Pls help dont answer if you don’t know i will give out brainliest please

Pls Help Dont Answer If You Dont Know I Will Give Out Brainliest Please

Answers

Answer 1

Answer:

34.65

Step-by-step explanation:

495x0.07=34.65

Answer 2
$34.65 is the correct answer495 x 0.07 = 34.65Please let me know if I am wrong.

Related Questions

I’m confused in the exponential

Answers

Answer:

this mean in case of multiplying exponents with same base you should add the exponent and keep base same.

example:

[tex] {6}^{4} \times {6}^{5 } = {6}^{4 + 5} \\ = {6}^{9} [/tex]

What is the angle of rotation of the following figure?

Answers

This snow flake-like figure can be generated by rotating an end 60° five times around the center of the hexagon. There are two forms: (i) clockwise, (ii) counterclockwise.

What is the angle of rotation of a snow flake?

Geometrically speaking, snow flakes represent regular hexagons. Regular hexagons can divided into six concentric regular triangles, whose central angles have a measure of 60°. This fractal figure can be generated by rotating 60° five times around the center.

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PLS HELP OR I WILL FAIL I BEG U HELP

Answers

Answer:

The first one, you cannot factor because the two values do not share any common factors. Hence, the answer would just be:

a. 51x-25

The other one, we can factorise to:

b. 3x(4-x)

Step-by-step explanation:

For the second option:

Common factor between 12x and 3x^2 is 3x.

Take this out to the front, we are left with:

3x(4-x)

A website I recommend you use (math calculator with some instructions) is Symbolab.

https://www.symbolab.com/solver/factor-calculator/factor%2012x-3x%5E%7B2%7D?or=input

Evaluate 2x − 2 for x = 0, x = 1, and x = 2. Question 1 options: A) −1, 0, 2 B) −1, 1, 2 C) 0, 1, 2 D) 1, 2, 4

Answers

The value of x in 2^x - 2 when x = 0, x = 1 and x = 2 are -1, 0 and 2 respectively. option A

Algebra

2^x - 2

when x = 0

2^x - 2

= 2^0 - 2

= 1 - 2

= -1

when x = 1

2^x - 2

=2^1 - 2

= 2 - 2

= 0

when x = 2

2^x - 2

= 2^2 - 2

= 4 - 2

= 2

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Between permanent life insurance and term life insurance, which typically has the lower premium and why?
a.
Term life insurance has the lower premium because term life insurance pays the face value to your beneficiary if you die within a certain set period of time, whereas whole life insurance covers you your entire life.
b.
Term life insurance has the lower premium because you cannot renew the insurance after your term has ended.
c.
Permanent life insurance has the lower premium because you are making more premium payments (your whole life versus a set period of time), so the amount per premium payment is less.
d.
Permanent life insurance has the lower premium because the amount you contribute is then invested and makes interest for the life insurance company.


Please select the best answer from the choices provided

A
B
C
D

Answers

Term life insurance has the lower premium because term life insurance pays the face value to your beneficiary if you die within a certain set period of time, whereas whole life insurance covers you your entire life. (Option A)

What is insurance?

Insurance is when a third-party (the insurer) promises to indemnify another party (the insured) for losses they might suffer in the future in exchange for agreed upon payments.

Permanent life insurance is a type of insurance that provides a coverage that never expires. The person with a permanent life insurance is covered until he or she passes on. Whole life insurance is a type of permanent life insurance that has a fixed and guaranteed premium and a fixed death benefit.

Term life insurance is a type of insurance that provides coverage to a person only for a scheduled period of time. For example, a person who buys a 10 year term life insurance, the person's insurance only lasts for 10 years. If the person passes on within the 10 years, his beneficiary receives payments. If the person passes on after 10 years, his beneficiary does not receive any payments.

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The soil samples for the next field indicate that fertilizer

Answers

In order to have a greater fertilizer coverage, you need to increase flow rate and: A. increase speed to approximately 7.1 mph so that you cover the field more quickly.

What is a flow rate?

A flow rate is an average rate and it can be defined as the number of flow units that are created per unit time such as fertilizer coverage on a farm.

In this context, we can infer and logically deduce that you have to increase flow rate and your increase speed to approximately 7.1 mph, so that you can cover the field more quickly and have a greater fertilizer coverage.

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Complete Question:

The soil samples for the next field indicate that fertilizer coverage needs to be greater. To achieve this, you need to increase flow rate. How would you achieve this?

A. Increase speed to approximately 7.1 mph so that you cover the field more quickly

B. Increase the engine speed to approximately 2,000 rpm

C. Decrease speed to approximately 6.0 mph so that you cover the field more slowly

D. Shift to second gear so that the engine speed slows

help me pleaseeeee (20 points)
what is the volume of this solid?

Answers

Answer:

A) 39

Step-by-step explanation:

If you calculate the volume of the cube which is the V=a^3 you get 27, then calculating the pyramid, the Length is 3, and the Width is also 3. Then the height is 4. so you put that into the formula to calculate the volume which is V=L*W*H
    --------

        3

you get 12. Now its simple, you just add the 2 volumes, so you do 27+12 and its 39.

39 is the answer by calculating the volume using formula!

Rationalize the denominator and simplify
√a+1-2/√a+1+2

Answers

5+a-4√(a+1)/(a-3) is the simplified form of the number. This can be obtained by multiplying numerator and denominator with conjugate of the denominator.

Simplify the number:

Given the number,

√a+1-2/√a+1+2

Denominator = √a+1+2

Conjugate of the denominator = √a+1 - 2

Now, (√a+1-2)(√a+1 - 2 )/√(a+1+2)(√a+1 - 2 )

=(√a+1 - 2 )²/(√a+1)² - 4

=(a+1 -4√a+1+5)/(a+1-4)

=5+a-4√(a+1)/(a-3)

Hence 5+a-4√(a+1)/(a-3) is the simplified form of the number.

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I need help to this it would be awesome if you could help.

Answers

In the given diagram, the value of JI is 6

Solving equations

From the question, we are to determine JI

From the given diagram, we can write that

JI + IH = x + 22

Also,

JI = 2x + 28

and

IH = 5

Then, we can write that

2x + 28 + 5 = x + 22

Collect like terms

2x - x = 22 -28 -5

x = -11

Now, substitute the value of x into the equation

JI = 2x + 28

JI = 2(-11) + 28

JI = -22 +28

JI = 6

Hence, the value of JI is 6

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Integral of
11-3x/
x²+2x-3
dx

Answers

Answer:

2x+2

Step-by-step explanation:

x²+2x-3

=2(x^2-1)+2*1(2x^1-1)

Find the circumference and the area of a circle with diameter 4 cm.
Use the value 3.14 for
, and do not round your answers. Be sure to include the correct units in your answers.

Answers

Answer:

Step-by-step explanation:

Since diameter x pi=3.14,this should be easy.

4x3=12

4x14/100=.56

12+.56=12.56

12.56 is the answer

Consider these two functions:
F(x) = 2cos(πx)
G(x) = 1/2cos(2x)
What are the amplitudes and periods of the two functions?

Answers

Answer:

[tex]\mathrm{pK}_{\mathrm{a}}+\mathrm{pK}_{\mathrm{b}}=\mathrm{pK}_{\mathrm{w}}[/tex] for [tex]\mathrm{HCl}[/tex] \& [tex]\mathrm{ClOH}[/tex]

Answer:

f(x):  Amplitude = 2, Period = 2

g(x):  Amplitude = ¹/₂, Period = π

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function:

f(x) = A cos(B(x + C)) + D

where:

A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shift

Function f(x)

[tex]f(x)=2 \cos (\pi x)[/tex]

Comparing this with the standard form of a cosine function:

Amplitude = 2[tex]\sf Period = \dfrac{2 \pi}{\pi}=2[/tex]

Function g(x)

[tex]g(x)=\dfrac{1}{2} \cos (2x)[/tex]

Comparing this with the standard form of a cosine function:

[tex]\sf Amplitude=\dfrac{1}{2}[/tex][tex]\sf Period = \dfrac{2 \pi}{2}=\pi[/tex]

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-4
-2
4
-2-
0
3
On which interval are both functions increasing?
2
-8
p
0
-X
-2
g(x) = -x - 3| +4
(,0)

Answers

Answer: [tex](3, \infty)[/tex]

Step-by-step explanation:

q(x) is increasing for [tex]x > 3[/tex].

p(x) is increasing for [tex]x \geq -2[/tex].

So, both functions are increasing for [tex](3, \infty)[/tex].

If A is a 2 × 2 matrix, then A × I =
and I × A =

Answers

Since the multiplication between two matrices is not commutative, then [tex]\vec A\, \times\,\vec I \ne \vec I \,\times \,\vec A[/tex], regardless of the dimensions of [tex]\vec A[/tex].

Is the product of two matrices commutative?

In linear algebra, we define the product of two matrices as follows:

[tex]\vec C = \vec A \,\times \vec B[/tex], where [tex]\vec A \in \mathbb{R}_{m\times p}[/tex], [tex]\vec B \in \mathbb{R}_{p\times n}[/tex] and [tex]\vec C \in \mathbb{R}_{m \times n}[/tex]     (1)

Where each element of the matrix is equal to the following dot product:

[tex]c_{ij} = \left[\begin{array}{cccc}a_{i1}&a_{i2}&\ldots&a_{ip}\end{array}\right]\,\bullet\,\left[\begin{array}{ccc}b_{1j}\\b_{2j}\\\vdots\\b_{pj}\end{array}\right][/tex], where 1 ≤ i ≤ m and 1 ≤ j ≤ n.     (2)

Because of (2), we can infer that the product of two matrices, no matter what dimensions each matrix may have, is not commutative because of the nature and characteristics of the definition itself, which implies operating on a row of the former matrix and a column of the latter matrix.

Such "arbitrariness" means that resulting value for [tex]c_{ij}[/tex] will be different if the order between [tex]\vec A[/tex] and [tex]\vec B[/tex] is changed and even the dimensions of [tex]\vec C[/tex] may be different. Therefore, the proposition is false.

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Find the slope of a line parallel to a line that contains the points (8, -3) and (2, 5).
Select the best answer from the choices provided.
OA
413
OB. 4
O D.
413
3
OC 3
3|4
314

Answers

Answer:

[tex]-\frac{4}{3}[/tex](Your answer choices were really confusing, so I just put the plain answer)

Step-by-step explanation:

To find the slope of a line with just two points, we can use the formula [tex]\frac{y2-y1}{x2-x1}[/tex]. In this case, [tex]\frac{5-(-3)}{2-8}[/tex]. This is [tex]\frac{8}{-6}[/tex]. This reduces to [tex]-\frac{4}{3}[/tex]

Joy wants to invest $3000 in a savings account. Determine the interest rate (simple interest) required for Joy 's investment to double in value in 18 years. Round your answer to the nearest tenth of a percent.

Answers

The interest rate needed to double the investment in 18 years is  6%.

What is the interest rate?

Interest earned is a function of the amount invested, interest rate and time. The future value of the investment is to be $6000 (3000 x 2). Interest earned would be $3000 (6000 - 3000)

Interest rate = interest earned / (amount invested x time )

$3000 / ($3000 x 18) = 6%

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A washer and a dryer cost $737 combined. The washer costs $37 more than the dryer. What is the cost of the dryer

Answers

Answer: $350

Step-by-step explanation:

$700 divided by 2 is 350

solve 4/7- (-4/7)
A. 8/7
B.-8/7
C.-4/7
D.4/7​

Answers

Answer:

A. 8/7

Step-by-step explanation:

Step 1    

4/7 - (-4/7) --> 4/7 + 4/7

The two minutes turn into a plus, removing the bracket.

Step 2

4/7 + 4/7 = 8/7

Add the two fractions together.

Answer:

A. 8/7

Step-by-step explanation:

Jakobe runs a coffee cart where he sells coffee for $1.50 tea for $2 , and donuts for $0.75 . On Monday, he sold 320 items and made $415 . He sold 3 times as much coffee as tea. How many donuts did he sell?

Answers

Jakobe sold 150 coffee, 50 tea and 120 donuts at the coffee cart on Monday.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of coffee, y represent the amount of tea and z represent the amount of donuts, hence:

x + y + z = 320    (1)

Also:

1.5x + 2y + 0.75z = 415     (2)

And:

x = 3y     (3)

From the equations:

x = 150, y= 50 and z = 120

Jakobe sold 150 coffee, 50 tea and 120 donuts at the coffee cart on Monday.

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You have customers of the following ages, what is the median age of your customer base? 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70​

Answers

The median age of customer age is 45

The median age of your customer base = 45

What is median?

The median is the value that divides a data sample, a population, or even a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set. The fundamental difference between the mean and the median when describing data is that the median is more representative of the "typical" value because it is not skewed by the a small proportion of extremely large or small values. Due to the fact that income distribution can be highly skewed, the median income, for instance, might be a better indicator of what is considered a "typical" income.

Mean = middle term

          = 6th term

          = 45

Hence, Median of age = 45.

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When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 2kg, the acceleration of the object is 12 m/s^2. When the same force acts upon another object, its acceleration is 8m/s^2. What is the mass of this object?

Answers

The mass of the second object exists at 3 kg.

How to estimate the mass of the second object?

Let, F be the Force

a be the acceleration

m be the mass

The formula of force exists F = m [tex]*[/tex] a

Since force exists constant, then:

[tex]$m_1 = 2 kg, a_1 = 12 m/s^2[/tex] subset 1 designates the first object

[tex]$m_2 = ? , a_2 = 8m/s^2[/tex] subset 2 designates the second object

To estimate the mass of the second object

A constant force indicates [tex]$ m_1 * a = m_2 * a[/tex]

The mass of second object [tex]m_2[/tex], we get

[tex]m_1 * a = m_2 * a[/tex]

[tex]$m_2 = \frac{m_1 * a}{a}[/tex]

[tex]$=\frac{2*12}{8}[/tex]

= 24/8 = 3 kg

Therefore, the mass of the second object exists at 3kg.

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The function h(x) is a transformation of the square root parent function,
f(t) = t. What function is H(x)?

Answers

Answer:

A. [tex]h(x)=\sqrt{x-3}[/tex]

Step-by-step explanation:

Step 1: Definition

The parent function of [tex]\sqrt{x}[/tex] is translated to the left when [tex]h[/tex] is positive in the transformation [tex]\sqrt{x+h}[/tex].

If [tex]h[/tex] is negative, the graph translates towards the left with the distance equal to the value of [tex]h[/tex].

Step 2: Implementation

Here the graph moved 3 units towards the right. This means that [tex]h[/tex] is negative and has the value of 3.

So, plugging that into the parent function for translation, the function becomes:

[tex]h(x)=\sqrt{x-3}[/tex]

During a flu epidemic a company with 200 employees had 1/3 on Monday and another 3/10 call in sick on Tuesday.

Answers

Part (a)

[tex]\frac{1}{10}+\frac{3}{10}=\frac{4}{10}=\boxed{\frac{2}{5}}[/tex]

Part (b)

[tex]200\left(\frac{2}{5} \right)=\boxed{80}[/tex]

a coin is flipped 10 times and the result is recorded. How many outcomes are in the event n(A)?

Answers

There are 1024 outcomes in the event

How to determine the number of outcomes?

The given parameters are:

Device = coin

Number of flips = 10

A coin has 2 faces.

So, the number of outcomes is

Outcome = Faces^Flip

This gives

Outcome = 2^10

Evaluate

Outcome = 1024

Hence, there are 1024 outcomes in the event

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Answer:

[tex]1024[/tex]

Step-by-step explanation:

Each and every flip of our coin has two possible outcomes on the whole: it is either the heads or the tails. Besides, it resembles the bit in computing, right? Indeed, it has two options likewise: it can be either [tex]0[/tex] or [tex]1[/tex]. For now on I suggest thinking neither in heads nor in tails, but in bits. Suppose the heads is [tex]0[/tex], the tails is [tex]1[/tex]. Let us slightly simplify the condition, namely: suppose that the number of flips is [tex]3[/tex]. Then, our possible outcomes:

[tex]000 \\ 001 \\ 010 \\ 011 \\ 100 \\ 101 \\ 110\\ 111[/tex]

Take a look at the first number. In case it is [tex]0[/tex], we have [tex]4[/tex] outcomes because we can put either [tex]0[/tex] or [tex]1[/tex] not only on the second place, yet also on the third one. Abiding by the same logic, we also have [tex]4[/tex] outcomes when the first one is [tex]1[/tex]. In mathematics: [tex]2 * 2 * 2 = 2^3 = 8[/tex] outcomes.
As for the initial condition, it does not globally differ from our simplification, it just has more flips, hence it is not just a walk in the park to list all the possible outcomes anymore in this case, it is time-consuming otherwise. Even though, it is still not a big deal to count it: [tex]2 * ... * 2 = 2^{10} = 1024[/tex] outcomes.

A trapezoid has an area given by A =1-2(b1-b2)h,where b1,is the length of one base, b2 is the length of the other
base, and h is the height. If the trapezoid has an area of 14 square units, solve for b in terms of the other variables.

Answers

The value of [tex]b_{1}[/tex] is 69/4h and value of [tex]b_{2}[/tex] is 43/4h if the area of trapezoid is 14 square units.

Given that area is equal to 1-2([tex]b_{1} -b_{2}[/tex])h and area is 14 square units.

We know that area of trapezoid is equal to (a+b)h/2.

We have to put the given equation equal to 14 to get our first equation.

14=1-2([tex]b_{1} -b_{2}[/tex])h

14=1-2[tex]b_{1}[/tex]h+2[tex]b_{2}[/tex]h

2[tex]b_{1}[/tex]h-2[tex]b_{2}[/tex]h=-13------------1

Now put the value of area in the formula of area of trapezoid.

14=[tex](b_{1} +b_{2})h/2[/tex]

[tex]b_{1}[/tex]h+[tex]b_{2}h[/tex]=28-----------------2

Multiply equation 2 by 2 and then subtract 2 from 1

[tex]2b_{1}h -2b_{2}h -2b_{1}h-2b_{2}h[/tex]=-13-56

-4[tex]b_{2}h[/tex]=-43

[tex]b_{2}[/tex]=43/4h

Put the value of [tex]b_{2}[/tex] in 2 to get the value of [tex]b_{1}[/tex].

[tex]b_{1} h+43/4h*h=28[/tex]

[tex]b_{1}[/tex]=69/4h

Hence The value of [tex]b_{1}[/tex] is 69/4h and value of [tex]b_{2}[/tex] is 51/4h if the area of trapezoid is 14 square units.

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Write down the 2×2 matrices representing the following transformations of the plane. (i) Reflection in the y-axis, (ii) Reflection in the line y = x (iii) Rotation through 180◦ about the origin (iv) Enlargement from the origin with scale factor λ.

Answers

The 2 x 2 matrices of the transformations are

[tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex], [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex], [tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right][/tex] and [tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right][/tex]

(i) Reflection in the y-axis

The rule of reflection in the y-axis is

(x, y) ⇒ (-x, y)

This is represented as:

[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]

When solved using a graphing calculator, we have:

[tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]

Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex]

(ii) Reflection in the line y = x

The rule of reflection in the line y = x is

(x, y) ⇒ (y, x)

This is represented as:

[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}y&x\end{array}\right][/tex]

When solved using a graphing calculator, we have:

[tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}y&x\end{array}\right][/tex]

Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex]

(iii) Rotation through 180◦ about the origin

The rule of rotation through 180◦ about the origin is

(x, y) ⇒ (-x, -y)

This is represented as:

[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&-y\end{array}\right][/tex]

When solved using a graphing calculator, we have:

[tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]

Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right][/tex]

(iv) Enlargement from the origin with scale factor λ.

The rule of the enlargement from the origin with scale factor λ.

(x, y) ⇒ (λx, λy)

This is represented as:

[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}\lambda x&\lambda y\end{array}\right][/tex]

When solved using a graphing calculator, we have:

[tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}\lambda x&\lambda y\end{array}\right][/tex]

Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right][/tex]

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Evaluate functions from their graph g(−9)=
See the Correct Answer Attached!

Answers

Evaluating the function from the given graph, g(-9) = 1.

How to Evaluate a Function?

To find the value of a function for a given x-value using a given graph, trace the x-value against the corresponding y-value on the y-axis.

To evaluate the function from the graph given, for g(-9), find the y-value that corresponds to the x-value of -9.

The graph shows that when x = -9, the corresponding y-value is 1.

Therefore, g(-9) = 1.

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Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 12 pieces and costs \$8 dollar sign, 8.
Let R represent the number of additional rolls that Sofia orders.

Answers

Sofia will order 7 more rolls of sushi (84 pieces) and pay $56St

Step-by-step explanation: im right

if Jill's age is 84 and johns age is 21 how many years ago was Jill 10 times older than john

Answers

not sure if this is right but i gave it a go. hope it helps

1. In a class of 60 students, a survey was conducted, 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities. Find 1.. number of students that applied for all the universities. 2 number of students that applied for at least two of the universities. 3 number of students that applied at most two universities. 4 number of students that applied for Addis Ababa but not Bahir Dar University? Please I need your help?​

Answers

1. Consult the linked question. [tex]n(A\cap B\cap W) = \boxed{3}[/tex].

2. We have

[tex]n(A\cap B) = n(A\cap B \cap W) + n(A\cap B \cap W') \\\\ \implies 11 = 3 + n(A\cap B \cap W') \\\\ \implies n(A\cap B\cap W') = 8[/tex]

Similarly we can find

[tex]n(A\cap B' \cap W) = 3[/tex]

[tex]n(A'\cap B\cap W) = 6[/tex]

[tex]n(A\cap B'\cap W') = 16[/tex]

[tex]n(A'\cap B\cap W') = 8[/tex]

[tex]n(A'\cap B'\cap W) = 12[/tex]

Then the total number of students that applied to at least two of the universities is

[tex]\underbrace{n(A\cap B\cap W') + n(A\cap B'\cap W) + n(A'\cap B\cap W)}_{\text{only 2}} + \underbrace{n(A\cap B\cap W)}_{\text{all 3}} = \boxed{20}[/tex]

3. There's a small ambiguity here. Are we interested in students that applied to zero universities? If so, there are

[tex]\underbrace{n(U\setminus(A\cup B\cup W))}_{\text{none}} + \underbrace{n(A\cap B'\cap W') + n(A'\cap B\cap W') + n(A'\cap B'\cap W)}_{\text{only 1}} = \boxed{40}[/tex]

If we want students that applied to at least 1 school, we omit the first term and get a total of 36.

4. Split this set of students into those that also applied to Wachemo and those that did not.

[tex]n(A \cap B') = n(A\cap B' \cap W) + n(A\cap B'\cap W') = \boxed{19}[/tex]

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