The measure of ∠S is 59.4° for trignometric identities
What are trigonometric identities?
There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
ΔSTU:
s = 50 inches
t = 58 inches
u = 630 inches
Applying the cosines rule on ΔSTU.
s² = t² + u² - 2 x t x u x cos S
cos S = (t² + u² - s²) / 2tu
cos S = (58² + 27² - 50²) / (2 x 58 x 27)
cos S = (3364 + 729 - 2500) / 3132
cos S = 0.5086.
∠S = (0.5086)
∠S = 59.4°
Thus,
∠s angle value is 59.4°.
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Calculate the number of whole years it takes for the population to decrease from 2180 to less than 1000
Answer:
Calculate the number of whole years it takes for the population to decrease from 2180 to less than 1000
Step-by-step explanation:
Let n be the least positive integer for which 149^n-2^n is divisible by 3^3.5^5.7^7.$ Find the number of positive integer divisors of n.
Calculating the LCM of all these, one gets 2^2. 3^2 . 5^4 .7^5. Using the factor counting formula, the answer is 3.3.5.6 = {270}
Step-by-step explanation:
Note that for all n, 149^n-2^n is divisible by 149-2=147 by difference of nth powers. That is 3.7^2, so now we can clearly see that the smallest n to make the expression divisible by 3^3 is just 3^2 Similarly, we can reason that the smallest n to make the expression divisible by 7^7 is just 7^5.
Finally, for 5^5, take (mod {5}) and ( mod {25} )of each quantity (They happen to both be -1 and 2 respectively, so you only need to compute once). One knows from Fermat's theorem that the maximum possible minimum n for divisibility by 5 is 4, and other values are factors of 4. Testing all of them(just 1,2,4 using mods-not too bad), 4 is indeed the smallest value to make the expression divisible by 5, and this clearly is NOT divisible by 25. Therefore, the smallest (n) to make this expression divisible by 5^5 is $2^2 .5^4.
Using the factor counting formula, 2^2. 3^2 . 5^4 .7^5 = 3.3.5.6 = {270}
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Judy tosses a coin four times. Draw a tree diagram showing the possible outcomes. Select the probability of getting at
least 2 tails.
A. 1/4 B. 11/16. C.3/8. D.5/16
Answer:
B. 11/16
Step-by-step explanation:
tossing a coin 4 times, with 2 possible outcomes each time: 2 x 2 x 2 x 2 = 16 total possible outcomes. All but 5 have at least 2 tails.
How much is 1470p in dollars ?
Answer:
$30.66
Step-by-step explanation:
Timmy lift a rock using 245 joules of work over 5 seconds . How much power was required to lift the rock?
Answer: 49Watt
Step-by-step explanation:
The formula for power is:
Power = Work/Time
where,
Work = 245 Joules
Time = 5 seconds
Power = Work / Time
= 245/5
= 49Watt
Therefore, the power required to lift the rock is 49W.
You deposit $1000 in an account that pays 2% annual interest compounded quarterly. How much will you have
after 8 years?
bat
Name
1. Complete each more or less statement.
2
a. 1 more than 66 is
b. 10 more
c. 1 less than 66 is
d. 10 less
e. 56 is 10 more than
f. 88 is 1
determine the number of 8x8x16 concrete masonry units needed to construct a foundation wall 104" high with a 120" perimeter. include 10% for waste
The number of concrete masonry units needed to construct a foundation wall is 102.
What is volume?The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Given, a foundation wall 104" high with a 120" perimeter.
Since, perimeter of square = 4 * side
120 = 4 * side
side = 30"
Hence area of the foundation wall = side²
area of the foundation wall = 30² = 900
volume of the foundation wall = area * height
the volume of the foundation wall = 104 * 900 = 93,600"
The volume of the concrete masonry whose length, width, and depth are 16, 8, and 8 respectively is
Volume of masonry = 8 * 8 * 16
The volume of masonry = 1024
since 10 % of masonry goes to waste.
Thus the effective volume of the masonry = 1024*0.9 = 921.6
total masonry required = 93600/ 921.6 = 101.56
therefore, To build a foundation wall, 102 concrete masonry units are required.
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In the figure shown, what is the value of x?
PLEASE HURRY JUST GIVE ME THE ANSWER THANK YOU
Answer: x= 23
Step-by-step explanation:
Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3. If each leasing center has 24 trucks, which auto leasing company has more cars? Main Street Auto Leasing has more cars since it has cars while Airport Auto Leasing has cars only
If the ratio of cars to truck in Main Street Auto Leasing Company is 9 to 4 and in the airport Auto Leasing Company is 5 to 3 , then the Main Street Auto Leasing Company has more number of cars .
The Ratio of cars to truck in Main Street Auto Leasing Company is = 9:4 ;
the ratio of cars to truck in Airport Auto Leasing Company is = 5:3 ;
the number of trucks in each Leasing Company is = 24 trucks ;
Case (i) : Main Street Auto Leasing Company ;
Since the ratio is = 9:4 ,
So , the number of cars is = 9x and
the number of trucks = 4x ;
That means , [tex]4x = 24[/tex] ;
[tex]x = 6[/tex] ;
the number of cars in Main Street company is = [tex]9 \times 6[/tex] = 54 cars .
Case (ii) : Airport Auto Leasing Company ;
the ratio is = 5:3 ;
So , the number of cars is = 5x and
the number of trucks = 3x ;
That means , [tex]3x = 24[/tex] ;
[tex]x = 8[/tex] ;
the number of cars in Airport Auto company is = [tex]5 \times 8[/tex] = 40 cars .
Therefore , the Main Street Auto Leasing Company has more number of Cars .
The given question is incomplete , the complete question is
Main Street Auto Leasing has a ratio of cars to trucks that is 9 to 4. Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3. If each leasing center has 24 trucks, which auto leasing company has more cars ?
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Josh has $252 in his bank account. This is $12 more than 6 times the amount of money that sally has in her bank account. What equation can be used to represent the relationship between the amounts of money josh and sally have in their bank accounts？
A) 12x+6 = 252
B) 6x+12=252
C) 18x = 252
D) 6x-12=252
Answer:
B
Step-by-step explanation:
12 more tells you that this adds 12 dollars and 6 times tells you that it is 6x so 12+6x=252
What is (-1)⁶?
O A. -i
O B.-1
O C. 1
O D. i
Mike has $21 to spend at the mall. He spends all of his money on bracelets for his sisters. Bracelets cost $3 each. How many bracelets dose he buy?
Answer:
7
Step-by-step explanation:
PLEASE HELP ILL BRAINLIEST YOU
Answer:
x=176.78
y=262.28
z=176.77
Sam is writing a report on cell phone usage. he collects data from a random sample of eight graders in his school, and finds that 18 out of 20 eight graders have cell phones. if there are 310 eight graders in his school,estimate the number of eighth graders who have cell phones.
A palindrome is an integer that reads the same forwards and backwards. How many positive 3-digit palindromes are multiples of $3$
There are total 30 positive 3-digit palindromes are multiples of 3.
The numbers are as follows,
111, 141, 171, 222, 252, 282, 303, 333, 363, 393, 414, 444, 474, 525, 555, 585, 606, 636, 666, 696, 717, 747, 777, 828, 858, 888, 909, 939, 969, 999.
Palindrome numbers
A palindromic number is a number that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis.
A palindrome number is a number that is same after reverse.
For example - 121, 34543, 343, 131, 48984 are the palindrome numbers.
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A guy wire attached to the top of a radio antenna
is bolted to the ground 48 m from the base of
the tower. If the wire makes an angle of 14°
with the ground. What is the length of the
guy wire? Round your answer to the nearest
hundredth of a meter.
1
The length of the guy wire is 48.87 m.
How to find the length?To find the length of the guy wire, you can use the formula for the length of a side of a right triangle (the Pythagorean theorem): [tex]c = sqrt(a^2 + b^2)[/tex]. In this case, c is the length of the guy wire, a is the distance from the base of the tower to the point where the guy wire is attached to the ground (48 m), and b is the distance from the point where the guy wire is attached to the ground to the top of the antenna.
To find b, you can use the tangent function: [tex]tan(14°) = b / 48.[/tex]
Solving for b gives b = 6.78 m
Then, length of wire can be calculated as
[tex]c = sqrt(48^2 + 6.78^2)[/tex]
[tex]c = 48.87 m (approx)[/tex]
Rounding it to the nearest hundredth of a meter, the length of the guy wire is 48.87 m.
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If PQR measures 75°, what is the measure of SQR?
22°
45°
The measure of the angle ∠PQS will be 53°. Then the correct option is C.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.
If angle ∠PQR measures 75°. And angle ∠PQS measures 22°.
Angle ∠SQR and angle ∠PQS are the adjacent angles. Then we have
∠PQS + ∠SQR = ∠PQR
∠PQS + 22° = 75°
∠PQS = 53°
The measure of the angle ∠PQS will be 53°. Then the correct option is C.
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Complete question is attached below.
What if Aya and Sakura could only afford a monthly payment of $1800?
What would be the maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same?
What is the total amount that would be paid to the lender over 25 years?
a) The maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same = $369,181.93.
b) The total amount that would be paid to the lender over 25 years = $540000
To find the maximum mortgage amount they could afford to borrow if they could only pay $1800.
Here, future value = 0
number of periods = 25 years
= 25 × 12 months per year
= 300
payment amount = -1800 dollars
interest rate = 4.25% per year
= 0.3542% per month
the maximum mortgage amount they could afford = $369,181.93.
And the total payments would be equal to 300 × 1800 = 540000
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The complete question is:
Aya and Harumi would like to buy a house and their dream house costs $500,000. They have $50,000 saved up for a down payment but would still need to take out a mortgage loan for the remaining $450,000 and they're not sure whether they could afford the monthly loan payments. The bank has offered them an interest rate of 4.25%, compounded monthly.
What if Aya and Harumi could only afford a monthly payment of $2,000?
What would be the maximum mortgage amount they could afford to borrow from the bank if all the other conditions were the same?
What is the total amount that would be paid to the lender over 25 years?
What is the area of the triangle?
Answer:
9 units^2
Step-by-step explanation:
The area of a triangle is 1/2hxb. 1/2(6)(3)=9.
Answer:
9
Formula for area - 1/2 times base times height
base - 3
height - 6
1/2 times 6 times 3
= 9
What is the area, in square inches, of a rectangle with a length of 21/2 inches and a width of 11/4 inches?
Answer:
28.875
Step-by-step explanation:
If you have a calculator on hand, then this kind of problem will be easy. If you multiply 10.5 by 2.75, then you would get 28.875.
Hope that this helps!
pleaseeeeeee someone help me asappp i need help so bad.
The slope of the linear equation that passes through the points (-6, -2) and (3, -2) is 0.
How to find the slope with the two known points?We can write a linear equation using the sope-intercept form as:
y = m*x + b
Where m is the slope and b is the y-intercept.
For any linear equation, if we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope is given by:
m = (y₂ - y₁)/(x₂ - x₁).
In this case we know that the line passes through the points (-6, -2) and (3, -2).
Then the slope will be:
m = (-2 + 2)/(3 + 6) = 0
m = 0
The slope is zero, meaning that this is an horizontal line.
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The sum of four consecutive multiples of 7 is 406.
Work out the values of these four numbers.
Examples of four consecutive multiples of 7 are: 7, 14, 21, 28
The value of all four numbers will be 91, 98, 105, 112 respectively.
Let the first multiple be 7x
As the multiple of any number can be determined by simply multiplying the given number by the natural number or the counting numbers.
So, the value of the second multiple of 7 will be 7(x+1)
The value of third multiple of 7 will be = 7(x+2)
The value of fourth multiple of 7 will be = 7(x+3)
As all the multiple are consecutive so we have taken the multiplying factor as x, (x+1), (x+2) and (x+3)
From the data given in the question:
Sum = 7x+7x+7+7x+14+7x+21 = 406
=>28x+42=406
=>28x=364
=>x=(364/28)=13
So, the value of first multiple = 7x = (7*13) =91
So, the value of the second multiple of 7 will be 7(13+1)=98
The value of third multiple of 7 will be = 7(x+2)=7(13+2)=105
The value of fourth multiple of 7 will be = 7(x+3)=7(13+3)=112
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What is the area of the figure?
Answer:
151/6
Step-by-step explanation:
How do you get from 4 to 4/3?
4 times what gives us 4/3?
m = the unknown value
4m = four times that unknown value
4m = 4/3
m = (4/3)*(1/4)
m = 4/12
m = 1/3
Therefore, we multiply 4 with 1/3 to end up with 4/3.
Suppose y varies directly with x, and y = 6.5 when x = 1.3. What direct variation equation relates x and y ?
Select one:
a.
y = − 5x
b.
y = x / 5
c.
y = 5x
d.
y = 1.5x
Answer:
c
Step-by-step explanation:
given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 6.5 when x = 1.3
6.5 = 1.3k ( divide both sides by 1.3 )
5 = k
y = 5x ← equation of variation
Question 4
Did you reach the same conclusion in both Question 2 and 3? Based on your work so far, what can you conclude about the measure of a central
angle and an inscribed angle that intercept the same arc on a circle?
Answer: The measure of a central angle is twice as big as the measure of an inscribed angle IF they intercept the same arc on a circle
Step-by-step explanation: See photo. A central angle’s vertex is at the center of the circle. The measure of a central angle is equal to the measure of the included arc. An inscribed angle’s vertex lies on the circle. The measure of an inscribed angle is equal to half the measure of the included arc. Therefore the measure of the central angle is double the measure of the inscribed angle that intercept the same arc on a circle
The measure of a central angle is twice the measure of an inscribed angle, they intercept the same arc on a circle.
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
A central angle’s vertex is at the center of the circle. The measure of a central angle is equal to the measure of the included arc.
An inscribed angle’s vertex lies on the circle. The measure of an inscribed angle is equal to half the measure of the included arc.
Therefore, the measure of the central angle is double the measure of the inscribed angle that intercept the same arc on a circle.
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What is the product of 2 and 2 √80 in simplest radical form?
show work
[tex]2 \times 2 \times 4 \sqrt{5} [/tex]
[tex]16 \sqrt{5} [/tex]
final answer is this
plz mark as brainliest
Answer:
..........
Step-by-step explanation:
What is the radius of a hemisphere with a volume of 5320\text{ in}^3,5320 in 3 , to the nearest tenth of an inch?
Answer:
13.6 in
Step-by-step explanation:
volume of a hemisphere = (2/3) x (n) x (r^3)
n = 22/7
r = radius
5320 = 2/3 x r^3 x 22/7
r^3 = 5320 x 3/2 x 7/22
find the cube root of both sides
r = 13.6
The four-digit numeral $3AA1$ is divisible by $9$. What digit does $A$ represent?
When the four - digit numeral is divisible by nine is given by 3AA1 the digit A represents 7
Properties of numbers divisible by 9A number itself is divisible by 9 if its digit's sum is also divisible by 9.
In mathematics, multiples are the results of multiplying an integer by a given number. number divisible by 9 is multiple of 9
using the above property we have that
3 + A + A + 1 = 9, OR 18, OR 27
4 +2A = 9, OR 18, OR 27
assuming 18
2A = 18 - 4
2A = 14
A = 7
hence the number is 3771
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