Write a congruence statement for the triangles

Answer: To construct a 99% confidence interval for the mean number of books people read, we can use the following formula:

CI = X ± Z*(S/sqrt(n))

where:

X = sample mean (11.3)

S = sample standard deviation (16.6)

n = sample size (1005)

Z = the z-score for the confidence level (99%)

To find the z-score for the 99% confidence level, we can look up the value in a standard normal distribution table or use a calculator. The z-score for a 99% confidence level is 2.576.

Substituting the values into the formula, we get:

CI = 11.3 ± 2.576*(16.6/sqrt(1005))

CI = 11.3 ± 2.576*(0.524)

CI = 11.3 ± 1.35

Therefore, the 99% confidence interval for the mean number of books people read is (9.95, 12.65). We can be 99% confident that the true population mean falls within this interval.

Step-by-step explanation:

Therefore, the general solution for the differential equation dy/dx cosx=ysinx+sin113x is y = log |sin(x) / sin(113x)| + C, where C is an arbitrary constant.

A differential equation explains the unknown derivative or derivatives of a function. Example: Think about the equation. The equation d y d x = x sin represents the derivative of an unknown function.

We can solve this differential equation by using separation of variables.

First, we'll rearrange the equation to isolate the y term on one side:

cos x = y sin x + sin 113x

cos x - sin 113x = y sin x

y = (cos x - sin 113x) / sin x

Now we can integrate both sides with respect to x:

∫dy = ∫(cos x - sin 113x) / sin x dx

Using integration by parts, we can integrate the second term on the right side:

∫dy = ∫cos x / sin x dx - ∫sin 113x / sin x dx

The first term on the right side can be integrated using substitution:

u = sin x, du/dx = cos x dx

∫cos x / sin x dx = ∫du/u = log |u| + C1 = log |sin x| + C1

The second term on the right side can be rewritten as:

∫sin 113x / sin x dx = - ∫sin 113x / sin 113x cos x dx

= - ∫csc x cos 113x dx

Using substitution again:

u = sin 113x, du/dx = 113 cos 113x dx

∫csc x cos 113x dx = - ∫du/u = - log |sin 113x| + C2

y = log |sin x| - log |sin 113x| + C

Simplifying:

y = log |sin(x) / sin(113x)| + C

Therefore, the general solution for the differential equation dy/dx cosx=ysinx+sin113x is y = log |sin(x) / sin(113x)| + C, where C is an arbitrary constant.

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Answer: a) To find the number of working days on which under 18,000 bottles are filled, we need to calculate the z-score for this value:

z = (18,000 - 20,000) / 2000 = -1

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -1 standard deviation is approximately 0.1587. Therefore, the approximate number of working days on which under 18,000 bottles are filled is:

0.1587 x 260 ≈ 41

b) To find the number of working days on which over 16,000 bottles are filled, we need to calculate the z-score for this value:

z = (16,000 - 20,000) / 2000 = -2

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -2 standard deviations is approximately 0.0228. Therefore, the approximate number of working days on which over 16,000 bottles are filled is:

0.0228 x 260 ≈ 6

c) To find the number of working days on which between 18,000 and 24,000 bottles are filled, we need to calculate the z-scores for these values:

z1 = (18,000 - 20,000) / 2000 = -1

z2 = (24,000 - 20,000) / 2000 = 2

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -1 standard deviation is approximately 0.1587, and the probability of a value being less than 2 standard deviations is approximately 0.9772. Therefore, the approximate number of working days on which between 18,000 and 24,000 bottles are filled is:

(0.9772 - 0.1587) x 260 ≈ 236

Step-by-step explanation:

The area of the triangles are 81.77 square units, 333.50 square units, 207 square units and 52.21 square units

Given the triangles as the parameters, the area can be calculated as

Area = 1/2absin(C)

Using the above formula as a guide, we have the following equations

Triangle 7 = 1/2 * 15 * 13 * sin(57 degrees)

Triangle 7 = 81.77 square units

Triangle 8 = 1/2 * 28 * 24 * sin(83 degrees)

Triangle 8 = 333.50 square units

Triangle 9 = 1/2 * 23 * 18 * sin(90 degrees)

Triangle 9 = 207 square units

Triangle 10 = 1/2 * 15 * 7 * sin(96 degrees)

Triangle 10 = 52.21 square units

Hence, the area of triangle 10 is 52.21 square units

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Answer: 1. 8.94

2. 13

3.  True

Step-by-step explanation:

The given sequence is a geometric sequence, where the common ratio (r) between any two consecutive terms is:

r = 3/1.5 = 2

We need to find the sum of the first 10 terms of this sequence. Let's denote the first term (a₁) as 1.5 and the tenth term (a₁₀) as a.

The formula to find the sum of the first n terms of a geometric sequence is:

Sₙ = a(1 - rⁿ)/(1 - r)

Substituting the values, we get:

a = 1.5 x 2^9 = 768

S₁₀ = 1.5(1 - 2¹⁰)/(1 - 2) = 1.5(1 - 1024)/(-1) = 1.5 x 1023

Therefore, the sum of the first 10 terms of the given sequence is 1.5 x 1023, which is approximately equal to 1.53 x 10³=1534,5

Based on the congruent angles theorem, the value of the variable x in the circle is 40 degrees

An angle is a figure formed by two rays that share a common endpoint, called the vertex of the angle

From the question, we have the following parameters that can be used in our computation:

The circle with center O

In the figure, angles with the same marks are congruent angles

Using the above as a guide, we have the following:

x =40

Hence, the value of x is 40 degrees

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She has 7 gallons of gas after driving for 2 hours.

What is Subtraction?

Subtraction is a mathematical operation that involves finding the difference between two numbers or quantities. It is the inverse of addition, which means that it is the opposite process of adding numbers.

In subtraction, a number or quantity (called the subtrahend) is subtracted from another number or quantity (called the minuend), resulting in the difference. The symbol used for subtraction is "-" and the resulting value is called the remainder or difference.

Katie had 12 gallons of gas.

She used 2 1/2 gallons of gas each hour.

Now, She drove 2 hours.

So, gallon of gas use for 2 hours = 2 × 2 1/2

                                                       = 2 × 5/2

                                                       = 5 gallons of gas.

Now, Gallons of gas left after 2 hours

        = total gallons of gas - Gallons used for 2 hours

        = 12 - 5

        = 7.

Hence, She is left with 7 (12-5) gallons of gas.

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From the quadratic equation, we found the new dimensions:

Length =  14.85 feet

Width = 18.85 feet.

What is a quadratic equation?

The polynomial equations of degree two in one variable of type

f(x) = ax² + bx + c = 0 and with a, b, c, ∈ R and a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of

f (x).

The current dimensions of the farm are 10 feet by 14 feet.

Length l = 10 feet

Width w = 14 feet

Area a = l * w = 10 * 14 = 140 sq. feet.

Now the new area is doubled.

A = 2a = 2 * 140 = 280 sq.feet

The new dimensions are:

L = l + x = 10 + x

W = w + x = 14 +x

A = (10+x)(14+x)

280 = 140 + 10x + 14x + x²

x² + 24x - 140 = 0

This is a quadratic equation.

Solving the equation, we get

x = 4.85, -28.85

Neglecting the negative value, we get the value of x as 4.85.

Therefore from the quadratic equation, we found the new dimensions:

L = 10 + 4.85 = 14.85 feet

W = 14 + x = 14 + 4.85 = 18.85 feet.

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Answer:

Step-by-step explanation:

1. 1 - 408

2. 15/136

3. 1/2

4. 24%

Hence, 7200 units were produced throughout the period equivalently as WIP multiplied by the percentage of completion.

The percentage sign (%) is used to indicate it. When a student receives a score of 80% on a test, for instance, it signifies that 80 of the 100 questions were properly answered by the student. Alternatively, the result can also be expressed as a fraction of 80/100, or as 0.8 in decimal form. In order to express a portion or component of a whole, percentages are utilized. It is a practical technique to contrast values of various magnitudes on an equivalent scale.

given

The steps to determine the equivalent production are as follows:

Total units input: 8000

A typical loss is 400 units, or 5% of 8000 units.

Consider there to be no anomalous loss because none has been reported.

Counted in total units: 8000 - 400 = 7600 units

Units completed: 7600 less 1000 (closing WIP) equals 6600 units.

Equivalent production equals completed units plus closing WIP multiplied by the percentage of completion, which equals 6600 + 1000 x 60%, or 6600 + 600, or 7200 units.

Hence, 7200 units were produced throughout the period equivalently as WIP multiplied by the percentage of completion.

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Answer:

it would be 70months when rounded up.

Step-by-step explanation:

if not then 69months 7days

Function is increasing in the domain of interval (1, ∞).

A quadratic function is a mathematical function of the form:

f(x) = ax² + bx + c

where "a", "b", and "c" are constants, and "x" is the variable.

From the given table of ordered pairs, we can see that the function k is a continuous quadratic function that passes through the points (-1, 0), (0, 2), (2, 5), (3, 4), and (4, 5).

We can estimate the slope of the function between each pair of consecutive points in the table. For example, between (-1, 0) and (0, 2), the slope is positive, so the function is increasing in the interval (-1, 0). Between (0, 2) and (2, 5), the slope is also positive, so the function is increasing in the interval (0, 2). However, between (2, 5) and (3, 4), the slope is negative, so the function is decreasing in the interval (2, 3).

Finally, between (3, 4) and (4, 5), the slope is positive, so the function is increasing in the interval (3, 4). Therefore, the function k is increasing over the intervals (-1, 0) and (3, 4).

So, the correct answer is option A: (1, ∞).

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Answer:

1a) Increment in price = 5500 - 4500 = 1000 Naira

1b) Percentage increase in price = (increment in price / old price) x 100%

= (1000 / 4500) x 100%

= 22.22%

2) Marked price = selling price / (1 - discount percentage)

= 3000 / (1 - 0.1)

= 3333.33 Naira

3) Total cost of 30 crates of eggs = 30 x 30 = 900 Naira

Commission = (4/100) x 900

= 36 Naira

4) Commission = (7/100) x 49000

= 3430 Naira

5) Discount = marked price - selling price

= 44.48 - 39.28

= 5.20 Naira

6) Discount = (245 - 225) / 245 x 100%

= 8.16%

7) Commission = (3/100) x 33

= 0.99 Naira

8) New salary = old salary + 5% of old salary

= 250 + (5/100) x 250

= 262.50 Naira

9) Marketed price = selling price / (1 - discount percentage)

= 55 / (1 - 0.05)

= 57.89 Naira

10) Marketed price = selling price + discount

= 845 + 55

= 900 Naira

Percentage discount = (discount / marked price) x 100%

= (55 / 900) x 100%

= 6.11%

Step-by-step explanation:

Answer:y=6-X

Step-by-step explanation:

To leave y on it’s on on the right hand side we need to subtract X
X+y-X= y

What you do on the left hand side, you do the same on the right hand side

6-X

final equation would be:

X+y-X=6-X

Simplifying we get :

y=6-X (FINAL ANSWER)

Answer:

8

Step-by-step explanation:

square the whole equation to get

[tex] {m}^{2} + \frac{1}{ {m}^{2} } = 9[/tex]

then minus one from both sides of the equation to get 8

Answer:

Step-by-step explanation:

Use the figure to complete the transformations.

1. Reflect the triangle across the y-axis.

2. Reflect the image across the x-axis.

The final image is the same as what single transformation?

a translation 2 units to the left and 2 units down

a reflection across the y-axis

a 180° rotation about the origin

a clockwise rotation 90° about the origin

Answer:

Step-by-step explanation:

The probabilities of picking the real numbers are 0.52 and 0.88, respectively

The probabilities in this case, is the area covered by each region

Using the above as a guide, we have the following:

Real number between 3 and 5

Here, we have the area to be

Region B

The area of region B is 0.56

So, we have

Probability = 0.56

Real number between 3 and 7

Here, we have the area to be

Region B and Region C

The areas of these regions are 0.56 and 0.32

So, we have

Probability = 0.56 + 0.32

Probability = 0.88

Hence, the probability is 0.88

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Answer:

B) [tex]\frac{3}{2}[/tex] % of 400

Step-by-step explanation:

A) 2% of 150 = 3

Start by expressing the percent as a decimal by dividing the percent by 100

2% -> 0.02

Next multiply the percent by the number given

0.02 * 150 = 3

B)  [tex]\frac{3}{2}[/tex] % of 400 = 6

Start by expressing the percent as a decimal by dividing the percent by 100

3/2% -> 0.015

Next multiply the percent by the number given

0.015 * 400 = 6

C) 5% of 60

Start by expressing the percent as a decimal by dividing the percent by 100

5% -> 0.05

Next multiply the percent by the number given

0.05 * 60 = 3

D) 6% of 50

Start by expressing the percent as a decimal by dividing the percent by 100

6% -> 0.06

Next multiply the percent by the number given

0.06 * 50 = 3

After calculating all of the questions, we can see that the common product is 3, making B) the one that is not equal to the rest.

Answer:

If 1, -5, and -1/2 are zeros of a polynomial function, then the factors of the polynomial are:

(x - 1), (x + 5), and (2x + 1)

To find the polynomial function, we multiply these factors together and simplify:

(x - 1)(x + 5)(2x + 1)

= (x^2 + 4x - 5)(2x + 1)

= 2x^3 + 9x^2 - 6x - 5

Therefore, the polynomial function of the least degree with integral coefficients that has the zeros 1, -5, and -1/2 is:

f(x) = 2x^3 + 9x^2 - 6x - 5

the minimum number of degrees that may be rotated to satisfy rotational symmetry in this figure is 60°.

What is rotational symmetry?

Rotational symmetry is a type of symmetry where a shape or object can be rotated by a certain angle and still appear exactly the same as it did before the rotation. The smallest angle of rotation for which the shape or object appears the same is called the angle of rotational symmetry or the order of the rotational symmetry.

In light of the posed query

There is rotational symmetry in the image.

This picture can be seen as a circle. A whole circle has 360 degrees.

Six wings cover the figure.

360/6

=60°

Hence, the minimum number of degrees that may be rotated to satisfy rotational symmetry in this figure is 60°.

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Combine like terms to create an equivalent expression.[tex]\frac{9}{8} m + \frac{9}{10} - 2m - \frac{3}{5}[/tex] then we formed the equation is [tex]= \frac{1}{8} m - \frac{3}{50}[/tex]

When two expressions can be reduced to a single third expression or when one of the statements can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variables and both expressions yield the same result, you may also tell if expressions are equal.

The final response is 2 x - 2; alternatively, you might write 2 x - 3. The ultimate response is -2 point to the right. You could see that choice d is right in this case.

In this expression, we have two terms with the variable m: [tex]9/8 m[/tex] and [tex]-2m[/tex]. We can combine these by subtracting [tex]2m[/tex] from [tex]9/8 m[/tex], which gives us [tex]1/8 m[/tex].

We also have two constant terms: [tex]9/10[/tex] and [tex]-3/5[/tex]. We can combine these by adding them, which gives us [tex]-3/50[/tex].

Putting it all together, we get:

[tex]\frac{9}{8} m + \frac{9}{10} - 2m - \frac{3}{5} = \frac{1}{8} m - \frac{3}{50}[/tex]

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Answer:-7/8m+3/10

Step-by-step explanation:

Answer:

We know that the formula for the circumference (C) of a circle is:

C = 2πr

where r is the radius of the circle.

We are given that the circumference is 8πm, so we can write:

8πm = 2πr

Simplifying this equation by dividing both sides by 2π, we get:

r = 4m

Now that we know the radius of the circle, we can use the formula for the area (A) of a circle:

A = πr^2

Substituting the value we found for r, we get:

A = π(4m)^2

Simplifying this equation, we get:

A = π(16m^2)

A = 16πm^2

Therefore, the area of the circle is 16πm^2. The answer is C

Answer:

θ = arctan(10/62) ≈ 8.8°

Step-by-step explanation:

Let's assume that the plane travels a distance of x km during take off and reaches a height of 10 km. Then, using trigonometry, we can find the angle θ between the ground and the path of the plane:

tan(θ) = 10/x

We want to find the smallest possible angle θ, which means we need to maximize x. From the given information, we know that x must be in the range 57 km to 62 km. Therefore, to maximize x, we choose x = 62 km.

We use the additiοn prοperty οf equality tο simplify this tο FA = RN, which is what we wanted tο prοve.

The substitutiοn prοperty οf equality states that if twο expressiοns are equal, then οne can be substituted fοr the οther in any equatiοn οr expressiοn withοut changing the truth οf that equatiοn οr expressiοn.

Step:

The prοοf starts with the given that FRAN. We want tο prοve that FARN is true. We start by using the segment additiοn pοstulate tο add RA tο bοth sides οf FR tο get FR + RA = FR + RA.

We then use the additiοn prοperty οf equality tο simplify this tο FR + RA = FR + RA. Next, we use the segment additiοn pοstulate again tο add AN tο bοth sides οf FR + RA tο get FR + RA + AN = FR + RA + AN.

We then use the substitutiοn prοperty οf equality tο replace AN with FR, which gives us FR + RA + FR = FR + RA + FR.

We simplify this tο FR + RA = FR + RA + FR and then use the segment additiοn pοstulate again tο add FA tο bοth sides οf RA tο get RA + FA = RA + FA.

Finally, we use the additiοn prοperty οf equality tο simplify this tο FA = RN, which is what we wanted tο prοve.

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Answer:

The total length of the 30 pencils in centimeters is:

30 x 16 = 480 cm

To convert centimeters to meters, we divide by 100:

480 cm / 100 = 4.8 m

Therefore, the combined length of the 30 pencils is 4.8 meters.

Step-by-step explanation:

Answer:

to find the height of the storage unit, we can use the formula for volume:

Volume = length x width x height

We know that the volume needs to be 400 cubic ft, the width is 10ft and the length is 8ft. So, we can plug in these values and solve for the height:

400 = 8 x 10 x height

400 = 80 x height

height = 400/80

height = 5 ft

Therefore, the height of the storage unit needs to be 5 ft.