Carlos built a rectangular fort that was 6 feet long and 4.5 feet wide. He determined that the area of his fort was 13.5 feet².

For your response, answer three questions.

1. What is the area of the fort?

2. Was Carlos correct? (yes or no)

3. If Carlos was not correct, what was his mistake? If Carlos was correct, how did he determine the area?

The true statements regarding the probability are:

Based on the given information, it is likely that the bag has at least one black marble (with a probability of 0.1). It is not certain or impossible, as the probability is not 0 or 1.

It is not certain or unlikely that the bag has at least one pink marble, as the probability is not 0 or 1. However, the probability of the bag having at least one pink marble is relatively high (0.79), so it is more likely than not that the bag has a pink marble.

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The area of the given triangle, given the height and the type of triangle would be E. 16 cm ²

To find the area of an equilateral triangle when given just the height, the formula is:

= ( height ² x  √ 3 ) / 2

We are given a height of 4 cm.

The area of the triangle is therefore :

= ( height ² x  √ 3 ) / 2

= ( 4 cm ² x  √ 3 ) / 2

= ( 16 x  √ 3 ) / 2

=  27. 712 / 2

= 13. 85

The closest option is 16 cm ² so this is the answer.

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The sine of an angle 0 in the third quadrant is -0.5. So the value of cos∅ is -√(3)/2.

In the third quadrant, both sine and cosine are negative. We know that the sine of ∅ is -0.5, so we can use the Pythagorean identity to find the cosine of ∅:

sin²(∅) + cos²(∅) = 1

Substituting -0.5 for sin(∅), we get:

(-0.5)² + cos²(∅) = 1

Simplifying:

0.25 + cos²(∅) = 1

cos²(∅) = 1 - 0.25

cos²(∅) = 0.75

Taking the square root of both sides:

cos(∅) = ±√(0.75)

Since we're in the third quadrant where cosine is negative, we take the negative square root:

cos(∅) = -√(0.75)

Simplifying the square root:

cos(∅) = -√(3/4)

cos(∅) = -√(3)/2

Therefore, the value of cos(∅) is -√(3)/2.

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The commutative sets of transformations are two translations, refelction over the y-axis, dilation with center (2,2) and two reflections over the x-axis​. B, D, and E.

The sets of transformations that result in the same image when performed in any order are called "commutative."

A set of transformations is commutative if the order of the transformations doesn't matter;

Performing the transformations in a different order still results in the same final image.

Based on this definition can select the commutative sets of transformations from the given choices:

Translation and dilation with center (0,0) are not commutative.

The order of the transformations matters.

Two translations are commutative.

The order of the transformations doesn't matter.

Vertical translations and reflection over the y-axis are not commutative. The order of the transformations matters.

Reflection over the y-axis and dilation with center (2,2) are commutative.

The order of the transformations doesn't matter.

Two reflections over the x-axis are commutative.

The order of the transformations doesn't matter.

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09. The total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals.

10. The total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.

In order to find the marginal frequencies, we need to calculate the totals for each category separately.

For question 9:

The marginal frequency for "Set Academic Goals - yes" is 64 + 54 = 118. This represents the total number of individuals who answered "yes" to setting academic goals.

The marginal frequency for "Set Academic Goals - no" is 168 + 142 = 310. This represents the total number of individuals who answered "no" to setting academic goals.

The marginal frequency for "Male" is 64 + 168 = 232. This represents the total number of males.

The marginal frequency for "Female" is 54 + 142 = 196. This represents the total number of females.

Interpretation:

The marginal frequencies provide us with the total counts for each category in a contingency table. In this case, we can see that out of the total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals. Additionally, there were 232 males and 196 females in the sample.

For question 10:

The marginal frequency for "Cat - yes" is 104 + 186 = 290. This represents the total number of individuals who have cats.

The marginal frequency for "Cat - no" is 208 + 98 = 306. This represents the total number of individuals who do not have cats.

The marginal frequency for "Dog - yes" is 104 + 208 = 312. This represents the total number of individuals who have dogs.

The marginal frequency for "Dog - no" is 186 + 98 = 284. This represents the total number of individuals who do not have dogs.

Interpretation:

The marginal frequencies reveal the total counts for each category in the contingency table. In this case, we can observe that out of the total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.

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After considering the given data we conclude that the area of the given figure is 62.2 cm², under the condition that x = 5 cm

Since the given figure comprises of two right angled triangle and one rectangle we can split them and calculate their area separately then apply summation at the ending.
Let us proceed with the triangle
Let us first name the whole figure, ABCD is the whole diagram out of which first we will deal with triangle CDG,
In triangle CDG
The height length (DG) = 7.5 cm
The base  length ( CG) = 2.4 cm
Then the area of the triangle CDG
[tex]Area =1/2 * base *height[/tex]
= 1/2 × 2.4 ×7.5
= 1/2 × 18
= 9 cm²
Now moving on to the other triangle ABE
The height length (AE) = 7.5 cm
The base  length (EB) = 4.2 cm
Then the area of the triangle ABE
[tex]Area =1/2 * base *height[/tex]
= 1/2 × 4.2 × 7.5
=1/2 × 31.5
= 15.7 cm²
Finally moving onto the rectangle AEGD,
Given
Length of the rectangle (DG) = 7.5 cm
Breadth of the rectangle ( GE) = x = 5 cm
Placing the values in the formula
[tex]Area = length * breathe[/tex]
Area = 7.5 × 5
Area = 37.5 cm²

Now applying summation to evaluate the total area of the quadrilateral ABCD
Area of CDG + Area of ABE + Area of AEGD
= ( 9 + 15.7 + 37.5)
= 62.2 cm²
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The weight of the 0.8-meter piece is 19.6 kilograms.

We can use the ratio of length to weight to determine the weight of the 0.8-meter piece.

Let's call the weight of the 2.8-meter piece "W₁" and the weight of the 0.8-meter piece "W₂". Then we have:

W₁/2.8m = 24.5kg/1m

Solving for W₁, we get:

W₁ = (24.5kg/1m) x 2.8m = 68.6kg

Now we can use the same ratio to find W₂:

W₂/0.8m = 24.5kg/1m

Solving for W₂, we get:

W₂ = (24.5kg/1m) x 0.8m = 19.6kg

Therefore, the weight of the 0.8-meter piece is 19.6 kilograms.

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Answer:

The original price of the shirt was Ksh 500 and it was sold for Ksh 550.

The discount is the difference between the original price and the selling price, which is Ksh 500 - Ksh 550 = Ksh -50.

To find the percentage discount, we can use the formula:

percentage discount = (discount ÷ original price) × 100%

percentage discount = (-50 ÷ 500) × 100%

percentage discount = -10%

Therefore, the percentage discount is 10%.

The per-unit reactance of the transformer is 0.0444 pu.

To calculate the per-unit reactance of the transformer, we need to use the following formula:

Xpu = X / (Vbas[tex]e^2[/tex] / Sbase)

where X is the reactance in ohms, Vbase is the base voltage in volts, and Sbase is the base power in volt-amperes.

In this case, the rated power of the transformer is 5 kVA, and the rated voltage on the high side is 400V. Therefore, the base power and base voltage are:

Sbase = 5 kVA

Vbase = 400V

The reactance of the transformer referred to the low voltage side is given as 2Ω. To convert this to per-unit, we substitute the values in the formula:

Xpu = 2Ω / (300[tex]V^2[/tex] / 5 kVA)

Xpu = 0.0444 pu

Therefore, the per-unit reactance of the transformer is 0.0444 pu.

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The area of the whole quilt is 441 in². of the whole quilt is 441 in².

We are given that;

Measure= 7*7

Now,

To find the area of the whole quilt, you need to multiply the length and width of the quilt.

The length and width of the quilt are both 7 times 3 in,

which is 21 in. So, the area of the quilt is 21 in x 21 in

= 441 in².

Therefore, by the area the answer will be 441 in².

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The correct statement is: c. Median is less than or equal to [tex]18[/tex].

Let's analyze the given range of values, which is [tex]5 \ to \ 18[/tex], and evaluate the statements:

a. Mean is less than [tex]6[/tex]:

To determine if the mean is less than [tex]6[/tex], we need to find the average of the given range.

The mean can be calculated as:

[tex]\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \][/tex]

In this case, the sum of the values is [tex]5 + 6 + 7 + \ldots + 18[/tex], and the number of values is [tex]18 - 5 + 1[/tex] (inclusive).

b. Range is greater than [tex]18[/tex]:

The range is the difference between the maximum and minimum values in a dataset. In this case, the range is [tex]18 - 5 = 13,[/tex] which is less than 18.

c. Median is less than or equal to [tex]18[/tex]:

The median is the middle value in a dataset when the values are arranged in ascending order. In this case, since the range starts from [tex]5[/tex] and ends at 18, the median is less than or equal to [tex]18[/tex].

d. IQR is greater than or equal to [tex]6[/tex]:

The interquartile range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3) of a dataset. Since we don't have the actual dataset or specific values beyond the range, we cannot determine if the IQR is greater than or equal to [tex]6[/tex].

Therefore, based on the given range, the correct statement is:

c. Median is less than or equal to [tex]18[/tex].

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The measures of angle 1 and angle 2 are 12.5 degrees

We have to find the measures of angle 1 and angle 2

The circle will have 360 degrees

The unknown arc length be taken as x

175+160+x=360

Add the like terms

335+x=360

Subtract 335 from both sides

x=360-335

x=25

So angle m∠1 = 1/2(25)

m∠1 is 12.5

m∠1 = m∠2 as both are equal.

m∠2 = 12.5 degrees

Hence, the measures of angle 1 and angle 2 are 12.5 degrees

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Answer:

Step-by-step explanation:

20=17+12+9 so the answer is 4982

Answer: 6

Step-by-step explanation:

set up a box plot.

To find the interquartile range: 3rd tile value subtracted by the first tile value. Basically: Q3-Q1=IQR

Q= Quartile

3 and 1 is the number

IQR = interquartile range

if you do incorrectly you should get 6 if not add me as a friend and I’ll show you and explain it better!

Answer:

Step-by-step explanation:

The equation to solve the problem is:

x + 550 = 750

Explanation:

The manager has already distributed $550, and the remaining amount to distribute is represented by the variable x. Adding the distributed amount to the remaining amount should equal the total amount of tips the manager has, which is $750. Therefore, the correct equation is x + 550 = 750.

The actual distance from A to the mid-point of BC is 42 m.

The actual distance from B to the mid-point of AC is 27 m.

A scale of 1 cm to 10 m can draw the triangular field ABC as follows:

        C

       / \

85 /   \ 90

    /      \

  A-------B

     30

Here, we draw AB as a horizontal line segment of length 9 cm (since AB is 90 m and the scale is 1 cm to 10 m), BC as a vertical line segment of length 3 cm (since BC is 30 m and the scale is 1 cm to 10 m) and AC as the hypotenuse of a right triangle with legs of length 8.5 cm and 9 cm (since AC is 85 m and AB is 90 m).

We can use a ruler to measure the actual distances from A to the mid-point of BC and from B to the mid-point of AC on the scale drawing.

The actual distance from A to the mid-point of BC, we first locate the mid-point of BC on the scale drawing is at a distance of 1.5 cm from B.

Then, we measure the distance from A to the mid-point of BC on the scale drawing is approximately 4.2 cm.

The scale of 1 cm to 10 m, we can convert this to the actual distance:

Actual distance = 4.2 cm × 10 m/cm

= 42 m

The actual distance from B to the mid-point of AC first locate the mid-point of AC on the scale drawing is at a distance of 4.25 cm from A.

Then, we measure the distance from B to the mid-point of AC on the scale drawing is approximately 2.7 cm.

Using the scale of 1 cm to 10 m, we can convert this to the actual distance:

Actual distance = 2.7 cm × 10 m/cm

= 27 m

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The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

The equation of the conic in xy-coordinates when the axes are rotated through the given angle can be determined by using a rotation matrix. Given that the conic is represented by the equation:

x^2 - y^2 = 2y

And the rotation angle is θ = arccos(3/5), we can proceed as follows:

1. Rewrite the given equation in matrix form:

[x, y] * [1  0] * [x]  = [2y]

        [-1 0]   [y]      [0]

2. Define the rotation matrix using the given angle θ:

R(θ) = [cos(θ)  -sin(θ)]

          [sin(θ)   cos(θ)]

3. Apply the rotation matrix to the equation:

[x, y] * R(θ)^T * R(θ) * [x] = [2y]

        [1  0]     [-1 0]   [y]     [0]

[x, y] * R(θ)^T * [1  0] * R(θ) * [x] = [2y]

                              [-1 0]   [y]     [0]

[x, y] * [cos(θ) sin(θ)] * [1  0] * [cos(θ)  -sin(θ)] * [x] = [2y]

        [-sin(θ) cos(θ)]   [-1 0]     [sin(θ)   cos(θ)]   [y]     [0]

Simplifying the expression:

[x * cos(θ) + y * sin(θ)] * [x * cos(θ) - y * sin(θ)] - [x * sin(θ) - y * cos(θ)] * [x * sin(θ) + y * cos(θ)] = 2y

Expanding and rearranging terms:

x^2 * cos^2(θ) - y^2 * sin^2(θ) - x^2 * sin^2(θ) + y^2 * cos^2(θ) = 2y

Combining like terms:

x^2 * (cos^2(θ) - sin^2(θ)) + y^2 * (cos^2(θ) - sin^2(θ)) = 2y

Using the trigonometric identity cos^2(θ) - sin^2(θ) = cos(2θ):

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

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Answer and Step-by-step explanation:

The given polygon can be referred to in multiple ways, though not all names may prove to be an accurate description:

1. Quadrilateral: A four-sided figure is accurately called a quadrilateral, as it includes any shape with four sides.

2. Rectangle: A type of quadrilateral with four right angles and opposite sides parallel.

3. Square: A special type of rectangle with all sides equal in length.

4. Parallelogram: A quadrilateral with opposite sides that are parallel.

5. Rhomboid: A parallelogram with no right angles and sides of unequal length.

6. Kite: A quadrilateral with two pairs of adjacent sides that are of equal length.

7. Irregular Quadrilateral: A quadrilateral that does not fit in any of the defined categories above.

It's important to note that some names provided in the question do not correctly classify a four-sided polygon:

- Rhombus: A quadrilateral with all sides of equal length and opposite sides parallel. However, it has been provided as a separate entry.

- Trapezoid: A quadrilateral with one pair of parallel sides. However, it has been provided as a separate entry.

- Pentagon: An incorrect classification for a four-sided figure as it refers to a five-sided polygon.

Hope that helps.

The values of a is 2, b is -6 and c is 7 from the quadratic equation  2x² - 6x + 7 = 0

The given quadratic equation is 2x² - 6x + 7 = 0

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

When we compare the given quadratic equation with standard form we get the values of a , b and c

a=2

b=-6

c=7

Hence, the values of a is 2, b is -6 and c is 7 from the quadratic equation  2x² - 6x + 7 = 0

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The difference between the interquartile range of Matt's and Linda's remaining vacation days is 1.5.

The interquartile range will be calculated through the formula -

[tex] Q_{3}[/tex] = [tex] Q_{2}[/tex] - [tex] Q_{1}[/tex]

Firstly calculating [tex] Q_{3}[/tex] for Matt

[tex] Q_{2}[/tex] = (4+5)/2

[tex] Q_{2}[/tex] = 4.5

[tex] Q_{3}[/tex] = (8+12)/2

[tex] Q_{3}[/tex] = 10

Finding interquartile range now -

[tex] Q_{3}[/tex] = 10 - 4.5

[tex] Q_{3}[/tex] = 5.5

Now, performing calculation for Linda

[tex] Q_{2}[/tex] = (0+10)/2

[tex] Q_{2}[/tex] = 5

[tex] Q_{3}[/tex] = (11+13)/2

[tex] Q_{3}[/tex] = 12

Finding interquartile range now -

[tex] Q_{3}[/tex] = 12 - 5

[tex] Q_{3}[/tex] = 7

The difference between the interquartile range of Linda and Matt will be calculated as:

Difference = Interquartile range of Linda - Interquartile range of Matt (as we see Linda has greater interquartile range than Matt)

Difference = 7 - 5.5

Difference = 1.5

Hence, the difference between interquartile range of days is 1.5.

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The correct statements are:

If "positive" end behaviour:

The arrows point in the same direction.

The right arrow is up.

The graph hits the y-axis.

If "negative" end behaviour:

The arrows point in opposite directions.

The right arrow is down.

The graph hits the X-axis.

In mathematics, a graph is a visual representation of a set of data, which consists of points, called vertices or nodes, and lines connecting them, called edges or arcs.

Graphs are often used to represent mathematical functions, data sets, or relationships between objects, and they can be used to model real-world phenomena.

Graphs can be drawn on a coordinate plane or in a more abstract form, and they can be used to analyze and understand complex systems and relationships.

The correct statements are:

If "positive" end behaviour:

The arrows point in the same direction.

The right arrow is up.

The graph hits the y-axis.

If "negative" end behaviour:

The arrows point in opposite directions.

The right arrow is down.

The graph hits the X-axis.

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Answer:

Step-by-step explanation:

There are many expressions that could have an answer of 14, but here’s one example:

(7 x 2) - 1 = 14

Let’s break it down step by step:

The first operation in this expression is multiplication. We multiply 7 by 2, which gives us 14.

7 x 2 = 14

The second operation in this expression is subtraction. We subtract 1 from the result of our multiplication, which gives us 14.

14 - 1 = 14

So, the final expression is (7 x 2) - 1 = 14, which has an answer of 14.

Keep in mind that there are many other expressions that could have an answer of 14 as well. This is just one example!

Answer:

(49÷7)2=14

(2×3.5)2=14

Step-by-step explanation:

I honestly don't know of this is exactly what our asking for but here are two equations that are equal to 14, hope this helps

The solution for x  in the circle is:

x = 6

Tangent-tangent theorem states that "The measure of an angle formed by a two tangents drawn from a point outside the circle is one-half the difference of the intercepted arcs".

Using the above theorem. We can say:

5x + 17 = 1/2 * [(37x+5) - (23x-5)]

5x + 17 = 1/2 * [37x + 5 - 23x + 5]

5x + 17 = 1/2 * [14x + 10]

5x + 17 = 7x + 5

7x - 5x = 17 - 5

2x = 12

x = 12/2

x = 6

Therefore, the solution for x is 6.

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Complete Question

Check attached image

The value of x is 53.  

We have,

From the figure,

There are two parallel lines.

This means,

44 and angle M are corresponding angles.

And,

We can consider a triangle as:

M + P + P = 180

Where P is the angle opposite to the equal sides.

So,

44 + P + P = 180

44 + 2P = 180

2P = 180 - 44

2P = 36

P = 18

Now,

x is the exterior angle.

This means,

x = 35 + P

x = 35 + 18

x = 53

Thus,

The value of x is 53.  

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Answer:

[tex]\large {\mbox{R = 3.6}}[/tex]

Step-by-step explanation:

The formula for finding a magnitude of an earthquake on the Richter Scale is given as
[tex]R = \log\left(\dfrac{A}{A_0}\right)\\[/tex]

[tex]\rm{where}\\\textrm{A - measure of amplitude of quake wave}\\\textrm{$A_0$ = amplitude of smallest detectable wave}\\[/tex]

Given A = 0.3954 and A₀ = 0.0001, we can plug in these values into the R equation to get

[tex]R = \log\left(\dfrac{0.3954}{0.0001}\right)\\\\= \log(3954)\\\\= 3.597\\\\= 3.6\text { rounded to the nearest tenth}[/tex]

Answer:

The rectangle is 7.9 meters by 2.9 meters.

Step-by-step explanation:

Let l be the length and w be the width

l = w + 5

A = 23 m²

Formula: A = lw

Solve for the dimensions

23 = (w+5)w

23 = w² + 5w

w² + 5w - 23 = 0

Use quadratic formula to find the possible value/s of w

[tex]w = \frac{-b+-\sqrt{b^2-4ac} }{2a}\\ w = \frac{-5+-\sqrt{5^2-4(1)(-23)} }{2(1)} \\w = \frac{-5+-\sqrt{25+92} }{2}\\ w = \frac{-5+-\sqrt{117} }{2} \\w = \frac{-5+-\sqrt{9(13)} }{2} \\w = \frac{-5+-3\sqrt{13} }{2}\\ w = \frac{-5+3\sqrt{13} }{2} = 2.9\\ w = \frac{-5-3\sqrt{13} }{2} = -7.9[/tex]

Since we're dealing with dimensions, take the positive value which is 2.9.

w = 2.9 m

Substitute the value to l = w + 5

l = 2.9 + 5

l = 7.9 m

The absolute value function y = |x| looks like a "V" shape, with the vertex at the origin and the arms going off to positive and negative infinity. To shrink this function vertically by a factor of 2/9, we can multiply the entire function by 2/9:

y = (2/9)|x|

This new function has the same "V" shape, but the y-values are only two-ninths as large as they would be for the original function at any given value of x. The vertex of the new function is still at the origin, and the arms still go off to positive and negative infinity.

Answer:

[tex]y = (x-1)^2-9[/tex]

Step-by-step explanation:

The form of a quadratic equation is  [tex]y = a(x-h)^2+k[/tex]. Lets identify each change in words before switching to the formula:

Shifted 1 right

Shifted 9 down

No stretch horizontally

No stretch vertically.

Our equation will be [tex]y = (x-1)^2-9[/tex].

+* Answer *+

$5,590

*+Step-by-step explanation:*+

$5,000 x 5.9% = $295
$95 x 2 (months), = 590

5,000 + 590 = 5,590

So therefore you have $5,590 dollars.

hope this helps! : )