3 pens cost $2.70.

What is the cost per pen?


Rectangle divided into 3 units. First unit blank with a note underneath: cost per pen. Second unit has entry: $2.70. Third unit is blank.

$_____per pen

The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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Since no equation of the line, or graph is provided in the question statement, considering the line to be [3x +4y = 12], the y-intercept of the line is 3.

[3x +4y = 12] and then, determine it's y-intercept.

To solve this question, we can use two methods:

The standard equation of line is (y = mx + c), where, "m" is the slope of the line, and "c" is the y-intercept. Converting [3x +4y = 12] to the form of the standard equation, we get,

3x+4y=12\\or,4y=-3x+12\\or,y=\frac{-3x+12}{4}\\ or,[y=(\frac{-3}{4})x+3]...(i)

Now comparing (i) to the standard equation of line, we can identify that

(c = 3), i.e., y-intercept of the line [3x +4y = 12] is 3.

Another way we can determine the y-intercept of a line is by, substituting (x = 0) and then solving the equation for "y".

Y-Intercept: The y-intercept is the point on a cartesian plane, where a graph crosses the y-axis, i.e., the value of y when (x = 0).

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So the different number has a 4 with a value of 40.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first identify the place value of the digit 4 in the given number.

The digit 4 is in the hundreds place in the number 431.67, so its value is 4 x 100 = 400.

According to the problem statement, the 4 in the different number represents a value which is one-tenth of the value of the 4 in 431.67. Therefore, the value of the 4 in the different number is:

400/10 = 40

To determine the value of the different number, we need to look at the other digits in the number. Since we don't have any information about the other digits, we cannot determine the value of the different number. The answer is that the value of the different number cannot be determined with the information given.

Therefore, So the different number has a 4 with a value of 40.

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Answer:

C

Step-by-step explanation:

functions can only have domains that are different numbers, (first number) the rest repeat the domain and that makes it not a function

Answer:

C

Step-by-step explanation:

A set of pairs is a function if and only if there is only one y-value for each x-coordinate. In other words, the x-coordinate cannot repeat. If it does, then it must equal the same thing.

Let's go through each of the choices.

For A, -5 repeats twice. It simultaneously equals both 4 and -2. This cannot be true if this is a function, so A is not correct.

For B, 2 repeats twice. It equals both 6 and -6. So, this is also not a function.

For C, no digits are repeating. Thus, this is a function.

To make sure, in D ,-3 is repeating. It is both -4 and 8, so this is not a function.

So, our answer is C.

And we're done!

Answer:

5

Step-by-step explanation:

the quadrtic formula says the x=y=z but it also argues

Answer:

4: [52, 58]

5:  16 ≤ y ≤ 50   where y is in km

Step-by-step explanation:

Answer:

0.308

Step-by-step explanation:

Given the data:

1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 6

We need to obtain the sample mean and sample standard deviation :

Sample mean, xbar = Σx/n

Where n = sample size (1+1+2+2+2+3+3+3+3+4+4+6) / 12 = 2.833

Sample standard deviation, s

Using the formula :

s = √Σ((x - xbar)² / n-1)

s = 1.40

Hypothesis :

H0 : μ = 2.4

H1 : μ ≠ 2.4

The test statistic :

(xbar - μ) ÷ (s/√(n))

(2.833 - 2.40) / (1.40/sqrt(12))

Test statistic = 1.0713

Using the Pvalue from Test score calculator :

df = n - 1 = 12 - 1 = 11 ; two tailed

Pvalue(1.071, 11)

= 0.3069

= 0.307

Answer:

Explanation: When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6). Putting these together means you have a total of 2×6=12 outcomes.

Answer:

OMGGG I NEED THIS QUESTIONNN TOOOOOOWANNA WORK ON IT

Answer:

225sqft with 1in -> 5ft  = 9sqin

147sqft with 1in -> 7ft = 3sqin

256sqft with 1in ->8ft = 4sqin

128sqft with 1in -> 4ft = 8sqin

Step-by-step explanation:

To change from feet to inches, you just divide by the scaling factor (5, 7, 8, or 4) in this problem.  But because it is square feet to square inches, you must divide by the square of the scaling factor:

5*5 = 25

7*7 = 49

8*8 = 64

4*4 = 16

So:

225/25=9

147/49 = 3

256/64 = 4

128/16 = 8

Answer:

Answer is explained in the photo

Answer:

y=6x

Step-by-step explanation:

direct variation equation is like y=kx (k: constant)

substitute (5,30) to solve k,

30=5k

k=6

Answer:y=6x

Step-by-step explanation:

The lifetime in hours of an electronic tube will be of 2 hours.

A probability density function, also known as the density of a continuous random variable, is a function used in probability theory whose value at any given sample (or point) in the sample space can be interpreted as giving a relative likelihood that the random variable's value would be close to that sample. While the absolute likelihood of a continuous random variable taking on any given value is 0, probability density (PDF) at two different samples can be used to infer, in any given draw of the random variable, how much more likely it would be that the random variable would be close to one sample compared to the other sample.

We have,

f(x) = xe^(-x)             x>0

= 0                     o.w.

Consider,

\(E(X) = \int\limits^a_0 {xf} (x)\, dx \\\\E(X) = \int\limits^a_0 {xxe}^{-x} \, dx \\\\E(X) = \int\limits^a_0 {x}^{2}e^{-x} \, dx \\\\E(X) = \int\limits^a_0 {x}^{b-1}e^{-mx} \, dx = \frac{n}{m^{n} } \\\\= 2! = 2\)

Therefore, a tube of this type should last for 2 hours.

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Cara's first error was not 7 - 13, leading to an incorrect result of -32.

Cara's first error was that she did not evaluate (Negative 4) squared.

The expression in question is not provided, so let's assume it is "6 - 2 × (-4)² + 7 - 13".

According to the order of operations (PEMDAS/BODMAS), we evaluate operations inside parentheses first, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

To evaluate the expression correctly, we follow the order of operations:

Evaluate the exponent (-4)².

Since (-4) squared is positive, (-4)² = 16.

Multiply 2 and 16.

2 × 16 = 32.

Evaluate the addition and subtraction from left to right.

6 - 32 + 7 - 13.

At this point, we see that Cara did not evaluate 7 - 13.

Therefore, her first error was not evaluating the subtraction correctly.

Continuing the evaluation:

6 - 32 + 7 - 13 = -32.

So, Cara's first error was not evaluating 7 - 13, leading to an incorrect result of -32.

It's important to carefully follow the order of operations to ensure accurate evaluations of mathematical expressions.

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answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Cost of the ad is $167.5

What is cost?

A cost is the worth of money that has been used up to create something or supply a service and is thus no longer accessible for use in production, research, retail, or accounting. In business, the cost might be one of acquisition, in which case the money spent to obtain it is recognized as cost. In this situation, money is the input that is used to purchase the item. This acquisition cost might be the total of the original producer's production expenses and the acquirer's additional transaction costs over and above the amount paid to the producer. Typically, the price includes a profit margin above the cost of manufacture.

The cost of the ad per column inch = $67

So, the cost of 2¹/₂ inch = 67 x 2¹/₂ = $167.5

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The inverse of the equation is determined as \(y = \log_{6}(-3x)\).

option D is the correct answer.

The inverse of the equation is calculated by applying the following method;

The given equation;

y = - 6ˣ/3

The inverse of the equation is calculated as;

multiply through by 3

\(-3x = 6^y\)

Take the logarithm of both sides of the equation with base -6:

\(\log_{6}(-3x) = y\)

Finally, replace y with x to obtain the inverse equation as follows;

\(y = \log_{6}(-3x)\)

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Answer: the width is 24/35 square mile

The measure of <MNL is (71 - 3x²)/2.

We have,

Far Arc = 59 - 2x²

Near Arc = 12 - x²

Angle = 180- 2x²

Using the Formula

Angle= Average of vertical chords

180 - 2x² = (59 - 2x² + 12 - x²)/2

360 - 4x² = 71 - 3x²

289 = x²

x= 17

So, the measure of <MNL

= (71 - 3x²)/2

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Answer:

7 hours

Step-by-step explanation:

here,

270/18=105/x

x=(105*18)/270

x=7

Chau made $270 for 18 hours of work. At the same rate,  Therefore Chau would have to work 7 hours at the same rate to make $105.

To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:

Let x be the number of hours Chau needs to work to make $105.

We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:

Rate = Total earnings / Number of hours

Rate = $270 / 18 hours

Rate = $15 per hour

Now, we can set up the proportion:

$15 per hour = $105 / x hours

To find x, we can cross-multiply:

$15 × x = $105

Now, solve for x:

x = $105 / $15

x = 7 hours

So, Chau would have to work 7 hours at the same rate to make $105.

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Answer:60.97

Step-by-step explanation: tan 49 = opposite/adjacent = x/53

tan 49 = x/53

tan 49/1 = x/53

53 tan 49 = x

x = 60.969

x = 60.97

The height of tree is 60.97 feet tall on the ground is 53 feet from the tree.

Trigonometry uses the first six fundamental trigonometric functions. Trigonometric proportions are these functions. The six fundamental trigonometric functions are the sin function, cosine function, secant function, and so on.

As per the data given in the question,

tan 49° = opposite/adjacent

tan 49° = x/53

tan 49/1 = x/53

x = 53 tan 49°

x = 60.969 or,

x = 60.97 feet. (rounding off value)

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Answer:

The coordinates of point B are : (-1, 1)

Step-by-step explanation:

\(\frac{-7+x^{2} }{2} = -4\\\frac{1+y^{2} }{2} =1\) You multiply -4 by 2 which gives you -8 then you multiply 1 by 2 which gives 2.

Then you create the equations \(-7 + x^{2} = -8\\1 + y^{2} = 2\) you substitute -7 for +7 and add 7 to -8 which gives -1 (\(x^{2}\)) and subtract 1 from 2 which gives you 1 (\(y^{2}\))

To check your answer use the midpoint formula \(\frac{-7+-1}{2} =\frac{-8}{2} =-4\\\frac{1+1}{2} =\frac{2}{2} =1\) which gives you your midpoint (-4,1)

The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Answer: 300a^3cb

Step-by-step explanation:

\($$Simplify the following:$$15 \times 4 \times 5 a^{2} c a b$$$$\begin{aligned}&15 a^{2} \times 4 c \times 5 a b=15 a^{2+1} \times 4 c \times 5 b: \\ \\&15 \times 4 \times 5 a^{2+1} c b\end{aligned}$$$$\begin{aligned}&2+1=3 \\ \\&15 \times 4 \times 5 a^{3} c b \end{aligned}$$$$\begin{aligned}&15 \times 4=60 \\ \\&60 \times 5 a^{3} c b\end{aligned}$$$$60 \times 5=300$$Answer:$$300 a^{3} c b$$\)

The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

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Step 1:

To find the derivative of the function, apply the chain rule.

Step 2:

Step 3:

Final answer

You would need an additional $3.88 to buy the skateboard.

We need to calculate the total cost, including sales tax.

The sales tax rate is 6%, so the tax on a skateboard costing $98 would be as follows:

tax = 0.06 x $98 = $5.88

Consequently, the skateboard would have a total cost of:

total cost = $98 + $5.88 = $103.88

Since you have $100 to spend, you do not have enough money to buy the skateboard. You would need:

additional money = $103.88 - $100 = $3.88

Therefore, you would need an additional $3.88 to buy the skateboard.

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The nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.

The percentage decrease theory suggests that a decrease in the price of a product or service will lead to an increase in demand for that product or service.

This theory is based on the idea that consumers are more likely to buy a product or service if its price is lower. This theory can be applied to both new and existing products or services.

For example, a retailer may decide to decrease the price of a product in order to attract more customers and increase sales. Similarly, a company may choose to reduce the cost of a service in order to make it more attractive to potential customers.

This question is using the percentage decrease theory. According to this theory,

you can calculate the percentage decrease by subtracting the current value from the original value and then dividing by the original value.

Step 1: Subtract the current number of wild tigers (3200) from the original number of wild tigers (20 years ago).

Original - Current = Change

120,000 - 3200 = 116,800

Step 2: Divide the change (116,800) by the original number of wild tigers (120,000)

Change / Original = Percentage Change

116,800 / 120,000 = 97%

Step 3: Multiply the percentage change (97%) by the original number of wild tigers (120,000)

Percentage Change x Original = Estimated Original

97% x 120,000 = 116,400

Therefore, to the nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.

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