Answer:
Rate is 1.1333 words per second
Step-by-step explanation:
We understand rating as frequency or speed of doing something per time (seconds mainly)
[tex]{ \green{ \tt{rate = \frac{item \: quantity}{time} }}} \\ [/tex]
Let's find rate in terms of seconds (words per second)
[tex]{ \rm{rate = \frac{34 \: words}{ (\frac{1}{2} \times 60) \: seconds} }} \\ \\ { \rm{rate = \frac{34}{30} }} \\ \\ { \rm{rate = 1.133 \: \: words \: per \: second}}[/tex]
The temperature, t, in degrees celsius, in a warehouse changes according to the function t(h) = 18 + 4sin(pi/12 (x = 8)).
where h is the number of hours since midnight. at what rate is the temperature changing at 9 a.m.?
Answer:
about 1.01 °C per hour
Step-by-step explanation:
We assume the intended temperature function is ...
t(h) = 18 +4·sin(π/12(h -8))
We are asked for the rate of change when h=9.
__
derivativeThe rate of change of temperature with respect to time is the derivative of t(h) with respect to h.
t'(h) = 4(π/12)cos(π/12(h -8)) = π/3·cos(π/12(h -8))
at 9 amFor h = 9 hours after midnight, the rate of change is ...
t'(9) = π/3·cos(π/12(9 -8)) = π/3·cos(π/12) ≈ (3.14159)(0.965926)/3
t'(9) ≈ 1.01152
The rate of change of temperature at 9 a.m. is about 1.01 °C/hour.
Which set of values could be the side lengths of a 30-60-90 triangle?
OA. (6,6 2,12}
OB. (6,6√3, 12)
OC. (6, 12, 12√√3}
D. (6, 12, 12 √2)
The correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle are (6,6√3, 12).
What is the right-angled triangle?A triangle has three angles of 30-60 and 90 degrees in which the two sides are perpendicular to each other.
The three sides of the triangle will be calculated by applying the Pythagorean theorem:-
The sum of the square sides will be equal to the square of the third side.
For sides (6,6√3, 12)
12² = 6² + (6√3)²
144 = 36 + (36 x 3)
144 = 36 + 108
144 = 144
Therefore the correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle (6,6√3, 12).
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I need help with this problem, please explain
Answer:
v = 164.64
Step-by-step explanation:
Your friend forgot to divide 6.8 by two as 6.8 is the diameter not the radius. The volume equation needs the radius so you divide 6.8 by 2 which equals 3.4 thats what inputed into the volume equation
Help please give a detailed answer!
Given that 2x³-5x² - 4x+8 = (Ax - 1)(x-B)(x + 1) + C for all values of x, find the
values of A, B and C.
Answer:
A=2, B=3, C=5
Step-by-step explanation:
Two polynomials are equal for all values of the variable if the corresponding coefficients are the same. The way to solve the problem is to multiply the RHS, rewrite it in a more orderly way
[tex](Ax-1)(x-B)(x+1)+C = \\Ax^3+(A-AB-1)x^2+(B-AB-1)x +B+C[/tex]
Now, for the two polynomials to be the same we need to have, at the same time
[tex]x^3: A=2\\x^2: A-AB-1= -5\\x:B-AB-1=-4\\1: B+C=8[/tex]
You might notice that we have more conditions than variables, but you can consider one of the two in the middle as a "check" option.
Now, grabbing the value from the first condition into the second we get B=3. Replacing both value in the third we see that the equality still holds, and replacing into the fourth we get C =5.
What is the absolute deviation of 4 in this data set?
{6, 22, 14, 9, 11, 4}
02
O 3
07
11
Answer:
n
6
Mean
11
Average Absolute Deviation (MAD)
4.6667
Step-by-step explanation:
Divide 8,382 ÷ 7 please answer
Answer:
The answer is 1197.42
Step-by-step explanation:
Which trigonometric function requires a domain restriction of [0, pi/2) ∪ (pi/2 , pi]
The ANSWER is f(x) = secx ----- PLEASE EXPLAIN THANK YOU!!!!!
The trigonometric function requires a domain restriction of [0, π/2) ∪ (π/2, pi] is tan x, sec x.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
tan x = (sin x)/(cos x)
sec x = 1/(cos x)
cos x becomes zero at {-π/2,π/2}
Therefore, the both of the function are undefined at {-π/2,π/2}
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please give me a good answer for 30 points
Answer:
[tex]measure \: [/tex]
ANSWER :3/50
Step-by-step explanation:
[tex] \sqrt{3 \: is \: a \: formula \: tht \: has \: equation} [/tex]
MEASURE:92-3 ) DEFIND THE "3"
ANSWER: 3/50
Which ratio is equivalent to cos U?
