Which of the following is NOT prime number? A 1057 B 3163 C 157 D263
Try this trick out on a friend! Tell your friend to place a dime in one hand and a penny in the other hand. Explain that you can determine which hand is holding the penny. Here’s how to do it: a. Ask the friend to multiply the value of the coin in his or her RIGHT hand by 4, 6, or 8 and then to multiply the value of the coin in his or her LEFT hand by 3, 5, or 7. 2. b. Now ask the friend to add the two results together and tell you the total. c. If the total is EVEN, the penny is in the RIGHT hand. If the total is ODD, the penny is in the left hand.
The question involves a mathematical trick to determine the location of a penny based on the parity of a sum and a take-home experiment on the balancing of pennies and torque. Additionally, it touches upon probability in the context of half-life and independent probabilities.
Explanation:Understanding Coin Experiments and ProbabilityIn the trick described, you are presenting a simple mathematical puzzle to determine the location of a penny based on the parity of the sum of two numbers. This is an application of basic arithmetic operations and the concept of even and odd numbers. However, for the take-home experiment involving balancing pennies on a ruler, this is related to physics and moment of force (torque). In this experiment, to balance one penny placed 8 cm away from the pivot, you would need to find a position where the total torque caused by the two or three pennies counterbalances the torque caused by the single penny. This involves understanding the principles of levers and torque.
the half-life coin activity mentioned in the question is an example of using probability to model physical phenomena, specifically radioactive decay. It explores independent probabilities when flipping coins multiple times.
These experiments and demonstrations help to illustrate various scientific and mathematical concepts using coins, which are familiar objects, making them more approachable and relatable to students.
Jack is selling wristbands and headbands to earn money for camp. He earns $2 for each wristband and $3 for each headband. He wants to earn at least $50. He needs to sell at least 5 wristbands. Which system of inequalities is shown in the graph of the solution below?
• 2x + 3y ≥ 50 x ≥ 5 x ≥ 0 y ≥ 0
•3x + 2y ≥ 50 x ≥ 5 x ≥ 0 y ≥ 0
•2x + 3y ≤ 50 x ≥ 5 x ≥ 0 y ≥ 0
•2x + 3y ≤ 50 x ≤ 5 x ≥ 0 y ≥ 0
Answer:
The correct option is A.
Step-by-step explanation:
Let number of sold wristbands and headbands be x and y respectively.
It is given that the jack earns $2 for each wristband and $3 for each headband. So, total revenue is
[tex]T=2x+3y[/tex]
He wants to earn at least $50.
[tex]2x+3y\geq 50[/tex]
He needs to sell at least 5 wristbands.
[tex]x\geq 5[/tex]
The number of sold wristbands and headbands can not be negative. so,
[tex]x\geq 0,y\geq 0[/tex]
The system of inequalities is
[tex]2x+3y\geq 50[/tex]
[tex]x\geq 5[/tex]
[tex]x\geq 0,y\geq 0[/tex]
Therefore, correct option is A.
Need help please. Just need my answers checked. Thanks in advance. My answers are in brackets.
1. The coordinates of the vertices of ΔJKL are J(-5, -1) , K(0, 1) , and L(2, -5). Which statement correctly describes whether ΔJKL is a right triangle?
a. ΔJKL is a right triangle because JK is perpendicular to JL.
b. ΔJKL is a right triangle because JL is perpendicular to KL.
c. ΔJKL is a right triangle because JK is perpendicular to KL.
[ d. ΔJKL is not a right triangle because no two of its sides are perpendicular. ]
2. The coordinates of the vertices of ΔJKL are J(0, 2) , K(3, 1) , and L(1, -5). Drag and drop the choices into each box to correctly complete the sentences.
The slope of JK is [ -¹/₃ ], the slope of KL is [ 3 ], and the slope of JL is [ -7 ]. ΔJKL [ is ] a right triangle because [ two of these slopes have a product of -1 ].
answer choices: -3 ; 3 ; -7 ; -¹/₃ ; ¹/₇ ; is ; is not ; two of these slopes have a product of -1 ; no two of these slopes have a product of -1
3. The coordinates of the vertices of quadrilateral DEFG are D(-2, 5) , E(2, 4) , F(0, 0) , and G(-4, 1). Which statement correctly describes whether quadrilateral DEFG is a rhombus?
a. Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.
[ b. Quadrilateral DEFG is not a rhombus because there is only one pair of opposite sides that are parallel. ]
c. Quadrilateral DEFG is not a rhombus because opposites sides are parallel but the four sides do not all have the same length.
d. Quadrilateral DEFG is not a rhombus because there are no pairs of parallel sides.
The slopes of the sides are:
DE = -¹/₄
EF = 2
FG = -¹/₂
GD = 2
I'm debating between A and B.
4. The coordinates of the vertices of quadrilateral ABCD are A(-4, -1) , B(-1, 2) , C(5, 1) , and D(1, -3). Drag and drop the choices into each box to correctly complete the sentences.
The slope of AB is [ 1 ], the slope of BC is [ -¹/₆ ], the slope of CD is [ 1 ], and the slope of AD is [ -²/₅ ]. Quadrilateral ABCD [ is not ] a parallelogram because [ only one pair of opposite sides is parallel ].
answer choices: -²/₅ ; -¹/₆ ; 1 ; ³/₂ ; is ; is not ; both pairs of opposite sides are parallel ; only one pair of opposite side is parallel ; neither pair of opposite sides is parallel
5. The coordinates of the vertices of quadrilateral PQRS are P(-4, 2) , Q(3, 4) , R(5, 0) , and S(-3, -2). Which statement correctly describes whether quadrilateral PQRS is a rectangle?
a. Quadrilateral PQRS is not a rectangle because it has only two right angles.
b. Quadrilateral PQRS is a rectangle because it has four right angles.
c. Quadrilateral PQRS is not a rectangle because it has only one right angle.
d. Quadrilateral PQRS is not a rectangle because it has no right angles.
I'm not sure about this one.
Thanks again.
Answer:
#1) d. ΔJKL is not a right triangle because no two of its sides are perpendicular; #2) -1/3, 3, -7, is, two of these slopes have a product of -1; #3) a. Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length; #4) 1, -1/6, 1, -2/5, is not, only one pair of opposite sides is parallel; #5) c. Quadrilateral PQRS is not a rectangle because it has only one right angle.
Step-by-step explanation:
#1) The slope of any line segment is found using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For JK, this gives us (1-1)/(-5-0) = 0/-5 = 0. For KL this gives us (1--5)/(0-2) = 6/-2 = -3. For LJ this gives us (-5-1)/(2--5) = -6/7. None of these slopes are negative reciprocals, so none of the angles are right angles and this is not a right triangle.
#2) The slope of JK is (2-1)/(0-3) = 1/-3 = -1/3. The slope of KL is (1--5)/(3-1) = 6/2 = 3. The slope of LJ is (2--5)/(0-1) = 7/-1 = -7. Two of these slopes have a product of -1, 3 and -1/3. This means they are negative reciprocals so this has a right angle; this means JKL is a right triangle.
#3) The slope of DE is (5-4)/(-2-2) = 1/-4 = -1/4. The slope of EF is (4-0)/(2-0) = 4/2 = 2. The slope of FG is (0-1)/(0--4) = -1/4. The slope of GD is (1-5)/(-4--2) = -4/-2 = 2. Opposite sides have the same slope so they are parallel.
Next we use the distance formula to find the length of each side:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Using our points, the length of DE is
[tex]\sqrt{(5-4)^2+(-2-2)^2}=\sqrt{1^2+(-4)^2}=\sqrt{1+16}=\sqrt{17}[/tex]
The length of EF is
[tex]d=\sqrt{(4-0)^2+(2-0)^2}=\sqrt{4^2+2^2}=\sqrt{16+4}=\sqrt{20}[/tex]
The length of FG is
[tex]d=\sqrt{(0-1)^2+(0--4)^2}=\sqrt{(-1)^2+(4)^2}=\sqrt{1+16}=\sqrt{17}[/tex]
The length of GD is
[tex]d=\sqrt{(1-5)^2+(-4--2)^2}=\sqrt{(-4)^2+(-2)^2}=\sqrt{16+4}=\sqrt{20}[/tex]
Opposite sides have the same length and are parallel, so this is a parallelogram.
#4) The slope of AB is (-1-2)/(-4--1) = -3/-3 = 1. The slope of BC is (2-1)/(-1-5) = 1/-6 = -1/6. The slope of CD is (1--3)/(5-1) = 4/4 = 1. The slope of DA is (-3--1)/(1--4) = -2/5. Only one pair of opposite sides is parallel, so this is not a parallelogram.
#5) The slope of PQ is (2-4)/(-4-3) = -2/-7 = 2/7. The slope of QR is (4-0)/(3-5) = 4/-2 = -2. The slope of RS is (0--2)/(5--3) = 2/8 = 1/4. The slope of SP is (-2-2)/(-3--4) = -4/1 = -4. Only one pair of sides has slopes that are negative reciprocals; this means this figure only has 1 right angle, so it is not a rectangle.
The answers provided for ΔJKL, ΔJKL as a right triangle, and quadrilateral ABCD are correct. For quadrilateral DEFG, the answer may be correct depending on side lengths, and for quadrilateral PQRS, slopes must be calculated to determine if it's a rectangle.
Explanation:To determine whether the given shapes are right triangles, rhombuses, rectangles, or parallelograms, we use properties such as the slopes of lines to check for perpendicularity, parallelism, and equal lengths.
For ΔJKL with vertices J(-5, -1), K(0, 1), L(2, -5), you calculated it's not a right triangle because none of the slopes of the sides are negative reciprocals of each other (indicating perpendicular sides). This is correct; no slopes have a product of -1, so answer (d) is correct.
In the second case, ΔJKL with vertices J(0, 2), K(3, 1), L(1, -5) has slopes -1/3, 3, and -7 for sides JK, KL, and JL respectively. Since -1/3 and 3 are negative reciprocals, ΔJKL is a right triangle due to the perpendicular sides JK and KL. So, the filled answers are correct.
Regarding quadrilateral DEFG, you might want to reconsider option (b), as you cannot determine whether it's a rhombus solely based on one pair of opposite sides being parallel. Instead, check if all sides have the same length using the distance formula, and if the opposite sides are parallel by comparing slopes. Since you didn't provide the side lengths, I will only address the slopes here, which you've noted. Answer (b) can be correct if the side lengths are not equal, but if they are, it should be (c).
For quadrilateral ABCD, your assessment of the slopes leads to the conclusion that it is not a parallelogram, which is correct as only one pair of opposite sides (AB and CD having a slope of 1) is parallel. The filled answers are appropriate.
Last, for quadrilateral PQRS, you must calculate the slopes of the sides to determine if the sides are perpendicular to each other by checking if the products of the corresponding slopes are -1. If the slopes of adjacent sides are negative reciprocals of each other, then PQRS has right angles, and it could be a rectangle. Calculate the slopes, and if none are negative reciprocals, then answer (d) is correct stating that PQRS is not a rectangle because it has no right angles.
leticia tretched for 8 minutes then jogged around her block several times .it takes her 6 minutes to run around the block once .she spent 38 minutes exercising how many tims did leticia jog aound the block ?
After stretching for 8 minutes, Leticia had 30 minutes left for running. Given that she takes 6 minutes to complete one round, she completed 5 rounds in the remaining time.
Explanation:The question asks how many times Leticia jogged around her block after stretching for 8 minutes within her total exercise time of 38 minutes. Let's deduct the time Leticia spent stretching from the total time to find out how much time she spent running. That is 38 - 8 = 30 minutes. Since we know that running around the block once takes Leticia 6 minutes, we then divide her running time by this to discover how many laps she was able to make.
We do this by 30 / 6 = 5. Therefore, Leticia jogged around her block 5 times.
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How many integers between 2000 and 3999 have a ones digit that is a prime number?
Lee works at a job where her pay varies directly with the number of hours she works. Her pay for 6.5 hours is 49.40. Write a direct variation equation relating lee's pay x to the hours worked y. Then find her pay if she works 25 hours in a week
Final answer:
The direct variation equation relating Lee's pay (x) to the hours worked (y) is y = 7.60x. Lee's pay for working 25 hours in a week is $190.
Explanation:
Let's define the direct variation equation:
y = kx
We can substitute the information given in the question:
When x = 6.5, y = 49.40
49.40 = 6.5k
k = 49.40 / 6.5
k = 7.60
Therefore, the direct variation equation relating Lee's pay (x) to the hours worked (y) is y = 7.60x.
To find Lee's pay if she works 25 hours, we can substitute x = 25 into the equation:
y = 7.60(25)
y = 190
Lee's pay for working 25 hours in a week is $190.
You parents gave you $50 to take your brother and sister to the movies. Your ticket cost $7.25 and your siblings cost $4.25. If you spent an additional $20 on soda and popcorn, how much money did you bring home with you?
Adults: 7.25
Seniors: 6.00
Children under 8: 4.25
Answer:
You bring home $14.25 with you.
Step-by-step explanation:
First we add the money spent in movie tickets and snacks.
Your ticket = $7.25
Brother's ticket = $4.25
Sister's ticket = $4.25
Soda and popcorn = $20.00
Total = 7.25 + 4.25 + 4.25 + 20.00 = $35.75
Your parents gave you = $50.00
You spent = $35.75
Balance = 50.00 - 35.75 = $14.25
You bring home $14.25 with you.
Susan's property is assessed at $97,500. The property tax rate in her city is 3.05%. Find her property tax.
WHAT IS 24.5 DIVIDED BY 7
Write a function rule the price p of a pizza is $6.75 plus $0.85 for each of the t toppings of pizza
Darryl has $5 left in his pocket. He spent $16 on a book, $20 on a compact disc, and $2 on a magazine. How much money did he have at the beginning of the day.
What is the property that justifies the illustrated step in solving the equation?
3x + 4 - 2x + 5 = 6x + 2
3x - 2x + 4 + 5 = 6x + 2
Multiplication Property of Equality
Addition Property of Equality
Commutative Property of Addition
Distributive Property of Addition
The property that justifies the step is the Commutative Property of Addition, which states that the order of addition does not affect the result.
Explanation:The property that justifies the illustrated step in solving the equation 3x + 4 - 2x + 5 = 6x + 2 as 3x - 2x + 4 + 5 = 6x + 2 is the Commutative Property of Addition.
This property states that the order in which numbers are added does not affect the result. So, we can rearrange the terms in any order without changing their sum.
In this step, we are rearranging the terms -2x and 5 so that like terms, namely 3x and -2x, and 4 and 5, are grouped together.
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They are 812 students in your school there are 36 more girls than boys how many girls are there
If there are 812 students in your school and there are 36 more girls than boys. Then there are 414 girls in the school.
Explanation:In this problem, let's denote the number of boys as B and the number of girls as G. We are given two pieces of information: there are 812 students in total, and there are 36 more girls than boys.
So, we can set up two equations based on these statements:
1. Total number of students: (B + G = 812)
2. The number of girls is 36 more than boys: (G = B + 36)
Now, we can substitute the expression for G from the second equation into the first equation:
[B + (B + 36) = 812]
Combine like terms:
[2B + 36 = 812]
Subtract 36 from both sides:
[2B = 776]
Now, divide by 2 to solve for B:
[B = 388]
Now that we know the number of boys, we can find the number of girls using the second equation:
[G = 388 + 36]
[G = 424]
So, there are 388 boys and 424 girls in the school. To find the number of girls, we add the number of boys (388) to the given difference (36):
[424 = 388 + 36]
Therefore, the final answer is that there are 424 girls in the school.
Which of the following has the steepest graph?
The equation which has the steepest graph is:
Option: A
A. [tex]y=11x-144[/tex]
Step-by-step explanation:We know that the slope-intercept form of a line is given by:
[tex]y=mx+c[/tex]
where m is the slope of the line and c is the y-intercept of a line.
If the absolute value of the slope is greatest then that line is most steep.A)
[tex]y=11x-144[/tex]
The slope is: 11
B)
[tex]y=\dfrac{1}{2}x+3[/tex]
The slope is: [tex]\dfrac{1}{2}[/tex]
C)
[tex]y=7x+16[/tex]
The slope is: 7
D)
[tex]y=3x+144[/tex]
The slope of this line is: 3
The line which has the largest absolute value of slope is:
[tex]y=11x-144[/tex]
Hence, the graph of this equation will be steepest.
The two-way table shows the number of sport utility vehicles with certain features for sale at the car lot.
What is the probability that a randomly selected car with no 4-wheel drive has third row seats?
0.3
0.4
0.7
0.8
Probability measures to determine the possibility of an event. In this case, the events are cars with no 4 wheels and cars with third row seats.
The probability that a randomly selected car with no 4-wheel drive has third row seats is 0.3
Let:
[tex]A \to[/tex] A car with no 4-wheel drive
[tex]B \to[/tex] A car that has third row seats
The probability that a randomly selected car with no 4-wheel drive has third row seats is represented as:
[tex]P(B|A)= \frac{n(A\ n\ B)}{n(A)}[/tex]
From the 2-way table, we have the following parameters:
[tex]n(A\ n\ B) = 12[/tex]
[tex]n(A) = 40[/tex]
So, the probability is:
[tex]P(B|A)= \frac{n(A\ n\ B)}{n(A)}[/tex]
[tex]P(B|A)= \frac{12}{40}[/tex]
[tex]P(B|A)= 0.3[/tex]
Hence, the probability that a randomly selected car with no 4-wheel drive has third row seats is 0.3
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A factory uses 15 pounds of steel for every 18 pounds of copper. How much copper will the factory use for 2,700 of steel. A.2,250lbs B.2,400lbs C.3,240lbs D.3,700lbs?
Write (1-i)-(4-5i) as a complex number in standard form. I don't exactly get how to do this.. Can anyone help?
Timothy explains to his brother that the model y=4mt has a constant of variation of 4 and is an example of _____ variation.
△ABC△ABC is similar to △QRS△QRS. Also, sideABsideAB measures 50 cm, sideACsideAC measures 60 cm, and sideQSsideQS measures 6 cm.
What is the measure of sideQRsideQR ?
Answer for 14 and 15 only
Find the area of the triangle with A =63°, b = 9 feet, and c =7 feet. Round to the nearest tenth.
Answer: 28.1ft^2 so it’s C
Answer: C
Step-by-step explanation:
solve:512^x-2/(1/64)^3x-512
x = –1
x = 0
x = 1
no solution
The answer is x=1. Just did the assignment
The equation is a complex exponentiation problem that can be solved by simplifying and rearranging the equation. By plugging in the given potential solutions, it can be determined that x = -1 is the correct answer.
Explanation:This equation is an exponential equation. You can start solving by simplifying the bases, as both bases are actually the 2, but to different powers (512 = 2^9 and 1/64 = 2^-6). The equation can be rewritten as (2^9)^x - 2 = (2^-18)x - 512. Simplifying this gives 2^(9x) - 2 = 2^(-18x) - 512. From the options given (x = -1, 0, or 1), we can plug these into the simplified equation to see which one gives a valid solution. Plugging these values in reveals that x = –1 is the valid solution to the equation. None of the other choices work out correctly.
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Approximately what percentage of iq scores falls between 70 and 130?
for the geometric sequence with a1=4 and r=5, find a5
This IS SO HARD
NEED HELP
I THINK ITS B.. Confirmation?
Answer:
22sqrt(3)/3
You are correct.
Step-by-step explanation:
You have a 30-60-90 triangle.
In a 30-60-90 triangle, the hypotenuse is twice the length of the short leg. The long leg is sqrt(3) times the length of the short leg.
You are given the length of the long leg.
1) Find the length of the short leg.
HG = GI/sqrt(3) = 11/sqrt(3)
2) Find the length of the hypotenuse, HI.
HI = 2HG = 2(11/sqrt(3)) = 2(11/sqrt(3))*(sqrt(3))/(sqrt(3)) = 22sqrt(3)/3
What construction can be used to identify a line of reflection?
A plane travels 600 miles in 3 hours. at this rate how far could the jet fly in 10 hours? math
What is the y-intercept of the equation 4×+2y=12?
Which statements are true about the ordered pair (5, −6) and the system of equations?
{x+y=−1
3x−y=21
Select each correct answer.
The ordered pair (5, −6) is a solution to the first equation because it makes the first equation true.
The ordered pair (5, −6) is a solution to the second equation because it makes the second equation true.
The ordered pair (5, −6) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (5, −6) is a solution to the system because it makes both equations true.