Bryan's lemon cookie recipe calls for 1 1/3 cups of sugar. How much sugar would Bryan use to make 3 1/2 batches of cookies?

The angle K for the Isosceles trapezoid is a supplementary angle to the angle J and the measure of angle K = 152°

This is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.

angle J and angle M are base angles for the Isosceles trapezoid and are equal, so:

23x + 5 = 13x + 15

23x - 13x = 15 - 5 {collect like terms}

10x = 10 {divide through by 10}

x = 1

angle J = 23(1) + 5 = 28°

Angle K and angle J are supplementary so:

K = 180 - 28

K = 152°

Therefore, the measure of the angle K for the Isosceles trapezoid JKLM is equal to 152°

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Answer:

Janet would save 4 dollars a month while Mike saves 2 dollars a month.

Step-by-step explanation:

5 x 2 = 10

4 x 2 = 8

10 + 8 = $18

Answer:

18

Step-by-step explanation:

The graph of the equation is a hyperbola, (-1, 1).

We have,

To identify the graph of the equation x² - 2x - 2 - 36 = 0 and find the point (h,k), we need to rearrange the equation into a standard form and analyze the coefficients.

x² - 2x - 38 = 0

By comparing this equation to the general form of an ellipse and a hyperbola, we can determine the correct graph.

The equation for an ellipse in standard form is:

((x - h)² / a²) + ((y - k)² / b²) = 1

The equation for a hyperbola in standard form is:

((x - h)² / a²) - ((y - k)² / b²) = 1

Comparing the given equation to the standard forms, we see that it matches the equation of a hyperbola.

Therefore,

The graph of the equation is a hyperbola, (-1, 1).

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Answer:

8

Step-by-step explanation:

6x+5=53

6x=48

6x/6=48/6

x=8

The specific critical value for a one-tailed dependent samples t-test at the p < .05 level for a study with 30 participants is :

1.699

To find the specific critical value for a one-tailed dependent samples t-test at the p < .05 level for a study with 30 participants, you will need to refer to the t-distribution table.

1. First, determine the degrees of freedom, which is the number of participants minus 1: df = 30 - 1 = 29.
2. Next, locate the appropriate row for 29 degrees of freedom in the t-distribution table.
3. Look for the value in the one-tailed (0.05) column.

After checking the t-distribution table for 29 degrees of freedom and a one-tailed test with a significance level of p < .05, the critical value is 1.699. Therefore, the answer to your question is 1.699.

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To find the expected number of sixes appearing on three die rolls, we can calculate the probability of rolling a six on each individual roll and then multiply it by the number of rolls.

The probability of rolling a six on a single roll of a fair die is 1/6, since there are six equally likely outcomes (numbers 1 to 6) and only one of them is a six.

Since the rolls are independent events, we can multiply the probabilities together to find the probability of rolling a six on all three rolls:

(1/6) * (1/6) * (1/6) = 1/216

Therefore, the probability of rolling a six on all three rolls is 1/216.

To find the expected number of sixes, we multiply the probability by the number of rolls:

Expected number of sixes = (1/216) * 3 = 1/72

So, the expected number of sixes appearing on three die rolls is 1/72.

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Therefore, according to the squeeze theorem, the limit of x^2 cos(1/x^2) as x approaches 0 is also 0: lim(x→0) x^2 cos(1/x^2) = 0.

To prove that lim(x→0) x^2 cos(1/x^2) = 0, we can use the squeeze theorem.

First, we establish the following inequalities:

-1 ≤ cos(1/x^2) ≤ 1

Since -1 ≤ cos(1/x^2) ≤ 1 for all values of x, we can multiply each side of the inequality by x^2 to obtain:

-x^2 ≤ x^2 cos(1/x^2) ≤ x^2

Now, we need to evaluate the limits of the lower and upper bounds as x approaches 0:

lim(x→0) -x^2 = 0

lim(x→0) x^2 = 0

Since both lower and upper bounds approach 0 as x approaches 0, we can conclude that the function x^2 cos(1/x^2) is "squeezed" between these two functions.

Thus, the statement is proven.

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Answer:

-19

Step-by-step explanation:

Given that:

Pencils: 5

Pens: 8

Ratio indicates how one value is compared to another value

The ratio of pens to pencils will be:

8:5

Answer: 28

Step-by-step explanation:

   First, we will write what the first line of text represents:

3x + 5 = 7

   Then, we will solve:

3x + 5 = 7

3x = 2

x = \(\frac{2}{3}\)

   Lastly, we will substitute this value of x into the expression and simplify:

12x + 20

12(\(\frac{2}{3}\)) + 20

8 + 20

28

Answer:

Option B.

Step-by-step explanation:

We have to find the quotient of the expression \((3x^4+6x^3+2x^2+9x+10)\) when divided by (x + 2) by synthetic division.

-2 | 3     6     2     9     10

   | ↓    -6     0    -4    -10

     3     0     2     5     0

Solution of the synthetic division will be = (3x³ + 2x + 5)

Therefore, quotient after division will be, (3x³ + 2x + 5) and the remainder is 0.

Therefore, (3x³ + 2x + 5) will be the answer.

Option (B) will be the correct option.

Answer:

B

Step-by-step explanation:

I did the work and this one is very tough

The result for the given normal random variables are as follows;

a. E(3X + 2Y) = 18

b. V(3X + 2Y) = 77

c. P(3X + 2Y < 18) = 0.5

d. P(3X + 2Y < 28) = 0.8729

Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Now, according to the question;

The given normal random variables are;

E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.

Part a.

Consider E(3X + 2Y)

\(\begin{aligned}E(3 X+2 Y) &=3 E(X)+2 E(Y) \\&=(3) (2)+(2)(6 )\\&=18\end{aligned}\)

Part b.

Consider V(3X + 2Y)

\(\begin{aligned}V(3 X+2 Y) &=3^{2} V(X)+2^{2} V(Y) \\&=(9)(5)+(4)(8) \\&=77\end{aligned}\)

Part c.

Consider P(3X + 2Y < 18)

A normal random variable is also linear combination of two independent normal random variables.

\(3 X+2 Y \sim N(18,77)\)

Thus,

\(P(3 X+2 Y < 18)=0.5\)

Part d.

Consider P(3X + 2Y < 28)

\(Z=\frac{(3 X+2 Y-18)}{\sqrt{77}}\)

\(\begin{aligned} P(3X + 2Y < 28)&=P\left(\frac{3 X+2 Y-18}{\sqrt{77}} < \frac{28-18}{\sqrt{77}}\right) \\&=P(Z < 1.14) \\&=0.8729\end{aligned}\)

Therefore, the values for the given normal random variables are found.

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The correct question is-

X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following:

a. E(3X + 2Y)

b. V(3X + 2Y)

c. P(3X + 2Y < 18)

d. P(3X + 2Y < 28)

Answer: B. 1178 cm²

What we are solving for:

   The lateral area is, put simply, the surface area of the cone not including the bottom.

    The formula is:

L = πr\(\sqrt{h^{2} +r^{2} }\)

Height of the cone:

    This calls for the height, since it is a right triangle we can use the Pythagorean theorem to solve.

a² + b² = c²

15² + b² = 25²

225 + b² = 625

b² = 400

b = \(\sqrt{400}\)

    The height is 20 cm

Solving:

    Back to the formula,

L = πr\(\sqrt{h^{2} +r^{2} }\)

L = π15\(\sqrt{(20)^{2} +(15)^{2} }\)

L ≈ 1178.1 cm²

              The lateral area of the cone is B. 1,178 cm².

The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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Since we cannot have a fraction of a student, we need to round up to the nearest whole number.

Therefore, the required sample size is 10 students.
Hence correct answer is D. 10.

To determine the sample size required for this study, we can use the formula for sample size estimation in a population with known standard deviation.

The formula is:
n = (Z * σ / E)^2
where:
n = sample size
Z = Z-score corresponding to the desired confidence level (90% in this case)
σ = standard deviation of the population (2.8)
E = margin of error (1.5 drinks)
First, we need to find the Z-score corresponding to the 90% confidence level.

Since we want a two-tailed probability, we will look up the Z-score for 95% (adding 5% to each tail of the distribution).

The Z-score for 95% is approximately 1.645.
Next, we plug the values into the formula:
\(n = (1.645 * 2.8 / 1.5)^2\)
\(n = (4.606 / 1.5)^2\)
\(n = 3.071^2\)
\(n = 9.43\)

So, the correct answer is D. 10.

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The Central Limit Theorem allows us to use the sample mean to estimate the population mean even when the population distribution is unknown. The standard deviation of the population, sigma, is an important factor in determining the spread of the sample means.

The statement you are referring to is known as the Central Limit Theorem. It states that when sampling from a population with an unknown distribution, if the sample size is sufficiently large (usually n>30), the sample mean will follow an approximately normal distribution regardless of the shape of the population distribution. This is particularly useful in statistics because it allows us to make inferences about the population mean based on the sample mean.

The standard deviation, sigma, plays an important role in the Central Limit Theorem because it determines how spread out the population is. If sigma is small, the sample means will be tightly clustered around the population mean, while if sigma is large, the sample means will be more spread out.

In conclusion, the Central Limit Theorem allows us to use the sample mean to estimate the population mean even when the population distribution is unknown. The standard deviation of the population, sigma, is an important factor in determining the spread of the sample means.

1. When sampling from a population with an unknown distribution, mean mu, and standard deviation sigma,

2. If the sample size (n) is sufficiently large,

3. The sample mean (x bar) will have approximately a normal distribution.

The CLT(central limit theorem) is a vital tool in many areas of statistical analysis, as it provides a foundation for making inferences about populations based on sample data, even when the original population distribution is unknown or non-normal.

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The concept which is the main idea of estimating a population​ proportion is

C. Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.

The concept stated in option C is not a main idea of estimating a population proportion.

Estimating a population proportion involves inferential statistics, which is concerned with making inferences or drawing conclusions about a population based on information from a sample. In this context, descriptive statistics refers to methods that summarize and describe the characteristics of a sample or population, such as measures of central tendency and variability.

The main ideas of estimating a population proportion include:

A. The sample proportion is the best point estimate of the population proportion: When estimating a population proportion, the sample proportion (the proportion observed in the sample) is commonly used as the point estimate for the population proportion. This is because it provides an unbiased estimate of the unknown population proportion.

B. Knowing the sample size necessary to estimate a population proportion is important: The sample size plays a crucial role in estimating a population proportion. A larger sample size generally leads to a more precise estimate with a smaller margin of error. Determining an appropriate sample size is essential to ensure the desired level of confidence and accuracy in the estimate.

D. We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion: Constructing a confidence interval is a common method to estimate the true value of a population proportion. By using the sample proportion along with the standard error and a chosen level of confidence, a range of values is calculated within which the true population proportion is likely to fall.

In contrast, option C refers to using a sample statistic to estimate the population proportion by utilizing descriptive statistics. However, estimating a population proportion typically involves inferential statistics rather than descriptive statistics.

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Answer:

Slop intercept form hopefully this helps

Answer:

-2

Step-by-step explanation:

I'm no mathematician, but i'm pretty sure the answer to that is 2. :)

Answer:the answer is A

Step-by-step explanation:

The step is

Real number - rational(irrational)_ - integer - whole - then natural

The true statement regarding number sets are b. all irrational numbers are real numbers.

Irrational numbers are those numbers which have a non-repeating, non-terminating pattern after decimal place.

According to the given statements we have to determine which is true.

a. all integers are not whole numbers as 0 contains in the set of whole numbers but not in the set of integers.

b. all irrational numbers are real numbers this is a true statement because all the real numbers consist of rational and irrational numbers.

We don't need to check other options because we have been asked which of the following is true not which of the following is/are true.

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Keegan's error is that he did not provide enough information to fully determine the result of the given composition of transformations, namely (R90•D2)(Triangle ABC).

To be able to graph the image of Triangle ABC under the composition of R90 (a 90-degree counterclockwise rotation) and D2 (a dilation with center the origin and scale factor 2), we need to know the center of rotation for the rotation R90.

The reason for this is that the composition of a rotation and a dilation is not commutative, meaning that the order of the transformations matters. Specifically, the result of the composition depends on whether the dilation is applied before or after the rotation. If the dilation is applied before the rotation, then the center of dilation becomes the center of rotation for the rotation. If the rotation is applied before the dilation, then the center of dilation is not affected by the rotation.

Therefore, without knowing the center of rotation for the rotation R90, we cannot determine the exact result of the composition (R90•D2)(Triangle ABC), and thus we cannot graph it accurately.

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The population median commute time of the employees of Asons is 40 minutes.

The median is a measure of central tendency that represents the middle value in a dataset when the data is arranged in ascending or descending order. In this case, the commute times provided are 47.4, 45, 35, and 40 minutes.

To determine the median, we arrange the commute times in ascending order: 35, 40, 45, 47.4. Since there are four values in the dataset, the middle value is the average of the two central values, which are 40 and 45. Taking the average of these two values gives us the median of 40 minutes.

Therefore, the population median commute time of the employees of Asons is 40 minutes, indicating that half of the employees have a commute time of 40 minutes or less, while the other half have a commute time of 40 minutes or more.

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Answer:

504 km

Step-by-step explanation:

The number that should be added to the polynomial 2x³ - 3x² - 8x is 12x

When a polynomial is divided by a linear factor, the remainder is equal to the constant term of the polynomial multiplied by the reciprocal of the linear factor.

In this case, the polynomial is 2x³ - 3x² - 8x, and the linear factor is 2x-1.

To find the remainder when this polynomial is divided by 2x-1, we need to multiply the constant term of the polynomial, which is -8, by the reciprocal of 2x-1, which is 1/(2x-1).

So the remainder should be -8*(1/(2x-1)) = -8/(2x-1) = -4/(x-0.5)

To make the remainder 12, we will add 12x to the polynomial so that the new constant term is 12.

The polynomial 2x³ - 3x² - 8x + 12x will have a remainder of 12 when divided by 2x-1.

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For a crosstabs analysis with a row variable of 4 groups and a column variable of 13 groups, the degrees of freedom for this test would be 36.

To determine the degrees of freedom for a crosstabs analysis, we need to consider the number of groups for each variable. The degrees of freedom in this context represent the number of independent pieces of information available for analysis.

In a crosstabs analysis, we create a contingency table that displays the frequency or count of observations falling into each combination of categories for the row and column variables. The table is typically organized in a grid format.

The degrees of freedom for a crosstabs analysis are calculated using the formula:

(df_row - 1) * (df_column - 1)

where df_row represents the degrees of freedom for the row variable and df_column represents the degrees of freedom for the column variable.

In this scenario, the row variable has 4 groups, so df_row = 4 - 1 = 3. Similarly, the column variable has 13 groups, so df_column = 13 - 1 = 12.

Plugging these values into the formula, we get:

(3) * (12) = 36

Therefore, for the given crosstabs analysis with a row variable of 4 groups and a column variable of 13 groups, there are 36 degrees of freedom available for this test. These degrees of freedom allow for the assessment of the relationship between the two variables and the evaluation of statistical significance.

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To guarantee accuracy within 0.00002 for trapezoidal and midpoint rule approximations for ∫21 1x dx, we must take n ≥ 92 for the trapezoidal rule and n ≥ 65 for the midpoint rule.

To guarantee that the trapezoidal and midpoint rule approximations for ∫21 1x dx are accurate to within 0.00002, we need to find the value of n that satisfies the following inequalities:

|ET| ≤ (b-a)³ / (12n²) * M₂ for the trapezoidal rule
|EM| ≤ (b-a)³ / (24n²) * M₂ for the midpoint rule

Where M₂ is the maximum value of the second derivative of the function f(x) = 1/x on the interval [1,2], b-a = 2-1 = 1, and ET and EM are the true errors for the trapezoidal and midpoint rules, respectively.

Taking the second derivative of f(x), we get f''(x) = 2/x³. The maximum value of this function on the interval [1,2] is M₂ = 2.

Plugging in the values of M₂, b-a, and the desired accuracy into the inequalities, we get:

|ET| ≤ (1)³ / (12n²) * 2 ≤ 0.00002
|EM| ≤ (1)³ / (24n²) * 2 ≤ 0.00002

Solving for n, we get:

n² ≥ (1)³ / (12 * 0.00002) * 2 = 8333.33 for the trapezoidal rule
n² ≥ (1)³ / (24 * 0.00002) * 2 = 4166.67 for the midpoint rule

Taking the square root of both sides, we get:

n ≥ 91.29 for the trapezoidal rule
n ≥ 64.55 for the midpoint rule

Therefore, to guarantee that the trapezoidal and midpoint rule approximations are accurate to within 0.00002, we should take n ≥ 92 for the trapezoidal rule and n ≥ 65 for the midpoint rule.

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Conduct a one-sample t-test to determine if the mean temperature of the cakes is statistically significantly above 200 F.

To test whether the mean temperature of the cakes is above 200 F, a one-sample t-test is suitable. In this case, the manufacturer has collected 100 data points, which allows for an adequate sample size. The one-sample t-test compares the sample mean to a hypothetical mean (in this case, 200 F) and determines if there is enough evidence to suggest that the true population mean is significantly different.

By performing this test, the manufacturer can assess whether the baking process consistently produces cakes with a mean temperature above the desired threshold. The results of the t-test will provide statistical evidence to support decision-making regarding the baking temperature.

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Using property of independent events, there should be 12 sophomore girls present in the class.

If the occurrence of one event has no bearing on the likelihood that the other will also occur, then the two events are independent. The likelihood that both occurrences A and B will occur is defined mathematically as being equal to the product of the probabilities of A and B (i.e., P) (A and B)

Given,

There are twelve freshmen boys, sixteen freshmen girls, and nine sophomore boys

and two events are independent if,

p(A ∩ B) = P(A). P(B)

Let sophomore girls present = x

               Freshmen       sophomore        Total

Boys              12                     9                    21

Girls               16                     x                    16 + x

Total              28                 9 + x                37 + x

P(Boys) = \(\frac{21}{37 + x}\)

P(Freshmen) = \(\frac{28}{37 + x}\)

P(Boys ∩ Freshmen) = \(\frac{12}{37 + x}\)

Using p(A ∩ B) = P(A). P(B),

\(\frac{12}{37 + x} = \frac{21}{37 + x} \times \frac{28}{37 + x}\)

\(12(37 + x) = 21 \times 28\\x = 12\)

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Answer:

98.9

Step-by-step explanation:

23x4.3=98.9 hours