Write the phrase as an algebraic
expression:
a. Seven times the difference of two and a
number
b. Six less than h

Each person buys a number of cakes

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy

So,

Andy has = x Cakes

Betty have = 4x Cakes

Clin has = x +3 Cakes

Since each cake costs 65p and the total cost of the cakes is £52.65

thus,

0.65( x + 4x + x +3) = 52.62

x + 4x + x +3 = 81

6x = 78

x = 13

Therefore,

Andy has = 13 cakes

Betty has = 4x = 4*13 = 52 cakes

Colin has = x + 3 = 16 cakes

Learn more about Mathematical operations here:

https://brainly.com/question/20628271

#SPJ1

To show that the projection maps π₁: X × Y → X and π₂: X × Y → Y are open maps, we need to demonstrate that for every open set U in X × Y, the sets π₁(U) and π₂(U) are open in X and Y, respectively.

Let U be an open set in X × Y. We can write U as the union of open sets U = U₁ × U₂, where U₁ is an open set in X and U₂ is an open set in Y. Since U is open, every point (x, y) in U has an open neighborhood contained within U.

Now, consider the image of U under the projection map π₁: X × Y → X. The set π₁(U) is the collection of all x-coordinates of the points in U. For any point x' in π₁(U), there exists a point (x', y') in U. Since U is open, there exists an open neighborhood N = N₁ × N₂ of (x', y') contained within U. The projection of N onto the x-coordinate, N₁, is an open neighborhood of x' contained within π₁(U). Therefore, π₁(U) is open in X.

Similarly, for the projection map π₂: X × Y → Y, we can show that π₂(U) is open in Y. For any point y' in π₂(U), there exists a point (x', y') in U. By a similar argument as above, there exists an open neighborhood N = N₁ × N₂ of (x', y') contained within U. The projection of N onto the y-coordinate, N₂, is an open neighborhood of y' contained within π₂(U). Therefore, π₂(U) is open in Y.

Since this holds for an arbitrary open set U in X × Y, we have shown that the projection maps π₁: X × Y → X and π₂: X × Y → Y are open maps.

Learn more about Sets here -: brainly.com/question/25369230

#SPJ11

Answer:

500

Step-by-step explanation:

company a looks like it costs 3000 to serve 800 students and company c looks like it costs 3500 to serve 800

Answer:

600

Step-by-step explanation:

Answer:

3394 ft.

Step-by-step explanation:

I don't know I used a web browser and found the answer on a website.

Answer:

9459.9771875106 ft.

Step-by-step explanation:

Took the test

Extra people required is 50.

Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Question 1 :

Number of associates = 30

Number of direct workers = 30 - 2 = 28

You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.

Direct rate = 150 units per hour

Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week

                                                            = 37.5 hours per week

Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units

28 people produce 5625 units in a week

Let x people produce 10,000 + 5625 = 15,625 units in a week

Using proportion,

28 : 5625 = x : 15,625

28 / 5625 = x / 15,625

x = (28 × 15,625) / 5625 = 77.78 ≈ 78

Extra people required = 78 - 28 = 50

Question 2 :

Number of sandwiches made in 10 minutes = 1

Number of sandwiches made in 10 hours = 60

5 workers are there. one worker makes 60/5 = 12 sandwiches

But Deli want number of sandwiches in 10 hours = 75

One worker should make 75/5 = 15 sandwiches instead of 12.

Number of sandwiches made in 8 minutes should be 1.

So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.

Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.

Learn more about Proportion here :

https://brainly.com/question/26974513

#SPJ1

Answer:

y-intercept(s):  ( 0 , − 5 )

Step-by-step explanation:

Hope this helps.

In an experiment, the variable being measured or tested is known as the dependent variable.

To learn more about dependent variable, refer to:

https://brainly.com/question/25223322

#SPJ4

Answer:

12 hours

Step-by-step explanation:

Let x hours be the time it will take you to mow the greens at the golf course.

Since Kim can mow twice as fast, it will take Kim x / 2 hours to mow the greens.

In 1 hour, you will mow 1 / x of the greens

in 1 hour, Kim will mow 1 / (x / 2) of the greens= 2 / x of the greens

In 4 hours, you will mow 4 * 1 / x of the course = 4 / x of the greens

In 4 hours, Kim will mow 4 * 1 / (x / 2) of the course = 4 / (x / 2) = 8 / x of the greens.

Since we are dealing in fraction, the sum of the amount of greens that they would individually mow in 4 hours should be 1. i.e

(4 / x) + (8 / x) = 1

12 / x = 1

Solve for x;

x = 12

Therefore, it will take you 12 hours to mow the greens alone.

the answer is 4.6 because I divided it

The quotient of the division are solved and A = 9.5/2 = 4.75

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the numerator of the fraction be p

where the value of p =  9.5

Let the denominator of the fraction be q

where q = 2

Now , the fraction is A = p/q

On simplifying the expression , we get

So , the left hand side of the equation is equated to the right hand side by the value of p/q

A = 9.5/2

On further simplification , we get

A = 4.75

Therefore , the value of A = 4.75

Hence , the fraction is A = 4.75

To learn more about fractions click :

https://brainly.com/question/29766013

#SPJ6

Malik's utility from his expected income is 793.0, and his expected utility of income is 818.5. The correct option is B.

To calculate Malik's utility from his expected income, we can use the weighted average of his utility from each possible income, with the probabilities as the weights:
Utility from expected income = (0.20 x 387.3) + (0.80 x 894.4) = 793.0
Finally, we can calculate Malik's expected utility of income by applying his utility function to his expected income:
Expected utility of income = √$710,000 = 818.5

First, we need to calculate Malik's expected income. We can do this using the probabilities and the given amounts of income for each outcome:
Expected income = (0.20 x $150,000) + (0.80 x $800,000) = $710,000
Next, we can use Malik's utility function to calculate his utility from each possible income:
Utility from $150,000 = √$150,000 = 387.3
Utility from $800,000 = √$800,000 = 894.4

To know more about income visit:-

https://brainly.com/question/29099506

#SPJ11

The probability that a student selected at random is a girl who chose apple as her favorite fruit is 0.32, or 32% rounded to the nearest hundredth.

To calculate the probability that a student is a girl who chose apple as her favorite fruit, we need to use the information provided in the table. First, we need to find the total number of girls who participated in the survey, which is the sum of the number of girls who chose apples, oranges, and mangoes as their favorite fruit, i.e., 46 + 41 + 55 = 142.

Next, we need to find the number of girls who chose apples as their favorite fruit, which is 46. Therefore, the probability that a student is a girl who chose apple as her favorite fruit is given by:

Probability = Number of girls who chose apples / Total number of girls in the survey

Probability = 46 / 142

Probability = 0.32

This means that out of all the girls who participated in the survey, 32% of them chose apple as their favorite fruit.

To learn more about probability click on,

https://brainly.com/question/30622026

#SPJ4

Complete question is:

three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. this table lists the results.

               Boys Girls

Apple    66     46

Orange   52     41

Mango    40     55

if a survey is selected at random, what is the probability that the student is a girl who chose apple as her favorite fruit?

Answer:

9, y=9

Step-by-step explanation:

So, there is one thing we always need to remember to find the y intercept.

This is that the y intercept can always be found on the middle line of the graph, when x is at 0.

What we must do is look at the graph, look at where the function hits x=0, and see what the y value is.

In this case, when x equals 0, we can see that y is 9.

So the y intercept is 9.

Hope this helps! :D

The amount that each person will contribute towards the concert that will be attended by the three friends would be = $43.

The total number of friends including Hank = 3

The total amount of money that will be spent which include funds for tickets and parking = $129.00

Therefore the amount that will be contributed by each of the friends = 129/3 = $43.

Learn more about division here:

https://brainly.com/question/25289437

#SPJ1

Answer:

11 months

26+33(11)=389

59+30(11)=389

The 11 is in going for x and represents the months.

A customer's likelihood of making a minimum monthly purchase of $20 is 0.93319.

The wealthiest 10% of consumers will part with $31.1262

Let X be a random variable that represents the monthly average of a customer's purchases. Given that X has a mean of $26 and a standard deviation of $4, i.e., it is normally distributed,

X ~ N (26, 4²)

We require the likelihood that a customer will make a purchase of at least $20, or

P (X ≥ 20)

After standardizing, we get:

= P [ Z ≥ (20 - 26) / 4]

= P (Z ≥ - 1.5)

=  P (Z ≤ 1.5)

= 0.93319

Therefore, If we use Z-table values then the required probability is 0.93319

Let x be the sum that the top 10% of consumers spend. Thus, we have

P (X ≥ x) = 0.1

On standardizing, we get:

= P [ Z ≥ (x - 26) / 4]

= P (Z ≥ 1.2816) = 0.1

On comparing the 2 values, we will get:
(x - 26) / 4 = 1.2816

x = 26 + 4 * 1.2816

x = 31.1264

Consequently, the top 10% spent $31.1264.

To know more about probability, refer to this link:

https://brainly.com/question/12629667

#SPJ4

Answer: approx. 75 cents / muffin

Step-by-step explanation: divide 6.8 by 9

Answer:

$0.75

Step-by-step explanation:

6.8 divide by 9=0.755555556 and so its 0.75 cents per muffin

Answer:

0 or 7

Step-by-step explanation:

hello,

we can write the following as n is a common factor

\(n^2-7n = n(n-7)\)

so

     \(n^2-7n = 0\\<=> n(n-7)=0\\<=> n = 0 \ or \ n = 7\)

hope this helps

Answer:

\( \boxed{\sf n = 7 \ \ \ \ or \ \ \ \ n = 0} \)

Step-by-step explanation:

\( \sf Solution \: set \: for \: equation : \\ \sf n^{2} - 7n = 0 \\ \\ \sf Factor \: n \: from \: the \: left \: hand \: side: \\ \sf n(n - 7) = 0 \\ \\ \sf Split \: into \: two \: equations: \\ \sf n - 7 = 0 \: \: \: \: or \: \: \: \: n = 0 \\ \\ \sf Add \: 7 \: to \: both \: sides: \\ \sf \boxed{ \sf n = 7} \: \: \: \: or \: \: \: \: n = 0\)

Answer:

x = 25°

Step-by-step explanation:

The angles are equal and opposite. This means that if the top angle is 150°, then the angle at the bottom must be 150° too. However, it is currently 2x° + 100°, which turns it into an equation. So far we have 100° as a known angle, so we subtract that from 150° to get the value of 2x.

2x° = 50

Now we divide 50 by 2, and that gives us 25°.

x = 25°

- Educationist

The equation of the new function will be: y = 2x + 5

The equation for a linear function with a slope of m and y-intercept of b is represented as y = mx + b.

We are Given a linear function graph passes the points (-0.5, 0) and (0, 1):

Y-intercept (b) = 1 (value of y when x = 0)

Thus Slope (m) = change in y/change in x = (1 - 0)/(0 - (-0.5)) = 2

If the slope (1) is multiplied by 2, the new slope would be: 2

If the y-intercept is increased by 3 units, the new y-intercept will be: 5

The equation of the new function will be: y = 2x + 5

Learn more about linear function on:

brainly.com/question/4025726

#SPJ1

The estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

To estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints, we can use the right Riemann sum method.

The width of each rectangle, Δx, is given by the interval width divided by the number of rectangles.

In this case, Δx = (π/2 - 0)/4 = π/8.

To calculate the right endpoint values, we evaluate f(x) at the right endpoint of each rectangle.

For the first rectangle, the right endpoint is x = π/8.

For the second rectangle, the right endpoint is x = π/4.

For the third rectangle, the right endpoint is x = 3π/8.

And for the fourth rectangle, the right endpoint is x = π/2.

Now, let's calculate the area for each rectangle by multiplying the width (Δx) by the corresponding height (f(x)):

Rectangle 1: Area = f(π/8) * Δx = 5cos(π/8) * π/8

Rectangle 2: Area = f(π/4) * Δx = 5cos(π/4) * π/8

Rectangle 3: Area = f(3π/8) * Δx = 5cos(3π/8) * π/8

Rectangle 4: Area = f(π/2) * Δx = 5cos(π/2) * π/8

Now, let's calculate the values:

Rectangle 1: Area = 5cos(π/8) * π/8 ≈ 0.2887

Rectangle 2: Area = 5cos(π/4) * π/8 ≈ 0.3142

Rectangle 3: Area = 5cos(3π/8) * π/8 ≈ 0.2887

Rectangle 4: Area = 5cos(π/2) * π/8 ≈ 0

Finally, to estimate the total area, we sum up the areas of all four rectangles:

Total Area ≈ 0.2887 + 0.3142 + 0.2887 + 0 ≈ 0.8916

Therefore, the estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

To know more about endpoints refer here:
https://brainly.com/question/31398203#

#SPJ11

The solution to the equation\(4^5 - 3x - \frac{1}{256 }\)is x = 128.

To solve the equation \(4^5 - 3x - \frac{1}{256}\) = 0, we need to isolate the variable x. We start by simplifying the expression \(4^5\), which is equal to 1024.

The equation then becomes 1024 - 3x - \(\frac{1}{256}\) = 0.

To eliminate the fraction, we can multiply the entire equation by 256, resulting in 256(1024) - 256(3x) - 1 = 0.

This simplifies to 262,144 - 768x - 1 = 0.

Combining like terms, we have -768x + 262,143 = 0. To isolate x, we subtract 262,143 from both sides, giving us -768x = -262,143.

Finally, we solve for x by dividing both sides by -768, yielding x = 128.

Learn more about basic algebraic principles.

brainly.com/question/29855331

#SPJ11

The extra number of people that should be engaged to reap the field in 10 days is given by A = 21 people

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the extra number of people that should be engaged to reap the field in 10 days be represented as A

Now , the number of people that should be engaged to reap the field in 10 days = n

The number of people that can reap the field in 17 days = 30 persons

So , the proportion is

30 x 17 = n ( 10 )

On simplifying , we get

Divide by 10 on both sides , we get

n = ( 30 x 17 ) / 10

n = 3 x 17

n = 51

And , the number of extra persons A = n - 30

So , the extra number of people that should be engaged to reap the field in 10 days A = 21 people

Hence , the proportion is A = 21 people

To learn more about proportion click :

https://brainly.com/question/7096655

#SPJ1

The concept time and work is used here to determine the number of people required to reap the same field in 10 days. The number of people required is 51.

The time and work represents the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the workdone by each of them.

If 30 persons can reap a field in 17 days

1 person can reap = 30 × 17 = 510 days

In 10 days, number of persons needed = 510 / 10 = 51 persons

Thus 51 persons can reap the field in 10 days.

To know more about time and work, visit;

https://brainly.com/question/444583

#SPJ1

Answer: never because they are both infinite.

The population scenario of Dhaka City presents a complex and challenging situation. Dhaka, the capital city of Bangladesh, has experienced rapid urbanization and population growth over the past few decades. With an estimated population of over 20 million people, Dhaka is one of the most densely populated cities in the world. This rapid population growth has resulted in various social, economic, and environmental challenges, with traffic congestion being one of the most pressing issues.

Dhaka City's population growth has outpaced its infrastructural development, leading to severe traffic congestion. The increasing number of vehicles on the roads, coupled with inadequate road infrastructure and limited public transportation options, has contributed to the worsening traffic jam situation. The traffic congestion not only causes inconvenience and frustration for commuters but also results in economic losses due to productivity decline and increased fuel consumption.

To mitigate the present traffic jam situation and restructure the population of Dhaka City, several measures can be considered:

Improve public transportation: Enhancing and expanding the public transportation system is crucial. This includes developing an efficient and reliable bus network, introducing mass rapid transit systems such as metro or light rail, and promoting the use of non-motorized transport modes like cycling and walking.

In conclusion, addressing the traffic jam situation in Dhaka City requires a comprehensive and multi-faceted approach. Restructuring the population of Dhaka City involves not only improving transportation infrastructure but also implementing sustainable urban planning strategies and promoting alternative modes of transport. By implementing these measures, Dhaka City can aim to mitigate traffic congestion, enhance mobility, and improve the overall quality of life for its residents.

To know more about population , visit

brainly.com/question/29159915

#SPJ11

No, lecture notes collected during a bachelor degree study are not a type of date. Lecture notes are a collection of the notes taken by a student during the lectures in the course of their bachelor degree study.

They are not the same as dates, which are the specified days on which something happens or is planned to happen. Lecture notes are usually written in the form of summaries of a lecture, which are usually made up of the important points that the student has noted down during the lecture.

They may also include diagrams, equations, and other visual aids that the student has used to illustrate the material covered. Lecture notes are not the same as dates, as they are not related to any specified days. They are simply summaries of the lecture topics discussed by the professor in the course of the student’s bachelor degree study.

know more about equations here

https://brainly.com/question/29657988#

#SPJ11

The probability that you pick exactly 2 juniors is 15/30 x 14/29 x 13/28 x 12/27, or 0.081.

1. Probability of picking the first junior: 15/30

2. Probability of picking the second junior: 14/29 (14 remaining juniors out of 29 total students after the first pick)

3. Probability of picking the third non-junior: 13/28 (13 remaining non-juniors out of 28 total students after the second pick)

4. Probability of picking the fourth non-junior: 12/27 (12 remaining non-juniors out of 27 total students after the third pick)

Therefore, the probability of picking exactly 2 juniors is

15/30 x 14/29 x 13/28 x 12/27

= 0.081.

The probability of picking exactly 2 juniors out of 4 slips of paper from a hat with the names of all 30 students in your statistics class is 0.081. This is calculated by taking the probability of picking the first junior (15/30) and multiplying it by the probability of picking the second junior (14/29, since there are 14 remaining juniors out of 29 total students after the first pick), the probability of picking the third non-junior (13/28, since there are 13 remaining non-juniors out of 28 total students after the second pick), and the probability of picking the fourth non-junior (12/27, since there are 12 remaining non-juniors out of 27 total students after the third pick).

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

option A by symmetry of figure.and then using formula of triangle and rectangle.

Step-by-step explanation:

Answer:

B.  \(x = -4\,\lor \,x = -1\)

Step-by-step explanation:

Let \(\sqrt{-4-5\cdot x} = x\), we solve for \(x\) by algebraic means.

1) \(\sqrt{-4-5\cdot x} = x\) Given

2) \(-4-5\cdot x = x^{2}\) Definition of power/Symmetry of equality

3) \(x^{2}+5\cdot x + 4 = 0\) Compatibility with addition/Commutative and associative properties/Existence of additive inverse/Modulative property

4) \((x+4)\cdot (x+1) = 0\)         \(x^{2}+(a+b)\cdot x +a\cdot b = (x + a)\cdot (x+b)\)

5) \(x = -4\,\lor \,x = -1\) Result

Hence, the correct answer is B.

As the degrees of freedom (DF) increase, the t distribution approaches the normal distribution. Therefore, the correct answer option is: C. normal distribution.

The degrees of freedom (DF) in a sample are typically used to correct a possible bias that exists between the alternative and null hypotheses because they are the maximum number of logically independent numerical values (data points) in the final calculation of a statistical problem.

A normal distribution is sometimes referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than data that are far from the mean.

In this context, we can reasonably infer and logically deduce that the t-distribution generally approaches the normal distribution as the degrees of freedom (DF) increase.

Read more on degrees of freedom here: https://brainly.com/question/22849398

#SPJ4