The median weight of a boy whose age is between 0 and 36 months can be approximated by the function w(t)=7.42+1.92t−0.0074t2+0.000446t3​, where t is measured in months and w is measured in pounds. Use this approximation to find the following for a boy with median weight in parts ​a) through ​c) below.a) The weight of the baby at age 7 months. The approximate weight of the baby at age 7 months is __________ lbs. (Round to two decimal places as needed.) b) The rate of change of the baby's weight with respect to time at age 7 months. The rate of change for the baby's weight with respect to time at age 7 months is approximately ________ lbs/month (Round to two decimal places as needed.)
Answers
Answer:
(a)20.65 lbs.
(b)1.88 lbs/month.
Step-by-step explanation:
The median weight of the boy can be approximated by the function:
\(w(t)=7.42+1.92t-0.0074t^2+0.000446t^3\)
Where t is measured in months; and
w is measured in pounds.
(a)When the baby is 7 months
Approximate Weight,
\(w(7)=7.42+1.92(7)-0.0074(7)^2+0.000446(7)^3\\=20.65$ pounds (to two decimal places)\)
The approximate weight of the baby at age 7 months is 20.65 lbs.
(b) If \(w(t)=7.42+1.92t-0.0074t^2+0.000446t^3\)
Rate of change, \(w'(t)=1.92-0.0148t+0.001338t^2\)
At t=7 months
\(w'(7)=1.92-0.0148(7)+0.001338(7)^2\\w'(7)=1.88$ lbs/month\)
The rate of change for the baby's weight with respect to time at age 7 months is approximately 1.88 lbs/month.
Related Questions
Amelia needs to buy some dog food. At the nearest store, 5 bags of dog food cost $11.25. How much
would Amelia spend on 3 bags of dog food?
Amelia would spend $on 3 bags of dog food.
Answers
Answer:
$6.75
Step-by-step explanation:
find the cost of each individual bag
11.25 ÷ 5 = 2.25
multiply that by the amount of bags needed
2.25 × 3 = 6.75
Omar wants to measure the width of a river. He marks off two right triangles, as shown in the figure. The base of the larger triangle has a
length of 64 m, and the base of the smaller triangle has a length of 31 m. The height of the smaller triangle is 19.8 m. How wide is the
river? Round your answer to the nearest meter. (The figure is not drawn to scale.)
19.8 m
River
A
31 m
64 m
?
A
m
X
Ś
Answers
Answer:
41 meters
Step-by-step explanation:
\(\frac{31}{64}\) = \(\frac{19.8}{x}\)
31x = (19.8)(64)
31x = 1267.2 Divide both sides by 31 and round
x = 41
Find the area of the triangle. Round to the
nearest tenth.
8 yd
98 percent
3 yd
Answers
Answer:
i NEED A PICTURE.
Step-by-step explanation:
27
3. A poll was conducted to find out whether people thought the United States should be involved (1 point)
in restrictions made on other countries' nuclear programs. Respondents who answered
positively were then asked to select a reason for this involvement. The respondents were
grouped into two age brackets. Using a 0.01 significance level, a test statistic of 19.529 and a
critical value of 9.210 were found. Use these values to test the claim that the age bracket is
independent of the choice for the cause of the United States' involvement in other countries'
nuclear programs.
OReject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the age
bracket is independent of the choice for the cause of the United States' involvement in other count
nuclear programs.
OFail to reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim
the age bracket is independent of the choice for the cause of the United States' involvement in oth
countries' nuclear programs.
Fail to reject the null hypothesis, this is sufficient evidence
Reject the null hypothesis, there is not sufficient evidence
Answers
Based on the information, the correct answer is B. Reject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the age bracket is independent of the choice for the cause of the United States' involvement in other countries' nuclear programs.
How to explain the hypothesisThe test statistic is greater than the critical value, so we reject the null hypothesis. This means that there is sufficient evidence to conclude that the age bracket is not independent of the choice for the cause of the United States' involvement in other countries' nuclear programs.
In other words, the age bracket of a respondent is related to the reason they believe the United States should be involved in restrictions made on other countries' nuclear programs.
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A direct mail appeal for contributions from a university’s alumni and supporters is considered to be too costly if less than 28%
28
%
of the alumni and supporters provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 165
165
people on the alumni and supporters mailing lists. They receive monetary contributions from 36
36
people. Does this evidence demonstrate that the direct mail campaign is not cost effective? Use a 0.05
0.05
level of significance.
Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
Answers
The test statistic is given as follows:
z = -1.77.
As the test statistic is less than the critical value for the left-tailed test, this evidence demonstrates that the direct mail campaign is not cost effective.
How to obtain the test statistic?
The equation for the test statistic is given as follows:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
In which:
\(\overline{p}\) is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The parameters for this problem are given as follows:
\(p = 0.28, n = 165, \overline{p} = 0.2182\)
The critical value for a left tailed test with a significance value of 0.05 is given as follows:
z = -1.645.
The test statistic is then given as follows:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
\(z = \frac{0.2182 - 0.28}{\sqrt{\frac{0.28(0.72))}{165}}}\)
z = -1.77.
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-10 (r + 16) =-30
what does the r equal
Answers
Answer:
YES DOOD TY FOIR THE COINS DOOD
Step-by-step explanation:
or steps
first divide both sides by -10
r + 16 = 3
subtract 16 from both sides
r= 3-16
r=-13
A rectangular city is 2 miles long and 7 miles wide. What is the distance between opposite corners of the city? The exact distance is ______________ miles How far is it to the closest tenth of a mile? Answer: The distance is approximately ___________ miles.
Answers
Answer:
The distance is approximately 10.4 miles.
Answer:
exact distance is = 7.28010988928
rounded to the tenth of a mile is
distance is approximately 7.3 miles
Step-by-step explanation:
hypotenuse of a triangle that's 2 by 7
Pythagorean theorem
a^2 + b^2 = c^2
2^2 + 7^2 = c^2
4 + 49 = c^2
c^2 = 53
c = √53
c = 7.28010988928
tenth of a mile is
c = 7.3
Thank you for the help!
Answers
Answer:
c 57
Step-by-step explanation:
A cereal box has dimensions of 12 inches, (7)3/4 inches, and 2 inches. A pastry box has a dimensions of (3)2/3 inches, (3)1/2 inches, and (2)1/3 inches. What is the difference in volume, cubic inches, between the two boxes. show your work
Answers
The difference in volume between the two boxes would be = 156in³
How to calculate the difference in volume between the boxes?To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;
Volume = length×width×height.
For box 1 = length = 12in, width = 7¾in, height= 2in
Vol = 12×7¾×2 = 186in³
For box 2; length = 3⅔in, width = 3½in, height= 2⅓in
Volume = 3⅔×3½×2⅓ = 30
The difference = 186-30 = 156in³
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what is the answer I need help
Answers
Answer:
Step-by-step explanation:
The vertex is at (-3, -1) and the leading coefficient is negative ( because the curve is inverted)
y = -a(x + 3)^2 - 1
One point on the curve is (-2, -3) so
-3 = -a(-2+3)^2 - 1
-3 = -a - 1
-a = -2
So we have
y = -2(x + 3)^2 - 1
y = -2(x^2 + 6x + 9) - 1
y = -2x^2 - 12x - 19.
Find the coordinates of the point 7/10 of the way from A (-3,-5) to B (9.4)
Answers
Answer:
(-2/17, 5/17)
Step-by-step explanation:
Given the coordinates A (-3,-5) to B (9,4), we are to find the coordinate of the point cutting the line using the ratio 7:10
Using the midpoint formula;
M(X,Y) = {(ax1+bx2/a+b, (ay1+by2/a+b))
Given
x1 = -3, y1 = -5, x2 = 9, y2 = 4, a = 7 and b = 10
get the required coordinates;
X = ax1+bx2/a+b
X = 7(-3)+10(9)/7+10
X = -21+19/17
X = -2/17
Get the Y coordinate;
Y = ay1+by2/a+b
Y = 7(-5)+10(4)/7+10
Y = -35+40/17
Y = 5/17
Hence the required coordinate is (-2/17, 5/17)
A single 6-sided die is rolled. Which BEST describes the probability of rolling a number 4 or less? 1) A ) impossible B) unlikely likely certains
Answers
Answer:
it is likely because the majority of the outcomes are in your favor
Answer:
A
Step-by-step explanation:
Impossible, did it on usatestprep
Find the area of a trapezoid with bases of 16 feet and 10 feet and a height of 3 feet. 39 ft2 78 ft2 240 ft2 480 ft2
Answers
Answer: 39 ft2
Step-by-step explanation:
The area of the trapezoid is 39 square feet.
To find the area of a trapezoid, you can use the formula:
Area = (1/2) × (base1 + base2) × height
Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:
Area = (1/2) × (16 + 10) × 3
Area = (1/2) × 26 × 3
Area = (1/2) × 78
Area = 39 ft^2
Therefore, the area of the trapezoid is 39 square feet.
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The ratio of the length to the width of a map is 5 to 2. The map is exactly 15 inches in length. What is the width of the map? A. 6 inches B. 7 inches C. 10 inches D. 12 inches
Answers
5:2 = 15:?
5 x 3 = 15, so 2 x 3 = your answer, 6.
How many solutions does this system have? no solutions one unique solution O O two solutions O or an infinite number of solutions
Answers
Answer:
no solutions
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
equation of blue line is y = x + 2 , in slope- intercept form
with slope m = 1
equation of red line is y = x - 3 , in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes
then the blue and red lines are parallel.
the solution to the system is at the point of intersection of the 2 lines
since the lines are parallel then they do not intersect each other.
thus the system shown has no solution.
a container of beads contains 8 red beads, 7 yellow beads, and 6 green beads. A bead will be drawn from the basket and replaced 60 times. What is a reasonable prediction for the number of times a green or a red bead is drawn?
Answers
Answer:
2/3
Step-by-step explanation:
8+6=14
14/21=2/3
mark me brainliest please
Which of the following equations best represents "y is directly related to the square of x"?
y = kx
y = kx2
y = k(1/x)
y = k(1/x2)
Answers
Answer:c.
Step-by-step explanation: its true
Answer:
the answer is y = k/x
Step-by-step explanation:
why? because I said so
10 points if you answer this
Answers
8. Their pizzas were all cut differently. Josh’s pizza was cut in half, Lisa’s was cut into 6 slices and Vicki’s was cut in 8 slices
Answer:
7. = 1/4 or 3 pieces left.
Step-by-step explanation:
If you take 12 pieces of pizza and divide it by 4 it equals 3. So 3 times 3 because there are 3 pieces left. Hope that makes sense!
Point C has a coordinate of (-4, -6) and point D has a coordinate of (1, -6), how far are they apart?
Answers
The distance between points C and D is given as follows:
5 units.
How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
The coordinates for this problem are given as follows:
(-4, -6) and (1, -6).
Hence the distance is given as follows:
\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)
D = 5 units.
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The length of a rectangle is shown below:
If the area of the rectangle to be drawn is 12 square units, where should points C and D be located, if they lie vertically below the line that connects B and A, to make this rectangle? (1 point)
A. C(−3, −2), D(1, −2)
B. C(−3, −1), D(1, −1)
C. C(−3, −4), D(1, −4)
D. C(−3, −5), D(1, −5)
Answers
Answer:
A - C(-3, -2), D(1, -2)
Step-by-step explanation:
Jen simplified a radical expression. Her work is shown.
√
50
x
3
y
5
5
Step 1:
√
10
x
3
y
5
Step 2:
√
10
⋅
x
2
⋅
x
⋅
y
2
⋅
y
2
⋅
y
Step 3:
x
y
2
√
10
x
y
Did Jen make an error?
A.
Jen made an error in Step 1.
B.
Jen made an error in step 2.
C.
Jen made an error in step 3.
D.
Jen did not make an error.
Answers
Answer:
im taking the same test lol
Step-by-step explanation:
y =4X +2 , y =2(2x -1)
Answers
Answer:
y =4x +2, y =4x-2
Step-by-step explanation:
according to this step we are not collecting like terms
WHAT ARE THE FACTORS OF 57
Answers
Solve the inequality.
|4x - 1| ≥ 23
I need some help if anyone knows it!
Answers
The value of the inequality |4x - 1| ≥ 23 will be
x ≥ 6.
How to calculate the inequality?It should be noted that the inequality given is expressed as:
|4x - 1| ≥ 23
This will be
|4x - 1| ≥ 23
4x ≥ 23 + 1
4x ≥ 24
Divide
4x/4 ≥ 24/4
x ≥ 6
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Ximena pays a flat cost of $44.50 per month and $4 per gigabyte. She wants to keep her bill at $50.10 per month. How many gigabytes of data can she use while staying within her budget?
Answers
Answer:
Ximena can use 1 gigabytes of data
Step-by-step explanation:
The first thing you want to do is subtract
51.10 - 44.50 = 5.6
5.6 is the amount of money she will have to spend on data
With each gigabyte costing 4 dollars and only 5 dollars to spend
she can only use one gigabyte
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 2 ft by 2 ft by 12.5 ft. If the container is entirely full and, on average, its contents weigh 0.22 pounds per cubic foot, find the total weight of the contents. Round your answer to the nearest pound if necessary.
Answers
Answer:
38.81 pounds
Step-by-step explanation:
Considering the definition of right rectangular prism and its volume, the total weight of the contents is 38.81 pounds.
Right rectangular prism
A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.
Volume of right rectangular prism
To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.
That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.
Volume of the container
In this case, you know that:
the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.
the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.
So, the volume of the container is calculated as:
7.5 ft× 11.5 ft× 3 ft= 258.75 ft³
Then, the total weight of the contents is calculated as:
258.75 ft³× 0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds
Finally, the total weight of the contents is 38.81 pounds.
Which of the following lines is perpendicular to the line 8x + 6y = 12 and passes through the point (-12,-2)?
Answers
Answer:
y = 3/4x + 7
Step-by-step explanation:
8x + 6y = 12
6y = -8x + 12
y = -4/3x + 2
Perpendicular slope: 3/4
y - y1 = m(x - x1)
y + 2 = 3/4(x + 12)
y + 2 = 3/4x + 9
y = 3/4x + 7
Learning Task 3 Answer the questions that follow. Put a check mark (/) on the space provided. Copy and answer in your math notebook. 1. The units for Volume are always ______squared _____cubed 2. Volume is the amount of space an object takes up. ___True ___False Calculate for the volume of solid. 3. Chona is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches. 4. A 3-tier cake with the same height of 10 in and radius of 12 in, 8 in, 5 in respectively is to be delivered to a birthday party. How much space does this cake take up? Use 3.14 for π. 5. A Styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth. Use 3.14 for π.
Answers
3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.
4. The cake takes up approximately 7317 cubic inches of space.
5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.
1. The units for Volume are always cubed.
2. Volume is the amount of space an object takes up. True.
3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:
V = 3.14 * (4.5)^2 * 32
V = 3.14 * 20.25 * 32
V ≈ 2034.72 cubic inches
4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.
Tier 1:
V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches
Tier 2:
V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches
Tier 3:
V3 = 3.14 * (5)^2 * 10 = 785 cubic inches
Total volume:
Total V = V1 + V2 + V3
Total V = 4521.6 + 2010.4 + 785
Total V ≈ 7317 cubic inches
5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:
V = (1/3) * 3.14 * (24)^2 * 12
V = (1/3) * 3.14 * 576 * 12
V ≈ 7234.08 cubic centimeters
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for the inequality Y is less than or equal to 9 Jasmine says 9 and 0 are both solutions is she correct
Answers
Vedant received two quotes for new carpet for his home. The quote from Company A is $0.15 less per square foot than the quote from Company B. If Vedant plans to buy 1,200 square feet of carpet, how do his total costs from the two companies compare?
Company A is cheaper by $180.
Company B is cheaper by $180.
Company A is cheaper by $8,000.
Company B is cheaper by $8,000.
Don’t make any funny jokes about this and don’t say idk or something like that or I’ll report you.
Answers
Answer:
Company B is cheaper by $180.
Step-by-step explanation:
just do 1,200 square feet x 0.15 = 180
Answer:
b as in big cat
Step-by-step explanation: