Answer:
a = -2/5 = -0.400
Step-by-step explanation:
Janine walks on a circular track whose radius is 60 meters. If she walks a total of 100 meters, which of the following represents the radian angle she rotates about the center of the track?
(1) 5/3
(2) 3/5
(3) 5π/3
(4) 3π/5
Answer: OPTION 1
Step-by-step explanation:
For this exercise you need to remember that, by definition, the Arc length can be calculated with the following formula:
[tex]arc\ length=rC[/tex]
where "C" is the central angle of the arc in radians and "r" is the radius.
Since you need to find the Central angle, you have to solve for "C" from that formula, as following:
[tex]C=\frac{arc\ length}{r}[/tex]
According to the information given in the exercise, you can identify that:
[tex]arc\ length=100\ m\\\\r=60\ m[/tex]
Therefore, the final step is to substitute these values into the formula and evaluate, in order to find the value of "C":
[tex]C=\frac{100\ m}{60\ m} \\\\C=\frac{5}{3}\ rad[/tex]
The volume of a cylinder is 180 cubic meters. The height of the cylinder is 11.25 meters. What is the radius of the cylinder?
Answer:
2.26 meters
Step-by-step explanation:
so the volume for a cylinder is
v= π r² x h
now just substitute in the numbers you know:
180= π r² x 11.25
now rearrange the formula:
180= r² x 11.25π
(rearranging allows you to do this next bit with ease)
now divide by 11.25π on both sides to get
[tex]\frac{180}{11.25\pi }[/tex]= r²
to maintain accuracy, don't divide yet
now you know what r² is but you want r, so square root it:
[tex]\sqrt{\frac{180}{11.25\pi } }[/tex]=r
type that into a calculator and i think the answer is ...
2.25675833419
write the long answer in case you make a mistake when rounding
round appropriately : 2.26 meters ( I've done it to 2 decimal places)
and hopefully that's the correct answer.
) Yoona gives guitar lessons for $70 per session. She gives a 10% discount to students who
come to her studio for the lesson.
The question is about calculating the price of guitar lessons after a 10% discount and the answer explains the steps to calculate the discounted price.
Explanation:The subject of this question is Mathematics and the grade level is High School.
To calculate the amount after the discount, subtract 10% of $70 from $70. 10% of $70 is $7, so the discounted price is $70 - $7 = $63.
Therefore, Yoona gives a 10% discount to students which means the price per session is $63.
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In rhombus ABCD, m∠XCB = 6a − 2 and m∠XBC = 4a + 12. What is the measure of ∠XCB?
Answer: Angle XCB = 46 degrees ( ∠XCB = 46°)
Step-by-step explanation: Please refer to the picture attached for details.
A rhombus basically is a parallelogram with a diamond shape. All four sides have equal length, opposite sides are parallel and opposite angles are equal.
The sides have been labelled ABCD as stated in the question, and the point X is extended to point B to form angle XBC and also extended to point C to form angle XCB. Upon careful observation we shall notice that a triangle has been formed with sides BXC and angle X is a right angle, which measures 90 degrees.
The sum of angles in a triangle equals 180, therefore,
Angle XBC + Angle XCB + Angle X = 180
Substituting for the given values we now have the following;
4a + 12 + 6a - 2 + 90 = 180
10a + 10 + 90 = 180
10a + 100 = 180
Subtract 100 from both sides of the equation
10a = 80
Divide both sides of the equation 10
a = 8
If XCB = 6a - 2,
Substitute for the value of a
XCB = 6(8) - 2
XCB = 48 - 2
XCB = 46
Therefore angle XCB measures 46 degrees.
Randomization in an experiment reduces bias between the treatment and control groups.
Answer:
True
Step-by-step explanation:
Answer: true
Step-by-step explanation:
A P E X
Evaluate the piecewise function for ƒ(4).
A) −7
B) 9
C) 16
D) 24
f(4)= 16.
The answer is **C) 16**.
Here's how to evaluate the piecewise function f(4):
1. **Identify the appropriate rule:**
- Since 4 is greater than 2 (4 > 2), we'll use the second rule of the function: f(x) = 5x - 4.
2. **Substitute x = 4:**
- f(4) = 5(4) - 4
3. **Simplify:**
- f(4) = 20 - 4 = 16
Therefore, f(4) = 16.
The other options are incorrect because they either use the wrong rule (A and D) or miscalculate the result (B).
The number whose 25% in 25 is?
Answer:
100 is the answer
Answer:
25/100= 150/x
1/4=150/x
x=150×4=600
600 is the number whose 25% is 150.
Step-by-step explanation:
Ariana just started a running plan where she runs 8 miles the first week and then
increases the number of miles she runs by 5% each week. If she keeps up this plan for
9 weeks, how many total miles would Ariana have run, to the nearest whole number?
Answer:
88
Step-by-step explanation:
simplify 12^3 over 12^7
Answer:
12^3/12^7= 1/12^(7-3)= 1/12^4
Step-by-step explanation:
The solution to the problem '12 to the power of 3 over 12 to the power of 7' is 12 to the power of negative 4 or written as a fraction, it is 1 over 12 to the power of 4 or 1 over 20736.
Explanation:The expression 123 over 127 refers to the mathematical concept of 'division of exponentials with the same base'. The rule in this case is to subtract the exponents. Therefore, 123 over 127 simplifies to 12-4. This can be understood as 1 over 124, or further simplified, 1 over 20736 if you multiply out the exponent.
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The ages of the members of four teams are summarized below. Answer the questions about them.
Team A: The mean age is 52 and the range of ages is 27.
Team B: The mean age is 49 and the range of ages is 28.
Team C: The mean age is 48 and the range of ages is 31.
Team D: The mean age is 54 and the range of ages is 33.
(a) Based on the information above, which team has the youngest members on average?
Team A
Team B
Team C
Team D
(b) Based on the information above, which team's ages have the least variability?
Team A
Team B
Team C
Team D
The answer the statement a and statement b is
a) the answer is team C
b)we can conclude that the answer is team A.
We have given that,
The ages of the members of the four teams are summarized below. Answer the questions about them.
Team A: The mean age is 52 and the range of ages is 27.
Team B: The mean age is 49 and the range of ages is 28.
Team C: The mean age is 48 and the range of ages is 31.
Team D: The mean age is 54 and the range of ages is 33.
We have to determine the a and b
a) The information above, which team has the youngest members on average
from the above observations we can conclude that the answer is team C.
What is the least variability?
A related measure of variability is called the semi-interquartile range. The semi-interquartile range is defined simply as the interquartile range divided by 2.
b) The information above, which team's ages have the least variability
from the above observations, we can conclude that the answer is team A.
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Find the length of the unknown side. Round your answer to the nearest whole number.
7 in
10 in
25 in
50 in
PLEASE HELP AND HURRY, IF ITS WRITE I WILL MARK YOU BRAINLIEST!!!
Answer: 7
Step-by-step explanation:
Pythagorean Theorem:
[tex]a^{2}+b^{2} =c^{2}[/tex]
[tex]5^{2} + 5^{2} = 50^{2}[/tex]
[tex]\sqrt{50} = 7.07[/tex]
7.07 rounds to 7
Answer:
7 in
Step-by-step explanation:
2 formula of Area of square
1/2 * c * c = 5 * 5
1/2 * c^2 = 25
c^2 = 25*2
c^2 = 50
c = square root 50
nearest to 7 in
The circumference of a 8in circle
Answer:
In pie: 16pie Regular: 50.24
Step-by-step explanation:
pie times 2 times radius
Solve for p
p/8=7/9
P=?
Answer:
56/9
Step-by-step explanation:
What is the x intercept of the graph of 3x-7y=24
The monthly energy use, in kilowatt hours, for two neighbors is shown in the box plots below.
A box plot titled Neighbor 1. The number line goes from 800 to 1400. The whiskers range from 825 to 1350, and the box ranges from 900 to 1025. A line divides the box at 950.
Neighbor 1
A box plot titled Neighbor 2. The number line goes from 800 to 1400. The whiskers range from 925 to 1400, and the box ranges from 950 to 1050. A line divides the box at 1025.
Neighbor 2
Which statements accurately compare the two data sets? Select three options.
Neighbor 1 tends to use fewer kilowatt hours each month.
The median value for Neighbor 2 is 75 kilowatt hours greater than the median value for Neighbor 1.
Neighbor 1 had greater variability in the number of kilowatt hours used per month.
Neighbor 2 had greater variability in the number of kilowatt hours used per month.
The median value for Neighbor 2 is 50 kilowatt hours greater than the median value for Neighbor 1.
Answer:
A B C
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Which of these numbers is in the solution set of x – 12 = 4? A. 3 B. 16 C. –8 D. 8
Answer:
x=16
so B
Step-by-step explanation:
Answer:
B. 16
Step-by-step explanation:
x-12=4
+12 +12
x=16
Oil prices are projected to increase by 100% by next june. A quart of oil currently costs $2.45. What is the projected cost of a gallon of oil next june?
Answer:
The projected cost of a gallon of oil by next june is $19.60.
Step-by-step explanation:
Given:
Oil prices are projected to increase by 100% by next june.
A quart of oil currently costs $2.45.
Now, to find the cost of a gallon of oil next june.
So, to get the projected cost of a quart of oil by next june:
Cost of one quart of oil currently = $2.45.
Rate of oil prices projected to increase by = 100%.
[tex]100\%\ of\ \$2.45+\$2.45\\\\=\frac{100}{100}\times 2.45+2.45\\\\=2.45+2.45\\\\=\$4.90.[/tex]
Now, to get the projected cost of a gallon of oil by next june we use conversion factor:
4 quart = 1 gallon.
If, 1 quart oil price = $4.90.
Then, 4 quarts oil price = [tex]\$4.90\times 4[/tex] = [tex]\$19.60.[/tex]
Thus, 1 gallon oil price = $19.60.
Therefore, the projected cost of a gallon of oil by next june is $19.60.
Answer:
19.60
Step-by-step explanation:
The area of a rectangular fountain is x2 + 9x + 20 square feet. A 3-foot walkway is built around the fountain. Find the dimensions of the outside border of the walkway. The dimensions of the outside border of the walkway are
Answer:
(x+11) by (x+10)
Step-by-step explanation:
We know that Area = Length x width
Given: Area = x²+9x+20
Lets sort this out first
Area = x²+5x + 4x + 20
Area = x(x+5) + 4(x+5)
Area = (x+5) (x+4)
Therefore, it is concluded that:
Length 'l' = (x+5) feet
Width 'w' = (x+4) feet
if a 3-foot walkway is built around the fountain, we'll add 3 feet on both sides
Therefore,
Outer Length = (x+5+3+3) = (x+11) feet
Outer Width = (x+4+3+3) = (x+10) feet
Answer:
The fountain is (x+5) by (x+4).
dimensions of the outside border of the walkway are (x+11) by (x+10)
A cruise ship can cover 21 nautical miles in 483 minutes. How many nautical miles will it travel in 161 minutes?
A. 7
B. 5
C. 9
D. 11
Answer:
A. 7
Step-by-step explanation:
483 ÷ 21 = 23. that means 1 nautical miles happens every 23 minutes. 7 × 23 = 161.
Answer:7
Step-by-step explanation:483 divided by 3 is 161 and 21 divided by 3 is 7
Akikta bought 25 trees for $15.40 each. Chloe bought 35 trees for $14.30 each. What was the difference between the total amounts that the girls paid for the trees?
Answer: $115.50
Step-by-step explanation:
500.5-385 = x
Answer:
$115.50
Step-by-step explanation:
(x + 3)2 + (x + 3) - 2 = 0
Answer:
x=-7/3
Step-by-step explanation:
2(x+3)+(x+3)-2=0
2x+6+x+3-2=0
3x+7=0
3x=-7
x=-7/3
Answer:
Step-by-step explanation:
Maricel is programming an archery component of a new video game. In her code, she has created an "auto aim" feature that helps players more easily hit their intended targets.
The code works such that if the player is aimed at
A
AA but instead should be aimed at target
T
TT, the game will automatically adjust the angle at which the arrow is fired directly at
T
TT.
If
A
AA and
T
TT are
15
1515 meters apart in the example below, how many degrees will Maricel's code adjust the shot?
Do not round during your calculations. Round your final answer to the nearest degree.
∘
∘
degrees
Archer
Archer
?
?
T
T
A
A
60
m
60 m
50
m
50 m
15
m
15 m
Show Calculator
Answer:
12 degrees
Step-by-step explanation:
[tex]b^2=a^2+t^2-2atCosB\\15^2=50^2+60^2-2(50)(60)Cos B\\Cos B=\frac{15^2-(50^2+60^2)}{-2(50)(60)} \\Cos B=0.9792\\B=arc Cos 0.9792\\B=11.7^0[/tex]
Maricel's code will adjust the shot by 12 degrees to the nearest degree.
If e = 9 cm and f = 40 cm, what is the length of g?
A. 43 cm
B. 39 cm
C. 31 cm
D. 41 cm
(9,40,41) is a Pythagorean Triple, farther down the list than teachers usually venture.
Answer: D. 41 cm
There's a subset of Pythagorean Triples where the long leg is one less than the hypotenuse,
a^2+b^2 = (b+1)^2
a^2 + b^2 = b^2 + 2b +1
a^2=2b+1
So we get one for every odd number, since the square of an odd number is odd and the square of an even number is even.
b = (a^2 - 1)/2
a=3, b=(3^2-1)/2=4, c=b+1=5
a=5, b=(5^2-1)/2 =12, c = 13
a=7, b=24, c=25
a=9, b=40, c=41
a=11, b=60, c=61
a=13, b=84, c=85
It's good to be able to recognize Pythagorean Triples when we see them.
Otherwise we'd have to work the calculator:
√(9² + 40²) = √1681 = 41
What are the length and width of a rectangular
traffic sign if the length exceeds the width by 6
inches and the perimeter is 112inches?
Answer:
width is 25 inches
length is 31 inches
Step-by-step explanation:
We will need the formula for perimeter of a rectangle:
P = 2(l + w)
"l" is length, "w" is width
If the length exceeds the width by 6, then:
l = w + 6 <= Substitute this into the equation
P = 2(l + w)
P = 2(w + 6 + w)
Remember we also know the perimeter is 112:
112 = 2(w + 6 + w)
Collect like terms:
112 = 2(2w + 6)
Start isolating "w" to find width.
56 = 2w + 6 Divided both sides by 2
50 = 2w Subtracted 6 from both sides
25 = w Divided both sides by 2
w = 25 Variable on left for standard formatting
The width is 25 inches.
Find the length using "length exceeds width by 6".
l = w + 6
l = 25 + 6 Substitute the width
l = 31
The length is 31 inches.
∴ The length is 31 inches and the width is 25 inches.
Check your answer with the perimeter formula.
P = 2(l + w)
112 = 2(31 + 25) Substitute all the variables.
112 = 2(56)
112 = 112 Same answer
LS = RS Left side equals right side
The answer is correct.
A coordinate grid with 2 lines. One line, labeled f(x) passing through (negative 4, 3), the point (negative 2, 1) and (0, negative 1). The other line is labeled g(x) and passes through (negative 4, negative 1), the point (negative 2, 1) and (0, 3). Which input value produces the same output value for the two functions on the graph? x = −3 x = −2 x = −1 x = 3
Answer:
b
Step-by-step explanation:
Answer:
The answer is B
Step-by-step explanation:
Question 2
If it takes 8 meters of fabric to make 5 pairs of curtains, how many meters are required to make 22 pairs?
Answer:
35.2m
Step-by-step explanation:
8 meters of fabric make 5 pairs of curtains so divide 8 by 5 to find that it takes 1.6 meters of fabric to make 1 pairs of curtains
multiply 1.6 by 22 to get 35.2 meters of fabric
Directions: Using the image and the scenario provided in the trajectory scenario activity Question #1, determine the trajectory the bullet traveled. Drawings are not to scale. Question #1. A bullet from a sniper struck and killed a controversial political figure who was waiting in a nearby car as a passenger. Crime scene investigators are unsure what floor of the building the shot came from. The first floor of the hotel is 25 ft. high. Each subsequent floor is 15 ft. tall. Entry point on car window above horizontal = 12 in. Distance from car window to victim = 42 in. Distance from building to victim’s car = 350 ft. Using the measurements from the scene, determine what floor of the building the shooter came from. Tips: Convert units to feet, Complete ratio to find the height of the shooter in feet. To determine the floor number from feet: 25 + 15x, The floor number = add one to x. Which means the shooter was on which floor? a 5 b 6 c 7 d 8
Answer: 6 floors
Step-by-step explanation: Given that:
The first floor height = 25ft
Where each subsequent floor is 15 ft. tall.
Entry point on car window above horizontal = 12 in.
Distance from car window to victim = 42 in.
Distance from building to victim’s car = 350 ft.
Using similarity in angle method, we have
(25 + 15x)/350 = 12 in/42 in
Convert inches to feet by dividing the value by 12
(25 + 15x)/350 = 1/3.5
Cross multiply
3.5(25 + 15x) = 350
87.5 + 52.5x = 350
52.5x = 350 - 87.5
52.5x = 262.5
X = 262.5/52.5
X = 5
Therefore,
The floor number = 1 + 5 = 6 floors
To determine the shooter's floor number, we divide the distance from the building to the victim's car by the height of each floor. Using the given measurements, the shooter was on the 6th floor.
Explanation:To determine the floor number from feet, we need to divide the distance from the building to the victim's car by the height of each floor. The height of the first floor is given as 25 ft, and each subsequent floor is 15 ft taller than the previous. We calculate the number of floors using the formula: floor number = (distance from building to car - height of first floor) / height of each subsequent floor. Plugging in the given values, we find that the shooter was on the 6th floor, so the correct answer is option b) 6.
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Four lines are drawn on a coordinate plane to form trapezoid WXYZ.
Which statements are true about the lines? Select three options.
Line WZ has the same slope as line XY.
Line YX has a greater slope than line ZY.
Line XW has a lesser slope than line YZ.
Line ZW has the same y-intercept as line YZ.
Line XY has a lesser y-intercept than line XW.
Answers: Line WZ has the same slope as line XY. Line XW has a lesser slope than line YZ. Line ZW has the same y-intercept as line WZ.
Please help, I’m not too smart
Answer:
x = - 4
Step-by-step explanation:
Given
r(x) = - 5x - 1 and r(x) = 19, then equating the right sides gives
- 5x - 1 = 19 ( add 1 to both sides )
- 5x = 20 ( divide both sides by - 5 )
x = - 4
what is the input for inverse trigonometric functions
Answer:
An inverse trigonometric function is a function in which you can input a number and get/output an angle (usually in radians). It is the inverse function of the basic trigonometric functions.
Step-by-step explanation:
Trigonometric functions are derived from ratios of certain sides of a right triangle in reference to an angle. The graph of which is a wave, with amplitude in the y-axis and angle in the x-axis. We will first define the sine function written as:
sin(θ)=oppositesidehypotenuse
As we can see, the sine function, together with all the other trigonometric functions, relates an angle to the ratio of an opposite side and the hypotenuse of right triangle. The input here is an angle, and the output is a ratio. Therefore, the inverse process to this is actually just a reverse process.
Let
y
=
s
i
n
(
θ
)
y=sin(θ)
Then inverse trigonometric function outputs an angle. However, we can set y to its original value via transitivity:
s
i
n
−
1
(
y
)
=
θ
s
i
n
−
1
(
o
p
p
o
s
i
t
e
s
i
d
e
h
y
p
o
t
e
n
u
s
e
)
=
θ
sin−1(y)=θsin−1(oppositesidehypotenuse)=θ
Thus we see, that the input to an inverse trigonometric function is a unitless ratio of two sides of a representative right triangle.
The input to an inverse trigonometric function is a unitless ratio of two sides of a representative right triangle.
We need to find what is the input for inverse trigonometric functions.
What is the input for an inverse trigonometric function?An inverse trigonometric function is a function in which you can input a number and get/output an angle (usually in radians).
The inverse trigonometric functions do the same thing as the inverse trigonometric relations, but when an inverse function is used, because of its restricted range, it only gives one output per input--whichever angle lies within its range.
Example:
Inverse sine of 1/2 is the angle of 30°
That is, [tex]sin^{-1}(\frac{1}{2} )=30^o[/tex]
As we can see, the sine function, together with all the other trigonometric functions, relates an angle to the ratio of an opposite side and the hypotenuse of the right triangle. The input here is an angle, and the output is a ratio. Therefore, the inverse process to this is actually just a reverse process.
Therefore, the input to an inverse trigonometric function is a unitless ratio of two sides of a representative right triangle.
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