equation (2).

x = 23 - 14

x = 9

So, the total number of nickels is 14 and the total number of quarters is 9.

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Answer:

3

Step-by-step explanation:

To estimate the number of students out of the next 10 who will support Julian, we can use the proportion of students who have supported Julian so far.

The total number of students who have been surveyed is:

15 + 9 + 16 + 10 = 50

Out of these 50 students, 15 have supported Julian. Therefore, the proportion of students who have supported Julian so far is:

15/50 = 0.3

To estimate how many of the next 10 students surveyed will support Julian, we can multiply the proportion of students who have supported Julian so far by 10:

0.3 x 10 = 3

Therefore, we can estimate that out of the next 10 students surveyed, about 3 will support Julian.

Answer: $50,750

Step-by-step explanation: To get the percentage of a number, you need to turn the percent into a decimal, then multiply it with the number you need the percentage of. 35% translates into 0.35. Then you would multiply 145,000 by 0.35, getting 50,750 as your answer!

A singular point occurs when the coefficient of the highest derivative term, in this case y'', becomes zero. At x=1, the coefficient (x²-16)³(x-1) becomes 0, making x=1 a singular point for the given equation.

To determine if x=1 is a singular point for the equation (x²-16)³(x-1)y'' - 2xy' y = 0, we can examine the coefficients of the equation.

In more detail, a singular point in a differential equation is a point where the coefficients of the highest derivative terms are either undefined or equal to zero. For our equation, the highest derivative term is y'' and its coefficient is (x²-16)³(x-1). When x=1, this coefficient becomes (1²-16)³(1-1) = (1-16)³(0) = (-15)³(0) = 0.

Since the coefficient is equal to zero at x=1, it confirms that x=1 is indeed a singular point for the given equation.

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Answer: √58 or about 7.6

Step-by-step explanation:

use the distance formula: √((x1 - x2)² + (y1 - y2)²)

√((3 - 0)² + (7 - 0)²)

√((3)² + (7)²)

√(9 + 49)

√58

hope this helps!

Answer:

about 7.6

Step-by-step explanation:

right on edge 2021

Answer:

1.x=90 degrees

2.smaller angles =30

3.larger angles =(30×2)=60

Step-by-step explanation:

Complement angle=90 degrees

90/3 (because need to separate into 3 parts) =30 degrees

1part =30 degrees

1:2

(1×30):(2×30)

30:60

The original dimensions of the metal piece are:

Let's say the length of the original metal piece is L and the width is W. The squares that are cut from the corners have sides of x. After the flaps are folded upward, the resulting dimensions of the box are L - 2x and W - 2x. The volume of the box is given as:

       (L - 2x) * (W - 2x) * x = x³

        LWx - 2Lx² - 2Wx² + 4x³ = x³

        LWx - 2Lx² - 2Wx² = 0

        LW = 2(L + W)x²

       LW / x² = 2(L + W)

       LW / V^(2/3) = 2(L + W)

        LW = 2(L + W) * V^(2/3)

        LW = 2V^(2/3) (L + W)

        LW = 2 * V^(2/3) * (L + W)

        L = W + t for some t > 0.

        W (W + t) = 2 * V^(2/3) * (W + t + t)

        W² + Wt = 2 * V^(2/3) * (2t + W)

        W² = 2 * V^(2/3) * 2t + 2 * V^(2/3) * W

        W² = 4 * V^(2/3) * t + 2 * V^(2/3) * W

        W^2 / (2 * V^(2/3) + 1) = 4 * V^(2/3) * t / (2 * V^(2/3) + 1) + 2 * V^(2/3)

        * W / (2 * V^(2/3) + 1)

        W * (2 * V^(2/3) + 1) = 4 * V^(2/3) * t + 2 * V^(2/3) * W

        W = 4 * V^(2/3) * t / (2 * V^(2/3) + 1)

        L = W + t = 4 * V^(2/3) * t / (2 * V^(2/3) + 1) + t

        L = 4 * V^(2/3) * t / (2 * V^(2/3) + 1) + t

        W = 4 * V^(2/3) * t / (2 * V^(2/3) + 1)

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Answer:

Step-by-step explanation:

can you get a bigger picture pls

Part A:

Jessica has 1/2 yard of ribbon

1/2 yd = 0.5 yd

She uses an equal amount of ribbon to decorate 3 picture frames.

So, basically we need to divide the total amount of ribbon by 3:

0.5 yd/ 3 = 1/6 yd

Part B:

Let's first express the mixed number as a fraction:

1 1/3 yd = 4/3 yd

Alex uses the same amount of ribbon for each frame. And he needs to decorate 6, Hence:

We multiply the amount of ribbon in each frame, by the total of frames:

4/3 yd * 6 = 8 yd

The system of linear inequalities represented by the graph are;

Inequality 1: y < 3

Inequality 2: x ≥ -1.

The equation of horizontal lines is always expressed in the form y = a where "a" is the point where the line cuts the y axis.

From the graph shown for line 1, we can see that the horizontal line cuts the y-axis at 3, hence the equation of the line will be y < 3.

Inequality sign is less than since the line is a broken line and shaded below the graph.

Similarly;

The equation of vertical lines is always expressed in the form x = b where "b" is the point where the line cuts the x-axis.

From the graph shown for line 2, we can see that the vertical line cuts the x-axis at -1, hence the equation of the line will be x ≥ -1.

The inequality sign is greater than and equal to since the line is a solid line and shaded to the right the graph.

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According to the question, the confidence interval does not include the value of 12 ozs, indicating that the true mean volume could be different. This provides some evidence to suggest that the advertised claim of 12 ozs may not hold true.

To determine if the confidence interval provides convincing evidence that the true mean volume is different than 12 ozs, we need to examine whether the interval contains the value of 12 ozs or not.

In this case, the confidence interval is constructed from the sample data and is given as 11.97 ozs. to 12.05 ozs. Since the interval does not include the value of 12 ozs, it suggests that the true mean volume may be different from 12 ozs.

When constructing a confidence interval, we specify a confidence level, which in this case is 95%. This means that if we were to repeat the sampling process multiple times and construct confidence intervals using each sample, approximately 95% of those intervals would contain the true mean volume.

However, in this particular instance, the confidence interval does not include the value of 12 ozs, indicating that the true mean volume could be different. This provides some evidence to suggest that the advertised claim of 12 ozs may not hold true.

The \(95\%\) confidence interval is constructed as (11.97, 12.05).

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Answer:

Step-by-step explanation:

It could be going at 49 MPH

(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

9514 1404 393

Answer:

Step-by-step explanation:

Plot the given points on the graph. Those that are on the (solid) boundary line or in the shaded area are solutions. Those in the white space are not solutions.

Answer:

12x³ - 7x² + 11x + 14

Step-by-step explanation:

(3x + 2)(4x² - 5x + 7)

Each term in the second factor is multiplied by each term in the first factor, that is

3x(4x² - 5x + 7) + 2(4x² - 5x + 7) ← distribute parenthesis

= 12x³ - 15x² + 21x + 8x² - 10x + 14 ← collect like terms

= 12x³ - 7x² + 11x + 14

Answer:

Step-by-step explanation:

Pedometer

The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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