Why is the hypotenuse always longer than the legs?
Answer:
its about the degrees.
Step-by-step explanation:
In a right triangle, the sum of the interior angles will always be 180°. Since a right angle is half that (90°), it has to be the biggest angle in the triangle and the side across from it will always be the longest.
Rewrite the triple integral ? 0 to 1 ? 0 to x ? 0 to y f(x,y,z) dzdydx as ? b to a ? g1(z) to g2(z) ? h1(y,z) to h2 (y,z) f(x,y,z) dxdydz a = _______ b = _______ g1(z) = ______ g2(z) = ______ h1(y,z) = ______ h2(y,z) = _______
A new form of the triple integral [tex]\int\limits^1_0 \int\limits^x_0 \int\limits^y_0 f(x,y,z)dzdydx[/tex] as a = 0 b = 1 g2(z) = 1 h2(y,z) = 1.
In other words, we want the integration order to be totally reversed for
[tex]\int\limits^1_0\int\limits^x_0 \int\limits^y_0 f (x,y,z) dz dy dx[/tex]
Keep in mind that this area is quite simple to define. The planes z = y and y = x, as well as the coordinate planes [tex]x=y=z=0[/tex], define our boundaries. We essentially have upper bounds z = y = x = 1 because x ∈[ 0, 1 ]. Therefore, we can alternatively express the region as:-
[tex]0\leq x\leq y\\0\leq y\leq z\\[/tex]
z∈ I0,1I. So
[tex]\int\limits^1_0 \int\limits^x_0 \int\limits^y_0 f(x,y,z)dzdydx = \int\limits^1_0 \int\limits^z_0 \int\limits^y_0 f(x,y,z)dxdydz[/tex]
Remember that a double integral could be set up in two different ways. Our number of alternative orders of integration increases from two to six when we include that third integral. We will rewrite the supplied integral in one of the other five possible orders in this exercise.
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the points (16, 12) and (12, 9) fall on a particular line. what is its equation in slope-intercept form?
Answer: y=3/4x
Step-by-step explanation:
1. Find slope using slope formula
2. Find b value by plugging a point to solve for b with
Lawson planted a tree when it was 14 inches tall and it will grow 3 inches per year. Ezra planted a tree when it was 8 inches tall and it will grow 5 inches per year. Determine how many years it will take for the trees to be the same height. Thanks
the lifetime in months of a transistor in a certain application is random with probability density function
The chance density characteristic of lifetime in months of a transistor in a positive utility is:
[tex]f(x)=0.4cdot e^x > 0f(x)=0.4⋅e −0.4x ;x>0[/tex]
The chance density characteristic shows that the random variable X follows a exponential characteristic with parameter λ = 0.4.
Compute the suggest lifetime as follows:
[tex]mu=frac=2.5μ= λ1 = 0.401 =2.5[/tex]
Thus, the suggest lifetime is months.
Compute the usual deviation of the lifetimes as follows:
[tex]sigma=2.5σ= λ 2 1 = 0.40 2 1 =2.5.[/tex]
Thus, the usual deviation of the lifetimes is 2.5 months.
Compute the sixtieth percentile of the lifetime as follows:
Thus, the sixtieth percentile of the lifetime is 2.3 months.
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if all sales are made on account, the only piece of information you would need to calculate the cash received from customers during the period is the net change in accounts receivable. State True or False your answer:
a. True
b. False
If all sales are made on account, the only piece of information you would need to calculate the cash received from customers during the period is the net change in accounts receivable.
It is False.
Information available from the question,
In the question:
If all sales are made on account, the only piece of information you would need to calculate the cash received from customers during the period is the net change in accounts receivable.
The answer in TRUE/FALSE
Now, According to the question:
Accounting for cash transactions:
Daily cash sheet: If cash transactions are a significant part of your business, you should also prepare a daily cash sheet to reconcile your cash received and paid out for the day. If you use a daily cash sheet, you can reconcile your cash receipts with your daily deposit into your bank account.
So, The given statement is False.
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PLEASE HELP MEE!!!! ASAP Im so confused on this problem! I'LL GIVE 50 POINTS!
The graph of the function over the interval -2 ≤ x ≤ 2 is given below:
What do you mean by step function?
A piecewise function is one that is broken up into smaller functions, each of which has its own equation. A very particular (and much simpler) type of piecewise function is called a step function (or staircase function), and it has parts that resemble steps or the stairs of a staircase.
