A certain amusement park ride requires riders to be at least 48 inches tall. If the heights of children in a summer camp are normally distributed with mean 52 and standard deviation 2.5, how many of the 140 campers will be allowed on the ride? Round to the nearest integer.

Answer:

It is a Quadralateral

Step-by-step explanation:

Answer:

quadralatural

Step-by-step explanation:

Volume = length x width x height.

4 x 1/2 = 2

2 x 3/2 = 3

colume = 3 cubic cm

Answer:

  \(\dfrac{\sqrt[3]{95^2}}{17\cdot95^4}=\dfrac{\sqrt[3]{9\,025}}{1\,384\,660\,625}\)

Step-by-step explanation:

The applicable rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)/(a^c) = a^(b-c)

__

  \(\dfrac{190^3}{68^2}\times\dfrac{34}{95^{\frac{19}{3}}}=\dfrac{(2\cdot 95)^3}{(2\cdot 34)^2}\cdot\dfrac{34}{95^6\cdot 95^{\frac{1}{3}}}=2^{3-2}95^{3-6-\frac{1}{3}}34^{1-2}\\\\=2\cdot 95^{-3\frac{1}{3}}\cdot 34^{-1}=2\cdot 95^{-4+\frac{2}{3}}\cdot 34^{-1}\\\\=\dfrac{2\sqrt[3]{95^2}}{95^4\cdot 34}=\dfrac{\sqrt[3]{95^2}}{17\cdot95^4}\\\\=\dfrac{\sqrt[3]{9\,025}}{1\,384\,660\,625}\)

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question

slope / m = 4/7

y intercept / c = 3

Substitute the values into the above formula

We have the equation as

\(y = \frac{4}{7} x + 3 \\ \)

Hope this helps you

Answer:

\(\boxed {\tt y=\frac{4}{7}x+3}\)

Step-by-step explanation:

Slope-intercept form is:

\(y=mx+b\)

where m is the slope and b is the y-intercept.

We know the slope is 4/7 and the y-intercept is (0,3). In this form, we can say the y-intercept is just 3. Therefore,

\(m=\frac{4}{7}\\b= 3\)

Substitute the values into the form.

\(y=\frac{4}{7} x+3\)

The equation of the line is:

y=4/7x+3

Answer:

The value 0.031 represents the interest rat, which means the annual compounded interest rate is 3.1%

First option

Step-by-step explanation:

The general equation for amount accrued A with a principal P at an annual compound interest rate of i%(r/100 in decimal) compounded n times a year for t years is given by

\(A = P\left(1 + \dfrac{r}{n}\right)^{nt}\)

Here r = i/100 which is a decimal

Looking at the specific equation
\(A = 2400\left(1 + \dfrac{0.031}{4}\right)^{4t}\)

we can see that P = 2440, the initial investment

0.031 is the annual interest rate in decimal

Expressed as percentage that would be 0.031 x 100 = 3.1% per year

So the correct answer is the first option which states
The value 0.031 represents the interest rat, which means the annual compounded interest rate is 3.1%

I. The solution to the system of equations using Gaussian elimination is x = 1, y = -1, and z = 2.

II. For the LU-decomposition method, we need to have a square coefficient matrix, which is not the case in the given system. Therefore, we cannot directly apply the LU-decomposition method.

III. For this method to converge, the coefficient matrix must be diagonally dominant, which is not the case in the given system. Therefore, the Gauss-Jacobi method cannot be directly applied either.

IV. It requires the coefficient matrix to be diagonally dominant, which is not satisfied in the given system. Hence, the Gauss-Seidel method cannot be directly used.

I. Gaussian Elimination Method:

To solve the system of linear equations using Gaussian elimination, we perform row operations to reduce the system into upper triangular form. The augmented matrix for the given system is:

| 6 2 -1 | 4 |

| 1 5 1 | 3 |

| 2 1 4 |27 |

We can start by eliminating the coefficients below the first element in the first column. To do this, we multiply the first row by a suitable factor and subtract it from the second and third rows to eliminate the x coefficient below the first row. Then, we proceed to eliminate the x coefficient below the second row, and so on.

After performing the necessary row operations, we obtain the following reduced row-echelon form:

| 6 2 -1 | 4 |

| 0 4 2 | -1 |

| 0 0 3 | 6 |

From this form, we can easily back-substitute to find the values of x, y, and z. We have z = 2, y = -1, and x = 1.

II. LU-Decomposition Method:

LU-decomposition is a method that decomposes a square matrix into a product of two matrices, L and U, where L is lower triangular and U is upper triangular.

III. Gauss-Jacobi Method:

The Gauss-Jacobi method is an iterative numerical method to solve systems of linear equations.

IV. Gauss-Seidel Method:

Similar to the Gauss-Jacobi method, the Gauss-Seidel method is an iterative method for solving linear systems.

Therefore, out of the four methods mentioned, only the Gaussian elimination method can be used to solve the given system of linear equations.

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The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

The number of terms in a polynomial helps when performing operations like simplification, factoring, or evaluating expressions.

The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

In order to determine the number of terms in a polynomial, we count the number of distinct algebraic expressions separated by addition or subtraction operations.

In this polynomial, we have:

Term 1: 18x³ (This is the term with the highest degree, which is 3 in this case, and it includes the coefficient 18.)

Term 2: -2x² (This term has a degree of 2 and a coefficient of -2.)

Term 3: 4x (This term has a degree of 1 and a coefficient of 4.)

Term 4: -1 (This is a constant term with a degree of 0.)

We can see that there are four distinct terms separated by addition and subtraction operations:

18x³, -2x², 4x, and -1.

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Answer:

Step-by-step explanation:

i belive its 3

Answer:

the person above me stole my answer

Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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The average movie ticket cost in Switzerland and Japan each of these​ countries is 46.97.

Let's assume that the average cost of a movie ticket in Japan is x, and the average cost of a movie ticket in Switzerland is y.

According to the problem statement, we can write two equations based on the given information:

3x + 2y = 78.5 ...(1)

2x + 3y = 74.1 ...(2)

We can solve these equations simultaneously to find the values of x and y. Here's how:

Multiply equation (1) by 2 and equation (2) by 3, then subtract equation (1) from equation (2):

(2x + 3y) - 2(3x + 2y) = 74.1 - 2(78.5)

Simplifying this equation, we get:

-y = -109.3

Therefore, y = 109.3.

Now substitute y = 109.3 into either equation (1) or (2) and solve for x:

3x + 2(109.3) = 78.5

Simplifying this equation, we get:

3x = -140.9

Therefore, x = -46.97.

However, we cannot have negative ticket prices.

Therefore, the average cost of a movie ticket is 46.97.

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The transformation is a translation (x + 7, y + 4) plus a dilation of scale factor 2.

We know that Circle 1 is centered at (-3,-2) and has a radius of 2 centimeters, and Circle 2 is centered at (4,2) and has a radius of 4 centimeters.

The radius of circle 2 is twice the radius of circle 1, then we need to have a dilation of scale factor 2.

Now let's apply a translation of (a, b) units such that:

(-3 + a, -2 + b) = (4, 2)

(a, b) = (4 + 3, 2 + 2)

(a, b) = (7, 4)

Then we have the translation (x + 7, y + 4) plus a dilation of scale factor 2.

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Answer:

7hrs 35mins

Step-by-step explanation:

addition 2hrs 15 mins +5hrs 20 mins

Answer:

x=5

Step-by-step explanation:

Answer : x = 5

3(х-2)= 9

(3)(x) - (3)(2) = 9

3x - 6 = 9

3x = 9 + 6

x = 15 ÷ 3

x = 5 Answer.

Solution set: {5}

Hope that helps...

Answer:

f(x) = 0.5x

Step-by-step explanation:

For this problem, we simply have to find the constant of proportionality between x and f(x). In other words, what x is multiplied by to get f(x).

Since this proportion is constant (meaning it doesn't change), all we have to do is divide an f(x) value in the table by its corresponding x value.

p = f(x) / x

p = -2 / -4

p = 1/2 = 0.5

We can show the relationship of x to f(x) with the equation f(x) = px, which can be simplified using the constant of proportionality that we just solved for.

f(x) = 0.5x

Answer:

Bert is 11 years old and Max is 17 years old.

Step-by-step explanation:

System of Equations

To solve the system of equations, we use two variables x and y. Let's make:

x = current age of Max

y = current age of Bert

x - 5 = age of Max five years ago

y - 5 = age of Bert five years ago

x + 1 = age of Max one year from now

y + 1 = age of Bert one year from now

According to the conditions of the problem, five years ago, Max was twice as old as Bert, thus:

x - 5 = 2(y - 5)        [1]

It's also known a year from now, the sum of their ages would be 30:

x + 1 + y + 1 = 30        [2]

Operating and simplifying [1]:

x - 5 = 2y - 10

x = 2y - 5       [3]

Operating and simplifying [2]:

x + y + 2 = 30

x + y = 28        [4]

Substituting [3] in [4]:

(2y - 5) + y = 28

Simplifying:

3y - 5 = 28

3y = 33

y = 33/3 = 11

y = 11

From [3]:

x = 2*11 - 5

x = 22 - 5 = 17

x = 17

Max is 17 years old and Bert is 11 years old

The number of ways to choose the 5 colors from a set of 17 is given as follows:

a) Order matters: 742,560.

b) Order does not matter: 6,188.

When the order matters, the permutation formula is used, given as follows:

\(P_{n,x} = \frac{n!}{(n - x)!}\)

Giving the number of permutations of x elements from a set of n elements.

5 elements are chosen from a set of 17 elements, hence the number of permutations is given as follows:

P = 17!/12! = 742,560.

When the order does not matter, the combination formula is used, given as follows:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

With the same parameters, the number of ways is given as follows:

C = 17!/(12! x 5!) = 6,188.

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The probability of selecting 50 jars is 0%

The z score determines by how many standard deviations the raw score is above or below the mean. It is given by:

\(z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where \mu=mean,\sigma=standard\ deviation, x=raw\ score,n=sample\ size\\\\Given\ that\ \mu=17,\sigma=0.68,n=50,x=16.8\\\\z=\frac{16.8-17}{0.65/\sqrt{50} } =-5\)

The P(z < -5) = 0%

Therefore the probability of selecting 50 jars is 0%

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Answer:

(1) Conjugate = -i8

(2) Conjugate = -i3+9

(3) Conjugate = i2+1

(4) Conjugate = -3-iy

Step-by-step explanation:

From the question,

Conjugate of a surd is formed by changing the sign between a rational number and a surd in an expression.

The conjugate of a surd is obtained by changing the sign of the surd in the expression.

Given

(1) i3+i5 = i8

Conjugate is -i8

(2) i3+9

Conjugate is -i3+9

(3) -i2+1

Conjugate is i2+1

(4) -3+iy

Conjugate is -3-iy

The perimeter of the rhombus in this problem is given as follows:

19.8 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The diagonal length can be obtained as follows:

RU + UT = 7.

Applying the Pythagorean Theorem, the side length is obtained as follows:

x² + x² = 7²

2x² = 49

\(x = \sqrt{\frac{49}{2}}\)

x = 4.95.

Then the perimeter is given as follows:

P = 4 x 4.95

P = 19.8 units.

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Answer:

14,200,000

Step-by-step explanation:

Answer:

There are 1,365 souvenir paperweights that need to be packed in boxes. Each box will hold 14 paperweights. How many boxes will be needed?

boxes will be needed to hold all the souvenir paperweights.

Step-by-step explanation:

The value of R(A) = 4, N(AT ) = 3, R(AT ) = 4, and N (A) = 3.

Given that

Dimension of matrix  = 7×5

Rank of matrix = 4

The range space of A,

Which is a subspace of R, is known as R(A).

It is made up of all conceivable linear combinations of A's columns.

The dimension of R(A) =  rank of A,

Which is 4 in this case.

The null space of the transpose of A,

Which is also a subspace of R, is designated as N(AT).

All potential answers to the equation ATx = 0,

Where x is a R column vector, are included in it.

N(AT) has a dimension = nullity of A,

which in this case is 3 in this example.

The range space of the transposition of A, is designated as R(AT).

The rows of A are arranged in all conceivable linear configurations.

The rank of A = 4

Thus it equal to dimension of R(AT).

N(A) is the null space of A.

Axe = 0, where x is a column vector in R, are included in it.

The nullity of AT, which is three, is likewise equivalent to the dimension of N(A).

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Answer:

David= 30

Maria= 15

Trey= 20

Step-by-step explanation:

If David sent 30 messages, then half as as many as that would be 15, the amount that Maria sent. 5 more than what Maria would be what Trey sent, 20.

A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:

(x, y)                                              →                 (-x, y).

\(f(x) = \frac{3}{8} (4)^x\)                               →              \(g(x) = \frac{3}{8} (4)^{-x}\)

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\({\large\begin{gathered} { \underbrace{\boxed { \rm {\blue {Concept \: \: Using}}}}}\end{gathered}}\)

The angle sum property of a triangle:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°

\( \underline {\mathcal {{{\color{orange}{\bf \large \rightarrow \: \angle \: 1 \: + \: \angle \: 2 \: + \: \angle \: 3 \: = \: 180 \degree}}}}} \)

\({\large\begin{gathered} { \underbrace{\boxed { \rm {\blue {Solution}}}}}\end{gathered}}\)

.

\(\bf \large\longrightarrow \: \: 50 \degree \: + \: 70 \degree \: + \: x \: = \: 180 \degree\)

\(\bf \large\longrightarrow \: \:120 \degree \: + \: x \: = \: 180 \degree\)

\(\bf \large\longrightarrow \: \: x \: = \: 180 \degree \: - \: 120 \degree\)

\(\bf \large\longrightarrow \: \: x \: = \: 60\degree\)

\(\bf \large\longrightarrow \: \: x \: + \: 60 \degree \: + \: 60 \degree \: = \: 180 \degree\)

\(\bf \large\longrightarrow \: \: x \: + \: 120 \degree \: = \: 180 \degree\)

\(\bf \large\longrightarrow \: \: x \: = \: 180 \degree \: - \: 120 \degree\)

\(\bf \large\longrightarrow \: \: x \: = \: 60\degree\)

Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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Answer:

The trigonometric ratios associated with (-5, -4) are \(\sin t \approx -0.625\), \(\cos t \approx -0.781\) and \(\tan t = 0.8\).

Step-by-step explanation:

Let \(\vec u = (x,y)\). From Trigonometry, we remember the following definitions for the trigonometric ratios, dimensionless:

\(\sin t = \frac{y}{\sqrt{x^{2}+y^{2}}}\) (1)

\(\cos t = \frac{x}{\sqrt{x^{2}+y^{2}}}\) (2)

\(\tan t = \frac{y}{x}\) (3)

If we know that \(x = -5\) and \(y = -4\), then the trigonometric ratios are, respectively:

\(\sin t = \frac{-4}{\sqrt{(-5)^{2}+(-4)^{2}}}\)

\(\sin t \approx -0.625\)

\(\cos t = \frac{-5}{\sqrt{(-5)^{2}+(-4)^{2}}}\)

\(\cos t \approx -0.781\)

\(\tan t = \frac{-4}{-5}\)

\(\tan t = 0.8\)

The trigonometric ratios associated with (-5, -4) are \(\sin t \approx -0.625\), \(\cos t \approx -0.781\) and \(\tan t = 0.8\).