The ratio 10:35 can be simplified to 2:7.
What is a Ratio?
A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
The ratio 10:35 can be simplified to 2:7.
To simplify a ratio, you can divide both values by the greatest common factor. In this case, the greatest common factor of 10 and 35 is 5, so 10 divided by 5 is 2, and 35 divided by 5 is 7.
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Simply the following ratio 10:35
The square root of a number is greater than the square of the number. For what set of numbers is this true?.
The set of numbers for which the statement that the square root of a number is greater than the square of the number is true, is equals to (0,1). So, right choice is option (a).
In mathematics, when we multiplying the number by itself, the result is called square of number. This is usually equivalent to raising a number to the power of 2. For example, square of 4 is 4² = 16. The square root of a number is that factor of a number which when multiplied by itself the original number. Square root of number is usually equivalent to raising a number to the power of 1/2. It is represented using the symbol '√'. Now, we have to check the options and determine where square root of a number is greater than the square of the number.
a) (0, 1), if we plug f(x) = √x , x∈(0,1) and g(x) = x² , x∈(0,1) on calculator then we get, the value of f(x) is greater than g(x), i.e, x = 1/2 , f(1/2) = 0.70 and g(1/2) = 0.25.
b) [0, 1], if we plug x = 0 then f(0) = 0 , g(0) = 0
that is f(x) is greater than and equal to g(x). But we have to consider only greater than not equal.
c) [1,∞), closed bracket again represents equality which is not consider. So, statement is false for it.
d) (1,∞), here number inbetween 1 and infinite but not for all reals it is true that square root of a number is greater than the square of the number, for example x = 2 , f(2) =1.414, g( 2) = 4 implies f(x)< g(x) for x = 2. So, the statement is false for it.
Hence, required option is option (a).
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Complete question :
The square root of a number is greater than the square of the number. For what set of numbers is this true?
a) (0, 1)
b) [0, 1]
c) [1, ∞ )
d) (1,∞)
The table shows the total numbers of visitors to a website t days after it is online.
a. Determine wether the table represents an exponential growth function, an exponential decay function, or neither.
b. How many people will have visited the website after it is online 47 days? Round to the nearest whole number.
a) The table represents an exponential growth function.
b) The number of people that will have visited the website after 47 days online is given as follows: 17,716 people.
How to model the exponential function?An exponential function is modeled as follows:
y = a(b)^x.
In which:
a is the initial value.b is the rate of change.The parameters for this problem are given as follows:
a = 11000.b = 12100/11000 = 1.1. > 1 -> exponential growth.Considering that the reference day is the day 42, the function is defined as follows:
y = 11000(1.1)^(x - 42).
Hence, after day 47, the number of visitors is given as follows:
y = 11000 x (1.1)^5.
y = 17,716.
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In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.
Somebody help, I don't get this!
The statements are (a) False, (b) True and (c) False
What are Right Angles?Right angles are angles whose measure is 90 degrees.
In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.
(a) ∠AHB and ∠AHG are vertical angles.
Vertical angles are angles which are formed on the opposite sides of two intersecting lines.
∠AHB and ∠AHG are not formed on the opposite sides, but are adjacent to each other.
So the statement is false.
(b) ∠EHF and ∠DHE are adjacent angles.
∠EHF and ∠DHE are two angles which are adjacent to each other. So they are adjacent angles.
So the statement is true.
(c) The measure of ∠FHG is equal to the measure ∠DHF.
We know that DG is a straight line.
∠FHG and ∠DHF are linear pair of angles.
So, ∠FHG + ∠DHF = 180°
Given that ∠FHG is right angle.
90° + ∠DHF = 180°
∠DHF = 180° - 90°
∠DHF = 90°
So the statement is true.
Hence the statements (a), (b) and (c) are false, true and true respectively.
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Your question is incomplete. The complete question with the figure is given below.
If a rock is thrown upward on an exoplanet of a nearby star with initial velocity…..
the displacement is 23.14m and the velocity is 21.28m/s
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The given equation y = 25t - 1.86t²
at t = 1
So the displacement y = 25-1.86 = 23.14
to find velocity dy/dt = 25- 2(1.86)t
v = 25 - 3.72 = 21.28m/s
Hence the displacement is 23.14m and velocity is 21.28m/s
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gerry's drawer has two black socks and 4 blue socks. if he selects two socks without looking what is the probability that both socks are black
Use the formula d= vt + 16t2, where d is the distance in feet, v is the initial velocity in feet per second, and it is the time in seconds.
An object is released from the top of a building 480 ft high. The initial velocity is 16 ft/s. How many seconds later will the object hit the ground?