The graph of the function over the interval -2 ≤ x ≤ 2 is given below:
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19. Select all tables that represent a proportional relationship between x and y.
From the given options, Option A and Option D will represent the proportionality relation between x and y.
The proportional relationship between 2 variables:Equivalence between two variables that are related to one another and preserve a particular amount is referred to as a proportional relationship.
It is a mathematical concept that describes how two variables are related when they do so in equivalency and is also known as the "Relation of Proportionality."
Let the variables x and y are proportional to each other
=> x ∝ y
=> x = ky
=> x/y = k [ where k is proportionality constant ]
Here we will use the formula x/y = k to check the given variables' proportionality
Now check given options given below
Option A
x 0 1/5 2/5 3/5
y 0 1/10 2/10 3/10
For x = 1/5 and y = 1/10
=> [tex]\frac{x}{y} = \frac{1}{5} \times \frac{10}{1}[/tex] = 2
For x = 2/5 and y= 2/10
=> [tex]\frac{x}{y} = \frac{2}{5} \times \frac{10}{2}[/tex] = 2
Therefore, Table A represents the proportionality relation
Option B:
x - 0 1/2 1/3 1/4
y - 0 1/3 1/4 1/5
For x = 1/2 and y = 1/3
=> [tex]\frac{x}{y} = \frac{1}{2} \times \frac{3}{1}[/tex] = 3/2
For x = 1/3 and y = 1/4
=> [tex]\frac{x}{y} = \frac{1}{3} \times \frac{4}{1}[/tex] = 4/3
Therefore, Table B doesn't represent the proportionality relation
Option C:
x - 0 1 3 5
y - 0 1 9 25
For x = 1 and y = 1
=> [tex]\frac{x}{y} = \frac{1}{1} = 1[/tex]
For x = 3 and 9
=> [tex]\frac{x}{y} = \frac{9}{3} = 3[/tex]
Therefore, Table C doesn't represent the proportionality relation
Option D:
x - 0 1 3 4
y - 0 5 15 20
For x = 1 and y = 5
=> [tex]\frac{x}{y} = \frac{1}{5} = 1/5[/tex]
For x = 3 and y = 15
=> [tex]\frac{x}{y} = \frac{3}{15} = \frac{1}{5}[/tex]
Therefore, Table D will represent the proportionality relation
Therefore,
From the given options, Option A and Option D will represent the proportionality relation between x and y.
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Which of the following is not a criterion for congruence of triangle Mcq? A
SAS
B
ASA
C
SSA
D
SSS
use the completed punnett square in part b to answer the questions below about the f2 generation. drag the probabilities on the left to the blanks on the right to answer the questions. terms can be used once, more than once, or not at all. view available hint(s)for part c resethelp 964964 2323 27642764 63646364 1414 164164 916916 1 0 3434 1212 1313 1. what is the probability that an f2 seed chosen at random will be yellow? blanktarget 1 of 4 2. what is the probablity that an f2 seed chosen at random from among the yellow seeds will breed true when selfed? blanktarget 2 of 4 3. what is the probability that three f2 seeds chosen at random will include at least one yellow seed? blanktarget 3 of 4 4. what is the probability that three f2 seeds chosen at random will include one green seed and two yellow seeds? blanktarget 4 of 4
1) The probability of F2 seed chosen at random will be yellow is the same as asking about the probability of forming a yellow seed in that generation. The answer is 3/4 (75%) because 1/4 = 25% GG is homozygous dominant and the rest 2/4 = 50% Gg are heterozygous.
2) In the F2 generation there are two genotypes that will breed true, which is homozygotic genotypes: GG and gg. But of these two, only one of them is yellow. The answer is 1/3 because from all the yellow seeds that resulted (GG, Gg and gG) only one has the genotype for true breeding.
3) The probability of taking out three seeds in which a least one is yellow can be calculated by subtracting the only probability that doesn't fit the criterion, which is taking out a green seed 3 times: = 1/64.
Then subtract that to 1 = 63/64
4) there are three possible groupings in which the green is taken once and the yellow seeds taken twice. The first possibility (follow the example) is the green being the first to come out, another possibility is being the second and the last possibility is being taken in the third time.
For example, Green yellow yellow- probability :
= 9/64
This is one possibily, but since there are 3, multiply it by 3 and you obtain the final answer:27/64.
