The angle of D is 98 degree.
Supplementary Angles:Any two angles that sum up to 180° are called supplementary angles. Observe the following figure which shows two angles 130° and 50° and since they add up to 180°, they are called supplementary angles. In other words, angle 1 and angle 2 are supplementary, if Angle 1 + Angle 2 = 180°. In this case, Angle 1 and Angle 2 are called 'supplements' of each other.
A quadrilateral ABCD is cyclic if and only if its opposite
angles are supplementary.
A and C are opposite angles, so they are supplementary
m ∠A + m ∠C = 180
9x - 1 + 64 = 180
9x + 63 = 180
9x = 117
x = 13
m ∠B = 6x+4 = 6(13)+4 = 82
B and D are opposite angles, so they are supplementary
m ∠B + m ∠D = 180
82 + m ∠D = 180
m∠D = 98°
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The function y = 575 (1.14)^t represents exponential growth and has a percent rate of change of __%
The function y = 575 (1.14)^t represents exponential growth and has a percent rate of change of 13.08 %
The given function is y = 575 \((1.14)^t,\) which represents exponential growth. We are asked to find the percent rate of change of this exponential function.
To determine the percent rate of change, we need to calculate the derivative of the function with respect to t. The derivative represents the instantaneous rate of change of the function.
Let's differentiate the function y = 575 (1.14)^t with respect to t using the power rule of differentiation:
dy/dt = 575 * ln(1.14) * (1.14)^t
Here, ln(1.14) is the natural logarithm of 1.14, which is approximately 0.1311.
Simplifying the expression, we have:
dy/dt ≈ 75.332 * \((1.14)^t\)
The percent rate of change can be calculated by dividing the derivative by the initial value of the function (y) and multiplying by 100:
Percent rate of change = (dy/dt) / y * 100
Substituting the values, we have:
Percent rate of change ≈ [75.332 * (1.14)^t] / [575 * (1.14)^t] * 100
The\((1.14)^t\) terms cancel out, leaving us with:
Percent rate of change ≈ 75.332 / 575 * 100
Simplifying further, we have:
Percent rate of change ≈ 13.08%
Therefore, the percent rate of change of the exponential growth function y = 575 (1.14)^t is approximately 13.08%.
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Which graph below is a function?
Answer:
the one below the the circle one
for a standard normal distribution, the probability of obtaining a z value between -2.4 to -2.0 is
The required probability of obtaining a z value between -2.4 to -2.0 is 0.0146.
Given, for a standard normal distribution, the probability of obtaining a z value between -2.4 to -2.0 is.
Now, we have to find the probability of obtaining a z value between -2.4 to -2.0.
To find this, we use the standard normal table which gives the area to the left of the z-score.
So, the required probability can be calculated as shown below:
Let z1 = -2.4 and z2 = -2.0
Then, P(-2.4 < z < -2.0) = P(z < -2.0) - P(z < -2.4)
Now, from the standard normal table, we haveP(z < -2.0) = 0.0228 and P(z < -2.4) = 0.0082
Substituting these values, we get
P(-2.4 < z < -2.0) = 0.0228 - 0.0082= 0.0146
Therefore, the required probability of obtaining a z value between -2.4 to -2.0 is 0.0146.
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A jar contains 125 marbles. Given 2% of the marbles are green, 54% of the marbles are blue, and the rest are red, how many red marbles are in the jar?
there are 55 red marbles in the jar
Answer:
There are 55 red marbles in the jar.
Step-by-step explanation:
Green marbles = 125 x 2/100 = 2.5
Blue marbles = 125 x 54/100 = 67.5
Red marbles = 125 - 67.5 - 2.5 = 55
Suppose f(x) = - 3x² + 9x − 2. Compute the following:
A.) ƒ( − 2) + f(1) =
B.) ƒ( − 2) – ƒ(1) =
Step-by-step explanation:
\( f(x) = - 3 {x}^{2} + 9x - 2\)
A) f(-2) + f(1) = -32 + 4 = -28
B) f(-2) - f(1) = -32 - 4 = -36
Chase is moving and must rent a truck. There is an initial charge of $35 for the rental plus a fee of $2.50 per mile driven. Make a table of values and then write an equation for C,C, in terms of m,m, representing the total cost of renting the truck if Chase were to drive m miles.
The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.
What is the equation?Equation: A declaration that two expressions with variables or integers are equal.
In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance.
The equation would be:
C is the total cost and m is the miles driven.
We know that:
Charge of the truck: $35
Charge per mile: $2.50
Then, form the equation as follows:
C = 35 + 2.50m
Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.
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use the Chain Rule to find ∂z/∂u when z = er cos θ and r= 6 uv , θ = √(u^2+v^2 )
This is the expression for ∂z/∂u using the Chain Rule.
To find ∂z/∂u using the Chain Rule, we first need to find the partial derivative of z with respect to r and θ.
∂z/∂r = e^(r cos θ) cos θ
∂z/∂θ = -e^(r cos θ) r sin θ
Next, we can use the Chain Rule to find ∂z/∂u:
∂z/∂u = (∂z/∂r) * (∂r/∂u) + (∂z/∂θ) * (∂θ/∂u)
We know that r= 6 uv and θ = √(u^2+v^2 ), so we can substitute those values in:
∂z/∂u = (e^(r cos θ) cos θ) * (6v) + (-e^(r cos θ) r sin θ) * (u/√(u^2+v^2 ))
Simplifying this expression, we get:
∂z/∂u = 6ve^(6uv cos(√(u^2+v^2 )))cos(√(u^2+v^2 )) - (u/√(u^2+v^2 ))e^(6uv cos(√(u^2+v^2 )))r sin(√(u^2+v^2 ))
We have z = e^(r cos θ), r = 6uv, and θ = √(u^2 + v^2). We need to find ∂z/∂u.
Using the Chain Rule, we get:
∂z/∂u = (∂z/∂r)(∂r/∂u) + (∂z/∂θ)(∂θ/∂u)
First, let's find the partial derivatives of z:
∂z/∂r = e^(r cos θ) cos θ
∂z/∂θ = -e^(r cos θ) r sin θ
Now, find the partial derivatives of r and θ with respect to u:
∂r/∂u = 6v
∂θ/∂u = u / √(u^2 + v^2)
Now, substitute these partial derivatives back into the Chain Rule formula:
∂z/∂u = (e^(r cos θ) cos θ)(6v) + (-e^(r cos θ) r sin θ)(u / √(u^2 + v^2))
This is the expression for ∂z/∂u using the Chain Rule.
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Let I and J be ideals and P a prime ideal of R. Prove that if I J ⊆ P then I ⊆ P or J ⊆ P.
We have shown that if IJ ⊆ P, then either I ⊆ P or J ⊆ P. Hence, the statement is proven, for I and J be ideals and P a prime ideal of R. Since P is prime, so we have the following inequality:(I intersection P) (J intersection P) ⊆ P²
Now, since P is prime so P² is a prime ideal too, thus one of the ideals I intersection P and J intersection P must be contained in P.
If I intersection P ⊆ P, then I ⊆ P. If J intersection P ⊆ P, then J ⊆ P. Therefore, I ⊆ P or J ⊆ P.
To prove the statement, let's assume that I and J are ideals of a ring R, and P is a prime ideal of R. We want to show that if IJ ⊆ P, then either I ⊆ P or J ⊆ P.
Suppose that IJ ⊆ P, We will proceed by contradiction.
Assume that I is not contained in P, which means there exists an element a ∈ I such that a ∉ P.
Since P is a prime ideal, it is closed under multiplication, so aJ ⊆ PJ ⊆ P.
Now consider the product (aJ)(a⁻¹). Since a ∉ P, a⁻¹ ∈ R\P (the complement of P in R).
Therefore, (aJ)(a⁻¹) ⊆ P(a⁻¹), and we have:
aJ ⊆ P(a⁻¹)
Multiplying both sides by a, we get:
a(aJ) ⊆ a(P(a⁻¹))
a²J ⊆ Pa⁻¹
Since J is an ideal, a²J ⊆ aJ ⊆ P(a⁻¹), and by induction,
we have aⁿJ ⊆ Pa⁻ⁿ for any positive integer n.
Consider the element aⁿ ∈ aⁿJ.
Since aⁿJ ⊆ Pa⁻ⁿ, aⁿ ∈ Pa⁻ⁿ.
This implies that aⁿ is an element of the prime ideal P for any positive integer n.
Since R is a ring, there exists a positive integer m such that aᵐ = aᵐ⁺¹ for some m⁺¹ > m.
This means that aᵐ (a - 1) = 0.
Since aᵐ ∈ P and P is a prime ideal, either a or (a - 1) must be in P.
If a is in P, then I ⊆ P, which is one of the conditions we want to prove.
If (a - 1) is in P, then consider the element 1 ∈ R. Since (a - 1) is in P, we have 1 - (a - 1) = a ∈ P.
This implies J ⊆ P, which is the other condition we want to prove.
In either case, we have shown that if IJ ⊆ P, then either I ⊆ P or J ⊆ P. Hence, the statement is proven.
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$700 is deposited in an account with 5% interest rate, compounded continuously. What is the balance after 12 years?
Step-by-step explanation:
Continuous compounding formula
FV = PV e^(rt) PV = $ 700 r = .05 t = 12
FV = future value = $ 700 e^(.05 * 12) = $ 1275.48
the smith family consists of a mother, father, and some children. the average age of the family is 20 yrs. old. the father is 48 yrs. old, and the average age of the mother and children is 16. how many children are in the smith family?
This is a contradiction, which means that our initial assumption that there are n children is incorrect. Therefore, there is no solution to this problem that satisfies the given conditions.
Let's assume that there are n children in the Smith family.
We know that the father is 48 years old, so the sum of the ages of the mother and children is:
Total age = (n + 1) * 20 (as there are n children and 1 father)
And we also know that the average age of the mother and children is 16, so we can write:
Total age / (n + 1) = 16
Combining these two equations, we get:
(n + 1) * 20 / (n + 1) = 16
Simplifying, we get:
20 = 16
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if answers correct you get brainist!
Two firms producing identical products engage in price competition. Cost of firm 1 is $20 per unit produced and cost of firm 2 is $15 per unit produced. There are no fixed costs. Firms produce only after they learn the quantity demanded. Each firm can choose any real number in the interval [15,25] as its price.
For tie-breaking we will assume that if both firms set the same price, all consumers purchase from firm 2.
The payoff/profit function of firm 1 is:
(p1 - 20)(100 - p1) if p1 is less than or equal to p2,
0 if p1 is greater than p2
The payoff/profit function of firm 2 is:
(p2 - 15)(100 - p2) if p2 is less than p1,
0 if p2 is greater than or equal to p1
Given all of this information, solve the following parts of the problem:
a) is p1 = 20, p2 = 19.50 a Nash Equilibrium?
b) is there a Nash Equilibrium in which Firm 2 makes a positive profit?
c) How many strategies does player 1 have?
d) is p1 = 15, p2 = 15 a Nash Equilibrium?
e) is p1 = 21, p2 = 21 a Nash Equilibrium?
a) No, p1 = 20, p2 = 19.50 is not a Nash Equilibrium.
b) Yes, there is a Nash Equilibrium in which Firm 2 makes a positive profit.
c) Player 1 has infinitely many strategies.
d) Yes, p1 = 15, p2 = 15 is a Nash Equilibrium.
e) No, p1 = 21, p2 = 21 is not a Nash Equilibrium.
What is Nash Equilibrium?Nash Equilibrium is a state of a strategic game where no player has an incentive to deviate from his or her chosen strategy after considering the strategies of other players. A game has more than one Nash equilibrium if players are unable to agree on a cooperative strategy to play.
Finding Nash Equilibrium
a) Is p1 = 20, p2 = 19.50 a Nash Equilibrium?No. Firm 1 has an incentive to decrease the price to 19.49, thus breaking the tie in its favour. So p1=20, p2=19.5 is not a Nash equilibrium.b) Is there a Nash Equilibrium in which Firm 2 makes a positive profit?Yes. There are several equilibria in which Firm 2 makes a positive profit. One such equilibrium is when both firms charge the same price of 15, at which both firms earn a profit of 375.c) How many strategies does player 1 have?Player 1 has infinitely many strategies to choose from as they can choose any real number in the interval [15,25] as their price.d) Is p1 = 15, p2 = 15 a Nash Equilibrium?Yes. This is a Nash Equilibrium because neither firm has an incentive to change their strategy as they are earning non-zero profits. Both firms earn a profit of 375.e) Is p1 = 21, p2 = 21 Nash Equilibrium?No. If Firm 1 changes its price to 20.99, its profit increases from 405 to 407.99. Therefore, p1=21 and p2=21 is not a Nash Equilibrium.Learn more about Nash equilibrium at
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Find all real numbers x such that 3x - 4 < 5 and -8x - 19 < 21
Answer:
the numbers are -5 and 3
Step-by-step explanation:
First of all, the question is asking you to find the values of x from the given inequalities.
-8x -19<21 and 3x - 4 < 5
group all liked terms, in other words, make x and its coefficient stand alone.
-8x < 21 + 19 and 3x < 5 + 4
-19 became +19 because it crossed the sign <, also -4 became +4 because it crossed the sign <.
so we get
-8x < 40 and 3x < 9
we divide each "x" by its coefficient
\( \frac{ - 8x}{ - 8} < \frac{40}{ - 8} \: and \: \frac{3x}{3} < \frac{9}{3} \)
then we get
x < -5 and x < 3
but x is positive so it's greater than -5 so we get
x > -5 and x < 3
triangle
please solve asap
a) since all the angles on the triangle are next to a given angle we just subtract the given angle from 180 to find the unknown angle
180-150=30=x
180-80=100=y
180-130=50=z
Sum of All triangles angles is always 180 degrees but we can still check
30+100+50
130+50=180
Now for the B triangle every angle is across from it like this means the triangle angle is equal to that
a= 40 degrees
b= 95 degrees
c= 45 degrees
And this also equal 180 degrees
Hopes this helps please mark brainliest
Answer:
1st Question Answer:
X=30
y=100
z=50
2nd Question Answer:
a=40
b=95
C=45
Step-by-step explanation:
1st Question : Since the angles of a straight line add up to 180 , we can subtract the degree of the angle given by 180 which gives us the answer . also we can make certain the angle is right because angles of a traingle add up to 180
2nd Question: Since the angles in the second question are parallel (which means they are the same) . we can easily find the answer . we can make sure the answer is right by using the same way ( angles of a triangle add up to 180)
PLS HELP ASAP I NEED IT PLS PLS PLS
I WILL MARK BRAINLIST AND SET THIS 100 POINTS BUT PLS ANSWER CORRECTLY.THIS IS GRADED OUT OF 100% I need 80% to pass for an A- PLS YALL!
Answer:
x=105
Step-by-step explanation:
The angles of a triangle add up to 180 degrees.
\(180 = 30 +45+x\)
\(x=105\)
which sampling method is being described
A store manger randomly choose a shopper entering her store to interview she then interview every 20th person after that contomer
to do the survey
Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants.
The sampling method described in the scenario is called systematic sampling.
Systematic sampling involves selecting every nth element from a population after randomly selecting a starting point. In this case, the store manager randomly chooses a shopper entering the store as the starting point and then proceeds to interview every 20th person after that initial selection.
Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants. By ensuring a regular interval between selections, systematic sampling provides a representative sample from the population.
However, it's important to note that systematic sampling can introduce a form of bias if there is any periodicity or pattern in the population. For example, if the store experiences a peak in customer traffic during specific time periods, the systematic sampling method might overrepresent or underrepresent certain groups of shoppers.
To minimize this potential bias, the store manager could randomly select the starting point for the systematic sampling at different times of the day or on different days of the week. This would help ensure a more representative sample and reduce the impact of any inherent patterns or periodicities in customer behavior.
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Find the absolute maximum and minimum for the given graph. Give your answer as an ordered pair. 4 3 -5 -4 -3 12 1 2 3 -2 -3 Y4 Absolute maximum: Absolute minimum:
Absolute maximum: (0,4) Since it is the highest point in the interval.
Absolute minimum: (-3,-5) Since it is the lowest point in the interval.
Choose all the fractions that are equivalent to 4/8 A.26 B.1/2 C.3/6 D.8/16 E.7/11 F.5/10
Answer:
B, C, D, F
Step-by-step explanation:
4/8 is equivilant to 1/2 because 4 is half of 8. Therefore, 3 is half of 6 and 8 is half of 16. 7 is half of 14 so 7/11 is not equivilant to 4/8.
Hope I helped.
describe these uses for the const keyword const distance d( 1, 2.2 )
The main use of the `const` keyword in the given code snippet is to declare a constant object named `d` of the class `distance`. This means that the object `d` cannot be modified once it is initialized.
In C++, the `const` keyword is used to define constants or variables that cannot be modified. When applied to an object, it ensures that the object's state remains constant and cannot be changed. In the context of the code snippet, the object `d` is declared as a constant object of the class `distance` with initial values of 1 and 2.2 for its member variables.
By declaring `d` as a constant object, the code expresses the intention to prevent any modifications to its values throughout the program execution. This can be useful in scenarios where the object represents a fixed measurement or a constant value that should not be altered accidentally or intentionally.
The `const` keyword provides benefits such as code clarity, as it clearly indicates the immutability of the object, preventing accidental modifications. It also helps enforce good programming practices by ensuring that the object's state remains constant, reducing potential bugs or unintended side effects.
Additionally, using the `const` keyword enables the compiler to perform optimizations, as it knows that the object's state won't change, allowing for potential code optimizations and improved performance.
Overall, the `const` keyword is used to declare constant objects, providing immutability and promoting code clarity and optimization.
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if we build a na¨ıve bayes classifier, how many independent parameters are there in total?
In summary, we are asked to determine the number of independent parameters in a Naive Bayes classifier. The Naive Bayes classifier is a probabilistic machine learning model that assumes independence between features given the class label.
To calculate the number of independent parameters, we need to consider the number of features and the number of classes in the dataset. For each feature, the classifier estimates the conditional probability of that feature given each class. . Therefore, the total number of independent parameters in the Naive Bayes classifier can be calculated by multiplying the number of features by the number of classes, and then multiplying the result by the number of possible values for each feature. For example, if we have m features, k classes, and n possible values for each feature, the total number of independent parameters would be m k n. Each independent parameter represents a specific conditional probability value in the Naive Bayes model. It's important to note that the Naive Bayes assumption of feature independence simplifies the model and reduces the number of parameters required for training. However, it also introduces a limitation in cases where the features are not truly independent.
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Enter the value that belongs in the
green box.
57°
Х
Z
33
25
tan 33
Answer:
x
Step-by-step explanation:
tan33° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{25}\)
Can Someone Please Help Me?
Answer:
The answer is c
Step-by-step explanation:
A couple decides to keep having children until they have a girl, at which point they will stop having children. They also agree to having a maximum of three children. The table below shows the probability distribution of X=, equals the number of children such a couple would have.
X=# of children 1 2 3
P(X), .5 .25 .25
Given that \mu_X=1.75μ
X
=1.75mu, start subscript, X, end subscript, equals, 1, point, 75 children, find the standard deviation of the children such a couple would have.
Round your answer to two decimal places.
\sigma_X\approxσ
X
≈sigma, start subscript, X, end subscript, approximately equals
children
Answer:.83
Step-by-step explanation:
Khan academy
From the discrete distribution given, the standard deviation is of 0.83 children.
The distribution is:
\(P(X = 1) = 0.5\)
\(P(X = 2) = 0.25\)
\(P(X = 3) = 0.25\)
The mean is 1.75.The standard deviation is the square root of the sum of the difference squared between each value and the mean, multiplied by it's respective probability.Hence:
\(\sqrt{V(X)} = \sqrt{0.5(1 - 1.75)^2 + 0.25(2 - 1.75)^2 + 0.25(3 - 1.75)^2} = 0.83\)
The standard deviation is of 0.83 children.
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Help please fast thank you
Answer:
if ur going left to right it would be d
Step-by-step explanation:
To study the effect of mindfulness meditation on mental health, an experimental investigation was done by comparing serum cortisol (as an indicator of stress level) between 2 groups of medical students who volunteered to participate in the study. Group 1 took a 4- day meditation program, while Group 2 did not. Volunteers from both groups then had a blood test and their serum cortisol was measured in nmol/L. Results were as follows: Group 1: 267 245 263 316 246 282 379 300 291 306 425 190 346 150 344 Group 2 470 222 443 506 455 518 360 408 375 246 189 368 Do the results support the hypothesis that meditation helps reduce stress level, with 95% confidence? You must properly identify and follow all the necessary steps for this investigation (Hint: for comparing variances, you can use 98% confidence.)
The results of the study suggest that the 4-day meditation program had a significant effect in reducing the stress levels of the medical students compared to the group that did not participate in the meditation program.
To determine if the results support the hypothesis that meditation helps reduce stress levels, we need to perform the necessary statistical analysis. Here are the steps involved:
Step 1: Define the hypothesis:
The null hypothesis (H₀) is that there is no significant difference in stress levels between the two groups.
The alternative hypothesis (Hₐ) is that there is a significant difference in stress levels between the two groups, with meditation reducing stress.
Step 2: Identify the appropriate statistical test:
Since we are comparing the means of two independent groups and want to test if there is a significant difference, we can use an independent samples t-test.
Step 3: Set the significance level:
The significance level (α) is the probability of rejecting the null hypothesis when it is true. In this case, we will use a significance level of 0.05, corresponding to a 95% confidence level.
Step 4: Calculate the sample statistics:
Calculate the means, standard deviations, and sample sizes for both groups.
Group 1:
Mean (x1) = (267 + 245 + 263 + 316 + 246 + 282 + 379 + 300 + 291 + 306 + 425 + 190 + 346 + 150 + 344) / 15 = 290.2
Standard deviation (s1) = 70.764
Sample size (n1) = 15
Group 2:
Mean (x2) = (470 + 222 + 443 + 506 + 455 + 518 + 360 + 408 + 375 + 246 + 189 + 368) / 12 = 377.5
Standard deviation (s2) = 109.057
Sample size (n2) = 12
Step 5: Conduct the statistical test:
We can now perform an independent samples t-test using the sample statistics.
Step 5a: Test for equal variances:
Before conducting the t-test, we need to check if the variances of the two groups are equal. We can use a F-test to compare the variances.
Null hypothesis (H₀): The variances of the two groups are equal.
Alternative hypothesis (Hₐ): The variances of the two groups are not equal.
Using a significance level of 0.02 (98% confidence), we can calculate the F-statistic and compare it to the critical F-value from the F-distribution table.
F = s1² / s2² = 70.764² / 109.057² = 0.428 (approximately)
The critical F-value for a 98% confidence level with (n1-1) = 14 and (n2-1) = 11 degrees of freedom is 3.72.
Since our calculated F-value is smaller than the critical F-value, we fail to reject the null hypothesis. Thus, we can assume equal variances.
Step 5b: Conduct the t-test:
Since the variances are assumed to be equal, we can perform the independent samples t-test using the sample means and pooled standard deviation.
Pooled standard deviation (sp) = √(((n1 - 1) × s1² + (n2 - 1) × s2²) / (n1 + n2 - 2)) = √(((15 - 1) × 70.764² + (12 - 1) × 109.057²) / (15 + 12 - 2)) = 90.362
t = (x1 - x2) / (sp × √(1/n1 + 1/n2)) = (290.2 - 377.5) / (90.362 × √(1/15 + 1/12)) = -2.227
Degrees of freedom (df) = n1 + n2 - 2 = 15 + 12 - 2 = 25
Using the t-distribution table or a statistical software, we can find the critical t-value for a two-tailed test at a significance level of 0.05 with 25 degrees of freedom. The critical t-value is approximately ±2.060.
Since our calculated t-value (-2.227) is smaller than the critical t-value (-2.060), we reject the null hypothesis and accept the alternative hypothesis. Therefore, there is evidence to support the claim that mindfulness meditation helps reduce stress levels, with a 95% confidence level.
In conclusion, the results of the study suggest that the 4-day meditation program had a significant effect in reducing the stress levels of the medical students compared to the group that did not participate in the meditation program.
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3.If a kilogram of pork cost Php 105.75,how much is the cost of 5.5 kilogram?
Answer:
581.625 php
Step-by-step explanation:
If 1 kilo of pork is 105.75, just multiply it by 5.5 to get the answer
Answer:
=5.5×105.75
=581.62
hope it helps
at the school festival , raffle tickets were sold at $1 each, or 3 for $2. At the end of the day, 15 books of tickets, each containing 20 tickets, were sold. the money collected from the sale was $236. How many tickets were sold at 3 for $2?
Answer:
you have to take away you word they said how many
An ice skater skates completely around the two circles shown in the diagram. Each circle has a diameter of 20 meters. What is the approximate total distance skated by the ice skater? Use 3.14 for π . Round your answer to the nearest meter.
A) 628 meters
B) 251 meters
C) 126 meters
D) 63 meters
The solution is Option C.
The total distance skated by the ice skater is 126 meters
What is a Circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the centre for every angle
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
Given data ,
Let the distance traveled by the skater be = D
Let the diameter of the circle A be = 20m
Let the diameter of the circle B be = 20m
So , the radius of circle A = 10 m
The radius of circle B = 10 m
Now , the value of π = 3.14
So , the distance traveled by the skater = perimeter of circle A + perimeter of circle B
Perimeter of Circle A = 2πr
Substituting the values in the equation , we get
Perimeter of Circle A = 2 x 3.14 x 10
Perimeter of Circle A = 62.8 m
And ,
Perimeter of Circle B = 2πr
Perimeter of Circle B = 2 x 3.14 x 10
Perimeter of Circle B = 62.8 m
Therefore , the distance traveled by the skater = Perimeter of Circle A + Perimeter of Circle B
Substituting the values in the equation , we get
The distance traveled by the skater = 2 x 62.8
The distance traveled by the skater = 125.6 meters
The distance traveled by the skater = 126 meters
Therefore , the value of D is 126 meters
Hence , The total distance skated by the ice skater is 126 meters
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determine the global extreme values of the (,)=11−5f(x,y)=11x−5y if ≥−8,y≥x−8, ≥−−8,y≥−x−8, ≤4.y≤4. (use symbolic notation and fractions where needed.)
The global maximum value is 44, and the global minimum value is -88.
To determine the global extreme values of the function f(x, y) = 11x - 5y subject to the given constraints, we need to analyze the function within the feasible region defined by the inequalities.
First, let's consider the boundary of the feasible region:
For x ≥ -8 and y ≥ x - 8, we have y ≥ -8 and y ≥ -x - 8. The feasible region is defined by the intersection of these two inequalities, which is a triangle with vertices (-8, -8), (-8, 0), and (0, -8).
For x ≤ 4 and y ≤ 4, we have y ≤ 4. The feasible region is the triangle with vertices (4, 4), (4, 0), and (0, 4).
Now, we need to evaluate the function at the vertices of the feasible region:
f(-8, -8) = 11(-8) - 5(-8) = -88 + 40 = -48
f(-8, 0) = 11(-8) - 5(0) = -88
f(0, -8) = 11(0) - 5(-8) = 40
f(4, 4) = 11(4) - 5(4) = 44 - 20 = 24
f(4, 0) = 11(4) - 5(0) = 44
From these evaluations, we can see that the maximum value of the function is 44, which occurs at the point (4, 0), and the minimum value is -88, which occurs at the point (-8, -8).
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The next model of a sports car will cost 5.3% less than the current model. The current model costs $51,000. How much will the price decrease in dollars? What
will be the price of the next model?
Decrease in price:
Price of next model
Х
?
The price of the next model will be $48,297.
To calculate the decrease in price of the next model of the sports car, we first need to find the amount by which the price of the current model will decrease.
We know that the current model costs $51,000 and the next model will cost 5.3% less. To find the decrease in price, we can multiply $51,000 by 5.3% expressed as a decimal:
$51,000 x 0.053 = $2,703
So the decrease in price will be $2,703.
To find the price of the next model, we can subtract the decrease in price from the current price:
$51,000 - $2,703 = $48,297
Therefore, the price of the next model will be $48,297.
It's worth noting that this calculation assumes a simple linear relationship between the current and next model prices, and does not take into account other factors that may affect pricing such as production costs, market demand, and competition.
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