Carlos read 4 books. How many children read fewer books. Than carlos?
Answers
Where the above pictogram is given, note that the number of children who read fewer books than Carlos are two in number. Namely:
Gwen - Two booksHenry - Four books.To derive the number of children who read fewer books than Carlos, we only need to count the number of people whose books are less than four.
Using the picture graph key, we know that:
Ryan read 4 books
Gwen = 2
Anna = 6
Henry = 3
Since 2 and 3 are less than 4 which was read by Carlos, then the number of children who read fewer books than Carlos are two in number.
Full Question:
Although part of your question is missing, you might be referring to this full question:
Read Picture Graphs
Use the picture graph above. Write or draw to explain.
4. Carlos read 4 books. How many children read fewer books than Carlos?
_ children ?
Related Questions
Suppose that the dollar cost of producing x radios is c(x) = 400 + 20x - 0.2x 2. Find the marginal cost when 30 radios are produced.
Answers
c(30) = 400 + 20(30) - 0.2(30)²
= 400 + 600 - 0.2(900)
= 1000 - 180
= 820
It costs $820 when 30 radios are produced.
Marginal cost is how much it would cost to make one MORE of the same product so now we find how much it costs to produce 31 radios and compare the two.
c(31) = 400 + 20(31) - 0.2(31)²
= 400 + 620 - 0.2(961)
= 1020 - 192.2
= 827.8 or ≈828.
Now we find the difference which means we subtract the two.
828 - 820 = 8.
Your marginal cost is $8.
To compare we can also do 29 radios.
c(29) = 400 + 20(29) - 0.2(29)² = 811.8 or ≈812
820 - 812 = 8.
The marginal cost when 30 radios are produced is $8.
Explanation:To find the marginal cost when 30 radios are produced, we need to differentiate the cost function with respect to x, which represents the number of radios produced. The cost function is given as c(x) = 400 + 20x - 0.2x^2. Differentiating c(x) with respect to x, we get c'(x) = 20 - 0.4x. Now, substitute x = 30 into c'(x) to find the marginal cost when 30 radios are produced. c'(30) = 20 - 0.4(30) = 20 - 12 = 8. Therefore, the marginal cost when 30 radios are produced is $8.
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Then find the area bounded by the two graphs of y=2x^2−24x+42 and y=7x−2x^2
Answers
[tex] \int\limits^a_b {(f(x)-g(x))} \, dx [/tex]
If you think about it, we are really doing this with all integration, only the second function is just y=0.
First, we need to figure out which function is on top. In this case we know that [tex]2x^2-24x+42[/tex] is a positive parabola while [tex]7x-2x^2[/tex] is negative, so the negative parabola will be on top. It is always a good idea to draw a rough sketch of the graphs because the curves could intercept multiple times, flipping which graph is on top at different intervals.
Next, we need to determine the bounds. These will be where the two graphs intercept, so we can just set them equal to each other and solve for x:
[tex]2x^2-24x+42=7x-2x^2[/tex]
Combine like terms:
[tex]4x^2-31x+42[/tex]
Now factor and find the zeros. We can use the quadratic formula:
[tex] \frac{31+ \sqrt{31^2-4(4)(42)} }{8} [/tex]
and
[tex] \frac{31- \sqrt{31^2-4(4)(42)} }{8} [/tex]
x = 1.75 and 6
[tex] \int\limits^6_{1.75} {((7x-2x^2)-(2x^2-24x+42))} \, dx [/tex]
[tex] \int\limits^6_{1.75} {(-4x^2+31x-42)} \, dx [/tex]
Solve:
[tex] \frac{-4x^3}{3} + \frac{31x^2}{2} - 42x [/tex]
Plug in bounds:
[tex]\frac{-4(6)^3}{3} + \frac{31(6)^2}{2} - 42(6)-(\frac{-4(1.75)^3}{3} + \frac{31(1.75)^2}{2} - 42(1.75))[/tex] = 51.17708
The mean of a curriculum committee is 34.8 years. A 15-year-old student representative is added to the committee. How does the student’s age affect the mean?
