A square garden has a length of (x+3) ft and a width of (x+2) ft. what is the perimeter and area of the garden?

Answer:

x = 8 and y = -4

Step-by-step explanation:

3x + 4y = 8    (call this equation '1')

x - y = 12      (call this '2')

multiply '2' by 3:

3x - 3y = 36  (call this '3')

subtract '1' from '3':

(3x - 3y = 36)  -  (3x + 4y = 8)

0x + -7y = 28

-7y = 28

y = -4.

sub that back into '1':

3x + 4y = 8

3x + 4(-4) = 8

3x - 16 = 8

3x = 8 + 16 = 24

x = 8.

sub both y =-4 and x =8 into '2' to check if everything adds up:

x - y = 12

8 - -4 = 8 + 4 = 12

so x = 8 and y = -4

Answer: 10 cheeseburgers

Step-by-step explanation: 25/2.5=10

Answer:

10

Step-by-step explanation:

To determine the number of cheeseburgers you can get with $25, you can divide the total amount of money by the cost of each cheeseburger.

$25 ÷ $2.50 = 10

Therefore, with $25, you can get 10 cheeseburgers if each cheeseburger costs $2.50.

The horizontal variance of sales between 2021 and 2022 is 340

By removing the sales figure of 2021 from that of 2022, we are able to arrive at the above figure.

That is Amount of 2022  – Amount of 2021 = Absolute Change.

Figure for 2022 = 3800

Less

Figure for 2021 = 3,460

Variance                340

Excel formula : = Cell no. of amount of 2022 - Cell no of amount of 2021

Note that a negative amount means decrease and positive amount means increase.

Learn more about variance:
https://brainly.com/question/9304306
#SPJ9

Work Shown:

LCM = (product of two numbers)/(HCF of the two numbers)

LCM = 1536/16

LCM = 96

Answer:

1) 5/6
2) 19/30
3) They are mutually exclusive.

Step-by-step explanation:

Let's break the diagram down.
We have four types of smoothies:

Contains apple but not blueberry - 12
Contains blueberry but not apple - 7
Contains both blueberry and apple - 3
Doesn't contain either - 8

From here, we find that there are 30 smoothies in total.

In addition, we know that the number of smoothies containing an apple is 15, and the number of smoothies containing blueberry is 10.

Therefore,

[tex]P(\text{contains apple}) = \frac{\text{contains apple}}{\text{total}} = \frac{15}{30} = \frac12\\\\P(\text{contains blueberry}) = \frac{\text{contains blueberry}}{\text{total}} = \frac{10}{30} = \frac13\\\\\text{a) } P(\text{contains apple}) + P(\text{contains blueberry}) = \frac12 + \frac13 = \frac36 + \frac26 = \frac56[/tex]

Now, the probability of getting apple OR strawberry is given by adding the probabilities of getting one of the flavors but not the other.

[tex]P(\text{apple, no blueberry}) = \frac{12}{30}\\\\P(\text{blueberry, no apple}) = \frac{7}{30}\\\\P(\text{apple or blueberry}) = \frac{12}{30} + \frac7{30} = \frac{19}{30}[/tex]

We can check if the events are mutually exclusive using the formula:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In our case, A means contains apple, and B means contains blueberry.
[tex]P(A \cup B)[/tex] resembles the case for exclusively apple or exclusively blueberry (AKA our answer for b).

[tex]P(A \cap B)[/tex] resembles the case for both apple and blueberry (AKA the intersection), which is equal to 3/30 = 1/10.

If the two sides are equal, the cases are not mutually exclusive.

[tex]\frac{19}{30} = \frac{15}{30} + \frac{10}{30} - \frac{3}{30}\\\\\frac{19}{30} \ne \frac{22}{30}[/tex]

Therefore, the events are mutually exclusive.

Answer:

Step-by-step explanation:

3.14 . 11= 150/360

Answer:

4

Step-by-step explanation:

A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)

The probability that event A or B takes place is 17/19

Probability is defined as the ratio of the required to the total possible outcomes of an event.

The probability of event A or B taking place can be defined as ;

P(A or B) = P(A) + P(B)

P(A) = 10/19

P(B) = 7/19

Hence,

P(A) + P(B) = 10/19 + 7/19

L.C.M of 19 and 19 = 1

P(A) + P(B) = (10 + 7)/19

P(A) + P(B) = 17/19

Therefore, the probability that event A or B takes place is 17/19

Learn more on probability ;https://brainly.com/question/13604758

#SPJ1

A graph of this quadratic equation x² + x - 6 = 0 is shown below.

The solutions to the equation x² + x - 6 = 0 are (-3, 0) and (2, 0).

In Mathematics, the graph of a quadratic function always form a parabolic curve or arc because it is u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive one (1) and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function x² + x - 6 = 0 is positive one (1), we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts (-3, 0) and (2, 0). Also, the value of the quadratic function f(x) would be minimum at -6.25.

Read more on quadratic functions here: brainly.com/question/29499209

#SPJ1

The job A is the best job based on pay scale

Given data ,

a) Job A:

Hours per week: 40

Hourly rate: $15

On simplifying the equation , we get

Gross pay per week: 40 hours * $15/hour = $600

b) Job B:

Hours per week: 30

Hourly rate: $5

On simplifying the equation , we get

Gross pay per week: 30 hours * $5/hour = $150

In addition to the base pay, Job B also offers tips averaging $350 per week.

Considering the total compensation for each job:

Total compensation for Job A: $600 per week (base pay)

Total compensation for Job B: $150 per week (base pay) + $350 per week (tips) = $500 per week

Based on the total compensation, Job A offers a higher gross pay of $600 per week, while Job B offers a total compensation of $500 per week.

Hence , if the decision is solely based on pay, Job A would be the better choice.

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The expression that can be used to find the amount of oatmeal in the container, obtained from the formula for the volume of a cylinder is π · 2² · 8. The correct option is therefore, the option C.

C. π · 2² · 8

The volume of a cylinder is; V = π × Radius² × Height

The part of the question that appear missing, obtained from a similar question on the internet, includes;

The radius of the can = 2 inches

The height to which the can was filled = 8 inches

The volume of oatmeal in the can is therefore;

V = π·r²·h

Where;

r = The radius of the can = 2 inches

h = The height to which the oatmeal is filled = 9 - 1 = 8 inches

Therefore;

V = π × 2² × 8

The expression that can be used to find the amount of oatmeal in the can is therefore;

C. π · 2² · 8

The possible question options, obtained from the online question are;

A. (4·π·9) - 1

B. 2·π·8

C. π·2²·8

D. (4·π·9)/3

Learn more on the volume of a cylinder here: https://brainly.com/question/14718960

#SPJ1

Answer: 132 cm cubed

Step-by-step explanation:

0.5*3*4*2=12

10*5=50

4*10=40

3*10=30

30+40+50+12=132 cm cubed

Answer:

Arc EG = 23.21 units

Step-by-step explanation:

Arc length:

Arc length could be found by the below mentioned formula.

         [tex]\boxed{\bf Arc \ length =\dfrac{\theta }{180}*\pi r}[/tex]

r - radius of circle = 19 units

Ф - central angle of arc = 70°

                             [tex]\sf arc \ EG = \dfrac{70}{180}*3.14*19\\\\[/tex]

                                         = 23.21 units

Answer:

The length of a side of the base of the box is 13 cm.

Step-by-step explanation:

To find the length of a side of the base of the box, we need to use the formula for the volume of a box.

The volume of a box is given by the formula:

V = l^2 * h

Where:

V is the volume,

l is the length of a side of the base, and

h is the height of the box.

Substituting the given values:

V = 1352 cm^3

h = 8 cm

1352 = l^2 * 8

Dividing both sides by 8:

l^2 = 169

Taking the square root of both sides:

l = √169

Calculating the length of a side of the base:

l = 13 cm

Therefore, the length of a side of the base of the box is 13 cm.

[tex]\cfrac{x}{4}-\cfrac{x+10}{2}=3\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{x}{4}-\cfrac{x+10}{2} \right)=4(3)}\implies x-(2x+20)=12 \\\\\\ x-2x-20=12-x-20=12\implies -20=12+x\implies \boxed{-32=x} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{2x+1}{5}-\cfrac{x-3}{7}=-2\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{2x+1}{5}-\cfrac{x-3}{7} \right)}=35(-2) \\\\\\ 14x+7-(5x-15)=-70\implies 14x+7-5x+15=-70 \\\\\\ 9x+22=-70\implies 9x=-92\implies \boxed{x=-\cfrac{92}{9}}[/tex]

The estimate for the number of females in marketing is given as follows:

225 females.

A bar graph shows the output considering a given input. In the context of this problem, the inputs are the prices, and for each input there are two outputs, which are the number of male employees and the number of females employees in each department.

For this problem, the second input is the number of male employees and the number of females employees in the marketing departments.

Hence the number of employees is given as follows:

More can be learned about bar graphs at brainly.com/question/28535024

#SPJ1

The mean increases from 9 to 10 because the value of 15 is greater than the mean of 9. When a larger value is added to a set of data, the mean will increase.

The mean of the data is 9 students because there are 45 students total and 5 meetings.

When 15 students attend the next meeting, the mean increases to 10.5 students because there are now 60 students total and 6 meetings.

Mean of the first 5 meetings:

There are 45 students total.

There are 5 meetings.

Therefore, the mean is:

= 45 / 5

= 9 students.

There are 60 students total.

There are 6 meetings.

Therefore, the mean is:

= 60/6

= 10 students.

The mean increases from 9 to 10 because the value of 15 is greater than the mean of 9. When a larger value is added to a set of data, the mean will increase.

Learn more about mean on

https://brainly.com/question/1136789

#SPJ1

Answer:

To calculate the value of (-3/4)^-4, we need to apply the exponentiation rules.

When a negative number is raised to an even power, the result is positive. Thus, we can rewrite (-3/4)^-4 as (4/-3)^4.

Now, let's evaluate the expression:

(4/-3)^4 = (4^4)/(-3)^4 = 256/81

So, the value of (-3/4)^-4 is 256/81

Step-by-step explanation:

Answer:

$60

Step-by-step explanation:

Based on the regression equation, the best prediction for the price of a 70-pound container of detergent can be found by substituting x = 70 into the equation:

y^ = 0.86x + 0.52

y^ = 0.86(70) + 0.52

y^ = 60.2 + 0.52

y^ ≈ $60.72

Therefore, the best prediction for the price of a 70-pound container of detergent is approximately $60.72. However, since we are dealing with prices, it is reasonable to round this value to the nearest dollar, which would be $61. But since none of the answers are 61 it would be $60.

Answer:

55°

Step-by-step explanation:

if angle 4 = 105°, then angle 3 must be 180 - 105 = 75° (angles in straight line add up to 180°).

angles in a triangle also add up to 180°.

so we expect angle 2 to be 180 - angle 6 - angle 3

= 180 - 50 - 75

= 55°.

The solution of the equation for B over the interval [0,2π] is undefined

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

-√3tan(β) = tan(β)sin(β)

Divide both sides of the equation by tan(β)

so, we have the following representation

-√3 = sin(β)

Rewrite as

sin(β) = -√3

Take the arc sin of both sides

β = undefined

Hence, the solution of the equation for B over the interval [0,2π] is undefined

Read more abiut trigonometry function at

https://brainly.com/question/24349828

#SPJ1

In my community, there are several situations where hypothesis testing can be applied. Here are three examples: Traffic Flow Optimization, Recycling Program Assessment, and Crime Prevention Strategy Evaluation

For the purpose of this response, let's choose Situation 1 (Traffic Flow Optimization) and go through the four steps.

1. Problem Statement: The local authorities want to determine if implementing a new traffic signal timing system will significantly reduce the average travel time for commuters passing through a busy intersection during peak hours.

2. Null Hypothesis (H0): The new traffic signal timing system has no effect on the average travel time for commuters passing through the intersection.

Alternative Hypothesis (H1): The new traffic signal timing system significantly reduces the average travel time for commuters passing through the intersection.

3. Level of Significance: α = 0.05

4. Rejection Region: The rejection region will depend on the specific test statistic used. Let's assume we are using a t-test to compare the mean travel time before and after implementing the new traffic signal timing system. In this case, we would calculate the t-statistic and determine the critical value(s) based on the degrees of freedom and the chosen level of significance. The rejection region would be in the tails of the t-distribution corresponding to the critical value(s).

Possible Type I Error: Rejecting the null hypothesis when it is actually true, indicating that the new traffic signal timing system is effective when it is not. In this case, it would mean concluding that the new system significantly reduces travel time when, in reality, it has no effect.

Possible Type II Error: Failing to reject the null hypothesis when it is actually false, indicating that the new traffic signal timing system is ineffective when it is actually effective. In this case, it would mean not detecting a significant reduction in travel time when the new system does indeed have a positive impact.

It's worthy of note that the specific test statistic and rejection region may vary depending on the nature of the data and the chosen statistical test. The above steps provide a general framework for conducting hypothesis testing in the given situation.

learn more about hypothesis testing: https://brainly.com/question/4232174

#SPJ1

The solution of the System of equation are,

⇒ x = 1

⇒ y = 5

We have to given that;

System of equation are,

⇒ 3x - 5y = - 22

⇒ 4x + 2y = 14

Now, We can simplify as;

From (ii);

2x + y = 7

y = 7 - 2x

Put above value in (i);

3x - 5 (7 - 2x) = - 22

3x - 35 + 10x = - 22

13x = - 22 + 35

13x = 13

x = 1

From (i);

⇒ 3x - 5y = - 22

⇒ 3 - 5y = - 22

⇒ 3 + 22 = 5y

⇒ 25 = 5y

⇒ y = 5

Learn more about systems of equations at:

brainly.com/question/14323743

#SPJ1

Step-by-step explanation:

A LOT of different outfits !
8  x  5  x  4  x  2   = 320 outfit possibilities

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -4}{2}~~~ ,~~~ \cfrac{ y +5}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(5~~,~~-1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -4 }{2}=5\implies x-4=10\implies \boxed{x=14} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +5 }{2}=-1\implies y+5=-2\implies \boxed{y=-7}[/tex]

Reema should use 3 hooks. The distance between the hooks is approximately 4 inches, and the distances of each hook from the left edge of the wood are approximately 1.75 inches, 5.75 inches, and 9.75 inches.

Given:

Wall length: 4 feet

Wood length: 28 inches

Space between hooks: about 7 or 8 inches

Minimum distance from each end: 1 3/4 inches

To center the coat rack on the wall, we need to find the remaining space on either side of the wood after accounting for the minimum distances from each end.

Convert measurements to inches:

Wall length: 4 feet = 48 inches

Calculate the available space for the wood on the wall:

Available space on each side = (Wall length - Wood length) / 2

Available space on each side = (48 inches - 28 inches) / 2

Available space on each side = 20 inches / 2

Available space on each side = 10 inches

Determine the number of hooks and the space between them:

Space between hooks: about 7 or 8 inches

Let's assume we choose a space of 8 inches between hooks for this calculation.

Remaining space for hooks = Wood length - (Minimum distance from each end × 2)

Remaining space for hooks = 28 inches - (1 3/4 inches × 2)

Remaining space for hooks = 28 inches - (3 1/2 inches)

Remaining space for hooks = 28 inches - 7/2 inches

Remaining space for hooks = 28 inches - 3.5 inches

Remaining space for hooks = 24.5 inches

Number of hooks = Remaining space for hooks / Space between hooks

Number of hooks = 24.5 inches / 8 inches (approximately)

Number of hooks ≈ 3.06 (rounded to the nearest whole number)

Since we cannot have a fraction of a hook, we'll round down to 3 hooks.

Calculate the distance between hooks:

Distance between hooks = Space between hooks / (Number of hooks - 1)

Distance between hooks = 8 inches / (3 hooks - 1)

Distance between hooks = 8 inches / 2

Distance between hooks = 4 inches

Calculate the distance of each hook from the left edge of the wood:

Hook 1 distance from the left edge = Minimum distance from each end

Hook 2 distance from the left edge = Minimum distance from each end + Distance between hooks

Hook 3 distance from the left edge = Minimum distance from each end + (Distance between hooks × 2)

Using the given minimum distance from each end of 1 3/4 inches (or 1.75 inches), we can calculate the distances for each hook:

Hook 1 distance from the left edge = 1.75 inches

Hook 2 distance from the left edge = 1.75 inches + 4 inches

Hook 2 distance from the left edge = 5.75 inches

Hook 3 distance from the left edge = 1.75 inches + (4 inches × 2)

Hook 3 distance from the left edge = 9.75 inches

So, Reema should use 3 hooks. The distance between the hooks is approximately 4 inches, and the distances of each hook from the left edge of the wood are approximately 1.75 inches, 5.75 inches, and 9.75 inches.

for such more question on distance

https://brainly.com/question/12356021

#SPJ8

Question

a Reema wants to build a coat rack for the front hallway. The wall is 4 feet long, and the piece of wood she has for the rack is 28  Checklist Did You... inches long. She wants to center the coat rack on the wall. There Draw a detalled needs to be an equal amount of space, about 7 or 8 inches, diagram? between the coat hooks. The first and last hooks should be no Check all your less than 1 inches from either end of the wood. How many calculations? Complete all parts hooks should Reema use? What is the distance between the of the problem? hooks? What is the distance of each hook from the left edge of the wood? Draw and label a diagram of the coat rack on the wall. Mark all the measurements for - inches placing the wood on the wall, and for attaching the hooks on the wood. You can use either fractions or decimals to label and calculate the measurements. Reflect Reflect on Mathematical Practices After you complete the task, choose one of the following questions to answer. • Model What models helped you to solve this problem? How did they help? • Be Precise When was it easier to use fractions, and when was it easier to work with decimal numbers? 213 1.75 left 1.75 edge Right edge

The number of squares that are in 384 sq ft is 0

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

Area expression = 384 sq ft

The above expression is an area expression

This means that it cannot be compared to quantities other then squares

The term "how many squares" is not an area expression

Hence, there are no squares in 384 sq ft

Read more about areas at

https://brainly.com/question/24487155

#SPJ9