The system of equations is inconsistent and has no solution.
Here's a step by step process to check for consistency:
2x + y = -5
82x + 3y = 1
Subtracting the first equation from the second gives us:
80x + 2y = 6, which can not be true for any values of x and y.
Therefore, the system of equations has no solution and no approximation of y can be made.
The arrangement of conditions gave doesn't have an answer, since it prompts clashing responses. Basically, when we plug in values for x, the conditions offer us two unique responses for y, and that implies there is definitely not a solitary point that fulfills the two conditions. This makes it difficult to track down an incentive for y that would make the two conditions right. It's like attempting to adjust two teeter-totters simultaneously with loads, yet the loads are different on each side, making it difficult to adjust the two sides. For this situation, there is no arrangement, so finding an incentive for y that works for the two equations is impractical.
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Please help me with this question.
We split a given vector by its magnitude to get a unit vector that has the same direction. Consider the vector v = (1, 4), which has a magnitude of |v|. The unit vector uv, which is in the same direction as v, is obtained by dividing each component of the vector v by |v|.
What is unit vector?The magnitude of a unit vector must be exactly one unit. They are quite helpful for a variety of reasons. The unit vectors [0,1] and [1,0] in particular can combine to generate any other vector. A vector of magnitude one is known as a unit vector. A vector's direction can be expressed using unit vectors regardless of the magnitude of the vector. Even though a unit vector must have a direction to be defined, even though it has a magnitude of 1, not all unit vectors will have the same direction. Now that we are aware that a unit vector is a vector whose magnitude is one, we will check to see whose magnitude is one and provide the response. [Right Arrow] Not a unit vector, it.To learn more about unit vector, refer to:
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A basketball team played a total of 28 games. The ratio of the total number of games they won to the number of games they lost is 43. How many games did they win? How many games did they lose?
Answer:
win=16, lose=12
Step-by-step explanation:
total is 28, and win to lose is 4:3
so 4+3=7 , which means we put them into 7 part
and 28/7=4, each part equal to 4
so the win= 4 time 4=16
lose = 3 time 4= 12
of the 90 gallons a average person uses a day,30% is used out doors. Mason wants to know how much water is used out doors .PLease complete the statement Since 30 percent of 90 is blank, the average person uses approximately blank gallons of water outdoors per day .
27 gallons of water is used outside everyday.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that of the 90 gallons a average person uses a day, 30% is used out doors.
Let the amount of water used outside be {x} gallons. Then, we can write -
{x} = 30% of 90
{x} = (30/100) x 90
{x} = 27
Therefore, 27 gallons of water is used outside everyday.
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two different ways to represent the expression -1/3x -17/3
Answer: -1/x-17 -1-17x
Step-by-step explanation:
In a typing class, the average number of words per minute N typed after t weeks of lessons was found to be
N =157/1 + 5.4e^-0.12t
Find the time necessary to type (a) 50 words per minute and (b) 75 words per minute
Answer:
i hope this helpes
Step-by-step explanation:
(a) To find the time necessary to type 50 words per minute, we need to solve the equation:
157/1 + 5.4e^-0.12t = 50
Rearranging the equation to isolate e^-0.12t and using the natural logarithm, we can find t:
ln(N - 157) = ln(5.4) - 0.12t
-ln(N - 157) = 0.12t - ln(5.4)
0.12t = ln(5.4) + ln(N - 157)
t = (ln(5.4) + ln(N - 157)) / 0.12
Plugging in N = 50, we get:
t ≈ 11.52 weeks
(b) To find the time necessary to type 75 words per minute, we follow the same steps as above:
157/1 + 5.4e^-0.12t = 75
ln(N - 157) = ln(5.4) - 0.12t
-ln(N - 157) = 0.12t - ln(5.4)
0.12t = ln(5.4) + ln(N - 157)
t = (ln(5.4) + ln(N - 157)) / 0.12
Plugging in N = 75, we get:
t ≈ 9.32 weeks
Answer:
For 50 wpm : 7.7 weeks approximately
For 75 wpm : 13.3 weeks approximately
Step-by-step explanation:
Given the relationship between N, the typing speed and t, the number of weeks of lessons as:
[tex]\mbox{\large N= \dfrac{157}{1+5.4e^{-0.12t}}}[/tex]
To solve for t for a particular N
cross-multiply the left side with the right side denominator to get
[tex]\mbox{\large 1+5.4e^{-0.12t } = \dfrac{157}{N}}[/tex]
For N= 50 this works out to
[tex]\mbox{\large 1+5.4e^{-0.12t } = \dfrac{157}{50}}[/tex]
[tex]\mbox{\large 5.4e^{-0.12t } = \dfrac{157}{50} - 1}\\[/tex]
[tex]\mbox{\large 5.4e^{-0.12t } = \dfrac{157-50}{50} } = \dfrac{107}{5} = 2.14[/tex]
Divide by 5.4 both sides:
[tex]\mbox{\large e^{-0.12t } = \dfrac{2.14}{5.4}} = 0.3963\\[/tex]
Take natural logs on both sides
[tex]\mbox{\large \ln(e^{-0.12t}) = \ln(0.3963)\\}[/tex]
[tex]\mbox{\large \ln(e^{-0.12t}) = -0.12 \;\textrm{since $ln(e^x)$ = x}}[/tex] since ln(eˣ) = x
ln(0.3963) = -0.9256
Therefore
[tex]t = \dfrac{-0.9256}{-0.12} = \dfrac{0.9256}{0.12} = {7.7133 \;weeks\approx \mbox{\large \boxed{7.7 \;weeks}}[/tex]
For N = 75, follow the same strategy and you will end up with
[tex]1+5.4e^{-0.12t}=\dfrac{157}{75} \\\\\\1+5.4e^{-0.12t}= 2.0933\\\\5.4e^{-0.12t} = 2.0933 - 1 = 1.0933\\\\e^{-0.12t} = \dfrac{1.0933}{5.4} = 0.2025\\\\[/tex]
Taking logs on both sides
[tex]-0.12t =-1.5971[/tex]
[tex]t = \dfrac{-1.5971}{-0.12} = 13.3097 \;weeks \approx \boxed{\mbox{\large 13.3 \;weeks}}[/tex]
Anyone good with geometry please help with as many questions ASAP. I would greatly appreciate it!
Answer: it is Konnachair, dm me there
Step-by-step explanation:
What’s negative one and one fourths subtract one and three eights
Answer:
negative two and five eights
Step-by-step explanation:
It usually helps to break down the equation like this:
-1 - 1 = -2
1/4 = 2/8
2 - 3 = 5, therefore 2/8 - 3/8 = 5/8.
Put it all together,
-1 1/4 - 1 3/8 = -2 5/8
The second side of a triangular deck is 4 feet longer than the shortest side, and the third side is 4 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 60 feet, what are the lengths of the three sides?
Answer:
15,19,26
Step-by-step explanation:
second side of a triangular deck is 4 feet longer than the shortest side,
shortest side = x
second side = x+4
third side = 2x-4
perimeter = 60 = x+x+4+2x-4 =4x
x=15
second side = x+4 =19
third side = 2x-4 =30-4 =26
Crossfire Company segments its business into two regions—East and West. The company prepared a contribution format segmented income statement as shown below: Total Company East West Sales $ 910,000 $ 650,000 $ 260,000 Variable expenses 637,000 468,000 169,000 Contribution margin 273,000 182,000 91,000 Traceable fixed expenses 133,000 70,000 63,000 Segment margin 140,000 $ 112,000 $ 28,000 Common fixed expenses 56,000 Net operating income $ 84,000 Required: 1. Compute the companywide break-even point in dollar sales. 2. Compute the break-even point in dollar sales for the East region. 3. Compute the break-even point in dollar sales for the West region. 4. Prepare a new segmented income statement based on the break-even dollar sales that you computed in requirements 2 and 3. Use the same format as shown above. What is Crossfire’s net operating income (loss) in your new segmented income statement? 5. Do you think that Crossfire should allocate its common fixed expenses to the East and West regions when computing the break-even points for each region?
1. Companywide break-even point in dollar sales = $910,000
2. Break-even point in dollar sales for the East region = $391,667
3. Break-even point in dollar sales for the West region = $225,000
How did we get the values?Companywide break-even point in dollar sales: Total fixed expenses / Contribution margin ratio = $189,000 / (273,000/910,000) = $910,000
Break-even point in dollar sales for the East region: Traceable fixed expenses / Contribution margin ratio = $70,000 / (182,000/650,000) = $391,667
Break-even point in dollar sales for the West region: Traceable fixed expenses / Contribution margin ratio = $63,000 / (91,000/260,000) = $225,000
New segmented income statement based on the break-even dollar sales:
Total Company
Sales $910,000
Variable expenses 637,000
Contribution margin 273,000
Traceable fixed expenses 133,000
Segment margin 140,000
Common fixed expenses 56,000
Net operating income $ 84,000
Total East
Sales $391,667
Variable expenses 258,250
Contribution margin 133,417
Traceable fixed expenses 70,000
Segment margin 63,417
Total West
Sales $225,000
Variable expenses 154,500
Contribution margin 70,500
Traceable fixed expenses 63,000
Segment margin 7,500
Net operating income in the new segmented income statement: $84,000
Yes, Crossfire should allocate its common fixed expenses to the East and West regions when computing the break-even points for each region as these expenses benefit both regions and affect the profitability of each region.
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What is the slope of the linear relationship? a graph of a line that passes through the points 0 comma 1 and 4 comma 0 one fourth negative one fourth four over 1 negative one fourth
The slope of the linear qeuation is -1/4 = -0.25
What is the slope of the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that if a line passes through (x₁, y₁) and (x₂, y₂) the slope will be:
a = (y₂ - y₁)/(x₂ - x₁)
We can see the points (0, 1) and (4,0). Then the slope is:
a = (0 - 1)/(4 - 0) = -1/4
The slope is -1/4.
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solve each integral using the information from groupwork question 2. (1) (0.25 points)z sin(x) cos3 (x) dx
The solution of the integral ∫sin ( x ) cos³( x )dx is equal to ( cos⁴(x) / 4 ) + c , where 'c' is the constant.
Solution of the integral is solved by substitution method :
∫∫sin ( x ) cos³( x )dx ___( 1 )
Let us consider cos ( x ) = t ____( 2 )
Now differentiate both the side we get,
-sin (x ) dx = dt
⇒ sin (x ) dx = -dt ____( 3 )
Substitute the value of ( 2 ) and ( 3 ) in ( 1 ) we get,
∫ t³ ( -dt )
= - ∫ t³ dt
= - t⁴ / 4 + c
Where 'c' is the integral constant .
Relace t = cos (x)
= - cos⁴ ( x ) / 4 + c
Therefore, the integral of the ∫sin ( x ) cos³( x )dx is equal to
( cos⁴(x) / 4 ) + c .
The above question is incomplete, the complete question is:
solve each integral using the information : ∫sinx cos³x dx
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How would you find x?
Step-by-step explanation:
n (TUB)=100-20
=80
from formula,
80 = x (x-5)+x+2x
80= x^2-5x+3x
80=x^2-2x
x^2-2x-80=0
x^2-10x+8x-80=0
x(x-10)+8 (x-10)=0
(x+8)(x-10)=0
either,
x+8=0
×=-8 (neglected)
Or,
x-10=0
×=10
Q1: For triangle ABC use the Triangle Proportionality Theorem to solve for x. Show all of your work for full credit.
Q2: What is the perimeter of triangle ABC? Show all of your work for full credit.
The value of x in the triangle is 17 .
The perimeter of the triangle ABC is 86 units.
How to use triangle proportionality theorem to find side of a triangle?Triangle Proportionality Theorem states that If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.
Therefore, let's use the theorem to find the value of x in the triangle.
Hence,
20 / 4 = 2x - 4 / 6
cross multiply
120 = 4(2x - 4)
120 = 8x - 16
120 + 16 = 8x
136 = 8x
divide both sides by 8
x = 136 / 8
x = 17
Hence, let's find the perimeter of the triangle ABC.
perimeter of the triangle ABC = 24 + 26 + 2(17) - 4 + 6
perimeter of the triangle ABC = 50 + 30 + 6
perimeter of the triangle ABC = 86 units
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A hose fills a hot tub at a rate of 3.99 gallons per minute. How many hours will it take to fill a 275-gallon hot tub?
The time taken to fill a 275-gallon hot tub is 69 minutes.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
A hose fills a hot tub at a rate of 3.99 gallons per minute.
This means,
3.99 gallons = 1 minute
Multiply 275/3.99 on both sides.
275 gallons = 275/3.99 x 1 minute
275 gallons = 69 minutes
Thus,
It will take 69 minutes to fill a 275-gallon hot tub
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tags are placed to the left leg and right leg of a bear in a forest. let be the event that the left leg tag is lost and the event that the right leg tag is lost. suppose these two events are independent and find the probability that exactly one tag is lost, given that at least one tag is lost (write it up to second decimal place).
The probability that at least one tag is lost is 0.75.
The probability that exactly one tag is lost is equal to the probability of the left tag being lost and the right tag being kept, plus the probability of the right tag being lost and the left tag being kept.
Using the formula for the probability of the union of two events, the probability that at least one tag is lost is:
P(A1 or A2) = P(A1) + P(A2) - P(A1 and A2) = 0.4 + 0.4 - 0.16 = 0.64
The probability of the left tag being lost and the right tag being kept is:
P(A1 and not A2) = P(A1) × (1 - P(A2)) = 0.4 × (1 - 0.4) = 0.24
The probability of the right tag being lost and the left tag being kept is:
P(A2 and not A1) = P(A2) × (1 - P(A1)) = 0.4 × (1 - 0.4) = 0.24
So, the probability of exactly one tag is lost, given that at least one tag is lost, is:
P(exactly one tag is lost | at least one tag is lost) = P(A1 and not A2 or A2 and not A1) / P(A1 or A2) = (0.24 + 0.24) / 0.64 = 0.75
Rounding to two decimal places, the answer is 0.75.
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A six-sided die is rolled, and the number N on the uppermost face is recorded. From a jar containing 10 tags numbered 1,2,...,10 we then select N tags at random without replacement. Let X be the smallest number on the drawn tags. Determine Pr{X=2}and E[X].
Please solve it step by step especially the expectation part. appreciate it.
You can draw some intuition graph and picture to help you explain
As per the probability the equation of E[X] = 2 * P(X=2) + 3 * P(X=3) + ... + 10 * P(X=10)
A die is a cube-shaped object with six faces numbered from 1 to 6. Each face has an equal chance of landing face up when the die is rolled. When you roll a die, you are randomly selecting one of the six numbers.
Let's first calculate the probability that X is equal to 2. To do this, we need to consider two cases:
The first case is when N = 2. In this case, there is only one way to select 2 tags, both with the number 2.
The second case is when N is greater than 2. In this case, there are 9 ways to select the first two tags, both with the number 2. The rest of the tags can be selected in any order.
The probability that X is equal to 2 can be calculated as follows:
P(X=2) = (1/45) + (9/45 * (9/44) * (8/43) * ... * ((10-N+1)/(10-N+2)))
Next, we calculate the expected value of X. The expected value of X is calculated as follows:
E[X] = sum of (each value of X multiplied by its probability)
E[X] = 2 * P(X=2) + 3 * P(X=3) + ... + 10 * P(X=10)
The expected value of X gives us an idea of the average value of X over many trials of rolling the die and selecting the tags.
In conclusion, the probability that X is equal to 2 is calculated by considering two cases, and the expected value of X is calculated by summing up each value of X multiplied by its probability.
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find all rational zeros
The zeros of a polynomial are the values of x for which the polynomial is equal to 0.
What is polynomial?
A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a non-negative integer power. It is an algebraic expression that can involve constants, variables, and exponents.
To find the rational zeros of a polynomial, use the Rational Zero Theorem. This theorem states that if the polynomial is written in standard form, ax^n + bx^n-1 + cx^n-2 + ... + k = 0, then the possible rational zeros are any rational number that can be expressed as p/q, where p is a factor of k (the constant) and q is a factor of a (the leading coefficient).
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Complete question is:
How to Find All Possible Rational Zeros Using the Rational Zeros Theorem With Repeated Possible Zeros?
whatcis 626362737287387287373 times 77474747743874837847348734463763786837
The result of 626362737287387287373 times 77474747743874837847348734463763786837 represented in scientific notation is 4.80498727057566113882339366151788673587 × 10⁹⁵.
The number you provided in your question can be represented in scientific notation. Scientific notation is a way of expressing numbers in a compact form that is especially useful for very large or very small numbers. The number you provided in your question can be represented in scientific notation as:
7.7474747743874837847348734463763786837 × 10⁷⁷
And 626362737287387287373 can be represented as:
6.26362737287387287373 × 10¹⁸
The product of these two numbers can be calculated as follows:
(7.7474747743874837847348734463763786837 × 10⁷⁷) × (6.26362737287387287373 × 10¹⁸) =
= (7.7474747743874837847348734463763786837 × 6.26362737287387287373) × (10⁷⁷ × 10¹⁸) =
= 48.0498727057566113882339366151788673587 x 10⁹⁵
So, the result of 626362737287387287373 times 77474747743874837847348734463763786837 in scientific notation is:
4.80498727057566113882339366151788673587 × 10⁹⁵
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Please help me with the following question.
The probability that an individual with a positive screening test will indeed have the disease is 0.9798.
What is probability?The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
A medical study team wanted to assess a suggested diabetic screening.
When administered to a random sample of 150 diabetic individuals, the test produced 34 positive findings.
While it produced 9830 negative findings when administered to a random sample of 9850 healthy people.
Assume that 30% of the population has diabetes.
The probability that an individual with a positive screening test will indeed have the disease is 0.9798.
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The answers please I’ll give you points fast
The length of the hypotenuse for all the right-angled triangles are found using trigonometric functions.
What is the hypotenuse?
The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
11) when angle = 30°
perpendicular = 3
sin 30 = perpendicular/ hypotenuse
0.5 = 3/hypotenuse
hypotenuse = 6
12) sin 30 =perpendicular/ hypotenuse
0.5 = 8/ hypotenuse
hypotenuse = 16
13) sin 60 = 11√3 / x
Hypotenuse = x = 11√3/ sin 60 = 11√3 / (√3/2) = 22
14) sin 30 = perpendicular/ hypotenuse
0.5 = 9/x
x = 18
15) cos 60 = base/ hypotenuse
0.5 = 1 /x
x = 2
16) sin 60 = 12√3/x
√3/2 = 12√3/x
Hypotenuse = x = 24
Therefore the length of the hypotenuse for all the right-angled triangles are found.
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Solve and reduce to lowest terms 2/7 x 5/6
Answer:
5/21
Step-by-step explanation:
2 x 5 = 10
--------
7 x 6 = 42
10 / 42 in simplest form is 5/21
What is 30° below sea level
30 degrees below sea level refers to a location that is 30 degrees lower in elevation than the average sea level, which is a reference point fomeasuring elevation and depth, and which can vary depending on the location.
Sea level is the average level of the surface of the ocean, which is used as a reference point for measuring elevation and depth. The term "sea level" can also refer to the specific measurement of the height of the ocean's surface at a specific location.
30 degrees below sea level refers to a location that is 30 degrees lower in elevation than the average sea level. This means that the location is 30 degrees lower in elevation than the reference point of the average surface of the ocean. This can be measured in either meters or feet, depending on the unit of measurement being used.
One way to think about 30 degrees below sea level is to imagine a point 30 degrees below the level of the water in a swimming pool. This would be considered a very deep point in the pool, and would be much lower than the surface of the water. Similarly, a location that is 30 degrees below sea level is much lower in elevation than the average sea level.
It's important to note that the concept of sea level can vary depending on the location, as sea level can vary due to factors such as ocean currents, tides, and the shape of the ocean floor. Therefore, the reference point for sea level can be different in different locations.
In summary, 30 degrees below sea level refers to a location that is 30 degrees lower in elevation than the average sea level, which is a reference point for measuring elevation and depth, and which can vary depending on the location.
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The area of of 20 yards
Correct option is D, using area of playground the length and width of the playground is length = 10 yd, breadth = 2 yd.
What is area in math?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy. A plane figure's area is the space that its perimeter encompasses. The area of a closed figure is the total number of unit squares covering its surface. Area is measured in square units like cm2 and m2.
The area of a shape is the area enclosed by its perimeter or boundary.
A = b × h is the formula for calculating the area, A, of a square or rectangle.
The playground's length is 5 times more than its breadth,
thus l=5w.
However, 10=2 x 5 allows us to write
l=5w, and
area = 20
=l x w
= (5x2) x 2
=20.
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Complete question -
The area of a playground is 20 square yards. The length of the playground is 5 times longer than its width. Find the length and width of the playground.
length = 1 yd, width = 20 yd
length = 2 yd, width = 10 yd
length = 10 yd, width = 2 yd
length = 20 yd, width = 1 y
Which Number line represents the solution set of the inequality
Answer:
Second option
Step-by-step explanation:
Given inequality
[tex]-8t\:+\:2\:\dfrac{1}{4}\ge 42\dfrac{1}{4}[/tex]
Convert mixed fractions to improper fractions:
[tex]2\dfrac{1}{4}=\dfrac{9}{4}[/tex]
[tex]2\dfrac{1}{4}=\dfrac{169}{4}[/tex]
The inequality becomes
[tex]-8t+\dfrac{9}{4}\ge \dfrac{169}{4}[/tex]
Multiply throughout by 4
[tex]-32t + 9 \ge 169[/tex]
[tex]\rightarrow -32t \ge 169-9\\\\-32t \ge 160\\\\-t \ge \dfrac{160}{32}\\\\-t \ge 5\\\\[/tex]
Multiply throughout by -1 (the inequality is reversed):
[tex]t \le -5[/tex]
The second option correctly represents this inequality
Option #1: Solve the inequality and graph the solution set.
Option #2: Test out the options to see which has solutions.
Let's do Option #2:
The first possible answer shows t < -5, so if we pick t = -10, we'd be in that interval. Let's test if t = -10 is a solution:
[tex]\begin{aligned}-8(-10) + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]80 + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]82\frac{1}{4} &\stackrel{\checkmark}{\geq} 42\frac{1}{4}\end{aligned}[/tex]
That checked!
So this alone tells us that the bottom two answers are not possible answers, since they do not include -10 in their sets.
But now we need to decide between the top answer or the one right below it. The only difference between the two number lines is that the top one does NOT include x = -5, while the second one does. So we need to test out if x = -5 is a solution, just like we did for x = -10.
[tex]\begin{aligned}-8(-5) + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]40 + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]42\frac{1}{4} &\stackrel{\checkmark}{\geq} 42\frac{1}{4}\end{aligned}[/tex]
Because of the "or equal to" in the inequality, this does check.
Our answer is the second number line, with a closed circle at x = -5 and the shading to the left.
If you wanted to do this by solving the inequality, that work would look like this:
[tex]\begin{aligned}-8t + 2\frac{1}{4} &\geq 42\frac{1}{4}\\[0.75em]-8t + 2\frac{1}{4}-2\frac{1}{4} &\geq 42\frac{1}{4}-2\frac{1}{4}\\[0.75em]-8t &\geq 40\\[0.75em]\dfrac{-8t}{-8}~ &{\boldsymbol{\leq}}~ \dfrac{40}{-8}\\[0.75em]t &\leq -5\end{aligned}[/tex]
Note that the inequality flipped because we divided both sides of the inequality by a negative number.
How many gallons of a 50% antifreeze solution must be mixed with 60 gallons of 25% antifreeze to get a mixture that is 40% antifreeze? Use the six-step method.
You need
gallons.
(Round to the nearest whole number.)
Answer:
Step-by-step explanation:
7877
Answer:
180 gallons is needed.
Step-by-step explanation:
8n = 120 − 8(5 + 2)
can someone help me with this, im too lazy lol
Answer:
Step-by-step explanation: First, do the multiplication inside the parenthesizes so 8x5 is 40, and 40+2 is 42. 120-42=78
8n=78
n=9.75
Jayden is handing out chocolate candies and bubble gum for Halloween. He wants to have a total of 8 pounds of candy, but he doesn't want to spend more than $19.00 total on the candy. If chocolate candies cost $1.50 per pound, and bubble gum cost $2.90 per pound, how many pounds of each type of candy should he buy?
He should buy (blank) pounds of chocolate candies and (blank) pounds of bubble gum.
Answer:
He should buy 4 pounds of chocolate candies and 4 pounds of bubble gum.
Step-by-step explanation:
1.50x4 (4 pounds) equals = $6
2.90x4 (4 pounds) equals = $11.6
$11.6 + $6 = $17.6
Hope this helps! <3 (so sorry if this is wrong :C)
#1. Which situation represents an example of a non-proportional Equation? A. A farmer sells fresh peaches for $0.71 a pound. B. Michael's Pizza charges a $5 fee for the delivery of each pizza. C. Emiliano's cell phone plan charges $40 per gigabyte of data used. D. The temperature in the morning was 49 F, and it increased by 3 F every hour.
When two variables' ratios are equivalent, proportional relationships between them emerge.The right response is option c.A $50 membership fee plus a $20 monthly cost is required to use a gym.
What is a proportional relationship?Because b, the w intercept, is zero in the linear exhaustion of a line, y=mx+b, a proportionate relationship would be something like y=mx+0.IHaving said that, the equation for a line is as follows: so that y=1.75x (because it is only charging per drink, and nothing else, there is no b value or y-intercept).Therefore, this is a y=0.10x for b) (because it is only charging per amount of texts, and nothing else, there is again no b value, so the y-intercept is 0, crossing the origin).(YET AGAIN, THIS IS NOT THE ANSWER)c) y=20x+50 (x is the number of months, and depending on how many months you go to the gym, the amount of money you spend there is determined). Additionally, you must include the $50 cost of the gym membership.In this instance, the b value or y-intercept would be 50 because 50 is being added to the 20x.To learn more about proportional relationship refer
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Manny and Patricia were working on a project in class they need to cut 4 lengths of 1 3/5 feet from the board. How long must the board be to allow this
The board in shape of rectangle must be at least 6.4 feet.
What is a rectangle?
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.
For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.
A rectangle has two diagonals, that bisects each other. Both the diagonals are equal in length.
Perimeter, P = 2 (Length + Width)
Area of Rectangle=Length*Breadth
Now,
Given length of board they want to cut=1 3/5 feet=8/5 feet.
No. of board they want to cut=4
so, length of rectangular board must be at least=4*8/5 feet
=32/5=6.4 feet
Hence,
The board in shape of rectangle must be at least 6.4 feet.
To know more about rectangles visit the link
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What is the answer 1/2 = 5d-1/2
Answer:
d=1/5
Step-by-step explanation:
Answer: d=2/5
Step-by-step explanation:
