The mistake he made was that he did not consider units of measurement while comparing the lengths
He has to convert the both quantities into the same unit to compare the lengths either centimeters to meters or meters to centimeters
Step-by-step explanation:
Length of desk = 1 meter
Henry's name tag = 8 cm
Henry says that his name tag is 7 cm longer than the desk. The mistake he made was that he did not compare the units of both quantities. He just subtracted 1 from 8 and got 7. Meter is a larger unit and centimeter is a smaller unit. In order to compare the lengths of the desk and his name tag the units have to be same.
Hence
The mistake he made was that he did not consider units of measurement while comparing the lengths
He has to convert the both quantities into the same unit to compare the lengths either centimeters to meters or meters to centimeters
Keywords: Measurement
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Final answer:
Henry mistakenly claimed his nametag was 7 centimeters longer than his desk due to a unit conversion error. His desk is 100 centimeters long, and his nametag is 8 centimeters long, making the nametag 92 centimeters shorter than the desk. The error is corrected by accurately comparing lengths in the same unit.
Explanation:
The question asks to identify the error Henry made in stating that his nametag is 7 centimeters longer than his desk and to explain how to correct it. Henry's desk is 1 meter long, which is equivalent to 100 centimeters, and his nametag is 8 centimeters long. The error Henry made is in the comparison of the lengths in different units and misunderstanding of the concept of length comparison. To correct this error, both lengths should be in the same unit, and then we compare or subtract to find the difference or relation.
The correct comparison is as follows:
Desk length in centimeters: 100 cm
Nametag length: 8 cm
So, rather than the nametag being 7 centimeters longer, it is 92 centimeters shorter than the desk. The correction is understanding unit conversion and accurately comparing lengths.
Divide 100 by 16 and write the answer as mixed number. Reduce the fraction part of the mixed number
Answer:
Step-by-step explanation:
100/16 = 25/4 = 6(whole number )1/4
In a survey, children were asked what flavor of ice cream they favored. 600 children, or 60% of the respondents, said chocolate was their favorite. How many children responded in the survey?
Answer:
1,000
Step-by-step explanation:
60% of 1,000 is equal to 600
Answer:
its 600%
Step-by-step explanation:
A car is driven 402.5 miles on 11.5 gallons of gas. Find the number of miles traveled per gallon of gas
Answer:
I believe it's 35 miles per gallon of gas
Answer:
35 miles per gallon
Step-by-step explanation:
Here we know that the car driven 402.5 miles on 11.5 gallons of gas, so we can write the following equivalence:
402.5 m = 11.5 g
With m being miles and g gallons.
We want to know the equivalent of miles for 1 gallon. So, lets take the equivalence and divide it by 11.5
402.5/11.5 m = 11.5/11.5 g
35 m = 1g
So, each gallon permits to travel 35 miles. If you want to verify it, just multiply 11.5 (the gallons) g by the number of miles, 35:
11.5 * 35 = 402.5
Which choices are real numbers? Check all that apply. (-22)½ (-16)⅓ (-16)⅕ (-10)¼
I am having a hard time figuring out how to check real numbers.
[tex](-22)^{\frac{1}{2}}[/tex] and [tex](-10)^{\frac{1}{4}}[/tex] are not real numbers
Solution:A real number is any positive or negative number. This includes all integers and all rational and irrational numbers
They are called "Real Numbers" because they are not Imaginary Numbers.
When you take an even root of a negative number, there is no real answer. (2 is an even number)
In the real number set, you can't take an even-indexed root of a negative number.
Given options are:
[tex]\begin{array}{l}{\text { A) }(-22)^{\frac{1}{2}}} \\\\ {\text { B) }(-16)^{\frac{1}{3}}} \\\\ {\text { C) }(-16)^{\frac{1}{5}}} \\\\ {\text { D) }(-10)^{\frac{1}{4}}}\end{array}[/tex]
Looking at the answer choices here, we can see that A and D use even roots, so they will give non-real answers.
Thus [tex](-22)^{\frac{1}{2}}[/tex] and [tex](-10)^{\frac{1}{4}}[/tex] are not real numbers
Answer:
(-16)^1/3 and (-6)^1/5
Step-by-step explanation:
each of 6 students ate 2/5 of a candy bar.how many candy bars were eaten in all?
Answer:
2 and 2/5 candy bars
Step-by-step explanation:
To figure this out, simply add the fractions together 6 times or multiply 2/5 by 6.
(2/5)(6/1)
Multiply the numerator
2*6=12
Multiply the denominator
5*1=5
so the answer is 12/5 or 2 and 2/5 candy bars.
Greta is 1 1/2 meters tall which of the following is equivalent to 1 1/2 meters
1 1/2 meters is equivalent to 1500 millimeters.
The correct option is (b).
To find out which option is equivalent to 1 1/2 meters, we need to convert 1 1/2 meters to millimeters.
Given:
- Gretta's height is 11/2 meters.
To convert meters to millimeters, we'll use the fact that 1 meter is equal to 1000 millimeters.
So, to convert 1 1/2 meters to millimeters:
[tex]\[ \text{1 1/2 meters} = (1 + 1/2) \times 1000 \text{ millimeters} \][/tex]
[tex]\[ = (1.5) \times 1000 \text{ millimeters} \][/tex]
[tex]\[ = 1500 \text{ millimeters} \][/tex]
So, 1 1/2 meters is equivalent to 1500 millimeters.
Therefore, the correct option is:
b. 1500 millimeters
complete question given below:
Gretta is 11/2 meters tall. Which of the following is equivalent to 1 1/2 meters?
a.150 millimeters
b.1,500 millimeters
c.100 millimeters
d.1,000 millimeters
Marty must pack 4,125 steel ball bearings into 10 boxes. Each box must contain an equal number of bearings. How many bearings does he have left over? (use long division to find the remainder)
A) 3
B) 5
C) 7
D) 9
Answer:
5 are left over
The drawing will help
Answer:
B
Step-by-step explanation:
d. Last year, Mr. Petersen was able to plant 4 rows of carrots with 13 plants in each row. This year, he
plans to plant twice as many rows with twice as many carrot plants in each. How many carrot plants
will he plant this year? Write a multiplication equation to solve. Assess the reasonableness of your
answer.
Please answer this!! (In your own words.) The best answer gets brainliest!
Find the area:
Answer:
97.5 sq. ft.
Step-by-step explanation:
Im presuming the question asks to find area of the shaded region.
First of all, the total figure is a rectangle. We can write an expression(in words) for the shaded area.
Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)
Now, we find respective areas.
Area of rectangle:
length * width = (5+10) * (12) = 15 * 12 = 180
Area of Small Triangle (white):
A = (1/2) * base * height = (1/2) * 5 * (12-3) = (1/2) * 5 * 9 = 22.5
Area of Large Triangle (white):
A = (1/2) * base * height = (1/2) * 10 * (12) = 60
Now, we find area of shaded region:
Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)
Shaded Area = 180 - 22.5 - 60 = 97.5 sq. ft.
Answer:
97.5 sq. ft.
Step-by-step explanation:
See the given diagram with given measurements.
The area of the shaded portion is to be determined.
Now, we have to first find the area of the two right triangles formed at the left and right sides.
We know that the area of a right triangle = [tex]\frac{1}{2} \times (\textrm {Base})\times (\textrm {Height})[/tex]
Then the area of the left side triangle = [tex]\frac{1}{2} \times 5 \times (12 - 3) = 22.5[/tex] sq. ft.
Now, the are of the right side triangle = [tex]\frac{1}{2} \times 10 \times 12 = 60[/tex] sq. ft.
Now, the area of non-shaded region = Total are of the two right triangles
= (60 + 22.5) = 82.5 sq. ft.
Therefore, the area of the shaded region is = (Area of the total rectangle - Area of the non-shaded region)
= [(10 + 5) × 12] - 82.5
= 97.5 sq. ft. (Answer)
what is the value of x, given that the two pyramids are similar?
Answer:
C
Step-by-step explanation:
Two pyramids are similar. It means that their side lengths are proportional.
So, let's see the proportionality constant from SMALL PYRAMID to LARGE PYRAMID.
The corresponding length of 8 in small pyramid is 24 in large pyramid. We ask ourself: "8 times WHAT gives us 24?"
This is the proportionality constant (aka "k").
So, 8 times "3" is 24. So the proportionality constant is "3".
k = 3
Now, the height of small pyramid is 6 and height of large pyramid is "x". These sides will be same way proportional. So, we can say:
6 times the proportionality constant (3) would give us x
So,
6 * 3 = x
x = 18
Correct answer is C
in a list of 7 consecutive integers, the sum of the first and last is 518. find the largest.
Answer:
262
Step-by-step explanation:
If x is the first integer, then x+1 is the second, x+2 is the third, and so on. Meaning the 7th term in the list is x+6.
x + x + 6 = 518
2x = 512
x = 256
The first integer is 256, so the last integer is 262.
Identify the prime factorization for the given number. 6 A. 2 × 2 × 3 B. 2 × 3 C. 1 × 6 D. 1 × 2 × 3 × 6
Answer:
B. 2 x 3
Step-by-step explanation:
Answer:
b i got it right on test
Step-by-step explanation:
Carlton and Will went fishing together. Carlton caught 2100
and 7 walleye. Will caught 13 bass and 8 walleye. How many
more fish did Carlton catch than Will?
Answer:
Carlton caught 2072 more fish than Will
Step-by-step explanation:
First you add how much fish Will caught: 7+13+8=28. Then you Subtract Carlton's number of fish minus Wills number of fish:
2100-28=2072! Hope it helped :) Please Mark Brainliest :)
Help ASAP!
What is the area of a triangle with a base of 5 1/2 cm and a height of 3 1/2 cm?
What is the area of a parallelogram with a base of 14.5 m and a height of 21 m?
Given that one ton is equal to 2000 pounds, what is 5 tons?
Answer:19.25
304.5
10000
Step-by-step explanation:
Higher Order Thinking
Mrs. Dryson
divided her collection of 52 glass bears
into equal groups. She had 1 bear
left over. How many groups did
Mrs. Dryson make? How many bears
are in each group?
Answer:
Mrs. Dryson made 3 groups with 17 glasses of bears each or she made 17 groups with 3 glasses of bears each.
Step-by-step explanation:
Let the number of groups is x and each group gets y number of bears.
Now, Mrs. Dryson distributed 52 glass bears equally in groups and there was 1 bear left over.
Therefore, xy = 52 - 1 = 51
Now, x and y both must be whole numbers.
Now, we have 51 = 3 × 17, which is the only possible factorization of 51.
So, if x = 3 then y = 17 and if x = 17, then y = 3.
Therefore, Mrs. Dryson made 3 groups with 17 glasses of bears each or she made 17 groups with 3 glasses of bears each. (Answer)
What is the midpoint of a line segment with endpoints at (3,-1) and (8, -4)?
The midpoint of a line segment with endpoints at (3,-1) and (8, -4) is [tex]\left(\frac{11}{2},-\frac{5}{2}\right)[/tex]
Solution:
We have been given 2 end points of a line which are: (3,-1) and (8, -4)
The midpoint of a line segment is half way from both the ends of the line segment.
The formula for midpoint for the two points [tex]P(x_1, y_1) \text{and} Q(x_2, y_2)[/tex] is given as:
[tex]\text {Midpoint}=(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})[/tex]
Here P(3, -1) and Q(8, -4)
[tex]\text { So } x_{1}=3 ; x_{2}=8 ; y_{1}=-1 ; y_{2}=-4[/tex]
Plugging in values in above formula, we get
[tex]\begin{array}{l}{\text {Midpoint}=(\frac{3+8}{2}, \frac{-1-4}{2}})\\\\ {\text {Midpoint}=(\frac{11}{2}, \frac{-5}{2}})\end{array}[/tex]
Hence, the midpoint of the line segment is [tex]\left(\frac{11}{2},-\frac{5}{2}\right)[/tex]
Change these times to the 12-hour clock.
a)
12 45
b)
19 30
Answer:
12:45 pm and 7:30 pm
Step-by-step explanation:
In a 24 hour clock, we don't use pm or am to identify time. But in a 12 hour clock , am or pm is used. Given time is in 24 hour clock.
So, for 12:45, in 12 hour clock it will be 12:45 pm because, when the time crosses 11:59, it becomes pm.
For, 19:30, it will 19:30-12:00= 7:30 pm.
Final answer:
To convert 12:45 from the 24-hour clock to the 12-hour clock, it remains 12:45 AM. To convert 19:30, you subtract 12 hours, making it 7:30 PM because it is after noon.
Explanation:
To convert times from the 24-hour clock to the 12-hour clock, you need to remember that the 24-hour clock runs from 0:00 (midnight) to 23:59, while the 12-hour clock repeats the cycle of AM and PM hours from 1 to 12.
Solution to (a):
12:45 in the 24-hour clock is straightforward. Since it's already in the AM range, it's the same in the 12-hour clock - 12:45 AM.
Solution to (b):
To convert 19:30 from the 24-hour clock to 12-hour clock format, subtract 12 hours from the 24-hour time if it is greater than 12. Thus, 19:30 becomes 7:30 PM because 19 - 12 = 7, and any time past noon is in the PM.
Point Q(-1, 5) is reflected across the line x = -1. What are the coordinates of its image? (5, -1) (1, 5) (-1, -5) (-1, 5)
Answer:
(-1,5)
Step-by-step explanation:
The line x = -1 is a vertical line parallel to the y-axis.
Therefore, if the point Q(-1,5) reflects on line x = -1, then the y-coordinate of the image point will not change.
Again, as the point Q(-1,5) is on the line x = -1, therefore, the image will be the point itself i.e. (-1,5). (Answer)
The horizontal distance from point (-1,5) to the line x = -1 is zero.
Answer:
(-1,5)
Step-by-step explanation:
please solve with steps how to do this exponets and signed fraction problem
( - 1/4) 2
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
Given
[tex](-1/4)^{2}[/tex]
= - [tex]\frac{1}{4}[/tex] × - [tex]\frac{1}{4}[/tex]
= [tex]\frac{1(1)}{4(4)}[/tex]
= [tex]\frac{1}{16}[/tex]
A diver is currently -5 feet from the surface of the water and plans to explore a shipwreck that is at -75 from the surface. If she moves at a rate of -8 feet per minute, how many minutes does it take the diver to reach the shipwreck?
Answer:
8.75 minutes
Step-by-step explanation:
This is a simple linear relation between two variables, time and depth
We can solve it by simple inspection like this.
If the diver is 5 feet deep and plans to go 75 feet deep, he must move 70 feet deeper.
At a rate of 8 feet/minute, it will take him/her
70/8= 8.75 minutes
It is 8 minutes and 45 seconds
Which pair of triangles below shows the ASA postulate. Explain
Answer:
We can conclude that Δ XYZ ≅ Δ RST by ASA postulate.
Step-by-step explanation:
Δ XYZ and Δ RST are congruents by ASA postulate because:
1. Their included sides XZ and RT are equal.
2. Their angles ∠Z and ∠T are equal (92° = 92°)
3. Their angles ∠X and ∠R are equal.
4. Their non-included sides XY and RS are equal.
Now, we can conclude that Δ XYZ ≅ Δ RST by ASA postulate.
The vertices of triangle ABC are A(−5, 1), B(−2.5, 7), and C(0, 1). Find the new coordinates of the vertices after the given translation.
Answer:
A'(-2,0) , B'(0.5,6) and C'(3,0)Step-by-step explanation:
The vertices of triangle ABC are A(−5, 1), B(−2.5, 7), and C(0, 1).
The given translation of vertices,
(x, y) → (x + 3, y − 1)This translation shows shift x-coordinate 3 unit right and y-coordinate 1 unit down.
First translate vertices A(-5,1)[tex]A(-5,1)\rightarrow A'(-5+3,1-1)[/tex]
New vertices A'(-2,0)
Now vertices B(-2.5,7)[tex]B(-2.5,7)\rightarrow B'(-2.5+3,7-1)[/tex]
New vertices B'(0.5,6)
Now vertices C(0,1)[tex]C(0,1)\rightarrow C'(0+3,1-1)[/tex]
New vertices C'(3,0)
Hence, the new coordinate of the vertices are A'(-2,0) , B'(0.5,6) and C'(3,0)
9.
Given that 4:5:8 is equivalent to 1:n:b. Find the ratio of n:b only.
Step-by-step explanation:
So 4:5:8
= 1:n:b
which means that 4/n= 1
n= 1x4 so n=4
Now we know that 4 is divided by 4 to get 1, so we do the same for the other two values.
5/4= 1.25 and 8/4= 2
So now place the values for n:b
n= 1.25 b=2
So n:b= 1.25:2
To check, multiply each of the values in 1:1.25:2 by 4 and see if the answer you get is the same as 4:5:8.
What is 6,051 x 10^5 written in standard form?
Answer:
605100
Step-by-step explanation:
6.051*10^5=605100
Write an inequality to represent the graph.
a solid line passing through points 0 comma 2 and 4 comma negative 1 with shading below the line
y is greater than or equal to negative four thirds times x plus 2
y is less than or equal to negative three fourths times x plus 2
y is greater than or equal to negative three fourths times x plus 2
y is less than or equal to negative four thirds times x plus 2
Answer:
[tex]y \leq -\frac{3}{4}x+2[/tex]
y is less than or equal to negative three fourths times x plus 2
Step-by-step explanation:
step 1
Find the equation of the solid line
we have the coordinates (0,2) and (4,-1)
Find the slope m
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{-1-2}{4-0}[/tex]
[tex]m=\frac{-3}{4}[/tex]
[tex]m=-\frac{3}{4}[/tex]
Find the equation of the line in slope intercept form
[tex]y=mx=b[/tex]
where
m is the slope
b is the y-intercept (value of y when the value of x is equal to zero)
we have
[tex]m=-\frac{3}{4}[/tex]
[tex]b=2[/tex] ---> is given
substitute
[tex]y=-\frac{3}{4}x+2[/tex]
Remember that
The shading area is below the line
therefore
The inequality is
[tex]y \leq -\frac{3}{4}x+2[/tex]
y is less than or equal to negative three fourths times x plus 2
Answer:
Y is less than or equal to negative three fourths times x plus 2
Step-by-step explanation:
The LCM of 3 and 8 is ______.
Answer: the lowest common multiple of 3 and eight is 24
Step-by-step explanation:
Answer:its 24 :)
Step-by-step explanation:
is -44 a rational or irrational
Answer: Rational
Step-by-step explanation: -44 is an integer and all integers are rational numbers. Therefore, -44 is classified as a rational number.
The set of integers includes the set of whole numbers {0, 1, 2, 3...} and they also include their negative counterparts.
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What is the fourth number in this pattern, and what is the rule?
Answer: Multiplied by 10
Step-by-step explanation:
To find the common difference (rate or slope) we can divide the 2nd term to the 1st term.
54.2 / 5.42 = 10 (rule)
Since the common difference is the same throughout the sequence, we can name this as a "arithmetic sequence".
We can multiply 10 to 542 to find the 4th term: 542 * 10 = 5,420
______
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Brian mix 8 cups of milk to make 6 dozen brownies at that rate how many cups of milk would he need to make 15 dozen brownies
Answer:
20 cups
Step-by-step explanation:
15 / 6 = 5/2
8 * 5/2 = 20
20 cups of milk would be required by Brian to prepare 15 dozen brownies. By utilizing ratios and proportions, this conclusion has been obtained.
Explanation:To solve this problem, we can use both proportions and ratio. Brian uses 8 cups of milk for every 6 dozen (or 72) brownies. This can be written as the ratio 8:72 or the proportion 8/72 = x/180. From the proportion, we know the cross products are equal, so 8*180 = 72*x. Solving for x gives us x = (8*180)/72. Therefore, Brian would need 20 cups of milk to make 15 dozen brownies.
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A metalworker has a metal alloy that is 30% copper and another alloy that is 55% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 50% copper alloy? The metal worker should use (blank) kilograms of the metal alloy that is 30% copper and (blank) kilograms of the metal alloy that is 55% copper. (show your work)
X+Y=100kg
X=100-Y
X*0.3+Y*0.55=100*0.5
(100-Y)*0.3+Y*0.55=50
30-0.3*Y+0.55*Y=50
0.25*Y=20
Y=80 kg
X=100-80
X=20 kg
The metal worker should use 20 kilograms of the metal alloy that is 30% copper and 80 kilograms of the metal alloy that is 55% copper.
Answer:
x=20kg
Step-by-step explanation: