Answer:
El monomio equivalente es [tex]\cos 5x \cdot \cos 2x[/tex].
Step-by-step explanation:
Un monomio es una entidad algebraica consistente en un componente, el polinomio dado puede ser transformado mediante el uso de la siguientes propiedades trigonométricas:
[tex]\cos (\alpha + \beta) = \cos \alpha \cdot \cos \beta - \sin \alpha \cdot \sin \beta[/tex]
Es decir:
[tex]\cos 7x + \sin 5x \cdot \sin 2x[/tex] Dado
[tex]\cos (5x+2x) + \sin 5x\cdot \sin 2x[/tex]
[tex]\cos 5x \cdot \cos 2x - \sin 5x \cdot \sin 2x + \sin 5x \cdot \sin 2x[/tex]
[tex]\cos 5x \cdot \cos 2x[/tex]
El monomio equivalente es [tex]\cos 5x \cdot \cos 2x[/tex].
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 247 days and standard deviation sigma equals 16 days. Complete parts (a) through (f) below.
Answer:
The answer is given below
Step-by-step explanation:
a) What is the probability that a randomly selected pregnancy lasts less than 242 days
First we have to calculate the z score. The z score is used to determine the measure of standard deviation by which the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that Mean (μ) = 247 and standard deviation (σ) = 16 days. For x < 242 days,
[tex]z=\frac{x-\mu}{\sigma}=\frac{242-247}{16}=-0.31[/tex]
From the normal distribution table, P(x < 242) = P(z < -0.3125) = 0.3783
(b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
If a sample of 17 pregnancies is obtained, the new mean [tex]\mu_x=\mu=247,[/tex] the new standard deviation: [tex]\sigma_x=\sigma/\sqrt{n} =16/\sqrt{17} =3.88[/tex]
c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 242 days or less
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{17} }=-1.29[/tex]
From the normal distribution table, P(x < 242) = P(z < -1.29) = 0.0985
d) What is the probability that a random sample of 49 pregnancies has a mean gestation period of 242 days or less?
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{49} }=-2.19[/tex]
From the normal distribution table, P(x < 242) = P(z < -2.19) = 0.0143
(e) What might you conclude if a random sample of 49 pregnancies resulted in a mean gestation period of 242 days or less?
It would be unusual if it came from mean of 247 days
f) What is the probability a random sample of size 2020 will have a mean gestation period within 11 days of the mean
For x = 236 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{236-247}{16/\sqrt{20} }=-3.07[/tex]
For x = 258 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{258-247}{16/\sqrt{20} }=3.07[/tex]
From the normal distribution table, P(236 < x < 258) = P(-3.07 < z < 3.07) = P(z < 3.07) - P(z < -3.07) =0.9985 - 0.0011 = 0.9939
Given that 8 <y< 12 and 1<x< 6, find the maximum possible value of
x+y/y-x
Answer:
Step-by-step explanation:
y = {9, 10, 11}
x = {2, 3, 4 , 5}
Maximum value of x + y = 11 + 5 = 16
Minimum value of y -x = 9 - 2 = 7
[tex]\frac{x+y}{y-x}=\frac{16}{7}[/tex]
Ice is placed around a bowl of water to lower the temperature. The equation D=−75t+22 shows the time, t, measured in minutes and temperature, D, measured in degrees Celsius. Which statement is correct?
Answer:
d) Before cooling begins, the temperature of the water is 22°C
Step-by-step explanation:
Option A
If t=7 minutes
D=-7/5t+22
=-7/5(7)+22
=-49/5+22
=-49+110/5
=61/5
=12.2°C
Change in temperature=12.2°C-22°C
=-9.8°C
Option B
If t=5 minutes
D=-7/5t+22
=-7/5*5+22
=-7+22
=15°
Change in temperature=15°-22°
=-7°
Option C
The temperature of the ice must be less than 22°C
Option D
D=-7/5t+22
When ice is not placed, t=0
D=-7/5t+22
=-7/5(0)+22
=0+22
=22
Temperature of the water before cooling=22°
Answer:
D
Step-by-step explanation:
For the diagram shown, which pairs of angles are vertical angles? Select all that apply. Angle1 and Angle3 Angle2 and Angle4 Angle2 and Angle3 Angle5 and Angle7 Angle5 and Angle8 Angle8 and Angle6
Answer:
2 & 4
1 & 3
5 & 7
8 & 6
Vertical angles are formed in a set of intersecting lines. They are two differrent angles that are opposite of eachother but have the same angle.
Angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:
<1 and <3
<2 and <4
<5 and <7; and
<8 and <6
Recall:
Angles that are regarded as pairs of vertical angles share the same vertex and are directly opposite each other at the point of intersection of two straight lines.
From the image given,<1 and <3 are directly opposite each other and share same vertex.
<1 and <3 are therefore are a pair of angles that are vertical angles.
In the same vein, the following pairs:<2 and <4; <5 and <7; and <8 and <6 are all directly opposite each other. They are vertical angles pair.
Therefore, angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:
<1 and <3
<2 and <4
<5 and <7; and
<8 and <6
Learn more here:
https://brainly.com/question/2889556
Matt has c baseball cards, and Jen has 9 fewer than 5 times as many cards as Matt. Jen gives Matt 14 cards. How many cards does Jen have now?
Answer:
Jen has 5c -23 cards now
Step-by-step explanation:
Matt has c baseballs.
Jen has 9 fewer than 5 times as Matt.
Mathematically, what Jen has will be 5c -9 baseballs
Now, Jen gives Matt 14 cards. This means that she lost 14 of her cards and we are going to subtract.
The number of cards she has now is thus 5c-9-14 = 5c -23 cards
Which one of the following numbers is divisible by 11?
A. 924711
B. 527620
C. 320793.
D. 435854
Answer:
320793
Step-by-step explanation:
320793 / 11 = 29163
An equilateral triangle has sides 8 units long. An equilateral triangle with sides 4 units long is cut off at the top, leaving an isosceles trapezoid. What is the ratio of the area of the smaller triangle to the area of the trapezoid? Express your answer as a common fraction.
Answer:
1:3
Step-by-step explanation:
Please study the diagram briefly to understand the concept.
First, we determine the height of the isosceles trapezoid using Pythagoras theorem.
[tex]4^2=2^2+h^2\\h^2=16-4\\h^2=12\\h=\sqrt{12}\\ h=2\sqrt{3}$ units[/tex]
The two parallel sides of the trapezoid are 8 Inits and 4 units respectively.
Area of a trapezoid [tex]=\dfrac12 (a+b)h[/tex]
Area of the trapezoid
[tex]=\dfrac12 (8+4)*2\sqrt{3}\\=12\sqrt{3}$ Square Units[/tex]
For an equilateral triangle of side length s.
Area [tex]=\dfrac{\sqrt{3}}{4}s^2[/tex]
Side Length of the smaller triangle, s= 4 Units
Therefore:
Area of the smaller triangle
[tex]=\dfrac{\sqrt{3}}{4}*4^2\\=4\sqrt{3}$ Square units[/tex]
Therefore, the ratio of the area of the smaller triangle to the area of the trapezoid
[tex]=4\sqrt{3}:12\sqrt{3}\\$Divide both sides by 4\sqrt{3}\\=1:3[/tex]
CD=17 AM=5 CD=? I've tried everything but I can't figure it out.
Answer:
We can prove that ΔTMB ≅ ΔTMD and ΔTMA ≅ ΔTMC by ASA. This means that BM = MD = BD / 2 = 8.5 and that AM = CM = 5 which means that CD = MD - CM = 8.5 - 5 = 3.5.
factorise this expression as fully as possible 2x^2+6x
Answer:
(Factor out 2x from the expression)
2x (x +3)
What is the x-intercept of the line with the equation y = 3 x minus 6?
a.2
c.-6
b.-2
d.3
Answer:A
Step-by-step explanation:
Find the values of the variables and the measures of the angles
Answer:
Add each given variable
(6x + 10) + (x + 2) + x = 8x + 12
The sum of all the angles equals 180ᴼ
8x + 12 = 180
Subtract 12 from both sides
8x = 168
Divide by 8 on both sides
x = 21
Now plug in 21 for each x to find the measure of each angle.
(6[21] + 10) = 126 + 10 = 136ᴼ
(21 + 2) = 23ᴼ
x = 21ᴼ
HELP please!!
“Find the volume of the sphere rounded to the nearest hundredth
Answer:
904.32 cm^3
Step-by-step explanation:
The formula for the volume of a sphere is V=4/3πr³. Since r is given, we can plug that in for r. I'm assuming that we are using 3.14 for pi, so when we plug in all the values in the equation we get V = 4/3*3.14*6³, which solves out to 904.32.
which of the following shows the correct steps to find the value of 8^1/3? (1 point)
Answer:
8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2
Step-by-step explanation:
Options are below
8 to the power of 1 over 3 equals 4 to the power of 3 whole to the power of 1 over 3 equals 4 to the power of 3 multiplied by 1 over 3 equals 4
8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2
8 to the power of 1 over 3 equals 2 to the power of 4 whole to the power of 1 over 3 equals 2 to the power of 4 multiplied by 1 over 3 equals 16
16 to the power of 1 over 4 equals 8 to the power of 2 whole to the power of 1 over 4 equals 8 to the power of 2 multiplied by 1 over 4 equals 8
Given:
8^1/3
if a power is raised to a power, we simplify it by multiplying the exponents; this will create a whole number exponent
if 8 can be rewritten as a number to the 3rd power.
We have
8 = 2*2*2 = 2³
Therefore,
8^1/3=(2^3)^1/3
=2^3×1/3
=2^3/3
=2^1
=2
there were 7 little cherries for every 2 big cherries. if there were 630 cherries in the box, how many little cherries were there? (please also answer the question in the picture)
Answer:
1)2205little cherries
2)0.5.
Step-by-step explanation:
1)7little=2big
?=630big
7×630=2205little cherries
2
2)²/5x=¹/10what is the value of 10x-2
first find the value of x that is ¹/10÷²/5=¼
so x is ¼
insert the value ie 10×¼-2
=2.5-2
=0.5
SNOG HELP OR SOMEONE THANK YOUUUU
Which unit rate is equivalent to 14 miles per gallon?
two gallons over thirty two miles
thirty two miles over two gallons
three gallons over forty two miles
forty two miles over three gallons
Answer:
forty two miles over three gallons
Step-by-step explanation:
2 gallons over 32 miles simplifies to 1 gallon over 16 miles, or 1 gallon per 16 miles. This is not the desired result, so we know the first choice is incorrect.
32 miles over 2 gallons simplifies to 16 miles over 1 gallon, or 16 miles per gallon. Again, this is not the desired result, so we know the second choice is also incorrect.
3 gallons over 42 miles simplifies to 1 gallon over 14 miles, or 1 gallon per 14 miles. While this may look correct, note that 1 gallon per 14 miles and 14 miles per gallon are not the same thing, so we know that the third answer is also incorrect.
By process of elimination, we know that the correct answer must be the last option, but let's still simplify it. 42 miles over 3 gallons simplifies to 14 miles over 1 gallon, or 14 gallons per mile. This is in fact the desired result, so we know that the correct answer is the last option. Hope this helps!
What are the solutions to the quadratic equation below? x^2+34x-72=0
Answer:
( x + 36 ) ( x - 2 ) = 0
Step-by-step explanation:
x^2 + 36x - 2x -72 = 0
x ( x + 36 ) - 2 ( x + 36 ) = 0
( x + 36 ) ( x - 2 ) = 0
The radius of a circle is 2 feet. What is the area of a sector bounded by a 180° arc?
Answer:
[tex]\boxed{Area = 3.14 ft^2}[/tex]
Step-by-step explanation:
Radius = r = 2 feet
Angle = θ = π/2 (In radians) = 1.57 radians
Area of Sector = [tex]\frac{1}{2} r^2 \theta[/tex]
Area = [tex]\frac{1}{2} (4)(1.57)[/tex]
Area = 2 * 1.57
Area = 3.14 ft²
Answer:
[tex]\bold{2\pi\ ft^2\approx6,28\ ft^2}[/tex]
Step-by-step explanation:
360°:2 = 180° so the area of a sector bounded by a 180° arc is a half of area of a circle of the same radius.
[tex]A=\frac12\pi R^2=\frac12\pi\cdot2^2=\frac12\pi\cdot4=2\pi\ ft^2\approx2\cdot3,14=6,28\ ft^2[/tex]
Evaluate: m - 12 when m = 23.
Answer:
11
Step-by-step explanation:
sub 23 with m
23 - 12 = 11
How is it that it is (-11/4,-1/2) ?
Answer:
Choice 3
Step-by-step explanation:
A(-5,-1) and B(4, 1)
Distance AB is calculated as x²+y², where x= 4-(-5)=9 and y= 1-(-1)=2
Point P is at 1/4 of distance from point A, so its coordinates will be at 1/4 of full distance from A to B in term of both coordinates:
-5 + 9/4= (-20+9)/4= -11/4-1 +2/4= (-4+2)/4= -2/4= -1/2So P= (-11/4, -1/2) and choice 3
A small community organization consists of 20 families, of which 4 have one child,8 have two children, 5 have three children, 2 have four children, and 1 has fivechildren. If one of these families is chosen at random, what is the probability it has`children,`= 1,2,3,4,5?
Answer and Step-by-step explanation:
According to the situation, The probabilities for each one is given below:
As there are 20 families
So the probabilities for each one is
For four families have one child is
[tex]= \frac{4}{20}\\\\ = \frac{1}{5}[/tex]
For eight families have two children is
[tex]= \frac{8}{20}\\\\ = \frac{2}{5}[/tex]
For five families have three children is
[tex]= \frac{5}{20}\\\\ = \frac{1}{4}[/tex]
For two families have four children is
[tex]= \frac{2}{20}\\\\ = \frac{1}{10}[/tex]
For one family have five children is
[tex]= \frac{1}{20}[/tex]
ASAP! A boat travelling at top speed upstream moves at 15km/hr. When it travels downstream, again at top speed< it moves at 25km/hr. What is the boat's top speed in still water?
Answer: 20km/h
Step-by-step explanation:
20km/h. Simply average 15 and 25 by doing (15+25)/2
Hope it helps <3
SOMEONE HELP PLEASE!! Will make as brainleist!??
Answer:
This is a geometric sequence and the common ratio is equal to ½.
Step-by-step explanation:
For a sequence to be termed to be in arithmetic progression, the difference between consecutive terms are the same and constant.
On the other hand, a sequence is termed to be in geometric progression if the ratio of a term to the term before it is the same as the ratio between the next term to it.
Let's consider the sequence given: 12, 6, 3 . . .
=>Let's try to find the common difference if it would be constant: 6-12 (-6) ≠ 3-6 (-3)
The sequence is not arithmetic.
=>Let's also try to find the ratio of the sequence to see if it is constant:
6/12 (½) = 3/6 (½)
Therefore we can conclude the sequence is geometric because the common ratio (½) is constant.
This is a geometric sequence and the common ratio is equal to ½.
Find the value of x. Round the length to the nearest tenth.
Answer:
[tex] x = 5.1 yd [/tex]
Step-by-step Explanation:
Angle of depression is congruent to angle of elevation.
Therefore, angle of elevation of the given figure, which is opposite to x is 25°.
Adjacent length = 11 yd
Opposite length = x
Trigonometric ratio formula for finding x is shown below:
[tex] tan(25) = \frac{opposite}{adjacent} [/tex]
[tex] tan(25) = \frac{x}{11} [/tex]
Multiply both sides by 11 to solve for x
[tex] 11*tan(25) = x [/tex]
[tex] 5.129 = x [/tex]
[tex] x = 5.1 yd [/tex] (to the nearest tenth)
Find an equivalent system of equations for the following system: 3x + 3y = 0 −4x + 4y = −8 PLZ HELP
Answer:
Answer:
3x + 3y = 0
7x - y = 8
Step-by-step explanation:
If you are given the graph of h(x) = log6x, how could you graph M(x) = log6(x+3)?
Answer:
Translate 3 units to the left
Step-by-step explanation:
Find the nth term -1 8 19 32 47
[tex]\bold{\text{Answer:}\quad \text{Recursive formula:}\ a_n=a_{-1}+2n+5}\\.\qquad \qquad \ \text{Explicit formula:}\ a_n=2n^2+3n-6[/tex]
Step-by-step explanation:
-1 → 8 = +9
8 → 19 = +11
19 → 32 = +13
32 → 47 = + 15
a₁ = -1
d = 2n + 5
Recursive formula is: the previous term plus the difference (d)
[tex]\large\boxed{a_n=a_{n-1}+2n+5}[/tex]
Explicit formula is the first term plus the product of d and n-1:
[tex]a_n=a_1+d(n-1)\\a_n=-1+(2n+5)(n-1)\\a_n=-1+2n^2-2n+5n-5\\\large\boxed{a_n=2n^2+3n-6}[/tex]
Anyone know please help!!
Answer:
only the inverse is a function
What is the recursive rule for this geometric sequence? 1/2 ,−2, 8, −32,
Answer:
an = an-1 * -4
Step-by-step explanation:
First we need to find the common ratio
r = second term / first term
= -2/ (1/2) = -4
The recursive formula is
an=an−1 * r
an = an-1 * -4
. Find the measure of angle A.
A
160°
Answer:
20°
Step-by-step explanation:
A= 360°- (160°+2*90°)= 20°
Mr. Ferrier invested $26,000. Some was invested in bonds that made a 5% profit, and the rest was put in stocks that made an 8% profit. How much did mr. Ferrier invest in bonds if his total profit on both types of investments was $1,420
Answer:
bonds=22000
stock=4000
Step-by-step explanation:
let b for bonds , and s for stock
b+s=26000
0.05 b +0.08 s=1420
to solve (by elimination)
1- multiply first equation with 0.05 to eliminate b
0.05 b+0.05 s=1300
0.05b+0.08s=1420
subtract two equations:
0.05b+0.05s-0.05b-0.08s=1300-1420
-0.03s=-120
s=120/0.03=4000
b+s=26000
b=26000-4000=22000
check:0.05(22000)+0.08(4000)=1420
Answer:
$22000
Step-by-step explanation:
x*0.05+(26000-x)*0.08= 1420
0.05x - 0.08x + 2080= 1420
0.03x=2080 -1420
0.03x= 660
x= 660/0.03
x= 22000
$22000 = 5% bonds
$4000 = 8% stocks