An athletic track is given in the figure.
The two straight parts are 80 m long.
The total length of the track is 400 m.
Find the radius of the curved part of the track
on both sides.
Subtract the length of the two straight parts
from the entire length of the track.
Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
The indicated IQ score, x, is enter your response here. (Round to one decimal place as needed.)
The indicated IQ score is given as 117.
How to solve for the IQ scoreThe area under the curve is given as 0.1431
the area to the left of x = 1 - 0.1431
= 0.8569
for 0.8569 the z stat is 1.07
u = 100
sd = 15
x = u + z * sd
= 100 + 0.8569 * 15
= 116.05
approximately 117
Read more on normal distribution here:https://brainly.com/question/4079902
#SPJ1
Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
xx
0.1431
A symmetric bell-shaped curve is plotted over a horizontal scale. A vertical line runs from the scale to the curve at labeled coordinate x, which is to the right of the curve’s center and peak. The area under the curve to the right of the vertical line is shaded and labeled 0.1431.
Read more on statistics here:https://brainly.com/question/15525560
#SPJ1
g a card game is made of 108 cards.25 each are red, yellow,blue and green and 8 are wild cards.each play- ers is dealt a seven card hand. a)what is the probability that hand will contain ex- actly 2 wild cards? b) what is the probability that hand contains seven yellow cards?
a) The probability that a hand will contain exactly 2 wild cards is 0.0246.
b) The probability of choosing a hand with seven yellow cards is 0.00056.
a) To find the probability that a hand will contain exactly 2 wild cards, we need to consider the number of ways we can choose 2 wild cards from 8 and the number of ways we can choose 5 non-wild cards from the remaining 100 cards. The total number of ways to choose 7 cards from 108 is:
C(108, 7) = 85,900,584
The number of ways to choose 2 wild cards from 8 is:
C(8, 2) = 28
The number of ways to choose 5 non-wild cards from the remaining 100 cards is:
C(100, 5) = 75,287,520
Therefore, the total number of ways to choose a hand with exactly 2 wild cards is:
28 * 75,287,520 = 2,108,196,160
The probability of choosing a hand with exactly 2 wild cards is:
2,108,196,160 / 85,900,584 ≈ 0.0246, or about 2.46%
b) To find the probability that a hand contains seven yellow cards, we need to calculate the number of ways we can choose 7 yellow cards from the 25 available, and divide this by the total number of ways to choose 7 cards from the 108 available. The number of ways to choose 7 yellow cards from 25 is:
C(25, 7) = 48,048
The total number of ways to choose 7 cards from 108 is:
C(108, 7) = 85,900,584
Therefore, the probability of choosing a hand with seven yellow cards is:
48,048 / 85,900,584 ≈ 0.00056, or about 0.056%
To learn more about probability click on,
https://brainly.com/question/14643921
#SPJ4
The lines intersect at
1 point.
different. The
parallel.
Do You Understand?
1. Essential Question How are slopes and
y-intercepts related to the number of solutions
of a system of linear equations?
The slopes and y-intercepts can be used to determine the type of relationship between the lines, and therefore the number of solutions.
What is linear equation ?
Linear equation can be defined as the equation in which the highest degree is one.
The number of solutions for a system of linear equations depends on the relationship between the slopes and y-intercepts of the lines represented by the equations. If the lines are intersecting, then there is exactly one solution where the lines cross. If the lines are parallel, then there are no solutions, as the lines will never intersect.
If the lines are coincident, then there are infinitely many solutions, as the lines represent the same line.
Therefore, The slopes and y-intercepts can be used to determine the type of relationship between the lines, and therefore the number of solutions.
To learn more about Linear equation from given link.
https://brainly.com/question/29739212
#SPJ1
Jayden measured a desk to be 4 feet. The actual measurement is 3. 2 feet. What is Jayden's percent error?
Jayden measured a desk to be 4 feet. The actual measurement is 3. 2 feet. Jayden's percent error is 25%.
To calculate the percent error, we first need to find the difference between the measured value and the actual value, then divide that difference by the actual value, and multiply the result by 100 to express it as a percentage.
Jayden measured a desk to be 4 feet. The actual measurement is 3. 2 feet.
The difference between Jayden's measurement and the actual measurement is:
4 ft - 3.2 ft = 0.8 ft
The actual value is 3.2 ft, so the percent error is:
(0.8 ft / 3.2 ft) x 100% = 25%
Therefore, Jayden measured a desk to be 4 feet. The actual measurement is 3. 2 feet. Jayden's percent error is 25%.
To learn more about percent error:
https://brainly.com/question/3105259
#SPJ4
A gardener has 10 pounds of soil. He used 5/8 of the soil for his garden. How many pounds of soil did he use in the garden? How many pounds did he have left?
Answer:
Step-by-step explanation:
The gardener used 5/8 of the soil, which is equal to 10 * 5/8 = 10 * 0.625 = 6.25 pounds.
So, he used 6.25 pounds of soil in the garden.
The gardener had 10 - 6.25 = 3.75 pounds of soil left.
T and W are the midpoints of the legs,
SU
and
VX
, of trapezoid SUVX.
If TW=30 and UV=40, what is SX?
Answer:
SX = 20
Step-by-step explanation:
the midsegment of a trapezoid is half the sum of the parallel bases, then
[tex]\frac{UV+SX}{2}[/tex] = TW , that is
[tex]\frac{40+SX}{2}[/tex] = 30 ( multiply both sides by 2 to clear the fraction )
40 + SX = 60 ( subtract 40 from both sides )
SX = 20
Find the volume of this prism.
Answer:
396cm^3
Step-by-step explanation:
use formula V=Area of base * Height that is V=1/2b*h *Height
W X
Y
Z
List the sample space for the experiment.
Os = {X, Y, Z}
Os = {W, Z, Z}
Os = {W.Y.Y. Z}
Os = {W, X, Y, Z}
Answer:
Os = {W, X, Y, Z}
Step-by-step explanation:
The sample space for the experiment is the set of all possible outcomes, in this case, W, X, Y, and Z. It represents all the outcomes that can occur in a single trial of an experiment. The sample space is usually denoted as a set, and the elements in the set are the individual outcomes. In this case, the sample space is the set {W, X, Y, Z}.
Answer:
the answer is the last one
Step-by-step explanation:
os= {w, x, y, z}
State if the lines are Parallel, Perpendicular, or Neither. 4x+y=5 3x+12y=-6
The lines 4x+y=5 and 3x+12y=-6are neither parallel nor perpendicular
How to determine the relationship between the linesFrom the question, we have the following parameters that can be used in our computation:
4x+y=5 3x+12y=-6
Make y the subject in the equations
So, we have
y = -4x + 5
y = -1/4x - 1/2
The slopes of the lines are -4 and -1/4
These numbers are not equal and they are not opposite reciprocals
This means that the lines are neither parallel nor perpendicular
Read more about linear equations at
https://brainly.com/question/2030026
#SPJ1
Please help! Thank you so much!
The non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.
The simplified expression that represents the total number of members after the third year is 4.5(53 + x).
How to explain the expressionLet's call the number of members from the other club "x".
After the first year, the total number of members is 20 + x, and it doubles to 2(20 + x) = 40 + 2x.
After the second year, half of the members from the other club leave, so there are 0.5x members left from the other club. And another 40 members join, so the total number of members is (40 + 2x - 0.5x) + 40 = 80 + 1.5x.
After the third year, the total number of members triples, so we have 3(80 + 1.5x) = 240 + 4.5x.
Therefore, the non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.
To simplify, we can factor out 4.5 from the expression to get 4.5(53 + x). So the simplified expression that represents the total number of members after the third year is 4.5(53 + x).
Learn more about expressions on;
https://brainly.com/question/1859113
#SPJ1
which sampling type will yield a representative sample? (choose one or more) group of answer choices stratified random snowball sample convenience simple random
Sampling type which will yield a representative sample is stratified random sampling.
A representative sample is a subset of a population that seeks to accurately reflect the characteristics of the larger group. For example, a classroom of 30 students with 15 males and 15 females could generate a representative sample that might include six students: three males and three females.
This method uses stratified random sampling to help identify its components. Other methods can include random sampling and systematic sampling. A representative sample seeks to choose components that match with key characteristics in the entire population being examined.
Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members' shared attributes or characteristics, such as income or educational attainment.
To know more about sampling
https://brainly.com/question/11045407
#SPJ4
PART G: Let c be the unknown side of the triangle. Use this triangle calculator to solve for c. Under Sides, enter 7 for side a and 9 for side b. Under Angles, enter 74 for angle C. Click Calculate once you have entered the information. What is the length of side c?
Part H
Now try to construct a triangle using a different set of measurements. This time, you’ll enter three angle measurements. Return to the Calculator tab, and click the Clear button to begin a new calculation.
Under Angles, enter 45 for A, 40 for B, and 95 for C. Then click Calculate. What happened? What message did the tool deliver? Explain the message in terms of the properties of a triangle and the given angles.
Part J
Return to the Calculator tab, and click the Clear button to begin a new calculation. This time, you’ll check for valid triangles given two angles and the side between them.
Under Sides, enter 5 for a. Under Angles, enter 30 for B and 50 for C. Then click Calculate. How many triangles can be created from the given conditions?
Part K
Return to the Calculator tab, and click the Clear button to begin a new calculation. This time, you’ll check for valid triangles given three sides of specified length.
Under Sides, enter 6 for a, 7 for b, and 13 for c. Then click Calculate. What happened? What message did the tool deliver? Explain the message in terms of the properties of a triangle and the given side lengths.
please help!
The solutions are given below.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Part A
the dotted line formes the thrid side of the triangle.
part B
The length is the unknon side increases while kepping the known side lenths fixed, measuremnt of anggle Z will increas. So, the tringle will not fir the given conditions anymore.
part c
If the length of he unknown side decrases while keeping h known side lengths fixed,the measure of angle will decrease so he tringle will not fit the given conditions anymore.
part D
You know the given conditions for the triangle are fixed you also know the unknown side length is fixed. What dose the this tell you angles adjacent to the unknown side.
part e
The given condiction are fixed and the unknown side lenghtis fixed, the angles adjacent to the unknown side must much also be fixed.
part f
Given two side lengths and the measurement of the angle between them, only one triangle can be constructed. Part G The length of the unknown side (c) is 9.76 centimeters
To learn more on triangle click:
brainly.com/question/29126067
#SPJ1
Hank came home from Trick-Or-Treating
with 8 Reece's, 12 Snickers, 5 Sour Patch
Kids, 4 Hershey's bars and 6 packs of
Skittles. Hank is allergic to chocolate.
Write the ratio of candy that Hank can
eat to the total amount Hank has.
Since Hank is allergic to chocolate, he cannot eat Reese's, Snickers, Hershey's bars, or any other type of chocolate candy.
Therefore, the only candy that Hank can eat is the Sour Patch Kids and Skittles.
The total number of Sour Patch Kids that Hank has is 5.
The total number of Skittles that Hank has is 6 packs, or 6 * the number of Skittles in one pack (let's assume it's 10 Skittles per pack). So, the total number of Skittles that Hank has is 6 * 10 = 60.
Adding the number of Sour Patch Kids and Skittles, the total number of candy that Hank can eat is 5 + 60 = 65.
The total amount of candy that Hank has is 8 Reece's + 12 Snickers + 5 Sour Patch Kids + 4 Hershey's bars + 6 packs of Skittles = 8 + 12 + 5 + 4 + 6 * 10 = 8 + 12 + 5 + 4 + 60 = 89.
The ratio of candy that Hank can eat to the total amount of candy he has is 65 / 89 = approximately 0.73, which can be expressed as a simplified fraction as 73 / 100.
Answer:
11:35
Step-by-step explanation:
no step by step explanation.
3x-1=5x+10x= 5 1/2
please explain to me what did i do wrong and correct it
The requried correct expression 3x - 1 + 5x + 10x = 5 1/2, and solution of the equation is x = 7.5/18
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
The equation as written doesn't have a unique solution, as the left-hand side and right-hand side are not equal.
To correct the equation, you would need to provide more information about what you intended to do with the two equations and format the right-hand side of the equation properly. For example, if you meant to add the two equations, you could write,
3x - 1 + 5x + 10x = 5 + 2.5
18x = 7.5
x = 7.5/18
Learn more about models here:
https://brainly.com/question/22591166
#SPJ1
simplify
1/2 - 1/4 + 1/8
The width of a rectangle is the length minus 8 units. The area of the rectangle is 9 square units. What is the length, in units, of the rectangle?
Answer: The length is 9 units and the width is 1 unit
Step-by-step explanation:
We can use the formula for the area of a rectangle to solve this problem. The formula is A = l * w, where A is the area, l is the length, and w is the width.
We have A = 9, and we know that w = l - 8. Substituting this into the formula, we get:
9 = l * (l - 8)
We can rearrange this to solve for l:
9 = l^2 - 8l
Adding 8l to both sides of the equation, we get:
9 + 8l = l^2
Subtracting 9 from both sides, we get:
8l = l^2 - 9
We can factor this to get:
l(l - 9) = 0
Since the product of two numbers is zero only when one of them is zero, we can set each factor equal to zero and solve:
l = 0 or l - 9 = 0
Adding 9 to both sides of the second equation, we get:
l = 9
Therefore, the length of the rectangle is 9 units.
if 3 is subtracted to a number and the sum is multiplied by 5 the number thus obtained is 575 find the original number
Answer:
(X-3)5=575
5x-15=575
5x=575+15
5x=590
X= 590:5
X= 118
200$ marked down 20% now increased by 20% is it equal to 200 again?
Answer: nope
Step-by-step explanation:
No, the 200$ marked down 20% would be 200 - 0.2 * 200 = 160$. Then, if it is increased by 20%, it would be 160 + 0.2 * 160 = 192$. So, 200$ is not equal to 192$.
Alexa is saving up to buy a new jacket. She already has $45 and can save an
additional $7 per week using money from her after school job. How much total
money would Alexa have after 8 weeks of saving? Also, write an expression that
represents the amount of money Alexa would have saved in w weeks.
Answer:
Step-by-step explanation:
Answer: 101because if you multipled 7 times 8 you will get 56 and if you add it with 45 you will get 101
i hope this help
After 8 weeks of saving, Alexa will have a total of $101. The expression to show the money Alexa saves in 'w' weeks is 45 + 7w.
Explanation:The subject of this question is
Mathematics
and it is geared towards
Middle School
grades. To solve this problem, we need to use
algebraic expressions
. Based on the problem given, Alexa has $45 initially and saves $7 per week additionally from her after school job. So if she saves for 8 weeks, Alexa would have accumulated an additional $7 times 8 = $56. Therefore, the total amount of money Alexa would have after 8 weeks is her initial amount of $45 plus the additional $56, which equals $101. To represent this in terms of an expression, where 'w' stands for weeks, you can write 45 + 7w. This expression lets us calculate the total savings for any number of weeks 'w'.
Learn more about Algebraic Expressions here:https://brainly.com/question/34192827
#SPJ2
Some of the world's smallest horses
include: Thumbelina, who stands
17 inches tall; Black Beauty, who stands
18 inches tall; and Einstein, who stands
14 inches tall.
a. How much taller is Black Beauty
than Thumbelina?
Black Beauty stands one inch taller than Thumbelina, measuring 18 inches in height compared to Thumbelina's 17-inch stature.
Black Beauty is 1 inch taller than Thumbelina.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Thumbelina, who stands 17 inches tall
Black Beauty, who stands 18 inches tall.
Einstein, who stands 14 inches tall.
We have to find how tall is Black Beauty than Thumbelina.
To find out, we can subtract Thumbelina's height from Black Beauty's height:
Black Beauty's height - Thumbelina's height
= 18 inches - 17 inches = 1 inch
Therefore, Black Beauty is 1 inch taller than Thumbelina.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
we need to survey a random sample of the 300 passengers on a flight from san francisco to tokyo. you randomly select a seat position (right window, right center, right aisle, etc.) and survey all the passengers sitting in those seats. what sampling technique best describes the process here?
The sampling technique best described here is systematic sampling. Systematic sampling is a type of probability sampling in which the elements in the population are selected in a systematic way
This sampling technique is used when the population size is too large to survey the entire population. In this example, the population size is 300 passengers and the sampling interval is determined by dividing the population size by the sample size. For example, if the sample size is 30, the sampling interval is[tex]10 (300/30=10).[/tex] This means that every 10th passenger is randomly selected for the survey. The selection starts with a randomly chosen passenger and then the ninth passenger after that is selected and so on. The formula for Systematic sampling is n = N/n, where N is the population size and n is the sample size.
Learn more about sampling technique here:
https://brainly.com/question/14546338
#SPJ4
What is the measure of the smallest angle?
(Image)
67°
69°
52°
61°
The measure of the smallest angle is 52 degrees
How to determine the measure of the smallest angle?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The triangle
The sum of angles in a triangle is 180
So, we have
2x + 3x - 11 + 2x + 9 = 180
Evaluate the like terms
7x = 182
So, we have
x = 26
This means that
2x = 2 * 26 = 52
3x - 11 = 3 * 26 - 11 = 67
Hence, the smallest is 52 degrees
Read more about angles at
https://brainly.com/question/25716982
#SPJ1
It takes Shawn 35 minutes by car to get to his grandma’s. The nearest parking area is a 4 minute walk from her apartment. One week, he realized that he spent 5 hours and 12 minutes traveling to her apartment and then back home. How many round trips did he make to visit his grandma?
Shawn made 4 round trips to visit his grandma.
How to calculate Travel Time?The travel time is the amount of time it takes to travel from one location to another. The specific method for calculating travel time depends on the mode of transportation being used. Here are some general guidelines for calculating travel time:
Estimate the distance between the starting location and the destination.Determine the average speed or pace of travel. This will depend on the mode of transportation being used.Calculate the travel time by dividing the distance by the speed or pace. This will give you the estimated travel time in hours.Let's start by converting the total travel time to minutes:
5 hours and 12 minutes = 5 × 60 + 12 = 312 minutes
Let's call the number of round trips that Shawn made "x".
For each round trip, Shawn has to travel to his grandma's apartment and then back home. The total time for each round trip is:
time per round trip = time to get there + time to get back + time to walk to/from parking
time per round trip = 35 + 35 + 4 + 4 = 78 minutes
So the total travel time for all of the round trips is:
total travel time = time per round trip x number of round trips
312 = 78x
Solving for "x", we get:
x = 312/78 = 4
Therefore, Shawn made 4 round trips to visit his grandma.
To know more about speed visit:
brainly.com/question/6280317
#SPJ1
can rectangle corner perpendicular diagonal lines of the rectangle?
if so can you draw a picture
Answer:
yes
Step-by-step explanation:
What is the area of this figure?
The area of the figure is given as follows:
100.56 mm².
How to obtain the area of the figure?The figure in this problem is composed as follows:
Rectangle of dimensions 4 mm and 12 mm.Rectangle of dimensions 2 mm and 7 mm.Rectangle of dimensions 4 mm and 12 - 7 = 5 mm.Rectangle of dimensions 3 mm and 2 mm.Semicircle of radius 2 mm.The areas for each region are given as follows:
Rectangle of dimensions 4 mm and 12 mm -> 4 x 12 = 48 mm²Rectangle of dimensions 2 mm and 7 mm -> 2 x 7 = 14 mm².Rectangle of dimensions 4 mm and 12 - 7 = 5 mm -> 4 x 5 = 20 mm².Rectangle of dimensions 3 mm and 2 mm -> 3 x 2 = 6 mm².Semicircle of radius 2 mm -> 3.14 x 2² = 12.56 mm².Hence the total area is of:
48 + 14 + 20 + 6 + 12.56 = 100.56 mm².
More can be learned about area at https://brainly.com/question/15673093
#SPJ1
a manufacturing production line breaks down two times a week on average. what is the probability that the interarrival times between breakdown will be less than 2 days?
The probability that there will be less than two days between manufacturing production line outages is approximately 0.553, or 55.3%.
We need to make some assumptions in order to calculate the probability that the time intervals between manufacturing production line breakdowns will be shorter than two days. Assume that the intervals between breakdowns have an exponential distribution with a mean of 3.5 days (1/2 times per week).
The probability that an interarrival time is fewer than two days can be calculated using the exponential distribution formula as follows:
P(X < 2) = 1 - e(-2/3.5)
where "X" stands for the duration in between breakdowns.
When we condense the expression, we get:
P(X < 2) = 0.553
Therefore, The probability that there will be less than two days between manufacturing production line outages is approximately 0.553, or 55.3%.
To learn more about exponential distribution, visit the link below:
https://brainly.com/question/20714221
#SPJ4
Use division to find which of the following fractions are equivalent to
6
24
? Select all that apply.
Answer: C and D are the correct ones
Step-by-step explanation:
nterpret the values of the mean and standard deviation. (round your answers to four decimal places.) a typical amount poured into a short, wide glass is ml. a typical deviation from the mean amount poured is ml. (b) the mean amount poured into a tall, slender glass for individuals asked to pour 44.3 ml (1.5 ounces) was 51.3167 ml. what do the values of the means for the two types of glasses suggest about the shape of glasses used? the mean amount for a short, wide glass is ---select--- the mean amount for a tall, slender glass. this suggests that individuals tend to pour ---select--- into a short, wide glass compared to a tall, slender glass.
The values of the means for the two types of glasses suggest about the shape of glasses used is 22ml on average.
When it comes to pouring drinks, bartenders are expected to pour a specific amount of liquid into each glass. However, there may be some variation in the amount poured depending on the shape of the glass. In this scenario, we have data on the actual amount poured by bartenders into a short, wide glass when asked to pour 44.3 ml. We will use this data to calculate the mean and standard deviation and interpret their values.
The mean is the average amount poured into the short, wide glass. To find the mean, we add up all the amounts poured and divide by the number of samples. Using the data provided, we get a mean of 57.889 ml, rounded to three decimal places.
However, the mean doesn't tell us the whole story. We also need to consider the standard deviation, which tells us how much the amounts poured vary from the mean.
To calculate the standard deviation, we first need to find the variance. We calculate this by subtracting the mean from each amount poured, squaring the differences, adding them up, and dividing by the number of samples minus one. Using the data provided, we get a variance of 479.716 ml², rounded to three decimal places.
To get the standard deviation, we take the square root of the variance. Using the data provided, we get a standard deviation of 21.904 ml, rounded to three decimal places.
Interpreting the values of the mean and standard deviation, we can say that a typical amount poured into a short, wide glass is 57.889 ml, while a typical deviation from the mean amount poured is 21.904 ml. This means that the amounts poured vary by about 22 ml on average, which could be due to differences in pouring technique or the shape of the glass.
To know more about standard deviation here.
https://brainly.com/question/16555520
#SPJ4
Forest rangers at a state park have observed a decline in the rate of trees per
acre over a 5-year period. At the beginning of their observations, there was an
average of 48 trees per acre. At the end of the 5-year period, there was an
average of 42 trees per acre. If this trend continues, how many trees per acre
will there be 4½ years from the end of the 5-year observation period?
helppp
There will be 36.6 trees per acre after 4½ years from the end of the 5-year observation period. The solution has been obtained by using unitary method.
What is the unitary method?
The value of each individual unit is first determined using the unitary method, and only then is the value of the required number of units determined.
We are given that at the beginning of their observations, there was an average of 48 trees per acre. At the end of the 5-year period, there was an average of 42 trees per acre.
So, decline in trees per acre in 5 years is 48 - 42 = 6 trees per acre
So, decline in 1 year = 6/5 = 1.2 trees per acre
Similarly, decline in 4.5 years = 1.2 * 4.5 = 5.4 trees per acre
Thus, trees left per acre = 42 - 5.4 = 36.6 trees
Hence, there will be 36.6 trees per acre after 4½ years.
Learn more about unitary method from the given link
https://brainly.com/question/28731562
#SPJ1
