12 1/2 divided by 5 1/2

The given expression:

The expression can be written as :

Take 9 common :

Since 3 x 3 = 9

Apply the property of factorization:

So, the expression can be written as :

So, the factorization is : 9(x + 3) (x - 3)

Answer :

Answer:

cosθ = \(\frac{12}{13}\)

Step-by-step explanation:

Given

sinθ = - \(\frac{5}{13}\) = \(\frac{opposite}{hypotenuse}\)

This is a 5- 12- 13 right triangle

with opposite = 5, adjacent = 12 , hypotenuse = 13

since θ is in 4th quadrant then cosθ > 0

cosθ = \(\frac{adjacent}{hypotenuse}\) = \(\frac{12}{13}\)

The trigonometric ratio of cos θ in quadrant IV is 12/13.

Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.

For the given situation,

Sin θ = -5/13, and

θ lies in the quadrant IV.

By trigonometric ratio,

\(sin \theta = \frac{opposite}{hypotenuse}\)

⇒ \(sin \theta = -\frac{5}{13}\)

Here opposite side = 5 and

hypotenuse side = 13

The adjacent side can be calculated by using the Pythagoras theorem,

\(Hypotenuse^{2} = opposite^{2} +adjacent^{2}\)

⇒ \(adjacent = \sqrt{hypotenuse^{2} -opposite^{2} }\)

⇒ \(adjacent = \sqrt{13^{2} -5^{2} }\)

⇒ \(adjacent = \sqrt{169 -25 }\)

⇒ \(adjacent = \sqrt{144}\)

⇒ \(adjacent = 12\)

Thus \(cos \theta = \frac{adjacent}{hypotenuse}\)

⇒ \(cos \theta = \frac{12}{13}\)

θ lies in the quadrant IV, so cos θ > 0.

Hence we can conclude that the trigonometric ratio of cos θ in quadrant IV is 12/13.

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To calculate the amount of money a friend's IRA will contain at a given age, we can use the savings plan formula. In this scenario, the IRA has an annual percentage rate (APR) of 7.25%, and monthly deposits of $35 are made.

The objective is to determine the value of the IRA at a specific age. The savings plan formula allows us to calculate the future value of an investment based on regular contributions and a fixed interest rate. Let's break down the information given:

- APR: The IRA has an annual percentage rate of 7.25%, which is the interest rate applied to the account.

- Monthly deposits: A friend makes deposits of $35 per month into the IRA.

- Age: We want to determine the value of the IRA at a specific age.

To calculate the value of the IRA at a given age, we need to consider the time period and the interest earned on the deposits. The savings plan formula is:

FV = P * ((1 + r)^n - 1) / r

Where:

FV = Future value of the IRA

P = Monthly deposit amount ($35)

r = Monthly interest rate (APR divided by 12)

n = Number of months from the start of the IRA until the desired age

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The area of the square is changing at 12√2 + 2√2t square inches/minute when the circle is increasing at 1 in/min.

Let us find the relationship between r and s using the Pythagorean theorem. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.

2r = s√2
Squaring both sides, we get:
4r² = 2s²or s² = 2r²
Dividing by 2 on both sides, we get:
s²/2 = r²
Differentiating both sides with respect to t, we get:
ds²/dt = 2r (dr/dt)
Dividing both sides by 2s, we get:
ds/dt = r (dr/dt) / s

Substituting r² = s²/2,

\(ds/dt = r (dr/dt) / √2s2s ds/dt = r (dr/dt)s ds/dt = (r/2) (dr/dt)2s ds/dt = r (dr/dt) or dA/dt = 2s ds/dt = 2r (dr/dt)\)

Now, substituting r² = s²/2,

dA/dt = 2s ds/dt = 2(√2 s) (dr/dt) = 2(√2) r (dr/dt)

Now, substituting dr/dt = 1 in/min and r = 6 in (since the circle is increasing at 1 in/min, the radius after t minutes is 6 + t),

dA/dt = 2(√2) (6 + t) (1) = 12√2 + 2√2t square inches/minute

Therefore, the area of the square is changing at a rate of 12√2 + 2√2t square inches/minute.

