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Each package weighs 6 pounds. Choose the best estimate of the total weight of the packages.2,400 pounds 240 pounds 200 pounds 20 pounds.

Answer:

Point U

Step-by-step explanation:

The center point of the angle

According to the scale on the map where 1 inch corresponds to 15 miles, the two cities that are 5 1/2 inches apart on the map would be separated by an actual distance of 82.5 miles.

To determine the actual distance between the two cities, we need to multiply the number of inches on the map by the corresponding distance in miles per inch. In this case, the scale indicates that 1 inch on the map represents 15 miles. So, when we multiply the distance on the map (5 1/2 inches) by the conversion factor (15 miles/inch), we get the actual distance between the two cities. Therefore, the calculation would be: 5.5 inches × 15 miles/inch = 82.5 miles. Thus, the two cities are 82.5 miles apart in reality.

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The confidence interval (149.2, 206.4) can be written as ¯x ± me, where ¯x = 177.8 and me = 28.6. The sample mean (¯x) is the midpoint of the confidence interval

To express the confidence interval (149.2, 206.4) in the form of ¯x ± me, we need to calculate the sample mean (¯x) and the margin of error (me).

The sample mean (¯x) is the midpoint of the confidence interval and can be calculated by taking the average of the upper and lower bounds of the interval:

¯x = (149.2 + 206.4) / 2 = 177.8

Next, we calculate the margin of error (me) by finding the half-width of the confidence interval:

me = (206.4 - 149.2) / 2 = 28.6

Therefore, the confidence interval (149.2, 206.4) can be expressed in the form of ¯x ± me as:

¯x ± me = 177.8 ± 28.6

Hence, the confidence interval (149.2, 206.4) can be written as ¯x ± me, where ¯x = 177.8 and me = 28.6.

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The area under the standard normal curve to the right of Z = 1.43 is 0.0764

The correct option is 0.0764

We will use the concept of probability and the Normal Distribution Formula.

Z = 1.43

According to the concept of probability:  P(Z > 1.43) + P(Z < 1.43) = 1

P(Z > 1.43) = 1 - P(Z < 1.43)

We have to use the z-table and locate 1.4 in the left-most column, move across the row to the right under 0.03 to find the value 0.9236.

⇒ P(Z < 1.43) = 0.9236

P(Z > 1.43) = 1 - P(Z < 1.43) = 1 - 0.9236

P(Z > 1.43) = 0.0764

Hence, the area under the standard normal curve to the right of Z = 1.43 is 0.0764

The correct option is 0.0764

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The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer:

The answer is below

Step-by-step explanation:

The scale for the drawing is 1 inch = 40 feet.

The right angled triangle has legs of 3 inches and 4 inches. Using the scale, the length of the legs is:

3 inches = 3 inch * 40 feet / inch = 120 feet and 40 inches =  4 inch * 40 feet / inch = 160 feet.

The area of a right angled triangle is half the product of the two legs. Hence:

Area of right angled triangle = 1/2 * 120 feet * 160 feet = 9600 ft²

The rectangle with dimensions of 1.5 inches and 2.5 inches. Using the scale, the length of the sides is:

1.5 inches = 1.5 inch * 40 feet / inch = 60 feet and 2.5 inches =  2.5 inch * 40 feet / inch = 90 feet.

The area of a rectangle is the product of the two sides. Hence:

Area of rectangle = 60 feet * 90 feet = 5400 ft²

Answer:

\(\overline{BC} \cong \overline{DC}\) because corresponding parts of congruent triangles ΔACD and ΔACB are Congruent

Step-by-step explanation:

Statements,                                                Reason

\(\overline{AC}\) bisects ∠BCD,                                      Given        

\(\overline{DC} \perp \overline{AD}\)                                                    Given

∠CDA ≅ ∠CBA                                           Right angles are ≅

\(\overline{AC} \cong \overline{AC}\)                                                     Reflexive property

ΔACD ≅ ΔACB                                           Hypotenuse Leg (HL) congrurency

\(\overline{BC} \cong \overline{DC}\)                                                    CPCTC

Where:

CPCTC = Corresponding parts of Congruent Triangles are Congruent

⊥ = Perpendicular to

≅ = Congruent

∠ = Angle

Δ = Triangle.

