To calculate the group admission prices for 5, 11, and 23 members at Wild World, we use the given equation p = 50 + 10n. The resulting prices are $100 for 5 members, $160 for 11 members, and $280 for 23 members.
Explanation:The group admission price at Wild World is determined by the equation p = 50 + 10n, where p is the total price and n is the number of members in the group. To find the prices for groups with 5, 11, and 23 members, we substitute the corresponding values of n into the equation.
For a group of 5 members: p = 50 + 10(5) = 50 + 50 = 100.For a group of 11 members: p = 50 + 10(11) = 50 + 110 = 160.For a group of 23 members: p = 50 + 10(23) = 50 + 230 = 280.The prices for groups with 5, 11, and 23 members are $100, $160, and $280 respectively.
You are a sports reporter interviewing an Olympic swimmer who lost the silver medal by a few hundredths of a
second. Write a one-page interview in which you discuss the meaning of time and the advanced instruments
used to measure time.
Final answer:
Time's accuracy is crucial in sports, and a high school track coach's new stopwatch with an uncertainty of ±0.05 s may not be suitable for distinguishing very close race outcomes, such as those within a few hundredths of a second apart.
Explanation:
Time is a fundamental measurement in athletic competitions, particularly in track and swimming events, where even hundredths of a second can determine the outcome. The precision of time measurements has become increasingly important with the advancement of athletes' abilities, pushing the limits of human performance. In recent history, various advanced instruments have been developed to ensure the accuracy of timing in these competitions.
For instance, a high school track coach who has recently acquired a new stopwatch might find it incredibly useful or not depending on its precision. If the manual states the stopwatch has an uncertainty of ±0.05 s, this could affect the outcome of close races. Given that the top runners on the coach's team regularly clock 100-m sprints with times that may only differ by a few hundredths of a second, this level of uncertainty could be problematic in accurately distinguishing winning times.
Considering a scenario where the first-place sprinter came in at 12.04 s and the second-place sprinter at 12.07 s, the new stopwatch’s uncertainty range may not clearly differentiate between the two, since the difference in their times is within the margin of error of the stopwatch. This is relevant when comparing a sprinter's 100-meter sprint time of 12.04 seconds one week and 11.96 seconds the next week; due to the uncertainty of the stopwatch, we cannot conclusively say that this week's time was faster.faster.
The radius of a circle is 1. What is the length of an arc that subtends an angle of a radians?
Answer:
1 unit
Step-by-step explanation:
We have the following formula to find the length of an arc that subtends an angle of radians is:
S = rΘ where:
r is the radiusΘ is the subtended central angle given in radiansGiven the information in this question, we have:
r = 1 unitΘ = a radian=> the length of an arc in this question is:
1*1 = 1 unit
Hope it will find you well
Final answer:
The length of an arc in a circle with radius 1 that subtends an angle of a radians is a units.
Explanation:
The student's question asks for the length of an arc in a circle with a radius of 1 that subtends an angle of a radians. The formula to calculate the arc length (s) is derived from the fact that the circumference of a circle (S) with radius r is S = 2πr. A full revolution around a circle results in an angular rotation of θ = 2π radians.
The arc length for an angle a radians in a circle with radius r is therefore s = r × a. Since the radius of the circle in this question is 1, the arc length is simply equal to the angle a in radians. Thus, the length of the arc is a units.
Express 900 as a product of its prime factors in index form.
Write the prime factors in ascending order.
Answer:
2^2*4*5^2*9=900
Step-by-step explanation:
900= 100*9
100=20*5
20=5*4
4=2*2
2*2*4*5*5*9=900=
2^2*4*5^2*9=900
Hope this helps!
Answer:
2×2×3×3×5×5
2²×3²×5²
Step-by-step explanation:
Hope this helped (:
What is the product of 36‾√cis(π8) and 25‾√cis(7π6) ?
