240 people are going to a charity event.

 
3535 of the guests have ordered chicken for their meals.

 
Of the remaining guests, 12.5% have ordered gluten-free meals.

 
How many people haven't ordered their meals yet?​

Answers

Answer 1

Answer:

First, find out how many guests have ordered chicken: 240 guests * 3535/10000 = 84 guests

Then subtract that number from the total number of guests to find the number of guests who haven't ordered chicken: 240 guests - 84 guests = 156 guests

Then find how many of those guests have ordered gluten-free meals: 156 guests * 12.5% = 19.5 guests

Then round down the number of guests who have ordered gluten-free meals to the nearest whole number to find the exact number of guests who ordered gluten-free meals: 19 guests

Then subtract that number from the number of guests who haven't ordered chicken to find the number of guests who haven't ordered their meals yet: 156 guests - 19 guests = 137 guests

So 137 people haven't ordered their meals yet.


Related Questions

Find median for average life of a particular brand of a T.V sets from the following data
life in years : 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40
No. of sets : 2 16 26 39 43 21 8 4

Answers

The median for average life of a particular brand of a T.V sets from the following data is given as follows:

17.5.

How to obtain the median of a data-set?

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.

The total number of observations in this problem is given as follows:

2 + 16 + 26 + 39 + 43 + 21 + 8 + 4 = 159.

This is an odd cardinality, hence the median is found in the class when the counter hits:

(159 + 1)/2 = 80.

Which is the class 15-20, as 2 + 16 + 26 < 80 and 2 + 16 + 26 + 39 > 80, and the median value is given as follows:

(15 + 20)/2 = 17.5.

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NO LINKS!!! NOT MULTIPLE CHOICE!!

59. You put $500 into a bank account that earns 2% interest. Determine each of the following.

a. The value of the account after 3 years if compounded annually.
b. The value of the account after 5 years if compounded quarterly.
c. The value of the account after 10 years if compounded monthly.
d. The value of the account after 20 years if compounded continously.

Answers

Answer:

[tex]a. \;\; \boxed{\$ 530.60}[/tex]

[tex]b.\; \;\boxed{ \$552.45}[/tex]


[tex]c,\;\;\boxed{\$610.60}[/tex]


[tex]d. \;\; \boxed{\$745.91}[/tex]


Step-by-step explanation:

All four cases deal with compound interest on the same amount of $500 and same interest rate of 2%.

The only difference is in the frequency of compounding and time

Compound Interest Formula

[tex]\boxed{A = P\left(1 + \dfrac{r}{n}\right)^{n\cdot t}\\\\}[/tex]

where

P = amount initially deposited - principal amountA = accrued value which is principal amount + interestr = interest rate expressed as a decimaln = number of compounding intervals.
This will depend on the frequency of compounding - daily, monthly, quarterly or yearly
t = number of number of years under consideration

In this particular problem we have
P = $500
r = 2% = 0.02

These are common for all parts of the question
Only n an t are different for each of the question sub-parts

Part a

Compounding is done annually (once a year) for 3 years

n = 1
t = 3 years
n · t = 3

[tex]A = 500\left(1 + \dfrac{0.02}{1}\right)^3\\\\A = 500\left(1.02\right)^3\\\\A = 500(1.061208)\\\\A=\boxed{\$ 530.60}[/tex]

For accuracy of calculations, I will not compute and store the exponent part, I will perform the calculations in one shot

Part b

Here the compounding is done quarterly (4 times a year) for 5 years


n = 4
t = 5 years
nt = 4 · 5 = 20

[tex]A = 500\left(1 + \dfrac{0.02}{4}\right)^{20}\\\\\\A = 500(1.005)^{20}\\\\A =\boxed{ \$552.45}[/tex]


Part c

Compounding done monthly(12 times a year) for 10 years

n = 12

t = 10

nt = 120

[tex]A = 500\left(1 + \dfrac{0.02}{12}\right)^{120}\\\\\\A = \boxed{\$610.60}[/tex]