Answer:

11/20

Step-by-step explanation:

16/20 - 1/4

rewrite 1/4 with same denominator (multiply by 5)

16/20 - 5/20 = 11/20

Step-by-step explanation:

If they are similar, then 10 is to 3      as  x is to 15

10/3 = x/15    multiply both sides by 15

 50 mm = x

Answer: (A) 1 Foot

Step-by-step explanation:

Travel per second = Distance/Time

So Look at the highest part of the graph. It says 6 Feet travelled after 6 seconds.

Thus 6 Feet / 6 Seconds = 1 Foot per second

This can be confirmed by the fact that 2 feet is travelled in 2 seconds, and 4 feet is travelled in 4 seconds, based on the graph.

Hope this helps!

If she already has 12 signatures: 60 - 12 = 48

48/3 = 16

so, she and her friends need at least 16 signatures each.

p being person;

p \(\geq\) 16 (p has to be greater or equal than 16)

Answer:

option 4

Step-by-step explanation:

Given Equation :-

=> -4| x + 9 | = -8

To FinD :-

=> Solution of the equation .

Solving it :-

=> -4| x + 9 | = -8

=> | x + 9 | = -8/-4

=> |x + 9| = 2

=> ( | x + 9 | )² = 2²

=> x + 9 = ±2

=> x = -9 +2 , -9-2

=> x = - 7 , -11

Option 4 is correct.

Answer:

x = - 7 , - 11

Step-by-step explanation:

\(-4 | x +9| = - 8\\\\\frac{-4}{-4} |x+9| = \frac{-8}{-4}\\\\1 | x+9| = 2\\\\x+9 = - 2\ , x + 9 = 2\\\\x + 9 - 9 = - 2 - 9 , \ x + 9 - 9 = 2 - 9\\\\x + 0 = - 1 1 \ , \ x + 0 = - 7\\\\x = -11 \ , \ x = - 7\)

Answer: C.   The drone is on the ground at 0 and 4 seconds.

you have a blessed thanksgiveing

Answer:

sorry i didn't understand

The area of the given triangle will be \(\dfrac{5\sqrt{2}}{2}\)

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

Given points of the triangle are:-

( -6,5 ) (-5,3 ) and (-8, 2)

Now we will apply the area formula for the triangle:-

\(A = \dfrac{1}{2} \times B\times H\)

The base will be = \(\sqrt{(-5++8)^2+(3-2)^2)}=\sqrt{9+1}=\sqrt{10}}\)

The Height will be = \(\sqrt{(-5+6)^2+(5-3)^2}=\sqrt5\)

The area will be calculated as:-

\(A =\dfrac{1}{2}\times \sqrt{10}\times \sqrt{5}=\dfrac{5\sqrt{2}}{2}}\)

Therefore the area of the given triangle will be \(\dfrac{5\sqrt{2}}{2}\)

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The regression analysis yielded a fitted line, y = 35 - 1.2x, with a coefficient of determination of 0.7632, a correlation coefficient of 0.8740, and a predicted mean of Y = 23 when X = 10.

To compute the coefficient of determination (r²), the correlation coefficient (r), and the predicted mean of Y when X = 10, we can use the given regression line y = 35 - 1.2x and the formulas related to regression analysis.

The coefficient of determination (r²) represents the proportion of the total variation in the dependent variable (Y) that can be explained by the independent variable (X). It is calculated by dividing the explained sum of squares (SSR) by the total sum of squares (SSY).

[a] To compute r²:

SSR = SSY - SSE

SSR = 2758 - 652 = 2106

r² = SSR / SSY

r² = 2106 / 2758 = 0.7632

Therefore, the coefficient of determination (r²) is 0.7632 (rounded to four decimal places).

[b] To compute the correlation coefficient (r):

We can use the formula:

r = √(r²)

r = √(0.7632) = 0.8740

Therefore, the correlation coefficient (r) is 0.8740 (rounded to four decimal places).

[c] To compute the predicted mean of Y when X = 10:

We can substitute the value of X = 10 into the regression line equation y = 35 - 1.2x:

y = 35 - 1.2(10)

y = 35 - 12

y = 23

Therefore, the predicted mean of Y when X = 10 is 23.

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Answer:

a) \(x = 10^{18}\,\mu m^{2}\), b) \(x = 10^{18}\), c) \(x = 10^{21}\,\mu m^{2}\), d) \(x = 10^{21}\), e) \(x = \frac{1}{10^{21}}\),  f) \(x = 10^{3}\,nm^{2}\), g) \(x = 10^{3}\,nm^{2}\)

Step-by-step explanation:

a) The product of one terameter and one micrometer is:

\(x = (1\,tm)\cdot (10^{12}\,\frac{m}{tm})\cdot (10^{6}\,\frac{\mu m}{m} ) \cdot (1\,\mu m)\)

\(x = (10^{18}\,\mu m)\cdot (1\,\mu m)\)

\(x = 10^{18}\,\mu m^{2}\)

b) The quotient of one terameter and one micrometer is:

\(x = \frac{(1\,tm)\cdot (10^{12}\,\frac{m}{tm} )\cdot (10^{6}\,\frac{\mu m}{m} )}{1\,\mu m}\)

\(x = \frac{10^{18}\,\mu m}{1\,\mu m}\)

\(x = 10^{18}\)

c) The product of terameter and one nanometer is:

\(x = (1\,tm)\cdot (10^{12}\,\frac{m}{tm})\cdot (10^{9}\,\frac{nm}{m} ) \cdot (1\,nm)\)

\(x = (10^{21}\,nm)\cdot (1\,nm)\)

\(x = 10^{21}\,\mu m^{2}\)

d) The quotient of one terameter and one nanometer is:

\(x = \frac{(1\,tm)\cdot (10^{12}\,\frac{m}{tm} )\cdot (10^{9}\,\frac{nm}{m} )}{1\,nm}\)

\(x = \frac{10^{21}\,nm}{1\,nm}\)

\(x = 10^{21}\)

e) The quotient of one nanometer and one terameter is:

\(x = \frac{1\,nm}{(1\,tm)\cdot (10^{12}\,\frac{m}{tm} )\cdot (10^{9}\,\frac{nm}{m} )}\)

\(x = \frac{1\,nm}{10^{21}\,nm}\)

\(x = \frac{1}{10^{21}}\)

f) The quotient of one nanometer and one micrometer is:

\(x = \frac{1\,nm}{(1\,\mu m)\cdot (10^{3}\,\frac{nm}{\mu m} )}\)

\(x = \frac{1\,nm}{10^{3}\,nm}\)

\(x = \frac{1}{10^{3}}\)

g) The product of one nanometer and one micrometer is:

\(x = (1\,nm)\cdot (1\,\mu m)\cdot (10^{3}\,\frac{nm}{\mu m} )\)

\(x = 10^{3}\,nm^{2}\)

Answer:

c. The graph has no​ x-intercepts.

Step-by-step explanation:

because it will never touch the x axis

A quadratic function is represented as: \(\mathbf{f(x) = ax^2 + bx + c}\)

The conclusion from \(\mathbf{b^2 - 4ac > 0}\) is that, the graph has two distinct x-intercepts

There are three possible roots of a quadratic function

When \(\mathbf{b^2 - 4ac > 0}\), it means that:

The function has distinct real roots

In other words, the function has 2 different values of x

This implies that,

The function crosses the x-axis two times

When the function cross the x-axis, it means that the function has an x-intercept

Hence, the conclusion is:

a. The graph has two distinct​ x-intercepts.

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The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer:

 a) cannot tell

  b) congruent

  c) not congruent

Step-by-step explanation:

You want to know if the triangles in the given figures are congruent.

In order to prove congruence, we must have information to establish one of SSS, SAS, ASA, AAS congruence.

Congruence only of corresponding angles demonstrates the triangles are similar, which means they may or may not be congruent.

These triangles have congruent corresponding angles, so are similar. It is impossible to tell if they are congruent.

These triangles meet the conditions for demonstrating AAS congruence. The triangles are congruent.

Looking at the figure from an AAS or ASA or SAS point of view, the corresponding sides are not congruent, but the corresponding angles are. These triangles are similar, but are not congruent.

__

Additional comment

In the triangles of (c), for the given long side, the short side shown will be 25.73 in the larger triangle and 16.73 in the smaller one. That is, the angles indicate the triangles should be similar, but the given side ratios are not proportional.

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The threshold price F * for insurance is F * = c1c2. If F >F *, it would not be rational for Nick to purchase insurance. If F < F *, it would be rational for Nick to purchase insurance as it provides a net benefit.

To find the threshold price F *  for insurance where Nick is indifferent over buying insurance, we need to determine the point at which Nick's expected utility is the same whether he purchases insurance or not.

Let's consider the two scenarios:

1. No insurance purchased (F' = 0):
In this case, if Nick consumes c1 chocolate bars in period 1 and c2 chocolate bars in period 2, his utility function becomes U(c1;c2;0) = c1c2.

2. Insurance purchased (F' = F):
If Nick purchases insurance by paying F upfront, his utility function becomes U(c1;c2;F) = c1c2 - F.

Now, let's find the threshold price F * by comparing the expected utilities for both scenarios:

1. No insurance:
The expected utility without insurance is the utility multiplied by the probability of not having his chocolate stolen (1 - 0.25 = 0.75):
E(U(c1;c2;0)) = 0.75 * (c1c2)

2. Insurance:
The expected utility with insurance is the utility multiplied by the probability of not having his chocolate stolen, minus the cost of insurance (F), multiplied by the probability of having his chocolate stolen (0.25):
E(U(c1;c2;F)) = 0.75 * (c1c2) + 0.25 * (c1c2 - F)

To find the threshold price F *, we set the expected utilities equal to each other and solve for F:
0.75 * (c1c2) = 0.75 * (c1c2) + 0.25 * (c1c2 - F)

By simplifying the equation, we get:
0 = 0.25 * (c1c2 - F)

Solving for F gives us:
F = c1c2

Therefore, the threshold price F * for insurance is F * = c1c2.

Now let's consider the scenarios when F > F * and F < F *:

- F > F *:
If the price of insurance (F) is greater than the threshold price (F *), it means that the cost of insurance is higher than the expected loss from chocolate being stolen. In this case, it would not be rational for Nick to purchase insurance because he would be paying more than the potential loss.

- F < F *:
If the price of insurance (F) is less than the threshold price (F *), it means that the cost of insurance is lower than the expected loss from chocolate being stolen. In this case, it would be rational for Nick to purchase insurance as it provides a net benefit by reducing the potential loss.

In summary, the threshold price F * for insurance is F * = c1c2. If F > F *, it would not be rational for Nick to purchase insurance. If F < F *, it would be rational for Nick to purchase insurance as it provides a net benefit.

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Answer:

95

Step-by-step explanation:

All interior angles of a square is equal to 360 so,

95+85+85+x=360

265+x=360

x=95

Answer:

3

Step-by-step explanation:

Slope m = (y2 - y1)/(x2 - x1)

m = (13 - 1)/(0 - -4) = 12/4 = 3

Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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Answer:

37.68.

Step-by-step explanation:

formula is C = 2 times pi times r

radius is half of diameter so radius is 6.

6 times 2 times 3.14 is 37.68.

Answer:

1

Step-by-step explanation:

Step 1:

2x + 5 = 7

Step 2:

2x = 2

Answer:

x = 1

Hope This Helps :)

Answer:

x = 1

Step-by-step explanation:

Step 1: Write equation

2x + 5 = 7

Step 2: Solve for x

Subtract 5 on both sides: 2x = 2

Divide both sides by 2: x = 1

Step 3: Check

Plug in x to verify if it's a solution.

Substitute: 2(1) + 5 = 7

Multiply: 2 + 5 = 7

Add: 7 = 7

Assuming that each of the sophomores, each of the juniors and each of the seniors is equally likely to be selected for the committee, there are b. 1211760 ways can the governance committee be selected, if it must be made up of 2 sophomores, 2 juniors and 3 seniors. The committee can be selected in 1,211,760 ways.

Combination formula:

Cn,x is the number of different combinations of x objects from a set of n elements, given by:

Cnₓ= n!÷ x! (n-x!)

In this problem:

2 sophomores from a set of 18.

2 juniors from a set of 12.

3 seniors from a set of 10.

They are independent, so we can just multiply them, thus:

T= C₁₈,₂ × C₁₂,₂× C₁₀,₃ = 18! ÷2!6! × 12!÷ 2!10! × 10!÷ 3!×7! = 1211760

The committee can be selected in 1,211,760 ways.

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After simplifying and rationalizing the expression 1 - √ 3 x / √ 6 x, we get the result as - (√ 2 / 2) + (√6 / 6) x .

We are given the expression:

1 - √ 3 x / √ 6 x

We need to simplify each expression by rationalizing the denominator.

Multiply √ 6 in both numerator and denominator, we get that:

(1 - √ 3 x)  / √ 6 x    ×    ( √ 6 / √ 6)

We get that:

= (√ 6 - 3 √ 2 x) / 6 x

= - (√ 2 / 2) + (√6 / 6) x

Therefore, after simplifying and rationalizing the expression 1 - √ 3 x / √ 6 x, we get the result as - (√ 2 / 2) + (√6 / 6) x .

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