Answer:
111 pounds
Step-by-step explanation:
A boy holding a stack of 9 identical books steps on a scale and weighs 138 pounds.
If the boy's weight is represented as B and the books are represented as b, this implies that:
B + 9b = 138
The boy then holding a stack of 3 of the same books again steps on the scale and weighs 120 pounds. This implies that:
B + 3b = 120
This has yielded two simultaneous equations:
B + 9b = 138
B + 3b = 120
We can solve by subtracting the second from the first.
B + 9b = 138
- (B + 3b = 120)
-----------------------
=> 6b = 18
b = 18 / 6 = 3 pounds
This means that each book weighs 3 pounds.
Putting b back in the second equation:
B + (3 * 3) = 120
B + 9 = 120
B = 120 - 9
B = 111 pounds
Therefore, the boy weighs 111 pounds.
Answer:
The boy would weigh 111 lbs.
Explanation:
Its complicated
What is the product of [2cis 33˚][3cis 22˚]
Answer:
The product of the complex numbers is 6cis55°Step-by-step explanation:
Given the complex numbers in polar cordinates
[2cis 33˚][3cis 22˚]
Generally, if z = rcis[tex]\theta\\[/tex], then z = r(cos[tex]\theta+isin\theta[/tex])
2cis33° = 2(cos33°+isin33°)
3cis22° = 3(cos22°+isin22°)
Taking tthe product of both complex numbers;
[2cis 33˚][3cis 22˚] = [2(cos33°+isin33°)][3(cos22°+isin22°)]
= 6{cos33cos22+icos33sin22+isin33cos22+i²sin33sin22}
since i² = 1
= 6{cos33cos22+icos33sin22+isin33cos22-sin33sin22}
= 6{(cos33cos22-sin33sin22)+i(cos33sin22+sin33cos22)}
Applying the trigonometric identity as shown;
cos(A+B)= cosAcosB-sinAsinB and;
sin(A+B)= sinAcosB + cosAsinB
[2cis 33˚][3cis 22˚] = 6{(cos(33+22)+ i(sin(33+22)}
[2cis 33˚][3cis 22˚] = 6(cos55°+isin55°)
[2cis 33˚][3cis 22˚] = 6cis55°
The product of the complex numbers is 6cis55°
Solve the equation y=2x^2-x-6 using the quadratic formula show the steps to solving
Answer:
[tex]x1 = 2 \\ x2 = - \frac{3}{2} [/tex]
Step-by-step explanation:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{1 + - \sqrt{ {( - 1)}^{2} - 4(2)( - 6) } }{2(2)} \\ x = \frac{1 + - \sqrt{1 + 48} }{4} \\ x = \frac{1 + - \sqrt{49} }{4} \\ x = \frac{1 + - 7}{4} \\ \\ x1 = \frac{1 + 7}{4} = \frac{8}{4} = 2 \\ x2 = \frac{1 - 7}{4} = - \frac{6 }{4} = - \frac{3}{2} [/tex]
Answer:
x = -1 ± √7
The picture explains the rest...
Which expression is equivalent to (x Superscript 27 Baseline y) Superscript one-third?
x cubed (RootIndex 3 StartRoot y EndRoot)
x Superscript 9 Baseline (RootIndex 3 StartRoot y EndRoot)
x Superscript 27 Baseline (RootIndex 3 StartRoot y EndRoot)
x Superscript 24 Baseline (RootIndex 3 StartRoot y EndRoot)
Answer:
x Superscript 9 Baseline (RootIndex 3 StartRoot y EndRoot)
OR x^9/(∛y)
Step-by-step explanation:
Given the indicinal equation
(x^27/y)^1/3
To find the corresponding expression, we will simplify the equation as shown:
(x^27/y)^⅓
= (x^27)^⅓/y⅓
= {x^(3×9)}^⅓/y⅓
= x^9/y⅓
= x^9/(∛y)
The right answer is x Superscript 9 Baseline (RootIndex 3 StartRoot y EndRoot)
A pizza with radius 7 in. is cut into 12 equal-sized pieces. What is the area of each piece? Round to the nearest hundredth of an inch.
Each pizza slice has an area of approximately 12.82 square inches, rounded to the nearest hundredth.
To find the area of each pizza slice, we first need to find the total area of the pizza and then divide it by the number of slices.
The formula for the area of a circle is [tex]\( A = \pi r^2 \)[/tex], where [tex]\( \pi \)[/tex] is approximately 3.14 and r is the radius of the circle.
Given that the radius of the pizza is 7 inches, we can calculate the total area of the pizza:
[tex]\[ A_{\text{total}} = \pi \times (7)^2 \]\[ A_{\text{total}} = 3.14 \times 49 \]\[ A_{\text{total}} \approx 153.86 \text{ square inches} \][/tex]
Now, to find the area of each pizza slice, we divide the total area by the number of slices (12):
[tex]\[ A_{\text{each slice}} = \frac{A_{\text{total}}}{12} \]\[ A_{\text{each slice}} \approx \frac{153.86}{12} \]\[ A_{\text{each slice}} \approx 12.82 \][/tex]
So, the area of each pizza slice is approximately 12.82 square inches.
A water balloon is shot into the air with an upward velocity of 95 ft/s. The balloon is released 12 feet above the ground. Write a function that represents the height h of the balloon in feet after t seconds. How long will it take the balloon to reach its maximum height? What will the maximum height be? (ALL ANSWERS SHOULD BE EXPRESSED TO THE NEAREST HUNDREDTH.)
Function: ____________________
Time to reach the maximum height: ___________________
Maximum Height: ______________________
Approximately how many whole seconds will it take to hit the ground?: _________________
Answer:
1. h = h₀ + u×t - 1/2×g×t²
2. 2.95 s
3. 152.14 ft
4. 3.07 s
Step-by-step explanation:
The given parameters are;
Vertical velocity of the balloon = 95 ft/s
Height from which the balloon is released = 12 feet
The function is h = h₀ + u×t - 1/2×g×t²
Where:
h = Height of the balloon at time t
h₀ = Initial height of the balloon = 12 feet
u = Initial upward velocity of the balloon = 95 ft/s
t = Time duration of motion
g = Acceleration due to gravity = 32.2 ft/s²
2. The time to maximum height is found from;
v = u - g·t
Where:
v = Final velocity = 0 m/s at maximum height
∴ 0 = 95 - 32.2 × t
32.2·t = 95
t = 95/32.2 = 2.95 s
Therefore, the time it will take to reach maximum height = 2.95 s
3. From h = h₀ + u×t - 1/2×g×t², we have;
h = 12 + 95×2.95 - 1/2×32.2×2.95² = 152.14 ft
4. Therefore;
152.14 = 0×t + 1/2 × 32.2 × t²
t² = 152.14/16.1 = 9.45 s
t = √9.45 = 3.07 s
Answer:
The function is: y(t) = 12 + 95*t - 16.085*t²
The time it'll take to reach the maximum height is: 2.95 s
The maximum height is: 152.27 ft
The time it'll take to hit the ground is: 12 s
Step-by-step explanation:
The water ballon is under the constant acceleration of gravity, therefore it's movement can be modelled by the equations that describe constant acceleration movement, as shown below:
y(t) = y(0) + v(0)*t - 0.5*g*t²
The acceleration is negative, because they are contrary to the movement. Applying the data form the problem, we have:
y(t) = 12 + 95*t - 0.5*32.17*t²
y(t) = 12 + 95*t - 16.085*t²
This equation describes a parabolla, therefore the time at which it achieves the maximum height is the "x" coordinate for the vertex, which can be found by using the formula below:
t = (-b)/[2*a]
t = (-95)/[2*(-16.085)] = -95/(-32.17) = 2.95 s
And the maximum height is:
y(2.95) = 12 + 95*2.95 - 16.085*(2.95)² = 152.27 ft
The time it'll take to reach the ground is:
y(0) = 12 + 95*0 - 16.085*(0)² = 12 s
People use water to cook, clean, and drink every day. An estimate of 32.5% of the water used each day is for drinking. If a family uses 68.9 gallons of water a day for drinking, how many gallons do they use every day
Answer:
they use 212 gallons
Step-by-step explanation:
(68.9/32.5)*100
the division by 32.5 is to determine the amount of water one percent would be, so multiplying it by 100 will give you the total amount
Final answer:
To find the total daily water usage of a family using 68.9 gallons per day for drinking, which is 32.5% of their total usage, you divide the amount of water for drinking by 0.325. The calculation shows the family uses about 212 gallons of water per day.
Explanation:
The question asks us to calculate the total daily water usage of a family if they use 68.9 gallons per day for drinking, which represents 32.5% of their total daily use. To find the total water use, we divide the amount of water used for drinking by the percentage that represents drinking water.
Step-by-step Calculation:
Convert the percentage to a decimal by dividing 32.5 by 100, giving us 0.325.
Divide the gallons used for drinking by this decimal: 68.9 gallons / 0.325 = 212 gallons (rounded to the nearest whole gallon).
Therefore, the family uses approximately 212 gallons of water every day for all purposes.
A cyclist rides her bike at a rate of 9 kilometers per hour. What is the rate in kilometers per minute? How many kilometers will the cyclist travel in 2 minutes
Answer: 0.15km/min and 0.3km in 2 mins
Step-by-step explanation:
Given Data:
Cyclists speed = 9km/hr
1. Some traveling 60 km/h is traveling one km/min
60/60= 1 km/min
Rate in km/min
= 9km/hr / 60min
= 3/20 km/min
= 0.15 km/min
Kilometers travelled in 2mins
= 2 / 60
= 1 / 30
= 9km/hr * 1 / 30
= 9 / 30
= 0.3 km in 2mins
Answer:
Rate(in km/min) = 0.15 km/min
Distance traveled in 2 mins = 0.3 km
Step-by-step explanation:
Rate = 9 km/hr
1 hr = 60 mins
In 60 minutes, the cyclist rides 9 km
in 1 minute, the cyclist will ride 9/60 km
Therefore, the rate in km/min = 9/60 km/min
Rate(in km/min) = 0.15 km/min
Since the cyclist rides 0.15 km in 1 min,
In 2 mins, the cyclist will ride 0.15 * 2 km = 0.3 km
Distance traveled in 2 mins = 0.3 km
A silo is a composite of a cylindrical tower with a cone for a roof. Find the volume of the silo if the
radius of the base is 120 feet, the height of the roof is 25 feet, and the height of the entire silo is 130
feet.
Answer:
5127079.21 cubic feet
Step-by-step explanation:
The silo is in the shape of a cylinder and a cone.
The volume of the silo will be the sum of the volumes of the cylinder and the cone.
Therefore, its volume is:
[tex]V = \pi r^2h + \frac{1}{3} \pi rH[/tex]
where r = radius of cylinder and cone
h = height of cylinder
H = height of cone
The radius of the base is 120 feet, the height of the roof (cone) is 25 feet. The height of the entire silo is 130 feet. This means that the height of the cylinder is:
130 - 25 = 105 feet
Therefore, the volume of the silo is:
[tex]V = (\pi * 120^2 * 105) + (\frac{1}{3} * 120^2 * 25)\\\\V = 4750088.09 + 376991.12\\\\V = 5127079.21 ft^3[/tex]
The volume of the silo is 5127079.21 cubic feet.
Select Not independent or Independent for each situation. (3)
A spinner is divided into three equally sized sections. The spinner is spun three times.
A number cube is rolled twice.
A bag contains 8 white balls and 3 yellow balls. Two balls are selected from the bag without replacement.
Answer:
A spinner is divided into three equally sized sections. The spinner is spun three times.
independent, since the outcome is not affected by previous spins.
A number cube is rolled twice.
independent, since the outcome is not affected by previous rollings.A bag contains 8 white balls and 3 yellow balls. Two balls are selected from the bag without replacement.
not independent, since the new outcome depends on the balls that were drawn before.Step-by-step explanation:
The outcome of an independent variable is not affected by previous outcomes or actions, while the outcome of dependent variables is affected by previous outcomes or actions.
The outcome from independent variable is not affected by old outcomes or actions, while the outcome of dependent variables is affected by old outcomes or actions.
What is Independent Variable?An independent variable is exactly when it sounds like. It is a variable that stands alone, changed by the other variables you are trying to measure.
A spinner is divided into three sections. The spinner is spun three times.
a. independent, since the outcome is not affected by previous spins. A number cube is rolled twice.
b. independent, since the outcome is not affected by previous rolling.
c. not independent, since the new outcome depends on the balls that were drawn before.
Thus, the outcome will be an independent variable which is not affected by previous outcomes.
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HELP!! ASAP!!! PLEASE!!!!!!
Answer:
It's 38
Step-by-step explanation:
I I don't know oh my God your thing is showing
Answer:
w = 8.
Step-by-step explanation:
Can't explain again did it in my head. :/
What is the volume of this cone?
Answer:
Volume of a cone: V = (1/3)πr2h.Step-by-step explanation:
Answer:
28.26
Step-by-step explanation:
volume = 1/3 * pi * r^2 * h
Find the arc length of the semicircle.
Either enter an exact answer in terms of n pi or use 3.14 for n pi and enter your answer as a decimal.
units.
* this is from Khan academy and the lesson is about ( circumstance of part of circles) PLEASE HURRY AND HELP ME!!!!!
Answer:
12.56
Step-by-step explanation:
Radius = 8/2 = 4
Arc length = pi × r
= 3.14 × 4
= 12.56
Express the shaded area as a fraction, a decimal, and a percent of the whole.
Fraction
Decimal
Percent
Answer: 30%
Step-by-step explanation:
Ive had this before the answer is 30%
What are the three ways a translation could be written?
Find the mean, median, mode, and range for the numbers 17, 22, 34, 3, 16, 16, 24, 55, 18, 3, 16, 12, and 18
Answer:
mean = 19.54
median = 17
mode 16
range 52
Step-by-step explanation:
17, 22, 34, 3, 16, 16, 24, 55, 18, 3, 16, 12, and 18
First put the numbers in order from smallest to largest
3, 3, 12, 16, 16, 16,17,18, 18,22,24, 34, 55
The mean is where you add up all the numbers and divide by the number of numbers
(3+ 3+ 12+ 16+ 16+ 16+17+18+ 18+22+24+ 34+ 55)/13
254/13
19.53846154
mean = 19.54
The median is the middle number
Since there are 13 numbers the middle number is 13/2 = 6.5 which rounds to 7
The 7th number is 17
median = 17
Mode is the number that appears most often
16 appears 3 times which is more often than any other number
mode 16
The range is the largest number minus the smallest number
55-3 = 52
range = 52
What is the range of the data below? A box-and-whisker plot. The number line goes from 50 to 100. The whiskers range from 52 to 93, and the box ranges from 60 to 89. A line divides the box at 82. 22 28 41 42want you inside now! LAURIE I walked down to the beach.
Answer:
42
Step-by-step explanation:
the is range is 42
Answer:
42
Step-by-step explanation:
A shipment to a warehouse consists of 2250 MP3 players. The manager chooses a random samle of 50 MP3 players and finds 6 that are defective. How many MP3 players in the shipment are likely to be defective?
Answer:
350
Step-by-step explanation:
Gimmie brainliest plzzz <3
Determine what type of model best fits the given situation:
A retirement account is expected to grow by 15% each year.
A. none of these
B. exponential
C. quadratic
D. linear
Answer:
I believe it is linear
Step-by-step explanation:
because if you are talking about percentage then it should be done on a linear graph so therefore i believe the answer is linear..................if i am incorrect i am very sorry but i believe i am correct.
Answer: Quadratic
Step-by-step explanation: I took the test
Jonas practices guitar 1 hour a day for 2 years. Bradley practices the guitar 2 hours a day more than Jonas. How many more minutes does Bradley practice the guitar than Jonas over the course of 2 years?
Answer:
Bradley practice 109500 more minutes than Jonas over the course of 2 years.
Step-by-step explanation:
Jonas practices guitar 1 hour a day for 2 years.
1 year = 365 days
2 years = [tex]365 \times 2 = 730 days[/tex]
1 hour = 60 minutes
So, Jonas practice for 60 minutes in 1 day
Jonas practice for minutes in 365 days =[tex]365 \times 60 =21900 minutes[/tex]
Bradley practices the guitar 2 hours a day more than Jonas.
So, Bradley practice the guitar for hours per day = 2+1=3 hours
3 hours = 3 \times 60 = 180 minutes
Bardley practice for minutes per day = 180 minutes
Bardley practice for minutes for 730 days = [tex]180 \times 730 =131400 minutes[/tex]
Difference in minutes in 2 years = 131400-21900=109500 minutes
Hence Bradley practice 109500 more minutes than Jonas over the course of 2 years.
I need help ASAP! Tysm
Step-by-step explanation:
solate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x≤193x≤193
Interval Notation:
(−∞,193]
If a sphere’s surface area is doubled, what is the corresponding change in radius?
Answer:
The radius has an increase of 41.4%
Step-by-step explanation:
We have that the surface area formula is equal to:
a = 4 * pi * r ^ 2
in this case if you assume an area of 100 and we calculate the radius it would be:
100 = 4 * pi * r ^ 2
we solve for r:
r ^ 2 = 100/4 * pi
r ^ 2 = 100 / (4 * 3.14)
r ^ 2 = 7.9617
r = 2,822
now if we double the area, that is 200:
r ^ 2 = 200 / (4 * 3.14)
r ^ 2 = 15.9236
r = 3,990
So the change of the radius would be:
3.99 / 2,822 = 1,414
That is to say that the radius has an increase of 41.4%
to rent a building for a school dance ava paid $120 plus $2.50 for each student who attended. If she paid a total cost of $325 how many students attended the dance
Answer:
82 students
Step-by-step explanation:
The total number of students who attended the dance can be found by subtracting the initial rental cost from the total cost, and then dividing this amount by the cost per student. The number of students who attended the dance was 82.
Explanation:This problem can be solved with a little bit of algebra. The initial cost of the building was $120, and there was an additional cost of $2.50 for each student who attended. The total cost was $325. Therefore, in order to determine how many students attended the dance, you would first need to subtract the initial cost of the building from the total cost. This leaves us with $325 - $120 = $205.
Next, you would divide this amount by the cost per student. $205 ÷ $2.50 = 82.
Therefore, the number of students who attended the dance was 82.
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what is the value of k
Answer:
k=10°
Step-by-step explanation:
<ZYX
<ZYM + <ZYX = 180° ( angle on straight line)
115° + <ZYX = 180°
<ZYX = 180° - 115°
<ZYX = 65°
k
<YZX + <ZXY + <ZYX = 180° ( sum of interior angles of a triangle)
(4k + 5)° + (6k + 10)° + 65° = 180°
10k + 80° = 180°
10k = 180° - 80°
10k = 100°
Multiplying both sides by 10
k = 100°
10
k = 10°
Answer:
a
Step-by-step explanation:
yes
pleas i need help as soon as possible!
Answer:
y = 2x-1
Step-by-step explanation:
The y intercept is -1
The slope is rise over run
Up 2 / right1
The slope is 2/1 = 2
The slope intercept form of the equation is
y = mx +b where m is the slope and b is the y intercept
y = 2x-1
If you have $10, and your money
doubles every year, how much
money will you have in 10 years?
Answer: $10240
Step-by-step explanation: 10 x 2^10 = 10240
_______________________________________________
Delisa is designing a website that will be viewable on both computers and mobile devices, so the website as it is seen on a mobile device is proportional to the website as it is seen on a computer. The diagonal of Delisa's computer monitor is 21 inches, and the diagonal of Delisa's tablet is 9.1 inches. If an image is 19 centimeters wide on the website when it's displayed on Delisa's computer, how wide should the image be on the tablet? Round to the nearest tenth of a millimeter, if necessary.
Final answer:
To find the width of the image on the tablet, set up a proportion using the diagonals of the computer monitor and the tablet. Solve for the unknown width using cross multiplication.So,on tablet it would be 0.84mm.
Explanation:
To determine the width of the image on the tablet, we can use a proportion based on the diagonals of the computer monitor and the tablet. The proportion can be set up as follows:
Computer Diagonal / Tablet Diagonal = Computer Width / Tablet Width
Substituting the given values, we have:
21 inches / 9.1 inches = 19 centimeters / x
Cross multiplying and solving for x, we get:
x = (9.1 inches * 19 centimeters) / 21 inches
Converting the units, the width of the image on the tablet should be approximately 8.43 centimeters=0.84mm
Plsss help me !!! 10 points giving for answer
Answer:
D
Step-by-step explanation:
each one can be multiplied by 4 to get the cost
Alex, an eighth grader, and Eric, a seventh grader, need to determine who came closer to their grade’s state record for the triple jump. Alex jumped 39.85 feet and Eric jumped 37 feet and 1 1/4 inches. Who was closer to the state record if the eighth-grade record is 42.25 feet and the seventh-grade record is 39 feet 3 inches? (2 points)
To determine who came closer to their grade's state record for the triple jump, calculate the difference between each jumper's distance and their grade's record. Alex jumped 39.85 feet, which is 2.4 feet away from the eighth-grade record. Eric jumped 37 feet and 1 1/4 inches, which is 1 foot 1 3/4 inches away from the seventh-grade record. Alex was closer to their grade's state record for the triple jump.
Explanation:To determine who came closer to their grade's state record for the triple jump, we need to calculate the difference between each jumper's distance and their grade's record.
Alex jumped 39.85 feet, which is 2.4 feet (42.25 - 39.85) away from the eighth-grade record.
Eric jumped 37 feet and 1 1/4 inches, which is 1 foot 1 3/4 inches (39 - 37 - 1 1/4) away from the seventh-grade record.
Therefore, Alex was closer to their grade's state record for the triple jump.
Final answer:
Alex, an eighth grader, was closer to his grade's state record for the triple jump than Eric, a seventh grader.
Explanation:
To determine who came closer to their grade's state record for the triple jump, we need to compare the distances jumped by Alex and Eric to their grade's respective records. Alex jumped 39.85 feet, which is 2.4 feet less than the eighth-grade record of 42.25 feet. Eric jumped 37 feet and 1 1/4 inches, which is 1.75 feet less than the seventh-grade record of 39 feet 3 inches.
By comparing the differences, we can see that Alex was closer to his grade's record by 2.4 feet, while Eric was closer to his grade's record by 1.75 feet. Therefore, Alex was closer to his grade's state record for the triple jump than Eric.
Logan wants to move to a new city. He gathered graphs of temperatures for two different cities. Which statements about the data
sets shown are true?
City A
City B
City A is likely to have a colder temperatures because the interquartile range is smaller than that of City B.
City Ais likely to have temperatures that remain fairly constant year round because it has a compact interquartile range
compared to that of City B.
Multi choice question hellllppppp
Answer:
we need the data to answer the question
Can someone please help me with this
Answer:
12 inches
Step-by-step explanation:
a^2 + b^2 = c^2
a=16
b=?
c=20
16^2 + b^2 = 20^2
256 + b^2 = 400
400 - 256 = b^2
144 = b^2
Square root 144 = b
12 = b