length of 6.6 meters. The width of it is 6 times shorter. What is the width?

Answer:

36 different salads can be ordered

Step-by-step explanation:

Answer:

x=-8, y=-1

Step-by-step explanation:

i aint in middle school no more so im not sure what operation ur doing, but this is my best guess.

3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

3⁴ / 3³ = (3 × 3 × 3 × 3) / (3 × 3 × 3) = 3

This means that 3⁴ is 3 times larger than 3³.

5³ is 5 times larger than 5².

5³ / 5² = (5 × 5 × 5) / (5× 5) = 5

7¹⁰ is 49 times larger than 7⁸.

7¹⁰/ 7⁸ = 7² =49

17⁶ is 289 times larger than 17⁴.

17⁶ /17⁴ = 289

Hence, 3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

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9 boxes *24 candybars = 216 candybars

$6* 216 candy bars = $1,296

Answer:

Step-by-step explanation:

Start with the piecewise definition of the absolute value function

y = f(x) = |x|

\(f(x) = \left \{ {f(x);\;{x\ge=0} \atop {{-f(x);\;{x < 0}} \right.\)

Substitute x + 5 for f(x)
\(|x+5| = \left \{ {x+5;\;{x+5\ge=0} \atop {{-(x+5);\;{x + 5 < 0}} \right.\)

Note that at x = 5, |x + 5| = 0 and therefore we have a unique point (-5, -2). This is where the function changes

Simplify the inequalities
x + 5 ≥ 0  ==> f(x) =  x ≥ -5

-(x+5) < 0 ==> -x -5 < 0 = -x < 5 or x >=5

Separate the two pieces
y = (x + 5); x ≥ -5
y = -x - 5; x < -5

Subtract 2 from both sides of the function
y = (x + 5) - 2 when x ≥ -5  or y = x + 3 when x ≥ -5

y = -x - 5 - 2 when x < -5   or y = - x - 7 when x < -5

Correct answer choice is the  last one
y = x + 3 for x ≥ -5 and y = -x -7 for x < -5

If you look at the attached graph of y = |x| -2  you will see this is consistent with the above piecewise function

For example at x = -3 which is greater than x = -5, y = 0 and x+3 = -3 + 3 = 0

At x = -7 which is less than -5, also y = 0 and -x -7 = -(-7) - 7 = 7-7 = 0

Answer:

The answer would be the first choice ; sides jh and tr are congruent

The fundamental theorem of arithmetic states that every natural number greater than 1 can be written as a product of primes. Using strong induction, we can prove this.

Let's proceed with the strong induction proof. We start by considering the base case, where m = 2. Since 2 is prime, it can be written as a product of primes itself.

Next, we assume that for all natural numbers k such that 2 ≤ k ≤ m, the statement holds true, i.e., k can be expressed as a product of primes. Now, we aim to prove that m+1 can also be expressed as a product of primes.

We know that m+1 is either prime itself or composite. If m+1 is prime, then it can be written as a product of a single prime, satisfying the theorem.

On the other hand, if m+1 is composite, it can be written as a product of two positive integers a and b, where 2 ≤ a ≤ b ≤ m. Since a and b are both less than or equal to m, we can apply the inductive hypothesis to express a and b as products of primes. Therefore, we can write m+1 as a product of primes by combining the prime factorizations of a and b.

By strong induction, we have shown that for any natural number m greater than 1, it can be expressed as a product of primes. This completes the proof of the fundamental theorem of arithmetic.

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The length of each side of the box is 10 centimeter.

Volume is the amount of space occupied by a three-dimensional figure as measured in cubic units.

Given,

The volume of the cubic box = 1 liter

We know 1 liter= 1000 cubic centimeter

Volume of the cubic box= \(x^3}\)

Then,

\(x^{3}=1000\\ x=\sqrt[3]{1000}\)

x=10 centimeter

Hence, the length of each side of the box is 10 centimeter.

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Answer:

See below ↓

Step-by-step explanation:

Information we need

Solving

The probability that we will roll exactly one number exactly three times is 125/7776.

Given a fair die is rolled six times.

A fair die has 6 faces, hence, the sample space will be {1, 2, 3, 4, 5, 6}

So, on rolling a die thrice, the number of elements in sample space is

6⁶ = 46,656

Let us assume that the die in the first roll shows 3, hence the second die and third die can show any of the other 5 numbers.

First, the probability of rolling a single value (in this case 3) on a fair 6-sided die would be one out of six = 1/6

The probability of NOT rolling that number would be five out of six.

Let P be the probability of getting 3 only once

P= 1/ 6 × 1/6 × 1/6 × 5/6 × 5/6 × 5/6 = 125/46656

The number 3 can be showed in any of the six dies at a time

Hence required probability ,

= 125/46656 + 125/46656 + 125/46656 + 125/46656 + 125/46656 + 125/46656  

= 750/46656

P = 125/7776

Therefore, the probability that exactly one 3 is rolled is 125 / 7776.

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After evaluating the given logical expression, we find that the value of the Boolean variable "b" is false.

The value of the Boolean variable "b" can be found by evaluating the given logical expression.

Given:

int x = 3;

int y = 4;

int z = 2;

boolean b = !((x > y) || ((y + z) >= (x - z)))

Let's break down the expression step by step:

1. Evaluate the sub-expression (x > y):

  Since x is 3 and y is 4, the expression (x > y) evaluates to false.

2. Evaluate the sub-expression ((y + z) >= (x - z)):

  We have y = 4, z = 2, and x = 3.

  Substituting the values, the expression ((y + z) >= (x - z)) becomes (4 + 2) >= (3 - 2), which simplifies to 6 >= 1.

  Thus, this sub-expression evaluates to true.

3. Negate the result of the entire expression:

  Since the expression ((x > y) || ((y + z) >= (x - z))) evaluates to false || true, which is true.

  Negating true gives us false.

Therefore, the value of the Boolean variable "b" is false.

In conclusion, after evaluating the given logical expression, we find that the value of the Boolean variable "b" is false.

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Given,

The initial balance in the checkbook is $463.18.

The deposite money is $265.

The amount of check is $198.73.

The charge paid for bank is $2.50.

The ending balance at the month end is,

Hence, option b ($526.95) is correct.

Answer:

So if 25% of the people go to work by bicycle then that means that 75% of people go to work by other means of transportation.

Therefore the odds against selecting someone who commutes by bicycle are 75% or 75/100 or 0.75.

Step-by-step explanation:

The odds against selecting someone who commutes by bicycle are 75%

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that In a certain town, 25% of people commute to work by bicycle. If a person is selected randomly from the town.

25% of the people go to work by bicycle then which means that 75% of people go to work by other means of transportation.

Therefore the odds against selecting someone who commutes by bicycle are 75% or 75/100 or 0.75.

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Answer:

x + x-1 + x-2 + x-3 =54.

x-1

Answer:

15

Step-by-step explanation:

Let the consecutive numbers be x, x + 1, x + 2, x + 3

==========

Greatest of the 4 integers:

The system can be solved using Gauss-Jordan method in a few steps.

Following is the step-by-step solution for the given system of equations

.2xy + 3z = 0 ...(1)     x + y + 3z = 3 ...(2)    x - 2y = -3 ...(3)

Using equations (1), (2) and (3), we can write the following matrix equation and use Gauss-Jordan method to solve the system.

[2xy 3z | 0][x y z | 3][x - 2y 0 | -3]

Subtracting equation (1) from (2),

we get

x + y + 3z - 2xy - 3z = 3 - 0

=> x + y - 2xy = 3 ...(4)

Adding equation (3) to (4), we get

2x - y - 2xy = 0

=> 2x - y(1+2x) = 0

=> y = 2x / (1+2x)

Substituting this value of y in equation (4),

we get

x + 2x / (1+2x) - 2x(2x / (1+2x)) = 3

=> x + 2x / (1+2x) - 4x^2 / (1+2x) = 3

=> (1+2x)(3x + 2) - 4x^2 = 3(1+2x)

=> 3x^2 - 4x + 3 = 0

Using quadratic formula,

we get

x = [4 ± sqrt(16 - 4*3*3)] / 6x

= [4 ± 2] / 6

=> x = 1 or x = 1/3

Substituting x = 1 in equation (4), we get y = 2/3 and using this in equation (2), we get z = 1.

Substituting x = 1/3 in equation (4), we get y = 1/5 and using this in equation (2), we get z = 8/5.

Hence, the solution of the system of equations is (x, y, z) = (1, 2/3, 1) or (1/3, 1/5, 8/5).

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To determine the moment of inertia of the area about the x-axis using rectangular differential elements, we can solve the problem in two ways: (a) with a thickness dx and (b) with a thickness dy. Here is a step-by-step explanation of both approaches:

(a) Using rectangular differential elements with thickness dx:

Divide the given area into small rectangular strips parallel to the x-axis, each having a width dx.

Consider a rectangular strip at a distance y from the x-axis, with a length L (in the y-direction) and a thickness dx.

The area of this rectangular strip is dA = L * dx.

The moment of inertia of this rectangular strip about the x-axis is given by dI = y^2 * dA = y^2 * L * dx.

Integrate the differential moments of inertia over the entire area to find the total moment of inertia about the x-axis: Ix = ∫y^2 * dA.

(b) Using rectangular differential elements with thickness dy:

Divide the given area into small rectangular strips parallel to the y-axis, each having a width dy.

Consider a rectangular strip at a distance x from the y-axis, with a length W (in the x-direction) and a thickness dy.

The area of this rectangular strip is dA = W * dy.

The moment of inertia of this rectangular strip about the x-axis is given by dI = x^2 * dA = x^2 * W * dy.

Integrate the differential moments of inertia over the entire area to find the total moment of inertia about the x-axis: Ix = ∫x^2 * dA.

In both cases, the integrals are evaluated over the appropriate limits of integration based on the given area and its dimensions. The resulting integrals will give the moment of inertia of the area about the x-axis using the respective methods.

The specific dimensions and shape of the area need to be provided to calculate the moment of inertia using either of these methods.

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Answer:

Therefore, the approximate monthly payment is $548.85

Step-by-step explanation:

The amount of student loans Erica currently has = $34,006.00

The duration over which Erica is to pay back the loan = 7 years

The annual interest rate for the loan = 9.1%

Therefore, we have the geometric sequence formula is given as follows;

\(A_n = P( 1 + r)^n - M \times \left [ \dfrac{(1 + r)^n-1}{r} \right ]\)

Where;

M = The monthly payment

P = The initial loan balance = $34,006.00

r = The annual interest rate = 9.1%

n = The number of monthly payment = 7 × 12 = 84

Aₙ = The amount remaining= 0 at the end of the given time for payment

Substituting the values into the above formula, , we get;

\(0 = 34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} - M \times \left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ]\)

\(M = \dfrac{34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} }{\left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ]} \approx 548.85\)

Therefore, the approximate monthly payment = $548.85

Unit Rate = 3 dollars/pound

D P

3 1

6 2

12 4

Unit Rate = 1/3 dollars/pound

p = 3d

Unit Rate = 9 dollars/pound

1/3 dollars/pound

&

D P

1    1/9

9     1

18    2

Based upon this information, the value of the test statistic is 0.23.

The term "test statistic" refers to a quantity obtained from the sample and used in statistical hypothesis testing.

The sample proportion, or ratio of the sample size to the number of "yes" responses (23), would be the test statistic in this situation (100). The sample proportion is computed in the following manner:

The test statistic is p = 23/100, or 0.23.

So, 0.23 is the test statistic. The percentage of dog owners that routinely feed their dogs Woof Chow dog food is represented by this sample estimate.

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Answer:

Step-by-step explanation:

Year >> Starting balance >>         prt            >>         Interest                      

1                    4200         4200*1.045 = 4389          4389 - 4200 = 189

2                   4389         4200*1.045² = 4586.51    4586.51 - 4200 = 386.51      

3                   4586.51     4200*1.045³ = 4792.90   4792.90 - 4200 = 592.90

4                   4792.90    4200*1.045⁴ = 5008.58   5008.58 - 4200 = 808.58

5                   5008.58    4200*1.045⁵ = 5233.96   5233.96 - 4200 = 1033.96  

6                   5233.96    4200*1.045⁶ = 5469.49   5469.49 - 4200 = 1269.49

Answer:

Angle 9 = 65°

Step-by-step explanation:

Given:

Angle 7 = 65°

Angle 7 is alternate to Angle 9

Find:

Angle 9

Computation:

We know that

alternate interior angles are equal and angle 7 is alternate to angle 9

So,

Angle 7 = Angle 9

So,

Angle 9 = 65°

Answer:

301.224 g

Step-by-step explanation:

Let's divide in the ratio 21:4 the volume of the medal (35cm^3)

copper = (21/25)(35cm^3) = 29.4cm^3

tin = (35 - 29.4)cm^3 = 5.6cm^3

FOR THE COPPER

8.84 : 1 = X : 29.4

X = 259.896(g)

FOR THE TIN

7.38 : 1 = X : 5.6

X = 41.328(g)

(259.896 + 41.328)g = 301.224 g

M = 5 - 4i

J = 3 + 2i

J* = -3 + 2i (Conjugate)

Therefore M + J*

= (5 + -3) + (-4i + 2i)

= 2 - 2i

the values of x in [0, 2π] where the graph of f(x) has a horizontal tangent are x = 2π/3, x = 4π/3, and x = π.

To find the values of x in [0, 2π] where the graph of f(x) = x + 2sin(x) has a horizontal tangent, we need to find where the derivative of the function is zero or undefined.

The derivative of f(x) is:

f'(x) = 1 + 2cos(x)

For the derivative to be zero, we need:

1 + 2cos(x) = 0

Solving for cos(x), we get:

cos(x) = -1/2

This is true when x = 2π/3 or x = 4π/3.

Now we need to check if the derivative is undefined at any point in the interval [0, 2π]. The derivative is undefined when cos(x) = -1, which occurs at x = π.

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Answer:

p=1/5

Step-by-step explanation:

Distribute -5 through the parenthese.

Move constant to the righ-hand side and change the sign.

Calculate the sum -5p=-1

Divide both sides by -5

Answer:

1/5

Step-by-step explanation:

Expand the equation

-5p -3= -4

Collect like terms

-5p = -4 +3

-5p = -1

Divide both sides by -5

p = 1/5

Answer:

The inequality for x is x > 36

(In interval notation form it is (36, ∞)

Step-by-step explanation:

Multiply to remove the fraction, then set equal to zero and solve.

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There is no significant difference in the average scores of two groups of SOC 390 students who took Exam 1 in the spring and fall semesters, respectively, as per the two-sample t-test with a p-value of 0.388.

The average score of the spring group of 50 students in SOC 390 on Exam 1 was 80, with a standard deviation of 12, while the average score of the fall group of 52 students was 81, with a standard deviation of 6. To determine if the difference in the means of the two groups is statistically significant, we can use a two-sample t-test.

Assuming unequal variances, the t-value for the two groups is 0.87, with a corresponding p-value of 0.388. Since the p-value is greater than the standard alpha level of 0.05, we fail to reject the null hypothesis that the two groups have equal means.

Therefore, we can conclude that there is no significant difference in the average scores of the two groups of SOC 390 students who took Exam 1 in the spring and fall semesters, respectively.

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The complete question is :

What is the difference between the average scores of two groups of students who took Exam 1 in SOC 390 in the spring and fall semesters, respectively, given that the spring group consisted of 50 students who scored an average of 80 with a standard deviation of 12, and the fall group consisted of 52 students who scored an average of 81 with a standard deviation of 6?