Quotients are used to represent the division of numbers
The number is -0.52
Let the number be represented with x.
So, the quotient of a number (x) and 0.2 is -2.6 is represented as:
[tex]\frac x{0.2} = -2.6[/tex]
Multiply both sides of the equation by 0.2
[tex]0.2 * \frac x{0.2} = -2.6 * 0.2[/tex]
Evaluate the quotient, on the left hand side
x = -2.6 * 0.2
Evaluate the product on the right hand side
x = -0.52
Hence, the number is -0.52
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Use cylindrical coordinates. find the volume of the solid that lies within both the cylinder x2 + y2 = 25 and the sphere x2 + y2 + z2 = 64.
The volume of the solid that lies within both the cylinder and the sphere is [tex]\( \pi \cdot 39^{3/2} \)[/tex].
To find the volume of the solid that lies within both the cylinder
[tex]\(x^2 + y^2 = 25\)[/tex] and the sphere [tex]\(x^2 + y^2 + z^2 = 64\)[/tex], we'll use cylindrical coordinates. The equations in cylindrical coordinates are
[tex]\(x = r\cos(\theta)\), \(y = r\sin(\theta)\), and \(z = z\)[/tex].
First, let's find the limits of integration for (r), [tex]\(\theta\)[/tex], and (z):
Limits for (r): The cylinder has a radius of 5 (r = 5), so [tex]\(0 \leq r \leq 5\)[/tex].
Limits for [tex]\(\theta\)[/tex]: Since the solid lies within the entire cylinder, [tex]\(0 \leq \theta \leq 2\pi\).[/tex]
Limits for (z): The sphere has a radius of [tex]\(\sqrt{64} = 8\)[/tex], so [tex]\(0 \leq z \leq \sqrt{64 - r^2}\)[/tex].
Now, the volume element (dV) in cylindrical coordinates is [tex]\(r \, dr \, d\theta \, dz\)[/tex].
So, the volume (V) is given by:
[tex]\[ V = \int_0^{2\pi} \int_0^5 \int_0^{\sqrt{64-r^2}} r \, dz \, dr \, d\theta \][/tex]
Let's calculate this:
[tex]\[ V = \int_0^{2\pi} \int_0^5 \left[ z \right]_0^{\sqrt{64-r^2}} \, dr \, d\theta \][/tex]
[tex]\[ V = \int_0^{2\pi} \int_0^5 \sqrt{64-r^2} \, dr \, d\theta \][/tex]
[tex]\[ V = \int_0^{2\pi} \left[ \frac{1}{2} (64-r^2)^{3/2} \right]_0^5 \, d\theta \][/tex]
[tex]\[ V = \int_0^{2\pi} \frac{1}{2} (64-25)^{3/2} \, d\theta \][/tex]
[tex]\[ V = \int_0^{2\pi} \frac{1}{2} (39)^{3/2} \, d\theta \][/tex]
[tex]\[ V = \frac{39^{3/2}}{2} \int_0^{2\pi} d\theta \][/tex]
[tex]\[ V = \frac{39^{3/2}}{2} \cdot 2\pi \][/tex]
[tex]\[ V = \pi \cdot 39^{3/2} \][/tex]
So, the volume of the solid that lies within both the cylinder and the sphere is [tex]\( \pi \cdot 39^{3/2} \)[/tex].
The volume of the solid that lies within both the cylinder [tex]\(x^2 + y^2 = 25\)[/tex] and the sphere[tex]\(x^2 + y^2 + z^2 = 64\) is \( \frac{40\pi}{3} \).[/tex]
To find the volume of the solid that lies within both the cylinder [tex]\(x^2 + y^2 = 25\)[/tex] and the sphere [tex]\(x^2 + y^2 + z^2 = 64\)[/tex], we can use cylindrical coordinates.
In cylindrical coordinates, the equations of the cylinder and the sphere become:
Cylinder: [tex]\(r^2 = 25\)[/tex]
Sphere: [tex]\(r^2 + z^2 = 64\)[/tex]
The limits of integration for r will be from 0 to 5 (since [tex]\(r^2 = 25\)[/tex] gives r = 5 in cylindrical coordinates). The limits of integration for z will be from [tex]\(-\sqrt{64 - r^2}\) to \(\sqrt{64 - r^2}\).[/tex]
The volume element dV in cylindrical coordinates is [tex]\(r \, dr \, dz \, d\theta\).[/tex]
So, the volume V of the solid is given by the triple integral:
[tex]\[V = \iiint dV = \int_{0}^{2\pi} \int_{0}^{5} \int_{-\sqrt{64 - r^2}}^{\sqrt{64 - r^2}} r \, dz \, dr \, d\theta\][/tex]
Let's evaluate this triple integral:
[tex]\[V = \int_{0}^{2\pi} \int_{0}^{5} \left[ r\sqrt{64 - r^2} - (-r\sqrt{64 - r^2}) \right] \, dr \, d\theta\]\[V = 2\pi \int_{0}^{5} 2r\sqrt{64 - r^2} \, dr\][/tex]
Now, we can use a substitution to solve this integral. Let [tex]\(u = 64 - r^2\),[/tex]then [tex]\(du = -2r \, dr\):[/tex]
[tex]\[V = -4\pi \int_{64}^{39} \sqrt{u} \, du\]\[V = -4\pi \left[ \frac{2}{3}u^{3/2} \right]_{64}^{39}\]\[V = -\frac{8\pi}{3} \left[ 39^{3/2} - 64^{3/2} \right]\]\[V = -\frac{8\pi}{3} \left[ 59 - 64 \right]\]\[V = \frac{40\pi}{3}\][/tex]
Thus, the volume of the solid that lies within both the cylinder [tex]\(x^2 + y^2 = 25\)[/tex] and the sphere[tex]\(x^2 + y^2 + z^2 = 64\) is \( \frac{40\pi}{3} \).[/tex]
WILL GIVE BRAINEST
Identify one characteristic of exponential growth.
Answer: Option 'd' is correct.
Step-by-step explanation:
Since we have given the exponential growth.
Properties of exponential growth are as follows:
1) The graph should pass through (0,1).
2) Domain of exponential growth function is the set of real numbers.
3) Range of exponential growth is greater than 0.
4) The graph is always increasing for the case of exponential growth.
Hence, Option 'd' is correct.
The difference between the number of customers in line at the express checkout and the number in line at the superexpress checkout is x1 − x2. calculate the expected difference.
(d) estimate p(x < 1.5), i.e., the proportion of all thickness values less than 1.5. [hint: if you knew the values of μ and σ, you could calculate this probability. these values are not available, but they can be estimated.] (round your answer to four decimal places.)
To estimate p(x < 1.5), we can use the concept of probability. Given the information provided, we can assume a uniform distribution between 1.5 and 4. The shaded area in Figure 5.20 represents the shortest 30 percent of repair times. Therefore, we can estimate that p(x < 1.5) is approximately 0.30.
Explanation:To estimate p(x < 1.5), we can use the concept of probability. Given the information provided, we can assume a uniform distribution between 1.5 and 4. The shaded area in Figure 5.20 represents the shortest 30 percent of repair times. Since we want to estimate the proportion of values less than 1.5, we can estimate it as the shaded area to the left of 1.5. This shaded area is equivalent to the shortest 30 percent of repair times, which is 0.30. Therefore, we can estimate that p(x < 1.5) is approximately 0.30.
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The actual probability is 0.159
To estimate the probability P(X < 1.5) without knowing the exact values of the mean (μ) and standard deviation (σ), we can use the empirical rule (also known as the 68-95-99.7 rule). This rule states that for a normally distributed variable:
Approximately 68% of the data falls within 1 standard deviation (σ) of the mean (μ).
Approximately 95% of the data falls within 2 standard deviations (2σ) of the mean.
Approximately 99.7% of the data falls within 3 standard deviations (3σ) of the mean.
Since the exact values of μ and σ are not available, we can estimate them using the sample mean (X) and sample standard deviation (s) of the data.
In this case, let's assume we have a sample of thickness values {x1, x2, ..., xn}. The sample mean (X) is the average of all the sample values:
X = (∑xi) / n
The sample standard deviation (s) is the square root of the variance (s^2), which is the average of the squared deviations from the mean:
s^2 = ∑(xi - X)^2 / n
Once you have the estimated values of μ (approximately equal to X) and σ (approximately equal to s), you can use the empirical rule to estimate P(X < 1.5).
For example, if you estimate that μ = 2 and σ = 0.5, then:
P(X < 1.5) = P(X < μ - σ) ≈ P(X < 2 - 0.5) ≈ P(X < 1.5) ≈ 0.159
Remember that this is just an estimate, and the actual probability may be slightly different.
(08.01)Maggie wants to know how many students in her school enjoy watching sports on TV. She asks all 25 students in her math class and finds that 60% of her classmates enjoy watching sports on TV. She claims that 60% of the school's student population would be expected to enjoy watching sports on TV. Is Maggie making a valid inference about her population? Yes, it is a valid inference because she asked all 25 students in her math class Yes, it is a valid inference because her classmates make up a random sample of the students in the school No, it is not a valid inference because her classmates do not make up a random sample of the students in the school No, it is not a valid inference because she asked all 25 students in her math class instead of taking a sample from her geography class
Answer:
c would be the right answer
Step-by-step explanation:
A company makes three types of candy and packages them in three assortments. Assortment I contains 4 cherry , 4 lemon , and 12 lime candies, and sells for a profit of $4.00 . Assortment II contains 12 cherry , 4 lemon , and 4 lime candies, and sells for a profit of $3.00 . Assortment III contains 8 cherry , 8 lemon , and 8 lime candies, and sells for a profit of $ 5.00 . They can make 4 comma 800 cherry , 3 comma 800 lemon , and 5 comma 600 lime candies weekly. How many boxes of each type should the company produce each week in order to maximize its profit (assuming that all boxes produced can be sold)? What is the
Final answer:
The company should produce 1,200 boxes of Assortment I per week to maximize its profit.
Explanation:
In order to maximize profit, the company should produce the assortment that yields the highest profit per candy sold. Let's calculate the profit per candy for each assortment:
Assortment I: Profit per cherry candy = $4.00/4 = $1.00Assortment II: Profit per cherry candy = $3.00/12 = $0.25Assortment III: Profit per cherry candy = $5.00/8 = $0.625From the calculations above, we can see that Assortment I has the highest profit per cherry candy. Therefore, the company should produce as many boxes of Assortment I as possible, given the available resources. To determine the number of boxes to produce, we need to calculate the maximum number of cherry candies that can be produced with the available resources:
Cherry candies produced: 4,800Lemon candies produced: 3,800Lime candies produced: 5,600Assortment I contains 4 cherry candies per box, so the maximum number of boxes of Assortment I that can be produced is 4,800/4 = 1,200 boxes. The company should produce 1,200 boxes of Assortment I per week to maximize its profit.
A rectangular field is 0.4 kilometers long and 0.3 kilometers wide. What is the area of the field in square meters?
The area of the rectangular field is 120,000 square meters.
How do we find the area of the rectangular field?We shall multiply the length by its width, to find the area of the rectangular field.
We can calculate like this:
Area = Length x Width
Area = 0.4 kilometers x 0.3 kilometers
Next, we convert the measurements to square meters, recalling that 1 kilometer = 1000 meters:
Area = (0.4 km * 1000 m/km) x (0.3 km * 1000 m/km)
Area = (400 m) x (300 m)
Then, multiplying the values, we have:
Area = 120,000 square meters
Hence, the area of the rectangular field is 120,000 square meters.
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What is the product of −2 1/4 and -4 1/2?
Enter your answer as a mixed number, in simplified form, in the box.
you add -2 1/4 + -4 1/2 = -6 3/4
so, your answer is -6 3/4
Answer:
10 1/4
Step-by-step explanation:
You want to install a 2 yd wide walk around a circular swimming pool. the diameter of the pool is 17 yd. what is the area of the walk? use 3.14 for π.
To find the area of the walk around a circular swimming pool with a given diameter and width, calculate the radius, add the walk width to it, and then compute the area of the walk using the area of a circle formula.
The area of the walk around the pool is:
Find the radius of the pool by dividing the diameter by 2. Radius = 17 yd / 2 = 8.5 yd.
Find the radius of the walk by adding 2 yards to the pool's radius. Walk's radius = 8.5 yd + 2 yd = 10.5 yd.
Calculate the area of the walk using the formula for the area of a circle: A = πr². Area = 3.14 x (10.5)² = 346.185 square yards.
The table shows the cost of a ski rental package for a given number of people. People Cost ($) 4 160 5 200 6 240 7 280 The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.
Number 13. Pls explain and give the answer
The highest point in colorado is mount elbert, at 14,433 feet.About how many miles is that
Which best describes the relationship between the successive terms in the sequence shown? 9, –1, –11, –21, … The common difference is –10. The common difference is 10. The common ratio is –9. The common ratio is 9.
Write -63.55 as a mixed number in simplest form.
5/6 ( 3/8 - x ) = 16
The value of x on solving the equation 5/6 (3/8 - x) = 16 is - 251 / 5.
What is the equation?In other terms, it is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.
Given:
5/6 (3/8 - x) = 16
Solve the above equation as shown below,
Use the distributive property to solve the equation,
5 / 6 × 3 / 8 - 5 / 6 x = 16
15 / 48 - 5 / 6 x = 16
5 / 16 - 5 / 6 x = 16
5 / 6 x = 5 / 16 - 16
5 / 6x = -251 / 16
x = -251 / 16 × 6 / 5
x = - 251 / 5
Thus, the value of x is - 251 / 5.
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Sarah bought a shirt on sale for $35 the original price of the shirt was 3 times that amount sarah also bought a pair of shoes on sale for $28 the original price of the shoes was 5 times that amount together how much money did the shirt and shoes cost before they went on sale
Write 1.12 repeating as a mixed number
A repeating mixed number is a mixed fraction, which after converted to decimal; the numbers after the decimal point repeat without end.
1.12 as a repeating mixed number is [tex]1\frac{13}{99}[/tex]
Given that
[tex]Number = 1.12[/tex]
First, we represent as a fraction
[tex]Number = \frac{112}{100}[/tex]
To represent the number as a repeating mixed number, we simply subtract 1 from the numerator
[tex]Number = \frac{112}{100 - 1}[/tex]
[tex]Number = \frac{112}{99}[/tex]
Represent as a mixed number
[tex]Number = 1\frac{13}{99}[/tex]
Hence, 1.12 as a repeating mixed number is [tex]1\frac{13}{99}[/tex]
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adam buy 9 gift card and gives 6 away.how many does he have left?
Peter can buy 5 juice bottles for $10 or 6 juice bottles for $12. How much do you think he would pay for 7 juice bottles? Why?
The number of applications for patents, n, grew dramatically in recent years, with growth averaging about 3.43.4% per year. that is, upper n prime left parenthesis t right parenthesisn′(t)equals=0.0340.034upper n left parenthesis t right parenthesisn(t). a) find the function that satisfies this equation. assume that tequals=0 corresponds to 19801980, when approximately 110 comma 000110,000 patent applications were received. b) estimate the number of patent applications in 20152015. c) estimate the doubling time for upper n left parenthesis t right parenthesisn(t).
Final answer:
The function [tex]N(t) = 110,000(1.034)^t[/tex] models patent applications yearly after 1980; in 2015 (t = 35), it predicts 354,496 applications. Doubling time, found when N(t) doubles from the initial value, is approximately 21 years
Explanation:
The given function [tex]N(t) = 110,000(1.034)^t[/tex] models the number of patent applications received at any year t after 1980, where t represents the number of years. In 2015, t = 35, so [tex]N(35) = 110,000(1.034)^35 = 354,496[/tex]. To find the doubling time, we set N(t) equal to twice the initial value: 2(110,000) = 220,000. Solving [tex]220,000 = 110,000(1.034)^t[/tex] yields [tex](1.034)^t = 2,[/tex]then log(1.034)t = log(2). Hence, t = log(2) / log(1.034) ≈ 20.73. Thus, the doubling time for N(t) is approximately 21 years.
The price of a new apple ipod has increased by 1/4. if the original price of the apple was $200, what is the price today? $150 $250 $200 $175 none of these
Answer: The price today = $250
Step-by-step explanation:
Given : The original price of apple was $200.
The price of a new apple ipod has increased by 1/4.
Then , the new price =(Original price) +([tex]\dfrac{1}{4}[/tex]) x (Original price)
= (Original price) ( [tex]1+\dfrac{1}{4}[/tex] )
[tex](\$200)(\dfrac{5}{4})=\$250[/tex]
Hence, the price of ipod today = $250
Thomas Vega offers to pay $59 of the March cell phone bill. Each of the other 4 members of the family agrees to split the rest of the bill equally among themselves. How much does each of the 4 family members owe? Show your work.
a certain type of nuts are on sale at $0.35 per pound tamara buys 2 pound of nuts how much will the nuts cost
To the nearest hundredth of a yard, determine the circumference of the given circle. Approximate as 3.14. r=9
The circumference of a circle with a radius of 9 yards is calculated using the formula C = 2πr, with π approximated as 3.14. After substituting the values, the circumference is found to be 56.52 yards to the nearest hundredth.
Explanation:To calculate the circumference of a circle with a radius (r) of 9 yards, you'll use the formula for the circumference of a circle, which is C = 2πr. Given that π (pi) is approximately 3.14, as the question suggests, you'll substitute this value and the given radius into the formula.
Step-by-step calculation:
Substitute the given values into the circumference formula: C = 2 * 3.14 * 9.Multiply 2 by 3.14 to get 6.28.Multiply 6.28 by 9 to get the circumference.The circumference C is 6.28 * 9 = 56.52 yards.Therefore, the circumference of the circle to the nearest hundredth of a yard is 56.52 yards.
write the slope-intercept form of the equation of each line given the slope and y-intercept 1) slope=-3/2 y-intercept=-1 2) slope=3 y-intercept=4 3) slope=-3 y- intercept=2. 4) slope=-2/5 y- intercept= 2
The subway train shown is traveling at a speed of 30 mi/h when the brakes are fully applied on the wheels of cars b and c, causing them to slide on the track, but are not applied on the wheels of car
a. the coefficient of kinetic friction is 0.35 between the wheels and the track.
The question deals with a physics scenario involving a subway train applying brakes, kinetic friction, and requires calculating stopping distances and average acceleration using mechanical principles.
The question involves a subway train traveling at a certain speed and then applying brakes on specific cars, leading to a scenario involving kinetic friction. It asks for an analysis of the situation using physics concepts such as speed conversion, coefficient of kinetic friction, and acceleration. A comprehensive understanding of these topics would be necessary to calculate quantities like stopping distance and average acceleration.
The provided references suggest that the problems are focusing on converting speeds from miles per hour to meters per second, the effects of friction on motion, and using equations of motion to determine the stopping distance of a vehicle with locked wheels on a wet surface. These problems demonstrate applications of concepts in mechanics, specifically Newton's laws of motion, frictional forces, and energy conservation.
The subway train will travel approximately 26.2 meters before coming to a stop due to the brakes causing the wheels to slide on the track with a coefficient of kinetic friction of 0.35.
To solve this problem, we need to use principles of physics, specifically those related to friction and acceleration.
Convert the Speed: First, convert the speed from miles per hour (mi/h) to meters per second (m/s) for ease of calculation.
30 mi/h = 30 * 1609 / 3600 m/s ≈ 13.4 m/s.
Identify the Variables:
Initial speed (u): 13.4 m/s
Final speed (v): 0 m/s (since the train stops)
Coefficient of kinetic friction (μ): 0.35
Calculate the Frictional Force: The kinetic frictional force can be calculated using the formula:
Frictional force (f_k) = μ * N, where N (the normal force) equals the weight of the sliding cars. Assuming we only need to calculate the proportion without specific mass of cars, we can denote N as m * g (mass * gravity). Therefore, f_k = 0.35 * m * g.
Determine the Deceleration: Using Newton's second law, f_k = m * a (mass * acceleration), we can solve for acceleration (a):
0.35 * m * g = m * a,
a = 0.35 * g (since m cancels out), where g is the acceleration due to gravity (≈ 9.8 m/s²).
a = 0.35 * 9.8 m/s² ≈ 3.43 m/s².
Use the Kinematic Equation: To find the stopping distance, we use the kinematic equation: v² = u² + 2 * a * s (where s is the stopping distance):
0 = (13.4)² + 2 * (-3.43) * s
0 = 179.56 - 6.86 * s
s = 179.56 / 6.86
s ≈ 26.2 meters.
what is the unknown factor 9Xp=45
Write 29/12 as a decimal if necessary use a bar to indicate which digit of group of digits repeats
What is the length of the radius of a circle with a center at 2 – i and a point on the circle at 8 + 7i?
Answer:
10
Step-by-step explanation:
The radius is the magnitude of the complex number that is the difference between any point on the circle and the center point. A suitable calculator can tell you that magnitude:
║(8+7i) - (2-i)║ = √((8-2)² +(7-(-1))²) = √(36+64) = √100 = 10
Answer:
10
Step-by-step explanation:
Kyle is six years older than Melissa. Nine years ago he was twice Melissa's age. How old is Kyle now?
Final answer:
Kyle is currently 21 years old. This was determined by setting up equations based on the information given and solving for Melissa's age first, which allowed us to find Kyle's age.
Explanation:
We are given that Kyle is six years older than Melissa. Also, nine years ago, he was twice her age. Let's represent Melissa's current age as M and Kyle's current age as K.
From the first piece of information, we can formulate the following equation:
1) K = M + 6
From the second piece of information, we get:
2) K - 9 = 2 * (M - 9)
Now, we substitute the expression from equation 1 into equation 2:
(M + 6) - 9 = 2 * (M - 9)
M - 3 = 2M - 18
After simplifying the equation, we find Melissa's current age:
M = 15
Using equation 1, we then calculate Kyle's current age:
K = 15 + 6
K = 21
Hence, Kyle is currently 21 years old.