At Antonio’s Pizzeria, the pizzas come in three sizes: large, massive, and
gargantuan. There are four varieties to choose from: Veggie Garden,
Carnivore’s Delight, Cheesy Wheezy, and Hawaiian Paradise. Use either a tree
diagram or a table to display all of the possible choices.

Answer:

(10, 5)

Step-by-step explanation:

The circle is located at (10, 5)

The parametric equations of y = 6x -1  are [x = t, y = 6t - 1].

Parametric equations divide an equation into two or more equations, depending upon the variables in the original equation, both dependent and independent.

In parametric equations we mostly use t as an independent variable and write all equations in terms of t.

To convert a rectangular equation in its parametric representation, the easiest way to do is to equate x with the variable t in the original equation. Now, our x is equal to t. Hence, the final answer is  [x = t, y = 6t - 1].

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Answer:

You can use Unit rate to find the answer. (Divide)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question got caught off. Can't read any of the other examples. I can tell you though that ice melting is a physical change, not a chemical change.

If functions f(x)=x² +16x-24 and g(x)=x²-5x-17 then (f+g)(x) is 2x² +11x-41.

A relation is a function if it has only One y-value for each x-value.

The given functions are f(x)=x² +16x-24 and g(x)=x²-5x-17.

We need to find  (ƒ + g)(x).

From properties we have (ƒ + g)(x)=f(x)+g(x)

(ƒ + g)(x)=x² +16x-24+x²-5x-17.

Add the like terms

(f+g)(x)=2x² +11x-41

Hence, if functions f(x)=x² +16x-24 and g(x)=x²-5x-17 then (f+g)(x) is 2x² +11x-41.

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Answer:

u(2t - 1) - u(-3t + 4)

= 2tu - u + 3tu - 4u

= 5tu - 5u

= 5u(t - 1)

Answer:

Therefore, the length of the ladder is 13 feet.

Step-by-step explanation:

This is a classic example of a right triangle problem in geometry. The ladder serves as the hypotenuse of the triangle, while the distance from the building to the ladder and the height of the window serve as the other two sides. Using the Pythagorean theorem, we can solve for the length of the ladder:

ladder^2 = distance^2 + height^2 ladder^2 = 5^2 + 12^2 ladder^2 = 169 ladder = √169 ladder = 13

Therefore, the length of the ladder is 13 feet.

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Answer:false

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

12 divided by .03 is 400

The double integral over the region R is zero

To evaluate the given double integral using symmetry, we can exploit the symmetry of the region of integration, R.

The region R is defined as R = {(x, y) | −2 ≤ x ≤ 2, 0 ≤ y ≤ 1}.

Since the limits of integration for y are from 0 to 1, we notice that the integrand 8xy does not depend on y symmetrically about the x-axis. Therefore, we can conclude that the integral over the entire region R is equal to twice the integral over the lower half of R.

So, we can evaluate the double integral as follows:

∬R (8xy / (1 + x⁴)) dA =  \(2\int_{-2}^2 \int_0^1\frac{8xy}{1+x^4} dydx\)

Now, let's evaluate the integral in terms of x:

\(\int_0^1\frac{8xy}{1+x^4}dy\)

This integral is independent of y, so we can treat it as a constant with respect to y:

=  \(\frac{8x}{1+x^4} \int_0^1ydy\)

= \(\frac{8x}{1+x^4}[\frac{y^2}{2}]_0^1\)

= (8x / (1 + x⁴)) * (1/2)

= 4x / (1 + x⁴)

Now, we can evaluate the remaining integral with respect to x:

\(2\int_{-2}^2\frac{4x}{1+x^4}dx\) =  \(8\int_{-2}^2\frac{x}{1+x^4}dx\)

We can evaluate this integral using symmetry as well. Since the integrand (x / (1 + x⁴)) is an odd function, the integral over the entire range [-2, 2] is equal to zero.

Therefore, the double integral over the region R is zero:

∬R (8xy / (1 + x⁴)) dA = 0.

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To find the number of three-letter initials with none of the letters repeated, we need to consider the number of choices for each position in the initials.

To determine the number of three-letter initials with none of the letters repeated, we can analyze each position in the initials. For the first letter, we have 26 choices since there are 26 letters in the English alphabet.

After selecting the first letter, for the second letter, we have 25 choices remaining since we cannot repeat the letter used in the first position. Similarly, for the third letter, we have 24 choices remaining since we cannot repeat either of the previous letters.

Therefore, the total number of three-letter initials with none of the letters repeated can be found by multiplying the number of choices for each position: 26 * 25 * 24 = 15,600. Hence, there are 15,600 different three-letter initials that people can have if none of the letters are repeated.

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The value(s) of k that make the function continuous over the given interval are k ≥ 0.

To determine the values of k that make the function f(x) continuous over the interval [0, 5] and (5, 10], we need to ensure that the function is defined and has no discontinuities at the endpoints and the transition point.

For the function f(x) = √(kx), the square root function is defined for non-negative values of its argument. Therefore, for the interval [0, 5], we require that kx ≥ 0 for all x in the interval. Since x is non-negative, it follows that k must also be non-negative or k ≥ 0.

For the interval (5, 10], the function is given by f(x) = x + 2, which is a linear function and is continuous for all real values of x. In this case, the value of k does not affect the continuity of the function.

In summary, for the function f(x) = √(kx) to be continuous over the interval [0, 5] and (5, 10], we need k to be non-negative or k ≥ 0.

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Answer:

Step-by-step explanation:

If z is any integer then the next integer to z would be: z+1

And the next:  z+1+1 = z+2 (the largest)

Their sum is 39 so:

z + z+1 + z+2 = 39

3z + 3 = 39

3z = 36

z = 12

z+2 = 12 + 2 = 14

check:

z+1=12+1=13,

14+13+12 = 39

Step-by-step explanation:

\( f(x) = - 3 {x}^{2} + 9x - 2\)

A) f(-2) + f(1) = -32 + 4 = -28

B) f(-2) - f(1) = -32 - 4 = -36

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:

0.98

Step-by-step explanation:

Assuming the number of questions on all the tests is 10,

9+9+10+10+10 / 50

You get 50 by doing 5 quizzes x 10 questions per quiz.

48/50 = 0.98

The mean, standard deviation, and the variance are respectively calculated as: a. μx = 2.96, σx ≈ 1.472; b. μy = 1.2, σy ≈ 0.693; c. μc = $8.88, σc² ≈ 29.97; d. μb = $8.00, σb² ≈ 2.40; e. μz = 4.16, σz² = 2.65; f. μw = $16.88, σw² = 32.37

To solve this problem, we'll use the given probability distributions and apply the formulas for mean and variance. Let's calculate each part step by step:

a. Compute the mean and standard deviation of x:

Mean of x (μx):

μx = ∑(x * p(x)) = (0 * 0.05) + (1 * 0.09) + (2 * 0.25) + (3 * 0.3) + (4 * 0.2) + (5 * 0.11) = 2.96

Variance of x (σx²):

σx² = ∑((x - μx)² * p(x)) = ((0 - 2.96)² * 0.05) + ((1 - 2.96)² * 0.09) + ((2 - 2.96)² * 0.25) + ((3 - 2.96)² * 0.3) + ((4 - 2.96)² * 0.2) + ((5 - 2.96)² * 0.11) ≈ 2.17

Standard deviation of x (σx):

σx = √(σx²) ≈ √(2.17) ≈ 1.472

b. Compute the mean and standard deviation of y:

Mean of y (μy):

μy = ∑(y * p(y)) = (0 * 0.4) + (1 * 0.2) + (2 * 0.4) = 1.2

Variance of y (σy²):

σy² = ∑((y - μy)² * p(y)) = ((0 - 1.2)² * 0.4) + ((1 - 1.2)² * 0.2) + ((2 - 1.2)² * 0.4) ≈ 0.48

Standard deviation of y (σy):

σy = √(σy²) ≈ √(0.48) ≈ 0.693

c. Compute the mean and variance of the total amount of money collected in tolls from cars:

Mean of cars toll (μc):

μc = ∑(x * $3 * p(x)) = (0 * $3 * 0.05) + (1 * $3 * 0.09) + (2 * $3 * 0.25) + (3 * $3 * 0.3) + (4 * $3 * 0.2) + (5 * $3 * 0.11) = $8.88

Variance of cars toll (σc²):

σc² = ∑(((x * $3) - μc)² * p(x)) = (((0 * $3) - $8.88)² * 0.05) + (((1 * $3) - $8.88)² * 0.09) + (((2 * $3) - $8.88)² * 0.25) + (((3 * $3) - $8.88)² * 0.3) + (((4 * $3) - $8.88)² * 0.2) + (((5 * $3) - $8.88)² * 0.11) ≈ 29.97

d. Compute the mean and variance of the total amount of money collected in tolls from buses:

Mean of buses toll (μb):

μb = ∑(y * $10 * p(y)) = (0 * $10 * 0.4) + (1 * $10 * 0.2) + (2 * $10 * 0.4) = $8.00

Variance of buses toll (σb²):

σb² = ∑(((y * $10) - μb)² * p(y)) = (((0 * $10) - $8.00)² * 0.4) + (((1 * $10) - $8.00)² * 0.2) + (((2 * $10) - $8.00)² * 0.4) ≈ 2.40

e. Compute the mean and variance of z = total number of vehicles (cars and buses) on the ferry:

Mean of z (μz):

μz = μx + μy = 2.96 + 1.2 = 4.16

Variance of z (σz²):

σz² = σx² + σy² = 2.17 + 0.48 = 2.65

f. Compute the mean and variance of w = total amount of money collected in tolls:

Mean of w (μw):

μw = μc + μb = $8.88 + $8.00 = $16.88

Variance of w (σw²):

σw² = σc² + σb² = 29.97 + 2.40 = 32.37

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Answer:

4.5 minutes or 36/8 minutes or 9/2 minutes

Step-by-step explanation:

So we simply find 3/8 of 12 by multiplying:

\(\frac{3}8} \times 12\)

This gives us 36/ 8

Now, depending on how you want your answer formulated, we just reduce it to either 9/2 minutes, or 4.5 minutes.

Hope this helpss!!!

The quotient of a division problem is the result obtained when one number is divided by another. In the given problem, we need to find the quotient of 136 divided by 21.

To solve this problem, we need to use the long division method. First, we divide the first digit of 136 (which is 1) by 21. We get 0 as the quotient. We then bring down the next digit (which is 3) to get 13. We divide 13 by 21 and get 0 as the quotient again. We bring down the next digit (which is 6) to get 136. We divide 136 by 21 and get 6 as the quotient.

Therefore, the answer to the problem is 6 with a remainder of 10. We write the answer as 6 r10.

In conclusion, the quotient of the division problem 136 / 21 is 6 with a remainder of 10. This means that we can divide 136 by 21 six times with a remainder of 10.

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Answer:

300

Step-by-step explanation:

20÷2=10

60÷2=30

30x10=300

Answer:

y= -3x + 7:)

Step-by-step explanation:

Hope this helps!

Answer:

y = - 3x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 3 , thus

y = - 3x + c ← is the partial equation

To find c substitute (4, - 5) into the partial equation

- 5 = - 12 + c ⇒ c = - 5 + 12 = 7

y = - 3x + 7 ← equation of line

The value of theta is tan theta equal to sin theta at A( π ).

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

Consider that the value of sinθ and tanθ is same.

sinθ = tanθ

sinθ = sin θ / cosθ

Cancel out the common factor.

1 = 1/cosθ

1 = cosθ

cos π = cosθ

π = θ

For  π = θ, the value of sinθ and tanθ is same.

Therefore the correct option is A( π ).

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Answer:

please see explanation.

Step-by-step explanation:

2268×2=4536

2268×3=6804

2268×4=9072

2268x5=11340

2268×6=13608

2268×7=15876

from the computation 15848 is a perfect square

√15848= 126

to calculate the 126= ✓126=11.225

50 million people instead of 25 million people make up the population. The degree of assurance is reduced from 95% to 90%.

What is confidence interval?

A confidence interval in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 95%, but other levels, such 90% or 99%, are occasionally used.

Because the standard error is reduced as sample size increases, confidence intervals are narrower.

Therefore, we may state that when the population standard deviation rises, the width of the confidence interval will also rise.

Hence, 50 million people instead of 25 million people make up the population. The degree of assurance is reduced from 95% to 90%.

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Answer: 60 ft

Step-by-step explanation:

Given

The perimeter of the garden is \(220\ ft\)

The width of the garden is \(50\ ft\)

Suppose the length of the garden is \(x\)

Perimeter is the sum of the lengths of the sides

\(\Rightarrow 220=2(x+50)\\\Rightarrow 110=x+50\\\Rightarrow x=60\ ft\)

So, the length of the garden is \(60\ ft\)

The value of an 8 in the tens place as a fraction of an 8 in the hundreds place is 1 / 10.

In the number system we use, each digit's value is determined by its position and is ten times the value of the digit to its right. Therefore, the value of an 8 in the tens place is 10 times the value of an 8 in the ones place.

Likewise, the value of an 8 in the hundreds place is 10 times the value of an 8 in the tens place, which in turn is 10 times the value of an 8 in the ones place. Therefore, the value of an 8 in the hundreds place is 10 x 10 times the value of an 8 in the ones place.

So in equation form, we have:

= 8 / 80

= 1 / 10

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Equilibrium is the term refers to coordination, balance, and balance in three dimensional space.

The equilibrium condition of an object exists when Newton's first law is valid. An object is in equilibrium in a reference coordinate system when all external forces (including moments) acting on it are balanced. This means that the net result of all the external forces and moments acting on this object is zero.

There are three types of equilibrium: stable, unstable, and neutral.

Examples of equilibrium in everyday life:

A book kept on a table at rest. A car moving with a constant velocity. A chemical reaction where the rates of forward reaction and backward reaction are the same.

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The intervals of concavity for f(x) = 3 cos x, with 0 < x < 21, are (0, π/2) and (3π/2, 2π).

To find the intervals of concavity for f(x) = 3 cos x, we need to analyze the second derivative of the function.

First, let's find the second derivative of f(x):

f'(x) = -3 sin x (derivative of cos x)

f''(x) = -3 cos x (derivative of -3 sin x)

Now, we can analyze the concavity of f(x) by considering the sign of the second derivative:

When x ∈ (0, π/2): In this interval, cos x > 0, so f''(x) < 0. The second derivative is negative, indicating concavity downwards.

When x ∈ (π/2, 3π/2): In this interval, cos x < 0, so f''(x) > 0. The second derivative is positive, indicating concavity upwards.

When x ∈ (3π/2, 2π): In this interval, cos x > 0, so f''(x) < 0. The second derivative is negative, indicating concavity downwards.

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Answer:

5

Step-by-step explanation:

By process of elimination, we can say for sure that C and D are not the right answers because as x- the numbers on the top- increases, y- the numbers on the bottom- increases. This means that the slope is not negative, because the slope is the rate of change and it does not have a negative rate of change.

The equation for slope is y2-y1 / x2-x1. Meaning, y is on top and x is on bottom. This creates a fraction. So let's take 0 and 1 for X, the first and second values, and 3 and 8 for y, the first and second values. We swap them, because the second y value comes first, so we have 8 - 3 for the top, the numerator. Then we have 1 - 0 for the bottom, the denominator. Solving 8 - 3 and 1 - 0, we have 5/1. 5/1 simplifies to 5, and thus 5 is your slope.