If θ=2 rad then the condition when θ=2 rad is that the arc length S is equal to twice the radius r.
In this problem, we are given that when the arc length is equal to the radius (S=r), the angle is 1 radian (θ = 1 rad). Now, we are asked to find the condition when the angle is 2 radians (θ = 2 rad).
If Θ=1 rad when S=r, it means that when the angle subtended by an arc of length r is 1 radian, then the radius of the circle is also r.
Now, if θ=2 rad, we can use the same proportionality to find the arc length S that corresponds to this angle. Since the angle has doubled, we can expect the arc length to double as well. Therefore, we have:
θ/Θ = S/r
2/1 = S/r
S = 2r
Thus, the condition when θ=2 rad is that the arc length S is equal to twice the radius r.
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Music streaming services are the most popular way to listen to music. Data gathered over the last 12 months show Apple Music was used by an average of 1.81 million households with a sample standard deviation of 0.47 million family units. Over the same 12 months Spotify was used by an average of 2.21 million families with a sample standard deviation of 0.32 million. Assume the population standard deviations are not the same. Using a significance level of 0.02, test the hypothesis of no difference in the mean number of households picking either service.
a. Compute the test statistic.
b. Compute the p-value.
PLEASE ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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YOU GET 100 POINTS
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Answer:
11
Step-by-step explanation:
You want the degree of the monomial -3q⁴rs⁶.
DegreeThe degree of a variable expression is its exponent. The degrees of the variables in the given expression are ...
q: 4
r: 1
s: 6
The degree of their product is the sum of the exponents:
monomial degree = 4 + 1 + 6 = 11
The degree is 11.
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The sales tax for an item was 11.70 and it cost 390 before tax.
Find the sales tax rate. Write your answer as a percentage.
The sales tax rate for the item is 3%.
How to find the sales tax rate?To find the sales tax rate, we can divide the sales tax amount by the original cost of the item, and then multiply by 100 to express the result as a percentage.
Given:
Sales tax amount = $11.70
Original cost of item = $390
Sales tax rate = (Sales tax amount / Original cost of item) x 100
Plugging in the given values:
Sales tax rate = (11.70 / 390) x 100
Calculating:
Sales tax rate = 0.03 x 100
Final result:
Sales tax rate = 3%
So, the sales tax rate for the item is 3%.
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What is 5a^2b + 15ab^2 factories fully
Answer:
[tex]5 {a}^{2} b + 15a {b}^{2} = [/tex]
[tex]5ab(a + 3b)[/tex]
You paid $6.99 for a shirt that was 70% off; what was the original price of the shirt?
Answer:
$23.30
Step-by-step explanation:
We Know
You paid $6.99
The shirt was 70% off
$6.99 = 30%
What was the original price of the shirt?
We Take
(6.99 ÷ 30) x 100 = $23.30
So, the original price is $23.30
What is the measure of angle XYZ
The calculated measure of the arc XYZ is 83 degrees
Calculating the measures of the angle XYZFrom the question, we have the following parameters that can be used in our computation:
The circle
The angles created by secants and tangents that intersect outside a circle, which states that
The size of the angle formed by these two lines is equivalent to half the numerical difference between the measures of the arcs that they cut out from the circle.
So, we have
XYY = 1/2 * (166 - 0)
Evaluate
XYY = 83
Hence, the measure of the angle is 83 degrees
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need help please thanks
Answer:
a)
[tex]y = 7( {1.03}^{t} )[/tex]
[tex]y = 7( {1.03}^{5} ) = 8.11[/tex]
There were about 8.11 billion subscribers in 2019.
b)
[tex]7( {1.03}^{t}) = 7.5[/tex]
[tex]t = 2.33 \: years \: after \: 2014[/tex]
sometime in 2016
Is (-6, 8) a solution to this system of equations?
y = 8
7x + 4y = -10
yes
Or
no
Answer:
7(-6) + 4(8) = -42 + 32 = -10, so (-6, 8) is the solution to this system of equations.
The answer is Yes.
If a 95% confidence interval for is calculated to be (21.4 , 27.9) , what would be the result of a hypothesis test at a 5% significance level performed on the set of hypotheses?
H0: mean = 27
Ha: mean different 27
If z is a standard normal variable, find P(z>.97)
Therefore, P(z > 0.97) = 0.166 using standard normal distribution table.
Standard normal distribution table explained.
A standard normal distribution table, also called a z-score table or a standard normal table, is a table that provides the area under the curve to the left of a specific z-score value in a standard normal distribution. A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.
The table usually includes positive z-score values in the right-hand column and the second decimal place in the top row. The intersection of a specific z-score value and decimal place provides the area under the curve to the left of that z-score value.
For example, if we want to find the area under the curve to the left of a z-score value of 1.32, we would locate the row with 1.3 in the top row and the column with 0.02 in the right-hand column. The intersection of this row and column gives the area under the curve to the left of 1.32, which is 0.9066.
Using a standard normal distribution table or calculator, we can find the probability of z being greater than 0.97 is approximately 0.166. Therefore, P(z > 0.97) = 0.166.
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What is the slope intercept of -2 and y-intercept (0,2)?
Answer:
The slope-intercept form of the equation of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
We are given that the y-intercept is (0,2), which means that the value of b is 2.
We are also given that the slope is -2, which means that the value of m is -2.
Substituting these values into the slope-intercept form, we get:
y = -2x + 2
Therefore, the slope-intercept form of the equation of the line is y = -2x + 2.
Step-by-step explanation:
Answer:
that is correct just to give you feedback on that
the combined sales tax rate for your country 7.25%
Answer: The California state sales tax rate is 7.25%. This rate is made up of a base rate of 6%, plus California adds a mandatory local rate of 1.25% that goes directly to city and county tax officials.
Step-by-step explanation:
Hope this helped! :)
NO LINKS!! URGENT HELP PLEASE!!
Express the angle in terms of degrees, minutes, and seconds, to the nearest second.
350.5527°
Answer:
350° 33' 10".
Step-by-step explanation:
To convert the decimal degree 350.5527° to degrees, minutes, and seconds, we can use the following steps:
The whole number part of the decimal degree is the degree. So, the degree is 350.Multiply the decimal part by 60 to get the minutes.0.5527 x 60 = 33.162The whole number part of the minutes is the minutes. So, the minutes are 33.Multiply the decimal part of the minutes by 60 to get the seconds.0.162 x 60 = 9.72Round the seconds to the nearest second. The nearest second is 10.Therefore, 350.5527° is equivalent to 350° 33' 10".
What is the length of the diagonal from P to Q ?
Step-by-step explanation:
Use a modified Pythagorean theorem for 3 -D
diagonal = sqrt ( 9^2 + 12^2 + 8^2 ) = sqrt(289) = 17 units
Find the surface area of the triangular prism. The base of the prism is an isosceles triangle.
The answer of the given question based on the Rectangular prism is , the surface area of the given triangular prism is 3360 cm².
What is Rectangular prism?A rectangular prism is a three-dimensional geometric shape with six rectangular faces. It is also known as rectangular parallelepiped or cuboid. A rectangular prism has a length (l), width (w), and height (h) and the formula for the volume of a rectangular prism is given as V = l * w * h.
To find the surface area of a triangular prism, we need to add up the areas of all of its faces. A triangular prism has two identical triangular bases and three rectangular faces.
First, let's find the area of the triangular base. We know that it is an isosceles triangle with a perpendicular height of 35 cm and base of 24 cm, and the length of the two equal sides is 37 cm. We can use the formula for the area of a triangle:
Area of base = (1/2) * base * height
Area of base = (1/2) * 24 cm * 35 cm
Area of base = 420 cm²
Since there are two identical bases, we can multiply this by 2 to get the total area of the triangular bases:
Total area of bases = 2 * 420 cm²
Total area of bases = 840 cm²
Now, let's find the area of the three rectangular faces. We know that the height of the prism is 35 cm, and the length of each rectangular face is equal to the base of the triangular base, which is 24 cm. To find the width of each rectangular face, we need to use the Pythagorean theorem to find the length of the altitude of the triangular base:
a² + b² = c²
where a and b are the two equal sides of the triangular base, and c is the base.
Substituting the given values, we get:
a² + b² = c²
37² + 12² = c²
1369 + 144 = c²
c² = 1513
c = √1513
c = 38.95 cm
Therefore, the altitude of the triangular base is approximately 35 cm, and we can use this value as the width of each rectangular face. So, area of each rectangular face is given:
Area of each rectangular face = length*width
Area of each rectangular face = 24 cm * 35 cm
Area of each rectangular face = 840 cm²
Since there are three identical rectangular faces, we can multiply this by 3 to get the total area of the rectangular faces:
Total area of rectangular faces = 3 * 840 cm²
Total area of rectangular faces = 2520 cm²
Finally, we can find the total surface area of the prism by adding the areas of the two triangular bases and the three rectangular faces:
Total surface area = Total area of bases + Total area of rectangular faces
Total surface area = 840 cm² + 2520 cm²
Total surface area = 3360 cm²
Therefore, the surface area of the given triangular prism is 3360 cm².
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Pat's Pizza made
21
2121 cheese pizzas,
14
1414 veggie pizzas,
23
2323 pepperoni pizzas, and
14
1414 sausage pizzas yesterday.
Based on this data, what is a reasonable estimate of the probability that the next pizza made is not a cheese pizza?
Choose the best answer.\
Therefore , the solution of the given problem of probability comes out to be pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.
What exactly is probability?Any considerations technique's fundamental objective is to determine the likelihood that a claim is true or that a particular incident will take place. Any number range from one to one, when 0 traditionally signifies a percentage and 1 typically implies the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The total number of pizzas made yesterday can be determined using the information provided as follows:
2121 cheese pizzas total.
Pizzas with vegetables: 1414
2323 pepperoni pizzas total.
1414 sausage pizzas were consumed.
Total pizzas produced were
=>2121 + 1414 + 2323 + 1414 = 7272.
Therefore, there were 2121 cheese pizzas prepared yesterday out of a total of 7272 pizzas.
The likelihood that the following pizza will be a cheese pizza is calculated as follows:
=> 2121 / 7272
The likelihood that the next pizza prepared won't be a cheese pizza is thus:
=> 1 - (2121 / 7272) = 5151 / 7272
Therefore, a conservative estimate of the likelihood that the following pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.
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PLEASE HELP ON QUESTION!(if answer and explanation is correct I'll rate you five stars a thanks and maybe even brainly. Also your very smart!)
What is value of x in this equation:
4x+15=33-2x
Answer: Simplifying
4x + 15 = 33 + -2x
Reorder the terms:
15 + 4x = 33 + -2x
Solving
15 + 4x = 33 + -2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2x' to each side of the equation.
15 + 4x + 2x = 33 + -2x + 2x
Combine like terms: 4x + 2x = 6x
15 + 6x = 33 + -2x + 2x
Combine like terms: -2x + 2x = 0
15 + 6x = 33 + 0
15 + 6x = 33
Add '-15' to each side of the equation.
15 + -15 + 6x = 33 + -15
Combine like terms: 15 + -15 = 0
0 + 6x = 33 + -15
6x = 33 + -15
Combine like terms: 33 + -15 = 18
6x = 18Divide each side by '6'.
x = 3
Simplifying
x = 3
so X=3 is your answer
A movie theater has a seating capacity of 257. The theater charges $5.00 for children, $7.00 for
students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket
sales was $ 1870, How many children, students, and adults attended?
The attendance at the movie theatre is;
Children = 142
Students = 44
Adults = 71
What is arithmetic?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
Given:
Seating capacity = 257
Charges: Children = $5.00; Students = $7.00; Adults = $12.00
Total sales of ticket = $1870
A number of children, students, and adults were present in the theatre.
Let A, C, and S represent adults, children, and students respectively.
There are half as many adults as there are children; this means that
A = ½C
If the total seat capacity is 257, then
A + C + S = 257
Also, if the total sales of tickets are $1870, then
12A + 7S + 5C = 1870
So, we have two equations to be solved simultaneously.
A + C + S = 257 --- (1)
12A + 7S + 5C = 1860 --- (2)
Substitute ½C for A in (1) and (2)
½C + C + S = 257
Multiply both sides by 2
2(½C + C + S) = 2 * 257
C + 2C + 2S = 514
3C + 2S = 514 ----- (3)
12(½C) + 7S + 5C = 1870
6C + 7S + 5C ,= 1870
6C + 5C + 7S = 1870
11C + 7S = 1870 --- (4)
Make S the subject of the formula in (3)
2S = 514 - 3C
S = ½(514 - 3C)
S = 257 - 1.5C
Substituton 257 - 1.5C for S in (4)
11C + 7(257- 1.5C) = 1870
11C + 1799 - 10.5C = 1870
Collect like terms
11C - 10.5C = 1870 - 1799
0.5C = 71
Multiply both sides by 2
2 * 0.5C = 2 * 71
C = 142
Recall that
S = 257 - 1.5C
S = 257 - 1.5(142)
S = 257 - 213
S = 44
Also, recall that
A = ½C
A = ½ * 142
A = 71
Hence, the attendance at the movie theatre is;
Children = 142
Students = 44
Adults = 71
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The 8th grade math team is having a bake sale as a fundraiser. Alan can make 5 cookies in 2 minutes. Abigail can make 8 cookies in 3 minutes. However, Katie eats 1 cookie every 6 minutes. How many minutes will it take to make 5 dozen cookies.
Answer: B. 12
Step-by-step explanation:
1) Alan can make 2.5 cookies per min
2) Abi can make 8/3 which is 2.7.
3) overall, 5.2 cookies per minute can be made.
multiple 5.2 x 6 and you get around 31.5?
then subtract =1. you have 30.5, now add onto that number 31.5, which is another 6 minutes. since you're still only subtracting 1, the answer would be above 60, which is 5 dozen, and it only took 12 mins
What is an equation of the line that passes through the points
(
5
,
−
6
)
(5,−6) and
(
−
5
,
−
4
)
(−5,−4)?
Answer:
y= -1/5x-5
Step-by-step explanation:
You can use the slope formula and the slope intercept form which is y=mx+b.
In this 30°-60°-90° right triangle, the length of the long leg is 9√3
What is the measure of the hypotenuse n and the short leg m?
30°
9√3
n
m
Answer:
30°
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
In a 30°-60°-90° right triangle, the sides are always in the ratio of 1: √3:2, where 1 is the length of the short leg opposite the 30° angle, √3 is the length of the long leg opposite the 60° angle, and 2 is the length of the hypotenuse opposite the 90° angle1234.
In this case, we are given that the long leg is 9√3, so we can use this value to find the other sides by setting up a proportion:
short leglong leg=13
short leg93=13
Cross-multiplying and solving for the short leg, we get:
short leg=393×1=9
Similarly, we can use another proportion to find the hypotenuse:
long leghypotenuse=32
93hypotenuse=32
Cross-multiplying and solving for the hypotenuse, we get:
hypotenuse=32×93=18
Therefore, the measure of the hypotenuse n is 18 and the measure of the short leg m is 9.
Based on the information in the table, what
was the approximate value of this item in
1980?
Answer:
B) 4,700
Step-by-step explanation:
6000 - 4000 = 2000
2000 in 15 year, find how much for each year
2000/ 15 = 133.3333333
133.3333333 estimated = 133
133 approximately for each year
1975 to 1980 is five years
133 x 5 = 665
4000 + 665 = 4665
4665 rounded the the nearest hundred
4700
The length of a rectangle is 4 meters less than 2 inches times width. The perimeter is 34 meters. Find the width
Answer:
7
Let's call the width = x
width : x
so (x + 2x-4)2 = 34 (perime formula of a rectangle) x+2x-4 = 7
3x = 21
x = 7
so x is 7
An object is thrown upward at a speed of 145 feet per second by a machine from a height of 2 feet off the ground. The height h of the object after t seconds can be found using the equation
When will the height be 230 feet?
seconds
When will the object reach the ground?
seconds
Answer:
Step-by-step explanation:
The equation for the height h of the object after t seconds is given by:
h = -16t^2 + 145t + 2
To find when the height will be 230 feet, we can set h = 230 and solve for t:
230 = -16t^2 + 145t + 2
We can simplify this equation by moving all the terms to one side:
16t^2 - 145t + 228 = 0
To solve for t, we can use the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 16, b = -145, and c = 228. Plugging in these values, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(228))) / 2(16)
t = (145 ± sqrt(21025 - 14592)) / 32
t = (145 ± sqrt(6433)) / 32
t ≈ 0.56 seconds or t ≈ 9.17 seconds
Therefore, the height of the object will be 230 feet at approximately 0.56 seconds or 9.17 seconds after it is thrown.
To find when the object will reach the ground, we can set h = 0 and solve for t:
0 = -16t^2 + 145t + 2
Again, we can simplify this equation by moving all the terms to one side:
16t^2 - 145t - 2 = 0
Using the quadratic formula again, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(-2))) / 2(16)
t = (145 ± sqrt(21249)) / 32
t ≈ 9.51 seconds or t ≈ 0.15 seconds
Therefore, the object will reach the ground at approximately 0.15 seconds or 9.51 seconds after it is thrown. However, since the negative solution does not make physical sense in this context, the object will reach the ground after approximately 9.51 seconds.
~~~Harsha~~~
Y can represent the distance Frog B hopped as y=x+ 8/3 x. Now rewrite the equation using the distributive property.
The rewritten expression of y = x + 8/3x using the distributive property is y = x(1 + 8/3)
Rewriting the equation using the distributive property.From the question, we have the following parameters that can be used in our computation:
Y can represent the distance Frog B hopped as y=x+ 8/3 x.
This means that
y = x + 8/3x
Factor out x from the equation
So, we have
y = x(1 + 8/3)
The above equation has been rewritten using the distributive property.
Hence, the rewritten expression using the distributive property is y = x(1 + 8/3)
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A person invested $840 in an account growing at a rate allowing the money to double every 10 years. How long, to the nearest tenth of a year would it take for the value of the account to reach $1,540?
It would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.
HOW CAN WE CALCULATE THE AMOUNT?To solve this problem, we can use the formula for exponential growth:
[tex]A = P * (1 + r)^t[/tex]
where:
A = final amount (in this case, $1,540)
P = principal amount (initial investment, in this case, $840)
r = rate of growth (as a decimal, in this case, the rate at which the money doubles every 10 years, or 1/10 = 0.1)
t = time (in years, which we need to find)
Plugging in the values:
[tex]1,540 = 840 * (1 + 0.1)^t[/tex]
Dividing both sides of the equation by 840:
[tex]1.83333... = (1.1)^tTaking the natural logarithm of both sides:ln(1.83333...) = ln((1.1)^t)Using the property of logarithms that ln(a^b) = b * ln(a), we get:ln(1.83333...) = t * ln(1.1)Finally, dividing both sides by ln(1.1) to solve for t:t = ln(1.83333...) / ln(1.1)[/tex]
Using a calculator, we can find that t ≈ 7.5 (rounded to the nearest tenth of a year).
So, it would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.
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XYZ Software employed three different salespeople last year. Person 1
earned $4700 in the first quarter, Person 2 earned $19,800 in the first quarter,
and Person 3 earned $6500 in the first quarter. What are the maximum FUTA
deductions for the first quarter?
OA. $291.40
OB. $1227.60
C. $403.00
D. $1128.40
The maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.
The Federal Unemployment Tax Act (FUTA) tax rate is 6% on the first $7,000 paid to each employee in a calendar year. Therefore, the maximum FUTA deduction for each employee is $420 ($7,000 x 0.06).
Person 1 earned $4700, so the FUTA deduction for Person 1 is $282 ($4700 x 0.06).
Person 2 earned $19,800, but only the first $7,000 is subject to FUTA. Therefore, the FUTA deduction for Person 2 is $420.
Person 3 earned $6500, so the FUTA deduction for Person 3 is $390 ($6500 x 0.06).
The total FUTA deduction for the first quarter is the sum of the FUTA deductions for each employee:
$282 + $420 + $390 = $1092
Therefore, the maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.
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If sam can swin 10 laps in 20 minutes, what would be his expected time for 15 laps?
Asnwer: 30 minutes
Explanation:
10 laps in 20 minutes is 1 lap every 2 minutes.
So we get this:
1 lap = 2 minutes
But we want 15 laps, so multiply both sides by 15 to get:
15 laps = 30 minutes
find the gcf of 8a^3b^2 and 12ab^4
Answer:
To find the greatest common factor (GCF) of 8a^3b^2 and 12ab^4, we need to factor each term into its prime factors and then find the common factors.
8a^3b^2 can be written as:
8a^3b^2 = 2^3 * 2 * a * a * a * b * b
12ab^4 can be written as:
12ab^4 = 2^2 * 3 * a * b * b * b * b
The common factors are 2, a, and b^2.
Therefore, the GCF of 8a^3b^2 and 12ab^4 is:
2 * a * b^2 = 2ab^2
Find the volume for each prism.
(7) The volume of the triangular based prism is 41.16 m³.
(8) The volume of the haxagonal based prism is 1793.4 cm³.
What is a volume?Volume is the space ocuppied by a solid shape.
(7) To calculate the volume of the triangular based prism, we use the formula below
Formula:
V = Hbh/2.................... Equation 1Where:
V = Volume of the triangular based prismH = Height of the prism = 7 mb = Base of the triangle = 4.2 mh = Height of the triangle = 2.8 mSubstitute these values into equation 1
V = 7×4.2×2.8/2V = 41.16 m³(8) Also, to calculate the volume of the hexagon based prism, use the formula below
V = 6Hpa/2................. Equation 2Where:
H = Height of the prism = 14 cmp = Apothom of the hexagon = 6.1 cma = Sides of the hexagon = 7 cmSUbstitute these values into equation 2
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