Stimultaneous elimination equations
4x + 2y = 10
X+ 2y = 7
The values of x and y on solving the two simultaneous equations are x = 1 and y = 3.
The simultaneous equations to be solved are 4x + 2y = 10 and x + 2y = 7.
Rearranging the above equations, we have,
- 4x - 2y = - 10 -----(A)
x + 2y = 7 -------(B)
Solving them, we have, -3x = -3
x = 1 ------(C)
Substituting (C) in (B), we have,
1 + 2y = 7
2y = 6
y = 3 ------(D)
Now, let us substitute the x and y values in (A) and (B) and then check.
4x + 2y = 10
4 + 2(3) = 10
A is checked.
x + 2y = 7
1 + 2(3) = 7
B is checked.
Thus, the values of x and y are checked to be correct.
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customers are used to evaluate preliminary product designs. in the past, 96% of highly successful products received good reviews, 50% of moderately successful products received good reviews, and 12% of poor products received good reviews. in addition, 40% of products have been highly successful, 35% have been moderately successful and 25% have been poor products. round your answers to four decimal places (e.g. 0.9876). (a) what is the probability that a product attains a good review? (b) if a new design attains a good review, what is the probability that it will be a highly successful product? (c) if a product does not attain a good review, what is the probability that it will be a highly successful product? (a) enter your answer in accordance to the item a) of the question statement
The probability that a product attains a good review is 0.6125
The given information can be tabulated as follows.
Success type High Moderate Low Total
0.40 0.35 0.25 1
Good reviews 0.95 0.60 0.10
Combined prob 0.4*0.95 0.35*0.6 0.25*0.1
0.38 0.21 0.025 0.6125
A)the likelihood that a product will receive a favorable review = Prob it is successful and receives a favorable review + Prob it is moderately successful and receives a favorable review + Prob it is unsuccessful and receives a favorable review = 0.6125
B) If a new design receives positive feedback, there is a 0.62 percent chance that it will be a highly successful product.
C) Chance of not receiving a favorable review: (0.40*0.05)
+0.35(0.4) +(0.25)*0.9\s= 0.385
Prob for successful but not receiving a favorable evaluation is 0.40(0.05) = 0.02; required prob is 0.0519.
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(4,0)
(5,3)
(6,0)
Identify the values of the variables in the equation when it is written in vertex form: y = a (x - h)² + k
1. What is the value of a?
2. What is the value of h?
3. What is the value of K?
Answer:
VALUES (5,6,12)
Step-by-step explanation:
A gym charges its customers an initial membership fee, plus an hourly fee. The graph shows the cost of using the gym
The initial fee charged to customers for using the gym, given the graph showing the charges to customers is $ 20.
How to find the initial membership fee ?To find the initial membership fee, you should look at the y - intercept of the graph.
The y - intercept is the point where the x vale is 0 and this case this point shows the cost when the customers have not worked out in the gym for any hour yet.
This y - intercept is therefore $ 20 as this is the point on the graph where the value of x is 0.
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The question is:
What is the initial fee charged to customers for using the gym?
Check all that apply
From the trigonometric function sec θ = 13/12, two more functions are derived -
Option C: cos θ = 12/13
Option D: tan θ = 5/12
What is trigonometric function?
Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.
The given trigonometric function is -
sec θ = 13/12
Sec function is written as the ratio of hypotenuse to adjacent.
sec θ = 1/cos θ
Cos function is written as the ratio of adjacent to hypotenuse.
cos θ = 12/13
To find the opposite, apply the Pythagoras theorem -
(Opposite)² = (Hypotenuse)² - (Adjacent)²
(Opposite)² = (13)² - (12)²
(Opposite)² = 169 - 144
Opposite = √25
Opposite = 5
Tan function is written as the ratio of opposite to adjacent.
tan θ = 5/12
Therefore, from sec function, cos and tan function are obtained.
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of five letters (a, b, c, d, and e), three letters are to be selected at random. how many possible selections are there?
Three letters will be selected from five letters. The number of possible selections is 10.
A combination is a method of picking elements from a collection where the order of selection is irrelevant. Assume we have three numbers P, Q, and R. The number of ways we can choose two numbers from each set is determined by combination.
Suppose we want to pick k elements from a set of n elements, then the number ways it can be chosen is:
C(n,k) = n! / k! (n-k)!
Where n! is n factorial.
In this case, there are 5 letters and we want to select three letters. Hence, k = 3, and n = 5.
C(5,3) = 5! / 3! (5-3)!
C(5,3) = 5! / (3! 2!) = 10
Thus, there are 10 possible selections.
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consider the equation y=100x+500 where y is the number of park visitors and x is the average daily temperature in degrees Fahrenheit.
these are the answer choices
A. 500 people will go out to the park when its 100F
B. even if its 0F, 500 people will still go to the park
C. when it is 0F, 100 people will go to the park
Answer:
A. 500 people will go out to the park when its 100F is incorrect.
Solve this (algebra) to the simplest form
Answer: b to the power of 3 / 8 Have a nice day!
someone help pls w this questions
Answer:
2
Step-by-step explanation:
count the grids, A is 4, B is 8, so scale =2
What does ordinal number mean.
Answer: Ordinal numbers are a designation of something's place in a series by a number, such as first or third. Ordinal numbers can function as pronouns, nouns, and adjectives.
Answer:
Step-by-step explanation:
It means what place something is in. For example the ordinal of 1 is 1st 2 is 2nd and 3 is 3rd and so on. I hope this helps.
Find the volume of the rectangular prism . Simplify
A rectangular prism has a volume of 2x ^ 3 + 19x ^ 2 + 24x
What is volume?the volume of the rectangular prism is
The area contained by an object's limits in three-dimensional space is referred to as its volume.
Thus, a rectangular prism having the following dimensions: 2x length, (x2) width, and (x + 2) height
L x B x H = volume
= x× (x +8 )(2x + 3)
= x(x + 8)(2x + 3)
(2x + 3) * x ^ 2 + 8x(2x + 3)
2x ^ 3 + 19x ^ 2 + 24x
The area contained by an object's limits in three-dimensional space is referred to as its volume.
A rectangular prism's volume is thus 2x ^ 3 + 19x ^ 2 + 24x
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Pls help me with this I am stuck cheers thanks
Answer:
x ≥ 10
Step-by-step explanation:
A solid dot on 10 means 10 is included.
An arrow pointing to the right of 10 means all numbers greater than 10 are included.
Answer: x ≥ 10
Answer:10 =< x
Step-by-step explanation:
Shaded circle means include that number so it is a <= or >= sign
Goes to x.
Think about it a bit, not quite sure if 50 is involved in this inequality
The circumference of a circle is 25π in. What is the area, in square inches? Express your answer in terms of pi
The area, in square inches, will be 156.25π
You would require the radius in order to get the circle's area. You would enter the circumference (25) into the equation for the circle's circumference, which looks like this:
C = 2πr
25π = 2πr
Then you would figure out how to solve for r. (the radius)
25π = 2πr
12.5π = πr
12.5 = r
After that, you would enter the radius into the equation for a circle's area.
A = π(r^2)
A = 12.5^2π
A = 156.25π
Due to the fact that meters were used as the unit of measurement, your response would be 156.25 meters.
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groups of 25 and more receive a 20% discount to the zoo. tickets range in price from $10.00 to $15.00 depending on your age. what is the range of the ticket prices after the discount is used
The range of the ticket prices after the discount is used is 1.
What is range?The difference between the lowest and highest values, is considered as range.
Given that, groups of 25 and more receive a 20% discount to the zoo. tickets range in price from $10.00 to $15.00 depending on your age.
The range of a data is given by, difference of lowest element and largest element.
Here, 20% discount is to be given, and ticket price ranges from $10 to $15
20% of 10 = 2
And
20% of 15 = 3
Therefore, range = 3-2
= 1
Hence, the range of the ticket prices after the discount is used is 1.
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Does anyone know the answer to this?? (pls give right answer I really need this one to be correct)
a) Equation would be 5x + (x - 6) + (x - 6) = 180°
b) m∠1 = 180° and m∠2 = 30°
What is the measure of angle?
The term "degree measure" refers to the measurement of an angle in degrees. Because one entire revolution equals 360°, it is divided into 360 parts. Each stage of the revolution represents a degree.
a) The angle measures in a triangle must add up to 180°.
Therefore, the equation to find x is:
5x + (x - 6) + (x - 6) = 180°
b) Solving for x, we get:
x = 36
Therefore, angle m∠1 = (5x) = (5 * 36) = 180° (major angle)
angle m∠2 = (x - 6) = (36 - 6) = 30° (minor angle)
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Can anyone help me ?
Answer:
C) 11
Step-by-step explanation:
Exterior angles in a triangle = the sum of the interior angles of the triangle
Here, the exterior angle is ∠BCT while the interior angles are ∠CAB and ∠ABC
Using the above theorem we can say that ∠BCT = ∠CAB + ∠ABC
Plugging in the given expressions and values of the angles we acquire
9x + 6 = 3x + 2 + 70
==> combine like terms
9x + 6 = 3x + 72
==> subtract 3x from both sides
6x + 6 = 72
==> subtract 6 from both sides
6x = 66
==> divide both sides by 6
x = 11
Which function represents the reflection over the x-axis of f(x)=x
The fourth option represents the reflection over the x-axis of f(x)=√x. The graph has been attached below. The solution has been obtained by the concept of reflections.
What is reflection?
A flip is the term for a reflection in geometry. The shape is mirrored in a reflection. The line of reflection is a line across which an image will reflect. A reflection is the shape's mirror image. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way.
We are given the function f(x)=√x.
When we replace x with -x, then the graph of the resulting equation i.e.
f(x)=√-x is captured by reflecting the graph of f(x)=√x vertically across the x-axis.
Thus, the reflection of the function f(x)=√x is a vertical reflection across the x-axis.
Hence, the graph below represents the reflection of the function f(x)=√x which is the fourth option.
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Consider a force F = 〈–1, 3〉 applied to an object that is moving from the point (3, –9) to the origin. Find the displacement vector of the object.
Answer:
d = 〈 -3 , 9 〉
W = 30 Joules
The displacement vector of the object is (-3, 9) and the work done is 30 Joules
The term called vector in math is defined as a quantity or phenomenon that has two independent properties such as magnitude and direction.
Here we know that the value of force F is (-1, 3) and the point is (3, -9)
Then the displacement from origin to (3, -9) is calculated as,
=> d = (0-3, 0-(-9))
Then the value of d is ( -3, 9)
Here the formula to Work done is written as,
=> F x d
=> (-1, 3) x (-3, 9) = 3 + 27
=> 30 joules.
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if this same population size wants to start decreasing over time, the population growth rate needs to be
Simon is a member of The Mighty Manatees, an outdoor swim team. Every practice, his coach tells him to swim a target number of laps. One day, Simon swims 45 laps before practice is canceled due to a thunderstorm. Simon still has 35 laps left to reach his target number. Use an equation to find Simon's target number of laps.
Simon's target number of laps will be 80.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this case, his coach tells him to swim a target number of laps and Simon swims 45 laps before practice is canceled due to a thunderstorm. Simon still has 35 laps left to reach his target number
Let the target number be x. This will be:
x - 45 = 35
x = 45 + 35
x = 80.
The Target number is 80
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Which value is equal to 4 square root 20- 3 square root 45?
Answer:-√ 5
Step-by-step explanation:
4√ 20 = 8√ 5
3√ 45 = 9√ 5
8√ 5 - 9√ 5 = -√ 5
473 determine the answer to the following questions using long division
There are other methods to write a division issue, such as using a / or a to denote "divided by." As a result, in the equation 473 / 2 = 1 the divisor is the quotient, the remainder is 236, and the divisor is 2.
How do you find the answer in long division?Divide the dividend's first digit, which should be on the left, by the divisor, then write the result as the quotient on top. Write the difference below after subtracting the outcome from the digit. Bring down the dividend's next digit (if present).
Long division strategy: lengthy division techniques. The same symbols are used for long division as they are for short division: dividend (the number being divided) under the "bus stop," divisor (the number the dividend is being divided by), quotient (the solution) on top, and each place value aligned with the dividend.
Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.
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The complete question is "Divide the given numbers 473 and 6 using our free online Long Division Calculator and determine the Quotient and Remainder as Q 78 R 5 instantly without any hurdles."
In triangle ABC, the measure of angle A is 35º and the measure of angle B is 20°. In triangle
DEF, the measure of angle D is 35º and the measure of angle F is 125. Are triangles ABC
and DEF similar? Explain or show your reasoning.
ΔABC and ΔDEF are not similar because corresponding angles are not equal.
Now, According to the question:
In triangle ABC :
The measure of angle A is 35º and
The measure of angle B is 20°.
In triangle DEF:
The measure of angle D is 35º and
The measure of angle F is 125
We know that :
Sum of interior angles of triangle is 180°
Now, In ΔABC:
∠A + ∠B + ∠C = 180°
35 + 20 + ∠C = 180°
55° + ∠C = 180°
∠C = 180° - 55°
∠C = 125°
Now, In ΔDEF:
∠D + ∠E + ∠F = 180°
35 + ∠E + 125 = 180°
160 + ∠E = 180°
∠E = 180° - 160°
∠E = 20°
So, ∠C ≠ ∠E as ∠C = 125° and ∠E =20°
Hence, No, Triangles are not similar .
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Side and angle properties of a parallelogram (level 2)
find x,y,z
7. At an office building, the amount of time it takes before the elevator door on the first floor opens when the button is pressed to go “up” ranges uniformly from 2 seconds to 70 seconds.
Determine the probability that the elevator door with take less than 30 seconds to open.
Determine the probability that the door will take exactly 55 seconds to open
The probabilities for this problem are given as follows:
Less than 30 seconds: 0.4118 = 41.18%.Exactly 55 seconds: 0%.What is the uniform probability distribution?It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The bounds for this problem are given as follows:
a = 2, b = 70.
Hence the probability of less than 30 seconds is given as follows:
P(X < 30) = (30 - 2)/(70 - 2)
P(X < 30) = 0.4118 = 41.18%.
The uniform distribution is a continuous distribution, meaning that the probability of an exact value is of 0.
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One angle measures 18°, and another angle measures (6d − 6)°. If the angles are complementary, what is the value of d?
The value of d in the given angles using the concept of complementary angles is; d = 13
How to find complementary angles?Complementary angles are defined as angles that add up to 90 degrees.
Now, we are told that one angle measures 18°, and another angle measures (6d − 6)°. This tells us that;
(6d - 6) + 18 = 90
Expanding the bracket gives us;
6d - 6 + 18 = 90
6d + 12 = 90
6d = 90 - 12
6d = 78
Use division property of equality to divide both sides by 6 to get;
6d/6 = 78/6
d = 13
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suppose we have a bag with $10$ slips of paper in it. eight slips have a $3$ on them and the other two have a $9$ on them. how many $9$'s do we have to add before the expected value is at least $8$?
There are a total of 10 slips.
8 slip with 3 on it
2 slips with 9 on it
value = Probability of 3 x 3 + Probability of 9 x 9.
= (8 / 11) x 3 + (2/ 11) x 9
24 / 11 + 24 / 11 = 4.36
probability
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
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what is the inequality?
Answer:
X < 250
Step-by-step explanation:
Inequalities:
> Greater/More than
< Less/Fewer than
= Equal to
>= Greater than/More than OR equal to
<= Less than/Fewer than OR equal to
Since it says fewer than, we'll use <
X in this case will be the actual number of people.
We know fewer than 250 will attend, making the inequality
X < 250
two numbers,thrice the first number minus the second number is 19 and twice the first number plus five times the second number is minus 10 find the product of the two numbers
Answer:
-20
Step-by-step explanation:
Line F passes through points (2, 8) and (9, 3). Line g passes through points (1, 8) and (10, 1). Are line f and line g parallel or perpendicular? Pls help I’m getting frustrated
The linear functions f(x) and g(x) are neither parallel nor perpendicular.
How to obtain if the lines are parallel or perpendicular?To obtain whether they are parallel of perpendicular, first we must obtain the slope of each line.
Given two points, the slope of a line is calculated as the change in y divided by the change in x.
Hence, the slope for each line is obtained as follows:
Line F: m = (3 - 8)/(9 - 2) = -5/7.Line G: m = (1 - 8)/(10 - 1) = -7/9.They would be:
Parallel if they have the same slope.Perpendicular if the product of the slopes was of -1.Hence they are neither.
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