An 8-ounce bag of pretzels
contains 68 pieces. How many
pieces would you expect in a 12-
ounce bag?

The number of different collections of writing utensils could Faruq bring to class if he doesn't want to show up empty-handed is ab + a + b

Since Faruq has a identical markers, b identical pencils, and no other writing utensils in his locker and we require the number of collections or ways he could bring them to school without coming to school empty-handed, we use combination mathematics since order does not matter.

Now, Faruq can either come to school with one marker and one pencil or one pencil or one marker.

So, the combination for one marker and one pencil is n = a × b = ab

The combination for one marker is n' = a

The combination for one pencil is n" = b

So, the total combination is N = n + n' + n"

= ab + a + b

So, the number of different collections of writing utensils could Faruq bring to class if he doesn't want to show up empty-handed is ab + a + b

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The figure shown can be divided into three rectangles , the two yellow ones and the blue one.

As the width of the yellow triangles is 1 unit and the length of the entire shape is 8 units , it can be calculated that the length of the blue triangle is 6 units ( as shown in second picture )

\(\therefore \: area \: of \: figure \: = \: area \: of \: two \: yellow \: triangles \: \times area \: of \: blue \: triangle\)

\(area \: of \: figure \: = 2( \: l \times b \: ) + ( \: l' \times b' \: ) \\ \dashrightarrow \: area \: = 2(5 \times 1) + (6 \times 1) \\ \dashrightarrow \: area = 10 + 6 \\ \dashrightarrow \: \boxed{area \: = 16 \: {units}^{2} }\)

hope helpful! :)

Answer:

A

Step-by-step explanation:

Hello!

The answer is attached with explanation. Please note me if you have any more questions.

Answer:

Letter A.

\( {f}^{ - 1} (x) = \frac{ x + 8}{9} \)

Answer:

$27.14

Step-by-step explanation:

Price of 1 DVD: $9.10

Price of 4 DVDs: 4 * $9.10 = $36.40

Discount: 25%

Now we find 25% of $36.40.

25% of $36.40 =

= 0.25 * $36.40

= $9.10

The 25% discount amounts to $9.10. We now subtract $9.10 from $36.40 to find the discounted price.

$36.40 - $9.10 = $27.30

Now we need to apply the 6.75% tax to $27.30.

6.75% of $27.30 =

= 0.0675 * $27.30

= $1.84

The sales tax is $1.84.

Now we add the sales tax amount to the total discounted price.

$27.30 + $1.84 = $29.14

Answer: $27.14

According to the given information, the answer is 1 / 10.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The frequency of card A is 8 and the frequency of card 2 is 12. Therefore, the total frequency of cards that are A or 2 is 8 + 12 = 20.

The total number of cards is the sum of the frequencies: 8 + 12 + 11 + 17 + 14 + 12 + 15 + 18 + 13 + 20 + 16 + 24 + 20 = 200.

So the experimental probability that the card selected was an A or 2 is:

Frequency of A or 2 / Total number of cards = 20 / 200 = 1/10

Therefore, the answer is 1 / 10.

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Answer:

2400

Step-by-step explanation:

You have to follow PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction).  Based off of this, you have to do the multiplication first, and then add.

263 × 24 - 164 × 24 + 24

6312 - 3936 + 24

2376 + 24

2400

The value of the expression 263 · 24 − 164 · 24 + 24 will be 2400.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The expression is given below.

⇒ 263 · 24 − 164 · 24 + 24

Simplify the expression, then the value of the expression is given as,

⇒ 263 · 24 − 164 · 24 + 24

⇒ 6312 − 3936 + 24

⇒ 6336 − 3936

⇒ 2400

The value of the expression 263 · 24 − 164 · 24 + 24 will be 2400.

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Answer:

Step-by-step explanation:

23.21

Answer:

23.208

Step-by-step explanation:

By applying the concept of corresponding angles in similar triangles, we were able to establish the value of x as 25 in the given scenario.

In the given problem, we are provided with information about the angles in two similar triangles: triangle ABC and triangle STU. It is stated that angle UTS in triangle STU is 100 degrees, and since corresponding angles of similar triangles are congruent, we can conclude that angle STU is also 100 degrees.

Next, we examine angle BAC in triangle ABC, which is given as 4x. Using the same logic, we know that angle BAC is also congruent to angle STU. Therefore, we can equate the two angles:

angle BAC = angle STU

4x = 100

To find the value of x, we divide both sides of the equation by 4:

x = 100/4

x = 25

Hence, we determine that x is equal to 25. This method allows us to leverage the known information about one triangle to infer the measurements of corresponding angles in the other similar triangle.

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Both of you are correct because using either way can solve the equation for the value of x.

In the case of solving for x in  2/5 x = 14, the goal is to get rid of the fraction that is multiplying x on the left side. This can be done by either multiplying both sides of the equation by the inverse of 2 / 5 ( which is 5 / 2 ) or by dividing both sides by 2 / 5.

Doing either of these things would get rid of the 2 / 5 and give an answer to x as shown below :

Multiplying :

2/5 x = 14

5 / 2 x 2 / 5 x = 14 x 5 / 2

x = 35

Dividing :

2/5 x = 14

2 / 5 x / 2 / 5 = 14 / 2 / 5

x = 35

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Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

The average value of the given function on the given interval is = 7/2 and 6.25 respectively

What is Average?

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

(a) f(x) = x2 – 8x + 10

f = 1/b-a \(\int\limits^b_a {f(n)} \, dx\)

f = 1/5-2 \(\int\limits^5_2 {x^{2} -8x+10} \, dx\)

Here, a=2

b=5

f(x) =x2 – 8x + 10

f = 1/3 (x³/3 - 8x²/2+10x)5/2

f = -25/9 -20/9

f = -45/9

= -5

Mean Value Theorem

If f(x) = continous on (a, b)

If f(x) = differentiable on (a, b)

Then f(c) = f(b) -f(a)/b-a

were c∈ (a,b)

Here, f(c) = f(-5)-f(2)/5-2

f(c) = -5+2/3

f(c) = -1 ......................(1)

Here, f(x) = x²-8x+10

f(c) = c²-8c+10

f(x) = 2c-8...................(2)

equating 1&2

2c -8 = -1

2c = -1 +8

c = 7/2

c∈ (2,5)

(b) f(x) = Vx on [1, 16]

f = \(\sqrt{x}\) on (1 ,16)

f= 1/b-a \(\int\limits^b_a {f(n)} \, dx\)

f = 1/16-1 \(\int\limits^6_1 {\sqrt{x} } \, dx\)

f = ( 2x (3/2)/45)₁¹⁶

f = 128/45-2/45

f = 126/45

= 14/5

Mean Value Theorem

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

f(c) =\(\sqrt{c}\)

f(c) = 1/2\(\sqrt{c}\)....................(1)

we know that

f(c) = f(b)-f(a)/b-a

f(c) = f(16)-f(1)/16-1

f(c) = \(\sqrt{16}\) -\(\sqrt{1}\)/15

f(c) = 4-1/15

= 3/15.....................(2)

Equating (1) and (2)

1/2\(\sqrt{c}\) = 3/15

2\(\sqrt{c}\) = 15/3

2\(\sqrt{c}\) = 5

\(\sqrt{c}\) = 5/2

c = (5/2)²

=25/4

c≅ 6.25

6.25 = (1 ,16)

The average value of the given function on the given interval is = 7/2 and 6.25 respectively

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Answer:

There is no picture but I think b

Step-by-step explanation:

The answer for it is diagram B because it does not cross or have parallel lines

Answer:

1008 cm²

Step-by-step explanation:

The triangular prism comprises:

Formulae

Area of a triangle = 1/2 × base × height

Area of a rectangle = width × length

Total surface area:

= 2 triangles + rectangle 1 + rectangle 2 + rectangle 3

= 2(1/2 × (9 + 5) × 12) + (15 × 20) + (13 × 20) + ((5 + 9) × 20)

= 2(1/2 × 14 × 12) + (15 × 20) + (13 × 20) + (14 × 20)

= 168 + 300 + 260 + 280

= 1008 cm²

Area of two side triangles

Area of atop rectangles

Area of base rectangle

TSA

Answer:

  9/2

Step-by-step explanation:

It is the ratio between y-values for consecutive x-values. Perhaps the easiest two points to work with are ...

  (x, y) = (0, 1), (1, 9/2)

The rate of change you're looking for is (9/2)/1 = 9/2.

Answer:

D. 9/2

Step-by-step explanation:

Edge 2021

Answer:

0

Step-by-step explanation:

It is 0 where t is the time in seconds after the ball leaves my hand

Thhe required steps to follow is given in the exlanation.

The copying of is to use your compass to sort of measure how wide the angle is open ; then you create another angle with the same amount of opening.

From the question the required step to be followed  to create a copy of ∠CAB.

1. Mark a point X that will be vortex of new angle.

2. Use a straightedge to draw XZ. This will become one side of the new angle.

3.Use a straightedge to draw a ray  with endpoint X.

4. Without changing the setting,place the compass point at X and draw an arc intersecting the ray. Mark the point Y at the intersection.

5. Without changing the setting,place the compass point at Y and draw an arc intersecting the ray. Mark the point Z at the intersection.

6. Place the point at A. Draw an arc that intersect both rays of ∠A. Label the points of intersection B and C.

7. Put the compass point at C, and opens the compass to the distance between B and C.

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Answer:

Option (D) : (3.5, 8.75)

Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

The solution to the system of equations is x = 6 and  y = -5, which is the same as we obtained using the elimination method.

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:

2x + y = 7 ---(1)

x + y = 1 ---(2)

To solve this system, we can use the method of elimination or substitution.

Method 1: Elimination

In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.

Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:

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

Multiplying equation

(2) by -2-2x - 2y = -2

Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:

2x + y = 7(-2x - 2y = -2)0x - y = 5

We now have a new equation in which y is isolated.

To solve for y, we can multiply both sides by -1:

-1(-y) = -1(5)y = -5

Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6

Therefore, the solution to the system of equations is (x,y) = (6,-5).

Method 2: Substitution

In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.

From equation (2), we can solve for y in terms of x:y = 1 - x

We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6

Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5

Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.

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The correct answer is option D. Which is the even function is f (x) = x⁴.

The function in which when the sign of the input variable is changed the output remains the same is called the even function. Mathematically we can write it as f(x) = f(-x ).

let us check the given four options:-

A f(x) = √x ;  f(-x) = √-x  here f(x) ≠ f(-x)

B f(x) = x ;  f(-x) = -x    here f(x) ≠ f(-x)

C f(x)  = x³ + 1 ; f(-x) = -x³ + 1  here f(x) ≠ f(-x)

D f(x)  = x⁴  ;  f(-x) = (-x)⁴ = x⁴  here f(x) = f(-x)

We can see that in the option D the f(x) = x⁴ is an even function because f(x) = f(-x).

Therefore the correct answer is option D. Which is the even function is f (x) = x⁴.

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Since we can choose 4 of the 15 toppings, we can order 1365 different types of pizzas with 4 toppings

Since the question says 'choose', it is a combination question and order is not important.

This is the number of ways in which x objects can be selected from n objects.

It is given mathematically as ⁿCₓ = n!/[r!(n - r)!]

Now given that we have 15 toppings for pizza and we want to choose any 4, So, we are choosing 15 toppings in 4 ways. So,

So, ¹⁵C₄ = 15!/4!(15 - 4)!

= 15!/4!11!

= 15 × 14 × 13 × 12 × 11!/4!11!

= 15 × 14 × 13 × 12/24

= 15 × 7 × 13

= 1365 ways

So, we can order 1365 different types of pizzas with 4 toppings

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The break-even point for the glide 5 hoverboard is 36670.4.

Given that:

We know that at break-even:

Now,

By subtracting "25.42x" from both sides, we get:

Then,

Therefore, the break-even point for the glide 5 hoverboard is 36670.4.

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Answer:

A) (x-4)(x+16)

Step-by-step explanation:

\(x^2+12x-64\\=x^2-4x+16x-64\\=x(x-4)+16(x-4)\\=(x+16)(x-4)\)

The expression arcctg(tg(x)) simplifies to arcctg(tan(x)).

To simplify the expression arcctg(tg(x)), we can apply trigonometric identities and properties.

The function arcctg(x) is the inverse cotangent function, which is the angle whose cotangent is x. Similarly, tg(x) represents the tangent function.

First, let's simplify the expression inside the arcctg function, which is tg(x):

tg(x) = sin(x) / cos(x)

Now, we can substitute this value into the original expression:

arcctg(tg(x)) = arcctg(sin(x) / cos(x))

Using the property of inverse trigonometric functions, we can rewrite this as:

arcctg(sin(x) / cos(x)) = arcctg(1 / tan(x))

Now, we can simplify further using the identity:

1 / tan(x) = cot(x)

Therefore:

arcctg(1 / tan(x)) = arcctg(cot(x))

Using another identity, we know that the cotangent function is the reciprocal of the tangent function:

cot(x) = 1 / tan(x)

Therefore, we can simplify the expression to:

arcctg(cot(x)) = arcctg(1 / tan(x)) = arcctg(tan(x))

Finally, we arrive at the simplified expression:

arcctg(tg(x)) = arcctg(tan(x))

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Answer:

I think 164

Step-by-step explanation:

1312/8

Answer:

rectangle= 22*9 = 198ft

triangle=11*10 = 110 ft

110+ 198 = 308 polygon

Answer:

a)-27/20

Step-by-step explanation:

3/5 ÷ (-4/9)

3/5 × (-9/4)

-27/20

Hope it will help

C) There is sufficient evidence to reject the claim i ¼- 486.(correct option)

Hypothesis=A hypothesis is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous observations that cannot satisfactorily be explained with the available scientific theories .A hypothesis  in a scientific context, is a testable statement about the relationship between two or more variables.

for that given problem we want to test that

There sufficient evidence to reject the Claim that  i¼-486.

Option C is correct

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Answer:

x = 27° , <EAF = 27°

Step-by-step explanation:

63° + x° = 90°

x = 27°

63° + <EAF = 90°

<EAF = 27°