Find the area of the triangle with vertices: Q(2,-1,1), R(3,-2,-2), S(5,1,-1).

a) no, not congruent

b) yes, congruent

c) yes <K + <J = 180

d) yes, based on c

e) no, not congruent

According to the Empirical Rule (68-95-99.7% Rule), approximately 68% percent of the values will be between 75 and 85.

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

\(P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%\)

Here, we had  where mean of distribution of X is \(\mu\) and standard deviation from mean of distribution of X is \(\sigma\).

A distribution of scores on an aptitude test is Normally distributed with a mean of 80 and a standard deviation of 5.

\(\mu=80\\\sigma=5\)

The percentage for the interval of values between 75 and 85 has to be found out. From the 68%, the interval is,

\(P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(80 - 5 < X < 80+ 5) = 68\%\\P(75 < X < 85) = 68\%\)

Thus, according to the Empirical Rule (68-95-99.7% Rule), approximately 68% percent of the values will be between 75 and 85.

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The compound Inequality for the given graph is; -2 < x ≤ 6

The graph in the attached file shows conjunction. This means that the two statements of the inequality are equally true at the same time. Therefore, it follows that:

x > -2 ("we use greater than sign" because the empty/unshaded circle indicates that -2 is not included)

The second inequality will be;

x ≤ 6 (we use greater than or equal to sign because the shaded circle indicates 6 is included)

Joining both statements together, we would have the compound inequality written as:

-2 < x ≤ 6

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Research that provides data which can be expressed with numbers is called quantitative research.

Quantitative research is a type of research that focuses on gathering and analyzing numerical data. It involves collecting information or data that can be measured and quantified, such as numerical values, statistics, or counts. This research method aims to objectively study and understand phenomena by using mathematical and statistical techniques to analyze the data.

Quantitative research typically involves the use of structured surveys, experiments, observations, or existing data sources to gather information. Researchers often employ statistical methods to analyze the data and draw conclusions or make predictions based on the numerical findings.

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\(y=mx+b\\y=x-2\)

Only y= x - 2 intercepts x-axis at 2 and y-axis at -2. Thus meaning that they intercept oppositely.

Find if both graphs are parallel, that means the equation must be false.

\(x-2=-\frac{5}{2}x+5\)

Multiply whole equation by 2 to get rid of the fractional 2.

\(2x-(2)(2)=-\frac{5}{2}(2)(x)+5(2)\\ 2x-4=-5x+10\\2x-4+5x-10=0\\7x-14=0\\7x=14\\x=2\)

Well, that doesn't seem to be parallel. This is called one solution answer. Both graphs intercept at (2,0). There are no linear graphs that intercept at (2,-2) except for y = x-2 so there are no graphs with (2,-2) that are parallel to the equation y = -5x/2+5

The value of the missing length in the image shown using the Pythagoras theorem is x = 1500

An equation is an expression that shows the relationship between two or more variables and numbers.

Let h represent the missing red line. Using Pythagoras:

x² = h² + 900²

h² = x² - 900²

Also:

r² = h² + 1600²

r² = x² - 900² + 1600²

And:

(1600 + 900)² = r² + x²

(1600 + 900)² = (x² - 900² + 1600²) + x²

x = 1500

The value of the missing length in the image shown using the Pythagoras theorem is x = 1500

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Answer:

∆y = 95 ft

the vertical distance the shark travels is 95 ft

Step-by-step explanation:

Given;

Initial position y1= 80 ft below the surface of water = -80ft

Final Position y2 = 15 ft above the surface = +15ft

The vertical distance travelled by the shark is;

∆y = y2 - y1 = 15 - (-80) ft

∆y = 15 +80 ft

∆y = 95 ft

the vertical distance the shark travels is 95 ft

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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Answer:

A (25)

Step-by-step explanation:

Pythagorean Theorm

\(7^{2} +24^{2} =x^{2}\)

Please vote brainliest!!!

Answer:

\( \frac{ {m}^3{} }{25} \)

Step-by-step explanation:

that is the answer

Answer:

Step-by-step explanation:

y=30x+65

y=30(3)+65

y=90+65

y=155

Answer:

The answer is: 9.50

Answer: $18.19

Step-by-step explanation:

Answer:

18 sticks will be the answer

hope this is helpful ^_^

Answer:

A. Length of the larger cake = 10.2 inches

B. Height of the larger cake = 5.1 inches

C. Volume scale factor = 4.91 : 1 or approximately 5 : 1

Note: The question is incomplete. The complete question is given below:

You work for a catering company making cakes. The catering company must create a hexagonal cake for a tool company. Your company currently makes a small cake that is hexagonal and serves 8 people. The tool company wants one cake to serve 40 people. To feed that many the length of each dimension of the larger cake will be about 1.7 times that of the smaller cake. Each edge of the small cake is 6 inches and the height of the cake is 3 inches.

a. What is the length of the edge of the larger cake?

b. What is the height of the large cake?

c. Your boss wants to know the scale factor of the volume of the cakes so that he can make sure you have enough materials to create the cake. What is the scale factor for the volume?