Answer:
The product of
36√cis(π/8) and 25√cis(7π/6)
is
(225√2)√[√(2 + √2) + i√(2 - √2)][√(3(-1 + i))]
Step-by-step explanation:
First note that
cis(π/8) = cos(π/8) + isin(π/8)
cis(7π/6) = cos(7π/6) + isin(7π/6)
cos(π/8) = (1/2)√(2 + √2)
sin(π/8) = (1/2)√(2 - √2)
36√cis(π/8) = (36/√2)√[√(2 + √2) + i√(2 - √2)]
cos(7π/6) = -(1/2)√3
sin(7π/6) = (1/2)√3
25√cis(7π/6) = (25/2)√3(-1 + i)
The product,
36√cis(π/8) × 25√cis(7π/6)
= (36/√2)√[√(2 + √2) + i√(2 - √2)] × (25/2)√3(-1 + i)
= (225√2)√[√(2 + √2) + i√(2 - √2)][√(3(-1 + i))]
Answer:
32.86 cis ( 4.06 )
Step-by-step explanation:
TTT
sort -3,-2.75,0,1/2,1,2 7/8 from least to greatest using ABSOLUTE VALUE. i do mark people brainliest !
Answer:
0 1/2 7/8 1 2 -2.75 -3
Explanation:
(1. Absolute value is the distance a number is from zero. It can only be positive. For example, the absolute value of -8 is 8 because it is 8 units away from zero. More examples: The absolute value of 5 is 5 because it is 5 units away from zero. The absolute value of -6.75 is 6.75 because it is 6.75 units away from zero.
(2. Because we know this, we can put the order as 0, 1/2, 7/8, 1, 2, -2.75, and -3. -3 is 3 units away from zero which is more than the absolute value of -2.75 which is 2.75 units away from zero.
(3. The absolute value of a number is basically just making the number positive. If the number is already positive then the absolute value of that number is that number.
Hope you understand!
Solve the quadratic equation below by finding square roots. Select all that apply.
Answer:
5
Step-by-step explanation:
That's all I could come up with
The solutions to the quadratic equation [tex]$x^2 = 25$[/tex] are x = 5 and x = -5. Thus, the correct options are 5 and -5.
To solve the quadratic equation [tex]\(x^2 = 25\)[/tex] by finding square roots, we take the square root of both sides.
Taking the square root of 25, we get [tex]\(x = \pm 5\)[/tex].
So, the solutions are [tex]\(x = \pm 5\)[/tex].
Therefore, the correct options are:
5
-5
A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. The standard deviation of the amount in each can is 0.12 ounce. The machine is overhauled with new components, and ten cans are filled to determine whether the standard deviation has changed. Assume the fill amounts to be a random sample from a normal population.
Perform a hypothesis test to determine whether the standard deviation differs from 0.12 ounce. Use the level of significance.
Answer:
[tex]\chi^2 =\frac{10-1}{0.0144} 0.0217 =13.54[/tex]
The degrees of freedom are:
[tex] df=n-1=10-1=9[/tex]
Now we can calculate the p value using the alternative hypothesis:
[tex]p_v =2*P(\chi^2 >13.54)=0.279[/tex]
Since the p value is higher than the signficance level assumed of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that the true deviation differs from 0.12 ounces
Step-by-step explanation:
Assuming the following data:"12.14 12.05 12.27 11.89 12.06
12.14 12.05 12.38 11.92 12.14"
We can calculate the sample deviation with this formula:
[tex]s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
[tex]n=10[/tex] represent the sample size
[tex]\alpha=0.05[/tex] represent the confidence level
[tex]s^2 =0.0217 [/tex] represent the sample variance
[tex]\sigma^2_0 =0.12^2= 0.0144[/tex] represent the value to verify
Null and alternative hypothesis
We want to determine whether the standard deviation differs from 0.12 ounce, so the system of hypothesis would be:
Null Hypothesis: [tex]\sigma^2 = 0.0144[/tex]
Alternative hypothesis: [tex]\sigma^2 \neq 0.0144[/tex]
The statistic can be calculated like this;
[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]
[tex]\chi^2 =\frac{10-1}{0.0144} 0.0217 =13.54[/tex]
The degrees of freedom are:
[tex] df=n-1=10-1=9[/tex]
Now we can calculate the p value using the alternative hypothesis:
[tex]p_v =2*P(\chi^2 >13.54)=0.279[/tex]
Since the p value is higher than the signficance level assumed of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that the true deviation differs from 0.12 ounces
Which is the definition of hyperbola?
A)it is a locus of points that is equidistant from a fixed point called center.
B)It is a locus of points such that the sum of its distance from two fixed points (foci) is constant.
C)It is a locus of points such that its distance from focus plus its distance from a directrix is constant.
D)It is a locus of points such that the difference of each point's distances from two fixed points is constant.
I believe that the answer is (A)
It is a locus of points that is equidistant from a fixed point called the center. Which is the correct answer would be an option (A)
What is the hyperbola?Hyperbola is defined as a conic section, a two-branched open curve, produced by the intersection of a circular cone.
(x-h)²/b² - (y-k)²/a² = 1
This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.
The variable h represents the x-offset from the origin,
and k represents the y-offset from the origin.
Here it is a locus of points that are all equal distance from the center, a constant point.
Therefore, it is a locus of points that is equidistant from a fixed point called the center.
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The number of branches on a tree demonstrates the Fibonacci sequence. How many branches would there be on the next two levels of this tree?
Answer:
In the next two levels the tree we have 8 branches
Step-by-step explanation:
In mathematics, the Fibonacci numbers, commonly denoted Fₙ, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones.
The Fibonacci numbers are given as 1,2, 3,5,8,13........n
The Second level according to the Fibonacci sequence indicates that the tree will have 8 branches
Answer:
21,34
Step-by-step explanation:
The blue dot is at what value on the number line?
Answer:
i would like to say the answer is 17
Step-by-step explanation:
30 is what percent of 180? round your answer to the nearest tenth
Answer:
54
Step-by-step explanation:
this is wrong don't mind it
Answer:
I got 16.7%
Step-by-step explanation:
i will mark brainliesttt!
Answer: 75 degrees
Step-by-step explanation: supplementary means 180 so you do 180-105 which is 75
find the value of each variable in the circle to the right. the dot represents the center of the circle.
We have been given an image of a circle. We are asked to find the value of each variable.
We can see that angle b corresponds to diameter of circle. We know that the measure of an angle that is inscribed to the diameter of a circle is 90 degrees . Therefore, the value of b will be 90.
we can see that angle is an inscribed angle of arc 99 degrees. We know that measure of an inscribed angle is half the measure of inscribed arc.
[tex]a=\frac{1}{2}\cdot 99[/tex]
[tex]a=49.5[/tex]
Therefore, the value of a is 49.5 units.
We know that measure of all angles of a triangle is 180 degrees. The measure of 3rd angle will be half the measure of c, so we can set an equation as:
[tex]a+b+\frac{1}{2}c=180[/tex]
[tex]49.5+90+\frac{1}{2}c=180[/tex]
[tex]139.5+\frac{1}{2}c=180[/tex]
[tex]139.5-139.5+\frac{1}{2}c=180-139.5[/tex]
[tex]\frac{1}{2}c=40.5[/tex]
[tex]\frac{1}{2}c\cdot 2=40.5\cdot 2[/tex]
[tex]c=81[/tex]
Therefore, the value of c is 81.
Find the area of the parallelogram shown below.
Answer:
88
Step-by-step explanation:
a wall in his bedroom and finds that it is 3 meters tall. How many centimeters is this?
Answer:
300 cm
Step-by-step explanation:
1 meter is 100 centimetres, so 3 meters would result in 3 x 100, which equals 300.
solve 5y(y-4)=0 please hurry!
Answer:
y = 4
y = 0
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
5y • (y - 4) = 0
Step 2 :
Theory - Roots of a product :
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
2.2 Solve : 5y = 0
Divide both sides of the equation by 5:
y = 0
Solving a Single Variable Equation :
2.3 Solve : y-4 = 0
Add 4 to both sides of the equation :
y = 4
Hope this helps
Answer:
Your question that I have solved:
y= 0,4
Step-by-step explanation:
Male and female high school students reported how many hours they worked each week in summer jobs. The data is represented in the following box plots:
two box plots shown. The top one is labeled Males. Minimum at 0, Q1 at 1, median at 20, Q3 at 25, maximum at 50. The bottom box plot is labeled Females. Minimum at 0, Q1 at 5, median at 6, Q3 at 10, maximum at 18
Identify any values of data that might affect the statistical measures of spread and center.
The females worked less than the males, and the female median is close to Q1.
There is a high data value that causes the data set to be asymmetrical for the males.
There are significant outliers at the high ends of both the males and the females.
Both graphs have the required quartiles.
Question:
1. The females worked less than the males, and the female median is close to Q1.
2. There is a high data value that causes the data set to be asymmetrical for the males.
3. There are significant outliers at the high ends of both the males and the females.
4. Both graphs have the required quartiles.
Answer:
The correct option is;
1. The females worked less than the males, and the female median is close to Q1
Step-by-step explanation:
Based on the given data, we have;
For males
Minimum = 0
Q1 = 1
Median or Q2 = 20
Q3 = 25
Maximum = 50
For females;
Minimum = 0
Q1 = 5
Median or Q2 = 6
Q3 = 10
Maximum = 18
Therefore, the values of data that affect the statistical measures of spread and center are that
The females worked less than the males as such the statistical data for the females have less variability than the males in terms of interquartile range
Also the female median is very close to Q1, therefore it affects the definition of a measure of center.
Answer:
the answer is the second one
Step-by-step explanation:
I need help! Please answer below on card B
Answer:
X = 12 - Angle EFG = 48
Find the area of a regular decagon whose apothem is 14 mm.
The area of a regular decagon whose apothem is 14 mm is 560 square milli meter
What is Polygon?A polygon is a plane figure made up of line segments connected to form a closed polygonal chain
We have to find the area of a regular decagon whose apothem is 14 mm and side length of 8m
Area of decagon = 1/2×Apothem×perimeter
Perimeter =Number of sides ×side length
=10×8
=80
Area of decagon = 1/2×14×80
=7×80
= 560 square mm
Hence, the area of a regular decagon whose apothem is 14 mm is 560 square milli meter
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The area of a regular decagon is approximately 605.5 mm².
Area of a regular decagon :
Area = (1/2) × Perimeter × Apothem
If we denote the side length by 's,' we can find it using the relationship between the number of sides, the side length, and the apothem:
The number of sides (n) is 10 because it is a decagon.
The formula for the side length of a regular polygon given its apothem (a) is:
[tex]s = 2a \times tan(\pi/n).[/tex]
Substitute n = 10 and a = 14 mm into the formula:
s = [tex]2 * 4 mm \times tan(\pi/10)[/tex]
≈ 8.65 mm.
Then, the perimeter (P) of the decagon is:
[tex]P = n \times s[/tex]
= 10 *8.65 mm
≈ 86.5 mm.
Now, use the area formula:
Area = (1/2) × P × a
= (1/2) × 86.5 mm × 14 mm
≈ 605.5 mm².
So, the area of the regular decagon is approximately 605.5 mm².
Which expressions show how to calculate the volume
of this prism? Check all that apply.
2(12 +21+28)
3(4) + 7
3(7)(4)
407)(3)
12(7)
21(28)
7 cm
4 cm
3 cm
Answer:its 3 (7)(4) 4(7)(3) 12(7) i just did it
Answer:
C,D,E
Step-by-step explanation:
Ross drives 240 miles in 4 hours. If Ross continues to drive at the same rate, how many miles can he drive in 8 hours?
A. 464
B. 480
C. 180
D. 960
Answer:
B
Step-by-step explanation:
240+240=480
yes
Answer:
B. 480
Step-by-step explanation:
You can find the answer to this by finding the unit rate of Ross's travel. 240:4=60:1, meaning that he drives at 60 miles per hour. Multiplying this by 8 hours, you get 480 miles. Hope this helps!
What is the actual distance
Answer:
B. 2.3
Step-by-step explanation:
Answer:
If the distance is 4.6 centimeters, then the actual distance has to be 2.3 kilometers.
Step-by-step explanation:
[tex]\frac{2 cm}{1 km}[/tex]
[tex]\frac{2}{1} * \frac{4.6}{?}[/tex]
[tex]\frac{4.6}{2}[/tex]
2.3 km
So, you answer is letter choice 2.3 kilometers.
Name the center of Circle R with an ordered pair. Type an ordered pair, including parentheses, into the space provided.
Do not type spaces in your answer.
NEXT QUESTION
ASK FOR HELP
TURN IT IN
Answer:
(0,0)
Step-by-step explanation:
Find the volume
12 poir
2.2 cm
A watch company is developing packaging for its new watch. The designer uses pentagons with a base area of 20 in2 and rectangles with a length of 10 in to create a prototype for the new package. What is the volume of the prototype?
Answer:
The volume of the prototype is 200 cubic inches.
Step-by-step explanation:
Hi, to answer this question we have to calculate the volume of the pentagonal prism:
Volume (V)= base area x height of the rectangular face
Replacing with the values given and solving for V (volume)
V = 20 in2 x 10 in = 200 cubic inches
The volume of the prototype is 200 cubic inches.
Feel free to ask for more if needed or if you did not understand something.
The volume of the prototype is 200 cubic inches.
Calculation of the volume:Since The designer uses pentagons with a base area of 20 in2 and rectangles with a length of 10 in
So, here the volume is
= 20(10)
= 200 cubic inches
Therefore, The volume of the prototype is 200 cubic inches.
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What is the area of this tile?
Is it in. or in2
Answer:
A = 4 in^2
Step-by-step explanation:
The area is given by
A = l*w
A = 1in * 4 in
A = 4 in^2
When compared with the independent variable, how many of the graphs represent a linear relationship? 0 1 2 3
Answer:2
Step-by-step explanation:
In relation to the independent variable, one graph represents a linear relationship, as shown by the linear equation examples provided. The remaining graphs depict quadratic, inverse, and exponential relationships.
Explanation:The question asks, 'When compared with the independent variable, how many of the graphs represent a linear relationship?' In the given examples, 'y = 6x + 8', '4y = 8', and 'y + 7 = 3x' are all linear equations. This means they represent a linear relationship between two variables, often plotted on horizontal and vertical axes of a graph. In such graphs, the independent variable is usually plotted on the horizontal (x) axis and the dependent variable on the vertical (y) axis.
If we look at the information regarding different types of relationships, the examples show a linear, quadratic, inverse, and exponential relationship graph. As the linear graph is the only one representing a linear relationship, the answer is that 1 out of 4 graphs, when compared with the independent variable, represents a linear relationship.
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which of the following rectangles have an area of 24 square meters? HELP ME PLS
Answer:
B and c.
Step-by-step explanation:
Area is: L x W.
8 x 3 = 24
6 x 4 = 24
Feel free to let me know if you need more help. :)
Answer:
b. and c.
Step-by-step explanation:
Area of a rectangle is wl
8 x 3 = 24
6 x 4 = 24
A circle has the equation (x−4)2+(y−1)2=34.
What are the coordinates of the center and the length of the radius?
The center is at (4,1), and the radius is 34−−√ units.
The center is at (4,1), and the radius is 34 units.
The center is at (1,4), and the radius is 34 units.
The center is at (1,4), and the radius is 34−−√ units.
Answer:
A
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x - 4)² + (y - 1)² = 34 ← is in standard form
with centre = (4, 1 ) and r² = 34 ⇒ r = [tex]\sqrt{34}[/tex] → A
Final answer:
The equation represents a circle with the center at (4,1) and a radius of 5.83 units.
Explanation:
The center of the circle is at (4,1) and the radius is 5.83 units.
To find the center of the circle, you simply take the opposite of the numbers inside the parentheses of (x - 4) and (y - 1), giving you the center (4, 1). The radius is the square root of the number on the right side of the equation, which is √34 = 5.83 units.
A 150 point exam has 54 questions. There are 2 point and 5 point questions. How many of each type of question are on the test?
Answer:
40 2-point questions and 14 5-point questions
On a 150 point exam with 54 questions, consisting of 2 point and 5 point questions, there are 40 two-point questions and 14 five-point questions.
Explanation:To determine how many 2 point and 5 point questions are on a 150 point exam with 54 questions, we need to set up a system of equations and solve it. Let x represent the number of 2 point questions and y represent the number of 5 point questions. We have two equations based on the information given:
The total number of questions is 54: x + y = 54The total number of points for all questions is 150: 2x + 5y = 150Solving these equations simultaneously, we multiply the first equation by 2, which gives us 2x + 2y = 108. Subtracting this from the second equation cancels out x, yielding 3y = 42. Dividing both sides by 3 gives us y = 14. Substituting the value of y back into the first equation, we have x + 14 = 54, which gives us x = 40.
Therefore, there are 40 two-point questions and 14 five-point questions on the exam.