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show work pls

Answer:

6 days.

Step-by-step explanation:

Given that in a home economics class, 6 girls worked together and sewed a dress in 4 days, to determine how long it would have taken for 4 girls to make the same dress, the following calculation must be performed:

X / 6 = 4

X = 4 x 6

X = 24

24/4 = 6

Thus, the 4 girls will take 6 days to make the same dress that 6 girls made in 4 days.

The fraction of the Journey that Kwame travelled by the train is found to be 4/15.

Let's start by finding the fraction of the journey that Kwame travelled by Lorry and taxi combined,

1/3 + 2/5 = 5/15 + 6/15 = 11/15

This means that Kwame travelled 11/15 of the journey by Lorry and taxi, and the remaining fraction of the journey by train. To find the fraction of the journey that Kwame travelled by train, we can subtract the fraction he travelled by Lorry and taxi combined from 1,

1 - 11/15 = 15/15 - 11/15 = 4/15

Therefore, Kwame travelled 4/15 of the journey by train.

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Complete question - Kwame travelled from Accra to Kumasi. He travelled from 1/3 of the journey by Lorry, 2/5 of the journey by taxi and the rest by train . what fraction of the journey did he travel by train.

Given:

Right triangle XYZ has right angle Z.

\(\sin(x)=\dfrac{12}{13}\)

To find:

The value of \(\cos x\).

Solution:

We know that,

\(\sin^2(x)+\cos^2(x)=1\)

\(\cos^2(x)=1-\sin^2(x)\)

\(\cos(x)=\pm\sqrt{1-\sin^2x}\)

For a triangle, all trigonometric ratios are positive. So,

\(\cos(x)=\sqrt{1-\sin^2x}\)

It is given that \(\sin(x)=\dfrac{12}{13}\). After substituting this value in the above equation, we get

\(\cos(x)=\sqrt{1-(\dfrac{12}{13})^2}\)

\(\cos(x)=\sqrt{1-\dfrac{144}{169}}\)

\(\cos(x)=\sqrt{\dfrac{169-144}{169}}\)

\(\cos(x)=\sqrt{\dfrac{25}{169}}\)

On further simplification, we get

\(\cos(x)=\dfrac{\sqrt{25}}{\sqrt{169}}\)

\(\cos(x)=\dfrac{5}{13}\)

Therefore, the required value is \(\cos(x)=\dfrac{5}{13}\).

Answer:

Step-by-step explanation:

The angle PKS is marked with a small square.

It is the indication of a right angle, hence the measure of this angle is:

The reflexive closure of a relation on a set is the smallest reflexive relation that contains the original relation. In other words, it is the addition of pairs that ensure every element in the set is related to itself. To form the reflexive closure, we need to add pairs that relate each element in the set to itself.

To form the reflexive closure of relation r on the set {0, 1, 2, 3}, we need to add ordered pairs that ensure every element in the set is related to itself. In other words, we need to add pairs of the form (x, x) for each element x in the set that is not already present in relation r.

In this case, the reflexive closure of relation r would require adding the following ordered pairs: (0, 0), (1, 1), (2, 2), and (3, 3). These pairs ensure that every element in the set {0, 1, 2, 3} is related to itself, making the relation reflexive. These pairs ensure that every element is related to itself, satisfying the reflexivity property.

By adding these additional ordered pairs, we have modified relation r to include reflexivity, as every element now has a direct relation to itself in the set.

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angle 1 + angle 2 = 180 degrees

Step-by-step explanation:

supplementary angles add up to 180

Answer:

As per above properties we have:

and

the length of sides AB of the triangle is sum of all sides..

A rectangle's length is 5 inches greater than its width. if the perimeter of the rectangle is 42 inches, then the length is 13 inch.

A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.

here, we have,

a rectangle's length is 5 inches greater than its width.

if the perimeter of the rectangle is 42 inches

let, width = x

then, length = x+5

so, perimeter= 2(x+5 +x)

                      = 4x+10

ATQ, 4x+10 = 42

solving we get,

x=8

the length = 13

Hence, A rectangle's length is 5 inches greater than its width. if the perimeter of the rectangle is 42 inches, then the length is 13 inch.

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The given limit involves a vector expression.  By applying the properties of limits and trigonometric identities, we can simplify the expressions and determine the final limit. The final limit is lim t→0 (sin 3t/3t i - e^(4t-1)/7t j + cos t + t^2/2 - 1/6t^2 k) = 1i + 1/7j - ∞k.

To evaluate the given limit lim t→0 (sin 3t/3t i - e^(4t-1)/7t j + cos t + t^2/2 - 1/6t^2 k), we consider the limit of each component separately.

For the first component, lim t→0 (sin 3t/3t), we can use the limit property lim x→0 (sin x/x) = 1. Therefore, the first component simplifies to 1i.

For the second component, lim t→0 (e^(4t-1)/7t), we can use the limit property lim x→0 (e^x-1/x) = 1. Thus, the second component simplifies to 1/7j.

For the third component, lim t→0 (cos t + t^2/2 - 1/6t^2), we evaluate each term separately. The limit of cos t as t approaches 0 is 1, the limit of t^2/2 as t approaches 0 is 0, and the limit of 1/6t^2 as t approaches 0 is infinity. Therefore, the third component simplifies to 1 + 0 - infinity = -∞.

Thus, the final limit is lim t→0 (sin 3t/3t i - e^(4t-1)/7t j + cos t + t^2/2 - 1/6t^2 k) = 1i + 1/7j - ∞k.

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Answer: 36

Step-by-step explanation:

If 5/6 = 180

lets find what 1/6 equals

To do this lets divide 180 by 5 to find 1/6

\(\frac{180}{5} =36\)

Therefore, 1/6 = 36

We know 180/5 will give us the answer because 180 is already 5/6 of the total; dividing by 5 will give us 1/6 of the total. Ex: if we had 4/6 of the total, we would divide by 4 to find 1/6.

Anyways, we can check our answer by doing:

36*5 = 216 then taking 5/6 of 216, which should equal 180

\(216*\frac{5}{6} =180\)

Therefore, we know 36 is the correct answer

Answer:

The answer is below

Step-by-step explanation:

The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is given by:

\(AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\)

Point J is at (-3, 3), point K is at (4, 3) and point L is at (1, -1). Hence:

The distance between K and L = KL = \(\sqrt{(-1-3)^2+(1-4)^2} =5\ units\)

The distance between J and L = JL = \(\sqrt{(-1-3)^2+(1-(-3))^2} =4\sqrt{2} \ units\)

The distance between K and J = JK = \(\sqrt{(3-3)^2+(-3-4)^2} =7\ units\)

Therefore, the perimeter of triangle JKL is:

Perimeter = KL + JL + JK = 5 + 4√2 + 7 = 17.66 units

Answer:

0.07

Step-by-step explanation:

To round a decimal to the nearest hundredth, look at the thousandths place.

If the number in the thousandths place is greater than or equal to 5, we will round up the hundredths place.

If it is smaller than 5, we will keep the number the same.

In the number 0.065, the thousandths place value is 0.005. So, we will round up the hundredths place.

The hundredths place value is 0.06, so we will round it up to 0.07.

So, 0.065 will round to 0.07.

Answer:

So you just calculate the distance from.point 1 to 2 and then from 2 to 3 and then from 3 to 1. then sum them all up and you get the perimeter

Answer:

f(f(x)) = 27\(x^{4}\) + 18x² + 4

Step-by-step explanation:

To find f(f(x)) substitute x = f(x) into f(x) , that is

f(3x² + 1)

= 3(3x² + 1)² + 1 ← expand parenthesis using FOIL

= 3(9\(x^{4}\) + 6x² + 1) + 1 ← distribute parenthesis by 3

= 27\(x^{4}\) + 18x² + 3 + 1 ← collect like terms

= 27\(x^{4}\) + 18x² + 4

Hello,

\((fof)(x)=f(f(x))\\\\=3(3x^2+1)^2+1\\\\=3(9x^4+6x^2+1)+1\\\\\boxed{=27x^4+18x^2+4}\)

The upward unit normal to the surface 7cosθ = 10−13 at (9, θ, 0) is (-7√3/13, 0, 2√3/13).

To find the upward unit normal to the given surface, we need to determine the gradient vector of the surface at the specified point. The gradient vector represents the direction of the steepest ascent on the surface.

First, we rewrite the equation of the surface as cosθ = (10−13)/7. Taking the derivative of both sides with respect to θ, we get -sinθ = 0. Rearranging, we have sinθ = 0, which implies θ = 0 or π.

Since we are interested in the point (9, θ, 0), we consider the case when θ = 0. Plugging this value into the equation, we have cos(0) = (10−13)/7, which simplifies to cos(0) = -3/7.

The gradient vector at the point (9, 0, 0) is (-7√3/13, 0, 2√3/13). This vector represents the direction of the upward unit normal to the surface at that point.

Therefore, the upward unit normal to the surface 7cosθ = 10−13 at (9, θ, 0) is (-7√3/13, 0, 2√3/13).

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You need to know the following:

1. The "difference" is the result of a subtraction.

2. The word "times" indicates a multiplication.

3. The sum is the result of an addition.

Let be "n" the number mentioned in the exercise.

Knowing the explained above, you know that "the difference of a number and 6" can expressed as:

And "5 times the sum of the number and 2" can be expressed as:

Therefore, "the difference of a number and 6 is the same as 5 times the sum of the number and 2" can be written as the following equation:

Now, in order to find the number, you must solve for "n":

Answer:

5 cm

Step-by-step explanation:

Answer:

\(\boxed {\tt 50 \ m/s}\)

Step-by-step explanation:

To find the speed, divide the distance by the time. We can use the following formula:

\(s=\frac{d}{t}\)

The racing car completed a 700 meter lap in 14 seconds. So, the distance is 700 meters and the time is 14 seconds.

\(d= 700 \ m \\t= 14 \ s\)

Substitute the values into the speed formula.

\(s=\frac{700 \ m }{14 \ s}\)

Divide.

\(s= 50 \ m/s\)

The speed of the racing car is 50 meters per second

Answer:

Step-by-step explanation:

The speed of an object can be found by using the formula

\(v = \frac{d}{t} \\ \)

where

v is the speed

d is the distance

t is the time

From the question

d = 700 m

t = 14 s

We have

\(v = \frac{700}{14} \\ \)

We have the final answer as

Hope this helps you

to find the number of plants in the pond at the time t we can use the equation N(t) = 150(3)^t.

        The equation that can be used to find the number of plants in the pond at time t, given that the number of plants is growing exponentially, is:

                      N(t)=ab^t.

         The given values in the table for the function N(t) are:

                      t  N(t)0  1501  450

         We can use these values to determine the values of constants a and b in the equation

                       N(t)=ab^t:

          Substitute t = 0 and N(t) = 150 in the equation

                      N(t)=ab^t.

          Then, 150 = a × b^0 → 150

                            = a × 1 → a

                            = 150

            Substitute t = 1 and N(t) = 450 in the equation N(t)=ab^t.

             Then, 450 = 150 × b^1 → b = 3.

     Now that we have found the values of a and b, we can write the equation that can be used to find the number of plants in the pond at time t as:  N(t) = ab^t = 150(3)^t.

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1. When t = 0, the position (displacement) of the object can be found by substituting t = 0 into the given equation of motion:d = 3sin(8π(0)) - 2 = 0 - 2 = -2 meters.2. The maximum displacement of the object from its t=0 position can be found by taking the amplitude of the displacement function. Since the function is of the form d = Asin(ωt) - B, where A is the amplitude, ω is the angular frequency and B is the vertical shift, it can be seen that the amplitude in this case is A = 3 meters. So, the maximum displacement is 3 meters.3. The time taken for one oscillation can be found by dividing the period, T, of the oscillation by the number of oscillations in that period. The period of the oscillation is the time taken for one complete cycle of the sine wave, which is 1/8 seconds. Thus, the time taken for one oscillation is:1 oscillation = T/1/8 s = 8T s4. The frequency of the oscillation is the reciprocal of the period, which is f = 1/T. Thus, the frequency is:f = 1/T = 1/(1/8) Hz = 8 Hz.

An U-tube is set up and three liquids A, B and C with densities of 13600 kg/m³, 5800 kg/m³ and 2400 kg/m³ respectively are poured into one end one by one. The U-tube is initially filled with liquid A. The height of liquid B and C in the U-tube is 6 cm and 7 cm respectively.

We are to sketch the diagram, mark the liquids and determine the column height of liquid A w.r.t the base of liquid B. Liquid A is denser than liquid B and liquid C That is, liquid B will be above liquid C.

This can be obtained by subtracting the height of liquid B from the height of liquid C. The height of liquid C is 7 cm. Liquid B is above liquid C, therefore its height can be obtained by subtracting the height of liquid B from that of liquid C. Hence, the height of liquid B is:7 - 6 = 1 cm.

Since the height of the U-tube is not given, we can assume any convenient value. Let us assume that the height of the U-tube is 14 cm.  \({{\rm{H}}_{{\rm{AB}}}}\) is the height of liquid B above the base of the U-tube.

\(h = 14 - (7 + 6 + 1) = 14 - 14 = 0 cm\) Therefore, the column height of liquid A w.r.t the base of liquid B is 0 cm.

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From the given information, cholesterol level X follows the N(222, 37) distribution.

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be calculated by using the z-score formula as follows:

z = (x - μ) / σ

For lower limit x1 = 200, z1 = (200 - 222) / 37 = -0.595

For upper limit x2 = 240, z2 = (240 - 222) / 37 = 0.486

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be computed as

P(200 ≤ X ≤ 240) = P(z1 ≤ Z ≤ z2) = P(Z ≤ 0.486) - P(Z ≤ -0.595) = 0.683 - 0.277 = 0.406

In this population, 90% of men have a cholesterol level that is at most X90.The z-score corresponding to a cholesterol level of X90 can be calculated as follows:

z = (x - μ) / σ

Since the z-score separates the area under the normal distribution curve into two parts, that is, from the left of the z-value to the mean, and from the right of the z-value to the mean.

So, for a left-tailed test, we find the z-score such that the area from the left of the z-score to the mean is 0.90.

By using the standard normal distribution table,

we get the z-score as 1.28.z = (x - μ) / σ1.28 = (X90 - 222) / 37X90 = 222 + 1.28 × 37 = 274.36 ≈ 274

The cholesterol level of 90% of men in this population is at most 274 mg/dl.

The distributions that we can consider to be approximately normal are the sampling distribution of mean BMI for random samples of 60 adults and the sampling distribution of mean BMI for random samples of 9 adults.

The reason for considering these distributions to be approximately normal is that according to the Central Limit Theorem, if a sample consists of a large number of observations, that is, at least 30, then its sample mean distribution is approximately normal.

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Answer:

Step-by-step explanation:

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Answer:

Approximately 7.2 kilometers

Step-by-step explanation:

4.5(miles walked)*1.6(kilometers in mile)=7.2(kilometers in 4.5 miles)

Answer:

7.2 kilometres

Step-by-step explanation:

4.5 * 1.6

To estimate the area under the graph of f(x) = 3√x from x = 0 to x = 4 using four approximating rectangles, we can divide the interval [0, 4] into four subintervals of equal width and calculate the area of each rectangle using either the right endpoints or the left endpoints.

(a) Using right endpoints:

The width of each rectangle is Δx = (4 - 0) / 4 = 1.

The right endpoints for the four subintervals are x = 1, 2, 3, and 4.

We can calculate the height of each rectangle by evaluating f(x) = 3√x at the right endpoints:

f(1) = 3√1 = 3

f(2) = 3√2

f(3) = 3√3

f(4) = 3√4 = 6

The area of each rectangle is then the product of the width and the height.

R1 = 1 * 3 = 3

R2 = 1 * f(2)

R3 = 1 * f(3)

R4 = 1 * 6

To estimate the total area, we sum up the areas of the four rectangles:

R4 = R1 + R2 + R3 + R4

(b) Using left endpoints:

Similar to part (a), the width of each rectangle is Δx = (4 - 0) / 4 = 1.

The left endpoints for the four subintervals are x = 0, 1, 2, and 3.

We can calculate the height of each rectangle by evaluating f(x) = 3√x at the left endpoints:

f(0) = 3√0 = 0

f(1) = 3√1 = 3

f(2) = 3√2

f(3) = 3√3

The area of each rectangle is the product of the width and the height.

L1 = 1 * 0 = 0

L2 = 1 * f(1)

L3 = 1 * f(2)

L4 = 1 * f(3)

To estimate the total area, we sum up the areas of the four rectangles:

L4 = L1 + L2 + L3 + L4

Now, to determine whether the estimates are underestimates or overestimates, we compare them to the actual area under the curve.

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Answer:

The value of x is 30 degrees.

Step-by-step explanation:

We know that angle 1 is 60 degrees, and that angle two is a right angle (meaning 90 degrees.) 60+90 is equal to 150 degrees. 180 degrees - 150 degrees is equal to 30 degrees. I hope this helps! :)

\(~~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\\implies \sin 60^{\circ} = \dfrac{x}{8}\\\\\\\implies x = 8 \sin 60^{\circ}\\\\\\\implies x = 8 \cdot \dfrac {\sqrt3}2\\\\\\\implies x = 4\sqrt 3\)