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​

The probability of the random variables being less than 23 will be 0.6.

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 a random variable has possible values of 20, 21, 22, 23, and 24 that are equally likely to occur.

Total sample = { 20, 21, 22, 23, 24 } = 5

Favourable outcome = { 20,21,22} = 3

The probability will be calculated as,

Probability = 3 / 5

Probability = 0.6

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Answer:

for ponits

Step-by-step explanation:

Answer:

U dry aint put a answer

Step-by-step explanation:

Transformation involves changing the position of a function.

The equation of the new function is: \(\mathbf{g(x) = -3\sqrt{x + 5} - 12}\)

The function is given as:

\(\mathbf{f(x) = \sqrt x}\)

The rule of reflection across the x-axis is:

\(\mathbf{(x,y) \to (x,-y)}\)

So, we have:

\(\mathbf{f'(x) = -\sqrt x}\)

The rule of translation, 4 units down and 5 units left is:

\(\mathbf{(x,y) \to ( x + 5,y-4)}\)

So, we have:

\(\mathbf{f"(x) = -\sqrt{x + 5} - 4}\)

The rule of vertical stretch by a factor of # is:

\(\mathbf{(x,y) \to (x,3y)}\)

So, we have:

\(\mathbf{g(x) = 3(-\sqrt{x + 5} - 4)}\)

\(\mathbf{g(x) = -3\sqrt{x + 5} - 12}\)

Hence, the equation of the new function is:

\(\mathbf{g(x) = -3\sqrt{x + 5} - 12}\)

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Answer:

∠ R = 30°

Step-by-step explanation:

The secant- secant angle R is half the difference of its intercepted arcs, so

∠ R = \(\frac{1}{2}\) (103 - 43)° = \(\frac{1}{2}\) × 60° = 30°

Answer: C

Step-by-step explanation:

Okay first set a comparison since the two triangles are similar

x-1/20=x-1+27/3x+8

x-1/20 = x+26/3x+8

cross multiply

20x+520=3x^2+8x-3x-8

3x^2-15x-528=0

3(x^2-5x-176)=0

im kinda lazy to factor this out so i used an online calculator right here but factor it out like a good kid

x=16, x=-11

it has to be positive so x=16

C

Answer:

Linear - 4

Quadratic - 1

Quartic - 3

Quintic - 2

Step-by-step explanation:

The total amount owed by the students for the week is $\($28\).

An amount owed refers to total of the money a person owe us from time to time which can include loan and any unpaid interest, fees and expenses. It can also be an ordinal expenses such as school fee etc.

The total amount owed by the student will be:

= $3.00 + $8.00 + $7.00 + $10.00

= $28

Full question "On the first Monday of each month, the school sends home a note that includes each student's lunch account balance. These students owe money. Student 1 =$3.00, Student 2 - $8.00, Student 3 - $7.00, Student 4 - $10.00. What is the total amount owed by the student?".

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The linear inequality that satisfies the point (1, 1) is y ≤ 2x – 1 option (D) y ≤ 2x – 1 is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The graph of the linear inequality is shown in the picture.

The point is (1, 1)

Take the equation:

y ≤ 2x – 1

Plug x = 1, y = 1

1 ≤ 2 – 1

1 ≤ 1  (True)

Thus, the linear inequality that satisfies the point (1, 1) is y ≤ 2x – 1 option (D) y ≤ 2x – 1 is correct.

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Answer:

After finding the sides of the triangle using sine law, we found that the height of the flagpole is found to be 110.89 ft.

What is meant by sine law?

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.

Given,

 The distance between two observers = 600 ft

The angle of elevation of the first observer = 19°

The angle of elevation of the second observer = 21°

We are asked to find the height of the flagpole.

The figure is given below.

There are 2 right triangles, ΔABD and ΔCBD.

We will start with ΔABC.

∠B = 180 - (∠A+∠C) = 180 - (21+19) = 140

Now using sine law, we can find lengths a and b.

According to sine law,

b/sin21 = a/sin 19 = 600/sin 140

From this,

b/sin 21 = 600/sin 140

b/0.36 = 933.43

b = 336.03ft

Also,

a/sin 19 = 600/sin 140

a/0.33 = 933.43

a = 308.03ft

Now using ΔABD,

sin 21  =h/a

0.36 = h/308.03

h = 110.89 ft

Therefore after finding the sides of the triangle using sine law, we found that the height of the flagpole is found to be 110.89 ft.

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C = Q/mT, where C is the specific heat capacity, Q is the heat energy, m is the mass, and T is the temperature change, is the equation for specific heat capacity. C = Q/mT is the function that must be used to solve for the variables related to temperature change.

C = Q/mT, where C is the specific heat capacity, Q is the heat energy, m is the mass, and T is the temperature change, is the equation for specific heat capacity. This equation can be used to determine how much energy is required to alter the temperature of a given mass by a certain amount. The formula C = Q/mT must be used to find the variables related to temperature change. According to this equation, the specific heat capacity (C) is multiplied by the temperature change (T) to determine the amount of heat energy (Q) required to create a temperature change (T) in a given mass (m). The specific heat capacity (C) and mass can be multiplied to find the heat energy (Q) by rearranging the equation (m).

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Please attached a diagram drawn with MS Word based on the question parameters, and from a diagram from a similar question.

The length of the rectangle that contains 10 identical squares and has a width of 15 centimeters is 21 centimeters

A square is a quadrilateral that has four sides of the same length and the the four interior angles are each equal to 90°.

Some parts of the question appear missing, please find attached the design of a rectangle based on a similar GCSE question online. The width of the rectangle = 15 cm

The number of squares = 10

The number of squares that make up the width from the drawing = 5

The side length of the square is therefore; 15 cm ÷ 5 = 3 cm

The number of squares that make up the length of the rectangle = 7

The length of the rectangle is therefore, L = 7 × 3 cm = 21 cm

The length of the rectangle = 21 centimeters

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Answer:

its 56 units square.

Step-by-step explanation:

(count the tiles in the shaded figure, you'll get the area)

In response to the given question, we can state that Rounding this to the  Pythagorean theorem nearest inch gives an answer of \($\boxed{\textbf{(D) }45}$\)

The Pythagorean Theorem is the foundational Euclidean geometry relationship among a right triangle's three sides. The area of a cube with the velocity vector side is the sum of something like the areas of squares that have the other two sides, according to this rule. The rectangle that spans the slope of a triangular shape across the sharp angle equals the total of the rectangles that span its sides, as defined by the Pythagorean Theorem. In general algebraic notation, it is written as a2 + b2 = c2.

The height of each triangle can be found using the Pythagorean theorem:

\($15^2 - \left(\frac{20}{2}\right)^2 = 225 - 100 = 125$, so the height of each triangle is $\sqrt{125} = 5\sqrt{5}$.\)

The overall height of the kite is the sum of the heights of the two triangles, which \(is $2 \cdot 5\sqrt{5} = 10\sqrt{5}$.\)

Rounding this to the nearest inch gives an answer of \($\boxed{\textbf{(D) }45}$\)

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If the denominator does not equal 0, the equivalent expression of \(\frac{14x^4y^6}{7x^8y^2}\) is \(\frac{2y^{4}}{x^{4}}\)\(\frac{x^{10} y^{14}}{729}\)

The expression is given as:

\(\frac{14x^4y^6}{7x^8y^2}\)

Divide 14 by 7

\(\frac{14x^4y^6}{7x^8y^2} = \frac{2x^4y^6}{x^8y^2}\)

Apply the law of indices

\(\frac{14x^4y^6}{7x^8y^2} = \frac{2y^{6-2}}{x^{8-4}}\)

Evaluate the differences in the exponents

\(\frac{14x^4y^6}{7x^8y^2} = \frac{2y^{4}}{x^{4}}\)

Hence, the equivalent expression of \(\frac{14x^4y^6}{7x^8y^2}\) is \(\frac{2y^{4}}{x^{4}}\)

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Answer:

A- The survey results will be inaccurate because lawns in one neighborhood do not represent all types of lawns in a large city.

Step-by-step explanation:

smile:)

Answer:

For this exercise we need to solve the next equation:

3 +6x = 2x + 27

We can start substracting 3 at both sides:

3 + 6x - 2 = 2x + 27 - 3

6x = 2x + 25

And then, we can substract 2x::

6x - 2x = 2x + 24 - 2x

4x = 25

Then, we divide by 4:

4x/4 = 24/4

x = 24/4 = 6

Now, we can see if we have done it correctly:

3 + 6*6 = 39

2 * 6 + 27 = 39

And we have seen our result is correct

Thus, the dimensions that will give the maximum enclosed area are:  x = (320 - 3w)/4 and y = 80 - 3w/2.

To find the dimensions that will give the maximum enclosed area, we need to use the formula for the area of a rectangle, which is A = lw (where A is the area, l is the length, and w is the width).

Let's call the length of one corral x and the length of the other corral y. Since the corrals are adjacent, they share a common side, which we'll call w.

So we have two equations:

2x + y + 3w = 320 (the total amount of fencing)

A = xy (the area we want to maximize)

We can solve the first equation for y:

y = 320 - 2x - 3w

Then substitute that into the equation for the area:

A = x(320 - 2x - 3w)

Now we need to find the value of x that will give us the maximum area. To do this, we'll take the derivative of A with respect to x, set it equal to zero, and solve for x:

dA/dx = 320 - 4x - 3w = 0

4x = 320 - 3w

x = (320 - 3w)/4

Now we can substitute that value of x back into our equation for y:

y = 320 - 2(320 - 3w)/4 - 3w

y = 80 - 3w/2

We know that w must be positive, so we can find the maximum value of the area by taking the second derivative of A with respect to x:

d^2A/dx^2 = -4

Since this is negative, we know that we have a maximum.

So the dimensions that will give the maximum enclosed area are:

x = (320 - 3w)/4

y = 80 - 3w/2

w > 0

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The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.

The given function is f(x) = e^x near x = 0.

To find the best linear approximation, L(x), we use the formula:

L(x) = f(a) + f'(a)(x-a),

where a is the point near which we are approximating.

Let a = 0, so that a is near the point x = 0.

f(a) = f(0) = e^0 = 1

f'(x) = d/dx (e^x) = e^x;

so f'(a) = f'(0) = e^0 = 1

Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1

Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.

For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.

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Answer:

Step-by-step explanation:

this is called a ratio and proportion or similar triangles

  21    =     35  

 31.5           x

do cross multiply:

21 x = 31.5 (35)

x = 1102.5 / 21

x = 52.5 cm

The second probability is affected by the first probability. So, we can say that this is a dependent probability.

Given,

Number of white gems = 7

Number of green gems = 5

Number of blue gems = 3

Total number of gems = 7 + 5 + 3 = 15

We have to find the probability when picking a green gem and then another green with out replacement are dependent.

Here,

Probability of choosing the first gem green = Number of green gems / total number of gems

Probability = 5/15 = 1/3

Now,

Number of green gems = 4

Total number of gems = 14

Probability of choosing the second gem green = Number of green gems / Total number of gems

Probability = 4/14 = 2/7

Here,

The second probability is affected by the first probability. So, we can say that this is a dependent probability.

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The given problem can be represented with the help of Venn diagrams. Since 5 of the total 32 students neither swim nor play softball, there are 27 students who either swim or play softball or do both.

Here is the diagram for the given data:We can represent the values for each category as:A = Number of students who swim onlyB = Number of students who play softball onlyC = Number of students who swim and play softball bothD = Number of students who do neitherSwim | Play Softball | TotalNumber of Students (A) | |Number of Students (C) | |Number of Students (B) | |Number of Students (D) | |Total | |We have been given that 22 students swim and 20 students play softball. Let us start filling up the table using the given data:Swim | Play Softball | TotalNumber of Students (A) | |Number of Students (C) | |Number of Students (B) | |Number of Students (D) | 5Total | |27So, we can say that the values that complete the table are:A = 12B = 10C = ?D = 5C can be found out using the fact that the total number of students who either swim or play softball is 27.A + B + C = 27Substituting the values of A and B, we get12 + 10 + C = 27C = 5 + 27 - 12 - 10C = 10Therefore, the complete table is:Swim | Play Softball | TotalNumber of Students (A) | 12 |Number of Students (C) | 10 |Number of Students (B) | 10 |Number of Students (D) | 5Total | 32 |In total, there are 12 students who swim only, 10 students who play softball only, 10 students who do both, and 5 students who do neither.

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The value of Acute angle is approximately 0.4049 radians or 22.6199 degrees.Option (1) is correct.

A polygon with three sides and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with points A, B, and C. In Euclidean mathematics, any three points that are not co-linear produce a distinct triangle and a distinct plane.

We have given In the diagram of ABC shown below, BC= 10 and AC = 24.

Let x be the acute angle

Then;

We know that

tanx = P/B = BC/AC

tanx = 10/24

tanx = 5/12

x = tan⁻¹(5/12)

Alternatively, we can use the identity:

tan(tan⁻¹(x)) = x

Applying this identity, we get:

tan(x) = 5/12

We can then use a calculator or a trigonometric table to find the exact value of x. In degrees, we have:

x = tan⁻¹(5/12) ≈ 22.6199°

Therefore, the value of x is approximately 0.4049 radians or 22.6199 degrees.

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The radius of convergence and interval of convergence of the series, [infinity] xn / 9^(7n!) n = 1, is  R = ∞.

To determine the radius of convergence and interval of convergence of the series, [infinity] xn / 9^(7n!) n = 1, we shall apply the ratio test.

Firstly, let's write down the series to be tested with the general term written explicitly.

[infinity] xn / 9^(7n!) n

= 1x_n

= x_n9^(7n!)x_(n+1)

= x_(n+1)9^(7(n+1)!)

Thus, we can write out the ratio as: |x_(n+1)|9^(7(n+1)!)|x_n|9^(7n!)

The above equation is only valid when n is sufficiently large. This is because for n < N (N some positive integer), the values of the ratio test might be undefined (or meaningless) for one reason or another.

To make the calculation of the ratio easier, we shall take the absolute value of each term in the above equation.

Hence, |x_(n+1)| / |x_n| = 9^(7n! - 7(n+1)!)

Now we are able to find the radius of convergence. The ratio test tells us that a series is convergent if the ratio of successive terms approaches zero as n approaches infinity.

We can write this mathematically as: lim_(n->∞) |x_(n+1)| / |x_n| < 1

For the series given in this question, this condition is equivalent to: lim_(n->∞) 9^(7n! - 7(n+1)!) < 1

Simplifying, we get: lim_(n->∞) 9^(-7n!) / 9^(-7(n+1)!) < 1lim_(n->∞) 1 / 9^7 < 1

Since the limit is less than 1, the series is convergent.

The radius of convergence is: R = ∞

Interval of convergence can be obtained from the formula: [-R, R].

Therefore, interval of convergence of the series is (-∞, ∞).

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Using the given formula, the sum of S(n) for the arithmetic series is 565.5.

In the given question we have to find the sum S(n) for the arithmetic series

The given formula is S(n)=n/2 {a(1)+a(n)}

The given values are a(1)=12, a(n)=75,n=13

We just have to put values in given formula

S(n)=n/2 {a(1)+a(n)}

S(n)=13/2 (12+75)

S(n)=6.5*87

S(n)=565.5

Hence, the sum of S(n) for the arithmetic series described is 565.5.

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