(c) What is the shortest possible distance between the building and the end of the ramp if the architect redesigns the building so that the doorway is 1.3 feet above the parking lot?
Answers
The required shortest distance between the building and the end of the ramp, if the doorway is 1.3 feet above the parking lot, is 1.3 feet.
What is the slope?The slope is defined as the ratio measure of rise to measure of the run.
Here,
The shortest possible distance between the building and the end of the ramp, if the doorway is 1.3 feet above the parking lot, is 1.3 feet.
This is because, if the doorway is 1.3 feet above the parking lot, the ramp will need to rise 1.3 feet in order for a person or vehicle to be able to enter the building. The length of the ramp will be equal to the rise, so in this case, the shortest possible distance between the building and the end of the ramp would be 1.3 feet.
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Related Questions
Daniel Davis Dillard is proud of the lawn care business he runs after school. He charges a flat rate of $10 plus $5 per quarter acre of lawn. After mowing Mr. Durant's lawn times, he made a total of $125. Write and solve an equation to determine how many acres of lawn Mr. Durant has.
Answers
Mr. Durant has 5.75 acres of lawn, therefore he was charged $125
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The slope intercept form of an equation is:
y = mx + b
where m is the rate of change and b is the y intercept.
Let y represent the total cost of charging for mowing x acres.
He charges a flat rate of $10 plus $5 per quarter acre of lawn. Therefore:
$5 = quarter acre; $(5 * 4) = $20 is for one acre.
y = 20x + 10
He made a total of $125; hence:
125 = 20x + 10
115 = 20x
x = 5.75 acres
Mr. Durant has 5.75 acres of lawn.
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Solve the system of linear equations by graphing.
y=-1/2x+2
y=1/2x-1
=negative 3 comma one half
=one half comma 3
=one half comma negative 3
=3 comma one half
Answers
From the graphs below, we can see that the solution of the given system of linear equations is (3,0.5).
What is meant by a system of linear equations?
A collection of one or more linear equations containing the same variables is known as a system of linear equations. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is invariably a straight line equation. A group of diverse straight line equations make up a system of linear equations.
We are given two linear equations:
y = -1/2 x + 2
y = 1/2x - 1
As mentioned earlier, these are equations of two straight lines with slopes -1/2 and 1/2.
Now the solution of the equation is the intersecting point of these straight lines. We graph these equations and found the intersecting point.
Therefore, from the graphs below, the solution of the given system of linear equations is (3,0.5).
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While going through some more data from the AP Stats survey, Meghan finds some
interest correlations between student participation in sports and their grades. Of the
students surveyed, 341 played at least one sport and were on honor roll; 121 played
at least one sport but weren't on honor roll; 363 played no sports and weren't on
honor roll; and 275 played no sports and were on honor roll.
Using a two-way frequency table, determine what percentage of respondents play at
least one sport for the school.
Answers
Answer: no answer
Step-by-step explanation:
If the two quantities on a coordinate graph are time and distance from home which quantity is a function of which?
Answers
The distance is a function of time and the slope of the distance time graph will give the speed
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the first quantity be represented as Distance D
Let the second quantity be represented as Time T
Now , the function is given as
The distance D is a function of time and the slope of the line between the x and y axis of the distance time graph will give us the speed
Substituting the values in the equation , we get
Let the y axis represent the distance D
And , let the x axis represent the time T
So , Slope m = y / x
On simplifying the equation , we get
Slope m = Distance / Time = Speed
Hence , the distance is a function of time
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on january 28, 1986, space shuttle challenger exploded on takeoff. all seven crew members were killed. following the disaster, scientists and statisticians helped analyze what went wrong. they determined that the failure of o-ring joints in the shuttle's booster rockets was to blame. under the cold conditions that day, experts estimated that the probability that an individual o-ring joint would function properly was 0.977. but there were six of these o-ring joints, and all six had to function properly for the shuttle to launch safely. assuming that o-ring joints succeed or fail independently, find the probability that the shuttle would launch safely under similar conditions. show your work.
Answers
The probability of the shuttle launching safely under similar conditions is 0.859, or approximately 86%.
Scientists and statisticians played a crucial role in analyzing the cause of the disaster, which was eventually attributed to the failure of O-ring joints in the shuttle's booster rockets.
To understand the probability of the shuttle launching safely under similar conditions, we need to consider the probability of all six O-ring joints functioning properly. According to experts, the probability of an individual O-ring joint working in cold conditions was 0.977.
Assuming that the O-ring joints succeed or fail independently, we can use the multiplication rule of probability to calculate the probability of all six joints functioning properly.
The multiplication rule states that the probability of two independent events occurring together is the product of their individual probabilities. In this case, the probability of all six joints working properly is:
P(all six joints work) = P(joint 1 works) x P(joint 2 works) x P(joint 3 works) x P(joint 4 works) x P(joint 5 works) x P(joint 6 works)
Plugging in the given probability of an individual O-ring joint working in cold conditions (0.977), we get:
P(all six joints work) = 0.977 x 0.977 x 0.977 x 0.977 x 0.977 x 0.977
P(all six joints work) = 0.977⁶
P(all six joints work) = 0.859
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6. there are many cones with a volume of cubic inches. the height in inches of one of these cones is a function of its radius in inches where . a. what is the height of one of these cones if its radius is 2 inches? b. what is the height of one of these cones if its radius is 3 inches? c. what is the height of one of these cones if its radius is 6 inches?
Answers
In all three cases, the height of the cone is proportional to the volume and inversely proportional to the square of the radius. So, if we know the volume and radius of a cone, we can use the formula for h to find its height.
[tex]\text{Height } = h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (2^2)} = \frac{3V}{4\pi}[/tex]
The volume of a cone is given by the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone.
If we rearrange this formula to solve for h, we get h = 3V / (πr²). This means that the height of a cone is directly proportional to the volume and inversely proportional to the square of the radius.
a. If the radius of a cone is 2 inches and its volume is given, we can find its height by plugging in the values of V and r into the formula for h.
[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (2^2)} = \frac{3V}{4\pi}[/tex]
b. Similarly, if the radius is 3 inches, the height would be:
[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (3^2)} = \frac{3V}{9\pi}[/tex]
c. If the radius is 6 inches, the height would be:
[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (6^2)} = \frac{3V}{36\pi}[/tex]
In all three cases, the height of the cone is proportional to the volume and inversely proportional to the square of the radius. So, if we know the volume and radius of a cone, we can use the formula for h to find its height.
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based on your knowledge of the two data sets described below, would you expect a scatter plot describing the two data sets to have a positive, a negative, or no correlation? hourly pay and total number of sick days allowed
Answers
Based on your knowledge of the two data sets described below, would you expect a scatter plot describing the two data sets to have a no correlation.
Based on my knowledge, I would not expect there to be a strong correlation between hourly pay and total number of sick days allowed. These two variables are not directly related to each other and there is no clear reason to expect a positive or negative correlation between them. Therefore, I would expect the scatter plot to show no correlation between the two variables. However, it's worth noting that without actually seeing the data, it's difficult to definitively determine whether there is any correlation present.
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Select the correct answer.
Consider this quadratic equation.
x² + 3 = 4x
Which expression correctly sets up the quadratic formula to solve the equation?
O A.
OB.
O C.
O D.
-(-4) ± √(-4)² - 4(1)(3)
2(1)
-(-4) ± √(-3)² - 4(1)(4)
2(1)
-(-4) ± √4²(1)(3)
2(1)
-4± √√42-4(1)(3)
2(1)
Answers
The equation can be solved using the quadratic formula when the following expression is used: [tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4(1)(3)}}{2(1)}$[/tex]
What is quadratic formula?The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic equation. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.
The following general quadratic equation is given:
ax² + bx + c = 0
As a result, a polynomial equation with exponent two is referred to as a quadratic ("square-like") equation. Quadratum is the Latin word for square, and since the area of a square with side length x is given by x2, this is the case.
A quadratic equation's solution(s) can be found using the quadratic formula in elementary algebra. Graphing, factoring (direct factoring, grouping, AC technique), completing the square, and other methods can be used to solve a quadratic equation in addition to the quadratic formula.
The given equation is x² - 4x + 3 = 0
When compared to the quadratic equation's general equation, we get a = 1, b = -4, c = 3.
When the coefficient values for the Sridhar Acharya formula are put in,[tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4(1)(3)}}{2(1)}$[/tex] which gives Option (A).
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shawna knows that a correlation between calories of sweeteners consumed and mortality rates among women does not, in itself, mean that drinking more soft drinks will lead to a higher chance of her dying. which of the following would not be a lurking variable in the above scenario? a.) shawna's weight b.) the time of day shawna exercises c.) the number of soft drink brands available for purchase d.) the amount of caffeine available in soft drinks
Answers
Answer: Musical preferences
A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely your musical preferences affect mortality or how much sweetener you consume.
The number of soft drink brands available for purchase is not a lurking variable in this scenario. Correct option is C.
The statement is asking which of the given variables is not a lurking variable in the scenario where Shawna is considering the correlation between the calories of sweeteners consumed and the mortality rates among women, and is trying to determine whether drinking more soft drinks will lead to a higher chance of her dying.
A lurking variable is a variable that is not included in the analysis, but has an effect on the relationship between the variables being studied. In this case, the variables being studied are the calories of sweeteners consumed and the mortality rates among women, and the effect of drinking more soft drinks on the chances of dying.
Out of the given variables, the number of soft drink brands available for purchase would not be a lurking variable, as it does not have an effect on the relationship being studied.
Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could all potentially have an effect on the relationship being studied, either as confounding variables or moderators.
For example, Shawna's weight could be a confounding variable, as it is associated with both sweetener consumption and mortality rates. The time of day she exercises could be a moderator, as exercise may affect the metabolism of sweeteners and caffeine, which could in turn affect mortality rates.
The amount of caffeine available in soft drinks could be a confounding variable, as caffeine consumption is associated with both sweetener consumption and mortality rates.
In summary, the number of soft drink brands available for purchase is not a lurking variable in this scenario, while Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could potentially be confounding variables or moderators that need to be accounted for in the analysis.
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A store charges a restocking fee for any returned item based upon the item price. An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9. If you return an item that has an original price of $180, how much is the restocking fee?
Answers
An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9. The restocking fee for an item priced at $180 is $10.
To solve this problem, we need to use a proportion to relate the item price to the restocking fee. The problem provides two pairs of corresponding item prices and restocking fees: $200 and $12, and $150 and $9. We can set up a proportion using these pairs:
$200/$12 = $150/$9
We can simplify this proportion by dividing both sides by 3:
$200/$4 = $150/$3
Now we can use the simplified proportion to find the restocking fee for an item priced at $180. We'll use cross-multiplication:
$200 x $3 = $150 x $4
$600 = $600
This tells us that the ratios are equivalent, and the restocking fee for an item priced at $180 is $10.
In other words, the restocking fee is proportional to the item price, and we can use the given pairs of prices and fees to find the fee for any given price using a proportion.
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Simplify the following expression:
3x − 4y + z − 2z + x − y
2x − 6z
4x − 5y − z
4x − 3y − z
4x − 5y − 3z
Answers
Answer:
4x - 5y - z
Step-by-step explanation:
3x − 4y + z − 2z + x − y
Add like terms
= 4x - 5y - z
Answer: 4x-5y-z
Step-by-step explanation: 3x + x -4y-y -2z + z
It becomes a lot easier to simplify if you reorganize the equation so that the same variables are next to each other
To make a strawberry banana smoothie, a recipe calls for 1.75 cups of strawberries and some bananas. TO make
the recipe taste more like banana, ; cup more banana was added to the blender. The smoothie now has 1.4 cups
of bananas. How many cups of bananas were in the original recipe?
cup
Answers
Based on the information, it can be inferred that the original recipe contained 0.9 cups of banana.
How to calculate the original amount of banana contained in the recipe?To calculate the original amount of banana contained in the smoothie recipe we must perform the following mathematical operation:
We know that the final recipe has 1.4 cups of banana and that to make it have a more intense banana flavor they added 1/2 cups of banana, that is, 0.5 cups.
According to the above, we must subtract the amount that was added to the final amount to find how much the recipe has as shown below:
1.4 drinks - 0.5 drinks = 0.9 drinks
According to the above, the original recipe would have 0.9 cups of banana.
Note: This question is incomplete. Here is the complete information:
To make a strawberry banana smoothie, a recipe calls for 1.75L cups of strawberries and some bananas. To make the recipe taste more like banana, 1/2 C cup more banana was added to the blender. The smoothie now has 1.4 cups of bananas. How many cups of bananas were in the original recipe?
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HELPPPPP i don't know how to do these, I missed the first quarter of math
Answers
The domain of the relation is 0, 2, 3, and 7.
The range of the relation is 1 and 3.
How to find the domain and range of a relation?The domain of a function is the set of all possible inputs for the function. The domain of a relation is the independent variable of the relation. The domain of the relation are the x values.
Therefore, the domain of the relation are 0, 2, 3 and 7.
The range of the relation is the set of the second coordinates from the ordered pairs. The range is the output of the relation. The range are the y axis values.
Therefore, the range of the relation are 1 and 3.
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A piece of sheet metal has dimensions 3 3/4ft x 4 2/3ft. What is the area in square inches?
Answers
Explanation: multiple the dimensions which gives you the answer in square feet then multiply your answer by 12 to convert it to square inches.
IM BEING TIMED PLS HURRRYYY
Use factoring to write an expression equivalent to
100x^2-49y^2
SHOW UR WORKKK
Answers
The equivalent expression is (10x - 7y)²
What are algebraic expressions?They are defined as expressions that are composed of variables, terms, coefficients, factors and constants.
They are also made up of arithmetic operations.
It is important to note that equivalent expressions are defined as expressions having the same solution but usually differ in the mood of their arrangement.
From the information given, we have that;'
100x^2-49y^2
Find the perfect squares of the values, we have;
(10x - 7y)²
Hence, the expression is (10x - 7y)²
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The quadratic expression 100x² - 49y² is equivalent to (10x - 7y)(10x + 7y)
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
Given the quadratic equation:
100x² - 49y²
Factorizing the polynomial:
100x² + 70xy - 70xy - 49y²
= 10x(10x + 7y) - 7y(10x + 7y)
= (10x - 7y)(10x + 7y)
The expression is equivalent to (10x - 7y)(10x + 7y)
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Need answersjjsjsjdjejejsjs
Answers
It takes 45 scoops of water.
V_bucket = π * r^2 * h = π * r^2 * r = π * r^3
V_scoop = (1/3) * π * r^2 * h = (1/3) * π * r^2 * r = (1/3) * π * r^3
Now that we have the volumes of the bucket and the scoop, we can find the number of scoops it would take to fill the bucket 15 times:
V_bucket * 15 = 15 * π * r^3
V_bucket * 15 / V_scoop = 15 * π * r^3 / (1/3) * π * r^3 = 45
So it would take 45 scoops of water to fill the bucket 15 times.
Shawna joined the bowling league at Bronze Lanes, a bowling alley. She scores a strike 75% of the time. For a perfect game, she needs to bowl a strike 12 times in a row. How likely is it that Shawna will bowl a perfect game at her next game?
Shawna simulates the situation by using a computer to randomly generate 12 numbers from 1 to 4. Each time 1, 2, or 3 appears, it represents a strike
Answers
The probability of Shawna bowling a perfect game is 7.23%.
Assuming that Shawna's chance of getting a strike is independent on each roll (which may not be entirely accurate in real life), the probability of her getting a strike on any given roll is 0.75.
To calculate the probability of Shawna bowling a perfect game (i.e., getting a strike on all 12 rolls), we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.
So, the probability of Shawna getting a strike on the first roll is 0.75. The probability of her getting a strike on the second roll, assuming she got a strike on the first roll, is also 0.75. Similarly, the probability of her getting a strike on the third roll, assuming she got strikes on the first two rolls, is also 0.75. We can continue this pattern for all 12 rolls.
Therefore, the probability of Shawna bowling a perfect game is:
0.75 x 0.75 x 0.75 x ... (12 times)
which is approximately equal to 0.0723, or about 7.23%.
Using a computer to randomly generate 12 numbers from 1 to 4 and treating 1, 2, or 3 as a strike is a reasonable way to simulate the situation and estimate the probability of Shawna bowling a perfect game. By repeating this process many times, we can get a better idea of the distribution of possible outcomes and the likelihood of different results.
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The local ferry takes cars across a bay. One day, the ferry transported a total of 610 cars over a 5 -hour period. The ferry took the same number of cars each hour. How many cars did it take each hour? Complete the bar diagram to help.
___ cars
c
c
c
c
___________
c
Answers
Answer:122 cars per hour
Step-by-step explanation:Get the total number of cars 610 get the time period 5 hours divide 610 divided by 5 equals 122 cars per hour.
Answer: the ferry took atleast 3,050 cars each hour
1. Cam has just completed her first year of
college, and she has decided to put her
possessions in a self-storage facility while
she's visiting her family during summer
vacation. She will be charged a flat fee of
$35.00 plus $0.45 for each day of storage. If
Cam stores her possessions for d days and
is charged a total of $63.80, which of the
following equations can be used to solve for
d?
A. 35+0.45 + d = 63.80
B. 35+0.45 = d+63.80
C. 350.45 + d + 63.80
D. 35+0.45d = 63.80
E. 35+0.45 = 63.80d
Answers
The equation that represents the given scenario is 35 + 0.45d = 63.80
What is Linear Equation:The linear equation is a mathematical statement that is solved for an unknown value. The linear equation is straight in a graph where the variable will represent an unknown value in the given problem.
To find the required equation, first calculated the charge according to the given problem and form the linear equation using the given variable.
Here we have
Cam will be charged a flat fee of $35.00 plus $0.45 for each day of storage.
If Cam stores her possessions for d days then the charge = $ 0.45d
After adding the fee the total charge will be $ 35 + $ 0.45d
Given that the total charge is $63.80
From the above calculations,
=> $ 35 + $ 0.45d = $ 63.80
=> 35 + 0.45d = 63.80
Therefore,
The equation that represents the given scenario is 35 + 0.45d = 63.80
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two messenger services deliver to a small town. service a has 75% of all the scheduled deliveries, and service b has the remaining 25%. their on-time rates are 80% and 60% respectively. calculate the probability that a package is delivered on time.
Answers
Service a has 75% of all the scheduled deliveries, and service b has the remaining 25%, their on-time rates are 80% and 60% respectively, the probability that a package is delivered on time is 0.75 or 75%.
To calculate the probability that a package is delivered on time, we need to use the law of total probability and the probabilities of on-time delivery for each messenger service.
Let A denote the event that a package is delivered by Service A, and B denote the event that a package is delivered by Service B. Then, we have:
P(on-time delivery) = P(on-time delivery | A) * P(A) + P(on-time delivery | B) * P(B)
where P(on-time delivery | A) is the probability that a package is delivered on time given that it was sent through Service A, and P(A) is the probability that a package is sent through Service A.
Similarly, P(on-time delivery | B) is the probability that a package is delivered on time given that it was sent through Service B, and P(B) is the probability that a package is sent through Service B.
From the information given in the question, we know that P(A) = 0.75, P(B) = 0.25, P(on-time delivery | A) = 0.8, and P(on-time delivery | B) = 0.6. Substituting these values into the above formula, we get:
P(on-time delivery) = 0.8 * 0.75 + 0.6 * 0.25
= 0.6 + 0.15
= 0.75
Intuitively, this result makes sense because Service A, which has a higher on-time rate and delivers 75% of the packages, dominates the total probability of on-time delivery. However, the contribution of Service B cannot be ignored completely and reduces the overall on-time rate slightly.
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9. Si a=1/2, b=1/3, entonces
a) 1/2
b) 6/5
a+b
es igual a:
c) 1/6
d) 6
Answers
Answer:
5/6 (No option is suitable)
Step-by-step explanation:
Given information,
→ a = 1/2
→ b = 1/3
We have to find,
→ a + b
Let's solve the problem,
→ (1/2) + (1/3)
→ (3/6) + (2/6)
→ (3 + 2)/6
→ 5/6
Hence, the answer is 5/6.
The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool
Answers
Answer:
Step-by-step explanation:
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The actual distance between the basketball court and the pool is 37.5 feet
Distance refers to the amount of space between two objects or points. It is a measure of how far apart two things are from each other.
The scale of the model is 3 inches = 5 feet. This means that every 3 inches on the model represents 5 feet in actual size. We are given that the distance between the basketball court and the pool on the model is 22.5 inches. To find the actual distance between these areas, we need to use the scale.
We can start by setting up a proportion using the scale. We know that 3 inches on the model represents 5 feet in actual size. Therefore, we can say that:
3 inches / 5 feet = 22.5 inches / x
We are trying to solve for x, which represents the actual distance between the basketball court and the pool. To solve for x, we can cross-multiply and simplify the equation:
3 inches x x = 5 feet x 22.5 inches
3x = 112.5
x = 37.5 feet
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Complete Question:
The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool?
Sketch and graph please
Answers
The graph of the linear inequality [tex]y\geq -3x+4[/tex] is given below.
What is linear inequality?
The expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities. A linear inequality, which is an inequality including at least one linear algebraic expression, is when a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1. There are numerous ways to depict various kinds of linear inequalities.
Given linear inequality is [tex]y\geq -3x+4[/tex] for which y region will be in the positive range.
Hence, the graph of the given linear inequality is given below.
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please help me! A business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually. After 30 years, the value of the bond will be $25,084.20. If the business owner's investment was compounded continuously instead of twice per year, what would be the difference in the account balance after 30 years? $345.31 $318.22 $286.74 $228.59
Answers
Using compounding we know that after 30 years, the account balance has changed by $345.31.
What is continually compounded?Theoretically, continually compounded interest indicates that interest is continuously earned on an account balance as well as reinvested into the balance so that additional interest is generated.
So, a business owner put $7,000 into a Treasury bond paying a semiannual compound interest rate of 4.3%.
The bond's value after 30 years is $25,084.20.
Instead of compounding twice a year, the investment made by the business owner was made continuously.
After 30 years, we must determine the difference in the account balance.
Think of the continuously compounding recipe:
A = Pe∧rt
We have, p = 7000.
r = 4.3% = 0.043
t = 30
Then,
A = 7000e∧(0.043*30) = 25429..51
A = $25429.51
Therefore, using compounding we know that after 30 years, the account balance has changed by $345.31.
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Correct question:
A business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually. After 30 years, the value of the bond will be $25,084.20. If the business owner's investment was compounded continuously instead of twice per year, what would be the difference in the account balance after 30 years?
Answer two questions about Systems AAA and BBB:
System AAA \text{\quad}start text, end text System BBB
\begin{cases}-3x+12y=15\\\\7x-10y=-2\end{cases}
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−3x+12y=15
7x−10y=−2
\begin{cases}-x+4y=5\\\\7x-10y=-2\end{cases}
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−x+4y=5
7x−10y=−2
1) How can we get System BBB from System AAA?
Answers
1. To get System BBB from System AAA, we can divide both sides of the first equation in System AAA by -3:
-3x + 12y = 15
-3x/ -3 + 12y/ -3 = 15/ -3
x + 4y = -5
So System BBB is obtained by dividing both sides of the first equation in System AAA by -3.
2. Are Systems AAA and BBB equivalent?
Yes, Systems AAA and BBB are equivalent. This means that they have the same solution set, despite having different coefficients in their equations. Equivalent systems of linear equations are systems that have the same solution set, regardless of the coefficients of the equations.
Sam is making a model of a stadium using a scale in which 2 centimeters equals 15 feet. If the model is 46.5 centimeters wide, what is the actual width of the stadium, in feet? your answer can be exact or rounded to two decimal places.
Answers
Answer:
348.75
Step-by-step explanation:
A maintenance worker needs to wax a restaurant floor shaped like the image shown. A six-sided figure. There is a horizontal base of 33 feet then another horizontal base below it of 19 feet. The longest side is to the right and is 37 feet. The top is 28 feet. There is a perpendicular from the vertex of the top to the first base of 33 that is labeled 14 feet. If the wax cost $1.67 a square foot, how much will the wax cost to cover the floor? $832.50 $1,300.10 $1,664.99 $2,600.19
Answers
If the wax was priced at $1.67 per square foot, it would cost $1,664.99 to wax the entire floor. The right answer is C.
How to calculate the area of the floor?The floor is made up of a trapezoid and a rectangle.
The area of a trapezoid can be calculated as:
A = (b₁ + b₂)/2 x h
Where b₁ and b₂ are the lengths of the bases and h is the height.
The trapezoid is 14 feet tall, and its bases are 33 feet long and (28 - 19) or 9 feet wide. Thus, its area is:
A = (33 + 9)/2 x 14
A = 294 square feet
The rectangle is 37 feet tall with a 19-foot base. Thus, its area is:
A = 19 x 37
A = 703 square feet
The area of the triangle and trapezoid together make up the overall area of the figure.
A = 294 + 703
A = 997 square feet
Finally, to find the cost of the wax, we multiply the area by the cost per square foot:
Cost = 997 * $1.67
Cost = $1664.99
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amit took part in an cycle race .he started at 1:25 pm and reached the finishing line at 1:50 . what was the duration of the race ?
amit took a part in cycle race .he started at 1:25 and he reached finishing lline at 1:50 pm what was the duration of the race .
Answers
Answer:
25 minutes
Step-by-step explanation:
The time difference between 1:25 and 1:50 is 25 min
a fitness club leases space at a major shopping center. the club has 10,500 square feet which represents 16% of the total leasable space at the shopping center. calculate the total leasable space at the center?
Answers
The shopping mall has 65,625 square feet of total leasable area. As stated in the problem, this indicates that the fitness club takes up 16% of the total leasable space.
According to the information provided, a fitness club occupies 10,500 square feet or 16% of the total leasable area at a sizable shopping mall. We can use the proportional and percentage approaches to determine the total leasable area.
Let's assume that the variable "x" stands for the whole amount of leasable space. Since we are aware that the area leased by the gym is 16% of the total leasable area, we can create the following equation:
10,500 = 0.16x
To solve for "x", we can divide both sides of the equation by 0.16:
10,500 / 0.16 = x
Simplifying this expression gives us:
x = 65,625
Therefore, The shopping mall has 65,625 square feet of total leasable area. As stated in the problem, this indicates that the fitness club takes up 16% of the total leasable space.
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The large tank begins with 600 gallons of oil. The flow rate is recorded as –4 gallons per minute. After a period of 32 minutes, how much oil has been moved and to which tank?
Answers
After a period of 32 minutes 128 gallons of oil is moved from a large tank to a small one.
What is the flow rate?
The quantification of bulk fluid movement is called flow measurement. The mass of a material that moves per unit of time is known as the mass flow rate. The amount of fluid moving per unit of time is known as the volumetric flow rate.
Here, we have
Given that the flow rate is recorded at -4 gallons per minute, which is negative.
It means that the oil is flowing in the small tank.
The rate of flow, r is 4 gallons per minute, here work is oil flowing into a tank
Rate of flow, r = oil flown in a tank/time taken
Given that time, t = 32 minutes
∴ rate of flow × time taken = Oil flown in small tank
⇒ r× t = oil flown in small tank = 4 × 32 = 128 gallons
Hence, after a period of 32 minutes 128 gallons of oil is moved from a large tank to a small one.
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