Step-by-step explanation:

Since  the length of each dimension of the larger cake will be about 1.7 times that of the smaller cake:

a. Length of the edge of smaller cake = 6 inches

Length of the larger cake will be 6 * 1.7 = 10.2 inches

b. Height of the smaller cake = 3 inches

Height of the larger cake will be 3 * 1.7 = 5.1 inches

c. Volume  of a hexagon = 3/2 × √3 × s² × h; where s is length of one side, h is height

Volume of the smaller cake = 3/2 * √3 * 6² * 3 = 349.06 in³

Volume of larger cake = 3/2 * √3 * 10.2² * 5.1 = 1714.94 in³

Volume scale factor = 1714.94/349.06 = 4.91 or approximately 5:1

Answer:

Step-by-step explanation:

Answer:

23a + 9b + 9c

Step-by-step explanation:

9a + 6b + 3b + 14a + 9c ( collect like terms )

= (9 + 14)a + (6 + 3)b + 9c

= 23a + 9b + 9c

-7x+4>-10

cancel out 4 by subtracting on both sides

-7x>-14

Now divide

-7x>-14

/-7  /-7

x>2

---

hope it helps

Logical Error: In computer programming language, a logic error is a bug or in a program or code that causes it to operate incorrectly, but not to terminate abnormally (or crash).

A logic error developed unintended or undesired output or other behavior, although it may not immediately be recognized as such.

For example, assigning a value to the wrong variable may cause a many of unexpected program errors.

These errors can be programmer mistakes or sometimes machine less memory to load the code.

if(x>=5) {

// program

}

else if(x==5) {

//program

}

else(x<=5) {

//program

}

they all do not give any error.

x=5 gave an error because it is value assigning to 5.

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in slope intercept form:

y=mx+b.

slope of line:

-3/4

y intercept:

(0, 5/2)

Therefore, P(X >= 5) = 1 - P(X < 5) ≈ 0.76, or 76%. This simulation design can be implemented using a computer program or a physical device, such as a spinner or a dice.

To find the probability that it will take at least 5 customers to find one who buys chocolate ice-cream, we can use the geometric distribution, which models the number of trials needed to get the first success in a series of independent trials.

Let p be the probability of success (i.e., the probability that a customer buys chocolate ice-cream), which is 0.3. Then, the probability that it will take at least 5 customers to find one who buys chocolate ice-cream is given by:

P(X >= 5) = 1 - P(X < 5)

where X is the number of trials needed to get the first success.

Using the formula for the geometric distribution, we can calculate P(X < 5) as follows:

P(X < 5) = (1 - p)^4 = (1 - 0.3)^4 ≈ 0.24

Therefore, P(X >= 5) = 1 - P(X < 5) ≈ 0.76, or 76%.

For simulating this problem, we can use a random number generator to simulate the outcomes of each trial, where success corresponds to a customer buying chocolate ice-cream, and failure corresponds to a customer not buying chocolate ice-cream. We can repeat this process until we get the first success and count the number of trials needed.

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Here, we use the property of multiplication of exponential expression which states when we multiply two exponential expressions with the same base, we keep the base and add the exponents.

Therefore,

\(x^(3+5) = x^8\)

Now,

\(x^(3+5) = x^8\)

is of the form:

\(x^b = x^p\)

When we have two equal expressions on either side of the equation, the power of the base remains the same. Therefore,

p = 8

There we have it. The value of p is 8. The full solution is shown below:

\(x^3 × x^5 \\= x^px^8\\ = x^p\)

We can see that the base of the exponential expression on either side is equal.

Therefore, the power of the base must be equal as well. In other words

,p = 8.

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Step-by-step explanation:

¹/25y²-81

(⅕y)²-9². apply a²-b²=(a+b)(a-b)

(⅕y+9)(⅕y-9)

hope this helps you.

Answer:

ummm

Step-by-step explanation:

Answer:

29.50

Step-by-step explanation:

Thus, the height of the water in the tank is increasing at a rate of approximately 4 / (9π) meters per minute

To solve this problem, we need to find the rate at which the height of the water is increasing. Let's call the height of the water in the tank h(t), and the rate at which it is increasing dh/dt. We know that the volume of a cylinder is given by the formula\( V = πr^2h\), where V is the volume, r is the radius, and h is the height.
Given information:
- The radius of the cylindrical tank, r, is 3 m.
- The volume of water, V, is being filled at a rate of 4 m^3/min.
We want to find dh/dt. First, we need to find the expression for the volume of the water in the tank with respect to time, V(t):
V(t) = π(3)^2*h(t)
V(t) = 9π*h(t)
Now, we can find the derivative of V(t) with respect to time:
dV/dt = 9π*dh/dt
We know that dV/dt = 4 m^3/min. Therefore:
4 = 9π*dh/dt
Now, we can solve for dh/dt:
dh/dt = 4 / (9π)

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The recursive formula for Lindsey's scores is aₙ = aₙ₋₁ \(\times\) r, and the explicit formula is aₙ \(= 67 \times r^{(n-1).\)

To find the recursive and explicit formulas for the given geometric sequence, let's analyze the pattern of Lindsey's scores.

From the given information, we can observe that Lindsey's scores are increasing at the same rate.

This suggests that the scores form a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio.

Let's denote the first term as a₁ = 67 and the common ratio as r.

Recursive Formula:

In a geometric sequence, the recursive formula is used to find each term based on the previous term. In this case, we can write the recursive formula as:

aₙ = aₙ₋₁ \(\times\) r

For Lindsey's scores, the recursive formula would be:

aₙ = aₙ₋₁ \(\times\) r

Explicit Formula:

The explicit formula is used to directly calculate any term of a geometric sequence without the need to calculate the previous terms.

The explicit formula for a geometric sequence is:

aₙ = a₁ \(\times r^{(n-1)\)

For Lindsey's scores, the explicit formula would be:

aₙ \(= 67 \times r^{(n-1)\)

In both formulas, 'aₙ' represents the nth term of the sequence, 'aₙ₋₁' represents the previous term, 'a₁' represents the first term, 'r' represents the common ratio, and 'n' represents the term number.

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The Bessel's differential equation are:

4xu'' + 4xu' + zu = 0

x³u'' + z - v⁴xu = 0

(a) Starting with the equation: y" + k²x²y = 0

Let's make the substitution y = u\(x^{(1/2)\) and (1/2)kx² = z.

First, we need to find the derivatives of y with respect to x:

y' = (1/2)u\(x^{(-1/2)\) + u'\(x^{(1/2)\)

y" = -(1/4)u\(x^{(-3/2)\) + (1/2)u'\(x^{(-1/2)\) + (1/2)u'\(x^{(1/2)\) + u''\(x^{(1/2)\)

Simplifying, we have:

y" = -(1/4)u\(x^{(-3/2)\) + u'\(x^{(-1/2)\) + u''\(x^{(1/2)\)

Now, substitute these expressions into the original equation:

-(1/4)u\(x^{(-3/2)\) + u'\(x^{(-1/2)\) + u''\(x^{(1/2)\) + k²x²u\(x^{(1/2)\) = 0

Next, simplify the equation by multiplying through by 4\(x^{(3/2)\) to eliminate the fractional powers:

-u + 4xu' + 4xu'' + 4k²\(x^{(5/2)\)u = 0

4xu'' + 4xu' + (4k²\(x^{(5/2)\) - 1)u = 0

Finally, let z = 4k²\(x^{(5/2)\) - 1, which simplifies the equation to:

4xu'' + 4xu' + zu = 0

This is the Bessel's differential equation.

(b) Starting with the equation: x²y" + (1 - 2v)xy² + v²(x²v + 1 - v²)y = 0

Let's make the substitution y = xu and x¹ = z.

First, we need to find the derivatives of y with respect to x:

y' = u + xu'

y" = 2u' + xu''

Now, substitute these expressions into the original equation:

x²(2u' + xu'') + (1 - 2v)xu² + v²(x²v + 1 - v²)xu = 0

2x²u' + x³u'' + xu² - 2vxu² + v²x³u + v²xu - v⁴xu = 0

x³u'' + (2x²u' - 2vxu² + v²x³u + v²xu - xu²) - v⁴xu = 0

Now, let z = 2x²u' - 2vxu² + v²x³u + v²xu - xu², which simplifies the equation to:

x³u'' + z - v⁴xu = 0

This is the Bessel's differential equation.

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Answer:

the area is 6

Step-by-step explanation:

Answer:

25 oz.

Step-by-step explanation:

4.5+5.01+5.3+4.75+4.9=24.46

Answer:

25 oz

Step-by-step explanation: