Answer:
{(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)
Step-by-step explanation:
Sample space is the set of all possible outcomes of an experiment.
Here a person should choose one meal and a hot drink. Hence, each element in the set includes one meal and one beverage, which eliminates 2,because it indicates person choses oatmeal and pancakes which has no beverage. Sets should have elements in pairs so ,We should eliminate 3 ,4,5.
As a result person can choose
oatmeal as meal and coffee as drink
oatmeal as meal and tea for drink
eggs for meal tea for drink
eggs for meal coffee for drink
pancakes for meal tea for drink finally
pancakes for meal and coffee for drink
The sample space of a distribution is the list of possible options.
The sample space for the meal and the beverage is (a) {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)
From the question, the meals are:
Meals: Oatmeal, Eggs, Pancakes
And the beverages are:
Beverages: Coffee, Tea
This means that, the available selections are:
Oatmeal and CoffeeOatmeal and TeaEggs and CoffeeEggs and TeaPancakes and CoffeePancakes and TeaHence, the sample space is (a)
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Joanne's age is two times Devin's age and Devin is eight years older than Christina. If the sum of their ages is 76, what is Christina's age? Joanne's age? Devin's age?
Answer: Christina's age is 13, Joanne's age is 42 and Devin's age is 21.
Step-by-step explanation: If Devin's age is represented by d, then Joanne's age will be 2d because Joanne is two times Devin's age. Also, if Devin is 8 years older than Christina, then Christina's age would be d - 8. If the sum of their ages is equal to 76, then;
2d + d + (d - 8) = 76
2d + d + d - 8 = 76
4d - 8 = 76
Add 8 to both sides of the equation
4d = 84
Divide both sides of the equation by 4
d = 21
Therefore, Devin is 21 years old
Joanne is 42 years old and
Christina is 13 years old.
Christina is 13 years old, Devin is 21 years old, and Joanne is 42 years old. This is found by defining Christina's age as x, then setting up and solving an equation based on the problem's provided relationships.
Explanation:In this math problem, we have three individuals: Joanne, Devin, and Christina, and we know their ages in relation to each other's.
We know that Joanne's age is two times Devin's. We also know Devin is eight years older than Christina. Finally, we know the sum of all three ages is 76.
Let's denote Christina's age as x. Consequently, Devin's age would be x + 8 because he is 8 years older than Christina. As Joanne's age is two times Devin's age, Joanne's age would be 2*(x + 8).
The sum of their ages is 76, which gives us the following equation:
x (Christina's age) + x + 8 (Devin's age) + 2*(x + 8) (Joanne's age) = 76.
Solving this equation, we get:
4x + 24 = 76
Subtract 24 from both sides gives us 4x = 52, and dividing both sides by 4 gives x = 13.
So, Christina's age is 13, Devin's age is 13 + 8 = 21, and Joanne's age is 2*21 = 42.
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Allysa spent $35 to purchase 12 chickens . She bought two different types of chickens. Americana chickens cost $3.75 each and Delaware chickens cost $2.50 each
Final answer:
To solve the problem, set up a system of equations representing the total number of chickens and the total cost. Solve the system using substitution or elimination method to find the number of Americana and Delaware chickens that Allysa bought.
Explanation:
Allysa spent a total of $35 to purchase 12 chickens. Let's denote the number of Americana chickens as 'x' and the number of Delaware chickens as 'y'. The cost of Americana chickens is $3.75 each, while the cost of Delaware chickens is $2.50 each. Based on this information, we can establish two equations:
x + y = 12 (equation 1, representing the total number of chickens)
3.75x + 2.50y = 35 (equation 2, representing the total cost)We can solve this system of equations using substitution or elimination method. Let's use substitution:
From equation 1, we can express x in terms of y: x = 12 - ySubstitute the value of x in equation 2: 3.75(12 - y) + 2.50y = 35Simplify and solve for y: 45 - 3.75y + 2.50y = 35Combine like terms: -1.25y = -10Divide both sides by -1.25 to solve for y: y = 8Substitute the value of y back into equation 1 to find x: x = 12 - 8 = 4Therefore, Allysa bought 4 Americana chickens and 8 Delaware chickens.
Alyssa purchased 4 Americana chickens and 8 Delaware chickens. By solving the system of equations, we determined the number of each type of chicken. At the end of the first week, she expects to take in $22.5 from selling eggs.
To determine the number of Americana chickens, A, and the number of Delaware chickens, D, Alyssa purchased, we set up a system of equations based on the given information:
The total number of chickens purchased is 12: A + D = 12.The total cost of the chickens is $35: 3.75A + 2.5D = 35.Now, to solve the system, we can use substitution or elimination. Let's use substitution:
From the first equation, we can express A in terms of D: A = 12 - D.Substitute this expression for A into the second equation: 3.75 x (12 - D) + 2.5D = 35.Simplify and solve for D: 45 - 3.75D + 2.5D = 35, which simplifies to D = 8.Substitute D back into the expression for A: A = 12 - 8 = 4.So, Alyssa purchased 4 Americana and 8 Delaware chickens.
To determine Alyssa's expected income from selling eggs at the end of the first week:
Total eggs per day: 2×4 (Americana chickens)+1×8 (Delaware chickens) = 8+8=16Total eggs in a week: 16 eggs/day x 7 days = 112 eggs.She sells eggs by the dozen, so 112 eggs / 12 = 9 dozens (approximately) . Income from selling 9 dozens at $2.50 each: 9 x $2.50 = $22.5.Therefore, Alyssa expects to take in $22.5 at the end of the first week from selling eggs.
Complete Question:
Alyssa spent $35 to purchase 12 chickens. She bought two different types of chickens. Americana chickens cost $3.75 each and Delaware chickens cost $2.50 each. Write a system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased. Determine algebraically how many of each type of chicken Allysa purchased. Each Americana chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day. Allysa only sells eggs by the full dozen for $2.50. Determine how much money she expects to take in at the end of the first week with her 12 chickens.
Help me Find the arc length of a circle in terms of pi
Answer:
3
Step-by-step explanation:
Recall that the full circumference of a circle can be represented by an angle of 360°.
In our case, we are asked to find the arc AB on the circumference of a circle that is represented by an angle of only 20°
hence the fraction of the circumference that is represented by arc AB
= 20° / 360°
= 1/18
we can thus say that the length of AB is 1/18 of the total circumference
Arc Length of AB
= (1/18) of total circumference
= (1/18) x 2π x radius
= (1/18) x 2π x 27
= 3π units
Answer:
3π Radian
Step-by-step explanation:
[tex]we \: have \: \: \: s = r \alpha \\ here \: s = arc \: length \\ r = radious \: of \: circle \\ \alpha = centre \: angle \: of \: current \: circle \\ so \\ s = 27 \times 20 \\ \: \: \: = 540 \\ \: \: \: \: \: = 540 \times \frac{\pi}{180} \\ \\ \: \: \: \: = 3\pi \: radian[/tex]
During statistical analysis, the investigator may consider searching for statistical associations among various groups that may suggest a cause–effect relationship, without having generated prior hypotheses about these groups. This is known as ____.
.
Answer:
This is known as Data dredging.
Step-by-step explanation:
In order for any statistical analysis to be significant, a researcher has to first generate a hypothesis.
Data dredging is trying to uncover patterns in data that can be presented statistically without devising a clear hypothesis by use data mining. It is also referred to as data fishing or p-hacking.
In this case any correlation (relationship between cause-effect)will be purely by chance.
Therefore, the investigator is Data dredging
Which graph represents g(x)=−(x−3)2−5 ?
Answer:
see below
Step-by-step explanation:
The leading minus sign tells you the graph opens downward. (x-3) in the squared term tells you the x-coordinate of the vertex is x=3. The graph that matches these characteristics is shown below.
A drive has a maximum speed of 10,000 revolutions per minute. If a disc has a diameter of 14 cm, what is the linear speed, in km/h, of a point 6 cm from the center if the disc is spinning at a rate of 6000 revolutions per minute?
The point 6 cm away from the center travels in a circle of circumference 2π*(6 cm) = 12π cm, so that it covers this distance per revolution, 12π cm/1 rev.
So the disk has a linear speed of
(6000 rev/min) * (12π cm/rev) = 72,000π cm/min
which is equivalent to
(72,000π cm/min) * (1/100,000 km/cm) * (60 min/h)
or approximately 135.7 km/h.
Determine whether the value given below is from a discrete or continuous data set. The volume of cola in a can is 12.1 oz?A. A discretediscrete data set because there are infinitely many possible values and those values can be countedvalues can be counted B. A continuouscontinuous data set because there are infinitely many possible values and thosethere are infinitely many possible values and those values cannot be countedvalues cannot be counted C. The data set is neither continuous nor discrete. D. A discretediscrete data set because there are a finite number of possible valuesthere are a finite number of possible values
Answer:
B. A continuous continuous data set because there are infinitely many possible values and those there are infinitely many possible values and those values cannot be counted values cannot be counted
Step-by-step explanation:
Given that the volume of cola in a can is 12.1 oz
We have to find out whether discrete or continuous.
We can say a random variable is discrete if it takes values which have one to one correspondence with the set of natural numbers.
continuous if a one to one correspondence with set of natural numbers cannot be established.
In our case, we have volume of cola as 12.1 oz. Between two readings say,12.1 oz and 12.15 oz. there may be infinite other values which the volume can take
i.e. this is a continuous data.
B. A continuous continuous data set because there are infinitely many possible values and those here are infinitely many possible values and those values cannot be counted values cannot be counted
is right answer
The volume of cola in a can, measured as 12.1 oz, is an example of continuous data because it could theoretically take any value in a certain range, unlike discrete data which can only have certain distinct values.
Explanation:The volume of cola in a can being 12.1 oz represents continuous data. This is because continuous data can take on any value within a certain range or interval. In this case, the volume of the cola in the can could theoretically have been any number between certain limits, for example, 0 to 12.2 oz. This differs from discrete data, which can only take certain distinct or separate values, such as the number of cans of cola you might buy (1,2,3, etc.).
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Elizabeth made a scale drawing of her school's basketball court before devising a winning strategy for her team. The dimensions of the court are 15\text{ m}15 m by 27\text{ m}27 m. Move points to recreate Elizabeth's drawing on the grid below.
Answer:
the answer is 16ft
step-by-step explanation:
in order to make a triangle with non-zero area, the sum of the shorter two sides must be greater than the longest side.
here, 4 + 4 > 7, so the lengths can form a triangle.
The correct answer was given: Brain
7+8= 15
hope this
The correct answer was given: Brain
36 cm is the final : )
The Answer is
5 by 9
The desert temperature, H, oscillates daily between 40◦F at 5 am and 80◦F at 5 pm. Write a possible for- mula for H in terms of ????, measured in hours from 5 am.
Answer:
[tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex]
Step-by-step explanation:
We have been given that the desert temperature, H, oscillates daily between 40◦F at 5 am and 80◦F at 5 pm. We are asked to write a formula H in terms of t, measured in hours from 5 am.
We will use cosine function to write our required formula.
[tex]y=A\text{cos}[B(x-C)]+D[/tex], where,
A = Amplitude,
[tex]\text{Period}=\frac{2\pi}{|B|}[/tex]
C = Phase shift,
D = Vertical shift.
First of all, we will find amplitude using maximum and minimum values as:
[tex]A=\frac{\text{Maximum value}-\text{Minimum value}}{2}[/tex]
[tex]A=\frac{80-40}{2}[/tex]
[tex]A=\frac{40}{2}[/tex]
[tex]A=20[/tex]
Since period is 24 hours (5 am to 5 pm), so let us find B as:
[tex]24=\frac{2\pi}{|B|}[/tex]
[tex]B=\frac{2\pi}{24}[/tex]
[tex]B=\frac{\pi}{12}[/tex]
[tex]\text{Vertical shift}=\frac{\text{Maximum value}+\text{Minimum value}}{2}[/tex]
[tex]D=\frac{80+40}{2}=\frac{120}{2}=60[/tex]
There is no phase shift.
Since temperature is minimum when [tex]t=0[/tex], so we will use negative cosine as:
[tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex]
Therefore, our required function would be [tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex].
To model the desert temperature, use the sinusoidal function H(t) = 20 * cos(π/12 * t) + 60, which captures daily temperature changes between 40°F and 80°F, with parameters tuned to fit the given data.
To write a formula for the desert temperature H in terms of t, measured in hours from 5 am, we can use a sinusoidal function that models the daily temperature oscillation.
We know:
The minimum temperature is 40°F at 5 amThe maximum temperature is 80°F at 5 pmThe period of the oscillation is 24 hoursThe general form for the sinusoidal function is:
H(t) = A * sin(B*(t - C)) + D
Where:
A is the amplitudeB is related to the periodC is the phase shiftD is the vertical shiftFrom the given data:
A (amplitude) = (80 - 40) / 2 = 20°FVertical shift D = (80 + 40) / 2 = 60°FThe period is 24 hours, so B = 2π / 24 = π / 12The temperature is minimum at 5 am (t = 0), we use a cosine function (which reaches the minimum at 0) shifted by 5 hours. Hence, C = 0Thus, the sinusoidal function becomes:
H(t) = 20 * cos(π/12 * t) + 60.
Billy left home at 9 a.M. And rode his bicycle to the park at an average speed of 10 miles per hour here I got the park at 9:30 a.M. How many miles from the park is Billy's home so I explain how you got your answer
Answer:
Park is 5 miles from Billy's home.
Step-by-step explanation:
Given:
Billy left home at 9 a.m. And rode his bicycle to the park at an average speed of 10 miles per hour here and got the park at 9:30 a.m.
Now, to find the distance from park to Billy,s home.
Time it took Billy to rode his bicycle from park to home is from 9.30 a.m to 9.30 p.m.
So, the time = (9.30 - 9.00) = 30 minutes
[tex]=\frac{30}{60}[/tex] [tex]=0.5\ hour.[/tex]
Speed = 10 miles per hour.
Now, to get the distance from park to Billy's home we put formula:
[tex]Distance=Speed\times Time.[/tex]
[tex]Distance=10\times 0.5[/tex]
[tex]Distance=5\ miles.[/tex]
Therefore, park is 5 miles from Billy's home.
Mr.Kork sold his car for $8,400. This was $200 more than two fifths of what he had paid for the car originally. How much had Mr. Kork paid for the car?
Answer:
He paid = $20,500
Step-by-step explanation:
Let the amount he bought the car originally be X
so from the statement,
(2/5)*X + $200 = $8,400
(2/5)*X = $8,400 - $200
solving for X
X = $8200 * 5/2
X = $20,500
A conveyor belt moves bottles at a constant speed of 120 centimeters per second. If the conveyor belt moves a bottle from a loading dock to an unloading dock, is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)(1) It takes the conveyor belt less than 1.2 minutes to move the bottle from the loading dock to the unloading dock.
(2) It takes the conveyor belt more than 1.1 minutes to move the bottle from the loading dock to the unloading dock.
Answer:
The distance that the conveyor belt moves the bottle is less than 90 meters
Step-by-step explanation:
Speed of the conveyor belt
120 cm/s
Time it takes to move the conveyor belt less than 1.2 minutes to move the bottle from the loading dock to the unloading dock.
But 60s = 1 minute
This gives
1.2 minutes = 1.2×60s seconds = 72 seconds
But speed = distance/time
so that distance = speed × time = 120cm/s ×(<72s)
From where distance = <8640cm<90m (90m×100=9000cm)
Time it takes to move the conveyor belt more than 1.1 minutes to move the bottle from the loading dock to the unloading dock.
Again 60s = 1 minute
This gives
1.1 minutes = 1.1×60s seconds = 66 seconds
Time it takes is more than 66s
But speed = distance/time
so that distance = speed × time = 120cm/s × (>66s)
From where distance >7920cm
However
7920cm < 90m (90m×100=9000cm)
So that
The distance that the conveyor belt moves the bottle is less than 90 meters
The distance between (0,5) and (6,-1) is
Answer:
6sqrt(2) units (exact form)
= 8.49 units (3 sf)
Step-by-step explanation:
sqrt[(-1-5)²+(6-0)²]
sqrt[(-6)² + 6²]
sqrt(36 + 36)
sqrt(72)
= 6sqrt(2) units (exact form)
= 8.49 units (3 sf)
Return the bottles: Shawna Return some bottles to the store. She received 1.85 in quarters, dimes, nickels. Use these clues to determine the number of each kind of coin. She received at least one of each coin. There are more dimes and nickels. There is an even number of quarters. There are as many quarters and nickels together as there are dimes.
Answer:
There are 7 dimes, 3 nickels, and 4 quarters.
Each peanut butter snack costs $2 each chocolate snack costs $3 how much does it cost to buy 6 peanut butter snacks and 8 chocolate snacks write an equation
A female bunny gained three pounds per week for six weeks. A male bunny gained 8 pounds per week for six weeks. How many more pounds did the male bunny gain than the female bunny?
Answer:
Step-by-step explanation:
A female bunny gained three pounds per. It means that the total number of pounds that the female bunny gained in 6 weeks would be
3 × 6 = 18 pounds.
A male bunny gained 8 pounds per week. It means that the total number of pounds that the male bunny gained in 6 weeks would be
8 × 6 = 48 pounds.
Therefore, the number of pounds that the male bunny gained more the female bunny would be
48 - 18 = 30 pounds
Step-by-step explanation:
Female Bunny: Doe
Male Bunny: Buck
A doe gained three lbs per week for six weeks.
3 x 6 = 18
A buck gained eight lbs per week for six weeks.
8 x 6 = 48
How many more lbs did the buck get than the doe?
48-18= 30
Answer:
The male bunny gained thirty more pounds than the female bunny.
The buck gained 30 more lbs than the doe.
Find all numbers such that the square of the number is 48 more than double the number. If you find more than one, then list all the numbers you find in increasing order, separated by commas.?
Answer:
-6, 8
Step-by-step explanation:
Let the numbers be represented by y
Square of y = y^2
Double y = 2 × y = 2y
Square of the number is 48 more than double the number is written mathematically as
y^2 = 2y +48
y^2 - 2y - 48 = 0
This is a quadratic equation and can be solved by method of factorisation
y^2 -2y - 48 = 0
y^2 + 6y - 8y - 48 = 0
(y^2 + 6y) - (8y - 48) = 0
y(y + 6) - 8(y + 6) = 0
(y + 6)(y - 8) = 0
y = -6, 8
The numbers are -6, 8
Answer:
8, -6
Step-by-step explanation:
Let the number be $n$, so we have $n^2 =48 + 2n$. Rearranging this equation gives $n^2 -2n-48=0$ and factoring gives $(n-8)(n+6)=0$. So, the numbers that fit the problem are $\boxed{n = -6~\text{and}~n = 8}$.
A phone company offers two monthly plans. In plan A, the customer pays a monthly fee of $35 and then an additional 9 cents per minute of use. In Plan B, the customer pays a monthly fee of $55.70 and then an additional 6 cents per minute of use. For what amounts of monthly phone use will Plan A cost less than Plan B? Use m for the number of minutes of phone use, and solve your inequality for m.
Answer:
Lesser than 6.9 minutes
Step-by-step explanation:
Let m represent the number of minutes of phone use with either plan A or plan B.
In plan A, the customer pays a monthly fee of $35 and then an additional 9 cents(9/100 = $0.09) per minute of use. This means that the total cost of m minutes would be
0.09m + 35
In Plan B, the customer pays a monthly fee of $55.70 and then an additional 6 cents(6/100 = $0.06) per minute of use. This means that the total cost of m minutes would be
0.06m + 55.70
Therefore, for the amounts of monthly phone use for which Plan A will cost less than Plan B, it becomes
0.09m + 35 < 0.06m + 55.70
0.09m - 0.06m < 55.70 - 35
0.03m < 20.7
m < 20.7/3
m < 6.9
Two horses ran from the same place at the same time. One horse ran at a speed of 16 m/sec and the other ran at a speed of 18 m/sec. How far apart were they in 1 minute? In 5 minutes? In 8 minutes?
Answer:
1 minute = 1080 - 960 = 120 m
5 minutes = 5400 - 4800 = 600 m
8 minutes = 8640 - 7680 = 960 m
Step-by-step explanation:
I think the easiest way is to just see how far they get at each time. So I'm going to go one horse at a time.
16 m/s
1 minute = 60 seconds, every second is 16 meters so 16 m/s * 60 s = 960 m
5 minutes = 300 seconds so 16 m/s * 300 s = 4800 m
8 minutes = 480 seconds, 16 m/s * 480 s = 7680 m
I also want to point out that unites cancel out. m/s * s is kinda like variables so the seconds being multiplied by m/s cancels witht eh seconds in the denominator.
Now the next horse
18 m/s
1 minute totals to 1080 m
5 minutes = 5400 m
8 minutes = 8640 m
Now we take the differences of each time
1 minute = 1080 - 960 = 120 m
5 minutes = 5400 - 4800 = 600 m
8 minutes = 8640 - 7680 = 960 m
Another way to do this is to take the difference of speed and then multiply that by the time. so 18-16 = 2, then multiply each time by 2. For me it just makes more intuitive sense the way I showed.
A and B play a game in which they alternately toss a pair of dice. The one who is first to get a total of 7 wins the game. Find the probability that (a) the one who tosses first wins the game
Answer: the probability that the first toss wins is:
P = 1/6 or 0.1667
Step-by-step explanation:
A die has six sides (that is 6 outcome per die)
For a pair of dice:
The Total number of possible outcomes = 6 × 6 = 36
The possible outcomes of 7 is:
(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)
= 6
The probability P of getting 7 is:
P = number of possible outcomes of 7/total number of possible outcomes
P = 6/36 = 1/6
The probability that the first toss wins
P = 1/6 or 0.1667
The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?a. 47.72%
b. 97.72%
c. 37.45%
d. 2.28%
e. 4.56%
Alexa is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Alexa will earn $20 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties on 8 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Alexa's songs were played. Define the variables that you use to write the system.
Answer:the equations are
x + y = 8
20x + 110y = 340
Step-by-step explanation:
Let x represent the number of commercials on which Alexa's songs were played.
Let y represent the number of movies on which Alexa's songs were played.
The total number of movies and commercials on which Alexa earned is 8. It means that
x + y = 8 - - - - - - - - - - - -1
Alexa will earn $20 every time one of her songs is played in a commercial and $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties. This means that
20x + 110y = 340 - - - - - - - - - - - -2
Answer:
variables:
c= the number of commercials
m= number of movies
system of equations:
20c+110m= 340
c+m= 8
A square that is 5yd on a side is placed inside a rectangle that has a width of 11yd and a length of 17 yd. What is the area of the region inside the rectangle that surrounds the square?
Answer: 162 sq. yds.
Step-by-step explanation:
Given : A square that is 5yd on a side is placed inside a rectangle that has a width of 11yd and a length of 17 yd.
Then , Area of rectangle = length x width
= 11 yd x 17 yd = 187 sq. yds.
Area of square = (side)²
= (5 yd)² = 25 sq. yds.
Now , the area of the region inside the rectangle that surrounds the square will be Area of rectangle - Area of square
= 187 sq. yds.- 25 sq. yds.
=162 sq. yds.
Hence, the area of the region inside the rectangle that surrounds the square is 162 sq. yds. .
The sum of three guys ages is 62. Angelo is two years younger than Aaron and Alfred is four years older than twice Aaron's age. What are the ages of each guy?
Answer: Angelo is 13 years old.
Aaron is 15 years old
Alfred is 34 years old
Step-by-step explanation:
Let x represent the age of Angelo.
Let y represent the age of Aaron.
Let z represent the age of Alfred
The sum of three guys ages is 62. It means that
x + y + z = 62 - - - - - - - - - - -1
Angelo is two years younger than Aaron. It means that
x = y - 2
Alfred is four years older than twice Aaron's age. It means that
z = 2y + 4
Substituting x = y - 2 and z = 2y + 4 into equation 1, it becomes
y - 2 + y + 2y + 4 = 62
4y + 2 = 62
4y = 62 - 2 = 60
y = 60/4 = 15
x = y - 2 = 15 - 2
x = 13
z = 2y + 4 = 2 × 15 + 4
z = 34
These triangle are similar find the value of x
A. 2
B.6
C.4
D.3
Answer:
4
Step-by-step explanation:
in similarity the ratio of the similar sides is the same i.e
10/5 =8/x
2x=8
x= 4
Use the ten-frame and a crayon to show how to decompose the numbers into tens and ones
Answer:
1 Suppose these numbers are boxes and the dots 2 represent the crayon color to show that they are filled.3 If we have 1 ten frame we will use it one ten and if we have 4 5 ones then they will not be a ten. 2 tens would make a5 twenty similarly 3 tens would make a thirty.6789101 If we add a single 10 and 5 ones the answer would be 152 Other examples would adding two tens and 7 ones which 3 would make 27.45Another way to decompose the number would be
43 taking the 4 of the left with tens like 40 ( 4*10) and 3 of the right as three separate ones ( 3*1= 3) .Adding 10s four times with three one times would make 43
Final answer:
The student's question deals with decomposing numbers into tens and ones and relates to the concept of powers of ten in mathematics. Powers of ten notation is foundational in understanding place value, large, and small numbers. By breaking down numbers into tens and ones, students can grasp numerical values more effectively.
Explanation:
The question pertains to the mathematical concept of decomposing numbers into tens and ones using a ten-frame and involves powers of ten. In mathematics, numbers can be broken down into tens and ones to understand their value better. It's essential to note that each place in our numbering system is ten times greater than the place to the right of it. This is part of the reason we use powers-of-ten notation.
Decomposing Numbers
When decomposing a number like 24, for example, we can break it down into two tens (20) and four ones (4). If we used a ten-frame, we would fill in two full ten-frame grids to represent the tens and then add four individual marks to represent the ones.
Understanding Powers of Ten
When we discuss powers of ten, we're talking about how the counting system is structured, with each place value being ten times greater than the one before it. The digital numbering system got started because humans have ten fingers and counted with them, leading to an increase by tens.
A positive exponent, like 10³, tells us to multiply the base (10) by itself the number of times indicated by the exponent (3), which results in 1000. On the other hand, a negative number as the power indicates a division, so a power like 10⁻¹=0.1. If we have 10⁻⁴, it means 0.0001, which is ten times smaller than 0.001 (10⁻³).
When dividing by powers of ten, we move the decimal point to the left by the number of zeros indicated by the power. This process simplifies understanding large and small numbers by expressing them in terms of powers of ten or powers of one thousand for very large numbers.
What is the value of x?
Answer:
x=22.5
Step-by-step explanation:
BM||DT
Using Intercept theorem/Intercept theorem
[tex]\frac{6}{6+15} =\frac{9}{9+x}[/tex]
6(9+x)=9*21
54+6x=189
6x=135
x=22.5
At least I think so
*Will Give Brainliest* Consider the Piece-Wise graph described by the following equation:
Determine the coordinates of the point on the graph where x=3.
A. (3, 1)
B. (3, 3)
C. (3, 5)
D. (3, 13)
The coordinates of the point on the graph when x=3 are C. (3, 5)
Step-by-step explanation:
Given piece-wise function is:
[tex]y = \left \{ {{4x+1\ \ \ x<3 } \atop {2x-1\ \ \ x\geq 3 }} \right.[/tex]
In order to determine the coordinates of the point on the graph where x=3 we will see which part of the function we have to consider as the function is in two pieces.
By observing we see that the second piece of function will be used as it is for x≥ 3 so it includes 3.
Putting x = 3 in y = 2x-1
[tex]y = 2(3) -1\\y = 6-1\\y = 5[/tex]
Hence,
The coordinates of the point on the graph when x=3 are C. (3, 5)
Keywords: Functions, graph
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PLEASE PLEASE HELP ME!!! WILL GIVE BRAINLIEST!!!!
The data to represent average test scores for a class of 19 students includes an outlier value of 81. If the mean, including the outlier of 81, equals 94, which statement is always true about the new data when the outlier is removed?
A. The median would increase.
B. The median would decrease.
C. The mean would increase.
D. The mean would decrease.
Answer:
the answer would be C. The mean would increase.
Step-by-step explanation:
The mean has increased, the correct option is C.
What is an Average?Average is the mean of the data set obtained by summing all the values of the data set and then dividing it by the number of data in the set.
The total number of students is 19.
The outlier is 81
An outlier is a number that is different from the other set of numbers, it is obtained due to variability in the observation or due to experimental error.
The mean including the outlier of 81 equals 94.
For the mean including the outlier, it can be observed that the outlier is the left outlier or the smallest number.
Let x represent the sum of all the test scores
x / 19 = 94
x = 94 * 19
x = 1786
The sum without the outlier is 1786 - 81 = 1705
The mean without the outlier is
= 1705 / 18
= 94 13 /18
This is greater than 94.
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A bus traveled 336 traveled 336 miles in 7 hours. If the continues at the same number of miles per hour, how many miles will the bus travel in 15 hours? Explain
Answer:
The bus traveled 720 miles with constant speed.
Step-by-step explanation:
Given,
Distance = 336 miles
time = 7 hrs
We have to find out the distance traveled by the bus in 15 hours with constant speed.
Solution,
Since we know that the speed is equal to distance divided by time.
So the equation can be framed as;
[tex]speed=\frac{336}{7}=48\ mi/h[/tex]
Now time = 15 hrs
Distance traveled is equal to speed multiplied with time.
So the equation can be framed as;
[tex]Distance\ traveled=48\times15=720\ miles[/tex]
Hence The bus traveled 720 miles with constant speed.