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Answer:

\(-8x^{10}\)

Step-by-step explanation:

\((2x^2)^3(-x^4)\)

Apply the rule \((-a)=-(a)\):

\(\implies -(2x^2)^3(x^4)\)

Apply the exponent rule \((a \cdot b)^c=a^cb^c\) :

\(\implies-(2^3\cdot x^{2 \times 3})x^4\)

\(\implies -8 \cdot x^6 \cdot x^4\)

Apply exponent rule \(a^b \cdot a^c=a^{b+c}\)

\(\implies -8x^{6+4}\)

\(\implies -8x^{10}\)

Answer:

20

Step-by-step explanation:

you add 15 and 5

Answer:

the answer could be B because ration represent as a fractional

Answer:

$54.3

Step-by-step explanation:

17% of 319.41

so u need only to multiply them

25.The correct answer is A. The subject has an extreme criterion.26. The correct answer is B. The criterion is negative.

Question 25:If you know the true underlying sensitivity (d') is 2, but you measure d' as 0, the most reasonable conclusion would be that the subject has an extreme criterion. The criterion refers to the decision threshold used to differentiate between signal and noise. In this case, the subject's criterion is likely set in such a way that they are more conservative or cautious, leading to a reduced sensitivity measure.Therefore, the correct answer is A. The subject has an extreme criterion.

Question 26:When there are more False Alarms than Hits in signal detection, it suggests that the criterion is negative. The criterion represents the decision threshold, and a negative criterion implies a more liberal or lenient approach to categorizing events as a signal. This leads to a higher likelihood of detecting false alarms (incorrectly identifying noise as a signal) while potentially missing some true signals.Hence, the correct answer is B. The criterion is negative.

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The price of a child ticket is $4 and the price of a senior citizen ticket is $10

Let's call the price of a senior citizen ticket "x" and the price of a child ticket "y".

On the first day, the school sold 3 senior citizen tickets and 4 child tickets for a total of $46, so we can write the equation:

3x + 4y =46

On the second day, the school took in $48 by selling 4 senior citizen tickets and 2 child tickets, so we can write another equation:

4x + 2y = 48

Now that we have two equations, we can use substitution or elimination to find the value of x and y.

For substitution, we can solve one equation for one variable and then substitute that expression into the other equation. For example, let's solve the first equation for x:

x = (46 - 4y)/3

Then, we can substitute this expression for x into the second equation:

4((46 - 4y)/3) + 2y = 48

Expanding the left side of the equation:

(184 - 16y)/3 + 2y = 48

Multiplying both sides by 3:

184 - 16y + 6y = 144

Combining like terms on the left side:

184 - 10y = 144

Subtracting 184 from both sides:

-10y = -40

Dividing both sides by -10:

y = 4

So the price of a child ticket is $4. To find the price of a senior citizen ticket, we can substitute this value back into the equation we solved for x:

x = (46 - 4y)/3 = (46 - 4 * 4)/3 = (46 - 16)/3 = 30/3 = $10

So the price of a senior citizen ticket is $10.

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Answer:

What are all the other numbers for up there

Step-by-step explanation:

The result of testing the given claim is; c) H₀: p = .5, Hₐ: p≠ .5; z = 0.8; Fail to reject H₀ at the 1% significance level

We are given;

Sample size; n = 100

Sample proportion; p' = 54/100 = 0.54

In general, population proportion is; p = 0.5

Thus;

The null hypothesis is, H₀: p = 0.5

Alternative hypothesis is; Hₐ: p ≠ 0.5

z-test statistic is defined as:

z = √[(p' - p)/(p(1 - p)/n)]

Plugging in the relevant values gives;

z = √[(0.54 - 0.5)/(0.5(1 - 0.5)/100)]

z = 0.8

From p-value from z-score calculator, we have;

p-value = 0.4237

The P-value is greater than the 1% level of significance. We fail to reject the null hypothesis at the 1% level of significance.

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By solving a linear equation, we can see that the deep of the layer will be 6.37 ft.

For a cylinder of radius R and deep D, the volume is:

V = pi*R^2*D

Where pi = 3.14

In this case, we know that the diameter is 3 ft, so the radius is:

R = 3ft/2 = 1.5ft

And the volume of dirt used is 45 cubic feet, then the deep D must be a solution of the following linear equation:

45 ft^3 = 3.14*(1.5ft)^2*D

Solving this for D, we get:

(45 ft^3)/(3.14*(1.5ft)^2) = D

6.37 ft = D

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The spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

To determine how much further the spring will stretch when a 0.60 kg block is added to the 1.2 kg block, we need to consider Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

Let's assume that the spring is initially stretched by a certain amount x when only the 1.2 kg block is attached. The force exerted by the spring is given by F = kx, where k is the spring constant.

When the 0.60 kg block is added, the total mass becomes 1.2 kg + 0.60 kg = 1.8 kg. The force exerted by the spring remains the same, but the total mass affects the acceleration of the system according to Newton's second law, F = ma.

Using F = ma, we can find the acceleration of the system: F = (1.8 kg)(9.8 m/s^2) = 17.64 N.

Since F = kx, we can rearrange the equation to find x: x = F/k.

Now, if we assume the spring constant k remains constant, the displacement x will increase by a factor of 1.8 kg/1.2 kg = 1.5.

Therefore, the spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

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Answer:

a - b = 9

steps and explanation:

Answer:

a - b = 9

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\) , then

\(\frac{2^{a} }{2^{b} }\) = \(2^{a-b}\) , so

\(2^{a-b}\) = 512 = \(2^{9}\)

since bases on both sides are equal, both 2 then equate exponents

a - b = 9

The Upper Control Limit (UCL) for the X-chart is approximately 14.028.

To calculate the control limits for the X-chart (also known as the process mean chart) in a Statistical Process Control (SPC) chart, we need the average moving range (MR-bar).

The control limits for the X-chart can be determined using the following formulas:

\(Upper $ Control Limit (UCL) = X-double-bar + A2 \times MR-bar\)

\(Lower $ Control Limit (LCL) = X-double-bar - A2 \times MR-bar\)

In these formulas:

X-double-bar represents the overall average measurement.

MR-bar represents the average moving range.

A2 is a constant that depends on the sample size.

The value of A2 can be obtained from statistical tables or calculated using the following formula for sample sizes greater than or equal to 2:

\(A2 = 3.267 - (0.15 \times \sqrt{(N)} )\)

In your case, the overall average measurement is 12.5, and the average moving range is 0.5.

Assuming you have a sample size greater than or equal to 2, we can calculate the value of A2 as follows:

\(A2 = 3.267 - (0.15 \times \sqrt{(N)} )\)

\(= 3.267 - (0.15 \times \sqrt{(2)} ) (assuming N = 2, the $ minimum sample size)\)

\(\approx 3.267 - (0.15 \times 1.414)\)

≈ 3.267 - 0.2121

≈ 3.0559

Now, we can calculate the control limits for the X-chart:

\(UCL = X-double-bar + A2 \times MR-bar\)

\(= 12.5 + 3.0559 \times 0.5\)

= 12.5 + 1.52795

≈ 14.028

Therefore, the Upper Control Limit (UCL) for the X-chart is approximately 14.028.

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Answer:

A=h(b)b/2

Step-by-step explanation:

Answer: To figure out the tip, you need to find 20% of $52.60.

0.2×52.6=10.52

Step-by-step explanation:

Answer:

After eating at your favorite restaurant, you know that the bill before tax is $52.60 and that the sales tax rate is 8%. You decide to leave a 20% tip for the waiter based on the pre-tax amount. How much should you leave for the waiter? How much will the total bill be, including tax and tip? Show work to support your answers.

Solutions

Solution: An exact answer

To figure out the tip, you need to find 20% of $52.60.

0.2×52.6=10.52

You should leave $10.52 for the waiter if you want to leave him exactly 20%.

To figure the tax, you need to find 8% of $52.60.

0.08×52.6=4.208

Next, add them up:

52.6+10.52+4.208=67.328

The total bill, including tax and tip, will be $67.33.

Solution: Estimating an answer

If you are not concerned whether you give the waiter exactly 20%, you can simply estimate the total bill. Tax and tip together are a little less than 30% and the bill is a little more than $50. Since 30% of 50 is 15, the tax and tip together are approximately $15. (Note that the exact calculation is $14.73.)

We can also estimate the total bill as $52 + $15 = $67, which is very close to the exact calculation of $67.33. This kind of estimating is a good way to check the answer to an exact calculation, and more like the way you would probably compute tax and a tip in a real restaurant.

Solution: Exact tax, approximate tip

In a real-world context, restaurant patrons generally estimate the tip, but pay the exact tax based on the calculation of their bill. Therefore, a third solution possibility is for students to estimate the tip portion of the calculations and to find the exact tax when calculating the total bill.

If you wish to estimate the tip, you can round $52.60 to $50. Twenty percent of $50 is $10. So, you would leave a $10 tip.

To figure tax, you need to find 8% of $52.60:

0.08×52.6=4.208.

Next, add the estimated tip, the calculated tax, and the pre-tax bill:

52.60+10+4.208=66.808.

The total bill will be $66.81.

Step-by-step explanation:

Answer:

3y - x = 3

Step-by-step explanation:

The slope intercept form of the equation is expression is y = mx+c

m is the slope

c is the y inercept

From the graph

c = 1

Using the coordinates (-3, 0) and (0, 1)

m = 1-0/0-(-3)

m = 1/3

Get the required equation

y = 1/3x + 1

Multiply through by 3

3y = x + 3

3y - x = 3

Hence the required equation is 3y - x = 3

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem the we have to convert the units with the given information.

1mm is equal to 1000 μm

5μm * (1 mm/1000μm) = (5*1) / 1000 = 5/1000 = 0.005 mm = 5x10^-3 mm

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

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Answer: A

Given that:

And the formula for finding the area of a triangle is

We can rewrite this as

*Solve for BC

Now, given that BC = CD,

Given that BC and CD are equal, this would mean that:

To find the Area of ACD, we will subtract the Area of ABC from the Area of ABD

We can rewrite this as:

Evaluate

Therefore, the Area of ACD is 6.

Alex can make a total of 180 different sandwiches by choosing one kind of meat from 10 options and two kinds of cheese from 9 options.

To determine the number of different sandwiches Alex can make, we need to consider the combinations of meat and cheese. Since Alex can choose one kind of meat from 10 options, there are 10 choices for the meat component of the sandwich. For the cheese component, Alex can choose two kinds of cheese from 9 options.

To calculate the total number of combinations, we can use the formula for combinations without repetition. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices. In this case, n is 9 (number of cheese options) and r is 2 (number of cheese choices). Thus, the number of combinations of two kinds of cheese is \(9C2\)= 9! / (2!(9-2)!) = 36.

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Converting 46.1031 to 4 significant figures, we have 46.10.

Rounding off numbers implies reducing the number of digits in a given number to a preferred length. The two modes are significant figures, or decimal places.

Decimal places requires reducing the numbers of digits in a given number to a required number but considering the position of the decimal point. In significant figures, the length of the given number is reduced to a required number by not considering the position of the decimal.

In the given question, we are to convert 46.1031 to 4 significant figures.

This can be done by counting four digits, and rounding off the digits after.

So that we have;

46.1031 = 46.10 (4 sf)

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The conversation of 46.1031 to 4 significant figures would be = 46.10

A four significant figures are those figures that shows that all zeros to the right of the last significant zero after the decimal point.

From the given figure such as 46.1031, to convert to four significant figures, 46.10

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The expression 0.8p+1 and 1 + 0.8p are equivalent to (0.5p + 7) + (0.3p-6).

We can simplify the given expression by combining like terms:

(0.5p + 7) + (0.3p-6) = 0.5p + 0.3p + 7 - 6

= 0.8p + 1

Therefore, 0.8p + 1 is equivalent to (0.5p + 7) + (0.3p-6).

Similarly, we can simplify the given expression in another way:

(0.5p + 7) + (0.3p-6) = 0.5p + 0.3p + 7 - 6

= 0.8p + 1

The other options (1 + 0.8p, 7.5p-5.7) are not equivalent to the given expression.

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The missing figures in the diagrams are:      88km                    616km²,   37.7km                      113.14km respectively

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

                Radis          diameter            circumference            area

S/N           r                        2r                         2πr                           πr²

Applying the above formulae in each of the questions we have as follows:

1             3                  2*3=6             2*3.14*3=18.84        3.14*3*3=28.26       2        3.5                   7                 2*3.14*3.5=21.98    3.14*3.5*3.5=38.47      

3       7.5                 15               2*3.14*7.5=47.1ft      3.14*7.5*7.5=176.25

4       14km           28km         2*3.14*14=87.92km    3.14*14*14=615.44km²

5        5mi           10mi        2*3.14*5=31.4mi               3.14*5*5= 78.5mi²

6       2.5cm         5cm         2*3.14*2.5=15.7cm          3.14*2.5*2.5=19.63cm²

7      

14                     14*2 28             2*22/7*14                    22/7*14*14  

                                                     88km                    616km²

6                             12                2*22/7*6                     22/7*6*6

                                                    37.7km                      113.14km

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Answer:

see explanation

Step-by-step explanation:

To determine if (3, 1 ) is a solution to the system

Substitute x = 3 into both equations and evaluate. If the result is y = 1 for both then the point is a solution.

y = \(\frac{4}{3}\) × 3 - 3 = 4 - 3 = 1

y = - 2(3) + 7 = - 6 + 7 = 1

Since both equations equal 1 then

(3, 1 ) is a solution to the system

a) Rocky Mountain should order 200 tires each time it places an order.

b) The total cost of this policy is $17,160.

a) To determine how many tires Rocky Mountain should order each time, we need to consider the different price levels and find the point where it is most cost-effective to order. Let's analyze the three price levels:

If fewer than 200 tires are ordered: The purchase price is $25 per tire.

If 200 or more, but fewer than 8,000 tires are ordered: The purchase price is $17 per tire.

If 8,000 or more tires are ordered: The purchase price is $13 per tire.

Since the ordering cost is $35 per order, it is most cost-effective to order the maximum quantity that falls within the second price level, which is 200 tires.

b) To calculate the total cost of this policy, we need to consider the ordering cost and the holding cost. The holding cost is 40% of the purchase price per tire per year. Let's calculate the total cost:

Total holding cost = (Purchase price per tire * Quantity ordered * Holding cost rate) / 2 = (($17 * 10,000 * 0.4) / 2) + (($13 * 2,000 * 0.4) / 2) = $34,000 + $5,200 = $39,200

Total cost = Total ordering cost + Total holding cost = (Ordering cost per order * Number of orders) + Total holding cost = ($35 * (10,000 / 200)) + $39,200 = $1,750 + $39,200 = $40,950

Therefore, the total cost of this policy is $40,950.

Rocky Mountain Tire Center should order 200 tires each time it places an order, resulting in a total cost of $40,950 for this policy. This ordering quantity and cost analysis allows Rocky Mountain to make efficient and cost-effective decisions in managing their inventory.

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Answer:

Option 1 and 2

The requirements to be a HL are:

Both triangles must right triangles (one angle of 90)

The congruent sides must be correspond

One of the congruent sides must be the hypotenuse (long side)

From the following options, the options 1 and 2 are the examples of HL shortcut.

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.

As per the given information in the question,

The conditions to be an HL(Hypotenuse Leg) are:

1. Triangles must be right-angled in both cases (one 90 angle in both cases.)

2. The congruent sides need to be matched.

3. The hypotenuse is required to be among the congruent sides (long side)

As we can see that option 1 and 2 are fulfilling the requirement for HL.

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Given: The dimension of a trapezoid as shown below

To Determine: The area of the given trapezoid

Solution

The formula for finding the area of a trapezoid is

Substitute the given into the formula

Hence, the area of the trapezoid is 30m²