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Answer:
1.4
Step-by-step explanation:
We want to find the multiplier n such that ...
arc length = n × radius
n = arc length / radius = (9.8 cm)/(7 cm)
n = 1.4
The subtended arc is 1.4 times as long as the circle's radius.
100 Points + Brainliest Again. They deleted my other for being too easy :P
What is the circumference of a circle with a radius of 20 inches?
Answer:
125.66 inches
Step-by-step explanation:
Step 1: Calculate the circumference
The circumference formula is: C = πd
Another way of saying that is: C = 2πr
C = 2π(20)
C = 40π
C ≈ 125.66 inches
Answer: 125.66 inches
Suppose f(x) = loga(x) and f(7) = 2. Find f(343)
Answer:
6
Step-by-step explanation:
The given function to us is ,
[tex]\rm\implies f(x)= log_a(x) [/tex]
And its value at 7 is 2 , that is ,
[tex]\rm\implies f(x)= log_a(7) =2[/tex]
Taking this ,
[tex]\rm\implies 2= log_a(7) [/tex]
In general we know that ,
[tex]\bf\to log_a b = c ,\ then \ a^c = b [/tex]
Using this , we have ,
[tex]\rm\implies a^2 = 7 [/tex]
Squarerooting both sides ,
[tex]\rm\implies a =\sqrt{ 7 }[/tex]
Therefore , when x is 343 ,
[tex]\rm\implies f(343)= log_{\sqrt7} ( 343) [/tex]
We can write , 343 as 7³ ,
[tex]\rm\implies f(343)= log_{\sqrt7}7^3 [/tex]
[tex]\rm\implies f(343)= log_{7^{\frac{1}{2}}} 7^3 [/tex]
This can be written as ,
[tex]\rm\implies f(343)= \dfrac{ 3}{\frac{1}{2}} [/tex]
[tex]\rm\implies \boxed{\blue{\rm f(343)= 6 }}[/tex]
Hence the required answer is 6.
Math IIIB Performance Task: Piecewise-Defined Functions
Question Set 2
A parking garage charges the following amounts for cars parked in the garage:
For the first hour that a car is parked in the garage, there is no charge.
After the first hour, for the next two hours that a car is parked in the garage, there is a $5 charge.
After the third hour, the garage charges $2 for each additional hour that the car is parked in the garage. If a car is parked in the garage for a fraction of an hour, the garage will charge that fraction of the additional hourly rate.
Use the information provided about the parking garage to answer each of the following questions. Refer to the responses you submitted for Question Set 1 for support.
Sketch a graph to model the total cost of parking in the garage over the domain [0, 12]. (10 points)
Write the piecewise-defined function for the total cost of parking in the garage. That is, state the function C(x), where x is the number of hours a car is parked in the garage. (10 points)
The parking garage plans to change the structure of how much it charges for cars that park in it. A graph of the new total cost is shown below. Describe in detail the new structure. (10 points)
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Explanation:
a) see the attachment for a graph (red curve)
__
b) The piecewise defined function can be ...
[tex]\displaystyle C(x)=\begin{cases}0&0\le x\le 1\\5&1<x\le 3\\2x-1&3<x\le12\end{cases}[/tex]
__
c) The new cost function is ...
[tex]\displaystyle C(x)=\begin{cases}10&0\le x\le5\\x+5&5<x\end{cases}[/tex]
The charge is a flat $10 for any period up to 5 hours, then $1 per additional hour after that, prorated for partial hours. There is apparently no upper limit on parking time as there was with the original function. (The graph shown goes beyond 15 hours; the domain of the original C(x) is 0 to 12 hours.) For reference, the new cost structure is shown in blue in the attachment.
_____
Additional comment
Under the new structure, costs are significantly higher for short-term parking, and lower once the term exceeds 6 hours.
What is the value if x
Answer:
Step-by-step explanation:
work out the value of (4√2)^2
Answer:
32
Step-by-step explanation:
(4[tex]\sqrt{2}[/tex] )²
= 4[tex]\sqrt{2}[/tex] × 4[tex]\sqrt{2}[/tex]
= 4 × 4 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex]
= 16 × 2
= 32
Use the Empirical Rule to answer the questions below:
The distribution of weights for newborn babies is approximately normally distributed with a mean of 7.6 pounds and a standard deviation of 0.7 pounds.
1. What percent of newborn babies weigh more than 8.3 pounds? %
2. The middle 95% of newborn babies weigh between and pounds.
3. What percent of newborn babies weigh less than 6.2 pounds? %
4. Approximately 50% of newborn babies weigh more than pounds.
5. What percent of newborn babies weigh between 6.9 and 9.7 pounds? %
Answer:
1. 16%
2. The middle 95% of newborn babies weigh between 6.2 and 9 pounds.
3. 2.5%
4. Approximately 50% of newborn babies weigh more than 7.6 pounds.
5. 83.85%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 7.6 pounds, standard deviation of 0.7 pounds
1. What percent of newborn babies weigh more than 8.3 pounds?
7.6 + 0.7 = 8.3.