Part d

First let's figure out what continuous compounding means

[tex]\fbox{\begin{minipage}[t]{1\columnwidth \fboxsep - 2\fboxrule}%\textsf{What is continuous compounding?} \\\textsf{Continuous compounding is the mathematicallimit that compound interest can reach if it's calculated and reinvestedinto an account's balance over a theoretically infinite number ofperiods. While this is not possible in practice, the concept of continuouslycompounded interest is important in finance. (Investopedia)}\}%\end{minipage}}[/tex]

The formula for continuous compounding can be determine by using the standard formula for periodic compounding and taking limits as
[tex]n \rightarrow \infty[/tex]

Therefore, for compounding continuously , the formula can be derived from
[tex]\lim _{n\to \infty } P\left(1 + \dfrac{r}{n}\right)^{nt}\\\\[/tex]

One of the limit formulas states

[tex]\lim _{x\to \infty } \left(1 + \dfrac{a}{x}\right)^{x} = e^a\\\\[/tex]

Therefore
[tex]\lim _{n\to \infty } \left(1 + \dfrac{r}{n}\right)^{n} = e^r\\\\[/tex]

So for the continuous compounding case, the formula is
[tex]\boxed{A = P \cdot e^{rt}}[/tex]

Here we have
r = 0.02
t = 20 years
rt = 20(0.02) = 0.4

Plugging in P = 500, and rt = 0.4 we get
[tex]A = 500 \cdot e^{0.4}\\\\A = \boxed{\$745.91}[/tex]


Answer:

a) $530.60

b) $552.45

c) $610.60

d) $745.91

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Part a

Given:

P = $500r = 2% = 0.02t = 3 yearsn = 1 (annually)

Substitute the given values into the compound interest formula and solve for A:

[tex]\implies A=500\left(1+\dfrac{0.02}{1}\right)^{1 \cdot 3}[/tex]

[tex]\implies A=500\left(1.02\right)^{3}[/tex]

[tex]\implies A=500(1.061208)[/tex]

[tex]\implies A=530.604[/tex]

Therefore, the value of the account after 3 years if interest is compounded annually is $530.60 (nearest cent).

Part b

Given:

P = $500r = 2% = 0.02t = 5 yearsn = 4 (quarterly)

Substitute the given values into the compound interest formula and solve for A:

[tex]\implies A=500\left(1+\dfrac{0.02}{4}\right)^{4 \cdot 5}[/tex]

[tex]\implies A=500\left(1.005\right)^{20}[/tex]

[tex]\implies A=500(1.10489557...)[/tex]

[tex]\implies A=552.447788...[/tex]

Therefore, the value of the account after 5 years if interest is compounded quarterly is $552.45 (nearest cent).

Part c

Given:

P = $500r = 2% = 0.02t = 10 yearsn = 12 (monthly)

Substitute the given values into the compound interest formula and solve for A:

[tex]\implies A=500\left(1+\dfrac{0.02}{12}\right)^{12 \cdot 10}[/tex]

[tex]\implies A=500\left(1.0016666...\right)^{120}[/tex]

[tex]\implies A=500(1.22119943...)[/tex]

[tex]\implies A=610.599716...[/tex]

Therefore, the value of the account after 10 years if interest is compounded monthly is $610.60 (nearest cent).

Part d

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Interest Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

P = $500r = 2% = 0.02t = 20 years

Substitute the given values into the continuous compounding interest formula and solve for A:

[tex]\implies A=500e^{0.02 \cdot 20}[/tex]

[tex]\implies A=500e^{0.4}[/tex]

[tex]\implies A=500(1.49182469...)[/tex]

[tex]\implies A=745.912348...[/tex]

Therefore, the value of the account after 20 years if interest is compounded continuously is $745.91 (nearest cent).

In a certain​ year, a movie and its sequel grossed a combined total of ​$1518 million. If the sequel grossed ​$116 million more than the​ movie, then how much did each movie​ gross?

Answers

The movie gross is $701

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total amount earned from the movie and the sequel = $1518

Amount earned from the movie = x

Amount earned from the sequel = x + $116

Now,

x + (x + 116) = 1518

2x + 116 = 1518

2x = 1518 - 116

2x = 1402

x = 1402/2

x = 701

Now,

x = $701

x + 116 = 701 + 116 = $817

Thus,

The movie gross is $701

The sequel gross is $817

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please help me i’ll give you brainlist!

Answers

X intercept: 10/5

Y intercept: 0

How to find  intercept of a linear equation?

To find the intercepts of a linear equation, you need to set either the X or Y variable to 0 and then solve for the other variable.

For example, if you have the equation 5x - 2y = 10, you can set X equal to 0 and solve for Y to find the Y intercept, or you can set Y equal to 0 and solve for X to find the X intercept.

X Intercept:

To find the X intercept, set Y equal to 0 and solve for X.

5x - 2(0) = 10

5x = 10

x = 10/5

X intercept = 10/5

Y Intercept:

To find the Y intercept, set X equal to 0 and solve for Y.

5(0) - 2y = 10

-2y = 10

y = -10/2

Y intercept = 0

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Find all the complex roots. Leave your answer in polar form with the argument in degrees. The complex fifth roots of 3. Zo= ___ (cos ___º + i sin ___º)z₁=___(cos___º + i sin ___º)z2=___(cos___º + i sin___º) z3=___ (cos___º + i sin___º) z4=___(cos___º + i sin___º)

Answers

The complex fifth roots of 3 are Z₀ = ∛3 (cos 0° + i sin 0°), Z₁ = ∛3 (cos 72° + i sin 72°), Z₂ = ∛3 (cos 144° + i sin 144°), Z₃ = ∛3 (cos 216° + i sin 216°) and Z₄ = ∛3 (cos 288° + i sin 288°)

The complex fifth roots of 3 can be found by finding the roots of the equation z^5 = 3. To find the roots in polar form, we first convert 3 to polar form:

3 = |3| (cos 0 + i sin 0) = 3 (cos 0 + i sin 0)

Next, we find the argument of the fifth roots, which is equal to 360°/5 = 72°. The polar form of the first root is then:

z₁ = ∛3 (cos 0° + i sin 0°) = ∛3 (cos 0° + i sin 0°)

The polar form of the other roots can be found by rotating the argument by 72°, 144°, 216°, and 288° respectively. The result is:

z₂ = ∛3 (cos 72° + i sin 72°)

z₃ = ∛3 (cos 144° + i sin 144°)

z₄ = ∛3 (cos 216° + i sin 216°)

z₅ = ∛3 (cos 288° + i sin 288°)

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A farmer has enough food to feed 20 animals in his cattle for 6 days. How long
would the food last if there were 10 more animals in his cattle?

Answers

Answer:

Food supply would only last 4 days

Step-by-step explanation:

(20 cattle)(6 days) = 120 cattle·days      (this is the current feed supply on hand)

20 cattle + 10 = 30 cattle total

(120 cattle·days) / (30 cattle) = 4 days

lan collects stamps. He put 34% of his stamp collection in an album. If there are
204 stamps in the album, how many stamps does he have in his collection?

Answers

well, there are a total of "x" stamps in his collection, which oddly enough is 100%.

now, we know that 34% of "x" is 204, what the heck is "x"?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 204& 34 \end{array} \implies \cfrac{x}{204}~~=~~\cfrac{100}{34} \\\\\\ \cfrac{ x }{ 204 } ~~=~~ \cfrac{ 50 }{ 17 }\implies 17x=10200\implies x=\cfrac{10200}{17}\implies x=600[/tex]

the charge of sphere 2 is twice that of sphere 1. which vector below shows the force of 2 on 1 if the distance

Answers

The vector representing the force of sphere 2 on sphere 1 is[tex]$\frac{2}{5} \vec{i}$[/tex] because the charge of sphere 2 is twice that of sphere 1 and they are separated by a distance of 5 cm.

Step 1: Calculate the charge of sphere 2. Since it is twice that of sphere 1, the charge of sphere 2 is 2 x the charge of sphere 1.

Step 2: Calculate the distance between the two spheres. This is given as 5 cm.

Step 3: Calculate the force. The force is equal to the product of the charges of the two spheres divided by the square of the distance between them.

Step 4: Construct the vector. The vector representing the force of sphere 2 on sphere 1 is[tex]$\frac{2}{5} \vec{i}$.[/tex]

The vector representing the force of sphere 2 on sphere 1 is [tex]$\frac{2}{5} \vec{i}$[/tex], as the charge of sphere 2 is twice that of sphere 1 and they are separated by a distance of 5 cm. This is calculated by multiplying the charges of the two spheres and dividing by the square of the distance between them.

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what is the answer!??

Answers

Answer:

8.75 miles

Step-by-step explanation:

using the equation for the line of best fit

y = 0.8x + 0.75

substitute x = 10 into the equation

y = 0.8(10) + 0.75 = 8 + 0.75 = 8.75

the equation predicts she will run 8.75 miles in week 10

all of the following are precautions to prevent static electricity damage when replacing a control module except

Answers

To stop electrostatic discharge from harming your hardware, fasten a wrist strap to a painted metal surface.

Static electricity discharge can damage disc drives, media drives, electronic boards, and adapters. To avoid this harm, these gadgets are enclosed in antistatic bags. Take the following safety measures to guard against static electricity discharge harming this equipment.

To stop electrostatic discharge from harming your hardware, fasten a wrist strap to a painted metal surface.

Be sure to observe all electrical safety precautions while utilizing a wrist strap. For static control, a wrist strap is used. When you use or work on electrical equipment, your risk of getting shocked by electricity is not increased or decreased.

If you do not have a wrist strap, you must touch an unpainted metal surface of the system for at least 5 seconds before removing it from the ESD packing and installing or replacing components.

When you're ready to install the device in the system, take it out of the antistatic bag.

Touch the gadget to the system's metal frame while it is still in its antistatic bag.

Grasp the edges of the cards and boards. On the adaptor, stay away from the parts and gold connectors.

The complete question is :-

All of the following are precautions to prevent static electricity damage when replacing a control module EXCEPT:

Touch a known good ground before opening the package.

Wipe the terminals clean before installing the component.

Ground the package to a known good ground before opening.

See Electronic Service Precautions

Open the package only when ready to install the component.

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if a pizza feeds 3 kids, but you need to feed 6, what would the scale factor be for calculating how many pizzas you need?

Answers

Answer:

2

Step-by-step explanation:

If a pizza feeds 3 kids and you need to feed 6 kids, the scale factor for calculating how many pizzas you need would be 2.

A scale factor is used to determine the relationship between the size of an object and a similar or corresponding object. In this case, you have a pizza that can feed 3 kids and you need to feed 6 kids, so the relationship between the number of kids that can be fed by one pizza and the number of kids you need to feed is 6/3 = 2

So, you need to double the quantity of pizza to feed 6 kids, therefore the scale factor would be 2.

THAT IS NEXT IN PATTERN 3,5,12,55,648

Answers

Note that the next number in the progression or sequence or pattern is 35,585.

What is progression?

Note that a number pattern is a series of numbers that adheres to a set of criteria. The rule might be mathematical, such as adding a constant value to each item in the series, or it can be based on some other logical relationship.

The next term in the sequence or pattern is derived as follows:

3x5 -3 = 12

5x12 -5 = 55

12x55 -12 = 648

55x648 -12 = 35,585

Therefore, it is correct to state that 35,585 is the next term in the sequence

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Which two of the following are not characteristics of surveys?
A. One or more treatment groups and a control group a
the study.
B. Two or more treatments are compared in the study.
C. The result of the study are analyzed statistically.
D. Data are gathering during the course of the study.

Answers

The following are not characteristics of surveys :

A. The study involves on or more treatment groups and a control group

B. The study compared two or more treatments

What is a survey

A survey is a research technique used to gather data from a predetermined sample of respondents in order to learn more and acquire insights into a range of interesting topics.

There are Characteristics of an Effective Survey :

measurable survey objectivessound research design.effective survey question designsound sampling strategy, when needed effective survey response strategy. meaningful data summary. effective data display and reporting.

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you drop a rock into a deep well. you can't see the rock's impact at the bottom, but you hear it after 6 seconds. the depth of the well is 285.9 feet. ignore air resistance. the time that passes after you drop the rock has two components: the time it takes the rock to reach the bottom of the well, and the time that it takes the sound of the impact to travel back to you. assume the speed of sound is 1100 feet per second. note: after seconds the rock has reached a depth of feet where

Answers

There is a distance of 656.088 feet to the bottom of the well.

What is Speed?

Speed is the ratio between the distance an object travels and the time it takes to cover that distance.

Since speed just has magnitude and no direction, it is a scalar quantity.

Because the amount of time that passes after you drop the rock is made up of both the amount of time it takes for it to fall to the bottom of the hole and the amount of time it takes for the sound of the impact to reach you,

Let t be the moment when a rock was attained at depth d, which is the well's bottom.

And this is the moment when you hear the sound of impact.

t + t' = 7 seconds

⇒ t' = 7 - t

Speed = Distance / Time

1100 feet per second = d / t'

d = 1100 t

Also d = 16t²

1100 t' = 16t²

1100 (7 - t) = 16t²

7700 - 1100t = 16t²

16t² + 1100t - 7700 = 0

4t² + 275t - 1925 = 0

This is a quadratic equation.

Discriminant = √(b² - 4ac) = √[275² - (4 × 4 × -1925)] = 326.228

t = (-275 ± 326.228) / (2 × 4)

t = 6.404 or t = -75.15

t = -75.15 is not possible because it is negative and t + t' = 7 seconds.

So t = 6.404 seconds

t' = 7 - 6.404 = 0.596 seconds

d = 16 × (6.404)² = 656.088 feet

Hence the distance from the well to the bottom is 656.088 feet.

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Which of the following are not linear equations in one variable?

A.x²-5x+6=0
B. x³ = x
C. 3x-4=0
D. 7x-6x = 3 + 9x

Answers

The  linear equations which are not  in one variable are x²-5x+6=0 and  x³ = x

What is linear equation ?

Linear equation can be defined as the equation in which highest degree is one.

Given Equations are

x^2 - 5x + 6 = 0

Here the highest degree is greater than one so it is not a linear equation

And x

x^3  = x

x^3 - x =  0

Here also the highest degree is greater than one so it is not a linear equation

3x-4=0

Here the highest degree is equals to one so it is  a linear equation

7x-6x = 3 + 9x

x = 3+9x

8x+3 = 0

Here the highest degree is equals to one so it is  a linear equation

Therefore , The  linear equations which are not  in one variable are x²-5x+6=0 and  x³ = x

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What is the perimeter of a rectengular park that measure 20 1/4 yards by 32 5/8

Answers

The perimeter of the rectangular park is 423/4 units.

What precisely is a perimeter?

The lengths of a shape's edges and sides are added to find its perimeter.

The length of a two-dimensional shape's boundary is its perimeter. It is frequently referred to as the sum of the lengths of the sides of the object. That shape's perimeter is equal to the side lengths added together algebraically.

The perimeter of a shape is equal to the length of its boundary or whole circumference. The perimeter of a closed 2D form is the product of its sides.

Given : Length = 20 1/4

                        = 81/4

          Width = 32 5/8

                     = 261/8

So, Perimeter = 2 ( L + B)

                      = 2 ( 81/4 + 261/8)

                      = 2 ( 423/8)

                     = 423/4 units.

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Build it #1
Drag the points to create a graph that satisfies the following requirements:

Answers

A graph that satisfies the given requirements 1 ≤ x ≤ 3 and 2 ≤ y ≤ 7 is shown in the image attached below.

What is a domain?

In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

For the domain of this graph, the x-value would be placed at point 1 and then dragged to point 3 on the x-coordinate. Similarly, the y-value for the range of this graph would be placed at point 2 and then dragged to point 7 on the y-coordinate as shown in the image attached below.

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Given f(x)=9/5 x + 32, find the folwing.

Answers

The inverse of the function as it has been written is f(x) = (x - 32) 5/9.

What is the inverse of the function?

We know that the inverse of a function can easily be obtained as long as we have the function as we do in the question here. The function has been given to us as; f(x)=9/5 x + 32.

Let y = f(x)

Hence;

y=9/5 x + 32

y - 32 + 5/9 = x

We would then have the inverse of the function as;

f(x) = (x - 32) 5/9

This is the procedure that would help us to obtain the inverse of the function that have been given here.

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Missing parts;

Given f(x)=9/5 x + 32, find the following;

Inverse of the function

You use beads to make design. Of the beads, 1/3 are red and 1/6 are blue. The rest are white. What fraction of the beads are red red or blue?

Answers

Answer:

1/2

Step-by-step explanation:

First, let's find the GCF of 3 and 6. In this case, it's 6.

Then, lets convert every fraction so that the denominator is 6. 1/6 already has this property, so let's convert 1/3. And to do that, we multiply the fraction by 2/2.

[tex]\frac{1}{3} * \frac{2}{2} = \frac{2}{6}[/tex]

Finally, we add the fraction of beads that are red and blue together, then simplify.

[tex]\frac{2}{6} + \frac{1}{6}=\frac{3}{6} =\frac{1}{2}[/tex]

Therefore, the answer is 1/2.

Help please
Determine whether the statement is true or false. If the statement is false, make the necessary changes) to produce a true statement.

Image attached

Answers

The complex number statement (3+8i)/(2+8i)=3/2 is false. The correct complex number statement is (3+8i)/(2+8i) = (24i + 6)/(-64i² + 16).

What is a complex number?

Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and i is a imaginary number called a "iota."

The given complex number equation is (3+8i)/(2+8i)=3/2

Simplify both sides of the equation.

On the left side, there is -

= (3+8i)/(2+8i)

= (3+8i)/(2+8i) × (2-8i)/(2-8i)

= (6+24i-24i-64i²)/(2² + 2×8i-8i²)

= (-64i² + 24i + 6)/(-64i² + 16)

= (24i + 6)/(-64i² + 16)

On the right side, there is -

3/2 = 3/2

It can be seen that the simplified forms of both sides are not equal, so the original statement is false.

To make the statement true, change the right side of the equation to the left side simplified form.

(3+8i)/(2+8i) = (24i + 6)/(-64i² + 16)

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consider the expresson 1/2x to the second power +x+7. complete 2 descriptions of the part of the expression

Answers

The entire expression is a sum with 0 factors

The coefficients are 1/2, 1 and 7

How to describe the expression

From the question, we have the following parameters that can be used in our computation:

1/2x² + x + 7

The above expression is a quadratic expression and it has three terms

Quadratic expressions with real roots have 2 factors, otherwise it would have 0 factor

The expression 1/2x² + x + 7 does not have a real root because

b² < 2ac

Also in the expression, the coefficients are 1/2, 1 and 7

i.e. a = 1/2, b = 1 and c = 7

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Complete question

consider the expresson 1/2x² + x + 7.

complete 2 descriptions of the part of the expression

The entire expression is a sum with __ factors

The coefficients are _

Can a slope have two negative signs

Answers

If the slope of the line has two negative signs, then it is positive.

How to obtain the slope of a linear function?

The slope of a linear function represents the rate of change of the linear function.

If we have two points on the linear function, then the slope is obtained by the division of the change in the output by the change in the input.

If both changes are negative, then we are dividing two negative numbers, meaning that the slope is positive, as the quotient of two negative numbers is positive.

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Two distinguishable fair dice are rolled: Define the following events: (sum of the numbers rolled is divisible by 4] (sum of the numbers rolled is less than 4} (a) What is the total number of possible outcomes in this experiment? (b) List the outcomes in A (c) List the outcomes in B (d) Find the probability P(A) (e) Find the probability P(B) (f) Find the probability P(AU B) (g) Find the probability P(AnB) (h) Are events A and B independent?

Answers

Event A is the event that the sum of the numbers rolled on the two dice is divisible by 4. Event B is the event that the sum of the numbers rolled on the two dice is less than 4.

(a) The total number of possible outcomes in this experiment is 36 (6 possible outcomes for each die).

(b) Outcomes in A are (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (12, 1), (12, 2), (12, 3), (12, 4), (12, 5), and (12, 6).

(c) Outcomes in B are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), and (2, 6).

(d) P(A) is 5/36. (e) P(B) is 6/36. (f) P(A U B) is 11/36. (g) P(A n B) is 0 (there are no outcomes that belong to both A and B). (h) Events A and B are not independent because P(A U B) does not equal P(A) + P(B).

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Zach had been walking for
distance.
when both boys had walked exactly the same
Place the correct value to complete the sentence.
Two boys, Zach and Carlos, go for a walk. Zach begins walking 20 seconds earlier
than Carlos

Answers

Two boys, Zach and Carlos, go for a walk. Zach begins walking 20 seconds earlier than Carlos and they both walked the same distance.

How to calculate the distance?

To calculate the distance that the boys walked, you would need to know their speed and the duration of their walk.

Speed is typically measured in units such as miles per hour (mph) or kilometers per hour (kph). If you know the speed of the boys and the duration of their walk in hours, you can calculate the distance they walked using the formula: distance = speed x time.

The sentence is describing a scenario in which two boys, Zach and Carlos, go for a walk. It is stated that Zach begins walking 20 seconds earlier than Carlos. This means that Zach starts his walk 20 seconds before Carlos does. It is also stated that both boys had walked exactly the same distance. This means that despite Zach starting his walk 20 seconds earlier than Carlos, they both covered the same distance during their walk.

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A rectangle has length x and width y. Select all the statements that must be true.

Answers

The area of a rectangle with length x and width y is xy unit square.

What is an equation?

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

Area is the amount of space occupied by a figure. Area is usually calculated for a two dimensional shape while volume is calculated for a three dimensional shape.

A rectangle have equal opposite sides which are parallel to each other and all angles are at 90 degrees.

Area of rectangle = length * width

Area = x * y = xy

The area is xy unit square.

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Solution set

2x + 4 / 2 - 3x / x - 2 = X

Answers

On solving the given equation,  the value of x = -4.

Finding the value of f(x) =... or y =... that corresponds to a certain value of x is what it means to evaluate a function.

Simply swap out all instances of x with the value of x to do this. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.

Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

Given,

[tex]\frac{2x + 4}{2} - \frac{3x}{x-2} = x\\ \\[/tex]

Taking LHS

⇒ [tex]\frac{2x^2 - 4x + 4x - 8 - 6x}{2(x-2)} \\[/tex]

⇒ [tex]\frac{x^2-4-3x}{(x-2)}[/tex]

Equating both sides,

⇒ [tex]\frac{x^2-4-3x}{(x-2)} = x\\x^2-4-3x = x^2 - 2x\\x = -4[/tex]

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I need the answers for this whole side work must be shown or you get reported please don’t make me waste my points

Answers

a. The percentage of the original price that the consumers are going to pay will be 8.57%.

b. The markup percentage of the gallons will be

c. The percentage that decided not to sell the juice is 41.7%.

d. The price of each bottle will be:

How to calculate the percentage?

a. The percentage of the original price that the consumers are going to pay will be:

= (3.50 - 3.20) / 3.50 × 100

= 0.30 / 3.50 × 100

= 8.57%

b. The markup percentage of the gallons will be:

= (3.20 - 2.70) / 2.70 × 100

= 0.50 / 2.70 × 100

= 18.5%

c. The percentage that decided not to sell the juice is:

= 125 / 300 × 100

= 41.7%

d. The price of each bottle will be:

= (1 - 15%) × $2.25

= $1.91

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Find the derivative of the summation from n equals 0 to infinity of the quotient of the product of negative 1 raised to the nth power and x raised to the quantity 2 times n plus 1 power and the product of 3 to the 2 times n power and the square of n factorial. Write your answer as a summation with lower limit of summation equal to 0.

Answers

The derivative of the summation with lower limit that equal to 0 is [tex]$$y^{\prime}=\sum_{n=0}^{\infty}(-1)^n \cdot \frac{(2 n+1)}{(n !)^2} \cdot\left(\frac{x}{3}\right)^{2 n}$$[/tex].

From the given data,

The derivative of the summation from n equals 0 to infinity of the quotient of the product of negative 1 raised to the nth power and x raised to the quantity 2 times n plus 1 power and the product of 3 to the 2 times n power and the square of n factorial is  [tex]$y=\sum_{n=0}^{\infty} \frac{(-1)^n x^{2 n+1}}{3^{2 n} \cdot(n !)^2}$[/tex]

The process of finding the derivative is called differentiation. The inverse process is called anti-differentiation. Let’s find the derivative of a function y = f(x).  It is the measure of the rate at which the value of y changes with respect to the change of the variable x. It is known as the derivative of the function “f”, with respect to the variable x.

Derivatives can be classified into different types based on their order such as first and second order derivatives.

Derivative⇒ [tex]$y^{\prime}=\sum_{n=0}^{\infty} \frac{(-1)^n \cdot(2 n+1)(x)^{2 n}}{3^{2 n} \cdot(n !)^2}$[/tex]

⇒ [tex]$$y^{\prime}=\sum_{n=0}^{\infty}(-1)^n \cdot \frac{(2 n+1)}{(n !)^2} \cdot\left(\frac{x}{3}\right)^{2 n}$$[/tex].

Therefore, the summation with lower limit that equal to 0 is [tex]$$y^{\prime}=\sum_{n=0}^{\infty}(-1)^n \cdot \frac{(2 n+1)}{(n !)^2} \cdot\left(\frac{x}{3}\right)^{2 n}$$[/tex]

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use left rectangles and delta (x) = 0.5 to approximate the area under f(x) = (2x)^2 +6 from x = 2 to x=4 . give one decimal place in your answer.

Answers

The estimated area under the curve is 112.

We can use the left rectangle method to approximate the area under the curve f(x) = (2x)^2 + 6 from x = 2 to x = 4.

First, we need to choose a value of Δx = 0.5, which will determine the width of the rectangles. Then, we can find the height of each rectangle by evaluating the function at the left endpoints of the intervals.

For x = 2, the height of the first rectangle is f(2) = (2 * 2)^2 + 6 = 20.

For x = 2.5, the height of the second rectangle is f(2.5) = (2 * 2.5)^2 + 6 = 28.25.

For x = 3, the height of the third rectangle is f(3) = (2 * 3)^2 + 6 = 42.

For x = 3.5, the height of the fourth rectangle is f(3.5) = (2 * 3.5)^2 + 6 = 57.75.

For x = 4, the height of the fifth rectangle is f(4) = (2 * 4)^2 + 6 = 76.

Finally, we can multiply the height of each rectangle by its width (0.5) to find the area of each rectangle:

Area of first rectangle = 20 * 0.5 = 10

Area of second rectangle = 28.25 * 0.5 = 14.125

Area of third rectangle = 42 * 0.5 = 21

Area of fourth rectangle = 57.75 * 0.5 = 28.875

Area of fifth rectangle = 76 * 0.5 = 38

The total area under the curve can be estimated by adding up the areas of the rectangles:

Estimated area = 10 + 14.125 + 21 + 28.875 + 38 = 112

So the estimated area under the curve using the left rectangle method and Δx = 0.5 is 112.

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You deposit $120 in an investment account that earns 6.4% annual interest compounded quarterly write a function that represents the balance y (in dollars) of the investment account after t years

Answers

Answer:

$ balance = 120*(1+6.4%/4) ^4t

Step-by-step explanation:

principal =120

r =6.4% annual = 1.6% per quarter compounding every quarter

so 4 times a year, for t years

$ balance = 120*(1+6.4%/4) ^4t

The function that represents the balance of the investment account after t years is  [tex]y = 120 (1.016)^{4t[/tex].

How to calculate the compound interest?

The formula for calculating the balance of an investment account that earns compound interest is:

[tex]A = P (1 + \dfrac{r}{n})^{nt}[/tex]

where:

A = the balance after t years

P = the principal (initial amount deposited)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time in years

In this case, we have:

P = $120

r = 6.4% = 0.064 (as a decimal)

n = 4 (compounded quarterly)

Therefore, the function that represents the balance y (in dollars) of the investment account after t years is:

[tex]y = 120 *(1 + \dfrac{0.064}{4})^{4t}[/tex]

Simplifying the expression inside the parentheses, we get:

[tex]y = 120 (1.016)^{4t[/tex]

This is the function that represents the balance of the investment account after t years.

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