22. Thomas lists all of the different arrangements of the letters in the word CABOOSE. How many of Thomas's arrangements begin with a C and end with an E?
(A) 100
(B) 120
(C) 80
(D) 90
(E)Other

If a b a♣︎b - a - b - 1, then what is the value of 284♣︎1001?
(A) 282435
(B) 283000
(C) 283283
(D) 282000
(E)Other

What is the product of 4% of 112 and 61% of 375?
(A) 144
(B) 90
(C) 120
(D) 105
(E)Other


. Josh rolls two standard six-sided dice. What is the probability that the product of the numbers shown on the dice is a multiple of six?
(A) 4/9
B) 1/3
(C) 5/12
D) 1/2
(E)Other

What is the remainder when the sum of the terms of the arithmetic series 101 108 + 115 + 290 is divided by 28?
(A) 7
(B) 0
(C) 14
(D) 21
(E)Other

Two right triangles have the same perimeter, and each triangle's side lengths are all whole numbers. One right triangle has legs of length 10 and 24. The other right triangle has a hypotenuse of length 25. What is the area of the second triangle?
A) 150
(B) 112
(C) 120
(D) 144
(E)Other .

A function f is defined for positive integers x as f(x) = 0 if x ≤ 2. Otherwise, f(x) = f(x - 1) if x is not divisible by 3, and f(x) = 2 + f (3) if x is divisible by 3. What is the value of f(2020)?
A) 16
B) 14
C) 12
D) 8
E)Other​

Answer:

m = -1

Step-by-step explanation:

Slope = rise/run = (y2 - y1) / (x2 - x1)

Points (-3, 4) (2, -1)

We see the y decrease by 5 and x increase by 5, so the slope is

m = -5/5 = -1

(E) Other

To make 144 slices of cake, Emma will need 18 large eggs.

To solve this problem, we need to know how much 2 dozen is.

So, for every 24 slices of cake, 3 eggs are needed.

To figure out how many slices of cake 1 egg can make, we can divide 24 by 3.

Now, for every 8 slices of cake, 1 egg is needed.

Now, taking 144, we can divide that by 8 to get the number of eggs needed.

Therefore, 18 eggs will be needed to make 144 slices of cake.

Answer: option c.

Step-by-step explanation:

The three possibilities for a linear system, in terms of free variables, rank and nullity, are

Three possibilities for a linear system.

No solution    Signal equation 0 = 1

Infinitely many solutions One or more free variables nullity ≥ 1

Unique solution Zero free variables nullity = 0

No Solution. There is no solution to a system of equations exactly when a signal

equation 0 = 1 occurs during the application of swap, multiply and combination

rules. We report the system inconsistent and announce no solution. Infinitely Many Solutions. The situation of infinitely many solutions occurs when

there is at least one free variable to which an invented symbol, say t1, is assigned.

Since this symbol takes the values −∞ < t1 < ∞, there are an infinity of solutions.

The condition rank less than n can replace a reference to the number of free variables.

Unique Solution. There is a unique solution to a system of equations exactly when

zero free variables are present. This is identical to requiring that the number n of

variables equal the number of lead variables, or rank = n.

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In poetry, the two main types of feet are iambic and trochaic.

Iambic foot: An iambic foot consists of two syllables, with the first syllable being unstressed and the second syllable being stressed. This creates a rhythmic pattern of "da-DUM" that gives iambic meter its characteristic "rising" sound. Iambic meter is one of the most common types of meter in English poetry, and is often associated with a natural, conversational rhythm.

Trochaic foot: A trochaic foot consists of two syllables, with the first syllable being stressed and the second syllable being unstressed. This creates a rhythmic pattern of "DA-dum" that gives trochaic meter its characteristic "falling" sound. Trochaic meter is less common than iambic meter in English poetry, but is still used in a variety of forms and styles. It can create a sense of tension or urgency, and is often used in poetry that is meant to be dramatic or suspenseful.

It's important to note that these two types of feet are just two of many possible metrical patterns that can be found in poetry. However, they are two of the most basic and widely recognized, and a good starting point for understanding the rhythms and structures of poetic meter.

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$10.66 is dollars was the discount .

How does discount work?

Discount is a term that describes a sum or a percentage subtracted from a product's usual selling price. Make sure you need all of the items you plan to buy before waiting until after the holiday when you can frequently find them at a significant discount.

                           Discount is a term that refers to a reduction in the cost of a commodity or service.

Discount:

(13 x 18)/100 = $2.34

13 - 2.34 = $10.66

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Answer:

20 miles in 1/2.  That would be 40 miles per hour

Step-by-step explanation:

6 ÷ 1/8 is the same at 6 x 8 = 48

11 ÷1/4 is the same as 11 x 4 = 44

16 x 3/8 is the same as 16 x 8/3 = 42 2/3

20 ÷ 1/2 is the same as 20 x 3 = 40

There are 120 ways that the letters from the word "world" can be arranged

It is the ordered arrangement of members belonging to a set with no repeats.

To solve this problem the formula and the permutation procedure we must use is:

nPr = n! / (n-r)!

Where:

Information about the problem:

Applying the permutation formula we have:

nPr = n! / (n-r)!

5P5 = 5! / (5-5)!

5P5 = 5! / 0!

5P5 = 5*4*3*2 / 1

5P5 = 5*4*3*2

5P5 = 120

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The population of foxes in the preserve after 42 years will be:

1620 foxes.

The function "y = 60 • 3^t" models the population growth of foxes in a wildlife preserve.

"y" represents the population size, "60" is the initial population size, "3" is the factor by which the population triples, and "t" is the number of 14-year periods that have passed.

In this case, we are told that 42 years have passed, so we can calculate the number of 14-year periods as "t = 42/14 = 3".

Substituting this value of "t" into the function, we get: So, t = 42/14 = 3

Substituting that into the function:

So, after 42 years, the population of foxes in the preserve will have grown to 1620 foxes.

Complete Question:

"A population of 60 foxes in a wildlife preserve triples in size every 14 years. The function y = 60 • 3^x models the population growth, where x is the number of 14-year periods. How many foxes will there be after 42 years?"

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Step-by-step explanation:

1/4096

0.000244140625

2^-12

1/(2^12)

All of the above expressions are equivalent to (12⁻₂)₈, which is a decimal representation of a number that is obtained by dividing 1 by 2 raised to the power of 12. The first and second expressions are decimal representation of the number, the third one is the representation of the number by using the base 2 logarithm, and the fourth one is the mathematical representation of the number by dividing 1 by 2 raised to the power of 12.

Answer:

The graph of the function is a parabolic function graph

Step-by-step explanation:

Formula for a parabolic function: ( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the graph be represented as A

Now , a parabola is a U-shaped curve that is drawn for a quadratic function, f(x) = ax² + bx + c.

The value of the graph increases and decreases in a format according to the quadratic equation.

So , the graph of the function goes downward when value of a < 0 and the graph of the function goes upward when the value of a > 0

The graph of the parabola is downward (or opens down), when the value of a is less than 0, a < 0. The graph of parabola is upward (or opens up) when the value of a is more than 0, a > 0

Therefore , the graph is a parabolic graph

Hence , The graph of the function is a parabolic function graph

Answer:

A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. Please select the best answer from the choices provided A B C D

Answer:

1/5

Step-by-step explanation:

1/7 * x = 1/35    multiply both sides by 7

x = 7/35 = 1/5

For (a), x must be the 98th percentile of T22. For (b), x must be the 85th percentile value  of T13. For (c), x must be the 26th percentile of T26. For (d), x must be the 97.5th percentile of T2.

For (a), the value of x must be the 98th percentile of T22, which is the value of x such that 98% of the data points of T22 are less than or equal to x. For (b), the value of x must be the 85th percentile of T13, which is the value of x such that 85% of the data points of T13 are less than or equal to x. For (c), the value of x must be the 26th percentile of T26, which is the value of x such that 26% of the data points of T26 are less than or equal to x. For (d), the value of x must be the 97.5th percentile of T2, which is the value of x such that 97.5% of the data points of T2 are less than or equal to x. In order to find these values of x, one must first calculate the percentiles of the given variables. This can be done by sorting the data points in ascending order and then calculating the percentile of each data point. After the corresponding percentile of each data point has been calculated, the desired values of x can be determined by finding the data point whose percentile matches the desired value.

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aₙ = 0.20aₙ₋₁ + 200 is the recursive formula for the above sequence.

Therefore, choice A is the right one.

Given:

A holiday tree farm is owned by Mahek.

Currently, the site has 800 trees.

200 saplings are planted together with the 20% of the trees that are harvested and sold each year.

a₁ = 800

The recursive formula is,

aₙ = 0.20aₙ₋₁ + 200

Hence, the correct formula is aₙ = 0.20aₙ₋₁ + 200

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When h=-17  is b in the plane spanned by a1 and a2.

For the plane spanned by a1 and a2, y is a linear combination of a1 and a2 if it is in the plane,

y = a a1 + b a2

where a and b are constants,

[4,1,h] = a[1,4,-2] + b[-2,-3,7]

[4,1,h] = [a - 2b,4a -3b,-2a+ 7b]

by the rules of vector addition and multiplication.

Vectors are equal if their components are equal:

4 = a - 2b

1 = 4a - 3b

h = -2a + 7b

solve for a and b from the first two equations so that we can find h,

b = -3

h = -17

We see that -2[1,4,-2] - 3[-2,-3,7] = [4,1,-17].

so ,the value of  h=-17  is b in the plane spanned by a1 and a2.

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The distances from the midpoint M to the vertices are all the same and equivalent to 5·√2, therefore, the diagonals of the quadrilateral bisect each other.

A diagonal is a line that joins the opposite corners of the quadrilateral.

The question is without the possible options for the response.

The vertices of the quadrilateral are;

P(1, -1), Q(3, -7), R(-9, -11), and S(-11, -5)

The midpoint of the side PR = ((-9 + 1)/2, (-11 + (-1))/2) = (-4, -6)

Midpoint of the diagonal SQ = ((3 + (-11))/2, (-7 - 5)/2) = (-4, -6)

Let M represent the point of intersection of the diagonals, we get;

PM = √((1 - (-4))² + (-1 - (-6))² = 5·√2

MR = √((-9 - (-4))² + (-11 - (-6))² = 5·√2

The length of PM = The length of MR, therefore, the diagonal SQ bisects PM

Similarly, we get;

SM = √((-9 - (-4))² + (-11 - (-6))²) = 5·√2

MQ = √((3 - (-4))² + (-7 - (-6))²) = 5·√2

The length PM = MR and the lengths SM = MQ, therefore, the diagonals bisect each other.

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Answer: the product of the slopes of the diagonals PR and QS is equal to 1. Hence, the diagonals of parallelogram PQRS bisect each other.

Step-by-step explanation:

The length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is a perpendicular vector to both a→ and b→, meaning that c→ is at a right angle to both a→ and b→.

This is due to the fact that the length of a vector is equal to the length of the hypotenuse of a right triangle, which is the sum of the lengths of the other two sides (a→ and b→). When c→ is perpendicular to both a→ and b→, the right triangle formed by a→, b→, and c→ is a special type of right triangle called a Pythagorean triangle, in which the length of the hypotenuse (c→) is equal to the sum of the lengths of the other two sides (a→ and b→). Thus, the length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is perpendicular to both a→ and b→.

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The solution to the differential equation is ln |y| = 4t - 4.

The given differential equation can be written as ∆y/∆t = y2(4t). This is a first-order separable differential equation, which can be solved using the separation of variables method. To do this, we first isolate the dy/dt term on one side of the equation. We can then separate the two variables (t and y) by moving all terms with t to one side and all terms with y to the other side. This gives us ∆y/y2 = 4∆t. We can then integrate both sides to find the solution.

Integrating both sides with respect to y gives us the following:

ln |y| = 4t + C,

where C is an integration constant. We can use the boundary condition to solve for C. The boundary condition states that y=8 when t=1, so substituting this into the equation above gives us ln |8| = 4 + C. Solving for C gives us C=-4.

Therefore, the solution to the differential equation is ln |y| = 4t - 4. Rearranging this equation gives us y = e4t-4, which is the solution to the differential equation.

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The third interior angle of the triangle is 119.9 degrees

Triangle is a closed polygon consist of three sides, three angle or three segment.

Triangle has three angle which if we sum all of those three angle it will be 180 degrees.

Triangle can be divided into several type :

1.  Equilateral triangle which all of the angle is equal ( 180 degrees / 3 = 60 degrees each )

2. Isosceles triangle which have two equal angle, and the third angle is different

3. Scalene triangle which all of the angle is different

From the question, we have data :

1. First Angle is 45.5 degrees

2. Second Angle is 14.6 degrees

For the Third angle, we just simply subtract 180 degrees with the first and second angle. So it will be :

Third Angle = 180 degrees - ( 45.5 degrees + 14.6 degrees )

                    = 180 degrees - 60.1 degrees

                    = 119.9 degrees

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Answer: 5^3

Step-by-step explanation: since we know that 5^2=5x5 (which equals to 5x5x5), our answer is 5^3

Answer:

2. a)

As per the Angle sum property

∠P +  ∠Q +  ∠R = 180°

22° +  ∠Q + 54° = 180°

∠Q = 180° - 76°

∠Q = 104°

b)

Now as per the question,

ΔABC ≅ ΔPQR

Which implies that

AB = PQ

So,

PQ = 8 cm

Step-by-step explanation:

The unique property of Pythagorean triplets is the square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base.

In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and base are Pythagorean triplets.

Here,
Pythagorean triplet's unique property is that,
The square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base for a right-angled triangle.
hypotenuse² = perpendicular² + base²

Thus, the unique property of Pythagorean triplets is the square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base.

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Answer:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. Since the line given in the question is parallel to y = 1/4x + 7, we know that the line has a slope of m = 1/4.

To find the equation of the line that passes through (4,-1), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1).

Therefore, the equation of the line passing through (4,-1) and parallel to y = 1/4x + 7 is:

y - (-1) = 1/4(x - 4)

y + 1 = 1/4x + 1

This is the equation of a line passing through (4,-1) and parallel to y = 1/4x + 7.