for a random sample of 85 such pairs, what is the (approximate) probability that the sample mean courtship time is between 95 min and 120 min? (round your answer to four decimal places.)

Answer:

There are several ways to make 45 cents using different coins:

Nine nickels

Four dimes and one nickel

Three dimes and six nickels

Two dimes and one quarter

One dime, two nickels, and three pennies

One quarter and two dimes

One quarter, one dime, and four nickels

One quarter, three nickels, and five pennies

45 pennies

So there are 9 ways to make 45 cents.

I Hope This Helps!

Answer:

5/6 x 48 is  40

Step-by-step explanation:

5/6×48/1=240/6

240/6 = 40

Since the p-value (0.034) is less than the significance level of 0.05, we reject the null hypothesis. This suggests evidence against the claim that the median percent of impurities in the brand of jam is 2.5%.

To perform the sign test, we compare the observed values to the hypothesized median value and count the number of times the observed values are greater or less than the hypothesized median. Here's how we can proceed:

State the null and alternative hypotheses:

Null hypothesis (H0): The median percent of impurities in the brand of jam is 2.5%.

Alternative hypothesis (Ha): The median percent of impurities in the brand of jam is not 2.5%.

Determine the number of observations that are greater or less than the hypothesized median:

From the given data, we can observe that 5 jars have impurity percentages less than 2.5% and 11 jars have impurity percentages greater than 2.5%.

Calculate the p-value:

Since we are performing a two-tailed test, we need to consider both the number of observations greater and less than the hypothesized median. We use the binomial distribution to calculate the probability of observing the given number of successes (jars with impurity percentages greater or less than 2.5%) under the null hypothesis.

Using the binomial distribution with n = 16 and p = 0.5 (under the null hypothesis), we can calculate the probability of observing 11 or more successes (jars with impurity percentages greater than 2.5%) as well as 5 or fewer successes (jars with impurity percentages less than 2.5%). Summing up these probabilities will give us the p-value.

Compare the p-value to the significance level:

Since the significance level is 0.05, if the p-value is less than 0.05, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

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To construct an interval, estimate for mu with 95% confidence for the first question, we use the formula:
Interval estimate = x ± (zα/2 * σ/√n)

where x is the sample mean, σ is the known population standard deviation, n is the sample size, zα/2 is the z-score corresponding to the desired confidence level (in this case, 1.96 for 95% confidence). Plugging in the values, we get:

Interval estimate = 850 ± (1.96 * 50/√100) = 850 ± 9.8
So the 95% confidence interval is from 840.2 to 859.8.

For the second question, where sigma is assumed to be 100, we use the same formula but with σ = 100:

Interval estimate = 850 ± (1.96 * 100/√100) = 850 ± 19.6
So the 95% confidence interval is from 830.4 to 869.6.

For the third question, where sigma is assumed to be 200, we again use the same formula but with σ = 200:

Interval estimate = 850 ± (1.96 * 200/√100) = 850 ± 39.2
So the 95% confidence interval is from 810.8 to 889.2.

As we can see, the confidence interval gets wider as sigma increases. This is because a larger standard deviation indicates greater variability in the population, which means there is more uncertainty in the sample mean as an estimate of the true population mean. Therefore, a wider interval is needed to account for this increased uncertainty.

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Answer:

21b

Step-by-step explanation:

To find the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2, we can use the following formulas:

New x-coordinate = -2 * old x-coordinate

New y-coordinate = -2 * old y-coordinate

Let's apply these formulas to each point in triangle ABC:

Point A: (-3, 4)

New x-coordinate of A = -2 * (-3) = 6

New y-coordinate of A = -2 * 4 = -8

New coordinates of A: (6, -8)

Point B: (1, 1)

New x-coordinate of B = -2 * 1 = -2

New y-coordinate of B = -2 * 1 = -2

New coordinates of B: (-2, -2)

Point C: (5, -2)

New x-coordinate of C = -2 * 5 = -10

New y-coordinate of C = -2 * (-2) = 4

New coordinates of C: (-10, 4)

Therefore, the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2 are:

A: (6, -8)

B: (-2, -2)

C: (-10, 4)

In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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Answer:

27.4 and 152.6

Step-by-step explanation:

Supplementary angles equal 180 degrees when placed together.

x+(x+125.2)=180

2x+125.2=180

2x=54.8

x=27.4

the angles are 27.4 and 152.6

The length of the segment NT is  4.5  units

What is isosceles triangle?

An isosceles triangle is one that has two sides of equal length.

The angles opposite to equal sides are equal.

Let RM=x, then  MS=RN=NT=x  ( because RS = RT )

RS=RT =2x

RST and RMN are two similar triangles

So, we have

ST/MN = RT/NT

=>  ST/3.5 = 2x/x

=> ST/3.5 = 2

=> ST = 2*3.5 = 7

Given , perimeter = 25

=> RS+ST+RT = 25

=> 2x+ST+ 2x = 25

=>  4x + 7 = 25

=> 4x= 25-7 = 18

=> x=18/4 = 4.5

NT=x= 4.5  units

The length of the segment NT is  4.5  units

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Answer:

4 1/2

Step-by-step explanation:

Answer:

A) 45°

Step-by-step explanation:

A) 45°

Answer:

1139621600

Step-by-step explanation:

The answer is 1139621600, because if it is in 2001. All you have to o is multiply by 4. I don't know if this is correct. If they gave you another year and another set of numbers I would be able to clarify it more. So...if this isn't correct. I'm so sorry.

If you think its incorrect please say so in comments below. Any questions? Say them below as well.

I hope this helped.

:)

Signed,

tyreefrankinjr

The partial fraction decomposition of f(x) is: f(x) = (2x² + x - 4) / (3x² - 2x)

To find the partial fraction decomposition, we first factor the denominator: 3x² - 2x = x(3x - 2)

Now we can perform the partial fraction decomposition: f(x) = A/x + (Bx + C)/(3x - 2)

To find the values of A, B, and C, we can equate the numerators: 2x² + x - 4 = A(3x - 2) + (Bx + C)x

Expanding and collecting like terms: 2x² + x - 4 = (3A + B)x² + (-2A + C)x + (-2A)

Equating coefficients of corresponding powers of x:

3A + B = 2

-2A + C = 1

-2A = -4

Solving this system of equations, we find A = 2/3, B = 4/3, and C = 5/3.

Therefore, the partial fraction decomposition of f(x) is: f(x) = 2/3x + (4x + 5)/(3x - 2)

C. To find the volume of the solid obtained by revolving the region R bounded by the curves y = √x, x = 3, y = 0, and x = 0 about the y-axis, we use the disk method.

The radius of each disk is the x-value, and the height is the difference between the top and bottom curves. Since the region is bounded by y = √x and y = 0, the height is √x - 0 = √x.

The limits of integration are x = 0 and x = 3.

The volume V is given by the integral: V = ∫[0,3] π(√x)² dx

Simplifying, we have: V = π∫[0,3] x dx

Evaluating the integral, we get:

V = π[x²/2] from 0 to 3

V = π(9/2 - 0)

V = (9π)/2

Therefore, the volume of the solid obtained is (9π)/2.

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Answer:

v=11

Step-by-step explanation:

Combined like terms and then divide at the end

Answer: V=11

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

2

Step-by-step explanation:

slope = rise/run

slope = (12-4)/(6-2) = 8/4 = 2

Answer:

60 mph

Step-by-step explanation:

240/ 4 hours= 60

Answer:

240/4 = 60 mph

Step-by-step explanation:

Answer:

the value of x is 43....

\(\tt Step-by-step~explanation:\)

\(\tt Area:\)

To solve for the area of a triangle, we multiply the length and height, then divide that by two. L = 10. H = 7.

\(\tt 10*7=70\\70/2=35\\35=A\)

\(\tt Perimeter:\)

\(\tt Step~1:\)

To solve for the perimeter, or edges, of the triangle, we need to use the Pythagorean Theorem: a² + b² = c² to solve for the third side. We already know two measures: 10 and 7. Now we need to square them, add them together to get c², then take the root of that number.

\(\tt 7^2=49\\10^2=100\\100+49=\sqrt{149}\\\sqrt{149\)

We cannot simplify √149, so we either leave it, or round it.

\(\tt \sqrt{149}\\12.2066\)

This is rounded to the nearest 10,000.

\(\tt Step~2:\)

Now that we have the measure of the longest side, we can add all three sides together to get the perimeter of the triangle.

\(\tt 10+7+\sqrt{149}=17+\sqrt{149}=P\\Rounded~to~the~nearest~1,000th:~29.207=P\)

\(\large\boxed{\tt Our~final~answer: ~A=35,~P=17+\sqrt{149}}\)

Based on the given side lengths (a=16 mm, b=63 mm, c=65 mm), the triangle is a(n) right triangle. This is because it satisfies the Pythagorean theorem: a² + b² = c² (16² + 63² = 65²).

A right triangle is a triangle with two perpendicular sides and one angle that is a right angle (i.e., a 90-degree angle). The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

The hypotenuse, or side c in the illustration, is the side that is opposite the right angle. Legs are the sides that meet at the correct angle. Side a may be thought of as the side that is opposite angle A and next to angle B, whereas side b is the side that is next to angle A and next to angle B.

A right triangle is considered to be a Pythagorean triangle and its three sides are referred to as a Pythagorean triple if the lengths of all three of its sides are integers.

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Using the concepts of domain and range of functions, we have that:

10. The range is y ≥ 2.

11. The domain is all real numbers, the range is y ≤ 3, and it is a function.

12. The domain is (-4,3], and the range is (-5,5).

Hence, for these problems:

10. The range is y ≥ 2.

11. The domain is all real numbers, the range is y ≤ 3, and it is a function.

12. The domain is (-4,3], and the range is (-5,5).

In item 11, we have that it is a function because it has no vertically aligned points, that is, each value of x is associated with only one value of y.

In item 12, the open intervals are due to the open circles at the extremes of the domain and the range on the graph.

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Holy will take 13/5 or 2.6 hours to finish the bookcase.

The relation between time and work is

Work Done = Time Taken × Rate of Work ·

or, Rate of Work = 1 / Time Taken ·

or, Time Taken = 1 / Rate of Work ·

Now it is given that,

Time taken by Fritz to build a bookcase =  8 hours

So, Bookcase build by Fritz in 1 hour = 1/8

Similarly,

Time taken by Holly to build a bookcase =  10 hours

So, Bookcase build by Holly in 1 hour = 1/10

So, bookcase build in 3 hours

Fritz = 3/8

Holly = 3/10

Total bookcase build in 3 hours =  3/8 + 3/10 =  27/40

So. remaining work =  1 - 27/40 =  13/40

Thus, Time taken by Fritz to complete the bookcase =  8 * (13/40) hours

                                                                                         =  13/5 or 2.6 hours

Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.

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Answer:

c

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

7(0)+y=10

y=10

Answer: (0, 10)

Step-by-step explanation:

The given expression is in the standard form of linear equations: Ax + By = C, where A and B are constants.

The definition of y-intercept is the point that intersects with the y-axis, meaning that the [x] value of the point will be zero.

To find the y-intercept of an equation, substitute the [x] variable with 0, as mentioned above, the [x] value of a y-intercept is 0.

\(7x+y=10\\\)

\(7(0)+y=10\)

\(0+y=10\)

\(y=10\)

As we find the [y] value is 10, while the given [x] value is 0, therefore, the y-intercept of \(7x+y=10\) is \(\boxed{(0,10)}\).

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Please let me know if you have any questions

Answer: ∞

Step-by-step explanation:

\(\displaystyle\\ \lim_{x \to 3-0} \frac{-5x^2+1}{x-3} =\\\\ \frac{-5(3-0)^2+1}{3-0-3} =\\\\\frac{-5(3)^2+1}{-0}=\\\\\frac{-5(9)+1}{-0}=\\\\\frac{-45+1}{-0} =\\\\\frac{-44}{-0} =\\\\\frac{44}{0} =\\\\\infty\)

The poetic line are Upon the shore, where whispers reside, We danced embraced, as the waves collide, Bound by love's current, our hearts confide, In sync with the rhythm of the eternal tide.

A poetic line is a fundamental unit of poetry, typically consisting of a sequence of words that form a single line within a poem. Poetic lines can vary in length, from a single word to several syllables or more.

They play a crucial role in shaping the structure, rhythm, and overall flow of a poem. The arrangement of words in a poetic line allows poets to convey their thoughts, emotions, and imagery in a condensed and impactful manner.

The choice of words, their order, and the use of techniques like rhyme, meter, and metaphor all contribute to the artistic expression and impact of a poetic line. The poetic lines are

Upon the shore, where whispers reside,

We danced embraced, as the waves collide,

Bound by love's current, our hearts confide,

In sync with the rhythm of the eternal tide.

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The domain and range of a function can be determined by analyzing its graph and also algebraically.

MAFS.912.F-IF.2.4 standard of Florida Mathematics State Standards is based on identifying the domain and range of a function. The domain is a set of input values that the function is defined for, while the range is a set of output values that the function produces. Here are the answers to the given question:35. State the domain and range for each function

.(a) f(x)

= 3x - 2

Domain: All real numbers Range:

All real numbers(b) g(x)

= x² - 5

Domain: All real numbers Range

: y ≥ -5(c) h(x)

= √(x + 4)

Domain: x ≥ -4

Range: y ≥ 0(d) k(x)

= 4

Domain: All real numbers Range: {4}.The domain and range of a function can be determined by analyzing its graph and also algebraically.

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After considering the given data we conclude that the coordinates of point C are (-0.5, 3), under the condition that they are located 1/4 of the distance from A(-1, 2) to B(4,8).

To evaluate the coordinates of point C that are located 1/4 of the distance from A(-1, 2) to B(4,8), we can use the midpoint formula to evaluate the coordinates of the midpoint M of the line segment AB, and then apply  the section formula to find the coordinates of point C that are 1/4 of the distance from A to B.
The midpoint formula projects  that the coordinates of the midpoint M of the line segment with endpoints (x₁,y₁) and (x₂, y₂) are given by:
M = ( x₁ + x₂ /2, y₁ + y₂ /2)
Applying this formula, we can evaluate the midpoint M of the line segment AB:
M = ( - 1 + 4 / 2, 2 + 8 / 2) = (1.5,5)
The section formula projects that if a point C divides the line segment AB in the ratio m:n, then the coordinates of C are given by:
C =( mx₂ + nx₁ /m + n, my₂ + ny₁ /m + n)
For the given case, we want to find the coordinates of point C that are 1/4 of the distance from A to B, so we can set m = 1 and n = 3.
Staging the coordinates of A, B, and the values of m and n into the section formula, we get:
C = ( 3(-1)+ 1.4 / 1 + 3, 3.2 + 1.8 / 1+3) = ( - 0.5, 3)
Therefore, the coordinates of point C that are located 1/4 of the distance from A(-1, 2) to B(4, 8) are (-0.5, 3).
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