Then, write the result as a binomial squared. a2+a

Answer:

[tex]z = -2.1875[/tex]

Step-by-step explanation:

The z score is given by the formula
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

where

[tex]z =[/tex] standard score

[tex]x[/tex] = data point = 45 for this problem
[tex]\mu[/tex] = mean = 52 for this problem
[tex]\sigma =[/tex] standard deviation = 3.2 for this problem

Therefore
[tex]z = \dfrac{45 - 52}{3.2} = -2.1875[/tex]

The length of PR is 4.8 units.

In geometry, a trapezoid, also known as a trapezium in some countries, is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs. The angle between the bases of a trapezoid determines its height.

Trapezoids can be classified into several types based on their properties, such as:

Isosceles trapezoid: a trapezoid with congruent legs.

Right trapezoid: a trapezoid with a right angle between one of its legs and one of its bases.

Scalene trapezoid: a trapezoid with no congruent sides.

Since QR is parallel to NO, we have:

∆PNQ ~ ∆PRO (by AA similarity)

So we can write:

PR/PQ = PO/PN

PR/7.2 = 6/9

PR = 7.2 × 6/9

PR = 4.8

Therefore, the length of PR is 4.8 units.

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1)

The value of x is 30.5.

The measure of each angle is:

∠1  = ∠3 = ∠6 = ∠4 = 94

∠2 = ∠5 = 86

2)

The measure of ∠b is 60.7.

The measure of ∠d is 43.1.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

1)

Since line m and line n are parallel.

(2x + 25) and 86 are alternate interior angles.

So,

2x + 25 = 86
2x = 86 - 25

2x = 61

x = 30.5

And,

∠2 and 86 are opposite angles.

So,

∠2 = 86

∠1 and ∠3 are opposite angles.

So,

∠1 = ∠3

And,

∠3 + 86 = 180

∠3 = 180 - 86

∠3 = 94

∠3 and ∠4 are alternate interior angles.

So,

∠3 = ∠4 = 94

∠1 and ∠6 are exterior alternate angles.

∠2 and ∠5 are exterior alternate angles.

So,

∠1 = ∠6 = 94

∠2 = ∠5 = 86

2)

Line m and line n are parallel.

So,

∠b and 60.7 are alternate interior angles.

∠d and 43.1 are alternate interiro angles.

So,

∠b = 60.7

∠d = 43.1

Thus,

1)

The value of x is 30.5.

∠1  = ∠3 = ∠6 = ∠4 = 94

∠2 = ∠5 = 86

2)

∠b = 60.7

∠d = 43.1

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[tex]\dfrac{x^2-15x+36}{5x-60}[/tex]

[tex]= \dfrac{(x-3)(x-12)}{5x-60}[/tex]

[tex]= \dfrac{(x-3)(x-12)}{5(x-12)}[/tex]

[tex]= \dfrac{(x-3)}{5}\\= \dfrac{x-3}{5}[/tex]

[tex]\dfrac{x-3}{5}[/tex], [tex]x\neq12[/tex]

If a nurse can visit 5 patients each hour. If he has 37 patients to visit in a day.  the nurse can visit all of his patients if he works for at least 8 hours in a day.

Let's start by figuring out how many hours the nurse would need to visit all 37 patients, assuming he could work for a continuous period of time without taking a break:

37 patients ÷ 5 patients/hour = 7.4 hours

However, since the nurse cannot work a fraction of an hour, we need to round up to the nearest hour. Therefore, the nurse would need to work for 8 hours in order to visit all 37 patients.

So, the nurse can visit all of his patients if he works for at least 8 hours in a day.

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The balance over the acceptable debt ratio is $1089.90.

A debt ratio calculates a company's leverage by comparing its total debt to its total assets.

Although this ratio varies greatly between industries, capital-intensive enterprises typically have significantly larger debt ratios than other types of businesses.

Divide total debt by total assets to find a company's debt ratio.

A debt ratio of less than 100% signifies a corporation has more assets than debt, and a debt ratio of larger than 1.0 or 100% means the opposite.

According to some sources, the debt ratio is calculated by dividing all obligations by all assets.

Given that, credit card balance = $3,589.90

credit limit = $5,000

Debt Ratio percentage = 50% = 0.50

The balance over is given as

balance = Current Balance - (Credit Limit × 0.50 )

balance = 3589.90 - (5000 × 0.5)

balance = 3589.9 - 2500

balance = 1089.9

Hence, the balance over the acceptable debt ratio is $1089.90.

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Answer:

(3/5) (30x - 15) = 72 ⇔ 18x - 9 = 72

(3/5) (30x - 15) = 72 ⇔ 3(6x - 3) = 72

(3/5) (30x - 15) = 72 ⇒ x = 4.5

Equation 1 and 2 have the same value.

Equations C and D have the same value.

A formula is given to us: 3/5 (30x -15) = 72. The equations with the same value of x are the ones we are to choose.

Let's tackle the issue at hand.

3/5 . 30x - 3/5 . 15=72

3.6x - 3.3= 72

18x - 9 = 72

As a result, option C is the best one.

As we factor 3 out of the equation above, we get:

3 . 6x - 3 . 3 = 72

3(6x-3)=72

As a result, option D is also a good decision.

Let's figure out what x is: 3(6x-3) / 3 = 72/3

6x-3=24

x = 4.5

As a result, the final choice is also right.

(3/5) (30x - 15) = 72⇔ 18x - 9 = 72

(3/5) (30x - 15) = 72 ⇔ 3(6x - 3) = 72

(3/5) (30x - 15) = 72 ⇒ x = 4.5

Equations C and D have the same value.

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Therefore, the regression equation best fits the data set is yˆ=0.728x2−20.213x+179.246.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides, the left-hand side and the right-hand side, connected by an equal sign (=). The expressions on either side of the equal sign can be made up of numbers, variables, mathematical operations, and other mathematical symbols. Equations are used to represent various mathematical relationships and can be solved to find the value of one or more variables. Solving an equation involves manipulating the expressions on either side of the equal sign to isolate the variable being solved for. This is often done by applying a series of mathematical operations to both sides of the equation, with the goal of eventually isolating the variable on one side of the equal sign and obtaining a numerical value for it.

Here,

Using a graphing calculator, we can plot the data set of x and y values and use the regression feature to find the quadratic regression equation that best fits the data. Here's how we can do it:

Enter the x and y values into the calculator.

Plot the points on a scatter plot.

Choose the regression feature on the calculator.

Select the quadratic regression option.

The calculator will display the quadratic regression equation that best fits the data.

After performing these steps, we get the following quadratic regression equation:

yˆ=0.728x2−20.213x+179.246

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The number of coins Mark have is 48.

Joey has 25 collectible coins which is 9 more than 1/3 the number Mark has. Therefore, the number of coins Mark have can be calculated as follows:

Let's write the equation for the word problem before solving.

Hence,

let

x = number of coins Mark has

Therefore,

Number of coins Joey have = 9 + 1  /3 x

Hence,

25 = 9 + 1  / 3 x

25 - 9 = 1 / 3 x

16 = 1 / 3 x

cross multiply

x = 16 × 3

x = 48 coins

Therefore,

number of coins Mark have = 48 coins

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Answer:

Step-by-step explanation:

Therefore , the solution of the given problem of test statistics comes out to be Using a z-table or calculator, we find the p-value to be approximately 0.0423.

The test statistic for anything akin to a Z-test has been the Z-statistic, which shows the ordinary normal neutral hypothesis is correct. Suppose you perform a 2 different X y test with a 0.05 threshold of significance and, based on your data, you obtain a 2.5 R t (also referred as a Z-value). 0.0124 is the p-value for the this Z-value.

Here,

To test Aaron's claim, we can use a two-sample proportion z-test.

Let p1 be the proportion of cat persons in the Orlando population, and p2 be the proportion of cat persons in the rural population.

Null hypothesis: p1 = p2 (there is no significant difference in how appealing owning a cat is between city residents and rural residents)

Alternative hypothesis: p1 ≠ p2 (there is a significant difference in how appealing owning a cat is between city residents and rural residents)

We can use the following formula to calculate the test statistic:

z = (p1 - p2) / sqrt(p * (1 - p) * (1/n1 + 1/n2))

where p is the pooled proportion, n1 and n2 are the sample sizes, and

p = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of cat persons in each sample.

Plugging in the values, we get:

p1 = 62/119 = 0.5210

p2 = 48/117 = 0.4103

n1 = 119, n2 = 117

p = (62 + 48) / (119 + 117) = 0.4661

z = (0.5210 - 0.4103) / sqrt(0.4661 * (1 - 0.4661) * (1/119 + 1/117)) ≈ 2.0296

Using a z-table or calculator, we find the p-value to be approximately 0.0423.

Since the p-value (0.0423) is less than the significance level (0.05), we reject the null hypothesis. We can conclude that there is a significant difference in how appealing owning a cat is between city residents and rural residents.

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The volume of grains stored in Adam's family farm in m³ is 14.374m³.

What is meant by volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. Knowing an object's volume can help us figure out how much a substance is needed to fill it, such as how much water is needed to fill a bottle. Cubic units are used to quantify a solid's volume. Volume is another word for capacity.

Given,

 The volume of grains stored in the farm = 18.8 yards³

It is given that 1 yard = 0.9144 m

We are asked to find the above volume of grains from yards³ to m³

if

1 yard = 0.9144 m

1 yard³ = 0.9144 m * 0.9144 m * 0.9144 m

18.8 yards³ = 18.8 * 0.9144*0.9144*0.9144 = 14.374 m³

Therefore the volume of grains stored in the farm in m³ is 14.374m³.

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Here, The amount $26,000 is being deducted or reduced from the account which means it is debit...

Answer:

$26,000 is being deducted from the account which means it is debit.

Explanation:

The journal entry to record a $26,000 reduction in inventory would depend on the reason for the reduction. In general, if the reduction is due to a sale of inventory, the journal entry would be:

Date: 1-Oct

Account: Inventory

Account Number: 1020

Debit: Cost of Goods Sold

Credit: Inventory

In this case, the debit entry would be to the Cost of Goods Sold (COGS) account, which is an expense account that is used to record the cost of goods that have been sold during a particular period. The credit entry would be to the Inventory account, which represents the value of inventory that the business currently holds.

If the reduction in inventory is due to some other reason, such as loss, theft, or damage, the journal entry would be:

Date: 1-Oct

Account: Inventory

Account Number: 1020

Debit: Loss or Expense account

Credit: Inventory

In this case, the debit entry would be to a Loss or Expense account that reflects the reason for the reduction in inventory. The credit entry would be to the Inventory account.

Answer:

The easiest way to divide two numbers is to use a calculator. All you need to do is enter the two numbers and press the division symbol (÷). Another method is to use long division, which involves breaking down the two numbers into individual digits and then systematically dividing them. This method is particularly useful when dividing large numbers.

The probability that the first winner lives in Wells and the second lives in Gaston 1/9.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Total number of customers entering the drawing = 9

Number of customers from Gaston = 4

Number of customers from Pike = 3

Number of customers from Wells = 2

Now the probability for the first winner to be from Wells will be

= 2/9

and,  Probability of second winner to be from Gaston will be

= 4/8

= 1/2

So, the probability is

= 2/9 x 1/2

= 1/9.

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Final answer is that there are 500 students in Math 6.

what is percentage ?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the % symbol. For example, 50% means 50 out of 100, or 0.5 as a decimal.

According to question:
A. Joey's answer of 180 is not correct. If 300 students are currently mastering their math lessons and this represents 60% of the total number of students in Math 6, we can use the following equation to find the total number of students in Math 6:

60% of the total number of students = 300

0.6 × Total number of students = 300

Total number of students = 300 ÷ 0.6

Total number of students = 500

Therefore, there are 500 students in Math 6, not 180.

B. It is possible that Joey used a method called "guess and check" to arrive at his answer of 180. This method involves guessing a number, plugging it into an equation or problem, and checking to see if it is the correct answer. While this method can be useful in some cases, it is not a reliable method for solving this problem since there are an infinite number of numbers to guess from and the probability of guessing the correct answer is low.

C. To solve this problem correctly, we can use a percent equation. We know that 60% of the students in Math 6 are mastering their math lessons, so we can write:

0.60 × Total number of students = 300

To solve for the total number of students, we can divide both sides of the equation by 0.60:

Total number of students = 300 ÷ 0.60

Total number of students = 500

Therefore, the final answer is that there are 500 students in Math 6.

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Answer:

middle set of data

Step-by-step explanation:

Answer:

c = -5

Step-by-step explanation:

[tex]\frac{1}{4} c+2=\frac{3}{4}[/tex]

Subtract 2 on both sides

[tex]\frac{1}{4} c=-1\frac{1}{4}[/tex]

Divide by [tex]\frac{1}{4}[/tex]

[tex]c=-5[/tex]

Answer:

Step-by-step explanation:

(a) To find the minimum possible mass of the four barrels, we want to arrange them in a way that minimizes the total mass. One way to do this is to put the two lightest barrels together and the two heaviest barrels together. This way, the total mass is minimized because the lighter barrels balance out the heavier ones.

So, the minimum possible mass of the four barrels is:

2(30 kg) + 2(30 kg) = 120 kg

(b) To find the maximum possible mass of the four barrels, we want to arrange them in a way that maximizes the total mass. One way to do this is to put the heaviest barrel with the lightest barrel and the other two barrels together. This way, the total mass is maximized because the heaviest and lightest barrels are paired together, making the total mass greater than if they were all paired together.

So, the maximum possible mass of the four barrels is:

30 kg + 90 kg + 30 kg + 30 kg = 180 kg

The exact perimeter of the triangle is 2√5 + √34 + 5√2.

To find the perimeter of the triangle, we need to find the distances between its vertices and add them up. Let's use the distance formula to find the three distances:

Distance between (2, -2) and (-2, 0):
d1 = √[(2 - (-2))^2 + (-2 - 0)^2]

= √[(4)^2 + (-2)^2]

= √(16 + 4)

= √20

= 2√5

Distance between (2, -2) and (-1, -7):

d2 = √[(2 - (-1))^2 + (-2 - (-7))^2]

= √[(3)^2 + (5)^2]

= √(9 + 25)

= √34

Distance between (-2, 0) and (-1, -7):

d3 = √[(-2 - (-1))^2 + (0 - (-7))^2]

= √[(-1)^2 + (7)^2]

= √(1 + 49)

= √50

= 5√2

Now, we can add up the distances to find the perimeter:

perimeter = d1 + d2 + d3

= 2√5 + √34 + 5√2

Therefore, the exact perimeter of the triangle is 2√5 + √34 + 5√2.

The perimeter of a triangle is the total length of its three sides. To find the perimeter, you simply add the lengths of the three sides together.

For example, if a triangle has side lengths of 5 cm, 6 cm, and 7 cm, its perimeter would be:

Perimeter = 5 cm + 6 cm + 7 cm

Perimeter = 18 cm

So the perimeter of the triangle is 18 cm.

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The interval in set builder notation is {x : x ≥ -2 and x < 3, where x ∈ R} and the graph of the interval is given below.

Set builder form is used to represent the numbers in a set especially infinite numbers in a set using a statement which describes all the elements in the set.

Given interval is [-2, 3).

This is a closed interval from -2 and open interval at 3.

So, this interval contains all the elements from -2 to 3 where 3 is not included.

So, the set builder form can be written as,

{x : x ≥ -2 and x < 3, where x ∈ R}

The graph of the interval on the number line will be a straight line with closed circle at -2 and open circle at 3.

Hence the set builder form is {x : x ≥ -2 and x < 3, where x ∈ R}.

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Among the options provided, the one that best describes the meaning of the y-intercept is:

The cab charges a base fee of $6.

The point where a line or curve contacts the y-axis in a graph is known as the y-intercept. The dependent variable's value is represented by the graph's vertical axis or y-axis.

The value of the dependent variable when the independent variable is zero is represented by the y-intercept. The y-intercept, for instance, depicts the cost of the taxi ride when the distance traveled is zero in a graph that shows the cost of a taxi ride as a function of the distance traveled. This amount can represent a set cost that is added to a variable cost, like a cost per mile, such as a base price.

Using the given investment method:

FV = P(1 + r/n)^(nt)

FV = 1000(1 + 0.03/4)^(4*15)

FV = $1,489.36

Using annual compounding:

FV = P(1 + r)^t

FV = 1000(1 + 0.03)^15

FV = $1,520.10

These calculations show that the future value of the investment using annual compounding is higher than the future value using the given investment method.

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Answer:

Decreased by 19%.

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

Decrease by of x 10% can be shown as a product of x and:

Same applies to the second decrease, then we get a final number:

It represent a one off decrease of:

Hence the answer is 19%.

Answer:

Step-by-step explanation:

100 - 100/10 = 90

90 - 90/10 = 91

100 - 81 = 19%

for a better understanding look at the figure

At the Culver City Trampoline Park, customers leave their shoes in cubbies shaped like rectangular prisms while they jump. Each cubby is 11 inches deep, 6 inches tall, and has a volume of 396 cubic inches. So, each cubby is 6 inch wide.

Three-dimensional space is quantified by volume. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or American customary units. 

Every object in three dimensions takes up that space. The volume of that kind of area is the one being measured. The area covered by such an object's boundaries in three-dimensional space generally said to as the volume. Other term for it would be an object's capacity.

Given that,

Each cubby is 11 inches deep,

6 inches tall, and

has a volume of 396 cubic inches.

Volume of rectangular prism = L × W × h

or, 396 = 11 × W × 6

or, W = 396 / 66

or, W = 6 inch

Thus, each cubby is 6 inch wide.

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Answer:

Step-by-step explanation:

Polynomials are a type of mathematical expression that involve variables raised to powers and added or subtracted together. They have many applications in the real world, ranging from science and engineering to finance and economics. Here are a few examples:

Physics: Polynomials are used to describe the motion of objects in space. For example, the position of a moving object over time can be represented by a polynomial function.

Engineering: Polynomials are used to design and analyze complex systems, such as electrical circuits and control systems.

Computer graphics: Polynomials are used to create curves and shapes in 3D modeling and computer graphics.

Finance: Polynomials are used in financial modeling to represent trends and make predictions. For example, a polynomial function could be used to model the growth of a company's revenue over time.

Data analysis: Polynomials are used to fit curves to data in order to make predictions or gain insights. For example, a polynomial function could be used to model the relationship between a company's advertising budget and its sales.

Overall, polynomials are a powerful tool in mathematics and have many practical applications in various fields.

Trains make up approximately 49.04% of the total journeys across all modes of transportation.

We must divide the total number of train trips by the total number of trips made using all modes of transportation, then multiply the result by 100 to get the percentage that trains make up of the total.

There have been 2320 train trips overall, and there have been 4730 trips overall using all forms of transportation.

Trains therefore account for the following proportion of the total:

(2320 / 4730) x 100% = 49.04%

Train travel thus accounts for roughly 49.04 percent of all travels made using all modes of transportation.

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It is proved that  [tex]tan^2(x)*sin^2(x) = tan^2(x) - sin^2(x)[/tex]

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It has applications in fields such as engineering, physics, and navigation.

We can use the trigonometric identity:

[tex]tan^2(x) + 1 = sec^2(x)[/tex]

to derive the identity:

[tex]tan^2(x) = sec^2(x) - 1[/tex]

We can also use the identity:

[tex]sin^2(x) + cos^2(x) = 1[/tex]

to derive the identity:

[tex]cos^2(x) = 1 - sin^2(x)[/tex]

Then, substituting the second identity into the first, we get:

[tex]tan^2(x) = sec^2(x) - 1 = 1/cos^2(x) - 1 = (1 - cos^2(x))/cos^2(x) = sin^2(x)/cos^2(x) = tan^2(x)*sin^2(x)/(1 - tan^2(x))[/tex]

Multiplying both sides by [tex](1 - tan^2(x))[/tex], we get:

[tex]tan^2(x)*(1 - tan^2(x))*sin^2(x) = tan^2(x)*(1 - tan^2(x)) - sin^2(x)*tan^2(x)tan^2(x)*sin^2(x) - tan^4(x)*sin^2(x) = tan^2(x) - tan^4(x) - sin^2(x)*tan^2(x)tan^2(x)*sin^2(x) = tan^2(x) - sin^2(x)[/tex]

Hence Proved

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The least number of bars of soap that must be made on any given day for the factory to make a profit that day is 369 bars.

Two expressions in an equation are combined using the equal symbol ("="). The "left-hand side" and "right-hand side," respectively, of the equation refer to the two expressions that are on either side of the equals sign. Usually, we consider an equation's right side to be zero.

We have the equation ,

y = 0.84 x + 428

Let n be the least number of bars required to make a profit.

then,

2n = 0.84n + 428

dividing both sides by 2

n = 0.42n + 214

0.58n = 214

n = 368.96

n ≈ 369 bars

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Answer:

y = (12 / (25/12)^7) * (25/12)^x

Step-by-step explanation:

To write an exponential model given two points, we can use the general form of an exponential function:

y = ab^x

where y is the dependent variable, x is the independent variable, b is the base or growth factor, and a is the initial value when x = 0.

Using the two given points, we can form a system of equations:

12 = ab^7 (1)

25 = ab^8 (2)

Dividing equation (2) by equation (1), we get:

25/12 = b^(8-7) = b

So the base of the exponential function is b = 25/12.

To find the initial value a, we can substitute b into either of the original equations. Let's use equation (1):

12 = a(25/12)^7

Simplifying, we get:

a = 12 / (25/12)^7

Therefore, the exponential model that fits the given points is:

y = (12 / (25/12)^7) * (25/12)^x