The following expressions (1+cosβ)(1−cosβ)sinβ is equivalent to sin³β
What are Trigonometric Ratios ?In a Right angled triangle , trigonometric ratios can be used to determine the value of angles and sides of the triangle.
The trigonometric expression given in the question is
(1+cosβ)(1−cosβ)sinβ
(a+b)(a-b) = a² - b²
( 1 - cos²β)sinβ
By the trigonometric Identity
1-cos²β = sin² β
sin² β x sin β
sin³β
Therefore Option B is the correct answer.
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5=1 2/3x how do I solve for x?
You'll first Cross multiply: 5× 3x
that'll give you 15x.
15x=12(12 is a numerical constant).
Divide both sides by the the coefficient of X .That is 15x/15= 12/15
Therefore the answer is 12/15= x
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{5 = 1 \dfrac{2}{3}x}[/tex]
[tex]\mathsf{1 \dfrac{2}{3}x = 5}[/tex]
[tex]\mathsf{\dfrac{1\times3 + 2}{3}x= 5}[/tex]
[tex]\mathsf{\dfrac{3 + 2}{3}x = 5}[/tex]
[tex]\mathsf{\dfrac{5}{3}x = 5}[/tex]
[tex]\large\text{MULTIPLY }\rm{\dfrac{3}{5}}\large\text{ to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{3}{5}\times\dfrac{5}{3}x = \dfrac{3}{5}\times5}[/tex]
[tex]\large\text{SIMPLIFY IT!}[/tex]
[tex]\mathsf{x = \dfrac{3}{5}\times5}[/tex]
[tex]\mathsf{x = \dfrac{3}{5}\times\dfrac{5}{1}}[/tex]
[tex]\mathsf{x = \dfrac{3\times5}{5\times1}}[/tex]
[tex]\mathsf{x = \dfrac{15}{5}}[/tex]
[tex]\mathsf{x = \dfrac{15\div5}{5\div5}}[/tex]
[tex]\mathsf{x = \dfrac{3}{1}}[/tex]
[tex]\mathsf{x = 3\div1}[/tex]
[tex]\mathsf{x = 3}[/tex]
[tex]\huge\text{Therefore, your answer: \boxed{\mathsf{x = 3}}}\huge\checkmark[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]A small country is comprised of five states, A, B, C, D, and E. The population of each state is given in the following table. Congress will have 57 seats divided among the five states according to their respective populations. Use Jefferson's method with d=32,920 to apportion 57 seats
Based on Jefferson's method and the value of d, the apportionment of the 57 seats will be:
A - 4 seats.B - 5 seats. C - 10 seats.D - 16 seats.E - 22 seats.How will the seats be allocated?This is done by dividing the population of the state by the d value and then rounding this off:
State A:
= 138,352 / 32,920
= 4.2
= 4
State B:
= 181,282 / 32,920
= 5.5
= 5
State C:
= 337,026 / 32,920
= 10.23
= 10
State D:
= 549,634 / 32,920
= 16.6
= 16
State E:
= 729,736 / 32,920
= 22.1
= 22
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The points (-15, r) and (-3, 16) lie on a line with slope 5/4. Find the missing coordinate r.
Answer:
r = 1
Step-by-step explanation:
we know that :
[tex]Slope=\frac{y_{B}-y_{A}}{x_{B}-x_A}[/tex]
Then
[tex]\frac{5}{4} =\frac{16-r}{-3-(-15)}[/tex]
Then
[tex]\frac{5}{4} =\frac{16-r}{12}[/tex]
Then
5×12 = 4×(16-r)
Then
60 = 64 - 4r
Then
4r = 64 - 60
Then
4r = 4
Then
r = 1
How many solutions exist for the given equation?
3(x - 2) = 22 -x
Answer:
One solution
Step-by-step explanation:
The equation can be rewrite as 3x - 6 = 22 - x
so we try to get all the x on one side so we add x and 6 to both sides so we get 4x = 28 then we divide by 4 both side and get x=7
On a walk through the woods, Mr. Finley saw 16 blue jays and 25 purple finches. Write the ratio of finches to blue jays three different ways.
Answer:
25:16
50:32
100:64
Step-by-step explanation:
In the diagram below, ABC~ DEC. What is the value of x?
The value of x will be 3
From given diagram, triangle ABC and EDC meet at a common vertex C.
So, triangle ABC and EDC both are congruent to each other.
Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.
Therefore,
[tex]\frac{AB}{ED} = \frac{AC}{EC} = \frac{BC}{CD}[/tex]
[tex]\frac{AC}{EC} = \frac{BC}{CD}[/tex]
Simplifying the expression,
We get
(18-x)/x = 25/5
(18-x)/x = 5
18-x = 5x
18-x-5x = 0
18 - 6x = 0
- 6x = -18
x = 3
Hence, the value of x is 3.
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Wei Xun bought 8 pieces of chocolates and 10 lollipops for $17. The average price of a piece of chocolate was S$1. What was the average price of a lollipop?
Answer:
$0.90
Step-by-step explanation:
If each piece of chocolate is $1, then 8 pieces is $8. Wei Xun bought 8 pieces of chocolate and 10 lollipops, which came out to $17. The chocolate was $8 total, leaving $9 for the 10 lollipops. 9/10 = 0.9. So, each lollipop was $0.90, or 90 cents.
the angle is 36.2 less than it’s complementary angle
Answer:
below
Step-by-step explanation:
Measure of each angle is 27 and 63 degrees.
2 more than product of a number and 9 is 8. variable w
Answer:
w (number) = 2/3
Step-by-step explanation:
Variable w means use the letter w as the unknown number :
This is the equation made from the question :
2+(9w) = 8
Let's subtract 2 from both sides :
9w = 6
Divide both sides by 9 :
w = 6/9
Simplify fraction :
w = 2/3
Hope this helped and have a good day
please help
0.06/1.71
Answer:
0.04
Step-by-step explanation:
0.03508772
Rewrite each of the following expressions without using absolute value: |x-5|+|x+5| if x<-5
For [tex]x < -5[/tex]:
[tex]x-5 < 0 \Rightarrow |x-5|=-(x-5)=-x+5\\x+5 < 0\Rightarrow |x+5|=-(x+5)=-x-5[/tex]
So
[tex]|x-5|+|x+5|=-x+5-x-5=-2x[/tex]
Write the integral and solve for the area under the curve:
Answer:
Integral: [tex]\int\limits^\pi _0 {3sinx} \, dx[/tex]
Area: 6
Step-by-step explanation:
[tex]\int\limits^\pi _0 {3sinx} \, dx = -3[cosx]_{0} ^{\pi} = 6[/tex]
for
If a study determines the difference in average salary
subpopulations of mechanical engineers and civil
engineers is NOT significant, then the subpopulations
of mechanical and civil engineers are
different
salaries.
A
Guaranteed not to be earning
B
Not earning
C) Earning very
D Definitely earning
A mean is an arithmetic average of a set of observations. The correct option is B.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
The average pay does not differ significantly since the average wage for subpopulations is not significant. As a result, the subpopulations of mechanical and civil engineers are Not earning different salaries.
Hence, the correct option is B.
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Hi supreme turtle this is the question
Answer:
< $0 --------------$35------ $50>
Step-by-step explanation:
wait that's not the full question but uh I assume that's 30% off $50?
it would be 0.3x50 which is 15 and 50-15 is 35.
the range is 0 - $50 if I'm not mistaken
< $0 -------------------------- $50> scuffed number line
but 35 is somewhere around here?
< $0 --------------$35------ $50>
A standard number cube with the numbers 1 through 6 is rolled. Find the probability of rolling a number greater than 2
Find the midpoint between the given points: (2,-1), (10,-9)
Answer: (6, -5)
Step-by-step explanation: I used the midpoint formula and this is what I got. I hope this helps!
The formula:
(xm, xy) = (x1 + x2/2, y1 + y2/2)
Each phrase in the table describes two variables whick are strongly correlated. Select all phases that imply correlation without causation.
The complete question is attached below.
The most correct phases that imply correlation without causation are 1, 5, and 6.
What is correlation?The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when another data value is increased or decreased respectively.
The most correct phases imply correlation without causation are;
The number of stuffed animals produced at a factory and the number of newborn babies.
The number of videos rented and the number of films in the theater.
The number of pets in the neighborhood and the amount of grass nearby.
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Sampling is used in the situations
A. Cooking rice in an utensil
B. Purchase of food commodity from
C. shopkeeper
D. All the above
E. Blood test of the patients
Answer:
all of the above
Step-by-step explanation:
please mark me as brainliest
please help to answer with working.
Answer:
When r=0.2, m=0.016g
When m=0.25, r=0.5cm
When r=0.7, m=0.686g
When m=11.664, r=1.8cm
Step-by-step explanation:
General outline of steps for proportionality problems:
Identify the type or proportionality.Find the proportionality constant using a known input/output pair.Use the proportionality equation to find other unknowns.Background on proportionality relationshipsThere are two main types of proportionality, "direct" and "inverse", and then there are modifications that can be made to them. Several examples are listed below:
Direct proportionality examples
y is directly proportional to x: [tex]y=kx[/tex]y is directly proportional to the square of x: [tex]y=kx^2[/tex]y is directly proportional to the cube of x: [tex]y=kx^3[/tex]Inverse proportionality examples
y is inversely proportional to x: [tex]y=\dfrac{k}{x}[/tex]y is inversely proportional to the square of x: [tex]y=\dfrac{k}{x^2}[/tex]In each case, irregardless of which type, the two quantities are related with some extra letter "k", called the proportionality constant. Either way, the proportionality constant "k" is always in the numerator, and the quantity is either multiplied to or divided from the proportionality constant "k".
Notice that for direct proportionality, in each case, the equation always ends up as "k times" the quantity.
On the other hand, notice that for inverse proportionality, in each case, the equation always ends up as "k divided by" the quantity.
Step 1. Identify the type or proportionality (Setting up our proportionality equation)The problem says "... the mass, m g, of a sphere is directly proportional to the cube of its radius, r cm...", so our equation will look like [tex]m=kr^3[/tex].
Step 2. Finding the proportionality constantTo find the proportionality constant for our situation, one must know a full input/output pair. Notice that in the 4th column, [tex]r=1.5[/tex] and [tex]m=6.75[/tex].
Substituting these values into our equation, we can find "k".
[tex](6.75)=k(1.5)^3[/tex]
[tex]6.75=k*3.375[/tex]
[tex]\dfrac{6.75}{3.375}= \dfrac{k*3.375}{3.375}[/tex]
[tex]2=k[/tex]
So, the proportionality constant for this situation is 2, and our equation for this situation becomes: [tex]m=2r^3[/tex]
Step 3. Finding the other inputs/outputsNow that we know the proportionality constant for this situation, if we have either the input OR the output, we can solve for the other unknown.
r=0.2
[tex]m=2r^3[/tex]
[tex]m=2(0.2)^3[/tex]
[tex]m=2(0.008)[/tex]
[tex]m=0.016[/tex]
Recall the the question said that the mass, m, was measured in grams, and the radius, r, was measured in centimeters. So, if the radius is 0.2cm, then the mass of the sphere would be 0.016g.
m=0.25
[tex]m=2r^3[/tex]
[tex](0.25)=2r^3[/tex]
[tex]\dfrac{0.25}{2}=\dfrac{2r^3}{2}[/tex]
[tex]0.125=r^3[/tex]
[tex]\sqrt[3]{0.125} = \sqrt[3]{r^3}[/tex]
[tex]0.5=r[/tex]
So, if the mass of the sphere were 0.25g, the radius of the sphere would be 0.5cm.
r=0.7
[tex]m=2r^3[/tex]
[tex]m=2(0.7)^3[/tex]
[tex]m=2(0.343)[/tex]
[tex]m=0.686[/tex]
So, if the radius is 0.7cm, then the mass of the sphere would be 0.686g.
m=11.664
[tex]m=2r^3[/tex]
[tex](11.664)=2r^3[/tex]
[tex]\dfrac{11.664}{2}=\dfrac{2r^3}{2}[/tex]
[tex]5.832=r^3[/tex]
[tex]\sqrt[3]{5.832} = \sqrt[3]{r^3}[/tex]
[tex]1.8=r[/tex]
So, if the mass of the sphere were 11.664g, the radius of the sphere would be 1.8cm.
use interval notation to express the following: the set of all numbers greater than or equal to 5 and less than or equal to 7
[5, +∞) ∪ (-∞,7] is the notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7.
We need to use interval notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7.
What is a set?A set is a mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Let x belong to the set of real numbers (R)
Now, x≥5 and x≤7.
So, x≥5⇒[5, +∞) and x≤7⇒(-∞,7]
Therefore, the notation will be [5, +∞) ∪ (-∞,7].
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A tea shop owner is mixing a blend of two teas, one of which costs $6.50 per pound, the other costing $4.00 per pound. The owner wants to have 20 pounds of a mixture that will sell for $5.50 per pound. How much of each type of teach should be used?
Answer:
12 pounds of tea-1 and 8 pounds of tea-2 should be used.
Step-by-step explanation:
A clinical psychologist is administering the Hamilton Rating Scale for Depression (Hamilton, 1967). The scale ranges from 0 to 52. Scoring is based on the 17-item scale and scores of 0–7 are considered as being normal, 8–16 suggest mild depression, 17–23 moderate depression and scores over 24 are indicative of severe depression (Zimmerman, Martinez, Young, Chelminski, & Dalrymple, 2013).
We have some evidence about the mean score for the Hamilton Rating Scale for Depression among the population of adolescents: μ = 6 with a standard deviation of σ =1.5. The clinical psychologist’s patient, a 14-year old girl, scores a 10 on the scale. How would you describe her score relative to the population of adolescents? (Please use your knowledge of z-scores to answer this question.)
Using the normal distribution, it is found that the girl's score of 10 is higher than 99.62% of the population.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 6, \sigma = 1.5[/tex].
Her z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 6}{1.5}[/tex]
Z = 2.67
Z = 2.67 has a p-value of 0.9962.
Hence her score is higher than 99.62% of the population.
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If $4500 is invested at 10% annual interest, which is compounded continuously, what is the account balance after 3 years, assuming no additional deposits or withdrawals are made?
Answer:
$6074.36
Step-by-step explanation:
The formula for continuous compounding is
F = Pe^(rt)
F = $4500 × e^(0.1 × 3)
F = $6074.36
Answer: $6074.36
An electrician charges a $40 fee to make a house call plus an hourly rate for labor. If the total bill that takes 2 hours comes to $99 what is the electrician hourly labor rate?
90ft×7ft requires1/2 ounces toof solution per square ft to clean.How much solution is necessary to clean floor
The amount of the cleaning solution is required to clean the hallway will be 315 ounces.
The complete question is given below.
A hallway measuring 90 feet by 7 feet requires 1/2 a fluid ounce of cleaning solution per square foot. How much cleaning solution is required to clean the hallway?
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L × W square units
A hallway measuring 90 feet by 7 feet requires 1/2 a fluid ounce of cleaning solution per square foot.
Then the amount of the cleaning solution is required to clean the hallway will be
Amount of cleaning solution = 1/2 × area of hallway
Amount of cleaning solution = 0.5 × (90 × 7)
Amount of cleaning solution = 315 ounces
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I don’t get this question
Simplify 4.5:9.9:8.1
Please help
Answer:
5:11:9
Step-by-step explanation:
Change the decimal to fractions
45/10:99/10:81/10
Multiply through by the Lowest Common Factor 10
10×45/10:10×99/10:10×81/10
Which makes it
45:99:81
They have a common factor which is 9, so divide through by 9
45/9:99/9:81/9
Your answer is
5:11:9
Hope it helps
How can triangles be proven similar by the SAS similarity theorem?
Answer: Option (2)
Step-by-step explanation:
We need the angle to be included between the two mentioned sides.
This eliminates the first and fourth options.Also, the sides need to be corresponding for the ratio, and both sides of the triangle need to be in either the numerators or the denominators.
This eliminates the third option.A decision at the margin Crystal is a hard-working college senior. One Thursday, she decides to work nonstop until she has answered 100 practice problems for her math course. She starts work at 8:00 AM and uses a table to keep track of her progress throughout the day. She notices that as she gets tired, it takes her longer to solve each problem. Time Total Problems Answered 8:00 AM 0 9:00 AM 40 10:00 AM 70 11:00 AM 90 Noon 100 Use the table to answer the following questions. The marginal, or additional, gain from Crystal’s first hour of work, from 8:00 AM to 9:00 AM, is problems. The marginal gain from Crystal’s third hour of work, from 10:00 AM to 11:00 AM, is problems. Later, the teaching assistant in Crystal’s math course gives her some advice. “Based on past experience,” the teaching assistant says, “working on 35 problems raises a student’s exam score by about the same amount as reading the textbook for 1 hour.” For simplicity, assume students always cover the same number of pages during each hour they spend reading. Given this information, in order to use her 4 hours of study time to get the best exam score possible, how many hours should she have spent working on problems, and how many should she have spent reading? 0 hours working on problems, 4 hours reading 1 hour working on problems, 3 hours reading 3 hours working on problems, 1 hour reading 4 hours working on problems, 0 hours reading
She should spend 1 hour working on problems , 3 hour reading , Option B is the right answer.
What is Margin gain ?The gain of the desired effect with respect to the previous gain is called margin gain
The marginal gain from 8:00 am to 9:00 am is
(40-0) = 40 problems
The marginal gain from 9:00 am to 10:00 am is
= 70-40 = 30 problems
The marginal gain from 10:00 am to 11:00 am is
(90-70) = 20 problems
As if she does more than one hour of problem solving her productivity decreases to 30 which is less than 1 hour of reading textbook
Therefore she should not spend more than 1 hour on problem solving.
Therefore Option B is the right answer.
1 hour working on problems , 3 hour reading
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Houses in an real estate are all identical however a person can purchase a new house with some all or none of a set of options as indicated by the set below
how many options are there for purchasing a house in this community
{ pool , alarm , lake view , balcony }
Considering the number of subsets of the set of options, it is found that there are 16 options for purchasing a house in this community.
What is the number os subsets of a set of cardinality n?The number of subsets is given by:
[tex]N_s = 2^n [/tex]
The set of options is given by:
O = { pool , alarm , lake view , balcony }
Which has cardinality n = 4.
The number of options for the purchased home is the number of subsets of set O, hence:
[tex]N_s = 2^4 = 16[/tex]
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Factor: 120u² + 125u + 30.
Answer:
5(3u+2)(8u+3)
Step-by-step explanation:
lmk if you want an explanation
Answer:
5(3u+2)(8u+3)
Step-by-step explanation:
Well you first want to factor out any GCF which in this case is 5
5(24u² + 25u + 6)
so now a, b, c = 24, 25, 6.
ac = 144
factors of 144 that add up to 25 are 9 and 16
rewrite equation
(24u² + 9u) + (16u + 6)
factor out GCF
3u(8u+3) + 2(8u + 3)
(3u+2)(8u+3)
plug that back into entire equation
5(3u+2)(8u+3)
