A printing company needs to ship 2,477 team calendars to the city's basketball team. The printing company can fit 24 calendars in each box. How many calendars will be in the partially filled box?
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Set up for proportion its not 9 or 6 or 2
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The value of x in the triangle is 2√13.
We have,
There are two similar triangles.
So,
The ratio of the corresponding sides is equal.
Now,
4/x = x/(9 + 4)
4/x = x / 13
4 x 13 = x²
x² = 4 x 13
x = √(4 x 13)
x = 2√13
Thus,
The value of x in the triangle is 2√13.
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The distribution of weigths of a sample of 1300 cargo containers is symmetric and bellshadped .what percent is above mean 2standard deviations
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Out of the 1300 cargo containers, approximately 30 containers (2.28% of 1300) are expected to weigh more than the mean by 2 standard deviations.
If the distribution of weights of a sample of 1300 cargo containers is symmetric and bell-shaped, we can assume that it follows a normal distribution. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, and approximately 95% of the data falls within two standard deviations of the mean.
Therefore, if we want to know what percent of the data is above the mean by 2 standard deviations, we need to calculate the area under the normal distribution curve to the right of the mean plus 2 standard deviations. This is equivalent to finding the area in the upper tail of the distribution.
Using a standard normal table or a calculator, we can find that the area to the right of mean plus 2 standard deviations in a standard normal distribution is approximately 2.28%. Since the given distribution is assumed to be a normal distribution, we can conclude that approximately 2.28% of the cargo containers weigh more than the mean by 2 standard deviations.
Therefore, out of the 1300 cargo containers, approximately 30 containers (2.28% of 1300) are expected to weigh more than the mean by 2 standard deviations.
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An article is sold in Rs 678 at a profit of 13%. Find its cost price.
Please help me
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Answer:
Rs 600.
Step-by-step explanation:
113% is equivalent to Rs 678 So by proportion:
100% .. ... .. .. to 678 * 100 / 113
= Rs 600.
One packet of hot cocoa weighs 1.38 ounces. How much will 8 packets weigh?
Answers
Answer:
Your answer will be 11.04
Step-by-step explanation:
1.38 × 8= 11.04
Use the information given in the diagram to prove that triangle PUX is congruent to triangle QSY. I have multiple photos I would like to upload on here.
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SOLUTION
We want to use the information in the diagram to prove that
\(\Delta PUX\cong\Delta\text{QSY}\)Now, we have been given for number 1
2.
\(\begin{gathered} RS=VU \\ \text{Definition of congruent segments } \end{gathered}\)3.
\(\begin{gathered} RU=RS+SU,VS=VU+SU \\ \text{Segment addition postulate } \end{gathered}\)4.
\(\begin{gathered} VS=RS+SU \\ Substitution\text{ property of equality} \end{gathered}\)5.
\(\begin{gathered} RU\cong VS \\ Transitive\text{ property of equality } \end{gathered}\)6.
\(\begin{gathered} RU=VS \\ \text{Definition of congruent segments} \end{gathered}\)7.
\(\begin{gathered} \Delta PUR\cong\Delta QSV \\ \text{ASA congruence theorem } \end{gathered}\)8.
\(\begin{gathered} m\angle RUX\cong m\angle VSY \\ m\angle PUR\cong m\angle QSV \\ \text{Corresponding parts of congruent triangles are congruent } \end{gathered}\)9. and 10. is good (correct)
11.
\(\begin{gathered} m\angle PUX=m\angle QSY \\ \text{Substitution property of equality} \end{gathered}\)12.
\(\begin{gathered} m\angle QSY=m\angle PUR+m\angle RUX \\ \text{Transitive property of equality} \end{gathered}\)13.
\(\begin{gathered} m\angle PUX=m\angle QSY \\ \text{Definition of congruent angles } \end{gathered}\)14.
\(\begin{gathered} \Delta PUX\cong\Delta\text{QSY} \\ \text{ASA congruence theorem} \end{gathered}\)What is a difference of squares that has a factor of x = 8? a. x2-4 b. x2-16 c. x2-64d. x2-256
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The difference of squares that has a factor of x = 8 is option c: x²-64.
The difference of square formula is an algebraic form of the equation used to express the differences between two
square values.
A difference of square is expressed in the form: a 2 – b 2, where both the first and last term is perfect squares.
factors are the positive integers that can divide a number evenly. Suppose we multiply two numbers to get a product.
The number that is multiplied are the factors of the product. Each number is a factor of itself.
1. Recall the difference of squares formula:
a² - b² = (a + b)(a - b).
2. In this case, we need to find the equation with a factor of x = 8.
3. Option c, x²-64, can be factored using the difference of squares formula:
x² - 64 = (x + 8)(x - 8).
4. As you can see, when x = 8, one of the factors is (x - 8), which equals 0, making the entire expression equal to 0.
So, the correct answer is c: x²-64.
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4x^4 - 3x^3 + 2x^2 - 5x +6 divided by (x-2)what is the remainder of this question
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The remainder is 44
Explanations:The given polynomial is:
\(4x^4-3x^3+2x^2-5x\text{ + 6}\)The function is to be divided by x - 2
The remainder of the division will be calculated using the remainder theorem
The remainder theorem states that " If a function g(x) is divided by x - a, the remainder of the division will be g(a)"
\(\text{Let g(x) = 4x}^4-3x^3+2x^2-5x+6\)The remainder when g(x) is divided by x -2 is g(2)
\(\begin{gathered} g(2)=4(2)^4-3(2)^3+2(2)^2-\text{ 5(2) + 6} \\ g(2)\text{ = 4(16) - 3(8) + 2(4) -5(2) + 6} \\ g(2)\text{ = 64 - 24 + 8 - 10 + 6} \\ g(2)\text{ = 44} \end{gathered}\)Suppose that X and Y are random variables and that X and Y are nonnegative for all points in a sample space S. Let Z be the random variable defined by Z(s)= max(X(s), Y(s)) for all elements s ? S. Show that E(Z) = E(X) + E(Y).
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We have shown that E(Z) = E(X) + E(Y) for nonnegative random variables X and Y.
What is variable?The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.
To show that E(Z) = E(X) + E(Y), we need to use the definition of the expected value of a random variable and some properties of max function.
The expected value of a random variable X is defined as E(X) = ∑x P(X = x), where the sum is taken over all possible values of X.
Now, let's consider the random variable Z = max(X, Y). The probability that Z is less than or equal to some number z is the same as the probability that both X and Y are less than or equal to z. In other words, P(Z ≤ z) = P(X ≤ z and Y ≤ z).
Using the fact that X and Y are nonnegative, we can write:
P(Z ≤ z) = P(max(X,Y) ≤ z) = P(X ≤ z and Y ≤ z)
Now, we can apply the distributive property of probability:
P(Z ≤ z) = P(X ≤ z)P(Y ≤ z)
Differentiating both sides of the above equation with respect to z yields:
d/dz P(Z ≤ z) = d/dz [P(X ≤ z)P(Y ≤ z)]
P(Z = z) = P(X ≤ z) d/dz P(Y ≤ z) + P(Y ≤ z) d/dz P(X ≤ z)
Since X and Y are nonnegative, we have d/dz P(X ≤ z) = P(X = z) and d/dz P(Y ≤ z) = P(Y = z). Therefore, we can simplify the above expression as:
P(Z = z) = P(X = z) P(Y ≤ z) + P(Y = z) P(X ≤ z)
Now, we can calculate the expected value of Z as:
E(Z) = ∑z z P(Z = z)
= ∑z z [P(X = z) P(Y ≤ z) + P(Y = z) P(X ≤ z)]
= ∑z z P(X = z) P(Y ≤ z) + ∑z z P(Y = z) P(X ≤ z)
Since X and Y are nonnegative, we have:
∑z z P(X = z) P(Y ≤ z) = E(X) P(Y ≤ Z) and
∑z z P(Y = z) P(X ≤ z) = E(Y) P(X ≤ Z)
Substituting these values in the expression for E(Z) above, we get:
E(Z) = E(X) P(Y ≤ Z) + E(Y) P(X ≤ Z)
Finally, we note that P(Y ≤ Z) = P(X ≤ Z) = 1, since Z is defined as the maximum of X and Y. Therefore, we can simplify the above expression as:
E(Z) = E(X) + E(Y)
Thus, we have shown that E(Z) = E(X) + E(Y) for nonnegative random variables X and Y.
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mercedes is running a special in which all SUVs are marked down for 15%. Mr. Estes purchased a G wagon for 160,000. What did he pay for the SUV after the discount was applied?
A.110,000
B.105,000
C.136,000
D. 125,000
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The required payment for the SUV after the discount was applied is 136,000. Option C is correct.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
All SUVs are marked down by 15%.
Cost of G wagon = 160, 000
Cost after discount = 160000 - 15% of 160,000
= 136000
Thus, the required payment for the SUV after the discount was applied is 136,000. Option C is correct.
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The amount after discount is $136000.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Mercedes is running a special in which all SUVs are marked down for 15%. Mr. Estes purchased a G wagon for 160,000.
The amount after the discount was applied is -
D = 15% of 160000
D = (15/100) x 16000
D = 15 x 160
D = 2400
A = 160000 - 2400 =
A = 136000
Therefore, the amount after discount is $136000.
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Find x in this 45°-45°-90° triangle. 12 X M 1 2 3 4 5 6 7 8 9 8197P
Answers
Solution
We can use the following identity:
\(\sin 45=\frac{x}{12}\)Solving for x we got:
\(x=12\cdot\sin 45=12\cdot\frac{\sqrt[]{2}}{2}=6\sqrt[]{2}=\sqrt[]{72}\)Help me with this 9 math
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The height of the cylinder is 4 feet.
How to find the height of a cylinder?The volume of a cylinder can be found as follows;
volume of a cylinder = base area × height
Therefore,
base area = πr²
volume of the cylinder = 48π ft³
base area = 12π ft²
Therefore, let's find the height of the cylinder as follows:
48π = 12π × h
divide both sides of the equation by 12π
h = 48π / 12π
h = 4 ft
Therefore,
height of the cylinder = 4 feet
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PLEASE HELP ASAP!!!
Question in photo
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please help me answer this question asap
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Answer:
It's quite easy
Step-by-step explanation:
people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23
Therefore there are 23 people less than 30 years old.
pls mark me as brainliest pls.
Discrete Structures in Mathematics(b) Solve the recurrence relation An = 6an-1 – 9an-2 = with initial conditions ao = 2 and ai = 3. [6 marks]
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First, let me explain some key terms related to the question.
- Discrete: This refers to mathematics that deals with countable or finite sets of numbers, rather than continuous sets. In other words, we're dealing with specific, separate values rather than a continuous range.
- Recurrence: This refers to a mathematical sequence where each term depends on one or more previous terms. In other words, we can use a formula to generate the next term based on previous terms.
- Relation: This refers to a mathematical expression that relates one or more variables. In this case, our recurrence relation relates the sequence An to its previous terms.
With that in mind, let's tackle the question!
We're given a recurrence relation: An = 6An-1 – 9An-2. This means that each term in the sequence An depends on the two previous terms, An-1 and An-2.
We're also given initial conditions: a0 = 2 and a1 = 3. This gives us a starting point for the sequence.
To solve the recurrence relation and find the values of An, we'll use a technique called iteration. Essentially, we'll use the recurrence relation to generate the next term in the sequence, then use that term to generate the next one, and so on.
Here's how it works:
- First, we use the initial conditions to find the first two terms of the sequence: a0 = 2 and a1 = 3.
- Next, we use the recurrence relation to generate the third term: a2 = 6a1 - 9a0 = 6(3) - 9(2) = 0.
- We continue this process, using the recurrence relation to generate each subsequent term. For example, to find a3, we use the formula An = 6An-1 – 9An-2 with n = 3: a3 = 6a2 - 9a1 = 6(0) - 9(3) = -27.
- We can keep going like this to find as many terms as we need.
Here's what the first few terms of the sequence look like:
a0 = 2
a1 = 3
a2 = 0
a3 = -27
a4 = -54
a5 = -162
a6 = -270
...
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for how many (not necessarily positive) integer values of $n$ is the value of $4000\cdot \left(\tfrac{2}{5}\right)^n$ an integer?
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There are 55 integer values of n for which the expression \(4000 * (2/5)^n\) is an integer, considering both positive and negative values of n.
To determine the values of n for which the expression is an integer, we need to analyze the factors of 4000 and the powers of 2 and 5 in the denominator.
First, let's factorize 4000: \(4000 = 2^6 * 5^3.\)
The expression \(4000 * (2/5)^n\) will be an integer if and only if the power of 2 in the denominator is less than or equal to the power of 2 in the numerator, and the power of 5 in the denominator is less than or equal to the power of 5 in the numerator.
Since the powers of 2 and 5 in the numerator are both 0, we have the following conditions:
- n must be greater than or equal to 0 (to ensure the numerator is an integer).
- The power of 2 in the denominator must be less than or equal to 6.
- The power of 5 in the denominator must be less than or equal to 3.
Considering these conditions, we find that there are 7 possible values for the power of 2 (0, 1, 2, 3, 4, 5, and 6) and 4 possible values for the power of 5 (0, 1, 2, and 3). Therefore, the total number of integer values for n is 7 * 4 = 28. However, since negative values of n are also allowed, we need to consider their counterparts. Since n can be negative, we have twice the number of possibilities, resulting in 28 * 2 = 56.
However, we need to exclude the case where n = 0 since it results in a non-integer value. Therefore, the final answer is 56 - 1 = 55 integer values of n for which the expression is an integer.
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Luna have c caramel then luna sister took 56 of the carmel write the expression that show the number of carmel luna have left brainly
Answers
Answer: \(c-56\)
Step-by-step explanation:
Given
Luna has c caramel
Her sister took 56 caramel
The number of caramel luna has left is the subtraction of initial and 56 i.e.
\(\Rightarrow c-56\)
Jonna ran a mile in a physical education class
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Which expression is equivalent to this polynomial? x^2-x-20
Answers
Answer:
(x-5)(x+4)
Step-by-step explanation:
hello :
x^2-x-20 = (x-5)(x+4)
pleeeeeeeaaaaseee heeelp meeeee
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The area A of a trapezoid is the height h times the average of the parallel bases a and b.
A = (1/2)(a + b)h
Solving for a,
2A = (a+b)h
2A/h = a+b
a = 2A/h - b
We have A=59.64, b=4, h=8.4
a = 2(59.64)/8.4 - 4
a = 10.2 yards
Answer: 10.2
Need some help pleaseee
Answers
Answer: A=56/5 ft^2
Step-by-step explanation:
A=Area of triangle. b=base. h=height
A=1/2 * b * h
A=1/2 * (5+3/5) * 4
A=1/2 * (25/5 + 3/5) * 4
A=1/2 * 28/5 * 4
A=28/10 * 4
A=28*4/10
A=112/10
A=56/5 ft^2
Assume an initial starting ft of 290 units, a trend (tt) of eight units, an alpha of 0.40, and a delta of 0.50. if actual demand turned out to be 278, calculate the forecast for the next period.
Answers
The forecast for the next period when the actual demand turned out to be 278 will be 294 units.
What is the forecast?The method of forecasting entails creating assumptions based on historical and current data. These might then be contrasted with what transpires.
Ft = 290, Tt = 8, α = 0.40, δ = 0.50, At = 278. Then the forecast for the next period will be
FITt = Ft + Tt
= 290 + 8
= 298 units
Ft + 1 = FITt + α(At − FITt)
= 298 + 0.40(278 − 298)
= 298 − 8
= 290 units
Tt + 1 = Tt + δ(Ft + 1 − FITt)
= 8 + 0.50(290 − 298)
= 8 − 4
= 4 units
FITt + 1 = Ft + 1 + Tt + 1
= 290 + 4
= 294 units
The forecast for the next period will be 294 units.
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help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
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Answer:
Shorter leg = 2.5 ft
Longer leg = 6.5 ft
Step-by-step explanation:
Pythagorean theorem:Let the shorter leg = x ft
Longer leg = (x + 4) ft
Hypotenuse = 7 ft
\(\sf x^2 + (x +4)^2 = 7^2\)
x² + x² + 2*x*4 + 4² = 49
x² + x²+ 8x + 16 = 49
2x² + 8x + 16 - 49 = 0
2x² + 8x - 33 = 0
This is a quadratic equation. We can use the below mentioned formula to find the value of x.
a = 2 ; b = 8 ; c = -33
b² - 4ac = 8² - 4 * 2 * (-33)
= 64 + 264
=328
\(\sf x = \dfrac{-b \± \sqrt{b^2-4ac}}{2a}\)
\(\sf x = \dfrac{-8 \±\sqrt{328}}{2*2}\\\\\\x= \dfrac{-8 \±18.11}{4}\\\\\\x =\dfrac{-8+18.11}{4} ; \ x=\dfrac{-8-18.11}{4} > > \text{this is rejected because sides of } \\\\ \text{a triangle cannot be measured in negative value}\)
\(\sf x = \dfrac{-8+18.11}{4}\)
\(\sf x = \dfrac{10.11}{4}\\\\x =2.5275\)
x+ 4 = 2.5275 + 4 = 6.5275
Shorter leg = 2.5 ft
Longer leg = 6.5 ft
Answer: the length of the shoter leg is 2,5 feet
the length of the longer leg is 6.5 feet
Step-by-step explanation:
Let the length of the shoter leg is x feet
Than the length of the longer leg is (x+4) feet
We use Pythagoras' theorem:
\(\displaystyle\\x^2+(x+4)^2=7^2\\\\x^2+x^2+2(x)(4)+4^2=7(7)\\\\2x^2+8x+4(4)=49\\\\2x^2+8x+16-49=49-49\\\\2x^2+8x-33=0\\\\D=b^2-4ac\\\\Hence,\\\\D=8^2-4(2)(-33)\\\\D=8(8)+8(33)\\\\D=64+264\\\\D=328\\\\\sqrt{D}=\sqrt{328} \\\\x=\frac{-bб\sqrt{D} }{2(a)} \\\\x=\frac{-8б\sqrt{328} }{2(2)} \\\\x=-6.5277\notin (x > 0)\\\\x=2.5277\ feet\\\\x+4=2.5277+4\\\\x+4=6.5277\ feet\)
What is 16% of 78? Round to the nearest tenth.
Answers
What is 16% of 78? Round to the nearest tenth.
16% = 0.16
so:
0.16 * 78 = 12.48
round:
12.5
Consider the logistic differential equation:
dy/dx = y/8(6 - y)
Let f(t) be the particular solution to the differential equationwith f(0) = 8
a. What is the limiting factor?
b. Use Euler's method, starting at t=0 with two steps of equalsize, to appropriate F(1).
c. What is the range of f for t > 0
Answers
The approximate value of f(1) using Euler's method with two steps of equal size is 6.636. The range of f for t > 0 is 0 < f(t) < 6.
a. The limiting factor in this logistic differential equation is the carrying capacity, which is 6 in this case. As y approaches 6, the growth rate of y slows down, until it eventually levels off at the carrying capacity.
b. To use Euler's method, we first need to calculate the slope of the solution at t=0. Using the given differential equation, we can find that the slope at t=0 is y(0)/8(6-y(0)) = 8/8(6-8) = -1/6.
Using Euler's method with two steps of equal size, we can approximate f(1) as follows:
f(0.5) = f(0) + (1/2)dy/dx|t=0
= 8 - (1/2)(1/6)*8
= 7.333...
f(1) = f(0.5) + (1/2)dy/dx|t=0.5
= 7.333... - (1/2)(7.333.../8)*(6-7.333...)
= 6.636...
Therefore, the approximate value of f(1) using Euler's method with two steps of equal size is 6.636.
c. The range of f for t > 0 is 0 < f(t) < 6, since the carrying capacity of the logistic equation is 6. As t approaches infinity, f(t) will approach 6, but never exceed it. Additionally, f(t) will never be negative, since it represents a population size. Therefore, the range of f for t > 0 is 0 < f(t) < 6.
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solve: 2(5-4A)=-2A+8-6A
Answers
Can anyone help me with my homework
Answers
Answer:
x = the number
Step-by-step explanation:
15.) 2x + 9 = 25
16.) 3x - 6 = 21
17.) 7x = 12 + 3x
18.) 4x = 18 + x
19.) 2x + 24 = 8x
20.) 30 - x = 4x
The population for a clinical study has 500 Asian, 1000 Hispanic and 500 Native American people. What is good way of sampling this population to ensure that the distribution of various sub-populations is maintained if only 200 samples have to be chosen? Give the distribution of the various sub-populations in the final sample.
Answers
A good way to sample this population while maintaining the distribution of various sub-populations is by using stratified sampling. In stratified sampling, the population is divided into homogeneous subgroups or strata based on certain characteristics, and then a random sample is selected from each stratum.
To ensure that the distribution of various sub-populations is maintained, the sample should include a proportional representation of individuals from each subgroup. In this case, the subgroups are Asian, Hispanic, and Native American.
Here's how the distribution of the various sub-populations can be maintained in the final sample:
1. Determine the proportion of each subgroup in the population:
- Asian: 500 / 2000 = 0.25 (25%)
- Hispanic: 1000 / 2000 = 0.5 (50%)
- Native American: 500 / 2000 = 0.25 (25%)
2. Calculate the number of samples to be chosen from each subgroup:
- Asian: 0.25 * 200 = 50 samples
- Hispanic: 0.5 * 200 = 100 samples
- Native American: 0.25 * 200 = 50 samples
3. Randomly select the specified number of samples from each subgroup.
By using stratified sampling with the specified proportions, the final sample of 200 individuals will have a distribution that reflects the proportions of Asian, Hispanic, and Native American subpopulations in the overall population.
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A parachute is descending at a rate of 28 feet per minute. Find the total change in altitude of the parachute after 4 minutes.
Answers
Answer:
The parachute descended 112 feet
Step-by-step explanation:
What is the surface area of the cylinder with height 7 cm and radius 4 cm? Round
your answer to the nearest thousandth.
Answers
Step-by-step explanation:
\(2 \pi4 ^{2} \times 7 + \pi \times 8 \times 7 \\ 219.94\)
in the figure below, points J, K, and L are the midpoints of the sides of XYZ. suppose YZ =76, JK =12, and XY =68. find the following lengths. JL, XZ, and LZ
Answers
Given data:
The first length given is YZ =76.
The second length given is JK =12.
The third length given is XY=68.
The JL length is,
\(\begin{gathered} JL=\frac{1}{2}(YZ) \\ =\frac{1}{2}(76) \\ =38 \end{gathered}\)The XZ length is,
\(\begin{gathered} XZ=2(JK) \\ =2(12) \\ =24 \end{gathered}\)The LZ length is,
\(\begin{gathered} LZ=\frac{1}{2}(XZ) \\ =\frac{1}{2}(24) \\ =12 \end{gathered}\)Thus, JL=38, XZ=24, and LZ=12.