A charity fair raised $6,000 by selling 500 lottery tickets. There were two types of lottery tickets: A tickets cost $10 each, and B tickets cost $60 each. How many tickets of each type were sold?
A.5, 185
B.370, 230
C.410, 90
D.480, 20
E.250, 250
What is the value of x?
a. 86.5°
b. 43.25°
c. 133.25°
d. 46.75°
Answer:
x = 43.25
Step-by-step explanation:
In the given figure :
In ΔDEF ,
DF = FE
⇒ ∠DEF = ∠FDE = x ( Angles opposite to equal sides are equal)
Now, using angles sum property of a triangle in ΔDEF
∠DEF + ∠FDE + ∠DFE = 180
⇒ ∠FDE + ∠FDE + 93.5 = 180
⇒ x + x = 180 - 93.5
⇒ 2x = 86.5
⇒ x = 43.25
Answer: D. 43.25
Step-by-step explanation:
I have just taken the test
Find two consecutive integers whose sum is 73. Which of the following equations could be used to solve the problem?
a:2x = 73
b: 2x + 1 = 73
c;2x + 2 = 73
d:x2 + 1= 73
Answer:
b: 2x + 1 = 73
Step-by-step explanation:
Let x be the smaller integer,
Then the larger integer consecutive to x is x + 1,
Sum of these integers = x + x + 1 = 2x + 1
According to the question,
The sum is 73
⇒ 2x + 1 = 73
Which is the required equation that could be used to solve the problem.
Option 'b' is correct.
What is the value of x, when -25(x - 4) = -55(x - 10)?
A) x = 5
B) x = -5
C) x = 81
8
D) x = 15
[tex] -25(x - 4) = -55(x - 10)\\\\-25x+100=-55x+550\ \ \ |-100\\\\-25x=-55x+450\ \ \ \ |+55x\\\\30x=450\ \ \ |:30\\\\x=15 [/tex]
Answer: D) x = 15
Hello! I'm in seventh grade and I just started Algebra and I do not know what "simplifying the expression" means. Could someone please explain it? Thanks in advance.
Answer:
To diminish a portion to its most minimal terms by dropping to the least regular factor for both numerator and denominator or to gather a mathematical articulation by gathering and joining comparative terms. Working on makes an algebric articulation effectively reasonable and resolvable.
Step-by-step explanation:
To simplify any algebraic expression, the following are the basic rules and steps:
1. Remove any grouping symbol such as brackets and parentheses by multiplying factors.
2. Use the exponent rule to remove grouping if the terms are containing exponents.
3. Combine the like terms by addition or subtraction.
4. Combine the constants.
Cody is twice as old as evan and seven years ago the sum of their age was 1010. find the age of each boy now.
Find slope of the line that passes through the points
(-2,-1) and (4,5)
How to rewrite the expression. With the steps. Use an exponent, rather than repeated multiplication. (–4)(–4)
For this case we have the following expression:
[tex](-4) (- 4)[/tex]
Using law of exponents we have:
[tex](a ^ m) (a ^ n) = a ^ {m + n}[/tex]
We use the definition to rewrite the given expression
Rewriting we have:
[tex](-4) (- 4) = (- 4)^{ 1 + 1}\\(-4) (- 4) = (- 4) ^ 2[/tex]
Answer:
The rewritten expression is given by:
[tex](-4) (- 4) = (- 4) ^ 2[/tex]
Use complete sentences to describe how a postulate becomes a theorem.
Final answer:
A postulate becomes a theorem through a process of logical deduction and proof. Starting from basic assumptions or postulates, mathematicians derive theorems using step-by-step logical inferences, forming the basis for further deductions, such as with Newton's second law or the Schrödinger equation in physics.
Explanation:
A postulate is a statement assumed to be true without proof and serves as a starting point for deducing and inferring other truths. The transformation from a postulate into a theorem involves a process of logical deduction and rigorous proof. When we establish a theorem, what we're doing is showing that the statement necessarily follows from the previously accepted postulates and theorems by a sequence of logical deductions. For example, in geometry, one might postulate that a straight line can be drawn between any two points, and from there, using a series of logical steps, derive the Pythagorean theorem. The Pythagorean theorem's validity is then supported by the fact that it can be derived from these fundamental postulates through a sequence of unassailable logical steps within a proof.
To illustrate, a textbook might first introduce a straightforward theorem like: "If we start out with four lines that form a rectangle, we can draw a new, fifth line that divides the rectangle into two identical triangles." From this, using the fifth line as a postulate, more complicated theorems can be constructed. Similarly, in physics, Newton's second law (f = ma) and the Schrödinger equation in quantum mechanics begin as postulates that explain a wide range of observations. Once propositions like these are established, they can be used to deduce further principles that build upon them.
Joe wants to saw a wooden plank into 3/4 -meter pieces. The length of the wooden plank is 15/4meters. How many 3/4 -meter pieces can Joe saw from the wooden plank?
Answer:
5 is your answer
Step-by-step explanation:
Consider △LNM below. Which statements are true for triangle LNM? Check all that apply. (Pick more than one!)
[] The side opposite ∠L is NM.
[] The side opposite ∠N is ML.
[] The hypotenuse is NM.
[] The hypotenuse is LN.
[] The side adjacent ∠L is NM.
[] The side adjacent ∠N is ML.
Answer:
A,B,D ON EDGE. ASSIGNMENT
The statements that are true for triangle LMN are the 1st, 2nd and fourth options. That is
[] The side opposite ∠L is NM.
[] The side opposite ∠N is ML.
[] The hypotenuse is LN.
The question as well as the accurate diagram is shown in the attachment below.
To determine which statements are true for triangle LNM, we will observe each of the options one after the other.
For the first option - [] The side opposite ∠L is NMIn the diagram, the side opposite angle L is side NM
∴ The statement "The side opposite ∠L is NM" is true
For the second option - [] The side opposite ∠N is MLIn the diagram, the side opposite angle N is side ML
∴ The statement "The side opposite ∠N is ML" is true
For the third option - [] The hypotenuse is NMIn a right triangle, the hypotenuse is the longest side. It is the side opposite the right angle.
In the diagram, NM is not the side opposite the right angle. LN is the side opposite the right angle.
∴ The statement "The hypotenuse is NM" is not true
For the fourth option - [] The hypotenuse is LNAs stated above, LN is the side opposite the right angle. That is, LN is the hypotenuse.
∴ The statement "The hypotenuse is LN" is true
For the fifth option -[] The side adjacent ∠L is NMThe side adjacent an angle is the side next to it.
In the diagram, side NM is not adjacent to angle L, it is opposite to angle L.
∴ The statement "The side adjacent ∠L is NM" is not true
For the sixth option - [] The side adjacent ∠N is MLIn the diagram, side ML is not adjacent to angle N, it is opposite to angle N.
∴ The statement "The side adjacent ∠N is ML" is not true
Hence, the statements that are true for triangle LMN are the 1st, 2nd and fourth options. That is
[] The side opposite ∠L is NM.
[] The side opposite ∠N is ML.
[] The hypotenuse is LN.
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If m <5=42, what is m <4?
A.42
B.48
C.128
D.138
For the following figure, complete the statement for the specified points.
Points A, B, C, and Q are _____.
collinear
coplanar
both collinear and coplanar
neither collinear nor coplanar
Points A, B and Q are coplanar.
What are coplanar points?Points or lines are said to be coplanar if they lie in the same plane. Example 1: The points P , Q , and R lie in the same plane A . They are coplanar.
What are coplanar lines?A line which is in the same plane as another line. Any two intersecting lines must lie in the same plane, and therefore be coplanar.
What are collinear points?Three or more points that lie on the same line are collinear points . Example : The points A , B and C lie on the line m.
From the figure we can observe
Points A, B and Q are not in the same line.
Three points are collinear only if they are on the same line
3 points are collinear if we can draw a line that connects the points.
In the image A, Q are in a same line but B is not in the line of A and Q.
Points A, B and Q are on the base, So the three points are coplanar but not collinear.
So, Points A, B and Q are coplanar.
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The table below shows the typical hours worked by employees at a company. A salaried employee makes $78,000 per year. Hourly employees get paid $26 per hour, but get $39 per hour for each hour over 40 hours.
Sun.
Mon.
Tues.
Wed.
Thurs.
Fri.
Sat.
0
8
8.5
9.5
10
8
3
Which of the payment options would you recommend to a new employee?
The recommended method of pay must be salaried because, salaried employee will get more money than hourly paid employee per week.
Further explanation:
Given:
The salary of an employee is [tex]\$\ 78,000[/tex].
The hourly employee get paid is [tex]\$26\text{ /hour}[/tex] and after [tex]40[/tex] hour the employee get [tex]\$39\text{ /hour}[/tex].
Calculation:
The number of week in a year is [tex]52[/tex].
Therefore the salary of the employee per week can be obtained as follows:
[tex]\begin{aligned}\text{Salary per week}&=\dfrac{78000}{52}\\&=15000\end{aligned}[/tex]
The salary of the employ per week is [tex]\bf \$\ 1,500[/tex].
The number of hours worked by the hourly paid employee in the week is [tex]47\text{ hours}[/tex] since the sum of all the hours of the week is [tex]47[/tex].
The hourly paid employee works extra [tex]7\text{ hours}[/tex] per week.
The amount earned by hourly paid employee can be obtained as follows:
[tex]\begin{aligned}\text{Amount earned}&=(26\cdot 40)+(7\cdot 39)\\&=1040+273\\&=1313\end{aligned}[/tex]
Therefore, the dollars earned by the hourly paid employ per week is [tex]\$\1,313[/tex]
Since, the salaried employee make more money than and hourly paid employee per week.
Therefore, the highly recommended method of pay for new employee must be salaried.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Linear Equation
Keywords: Employee, $26, hourly, 40 hours, $78,000, Salaried, per year, hours, payment ,working hours, hourly, hourly paid employee, more money.
The payment options would you recommend to a new employee is $1150.
The salary of $67,000, when divided by 52 weeks, results in a weekly payment of $1288.
For standard hourly employees working 44 hours per week, the breakdown is as follows: 40 regular hours at $25 per hour amounting to $1000, with an additional 4 hours of overtime at $37.50 per hour, totaling $150.
This computation reflects a fair compensation structure that considers both regular working hours and overtime, ensuring equitable remuneration for employees based on their hourly rates and the hours worked beyond the standard weekly timeframe.
Consequently, the total weekly compensation for hourly employees is $1150.
the length of a Rectangle is 6 cm more than the width. the area is 11cm2 find the length and width
A plane that carries mail makes a round trip each day from Chicago to New York. It makes 3 intermediate stops on the way to New York and 1 intermediate stops on the way back to Chicago. Suppose you make a graph on the altitude of the plane for one day, whit time on the horizontal axis and altitude on the vertical axis. How many times will the graph touch the horizontal axis?
Answer:
7
Step-by-step explanation:
The graph that is drawn here shows the altitude as a function of time. When the plane takes off from Chicago, the graph will start from the horizontal axis.
Next, when the plane takes 3 intermediate stops, altitude will touch the horizontal axis 3 times.
Next, when the plane lands in New York the altitude will touch the horizontal axis.
Next, when plane takes off from New York and takes an intermediate stop, altitude will touch horizontal axis.
Lastly the altitude will touch the axis when plane lands back in Chicago.
So, cumulatively the altitude will touch the horizontal axis seven times.
The altitude vs time graph for the plane's journey will touch the horizontal axis 6 times - at each landing during the round trip from Chicago to New York and back.
Explanation:The graph of the plane's altitude versus time will touch the horizontal axis each time the plane lands. The plane lands at the 3 intermediate stops on the way to New York, once in New York, at the 1 intermediate stop on the way back, and once back in Chicago. This totals up to 6 times. Skyward journeys will create upward curves on the graph while the landings create points where the graph touches the horizontal axis (indicating an altitude of 0 at landing).
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What are the amplitude and midline?
Amplitude: 1; midline: y = 1
Amplitude: 1; midline: y = 2
Amplitude: 2; midline: y = 1
Amplitude: 2; midline: y = 2
Answer:
D) Amplitude;2 ; midline: y= 2
Step-by-step explanation:
The total height of the curve = 4
Amplitude = 4/2 = 2
The middle line is y = 2
Therefore, answer is D) Amplitude;2 ; midline: y= 2
Hope this will helpful.
Thank you.
Find the average rate of change for f(x) = x2 − 3x − 10 from x = 4 to x = 6
Answer:
what's the answer
Step-by-step explanation:
Solve for x. x−2.7≥10.3 Enter your answer, as an inequality, in the box.
The radius of a cylinder is increased from 9 to 9.03 inches. if the height remains constrant at 12 inches. Estimate the change in volume
∠A and ∠B are vertical angles with m∠A=x and m∠B=3x−60 .
What is m∠A ?
Enter your answer in the box.
If a(x) = 3x + 1 and b(x)= √x-4 , what is the domain of (b*a)(x)
Answer: The correct option is C. The domain of [tex](b\circ a)(x)[/tex] is [tex][0,\infty)[/tex].
Explanation:
It is given that,
[tex]a(x)=3x+1[/tex]
[tex]b(x)=\sqrt{x-4}[/tex]
First we have to find the composite function [tex](b\circ a)(x)[/tex].
[tex](b\circ a)(x)=b(a(x))[/tex]
[tex](b\circ a)(x)=b(3x+1)[/tex]
[tex](b\circ a)(x)=\sqrt{3x+1-4}[/tex]
[tex](b\circ a)(x)=\sqrt{3x-3}[/tex]
We know that a root function is defined for only positive values therefore the composite function is defined if,
[tex]3x-3\geq 0[/tex]
[tex]3x\geq 3[/tex]
[tex]x\geq 1[/tex]
The function is defined for all the values of x which are greater than or equal to 1. Therefore the domain of [tex](b\circ a)(x)[/tex] is [tex][0,\infty)[/tex] and option C is correct.
A student has passed 60 percent of the 20 quizzes he has written so far successfully. if the student writes 50 quizzes during the year, and passes 80 percent of the remaining quizzes successfully, what would his average percentile be?answer:
His average percentile is 72%
A student passed 60 percent out of 20 quizzes50 quizzes in a year and passed 80 percent of the remaining quizzesThe success rate for all his quizzes for the entire year is unknown.Further ExplanationA student passed 60 percent out of 20 quizzes, which can be expressed as
[tex]\frac{60}{100}[/tex] x [tex]20[/tex]
[tex]60[/tex] x [tex]\frac{20}{100}[/tex]
[tex]\frac{1200}{100}[/tex]
[tex]12[/tex]
Therefore the remaining quizzes will be:
[tex]50[/tex] - [tex]20[/tex]
[tex]30[/tex] quizzes
Also, we have to determine the 80% of 30 quizzes, which can also be expressed as
[tex]\frac{80}{100}[/tex] x [tex]30[/tex]
[tex]80[/tex] x [tex]\frac{30}{100}[/tex]
[tex]\frac{2400}{100}[/tex]
[tex]24[/tex]
To find the total remaining quizzes, then we have to add both value together
Therefore, we have
[tex]30[/tex] + [tex]24[/tex]
[tex]36[/tex]
Thus, the total remaining quizzes is 36.
Now, if the student writes 50 quizzes during the year, his average percentile would be:
[tex]\frac{36}{50}[/tex] x [tex]100%[/tex]
[tex]0.72[/tex] x [tex]100%[/tex]
[tex]72%[/tex]
Therefore, his average percentile is 72%
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The coordinates of the vertices of quadrilateral JKLM are J(−3, 2) , K(3, 5) , L(9, −1) , and M(2, −3) .
Which statement correctly describes whether quadrilateral JKLM is a rhombus?
Quadrilateral JKLM is not a rhombus because there is only one pair of opposite sides that are parallel.
Quadrilateral JKLM is a rhombus because opposite sides are parallel and all four sides have the same length.
Quadrilateral JKLM is not a rhombus because there are no pairs of parallel sides.
Quadrilateral JKLM is not a rhombus because opposite sides are parallel but the four sides do not all have the same length
Using the distance formula, we can calculate the distances between the vertices of quadrilateral JKLM. After performing these calculations, we can determine that not all sides have the same length, thus quadrilateral JKLM is not a rhombus.
Explanation:To determine if quadrilateral JKLM is a rhombus, we need to check if all four sides are of equal length because a defining property of a rhombus is that it has all sides of equal length. The length between two points (x1, y1) and (x2, y2) can be found using the distance formula which is √[(x2-x1)² + (y2-y1)²].
After calculating, we find:
J-K distance = √[(5-2)² + (-3-3)²] = √42
K-L distance = √[(-1-5)² + (9-3)²] = √52
L-M distance = √[(-3- -1)² + (2-9)²] = √52
M-J distance = √[(2- -3)² + (-3-2)²] = √42
Therefore, the distance between vertices J-K and L-M are the same, and the distance between vertices K-L and M-J are the same, but the two pairs are not in themselves equal to each other. As such, quadrilateral JKLM is not a rhombus because all sides do not have the same length.
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Mr. Battles raised all of his students' scores on a recent exam by 5 points. What effect did this have on the mean and standard deviation of the scores?
describe a real life representation of the following 12/140 = 0.09
Number 5555555555555
What is the algebraic expression for the difference of 17 and 5 times a number?
Nick and his cousin Sara have the same birthday, but Nick is is eight years older than Sarah. Let the variable x represents nicks age and y represents Sara’s age. Which graph represents the relationship between nicks age and Sara’s age
An 8-ounce bottle of lotion costs $4.50. What is the cost per ounce?