The correct responses found using trigonometric ratios are as follows;
Brooke's cannot bring the boat back without getting water over her boots.The plan will not be approvedThe plane will not disturbThe company can not use the chimney legallyThe Long company will build the bridgeThe fireman can reach her.The lift does not take the skiers up to the bar.Eric will be able to see his Dad's plane.The 73 m. braceHow can trigonometric ratios be used to find the right responses?1. The depth of the water = 15 × tan(4°) = 1.049 m
The height of Brooke's boot = 1 m
Therefore;
Brooke's cannot bring the boat back without getting water over her boots.2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°
Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;
The plan will not be approved.3. Height reached by the plane = 9 × tan(21°) = 3.455
Therefore;
The plane will not disturb.4. Height of the chimney at the factory = 50 × tan(51°) = 61.745
The minimum chimney height = 65 m.
Therefore;
The company can not use the chimney legally.6. Length of the bridge = 72 × tan(55°) ≈ 102.83
Therefore;
The Long company will build the bridge because it is longer than 100 m. but not more than 103 m.7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7
Therefore;
The fireman can reach her.8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8
Therefore;
The lift does not take the skiers up to the bar.9. Height reached by plane = 26 × tan(9°) ≈ 4.12
The plane flies under the cloud therefore;
Eric will be able to see his Dad's plane.10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83
Therefore;
The brace that wastes less metal is the 73 m. brace, because the 71 m. brace is not long enough and two braces will be required.Learn more about trigonometric ratios here:
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Find the volume of the composite figure. Round to the nearest tenth. 3cm 4cm 10cm 5 cm
The volume of the composite figure is 655.44 unit³.
How to illustrate the volume?The information is incomplete. An overview will be given. Let's assume that the shape is a cylinder.
The volume of a cylinder is πr²h
Assumed radius = 7
Assumed height = 4
The volume will be:
= πr²h
= 3.14 × 7² × 4
= 615.44 unit³
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What is the difference between 89.4 and 13.621 do not round your answer
Answer:
89.4 - 13.621 = 75.779
Explanation:
Subtract 13.621 from 89.4 to get 75.779.
One-fifth of a number x is less than 8. Find the greatest possible prime number x.
Suppose that $6500 is placed in an account that pays 12% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
The amount after 1 year is $7280 and the amount after two year is $8153.
Given that $6500 is placed in an account that pays 12% interest compounded each year.
Compounding is the addition of interest to the principal of a loan or deposit, or in other words, interest on principal plus interest.
Compounded interest=12%
Principal amount=$6500
Time period = 1 year
[tex]A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]
where P is Principle amount, r is annual interest, n is number of times the interest compounded monthly, t is number of years
Here P=6500, r=12%, n=1, t=1
Substitute these values in the formula, we get
A=6500(1+(0.12/1))¹⁽¹⁾
A=6500(1+0.12)¹
A=6500×1.12
A=7280
Now we have to calculate for two years.
That is if n=2 , then
A=6500(1+(0.12/1))¹⁽²⁾
A=6500(1+0.12)
A=6500×1.2544
A=8153.6
Hence, the amount for one year and two year when $6500 is placed in an account that pays 12% interest compounded is $7280 and $8153.60.
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The total area of a picture and its frame can be represented by ^l + 2f h^w + 2f h, where l and w represent the length and width of the picture, respectively, and f represents the thickness of the frame.
a. Sketch a diagram to represent this scenario.
b. What binomial multiplication represents the area of an 8" # 12" picture and its frame?
c. Multiply the binomials from b., and combine like terms to simplify.
d. What is the total area of an 8" # 12" picture and its frame if the frame is 1.5" thick?
The answers to the question are
b. (l + 2f) (w + 2f)
c. f + 4, f + 6
d. 52.25
a. The diagram is an attachment.
B. How to solve for the binomial multiplicationThe equation says
(l + 2f) (w + 2f)
We have the lengths of w and l as 8 and 12 respectively. Hence we have
(8 + 2f) (12 + 2f) as the area
c. (8 + 2f) (12 + 2f)
= 96 + 16f + 24f + 4f²
= 4f² + 40 f + 96
We have to factorize this using the quadratic equation calculator
f + 4, f + 6
= f = -4 and f = -6
d. If it is 1.25 thick we would have
1.25 x 2 = 2.5
12 - 2.5 = 9.5
8 - 2.5 = 5.5
Area = l * w
= 5.5 * 9.5
= 52.25
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Officially, variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ). An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit. Python’s most-followed style guide, PEP8 also suggests we limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.How many variable names can there be in Python if we abide by these two rules?
Abiding by the two rules, the number of variable names we can have in Python are; 63
How to name variables in Python Programming?The rules for python are given as;
1) Variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ).
1b) An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit.
2) We limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.
Now, abiding by the two rules above, the number of variable names we can have in Python are;
26( A-Z) + 26(a-z) + 10(0-9) + 1 ( _ ) = 63 variable names
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expand (x-4)^5 using the binomial theorem and pascal’s triangle show all necesssry steps
The binomial expansion of the [tex](x-4)^5[/tex] is [tex]x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
According to the statement
we have given that a equation and we have to expand it by use of the binomial theorem.
So, For this purpose we know that the
A binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form.
And the general formula is
[tex](x+y)^n= ^nC_0x^ny^0+^nC_1x^(n-1)y^1+^nC_2x^(n-2)y^2+...+^nC_nx^0y^n[/tex]
And we have to solve it with the given equation (x-4)^5.
Then
[tex](x-4)^5=x^5+20x^4+(20)/(2)x^3(4^2)+(60)/(6)x^2(4)^3+(120)/(24)x^1(4)^4+(120)/(120)x^0(4)^5[/tex]
Now after solving the equation become
[tex](x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
So, The after expanding the given statement with the binomial theorem the result output is
[tex](x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
So, The binomial expansion of the [tex](x-4)^5[/tex] is [tex]x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
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Find the value of x. (5x-40) (5x)
the first equation is inside the triangle at the bottom left but "5x" is at the bottom right on the outside of the triangle.
The value of x is 22
How to solve for x?Based on the description in the question,
The angles 5x -40 and 5x are angles on a straight line
So, we have:
5x - 40 + 5x = 180
Evaluate the like terms
10x = 220
Divide by 10
x = 22
Hence, the value of x is 22
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In a stock of 12 blouses, 90 are sleeveless. How many percent of the stock are sleeveless?
75 percent of the stock are sleeveless
How to determine the percentage?The given parameters are:
Blouse = 120
Sleeveless = 90
The percentage is calculated as:
Percentage = Sleeveless/Blouse * 100%
So, we have:
Percentage = 90/120* 100%
Evaluate the expression
Percentage = 75%
Hence, 75 percent of the stock are sleeveless
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the ammount of time between interest payments is know as
The amount of time between interest payments is know as period.
What is period?Period is the time between when interests are paid. Period can vary depending on the terms of the investment. Periods can be yearly, quarterly, semi-annually, biweekly or weekly.
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Multiply.
x²+3x+2
x 2x²+3x-1
OA. 2x¹ +9x² + 12x² + 3x-2
OB. 2x¹ +9x2 - 2
OC. 3x2 + 6x +1
OD. 2x¹ +21x² + 3x-2
The multiplication of the expression (x² + 3x + 2) (2x² + 3x + 1) is 2x⁴ + 9x³ + 14x² + 9x + 2
Multiplication(x² + 3x + 2) (2x² + 3x + 1)
= 2x⁴ + 3x³ + x² + 6x³ + 9x² + 3x + 4x² + 6x + 2
collect like terms= 2x⁴ + 3x³ + 6x³ + x² + 9x² + 4x² + 3x + 6x + 2
= 2x⁴ + 9x³ + 14x² + 9x + 2
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A and B are independent events. P(A) = 0.60 and P(B) = 0.30.
What is P(A and B)?
A. 0
B. 0.18
C. 0.90
D. 0.018
Answer: 0.18
Step-by-step explanation:
The probability of the event P(A and B) is equal to 0.18.
The correct option is (C).
What is Probability?A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Probability has been introduced in Arithmetic to forecast how likely occurrences are to happen.
As per the given data:
We are given the probability of two events:
P(A) = 0.60 and P(B) = 0.30
We are also given that A and B are independent events.
To find the probability of P(A and B):
The term and is equivalent to the term intersection.
P(A and B) = P(A∩B)
For any 2 independent events A and B the probability P(A∩B) is given by:
= P(A) × P(B)
By substituting the given values in the question
= 0.60 × 0.30
= 0.18
The probability of the event P(A and B) is equal to 0.18.
Hence, The probability of the event P(A and B) is equal to 0.18.
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: A native wolf species has been reintroduced into a national forest. Originally 210 wolves were transplanted. After 10 years, the population had grown to 410 wolves. If the population grows exponentially, write an explicit formula for the number of wolves, where w is the number of wolves and t is the number of years.
The explicit formula that can be used to determine the number of wolves is w = 210 (1.0692^t) .
What is the explicit formula?The first step is to determine the growth rate of the wolf species.
Growth rate = [(future population / present population)^(1/number of years)] - 1
[(410 / 210)^(1/10)] - 1 = 6.92
The exponential function would have the form:
FV = P (1 + r)^t
FV = Future population P = Present populationR = rate of growtht = number of yearsw = 210 (1.0692^t)
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Simplify the ratio 0.40 to 0.60
The ratio 0.40 to 0/60 is equivalent to a simplified ratio..?
(Simplify your answer. Type a whole number or fraction)
The simplified firm of the ratio 0.40 to 0.60 is 2 : 3
Ratio0.40 : 0.60
= 0.40 / 0.60
divide both numerator and denominator by 0.20
= 2 / 3
= 2 : 3
Therefore, the simplified form of the ratio 0.40 to 0.60 is 2 : 3
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To find the driver's initial speed
The speed of the driver is 200km/hr.
How to calculate the speed?The information is incomplete and an overview will be given since the complete information wasn't found online.
It should be noted that speed is calculated as:
= Distance / Time
Let distance = 2000km
Let time = 10 hours.
Speed = Distance/Time
Speed = 2000/10
Speed = 200km/hr
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Which of the following are equations for the line shown below? Check all that
apply.
(-4,3)
(4,-5)
A. y=-x-1
B. y+ 5=-(x-4)
C. y-3 = -(x+4)
D. y=-x-9
Answer: A, B, C
Step-by-step explanation:
[tex]m=\frac{-5-3}{4-(-4)}=-1[/tex]
Substituting into point-slope form, we get [tex]y-3=-(x+4)[/tex] and [tex]y+5=-(x-4)[/tex]. Rearranging this into slope-intercept form,
[tex]y-3=-(x+4)\\\\y-3=-x-4\\\\y=-x+1[/tex]
FRAME AN EQUATION AND SOLVE IT .NEED ASAP
3 is added to a number and the result is multiplied by 4 to get 20.
Answer:
[tex]\fbox {Required equation : 4(x + 3) = 20}[/tex]
[tex]\fbox {Result : x = 2}[/tex]
Step-by-step explanation:
Let our number be x.
1) 3 is added to this number.
x + 32) It is multiplied by 4.
4(x + 3)3) It is equated to 20.
4(x + 3) = 20∴ This is our framed equation.
Steps to solve :
1) Divide by 4 on both sides.
1/4 x 4(x + 3) = 20/4x + 3 = 52) Subtract 3 on both sides.
x + 3 - 3 = 5 - 2x = 2∴ The number is 2.
A line is parallel to the line y = x and passes
through the parabola y = x² - 3 at
(4, 13). What is the other point at which the two
functions intersect?
Answer:
Step-by-step explanation:
hello here is an solution
A sweater is selling for ½ off the original
price. Which number is equivalent to
A 0.23
B 33.3%
C 6.6
D 66.6%
Answer:
Step-by-step explanation:
it would be D
Using the following table, construct and interpret a 90% confidence interval for the population standard deviation of the carbon in metric tons.
Nation
Brazil
Germany
Mexico
Emissions
Canada
361
844
398
Great Britain 577
631
The 90 percent confidence interval for the data is given as 396.02, 727.98
First we have to find the meanThe formula is fx/n
= Mean, μ = 562.2
sum up the data and divide by 5
sd =
Σ(xi - μ)2/N
= (361 - 562.2)² + ... + (631 - 562.2)²/5
= 151806.8/5
= 30361.36
sd = √30361.36
= 174.24511470914
1 - confidence level
= 1 - 0.90
= 0.1
df = 4
Using excel
T.INV.2T(0.1, 4) = ±2.13
562 +- 2.13 x 174.245/√5
562- 165.98, 562+ 165.98
= 396.02, 727.98
Hence the confidence interval can be calculated to be 396.02, 727.98
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The base of a triangle is twelve more than twice its height. If the area of the triangle is 43 square centimeters, find its base and height.
Answer:
B=37
H=66
Step-by-step explanation:
Use algebra and find the answer.
I need to find the area for this shape I’ve tried several different ways and still no answer please help
Answer:
c) 212 sq ft
Step-by-step explanation:
I don't know which ways you tried, but I will show you three different ways, and the answer will be the same using all three ways.
1) The length of the upper horizontal side is 8 ft + 12 ft = 20 ft
Think of a rectangle 20 ft by 16 ft with a rectangle 12 ft by 9 ft missing at the lower right corner.
area = 20 ft × 16 ft - 12 ft × 9 ft
area = 320 ft² - 108 ft²
area = 212 ft²
2) Break up the shape into an upper horizontal rectangle 20 ft long by (16 ft - 9 ft) = 7 ft wide and a lower left rectangle 9 ft high and 8 ft wide.
area = 20 ft × 7 ft + 9 ft × 8 ft
area = 140 ft² + 72 ft²
area = 212 ft²
3) Break up the shape into an left vertical rectangle 16 ft high by 8 ft wide and an upper right rectangle 7 ft high and 12 ft wide.
area = 16 ft × 8 ft + 7 ft × 12 ft
area = 128 ft² + 84 ft²
area = 212 ft²
Answer: c) 212 sq ft
Answer:
Step-by-step explanation:
espero ter ajudado
Question 15 of 15
Convert 1,056 yards into miles. Round your answer to the nearest tenth.
Hint. There are 1,760 yards in a mile.
A. 150 miles
O B. 1.6 miles
O C. 0.6 miles
SUBMIT
Answer:
0.6
Step-by-step explanation:
Given what we know, we can set up a proportion to convert 1,056 yards into miles
[tex]\frac{1760 yd}{1mi} =\frac{1056 yd}{x mi} \\\\1760x=1056\\\\x=0.6[/tex]
A trapezoid has an area given by A =1-2(b1-b2)h,where b1,is the length of one base, b2 is the length of the other
base, and h is the height. If the trapezoid has an area of 14 square units, solve for b in terms of the other variables.
The value of [tex]b_{1}[/tex] is 69/4h and value of [tex]b_{2}[/tex] is 43/4h if the area of trapezoid is 14 square units.
Given that area is equal to 1-2([tex]b_{1} -b_{2}[/tex])h and area is 14 square units.
We know that area of trapezoid is equal to (a+b)h/2.
We have to put the given equation equal to 14 to get our first equation.
14=1-2([tex]b_{1} -b_{2}[/tex])h
14=1-2[tex]b_{1}[/tex]h+2[tex]b_{2}[/tex]h
2[tex]b_{1}[/tex]h-2[tex]b_{2}[/tex]h=-13------------1
Now put the value of area in the formula of area of trapezoid.
14=[tex](b_{1} +b_{2})h/2[/tex]
[tex]b_{1}[/tex]h+[tex]b_{2}h[/tex]=28-----------------2
Multiply equation 2 by 2 and then subtract 2 from 1
[tex]2b_{1}h -2b_{2}h -2b_{1}h-2b_{2}h[/tex]=-13-56
-4[tex]b_{2}h[/tex]=-43
[tex]b_{2}[/tex]=43/4h
Put the value of [tex]b_{2}[/tex] in 2 to get the value of [tex]b_{1}[/tex].
[tex]b_{1} h+43/4h*h=28[/tex]
[tex]b_{1}[/tex]=69/4h
Hence The value of [tex]b_{1}[/tex] is 69/4h and value of [tex]b_{2}[/tex] is 51/4h if the area of trapezoid is 14 square units.
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NEED FAST AND CORRECT!! Use the box plots comparing the number of males and number
of females attending the latest superhero movie each day for a
month to answer the questions.
Males
10
H
Females
20
30
Part A: Describe the shape of each plot
Part B: What is the best measure of center for Males? Females?
How do you know?
Part C: What is the best measure of spread for Males? Females?
How do you know?
Part D: Provide a possible reason for the outlier in the data set. Table
The description of the box plots are as follows:
The Interquartile Range is given as 23; and the difference between the median values is 14What is the calculation for the above?IQR = 25 - 2
= 23
The difference between the median values
= 20 - 6
= 14
What are the respective best measure of center for males? females?The mean would be a better measure of center for Females because the data has no outliers.The median would be a better measure of center for Males because the data has outliers.What is the reason for the outlier in the data set?That female admires those movie stars and has a large group of pals with whom she goes out on a regular basis to keep them company.
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If f(x) = 4x, which statements are true of g(x)? Select two options.
The two statements that are true for g(x ) are:
g(x) = [tex]4^{x}[/tex] - 1
g(x) is translated both vertically and horizontally.
What is a function?A function is a relation showing the relationship between two or more variables.
A function produces a unique output when a unique input is given to it. The input is called the domain and the output is called the Range.
Analysis:
If we use the values of x as 0,1,2,3
for x = 0
g(0) = [tex]4^{0}[/tex] -1 = 1 -1 = 0
for x = 1
g(1) = [tex]4^{1}[/tex] -1 = 4 - 1 = 3
for x = 2
g(2) = [tex]4^{2}[/tex] - 1 = 16 - 1 = 15
for x = 3
g(3) = [tex]4^{3}[/tex] - 1 = 64 - 1 = 63
Therefore g(x) = [tex]4^{x}[/tex] - 1
Also since the values of g(x) changes along the y - axis and x-axis also changes, therefore, g(x) is translated along both axes.
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An ice chest contains 9 cans of apple juice6 cans of grape juice5 cans of orange juiceand 4 cans of pineapple juice Suppose that you reach the container and randomly select three cans in successionFind the probability of selecting no grape juice Select one 243 506 6 17/45; c * 5/506; d * 102/253
Answer:
243/506
Step-by-step explanation:
There are 24 total juice boxes.
18 of them are not grape
You have an 18/24 chance of picking not grape juice
The second time, 1 is removed, then another is removed. This creates:
(18/24)*(18/23)*(18/22) = 243/506
what is the least common denominator of 1/2 5/6
Answer:
Multiples of 4:4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, …
Multiples of 6:6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …
Answer: The least common denominator of 1/4 and 1/6 is 12.
Prime factorisations of 8= 2 × 2 × 2.
Prime factorisations of 12= 2 × 2 × 3.
More items...
Hi! ⋇
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To find the least common denominator of [tex]\sf{\frac{1}{2}}[/tex] and [tex]\sf{\frac{5}{6}}[/tex], we should first find the least common multiple of 2 and 6, which is 6:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16... ∞
Multiples of 6: 6, 12, 18, 24... ∞
(all common multiples are in bold-face; all multiples of 6 are in bold-face because all multiples of 6 are also multiples of 2)
· In both sets, 6 is the least common multiple, and it's also the least common denominator.
Hope this made sense to you !!
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WILL GIVE BRAINLIEST
given: RTSU is a rectangle with vertices R (0,0), S (0, a), T(a,a) and U, (a,0) where a ≠ 0
Prove: RTSU is a square
look at image
The missing parts of the proof are: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
What is a Square?A square is a special type of rectangle whose consecutive sides are congruent. All four sides of a square are congruent.
In the proof given, the distance formula [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] was used to find ST = a units in step 2.
By the definition of congruence, RS = ST in step 4.
Finally, RSTU is stated to be a square because if two consecutive sides of a rectangle are congruent, then it is a square.
The option that completes the proof in the right order is: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
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Answer:
distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it’s a square
Step-by-step explanation:
so its c for me
I need help to this it would be awesome if you could help.
In the given diagram, the value of JI is 6
Solving equations
From the question, we are to determine JI
From the given diagram, we can write that
JI + IH = x + 22
Also,
JI = 2x + 28
and
IH = 5
Then, we can write that
2x + 28 + 5 = x + 22
Collect like terms
2x - x = 22 -28 -5
x = -11
Now, substitute the value of x into the equation
JI = 2x + 28
JI = 2(-11) + 28
JI = -22 +28
JI = 6
Hence, the value of JI is 6
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