Step-by-step explanation:
Right away i notice the 45° angle and the 90° angle in triangle RTQ, this means that the remaining angle must be 180-(90+45)=45°.
If it isn't obvious yet, triangle RTQ is a right isosceles triangle where RT=RQ=x.
Now looking at my other triangle RST
I know that RT=x, RS=2√3 and ST is unknown.
So i cannot apply my Pythagorean theorm.
HOWEVER i do notice 60 degree angle and the 90 degree angle, which means that the last angle must be 180-(90+60)=30° and this triangle (RST) must be a half equilateral triangle;,
Now i can use the relation which describes the relation between the hypotenuse(x) and the side opposite or facing the 60° angle (RS=2√3).
RS=x√3/2
2RS=x√3
2×2√3=x√3
4√3=x√3
4√3/√3=x
x=4 :P
A bicycle helmet cost $41.40 in 1983. what will a bicycle helmet cost when the cpi is 186? round to the nearest cent. a. $222.58 b. $144.60 c. $77.00 d. $72.30
Answer:
77.00
Step-by-step explanation: just round and subtract
The price of the bicycle helmet cost at the time when CPI is 186 is given by: Option C; $77
What is consumer price index?The consumer price index is the new cost of market basket in terms of percentage of old cost of market basket.
[tex]CPI_t[/tex] = consumer price index in current period[tex]C_t[/tex] = cost of market basket in current period[tex]C_0[/tex] = cost of market basket in base periodThen, we have:
[tex]CPI_t = \dfrac{C_t}{C_0} \times 100[/tex]
For this case, we're given that:
[tex]CPI_t[/tex] = 186[tex]C_t[/tex] = To find[tex]C_0[/tex] = $41.40Thus, we get:
[tex]186 = \dfrac{C_t}{41.4} \times 100\\\\C_t = \dfrac{186 \times 41.4}{100} \approx \$77[/tex]
Thus, the price of the bicycle helmet cost at the time when CPI is 186 is given by: Option C; $77
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Please Help! What is the measure of the reference angle that corresponds to an angle of measure 278°
Answer:
82 degrees
Step-by-step explanation:
Reference Angle: the acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive.
82 DEGREES
Find the area of the triangle. Enter your answer in the box. 27 mm 12 mm 14 mm sq mm
Answer:
84 cm^2
Step-by-step explanation:
The area of a triangle is calculated using the following formula:
1/2 * b*h (b: base, h: height)
1/2 * 14 * 12 = 84 the area is indicated with cm^2 so the answer is 84 cm^2
PLEASE HELP
Which is the graph of f(x) = 1/4 (4)x?
No links
Answer:
3rd
Step-by-step explanation:
Answer: graph 3
Step-by-step explanation:
The lengths of the diagonals of a rhombus are 24cm and 18 cm respectively. What is the perimeter/
keeping in mind that in a rhombus all sides are equal, Check the picture below.
The perimeter of the rhombus is 60 cm if the lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively.
What is a rhombus?A rhombus is a two-dimensional shape with four straight, equal sides and parallels opposite pairs.
This form is similar to a diamond and is what you'd expect to see on a deck of cards to symbolize the diamond suit. Rhombuses can be found in a variety of settings in everyday life.
We have:
The length of the diagonals of the rhombus is 24 cm and 18 cm
As we know in the rhombus the diagonals intersect at the right angle so it makes a right-angle triangle.
So half of the right-angle 24 cm will be perpendicular to the right-angle triangle and half of the 18 cm will be the base of the right-angle triangle.
a = 24/2 = 12 cm
b = 18/2 = 9 cm
From the Pythagoras theorem the length of the hypotenuse:
[tex]c = \sqrt{12^2+9^2}[/tex]
c = 15 cm
Now the perimeter will be:
The perimeter of the rhombus = 4(15) = 60 cm
Thus, the perimeter of the rhombus is 60 cm if the lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively.
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A triangle has two sides of length 19 and 18. What is the largest possible whole-number length for the third side?
Answer:
36
Step-by-step explanation:
For the largest possible whole number length, this means it would have to be the longest side. Let's let this third side have a length of x.
By the triangle inequality theorem, 19+18>x, which means x<37.
So, the largest possible whole number length for the third side is 36.
Please help
brainliest for correct answer
x + y = 6
y = 6 - x
substitute the x values to find the value of y
x ║ -2 ║ -1 ║ 0 ║ 1 ║ 2 ║ 3
========================
y ║ 8 ║ 7 ║ 6 ║ 5 ║ 4 ║ 3
Graph:
The area of a circle is 100π ft². What is the circumference, in feet? express your answer in terms of \piπ
Answer:
20π ft
Step-by-step explanation:
To find the circumference of the circle given its area, first find its radius.
[tex]\textcolor{steelblue}{\boxed{\text{Area of circle =}\pi {r}^{2} }}[/tex]
Substitute given area into the formula:
100π= πr²
Divide both sides by π:
100= r²
Square root both sides:
[tex]r = \sqrt{100} [/tex]
r= 10 ft
[tex]\textcolor{steelblue}{\boxed{\text{Circumference of circle = }2\pi {r}}}[/tex]
Since we have found the value of the radius, we can substitute r= 10 into the formula above to find the circumference.
Circumference of circle
= 2(π)(10)
= 20π ft
Help what's the correct question
You have $1000 invested for 3 years and get 10% interest.
Answer:
$1331 compounded annually after three years
Step-by-step explanation:
Given the following question:
1000 dollars invested (princpal)....
You invest that 1000 dollars for three years (time)....
Assuming it's compounded annually we need to substitute the values into the formula to calculate compound interest.
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
[tex]P=1000[/tex]
[tex]\frac{r}{n} =\frac{10}{100} =10\div100=0.1[/tex]
[tex]nt=(1)(3)[/tex]
[tex]A=1000(1+0.1)^{(1)(3)}[/tex]
[tex]1\times3=3[/tex]
[tex]A=1000(1+0.1)^{3}[/tex]
[tex]1+0.1=1.1[/tex]
[tex]1.1^3=1.1\times1.1\times1.1=1.331[/tex]
[tex]A=1000\times1.331[/tex]
[tex]1000\times1.331=1331[/tex]
[tex]=1331[/tex]
Which means after a intital investment of 1000 dollars you will have "1331 dollars" after three years compounded annually.
Hope this helps.
Mia gets 15 out of 18 questions correct on a test. What is the ratio of correct
answers to the total number on the test in simplest form?
Answer:
5/6
Step-by-step explanation:
it's a 15:18 ratio, just needs simplification
A store sells two cone-shaped funnels. What is the height of each funnel? Round your answer to the nearest tenth
(1 pt=28.875 in)
45 in
5 in
Volume 0.5 pint
Volume 1 pint
The height of the smaller funnel is about
inches.
The height of the larger funnel is about
inches.
Considering the volume of a cone, it is found that:
The height of the smaller funnel is about 2.72 inches.The height of the larger funnel is about 3.06 inches.What is the volume of a cone?
The volume of a cone of radius r and height h is given by:
[tex]V = \frac{\pi r^2h}{3}[/tex]
For cone 1, we have that V = 0.5 x 28.875 = 14.4375 in³ and r = 2.25 in(half the diameter), hence:
[tex]\frac{\pi (2.25)^2h}{3} = 14.4375[/tex]
[tex]h = \frac{14.4375 \times 3}{\pi \times (2.25)^2}[/tex]
[tex]h = 2.72[/tex]
For cone 2, we have that V = 28.875 in³ and r = 3 in, hence:
[tex]\frac{\pi (2.25)^2h}{3} = 28.875[/tex]
[tex]h = \frac{28.875 \times 3}{\pi \times (3)^2}[/tex]
[tex]h = 3.06[/tex]
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Dennis biked 8 km and Patrick ran 6,172 m. Who traveled farther and by how much?
Answer:
Dennis : 4.971 miles
Patrick : 3.835 miles
Dennis ran 1.136 miles farther
find two z values so that the middle 65% of the area is bounded by them
Answer: Firstly in this question, we need to solve for
α
which is the part of the distribution of which we not looking for.
we can do this with the sum:
α
=
1
−
0.76
=
0.24
as
0.76
=
76
%
we also know that our Standard Normal Distribution is symmetric, so we must divide that
α
to be split on either side of our distribution. so we solve for:
α
2
=
0.24
2
=
0.12
then we find a correlating
z
-score for the value
0.12
and we get that
−
z
=
−
1.175
and
z
=
1.175
This becomes easier to understand when visualized, so observe how we do this sum.
Step-by-step explanation:
Find the value of x and y
Answer:
x=120
y=60
Step-by-step explanation:
i) y=60 [ corresponding angles]
ii) x + 60 = 180 [linear pair]
or, x = 180- 60
therefore, x is equal to 120
INDEPENDENT or DEPENDENT?
Two marbles are drawn from a container in such a way that the first marble drawn is
replaced before selecting the second marble.
Answer:
what is 2dimes and one nickle and one quarter makes
On Tuesday afternoon at camp, Walter did archery and sailing before dinner. He spent 1 hour at archery and 1 hour and 20 minutes sailing. Sailing ended at 2:30 P.M. when it was time for dinner. What time did archery start?
Answer:
12:10
Step-by-step explanation:
1 hour and 20 minutes sailing- sailing ended at 2:30 pm when it was time for dinner.
For this, you simply have to subtract nd hour and 20 minutes from 2:30:
That is 1:10 pm.
Then, Walter spent an hour doing archery, so you take an hour off- which turns it back to 12:10 pm.
or 10 minutes after noon.
Thus, Archery started at 12:10 pm
Hope this helps, brainliest is always appreciated! :)
Have a nice day! cx
~Mitsuna
F(X)= -x^2 + 10x - 12
Answer:
(0, -22)
Step-by-step explanation:
The y-intercept is the value of y when x is 0,
f(x) = -x² + 10x - 22
f(0) = -(0)² + 10(0) - 22
f(0) = - 22
The y-intercept is -22 at point (0, -22).
-> We can also see this when graphing, please see attached.
Note: If you want me to solve for f(x) = -x² + 10x - 12 as you wrote in text and not f(x) = -x² + 10x - 22 as the picture shows, let me know.
Y=x-12, y=14 what is x I need someone to answer fast please
Answer:
x = 26
Step-by-step explanation:
If Y= x - 12 and Y = 14
Then we input the value of y which gets us the equation of: 14 = x - 12
Now we add 12 on both sides to isolate the variable.
We ADDED 12 because we needed a way to cross out the - 12 on the right side. Now the equation would be 14+12 = x
Easily we can find that 26=x
Answer the question based on the graph
What is the Y-intercept?
What is the asymptote?
number 13 ..........
Answer:
See below
Step-by-step explanation:
Scale it by -4/3 then shift it left by 3
scale by - 4/3 is the same as flipping the function about the x-axis
and scaling it by 4/3
Please help I need to complete this today
GUYS I NEED HELP ASAP IVE BEEN STUCK ON THIS MATH PROBLEM
The cylinder shown has a volume of 695 cubic inches.
What is the radius of the cylinder?
Step-by-step explanation:
[tex]volume = \pi {r}^{2}h[/tex]
[tex]695 = 3.14 \times {r}^{2} \times 11.5[/tex]
[tex] {r}^{2} = 19.2[/tex]
[tex]r = \sqrt{19.2} = 4.3[/tex]
How to find the surface area of a rectangular prism?.
Answer;
A=2(W·l+h·l+h·w)
Step-by-step explanation:
multiply all the numbers by eachother and multiply by 2
· is multiply
For example:
length-12
height-5
width-7
12×5+5×7+7×12=179
179×2=358
In a rhombus, the difference of the measures of the two angles between a side and the diagonals is 32°. What are the measures of the angles of the rhombus?
Answer:
122 and 58
Step-by-step explanation:
A large automobile manufacturing plant produces 1200 new cars every day. a qualitycontrol inspector checks a random sample of 90 cars from one day’s production and finds that 12 of them have minor paint flaws. calculate and interpret a 99% confidence interval for the proportion of all cars produced that day with minor paint flaws.
Using the z-distribution, it is found that the 99% confidence interval is (0.041, 0.2256), and it means that we are 99% sure that the population proportion is in this interval.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The other parameters are given by:
[tex]n = 90, \pi = \frac{12}{90} = 0.1333[/tex]
Then, the bounds of the interval are found as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1333 - 2.575\sqrt{\frac{0.1333(0.8667)}{90}} = 0.041[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1333 + 2.575\sqrt{\frac{0.1333(0.8667)}{90}} = 0.2256[/tex]
The 99% confidence interval is (0.041, 0.2256), and it means that we are 99% sure that the population proportion is in this interval.
More can be learned about the z-distribution at https://brainly.com/question/25890103
What is the volume of this figure?
2520 in³
1638 in³
1323 in³
935 in³
A right rectangular prism with a right triangular prism. The rectangular prism has a length of 14 inches, a width of 9 inches, and a height of 8 inches. The triangular prism shares a face with the rectangular prism. The triangular prism base has a length of 14 inches and a height of 5 inches. The height of the triangular prism is 9 inches.
Answer:
the answer is 1323. i took the quiz on k12 and this was the answer
Step-by-step explanation:
hi
1323
bye (disco lovely_jinni #2028
Evaluate the expression. Write your answer in scientific notation.
6 (6 x 10^-3) + 0.23 – (5 x 10^-2) =
A city has a population of 360,000 people. Suppose that each year the population grows by 3.75% What will the population be after 11 years?
Answer:
508,000 in 11 years
Step-by-step explanation:
3.75% of 360,000 is 13500
So every year the population grows 13500 people
13500 * 11 = 148,500
148,500+360,000=508,000
So in 11 years the population would be 508,000
What is the displacement current between the plates if the separation of the plates is r and they have an area of a?
A displacement current simply means the limited shift of electric components which occur when the voltage is applied to the capacitor.
What is displacement current?Your information is incomplete. Therefore, an overview of the displacement current will be given.
A displacement current simply defines the terms of the rate of change of the electric displacement field.
It's the current due to the changing of the electric field that is inside the plate of the capacitor.
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