Mei is thinking of a 2-digit multiple of 2. Ben is thinking of a 2-digit multiple of 3. Xander is thinking of a 2-digit multiple of 4. Dom is thinking of a 2-digit multiple of 6. Alice is thinking of a 2-digit multiple of 8. They are all thinking of the same number.
The only 2-digit multiple of 2, 3, 4, 6, and 8 is the number 24.
What is multiple ?Multiple is a term that refers to an amount that is greater than one or a collection of two or more items. It is often used to describe a quantity of objects, people, or events that are distinct from each other. For example, a multiple of five would be five, ten, fifteen, twenty, etc. Similarly, a multiple of three would be three, six, nine, twelve, etc.
Therefore, all five people are thinking of the same number: 24.
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(2) Melissa and Ron entered a competition as a team Ron's score was 4/9 of Melissa's score. Melissa scored 50 more points than Ron. How many points did Melissa score?
The number of points that Melissa scored would be = 89 points.
How to calculate the number of point scores by Melissa?The competition was carried out by these two individuals that had different scores such as follows:
The total number of scores for Melissa = 50 point + Ron's score. That is , y = 50+X. ---> eq 1
The total number of Ron's score X = 4/9 × y --> 2
substitute y into equation 2.
X = 4/9× (50+X)
X= 22 + 0.44x
0.56x= 22
X= 22/0.56
X= 39.
substitute X into equation 1;
y= 50+39
y = 89
Therefore, the total number of points for Melissa = 89 point.
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Given the following definitions: U = {1, 2, 3, 4, 5, 6, 7} A = {1, 2, 4, 5} B = {1, 3, 5, 7} How many elements are in A ∩ B' ?
Read the following problem carefully! The amount of work, W, required to move a particle of mass M a vertical distance d above its starting height is given by the formula,W=Mgdwhere g is the acceleration due to gravity. A heavy rope is 15 m long and has a constant (linear) density of rho=2 kg/m. The rope hangs over the edge of a 25 m building, as shown below: The work required to pull the rope to the top of the building cannot be computed using the above formula because the distance each part of the rope must be moved is different! Answer the following questions and put your final answer for each part in the box. I. (The Approximate Work) A. On the figure above, the rope has been divided into three segments of equal length,Δy. Calculate Δy.Δy=B. Find the mass, M2, of the middle segment of the rope.M2 =C. The y values of the bottom of each segment of rope are indicated above. Find the valuesy0, y1, and y2 and label them on the figure (No justification is necessary). By approximating that the middle segment is a particle located at y2: D. Find the distance d2 the middle segment must be moved to reach the top of the building.d2 =
A. The length of each segment of the rope is 5 m.
B. The mass of the middle segment is the length of the segment 10 kg.
C. The y values of the bottom of each segment are y₀ = 0, y₁ = 5 m, and y₂ = 10 m.
D. The distance d₂ the middle segment must be moved is 15,
What do you mean by acceleration?Acceleration is a measure of the change in velocity over time. In physics, acceleration is defined as the rate of change of velocity, or the second derivative of position with respect to time. Acceleration is a vector quantity that has both magnitude and direction, and its unit is meters per second squared (m/s²).
A positive acceleration indicates an increase in speed, while a negative acceleration indicates a decrease in speed or a change in direction. In everyday life, we encounter examples of acceleration in movements such as starting a car, stopping a car, or changing direction while driving.
A. The length of each segment of the rope is 15 m / 3 = 5 m.
B. The mass of the middle segment is the length of the segment multiplied by the density of the rope: M2 = 5 m × 2 kg/m = 10 kg.
C. The y values of the bottom of each segment are y0 = 0, y1 = 5 m, and y2 = 10 m.
D. The distance d2 the middle segment must be moved is 25 m - 10 m = 15 m.
Therefore, the work required to move the middle segment can be approximated using the formula W = M2 × g × d2, where g is the acceleration due to gravity. The exact value of the work required to move the entire rope would need to take into account the different distances that each segment must be moved.
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I NEED HELP ASAP PLEASE!!! Determine which integer will make the inequality x − 3 > 15 true.
S:{15}
S:{17}
S:{18}
S:{30}
Answer:
c) S : {30}
So, it is correct answer.
Step-by-step explanation:
mental math be like :-)
Let X be a continuous random variable taking values between 0 and 2 with probability density function p(x) = 0.5. Find E(X) and Var(X). Plot its Cumulative Distribution Function.
E(X) = 2 and Var(X) = 4/3.
And then, Here's a plot of the CDF of X:
[Plot of the CDF of X with x on the x-axis and F(x) on the y-axis, showing a line with slope 0.5 for x in [0,2]]
Continuous Random Variable ExpectationsThe expected value (mean) of a continuous random variable X with probability density function p(x) is given by:E(X) = ∫x*p(x)dx, where the integral is taken over the range of X.
In this case, since p(x) = 0.5 for all x in [0,2], we have:E(X) = ∫x*0.5dx = 0.5∫xdx = 0.5(x²/2)|0 to 2 = (2²/2 - 0²/2)*0.5 = 2.
The variance of X is given by:Var(X) = E((X - E(X))²) = E(X²) - (E(X))².
We have to calculate E(X²), which can be found as:E(X²) = ∫x²*p(x)dx = 0.5∫x²dx = 0.5(x²/3)|0 to 2 = (2²/3 - 0³/3)*0.5 = 8/3.
So, Var(X) = E(X²) - (E(X))² = 8/3 - (2)² = 8/3 - 4 = 4/3.
The cumulative distribution function (CDF) of a continuous random variable X is given by:F(x) = P(X <= x) = ∫p(t)dt for all t <= x.
In this case, since p(x) = 0.5 for all x in [0,2], we have:F(x) = 0.5x for x in [0,2].
The CDF of X is a monotonically increasing function, and it tells us the probability that X takes a value less than or equal to x.
Now, Here's a plot of the CDF of X:
[Plot of the CDF of X with x on the x-axis and F(x) on the y-axis, showing a line with slope 0.5 for x in [0,2]]
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What is the answer to 19-6(-k-2)?
Answer: 6k + 31
Step-by-step explanation:
19 - (-6k - 2(6))
19 - (-6k - 12)
19 + 6k + 12
6k + 31
Answer: 6k + 31
Step-by-step explanation:
= 19-6(-k-2)
= 19+6k +12
= 6k + 31
Patsy Bonner buys 200 shares of Target at $ 56.30 and 100 shares of Pepsico at $68.73. Find the total cost ignoring commissions.
Answer:
[tex]\$25,006[/tex]
Step-by-step explanation:
The total cost of Target shares is [tex](200)(\$56.30)=\$11,260[/tex].
The total cost of Pepsico shares is [tex](200)(\$68.73)=\$13,746[/tex].
Adding these costs together yields [tex]\$11,260+\$13,746=\$25,006[/tex].
Which division problem can be described using this model? Responses 3÷4 , 3 divided by 4, 3÷1/4 3 divided by 1 fourth 1÷1/12 , 1 divided by fraction 1 over 12, 3÷1/12
The model represent here gives the division problem is 3÷1/4.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
We have three section 1+ 1 + 1= 3.
and, Each section have the fraction
= 4/12
= 1/3
so, the model represent here gives the division problem
3÷1/4.
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The Bitcoin economy had reported year-on-year growth from 2017 to 2019 at a yearly rate of 7%. In 2020 it went into a downward trend. That year the growth turned negative at -5%. If the negative growth doubled the next year, what was the approximate percentage increase or decrease of the bitcoin economy in that year, compared to 2018?
SELECT ONLY ONE
Approximately 9% decrease
Approximately 13% decrease
Approximately 3% increase
Approximately 5% increase
If the Bitcoin economy had a yearly growth rate of 7% from 2017 to 2019, then the value in 2019 would be $1.07^3 = $1.225. If the economy had a negative growth rate of 5% in 2020, then the value in 2020 would be $1.225 x 0.95 = $1.1638. If the negative growth rate doubled in the next year, then the value in the next year would be $1.1638 x 0.9 = $1.04742.
To calculate the percentage change from 2018 to the next year, we can compare the values of the Bitcoin economy in those two years. The value in 2018 would be $1.07^2 = $1.1449. The percentage change would be ((value in next year - value in 2018) / value in 2018) x 100%. Substituting the values, we get ((1.04742 - 1.1449) / 1.1449) x 100% = -8.5%.
Therefore, the approximate percentage decrease of the Bitcoin economy in the next year, compared to 2018, is approximately 9%. The closest option is "Approximately 9% decrease".
can someone help me pls
a. The two pentagons are congruent as the transformations they underwent were only translation and rotation, which are rigid motions.
b. The side lengths of ABCDE are given as follows:
CD = 3.2.DE = 4.1.EA = 2.8.AB = 2.2.BC = 1.4.The angle measures of FGHIJ are given as follows:
<F = 59º.<J = 162º.<I = 108º.< H = 117º.<G = 94º.What are the effects of each transformation?Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.Congruence is only changed with a dilation, as the side lengths are changed.
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The students in Class 6 vote to pick a class captain. The choice is Anton, Eva, Kofi or Petra. Anton gets 0.2 of the votes. Eva gets 10% of the votes. Petra gets of the votes. Kofi gets 9 votes. How many students are in class 6?
Answer:
Step-by-step explanation:
Let's say there are "x" students in class 6.
Since Anton got 0.2 of the votes, he got 0.2 * x votes.
Eva got 10% of the votes, which is equal to 0.1 * x votes.
Petra got 0.3 of the votes, which is equal to 0.3 * x votes.
Kofi got 9 votes.
So, the total number of votes in class 6 is x.
By adding up the number of votes each candidate received, we can write an equation:
0.2x + 0.1x + 0.3x + 9 = x
Simplifying the equation:
0.6x + 9 = x
Subtracting 0.6x from both sides:
9 = 0.4x
Dividing both sides by 0.4:
x = 22.5
Since the number of students must be a whole number, we round up to the nearest whole number:
x = 23
So there are 23 students in Class 6.
I. Need.The.Answer
ASAP
Congratulations! You have been selected to be an emergency substitute teacher. You are given a lesson plan on writing parallel line equations. However the answer key is missing. Opps!
1) Start by writing this equation on the virtual white board: y = 1/2x -3
2) You then need to write an equation of a line using slope-intercept format that is parallel to this line and goes through the point (4,2).
An equation of a line in a slope-intercept format that is parallel to
y = (1/2)x - 3 line and goes through the point (4, 2) is y = (1/2)x
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know parallel lines have equal slopes.
The equation of the line given is y = (1/2)x - 3 and our required equation is parallel to it and passes through (4, 2).
So, 2 = (1/2)(4) + b.
2 = 2 + b.
b = 0.
Hence, y = (1/2)x is the required equation of the line.
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A researcher is studying a group of field mice. the distribution of the weight of the field mice is approximately normal with mean 25 g and standard deviation 4 g. which of the following is closest to the proportion of the field mice with a weight greater than 33 g? A 0.023 B 0.046 С 0.954 D 0.977 E 1.000
The probability of the field mice having a weight greater than 33 g is 0.977, the field mice have a weight greater than 33 g.
The proportion of field mice with a weight greater than 33 g can be calculated using the formula for a standard normal distribution. This formula states that the probability of an event with a normal distribution occurring can be calculated by subtracting the area under the normal curve from the mean to the given value and dividing by the standard deviation.
In this case, the mean of the distribution is 25 g, the standard deviation is 4 g and the given value is 33 g.
Therefore, the probability of the field mice having a weight greater than 33 g is 0.977. This means that 0.977, or 97.7%, of the field mice have a weight greater than 33 g.
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I need help………………………
Step-by-step explanation:
could you answer to my question
I'll need more than I need help in a picture to answer your question
please answer to this with what you need help with I am only seeing a question which I do not know and what I need to focus
thank you for cooperating - yuri
20 customers are eating dinner at a local restaurant. The restaurant accepts cash or credit as forms of payment. Of the 2020 customers, 44 have enough cash to pay for their meal, 1616 have a credit card, and 33 have enough cash and a credit card. Using this information, answer each of the following questions.
Let AA be the event that a randomly selected customer has enough cash and BB be the event that a randomly selected customer has a credit card.
What is P(A)P, left parenthesis, A, right parenthesis, the probability that a customer has enough cash?
the value of P(A∪B) is 17/20.
What is probability?Probability is a number expressing the likelihood or chance that a specific event will occur. Proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, A neighborhood restaurant is serving dinner to 20 patrons.
Both cash and credit are accepted as modes of payment at the restaurant. Of the 20 customers, 3 have enough cash and a credit card to pay for their dinner, 16 have a credit card, and 4 have enough cash to cover the cost of their meal.
From the general formula of probability:
Probability = (desired outcomes)/(Total outcomes)
Let "A" represent the situation in which a randomly chosen consumer has enough cash,
"B" represents the situation in which a randomly chosen customer has a credit card.
thus,
P(A) = 4/20
P(A) = 1/5
P(B) = 16/20
Also given,
P(A∩B) = 3/20
Since,
P(A∪B) = P(A) + P(B) -P(A∩B)
P(A∪B) = 4/20 + 16/20 - 3/20
P(A∪B) = 17/20
therefore, the value of P(A∪B) is 17/20.
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The triangle below is equilateral. Find the length of side x in simplest radical form with a rational denominator.
The length of side x is √3 units.
How to find the value of x?We know that the larger triangle is an equilateral triangle, and it is divided into two equal right triangles.
Now, let's analyze these, we can see that the catheti are:
x and 3.
And the hypotenuse must have a length of 2x (if the triangle is equilateral).
Now we can use Pythagorean's theorem.
Then we will get:
(2x)^2 = x^2 + 3^2
4x^2 = x^2 + 9
4x^2 - x^2 = 9
3x^2 = 9
x^2 = 9/3 = 3
x = ± √3
We only care for the positive value, then:
x = √3
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16. The elevation of City of Santa Clara is approximately 75 ft. What is the elevation in centimeters? (1ft = 12in; 1in = 2.54cm)
Answer:To convert the elevation of the City of Santa Clara from feet to centimeters, you can use the conversion factors:
1 ft = 12 in
1 in = 2.54 cm
First, convert feet to inches:
75 ft * 12 in/ft = 900 in
Then, convert inches to centimeters:
900 in * 2.54 cm/in = 2286 cm
So, the elevation of the City of Santa Clara is approximately 2286 cm.
Step-by-step explanation:
find the absolute value!! Need asap!!
Answer:
|-1/7| = 1/7 or approx .14
Helpppopoooooopppppppp
A. The solution set of the system is {7, 3}
About elimination methodThe elimination method is a method used to solve or find a set of solutions to a system of linear equations of two variables by eliminating one of the variables. If the variables are x and y, to determine the x variable we must first eliminate the y variable, or vice versa, if we want to find the y variable, we must first eliminate the x variable.
To eliminate a variable, it must have the same coefficient. So if the coefficients of the variables are not the same then first equate the coefficients by multiplying or dividing them. Then only can determine other variables that will be determined. So in the elimination method you need to eliminate the variable twice.
To eliminate y in order to find the value of x.
9x-y=60 (i) 9x-y=60
x+y=10 (ii) | times (-1)| -x-y= -10
___________ __________ _
10x=70
x=7
Substitute the value x=7 into equation (ii)
x+y=10
7+y=10
y=3
So the solution set is {7, 3}
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1×0.1+6×0.01+8×0.001 in standard form
Answer:
the answer is 0.168
Step-by-step explanation:
have a good day!
I keep messing up somebody please help me
Answer:
23 and 16
Step-by-step explanation:
The pattern is to subtract 7 each time.
51 - 7 = 44
44 - 7 = 37
37 - 7 = 30
30 - 7 = 23
23 - 7 = 16
Solve the triangle:
Answer:
Step-by-step explanation:
we will find the first angle in the larger triangle;
180⁰-60⁰= 120⁰
120⁰
the second angle will be;
120⁰+30⁰=150⁰
180⁰-150⁰=30⁰
30⁰ this means that the second triangle is isosceles triangle, when we find the hypotenuse of the smaller triangle it will be equal to x since the sides are equal
88/sin60⁰=x/sin90⁰
88sin 90⁰=xsin60⁰
88/0.8660=0.8660x/0.8660
x=101.62
find the value of x in 2/3 (2x+4) +6=10
Answer:
x = 1
Step-by-step explanation:
2/3 (2x + 4) + 6 = 10
2/3 (2x + 4) = 10 - 6
1⅓x + 2⅔ = 4
1⅓x = 4 - 2⅔
1⅓x = 1⅓
x = 1
The height of a rectangular box is 4 times its length, and its width is 7 in more than its length. The volume of the box is 102 in^3. Use the ALEKS graphing calculator to find the length of the box. Round your answer to two decimal places.
Answer: Let's call the length of the box "x". Then, the height of the box is 4x and the width is x + 7. The volume of the box is given by the equation:
x * 4x * (x + 7) = 102
Expanding and simplifying the equation, we get:
4x^3 + 28x^2 - 102 = 0
To find the length of the box, we need to solve for x in this equation. One way to do this is to use the cubic formula. However, this formula can be quite complex, so a simpler method would be to use numerical methods such as the bisection method or Newton's method.
Step-by-step explanation:
You might have noticed that the numbers, or frequencies, on an old radio dial are not evenly spaced. There is, however, some pattern to the placement of these frequencies. You will analyze this data and answer the following questions.
frequency reading on the radio dial (kilohertz)
distance from the left end of the radio dial (centimeters)
53
1.54
60
2.17
70
2.95
80
3.62
100
4.75
120
5.67
140
6.45
170
7.43
1. a. What is the independent variable and what are its units?
b. What is the dependent variable and what are its units?
2. Make a scatter plot of the data. Describe the data set based on the scatter plot.
b. What do you expect to happen to the distance from the left end of the radio as the frequency gets higher?
c. What do you expect to happen to the distance from the left end of the radio as the frequency gets smaller?
Answer:
j3jejej
jwjitygueiejjejrjejejrjrjtjjturuejdvr7uejfnfnnrkrjdvev4j
Turning yards into feet
To convert yards to feet we multiply the given value by 3.
How is this determined?A yard is one linear yard. "Yd" is the yard symbol. It is equivalent to 36 inches or 3 feet. 1 yard equals 0.9144 metres in metres when measured in metres. Both the imperial and US customary systems of measuring use this unit. The most common use of yards is to measure the length of a field, such a sports field.
A foot can also be used to measure length. The letter "ft" stands for the foot. Twelve inches and one third of a yard make up one foot. Additionally, one foot is equal to 0.3048 metres. We must divide the provided value by 3.281 to translate the given value from feet to metres. In aviation and elevation, the foot is typically used to measure height or altitude. The height of a person is also expressed in feet and inches.
Hence, to convert yards to feet we multiply the given value by 3.
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The water rate for a city in North Carolina is $1.39 per 755 gallons of water used. a) What is the water bill if a resident of that city uses 30,000 gallons? b) How many gallons of water can a customer use if the water bill is not to exceed $150?
The gallons of water a customer can use if the water bill is not to exceed $150 is 81474.82 gallons
What is the water bill if a resident of that city uses 30,000 gallons?
In order to determine the water bill, we need to calculate the price of one gallon of water (rate) using the given information.
Since $1.39 per 755 gallons
rate = 1.39/ 755
The water bill if a resident of that city uses 30,000 gallons will be:
1.39/ 755 * 30000 = $55.23
The gallons of water a customer can use if the water bill is not to exceed $150 will be:
Let x be gallons of water
(1.39/ 755)x ≤ 150
x ≤ 150/(1.39/ 755)
x ≤ 81474.82 gallons
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is the data below at represented by a comparative bar chart, the bar representing which of these will be the tallest
If the data below are represented by a comparative bar chart, the bar representing the following will be the tallest:
Cat Failed
Which bar will be the tallest?The tallest bar of all of these will be the cat failed bar. A comparative bar chart is often designed to compare a set of observations.
From what we can see in the passage, it is clear that the bar chart representing the cat failed group contains the highest number and will likely have the tallest chart of all the others listed. So, the point is to look out for the observation with the highest number and the cat failed group meets the requirement.
Complete Question:
If the data below are represented by a comparative bar chart, the bar representing which of these will be the tallest?
Passed Failed
Cat. 24. 30
Dog 26. 28
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a hot air balloon decends 305 feet per minute for 4minutes then ascends at a rate of 215 per minute for another 2 minutes. find the total feet in altitude
The total feet in altitude is given by the equation A = -790 feet
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total feet in altitude be represented as A
Now , the equation will be
The hot air balloon descends 305 feet per minute for 4 minutes
So , the total descending will be a negative value , where
The feet in altitude descended = -305 x 4 = -1220 feet
Now , hot air balloon ascends 215 feet per minute for 2 minutes
So , the total ascending will be a positive value , where
The feet in altitude ascended = 215 x 2 = 430 feet
And , the total feet in altitude A = feet in altitude descended + feet in altitude ascended
Substituting the values in the equation , we get
The total feet in altitude A = -1220 + 430
On simplifying the equation , we get
The total feet in altitude A = -790 feet
Hence , the equation is A = -790 feet
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