Laura baked a cake. She gave 1/5 of the cake to Alex, 1/3 of the cake to Erikson, and 1/10 of the cake to Autumn. How much is left for herself? need help asap

If we want to provide a 99% confidence interval for the mean of a population, the confidence coefficient will be 0.99. This means that there is a 99% probability that the true population mean falls within the calculated interval.

The confidence coefficient for a confidence interval represents the level of confidence we have in our estimate.

In the case of a 99% confidence interval, the confidence coefficient is 0.99. This means that we are 99% confident that the true population mean falls within the calculated interval. The confidence coefficient is derived from the desired level of confidence, which is typically expressed as a percentage.

A higher confidence level corresponds to a larger confidence coefficient. In practical terms, a 99% confidence interval indicates that if we were to repeat the sampling process multiple times and construct 99% confidence intervals, approximately 99% of those intervals would contain the true population mean.

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The function y = sin x / (1 + cos x) has a domain of all real numbers except for x = (2n + 1)π. It intersects the x-axis at x = nπ and the y-axis at y = 0. The function is symmetric about the y-axis. There  is a horizontal asymptote at y = -1. It increases on intervals where -π/2 < x < π/2 and decreases on intervals where π/2 < x < 3π/2. There are no local maximum or minimum values. The concavity of the function changes at x = nπ and there are no points of inflection.

A. The domain of the function y = sin x / (1 + cos x) includes all real numbers except for values of x that make the denominator equal to zero. In this case, the denominator is 1 + cos x, which is equal to zero when cos x = -1. Solving for x, we find x = (2n + 1)π, where n is an integer. Therefore, the domain is all real numbers except for x = (2n + 1)π.

B. To find the x-intercepts, we set y = 0 and solve for x. Setting sin x / (1 + cos x) = 0, we have sin x = 0. This equation is satisfied when x = nπ, where n is an integer. Hence, the function intersects the x-axis at x = nπ. The y-intercept is found by substituting x = 0 into the function, which gives y = 0 / (1 + 1) = 0.

C. The function y = sin x / (1 + cos x) is symmetric about the y-axis. This can be observed from the fact that replacing x with -x in the function does not change its value.

D. There are no vertical asymptotes for this function since the denominator is never zero. However, as x approaches positive or negative infinity, the function approaches a horizontal asymptote at y = -1.

E. The function increases on intervals where -π/2 < x < π/2 because the value of sin x is positive and the value of cos x is always greater than or equal to -1. It decreases on intervals where π/2 < x < 3π/2 because the value of sin x is negative while the value of cos x remains greater than or equal to -1.

F. The function y = sin x / (1 + cos x) does not have any local maximum or minimum values since it is always changing and never reaches a maximum or minimum point.

G. The concavity of the function changes at x = nπ, where n is an integer. Specifically, the function changes from concave up to concave down or vice versa at these points. However, there are no points of inflection where the concavity changes from concave up to concave down or vice versa.

H. Based on the information above, we can sketch the curve of the function. The curve will be symmetric about the y-axis, intersecting the x-axis at x = nπ and the y-axis at y = 0. It will approach a horizontal asymptote at y = -1 as x approaches positive or negative infinity. The curve will increase on intervals where -π/2 < x < π/2 and decrease on intervals where π/2 < x < 3π/2. There are no local maximum or minimum points, and the concavity changes at x = nπ, but there

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The approximate measure of the largest angle in the triangle is of:

θ = 63.4º.

The vertices of the triangle are given as follows:

N(2,2) and P(0,-2).

The triangle is symmetric over the y-axis, hence the remaining vertex is given as follows:

M(-2,2).

The side lenghts of the triangle are given as follows:

The height of the triangle is of:

4 units.

Hence the base angle is:

The tangent is:

tan(θ) = opposite side/adjacent side

Hence:

tan(θ) = 4/2

tan(θ) = 2

θ = arctan(2)

θ = 63.4º.

The diagram given by the image at the end of the answer represents the situation.

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1) In this question, we need to remember that in any boxplot the line in the middle of the box indicates the median.

Based on that, we can tell the Median is 140

2) In the Interquartile Range, we need to find the range between the lower quartile and the upper one, based on that boxplot. We can tell the IQR is:

Note that the boundaries of the box show us the lower and the upper quartile:

The predicted number of runs for the player with only 86 hits can be calculated using the equation Runs = Hits + Walks - Home Runs. Plugging in the values given, we get: Runs = 86 + Walks - Home Runs. Therefore, the predicted number of runs for the player is dependent on the number of walks and home runs they have.

To solve for the predicted number of runs, we can use the following steps:

Therefore, the predicted number of runs for the player with only 86 hits can be calculated by plugging in the values of the number of walks and home runs into the equation Runs = Hits + Walks - Home Runs.

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Answer:

\(\frac{41}{100}\)

Step-by-step explanation:

It cannot be simplified.

Ex: 50% can be simplified to \(\frac{1}{2}\)

After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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Answer:

\(\sqrt{x^{2}-7\)

Step-by-step explanation:

Negative exponents flip the fraction, fraction exponents imply a radical to the denominator's degree, so flip the fraction and take the square root of what is in parentheses

We know that :

\(\bigstar \ \ \boxed{\mathsf{a^{-1} = \dfrac{1}{a}}}\)

\(\mathsf{Given \ question \ is : \dfrac{1}{(x^2 - 7)^{\frac{-1}{2}}}}\)

Using the above formula, we can write it as :

\(\implies \mathsf{\dfrac{1}{\dfrac{1}{(x^2 - 7)^{\frac{1}{2}}}}}\)

\(\implies \mathsf{(x^2 - 7)^{\frac{1}{2}}}\)

\(\implies \mathsf{\sqrt{x^2 - 7}}\)

If the sample has the same mix of people, in the same proportions, as the population being studied then sociologists know if the sample they are using is representative. So the option c is correct.

No subject is off-limits when sociologists use the sociological lens and start asking questions. Every facet of human behaviour has the potential to be studied. Sociologists cast doubt on the society that people have built and inhabit. They observe behavioral patterns as individuals navigate that world.

Sociologists have uncovered workplace patterns that have revolutionized industries, family patterns that have educated parents, and educational patterns that have supported structural changes in classrooms by using sociological methodologies, methodical research, and a scholarly interpretive approach.

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The complete question is;

How do sociologists know if the sample they are using is representative?

a. If the people in the sample freely volunteered to serve as representatives

b. If the sample has an even number, decided by the researcher, of people from several different categories or backgrounds

c. If the sample has the same mix of people, in the same proportions, as the population being studied

d. If the participants have been interviewed to reveal possible bias.

Answer:

a.divide the amount by the percentage.

$2700× 25%

Ans:$675

subtract the selling price from the profit.

$2700 - $675

Ans:$2025

b.divide the 15% from selling price.

$2700 × 15%

Ans: 405

deduct the selling from from the discount given.

$2700 - $405

Ans: $2,295

x and x⁴-16x²+56 are the resulting composite functions respectively.

Given the following functions below

f(x) = 7/x

g(x) = x² - 8

We need to determine the composite functions (fof)(x) and (gog)(x)

(fof)(x) = f(f(x))

f(f(x)) = f(7/x)

Replace x with 7/x

f(7/x) = 7/(7/x)

f(7/x) = 7 * x/7

f(7/x) = x

Similarly:

(gog)(x) = g(g(x))

g(g(x)) = (x² - 8)² - 8

g(g(x)) = x⁴-16x²+64 - 8

g(g(x)) = = x⁴-16x²+56

Hence the resulting composite functions of f(f(x) and g(g(x)) are x and x⁴-16x²+56

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Answer:

Step-by-step explanation:

The sum of the angles in a triangle is 180

So, (19x-1)+(13x-5)+90(right angle) =180

32x+84=180

32x=96

x=3

19x3-1=56

13x3-5=34

answer : 56, 34

Answer:

Step-by-step explanation:

1) "The length of a rectangle is three more than twice the width." This can be written in a math sentence as  

L = 2W + 3

 where "twice the width" is 2W and "three more" is just adding 3.

 2) "Perimeter is 36 inches". Recall the formula for the perimeter of a rectangle

 P = 2W + 2L

  set the formula to 36 and that gives us our second equation: 36 = 2W + L

then use substitution do solve

Answer:

ST= 5.2

RT= 23.6

Step-by-step explanation:

Answer:

ST= 5.2

RT= 23.6

Step-by-step explanation:

The value of the equation A = 154,504 / 28 = 5518

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Let the dividend be p = 154,504

Let the divisor be q = 28

Substituting the values in the equation , we get

A = p / q

A = 5,518

     5518

28 | 154504

1 4 0      

 1 4 5    

 1 4 0    

     5 0  

     2 8  

     2 2 4

     2 2 4

         0

So , the remainder of the equation is 0 and the quotient is 5518

Hence , the equation is A = 5518

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Answer: I believe he could wear 768 outfits

Step-by-step explanation: I had a similar question consisting of the same numbers.

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(y = \frac{1}{2} x - \frac{9}{2} \\ \)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

10/3

Step-by-step explanation:

The length of the path described by the parametric equations

 is 3/2units.

We can find the length of the path described by the parametric equations x=cos³t and y=sin³t by using the arc length formula.

The arc length formula for a parametric curve given by:

x=f(t) and y=g(t) is given by:

L = ∫[a,b] √[f'(t)² + g'(t)²] dt

where f'(t) and g'(t) are the derivatives of f(t) and g(t), respectively.

In this case, we have:

x = cos³t, so x' = -3cos²t sin t

y = sin³t, so y' = 3sin²t cos t

Therefore,

f'(t)² + g'(t)² = (-3cos²t sin t)² + (3sin²t cos t)²

= 9(cos⁴t sin²t + sin⁴t cos²t)

= 9(cos²t sin²t)(cos²t + sin²t)

= 9(cos²t sin²t)

Thus, we have:

L = ∫[0,2π] √[f'(t)² + g'(t)²] dt

= ∫[0,2π] √[9(cos²t sin²t)] dt

= 3∫[0,2π] sin t cos t dt

Using the identity sin 2t = 2sin t cos t, we can rewrite the integral as:

L = 3/2 ∫[0,2π] sin 2t dt

Integrating, we get:

L = 3/2 [-1/2 cos 2t] from 0 to 2π

= 3/4 (cos 0 - cos 4π)

= 3/2

Therefore, the length of the path described by the parametric equations x=cos³t and y=sin³t is 3/2 units.

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Answer:

Step-by-step explanation:

B

x is approximately equal to 6.

The ratios of the sides of a right triangle are called trigonometric ratios.

Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

sin = Perpendicular/ Hypotenuse

Cos = Base / Hypotenuse

tan = Perpendicular/Base

In the figure attached with the answer we can see that in Triangle ABC ,

tan 50.1 = x / 5

5(tan 50.1) = x

Therefore x is approximately equal to 6.

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The maximum number of gift packages that Rodarius can make is 30. Each gift package will contain 4 mini footballs and 1 signed autograph from the Titans.

To determine the maximum number of gift packages Rodarius can make so that each recipient gets an equal number of footballs and autographs, we need to find the greatest common factor (GCF) of the two numbers, 120 and 30.

The prime factorization of 120 is:

120 = 2³ x 3 x 5

The prime factorization of 30 is:

30 = 2 x 3 x 5

To calculate the GCF, multiply the product of the common factors by the lowest exponent:

GCF = 2 x 3 x 5 = 30

So the maximum number of gift packages that Rodarius can make is 30. Each gift package will contain 4 mini footballs and 1 signed autograph from the Titans.

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Using the concepts of standard normal distribution,43 people height is in between 160 and 180 and 31 people height is taller than 165cm

The standard normal distribution is actually  of the forms of the normal distribution. It occurs when  normal random variable has a mean equal to zero and a standard deviation equal to one. Or a normal distribution with a mean 0 and standard deviation of 1 is known as the standard normal distribution. Also, the standard normal distribution is concentrated at zero, and the standard deviation gives the degree to which a given measurement deviates from the mean.

Now, we find the Z score of the given heights range

We know that Z score is given by formula

Z=(\(\frac{X-\alpha }{\beta }\))

where X is normal random variable,\(\alpha\) is mean of given sample and \(\beta\) is standard deviation of given sample.

Therefore, Z score is

z(160) = (170-160)/5 = 2

z(180) = (180-170)/5 = 2

P(160<= x <=180) = P(2<= z <=2) = 0.4772(from standard distribution table)

Therefore for 90 people=90×0.4772= 43 people after rounded up.

b) Similarly, we need to find Z value for people height greater than 165 cm.

Therefore, by using the above formula, we get

z(165) = (170-165)/5 = 1

P(x > 165) = P(z > 1) = 0.3438(from standard distribution table)

Therefore, for 90 people=0.3438×90=31 after rounded up

Hence, number of people whose height is in between 160 and 180cm is 43 and number of people whose height greater than 165cm is 31

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The probability is 0.6480.

The probability is 0.9629.

1. This can be computed using the standard normal distribution as follows:

z = (70 - 69.0) / 2.8 = 0.357

Using a standard normal table or calculator, we find that P(Z ≤ 0.357) ≈ 0.6480. Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.6480.

2. = 2.8/√25 = 0.56 inches.

We want to find P(x < 70), which is the probability that the mean height of the 25 men is less than 70 inches. This can be standardized using the standard normal distribution as follows:

z = (70 - 69.0) / 0.56 = 1.79

Using a standard normal table or calculator, we find that P(Z < 1.79) ≈ 0.9629. Therefore, the probability that the mean height of the 25 men is less than 70 inches is approximately 0.9629.

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Answer:

The correct answer is 672.

Step-by-step explanation:

Plz mark as brainliest ! :D

Answer:

Marking braily:)

Step-by-step explanation:

Answer:

25°

Step-by-step explanation:

25° because opposite angles are equal

the blue angle 25° is opposite the yellow angle x° making x=25°

Answer:

x = 25°

Step-by-step explanation:

We can see that the 25° and x° are vertical to each other and vertical angles are angles that are the same size and directly opposite each other thus they are equal!

The expression \(2- \dfrac{x-1}{x+2}\)  is equivalent to \(1 + \dfrac{3}{x+2}\).

We have to find, which equation is equivalent to the given expression.

The given expression is,

\(= 2- \dfrac{x-1}{x+2}\)

To determine the equivalent expression following all the steps given below.

                   \(\rm = 2-\dfrac{x-1}{x+2}\\\\= \dfrac{2(x+2) - (x-1)}{x+2}\\\\= \dfrac{2x+4-x+1}{x+2}\\\\\)

                    \(= \dfrac{2x+4-x+1}{x+2}\\\\= \dfrac{x+5}{x+2}\\\\\)

                    \(=\dfrac{x+5}{x+2}\\\\= \dfrac{x+ 2+3}{x+2}\\\\\)

                    \(= \dfrac{x+2}{x+2} + \dfrac{3}{x+2}\\\\= 1 + \dfrac{3}{x+2}\)

Hence, The expression \(2- \dfrac{x-1}{x+2}\)  is equivalent to \(1 + \dfrac{3}{x+2}\).

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Answer:

1/5

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

\( \frac{j}{4} = \frac{12}{4} = 3\)

4*3=12

3*4=12

12/4=3

12/3=4

Hope this helps ;) ❤❤❤

Answer:

We need to evaluate \(\frac{j}{4}\) for j = 12.

First, we need to replace j by 12 on \(\frac{j}{4}\), so we get \(\frac{12}{4}\) and now, we only need to divide:

\(\frac{12}{4}=3\)

So the result is 3

Answer:

you would need 6 scoops of sugar

Answer:

You would need 15 scoops of sugar per 3.5 oz

Step-by-step explanation: