[ 25 , 1.581 ] is the pair that is the mean and standard error of x.
What does standard error mean?
A statistical concept known as the standard error uses standard deviation to assess how well a sample distribution represents a population.
The standard error of the mean describes the statistical variation between a sample mean and the population's actual mean. Measures of variability include standard error and standard deviation: The standard deviation describes variation within a single sample.
n = 80
μ = 25
σ² = 200
mean of x = μ = 25
standard error = √ σ²/n
= √200/80
= 1.581
= [ 25 , 1.581 ]
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The standard form of an absolute value function is f(x) = a|x -h| + k.Which of the following represents the vertex?
A. (-k,h)
B. (-h,k)
C. (k,h)
D.(h,k)
Please help ASAP
Answer:
The correct answer:
D. (h, k)
Complete the sentences.
A rotation is a transformation that
OA. turns; shape and size
OB. turns; position
OC. flips; position
D. flips; shape and size
a figure. It changes its
SUBMIT
A rotation can be transformation which turns a figure. It changes its position
what is rotation ?
Rotation is the act of turning or moving something around a fixed point or axis. It is a fundamental concept in mathematics, physics, and engineering, and is used to describe the movement of objects in space.
In the given question,
Rotation is the act of turning or moving something around a fixed point or axis. It is a fundamental concept in mathematics, physics, and engineering, A rotation can be transformation which turns a figure. It changes its position
when their is rotations it turns around its axis and their will be change in its position
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A Ferris Wheel is 60 meters in diameter and rotates once every four minutes. The center axle of the Ferris Wheel is 40 meters. from the ground. Write at least 2 mathematical models that represent the motion of the passenger on this Ferris wheel.
y = acos bx +c
y=-25 cos
C. where X = 2.3 min
Another mathematical representation of how a rider on this Ferris wheel might move is :y = cos(0.25x) + 40
What more uses does trigonometry have?Trigonometry is widely used in many fields, including physics, engineering, architecture, surveying, oceanography, and more. Here are several examples:
In astronomy and physics, trigonometry is used to compute the motions of moving objects, gauge the separations between planets and stars, and examine waves. Trigonometry is used in architecture and engineering to determine angles and distances for building structures like bridges and buildings.
In surveying, trigonometry is a tool used to determine angles and separations between points on the surface of the ground.
.
The function y = a cos(bx) + c, where an is the function's amplitude, b is its frequency, and c is its vertical shift, can be used to mimic the height of a rider on a Ferris wheel.
Given that the Ferris wheel's diameter in this instance is 60 meters, its radius is 30 metres. The Ferris wheel's center axle is 40 metres off the ground. This indicates that a rider is 70 metres above the earth when they are at the top of the Ferris wheel (30 + 40). A rider is 10 metres above the ground when they reach the bottom of the Ferris wheel. (40 - 30).
We can determine that the Ferris wheel's period is four minutes because it rotates once every four minutes. The following formula can be used to get our function's frequency:
f = 1/T, 1/4, and 0.25 Hz
Therefore, our function has a frequency of 0.25 Hz.
The vertical shift of our function is equivalent to 50% of the difference between a Ferris wheel passenger's maximum and minimum heights:
, c = (a_max + a_min) /2
c = (70 + 10) /2
c = 40
Therefore, 40 is the vertical shift of our function.
Finally, we must ascertain the function's amplitude. The difference between a Ferris wheel passenger's maximum and minimum heights is equal to half of the amplitude:
For example, c = (a_max + a_min) / 2 c = (70 + 10) / 2 c = 40
Therefore, 40 is the vertical shift of our function.
Finally, we must ascertain the function's amplitude. The difference between a Ferris wheel passenger's maximum and minimum heights is equal to half of the amplitude:
A=(a_max - a_min) / 2 A=(70 - 10) / 2 A=30
Therefore, our function has an amplitude of 30.
When you combine everything, you get:
Y equals a cos(0.25x) + 40
y = -25 cos(C), where C is the time in minutes since the motion started at position, is another potential mathematical model that could describe this motion. (0,-25).
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What is the measure of an inscribed angle that intercepts an arc whose measure is 200?
A. 100
B. 200
C. 300
D. 50
The answer to the given question about inscribed angles intercepting an arc is option A. 100
As we know that the measure of an inscribed angle is half the measure of the intercepted arc, we can use the formula:
Measure of inscribed angle = 1/2 × Measure of intercepted arc
So, if the intercepted arc has a measure of 200 degrees, then the measure of the inscribed angle is:
Measure of inscribed angle = 1/2 × 200 degrees
= 100 degrees
Therefore, the answer is A. 100 degrees. In a circle, an inscribed angle is an angle formed by two chords of the circle that have a common endpoint on the circle. The measure of an inscribed angle is half the measure of the intercepted arc. Therefore, if an arc has a measure of 200, then an inscribed angle that intercepts that arc will have a measure of half of 200, which is 100 degrees.
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HELP PLEASEEEEEEEEEE
One side of the triangle is 1 inch less than three times the length of the altitude to that side. Write a polynomial that represents the area of this triangle.
By answering the presented question, we may conclude that the answer of the triangle [tex]A = (3/2)h^2 - (1/2)h\\[/tex] => [tex]A(h) = (3/2)h^2 - (1/2)h[/tex]
What precisely is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle may be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
x = 3h - 1
A = (1/2)bh
A = (1/2)xh
A = (1/2)(3h - 1)h
[tex]A = (3/2)h^2 - (1/2)h\\[/tex]
[tex]A(h) = (3/2)h^2 - (1/2)h[/tex]
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Amadou and Olivia are making fruit salads for a picnic. Amadou mixes 9 cups of melon and 10 cups of apple and Olivia mixes 2 cups of melon and 3 cups of apple. Use Amadou and Olivia’s percent of apple to determine whose fruit salad will taste more appley.
Given that 60% of Olivia's fruit salad is made up of apples as opposed to Amadou's fruit salad's 52.63%, Olivia's fruit salad will have a more apple-forward flavor based on percent.
The amount of apples in each fruit salad needs to be compared in order to determine which salad will taste more apple-like.
There are 19 cups of fruit in Amadou's fruit salad, of which 10 cups are apples. By dividing the total number of cups of fruit by the number of cups of apples, and multiplying the result by 100, we can get the proportion of apples in Amadou's salad:
Apple's percent of Amadou's fruit salad is equal to (10/19) x 100, or 52.63%.
There are 5 cups of fruit in Olivia's fruit salad, of which 3 cups are apples. We can use the same formula to determine how much apple is in Olivia's salad:
Olivia's fruit salad contains 60% apples, or (3/5) x 100.
As a result, Olivia's fruit salad will taste more apple-like because apples make up 60% of it as opposed to only 52.63% of Amadou's fruit salad.
It is important to keep in mind that the maturity, sweetness, and freshness of the fruits used, as well as other elements like the dressing and presentation, may all affect how the fruit salad tastes.
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Calculate the area of the shaded region below
Answer:
Step-by-step explanation:
According to the given situation,
the area of figure A= l*b
=4m * 5m
=20m²
As the measures of the figure A and B is same,
the area of figure B = the area of figure A=20m²
the length of the side C and D are = 16m-8m-4m=4m
the area of figure C = l * b
=4m*5m
=20m²
As the measures of the figure C and D is same,
the area of figure D = the area of figure C=20m²
Area of the figure E=l * b
=8m * 13m
=104m²
∴ the area of the shaded region is =184m²
Yolanda hiked each day for a week. The first day she hiked mile, the second day she hiked mile, and the third day she hiked 1 mile. By how much did she increase the distance she hiked each day?
the distance she hiked each day, we need to calculate the difference between the distance she hiked on consecutive days. Yolanda increased the distance she hiked by 1 mile each day.
What is the total distance?To find the increase in the distance Yolanda hiked each day, we need to calculate the difference between the distance she hiked on each consecutive day.
The distance Yolanda hiked each day for the first three days can be represented as:
Day 1: d miles
Day 2: [tex]d + 1[/tex] miles
Day 3: [tex]d + 2[/tex] miles
The increase in distance from day 1 to day 2 is [tex](d + 1) - d = 1[/tex] mile.
The increase in distance from day 2 to day 3 is [tex](d + 2) - (d + 1) = 1[/tex] mile.
Therefore, Yolanda increased the distance she hiked by 1 mile each day.
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HELP PLSSS!!!!!!
A student missed 88
problems on a English test and received a grade of 2%. If all the problems were of equal value, how many problems were on the test? Follow the problem-solving process and round your answer to the nearest integer.
Answer:
Let's start by using the formula for finding the percentage: percentage = (part/whole) x 100 In this case, we know the percentage (2%) and the part (88 problems), but we don't know the whole (total number of problems on the test). So we can write: 2% = (88/whole) x 100 Simplifying, we get: 0.02 = 88/whole Multiplying both sides by the whole, we get: whole x 0.02 = 88 Dividing both sides by 0.02, we get: whole = 4400 Therefore, there were 4400 problems on the English test.
Answer:90 problems
Step-by-step explanation:
To solve the problem, we can use the formula:% correct = (number of correct answers / total number of questions) * 100%Since the student received a grade of 2%, we can write:2% = (number of correct answers / total number of questions) * 100%Simplifying this equation, we get:total number of questions = number of correct answers / 0.02We know that the student missed 88 problems, so the number of correct answers is:number of correct answers = total number of questions - 88Substituting this into the equation above, we get:total number of questions = (total number of questions - 88) / 0.02Simplifying this equation, we get:total number of questions = 50 * (total number of questions - 88)Solving for the total number of questions, we get:total number of questions = 90Therefore, there were 90 problems on the English test
Ximena decides to estimate the volume of an apple by modeling it as a sphere. She measures its diameter as 11.9 cm. Find the apple's volume in cubic centimeters. Round your answer to the nearest tenth if necessary
The volume of the apple is approximately 832.2 cubic centimeters.
What is volume of sphere?The following equation determines a sphere's volume:
V = (4/3)πr³
When V denotes the sphere's volume, r denotes its radius, and denotes the mathematical constant pi (approximately 3.14). By seeing the sphere as an unlimited number of little cylinders piled on top of one another, the formula may be created. Each cylinder has a height equal to the sphere's shell thickness and a radius equal to the sphere's radius.
The volume of a sphere:
V = (4/3)πr³
Here, r = d/2 = 11.9 cm / 2 = 5.95 cm
Substituting the values we have:
V = (4/3)π(5.95 cm)³ ≈ 832.2 cm³
Therefore, the volume of the apple is approximately 832.2 cubic centimeters.
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In how many ways cam 2 students be chosen from a group of 15?
Answer:
you could do 2 students in each group with one group of 3
Step-by-step explanation:
sorry if i didn't answer correctly
In a village, 80% of people are Hindus and 2% are Muslims. If 36 people do not follow these two religions, by drawing a Venn diagram find the number of the Hindu.
Explanation:
Assuming the two religions are mutually exclusive, this would mean 80%+2% = 82% of people are either Hindu or Muslim (but not both).
The remaining 100% - 82% = 18% of people are neither religion mentioned.
x = number of people in the village
18% of x = 36
0.18x = 36
x = 36/0.18
x = 3600/18
x = 200
Then,
80% of x = 0.80*x = 0.80*200 = 160 people are Hindu
The Venn diagram is shown below.
I can’t find the answer pls help me!
Answer:
what is it
Step-by-step explanation:
how do you solve 11P3 and 11C3? i dont have right calculator and im typing this on my laptop
Answer:
Step-by-step explanation:
11P3=11×10×9=990
[tex]11C_{3}=\frac{11 \times 10 \times 9}{3 \times 2 \times 1} =165[/tex]
At a seminar, 2/5 of the audience were students, 3/10 of them were retirees. The rest were professionals. There were 18 more students than professionals. How many audience were at the seminar?
Answer:
There were 60 audience members at the seminar.
Step-by-step explanation:
Let's assume that the total number of audience members at the seminar is "x".
From the given information, we know that:
2/5 of the audience were students, so the number of students was (2/5)x
3/10 of the audience were retirees, so the number of retirees was (3/10)x
The rest were professionals, so the number of professionals was x - (2/5)x - (3/10)x = (1/10)x
We also know that there were 18 more students than professionals, so:
(2/5)x - (1/10)x = 18
Multiplying both sides by 10, we get:
4x - x = 180
Simplifying, we get:
3x = 180
x = 60
Therefore, there were 60 audience members at the seminar.
Fingerprint analysis and blood grouping are features that do not change through the lifetime of an individual. Fingerprint features appear early in the development of a fetus, and blood types are determined by genetics. Therefore, each is considered an effective tool for identification of individuals. These characteristics are also of interest in the discipline of biological anthropology—a scientific discipline concerned with the biological and behavioral aspects of human beings. The relationship between these characteristics was the subject of a study conducted by biological anthropologists with a simple random sample of male students from a certain region with a large student population. Fingerprint patterns are generally classified as loops, whorls, and arches. The four principal blood types are designated as A, B, AB , and O. The table shows the distribution of fingerprint patterns and blood types for the sample. Expected counts are listed in parentheses. The anthropologists were interested in the possible association between the variables. Blood Type A B AB O Total Loops 66 (71.69) 99 (112.19) 35 (32.29) 101 (84.83) 301 Whorls 51 (47.16) 91 (73.80) 15 (21.24) 41 (55.80) 198 Arches 14 (12.15) 15 (19.01) 9 (5.47) 13 (14.37) 51 Total 131 205 59 155 550 (a) Is the test for an association in this case a chi-square test of independence, or a chi-square test of homogeneity? Justify your choice. 0 / 10000 Word Limit0 words written of 10000 allowed Question 2 (b) Identify the conditions for the chi-square inference procedure selected in part (a), and indicate whether the conditions are met. B) 1 / 10000 Word Limit Question 3 (c) The resulting chi-square test statistic from the appropriate test is approximately 18.930. What are the degrees of freedom and p -value of the test? 0 / 10000 Word Limit Question 4 (d) Biological anthropology is concerned with the comparative study of human origin, evolution and diversity. Considering the sampling design in this study, to what population is it reason
a) The association test, in this case, is a chi-square test of independence,
b) The conditions for the chi-square inference procedure are:
Independence
Sample size
c) In this case, the degrees of freedom are (3-1) x (4-1) = 6.
d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.
What is the association test?
An association test is a statistical test used to determine whether there is a relationship or association between two or more variables. The type of association test used depends on the nature of the variables being examined.
a) The association test, in this case, is a chi-square test of independence, which is used to determine whether there is a significant association between two categorical variables.
b) The conditions for the chi-square inference procedure are:
Independence: The sample is a simple random sample, so independence is satisfied.
Sample size: The expected count for each cell should be at least 5, which is satisfied for all cells in the table.
c) The degrees of freedom for the chi-square test are (r - 1) x (c - 1), where r is the number of rows and c is the number of columns in the table.
In this case, the degrees of freedom are (3-1) x (4-1) = 6. The p-value associated with a chi-square test statistic of 18.930 and 6 degrees of freedom is less than 0.01.
d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.
However, it may not be appropriate to generalize to other populations without further research to ensure the characteristics of the population are similar to those of the sample.
Hence, a) The association test, in this case, is a chi-square test of independence,
b) The conditions for the chi-square inference procedure are:
Independence
Sample size
c) In this case, the degrees of freedom are (3-1) x (4-1) = 6.
d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.
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ala Manufacturing purchases land for $445,000 as part of its plans to build a new plant. The
Ompany pays $37,600 to tear down an old building on the lot and $55,583 to fill and level
me lot. It also pays construction costs of $1,402,600 for the new building and $88,536 for
ghting and paving a parking area.
repare a single journal entry to record these costs incurred by Cala, all of which are paid in
ash.
View transaction list
No
A
View journal entry worksheet
Transaction
1
No Transaction Recorded
General Journal
D
Note that the journal for the above transaction is attached accordingly.
What is the explanation for the above journal?The journal entry records the purchase of land for $445,000, demolition expense of $37,600, land improvement cost of $55,583, building construction cost of $1,402,600 and lighting and paving cost of $88,536, all paid in cash.
Therefore, the amounts are debited to their respective accounts and credited to cash.
The total credit amount is equal to the total debit amount, ensuring the accounting equation remains in balance.
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5.2, 5.2, 4.7, 5.4, 3.9, 3.5, 4.1, 4.2, 5.4, 4.7, 4.8, 4.2, 4.6, 5.1, 3.8, 3.9, 4.6, 5.1, 3.6,
4.6, 4.3, 3.4, 4.9, 4.2, 4.0
A manufacturer of pencils randomly selects 25 pencils and measures their length (in
inches). Their data is shown. Create a frequency distribution with 6 classes and a
class width of 0.4 inches. What is the shape of the frequency histogram?
A The histogram is bimodal.
B The histogram is roughly symmetrical.
C histogram is skewed right.
D The histogram is uniform.
E The histogram is skewed left.
Since the sample size is relatively small (n=25), the shape οf the histοgram may nοt perfectly reflect the underlying distributiοn οf the pοpulatiοn.
What is frequency distributiοn?The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.
The range οf the data is the difference between the maximum and minimum values:
Maximum value: 5.4
Minimum value: 3.4
Range: 5.4 - 3.4 = 2.0
Next, we divide the range by the desired number οf classes tο find the class width:
Class width = 2.0 / 6 = 0.3333 (rοunded tο 0.4)
Based οn the given data, we can expect the histοgram tο be apprοximately bell-shaped, with a peak arοund the middle classes (4.0-4.8) and fewer pencils in the extreme classes (3.4-3.8 and 5.4-5.8).
Hοwever, since the sample size is relatively small (n=25), the shape οf the histοgram may nοt perfectly reflect the underlying distributiοn οf the pοpulatiοn.
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El 15% de una cantidad es 216 cuál es esa cantidad ?
la cantidad buscada es 1440.
Calculating the value of the quantityPara encontrar la cantidad dada el 15% de la misma, podemos usar una ecuación:
15% de x = 216
Podemos convertir el porcentaje a decimal dividiendo por 100:
0.15x = 216
Luego, para despejar x, podemos dividir ambos lados de la ecuación por 0.15:
x = 216 / 0.15
x = 1440
Por lo tanto, la cantidad buscada es 1440.
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Find the least possible degree shown on the graph
Answer:
The least possible degree is 5.
Select all the properties that both rectangles and parallelograms share.
A. 4 right angles
B. 4 sides of equal length
C. 2 pairs of parallel sides
D. 2 pairs of sides with equal length
E. 2 acute angles and 2 obtuse angles
The prοperties that bοth rectangles and parallelοgrams share are 2 pairs οf parallel sides & 2 pairs οf sides with equal length.
Thus, οptiοn C & D is cοrrect.
Prοperties οf bοth rectangles and parallelοgrams:
Rectangles and parallelοgrams are bοth types οf quadrilaterals, which are pοlygοns with fοur sides.
Certain prοperties are unique tο each type οf quadrilateral, as well as sοme that they share in cοmmοn. Here are the prοperties that rectangles and parallelοgrams share:
1. Bοth rectangles and parallelοgrams have parallel οppοsite sides.
2. Bοth rectangles and parallelοgrams have cοngruent οppοsite sides
3. Bοth rectangles and parallelοgrams have cοngruent, οppοsite angles
4. Bοth rectangles and parallelοgrams have cοnsecutive angles that are supplementary
Therefοre,
The prοperties that bοth rectangles and parallelοgrams share are
C. 2 pairs οf parallel sides
D. 2 pairs οf sides with equal length
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The selling price of an article is N8,000.00. If it is sold at a loss of 20%. What was the cost price?
Answer:
sp= 8000.00.
loss percent= 20%
loss amount = 20% of sp
= 20÷100 × 8000
= 1600
now,
costprice = sp + loss amount
= 8000 + 1600
= 9600
A large mixing tank currently contains 300 gallons of water, into which 8 pounds of sugar have been mixed. A tap will open,
pouring 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 2 pounds
per minute. Find the concentration (pounds per gallon) of sugar in the tank after 10 minutes.
Answer:
the concentration of sugar in the tank after 10 minutes is approximately 0.056 pounds per gallon.
Step-by-step explanation:
Let's first calculate the amount of sugar that will be added to the tank during the 10 minutes:Amount of sugar added = rate of sugar * time = 2 pounds/minute * 10 minutes = 20 poundsThe initial amount of water in the tank is 300 gallons, and 20 gallons per minute are being added, so after 10 minutes, the amount of water in the tank will be:Amount of water in the tank = initial amount of water + rate of water * time = 300 gallons + 20 gallons/minute * 10 minutes = 500 gallonsTherefore, after 10 minutes, the total volume of the mixture in the tank will be 500 gallons, and the total amount of sugar in the tank will be 8 + 20 = 28 pounds.To find the concentration of sugar in the tank, we divide the total amount of sugar by the total volume of the mixture:Concentration of sugar = total amount of sugar / total volume of mixture = 28 pounds / 500 gallons ≈ 0.056 pounds per gallon
We can use the formula:
concentration = (total sugar added in pounds) / (total water in gallons)
First, we need to find out how much sugar is added in 10 minutes. Since sugar is being added at a rate of 2 pounds per minute , in 10 minutes, we will have:
total sugar added = 2 pounds/minute * 10 minutes = 20 pounds
Next, we need to find out how much water is in the tank after 10 minutes. Since water is being added at a rate of 20 gallons per minute , in 10 minutes, we will have:
total water added = 20 gallons/minute * 10 minutes = 200 gallons
Therefore, the total amount of water in the tank after 10 minutes is:
total water = 300 gallons (initial water) + 200 gallons (water added) = 500 gallons
Finally, we can calculate the concentration of sugar in the tank by plugging in the values:
concentration = total sugar added / total water
concentration = 20 pounds / 500 gallons
concentration = 0.04 pounds/gallon
Therefore, after 10 minutes, the concentration of sugar in the tank is 0.04 pounds per gallon.
THIS IS CONFUSSING!!! Select all the expressions that equivalent to 2 5/8.
262.5%
2.36
42 / 16
26.25%
2.625%
Step-by-step explanation:
The answer is 262.5%
5/8=5÷8=0.625
2 5/8=2.625
2.625=262.5%
262.5% and 2.625
Steps:5/8=5÷8=0.625 then 2 5/8=2.625 then we get 2.625=262.5%
All we do here Is divide then round It to the nearest 1, 10, or 100.
What Is Divide?
Division Is separate or be separated into parts, and noun of division Is a wide divergence between two groups, typically producing tension or hostility.
What Is round?
Adjusting the digits (up or down) to make rough calculations easier.
Hope This Helps!
I
I need to know this
The measures of the angles and arcs of the circle are;
11320317597824260853224The sum of the digits in the shaded = 1 + 3 + 7 + 2 + 3 + 4 + 6 = 26
26 - 14 = 12
Using the decoder wheel, we get; FVMMO
What is an arc of a circle?An arc is a portion or part of the circumference of the circle.
The arc angles from the diagrams indicates;
1. mPR = 90 + (90 - 67) = 113
2. mQST = mQR + mRST
mQST = 23 + 180 = 203
3. 8·x - 15 + (3·x + 8) = 180 (Linear pair angles)
11·x - 7 = 180
11·x = 187
x = 187/11 = 17
x = 17
4. LM = 3·x + 8
Therefore; LM = 3 × 17 + 8 = 59
LM = 59
5. m∠DAC = 156/2 = 78
6. mBC = 180 - 156 = 24
7. m∠ADB = 43
mAB = 43 × 2 = 86
mABD = 180 + 86 = 266
8. 2 × (7·x -3) = 17·x - 30
14·x - 6 = 17·x - 30
17·x - 14·x = 3·x = 30 - 6 = 24
x = 24/3 = 8
x = 8
9. m∠YZX = 7·x -3
m∠YZX = 7 × 8 - 3 = 53
m∠YZX = 53
10. m∠WXZ = 62/2 = 31
The angle formed by the intersection of WY and XZ is therefore;
mWZY = 180 - (2 × 53) + 63 = 137
mWXY = 180 - (2 × 31) + (17 × 8 - 30) = 224
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A rectangular piece of paper with length 30ft and width 24ft has two semicircles cut out of it. Find the area of the paper that remains. Use the value 3.14 for PIE , and do not round your answer.
Remark
I take it the semicircles cover the full width of the paper.
So the radius is [tex]24\div2 = 12 \ \text{cm}[/tex]
Since there are two of them, the area = a full circle.
Step One
Find the area of the rectangle before the cuts were made.
[tex]\text{Area = L} \times \text{W}[/tex]
[tex]\text{L = 30}[/tex]
[tex]\text{W = 24}[/tex]
[tex]\text{Area} = 30 \times 24 = 720 \ \text{cm}^2[/tex]
Step Two
Find the area of the circle cut outs.
[tex]\text{r} = 12[/tex]
[tex]\text{Area} = \pi \times \text{r}^2[/tex]
[tex]\text{Area} = 3.14 \times 12^2[/tex]
[tex]\text{Area} = 3.14 \times 144[/tex]
[tex]\text{Area} = 452.16 \ \text{cm}^2[/tex]
Step Three
Find the total area left
[tex]\text{Total Area Left = rectangle - circle}[/tex]
[tex]\text{Total Area Left} = 720 - 452.16[/tex]
[tex]\text{Total Area left} = 267.84 \ \text{cm}^2[/tex] Answer
The probability that Gerald makes a three-point shot in basketball is
20
%
20%20, percent. For practice, Gerald will regularly shoot a series of these shots until he succeeds at one. He's curious how many shots it will typically take him to get his first successful shot.
He simulated
40
4040 trials of three-point shots where each shot had a
0.2
0.20, point, 2 probability of being successful, and in each trial, he counted how many shots it took to get the first successful shot. Here are his results:
A dot plot for number of shots taken has a scale from 0 to 16. The number of dots for each is as follows. 0, 0. 1, 9. 2, 6. 3, 5. 4, 4. 5, 4. 6, 2. 7, 2. 8, 0. 9, 1. 10, 1. 11, 1. 12, 2. 13, 1. 14, 0. 15, 1. 16, 1.
Use his results to estimate the probability that it takes
10
1010 or fewer shots to get his first successful shot.
Give your answer as either a fraction or a decimal.
�
(
10
or fewer shots
)
≈
P(10 or fewer shots)≈P, left parenthesis, 10, start text, space, o, r, space, f, e, w, e, r, space, s, h, o, t, s, end text, right parenthesis, approximately equals
The estimated probability that it takes 10 or fewer shots to get his first successful shot is:
P(10 or fewer shots) ≈ 0.825
What is probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
To estimate the probability that it takes 10 or fewer shots to get his first successful shot, we need to add up the number of dots for the first 10 bars on the dot plot.
From the given dot plot, we can see that the number of dots for each value up to 10 shots are:
0 + 9 + 6 + 5 + 4 + 4 + 2 + 2 + 0 + 1 = 33
Therefore, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:
P(10 or fewer shots) ≈ 33/40
This can also be written as a decimal:
P(10 or fewer shots) ≈ 0.825
Hence, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:
P(10 or fewer shots) ≈ 0.825
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The total price of a shirt and a cap is $12. If the price of the shirt was doubled and the price of the cap was three times its original price, the total price of a shirt and a cap would be $26. The following system of equations models this scenario:
x + y = 12
2x + 3y = 26
What is the price of each shirt and cap?
1 The price of a shirt is $7, and the price of a cap is $5.
2 The price of a shirt is $8, and the price of a cap is $4.
3 The price of a shirt is $9, and the price of a cap is $3.
4 The price of a shirt is $10, and the price of a cap is $2.
Answer: Number 4 is the answer.
Hope this helps!
There was a sample of 600 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 8.4% each year.
Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams.
Write an exponential function showing the relationship between Y and t.
Answer: The decay rate is 8.4%, which means that the sample will have 91.6% of its original mass after one year, 91.6% of that amount after two years, and so on.
Therefore, we can write the relationship between y and t as:
y = 600 * (0.916)^t
This is an exponential decay function, where the initial value is 600 milligrams and the decay factor is 0.916 (1 minus the decay rate of 8.4%). As time t increases, the mass of the sample y decreases exponentially.
Step-by-step explanation: