Answer:
To find the greatest possible value of x + y, we need to maximize the values of x and y such that they are still positive integers and satisfy the given equation 18x + 11y = 2020.
We can start by rearranging the equation to solve for y:
11y = 2020 - 18x
y = (2020 - 18x)/11
For y to be a positive integer, 2020 - 18x must be divisible by 11. We can test values of x starting from x = 1 and increasing by 1 until we find the largest possible value of x that satisfies this condition.
When x = 1, 2020 - 18x = 2002, which is divisible by 11. This gives us a value of y = 182/11, which is not a positive integer.
When x = 2, 2020 - 18x = 1984, which is divisible by 11. This gives us a value of y = 180/11, which is not a positive integer.
When x = 3, 2020 - 18x = 1966, which is divisible by 11. This gives us a value of y = 178/11, which is not a positive integer.
When x = 4, 2020 - 18x = 1948, which is divisible by 11. This gives us a value of y = 176/11, which is not a positive integer.
When x = 5, 2020 - 18x = 1930, which is divisible by 11. This gives us a value of y = 174/11, which is not a positive integer.
When x = 6, 2020 - 18x = 1912, which is divisible by 11. This gives us a value of y = 172/11, which is not a positive integer.
When x = 7, 2020 - 18x = 1894, which is divisible by 11. This gives us a value of y = 170/11, which is not a positive integer.
When x = 8, 2020 - 18x = 1876, which is divisible by 11. This gives us a value of y = 168/11, which is not a positive integer.
When x = 9, 2020 - 18x = 1858, which is divisible by 11. This gives us a value of y = 166/11, which is not a positive integer.
When x = 10, 2020 - 18x = 1840, which is divisible by 11. This gives us a value of y = 164/11, which is not a positive integer.
When x = 11, 2020 - 18x = 1822, which is divisible by 11. This gives us a value of y = 162/11, which is not a positive integer.
When x = 12, 2020 - 18x = 1804, which is divisible by 11. This gives us a value of y = 160/11, which is not a positive integer.
When x = 13, 2020 - 18x = 1786, which is divisible by 11. This gives us a value of y = 158/11, which is not a positive integer.
When x = 14, 2020 - 18x = 1768, which is divisible by 11. This gives us a value of y = 156/11, which is not a positive integer.
When x = 15, 2020 - 18x = 1750, which is divisible by 11. This gives us a value of y = 154/11, which is not a positive integer.
When x = 16, 2020 - 18x = 1732, which is divisible by 11. This gives us a value of y = 152/11, which is not a positive integer.
When x = 17, 2020 - 18x = 1714, which is divisible by 11. This gives us a value of y = 150/11, which is not a positive integer.
When x = 18, 2020 - 18x = 1696, which is divisible by 11. This gives us a value of y = 148/11, which is not a positive integer.
When x = 19, 2020 - 18x = 1678, which is divisible by 11. This gives us a value of y = 146/11, which is not a positive integer.
When x = 20, 2020 - 18x = 1660, which is divisible by 11. This gives us a value of y = 144
What is the slope of the line?
-2
-1
1
2
Answer: positive 2
Step-by-step explanation:
Which statement is true?
Please help
call a positive integer kinda-prime if it has a prime number of positive integer divisors. if there are $168$ prime numbers less than $1000$, how many kinda-prime positive integers are there less than $1000$?
There are 173 kinda-prime positive integer less than 1000.
To find the number of kinda-prime positive integer less than 1000, we'll follow these steps:
1. Understand the definition of a kinda-prime number: A positive integer is kinda-prime if it has a prime number of positive integer divisors.
2. Determine the number of prime numbers less than 1000: There are 168 prime numbers less than 1000, as given.
3. Determine the possible prime number of divisors: Since 168 is not too large, we only need to consider 2 and 3 as possible prime numbers of divisors for a kinda-prime number.
4. Analyze the cases:
Case 1: Kinda-prime numbers with 2 divisors (prime numbers)
All prime numbers have exactly 2 divisors (1 and itself). Thus, all 168 prime numbers less than 1000 are kinda-prime.
Case 2: Kinda-prime numbers with 3 divisors
Let N be a kinda-prime number with 3 divisors. Then, N = p^2 for some prime number p. To find the suitable prime numbers p, we need[tex]p^2 < 1000[/tex]. The prime numbers that meet this condition are 2, 3, 5, 7, and 11 (since 13^2 = 169 > 1000). Therefore, there are 5 additional kinda-prime numbers ([tex]2^2, 3^2, 5^2, 7^2, and 11^2[/tex]).
5. Add the total number of kinda-prime numbers from both cases: 168 + 5 = 173.
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[tex]$(\pi(1000)-1)+11=\boxed{177}$[/tex] "kind a-prime" positive integers less than $1000$.
Let [tex]$n$[/tex] be a positive integer with[tex]$k$[/tex] positive integer divisors.
If [tex]$k$[/tex] is prime, then.
[tex]$n$[/tex] is a "kind a-prime" integer.
[tex]$k$[/tex] must be of the form.
[tex]$k=p$[/tex] or [tex]$k=p^2$[/tex] for some prime [tex]$p$[/tex].
If [tex]$k=p$[/tex], then [tex]$n$[/tex] must be of the form.
[tex]$p^{p-1}$[/tex] for some prime [tex]$p$[/tex]. Since [tex]$p < 1000$[/tex], there are.
[tex]$\pi(1000)$[/tex]possible values of [tex]$p$[/tex].
[tex]$p=2$[/tex] gives [tex]$2^1$[/tex], which is not prime, so we have to subtract.
[tex]$1$[/tex] from [tex]$\pi(1000)$[/tex] to get the number of possible.
[tex]$p$[/tex].
[tex]$\pi(1000)-1$[/tex] values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.
If [tex]$k=p^2$[/tex], then [tex]$n$[/tex] must be of the form.
[tex]$p^{p^2-1}$[/tex] for some prime[tex]$p$[/tex].
There are.
[tex]$\pi(31)=11$[/tex] primes less than [tex]$31$[/tex], and each of them gives a different "kind a-prime" integer of this form.
Since [tex]$31^5 > 1000$[/tex], no primes larger than [tex]$31$[/tex]can be used to form a "kind a-prime" integer of this form.
[tex]$11$[/tex] possible values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.
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fuel efficiency of manual and automatic cars, part i. each year the us environmental protection agency (epa)releases fuel economy data on cars manufactured in that year. below are summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions. do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? assume that conditions for inference are satisfied.
Given the above prompt on hypothesis testing, we can state that specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.
What is the explanation for the above response?
To determine if there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage, we can conduct a two-sample t-test assuming unequal variances. The null hypothesis is that there is no difference in the average city mileage between the two types of transmissions, and the alternative hypothesis is that there is a difference.
The t-test statistic is calculated as follows:
t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Plugging in the values from the given statistics, we get:
t = (16.12 - 19.85) / sqrt((3.85^2/26) + (4.51^2/26))
t = -3.31
Using a significance level of 0.05 and 50 degrees of freedom (approximated by n1+n2-2), the critical t-value is ±2.01.
Since the calculated t-value (-3.31) is less than the critical t-value, we can reject the null hypothesis and conclude that there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage.
Specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
. imagine you had a research question in which you wanted to compare a sample mean to the mean of a population. under these circumstances you would either do a z-test or a one-sample t-test. what key piece of information would be missing if you needed to do a one-sample t-test?
Sample size and sample standard deviation are the key information needed for a single-sample t-test.
In the event that you need to compare the test cruel with the populace cruel, and you perform a single-sample t-test rather than a z-test, the vital piece of data that will be lost is the populace standard deviation.
Within the z-test, the populace standard deviation is known and the standard mistake of the cruel is calculated utilizing the populace standard deviation.
In a single-sample t-test, the populace standard deviation is obscure, and the standard mistake of the cruel is evaluated from the test standard deviation.
Therefore, sample size and sample standard deviation are the key information needed for a single-sample t-test.
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in an integer overflow attack, an attacker changes the value of a variable to something outside the range that the programmer had intended by using an integer overflow.T/F
True. An integer overflow attack occurs when an attacker manipulates a variable in a way that causes it to exceed its maximum value or minimum value, leading to unexpected and potentially harmful behavior.
