If a recipe for one batch of cookies uses 5 cups of flour and 2 teaspoons of vanilla, how many teaspoons of vanilla would you use for 20 cups of flour? (Hint: Draw a double number line on a piece of paper to help identify an equivalent ratio.)
Group of answer choices

10

4

6

8
MATH
6TH GRADE

Answer:

The area of the trapezoid shown above is 660 square inches.

Step-by-step explanation:

It already gives you the formula, so just plug in the numbers given.

\(h\) - height (20)

\(B_1\) - Base (30)

\(B_2\) - Other base (36)

\(\frac{1}{2}(20)(30+36)\\\frac{1}{2}(20)(66)\\=660\)

a) The test statistic is -2.32. The p-value is 0.0104.

b) Yes, the above sample evidence enable us to reject the null hypothesis at α = 0.10.

c) Yes, the above sample evidence enable us to reject the null hypothesis at α = 0.05.

d) Population mean is less than 189 at a significance level of 0.05.

a-1) The test statistic can be calculated as:

z = (X - μ) / (σ/√n) = (187 - 189) / (15/√74) = -2.32

where X is the sample mean, μ is the hypothesized population mean, σ is the population standard deviation, and n is the sample size.

a-2. The p-value can be found by looking up the area to the left of the test statistic in the standard normal distribution table. The area to the left of -2.32 is 0.0104. Therefore, the p-value is 0.0104.

b. At α = 0.10, the critical value for a one-tailed test with 73 degrees of freedom is -1.28. Since the test statistic (-2.32) is less than the critical value, we can reject the null hypothesis at α = 0.10.

c. At α = 0.05, the critical value for a one-tailed test with 73 degrees of freedom is -1.66. Since the test statistic (-2.32) is less than the critical value, we can reject the null hypothesis at α = 0.05.

d. At α = 0.05, we have sufficient evidence to reject the null hypothesis that the population mean is greater than or equal to 189 in favor of the alternative hypothesis that the population mean is less than 189. Therefore, we can conclude that the sample provides evidence that the population mean is less than 189 at a significance level of 0.05.

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Answer:

Go to photo math thank me later

Step-by-step explanation:

Answer:

if your trying to find the area of 10ft and 2 1/2 all you gotta do is turn the 2 1/2 in a decimal and multiply it by 10 which is 25

Step-by-step explanation:

Step-by-step explanation:

To find the angle between a line and the x-axis, we need to calculate the slope of the line first. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the points (-2, 2) and (8, 9), we can substitute the values into the formula:

m = (9 - 2) / (8 - (-2))

= 7 / 10

= 0.7

The slope of the line is 0.7. The angle between the line and the x-axis can be found using the inverse tangent (arctan) function. The tangent of an angle is equal to the slope of the line, so we can write:

tan(θ) = 0.7

Taking the inverse tangent of both sides, we find:

θ = arctan(0.7)

Using a calculator, we can evaluate this to be approximately:

θ ≈ 35.87 degrees

Therefore, the angle between the line and the x-axis is approximately 35.87 degrees.

Frequency and wavelength are related by the equation f=cλ, where c is the speed of light in a vacuum. The speed of light in a vacuum is 2.9979×108 m/s. Wavelength must be converted from kilometers to meters, then the values can be plugged into the equation. f=2.9979×108 m/s5,700 m=52,594 Hz. The resulting frequency is 52,594 Hz or 5.3×104 Hz when rounded to the correct number of significant figures.

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Answer:

u < -5

Step-by-step explanation:

-2u > 10 (Divide both sides by -2)

u > -5 (Change the greater than sign to a less than sign since we divided by a negative number)

Final Answer: u < -5

Answer:

b or 1.2*10⁻1

Step-by-step explanation:

10^8=one hundred million and that *3=three hundred million

10^7=ten million*3.6=36 million.

it has to be about 0.1 seconds so b

Answer:

1.2 × \(10^{-1}\) of a second

Step-by-step explanation:

d = vt , t = d / v

t = ( 3.6 × \(10^{7}\) )( 3 × \(10^{8}\) ) = (3.6 ÷ 3) × ( \(10^{7}\) ÷ \(10^{8}\) ) = 1.2 × \(10^{7 - 8}\) = 0.12 of second

t = 1.2 × \(10^{-1}\) of a second

Answer:

16

Step-by-step explanation:

If you divide 8 by 2 it is 4 and 4 times itself is 16. Because to complete the square you find half of b and square it for c.

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

Explanation:

The given angle is ∅ = 300. This x value is between 270 and 360, so we're in quadrant IV (the southeast quadrant)

The rule to get the reference angle y for this quadrant is

Ф = 360-∅

This tells us the angle made with the positive x axis

Ф = 360-∅

Ф = 360-300

Ф = 60

A 60 degree angle forms with the positive x axis as shown in the diagram below.

Answer:

MP=(6,8)

Step-by-step explanation:

\(MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )\\MP= (\frac{9+3}{2} )(\frac{7+9}{2})\\MP= (\frac{12}{2} )(\frac{16}{2} )\\MP= (6,8)\)

The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

You failed to make the minimum payment by the due date. This is an action that can result in a message that "you've triggered the Penalty APR so that it has now climbed to 28.99%."

A charge APR is a charge that can be applied if you don't pay your bills on time. It may be set up so that future transactions may be subject to a penalty APR that is higher than the card's standard rate.

If the minimum payment was not made by the due date, Penalty APR would be applied.

But if the card also has a penalty APR and you trigger it, you will likely lose that promotional offer. Federal consumer protections that limit penalty APRs don't apply to small-business credit cards. That means issuers can be more punitive, such as applying penalty APRs sooner than 60 days after not making payments.

Therefore,

The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

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DNE in each coordinate of the ordered triplet are y is -7 , DNE ,y is-2.

1.) 2+3 = y + 12

Make y the formula's subject after adding the LHS.

5 = y + 12

Y = 5 - 12

Y = - 7

The answer to the equation is -7

2.) 2 + 13 = 1 +8

The equation cannot have a solution since there is no unknown variable and the sum of the numbers on the left hand side (LHS) does not equal the sum of the numbers on the right hand side (RHS).

3.) y - 7 = 2 - 11

RHS is added, and y is become the formula's subject.

Y - 7 = -9

Y = -9 + 7

Y = -2

The equation's answer is -2.

The complete question is:Solve the following system of equations. If there is no solution, write DNE in each coordinate of theordered triplet. If there are an infinite number of solution, write each coordinate in terms of z.2+3 = y + 12

2 + 13 = 1 +8

y - 7 = 2 - 11

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tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

  see the attachment

Step-by-step explanation:

You want graphs of f(x -5) and f(x)+2 and their asymptotes, given exponential function f(x).

The subtraction of 5 from the argument x causes the graph to be shifted to the right 5 units. The horizontal asymptote at y=0 is unchanged.

The addition of 2 to every function value causes the graph to be shifted up 2 units. The horizontal asymptote is likewise shifted up 2 units to y=2.

The red and blue graphs are attached. The asymptotes are dashed lines.

The capacity of fish tank in quarts is 246.

Therefore the answer is 246.

A pint is a unit of volume in the US customary system of measurement and is equal to 16 fluid ounces. A quart is also a unit of volume in the US customary system of measurement and is equal to 32 fluid ounces or 2 pints.

There are 2 pints in 1 quart, so to convert from pints to quarts, we need to divide by 2.

The capacity of the fish tank in pints is 492.

Therefore, the capacity of the fish tank in quarts is

= 492 pints / 2 pints per quart

= 246 quarts

So, the capacity of the tank in quarts is 246 quarts.

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Answer:

7 and 4

Step-by-step explanation:

i think

Answer:

Step-by-step explanation:

To calculate the probability of the union of mutually exclusive events A and B (P(A or B)), we can use the formula:

P(A or B) = P(A) + P(B)

However, since events A and B are mutually exclusive, meaning they cannot occur simultaneously, the probability of their union is simply the sum of their individual probabilities.

Given that P(A) = 1/3 and P(B) = 1/2, we can calculate the probability of their union:

P(A or B) = P(A) + P(B)

         = 1/3 + 1/2

         = 2/6 + 3/6

         = 5/6

Therefore, the correct answer is c. 5/6.

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The ordered pair that can be plotted together with these four points is

(0, 3).

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The following coordinates are from the graph.

(3, -1), (2, 3), ), (-4, 2), and (-2, -3)

We know that,

A function can have many-to-one but not one-to-many.

So,

We can not have (-2, 0), (-2, 3). and (3, 0) because we already have (-2, 3) and (3, -1).

This is an indication of a one-to-many function that is not possible.

(0, 3) is possible.

Thus,

The ordered pair that can be plotted together with these four points is

(0, 3).

Option C is the correct answer.

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Answer:  80 miles

Step-by-step explanation:

10mph + 30mph = 40 mph

Distance = Speed × time

D = 40m/h × 2 h

D = 80 m

Answer:

Step-by-step explanation:

true i think

The statement that the blue radius is perpendicular to the green cord is false.

The radius of a circle is any line segment connecting the centre of the circle to any point on the circle. The chord of a circle is a line segment joining any two points on the circle.

From the complete question,

The blue radius does not bisect the green chord

This means that the blue radius and the green chord do not meet at 90 degrees

Since both lines do not meet at 90 degrees, then they are not perpendicular

Hence, the statement that the blue radius is perpendicular to the green cord is false

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The search direction that is both improving and feasible while providing the most rapid objective function improvement is to increase the value of y₁.

To determine the search direction that improves the objective function most rapidly while remaining feasible, we need to calculate the reduced costs for each variable and choose the variable with the most negative reduced cost.

The reduced cost of a variable represents the amount by which its coefficient in the objective function can be decreased before it becomes profitable to include it in the solution.

In this case, the objective function is minimized, so we want to identify the variable with the most negative reduced cost. The reduced cost of a variable is calculated as the difference between its coefficient in the objective function and the dual price (shadow price) of the corresponding constraint.

For y₁: reduced cost = 2 - 1 = 1

For y₂: reduced cost = 3 - 0 = 3

For y₃: reduced cost = 5 - 1 = 4

Among the variables, y₁ has the lowest reduced cost of 1. By increasing the value of y₁, the objective function will improve by 1 unit for every unit increase in y₁, while keeping all the constraints satisfied.

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(a) The sample space for this game is the set of numbers on the wheel are 00, 0, 1, 2, ..., 38.

For this game of chance with a wheel consisting of 40 slots, the sample space is defined as the set of all possible numbers that the metal ball can fall into. The numbers range from 00 to 38, including both the double zero and single-digit numbers.

(b) The probability of the ball landing in the slot marked 4 is 1/40, which is equivalent to 0.025 when rounded to four decimal places.

To determine the probability that the metal ball falls into the slot marked 4, we need to calculate the ratio of the favorable outcomes (the ball landing in slot 4) to the total number of possible outcomes.

There is only one slot marked 4, so the number of favorable outcomes is 1. The total number of possible outcomes is 40 since there are 40 slots on the wheel.

This means that if the game is played many times, we can expect the ball to land in slot 4 approximately 0.025 (or 2.5%) of the time.

(c) The probability that the metal ball lands in an odd slot is 0.5.

To determine the probability that the metal ball lands in an odd slot, we count the number of odd slots on the wheel. Odd numbers occur every other slot starting from 1, so there are a total of 20 odd slots on the wheel.

The probability of the ball landing in an odd slot is given by the ratio of the number of odd slots to the total number of possible outcomes. Therefore, the probability is 20/40, which simplifies to 1/2 or 0.5 when rounded to four decimal places.

This means that if the game is played many times, we can expect the ball to land in an odd slot approximately 0.5 (or 50%) of the time.

The correct choices are:

(b) If the wheel is spun 1000 times, it is expected that about 25 of those times result in the ball landing in slot 4.

(c) If the wheel is spun 100 times, it is expected that exactly 50 of those times result in the ball landing on an odd number.

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The probability that exactly 28 of the employees work over forty hours per week using the binomial distribution is given below. Information required to find the probability of employees working over forty hours per week are as follows:

n = 54

x = 28

p = 0.35

Formula used in the binomial distribution is given below:

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

Where:

P(X=x) is the probability of exactly x successes in n trialsn

Cx = n! / x!(n-x)!p = probability of success q = 1 - p = probability of failure.

The probability that exactly 28 of the employees work over forty hours per week can be found as:P(X=28) = 54C28 * 0.35^28 * 0.65^26= 0.1646Therefore, the probability that exactly 28 of the employees work over forty hours per week using the binomial distribution is 0.1646.

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The angles between the edges of the resulting pieces are approximately \($56.1^\circ$ and $42.5^\circ$.\)

We know that the rectangle has sides of length 4 ft and 5.5 ft, so we can use the Pythagorean Theorem to find the length of the diagonal \($BD$\):

\($$ BD^2 = 4^2 + 5.5^2 $$\)

\($$ BD^2 = 16 + 30.25 $$\)

\($$ BD^2 = 46.25 $$\)

\($$ BD = \sqrt{46.25} $$\)

\($$ BD = 6.8 \text{ ft (rounded to one decimal place)} $$\)

Now, we can use the Law of Cosines to find the angle between sides \($AB$\)and \($AD$\) in triangle \($ABD$\):

\($$ \cos(A) = \frac{BD^2 + AB^2 - AD^2}{2 \cdot BD \cdot AB} $$\)

\($$ \cos(A) = \frac{6.8^2 + 4^2 - 5.5^2}{2 \cdot 6.8 \cdot 4} $$\)

\($$ \cos(A) = 0.5471 $$\)

\($$ A = \cos^{-1}(0.5471) $$\)

\($$ A = 56.1^\circ \text{ (rounded to one decimal place)} $$\)

Similarly, we can use the Law of Cosines to find the angle between sides \($BC$\) and \($CD$\) in triangle:

\($$ \cos(B) = \frac{BD^2 + BC^2 - CD^2}{2 \cdot BD \cdot BC} $$\)

\($$ \cos(B) = \frac{6.8^2 + 5.5^2 - 4^2}{2 \cdot 6.8 \cdot 5.5} $$\)

\($$ \cos(B) = 0.7416 $$\)

\($$ B = \cos^{-1}(0.7416) $$\)

\($$ B = 42.5^\circ \text{ (rounded to one decimal place)} $$\)

Therefore, the angles between the edges of the resulting pieces are approximately \($56.1^\circ$ and $42.5^\circ$.\)

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The likelihood of each utility function representing actual investor preferences varies based on different factors such as risk aversion, wealth accumulation, and personal preferences.

Utility function (a) U(W) = \(W^2\) represents a preference for increasing wealth at an increasing rate, indicating risk aversion and a desire for wealth accumulation. This is a commonly observed preference among investors.

Utility function (b) U(W) = 1/W represents a preference for wealth preservation and risk aversion. It implies that the marginal utility of wealth decreases as wealth increases, which aligns with the concept of diminishing marginal utility.

Utility function (c) U(W) = -W represents a preference for taking on risk and potentially incurring losses. This utility function implies a risk-seeking behavior, which is less common among investors who typically aim to maximize their wealth.

Utility function (d) U(W) = W represents a preference for increasing wealth linearly. This utility function suggests a risk-neutral attitude where investors are indifferent to risk and aim to maximize their wealth without considering risk factors.

Utility function (e) U(W) = ln(W) represents a preference for wealth accumulation, but with a decreasing marginal utility. This logarithmic utility function reflects risk aversion and diminishing sensitivity to changes in wealth.

Utility function (f) U(W) = \(W^(1-γ)\)/(1-γ), with γ = 2, represents risk-neutral behavior. However, the likelihood of this utility function representing actual investor preferences depends on the specific value of γ chosen. If γ is different from 2, it may represent risk aversion or risk-seeking behavior.

Overall, utility functions (a), (b), (d), and (e) are more likely to align with actual investor preferences due to their consistency with risk aversion and wealth accumulation. Utility function (c) represents a less common risk-seeking behavior, and utility function (f) depends on the chosen value of γ, making it less likely to represent typical investor preferences.

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Answer:

48

Step-by-step explanation:

(9*4) + (6*2)

36 + 12

= 48

Step-by-step explanation:

no:questions=15

correct questions =9

marks for correct answers =9×4=36

incorrect answers=6

marks for incorrect answers =(-2)×6=(-12)

full marks =36 - (-12)

=36 + 12

=48

Answer:

(6, 2)

Step-by-step explanation:

I did this over 10 times it's so easy it is like a breeze

Answer:(-2,5)

Step-by-step explanation: