Answer: The children weighing 10 pounds, 15 pounds and 30 pounds require 12 teaspoons , 18 teaspoons, 36 teaspoons respectively.
Step-by-step explanation:
Given, The recommended dosage is 40 milligrams per 2.2 pounds of body weight, divided into three daily doses and taken every 8 hours.
i.e. for 1 pound of body weight required dosage per day= [tex]\dfrac{40}{2.2}=18.18\ ml[/tex]
Each dose consist = [tex]\dfrac{18.18}{3}=6.06\ ml[/tex] drug.
so, 1 pound of body weight required 6.06 ml for each dose.
Then, 10 pounds of body weight require 10 x 6.06 ml drug= 60.6 ml
If 1 teaspoon = 5 ml, then 10 pounds of body weight require (60.6 ml ÷5) = 12.12 ≈12 teaspoons.
15 pounds of body weight require 15 x 6.06 ml drug= 90.9 ml
Then 15 pounds of body weight require (90.9 ml ÷5) = 18.18≈18 teaspoons.
30 pounds of body weight require 30 x 6.06 ml drug= 181.8 ml
Then 30 pounds of body weight require (181.8 ml ÷5) = 36.36 ≈ 36 teaspoons.
Hence, the children weighing 10 pounds, 15 pounds and 30 pounds require 12 teaspoons , 18 teaspoons, 36 teaspoons respectively.
Answer:
A. 1, 1 1/2 , 2 3/4
Step-by-step explanation:
REMEMBER: 1 teaspoon = 5 ml.
For 1 pound of body weight required dosage per day= {40}{2.2}=18.18 ml
Each dose consist = {18.18}{3}=6.06 ml drug.
so, 1 pound of body weight required 6.06 ml for each dose.
Then, 10 pounds of body weight require 10 x 6.06 ml drug= 60.6 ml
If 1 teaspoon = 5 ml, then 10 pounds of body weight require (60.6 ml ÷5) = 12.12 ≈12 teaspoons.
15 pounds of body weight require 15 x 6.06 ml drug= 90.9 ml
Then 15 pounds of body weight require (90.9 ml ÷5) = 18.18≈18 teaspoons.
30 pounds of body weight require 30 x 6.06 ml drug= 181.8 ml
Then 30 pounds of body weight require (181.8 ml ÷5) = 36.36 ≈ 36 teaspoons.
Hence, the children weighing 10 pounds, 15 pounds and 30 pounds require 12 teaspoons , 18 teaspoons, 36 teaspoons respectively which deduct to 1, 1 1/2 , 2 3/4 when converted to the fraction requested in the problem.
Choose the best estimate for the division problem below.
38.064/6.12
A. 9
B. 4.
c. 6
Answer:
c.6
Step-by-step explanation:
I would estimate 6.12 to 6 and 38.064 because I know 36 is a common denominator of 6. 36/6=6
Hope this helps.
Solving Exponential Equations using Logarithms
Answer:
6 weeks
Step-by-step explanation: set the equation to be 1458=2(3^t). Do the division property of equality by 2.
729=3^t
Divide 729 by 3 until you get a 1 as the answer.(Count the number of times that you did it, and that will be your answer)
to solve the equation 3 x + 1 = 4 x + (negative 4)
Answer:
x=5
Step-by-step explanation:
3x+1 = 4x -4
Subtract 3x from each side
3x+1-3x = 4x-3x-4
1 = x-4
add 4 to each side
1+4 = x-4+4
5 =x
Answer: x=5
Step-by-step explanation:
3x+1=4x+(-4)
3x+1=4x-4
3x+5=4x
5=x
Maki uses 20 gallons of a solution with an unknown ethanol concentration and 60 gallons of a 12% ethanol solution to make 80 gallons of a 10% solution. The table shows the amount of each solution. A table titled Ethanol Mixture, showing Gallons, Ethanol Concentration, and Total. The first row shows x percent Ethanol, 20, x, and blank. The second row shows, 12 percent Ethanol, 60, 0.12, and 7.2 The third row shows Mixture, with 80, 0.10, and blank. What is the value of x, the concentration of the unknown ethanol solution? 0.02 0.04 0.05 0.08
Answer:
4%
Step-by-step explanation:
We can write the following equation:
20 * (x / 100) + 60 * 0.12 = 80 * 0.10 (Note that since we're writing the percentages as decimals, x% becomes x / 100 as a decimal.)
x / 5 + 7.2 = 8
x / 5 = 0.8
x = 4%
Answer:
Its B. on edge
Step-by-step explanation:
got it right on my test
Please help ASAP. The question is down below. Thanks
Answer:
B
Step-by-step explanation:
there is three sections to be fenced using 78 m of fence so it would be letter B.
I believe this is pretty easy but it's: solve for x using common denominators 3/4(x+2)=x/(x+3) Answer choices below:
Answer:
x = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{3}{4(x+2)}[/tex] = [tex]\frac{x}{x+2}[/tex]
multiply numerator/ denominator of [tex]\frac{x}{x+2}[/tex] by 4, thus
[tex]\frac{3}{4(x+2)}[/tex] = [tex]\frac{4x}{4(x+2)}[/tex]
Since the denominators are common , equate the numerators, that is
4x = 3 ( divide both sides by 4 )
x = [tex]\frac{3}{4}[/tex]
Mr. Duncan bought a table at a discount if 30% thus saving $42. what was the marked price of the table?
Answer:
$140
Step-by-step explanation:
if 30% of full price = $42 then 100% = 42/0.3 = 140
Answer:
$140
Step-by-step explanation:
1. Set up the equation
[tex]\frac{42}{x}[/tex] = [tex]\frac{30}{100}[/tex]
Percentage is out of 100 this equation says 42 of x number is equal to 30%.
2. Cross multiply
30x = 4200
3. Solve for x by dividing both sides by 30
x = 140
Write an equation of the line that passes through the point (-6, -5) with slope 6.
A. y +5= -6(x+6)
B.y+6= -6(x+5)
C. y+6=6(x+5)
D.y+5= 6(x+6)
Answer:
Option (D) is the correct option.
Step-by-step explanation:
Let the equation of a line which passes through (x', y') and slope 'm' is,
y - y' = m(x - x')
If this line passes through a point (-6, -5) and slope 'm' = 6
Equation of the line will be,
y -(-5) = 6[x - (-6)]
y + 5 = 6(x + 6)
Therefore, equation the line will be y + 5 = 6(x + 6).
Option (D) will be the answer.
Which statements are true about the solution of 15 greater-than-or-equal-to 22 + x? Select three options. x greater-than-or-equal-to negative 7 x less-than-or-equal-to negative 7 The graph has a closed circle. –6 is part of the solution. –7 is part of the solution.
Answer:
[tex]x \leq -7[/tex]
The graph has a closed circle.
–7 is part of the solution.
Step-by-step explanation:
Given
[tex]15 \geq 22 + x[/tex]
Required
Select 3 options from the given list of options
[tex]15 \geq 22 + x[/tex]
Subtract 22 from both sides
[tex]15 - 22 \geq 22 - 22+ x[/tex]
[tex]-7 \geq x[/tex]
Swap positions of the expression; Note that the inequality sign will change
[tex]x \leq -7[/tex]
This means x less-than-or-equal-to negative 7
There are two options left to select;
The inequality sign in [tex]x \leq -7[/tex] implies that the graph has a close circle.
Inequality signs such as [tex]\leq[/tex] and [tex]\geq[/tex] signifies a close circle
There is only one option left to select;
Lastly;
Split the expression [tex]x \leq -7[/tex] into two
We have:
[tex]x < -7[/tex] or [tex]x = -7[/tex]
Because [tex]x = 7[/tex],
Then, -7 is also a part of the solution
Answer:
B) x less-than-or-equal-to negative 7
C) The graph has a closed circle.
E) –7 is part of the solution.
Step-by-step explanation:
Im not 100% sure but i am 95% sure they r
Rewrite the following radical expression in rational exponent form.
Answer:
[tex]x^\frac{3}{7}[/tex]
Step-by-step explanation:
we can write [tex]\sqrt[7]{x}[/tex] as [tex]x^\dfrac{1}{7}[/tex] and we multiply 1 by 3 to get [tex]x^\frac{3}{7}[/tex]
The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. Admissions Probability 1,100 .2 1,400 .3 1,300 .5 Click here for the Excel Data File What is the expected number of admissions for the fall semester? Compute the variance and the standard deviation of the number of admissions. (Round your standard deviation to 2 decimal places.)
Answer:
Variance =10900.00
Standard deviation=104.50
Step by step Explanation:
Admissions Probability for 1100= 0.2
Admissions Probability for 1400=0.3
Admissions Probability for 1300 =0.5
To find the expected value, we will multiply each possibility by its probability and then add.
mean = 1100*0.2 + 1400*0.3 + 1300*0.5 = 1290
To find the variance, we will start by squaring each possibility and then multiplying it by its probability. We will then add these and subtract the mean squared.
E(X^2)=( 1100²*0.2)+ (1400²*0.3 )+ (1300²*0.5) = 1675000
Variance(X)=E(X²)- [E(X)]²
= 1675000 - (1290)²
=10900
Hence, the Variance(X)=10900
Then to calculate the standard variation , we will use the formular below,
standard variation (X)=√ var(X)= √10900
=104.5
Hence the standard variation=104.5
among the following, a perfect number a) 6 b)28 c) 625 d) 100
this question comes under more than one correct answer
Answer:
28 and 6
Step-by-step explanation:
List the factors (excluding itself):
6: 1, 2, 3,
28: 1, 2, 4, 7, 14
Add them up!
1+2+3=6
1+2+4+7+14=28
if they add up to the original number then the number is perfect.
========================================
Explanation:
By definition, a perfect number is one where the factors smaller than itself add to the number in question.
The factors of 6, smaller than 6, are {1,2,3}. We can see that 1+2+3 = 6. Therefore, 6 is a perfect number.
Similarly, 1+2+4+7+14 = 28 showing that 28 is also a perfect number.
------
The factors of 625, that are smaller than 625, are 1,5,25,125. They add to 1+5+25+125 = 156. This isn't equal to 625, so 625 isn't a perfect number.
A similar issue happens with 100 as well. The smaller factors are 1,2,4,5,10,20,25,50, meaning we get a sum of 1+2+4+5+10+20+25+50 = 117, which is too large.
------
The first four perfect numbers are: {6, 28, 496, 8128}
Write an inequality:
from (–5) to (–1) inclusive
Answer:
Inclusive means that we'll use the signs ≤ and ≥. Let's call the variable in our inequality as x. Therefore, the answer is -5 ≤ x ≤ -1.
Courtney constructed this figure using a compass with its width set equal to PR, the radius of the circle. She claims triangle PRS is equilateral because all three sides of the triangle are equal to PR. She also claims that applying the same argument to prove each triangle in the figure is equilateral proves that the inscribed hexagon is also equilateral. Which statement is true? A. Courtney's reasoning about triangle PRS is correct, but the hexagon is not equilateral. B. Courtney's reasoning about triangle PRS is correct, and the hexagon is equilateral. C. Courtney's reasoning about triangle PRS is incorrect, and the hexagon is not equilateral. D. Courtney's reasoning about triangle PRS is incorrect, but the hexagon is equilateral.
Answer:
B
Step-by-step explanation:
It helps if you have the figure included. However, since it is not, we can assume that she has gone around the circle with all six sides of the hexagon is set to PR.
That makes the hexagon with 6 equal sides. It also makes each triangle using one of the sides equal to PR. The radii are all equal. There are 6 triangles making up the hexagon.
Both statements she makes are true and that makes B the answer.
The ratio of figure A to B is 4:1. The volume of figure A is 4,032π in3. What is the volume of figure B?
Answer:
The volume of figure B is 1008π in³Step-by-step explanation:
The ratio of figure A to B is 4:1
That's
[tex] \frac{4}{1} [/tex]
Volume of figure A is 4.023π in³
To find the volume of figure B we compare the volumes of the two figures to the ratio
That's
[tex] \frac{4}{1} = \frac{4032\pi}{B} [/tex]
Cross multiply
That's
4B = 4032π
Divide both sides by 4
B = 1008π
The volume of figure B is 1008π in³Hope this helps you
Which example illustrates the commutative property of addition for polynomials?
Answer:
The fourth.Step-by-step explanation:
The alternation of addition means you can swap places of components of sum.
(2x²+5x) and (4x²-4x) are polynominal components of the sum: (2x²+5x)+(4x²-4x)
Answer:
D
Step-by-step explanation:
got it right on edge
the product of five and a certain number is twelve
Answer:
Step-by-step explanation:
Hello
5 * [tex]\boxed{ }[/tex] = 12
so this number is
[tex]\boxed{ \ } = \dfrac{12}{5}[/tex]
Hope this helps
Answer:
[tex]\frac{12}{5}[/tex] or 2.4
Step-by-step explanation:
→ Form an equation
5 × ? = 12
→ Divide both sides by 5
? = [tex]\frac{12}{5}[/tex] or 2.4
Which function is graphed below?
Answer:
The function graphed below is [tex]x = y^{2} - 2[/tex] or [tex]y = \pm \sqrt{x+2}[/tex].
Step-by-step explanation:
The graph represents a second order polynomial function (a parabola), whose axis of symmetry is the x-axis and whose form is presented as follows:
[tex]x - h = C\cdot (y-k)^{2}[/tex]
Where:
[tex]x[/tex], [tex]y[/tex] - Dependent and independent variable, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the vertex, dimensionless.
[tex]C[/tex] - Vertex constant, dimensionless. If [tex]C > 0[/tex], then vertex is an absolute minimum, otherwise it is an absolute maximum.
After a quick observation, the following conclusions are done:
1) Vertex is an absolute minimum ([tex]C > 0[/tex]) and located at (-2, 0).
2) Parabola pass through (2, 2).
Then, the value of the vertex constant is obtained after replacing all known values on expression prior algebraic handling: ([tex]x = 2[/tex], [tex]y = 2[/tex], [tex]h = -2[/tex], [tex]k = 0[/tex])
[tex]2+2 = C\cdot (2-0)^{2}[/tex]
[tex]4 = 4\cdot C[/tex]
[tex]C = 1[/tex]
The function is:
[tex]x = -2 + 1\cdot y^{2}[/tex]
[tex]x = y^{2}-2[/tex]
The inverse function of this expression is [tex]y = \pm \sqrt{x+2}[/tex]
The function graphed below is [tex]x = y^{2} - 2[/tex] or [tex]y = \pm \sqrt{x+2}[/tex].
need help use the screen shot
Answer:
6.5 < 3rd side < 19.9.
Step-by-step explanation:
For a triangle, the third side must be more than the difference between the given side lengths, but less than the total of the given side lengths.
So, the third side must be more than...
13.2 - 6.7 = 6.5.
The third side must be less than...
13.2 + 6.7 = 19.9.
6.5 < 3rd side < 19.9.
Hope this helps!
a subway train with 47 people stops at a station and picks up 20 more people at the same station p people get off. there are 52 people left on the train. which equation shows how to find the value of p
Answer:
67 - p = 52
Step-by-step explanation:
the train starts with 47 people: 47
it picks up 20 more: 47 + 20 = 67
p people get off: 67 - p
52 people are left on train: 67 - p = 52
3/x-2, i'm confused as to what the horizontal asymptote is. The resources I found online conclude that it has a horizontal asymptote of y=0. I know that in order for a horizontal asymptote to be y=0, the denominator has to have a greater degree than the numerator. Im confused because doesn't the numerator have the same degree as the denominator (degree of 1)?
Answer:
y = 0
Step-by-step explanation:
Given
f(x) = [tex]\frac{3}{x-2}[/tex]
The degree of the numerator is zero 0 ( 3[tex]x^{0}[/tex] )
The degree of the denominator is 1
Since the degree of denominator > degree of numerator.
Then there is a horizontal asymptote at y = 0
Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 0.35 m3 of fluffy
material.
0.5 m
? m
1 m
What is the length of the pillow?
Give an exact answer (do not round).
HELP PLEASE
Complete Question
Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 0.35 m³ of fluffy
material. The base is 0.5m² and the height is 1m.
What is the length of the pillow?
Give an exact answer (do not round).
Answer:
1.4m
Step-by-step explanation:
A wedge comes in the shape of a Triangular prism. Hence,
Volume of a wedge(Triangular prism) = 1/2 × B × H × L
b = 0.5m
h = 1 m
l = ??
Volume of a wedge = 0.35m³
0.35 = 1/2 × 0.5 × 1 × L
0.35 = 0.25 × L
L = 0.35/0.25
L = 1.4m
¡Ayuda!
1. Método del Triángulo: Una embarcación navega a una distancia de 800 km hacia el Oeste y después avanza 1400 km a 135 °. ¿Cuál es la magnitud, dirección y sentido del desplazamiento resultante? R /. 2,080 km, 155 ° NO.
Answer:
La magnitud del desplazamiento resultante es 2045.463 kilómetros. La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.
Step-by-step explanation:
En primer lugar, se construye el triángulo. La figura resultante se encuentra incluida como archivo adjunto. La magnitud del desplazamiento resultante se determina mediante la Ley del Coseno:
[tex]r = \sqrt{(800\,km)^{2}+(1400\,km)^{2}-2\cdot (800\,km)\cdot (1400\,km)\cdot \cos 135^{\circ}}[/tex]
[tex]r \approx 2045.463\,km[/tex]
La magnitud del desplazamiento resultante es 2045.463 kilómetros.
La dirección del desplazamiento resultante es hallada por medio de la Ley del Seno, sabiendo que el ángulo del desplazamiento resultante a la recta de 1400 kilómetros:
[tex]\frac{1400\,km}{\sin \alpha} = \frac{2045.463\,km}{\sin 135^{\circ}}[/tex]
Se despeja el ángulo correspondiente:
[tex]\alpha = \sin^{-1}\left(\frac{1400\,km}{2045.463\,km}\times \sin 135^{\circ} \right)[/tex]
[tex]\alpha \approx 28.945^{\circ}[/tex]
La dirección absoluta del desplazamiento resultante es:
[tex]\alpha' = 180^{\circ}-\alpha[/tex]
[tex]\alpha' = 180^{\circ}-28.945^{\circ}[/tex]
[tex]\alpha' = 151.055^{\circ}[/tex]
La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.
3. The diagram shows a piece of rectangular tile
PQRS. A kite shape TUVW is inscribed in the
rectangle. Given that the perimeter of PQRS is
120 cm, find the area of TUVW.
Answer:
432cm²
Step-by-step explanation:
If the Perimeter is 120cm, PT=8 (120-28-12-12-28-12-12)/2
This means the rectangle is 24x36.
area of a kite is the diagonals divided by 2 (or half of the rectangle).
24x36=864
864/2=
432 cm²
Is y = 75 x + 52 increasing or decreasing.
Answer:
Increasing if X is positive decreasnig if X is negative
Step-by-step explanation:
Answer:
increasing
Step-by-step explanation:
positive slope of 75 so line goes up to the right
Which equations represents inverse variation? Check all that apply
An inverse variation can be represented by the equation xy=k or y=kx . That is, y varies inversely as x if there is some nonzero constant k such that, xy=k or y=kx where x≠0,y≠0
solve : 3/2 X -7/2 = 5x +14
Answer:
The answer to your question is -5
Step-by-step explanation:
Data
[tex]\frac{3}{2}x - \frac{7}{2} = 5x + 14[/tex]
Process
1.- Subtract 5x in both sides
[tex]\frac{3}{2} x - \frac{7}{2} - 5x = 5x -5x + 14[/tex]
2.- Simplify
[tex]- \frac{7}{2} x - \frac{7}{2} = 14[/tex]
3.- Add 7/2 in both sides
[tex]-\frac{7}{2} x = 14 + \frac{7}{2}[/tex]
4.- Simplify
- [tex]\frac{7}{2} x = \frac{35}{2}[/tex]
5.- Solve for x
x = [tex]\frac{35}{2} / - \frac{7}{2}[/tex]
6.- Simplify
x = -5
Answer: x = -3.71
Step-by-step explanation:
3/2*-7/2=5x+14
-4.55=5x+14
Subtract 14
-18.55=5x
Divide by 5
x = -3.71
Hope it helps <3
PLEASEEEEEEEEEEEEE HELPPPPPPPPPPP!
Susan and Mark are standing at different places on a beach and watching a bird. The angles of elevation they make are 20º and 50º, respectively. If Susan and Mark are 7 kilometers apart and the bird is between them, the bird is at a height of kilometers from the ground.
Answer:
The bird is 2.44km high
Step-by-step explanation:
Hello,
To solve this question, we need to understand how they are and we can only get this with a correct pictorial diagram.
See attached document for better understanding.
From the first diagram, we understand that the bird is between them and also on top of them.
Assuming Susan, Mark and the bird all form a triangle at each other and the bird at the top, we can divide the the triangle into two equal parts.
But before then, we should know that sum of angles in a triangle is equal to 180°
Therefore,
20° + 50° + b° = 180
70° + b = 180
b = 180° - 70°
b = 110°
Dividing angle b into two equal parts = 55° on each side.
See the last attached document for better illustration.
Using SOHCAHTOA, we can find the adjacent of the triangle which corresponds to the height of the bird.
We have opposite = 3.4km and we're looking for adjacent. We can use tangent of the angle to find the adjacent.
Tanθ = opposite / adjacent
Tan 55° = 3.5 / adj
Adjacent = 3.5 / tan55
Adjacent = 3.5 / 1.43
Adjacent = 2.44km
The height of the bird is 2.44km
Answer:
A. 1.95
Step-by-step explanation:
PLATO
Unit 6 Test Part B
MCR3U Summer
4. Sophie is riding her bike home when she runs over a nail. It gets stuck to the tire of her bike but does not pop
the tire. As she continues to cycle home, the nail hits the ground every 2 seconds and reaches a maximum
height of 48 cm
Answer:
You did not ask anything, i guess that you want to find the equation of the height of the nail as a function of time.
Data that we have:
The nail is in a circular object.
the nail hits the ground every 2 seconds, then the weel does a full cycle every 2 seconds.
The maximum height of the nail is 48cm, and as the nail is stuck on the weel, the maximum height will be when the nail is on top of the weel.
From this, we can conclude that the diameter of the weel is 48cm.
Now, with this we could write the equation of the height of the nail as a function of time.
We know that this is a periodic function, so let's write it as:
f(t) = A*cos(c*t) + B
where A, B and c are constanst.
At t = 0, when the byke hits the nail, the nail must be in the ground, so we have that:
0 = A*cos(c*0) + B
A + B = 0
A = - B
and we also know that the function is periodic with T = 2s
cos(c*t) = cos(c*(t + 2s) = cos( c*t + 2s*c)
and we know that the period of the cosine function is 2*pi
then:
c*2s = 2*pi
c = (2pi/2s) = pi/s
then our function is:
f(t) = -B*cos(t*pi/s) + B
now, the maximum heightwill be when cos(t*pi/s) = -1, and this happens at t = 1s
f(1s) = -B*cos(pi) + B = 2B
And we know that the maximum height is 48cm
2*B = 48cm
B = 24cm
Then the function of the height of the nail is:
f(t) = -24cm*cos(t*pi/s) + 24cm