This can happen if a programmer fails to properly check and validate the input values that are being used in their code, allowing an attacker to inject a value that triggers an overflow.
As a result, the variable may be assigned a value that is outside the intended range, leading to unpredictable behavior and potentially causing the program to crash or execute unintended code. It is important for programmers to take steps to prevent integer overflow attacks, such as validating input values and using data types with sufficient capacity to hold the expected range of values.
This occurs when an arithmetic operation results in a value that is too large to be stored in the allocated memory, causing the value to wrap around and become smaller, or even negative. This can lead to unintended consequences in a program's behavior, which an attacker can exploit to gain unauthorized access or cause other security issues.
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brainliest+100 points
2x + 2y = 4xy is wrong
2x + 2y = 2(x+y) is correct
b.3x+4= 7x wrong
c4x²+5x = 9x² wrong
23x²+3x²+4x = 6x² + 4x = 2x(3x + 2)
3sorry I don't understand this one.....
4-4(3x-5) = -12x + 20
5 120 12 10 4 3 5 26Answer:
120
12 10
4 2 5 2
2 2
Lucia has three separate pieces of ribbon. Each piece is 5 yards long. She needs to cut pieces that are 27 inches long to decorate folklorico dance dresses. What is the greatest number of 27-inch pieces that she can cut from three pieces of ribbon?
A 20
B 18
C 7
D 6
The greatest number of 27-inch pieces that she can cut from three pieces of ribbon is found to be 19. So, option B is the correct answer choice.
Each yard is equal to 36 inches, so 5 yards are equal to 180 inches. Therefore, each piece of ribbon is 180 inches long.
To find out how many 27-inch pieces Lucia can cut from each piece of ribbon, we divide 180 by 27.
180/27 = 6.67
Since Lucia can only cut whole pieces, she can cut 6 pieces of ribbon from each piece of ribbon.
Therefore, she can cut a total of 6 x 3 = 18 pieces of ribbon from the three separate pieces of ribbon.
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the random variable x is the number of occurrences of an event over an interval of 10 minutes. it can be assumed the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in 10 minutes is 5.3. the probability there are 8 occurrences in 10 minutes is . a. .0771 b. .0241 c. .1126 d. .9107
The probability of having 8 occurrences in 10 minutes is approximately 0.0241, which means the answer is (b).
The number of occurrences of an event in 10 minutes as a Poisson distribution with mean lambda = 5.3.
The probability of having 8 occurrences in 10 minutes is:
[tex]P(X = 8) = (e^(-5.3) * 5.3^8) / 8![/tex]
where X is the random variable representing the number of occurrences of the event in 10 minutes.
Using a calculator, we can evaluate this expression:
[tex]P(X = 8) = (e^(-5.3) * 5.3^8) / 8! ≈ 0.0241[/tex]
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The data for the height and weight of different people was collected the line of best fit for this date it was determined to be Y equals 0. 9 1X -65. 5 where X is the height in centimeters and why is the weight in kilograms is in the equation predict the height of a person who weighs 63 kg
According to the equation, a person who weighs 63 kg is predicted to be approximately 141 centimeters tall.
The equation given is Y = 0.91X - 65.5, where X represents the height in centimeters and Y represents the weight in kilograms. To predict the height of a person who weighs 63 kg, we need to solve for X, the height in centimeters.
To do this, we can plug in the given weight of 63 kg for Y in the equation and then solve for X. So, we have:
63 = 0.91X - 65.5
Adding 65.5 to both sides, we get:
63 + 65.5 = 0.91X
Simplifying, we have:
128.5 = 0.91X
Finally, to solve for X, we divide both sides by 0.91, giving:
X = 141.21
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A pancake company uses the
function f(x) = 1.5x² to calculate
the number of calories in a
pancake with a diameter of x cm.
What is the average rate of change
for the function over the interval
10
A.) 150 calories per cm of diameter
B.) 33 calories per cm of diameter
C.) 65calories per cm of diameter
D.) 215 calories per cm of diameter
Answer:
To find the average rate of change of the function f(x) = 1.5x² over the interval [10, 11], we need to calculate the change in f(x) over the interval, and divide by the change in x.
The change in f(x) over the interval [10, 11] is:
f(11) - f(10) = (1.511^2) - (1.510^2) = 165 - 150 = 15
The change in x over the interval [10, 11] is:
11 - 10 = 1
Therefore, the average rate of change of the function over the interval [10, 11] is:
(15/1) = 15
This means that for every 1 cm increase in diameter (i.e., for every 1 unit increase in x), the number of calories in the pancake increases by an average of 15 calories per cm of diameter.
Therefore, the answer is (A) 150 calories per cm of diameter.
A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. Which of these best describes the volume of this rectangular prism? (5 points)
1 unit cube and 15 smaller cubes of volume fraction 1/125 cubic inch each
1 unit cube and 75 smaller cubes of volume fraction 1/125 cubic inch each
7 unit cubes and 25 smaller cubes of volume fraction 1/125 cubic inch each
7 unit cubes and 125 smaller cubes of volume fraction 1/125 cubic inch each
The volume of the rectangular prism is 1.6 cubic inches.
Let's start by finding the number of cubes that can fit in each dimension of the rectangular prism. Since each cube has an edge length of 1/5 inch, the length, width, and height of the rectangular prism must be multiples of 1/5 inch. Let's call the length of the rectangular prism "L", the width "W", and the height "H". Then we have
L = 1/5 × x
W = 1/5 × y
H = 1/5 × z
where x, y, and z are integers.
Since the rectangular prism is completely packed with 200 cubes, we have
x × y × z = 200
We want to find the volume of the rectangular prism, which is given by
V = L × W × H = 1/5 × x × 1/5 × y × 1/5 × z = 1/125 × x × y × z
Substituting x × y × z = 200, we get
V = 1/125 × 200 = 8/5 = 1.6 cubic inches
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The given question is incomplete, the complete question is:
A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. find the volume of this rectangular prism
these four geometry questions i’m not quite sure how to do and have been struggling in them for a while and it’s due tomorrow!!!!
The total areas of each composite shape are:
1) 121 in²
2) 150m²
3) 14.03 ft²
4) 538.36 cm²
How to find the area of the composite figure?1) Formula for area of a rectangle is:
Area = Length * width
Thus:
Area of composite shape = (9 * 8) + (7 * 7)
= 121 in²
2) Formula for area of rectangle is:
Area = Length * width
Area = 12 * 5 = 60 m²
Area of triangle = ¹/₂ * base * height
Area = ¹/₂ * 12 * 15
Area = 90 m²
Area of composite shape = 60 + 90 = 150m²
3) Area of triangle = ¹/₂ * 3 * 7 = 10.5 ft²
Area of semi circle = ¹/₂ * πr²
= ¹/₂ * π * 1.5²
= 3.53 ft²
Total composite area = 10.5 ft² + 3.53 ft²
Total composite area = 14.03 ft²
4) Total composite area = (¹/₂ * π * 7.5²) + (30 * 15)
= 538.36 cm²
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please help!
If r=0.5 m, A = ???
(Use the r key.)
The area of a circle of radius of 0.5 meters is 0.785 square meters.
How to find the area of the circle?Remember that for a circle of radius r, the area is:
A = pi*r²
Where pi = 3.14
Here we know that r = 0.5m, then we can input that in the formula for the area that is above, we will get.
A = 3.14*(0.5m)²
A = 3.14*0.25 m²
A = 0.785 m²
That is the area of the circle.
Complete question: Let's say that r is the radius of a circle and A is its area, then: If r=0.5 m, A = ?
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if p is a prime number and a is a positive inte- ger, how many distinct positive divisors does pa have?
If p is a prime number and a is a positive integer, then pa has (a+1) distinct positive divisors.
A prime number is a positive integer greater than 1, which is divisible only by 1 and itself. Divisors are the numbers that evenly divide a given number.
For a prime number p raised to the power of a (p^a), the number of distinct positive divisors can be found using the following formula:
Number of divisors = (a + 1)
This is because each power of p from 0 to a can divide p^a without any remainder, giving us a total of a + 1 distinct divisors. These divisors are:
1, p, p^2, p^3, ..., p^(a-1), p^a
For example, if p = 2 (a prime number) and a = 3 (a positive integer), then the number of distinct positive divisors for 2^3 (which is 8) would be:
Number of divisors = (3 + 1) = 4
The divisors for 2^3 (8) are 1, 2, 4, and 8.
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A helicopter hovering above a command post shines a spotlight on an object on the ground 250 feet away from the command post as shown in the diagram how far is the object from the helicopter to the nearest foot
The distance of the object from the helicopter is 698 ft.
What is distance?Distance is the length between two points.
To calculate how far the object is above the helicopter, we use the formula below.
Formula:
Sin∅ = O/H..................... Equation 1Where:
∅ = AngleO = OppositeH = Hypotenus = Distance of the object from the HelicopterFrom the question,
Given:
O = 250 ft∅ = 21°Substitute these values into equation 1 and solve for H
H = 250/Sin21°H = 697.61 ftH ≈ 698 ftHence, the distance is 698 ft.
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armer abe has a budget of $300 to build a rectangular pen to protect his rambunctious sheep. he decides that three sides of the pen will be constructed with chain-link fence, which costs only $1 per foot. farmer abe decides that the fourth side of the pen will be made with sturdier fence, which costs $5 per foot. find the dimensions of the largest area the pen can enclose.
Let x be the length of the pen and y be the width of the pen.
The total cost of the pen is given by:
Cost = 3x + 5y = 300
3x + 5y = 300
3x = 300 - 5y
x = (300 - 5y)/3
The area of the pen is given by:
Area = xy = (300 - 5y)/3 * y
If r=0.5 m, A = ???
(Use the r key.)
The calculated value of the angular velocity of the object is 2 rad/s.
Calculating the angular velocityThe angular velocity, denoted by the Greek letter omega (ω), represents the rate of change of the angle with respect to time.
For an object moving in a circular path, the angular velocity is related to the linear speed and the radius of the circle by the equation:
ω = v/r
where v is the linear speed and r is the radius.
In this case, the radius is 0.5m and the speed is 1ms−1. Thus, the angular velocity is:
ω = v/r = 1/0.5 = 2 radians per second (rad/s)
Therefore, the angular velocity of the object is 2 rad/s.
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Complete question
An object moves in a circular path of radius 0.5m with a speed of 1ms−1. What is its angular velocity (A)?
If r = 0.5 m, A = ???
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups. She writes the equation r = 2/5 to describe the relationship.
In the given equation r = 2/5 t "r" is the dependent variable.
Dependent variables:In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.
An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.
A dependent variable is a variable whose value depends on the value of one or more other variables in the equation
Here we have
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups.
She writes the equation r = 2/5 t to describe the relationship.
In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.
Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.
The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.
Therefore,
In the given equation r = 2/5 t "r" is the dependent variable.
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Complete Question:
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.
in a recent basketball game, shenille attempted only three-point shots and two-point shots. she was successful on 20% of her three-point shots and 30% of her two-point shots. shenille attempted 30 shots. how many points did she score?(2013 amc 12a
The probability of a score for a recent basketball game, shenille attempted only three-point shots and two-point shots is 18 points in the game. The answer is Option B.
Let x be the number of three-point shots and y be the number of two-point shots attempted by Shenille.
Then, we have:
x + y = 30 (total number of shots attempted)
Let's solve for one of the variables. For example, we can solve for x by subtracting y from both sides of the equation:
x = 30 - y
Now, we can express Shenille's points in terms of x and y:
Points = 3x + 2y
Substituting x = 30 - y, we get:
Points = 3(30 - y) + 2y
Points = 90 - y
Shenille's success rate for three-point shots is 20%, so the number of successful three-point shots she made is 0.2x. Similarly, the number of successful two-point shots she made is 0.3y.
Total points scored = (0.2x)(3) + (0.3y)(2)
Substituting x = 30 - y, we get:
Total points scored = (0.2(30 - y))(3) + (0.3y)(2
Total points scored = 18 + 0.4y
Now we need to maximize the total points scored by Shenille. Since she attempted 30 shots in total, we have:
y = 30 - x
Substituting this into the equation for total points, we get:
Total points scored = 18 + 0.4(30 - x)
Total points scored = 30 - 0.4x
This is a linear function, which is maximized at its endpoint. The maximum value of this function occurs at x = 0, which means Shenille attempted all two-point shots. In this case, y = 30, and the total points scored would be:
Total points scored = 0 + 0.3(30)(2)
Total points scored = 18
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The question is -
In a recent basketball game, Shenille attempted only three-point shots and two-point shots. She was successful on 20% of her three-point shots and 30% of her two-point shots. Shenille attempted 30 shots. How many points did she score?
(A) 12
(B) 18
(C) 24
(D) 30
(E) 36
If you spin the spinner 36 times, what is the best prediction possible for the number of times
it will land on green or blue?
The best prediction possible for the number of times the spinner will land on green or blue is given as follows:
30 spins.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Out of six regions, three are green and two are blue, hence the probability of one spin resulting in green or blue is given as follows:
p = (3 + 2)/6
p = 5/6.
Thus the expected number out of 36 trials of spins resulting in green or blue is given as follows:
E(X) = 5/6 x 36
E(X) = 30 spins.
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Solve the following problem. Be sure to show all the steps (V. E. S. T. ) and work in order to receive full credit.
The sum of three numbers is 26. The second number is twice the first and the third number is 6 more than the second. Find the numbers.
Please help due tomorrow
The three numbers are 4, 8, and 14.
Let's use variables to represent the three numbers
Let x be the first number.
Then the second number is twice the first, so it is 2x.
The third number is 6 more than the second, so it is 2x + 6.
We know that the sum of the three numbers is 26, so we can write an equation:
x + 2x + (2x + 6) = 26
Now we can solve for x
5x + 6 = 26
5x = 20
x = 4
So the first number is 4.
To find the second number, we can use the equation we wrote earlier:
2x = 2(4) = 8
So the second number is 8.
To find the third number, we can use the other equation we wrote earlier
2x + 6 = 2(4) + 6 = 14
So the third number is 14.
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14. An airplane flew 2,800 miles from Los Angeles to New York. The airplane flies at approximately 500
mi/hr. How many hours did it take the plane to reach New York?
Answer:
Speed= 500ml/hr
total distance= 2800 m
total time = d/t
2800/500= 5.6hrs
Step-by-step explanation:
What are the cross-products of the proportion 6/40 = 9/60? Is the proportion TRUE?
54 and 2,400; the proportion is false.
54 and 540; the proportion is true.
360 and 360; the proportion is true.
Therefore, the answer is: 360 and 360; the proportion is true.
54 and 540; the proportion is true.
360 and 360; the proportion is true.
To find the cross-products of the proportion 6/40 = 9/60, we multiply the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.
So we have:
6 × 60 = 360
9 × 40 = 360
The cross-products are 360 and 360.
To check if the proportion is true, we compare the cross-products. If they are equal, then the proportion is true; otherwise, it is false.
Since the cross-products are equal, the proportion is true.
Therefore, the answer is:
360 and 360; the proportion is true.
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As a nurse working in a hospital one of the jobs is to give appropriate doses of medicine
before surgery so the patient doesn't wake up during surgery. 4cc of this particular medicine is
meant for a 180lb man, what would be the correct dosage for a 145 lb. woman?
Answer:
the correct dosage of the medicine for a 145 lb. woman would be approximately 3.22 cc
Step-by-step explanation:
To calculate the correct dosage of the medicine for a 145 lb. woman, we can use the following formula:
dosage = (weight of patient / weight of reference patient) x reference dosage
where the weight of the reference patient is 180 lb. and the reference dosage is 4 cc.
Plugging in the given values, we get:
dosage = (145 / 180) x 4
= 3.22 cc (rounded to two decimal places)
Therefore, the correct dosage of the medicine for a 145 lb. woman would be approximately 3.22 cc. However, it's important to note that dosages of medications should only be determined by a qualified medical professional based on a number of factors, including the patient's weight, medical history, and current condition.
What is the argument of z = StartFraction 1 Over 16 EndFraction minus StartFraction StartRoot 3 EndRoot Over 16 EndFraction i?
To find the argument of the complex number z = 1/16 - (sqrt(3)/16)i, we need to find the angle that the complex number forms with the positive real axis in the complex plane.
We can start by finding the magnitude of z, which is the distance between the origin and the point representing z in the complex plane:
|z| = sqrt( (1/16)^2 + (sqrt(3)/16)^2 )
= sqrt(1/256 + 3/256)
= sqrt(4/256)
= 1/4
Next, we can find the argument of z using the formula:
arg(z) = tan^(-1)(Im(z)/Re(z))
where Im(z) is the imaginary part of z, and Re(z) is the real part of z.
In this case, we have:
Re(z) = 1/16
Im(z) = -(sqrt(3)/16)
Therefore, we get:
arg(z) = tan^(-1)(Im(z)/Re(z))
= tan^(-1)(-(sqrt(3)/16)/(1/16))
= tan^(-1)(-sqrt(3))
= -60° (in degrees)
So, the argument of z is -60 degrees (or -π/3 radians).
Answer:
A
Step-by-step explanation:
HELP PLS EXPLAIN THISSSSS
Plugging in the values given into the expression, and simplifying, we would have our answer as: B. [tex]\frac{9}{25}[/tex]
How to Evaluate an Expression?To evaluate an expression, follow these steps:Identify the variables and constants in the expression.Substitute the given values for each variable in the expression.Simplify the expression until there are no more operations left.Given that, a = 5 and k = -2, substitute the values into the expression given and simplify:
[tex](\frac{3^2(5^{-2})}{3(5^{-1})} )^{-2}[/tex]
Simplify:
[tex](\frac{9 * \frac{1}{25} }{3* \frac{1}{5} } )^{-2}[/tex]
[tex](\frac{\frac{9}{25} }{\frac{3}{5} } )^{-2}\\\\(\frac{9}{25} * \frac{5}{3} } )^{-2}\\\\(\frac{3}{5} )^{-2}\\\\ = \frac{9}{25}[/tex]
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Find the volume of a pyramid with a square base, where the area of the base is 19. 6 ft 2 19. 6 ft 2 and the height of the pyramid is 11. 6 ft 11. 6 ft. Round your answer to the nearest tenth of a cubic foot
If the area of the base is 19. 6 ft^2 and the height of the pyramid is 11. 6 ft, the volume of the pyramid is approximately 79.1 cubic feet.
The formula for the volume of a pyramid is given by:
V = (1/3) × base area × height
In this case, we are given that the pyramid has a square base, so the base area is simply the area of a square with side length s:
base area = s^2 = 19.6 ft^2
We are also given the height of the pyramid:
height = 11.6 ft
Substituting these values into the formula for the volume of a pyramid, we get:
V = (1/3) × base area × height
= (1/3) × 19.6 ft^2 × 11.6 ft
≈ 79.1 ft^3 (rounded to the nearest tenth)
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The volume of a cylinder is given by the formula v - pi^h, where r is the radius of the cylinder and h is the height.
Which expression represents the volume of this cylinder?
The expression that represents the volume of the cylinder is:
V = π[tex]r^{2}[/tex]h
What is cylinder?
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases. The cylinder can be thought of as a tube or a can. The lateral surface of the cylinder is formed by "unrolling" a rectangular shape along the circumference of the base.
There appears to be a typographical error in the given formula for the volume of a cylinder. The correct formula is:
V = π[tex]r^{2}[/tex]h
where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.
Using this formula, the expression that represents the volume of the cylinder is:
V = π[tex]r^{2}[/tex]h
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From a horizontal distance of 80.0 m, the angle to the top of a flagpole is 18°. Calculate the height of the flagpole to the nearest tenth of a meter.
1. 24.7 meters
2. 76.1 meters
3. 26.0 meters
4. 25.3 meters
Answer:
The figure is omitted--please sketch it to confirm my answer.
Set your calculator to degree mode.
Let h be the height of the flagpole.
[tex] \tan(18) = \frac{h}{80} [/tex]
[tex]h = 80 \tan(18) = 25.994[/tex]
The height of the flagpole is approximately 26.0 meters. #3 is correct.