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Find the difference of 10x2y and 2x2y
Answer: 8x
Step-by-step explanation: We will start by writing out our equation which is 10x2y-2x2y. Next we will subtract using only like terms
10x - 2x = 8x
2y-2y=0
8x plus 0 = 8x.
find the probability of getting 5 face cards (king, queen, or jack) when 5 cards are drawn from a deck without replacement.
The probability of getting 5 face cards when taken without replacement is 0.00030473728.
There are 12 face cards in the deck overall.
When six cards are dealt, 12C5 equals 792.
without a replacement
P (5 face cards) = 12/5
P(5)=792 / 2598960 for five face cards.
P(5)=0.00030473728 for five face cards.
When 6 cards are picked from a deck without replacement, the likelihood of getting 6 face cards (a king, queen, or jack) is therefore 0.00030473728.
Probability is a branch of mathematics that deals with numerical descriptions of the likelihood that an event will occur or that a claim is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 indicates the event's impossibility and 1 indicates its certainty.
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The parent function f(x)=x^2 is translated 2 units left and 3 units up. Write the quadratic function in vertex form.
The quadratic function in vertex form is formed as: f(x)=a(x + 2)² + 2.
Explain the vertex form of quadratic function?In the linear model, k defines the vertex of the parabola, just as adding or subtracting b would decide where the line crosses.f(x)=a(x - h)² + k
K functions like b with in slope-intercept formula, just like a linear function would.For the stated question-
Whether you're going to increase by 2, you must also add 2.
The horizontal movement is determined by the h. It goes left or right depending on what you enter in h.
Finding the value that will cause the parenthesis to equal 0 when x equals -2 is necessary to make the necessary adjustments because shifting the vertex point to a left implies subtraction and negatives
x - h = 0
-2 - h = 0
-h = 2
h = -2
As a result, the function appears as follows:
f(x)=a(x - (-2))² + 2
A negative is subtracted to eliminate the signs and create a positive:
f(x)=a(x + 2)² + 2
Thus, the quadratic function in vertex form is formed as: f(x)=a(x + 2)² + 2.
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What if the elimination method results in 0=0?
Answer:
If the elimination produces the equation 0=0, then the two equations are for the same line.
Step-by-step explanation:
This means that there are an infinite number of solutions.
How do I do this? , it’s making me confused
Answer:
you remember vertex: h,k in (x-h)²+k..
replace in that. In that graph vertex: (10, -20)
So in that Equation, a(x-10)²-20, a<0 since it is maximum graph.
I cannot find the full Equation but from what I can see you can find h,k and the fact that a<0
How do you solve 1.4f+1.1=8.3−f?
For the given algebaric expression, 1.4f+1.1=8.3−f where "f " is variable the solved value of "f" is 3..
We have an algebraic expression of one variable say f ,
1.4 f + 1.1 = 8.3 - f --(1)
we have to solve it
Step 1 : Multiply both sides by 10
1.4 f ×10 + 1.1 ×10 = 8.3×10 - f ×10
=> 14/10(10f) + 11/10(10) = 83/10(10) - 10f
=> 14f + 11 = 83 - 10f
Step 2 : Subtract 11 from both sides
=> 14f + 11 - 11 = 83 - 10f -11
=> 14f = 72 - 10f
Step 3 : Add 10f both sides
=> 14f + 10f = 72 - 10f + 10f
=> 24f = 72
Step 4 : Divide both sides by 24
=> 24f/24 = 72/24
=> f = 3
Hemce,the solved value of "f" is 3 ..
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The perimeter of a rectangular parking lot is 302 meters. The parking lot is 86 meters long.
How wide is it?
Submit
meters
In addition to the 407 inch diagonal, the rectangle slab is 379 inches wide.
What is the length of the side of the slab in inches?
By using Pythagorean theorem ,148 is the length of the side of the slab in inches .
What is the Pythagorean theorem in plain English?
The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.
This is written as a2 + b2 = c2 in the usual algebraic notation.
12 inches = 1 feet
feet measurment = 407/12 = 33.91 feet
In triangle ABC
Using PYTHAOREAN THEOREM
l² + b² = h²
l = √h² - b²
l = √407² - 379²
l = √165649 - 143641
l = √22008
l = 148.35
l ≈ 148
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A third friend offers you a flat $20 to watch his dog during the same time. Tell whether you would choose this job over either of the other two.
Group of answer choices
$10 plus $2 per day
$15 plus $1 per day
A flat $20
It depends on the length of their vacations.
The job paying a flat $20 should be chosen instead of the other two options for periods of at most 5 days.
How to choose the best job?The daily pay for each job is constant, hence they can be modeled by linear functions, in the slope-intercept format, as follows:
y = mx + b.
The coefficients of the linear functions are given as follows:
m is the slope, representing the daily pay rate.b is the intercept, representing the flat fee.Hence the functions for each option are given as follows:
$10 plus $2 per day: y1(x) = 10 + 2x.$15 plus $1 per day: y2(x) = 15 + x.A flat $20: y3(x) = 20.The third option is better when:
First: 20 >= 10 + 2x -> 2x <= 10 -> x <= 5.Second 20 >= 15 + x -> x <= 5.Which is why it should be chosen for periods of at most five days.
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does anyone know what
3m−7=5
is?
Answer: m=4
Step-by-step explanation:
3m−7=5
3m = 12
m= 4
Answer:
m = 4
Step-by-step explanation:
add 7 to both sides > 3m - 7 + 7 = 5 + 7simplify > 3m = 12divide coefficient > 3m / 3 = m & 12 / 3 = 4 m = 4Two similar triangles, ABC and A JKL, are shown.
B
3.5
5
A 2.5 C
What is the length of side JL?
?
I 15
10.5
Answer:
JL = 7.5
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion , that is
[tex]\frac{JL}{AC}[/tex] = [tex]\frac{JK}{AB}[/tex] ( substitute values )
[tex]\frac{JL}{2.5}[/tex] = [tex]\frac{10.5}{3.5}[/tex] ( cross- multiply )
3.5 × JL = 2.5 × 10.5 = 26.25 ( divide both sides by 3.5 )
JL = 7.5
Some kids scored a 70% on a tesst and some scored a 90%. If the overall average was 76%, what percent of the kids scored a 90%?
The percent of the kids scored a 90% is 82%.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, some kids scored a 70% on a test and some scored a 90%.
Let x percent of the kids scored a 90%.
Now, x% of 76%=90%
0.01x×0.76=0.9
0.01x=0.9/0.76
0.01x=1.184
x=1.184/0.01
x=118%
So, 100-18=82%
Therefore, the percent of the kids scored a 90% is 82%.
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Which of the following is quadratic equations √ 3x² - 2x + 1/2 = 0?
The following equation √ 3x² - 2x + 1/2 = 0 is quadratic
What is quadratic?The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.
Is a quadratic 2 or 4?Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."
As the expression √ 3x² - 2x + 1/2 = 0 has square root so it is a quadratic equation.
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How do you write 31/25 as a decimal?
To write 31/25 as a decimal, we can divide 31 by 25 using long division or a calculator and we get 1.24
what is decimal?A decimal is a way of expressing a number as a fraction of one.
What is round off?Rounding off is a mathematical process that involves replacing a number with an approximate value that is easier to work with. When you round off a number, you choose the nearest whole number, ten, hundred, etc., depending on the place value you are rounding to.
For example, if you are asked to round the number 3.6 to the nearest whole number, you would round it off to 4, because 4 is the nearest whole number to 3.6.
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which expression shows a way to factor 16 + 72
The expression that shows a way to factor 16 + 72 is 8(2 + 9)
How to determine the way to factor the expression?From the question, we have the following parameters that can be used in our computation:
16 + 72
Express the terms of the expression as products
So, we have the following representation
16 + 72 = 8 * 2 + 8 * 9
Factor out 8 from the expression
This gives
16 + 72 = 8 * (2 + 9)
Hence, the factored expression of 16 + 72 is 8 * (2 + 9)
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the time to fly between new york city and chicago is uniformly distributed with a minimum of 66 minutes and a maximum of 100 minutes. what is the probability that a flight is less than 71 minutes? a) 1.00 b) 0.15 c) 0.07 d) 0.00
The probability that the flight is less than 71 minutes is 0.1471
Let the distribution of the time to fly between New York City and Chicago be X
X~U(66,100)
where,
66 = minimum
100 = maximum
We need to find P(X<71)
We know that in the case of uniform distribution,
P(X<x) = (x - a) / b -a
where,
a = min value
b = max value.
Hence P(X<71)
= (71 - 66) / (100 - 66)
= 5/34
= 0.1471
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a ball is thrown vertically upward from the ground with an initial velocity of 109 ft/sec. use h=−16t2 v0t h0.
Initial velocity of the function = 109 ft/sec.
The given quadratic function is-
h(t) = -16t² + 109t
maximum height;
dh/dt = 0 and d²h/dt² < 0.
Then,
dh/dt = -32t + 109
dh/dt = 0
-32t + 109 = 0
t = 3.4 seconds.
Time when maximum height is reached by the ball is 3.4 second.
Maximum height;
h(t) = -16(3.4)² + 109(3.4)
h(t) = 185.6 ft
Thus, the maximum height obtained by the ball is 185.6 ft.
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The complete question is-
A ball is thrown vertically upward from the ground with an initial velocity of 109 ft/sec. Use the quadratic function
h(t) = -16t2 + 109t to find how long it will take for the ball to reach its maximum height, and then find the maximum height.
the quality-control manager of a chemical company randomly sampled twenty 100-pound bags of fertil- izer to estimate the variance in the pounds of impuri- ties. the sample variance was found to be 6.62. find a 95% confidence interval for the population variance in the pounds of impurities.
The 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).
In the given question, the quality-control manager of a chemical company randomly sampled twenty 100-pound bags of fertilizer to estimate the variance in the pounds of impurities.
The sample variance was found to be 6.62.
We have to find a 95% confidence interval for the population variance in the pounds of impurities.
From the question,
N=20,
s^2=6.62
So, the Standard Deviation(SD) = √s^2
SD = √6.62
SD = 2.573
The confidence interval for the population variance is given by the following formula:
[tex]\frac{(n-1)s^2}{ \chi_{\alpha/2}} \leq\sigma^2\leq \frac{(n-1)s^2}{ \chi_{1-\alpha/2}}[/tex]
On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.
The next step would be calculating the critical values. First we need to calculate the degrees of freedom given by:
df = n-1
df = 20-1
df = 19
Since the Confidence is 0.95 or 95%, the value of α=0.05 and α/2=0.025, and we can use excel, a calculator or a table to find the critical values.
The excel commands would be: "=CHISQ.INV(0.025,19)" "=CHISQ.INV(0.975,19)".
So for this case the critical values are:
[tex]\chi_{\alpha/2}[/tex] = 32.852
[tex]\chi_{1-\alpha/2}[/tex] = 8.907
Now putting the value in the formula:
[tex]\frac{19\times6.62}{32.852}\leq\sigma^2\leq\frac{19\times6.62}{8.907}[/tex]
3.829≤σ^2≤14.121
So the 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).
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An investor invested a total of $2,300 in two mutual funds. One fund earned a 6% profit while the other eamed a 4% profit. If the investor's total profit was $102, how much was invested in each mutual fund?
The amounts in each mutual fund are $500 and $1800. By using a system of equations, the required values are evaluated.
What is a system of equations?The system of equations is a set of one or more equations that intersects at locations called solutions of the system.
The system of equations is solved for solutions in three different methods. They are the Elimination method, Substitution method, and Graphing method.
Calculation:It is given that, an investor invested $2300 in two mutual funds.
Consider the amount invested in two mutual funds as fund1 = x and fund2 = y.
So, we can write the equation for the total investment is
x + y = 2300 ...(1)
The percentage of profit earned from the fund1 = 6% = 0.06
The percentage of profit earned from the fund2 = 4% = 0.04
The total profit for the investor = $102
Then, the equation from this statement is
0.06x + 0.04y = 102 ...(2)
Then the system of equations is
x + y = 2300 ...(1)
0.06x + 0.04y = 102 ...(2)
Applying the substitution method to solve the obtained system of equations.
So, from (1), we can write x = 2300 - y
Then, equation (2) becomes
0.06(2300 - y) + 0.04y = 102
⇒ 6(2300 - y) + 4y = 10200
⇒ 13800 - 6y + 4y = 10200
⇒ 13800 - 2y = 10200
⇒ 2y = 13800 - 10200 = 3600
∴ y = 3600/2 = $1800
So, the value of x is x = 2300 - 1800 = $500
Thus, the amount of investment in two mutual funds is $500 and $1800.
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Geometry-need help i dont get it
Answer:
z = 11
Step-by-step explanation:
To find the answer we need to set up an expression with the two values they gave us:
8z = z + 77
This works because side IJ is the same length as side JK. So, all we have to do is solve for z:
8z = z + 77
-z - z
7z = 77
/7 /7
z = 11