Answer:
5 seconds
Step-by-step explanation:
d = vt + 16t² , that is
vt + 16t² = d
substitute d = 480, v = 16 into the equation
16t + 16t² = 480 ( divide through by 16 )
t + t² = 30 ( subtract 30 from both sides )
t² + t - 30 = 0 ← in standard form
(t + 6)(t - 5) = 0 ← in factored form
equate each factor to zero and solve for t
t + 6 = 0 ⇒ t = - 6
t - 5 = 0 ⇒ t = 5
t > 0 , then t = 5
the object will hit the ground 5 seconds later
Answer:
5 seconds.-------------------------
As per given we have:
d = 480 ft,v = 16 ft/s.Substitute these into given equation and solve for t:
480 = 16t + 16t²30 = t + t²t² + t - 30 = 0t² + 6t - 5t - 30 = 0t(t + 6) - 5(t + 6) = 0(t + 6)(t - 5) = 0t + 6 = 0 or t - 5 = 0t = - 6 or t = 5The first value of t is discarded as time can't be negative, so the answer is 5 seconds.
graph the inequality p < -8.
Answer:
I have graphed it and attached an image in the explanation part.
Step-by-step explanation:
Use calculator to find 61.6 to the nearest hundredth
Answer : 61.60
Step-by-step explanation:
Answer:61.60
Step-by-step explanation:
i just typed it in
i need help on this pleaseee!!
The value of each variable in the quadrilateral can be found such that :
y = 73 degrees z = 101 degrees How to find the value of the variables ?Angle 107 degrees and z degrees will add up to 180 degrees which means that the value of z is:
= 180 - 107
= 73 degrees
Using this value of z as 73 degrees, we can then solve for y because the sum of the interior angles of a quadrilateral need to add up to 360 degrees.
The value of y variable is therefore:
= 360 - 83 - 103 - 73
= 101 degrees
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Here is a triangle.
4x + 20
x +32
4x + 20
Does the triangle contain an obtuse angle?.
Explain your reasoning.
Please help me urgent need
Answer:
No
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
x + 32 + 4x + 20 + 4x + 20 = 180
9x + 72 = 180 ( subtract 72 from both sides )
9x = 108 ( divide both sides by 9 )
x = 12
then the 3 angles are
x + 32 = 12 + 32 = 44°
4x + 20 = 4(12) + 20 = 48 + 20 = 68°
4x + 20 = 68°
an obtuse angle is greater than 90°
none of the 3 angles in the triangle are obtuse
Answer:
No
Step-by-step explanation:
All angles of a triangle add up to 180°.
4x + 20 + 4x + 20 + x + 32 = 180
1. Simplify
9x + 72 = 180
2. Subtract 72 from both sides.
9x = 108
3. Divide both sides by 9.
x = 12
Replace x by 12 in each angle.
- 12 + 32 = 44°
- 4(12) + 20 = 68°
- 4(12) + 20 = 68°
All of the angles are less than 90°, so they aren't obtuse.
Find echelon form of this augmented matrix written so 1's on the diagonal
1 -1 2 400
1 0 0 900
1 -3 7 -300
The echelon form of the given augmented matrix with 1's on the diagonal is:
1 -1 0 1000
0 1 0 1100
0 0 1 300
What is the echelon form of this matrixTo find the echelon form of the given augmented matrix with 1's on the diagonal, we perform row operations to eliminate the entries below the diagonal. The goal is to get the matrix in row echelon form. Here are the steps:
Step 1: Subtract the first row from the second and third rows to eliminate the 1's in the first column below the diagonal:
1 -1 2 400
0 1 -2 500
0 -2 5 -700
Step 2: Add twice the second row to the third row to eliminate the -2 below the diagonal:
1 -1 2 400
0 1 -2 500
0 0 1 300
Step 3: Add 2 times the third row to the first row and add 2 times the third row to the second row to eliminate the entries above the diagonal:
1 -1 0 1000
0 1 0 1100
0 0 1 300
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Rosetta averages 148 points per bowling game with a standard deviation of 14 points. Suppose Rosetta's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(148,14). If necessary, round to three decimal places
The statistical measurement known as the Z-score describes the connection between a value and the mean of a set of values and the required z-score to the three decimal places is −2.714.
What is the z-score?The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score.
Standard deviations from the mean are used to measure Z-score.
A Z-score of zero means the data point's score is the same as the mean score.
Your observed value is 2.5 standard deviations from the mean if your Z-score is 2.5, and so on.
Your value is more closely aligned with the mean the closer your Z-score is to zero.
Your value is further from the mean the farther your Z-score is from zero.
So, let's say Rosetta wins the game on Thursday with 110 points.
When x=110, the z-score is -2.714.
The average is 148.
You can see from this z-score that x=110 is 2.714 standard deviations away from the mean.
This formula can be used to determine the z-score:
z = x−μ/σ
=110−148/14
=−38/14
≈−2.714
Therefore, the required z-score to the three decimal places is −2.714.
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Linear Functions Question! Please Help Asap!
The value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.
What is union of sets?We carry out specific operations in mathematics, such as addition, subtraction, multiplication, etc. Generally speaking, these operators accept two or more operands and output a result dependent on the operation carried out. Similar to this, in set theory, several operations are typically done on two or more sets to obtain a new set of elements depending on the operation. The number of elements supplied by the operation and processing the result of a collective set is represented by the union and overlap of sets. All of the components are taken into account in the outcome when there is a union, but only the ones that are shared when there is an intersection.
The union of the two sets depict all the terms present in both the sets.
Thus, the value of (A ∪ B) is:
(A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18}
The intersection of the sets depict all the common terms present in the two sets thus the value of (A ∩ B) is:
(A ∩ B) = {7}
Hence, the value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.
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6. Linden shared 237 litres of milk in 3 smaller litre containers. How many 3 litre containers would he get from his supply of milk?
Using division operation, the number of containers that Linden would get from his supply of milk is 79 containers.
What is division operation?Division operation involves the dividend divided by the divisor to obtain a result called the quotient.
Division operation is one of the four basic mathematical operations, including multiplication, addition, and subtraction.
Total liters of milk = 237
The content of the liter containers = 3 liters
The number of containers = 79 (237 ÷ 3)
Thus, based on division operation, Linden, who is sharing 237 liters of milk in containers will need 79 3-liter containers.
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EDAT: COMBINATION
An engineering faculty is going to form a committee for accreditation. The faculty is currently made up of 20 engineers. Exactly seven (7) engineers are needed to form the committee. In how many ways can they form the committee if:
1. Engr. Marzo and Engr. William refuses to work in the committee together. (10 pts)
2. Engr. Cara wants to be part of the committee with Engr. Danny but Engr. Danny will refuse to be part of the committee if Engr. Hillary is part of the committee. (10pts)
3. Engineers Gillian, Fernando and Ophelia will work in the committee if all three of them is part of the committee. (10 pts)
The number of combinations of different engineers is found to form a 7 member committee according to the given conditions.
What is meant by combination?
Combinations are ways to choose things from a collection where the order of the choices is irrelevant. It is described as an arrangement of items where the order in which they are chosen is irrelevant.
Given,
Number of engineers in the faculty = 20
Number of engineers required to form a committee = 20
1) Number of ways when either engr. Marzo or engr. William is only present.
Excluding Marzo and William, we have 18 engineers.
So we can select 6 engineers from these 18 = 18C6 = [tex]\frac{18!}{6!12!}[/tex] = 18564
Number of ways we can select only one from Marzo and William = 2C1 = 2
So the total number of combinations for forming a committee = 18564 + 2 = 18566
2) Engr. Cara and Eng. Danny are present.
Engr. Hillary is not considered.
So we have to select 5 members from the rest of the 15 people
Number of combinations are = 15C5 = 3003
3) Engineers Gilliam, Fernando and Ophelia are selected.
Now we have to select the rest of the 4 members from the remaining 15 people
Number of combinations = 15C4 = 1365
Therefore the number of combinations of different engineers are found to form a 7 member committee.
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What would you need to invest to produce $23711 if your interest rate is 3.6% compounded monthly for 15 years? Round your answer to the nearest dollar.
Answer:
$10576.38
Step-by-step explanation:
To calculate the investment amount required to produce $23711 at an interest rate of 3.6% compounded monthly for 15 years, you can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A is the amount of money you have after "t" years,
P is the initial investment amount (what you want to find),
r is the interest rate as a decimal,
n is the number of times the interest is compounded per year,
t is the number of years the investment will be compounded for.
In this case,
r = 0.036
n = 12 (because the interest is compounded monthly)
t = 15
So, we can plug in the values into the formula and solve for P:
A = P * (1 + 0.036/12)^(12 * 15)
$23711 = P * (1.003)^(180)
$23711 = P * 2.2375
Dividing both sides by 2.2375:
P = $23711 / 2.2375
P = $10576.38
So, to produce $23711 at an interest rate of 3.6% compounded monthly for 15 years, you would need to invest $10576.38. Rounded to the nearest dollar, this amount is $10576.
10. Susan has $800 in her bank account. Every week, she withdraws $100 for spending money.
A) What is the rate of change (or slope) in this situation?
B)
How much will she have left in her account after five weeks?
A) The rate of change in this situation is -$100 per week.
B) She will have $300 left in her account after five weeks.
Square ABCD has diagonal AC with vertices A(1, 1) and C(3, — 1). Find the coordinates of the
remaining vertices.
The coordinates are
Answer:
The coordinates of the remaining vertices are (1, -1) and (3, 1).
Step-by-step explanation:
A square is a quadrilateral with with four sides of equal length. It has two sets of parallel sides and its interior angles are all right angles. Therefore, each vertex shares its x-coordinate with one adjacent vertex, and its y-coordinate with the other adjacent vertex.
If AC with vertices A(1, 1) and C(3, -1) is the diagonal of a square, the coordinates of the remaining vertices will be:
[tex](x_A, y_C)=(1,-1)[/tex][tex](x_C, y_A)=(3,1)[/tex]Based on the scatter plot above, which three statements are true?
A
The graph shows a positive association.
B
The graph shows a negative association.
C
As the cost of a t-shirt increases, the # of t-shirts sold increases.
D
As the cost of a t-shirt increases, the # of t-shirts sold decreases.
E
There is a linear association shown.
F
There is a nonlinear association shown.
G
There is no correlation shown on the scatter plot.
The graph shows a positive association. There is a nonlinear association shown. There is no correlation shown on the scatter plot.
What is a nonlinear?A nonlinear system is one in mathematics and science where the change in the output is not proportional to the change in the input. Since the majority of systems are fundamentally nonlinear, engineers, biologists, physicists, mathematicians, and many other scientists are interested in nonlinear problems. A nonlinear equation is one in which the highest degree of any term is two or more. For instance, 3x2. + 2x + 1 = 0, 3x + 4y = 5, is an example of a nonlinear equation since equation 1 has the greatest degree of 2, while equation 2 involves variables x and y. Anything connected to a line is considered linear. To construct a line, one uses all of the linear equations. Unable to form a straight line is a non-linear equation. With a fluctuating slope value, it resembles a graphed curve.To learn more about nonlinear refer to:
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23 inches of wire cost 92 cents at the same rate, how much (in cents) will 34 inches of wire cost?
Answer:
Step-by-step explanation:
Let's use the formula rate = cost/length to find the cost of one inch of wire. We know that 23 inches of wire cost 92 cents, so the rate of one inch of wire can be found by dividing 92 cents by 23 inches:
rate = cost/length = 92 cents/23 inches = 4 cents/inch
Now that we have found the rate of one inch of wire, we can use it to find the cost of 34 inches of wire. We simply multiply the rate by the length:
cost = rate * length = 4 cents/inch * 34 inches = 136 cents
So, 34 inches of wire will cost 136 cents.
Step-by-step explanation:
the trick is to find the "norm" rate, which is the rate for one unit.
from there we can get the rate for any number of units just by multiplying.
so,
23 in for 92 cents.
that means the rate is
23/92 = 23/(23×4) = 1/4
so, by dividing numerator and denominator by 23 (in this case it has an integer result also for the denominator) we get the price for 1 inch of wire : 4 cents.
so, 34 inches then have the length/price ratio (we multiply numerator and denominator by 34)
1/4 × 34/34 = 34/136
that means 34 inches cost 136 cents (= $1.36).
If the percentage increase between 2017 of 9,640,000 and 2018 of 9,960,000 continued in 2018 and 2019 , how many households would be there be in 2019 ? Round to the nearest ten thousand
Answer:
Step-by-step explanation:
To determine the percentage increase between 2017 and 2018, we need to calculate the difference between the two years and then divide by the 2017 value and multiply by 100. So, the calculation would be:
(9960,000 - 9640,000) / 9640,000 * 100 = 3.125%
So, the number of households increased by 3.125% from 2017 to 2018.
To find the number of households in 2019, we need to find the increase from 2018 to 2019. We can do this by multiplying the number of households in 2018 by the percentage increase, and then add that to the 2018 value. So, the calculation would be:
9960,000 * (3.125 / 100) + 9960,000 = 10,298,800
Therefore, there would be approximately 10,298,800 households in 2019, rounded to the nearest ten thousand.
Question 5b
A trailer truck carries 11, 430 bottles, each weighing 14 ounces. To the nearest ton,
how much weight does the truck carry?
The truck carries
tons.
The total weight of the bottles the truck carries is 6020 ounces.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
Example:
2 + 1x + 4y = 7 is an expression.
3 + 3x + 3 = 7 is an expression.
We have,
Number of bottles the truck carries = 430
One bottle weight = 14 ounces
Now,
The total weight of the bottles.
= Number of bottles x Weight of one bottle
= 430 x 14
= 6020 ounces
Thus,
The total weight of the bottles the truck carries is 6020 ounces.
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the table shows the rate at which justin can make widgets. how many widgets can justin make in 36 minutes?
The number of widgets that Justin can make in 36 minutes is given as follows:
y = 36k.
In which the constant k is the number of widgets that can be made per minute, and is obtained dividing a value of y by it's respective value of x from the table.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
Input x: number of minutes.Output y: number of widgets.The constant is obtained as follows:
k = y/x.
For a time of 36 minutes, we have that x = 36, hence the number of widgets is given as follows:
y = 36k.
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The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S. In 2018, the Bureau reported that Wisconsin police officers had a mean yearly salary of $62,040. Calculate the average hourly wage for police officers. Round to the nearest cent. Assume that police officers generally work 40 hours a week. There are 52 weeks in the year.
The average hourly wage for police officers is $30.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S.
In 2018, the Bureau reported that Wisconsin police officers had a mean yearly salary of $62,040.
Assume that police officers generally work 40 hours a week.
There are 52 weeks in the year.
The average hourly wage for police officers is,
= 62040 ÷ (52 x 40)
= 62040 / 2080
= 29.8
≈ $30
Therefore, $30 is the hourly wage.
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Of the 125 persons applying for a certain job at data processing center,79 had previous work experience and 62 had college degree, while 38 has both work experience and college degree.
i)How many applicants did not have college degree
ii)how many applicants did not have experience
iii) how many applicants had college degree but no experience
iv)how many applicants had either college degree or experience but not both
1. the number ( of people without college degree ) = 125 - (24 +38)= 63
2. number of people without experience ) = 125- ( 41+38) = 46
3. number ( of applicants with college degree but no experience) = 24
4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103
What is set?A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
number of people that have previous work experience only) = 79-38 = 41
number ( of persons that have college degree only) = 62- 38 = 24
1. the n( of people without college degree ) = 125 - (24 +38)= 63
2. n( of people without experience ) = 125- ( 41+38) = 46
3. n( of applicants with college degree but no experience) = 24
4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103
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The temperatures, in °C , at midnight on 10 consecutive days were 4, 1, 0, –2, –1, –3, 1, –2, 3, –1. (a) Find the difference between the highest and the lowest temperature
Answer:
7 degrees C
Step-by-step explanation:
To solve this question, we can start by ordering the temperatures from least to greatest:
4, 1, 0, -2, -1, -3, 1, -2, 3, -1 --> -3, -2, -2, -1, -1, 0, 1, 1, 3, 4
the lowest temperature would be -3 in this list, and the highest temperature in this list would be 4. We can find the difference in temperature using subtraction:
4-(-3) = 4+3=7
The difference is 7 degrees C.
Please solve quickly thanks
Answer:
Step-by-step explanation:
I believe that you put the right answer in.
please help question below
Answer:
Step-by-step explanation:
22
You can work a total of no more than 32 hours each week at your two jobs. Tutoring pays $7 per hour and babysitting pays $8 per hour. You need to earn at least $256 each week to pay your bills.
Let X = the number of hours tutoring. Let Y = the number of hours babysitting
Answer: The correct system of linear inequalities that represents this situation is:
X + Y ≤ 32 (to represent the maximum number of hours you can work)
7X + 8Y ≥ 256 (to represent the minimum amount of money you need to earn)
X ≥ 0, Y ≥ 0 (to represent that you can only work a non-negative number of hours at each job)
Where X represents the number of hours you spend tutoring and Y represents the number of hours you spend babysitting. The first inequality represents the maximum number of hours you can work, and the second inequality represents the minimum amount of money you need to earn. The last two inequalities represent that you can only work a non-negative number of hours at each job.
Step-by-step explanation:
DUE TODAY PLS I JUST NEED HELP
Answer:
(a)
smaller value = 125 ft
larger value = 250 ft
(b)
31250 ft²
Step-by-step explanation:
(a)
In total, the farmer used 875ft worth of fencing.
In terms of x, the total fencing used is: 2x + x + x + x + 2x = 7x
This means 7x=875ft. Dividing both sides by 7, we find x=125ft
The dimensions of the rectangular enclosure in terms of x are "x and 2x". Subbing in 125ft for x, these dimensions become "125ft and 2(125ft)" or "125ft and 250ft".
(b)
Since we know the enclosure is 125ft long and 250ft wide, and since the area of a rectangle is its length times its width, the are of the enclosure is:
125ft * 250ft = 31250 ft²
Answer:
(a)
smaller value =125 ft
larger value = 250 ft
(b)
31250 ft?
