A doctor wanted to study the effect of four different treatments on mental health. A group of 100 adults experiencing depression volunteered for the study. The doctor randomly assigned one-fourth of them to each of four groups. Group 1 followed a specific exercise plan, group 2 followed a specific diet plan, group 3 followed an exercise and diet plan, and group 4 did not follow any plan. After 4 weeks, the doctor contacted each participant and asked them if they felt any better. The results are displayed in the table.



The doctor would like to know if these data provide convincing evidence that the distribution of responses differs across the treatment groups in the population of all patients like these. The random condition is met. The 10% condition is not needed because random sampling did not take place. This table of expected counts shows that all expected counts are at least 5.



What is the value of the chi-square test statistic?

χ‑2 = 5.03
χ‑2 = 6.26
χ‑2 = 25.33
χ‑2 = 39.22
Mark this and return

If the price of the stock is now $2.40 then the original stock price was $10.

In order to determine the original stock price, we need to work backwards from the current price of $2.40 and the percentage drops of 40% and 60%.

Let's assume that the original stock price was "x".

Then, we know that the stock price fell by 40% when the company overestimated demand.

This means that the new stock price was 60% of the original price (100% - 40% = 60%).

So, after the first drop, the stock price was:0.6x

Next, the company was forced to recall the seats due to them deflating in heat.

This caused the stock price to drop by another 60%, but from the new lower price of 0.6x.

This means that the new stock price was 40% of the previous price (100% - 60% = 40%).

So, after the second drop, the stock price was:0.4(0.6x) = 0.24x

Finally, we are given that the current stock price is $2.40.

Setting this equal to the second drop price, we can solve for "x":0.24x = 2.40x = $10

Therefore, the original stock price was $10.

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16.3 degrees is the angle that the ramp makes with the ground.

Draw a diagram: Draw a right-angled triangle with the ramp as the hypotenuse, the height of the truck as one of the other sides, and the horizontal distance from the bottom of the ramp to the truck as the other side.

Use trigonometry: We can use the trigonometric function tangent to find the angle the ramp makes with the ground. tan(theta) = opposite/adjacent = height of truck/horizontal distance

Let's substitute the given values:

tan(theta) = 6/21

Solve for theta: We can use the inverse tangent function to solve for theta.

theta = tan^-1(6/21)

theta ≈ 16.3 degrees

Therefore, the angle that the ramp makes with the ground is approximately 16.3 degrees.

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Answer:

x = -4 ± √2

Step-by-step explanation:

x^2+8x+16=2

(x + 4)^2 = 2

x + 4 = ±√2

x = -4 ± √2

A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.

a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`

Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`

b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)

`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)

`Simplifying:`S_n = 2*(2^n - 1)

`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.

Thus, the sum is getting closer and closer to infinity.

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B is the answer y2=-12x

if that helps

Answer:

Hey i believe this is the answer

Step-by-step explanation:

Take a look at the screenshot

Also Desmos graphing calculator is a big help :) It might make you a little more confident

Particular solution that satisfies the given differential equation is: f(x) = 6x⁴ - 3x² + (f(1) - 3).

To find the particular solution for the equation above follow these steps:

1. Integrate the given differential equation: Integrate f'(x) = 24x³ - 6x with respect to x to find f(x).

∫(24x³ - 6x) dx = 6x⁴ - 3x² + C, where C is the constant of integration.

2. Apply the initial condition: Now, we will use the initial condition f(1) to find the value of the constant C. Plug x = 1 into the equation:

f(1) = 6(1)⁴ - 3(1)² + C = 6 - 3 + C = 3 + C.

3. Solve for the constant C: Since we don't have the value of f(1), we can't solve for C. However, we can write the particular solution in terms of f(1):

f(x) = 6x⁴ - 3x² + (f(1) - 3).

This is the particular solution that satisfies the given differential equation and initial condition f(1).

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It takes 72 minutes for Nikki to paint the room working alone and 90 minutes for Greg to paint the room working alone given that Greg and Nikki takes a total of 40 minutes to paint a room if they work together and if Greg works alone, he takes 18 minutes longer to paint he room than Nikki takes if she works alone. This can be obtained by using suitable algebraic equation and quadratic formula.

Here in the question it is given that,

⇒  \(\frac{1}{time(Greg)} +\frac{1}{time(Nikki)} =\frac{1}{40}\)

⇒  time(Greg) = time(Nikki) + 18 ⇒ time(Greg) = x + 18

    ⇒    \(\frac{1}{x} +\frac{1}{x+18}= \frac{1}{40}\)

By simplifying the equation we get the quadratic equation,

⇒ \(\frac{x+18+x}{x(x+18)} =\frac{1}{40}\)

⇒ 40(2x + 18) = x(x + 18)

⇒ 80x + 720 = x² + 18x

⇒ x² - 62x - 720 = 0

By using quadratic formula we can find the value of x,

a = 1, b = - 62, c = - 720

⇒ b² - 4ac = (- 62)² - 4(1)(-720)

⇒ b² - 4ac = 3844 + 2880

⇒ b² - 4ac = 6724

√b² - 4ac = √6724

√b² - 4ac = 82

\(x = \frac{-b+\sqrt{b^{2}-4ac} }{2a}\) or \(x = \frac{-b-\sqrt{b^{2}-4ac} }{2a}\)

\(x = \frac{62+82}{2}\) or \(x = \frac{62-82}{2}\)

x = 144/2 or x = - 20/2

x = 72 or x = - 10

Since time taken cannot be negative we take the value of x as 72 min.

That is, time(Nikki) = x = 72 min

time(Greg) = x + 18

time(Greg) = 72 + 18

time(Greg) = 90 min

Hence it takes 72 minutes for Nikki to paint the room working alone and 90 minutes for Greg to paint the room working alone given that Greg and Nikki takes a total of 40 minutes to paint a room if they work together.

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Answer:

See photo #11

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

4-3=7 7x3= 54 54-13= 47

Answer:

Step-by-step explanation:

\(a^{m}*a^{n}= a^{m+n}\\\\\\(-3)^{5}*(-3)^{2}=(-3)^{5+2}=(-3)^{7}\)

Answer:

\(\Huge \boxed{\mathrm{(-3)^7}}\)

Step-by-step explanation:

\((-3)^5 \times (-3)^2\)

When bases are same for exponents in multiplication, the exponents are added.

\(a^b \times a^c=a^{b+c}\)

\((-3)^{5+2}\)

Add the exponents.

\((-3)^7\)

Answer:

a) Monica's error was she used the formula = Base × Height

This formula is wrong formula

b) The unit for area of a triangle is square inches not inches

Step-by-step explanation:

Monica has a triangular piece of fabric. The height of the triangle is 15 inches and the triangle's base is 10 inches. Monica says that the area of the fabric is 150 inches. What error did Monica make

The area of a triangle is = 1/2 × Base × Height

From the question

Base = 10 inches

Height = 15 inches

Area of the triangular fabric = 1/2 × 10 × 15

= 75 square inches

a) Monica's error was she used the formula = Base × Height

This formula is wrong formula

b) The unit for area of a triangle is square inches not inches

i. Range (A): The space spanned by the columns of matrix A. It represents all possible linear combinations of the columns of A.

ii. Null (A): The set of all vectors x such that Ax = 0. It represents the solutions to the homogeneous equation Ax = 0.

iii. Row (A): The space spanned by the rows of matrix A. It represents all possible linear combinations of the rows of A.

iv. Null (A): The set of all vectors y such that ATy = 0. It represents the solutions to the homogeneous equation ATy = 0.

The equation Ax = b has a solution only when b is in the Range (A). It has a unique solution only when the Null (A) contains only the zero vector.

The equation ATy = d has a solution only when d is in the Row (A). It has a unique solution only when the Null (A) contains only the zero vector.

Assuming the size of A is m × n:

When Ax = b has a unique solution, the space Null (A) must be equal to Rn. This means there are no non-zero vectors that satisfy Ax = 0, ensuring a unique solution.

When ATy = d has a unique solution, the space Null (AT) must be equal to Rm. This means there are no non-zero vectors that satisfy ATy = 0, ensuring a unique solution.

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Answer:

If, he got 94 marks for his sixth quiz, then, he will be able to maintain his required grade for his scholarship.

Step-by-step explanation:

given-

Joven's scores in five of his quizzes in mathematics are 85, 88, 95, 86, and 92.

let, the x score he gets for his sixth quiz.

then, he will be able to maintain his required grade for his scholarship.

he needs an average quiz grade of 90 to maintain his required grade for his scholarship.

according to the question--

using the formula of average=>

(85+88+95+86+92+x)/6=90

=>x=540-446

=>x=94

if, he got 94 marks for his sixth quiz, then, he will be able to maintain his required grade for his scholarship.

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The polynomial, so d can be any value less than b.

A polynomial is an expression made up of multiple terms, each of which is a number, a variable, or the product of a number and one or more variables. Polynomials are typically used to model real-world scenarios including, but not limited to, population growth, force and acceleration, and angles of elevation. Each term of the polynomial is separated from the others by an addition or subtraction sign.

Given the polynomial 4x^3 + ax^2 + bx + c,
a = 4, b = -3, c = 5, d = -2.
To find the values of a, b, c, and d, we need to compare the coefficients of the polynomial to the given values.
The coefficient of the term with the highest degree (x^3) is 4, so a = 4.
The coefficient of the next degree (x^2) is a, so a = -3.
The coefficient of the next degree (x) is b, so b = 5. The coefficient of the constant term is c, so c = -2. Finally, d is not given in the polynomial, so d can be any value less than b.

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Answer:

sorry I don't know about this

Step-by-step explanation:

sorry I don't know about this

(x, y) is an element of the set c × d, since x is an element of c and y is an element of d.

Since (x, y) was an arbitrary element in a × b, we can conclude that every element in a × b is also in c × d. Thus, we have shown that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d.

To show that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d, follow these steps:

Step 1: Understand the notation.
a ⊆ c means that every element in set a is also in set c.
b ⊆ d means that every element in set b is also in set d.

Step 2: Consider the Cartesian products.
a × b is the set of all ordered pairs (x, y) where x ∈ a and y ∈ b.
c × d is the set of all ordered pairs (x, y) where x ∈ c and y ∈ d.

Step 3: Show that a × b ⊆ c × d.
To prove this, we need to show that any ordered pair (x, y) in a × b is also in c × d.

Let (x, y) be an arbitrary ordered pair in a × b. This means that x ∈ a and y ∈ b.

Since a ⊆ c, we know that x ∈ c because every element in set a is also in set c.
Similarly, since b ⊆ d, we know that y ∈ d because every element in set b is also in set d.

Now, we have x ∈ c and y ∈ d, so the ordered pair (x, y) belongs to c × d.

Step 4: Conclusion
Since any arbitrary ordered pair (x, y) in a × b also belongs to c × d, we can conclude that a × b ⊆ c × d.

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a)

The expression that represents the number of lawns Eve mows in those 8 weeks is 8(L- 2)

b)

The value of the expression is 8.

c)

The tabular table is given above.

d)

Eve mowed 24 lawns in 8 weeks.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Logan:

Number of lawns each week = L

Number of lawns 8 weeks = 8L

Eve:

Number of lawns each week = )L - 2)

Number of lawns 8 weeks = 8(L- 2)

a)

The expression represents the number of lawns Eve mowed in those 8 weeks.

= 8(L -2)

b)

When L = 3,

8 (L - 2)

= 8 (3 - 2)

= 8 x 1

= 8

c)

Tabular table

                Number of weeks     Number of lawns

Logan         x                                xL

Eve            x                                 x(L - 2)

d)

Logan:

Number of lawns in one week = 5

L = 5

Eve:

Number of lawns in 8 weeks.

= 8 (L - 2)

= 8 (5 - 2)

= 8 x 3

= 24

Thus,

a) 8(L- 2)

b) 8

c) Tabular table is given above.

d) Eve mowed 24 lawns in 8 weeks.

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Answer: #x^3

Step-by-step explanation:

        x^3

note: An algebraic expression doesn't have an equal sign (=)

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Answer:

$11.24

Step-by-step explanation:

Given data

Original cost of tire=  $74.95

DIscount= 15%

Required

The amount of the discount

=15/100*74.95

= 0.15*74.95

= 11.24

Hence the amount saved is $11.24

Answer:

166.5

Step-by-step explanation:

Answer: 160

Step-by-step explanation:

12+37+78

Answer: 14 percent

Step-by-step explanation:

Not really needed.

Answer:

-15

Step-by-step explanation:

Hope this Helps

Answer: -335

Step-by-step explanation:

If P(E1) + P(E2) = 1, then E1 n E2 = 0 and E1 U E2 = 1. The above statement is also true.

E1 U E2 = 1 means either E1 or E2 can occur. E1 n E2 = 0 means the events are mutually exclusive, meaning that they cannot happen at the same time.

The following statements that are true are the following:

If E = 0, then P(E) = 0.If P(E1) + P(E2) = 1, then E1 U E2 = 1.If P(E1) + P(E2) = 1, then E1 n E2 = 0 and E1 U E2 = 1.The probability is a measure of the likelihood of an event happening. An event with a probability of 0 means that the event cannot happen. Therefore, if P(E) = 0 for event E, then E = 0.

Therefore, If E = 0, then P(E) = 0. The above statement is true. If E = 0, it is the same as stating that event E can not happen. Thus, there is no chance of P(E).

Therefore, P(E1) + P(E2) = 1, then E1 U E2 = 1. The above statement is true as well. Here, E1 U E2 means the probability of both E1 and E2 occurring. Hence, it is the sum of the probability of E1 and E2, which is equal to 1.

It means that one of the events has to happen, or both events have to happen.

Hence, if P(E1) + P(E2) = 1, then E1 n E2 = 0 and E1 U E2 = 1. The above statement is also true.

E1 U E2 = 1 means either E1 or E2 can occur. E1 n E2 = 0 means the events are mutually exclusive, meaning that they cannot happen at the same time.

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These are the polynomial equations:

A = x^ (1/4) - ∛x + 4√x - 8x + 16

B = 3x² - 5x⁴ + 2x - 12

C = x³ - 7x² + 9x - 5x⁴ - 20

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

These are the non-polynomial equations:

E = 4/x⁴ + 3/x³ - 2/x² - 1

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

Polynomials are mathematical expressions that only use addition, subtraction, multiplication, and non-negative exponentiation of the variables, along with coefficients (constants that multiply with the variables), coefficients, and constants.

Some of the elements of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.

Let the polynomial equations be represented by the following letters: A, B, C, D, E, and F.

In the equation, we can solve for other values to obtain:

Moreover, a polynomial equation is not an algebraic equation that has a negative exponent or an exponent that is fractional. Thus, negative exponent expressions are not polynomials.

A = x^ (1/4) - ∛x + 4√x - 8x + 16

This polynomial exists.

B = 3x² - 5x⁴ + 2x - 12

This polynomial exists.

C = x³ - 7x² + 9x - 5x⁴ - 20

This polynomial exists.

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

It is a polynomial.

E = 4/x⁴ + 3/x³ - 2/x² - 1

It is not a polynomial.

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

A polynomial is not what it is.

The polynomials are thus resolved.

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The standard deviation of the number of defective bulbs in a sample of 11 light bulbs, where 60% are defective, is 1.53, rounded to two decimal places.

The number of defective bulbs in a sample of 11 light bulbs follows a binomial distribution with parameters n = 11 and p = 0.6, where n is the sample size and p is the probability of a defective bulb.

The standard deviation of the binomial distribution is given by the formula:

σ = sqrt(np(1-p))

where σ is the standard deviation, n is the sample size, p is the probability of success (defective bulb), and (1-p) is the probability of failure (non-defective bulb).

Substituting the values into the formula, we get:

σ = sqrt(11 * 0.6 * 0.4) = 1.53

Therefore, the standard deviation of the number of defective bulbs in the sample is 1.53, rounded to two decimal places.

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Answer:

y = -2x + 17

Step-by-step explanation:

y has to equal 5:

incorrect

y = -2x - 17

y = -2(6) - 17

y = -12 - 17

y = -29

incorrect

y = -2x - 16

y = -2(6) - 16

y = -12 - 16

y = -28

incorrect

y = -2x + 16

y = -2(6) + 16

y = -12 + 16

y = 4

correct

y = -2x + 17

y = -2(6) + 17

y = -12 + 17

y = 5

In a continuous probability distribution, a random variable can take any value in a specified range. (Option D)

A probability distribution refers to the mathematical function that provides the probabilities of occurrence of different possible outcomes for an experiment. Continuous probability distribution refers to a probability distribution with continuous types of data or random variables where the random variable can take on any value and is continuous. As there are infinite values that the variable can assume, the probability of the variable assuming any one specific value is zero. A continuous distribution is characterized by a range of values that are infinite, and therefore uncountable. The normal distribution is one example of a continuous distribution.

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Topic : Linear equations in two variables.

Given :

Solution :

Now,

(i) + (ii)

\( \qquad \sf \: { \dashrightarrow 3x + 2y + (x - 2y) = - 4 + 4}\)

\( \qquad \sf \: { \dashrightarrow 3x + 2y + x - 2y = 0}\)

\( \qquad \sf \: { \dashrightarrow 3x \: \cancel{ + 2y} + x \: \cancel{- 2y} = - 4 + 4}\)

\( \qquad \sf \: { \dashrightarrow 4x = 0}\)

\( \qquad \bf \: { \dashrightarrow x = 0}\)

Now, substituting the value of x in Eq (i) :

\(\qquad \sf \: { \dashrightarrow 3x + 2y = -4}\)

\(\qquad \sf \: { \dashrightarrow 3(0) + 2y = -4}\)

\(\qquad \sf \: { \dashrightarrow 0 + 2y = -4}\)

\(\qquad \sf \: { \dashrightarrow 2y = -4}\)

\(\qquad \sf \: { \dashrightarrow y = \dfrac{ - 4}{2} }\)

\(\qquad \bf \: { \dashrightarrow y = -2}\)

Therefore, The value of x = 0 and y = -2

The solution to the two given simultaneous equations are; x = 0 and y = -2

We are given the simultaneous equations;

3x + 2y = -4   -----(eq 1)

x - 2y = 4      ------(eq 2)

Add eq1 and eq2 to get;

4x = 0

x = 0/4

x = 0

Substitute 0 for x in eq 2 to get;

0 - 2y = 4

-2y = 4

y = -4/2

y = -2

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