Answer:
40 mg
Step-by-step explanation:
Given,
The prescribed dosage the medicine for an adult = 180 milligrams,
Since, the minimum age of an adult = 18 years,
So, the prescribed dosage of the medicine for 18 years old person = 180 milligrams,
Thus, the ratio of prescribed dosage of medicine ( in mg ) and age of person ( in years ) = [tex]\frac{180}{18}[/tex]
Suppose prescribed dosage of a certain medicine for a child 4 years old is x mg,
So, ratio of prescribed dosage of medicine and age = [tex]\frac{x}{4}[/tex]
[tex]\frac{x}{4}=\frac{180}{18}[/tex]
[tex]\frac{x}{4}=10[/tex]
[tex]\implies x = 4\times 10 = 40[/tex]
Hence, the prescribed dosage of a certain medicine for a child 4 years old would be 40 mg.
Write a two column proof
Answer:
see the explanation
Step-by-step explanation:
The correct question is
Prove ∠H≅∠J
we know that
The Angle-Side-Angle postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent,
we have
∠HIG≅∠JKI ----> given problem
∠HGI≅∠JIK ----> by corresponding angles (HG and JI are parallel lines)
GI≅IK ----> given problem
so
two angles and the included side of triangle HIG are congruent to two angles and the included side of triangle JKI
therefore
triangle HIG ≅ triangle JKI ---> by ASA postulate
Remember that
If two figures are congruent, then its corresponding sides and corresponding angles are congruent
Hence
∠H≅∠J ----> by definition of congruence (corresponding angles are congruent)
May someone please help me?
Answer:
grapes cost $1.25 per pound
blueberries cost $4 per pound
Step-by-step explanation:
We have two unknowns, the cost of grapes and the cost of blueberries.
I'll call grape g and blueberries b.
since 21lb grapes and 44lb of blueberry cost $202.25, we can set up our first equation.
21g + 44b = 202.25
and the question also said 30lb grape and 22lb blueberries cost $125.50, we can set up our second equation.
30g + 22b = 125.5
now that we have two equations, you can use any methods you want to solve for the variable. I'm gonna use elimination.
21g + 44b = 202.25
-2(30g + 22b = 125.50)
━━━━━━━━━━
-39g = -48.75
g = 48.75/39
g = 1.25, grapes cost $1.25 per pound
now use substitution to find the cost of blueberries. you know the value of g now so plug it back in to one of the equation.
21g + 44b = 202.25
21(1.25) + 44b = 202.25
26.25 + 44b = 202.25
44b = 176
b = 4 , blueberries cost $4 per pound
if there are 170 students in 12th grade what percentage of 12th grade students have more then one college in mind? round to the nearest percent
Answer:
nearest percent is about 56%
Answer:
56
Step-by-step explanation:
Complete the inequality statement.
14 ft ____ 4 1/2 yd.
<
>
=
14 ft > [tex]4\frac{1}{2}[/tex] yards
Step-by-step explanation:
Given,
14 ft ____ 4 1/2 yd.
We will convert yards into feet to determine the inequality.
1 yard = 3 feet
[tex]4\frac{1}{2}[/tex] yards = [tex]3*4\frac{1}{2}[/tex]
[tex]4\frac{1}{2}[/tex] yards = [tex]3*\frac{9}{2}[/tex]
[tex]4\frac{1}{2}[/tex] yards = 3*4.5 = 13.5 feet
which is less than 14 feet, making 14 feet greater, therefore, we will use 'greater than' inequality.
14 ft > [tex]4\frac{1}{2}[/tex] yards
Keywords: inequality, conversion
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Answer:
>
Step-by-step explanation:
The leader board at the Lakeside Golf Tournament shows that Mei's score is 3 and Noah's score is -6. How many more strokes did Mei take than Noah?
A. 3
B. 9
C. 10
D. 8
Part B.
Find the total score made by Mei and Noah together.
Mai take 9 more strokes than Noah.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
The leader board at the Lakeside Golf Tournament shows that,
Mei's score is 3 and Noah's score is -6.
Now,
Since, Mei's score is 3 and Noah's score is -6.
Hence, The number of more scores of Mei's than Noah is,
⇒ 3 - (-6)
⇒ 3 + 6
⇒ 9
Thus, Mei take 9 strokes more than Noah.
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This scatter plot for a fund-raiser shows the time spent raising money for 9 student events. Noting the trend in the scatter plot, which is the most reasonable approximation of the money raised in the 11-hour fund-raiser?
Answer:
About $90, because the trend line shows that value for $11.
Step-by-step explanation:
It is the only one that shows a constant rate of change.
Answer:
the first one ( the line closest to 90)
Step-by-step explanation:
Matthew has 2 dozen eggs. He uses 3/4 of the first dozen and 5/6 of the second dozen for baking.
How many eggs were left over?
Answer:
5 eggs.
Step-by-step explanation:
Well, 3/4 of 12 is 9 and 5/6 of 12 is 10. So, 12 - 9 = 3 and 12 - 10 = 2
Therefore, Matthew has 5 eggs left over.
I hope I helped ^^
Answer:
5/12 dozen eggs
Step-by-step explanation:
confirmed!
simplify the expression-
3k+ -9k+ -6+10k
Answer:
4k-6
Step-by-step explanation:
[tex]3k+ -9k+ -6+10k=3k-9k-6+10k=4k-6[/tex]
Answer:
4k-6
Step-by-step explanation:
3k+-9k=-6k ; -6k + 10k = 4k ; 4k+ -6 = 4k-6
PLZ help super really super fast
Answer:
The one in the top left corner and bottom middle
Which expressions are equivalent to (7^-2)*(7^6)
A. 7^2/7^-2
B. 7^6/7^-2
C. 7^-12
D. (7^2)^2
Answer:
D
Step-by-step explanation:
(7^-2)*(7^6)=7^-2+6
......since the base 7 is the same, when u multiply them, you should add the exponents and keep 7 as it is. That will be 7^4, which in equivalent to ans D(7^2)^2.
HELP ASAP PLEASE
Which types of dilation are the given scale factors?
Select Expansion or Contraction to correctly describe the type of dilation for each given scale factor.
-4= Contraction
2.5=Expansion
2/3= Contraction
-3/4= Contraction
Best way to solve this, if the scale factor is less than one, is a contraction. If it is greater than one, than it is an expansion.
A tile pattern has 5 tiles in Figure 0 and adds 7 tiles in each new figure. Write the equation of the line that represents the growth of this pattern
For all values of x, which expression is equivalent to 2x + 5 − x + 3x + x − 2?
Answer:
5x + 3
Step-by-step explanation:
1) Collect like terms.
(2x − x + 3x + x) + (5 − 2)
2) Simplify
5 x + 3
Answer:
D.) hope this help if i don´t then o well
Step-by-step explanation:
What is the equation of the graph below?
y = cos(x/0.4)
y = cos(5x)
y = cos(0.4x)
Answer:
The answer is C. y=cos(0.4x)
Step-by-step explanation:
took the test
Answer: c
Step-by-step explanation:
y=cos(0.4x)
Y/4-9=-3please explain how you got the answer in detail if what you did to get the answer you got.
Answer:
24
Step-by-step explanation:
y/4-9=-3
y/4=-3+9
y/4=6
y=6*4
y=24
What is the reason for the last step in the argument?
A) division
B) addition
C) subtraction
D) symmetric property
Answer:
A) division
Step-by-step explanation:
4x=-4
4x/4=-4/4 (dividing by 4 on both sides)
x=-1
What expression is equivalent to 2x^2+2x-4/2x^2-4x+2
You need to factor the numerator and denominator...
(2x^2+4x-2x-4)/(2x^2-2x-2x+2)
(2x(x+2)-2(x+2))/(2x(x-1)-2(x-1))
((2x-2)(x+2))/((2x-2)(x-1)) so the (2x-2)s cancel out leaving
(x+2)/(x-1)
Answer:
[tex]\large\boxed{\dfrac{2x^2+2x-4}{2x^2-4x+2}=\dfrac{x+2}{x-1}}[/tex]
Step-by-step explanation:
[tex]\dfrac{2x^2+2x-4}{2x^2-4x+2}=\dfrac{2(x^2+x-2)}{2(x^2-2x+1)}=\dfrac{x^2+x-2}{x^2-2x+1}\\\\=\dfrac{x^2+2x-x-2}{x^2-x-x+1}=\dfrac{x(x+2)-1(x+2)}{x(x-1)-1(x-1)}\\\\=\dfrac{(x+2)(x-1)}{(x-1)(x-1)}\qquad\text{cancel}\ (x-1)\\\\=\dfrac{x+2}{x-1}[/tex]
The expression 4x gives the perimeter of a square with a side length of x units.
What is the perimeter of a square with a side length of 5/7?
Answer:
Perimeter of square is [tex]\frac{20}{7} \ units \approx2.86\ units.[/tex]
Step-by-step explanation:
Given:
Perimeter of square = [tex]4x[/tex]
where side length = 'x' units.
We need to find the Perimeter of square with side length[tex]\frac{5}{7}[/tex]
Now We know that;
[tex]x= \frac{5}{7}[/tex]
Substituting the value of x in perimeter of square formula we get;
Perimeter of square = [tex]4\times\frac{5}{7} = \frac{20}{7} \ units \approx2.86\ units.[/tex]
Hence Perimeter of square is [tex]\frac{20}{7} \ units \approx2.86\ units.[/tex]
Plz help me really really fast 2 mins left
Answer:
C
Step-by-step explanation:
The diagonal of the square creates 2 right triangles with the diagonal as the hypotenuse.
Using Pythagoras' identity in either of the right triangles.
The square on the hypotenuse is equal to the sum of the squares of the other 2 sides.
Let x be the side of the square, then
x² + x² = 40², that is
2x² = 1600 ( divide both sides by 2 )
x² = 800 ( take the square root of both sides )
x = [tex]\sqrt{800}[/tex]
= [tex]\sqrt{100(8)}[/tex]
= = 10[tex]\sqrt{8}[/tex]
= 10 × [tex]\sqrt{4(2)}[/tex]
= 10 × 2[tex]\sqrt{2}[/tex] = 20[tex]\sqrt{2}[/tex] → C
The average growth of human hair is 0.5 inch
per month. Find how long it takes a human to
grow 3 inches of hair.
Equation:
Solution:
Answer:6
Step-by-step explanation:
Answer:
6 months
Step-by-step explanation:
3 divided .5 = 6
2 months = 1 inch
1 inch x 3 = 3 inches
2 months x 3 = 6 months
please what is the derivative of y=cos(^7)base x
The derivative of y=cos(^7)base x is
Dydx = (cos(7x))x⋅(ln(cos(7x))−7x(tan(7x)))
Step-by-step explanation:
step 1 :
y= (cos(7x))x
Take the natural logarithm of either side, bringing the t x down to be the coefficient of the right hand side we get the answer:
step 2 :
⇒ln y = xln (cos (7x))
Differentiate each side with respect to x. The rule of implicit differentiation: ddx (f(y)) = f'(y) ⋅ dydx
step 3 :
∴1y ⋅ dydx = ddx (x) ⋅ln (cos(7x)) + ddx (ln (cos(7x)))⋅x
Use the chain rule for natural logarithm functions – ddx ( ln (f(x)) )= f'(x)f(x) - we can differentiate the ln (cos (7x))
step 4 :
Ddx (ln (cos(7x))) = −7xsin (7x) cos( 7x 7tan (7x)
Returning to the original equation:
1y ⋅dydx = ln (cos(7x))−7xtan(7x)
Substitute the original y as a function of x value from the start back in.
Dydx = (cos(7x))x⋅(ln(cos(7x))−7x(tan(7x)))
The width of a rectangle is seven meters less than the length. The perimeter is 58 meters. Find the length and width.
The length of rectangle will be 18 meters and width of rectangle will be 11 meters.
It is given that width of a rectangle is seven meters less than the length.
If perimeter of rectangle is 58 meters then find the value of length and width.
What are the area and perimeter of a rectangle ?
The area of rectangle is A = L × B and the perimeter is 2 ( L + B ) , where ; L = length and B = width.
Let's assume the length of the rectangle is x.
The width of the rectangle will be ;
= x - 7
Also ; the perimeter of triangle is given which is equal to 58 meters.
We know that ; the perimeter of triangle is given by ;
Perimeter = 2 × ( length + width )
So ;
58 = 2 [ x + (x - 7)]
58 = 2 ( 2x - 7 )
58 = 4x - 14
or
4x = 58 + 14
4x = 72
x = 72 ÷ 4
x = 18 meters
So ;
Length = 18 meters
and
Width = 18 -7 = 11 meters
Thus , the length of rectangle will be 18 meters and width of rectangle will be 11 meters.
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Kenny wants to place a picture frame in the center of a wall that is 17 3/4 feet wide. The picture is 2 3/4 feet wide. How many feet from each side of the wall must the frame be so that it is centered?
Answer:
The distance of frame from each side of the wall so that it is at centered is 7.5 feet
Step-by-step explanation:
Given as :
The measure of the wall = 17[tex]\dfrac{3}{4}[/tex] feet
i.e The measure of the wall =[tex]\dfrac{71}{4}[/tex] feet
The measure of the picture = 2[tex]\dfrac{3}{4}[/tex] feet
i.e The measure of the picture =[tex]\dfrac{11}{4}[/tex] feet
Let The distance from each side of wall so that frame at centered = x feet
Now, According to question
x = The measure of the wall - measure of the picture
Or, x = [tex]\dfrac{71}{4}[/tex] feet - [tex]\dfrac{11}{4}[/tex] feet
Or, x = [tex]\dfrac{71 - 11}{4}[/tex] feet
Or, x = [tex]\dfrac{60}{4}[/tex] feet
∴ x = 15 feet
Now, For each side so that frame st centered = [tex]\dfrac{15}{2}[/tex] feet
Or, For each side so that frame st centered = 7.5 feet
Hence,The distance of frame from each side of the wall so that it is at centered is 7.5 feet Answer
Steve made a sign for his room that is shaped like a triangle. It is 4.5 feet long and 3 feet high. He wants to make another sign that is shaped like a triangle and similar to the first sign. The new sign will be 4 feet high.
Part A
Write a proportion that Steve can use to find the length, x, of the new sign.
Part B
What is the length, in feet, of the new sign? Make sure to show your work and explain your reasoning.
Answer: PART A : [tex]\frac{4.4}{x}[/tex] = [tex]\frac{3}{4}[/tex]
PART B : 5.9 FEET
Step-by-step explanation:
Length of the first sign = 4.4 feet
height of the first sign = 3 feet
Length of the second sign = x feet
height of the second sign = 4 feet
If two shapes are similar , then the ratio of their sides are equal,
That is ;
[tex]\frac{h_{1}}{h_{2} }[/tex] = [tex]\frac{L_{1}}{L_{2} }[/tex]
PART A
[tex]\frac{4.4}{x}[/tex] = [tex]\frac{3}{4}[/tex]
PART B
[tex]\frac{4.4}{x}[/tex] = [tex]\frac{3}{4}[/tex]
cross multiplying , we have
3x = 4.4 x 4
3x = 17.6
Divide through by 3
x = 17.6/3
x = 5.86666666666667
x≈ 5.9 feet
Therefore , the length of the new sign is 5.9 feet
solve the system of equations below.
2 x 4 y = 10
2 x 4y = -10
A. X=3, Y=1
B. X=6, Y= -4
C. No solution
D. Infinitely many solutions
How many ounces does a 2-ton rhinoceros weigh?
Answer:
64,000 ounces
Step-by-step explanation:
1 ton = 32,000 ounces
2 tons x 32,000 ounces (which is equal to one ton)
=64,000 ounces
2 tons = 64,000 ounces
A 2-ton rhinoceros weighs 64,000 ounces, which is calculated by converting tons to pounds and then pounds to ounces.
Explanation:The weight of a rhinoceros weighing 2 tons can be calculated in ounces by first converting the weight to pounds. As we know from previous examples, 1 ton = 2,000 pounds. So, a 2-ton rhinoceros weighs 2 × 2,000 = 4,000 pounds. Now, to convert pounds to ounces, we use the conversion factor that 1 pound = 16 ounces. Therefore, a 2-ton rhinoceros weighs 4,000 × 16 = 64,000 ounces.
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A charity organization is having a fundraiser.
PPP represents the fundraiser's profit (in dollars) if nnn tickets are sold. A negative profit means the expenses exceeded the income from tickets.
P=70n-1500P=70n−1500
Answer:
Hence, the price of single ticket is $70.
Step-by-step explanation:
Consider the provided equation.
[tex]P(n) = 70n - 1500[/tex]
As we know that: Profit = Income – Cost
Here, P(n) represents the fundraiser's profit (in dollars) and n represents the number of tickets sold and cost is 1500
Since, n is multiplied by 70 that represents the price of per ticket is $70.
Hence, the price of single ticket is $70.
The expenses of the fundraiser are $40.
Step 1:
To find the expenses of the fundraiser, we can use the given equation:
[tex]\[ P = 70n - 1500 \][/tex]
Here, P represents the profit and n represents the number of tickets sold.
Step 2:
Since profit is the difference between income and expenses, and a negative profit means expenses exceeded income, we can set the profit P to zero and solve for the number of tickets n. Then, we can use the value of n to find the expenses.
When [tex]\( P = 0 \)[/tex]:
[tex]\[ 0 = 70n - 1500 \][/tex]
Solving for n:
[tex]\[ 70n = 1500 \][/tex]
[tex]\[ n = \frac{1500}{70} \][/tex]
[tex]\[ n \approx 21.43 \][/tex]
Since you can't sell a fraction of a ticket, we take the next whole number, which is 22.
Step 3:
Now, we can find the expenses using the value of [tex]\( n \)[/tex]:
[tex]\[ P = 70 \times 22 - 1500 \][/tex]
[tex]\[ P = 1540 - 1500 \][/tex]
[tex]\[ P = 40 \][/tex]
Therefore, the expenses of the fundraiser are $40.
Complete Correct Question:
A charity organisation is having a fundraiser. P represents the fundraiser's profit in dollars if 7 tickets are sold. A negative profit means the expenses exceeded the income from tickets. P=70n-1500 What are the expenses of the fundraiser?
A laptop case has an original price of $45. Ellen has a
coupon for 35% off the original price. Find how much
Ellen paid for the laptop case.
Answer:
29.25
Step-by-step explanation:
you need to take 35 and turn it into a decimal making it .35 then multiply 45 by .35 and you get 15.75 then subtract that from 45
Round 1.143 to the nearest hundredth
Answer:
1.14
Step-by-step explanation:
hundreth = 0.01
so we ignore the 3 because it is in teh thousandths
hope this helps :)
List ways to show 46 as tens and ones
Answer:
4 tens 6 ones
Step-by-step explanation:
those are the only way
The number 46 can be expressed as 4 tens and 6 ones, representing the value 40 plus 6, utilizing the powers of ten place value system.
Explanation:When expressing the number 46 in terms of tens and ones, we use the place value system which is based on powers of ten.
In this system, each place in the number represents a power of 10.
To represent 46 as tens and ones, we look for the highest power of ten that fits into the number without exceeding it.
In the case of 46, that value is 40, because 4 tens (4 x 10) equal 40, and there are 6 ones left over.
Therefore, we can say that 46 consists of 4 tens and 6 ones. This can be shown visually as: