Tammy made a 6-ounce milkshake. Two-thirds of the milkshake was ice cream. How many ounces of ice cream did
Tammy use in the shake?

The associated right triangle has one angle θ whose tangent is x/6, and the adjacent side has length 6 while the opposite side has length x.

To evaluate the integral, we use the trigonometric substitution x = 6 tan(θ). Then, dx = 6 sec2(θ) dθ, and substituting in the integral we get:

∫(x^2)/(36+x^2) dx = ∫(36 tan^2(θ))/(36 + 36 tan^2(θ)) (6 sec^2(θ) dθ)

= ∫tan^2(θ) dθ

To solve this integral, we use the trigonometric identity tan^2(θ) = sec^2(θ) - 1, so we get:

∫tan^2(θ) dθ = ∫(sec^2(θ) - 1) dθ

= tan(θ) - θ + C

Substituting back x = 6 tan(θ) and simplifying, we get the final result:

∫(x^2)/(36+x^2) dx = 6(x/6 * √(1 + x^2/36) - atan(x/6) + C)

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Answer:I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000

Step-by-step explanation:

Answer:

66 cm²

Step-by-step explanation:

From the given figure, and the question statement we have;

BD = 11 cm, AE = 7 cm, CF = 5 cm

The given quadrilateral ABCD consists of two triangles; ΔABD and ΔBCD

The area of quadrilateral ABCD = The sum of the areas of ΔABD and ΔBCD

The base length of the two triangles equals segment BD = 11 cm

The height of triangle ΔABD = 7 cm

The area of a triangle = (1/2) × Base length × Height

∴ The area of triangle ΔABD = (1/2) × 11 cm × 7 cm = 38.5 cm²

Similarly;

The area of triangle ΔBCD = (1/2) × 11 cm × 5 cm = 27.5 cm²

∴ The area of quadrilateral ABCD = 38.5 cm² + 27.5 cm² = 66 cm²

The area of the given figure (quadrilateral ABCD) = 66 cm².

Answer:

The concept of identity, the meaning we give to ourselves and our sense of purpose, connects us to others. This concept best illustrates the link between the psychological and ____ system

Answer:25

Step-by-step explanation:

Answer:

3.68 cm ^2

Step-by-step explanation:

A= b x h

A= 1.6 cm x 2.3 cm

A= 3.68 cm ^2

To determine the fraction of their journey that they drove, we need more information about the specific distances covered by each mode of transportation.

In order to calculate the fraction of their journey that the Robinson family drove, we need to know the distances covered by each mode of transportation. Let's assume that the distances covered by air and train are given as fractions or percentages of the total journey.

For example, if they traveled by air for 1/4 of the journey and by train for 2/5 of the journey, we can calculate the fraction of the journey they drove by subtracting the sum of the fractions covered by air and train from 1. In this case, the fraction they drove would be 1 - (1/4 + 2/5) = 1 - (5/20 + 8/20) = 1 - (13/20) = 7/20.

However, without specific information about the distances covered by each mode of transportation, it is not possible to determine the exact fraction they drove. The fraction would depend on the actual distances covered and cannot be calculated without those details.

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Answer:

  height = 2/5h

Step-by-step explanation:

You want the height of a frustum if the volume of the frustum is 98/125 times the volume of the original cone, which was of height h.

Let h' represent the height of the part of the cone that is removed to leave the frustum. Then its volume (v') is ...

  v' = (volume of large cone)(1 - 98/125) = v·(27/125)

The scale factor between h' and h is ...

  (h'/h)³ = v'/v = 27/125

  h'/h = ∛(27/125) = 3/5

The height of the frustum in terms of the height of the original cone is ...

  frustum height = (height of large cone) - (height of small cone)

  frustum height = h - (3/5)h

  frustum height = 2/5h

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Answer:

A, C, E

Step-by-step explanation:

remember to law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

or the "upside-down" version :

sin(A)/a = sin(B)/b = sin(C)/c

with a, b, c being the sides of the triangle, and A, B, C being the corresponding opposite angles in the triangle.

so, as you can clearly see, we always need at least one angle and one side (in fact either 2 angles one side or 1 angle 2 sides) to use the law of sine to solve the rest of the triangle.

therefore, the answer options A, C, E are correct.

for SSS (all 3 sides are known) we need the law of cosine to solve the angles (at least one of them, and then we could continue with either law).

remember :

c² = a² + b² - 2ab×cos(C)

again, a,b,c are the sides, and C is the opposite angle of whatever side we define as "c".

that's why I always call this the extended Pythagoras.

for AAA (all 3 angles are known) we cannot solve the triangle, because dilated triangles all have the same angles. and therefore there are infinitely many triangles with the same angles.

The surface area of the cylinder is approximately 401.92 square centimeters. To find the surface area of the cylinder, we need to add the area of the top and bottom circles to the area of the lateral surface.

The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

where r is the radius of the base, h is the height of the cylinder, and π ≈ 3.14.

Given that the radius is 8 cm and the height is also 8 cm, we can plug in the values in the formula:

SA = 2π(8²) + 2π(8)(8)

SA = 401.92

Rounding to the nearest hundredth, we get:

SA ≈ 401.92 square centimeters

Therefore, the surface area of the cylinder is approximately 401.92 square centimeters.

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For an exponential probability distribution of time (in years) until part failure for a certain car, probability that the time until the first critical-part failure is 6 year or more is equals to the 0.181.

The exponential distribution is a type of continuous probability distribution that is used to measure the expected time for an event to occur. Formula is written as \(f(X)=\lambda e^{-\lambda x}; X >0, \)

where λ --> rate parameter

X --> observed value

We have time (in year) first critical-part failure for a certain car is exponentially distributed. Let X be the time part failure for a certain car. Now, X follows the exponential distribution with mean 3.5 years. The probability density function of X is \(f(X) = \lambda e^{- \lambda x} ;X > 0 \), Here in this problem,

\(\lambda = \frac{1}{3.5} \)

= 0.285

Using the formula the probability of

X more than and equal to 6 years is \(P( X≥ 6) = 1 - P( X≤6) \)

\(= 1- (1 – e^{−0.285×6})\)

\(= e^{−0.285×6})\)

= 0.180865 ~ 0.181. Hence, the required probability value is 0.181.

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Using the given information and what we know about linear equations, we will find the sketch below.

Here we need to analyze each part separately.

In a coordinate axis where the y-axis represents distance and the x-axis represents time, we will have that:

First, we know that he rides for 30 minutes at a given speed, this will be represented with an increasing linear function.

Then he stops for 20 minutes, this is represented with a horizontal line.

Finally, he returns the motion, but slower than before, so the slope of this line will be smaller than the first one.

So for 0 to 30 we have an increasing linear equation, then for 30 to 50 we have a constant horizontal line, then for 50 to 80 we have another increasing linear equation

The sketch can be seen below.

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The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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Answer:

okay the answer is your mom ohhhhhhhhhhhhhhhhhh

Step-by-step explanation:

hi

Answer:

whatssssssssssssssssssss

The critical value of the standard normal distribution at α/2 = 0.025 is approximately 1.96.

To conduct a survey to verify the share value of 25%, the advertiser can use hypothesis testing. Let p be the true proportion of households with TV sets tuned to Pretty Betty, and let p0 = 0.25 be the hypothesized value of p. The null and alternative hypotheses are:

H0: p = 0.25

Ha: p ≠ 0.25

Using the pilot survey of 13 households, let X be the number of households with TV sets tuned to Pretty Betty. Assuming that the households are independent and each has probability p of being tuned to the show, X follows a binomial distribution with parameters n = 13 and p.

Under the null hypothesis, the mean and standard deviation of X are:

μ = np0 = 3.25

σ = sqrt(np0(1-p0)) ≈ 1.954

To test the null hypothesis, we can use a two-tailed z-test for proportions with a significance level of α = 0.05. The test statistic is:

z = (X - μ) / σ

If the absolute value of the test statistic is greater than the critical value of the standard normal distribution at α/2 = 0.025, we reject the null hypothesis.

For this pilot survey, suppose that 3 households had TV sets tuned to Pretty Betty. Then, the test statistic is:

z = (3 - 3.25) / 1.954 ≈ -0.1289

The critical value of the standard normal distribution at α/2 = 0.025 is approximately 1.96. Since the absolute value of the test statistic is less than the critical value, we fail to reject the null hypothesis. This means that there is not enough evidence to suggest that the true proportion of households with TV sets tuned to Pretty Betty is different from 0.25 based on the pilot survey of 13 households.

However, it is important to note that a pilot survey of only 13 households may not be representative of the entire population, and larger sample sizes may be needed for more accurate results.

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Answer:

\(\frac{-y-1}{8}\)

Step-by-step explanation:

1/2y - 5/8y = 4/8y - 5/8y = -1/8y

3/4 - 7/8 = 6/8 - 7/8 = -1/8

-1/8y - 1/8 =

-y/8 - 1/8 =

\(\frac{-y-1}{8}\)

Answer:

Because Rhomboids have adjacent sides that makes it equal, and also both sides have the same meeting point which is M.

Step-by-step explanation:

Interactions involving dummy variables can provide insights into the different effects of independent variables across categories.

1. Dummy variables are binary variables that represent categorical variables in a regression analysis. When interactions are included between dummy variables and other independent variables, it allows for differential effects of the independent variables based on the different levels of the categorical variable.

For example, let's consider a regression model to predict income based on education level and gender. We can include an interaction term between education level (represented by dummy variables for different levels) and gender. This interaction term allows us to examine whether the effect of education level on income differs between males and females. It helps capture any gender-specific differences in the relationship between education and income.

1.2 The linear probability model (LPM) is a common approach to estimate the probability of an event occurring using a linear regression framework. However, it has several problems:

1. The predicted probabilities from the LPM can fall outside the [0, 1] range: Since the LPM does not impose any restrictions on the predicted probabilities, they can sometimes exceed the valid probability range. This violates the assumption of probabilities being bounded between 0 and 1.

2. Heteroscedasticity: The LPM assumes constant error variance across the range of the predictors. However, in practice, the variability of the error term may change with different levels of the predictors, resulting in heteroscedasticity. This violates the assumption of homoscedasticity.

3. Non-linearity: The LPM assumes a linear relationship between the predictors and the probability of the event. However, this may not always be the case, and using a linear model can result in misspecification.

To remedy these problems, an alternative to the LPM is to use logistic regression or probit regression models. These models explicitly model the probability of an event occurring and address the issues mentioned above. They provide predicted probabilities that fall within the valid range of 0 to 1, account for heteroscedasticity, and allow for non-linear relationships between the predictors and the probability of the event.

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Therefore , the solution of the given problem of  surface area comes out to be  unused space is equal to 2π - (5π/6 + √3/2) m² .

Its surface area serves as a proxy for how much overall space it occupies. The whole environment of a three-dimensional shape is taken into account when calculating its surface area. The overall size of something is its surface area. The volume of water in a cuboid can be determined by summing the face on each of the six rectangular sides. To determine the box's measurements, apply the following formula: For 2lh, 2lw, & 2hw, the surface is exactly the same (SA). The region is represented by the surface area of the muti form.

Here,

Given:

AB = D = 4 m (R = 2 m)

The size of the AB semicircle is:

=> Area = πr²/2

=>A = 2π

The dimensions of the little semicircle are a=5/6 + 2/3/2 m2 and a=5/6 + 3/2 m2.

The remainder area is therefore equal to A- a.

= 2π - (5π/6 + √3/2) m²

The unused space is equal to 2π - (5π/6 + √3/2) m²

Therefore , the solution of the given problem of area comes out to be  unused space is equal to 2π - (5π/6 + √3/2) m² .

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The length of the repel line using one of the 3 trigonometry ratios will be 186.78 feet.

From the information given, Peyton is walking her dog, Willow, on a local trail and the dog falls 153 feet down a ravine.

The length will be calculated thus:

Cos 35° = 153/AC.

AC = 153/cos 35°

AC = 153/0.819

AC = 186.78 feet.

Therefore, the length is 186.78 feet.

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Answer:

x= r/s+t

Step-by-step explanation:

Answer:

(A) First table

___________

Input: 6, 9, 12

Output: 8, 12, 16

Step-by-step explanation:

To determine whether or not a function is a direct variation, x and y must divide evenly and have a constant factor or factor that stays the same.

B and C don't divide evenly so those are already wrong, and D is wrong because x and y do not divide by the same factor every time.

The correct statement among the given options is A. "Research cannot use both qualitative and quantitative methods in a study."

This statement is not correct because research can indeed use both qualitative and quantitative methods in a study. Qualitative research focuses on collecting and analyzing non-numerical data such as observations, interviews, and textual analysis to understand phenomena in depth. On the other hand, quantitative research involves collecting and analyzing numerical data to derive statistical conclusions and make generalizations.

Many research studies employ a mixed methods approach, which combines both qualitative and quantitative methods, to provide a comprehensive understanding of the research topic. By using both qualitative and quantitative data, researchers can gather rich insights and statistical evidence, allowing for a more comprehensive analysis and interpretation of their findings.

Therefore, option A is the statement that is not correct concerning qualitative and quantitative research.

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Answer:

your answer would be B I hope it's right

Answer:

B)

Step-by-step explanation:

I hope this helps:)

Answer:

c. y = 1/2x - 2

Step-by-step explanation:

they have the same gradient so are parallel

Answer:

dhdt≃0.283ft3s

Step-by-step explanation:

dhdt≃0.283ft3s

The draining from the tank when the water depth is 8 ft will be negative 1/π feet per minute.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

An inverted conical water tank with a height of 12 ft and a radius of 3 ft is drained through a hole in the vertex. If the water level drops at a rate of 1 ft/min.

\(\rm \dfrac{dV}{dt} = -1 \ ft/min\)

The volume of the cone is given as,

V = (1/3) πr²h

The relation between r and h is given as,

r / h = 3 / 12

r = h / 4

Then the volume is written as,

V = (1/3) π (h/4)² × h

V = (π / 48) h³

Differentiate the volume with respect to time. Then we have

(dV)/(dt) = (π/48) x 3h² x (dh / dt)

- 1 = (π/48) x 3(4)²  (dh / dt)

- 1/π = dh / dt

The draining from the tank when the water depth is 8 ft will be negative 1/π feet per minute.

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Answer: 6 days and 18 hours

Step-by-step explanation: 9/4=1.25 1.25x3=6.75 and so on

After 35 minutes there will be 40 bacteria remaining.

The process of a constant percentage rate decrease in an amount over time is referred to as "exponential decay." The formula to calculate exponential decay is given as, \(N_t=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}\). Here, Nt is the quantity after time t, N0 is the initial quantity, t1/2 is the half-life, and t is time.

For the first situation, Nt=360, N0=900, t=10 minutes. Therefore, substituting the given values get the value of t1/2. So,

\(\begin{aligned}360&=900\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}} \\\frac{360}{900}&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\0.4&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\ \ln(0.4)&=\frac{10}{t_{1/2}}\ln(0.5)\\t_{1/2}&=10\times\frac{\ln(0.5)}{\ln(0.4)}\\&=7.6\end{aligned}\)

Now, for the second situation,  Nt=40.  We have to find the time at which there will be 40 bacteria remaining. Then,

\(\begin{aligned}40&=900\left(\frac{1}{2}\right)^{t/7.6}\\0.04&=\left(\frac{1}{2}\right)^{t/7.6}\\\ln(0.04)&=\frac{t}{7.6}\ln(0.5)\\t&=7.6\times\frac{\ln(0.04)}{\ln(0.5)}\\&=7.6\times4.64\\&=35.26\\&\approx35\end{aligned}\)

The answer is 35 minutes.

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