a. The scatter plot of the data shows the incidence of diagnosed cases of celiac disease since 1950.
b. A linear regression model would best fit this data.
c. The equation for the curve of best fit is y = 0.603x + 8.821, where y represents the number of diagnosed cases of celiac disease (per 1000) and x represents the years since 1950.
d. Using the regression model, approximately 10.835 cases of celiac disease may be diagnosed in 2020.
a. To create a scatter plot of the data, we plot the number of diagnosed cases of celiac disease (y-axis) against the years since 1950 (x-axis). Each data point represents a pair of (x, y) values. For example, the first data point would be (0, 10), the second (8, 11), and so on.
b. In this case, a linear regression model would best fit the data because the scatter plot suggests a roughly linear relationship between the years since 1950 and the number of diagnosed cases of celiac disease.
c. To find the equation for the curve of best fit, we can use linear regression. We calculate the slope and intercept of the line that minimizes the sum of squared distances between the data points and the line. The equation of a line is y = mx + b, where m is the slope and b is the intercept. By performing linear regression on the given data points, we obtain the equation y = 0.603x + 8.821.
d. To estimate the number of diagnosed cases of celiac disease in 2020, we substitute x = 70 (since 2020 is 70 years since 1950) into the equation y = 0.603x + 8.821. Solving the equation, we find that y is approximately equal to 10.835. Therefore, using the regression model, around 10.835 cases of celiac disease may be diagnosed in 2020.
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Three of the cylinders in an eight-cylinder car are defective and need to be replaced. If two cylinders are selected at random (without replacement), what is the probability that two defective cylinders are selected? If two cylinders are selected at random (without replacement), what is the probability that at least one defective cylinder is selected?
Probability of selecting two defective cylinders ≈ 0.1071. Probability of selecting at least one defective cylinder ≈ 0.6429
To calculate the probability of selecting two defective cylinders when two cylinders are chosen at random without replacement, we need to consider the total number of cylinders and the number of defective cylinders. Given: Total number of cylinders: 8, Number of defective cylinders: 3. Probability of selecting two defective cylinders: To calculate this probability, we first need to determine the total number of ways to choose two cylinders out of the eight available. This can be calculated using the combination formula (nCr). Total ways to choose two cylinders out of eight: C(8, 2) = 8! / (2! * (8-2)!) = 28.
Next, we need to determine the number of ways to choose two defective cylinders out of the three available. Number of ways to choose two defective cylinders out of three: C(3, 2) = 3! / (2! * (3-2)!) = 3. Therefore, the probability of selecting two defective cylinders is: P(Two defective cylinders) = Number of ways to choose two defective cylinders / Total ways to choose two cylinders = 3/28 ≈ 0.1071 (rounded to four decimal places). Probability of selecting at least one defective cylinder: To calculate this probability, we can consider the complementary event, which is the probability of selecting no defective cylinders. Then, we subtract this probability from 1 to obtain the probability of selecting at least one defective cylinder.
Number of ways to choose two non-defective cylinders out of five remaining non-defective cylinders: C(5, 2) = 5! / (2! * (5-2)!) = 10. Total ways to choose two cylinders out of eight: C(8, 2) = 28 (as calculated earlier). Number of ways to choose at least one defective cylinder = Total ways to choose two cylinders - Number of ways to choose two non-defective cylinders= 28 - 10 = 18. Therefore, the probability of selecting at least one defective cylinder is: P(At least one defective cylinder) = Number of ways to choose at least one defective cylinder / Total ways to choose two cylinders= 18/28 ≈ 0.6429 (rounded to four decimal places).
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Scott and Letitia are brother and sister. After dinner, they have to do the dishes, with one washing and the other drying. They are having trouble deciding who will do what task, so they came up with a method based on probability. Letitia grabs some spoons and puts the is a bag. Some have purple handles and others have green handles. Scott has to pick two of the spoons. If their handles are the same, Scott will wash. If they are different colors, he will dry. It turns out there are two purple spoons and three green ones. What is the probability of Scott washing the dishes?
Answer:
The probability that Scott will wash is 2.5
Step-by-step explanation:
Given
Let the events be: P = Purple and G = Green
[tex]P = 2[/tex]
[tex]G = 3[/tex]
Required
The probability of Scott washing the dishes
If Scott washes the dishes, then it means he picks two spoons of the same color handle.
So, we have to calculate the probability of picking the same handle. i.e.
[tex]P(Same) = P(G_1\ and\ G_2) + P(P_1\ and\ P_2)[/tex]
This gives:
[tex]P(G_1\ and\ G_2) = P(G_1) * P(G_2)[/tex]
[tex]P(G_1\ and\ G_2) = \frac{n(G)}{Total} * \frac{n(G)-1}{Total - 1}[/tex]
[tex]P(G_1\ and\ G_2) = \frac{3}{5} * \frac{3-1}{5- 1}[/tex]
[tex]P(G_1\ and\ G_2) = \frac{3}{5} * \frac{2}{4}[/tex]
[tex]P(G_1\ and\ G_2) = \frac{3}{10}[/tex]
[tex]P(P_1\ and\ P_2) = P(P_1) * P(P_2)[/tex]
[tex]P(P_1\ and\ P_2) = \frac{n(P)}{Total} * \frac{n(P)-1}{Total - 1}[/tex]
[tex]P(P_1\ and\ P_2) = \frac{2}{5} * \frac{2-1}{5- 1}[/tex]
[tex]P(P_1\ and\ P_2) = \frac{2}{5} * \frac{1}{4}[/tex]
[tex]P(P_1\ and\ P_2) = \frac{1}{10}[/tex]
Note that: 1 is subtracted because it is a probability without replacement
So, we have:
[tex]P(Same) = P(G_1\ and\ G_2) + P(P_1\ and\ P_2)[/tex]
[tex]P(Same) = \frac{3}{10} + \frac{1}{10}[/tex]
[tex]P(Same) = \frac{3+1}{10}[/tex]
[tex]P(Same) = \frac{4}{10}[/tex]
[tex]P(Same) = \frac{2}{5}[/tex]
12.75 x 2 plus 13 x 3 plus 13.25 x 4 plus 13.5 x 3 PLEASE HELPPP QWICKKKK
Answer:
158
Step-by-step explanation:
In OK, which arc is a major arc?
G
H
74
K
A GEI
C FJG
D IJF
B HIJ
Answer:
D
i thank
Step-by-step explanation:
A.
f(x) = -4|x + 2| + 3
B.
f(x) = 4|x + 2| + 3
C.
f(x) = -4|x − 2| − 3
D.
f(x) = 4|x + 2| − 3
Answer:
D
Step-by-step explanation:
Which rule can be used to show that the two triangles above are similar?
SSS
SAS
ASA
Answer:
Step-by-step explanation: 675 ssa SAS 342w
Help me please....... :(
Answer:
The Degree of the polynomial is 3
A project has the following projected outcomes in dollars: $240, $310, and $560. The probabilities of their outcomes are 20%, 60%, and 20% respectively. What is the expected value of these outcomes?
If the probabilities of their outcomes are 20%, 60%, and 20% respectively, the expected value of these outcomes is $346.
To calculate the expected value of the outcomes, we multiply each outcome by its corresponding probability and then sum up the results.
In this case, the projected outcomes are $240, $310, and $560, with probabilities of 20%, 60%, and 20% respectively.
To calculate the expected value, we use the formula:
Expected value = (Outcome 1 * Probability 1) + (Outcome 2 * Probability 2) + (Outcome 3 * Probability 3) + ...
Expected value = ($240 * 0.20) + ($310 * 0.60) + ($560 * 0.20)
Expected value = $48 + $186 + $112
Expected value = $346
The expected value represents the average value or the long-term average outcome we can expect from the given probabilities and outcomes. It provides a summary measure that helps in understanding the central tendency of the distribution of outcomes.
In this case, the expected value indicates that, on average, we can expect the project's outcome to be around $346.
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Given m
n, find the value of x and y.
(37-18)
(8x+12)
m
(2X+18)
n
Answer:
Step-by-step explanation:
The two inside angles will sum to 180°.
The top to angles are equal.
Think about this as what if both of the parallel lines were intersected by a perpendicuar line. Every angle would be a right triangle 90°. The inside angles will sum to 180° and the opposite angles are again equal.
(2x + 18) + (8x + 12) = 180
10x + 30 = 180
10x = 150
x = 15
-------------------------
(3y - 18) = (8x + 12) x = 15
(3y - 18) = (8(15) + 12)
(3y - 18) = (120 + 12)
(3y - 18) = 132
3y = 132 + 18
3y = 150
y = 50
Juan earns a flat fee of $150 plus $20 for every hour he works decorating 5 points
a house. Which graph correctly displays Juan's earnings?
Answer: The 3rd one is the correct answer
Step-by-step explanation:
What's the number between 1.35 and 1.351
Answer: + 1000
Step-by-step explanation:
Describe this sampling method: "Survey the first 40 students who enter the main
office".
Answer:
Convenience sampling
Step-by-step explanation:
From the question, we understand that 40 of all students are to be surveyed. This implies that from the 41st till the last student will not be a part of the survey.
When sampling is done, taking a part of the whole population that is near or readily available; such sampling is referred to as convenience sampling.
The whole population, in this case are all students while the convenience being selected are the first 40 students.
Write the equation of a line that passes through the points (-2,-9) and (2,-9).
Answer:
mhmm feels so good
Step-by-step explanation:
The table below shows the number of families living in the city of Sunnyvale from 1965 to 2000. Year (after 1900) Number of Families (thousand) 65 O 31.1 70 T 30.5 75 2 30.1 80 2 28.7 85 4 27.1 90 5 25.7 95 6 23.2 20.3 2000 100 7 2015+7 -22 According to the best-fit quadratic model, approximately how many families will live in Sunnyvale in 2015? A. 18,000 y=-0.19378x² -0.15x65x +31.0148 B. 16,000 C. 14,000 D. 10,000 TI-84 Plus CE NORMAL FLOAT AUTO REAL RADIAN MP L1 L2 L3 L5 L4 0 123H567 4 ‒‒‒‒‒‒ L1(1)=0 31.1 30.5 30.1 28.7 27.1 25.7 23.2 20.3 TI-84 Plus CE NORMAL FLOAT AUTO REAL RADIAN MP QuadReg y=ax2+bx+c a= -0.1937822868 b=-0.1526507689 c=31.01480998
The best-fit quadratic model is given by the equation y = -0.19378x² - 0.15265x + 31.0148, where x represents the year after 1900.
According to the best-fit quadratic model obtained from the data, approximately 14,000 families will live in Sunnyvale in 2015.
To estimate the number of families in 2015, we substitute x = 115 (2015 - 1900) into the quadratic model:
y = -0.19378(115)² - 0.15265(115) + 31.0148
≈ 14,000
Therefore, based on the best-fit quadratic model, it is estimated that approximately 14,000 families will live in Sunnyvale in 2015. The model is obtained by performing a quadratic regression using the given data points, and it provides a reasonable estimate for the number of families in 2015 based on the trend observed in the data.
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Paulie’s pizza is considering expanding into the pizza truck business. They calculate that the costs of a pizza truck will be $1,420 per month. If they sell pizzas for $12 each, how many will they have to sell in a month to make a profit of at least $3,400
Answer:
283 1/3 pizzas
Step-by-step explanation:
I did 3,400 div 12 = 1,420
Just look at the picture
Answer:
I believe it is 60
Step-by-step explanation:
It's going to be COS and since you don't have and angle you are going to click [tex]cos^{-1}[/tex] and then type in 9/18 so it should look like this
[tex]cos^{-1}(9/18) = 60[/tex]
Which pair shows equivalent expressions?
2(x+2) = 2x+1
02(x+2) = x+4
02(x+4)=x+2
02(x+4)= 2/x+8
Answer:
2(x+2) = x+4
Step-by-step explanation:
The pair that shows equivalent expressions is:
2(x+2) = x+4
This is because when we distribute the 2 to the terms inside the parentheses, we get:
2x + 4 = x + 4
By subtracting x from both sides of the equation, we get:
2x - x + 4 = 4
Simplifying further, we have:
x + 4 = 4
Therefore, the expression 2(x+2) is equivalent to x+4.
Hope this helps!
bill is trying to plan a meal to meet specific nutritional goals. he wants to prepare a meal containing rice, tofu, and peanuts that will provide 312 grams of carbohydrates, 328 grams of fat, and 180 grams of protein. he knows that each cup of rice provides 46 grams of carbohydrates, 0 grams of fat, and 2 grams of protein. each cup of tofu provides 6 grams of carbohydrates, 12 grams of fat, and 15 grams of protein. finally, each cup of peanuts provides 26 grams of carbohydrates, 70 grams of fat, and 28 grams of protein. how many cups of rice, tofu, and peanuts should he eat?
Bill should eat 4 cups of rice, 4 cups of tofu, and 4 cups of peanuts to meet his specific nutritional goals.
To determine how many cups of rice, tofu, and peanuts Bill should eat, we need to set up a system of equations based on the given nutritional information. Let's denote the number of cups of rice, tofu, and peanuts as x, y, and z respectively.
Based on the given information, we can establish the following equations
Carbohydrate equation: 46x + 6y + 26z = 312
Fat equation: 0x + 12y + 70z = 328
Protein equation: 2x + 15y + 28z = 180
We now have a system of three equations that we can solve to find the values of x, y, and z.
Using any appropriate method to solve the system of equations, we find
12y + 70z = 328
y = 328 - 70z/12
y = 27.33 - 5.833z
putting the value of y in both equation
2x + 15(27.33 - 5.833z ) + 28z = 180
2x + 28z + 409.95 - 87.45z = 180
(2x - 59.45z = -391.95)23
46x - 1367.35z = - 9014.85
46x + 6(27.33 - 5.833z) + 26z = 312
46x + 163.98 - 34.998z + 26z = 312
46x - 8.998z = 148.02
equation both equation
- 8.998z + 1367.35z = 9014.85 + 148.02
z = 9162.87/1358.352
z ≈ 4
Solving equation we get
x = 4 cups of rice
y = 4 cups of tofu
z = 4 cups of peanuts
Therefore, Bill should eat 4 cups of rice, 4 cups of tofu, and 4 cups of peanuts to meet his nutritional goals.
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A number of days, d, of sunshine is not 28.
Answer:
D<28
Step-by-step explanation:
The required inequality for the given situation can be, d > 28 or d < 28
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, write an inequality for the situation.
Situation :-
A number of days, d, of sunshine is not 28.
Here, the number of days is said to be not equal to 28, we are not given if is less or more,
It can be less or more than 28 but not 28
So, here we get two situations,
Either, the number of days, d, of sunshine is less than 28, or the number of days, d, of sunshine is more than 28.
If we write these situations, mathematically, the inequalities we will have, are :-
1) The number of days, d, of sunshine is less than 28 :-
d < 28
2) The number of days, d, of sunshine is more than 28 :-
d > 28
Therefore, the two inequalities, are :- d < 28 or d > 28
Hence, the required inequality for the given situation can be, d > 28 or d < 28
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The complete question is :-
Write an inequality for the situation.
A number of days, d, of sunshine is not 28 .
graph the solution to the inequality on the number line. y<43.5
The solution to the inequality y < 43.5 can be graphed on a number line. The graph will show all the values of y that are less than 43.5.
To graph the solution to the inequality y < 43.5 on a number line, we start by marking the point 43.5 on the number line. Since the inequality is y < 43.5, we represent it with an open circle at 43.5 to indicate that 43.5 itself is not included in the solution.
Next, we shade the region to the left of the open circle. This shaded region represents all the values of y that are less than 43.5, including any negative values and values approaching negative infinity.
The resulting graph on the number line will show a shaded region to the left of the open circle at 43.5, indicating that all values of y in that region satisfy the inequality y < 43.5.
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PLEASE HELP ME ANSWER QUICK!! (Volume)
Answer:
V = 50 m³
Step-by-step explanation:
The formula for the volume of a pyramid of base area b and height h is V = (1/3)(b)(h).
Here the volume is V = (1/3)(5 m)²(6 m), or V = 50 m³
I NEED HELP!!! :((((
Answer:
it represents a polynomial
Can someone please help
Answer:
First row of blanks: -3 -3
Second row of blanks: 2 2 3
Third row blank: 6
Step-by-step explanation:
x/2 + 3 = 6
The objective is to isolate the variable:
Subtract both sides by 3
x/2 = 3
Multiply both sides by 2
x = 6
B.
The number of flowers in Lito's garden is represented as follows.
Gumamela
Orchid
Answer:
5 :12 ; what is the ratio of the number of gumamela to the total number of flowers
5 : 7 ; what is the ratio of the number of gumamela to the number of orchids
7:5 ; what is the ratio of the number of orchids to the number of gumamela
12 : 5 ; what is the ratio of the total number of flowers to the number of gumamela
12 : 7 ; what is the ratio of the total number of flowers to the number of orchid
Step-by-step explanation:
Ratios of a to b ;is written as a : b
Ratio of b to a is written as b : a
The ratio of a to the sum of a and b equals ;
a : (a + b)
Number of orchids = 7
Number of gumamela = 5
Total number of flowers = 7 + 5 = 12
Ratio two quantities are compared. A number of times a number contains another. It makes value comparisons. When two components of the same unit are compared, it is possible to determine how much of one number is represented in the other. The quotient of two mathematical equations is shown.
5:12 And what's the proportion from gumamela the total flowers in the garden?7:12 And what's the proportion of orchids in the field to the total number of flowers?5:7 And what's the number of gumamela to orchids ratio?7:5 And what's the orchid-to-gumamela ratio?12:12 What is the proportion of gumamela or orchids in the field to the overall flowers?Learn more:
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A function that increases proportionally to its current value. The larger the function gets, the faster it increases.
is it a science question
10 people can paint a building in 5 days. If each person paints as quickly as the others then how much of the building could 7 people paint in 5 days?
A.7/5
B.5/7
C.7/10
D.10/7
Answer:
C
20 character minimum
Un conductor circula a 12 m/s. Acelera y pasa a circular a 20 m/s al cabo de 10 segundos. Calcula la aceleración del coche.
Answer:
Aceleracion = 0.8 m/s²
Step-by-step explanation:
Dados los siguientes datos;
Velocidad inicial = 12 m/s
Velocidad final = 20 m/s
Tiempo, t = 10 segundos
Para encontrar la aceleración;
Aceleración se puede definir como la tasa de cambio de la velocidad de un objeto con respecto al tiempo.
Esto simplemente significa que la aceleración viene dada por la resta de la velocidad inicial de la velocidad final a lo largo del tiempo.
Por lo tanto, si restamos la velocidad inicial de la velocidad final y la dividimos por el tiempo, podemos calcular la aceleración de un objeto. Matemáticamente, la aceleración viene dada por la fórmula;
[tex] Aceleracion = \frac{final \; velocidad - inicial \; velocidad}{tiempo}[/tex]
Sustituyendo en la fórmula, tenemos;
[tex] Aceleracion = \frac{20 - 12}{10}[/tex]
[tex] Aceleracion = \frac{8}{10}[/tex]
Aceleracion = 0.8 m/s²
A student deposited money into a savings account. The following equation models the amount of money in the account, A(1), after t years. A(1)-1575 (1.045) a. State the initial amount of money deposited into the account. b. Determine the annual interest rate being paid on the account. C. Use the equation to find the amount of money, to the nearest dollar, in the account after 15 years. d. How many years, to the nearest whole year, will it take for the account to have at least $4000?
a. The initial amount of money deposited into the account is $1575.
b. The annual interest rate being paid on the account is 4.5%.
c. The amount of money in the account after 15 years is approximately $2946.27.
d. It will take approximately 20 years for the account to reach a balance of at least $4000.
To answer these questions, let's analyze the given equation:
A(1) = 1575 * (1.045)^t
a. The initial amount of money deposited into the account is $1575. This is evident from the equation, where A(1) represents the amount of money after 1 year.
b. To determine the annual interest rate, we can compare the given equation with the general formula for compound interest:
A = P * (1 + r)^t
Comparing the two equations, we can see that the interest rate in the given equation is 4.5% (0.045) since (1 + r) is equal to 1.045.
c. To find the amount of money in the account after 15 years, we can substitute t = 15 into the equation and calculate the result:
A(15) = 1575 * (1.045)^15 ≈ $2946.27 (rounded to the nearest dollar)
Therefore, after 15 years, the amount of money in the account will be approximately $2946.
d. To find the number of years it will take for the account to have at least $4000, we need to solve the equation for t. Let's set up the equation and solve for t:
4000 = 1575 * (1.045)^t
To solve this equation, we can take the logarithm of both sides (with base 1.045):
log(4000) = log(1575 * (1.045)^t)
Using logarithm properties, we can simplify the equation:
log(4000) = log(1575) + log((1.045)^t)
log(4000) = log(1575) + t * log(1.045)
Now, we can isolate t by subtracting log(1575) from both sides and then dividing by log(1.045):
t = (log(4000) - log(1575)) / log(1.045)
Calculating this expression, we find:
t ≈ 19.56 (rounded to two decimal places)
Therefore, it will take approximately 20 years (rounded to the nearest whole year) for the account to have at least $4000.
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Solve 3(x - 2) < 18
Hi there!
[tex]\large\boxed{x < 8}[/tex]
3(x - 2) < 18
Begin by dividing both sides by 3:
3(x - 2)/3 < 18/3
x - 2 < 6
Add 2 to both sides:
x - 2 + 2 < 6 + 2
x < 8
x< 8
Hope this is the answer you are looing for.
When two basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical order? Assume each player has a different name. P(shoot free throws in alphabetical order) - (Type an integer or a simplified fraction)
The probability that they shoot free throws in alphabetical order depends on the number of players participating. If there are only two players, the probability would be 1/2 or 0.5.
Since each player has a different name, there are only two possible orders in which they can shoot free throws: alphabetical order or reverse alphabetical order. Out of these two possibilities, only one is the desired outcome (alphabetical order). Therefore, the probability of shooting free throws in alphabetical order is 1 out of 2, which can be expressed as 1/2 or 0.5
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