A.) The new mean age will be less than 34.8
B.) The new mean age will be greater than 34.8
C.) The new mean age will still be 34.8
D.) The new mean age will be 24.9
Answers
A.) The new mean age will be less than 34.8
_____
Any new members whose age is less than the mean will reduce the mean. Any new members whose age is greater than the mean will increase the mean.
Answer:
The correct option is A. The new mean age will be less than 34.8
Step-by-step explanation:
The mean of a curriculum committee is 34.8 years
Now, A 15-year-old student representative is added to the committee
Number of students in the curriculum committee is not known so if a student of 15 year age is added into the society we cannot find the exact new mean of the curriculum committee.
But, As the 15 is added to the sum of all observations but only 1 is added to the number of observations
So, The mean of the curriculum committee will obviously decrease
Since, Th mean of the curriculum committee is 34.8
Therefore, the new mean of the curriculum committee will be less than 34.8
Hence, The correct option is A. The new mean age will be less than 34.8
Annette is stacking boxes in her closet. There are 15 boxes in all. If each box weighs 7.5 pounds, his much do the boxes weigh together
Answers
15*7.5
Multiply:
112.5
15 boxes weight 112.5 pounds
The graph shows the function f(x).
Which value is closest to the average rate of change from x = 1 to x = 4?
A.−3.5
B.−2.3
C. −1.4
D .−0.3
Answers
Answer:
Option B is correct
-2.3
Step-by-step explanation:
Average rate of change(A(x)) for the function f(x) over the interval [a, b] is given by:
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex] ....[1]
We have to find the average rate of change from x = 1 to x = 4.
From the graph as shown below
For x = 1
f(1) = 3
and
For x = 4
f(4) = -3.9
Using [1] we have;
[tex]A(x) = \frac{f(4)-f(1)}{4-1}[/tex]
Substitute the given values we have;
[tex]A(x) = \frac{-3.9-3}{3}[/tex]
⇒[tex]A(x) = \frac{-6.9}{3}[/tex]
Simplify:
[tex]A(x) = -2.3[/tex]
Therefore, -2.3 value is closest to the average rate of change from x = 1 to x = 4
Jordana is putting a fence around a garden that is shaped like a half circle and a rectangle.How much fencing will Jordana need? Use 22/7 for pi
64 ft
86 ft
92 ft
114 ft
Answers
28 ft + 14 ft + 28 ft = 70 feet for the straight sides.
To find the distance around the circular side, you will need to find half of the circumference of the circle.
1/2 x pi x d
1/2 x 22/7 x 14 = 22 feet
70 feet + 22 feet = 92 feet
Jordana will need 92 feet of fencing to enclose this space.
Answer:
awnser c on edge 2020
Step-by-step explanation:
92
Which figure has all sides of equal measure but not necessarily all angles of equal measure?
Answers
The correct figure which has all sides of equal measure but not necessarily all angles of equal measure are ''Rhombus'' and ''parallelogram''.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
To find figure which has all sides of equal measure but not necessarily all angles of equal measure.
Now, We know that;
In a Parallelogram, A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length.
And, In a Rhombus, A rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides the same length,
Thus, The correct figure which has all sides of equal measure but not necessarily all angles of equal measure are Rhombus and parallelogram.
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he radius of a circle is 2 kilometers. What is the area of a sector bounded by a 45° arc?
Answers
area of a circle=pi*r²
for r=2 km
area of a circle=pi*2²-----> 12.56 km²
if 360° (full circle) has an area of---------> 12.56 km²
45°---------------------------------> x
x=45*12.56/360-----> x=1.57 km²
the answer is
1.57 km²
The area of a sector bounded by a 45° arc in a circle with a radius of 2 kilometers is π/² square kilometers.
To calculate the area of a sector bounded by a 45° arc in a circle with a radius of 2 kilometers, we will use the formula for the area of a sector, which is (θ/360) × π × r², where θ is the central angle in degrees and r is the radius of the circle. The central angle for our sector is 45° and the radius r is given as 2 km.
Plugging these values into the formula, we have:
Area of sector = (45/360) × π × (2²) = (1/8) × π × 4 = (1/2) × π = π/2 km².
Therefore, the area of the sector bounded by a 45° arc in a circle with a radius of 2 kilometers is π/²square kilometers.
Use part 1 of the fundamental theorem of calculus to find the derivative of the function. y = 5 u3 1 + u2 du 4 − 3x
Answers
[tex]y(x)=\displaystyle\int_5^{4-3x}u^3(1+u^2)\,\mathrm du[/tex]
in which case the FTC asserts that
[tex]\dfrac{\mathrm dy}{\mathrm dx}=(4-3x)^3(1+(4-3x)^2)\cdot\dfrac{\mathrm d(4-3x)}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=-3(4-3x)^3(1+(4-3x)^2)[/tex]
Using part 1 of the fundamental theorem of calculus to find the derivative of the function. The derivative of the given function is:
[tex]\mathbf{\dfrac{dy}{dx} =3\Big (\dfrac{(4-3x)^3}{1+(4-3x)^2}\ \Big) \ }[/tex]
Consider the given function:
[tex]\mathbf{y = \int^5_{4-3x} \ \dfrac{u^3}{1+u^2}\ du}[/tex]
The objective is to find [tex]\mathbf{\dfrac{dy}{dx}}[/tex] by using the fundamental theorem of calculus.
Suppose v = 4 - 3x; Then dv = -3dx[tex]\mathbf{\dfrac{dv}{dx}= -3}[/tex]Using chain rule:
[tex]\mathbf{\dfrac{dy}{dx} = \dfrac{dy}{dv}\times \dfrac{dv}{dx}}[/tex]
[tex]\mathbf{ =\dfrac{d}{dv}\Big (\int^5_{4-3x} \dfrac{u^3}{1+u^2}\ du\Big) \dfrac{dv}{dx}}}[/tex]
[tex]\mathbf{ =\dfrac{d}{dv}\Big (\int^5_{v} \dfrac{u^3}{1+u^2}\ du\Big) \dfrac{dv}{dx} \ \ \ \ \ since \ v \ = 4 - 3x} }[/tex]
[tex]\mathbf{ =-\dfrac{d}{dv}\Big (\int^v_{5} \dfrac{u^3}{1+u^2}\ du\Big) \dfrac{dv}{dx} }[/tex]
[tex]\mathbf{ =-\dfrac{d}{dv}\Big (\int^v_{5} \dfrac{u^3}{1+u^2}\ du\Big) \ (-3)}[/tex]
[tex]\mathbf{ =3\dfrac{d}{dv}\Big (\int^v_{5} \dfrac{u^3}{1+u^2}\ du\Big) \ }[/tex]
From the fundamental theorem of calculus;
[tex]\mathbf{\dfrac{d}{dx} \Big( \int^x_1 \ g(t) dt \Big) = g(x)}[/tex]
∴
[tex]\mathbf{ =3\dfrac{d}{dv}\Big (\int^v_{5} \dfrac{u^3}{1+u^2}\ du\Big) \ }[/tex] will be:
[tex]\mathbf{ =3\times \Big (\dfrac{(4-3x)^3}{1+(4-3x)^2}\ \Big) \ }[/tex]
∴
[tex]\mathbf{\dfrac{dy}{dx} =3\Big (\dfrac{(4-3x)^3}{1+(4-3x)^2}\ \Big) \ }[/tex]
Therefore, we can conclude that the derivative of [tex]\mathbf{y = \int^5_{4-3x} \ \dfrac{u^3}{1+u^2}\ du}[/tex]
using the fundamental theorem of calculus is [tex]\mathbf{\dfrac{dy}{dx} =3\Big (\dfrac{(4-3x)^3}{1+(4-3x)^2}\ \Big) \ }[/tex]
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What fuction respersents a slope of -4 and yintrersection -2?
Answers
y = -4x -2
A half cylinder lies on its side. What is the exact volume of the half cylinder?
150 π in3
300 π in3
450 π in3
600 π in3
Answers
pi*r²*h
pi*r²*h/2
r=10/2-----> r=5 in
h=12 in
=pi*5²*12/2----> 150*pi in³
so finally the correct answer would be the first option
150*pi in3
The required exact volume of the half cylinder is 150 π in³. Option A is correct.
To calculate the volume of a half cylinder, we need to find the volume of a full cylinder and then divide it by 2.
The formula for the volume of a cylinder is given by:
Volume = π * r² * h
where π is a constant approximately equal to 3.14159, r is the radius of the cylinder, and h is the height or length of the cylinder.
Given that the diameter of the cylinder is 10 inches, we can find the radius by dividing the diameter by 2:
Radius (r) = 10 in / 2 = 5 in
The height or length of the cylinder is given as 12 inches.
Now we can calculate the volume of the full cylinder:
Volume = π * (5 in)² * 12 in = 300 π in^3
Finally, to find the volume of the half cylinder, we divide the volume of the full cylinder by 2:
Volume of Half Cylinder = (300 π in³) / 2 = 150 π in³
Therefore, the exact volume of the half cylinder is 150 π in³.
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(3) (-4) + (3) (4) -1
Answers
(-12) + (12) - 1
0 - 1
-1
Hope this helps.
How many lines of symmetry does a regular polygon with 32 sides have
Answers
A regular polygon with 32 sides has 16 lines of symmetry.
What is Polygon?A polygon is a plane figure made up of line segments connected to form a closed polygonal chain.
We need to find the number of lines of symmetry does a regular polygon with 32 sides have.
The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry
A regular polygon with 32 sides has 16 lines of symmetry.
This is because each side is equal in length and angles, creating a mirrored effect when each side is divided in half.
Hence, a regular polygon with 32 sides has 16 lines of symmetry.
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What does point A represent in this box plot?
A. first quartile
B. third quartile
C. the smallest value
D. the largest value
*Don't troll on these answers.
Answers
answer
C. the smallest value
Answer:
point A that is the first point represents the smallest value
Step-by-step explanation:
find point A represent in this box plot
first point is the smallest value of all the data
last point is the largest value of all the data
second point is the first quartile
Middle point is the second quartile
fourth point is the third quartile
So point A that is the first point represents the smallest value
What were the total earnings of all five of these movies in the given week?
Movie
Earnings
Average Ticket Price
A
$26,088,808.74
$8.35
B
$60,394,938.12
$9.72
C
$23,659,617.52
$8.12
D
$34,311,887.98
$7.57
E
$10,505,611.08
$8.46
Answers
Answer:
$154,960,863.44
Step-by-step explanation:
Add the 5 earnings numbers using a suitable calculator.
_____
In this case, a "suitable calculator" is one that will display numbers of 11 digits or more. Apparently the one at the Google search box is up to the task.
The total earnings of all five movies in the given week were approximately $155,950,863.44.
To find the total earnings of all five movies in the given week, you can simply add up their individual earnings:
Total Earnings = Earnings of Movie A + Earnings of Movie B + Earnings of Movie C + Earnings of Movie D + Earnings of Movie E
Total Earnings = $26,088,808.74 + $60,394,938.12 + $23,659,617.52 + $34,311,887.98 + $10,505,611.08
Now, calculate the sum:
Total Earnings = $155,950,863.44
So, the total earnings of all five movies in the given week were approximately $155,950,863.44.
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Why is a/0 not defined?
Answers
a/b = c
then
a = b*c
Division by 0 is undefined because it has no inverse operation. If
a/0 = c
it is not true that
a = 0*c
Final answer:
Division by zero is undefined because a/0 would imply an infinite value not included in the real numbers, and 0/0 is an indeterminate form lacking unique value, requiring advanced techniques in calculus for evaluation.
Explanation:
The concept of division by zero, specifically when discussing expressions like a/0 and 0/0, is a fundamental aspect of mathematics that leads to the undefined nature of these operations. In the case of 1/0, this division is not defined within the real number system, as a non-zero number divided by zero would imply an infinite value, which is outside the bounds of real numbers.
Conversely, the expression 0/0 is an example of an indeterminate form because it doesn't present enough information to deduce a unique value for the division, as zero divided by zero could represent any number.
Indeterminate forms such as these necessitate a more nuanced approach, particularly in calculus where the evaluation of limits often brings these expressions into play. In some contexts, sophisticated mathematical techniques must be employed to determine the behavior of functions as they approach these forms.
Given: PSTR is a parallelogram m∠T:m∠R=1:3, RD ⊥ PS , RM ⊥ ST Find: m∠DRM
Answers
Answer:
m∠DRM = 45°
Step-by-step explanation:
∵ PSTR is a parallelogram
∴ TS // RP ⇒ opposite sides
∴ m∠T + m∠R = 180° ⇒ (1) (interior supplementary angles)
∵ m∠T : m∠R = 1 : 3
∴ m∠R = 3 m∠T ⇒ (2)
- Substitute (2) in (1)
∴ m∠T + 3 m∠T = 180
∴ 4 m∠T = 180
∴ m∠T = 180 ÷ 4 = 45°
∴ m∠R = 3 × 45 = 135°
∵ m∠R = m∠S ⇒ opposite angles in a parallelogram
∴ m∠S = 135°
∵ RD ⊥ PS
∴ m∠RDS = 90°
∵ RM ⊥ ST
∴ m∠RMS = 90°
- In quadrilateral RMSD
∵ m∠S = 135°
∵ m∠RDS = 90°
∵ m∠RMS = 90°
∵ The sum of measure of the angles of RMSD = 360°
∴ m∠DRM = 360 - ( 135 + 90 + 90) = 45°
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Which calculation will always give a result greater than 1
Answers
Answer:
the answer is 1 3/4 - less than 3/4
Step-by-step explanation:
ik bc i used ttm and got this answer and it was correct
derivative, by first principle
[tex] \tan( \sqrt{x } ) [/tex]
Answers
Employ a standard trick used in proving the chain rule:
[tex]\dfrac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\cdot\dfrac{\sqrt{x+h}-\sqrt x}h[/tex]
The limit of a product is the product of limits, i.e. we can write
[tex]\displaystyle\left(\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\right)\cdot\left(\lim_{h\to0}\frac{\sqrt{x+h}-\sqrt x}h\right)[/tex]
The rightmost limit is an exercise in differentiating [tex]\sqrt x[/tex] using the definition, which you probably already know is [tex]\dfrac1{2\sqrt x}[/tex].
For the leftmost limit, we make a substitution [tex]y=\sqrt x[/tex]. Now, if we make a slight change to [tex]x[/tex] by adding a small number [tex]h[/tex], this propagates a similar small change in [tex]y[/tex] that we'll call [tex]h'[/tex], so that we can set [tex]y+h'=\sqrt{x+h}[/tex]. Then as [tex]h\to0[/tex], we see that it's also the case that [tex]h'\to0[/tex] (since we fix [tex]y=\sqrt x[/tex]). So we can write the remaining limit as
[tex]\displaystyle\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan\sqrt x}{\sqrt{x+h}-\sqrt x}=\lim_{h'\to0}\frac{\tan(y+h')-\tan y}{y+h'-y}=\lim_{h'\to0}\frac{\tan(y+h')-\tan y}{h'}[/tex]
which in turn is the derivative of [tex]\tan y[/tex], another limit you probably already know how to compute. We'd end up with [tex]\sec^2y[/tex], or [tex]\sec^2\sqrt x[/tex].
So we find that
[tex]\dfrac{\mathrm d\tan\sqrt x}{\mathrm dx}=\dfrac{\sec^2\sqrt x}{2\sqrt x}[/tex]
Identify the type of conic section whose equation is given. x2 = y + 3
Answers
PLEEEEEEEEEEEEEEAAAAAASSSSSSSSSSSSSEEEEEEEEEEEEEEEEE HELP!!!
The figure below is an oblique triangular prism. The expression below represents the volume of the figure written in standard form.
What are the missing values? axb + cx a = b = c =
Answers
B.3
C.3
Just did this assignment.
the answers are:
1. 1
2. 3
3. 3
Have a great day! hope I helped!
p.s: just completed this assignment, so I know these are 100% correct.
hey can you please help me posted picture of question
Answers
y² = 4 - [tex] \frac{4x^2}{25} [/tex]
Explanation:
The given expression is:
4x² + 25y² = 100
We need to isolate the y².
This can be done as follows:
4x² + 25y² - 4x² = 100 - 4x²
25y² = 100 - 4x²
[tex] \frac{25y^2}{25} = \frac{100-4x^2}{25} [/tex]
y² = [tex] \frac{x100-4x^2}{25} [/tex]
y² = [tex] \frac{100}{25} - \frac{4x^2}{25} [/tex]
y² = 4 - [tex] \frac{4x^2}{25} [/tex]
Hope this helps :)
the angle of elevation of an object from a point 200 meters above a lake is 30 degrees and the angle of depression of it's image in the lake is 45 degrees. Find the height of the object above the lake.
Answers
Looking at the reflection of the object in the lake's surface is equivalent to observing the object at distance h below the lake's surface, or observing it from 200 m below the lake's surface. Considering the latter case, we have
(h+200)/d = tan(45°)
(h -200)/d = tan(30°)
Solving these for d and equating the results gives
(h+200)/tan(45°) = (h -200)/tan(30°)
Solving for h, we get
h(1/tan(30°) -1/tan(45°)) = 200(1/tan(45°) +1/tan(30°))
h = 200(tan(45°) +tan(30°))/(tan(45°) -tan(30°))
h ≈ 746.41
The object is about 746.4 meters above the lake.
the two figures are congruent find the measure of the requested side or angle
Answers
The length of AB is approximately 14.68 which is option B. 15.
To find the length of side AB in the congruent figures where AC is 6, angle C is 119 degrees, AB is 15, angle B is 22 degrees, and BC is 12, we can use the Law of Cosines.
The Law of Cosines states:
[tex]\[ c^2 = a^2 + b^2 - 2ab \cos(C) \][/tex]
where:
- c is the side opposite the angle C,
- a and b are the other two sides,
- c is the angle opposite side c.
In this case, we have AC as side a, BC as side b, and AB as side c. We also know that angle C is 119 degrees.
[tex]\[ AB^2 = AC^2 + BC^2 - 2 \cdot AC \cdot BC \cdot \cos(C) \][/tex]
Substitute the given values:
[tex]\[ AB^2 = 6^2 + 12^2 - 2 \cdot 6 \cdot 12 \cdot \cos(119^\circ) \][/tex]
Now, calculate the expression to find the length of AB.
[tex]\[ AB^2 = 36 + 144 - 2 \cdot 6 \cdot 12 \cdot \left(\cos(119^\circ)\right) \]\\AB^2 = 36 + 144 - 2 \cdot 6 \cdot 12 \cdot \left(-0.492403\right) \]\\AB^2 = 36 + 144 + 35.4234 \]\\AB^2 = 215.4234 \][/tex]
Now, take the square root of both sides to find AB:
[tex]\[ AB = \sqrt{215.4234} \approx 14.68 \][/tex]
So, the length of AB is approximately 14.68.
Which polynomial function has a leading coefficient of 1, roots –3 and 8 with multiplicity 1, and root 4 with multiplicity 2?
f(x) = 2(x + 3)(x + 4)(x – 3)
f(x) = 2(x – 8)(x – 4)(x + 3)
f(x) = (x + 8)(x + 4)(x + 4)(x – 3)
f(x) = (x – 8)(x – 4)(x – 4)(x + 3)
Answers
Answer:
f(x) = (x – 8)(x – 4)(x – 4)(x + 3)
Step-by-step explanation:
A polynomial function with roots [tex]x_{1}, x_{2}, ..., x_{n}[/tex] has the following format:
[tex]f(x) = a(x - x_{1})(x - x_{2})...(x - x_{n})[/tex]
In which a is the leading coefficient.
In this problem, we have that:
Leading coefficient 1, so [tex]a = 1[/tex]
roots -3 and 8 with multiplicity 1, so [tex](x + 3)(x - 8)[/tex].
root 4 with multiplicity 2, so [tex](x - 4)^{2} = (x - 4)(x - 4)[/tex]
So the correct answer is:
f(x) = (x – 8)(x – 4)(x – 4)(x + 3)
Which side of XYZ is the longest ?? Please Help
Answers
due to it having the largest angle.
Answer:
XY is the longest side in the given ΔXYZ.
Step-by-step explanation:
We are given the following information in the question:
We have to find the longest side in the given triangle ΔXYZ.
The three angles of the triangle are:
[tex]\angle X = 62^\circ\\\angle Y = 55^\circ\\\angle Z = 63^\circ\\[/tex]
We know that in a triangle the side opposite to smallest triangle is smallest and the side opposite to largest angle is longest in length.
Angle Z in the given triangle is the largest angle and therefore, the side opposite to this angle is the longest side of the triangle.
Hence, XY is the longest side in the given ΔXYZ.
Determine whether quantities vary directly or inversely and find the constant of variation.
It takes four identical water pumps 6 hours to fill a pool. How long would it take three of these same pumps to fill the pool, assuming they all pump at the same rate?
Answers
Time taken by 1 pump will be:
4×6=24 hours
fraction of pool filled by a single pump in 1 hour will be:
1/24
To calculate how long it would take 3 pumps to fill the pool we proceed as follows:
Fraction of pool filled with water in 1 hour is:
3×1/24
=1/8
thus the time taken to fill the pool by 3 pumps is:
8/1=8 hours
Suppose a city has 810 high-rise buildings, and 29 of these buildings have rooftop gardens. Find the percentage of high-rise buildings with rooftop gardens in this city. Round your answer to the nearest tenth of a percent.
Answers
810 ---------> 100%
29 -----------> x
From here, we clear the value of x.
We have then:
x = (29/810) * (100)
x = 3.580246914%
Round to the nearest tenth of a percent:
x = 3.6%
Answer:
The percentage of high-rise buildings with rooftop gardens in this city is:
x = 3.6%
To find the percentage of high-rise buildings with rooftop gardens, divide the number of buildings with gardens (29) by the total number of buildings (810), and then multiply by 100. Round the final result to the nearest tenth, which is approximately 3.6%.
To calculate the percentage of high-rise buildings with rooftop gardens, we use the formula:
Percentage = (Part / Whole) imes 100
Where the Part is the number of buildings with rooftop gardens, and the Whole is the total number of high-rise buildings.
Substituting the given values:
Percentage = (29 / 810) times 100
Carrying out the division first gives us:
Percentage ≈ 0.035802469 times 100
Finally, multiplying by 100 to find the percentage, we get:
Percentage ≈ 3.58
After rounding to the nearest tenth of a percent, we obtain:
Percentage ≈ 3.6%
3.6% of the high-rise buildings in the city have rooftop gardens.
average of 1.99 3.29 2.45
Answers
[tex]1.99 + 3.29 + 2.45 = 7.73 \\ 7.73 \div 3 = 2.58[/tex]
Hope this helps! :)
Resting heart rate was measured for a group of subjects; the subjects then drank 6 ounces of coffee. ten minutes later their heart rates were measured again. the change in heart rate followed a normal distribution, with mean increase of 7.3 beats per minute and a standard deviation of 11.1 beats per minute. let latex: y y denote the change in heart rate for a randomly selected person. find latex: \text{p}(y<10)
Answers
Calculate the probability that the change in heart rate is less than 10 beats per minute using z-scores and the standard normal distribution table.
The probability (P) that the change in heart rate (y) is less than 10 beats per minute is calculated by finding the z-score for 10, then using the z-table or a calculator to find the corresponding probability.
First, calculate the z-score: z = (10 - 7.3) / 11.1 = 0.2432. Next, find the probability by looking up this z-score in the standard normal distribution table, which corresponds to approximately 59.93%.
Therefore, the probability that the change in heart rate is less than 10 beats per minute is approximately 59.93%.