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER
Answer:
(a) SW/VW
Step-by-step explanation:
In similar triangles ΔTUS and ΔVWS, corresponding angles are congruent. That means angle W will have the same measure and trig function values that angle U has.
The mnemonic SOH CAH TOA reminds you that the cosine ratio in this right triangle is ...
Cos = Adjacent/Hypotenuse
__
In ΔVWS, the side adjacent to angle W is side SW. The hypotenuse of the triangle is side VW. Then the cosine of interest is ...
cos(U) = cos(W) = SW/VW
A survey was taken of children between the ages of 7 and 12. Let A be the event that the person rides the bus to school, and let B be the event that the person has 3 or more siblings. A 6-column table has 5 rows. The first column has entries walks to school, bikes to school, rides bus to school, driven to school, total. The second column is labeled 0 siblings with entries 24, 8, 18, 32, 82. The third column is labeled 1 sibling with entries 37, 9, 36, 58, 140. The fourth column is labeled 2 siblings with entries 12, 8, 12, 22, 54. The fifth column is labeled 3 or more siblings with entries 3, 2, 9, 10, 24. The sixth column is labeled Total with entries 76, 27, 75, 122, 300. Which statement is true about whether A and B are independent events
The statement that is true about whether A and B are independent events is D. A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25.
How to depict the events?Let A be the event that the person rides the bus to school, then:
P(A) = 75/300
P(A) = 0.25
Let B be the event that the person has 3 or more siblings, then:
P(B) = 24/300 = 0.25
P(A/B)=9/24
P(A/B)=0.375
Since P(A/B)=0.375 is different from P(A)=0.25 the events are not independent.
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I'm struggling on finding a step-through for this question, can anyone help? (x+5)(2x+3)-3(x-2)(6x+5)
[tex]~~(x+5)(2x+3)-3(x-2)(6x+5)\\\\=2x^2 +3x + 10x +15 - (3x-6)(6x+5)\\\\=2x^2 +13x +15 - (18x^2 +15x -36x -30)\\\\=2x^2+13x+15-(18x^2 -21x-30)\\\\=2x^2 +13x+15-18x^2 +21x +30\\\\=-16x^2 + 34x+45[/tex]
please help... Explain how you would find the volume of the octagonal prism.
Answer:
Formula for the volume id the octagonal prism .......
Step-by-step explanation:
To calculate the area of octagon ( base area) , multiply the perimeter of the octagon by its apothem and divide by 2 .Then, ti get the volume of the octagonal prism u need to multiply the result by the length of the.prism
Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.
f (x) = 5 x squared minus 3. g (x) = 5 x squared + 3.
a.
both f and g open downward; low point of f is 3 units below the x-axis; the low point of g is 3 units above the x-axis
b.
both f and g open upward; low point of f is 3 units above the x-axis; the low point of g is 3 units below the x-axis
c.
both f and g open upward; low point of f is 3 units below the x-axis; the low point of g is 3 units above the x-axis
d.
both f and g open downward; low point of f is 3 units above the x-axis; the low point of g is 3 units below the x-axis
The similarities/differences observed in the graph is (c) both f and g open upward; low point of f is 3 units below the x-axis; the low point of g is 3 units above the x-axis
How to describe the similarities/differences?The equations are given as:
f(x) = 5x² - 3
g(x) = 5x² + 3
Next, we plot the above equations on the same plane (see attachment)
From the attached graph, we can see that:
Both functions open upwardThe lowest point of f(x) is at y = 3; i.e 3 units above the x-axisThe lowest point of g(x) is at y = -3; i.e 3 units below the x-axisHence, the similarities/differences observed in the graph is (c)
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Please answer this question
[tex]\text{L.H.S}\\\\=\cot^2 \dfrac{\pi}6 -2\cos^2 \dfrac{\pi}{3}-\dfrac 34 \sec^2 \dfrac{\pi}4-4\sec^2 \dfrac{\pi}6\\\\\\=\cot^2 30^\circ -2 \cos^2 60^\circ- \dfrac 34 \sec^2 45^{\circ} -4 \sec^2 30^{\circ}~~~~~~~;[\pi= 180^{\circ}]\\\\\\=\left(\sqrt 3 \right)^2 -2 \left( \dfrac 12 \right)^2 -\dfrac 34 \left(\sqrt 2 \right)^2 -4 \left(\dfrac 2{\sqrt 3} \right)^2\\\\\\=3-2 \cdot \dfrac 14 - \dfrac 34 \cdot 2 -4 \cdot \dfrac 43\\ \\\\=3-\dfrac 12-\dfrac 32 - \dfrac{16}3\\\\\\[/tex]
[tex]\\=\dfrac{9-16} 3 - \dfrac 42 \\\\\\=\dfrac{-7}{3}-2\\\\\\=\dfrac{-7-6}3\\\\\\=-\dfrac{13}3\\\\\\=-4\dfrac 13 \\\\\\=\text{R.H.S}\\\\\\\text{Proved.}[/tex]
Lulu has 10 feet of ribbon. She uses 1 feet of ribbon for a project. She uses the
rest of the ribbon to make bows. She uses 8 inches of ribbon for each bow.
How many bows does Lulu make? Show your work.
10-1 = 9 feet left
9 x 12 = 108 inches
108 / 8 inches per bow = 13.5 bows
she can make 13 bows
simplify the following expression 5‐³
1/5×1/5×1/5=1/125
$ give me a dollar $
300% of 7 is what percent of 42?
A. 30%
B. 50%
C. 60%
D. 12.5
Pls show work or don’t answer thanks
Answer:
B) 50%
Step-by-step explanation:
300% is the same as 3. So to find 300% of 7 you do 3 times 7 and get 21.
Now you need to find _% times 42 = 21. Divide 21/42 to get 0.5. This is the same thing as 50%.
Hope it helps and have a nice day! :)
According to the general equation for conditional probability, if P(AB) =
4/5
and P(B) = 5/6, what is P(AIB)?
A.15/16
B.35/36
C.8/9
D.24/25
Answer:
[tex]\sf D. \quad P(A|B)=\dfrac{24}{25}[/tex]
Step-by-step explanation:
General equation for conditional probability
[tex]\sf P(A \cap B)=P(A)\:P(B|A)[/tex]
As we need to find P(A|B) we can rewrite the equation:
[tex]\implies \sf P(B \cap A)=P(B)\:P(A|B)[/tex]
Given:
[tex]\sf P(A \cap B)=\dfrac{4}{5}[/tex]
[tex]\sf P(B)=\dfrac{5}{6}[/tex]
Remember that [tex]\sf P(A \cap B)=P(B \cap A)[/tex]
Substitute the given values into the formula:
[tex]\implies \sf P(B \cap A)=P(B)\:P(A|B)[/tex]
[tex]\implies \sf \dfrac{4}{5}=\dfrac{5}{6}\:P(A|B)[/tex]
[tex]\implies \sf P(A|B)=\dfrac{4}{5} \div \dfrac{5}{6}[/tex]
[tex]\implies \sf P(A|B)=\dfrac{4}{5} \times \dfrac{6}{5}[/tex]
[tex]\implies \sf P(A|B)=\dfrac{24}{25}[/tex]
Help please
1.In ∆ABC, how many triangles are formed given: a=10 cm, b=18 cm, c=105°?
A. 1
B. 2
C. 3
D. None
2. In ∆ABC, if <A is obtuse and a<c, then how many triangle/s can be formed?
A. 1
B.2
C. 3
D. None
For questions 1 and 2 options, A and D are correct respectively.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
1. In ∆ABC,
a=10 cm, b=18 cm, c=∠105°
For the given data only one triangle is formed. Option A is correct.
2. In ∆ABC, if <A is obtuse and a<c,
An obtuse angle is an angle more than the 90°.The given condition is wrong. None of the triangle is formed from the given options.
Hence for questions 1 and 2 options A and D are correct respectively.
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I need this answer quickly please :)
monkey B
Step-by-step explanation:
f(x) = 16x2 + 32x − 9?
Step-by-step explanation:
c beacuse if you subtract 8 by 2 you get 6 times x
using the equation y^2=-5/4(x-2), find the equation of the directrix
Answer:
Step-by-step explanation:
since its a horizontal parabola opening to the right we use a formula for the directrix
x=h-p 4p=5/4 p=5
X= -3 v(h,k)=(2,0)
what’s the best necklace length for a 5’0 female?
A. 16 inches
B. 18 inches
Answer:
18 inches
Step-by-step explanation:
The most frequent chain length for women's necklaces is 18 inches. This size is appropriate for a lady of medium height and weight.
HELP PLS….Volume of cones
Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for and round your final answer to the nearest hundredth.
Answer:
20.93 units cubed
Step-by-step explanation:
[tex]V = \frac{3.14(2)^{2}(5) }{3} \\V = \frac{3.14(4)(5) }{3}\\V = \frac{62.8 }{3}\\V = 20.93[/tex]
A system of two linear inequalities is graphed as shown, where the solution region is shaded. Complete the sentences below by determining whether each point is, or is not. located in the solution region.
The point (-3.2)
The point (-7.5)
The point (2.-5)
The point (-14,6)
All the points The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) is located in the solution region.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
When we plot all the points on the graph we can see that all the points The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) are located in the solution region.
Therefore all the points The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) is located in the solution region.
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In general, when solving a radical equation with square roots, you should first
isolate the __and then square both sides.
A. variable
B. radical
C. operator
D. coefficient
The correct answer is option B which is when solving a radical equation with square roots, you should first.isolate the radical and then square both sides.
How to solve radical equations?To solve radical equations, one common technique is to isolate the radical term first, then take both sides of the equation to a power to remove the radical.
Therefore the correct answer is option B which is when solving a radical equation with square roots, you should first.isolate the radical and then square both sides.
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Find 5-(-7).
5-(-7)=5+
Write as addition.
Answer: The answer is 5+28.
Step-by-step explanation:
First of all, you have to distribute the term in front of the parenthesis into the term(s) inside of it. In this case, “5-” is not a term because the “-” symbol is following it. However, we can distribute that particular symbol into the parenthesis. We then have 5+ 28 because - x - = +, and 5 x 7 - 5 = 28.
The amount of parts, p, that a shop produced in d days is shown in the table below.
d
1 2 3 4 5
p(d) 66 132 240 326 455
Select the average rate of change for the number of parts that the company produced from day 1 to day 3.
87
91
66
146
Using it's concept, it is found that the average rate of change for the number of parts that the company produced from day 1 to day 3 is of 87.
What is the average rate of change?It is given by the change in the output divided by the change in input.
In this problem, in 2 days, from day 1 to day 3, the number of parts increased from 66 to 240, hence the rate of change is given by:
r = (240 - 66)/2 = 87.
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Morgan wants to draw a right triangle two side lengths are 6 unites and 8 units. select all the possible dimensions of the third side
2 units 14 units
28units 10 units
√28 units
The possible dimension of the third side is 10 units.
What is the possible dimension of the third side?
A right triangle is a triangle that has three sides known as the opposite, adjacent and hypotenuse. The hypotenuse is the longest sides of the triangle. The opposite side is the side that faces an angle. The adjacent side is the third side.
If two side lengths are given, the third side can be determined using the Pythagoras theorem.
√a² + b ² = c
√6² + 8² = √36 + 64 = 10 units
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Use a net to find the surface area of the cone to the nearest square centimeter. Use 3.14 for л. The surface area of the cone is about cm². (Round to the nearest whole number as needed.) 19 cm 4 cm (The figure is not drawn to scale.)
The surface area of the cone rounded to the nearest whole number is; 289 cm².
How to determine the cone surface area?We are given the parameters:
Radius; r = 4 cm
Slant height; l = 19 cm
Let us first calculate the base area;
The base is a circle and the area formula for a circle is;
A = πr²
Thus;
A = π(4 cm)²
A = 50.24 cm²
Lateral area;
The circumference of a circle is given by the formula;
C = 2πr
C = 2(π)(4 cm)
C = 25.12 cm
This circumference is the arc length of the sector
The area of the sector is;
A = 1/2hs
where;
h is the radius of the sector.
s is its arc length
Thus;
A = ¹/₂(19 cm)(25.12 cm)
A = 238.64 cm²
The total surface area is;
SA = 50.24 cm² +238.64 cm²
S.A = 288.88 cm² ≈ 289 cm²
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Answer:
289 cm²
Step-by-step explanation:
The net for the surface area of a cone is a circular sector representing the lateral area, together with a circle representing the area of the base. The arc length of the sector is equal to the circumference of the base.
__
base areaThe area of the circular base is given by the area formula for a circle:
A = πr²
For the given radius, the area is ...
A = (3.14)(4 cm)² = 50.24 cm²
lateral areaThe circumference of the circular base is ...
C = 2πr = 2(3.14)(4 cm) = 25.12 cm . . . . also the arc length of the sector
The area of the sector is ...
A = 1/2hs . . . . where h is the radius of the sector, and s is its arc length
A = (1/2)(19 cm)(25.12 cm) = 238.64 cm²
total surface areaThe total surface area is the sum of the base area and the lateral area:
SA = 50.24 cm² +238.64 cm² = 288.88 cm² ≈ 289 cm²
The surface area of the cone is about 289 cm².