He is ordering the pizzas from a place that has 12 different topping options.
7 options are vegetarian and 5 are meats.
Write the ratio of vegetarian options to the total of options in three different ways

Answer:

Two events that are mutually exclusive when rolling two number cubes are:

Getting an odd number on the first cube and getting an even number on the second cube.

Getting a 1 on the first cube and getting a 2 on the second cube.

Two events that are not mutually exclusive when rolling two number cubes are:

Getting a 4 on the first cube and getting a 3 on the second cube.

Getting a 5 on the first cube and getting an odd number on the second cube.

Step-by-step explanation:

y = (x - 6) / 3 is the inverse function of f(x) and its domain is all real numbers.

The inverse of a function is a new function that "undoes" the original function. In other words, if the original function maps an input x to an output y, the inverse function maps the output y back to the input x.

To find the inverse of the function f(x) = 3x + 6, we need to solve for x in terms of y and then interchange x and y.

Starting with the function:

f(x) = 3x + 6

Replace f(x) with y:

y = 3x + 6

Solve for x:

y - 6 = 3x

x = (y - 6) / 3

Interchange x and y:

y = (x - 6) / 3

Hence, y = (x - 6) / 3 is the inverse function of f(x).

The domain of the inverse function is the range of the original function, which is all real numbers.

Therefore, the inverse function of f(x) = 3x + 6 is:

f⁻¹(x) = (x - 6) / 3

and its domain is all real numbers.

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Using the Central Limit Theorem, it is found that since the sample size is greater than 30, a normal approximation can be used, hence the test can be made.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

In this problem, the distribution of lengths is skewed, however, since the sample size is of 100 greater than 30, a normal approximation can be used, hence the test can be made.

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Answer:

The picture shows what you're looking for.

Step-by-step explanation:

Answer:

18 pencils in 3 packs.

Step-by-step explanation:

Assuming that each pack will have the same amount of pencils. It is given that there are 36 pencils in all when one has 6 packs. Find the amount in each pack by dividing (total amount of pencils)/(amount of packs) = Amount of pencils per pack:

36/6 = 6

There are 6 pencils in each pack.

Now, Elsa wants to know how much pencils are in 3 packs. Multiply the amount of packs with the amount of pencils in each pack:

Total amount of pencils = amount of packs (3) x amount of pencils per pack (6)

                                       = 3 x 6

                                       = 18

There are 18 pencils in 3 packs.

~

The solution to the problem is the simplified expression: 5x³ - x² - 3x + 13.

To solve the given problem, you need to simplify and combine like terms. Start by adding the coefficients of the same degree terms.

(3x³ - x² + 4) + (2x³ - 3x + 9)

Combine the like terms:

(3x³ + 2x³) + (-x²) + (-3x) + (4 + 9)

Simplify further:

5x³ - x² - 3x + 13

In this expression, the highest power of x is ³, and the corresponding coefficient is 5. The term -x² represents the square term, -3x represents the linear term, and 13 is the constant term. The simplified expression does not have any like terms left to combine, so this is the final solution.

Remember to check for any specific instructions or constraints given in the problem, such as factoring or finding the roots, to ensure you address all requirements.

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From the question;

we are given

Initial balance = $1,500.00 and a 2.50% interest

This implies that the

interest rate = 2.50%

We are to find the effective annual yield

The effective annual yield is calculated using

Where

r = interest rate

n = number of compounds per year

Therefore

r = 2.5%

n = 1

Hence

Therefore the effective annual yield is 2.5%

The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%

Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.

Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.

The total weight of a group of 16 individuals can be estimated as follows:

Total weight = 16 x average weight = 16 x 155 = 2480 pounds

To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:

Standard deviation of total weight = square root of (n x variance)

where n is the sample size (16) and variance is the square of the standard deviation (29 squared).

Standard deviation of total weight = square root of (16 x 29^2) = 232.74

Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:

Z-score = (2,500 - 2,480) / 232.74 = 0.86

Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.

Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.

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Answer:

5/26.

If you count y as a vowel it is 3/13

Step-by-step explanation:

After combining like terms to create equivalent expression we get (-1.9 + 1.2) + (5.1 - 3.6)t. Simplifying further, we get: -0.7 + 1.5t.

To combine like terms, we add or subtract the coefficients of the same variables. In this case, the variables are t and the constant terms (without variables) are -3.6, -1.9, and 1.2.

So the equivalent expression after combining like terms is:

(-1.9 + 1.2) + (5.1 - 3.6)t

Simplifying further, we get:

-0.7 + 1.5t

A coefficient is a numerical factor that is multiplied by a variable in an algebraic expression. It tells you how many times the variable appears in the expression. For example, in the expression 3x + 2, the coefficient of x is 3. Variables are symbols used to represent unknown quantities in mathematical equations or expressions. They can take on different values, and their value can be solved for using algebraic techniques. Equivalent expressions are expressions that have the same value for all possible values of the variables involved. For example, 2x + 4 and 4 + 2x are equivalent expressions since they simplify to the same value. Equivalent expressions can be useful in simplifying and solving algebraic equations.

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Complete Question

Combine like terms to create an equivalent expression. −

3. 6−1. 9+1. 2+5. 1 −3. 6−1. 9t+1. 2+5.

The variable associated with the interior and exterior angles in the triangle is equal to 56.

The value of the exterior angle is equal to 116°.

This question presents the case of a geometric system formed by a triangle and a semirray that includes two interior angles and a exterior angle. Please notice that the sum of the measures of interior angles in a triangle equals 180° and the sum of two supplementary angles equals 180°.

First, derive the equation of the missing interior angles in triangle PQR:

m ∠ R = 180° - 60° - x

m ∠ R = 120° - x

Second, obtain the equation for the two supplementary angles:

(120° - x) + (2 · x + 4°) = 180°

124° + x = 180°

x = 56

Third, determine the value of the exterior angle:

θ = 2 · x + 4

θ = 2 · 56 + 4

θ = 116°

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Answer:

Step-by-step explanation:

we have to know what the numbers are

Answer:

Less

Step-by-step explanation:

Answer:

if 1 represents 100% then it would be less than

Step-by-step explanation:

that would make the .90 90% and thus less than 95%

Answer:

1.00 significant figures

The required, 0.9967 rounded to 2 significant figures is approximately 1.0.

To round 0.9967 to 2 significant figures, we look at the first two non-zero digits: 0.9967

The first two non-zero digits are 99. Since there is no third significant digit, we round according to the following rules:

If the third digit is 5 or greater, round up the second digit.

If the third digit is less than 5, leave the second digit unchanged.

In this case, the third digit is 6, which is greater than 5. So, we round up the second digit:

Thus, 0.9967 rounded to 2 significant figures is approximately 1.0.

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Answer:

x <3

Step-by-step explanation:

–2(5 – 4x) < 6x – 4

Distribute

-10 +8x < 6x-4

Subtract 6x from each side

-10+8x-6x < 6x-6x-4

-10 +2x < -4

Add 10 to each side

-10+2x+10 < -4+10

2x< 6

Divide by 2

2x/2 < 6/2

x <3

Answer:

(6-2)÷3=1

this is the answer

follow me :)))

Answer:

140 > y

Step-by-step explanation:

19 >y/5 - 9

19+9 > y/5

28 >y/5

cross multiply

28×5 > y×1

140 > y

9514 1404 393

Answer:

  (2/5)√10 ≈ 1.26491

Step-by-step explanation:

The geometric mean of a set of n numbers is the n-th root of their product. For two numbers, it is the square root of their product.

  g = √((4/5)(2)) = √(8/5) = √(40/25)

  g = (2/5)√10 . . . the geometric mean

Answer:

60⁰

Step-by-step explanation:

A triangle has three angles.

The sum of its angles = 180⁰

[ By angle sum property ]

Let the unknown angle be 'x'

Then,

30⁰ + 90⁰ + x = 180⁰

120⁰ + x = 180⁰

x = 180⁰ - 120⁰

x = 60⁰

Therefore, the unknown angle will be equal to 60⁰

Answer:

$10,530

Step-by-step explanation:

I = Prt

P = 19500

r = 0.06

t = 9

I= 19500 x 0.06 x 9

I = 10530

Two marbles are selected at random with replacement.

the probability that both marbles are red in colour is 1/4..

Probability:

Probability multiply helps in visualize the multiple trials involved in a probability situation. The joint and conditional probabilities are easier to see and calculate with the use of the tree.

We have given that,

Number of Red marbles = 5

Number of Green marbles = 3

Number of blue marbles = 2

Total number of marbles = 10

i.e, total possible outcomes for selecting marbles = 10

Two marbles are selected at random with replacement.

we have to calculate probability that both marbles are red.

firstly, we consider that first selected marble is red.

Probability that the first selected marble is red

= 5/10

Then it put again with other marbles i.e with replacement.

second marble is selected from random.

Probability that both marbles are red in colour

= 5/10 ×5/10 = 25/100 = 1/4

Hence, the required probability is 1/4 .

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Answer:

143 oil changes

Step-by-step explanation:

We first find the unit rate.

(91 oil changes)/(7 days) = 13 oil changes/day

Since we want to know the number of oil changes in 11 days, we multiply the unit rate by 11 days.

13 oil changes/day * 11 days = 143 oil changes

The power of a that makes it equal to b is x = 5/6

The square root of a number is a number when multiplied by itself gives another number.

The cube root of a number is a number when multiplied by itself three times gives another number.

The power of a number is the exponent of that number

Since two numbers, a and b, are each greater than zero, and 4 times the square root of a is equal to 9 times the cube root of b. It follws that

4√a = 9∛b

⇒∛b = 4√a/9

⇒ b = ∛[4√a/9]

Since we require the  of x is a, to the x power equal to b if a = 2/3.

This implies that

aˣ = b

Substituting b into the equation, we have

aˣ =  ∛[4√a/9]

Since a = 2/3, we have

(2/3)ˣ =  ∛[4√(2/3)/9]

(2/3)ˣ =  ∛[4/9 × √(2/3)]

(2/3)ˣ =  ∛[2²/3² × √(2/3)]

(2/3)ˣ =  ∛[(2/3)² × √(2/3)]

(2/3)ˣ =  ∛[2/3)

\((\frac{2}{3} )^{x} = \sqrt[3]{(\frac{2}{3} )^{2 + \frac{1}{2}} } \\(\frac{2}{3} )^{x} = \sqrt[3]{(\frac{2}{3} )^{\frac{5}{2}} } \\(\frac{2}{3} )^{x} = (\frac{2}{3} )^{\frac{5}{2} \times \frac{1}{3} } \\(\frac{2}{3} )^{x} = (\frac{2}{3} )^{\frac{5}{6}\)

Equating both powers, we see that x = 5/6

So, the power of a is x = 5/6

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The correct critical value to use when finding a 90 percent confidence interval estimate for the mean is 1.7291.

The correct critical value to use when finding a 90 percent confidence interval estimate for the mean depends on the sample size and the desired level of confidence. In this case, since the sample size is 20 and the desired level of confidence is 90 percent, we need to use a t-distribution to find the critical value.
To find the critical value, we need to determine the degrees of freedom, which is equal to the sample size minus 1. In this case, the degrees of freedom would be 20 - 1 = 19.

Next, we need to find the critical value from the t-distribution table or a statistical calculator. The critical value for a 90 percent confidence interval with 19 degrees of freedom is approximately 1.7291. Therefore, the correct critical value to use in this case is 1.7291.

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Answer:

\(\sin(x)=-\dfrac{1}{2}\)

Step-by-step explanation:

The tangent function, tan(x), can be expressed as the ratio of sin(x) to cos(x):

\(\tan(x) = \dfrac{\sin(x)}{\cos(x)}\)

We are told that tan(x) = -1/√3.

There are two ways that tan(x) can be negative:

As we have been told that cos(x) is positive, then sin(x) must be negative.

To find the value of sin(x), equating the tan(x) ratio to the given value of tan(x), and rearrange to isolate cos(x):

\(\tan(x) = -\dfrac{1}{\sqrt{3}}\)

\(\dfrac{\sin(x)}{\cos(x)}=-\dfrac{1}{\sqrt{3}}\)

\(\cos (x)=-\sqrt{3}\sin(x)\)

Substitute the found expression for cos(x) into the trigonometric identity sin²(x) + cos²(x) = 1 and solve for sin(x):

\(\begin{aligned}\sin^2(x)+\left(-\sqrt{3} \sin(x)\right)^2&=1\\\\\sin^2(x)+3\sin^2(x)&=1\\\\4\sin^2(x)&=1\\\\\sin^2(x)&=\dfrac{1}{4}\\\\\sin(x)&=\sqrt{\dfrac{1}{4}}\\\\\sin(x)&=\pm \dfrac{1}{2}\end{aligned}\)

As we have already determined that sin(x) is negative, this means that the value of sin(x) is:

\(\boxed{\sin(x)=-\dfrac{1}{2}}\)

The stack pointer is decremented by a multiple of 4, as required by the MIPS architecture.

To solve the MIPS stack pointer question, we need to reserve enough space on the stack for 2 integers and the\(`$ra`\)register. Each integer and the ra register occupy 4 bytes, so the total space required is 12 bytes.

However, since the stack pointer is manipulated in multiples of 4, we need to find the closest multiple of 4 to -12, which is -16.

Hence, the value of XX in the instruction \(`addiu $sp, $sp, XX`\) should be -16 to reserve enough room on the stack for 2 integers and the ra register.

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Answer:

Substitute

18(14) + 13(12)

252 + 156

409

Answer:

252 + 156 = 408

Step-by-step explanation:

Answer:

x+12 The length of a rectangle

Step-by-step explanation:

The perimeter should be 4x+12, the x being the the width. If the length is the  is 12 inches more than the width, the length should be x+12

Answer:

\(y= \frac12 x^2 -2x +\frac32\)

Step-by-step explanation:

From the two zeroes, you can tell that the polynomial factors as \(y= A(x-1)(x-3)\). You have still one degree of freedom (determining how wide the parabola is. You can determine it with the other condition:

\(4 = A(5-1)(5-3) \rightarrow 4= A(4)(2) \rightarrow A= \frac12\)

Your function is \(y= \frac12 (x-1)(x-3) = \frac12 x^2 -2x +\frac32\)

\(4^x=3 \\\\[-0.35em] ~\dotfill\\\\ 4^{2x-2}\implies 4^{2x}\cdot 4^{-2}\implies (4^x)^2\cdot \cfrac{1}{4^2}\implies \cfrac{(4^x)^2}{16}\implies \cfrac{(3)^2}{16}\implies \cfrac{9}{16}\)

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, & The mass-normalised mode shapes can be  normalising the mode shape vectors f1, f2, and f3.

Part (a)

In Equation Q2, the spectral matrix, undamped natural frequencies, damping ratios, and fundamental frequency need to be calculated.

The mass matrix is given by [85.16400 083.3770 0046.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The stiffness matrix is given by [0.16400 00.3770 000.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The damping matrix is given by [0 0 0; 0 0 0; 0 0 0].The undamped natural frequencies, damping ratios, and fundamental frequency for the system in Equation Q2 can be calculated from the spectral matrix.

The characteristic equation can be written as det(K-mω^2M)=0.where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and m is the mass-normalised mode shape.

The roots of this equation are the undamped natural frequencies, and the damping ratios can be calculated from the undamped natural frequencies and mode shapes.

The mass-normalised mode shapes can be calculated by normalising the mode shape vectors f1, f2, and f3.

Part (b)

The mass-normalised mode shapes can be calculated using the mode shape vectors f1, f2, and f3.Part (c)The response of the system for the first physical coordinate y1 can be calculated using the mode superposition method. The initial modal displacements and velocities are given in terms of the modal coordinates.

The response is then calculated using the equation y(t)= Σ ai φi(t), where ai are the modal amplitudes, and φi(t) are the modal shapes given by the mode shape vectors f1, f2, and f3.

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, where Y is the vector of physical coordinates. The modal amplitudes can be calculated from the initial modal displacements and velocities.

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