What is the vertex, Line of symmetry, and how many x intercepts are there?

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

53 people

Step-by-step explanation:

\(\frac{2}{5}\)  × 120 = = 48
48 + 5 = 53 people
____

You've made your grade level high school, lower it to Grade 4. Thank you!

Answer:

11/10 is greater than 1

Step-by-step explanation:

For reference, 10/10 = 1, 8/8 = 1. So when looking at these:

11/10 is 1 and 1/10

7/8 is less than 1

Answer:

$9.50

Step-by-step explanation:

i am 100% sure

Answer:

9m*10m=

90m²

Step-by-step explanation:

Area is just multiplying length * width with rectangular shapes!

The common difference between each term is -5. The nth term of the sequence as follows: aₙ = 18 - 5(n-1)

The given sequence is 18, 13, 8, 3, -2.

To identify the pattern in the sequence, we can observe that each term is decreasing by 5. Starting from 18, we subtract 5 to get the next term, and so on. The common difference between each term is -5.

Using this pattern, we can continue the sequence as follows:

-2 - 5 = -7

-7 - 5 = -12

-12 - 5 = -17

-17 - 5 = -22

The extended sequence would be -2, -7, -12, -17, -22.

In terms of the general formula, we can represent the nth term of the sequence as follows:

aₙ = 18 - 5(n-1)

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Answer:

Step-by-step explanation:

x² + 2x - 3 = 5                                   >You cannot start factoring until you

                                                            set =0

(x - 1)(x + 3) = 5

x - 1 = 5 or x + 3 = 5

x = 6 or x = 2

Should be:

x² + 2x - 3 = 5                                    >Subtract 5 from both sides

x² + 2x - 8 = 0                                    >Now factor

(x - 2)(x + 4) = 0                                  >Set each parenthesis =0

x - 2 = 0 or x + 4 = 0                           >Solve for x's

x = 2 or x = -4

Answer:

Step-by-step explanation:

To increase the difference between 456.674 and 234.458 by 345.856, we follow the following steps :

Step 1: Subtract 456.674 from 234.458 and,

Step 2:  Add 345.856 to the result.

so,  456.674 - 234.458 = 222.216

222.216 + 345.856 = 568.072

Therefore, the increased difference between 456.674 and 234.458 by 345.856 is 568.072

Answer:

92

Step-by-step explanation:

Answer:

  (-2, 2)

Step-by-step explanation:

You want the circumcenter of the triangle with vertices A(2, -3), B(2, 7), and C(-6, -3).

The circumcenter is the center of  the circle that circumscribes the triangle. Here, the triangle is a right triangle, so the circumcenter is the midpoint of the hypotenuse.

The midpoint of segment BC is the average of the coordinates of B and C:

  X = (B +C)/2 = ((2, 7) +(-6, -3))/2 = (2 -6, 7 -3)/2 = (-4, 4)/2

  X = (-2, 2)

The circumcenter is (-2, 2).

__

Additional comment

The right angle subtends an arc of twice its measure, 180°, so the circumscribed triangle occupies a semicircle, and the hypotenuse is a diameter. That puts the center of the circle at the midpoint of the hypotenuse.

The interquartile range of the data will be 13

When arranged from lowest to highest, the IQR reflects the median 50% of values. To calculate the interquartile range (IQR), firstly compute the median (middle value) of the data's lower and upper halves. All those are quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The interquartile range is the difference between quarters three and then one.

first, let us sort the data from lowest to highest

25,25,29,31,33,37,38,42,46

Q1- median of the lower half of the data=(29+25)/2=27

Q3-median of the upper half of the data=(38+42)/2=40

the interquartile range of the data will be Q3-Q1

40-27= 13

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Answer:

Step-by-step explanation:

Answer:

Rachel is correct

Step-by-step explanation:

I hope this helps!

Answer:

_

| x+y(less than or equal to)17

| 11x+8y(greater than or equal to)160

~

Step-by-step explanation:

A. There is a weak negative linear relationship between Y and X, and there is significant scatter in the data points around a line.

Based on the given information, the sample variance of X is 9, the sample variance of Y is 16, and the covariance of X and Y is -10.

To determine the nature of the relationship between X and Y, we need to consider the covariance and the variances.

Since the covariance is negative (-10), it suggests a negative relationship between X and Y.

This means that as X increases, Y tends to decrease, and vice versa.

Now, let's consider the variances.

The sample variance of X is 9, and the sample variance of Y is 16. Comparing these variances, we can conclude that the scatter in the data points around the line is significant.

Therefore, based on the given information, the correct statement is:

A. There is a weak negative linear relationship between Y and X, and there is significant scatter in the data points around a line.

This option captures the negative relationship between Y and X indicated by the negative covariance, and it acknowledges the significant scatter in the data points around a line, which is reflected by the difference in variances.

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Answer:

It would be:

\(2.11 \times {10}^{8} \)

Step-by-step explanation:

You just subtract the regular numbers so 4.31-2.2 and keep the same scientific notation.

Answer:

Step-by-step explanation:

Answer:B

Step-by-step explanation: Reducing 2x-2+3x results in 5x-2 because 2x+3x is 5x

Answer:

B)

Step-by-step explanation:

The answer is option B)

2x - 2 + 3x = 5x - 2

Using the plus 4 method, the 95% confidence interval for the difference in proportion of individuals developing a cold after viral exposure between the Echinacea and the placebo is (-0.158, 0.397). Based on this confidence interval, we can conclude that there is no significant difference in the proportion of individuals developing a cold between the Echinacea and the placebo groups.

To determine the 95% confidence interval for the difference in the proportion of individuals developing a cold between the Echinacea and placebo groups, we can use the plus 4 method for small sample sizes.

First, we calculate the proportions of individuals who developed a cold in each group.

In the placebo group, out of 103 subjects, 88 developed a cold, giving a proportion of 88/103 ≈ 0.854.

In the Echinacea group, out of 48 subjects, 44 developed a cold, giving a

proportion of 44/48 ≈ 0.91

Next, we add 2 to the number of successes and 2 to the total number of observations in each group to apply the plus 4 adjustment.

This gives us 90 successes out of 107 observations in the placebo group (0.841) and 46 successes out of 52 observations in the Echinacea group (0.885).

To calculate the 95% confidence interval, we can use the formula:

\(CI = (p1 - p2) \pm Z \times \sqrt{(p1(1-p1)/n1} + p2(1-p2)/n2)\)

where p1 and p2 are the adjusted proportions, n1 and n2 are the respective sample sizes, and Z is the critical value for a 95% confidence interval (approximately 1.96).

Substituting the values into the formula, we get:

\(CI = (0.841 - 0.885) \pm 1.96 \times \sqrt{((0.841(1-0.841)/107) + (0.885(1-0.885)/52))}\)

Calculating the values within the square root and the overall expression, we can find the lower and upper bounds of the confidence interval.

Interpreting the results, if we repeat this experiment many times and construct 95% confidence intervals, we can expect that approximately 95% of these intervals will contain the true difference in proportions

In this case, if the interval contains 0, it suggests that there is no significant difference between Echinacea and placebo in terms of the proportion of individuals developing a cold after viral exposure. However, if the interval does not include 0, it indicates a significant difference, suggesting that Echinacea may have an effect on reducing the likelihood of developing a cold.

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Answer:

Quadrant IV..............

Answer:

what's the problem i know that "tickets for the school play cost 6 dollars for the adults and 3.50 for the students" but you didn't say how many people are going

Step-by-step explanation:

The value of the yakubu and bello business is N80,000.

Let's start by determining the original value of Yakubu and Bello's shares in the business before the sale took place.

The ratio of their shares is given as 3:5, which means Yakubu owns 3 parts and Bello owns 5 parts out of a total of 3+5 = 8 parts.

Now, let's assume the value of the business is represented by "V" (to be determined).

Since Yakubu later sold 3/4 of his share to Bello, this means he sold 3/4 * 3 = 9/4 parts of the business to Bello.

The value of 9/4 parts of the business is N180,000, so we can set up the following equation:

(9/4) * V = N180,000

To solve for V, we multiply both sides of the equation by 4/9:

V = (4/9) * N180,000

V = N80,000

Therefore, the value of the business is N80,000.

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what quadrants

Step-by-step explanation:

20,13 and 12,-8 is 2008 ,5

We need to solve the next system of equations by using elimination:

1) x + 4y = 10

2) x -+7y = 16

Subtract both equations:

x + 4y = 10

-

( x - 7y = 16)

------------------------

x-x + (4y-7y) = 10-16

0 -3y = -6

Solve for y

-3y = -6

Divide both sides by -3

-3y/ -3 = -6/-3

Then:

y = 2

Now, replace this y-value on the first equation:

1) x + 4y = 10

x + 4(2) = 10

x + 8 = 10

Solve the equation for x:

Subtract both sides by 8

x + 8 -8 = 10 -8

x = 2

Therefore, x =2 and y =2

Answer:

\(6+ \sqrt{29},6-\sqrt{29}\)

Step-by-step explanation:

The given quadratic equation is \(x^2-12x+7=0\)

The general form of quadratic equation is given by :

\(ax^2+bx+c=0\)

Comparing both the equations,

a = 1, b = -12 and c = 1

The solution of a quadratic equation is given by :

\(x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\)

Put all the values,

\(a=\dfrac{-(-12)\pm \sqrt{(-12)^2-4\times 1\times 7} }{2(1)}\\\\=\dfrac{12\pm \sqrt{116}}{2}\\\\=\dfrac{12\pm 2\sqrt{29}}{2}\\\\=6\pm \sqrt{29}\)

So, the solutions of the given equation is \(6+ \sqrt{29},6-\sqrt{29}\). Hence, the correct option is (d).  

The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

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Solution:

We are given an irregular pentagon. To calculate the area, we will have to break the pentagon into component shapes

We can break the pentagon into a trapezium and a triangle

The dimensions of the trapezium are :

1st base = 3 units

2nd base = 4 units

Height = 3 units

The dimensions of the triangle are:

Base= 4 units

Height=2 units

Area of the polygon = area of trapezium + area of triangle

= 10.5 square unit + 4 square unit = 14.5 square unit

The answer is 14.5 square units

Answer:   To find the average rate of change, divide the change in y-values by the change in x-values

Step-by-step explanation:

To find the equilibrium tuition price, we need to set the demand and supply equations equal to each other:

Demand equation: q = 20000 - 2p

Supply equation: q0 = 7500 + 0.5p

Setting these equations equal, we have:

20000 - 2p = 7500 + 0.5p

To solve for p, we can simplify and rearrange the equation:

20000 - 7500 = 2p + 0.5p

12500 = 2.5p

p = 12500 / 2.5

p = 5000

So the equilibrium tuition price is $5000.

To find the consumer surplus at the equilibrium price, we substitute the equilibrium price into the demand equation:

q = 20000 - 2p

q = 20000 - 2(5000)

q = 20000 - 10000

q = 10000

The consumer surplus is the area between the demand curve and the equilibrium quantity. To calculate it, we use the formula for the area of a triangle:

Consumer Surplus = (1/2) * (Equilibrium Quantity) * (Difference between Maximum Price and Equilibrium Price)

Consumer Surplus = (1/2) * 10000 * (5000 - 0)

Consumer Surplus = (1/2) * 10000 * 5000

Consumer Surplus = 25,000,000

So the consumer surplus at the equilibrium price is $25,000,000.

To find the producer surplus at the equilibrium price, we substitute the equilibrium price into the supply equation:

q0 = 7500 + 0.5p

q0 = 7500 + 0.5(5000)

q0 = 7500 + 2500

q0 = 10000

The producer surplus is the area between the supply curve and the equilibrium quantity. To calculate it, we again use the formula for the area of a triangle:

Producer Surplus = (1/2) * (Equilibrium Quantity) * (Difference between Equilibrium Price and Minimum Price)

Producer Surplus = (1/2) * 10000 * (5000 - 0)

Producer Surplus = (1/2) * 10000 * 5000

Producer Surplus = 25,000,000

So the producer surplus at the equilibrium price is $25,000,000.

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Using the simplex method, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.

To solve the linear program using the simplex method, we start by converting the problem into standard form with all constraints in the form of inequalities and non-negative variables. The initial tableau for the problem is as follows:

 |   x1  |   x2  |   s1   |   s2   |   b   |

--------------------------------------------

z |  -3   |   6   |   0    |   0    |   0   |

--------------------------------------------

s1|   5   |   7   |   1    |   0    |   35  |

--------------------------------------------

s2|  -1   |   2   |   0    |   1    |   2   |

--------------------------------------------

Next, we perform the simplex iterations to improve the objective function value. After performing the necessary row operations, we arrive at the final tableau:

 |   x1  |   x2  |   s1   |   s2   |   b   |

--------------------------------------------

z |   0   |   1   |  3/2   |  -1/2  |   14  |

--------------------------------------------

s1|   0   |   0   |   4    |   3    |   5   |

--------------------------------------------

s2|   1   |   0   |  -1/2  |   5/2  |   3   |

--------------------------------------------

From the final tableau, we can see that the optimal solution is z = 14, with x1 = 0 and x2 = 5. The decision variable x1 is at its lower bound, indicating that it is non-basic. Therefore, there are no alternative optimal solutions in this case.

In summary, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.

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