This means that if 7 or more teachers attend the training, it will be a good decision, as the cost of sending them will be less than the cost of not sending them.
What is an algebraic manipulation?
Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.
To determine if sending teachers to the summer training on mentor groups is a good decision, the committee needs to calculate the break-even point. This is the point at which the cost of sending the teachers is equal to the cost of not sending them. The break-even point can be calculated by dividing the advanced payment by the difference between the cost at registration and the advanced payment.
In this case, the break-even point is: $1,250 ÷ ($175 - $1,250) = $1,250 ÷ -$1,075 = 7 teachers.
Hence, This means that if 7 or more teachers attend the training, it will be a good decision, as the cost of sending them will be less than the cost of not sending them.
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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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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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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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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
A businessperson is returning from a trip to China and has 337 54 yuan in their wallet. The most current currency conversion rate is 1 US dollar 6.4651 yuan. How much money will the businessperson have when they convert ther
money to U.S. dollars?
O$52.21
O$331.07
O$344.01
O$2182.23
The required money will the businessperson have when they convert the money to U.S. dollars is 5220.96 dollar.
What is currency system?Commodities and services can be exchanged using money. Currency is defined as a unit of account that is issued by a government and is accepted at face value. When bartering, products and services were directly exchanged for one another.
According to question:We know that
1 US dollar = 6.4651 yuan
To find US dollar value of given yuan
1 yuan = 1/6.4651 US dollar
337 54 yuan = 337 54/6.4651 = 5220.96 dollar
Thus, required dollars are 5220.96.
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Answer:
the answer is 52.21 all u gotta do is divide 337.54 by 6.4651 and u get 52.20955592334225 and just round it and u get the answer which is 52.21
Step-by-step explanation:
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
Rewrite the expression 7(×-20)
Answer: 7x - 140
The expression 7(x-20) is a product of 7 and a grouping of x-20. To simplify this expression, we use the distributive property, which states that we can multiply the 7 by each term inside the grouping. So, 7(x-20) becomes 7x - 140. This is because 7x is the product of 7 and x, and 140 is the product of 7 and 20.
Step-by-step explanation:
i don’t know this answer i need help
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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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."
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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Solve this (algebra) to the simplest form
Answer: b to the power of 3 / 8 Have a nice day!
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
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.
The graph shows membership costs at a gym. How much was the initial membership fee?
Answer: 30$
Step-by-step explanation:
To find the slope of the equation, you can use the formula (y2-y1)/(x2-x1). Plugging the points the question gives us we can get:
(205-100)/(5-2)
= 105 / 3
= 35
Plugging this information along with a point into the formula y = mx + b:
100 = 35*2 + b
100 = 70 + b
b = 30
y = 35x + 30
To double check this is correct:
y = 35 * 5 + 30
y = 175 + 30
y = 205
(5,205) is a point therefore y = 35x + 30 is the equation
Because the x of the graph represents the number of months, the initial membership fee would be when x = 0.
y = 35*0 + 30
y = 30$
Find the distance between G and H on the number line below -12 and -2
The distance between G and H on the number line -12 and -2 is -10.
What is Distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language .
The phrase is widely used metaphorically to refer to a measurement of the degree of difference between two similar objects since spatial cognition is a rich source of conceptual metaphors in human thought.
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
What is number line?
A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that each real number and each point on a number line relate to one another.
We are given two point G and H which are represented on number line;
The value G = -12 and H = -2
We have to find the distance between them;
So , we can simply subtract these two values of G and H to get the distance between them;
distance = -12-(-2)
= -12 + 2
= -10
Therefore, the distance between G and H on the number line -12 and -2 is -10.
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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
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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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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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?
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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Candice is an interior designer and she is currently trying to change the look of a room. Candice found that the area of a room could be given by the expression 32+2 and that the area of a rug, which she wants to spread on the floor, is given by the expression 2+24−144. What expression represents the area of the room not covered by the rug?
The expression represents the area of the room not covered by the rug is A(x) = 2x² - 22x + 144.
Area of room = 3x² + 2x
Area of rug = x² + 24x - 144
We have to find the area of the room not covered by the rug.
Area of the room not covered by the rug = Area of the room - Area of rug
= (3x² + 2x) - (x² + 24x - 144)
= 3x² + 2x - x² - 24x + 144
= (3x² - x²) + (2x - 24x) + 144
= 2x² - 22x + 144
Hence, 2x² - 22x + 144 is the required expression for the area of the floor not covered by the rug.
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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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Find X and Y.
TEACHING TEXTBOOKS GEOMETRY
The value of the variables 'x' and 'y' will be 47° and 27°, respectively.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.
The equations are given below.
2y = 180° - 126°
2y = 54°
y = 27°
2x + 1 = 180° - 85°
2x + 1 = 95°
2x = 94°
x = 47°
The value of the variables 'x' and 'y' will be 47° and 27°, respectively.
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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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frankie already has a pair of basketball shoes that he can wear for the tryout, which makes the new pair a
The new pair of basketball shoes become a "desire" because Frankie already owns a pair that he can use for the tryout. Frankie's new basketball shoes would be viewed as a "need" if he didn't already have a pair for the tryout.
When referring to possessing or acquiring specific commodities, people frequently use the terms "want" and "need" interchangeably. In terms of economics, a need is what a person needs in order to survive. If a certain need is not met, a person may get sick or perhaps pass away. On the other hand, a desire is something that a person hopes to achieve in the near or distant future. In the first instance, Frankie is able to attend the tryout in a pair of basketball shoes that he already has. He could wear the shoes he already owns, thus the new pair of shoes would be his desire. In contrast, Frankie needs a new pair of sneakers in the second scenario because he doesn't have any basketball shoes for the tryout.
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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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What is the equation of the circle with a center located at ( 5, 2) and is tangent at the y-axis?
a. x2 + y2 – 10x – 4y + 4 = 0
b. x2 + y2 + 10x – 4y + 25 = 0
c. x2 + y2 + 10x – 4y + 4 = 0
d. x2 + y2 – 10x – 4y + 25 = 0
The equation of a circle with center located at (5,2) and that is tangent to the y-axis is given as follows:
C. x² + y² - 10x - 4y + 4 = 0.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
Considering the center, we have that:
(x - 5)² + (y - 2)² = r².
The circle is tangent to the y-axis, meaning that it passes through the point (0, 2), thus the radius is obtained as follows:
r² = 25.
Then the equation in standard form is given as follows:
x² - 10x + 25 + y² - 4y + 4 - 25 = 0.
x² + y² - 10x - 4y + 4 = 0.
Meaning that option C is correct.
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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.