Answer:36 females in the classroom
y
4
Solve for y.
Then, find the side lengths of the
largest triangle.
Fill in the green blank.
8
X
2
+
2
8
y
y
[?]
X
Enter
Help
Skip
Answer:
y = 4\(\sqrt{5}\) , ? = 10
Step-by-step explanation:
using Pythagoras' identity on the smallest right triangle
x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )
x = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)
using Pythagoras' identity on the middle right triangle
y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )
y = \(\sqrt{80}\) = \(\sqrt{16(5)}\) = \(\sqrt{16}\) × \(\sqrt{5}\) = 4\(\sqrt{5}\)
using Pythagoras' identity on the largest right triangle
?² = x² + y² = (2\(\sqrt{5}\) )² + (4\(\sqrt{5}\) )² = 20 + 80 = 100
Take square root of both sides
? = \(\sqrt{100}\) = 10
Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)
$300/week for 9 1/2
years at 5.5%/year compounded weekly
Answer: $227,226.51
Step-by-step explanation:
First, we need to convert the period to weeks.
9 1/2 years = 9.5 years
1 year = 52 weeks
9.5 years = 494 weeks
Next, we can use the formula for the future value of an annuity:
FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)
where:
PMT = payment amount per period
r = annual interest rate
n = number of compounding periods per year
t = number of years
Plugging in the given values:
PMT = $300
r = 0.055 (5.5% expressed as a decimal)
n = 52 (compounded weekly)
t = 9.5 years = 494 weeks
FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)
FV = $227,226.51
Therefore, the future value of the annuity is approximately $227,226.51.
Complete this table so it shows a relation 7 3 4 8 3
In order to be a function, each input must have only one output value,
If an input value has 2 output values, it's not a function.
So, we can repeat any input number to make it not a function.
For example:
4
Now input 4 hast 2 output values , 8 and 9. therefore is not a function
In the year 2012, 12\%12%12, percent of the residents of the US moved to a different residence. Suppose that several census workers took random samples of n=150n=150n, equals, 150 residents from the population and computed the proportion \hat p
p
^
p, with, hat, on top of residents in each sample who had moved in 2012.
What would be the shape of the sampling distribution of \hat p
p
^
p, with, hat, on top?
Answer: approximately normal (c) trust me-khan academy
Step-by-step explanation:
The accompanying figure shows the velocity v= ds/dt=f(t) (m/sec) of a body moving along a coordinate line.
a. When does the body reverse direction?
b. When is it moving at a constant speed?
c. Graph the body's speed for 0≤t≤10.
d. Graph the acceleration, where defined.
The values on the graph of the velocity of the body, indicates that we get;
a. t = 2 seconds and t = 7 seconds
b. 3 ≤ t ≤ 6
c. Please find attached the speed of the body in the interval 0 ≤ t ≤ 10 created with MS Excel
b. Please find attached the acceleration of the body in the interval 0 ≤ t ≤ 10
What is velocity?Velocity is the rate of change of the position of an object with respect to a specified reference frame and time.
The figure is a velocity time graph, and the velocity of an object is the rate of change of the displacement with time, such that when graph is above the horizontal axis, the velocity is positive, and when the velocity is below the horizontal axis, the velocity is negative, therefore, we get;
a. When the velocity of the changes sign, the direction of the body reverses. The points at which the velocity changes sign, which are the x-intercepts are at t = 2, and t = 7
b. The speed is constant when the velocity remains the same, which are locations on the graph, where the graph is an horizontal line. Therefore, the interval at which the body is moving at a constant velocity is; 3 ≤ t ≤≤6
c. The speed of a body is its absolute velocity, which can be found from the graph by taking the absolute value of the velocity at each point on the graph as follows;
The points on the resulting graph will therefore be; (0, 0), (1, 4), (3, 4), (6, 4), (8, 4) and (10, 0).
Please find attached the speed of the body in the interval 0 ≤ t ≤ 10
d. The acceleration is the rate of change of the velocity of the body with time. The acceleration of the body which has a velocity graph consisting of straight lines is a piecewise constant graph, such that we get;
From t = 0 to t = 1, a = (4 - 0)/(1 - 0) = 4
From t = 1 to t = 3, a = (4 - (-4))/(1 - 3) = -4
From t = 3 to t = 6 , a = (-4 - (-4))/(6 - 3) = 0
From t = 6 to t = 8, a = (4 - (-4))/(8 - 6) = 4
From t = 6 to t = 10, a = (0 - 4)/(10 - 8) = -2
Please find attached the graph of the acceleration of the body, created with MS Excel
Learn more on velocity here: https://brainly.com/question/30046122
#SPJ1
Kate is refilling her hummingbird feeder with
sugar water. She needs 4 times as much water
as sugar. This can be modeled with the
following equation.
W = 45
Solve the equation for the amount of
sugar, S.
Enter the variable that belongs in the green box.
S =
?]
=
Answer:
S = W/4
Step-by-step explanation:
To solve the equation for S, divide by its coefficient.
W = 4S
W/4 = (4S)/4 . . . . . . . . . . divide both sides by 4
W/4 = S(4/4) = S(1) = S . . . simplify
S = W/4
A railroad tunnel is shaped like a semiellipse, as shown below. The height of the tunnel at the center is 35 ft, and the vertical clearance must be 21 ft at a point 8 ft from the center. Find an equation for the ellipse
Answer: x^2 / (8 - 2sqrt(190))^2 + y^2 / 1225 = 1
Step-by-step explanation:
To find the equation of the semiellipse, we need to determine the horizontal and vertical radii of the ellipse. We know that the center of the ellipse is at the origin, so we can use the standard form of the equation for a horizontal ellipse:
x^2/a^2 + y^2/b^2 = 1
where a is the horizontal radius and b is the vertical radius.
From the problem statement, we know that the height of the tunnel at the center is 35 ft, so the vertical radius is b = 35 ft. We also know that the vertical clearance must be 21 ft at a point 8 ft from the center, which means that the distance from the center to this point is 8 ft plus the horizontal radius. Using the Pythagorean theorem, we can write:
(8 + a)^2 + 21^2 = 35^2
Expanding and simplifying, we get:
64 + 16a + a^2 + 441 = 1225
a^2 + 16a - 720 = 0
We can solve this quadratic equation using the quadratic formula:
a = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 16, and c = -720. Plugging in these values, we get:
a = (-16 ± sqrt(16^2 - 4(1)(-720))) / 2(1)
a = (-16 ± sqrt(16^2 + 4(1)(720))) / 2
a = (-16 ± sqrt(3040)) / 2
We can simplify this expression by factoring out 4 from the radical:
a = (-16 ± 4sqrt(190)) / 2
a = -8 ± 2sqrt(190)
Since a is the horizontal radius of the ellipse, we take the positive value:
a = -8 + 2sqrt(190)
Therefore, the equation of the semiellipse is:
x^2 / (8 - 2sqrt(190))^2 + y^2 / 35^2 = 1
Simplifying the expression under the square root:
x^2 / (8 - 2sqrt(190))^2 + y^2 / 1225 = 1
This is the equation of the semiellipse.
Need help with number 3 please
Answer:
I believe the answer is 7 for the rate of change
Step-by-step explanation:
What is the common difference in the arithmetic sequence 1,1.25,1.5,1.75,… ?
Answer:
0.25.
Step-by-step explanation:
To find the common difference, you need to find the number that each value increases by.
1.75 - 1.5 = 0.25.
1.5 - 1.25 = 0.25.
1.25 - 1 = 0.25.
All values apparently increase by 0.25. So, that is your common difference.
Hope this helps!
Answer:
0.25
Step-by-step explanation:
The common difference is the value added to the first term to get the second term, then added to the second to get the third and so on.
To find the common difference, subtract the first term from the second. Then check by subtracting the second term from the third.
The sequence is: 1,1.25,1.5,1.75
second term - first term
1.25- 1= 0.25
third term- second term
1.5 -1.25= 0.25
The common difference in the arithmetic sequence is 0.25
Explain how each pair of division and multiplication equations are the same, and how they are different.
Answer:
they differ when they are in different sign's but Will be same if the division sign change and the forward number will be reciprocal so it will be the same
(2 x 6) x 4 = 48 = 2 x (6 x 4) shows the ______ property? Associative
Answer:
Associative
Step-by-step explanation:
The associate property for multiplication states that \(a\times(b\times c)=(a\times b)\times c\), thus, \((2\times 6)\times 4 = 2\times (6\times 4)\). The way factors are grouped does not change the product, essentially.
Review the image below. Based on the image, what type of transformation is
this? Be specific and detailed and explain how/why you know. Use details, correct
vocabulary and coordinates to justify your reasoning. Your answer should be in
paragraph form using complete sentences.
Answer:
When you read a sentence, you may first look for the subject or what the sentence is about. The subject usually appears at the beginning of a sentence as a noun or a pronoun. A noun is a word that identifies a person, place, thing, or idea. A pronoun is a word that replaces a noun. Common pronouns are I, he, she, it, you, they, and we. In the following sentences, the subject is underlined once.
Step-by-step explanation:
You will often read a sentence that has more than one noun or pronoun in it. You may encounter a group of words that includes a preposition with a noun or a pronoun. Prepositions connect a noun, pronoun, or verb to another word that describes or modifies that noun, pronoun, or verb. Common prepositions include in, on, under, near, by, with, and about. A group of words that begin with a preposition is called a prepositional phrase. A prepositional phrase begins with a preposition and modifies or describes a word. It cannot act as the subject of a sentence. The following circled phrases are examples of prepositional phrases.
Answer:
this is a rotation. you can tell because point Z is (-5,2) and Z' is (2,5)
Point X was (-5,7) and X' is (7,5) and Point Y was (-2, 2) and Y' is (2,2).
by looking at the picture it was rotated 90 degrees counterclockwise
Step-by-step explanation:
2x+3>23
Solve the inequality.
Answer:
\( \boxed{\tt\orange{x > 10 }}\)
Step-by-step explanation:
Let's solve the inequality step-by-step.
2x+3>23
Step 1: Subtract 3 from both sides.
2x+3−3>23−3
2x>20
Step 2: Divide both sides by 2.
\( \bf \bold {\frac{2x}{2} } > \frac{20}{2} \)
Result:
\( \boxed{\tt \: x > 10 }\)
Fred is standing at a point looking north. He walks on a bearing 056° for 9.8km before stopping. He then walks an additional 3.5 km on a bearing of 112° before stopping to rest. (a) Find out how far he is away from his start point using sine or cosine rule (b) Determine the area of the enclosed shape (c) Draw neat labeled scale diagram of the same
The area of the enclosed shape is about 14.47 km^2.
We are given that;
056° for 9.8km and 3.5 km on a bearing of 112°
Now,
We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:
y = 180° - 56° - 112°
y = 12°
Now we can use the cosine rule to find z:
z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)
z^2 ≈ 101.87
z ≈ 10.09
Therefore, Fred is about 10.09 km away from his start point.
To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:
sin(56°) = x/9.8
x = 9.8 sin(56°)
x ≈ 8.27
The area of a triangle is given by half the base times the height, so:
A = (1/2)(3.5)(8.27)
A ≈ 14.47
Therefore, by trigonometric ratios the answer will be 14.47 km^2.
Learn more about trigonometric;
https://brainly.com/question/21286835
#SPJ1
Find the value of × in each of the following
a)5+1=11
b) 2x-3=2
Step-by-step explanation:
a,it doesn't have variable
b,2x-3=2
2x=2+3
2x=5
2x/2=5/2
x=5/2
What value of b makes this equation true? -2b + 3 = b - 9
-2b + 3 = b - 9
To Find:The value of b.
Solution:-2b - b = -9 - 3
or, -3b = -12
or, b = -12/-3
or, b = 4
Answer:The value of b is 4.
Answer:
b=4
Explanation:
1. Add 2b to each side: 3=3b-9
2. Add 9 to each side: 12=3b
3. Divide by 3: b=4
Evaluate the definite integral of sin^5(x)dx from 0 to pi/2.
Step-by-step explanation:
The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.
Let u = sin(x), then du = cos(x)dx
The integral becomes:
∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)
= (u^6)/6 evaluated at sin(π/2) and 0
= (sin^6(π/2))/6 - 0
= (1^6)/6
= 1/6
So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.
3x³ = -16x² - 21x
Solve for x
Answer:
x=0, x=-7/3, x=-3
Step-by-step explanation:
Use the order of operations to simplify 3 + 8(2.5 – 0.5).
O A. 163
O B. 201
O c. 4
D. 2
Answer:
A. 16 3/4
Step-by-step explanation:
it just is
Select the correct answer.
Julia is planning to sell her old car to buy a new one. When she bought her car five years ago, she paid $35,000. If the value of her car
depreciated at the rate of 15 percent per year, which graph models the given situation?
y
40,000
30,000
36,000
34,000
32,000
$0,000
30,000
126,000
000
Graph A
Cost (Dollars)
+22,000
+350,000
40,000
16,000
4,000
12,000
-10,000
te,pop
6,000
+4,000-
+2,000
tum. All rights reserved.
Graph B
Graph C
The graph that models the exponential function \(A(t) = 35000(0.85)^t\) is given at the end of the question.
What is an exponential function?A decaying exponential function is modeled by:
\(A(t) = A(0)(1 - r)^t\)
In which:
A(0) is the initial value.r is the decay rate, as a decimal.The initial value and the growth rate are given, respectively, by:
A(0) = 35000, r = 0.15.
Hence the equation is given by:
\(A(t) = 35000(0.85)^t\)
The graph is given at the end of the question.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
Answer: graph A
at the end of 5 years the cars worth 15,373.2
Step-by-step explanation:
Plato/Edmentum
The sum of deviations of n observations about 25 is 25 and the sum of deviations of the same n observations about 35 is −25. The mean of observations.
Answer:
30Step-by-step explanation:
please refer to the attachment above
The point P=(1/2,y)lies on the unit circle shown below. What is the value of y in simplest form?
The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.
To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.
Plugging in the coordinates of the point P = (1/2, y), we get:
(1/2)^2 + y^2 = 1
1/4 + y^2 = 1
y^2 = 1 - 1/4
y^2 = 3/4.
To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).
Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.
for more search question point
https://brainly.com/question/28162977
#SPJ8
3.
Name the image
Line
Line segment
Ray angle
Answer:
ray
Step-by-step explanation:
Construct one table that includes relative frequencies based on the frequency distributions shown below, then compare the amounts of tar in nonfiltered and filtered cigarettes. Do the cigarette filters appear to be effective? (Hint: The filters reduce the amount of tar ingested by the smoker.)
Based on the relative frequency table that compares nonfiltered and filtered cigarettes, we can infer that cigarette filters are effective because they reduce larger tar amounts.
How can the relative frequency table be drawn?Tar (mg) Relative Frequency Relative Frequency
(nonfiltered) (filtered)
6 - 11 0/ 25 = 0% 1 / 25 = 4%
12 - 17 0/ 25 = 0% 1 / 25 = 4%
18 - 23 2/ 25 = 8% 5 / 25 = 20%
24 - 29 1/ 25 = 4% 18 / 25 = 72%
30 - 35 13/ 25 = 52% 0 / 25 = 0%
36 - 41 6/ 25 = 24% 0 / 25 = 0%
42 - 47 3 / 25 = 12% 0 / 25 = 0%
Total 25 / 25 = 100% 25 / 25 = 100%
From the table, we can see that the unfiltered cigarette has higher tar amounts which means that cigarette filters are effective in reducing tar content.
Find out more on relative frequency at https://brainly.com/question/1094036.
#SPJ1
The Heflin household is laying down mulch around their garden. The following image depicts the shape and dimension of their garden and the area they want to place the mulch:
A triangular garden inside a rectangular mulch area. The garden has a base of 6 feet and a height of 5 feet, and the mulch area has a height of 9 feet and a base of 12 feet.
If the mulch costs $0.59 per square foot, determine the total cost.
Answer:
$54.87
Step-by-step explanation:
The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.
The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.
The total area to be covered with mulch is 108 - 15 = 93 square feet.
The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.
Therefore, the total cost of the mulch will be $54.87.
I am lost please help thank you all
Answer:
Step-by-step explanation:
At least 9 means more than 9 and includes 9
x ≥ 9 and [9, +∞)
At most 9 means numbers less than 9
x≤9 and (-∞, 9]
more than 9 means bigger than 9 but not including 9
x > 9 and (9, +∞)
fewer than 9 means less than 9 but not including 9
x<9 and (-∞, 9)
strictly between 7 and 9 means between 7 and 9 but not including
7<x<9 and (7,9) (This is the only one I'm unsure of. Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)
between 7 and 7 inclusive. means it's just =7 There's no boundaries
x=7
no more than 7 means less than 7 and includes 7
x ≤ 7 and (-∞, 7]
Please look at the photo. Thank you.
The output value of (f∘g)(x) is: \((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)
The domain of (f∘g)(x) is (-∞, -3) U (-3, ∞).
How to determine the corresponding output value for this function?In this scenario, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations (multiplication) in simplified form as follows;
\(f(x) = \frac{x-6}{x +3}\)
g(x) = 4x - 15
Next, we would write the numerators and denominators in factored form as follows;
(x - 6)(4x - 15)
4x² - 15x - 24x + 60
4x² - 29x + 60
Now, we can derive the corresponding composite function of f(x) and g(x);
\((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)
For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;
x + 3 ≠ 0
x ≠ -3
Domain = (-∞, -3) U (-3, ∞).
Read more on domain here: brainly.com/question/17440903
#SPJ1
determine the base funciton f(x)=2(4)^x+5 NEED ASAP
The base of the function given 2(4)ˣ+5 is 4ˣ
What is the base of a function?The base of an exponential function. If f(x) = ax, then we call a the base of the exponential function. The base must always be positive. Base 1. If f(x) is an exponential function whose base equals 1 – that is if f(x)=1x.
Given is a function, 2(4)ˣ+5, we need to find the base of the function,
With the multiplication of 4ˣ with 2, the rate at which f(x) changes is 2 times larger. Now it is added by 5, by adding 5 the value of f(x) is always 5 greater than the value of f(x).
This reverses the value of y for each corresponding value of x and increases the rate at which f(x) changes 8 times that of the original function.
Hence, the base of the function given 2(4)ˣ+5 is 4ˣ
Learn more about base of a function, click;
https://brainly.com/question/2456547
#SPJ1
what is 7,548,392 rounded to 100
Answer:
7,548,400
Step-by-step explanation:
Find the value of y
pls let me know how u solve this
Answer:
X° = 45°
Y = 8√2
Step-by-step explanation:
Angle of this triangle 45°:45°:90° so ratio of the triangle = 1:1:√2
8:8:8√2
I hope you understand it and sorry if it is wrong