It needs 1 [tex]\frac{3}{4}[/tex]gallons of 40% gloss and 3 [tex]\frac{1}{2}[/tex] gloss gallons of 25% gloss.
System of equations is a set or collection of equations that are dealt together. These equations can be solved graphically and algebraically. The point where two lines intersect is the solution to the system of equations. This article elaborates on Algebraic Technique To Solve System Of Equations.A linear equation is the one which has one or more variables and when plotted gives a straight line. Two or more linear equations consisting of two or more variables such that all equations are considered at the same time is called the system of linear equations.
Asume it needs x gallons of 40% gloss and y gallons of 25% glass
x+y=5.25
40% X+25% y = 30%×5.25
So x+y=5.25 ----------(i)
0.4x+0.25y = 15.75----------(ii)
(ii)*4 - (i)
4*(0.4x+0.25) - (x+y)=15.75*4 - 5.25
0.6x=1.05 (elimination y)
x=1.75=1 [tex]\frac{3}{4}[/tex] So
y=5.25-X=3.5 = 3 [tex]\frac{1}{2}[/tex]
So,it needs 1 [tex]\frac{3}{4}[/tex] gallons of 40% gloss and 3 [tex]\frac{1}{2}[/tex] glass gallons of 25% gloss.
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To mix paint that is 40% gloss with paint that is 25% gloss to make 5.25 gallons of paint that is 30% gloss, the paint mixer should mix 1.75 gallons of paint that is 40% gloss with 3.5 gallons of paint that is 25% gloss.
Let x be the number of gallons of paint that is 40% gloss and y be the number of gallons of paint that is 25% gloss. To mix paint that is 40% gloss with paint that is 25% gloss to make 5.25 gallons of paint that is 30% gloss, we can set up the following system of equations:
0.40x + 0.25y = 0.30 × 5.25
x + y = 5.25
To solve this system of equations, we can first multiply the second equation by 0.4 to eliminate the x term, and then we can subtract the first equation from the resulting equation to solve for y:
0.4x + 0.25y = 0.3×5.25
0.4x + 0.4y = 0.4×5.25
0.15y = 0.1×5.25 = 0.525
y = 0.525/ 0.15
y = 3.5
Then we can substitute this value of y back into one of the original equations to solve for x:
x = 5.25 - y
x = 5.25 - 3.5
x = 1.75
Therefore, the paint mixer should mix 1.75 gallons of paint that is 40% gloss with 3.5 gallons of paint that is 25% gloss to make 5.25 gallons of paint that is 30% gloss.
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The vertices of ABC are A(-4,4), B(-2,4), and C(-3,2). If ABC is reflected across the y-axis to produce the image A'B'C', find the coordinate of the vertex A'.
The vertices of ABC shown as A(-4, 4), B(-2, 4), and C(-3, 2). when reflected across the y-axis to produce the image A'B'C', the coordinate of the vertex A is
A' (4, 4)How to find the coordinates of the reflected imageReflection is one of the movements in transformation that involve creation of mirror image
Transformation rule for reflection over x-axis at origin (0, 0)) is
(x, y) → (x, -y)
Transformation rule for reflection over line y-axis at origin (0, 0)) is
(x, y) → (-x, y)
The problem involves reflection over y axis hence we use the rule
(x, y) → (-x, y)
Vertex A has the coordinate of the preimage as A(-4, 4) then after reflection the coordinate of the image will be A' (4, 4)
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(BRAINLIEST IF CORRECT) Brice has twice as many stamps in his collection as his friends Anthony and Paul
combined.
Paul has 32 stamps in his collection Brice has 96 stamps in his
collection. How many stamps does Anthony have in his collection?
The equation 2(x +32)=96 models this situation. Which choice
shows the sequence of operations needed to solve this problem, using
both arithmetic and algebra?
Answer: B is correct
Step-by-step explanation:
Answer:
Step-by-step explanation:
96=(32+x)x2=?
Gente me ajuda no projeto de matemática quanto é 3743÷250=???
rosie the ribbeter loves the three-jump,two-step event. if she completes the three-jump,two-step cycle 5 times, alex thinks the sequence can be written as 15j +2 Sara doesn't agree
Alex's expression about the sequence is incorrect and Sara's thought is correct
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Event: Three-jump, two-step cycle
Represent the number of jumps with x
So, we have the following representation
Event: Three- x, two-step cycle
When represented as an equation, we have
Event = 3x + 2
The number of times is 5
So, the sequence is represented as
Sequence = Event * 5
Substitute the known values in the above equation, so, we have the following representation
Sequence = (3x + 2) * 5
Evaluate the product
Sequence = 15x + 10
This means that the sequence is 15x + 10
Hence, Alex is incorrect and Sara is right
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Interpreting the meaning of the derivative in context Due to the tide, the water level rises and falls daily in Buzzard's Bay. D gives the depth of the water, in meters, t hours after midnight on a certain day. What is the best interpretation for the following statement? The value of the derivative of D at t = 8 is equal to -0.5. Choose 1 answer At 8 a.m. the water level decreased at a rate of 0.5 meters per hour. At 8 a.m. the water level decreased at a rate of 0.5 meters. At 8 a.m. the water level was 0.5 meters below sea level. D Until 8 a.m. the water level decreased at a rate of 0.5 meters per hour.
The value of the derivative of D at t = 8 is equal to -0.5 is At 8 a.m. the water level decreased at a rate of 0.5 meters per hour.
A function that has a derivative at each point in its domain is referred to as a differentiable function of one real variable in mathematics.
In other words, a graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function has no break, angle, or cusp and is smooth (it is locally well approximated as a linear function at each interior point).
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The diagram shows a convex polygon. What is the sum of the interior angle measures of this polygon?
The sum of the interior angle measures of the given polygon , given that it is a convex polygon is 540 °
How to find the sum of the angles ?The polygon given is a convex polygon , and has 5 sides . This means that it is a Pentagon .
Each interior angle in a regular convex pentagon, measures 108 ° . This means that the sum of the interior angle measures is therefore :
= Measure of interior angles x Number of angles in Pentagon
= 108 x 5
= 540 °
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Differentiate Implicitly To Find dy/dx.
2x^2+8xy+6y^2+13y-2=0
dy/dx= ___
The implicit differentiation of the given function is dy/dx = ((-4x-8y))/((8x +12y+ 13)).
In implicit differentiation, each side of an equation with two variables (usually x and y) are differentiated by treating one of the variables as a function of the other. The technique of implicit differentiation enables the determine the derivative of y with respect to x without having to solve the given equation for y. The chain rule must be used whenever the function y is being differentiated because of the assumption that y may be expressed as a function of x.
In order to find the differentiate implicitly,
d/dx (2x^2+8xy+6y^2+13y-2)=0
4x + 8y + 8xdy/dx + 12ydy/dx + 13dy/dx = 0
dy/dx (8x + 12y + 13) = -4x -8y
dy/dx = ((-4x-8y))/((8x +12y+ 13))
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A set of sides that creates a right triangle has sides in a ratio of 5 : 12 :13. Find two different sets of sides in feet that would create a right triangle using this ratio.
Answer:
10 : 24 : 26
15 : 36 : 39
Step-by-step explanation:
You can multiply all numbers in the ratio to find equivalent ratios that would function as different sets of sides because it's just a larger version of the 5: 12 : 13 triangle
One car travels 30 miles in the same amount of time it takes another car to travel 25 miles. If the second car travels fuse ante per hour slower, how fast does the first car travel?
After 15 hours, the faster car will be 75 miles ahead of the slower car.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken
We are Given,
Speed of first car = 30 miles per hour
Speed of second car = 25 miles per hour
Let, x be the number of hours.
Distance covered by first car = Speed x time = 30x
Distance covered by second car = 25x
According to given statement;
Difference between distance covered by both cars = 75 miles
Distance of faster car - Distance of slower car = 75 miles
30x - 25x = 75
5x = 75
x = 15
Hence, After 15 hours, the faster car will be 75 miles ahead of the slower car.
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GIVING AWAY FREE CREDS!! JUST ANSWER WITH ANYTHING AND GET REWARDED!!
Answer:
1+1=2
Step-by-step explanation:
2=1+1
the organizer of a potluck dinner sends 6 people a list of 10 different recipes and asks each person to bring one of the items on the list. if all 6 people randomly chose a recipe from the list, what is the probability that at least 2 will bring the same thing?
The probability of at least two people bringing the same item is 0.19.
The probability of two people bringing the same item can be calculated using the formula P(A∩B) = P(A) × P(B). In this case, P(A) and P(B) are both 1/10, since each person has the same chance of choosing any one of the 10 items on the list. Therefore, the probability of two people bringing the same item is 1/100. To calculate the probability of at least two people bringing the same item, we can use the formula P(A∪B) = P(A) + P(B) - P(A∩B). In this case, P(A∪B) = 1/10 + 1/10 - 1/100 = 0.19. Therefore, the probability of at least two people bringing the same item is 0.19.
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Using a ____ strategy, knowledgeable users can be selected who then conduct sessions for others.
A) structured walkthrough
B) train-the-trainer
C) desk checking
D) top-down design
The correct answer is option B) Train-the-trainer.
Using a train-the-trainer strategy, knowledgeable users can be selected who then conduct sessions for others.
Train-the-trainer is a strategy where knowledgeable users are selected to conduct sessions for others. This strategy is effective because it allows the users to become knowledgeable in the topic and learn how to teach it to others. This ensures that the users become comfortable with the material and can answer any questions that might come up during the sessions.
Additionally, the trainer can provide feedback to the users and help them understand the material better. This is especially beneficial for more complex topics that require a deeper understanding.
Furthermore, the train-the-trainer strategy is cost-effective because it eliminates the need for multiple instructors. The trainer can then provide the necessary training materials and resources to the users and help them learn in a more efficient manner.
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help with geometry please fast
Answer: 10
Step-by-step explanation:
Using the Pythagorean theorem we know a^2 + b^2 = c^2.
We can plug in 8 and [tex]2\sqrt{41[/tex] for b and c.
a^2 + 8^2 = [tex]2\sqrt{41}[/tex]^2
a^2 + 64 = 164
a^2 = 100
a = 10
The Bobcats football coach logged the following yardage gains, and losses over four game plays.
Gain 25x yards.
Gain 0.9y yards.
Lose 12y yards.
Lose 5.2x yards.
What is the net yardage for these four plays?
Answer:
lose 12y yards AKA( 3rd option)
Step-by-step explanation:
Answer: 77x+21y
Step-by-step explanation:
Ms. Johnson is throwing the entire class a pizza party (not really, keep reading)! When she places the order from Tony's pizza across the street, she learns that each medium pizza has 6 slices, and each large pizza has 8 slices. If Ms. Johnson orders 9 total pizzas with a total of 66 slices, how many of each size pizza did she buy? Let x represent the number of medium pieces and let y represent the number of large pizzas
There are 3 medium pizzas and 6 large pizza.
How to illustrate the equation?Let medium pizza = x
Let large pizza = y
Since she she places the order from Tony's pizza across the street, she learns that each medium pizza has 6 slices, and each large pizza has 8 slices and Ms. Johnson orders 9 total pizzas with a total of 66 slices
This will be:
x + y = 9 ..... i
6x + 8y = 66 ..... ii
From i, x = 9 - y
Put this into equation ii
6x + 8y = 66
6(9 - y) + 8y = 66.
54 - 6y + 8y = 66.
2y = 12
Divide
y = 12/2
y = 6.
Therefore there are 6 large pizzas
Medium pizza = 9 - 6 = 3
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Select all the expressions that can be used to find the price of a $320 tablet after a 45% markup.
A 320 . 4.5
B 320 . 1.45
C 320 . 0.45
D 320 + 320(1.45)
E 320 + 320(0.45)
The markup price is $464 and the expression to find the markup price is 320×1.45
What is markup price?Markup shows how much more a company's selling price is than the amount the item costs the company.
Given that, the price of a $320 tablet after a 45% markup.
This mean that, the tablet price is being hiked by 45%,
Therefore,
Total price will be = 45% of 320 + 320
= 45 / 100 x 320 + 320
= 144 + 320
= 464
Hence, the markup price is $464 and the expression to find the markup price is 320×1.45
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a student is working in an optics lab and has a light bulb which is 90 cm from a screen. She needs to make a real image of the bulb on the screen and shehas a positive lens witha focal length of 12.5 cm. Find two places she can put the lens andgive object and imagedistances to both setups.
The two places she can put lens and give object and image distances are 15cm and 75cm.
The Lens equation gives us:
1/f = 1/u + 1/v
From the problem we know that,
v=90-u
By solving
u² - 90u + 1125 = 0.
An optical system's focal length, which is the inverse of the system's optical power, indicates how strongly the system converges or diverges light. A system with a positive focal length is said to converge light, and one with a negative focal length is said to diverge light.
A negative focal length, on the other hand, indicates how far in front of the lens a point source must be located to form a collimated beam, for the special case of a thin lens in air, where a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus. For more generic optical systems, the focal length is merely the inverse of optical power and lacks any intuitive significance.
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a pen at a pet store contains male and female guinea pigs. The ratio of female guinea pig s to male guinea pigs is 7 to 3. Find the percent of guinea pigs in the pen that are male. Justify your answer.
The percentage of male guinea pigs in the pen at the pet store is 30%.
What is the percentage?The percentage refers to the ratio of a number or value compared to another.
Percentages are the results of division operations multiplied by 100.
The ratio of female to male guinea pigs = 7:3
The sum of ratios = 10
The percentage of female guinea pigs = 70% (7/10 x 100)
The percentage of male guinea pigs = 30% (3/10 x 100)
Thus, we can conclude that whereas there are 70% of female guinea pigs in the pet store's pen, 30% are male.
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A consumer organization was concerned that an automobile manufacturer was misleading customers by overstating the average fuel efficiency measured in miles per gallon or mos) of a particular car model. The model was advertised to get 27 mpg. To investigate the researchers selected a random sample of 10 cars of the model. Each car was then randomly assigned a different driver. Each car was driven for 5000 miles and the total fuel consumption was used to compute the mpg for the car. What is the parameter of interest? O the mean mpg of the 10 carsO the mpg measurements of this car model O the population of all cars of this particular model O the mean mog of all cars of this particular model
The correct answer is option a). The parameter of interest is the mean mpg of the 10 cars.
This parameter is important because it is the average mpg of the sample that is being used to measure the fuel efficiency of the car model. This parameter is important because it provides an indication of how efficient the car model is. By measuring the mpg of a sample of 10 cars, the researchers can get an indication of how the entire population of cars of this particular model perform.
The mean mpg of all cars of this particular model is the population parameter and is the overall average mpg of all cars of this particular model. The mpg measurements of this car model is the individual measurements for each car in the sample, which are used to calculate the mean mpg of the 10 cars.
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The scalar product of two parallel unit vectors, is equals to one i.e., i.e., = 1 , = 1 and = 1 .
Scalar Product: The scalar product is also known as dot product. The scalar product of two vectors can be constructed by taking the component of one vector in the direction of the other vector and multiplying it by magnitude of other vector. That gives scalar as a result. Scalar don't have a direction associated with them. The scalar product of vector A and vector B is equal to |A| |B|Cosθ , where |A|, |B| represent magnitude of vector A and vector B and θ angle between the two vectors direction.
We have to determine the scalar product of , and Here and are the unit vectors in the direction along the x-axis. So, they are parallel to each other, that's why θ = 0° and = 1 . Therefore, = (1) (1) cos 0° = 1. Similarly, = 1 ( unit vectors in direction along the y-axis) and = 1 ( along z-axis). Hence, the dot product of the two unit vectors and is equal to one for each
The average of 3 unique numbers is 50. If the lowest number is 30, what is the sum of the other two numbers?.
The sum of the other two numbers, x and y, is 120.
To solve this problem, we need to use the fact that the average of three numbers is the sum of the numbers divided by 3. Since the average of the three numbers is 50, and one of the numbers is 30, we can set up the equation:
(30 + x + y)/3 = 50
To solve for x and y, we need to multiply both sides of the equation by 3 to get:
30 + x + y = 150
We can then subtract 30 from both sides of the equation to get:
x + y = 120
So, the sum of the other two numbers, x and y, is 120.
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If the lowest number is 30, the sum of the other two numbers is 150
Let x1, x2 and x3 be three unique numbers with x1 is the lowest number and x3 is the largest number.
Let x{bar} be the average of numbers x1, x2 and x3
Given that the average of three unique numbers is 50.
So, x{bar} = 50
And the lowest number is 30
i.e., x1 = 30
Using the formula of average,
x{bar} = (x1 + x2 + x3) / 3
50 = (30 + x2 + x3)/3
50 × 3 = x2 + x3
x2 + x3 = 150
Therefore, the sum of the other two numbers is 150
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The square of z varies inversely as the square root of w. if z = 36 when w = 16, what is the value of z when w = 81?
Answer:
24
Step-by-step explanation:
PLEASE HELP ASAP
Consider the numbers -1, 0, 1, and 3. Which are solutions of the inequality?
13 - 7y ≤ 6
Use our free online step-by-step algebra calculator to resolve linear or quadratic inequalities.
How do I find the solution to an inequality?Use the steps below to solve an inequality: Step 1: Subtract all fractions by multiplying each term by the sum of all fractions' least common denominators. Step 2: Simplify the inequality by merging like terms on each side. Step 3: Add or subtract amounts to get the unknown and the numbers on either side.
A number is a "solution" to an inequality if it can be used as the variable to make the inequality true. The inequality changes to 8-2 > 5 when we replace x with 8. As a result, the inequality's solution is x=8. Here, x equals 3. Thus, 3x-2 > 0 produces the inequality. The inequality (4x-3)(2x-1) higher than 0 has the value 3, 2 as the solution set.
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Chocolate bars are $0.85 each. Gummy worms are $1.15 per package. Cora buys some of each.
If c represents the number of chocolate bars and g represents the number of packages of gummy
worms, what expression could be used to find how much Cora spent?
The expression that represents how much Cora spent = $0.85c + $1.15 g
What is expression?
An expression is a mathematical statement used to represent the method of a mathematical operation in a symbolic form.
Mathematical terms and operators are combined to form an expression.
Terms can be numerical or numerical and variables both.
As example 3y + 5 z + 10 is an expression that has been developed based on two variables y and Z, three numbers 3, 5 and 10.
How can be the expression given in question?Given, cost of each chocolate bar = $0.85
cost of Gummy worms per package = $1.15
If c is the numbers of chocolate bar and g is the number of packages of Gummy worms that Cora bought, then the expression will be
$0.85 c + $1.15 g
which has two variables and two decimal numbers
hence, Cora spent $0.85c + $1.15g
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IfMNO~ QRS, find x. Round to the nearest tenth.
MN = 10
NO=x
QR=5
RS 7
Answer:
x = 14
Step-by-step explanation:
given Δ MNO and Δ QRS are similar then the ratios of corresponding sides are in proportion , that is
[tex]\frac{NO}{RS}[/tex] = [tex]\frac{MN}{QR}[/tex] ( substitute values )
[tex]\frac{x}{7}[/tex] = [tex]\frac{10}{5}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )
x = 7 × 2 = 14
I NEED HELP, GUYS DO WHAT YOU DO BEST.
Answer:
Geometric -64, 128,-256
Step-by-step explanation:
It follows the same pattern of alternating + and - and has the quadratic increase as the others
Answer: B
Step-by-step explanation:
Rahul bought a sweater and saved rs20 when a discount of 25% was given. what was the price of the sweater before the discount ?
Answer: To find the price of the sweater before the discount, you need to determine how much the discount saved Rahul and divide that amount by the discount rate.
The discount saved Rahul 20 / 0.25 = 80 rupees.
So, the price of the sweater before the discount was 80 + 20 = 100 rupees.
Step-by-step explanation:
1. Find the limit, if it exists. (If an answer does not exist, enter DNE.)(a)lim x→[infinity] [ln(5 + 3x2) − ln(8 + x2)](b)lim x→[infinity] [ln(5 + 3x2) − ln(8 + x)] (c)lim x→[infinity] [ln(5 + 3x) − ln(8 + x2)]2. Find the limit, if it exists. (If an answer does not exist, enter DNE.)lim x → [infinity] arctan(ex)
Pat does a lot of traveling in her car, she keeps records on how often she fills her car with petrol. The table alongside shows the frequencies of the number of days between refills. Estimate the likelihood that:
A) there is a four day gap between refills.
B) there is at least a four day gap between refills.
At least 4 days means 4 or more; in this example, 4, 5, or 6
a 17/190 ≈ 0.089
b 24/190 ≈ 0.126
How often she fills her car with petrol?Step 1:
At least 4 days means 4 or more; in this example, 4, 5, or 6. So
Estimated Probability (Car Refill Gaps)
in general ,estimated probability observe =The frequency of a particular
outcome/The no: of times an
experiment is
repeated
This particular task observes=The no: of time a 4 day refill gap occurs/
The total frequency of refill gap
days
Case a total of 190 refill gap days occurred. Of those 17 were 4 days gap
Estimated probability in these case 17/190 or 0.089
This particular task observe= The no : of times 4 day or more refill gap
occurs/The total frequency of refill gap
day
Case a total of 190 refill gap day occurred of these 24 were 4+ day gap
Estimated probability in these case 24/190 or 0.126
Step 2:
a 17/190 ≈ 0.089
b 24/190 ≈ 0.126
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How do you find triangle pairs congruent by the HL?
To find triangle pairs congruent by the HL (Hypotenuse-Leg) condition, first identify the hypotenuse (the longest side) and the leg (the side adjacent to it).
Finding Triangle Pairs Congruent by the HL ConditionTo find triangle pairs congruent by the HL condition, first identify the hypotenuse and the leg in each triangle. The hypotenuse is the longest side, while the leg is the side adjacent to it. Once the hypotenuse and leg have been identified in both triangles, measure them to ensure they are the same length. If they are the same length, then the triangles are congruent by the HL condition. If the hypotenuse and leg of both triangles match in length, then the two triangles are congruent to each other. This means all three sides of the two triangles will be the same length, making them congruent by the HL condition.
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How do you solve exponential decay questions?
You can solve exponential decay questions using the decay rate and the exponential decay formula.
Exponential decay is a common mathematical concept that can be difficult to master. Fortunately, there are some key strategies that can help you solve exponential decay questions.
To begin, it’s important to understand the concept of exponential decay, which is the decrease in the value of a quantity over time.
From there, you’ll need to identify the decay rate, or the speed at which the quantity is decreasing.
Next, you’ll want to use the exponential decay formula to calculate the final value of the quantity.
The formula is
dN/dT = -λN
where
N = quantity
λ= exponential decay constant
T= time
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