how do I find the value of x so f(x)=7​

C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

Answer:

-8

Step-by-step explanation:

-2*(x+5)=6

Divide both sides by -2

x+5=-3

x=-3-5

x=-8

The correlation analysis indicates a moderate positive relationship between Column X and Column Y.

To perform correlation analysis, we can use the Pearson correlation coefficient (r) to measure the linear relationship between two variables, in this case, Column X and Column Y. The value of r ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

Here are the steps to calculate the correlation coefficient:

Calculate the mean (average) of Column X and Column Y.

Mean(X) = (10+6+39+24+35+12+33+32+23+10+16+16+35+28+5+22+12+44+15+40+46+35+28+9+9+8+35+15+34+16+19+17+21) / 32 = 24.4375

Mean(Y) = (37+10+18+12+11+34+26+9+42+24+40+1+39+24+42+7+17+17+27+47+35+14+38+18+17+22+12+30+18+43+24+45+24) / 32 = 24.8125

Calculate the deviation of each value from the mean for both Column X and Column Y.

Deviation(X) = (10-24.4375, 6-24.4375, 39-24.4375, 24-24.4375, ...)

Deviation(Y) = (37-24.8125, 10-24.8125, 18-24.8125, 12-24.8125, ...)

Calculate the product of the deviations for each pair of values.

Product(X, Y) = (Deviation(X1) * Deviation(Y1), Deviation(X2) * Deviation(Y2), ...)

Calculate the sum of the product of deviations.

Sum(Product(X, Y)) = (Product(X1, Y1) + Product(X2, Y2) + ...)

Calculate the standard deviation of Column X and Column Y.

StandardDeviation(X) = √[(Σ(Deviation(X))^2) / (n-1)]

StandardDeviation(Y) = √[(Σ(Deviation(Y))^2) / (n-1)]

Calculate the correlation coefficient (r).

r = (Sum(Product(X, Y))) / [(StandardDeviation(X) * StandardDeviation(Y))]

By performing these calculations, we find that the correlation coefficient (r) is approximately 0.413. Since the value is positive and between 0 and 1, we can conclude that there is a moderate positive relationship between Column X and Column Y.

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Answer:

x=-1/2

Step-by-step explanation:

Answer:

:Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded

Step-by-step explanation:

Answer:  Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded to the nearest hundreth.

Step-by-step explanation:

Answer:

\(\frac{1}{36}\)

Step-by-step explanation:

The probability of rolling a 4 is 1/6.

Using the multiplication rule, the required probability is \((1/6)^2=\frac{1}{36}\).

The surface area of the parachute is 628.4 cm.

The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface. It's also expressed in square units.

Given:

Slant Height = 14.1 cm

Base = 20 cm

Using

l² = r² + h²

h² = l² - r²

h = 10.08 cm

Now, Surface area of a square pyramid = a² + 2al

                                                                  = 40 + 2(20)(14.71)

                                                                  = 628.4 cm

Thus, the surface Area is 628.4 cm.

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 the correct option is d) square root of five divided by five.

Cotangent (cot) is one of the six trigonometric functions that are used to represent the ratio of two sides of a right-angled triangle.

Cot is equal to the ratio of adjacent to opposite sides of a right-angled triangle. The reciprocal of tan (tangent) is cot and is written as cot(θ).

The given trigonometric ratio of cot θ and cos θ can be used to determine the value of sin θ. Given that cot θ = - 2 and cos θ < 0.

Since cot θ = adjacent/opposite, we can use the Pythagorean theorem to find the hypotenuse.

For instance:Assume that the opposite side of θ is y and that the adjacent side is x.Therefore:cot θ = x/y => y = x/cot θ => y = - x/2We can use the Pythagorean theorem to find the hypotenuse, as follows:

cos θ = adjacent/hypotenuse => hypotenuse = adjacent/cos θ => hypotenuse = - 1/cos θ Also, hypotenuse squared = opposite squared + adjacent squared:

(- 1/cos θ)^2 = x^2 + (- x/2)^2=> 1/cos^2θ = 5x^2/4=> cos^2θ = 4/5 => sin^2θ = 1 - cos^2θ=> sin^2θ = 1 - 4/5 => sin^2θ = 1/5 => sinθ = ± √5/5

Since cos θ is less than 0, sin θ is less than 0.

Therefore, the correct option is d) square root of five divided by five

Let us first understand what is cotangent. Cotangent (cot) is one of the six trigonometric functions that are used to represent the ratio of two sides of a right-angled triangle.

Cot is equal to the ratio of adjacent to opposite sides of a right-angled triangle. The reciprocal of tan (tangent) is cot and is written as cot(θ).The given trigonometric ratio of cot θ and cos θ can be used to determine the value of sin θ.

Given that cot θ = - 2 and cos θ < 0, we can use these ratios to determine the value of sin θ.Since cot θ = adjacent/opposite, we can use the Pythagorean theorem to find the hypotenuse.

For instance, assume that the opposite side of θ is y and that the adjacent side is x. Therefore, cot θ = x/y => y = x/cot θ => y = - x/2. We can use the Pythagorean theorem to find the hypotenuse, as follows:

cos θ = adjacent/hypotenuse => hypotenuse = adjacent/cos θ => hypotenuse = - 1/cos θ.

Now, hypotenuse squared = opposite squared + adjacent squared: (- 1/cos θ)^2 = x^2 + (- x/2)^2 => 1/cos^2θ = 5x^2/4 => cos^2θ = 4/5 => sin^2θ = 1 - cos^2θ => sin^2θ = 1 - 4/5 => sin^2θ = 1/5 => sinθ = ± √5/5.

Since cos θ is less than 0, sin θ is less than 0. Therefore, the correct option is d) square root of five divided by five.

Therefore, the correct option is d) square root of five divided by five.

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Answer: 2, 3, 5, 6, -2, -3

Step-by-step explanation:

y = (x + 2)(x + 3)

y = x² + 5x + 6

x + 2 = 0      x + 3 = 0

    x = -2            x = -3

Answer:

4,6,10,24,-4,-6

Step-by-step explanation:

y=(x +4)(x+6)

y=x² + 10x + 24

Solutions:

x+4=0    x+6=0

x=-4       x=-6

Hope this helps ^-^

Answer: its 73,000

Step-by-step explanation: the answer sheet has the answers...

Answer:

  54880/27 = 2032 16/27

Step-by-step explanation:

You want the maximum value of 5x²y, subject to the constraints {x+y=14, x≥0, y≥0}.

Using the constraint to write an equation for y in terms of x, we have ...

  5x²(14 -x) = -5x³ +70x²

The value will be maximized at a point where the derivative is zero:

  -15x² +140x = 0 . . . . . derivative

  -5x(3x -28) = 0 . . . . . factored

  x = 0  or  28/3 . . . . . the left solution is a minimum

The value of 5x²y is maximized at x = 28/3. That maximum value is ...

  5(28/3)²(42-28)/3 = 54880/27

The maximum value of 5x²y is 54880/27.

<95141404393>

The maximum value of 5x²y, given that x + y = 14, occurs when x = 10 and y = 4, resulting in a maximum value of 2000.

To find the maximum value of 5x²y, we can use the method of optimization by substitution. Since we know that x + y = 14, we can rearrange this equation to express y in terms of x, giving us y = 14 - x. Substituting this into the expression for 5x²y, we get 5x²(14 - x). Expanding and simplifying this expression yields 70x² - 5x³.

To find the maximum value of this expression, we can take its derivative with respect to x and set it equal to zero. Differentiating 70x² - 5x³ gives us 140x - 15x². Setting this equal to zero, we can factor out x to get x(140 - 15x) = 0. This equation has two solutions: x = 0 and x = 140/15 = 28/3.

Since we are looking for nonnegative values, x = 0 is not feasible. Therefore, we consider x = 28/3. Plugging this value back into the expression 5x²y, we can solve for y, giving us y = 14 - (28/3) = 2/3. Thus, the maximum value of 5x²y occurs when x = 28/3 and y = 2/3, resulting in a value of 2000.

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Step-by-step explanation:

The volume of the container is:

V = l × w × h = 5m × 5m × 8m = 200 m³

The density is:

density = mass / volume

We are given the mass is 100 kg.

density = 100 kg / 200 m³ = 0.5 kg/m³

Therefore, the density of the shipping container is 0.5 kg/m³.

Answer: 0.5 kg/m^3

Step-by-step explanation:

To find the density of the shipping container, we need to divide its mass (weight) by its volume. The mass of the container is given as 100 kg.

To find the volume of the container, we need to multiply its length, width, and height. Therefore, the volume is:

V = l × w × h = 5 m × 5 m × 8 m = 200 m^3

Now we can find the density by dividing the mass by the volume:

Density = Mass / Volume = 100 kg / 200 m^3

Density = 0.5 kg/m^3

we will use the formula of tan(A+B)= (tanA+tanB)/(1-tanAtanB)

and tan(A-B)= (tanA-tanB)/(1+tanAtanB)

tan[(pie/4)+(x/2)]= [1+tan(x/2)]/[1-tan(x/2)] ......(1)

tan[(pie/4)-(x/2)]= [1-tan(x/2)]/[1+tan(x/2)]......(2)

now add the equation (1) and (2) which is LHS of question. So we get:

{[1+tan(x/2)]^2 + [1- tan(x/2)]^2}/1-tan^2(x/2)=2[1+tan^2(x/2)]/1-tan^2(x/2)= 2/cosx = 2secx =RHS

Hence proved.

Answer:

48 hours

Step-by-step explanation:

1 x 12 = 12, 12 inches in a foot

4 x 12 = 48

Function: y = 1/4x

The dependent variable is the amount of snowfall and the independent variable is the counting of hours.

pls mark brainliest!

<3

The year when about 20 pounds of apples were consumed per person using the equation would be around 2109.

The year when about 20 pounds of apples were consumed per person using the equation y = (√22x + 180) can be determined as follows.

1. Set y variable equal to 20, as we want to find the year when 20 pounds of apples were consumed per person:

20 = (√22x + 180).

2. Now, solve for x. Start by subtracting 180 from both sides:

-160 = √22x.

3. Square both sides to eliminate the square root:

(-160)^2 = (22x)^2, which gives 25600 = 22x.

4. Divide both sides by 22:

25600/22 = x, which gives

x ≈ 1164/9 ≈ 129.33.

Since x represents the number of years since 1980, and we got x ≈ 129.33, the year when about 20 pounds of apples were consumed per person would be around 1980 + 129.33 ≈ 2109 (rounding down to the nearest whole number).

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Answer:

\(m = \frac{5}{2} \)

Step-by-step explanation:

Here are the laws which would be used in this question:

Indices:

• \( \sqrt{a} = {a}^{ \frac{1}{2} } \)

• \( \frac{1}{a} = {a}^{ - 1} \)

Logarithm

• \( log_{a}( {x}^{n} ) = n log_{a}(x) \)

\( log_{m}( \sqrt{2} ) + log_{m}(8) + log_{m}( \frac{1}{2} ) \)

\( = log_{m}( {2}^{ \frac{1}{2} } ) + log_{m}( {2}^{3} ) + log_{m}( {2}^{ - 1} ) \)

\( = \frac{1}{2} log_{m}(2) + 3 log_{m}(2) - log_{m}(2) \)

\( = \frac{5}{2} log_{m}(2) \)

The probability that a string of 15 people passes through screening successfully before an individual is caught with a questionable object is 0.3040 and the expected number of people to pass through be- fore an individual is stopped 49

3% of people whose luggage is screened at an airport have questionable objects in their luggage i.e

P(x)=3/100=0.03

The probability of people whose luggage is screened at an airport and have no questionable object in their luggage is

〖P(x)〗^1=1-P(x)

〖P(x)〗^1=1-0.03

〖P(x)〗^1=0.97

Using Binomial probability which states that

P(x)=(nCx) (p)^x (q)^(n-x)

N= 16 total number in consideration

p= probability with no questionable luggage

q= probability with questionable luggage

P(15)=(16C15) (p)^15 (q)^(16-15)

P(15)=(16C15) (0.97)^15 (0.03)^(16-15)

16C15=16!/((16-15)!(15!))

15C15=15!/((1)!(15!))

16C15=20922789888000/((1)(1307674368000))

16C15=20922789888000/1307674368000

16C15=16

P(15)=(16) (0.97)^15 (0.03)^1

P(15)=(16)(0.63325)(0.03)

P(15)=0.3040

P(x) =(Required outcome)/(Total outcome)

0.3040 =15/(Total outcome)

Total outcome=15/0.3040

Total outcome=49.34

Total outcome=49

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Explanation:

We have 6 green out of 6+6+6 = 18 total

The probability of getting green is 6/18 = 1/3.

After selecting that green jelly bean and not putting it back, we have 6-1 = 5 green out of 18-1 = 17 total.

The probability of selecting another green is 5/17.

Multiply the two fractions 1/3 and 5/17

(1/3)*(5/17) = (1*5)/(3*17) = 5/51

The probability of selecting two greens in a row is 5/51 where we do not put the first selection back. We also do not replace the green jelly bean with some other identical copy.

Note: 5/51 = 0.098039 approximately

Answer:

The answer is your face try again loser

Step-by-step explanation:

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

The radius of the cone is 783.84/√h

A cone is the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cone is expressed as;

V = 1/3πr²h

643072 × 3 = 3.14 × r²h

r²h = 614400

r² = 614400/h

r = 783.84/√h

therefore the radius of the cone is 783.84/√h

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Answer:

10√2

Step-by-step explanation:

This is a 45-45-90 triangle which means that the two non-hyptonouse lenghts are the same which means that the bottom lenght of the triangle is also 10 units

We can then use a^2+b^2=c^2 to solve for the last side

so we have

10^2+10^2=x^2

200=x^2

sqrt200=x

and I see that they want an exact answer so you simplify sqrt200 to

10√2

==========================================================

Explanation:

The team won 16 games and lost 11 so far. At this point in the season, they played 16+11 = 27 games total. Their win rate is 16/27.

Set this equal to x/162 which is the win rate for winning x games out of 162 played over the entire season.

Solve for x.

x/162 = 16/27

27x = 162*16 ... cross multiplication

27x = 2592

x = 2592/27

x = 96

The team would win 96 games if it kept the same winning rate going.

Notice that 16/27 = 0.5926 = 59.26% and how 96/162 = 0.5926 = 59.26% as well (both are approximate). This helps confirm we have the correct answer.

-------------------------

Here's another slightly longer way to solve. If you prefer the first method above, then ignore this section.

w = number of games won over the entire 162 game season

162-w = number of games lost over the entire season

w/(162-w) = win to loss ratio

16/11 = win to loss ratio after winning 16 games and losing 11

Setting those last two expressions equal to each other and solving for w gets us...

w/(162-w) = 16/11

11w = 16(162-w)

11w = 2592-16w

11w+16w = 2592

27w = 2592 ... this hopefully looks a bit familiar from before

w = 2592/27

w = 96 games won

Answer: C: Expression B and D

Step-by-step explanation:

Say the item is $100. 20% of 100 is equal to 100 (20/100)

When you simplify, it equals 20. So 20% of 100 is 20. This $20 is the amount of discount you receive.

So you have to subtract $20 from the $100 to find the sale price. The sale price is $80.

Now plug in 100 for p in each equation. The equation that equals 80 is the answer.

Only equation B and D equals 80 when 100 is plugged in.

Answer:

$4/hour

Step-by-step explanation:

From 7:30 am to 10:00 am it's 2.5 hours.

10 * 2.5 hours = 25 hours

He worked a total of 25 hours.

$100/(25 hours) = $4/hour

There are 26 letters in the English alphabet and no it’s not a statistical question

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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Answer:

see explanation

Step-by-step explanation:

Any term in a Fibonacci sequence is the sum of the previous 2 terms.

Given the first 3 terms then

a₄ = a₂ + a₃ = x + y + y = x + 2y

a₅ = a₃ + a₄ = y + x + 2y = x + 3y

a₆ = a₄ + a₅ = x + 2y + x + 3y = 2x + 5y

a₇ = a₅ + a₆ = x + 3y + 2x + 5y = 3x + 8y

Thus the next four terms are

x + 2y, x + 3y, 2x + 5y, 3x + 8y

c) Data can sometimes be accurately represented by several regression models.

The statement "Data can sometimes be accurately represented by several regression models" is the correct answer. Regression models are statistical tools used to analyze the relationship between variables and make predictions based on observed data. In some cases, different regression models can accurately represent the same data.

This is because the choice of regression model depends on the underlying assumptions and the nature of the data. Different models may capture different aspects of the relationship between variables and provide varying degrees of accuracy in representing the data.

While extrapolation, which involves extending predictions beyond the observed data range, is generally not reliable for non-linear regression models (option a), it does not apply to all cases. The coefficient of determination (R-squared) measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s), and it does not need to be exactly 1 for a regression model to be useful (option b).

Polynomial regression models (option d) can be used to fit data points, but the required degree of the polynomial depends on the complexity and patterns present in the data, and it does not necessarily have to match the number of data points.

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The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.

In the given regression model:

\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)

Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.

The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).

Let's denote the variance as Var(U\(_{i}\)) = σ².

The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:

σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.

Taking the expectation (E) of the MLE for the variance:

E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

Now, let's break down the expression inside the expectation:

[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²

= \(U_{i}\)²

Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).

Therefore, we can rewrite the expectation as:

E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]

= (1 / n) × Σ[ E[\(U_{i}\)²] ]

= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]

= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)

Simplifying further:

E[σ²] = (1 / n) × n × σ²

= σ²

From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.

Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

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