So more than 1 standard deviation above the mean.
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
Of those above the mean, 100 - 68 = 32% are more than one standard deviation above the mean. So
[tex]0.32*0.5 = 0.16[/tex]
16% of newborn babies weigh more than 8.3 pounds.
2. The middle 95% of newborn babies weigh between and pounds.
Within 2 standard deviations of the mean, so:
7.6 - 2*0.7 = 6.2 pounds
7.6 + 2*0.7 = 9 pounds.
The middle 95% of newborn babies weigh between 6.2 and 9 pounds.
3. What percent of newborn babies weigh less than 6.2 pounds?
More than 2 standard deviations below the mean, which is 5% of the 50% below the mean, so:
[tex]p = 0.05*0.5 = 0.025[/tex]
2.5% of newborn babies weigh less than 6.2 pounds.
4. Approximately 50% of newborn babies weigh more than pounds.
Due to the symmetry of the normal distribution, the mean, so 7.6 pounds.
Approximately 50% of newborn babies weigh more than 7.6 pounds.
5. What percent of newborn babies weigh between 6.9 and 9.7 pounds?
6.9 = 7.6 - 0.7
9.7 = 7.6 + 3*0.7
Within 1 standard deviation below the mean(68% of the 50% below) and 3 standard deviations above the mean(99.7% of the 50% above). So
[tex]p = 0.68*0.5 + 0.997*0.5 = 0.8385[/tex]
83.85% of newborn babies weigh between 6.9 and 9.7 pounds.
The measures of the exterior angles of a convex pentagon can be represented as follows: angle 1=X, angle 2= 2x+9, angle 3=3x+4, angle 4=4x+11, angle 5=5x+18
Find the measure of each angle
Mr. Olaffsen opened a sandwich shop and a smoothie stand in his neighborhood.
The following table and equation show function f, representing Mr. Olaffsen's profit, in dollars, x months since opening the sandwich shop.
x 1 2 3 4 5 6 7
f(x) 12,000 15,500 18,000 19,500 20,000 19,500 18,000
The following table and equation show function g, representing Mr. Olaffsen's profit, in dollars, x months since opening the smoothie stand.
x 1 2 3 4 5 6 7
g(x) 9,300 12,000 14,100 15,600 16,500 16,800 16,500
Select the true statement.
A.
The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,200.
B.
The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,500.
C.
The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,000.
D.
The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $2,700.
Answer: the difference between the max is 3,200.
Step-by-step explanation:
20,000-16,800= 3,200
Answer:
the difference between the max is 3,200.
Step-by-step explanation:
20,000-16,800= 3,200
f(x+h)-f(x)
Find the difference quotient
h
where h# 0, for the function below.
f(x) = 4x? -
-8
Simplify your answer as much as possible.
f(x + h) - f(x)
:
h
Х
Okay
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Answer:
8x +4h
Step-by-step explanation:
[tex]\dfrac{f(x+h)-f(x)}{h}=\dfrac{(4(x+h)^2-8)-(4x^2-8)}{h}\\\\=\dfrac{(4x^2 +8xh+4h^2)-(4x^2-8)}{h}=\dfrac{8xh+4h^2}{h}\\\\=\boxed{8x+4h}[/tex]
I need help solving 10gallons = miles
Answer:
50?
Step-by-step explanation:
Because its 50 miles per gallon, so gallon time 50 will be the miles? I'm not sure but i think it is
Draw the image of the rotation of quadrilateral SORT by 270° about the origin.
I need visual help, not a number answer please :)
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Answer:
see attached
Step-by-step explanation:
A rotation 270° CCW is the same as a rotation 90° CW. To see what the figure looks like in its new location, make a copy on a semi-transparent medium, then align the +x axis on the copy with the -y axis on the original graph, keeping the origin in the same place.*
Algebraically, the transformation is ...
(x, y) ⇒ (y, -x)
For example, ...
S(7, -6) ⇒ S'(-6, -7)
In the attachment, the rotated figure is in red.
_____
* The exercise of physically doing this on paper or with transparencies can give you the insight you need to learn to do it mentally.
⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆
THAT IS THE RIGHT ANSWER
Shelley sells 5 bone shaped treats for $3.50. How much should she charge for a package of 12 treats?
Which proportion is needed to solve the problem?
what are the solutions to the quadratic equation (5y + 6)² = 24
Answer:
no solution
Step-by-step explanation:
25y² +36 = 24
(5y + 6) (5y + 6)
roots -6/5, -6/5
solution is always a positive root
Pls help me? I’m struggling
Answer: Number 1 is 150
Step-by-step explanation: If you put 72 / 48% in your calculator, you will get your answer.
Please help me…………….
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Answer:
54.8 km
Step-by-step explanation:
The sketch and the applicable trig laws cannot be completed until we understand what the question is.
Given:
two boats travel for 3 hours at constant speeds of 22 and 29 km/h from a common point, their straight-line paths separated by an angle of 39°
Find:
the distance between the boats after 3 hours, to the nearest 10th km
Solution:
A diagram of the scenario is attached. The number next to each line is the distance it represents in km.
The distance (c) from B1 to B2 can be found using the law of cosines. We can use the formula ...
c² = a² +b² -2ab·cos(C)
where 'a' and 'b' are the distances from the dock to boat 1 and boat 2, respectively, and C is the angle between their paths as measured at the dock.
The distance of each boat from the dock is its speed in km/h multiplied by the travel time, 3 h.
c² = 66² +87² -2·66·87·cos(39°) ≈ 3000.2558
c ≈ √3000.2558 ≈ 54.77
The boats are about 54.8 km apart after 3 hours.
Fine the area and circumference of each circle and round to the nearest tenth.
Answer: A=πr²
A=3.14(1.6inch)² r=d/2⇒3.2/2⇒1.6
A=3.14×2.56in²
A=8.0384in²
A≈8.04
now circumference,
C=2πr
C=2×3.14×1.6in
C=10.048in
C≈10.05
Find the missing length indicated
Answer:
x = 15
Step-by-step explanation:
There are 43 students in the orchestra and twice that number in the band. There are 31 boys and 10 girls in the choir. If each student only participates in one group, how many students total are there in the orchestra, the band, and the choir?
Answer:
170 students total
Step-by-step explanation:
43x2=86
86+43+31+10=170
If m ∥ n and n ⊥ p, then _____
Answer:
If m is parallel to n and n is perpendicular to p, then m is perpendicular to p.
Step-by-step explanation:
If you draw m parallel to n and then you run a line p through n such that n and p are perpendicular. The line p will also cross over m since lines go on forever and it will be perpendicular to m as well.
What is the solution to -41-2x + 6 = -24?
O x = 0
O x = 0 or x = -6
0 x = 0 or x = 6
Ono solution
Hello!
-41 - 2x + 6 = -24 <=>
<=> -35 - 2x = -24 <=>
<=> -2x = -24 + 35 <=>
<=> -2x = 11 <=>
<=> x = -11/2 or -5.5
Good luck! :)
The solution of the equation is only one solution.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have,
-41 - 2x + 6 = -24
Now, solving for x we get
-41 + 6 -2x = -24
-35 - 2x = -24
-2x = -24 + 35
-2x = 11
x = -11/2
x= -5.5
As, the equation of linear and have x= -5.5.
Thus, the equation have only one solution.
Learn more about Equation here:
https://brainly.com/question/29538993
#SPJ7
prove ||a+b|| ≤ ||a||+|b||
Step-by-step explanation:
|a+b|=✓(a²+b²)
|a|+|b|=a+b
||a+b|| ≤ ||a||+|b||
Which equation does the graph represent?
A. x^2 + y^2 = 4
B. x^2/3^2 + y^2/4^2 = 1
C. (X - 1)^2 / 3^2 + y^2/4^2 = 1
D.X^2 / 4^2 + (y + 1)^2 / 3^2 = 1
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Answer:
B. x^2/3^2 + y^2/4^2 = 1
Step-by-step explanation:
The graph looks like a circle, but is not. It is a unit circle scaled by a factor of 3 in the x-direction and a factor of 4 in the y-direction. Thus, its equation is ...
(x/3)^2 +(y/4)^2 = 1
x^2/3^2 +y^2/4^2 = 1
A driveway is in the shape of a rectangle 20 feet wide by 25 feet long.
(a)
Find the perimeter in feet.
(b)
Find the area in square feet.
50 POINTS
Use the function f(x) to answer the questions.
f(x) = −16x2 + 22x + 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
work and answers below
Answer:
[tex]\text{Part A.}\\(-\frac{1}{8},0),\\(\frac{3}{2},0)\\\\\text{Part B.}\\(\frac{11}{16},\frac{169}{16})\\\\\text{Part C.}[/tex]
Draw a parabola concave down with vertex at [tex](\frac{11}{16},\frac{169}{16})[/tex]. Since the leading coefficient of the equation is -16, the parabola should appear thinner than its parent function [tex]y=x^2[/tex]. Ensure that the parabola passes through the points [tex](\(-\frac{1}{8},0)[/tex] and [tex](\frac{3}{2},0)[/tex].
Step-by-step explanation:
Part A:
The x-intercepts of a function occur at [tex]y=0[/tex]. Therefore, let [tex]y=0[/tex] and solve for all values of [tex]x[/tex]:
[tex]0=-16x^2+22x+3[/tex]
The quadratic formula states that the real and nonreal solutions to a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].
In [tex]-16x^2+22x+3[/tex], assign:
[tex]a\implies -16[/tex] [tex]b\implies 22[/tex] [tex]c\implies 3[/tex]Therefore, the solutions to this quadratic are:
[tex]x=\frac{-22\pm\sqrt{22^2-4(-16)(3)}}{2(-16)},\\x=\frac{-22\pm 26}{-32},\\\begin{cases}x=\frac{-22+26}{-32}=\frac{4}{-32}=\boxed{-\frac{1}{8}},\\x=\frac{-22-26}{-32}=\frac{-48}{-32}=\boxed{\frac{3}{2}}\end{cases}[/tex]
The x-intercepts are then [tex]\boxed{(-\frac{1}{8},0)}[/tex] and [tex]\boxed{(\frac{3}{2},0)}[/tex].
Part B:
The a-term is negative and therefore the parabola is concave down. Thus, the vertex will be the maximum of the graph. The x-coordinate of the vertex of a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b}{2a}[/tex]. Using the same variables we assigned earlier, we get:
[tex]x=\frac{-22}{2(-16)}=\frac{-22}{-32}=\frac{11}{16}[/tex]
Substitute this into the equation of the parabola to get the y-value:
[tex]f(11/16)=-16(11/16)^2+22(11/16)+3,\\f(11/16)=\frac{169}{16}[/tex]
Therefore, the vertex of the parabola is located at [tex]\boxed{(\frac{11}{16},\frac{169}{16})}[/tex]
The price of a car was decreased from $13,000 to $11,830. The price is decreased by what percentage?
Answer:
It is decreased by 9%
Step-by-step explanation:
First, find out how much money is decreased. To do this, subtract 13,000-11,830=1170. Finally, figure out how much percent 1170 is of the original price of $13,000.
The answer is 7%.
Hope this helps :)
help pls!!!!!
What is the inequality for this verbal description?
The value of y is greater than or equal to the sum of five times the value of x
and negative three.
Answer:
y ≥ 5x+ (-3)
Step-by-step explanation:
greater than or equal to ≥
The sum means add
y ≥ 5x+ (-3)
Answer:
Option D, y ≥ 5x + (-3)
Step-by-step explanation:
Step 1: Make an expression
The value of y is greater than or equal to the sum of five times the value of x and negative three.
The value of y is greater than or equal to ← y ≥
The sum of five times the value of x and negative three ← 5x + (-3)
y ≥ 5x + (-3)
Answer: Option D, y ≥ 5x + (-3)
ESSE
Combine these radicals.
27-3
O √24
O 23
O-23
0 -3/2
here's the answer to your question
What is the area if measurements are 6m x 5.2m
Answer:
33.00 355.2
5.0m x 6.7m 33.50 360.6
5.0m x 6.8m 34.00 366.0
5.0m x 6.9m 34.50 371.4
5.1m x 6.0m 30.60 329.4
5.1m x 6.1m 31.11 334.9
5.1m x 6.2m 31.62 340.4
5.1m x 6.3m 32.13 345.8
5.1m x 6.4m 32.64 351.3
5.1m x 6.5m 33.15 356.8
5.1m x 6.6m 33.66 362.3
5.1m x 6.7m 34.17 367.8
5.1m x 6.8m 34.68 373.3
5.1m x 6.9m 35.19 378.8
Which statement can be proved true using the given theorem?
Answer:
BF = 16
Step-by-step explanation:
18/12 = 1.5 * 6 = 9
Since DE and BF are parallel and DB and EF are parallel, they comprise a parallelogram. This means that DB = EF
DB = EF = 9
24/1.5 = 16
DE = 16
BF = 16
The statement which can be proven true using the given theorem (congruence) is Segment BF = 16.
Congruence theoremBy the congruence theorem;
We can conclude that triangles ABC and EFC are congruent triangles and as such have the ratio of corresponding sides to be equal.Hence, AE/EC = BF/FC.
Therefore; 12/18 = BF/24
Hence, BF = 24× 12/18
BF = 16Read more on congruent triangles;
https://brainly.com/question/1675117
What is the y-intercept of the line y+11= -2(x+5)?
Answer:
y-intercept is (0, -21)
Step-by-step explanation:
For y-intercept, x = 0:
[tex]{ \sf{y + 11 = - 2(0 + 5)}} \\ { \sf{y + 11 = - 10}} \\ { \sf{y = - 21}}[/tex]
