A club had 600 members. 60% of them were males. When 200 new members joined the club, the percentage of male members was reduced to 50%. How many of the new members were males?

1. The diagonal of the base of the box is shorter than the length of the wind chime. 2. The interior diagonal of the box shorter than the length of the wind chime. 3.  The wind chime will not fit in the box.

A diagonal is a line segment that connects two polygonal corners (vertexes), although it is not an edge (side). In other words, it connects any two polygonal vertices that are not neighboring. So, when we directly link any two vertices that are not connected by any sides, we may draw the diagonals in a polygon. A diagonal is a line that runs straight across the vertices of a polygon and joins its opposing corners. In other terms, a line segment connecting any two non-adjacent corners is a polygon's diagonal. Depending on how many sides a polygon has, distinct polygons may have a variable number of diagonals.

Given that the length of the wind chime is 16 inches thus,

1.  diagonal of base of the box = √10²+8² = √164 = 12.8

Hence, the diagonal of the base of the box is shorter than the length of the wind chime.

2.  interior diagonal of the box = √6²+8²+10² = √200 = 14.14

The interior diagonal of the box shorter than the length of the wind chime

3.  The wind chime will not fit in the box

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Answer:

B?

Step-by-step explanation:

It asserts that if the sky is clear, then it is not possible for the plane to be on time.

In general, a hypothesis is a proposed explanation or tentative answer to a research question or problem. It is a statement that can be tested through investigation and analysis of data.

The statement "q -> ~p" can be interpreted as "If the sky is clear, then the plane is not on time."

This is a conditional statement, where q represents the hypothesis or condition ("the sky is clear") and ~p represents the conclusion or result ("the plane is not on time").

It asserts that if the sky is clear, then it is not possible for the plane to be on time.

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Answer: V(x) = -5x^2 + 70x

Step-by-step explanation:

Let the length and width of the rectangular base be represented by x and y, respectively.

Since the perimeter of the rectangular base is 28 cm, we have:

2x + 2y = 28

x + y = 14

The height of the box is given as 5 cm.

The volume of the box is given by:

V = lwh = xy(5)

V = 5xy

We can solve for y in terms of x from the equation x + y = 14:

y = 14 - x

Substituting this into the equation for the volume, we get:

V = 5x(14 - x)

Simplifying:

V = 70x - 5x^2

The probability of picking a 7 and then picking a 7 is 8.33%.

Since we are not replacing the first card before drawing the second one, the probability of drawing a 7 on the first card is 1/4. After drawing the first card, there are three remaining cards, and only one of them is a 7. Therefore, the probability of drawing a 7 on the second card given that the first card was a 7 is 1/3.

Using the multiplication rule of probability, the probability of drawing a 7 on the first card and then drawing a 7 on the second card without replacement is

P(7 on the first card) x P(7 on the second card | 7 on the first card) = (1/4) x (1/3) = 1/12

P(7 on the first card and then a 7 on the second card) = 1/12 x 100% = 8.33%

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Answer:   To find the time at which the temperature is maximum, we need to find the vertex of the quadratic function T(x) = -0.07x^2. Recall that the x-coordinate of the vertex of a quadratic function f(x) = ax^2 + bx + c is given by -b/2a. In this case, a = -0.07 and b = 0 (since there is no linear term), so the x-coordinate of the vertex is x = -b/2a = -0/(-0.14) = 0.

Since x is the number of hours after 6 a.m., the time corresponding to x = 0 is 6 a.m. Therefore, the temperature is a maximum at 6 a.m.

To find the maximum temperature, we evaluate T(0) = -0.07(0)^2 = 0. Therefore, the maximum temperature is 0 degrees Fahrenheit. Note that this result makes sense, since the quadratic function T(x) = -0.07x^2 is a downward-facing parabola, which means that the temperature decreases as the number of hours after 6 a.m. increases.

Step-by-step explanation:

Answer:
x > 53

30 + x > 83

Subtract 30 from both sides:

x > 53

Therefore, the solution is:

x > 53

Answer:

36hrs is 36/6.5=5.538 doubling periods. Initial population x0=100

Step-by-step explanation:

The rate of exponential growth of a bacterial culture is expressed as generation time, also the doubling time of the bacterial population. Generation time (G) is defined as the time (t) per generation (n = number of generations). Hence, G=t/n is the equation from which calculations of generation time (below) derive.

Answer: While I cannot give an exact answer without additional context, the answer should have a slope of 12, and should look like the image below.

Answer:

12

Step-by-step explanation:

The leading coefficient of the polynomial is 4.

The leading coefficient of a polynomial, we first need to understand what the leading term of the polynomial is.

The leading term is the term with the highest degree in the polynomial.

For example, in the polynomial [tex]3x^4 + 2x^3 - 5x^2 + 4x - 1[tex], the leading term is 3x^4.
To determine the leading coefficient of a polynomial, we simply look at the coefficient of the leading term. For example, in the polynomial [tex]3x^4 + 2x^3 - 5x^2 + 4x - 1[/tex], the leading coefficient is 3.
Now, let's apply this concept to the polynomial graphed below. From the graph, we can see that the polynomial has a degree of 2, meaning that the highest power of x in the polynomial is 2.

Therefore, the leading term of the polynomial is [tex]ax^2[/tex], where a is the leading coefficient.
The vertex is the point on the graph where the polynomial reaches its maximum or minimum value. In this case, the vertex is located at [tex](-2, 4)[/tex]
Since the vertex is the highest point on the graph, we know that the coefficient of x^2 must be positive.

In this case, the value of y at the vertex is 4.

Therefore, the leading coefficient of the polynomial is 4.

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Answer:20

Step-by-step explanation:

Answer:

[tex]-x^{5} -5x+6[/tex]

Step-by-step explanation:

The square of the binomial that represents the trinomial is [tex](0.1b+10c)^{2}[/tex], and the missing monomial is 10bc.

What is Trinomial ?

A trinomial is a polynomial that consists of three terms. In algebra, a term is a combination of a constant and one or more variables, multiplied together. A trinomial, therefore, is a polynomial that has three such terms.

To represent the trinomial 0.01[tex]b^{2}[/tex]+ ∗ +100[tex]c^{2}[/tex] as a square of a binomial, we need to find a monomial that can be added to it to form a perfect square trinomial.

To do this, we can take the square root of the first and last terms of the trinomial and multiply them together:

√(0.011[tex]b^{2}[/tex]) = 0.1b

√(100[tex]c^{2}[/tex]) = 10c

Multiplying these square roots together, we get:

0.1b * 10c = b * 1c * 10 = 10bc

So, the missing monomial is 10bc. Adding this monomial to the original trinomial gives us:

0.011[tex]b^{2}[/tex] + 10bc + 100[tex]c^{2}[/tex] =  [tex](0.1b+10c)^{2}[/tex],

Therefore, the square of the binomial that represents the trinomial is   [tex](0.1b+10c)^{2}[/tex], and the missing monomial is 10bc.

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Answer:

117in

Step-by-step explanation: 9in x 13in=117in

So, Edward needs to use a round cast iron pan with a radius of 177 inches to have the same area as the rectangular pan. correct answer is (d).

To find the area of a circle, you need to know its radius (the distance from the center of the circle to any point on its perimeter). Once you know the radius, you can use the following formula:

[tex]Area = \pi * radius^2[/tex]

where π (pi) is a mathematical constant approximately equal to 3.14159.

So, to find the area of a circle, follow these steps:

Measure the radius of the circle.

Square the radius (multiply it by itself).

Multiply the squared radius by π.

Round your answer to the desired number of decimal places (usually 1 or 2).

The area of a 9-in. by 13-in. rectangular pan is:

Area = length x width = 9 in. x 13 in. = 117 in.²

So, the area of the rectangular pan is 117 in.².

To use a round cast iron pan with the same area, Edward needs to find the radius of the circle with an area of 117 in.²:

Area of a circle = πr²

[tex]= \pi r^2[/tex]

[tex]= 117 in.^2 /[/tex]

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the complete question: Edward's grandmother used to make him Pannukakku when he was little. He wants to surprise.

her by making it himself. The recipe he found requires a 9-in. by 13-in. rectangular pan.

Edward would like to use a round cast iron pan like his grandmother does.

What is the area of a 9-in. by 13-in. pan?

[tex](a) 22in^{2} \\(b)44in^{2} \\(c)108in^{2} \\(d)117in^{2}[/tex]

Answer:

y = 3 cot (1x)?

Step-by-step explanation:

Answer:

The mass of a 5-year-old child is 20 kg. We can express this mass in scientific notation as:

2 x 10^1 kg

To find approximately how many times larger an elephant is than a 5-year-old child, we need to know the mass of an elephant. According to National Geographic, an average elephant can weigh between 2,700 and 6,000 kg. Assuming an average weight of 4,350 kg for an elephant, we can calculate the ratio of elephant mass to child mass as follows:

4,350 kg / 20 kg ≈ 218

Therefore, an elephant is approximately 218 times larger than a 5-year-old child in terms of mass.

To determine approximately how many water drops equal the mass of a child, we need to know the mass of a single water drop. This can vary depending on the size of the drop and the substance it is made of. However, for the purposes of estimation, we can assume that the mass of a water drop is approximately 0.05 grams.

First, we need to find the cross-sectional area of each figure:

Since the cross-sectional areas are equal at every level, we can set up the following equation:

5x = 9π

Solving for x, we get:

x = 9π/5

Now, we can find the volume of the rectangular prism:

V = 5x * 8 = 72π cubic meters

And the volume of the cylinder:

V = π(3^2) * 8 = 72π cubic meters

Since the volumes are equal, we can set up the following equation:

72π = 72π

Simplifying, we get:

9πx = 40π

Solving for x, we get:

x = 40/9

Rounding to the nearest tenth, we get:

x ≈ 4.4 meters

Therefore, the width of the rectangular prism is approximately 4.4 meters.

Answer 6

Step-by-step explanation:  A = 1/2 bh, 6 x 2 is 12 and 1/2 of 12 is 6

DH is radius.

EG is a chord

FI line is tangent to the circle

H is the point of tangency

The point of tangency is the point where a tangent line touches a curve or a circle at a single point, without intersecting it. At this point, the tangent line is perpendicular to the curve or circle at that specific point. The point of tangency is important in calculus and geometry, as it is used to calculate derivatives and solve problems related to circles, curves, and other geometrical figures.

In the given circle,

DH is radius.

(As it passes through center of circle and touches its circumference)

EG is a chord

(It divides the circle into two parts)

FI line is tangent to the circle

(It touches the line externally)

H is the point of tangency

(It is a point where the tangent of circle and circle meets)

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Answer:

2nd option

Step-by-step explanation:

Answer:

a)

 103

         |

       96 +

         |

       92 |     *  

         |    * *  

       88 +--*    

         | *      

       84 |        

         |*        

       80 +        

         |        

       79 |        

         |        

       72 +        

         |        

       70 |

         |

b)b. The range is the difference between the highest and lowest scores: 103 - 45 = 58.

The IQR is the interquartile range, which is the range of the middle 50% of the scores. To find it, we first need to find the first and third quartiles:

   The first quartile (Q1) is the median of the lower half of the scores, which are 45, 70, 72, 79, and 80. The median of this set is (72+79)/2 = 75.5.

   The third quartile (Q3) is the median of the upper half of the scores, which are 84, 87, 88, 92, and 96. The median of this set is (88+92)/2 = 90.

Therefore, the IQR is 90 - 75.5 = 14.5.

c)c. To find any outliers, we need to first define the "fences" of the box and whisker plot. The lower fence is Q1 - 1.5IQR = 75.5 - 1.514.5 = 53.25. The upper fence is Q3 + 1.5IQR = 90 + 1.514.5 = 112.75.

There is one score that is outside the fences: 103. Therefore, 103 is an outlier.

Step-by-step explanation:

The average change in field position on each run was a loss of 7/4 yards.

A mixed number in mathematics is a number that combines a whole number and a fraction. The entire number and the fraction are often separated by a space or a plus sign when writing mixed numbers. As an illustration, the mixed number 2 1/3 stands for the sum of 2 and 1/3. By dividing the entire number by the fraction's denominator and adding the numerator, mixed numbers can be transformed into improper fractions. For instance, we would multiply 2 by 3 and add 1 to get 7, which is an incorrect fraction of 2 1/3. In order to obtain 7/3, we would then write the fraction using the same denominator as the original fraction.

The total change in position for a total loss of 15/3/4 yards is:

Total change in field position = - (15 + 3/4) yards

Given the, number of runs = 9

Thus:

Average change in field position = Total change in field position / Number of runs

Average change in field position = (- 15 - 3/4) yards / 9

Average change in field position = (- 63/4) yards / 9

Average change in field position = - 7/4 yards

Hence, the average change in field position on each run was a loss of 7/4 yards.

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Answer:

Step-by-step explanation:

If 15 out of 50 students are twelve years old, we can estimate the proportion of twelve-year-olds in the whole school as follows:

Proportion of twelve-year-olds = 15/50

Simplifying this fraction by dividing both numerator and denominator by 5, we get:

Proportion of twelve-year-olds = 3/10

Similarly, if 20 out of 50 students are thirteen years old, we can estimate the proportion of thirteen-year-olds in the whole school as:

Proportion of thirteen-year-olds = 20/50

Simplifying this fraction by dividing both numerator and denominator by 10, we get:

Proportion of thirteen-year-olds = 2/5

Finally, if 15 out of 50 students are fourteen years old, we can estimate the proportion of fourteen-year-olds in the whole school as:

Proportion of fourteen-year-olds = 15/50

Simplifying this fraction by dividing both numerator and denominator by 5, we get:

Proportion of fourteen-year-olds = 3/10

Therefore, the best estimate of the proportion of students who are twelve, thirteen, and fourteen years old in the school, respectively, is:

3/10 are twelve years old

2/5 are thirteen years old

3/10 are fourteen years old

Part (a)

Answers:

A' = (0, 2)

B' = (-1, -2)

C' = (-3, -2)

D' = (-4, -1)

Explanation:

Multiply each coordinate by 1/3.

For instance,

[tex]B(-3,-6) \to B( -3*(1/3), -6*(1/3) ) \to B \ '(-1, -2)[/tex]

====================================================

Part (b)

Answers:

A' = (-5, 5)

B' = (-8, -7)

C' = (-14, -7)

D' = (-17, -4)

Explanation:

Subtract 5 from the x coordinate. Subtract 1 from the y coordinate. This moves each point 5 units to the left and 1 unit down.

I'll show an example using point C.

[tex](\text{x},\text{y})\to(\text{x}-5,\text{y}-1)\\\\(-9,-6)\to(-9-5,-6-1)\\\\(-9,-6)\to(-14,-7)\\\\[/tex]

Therefore, C(-9,-6) moves to C ' (-14,-7)

These are just a few examples of real life situations where you might need to find the volume or surface area of a shape. There are many other situations where this knowledge is useful, including in scientific research, medical imaging, and many other fields.

In mathematics, volume is the amount of space occupied by an object or a shape. It is a measure of how much three-dimensional space an object or a shape takes up. Volume is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or cubic inches (in³).

Here,

There are many real life situations where you might need to find the volume or surface area of a shape. Here are some examples:

Packaging and Shipping: In order to package and ship products, companies need to know the volume and surface area of the products and their packaging. For example, a shipping company needs to know the volume and surface area of a package in order to determine how much space it will take up in a truck or airplane, and how much packaging material will be required.

Construction: Architects, engineers and builders need to know the volume and surface area of building materials such as concrete, steel, bricks, and insulation in order to estimate the amount of materials required for a project. They also need to know the volume of a space to determine the amount of materials required to fill it, such as the amount of concrete required to fill a foundation or the amount of insulation needed to insulate a room.

Cooking and Baking: When cooking or baking, you may need to measure the volume or surface area of a container or cooking vessel to ensure that the recipe will fit and cook or bake properly. For example, you might need to measure the volume of a baking dish to know how much batter to use, or measure the surface area of a frying pan to know how much oil is needed.

Gardening and Landscaping: In gardening and landscaping, you may need to know the volume of soil required to fill a raised bed or the surface area of a lawn in order to determine the amount of fertilizer or weed killer required.

Industrial Design: In industrial design, designers need to know the volume and surface area of products in order to determine the materials required for production and to ensure that the product will fit in its intended location. For example, a designer may need to know the volume and surface area of a water tank to determine its capacity and the amount of materials required to build it.

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Smithson will recognize the loss. So,the amount of loss will Smithson recognize on retirement of the liability is $309,248.85.

Profit or loss is the financial gain or loss resulting from the difference between revenue and expenses in a business or financial context.

Book value of ARL = Present value of estimated cash flows for ARL - Accumulated depreciation and amortization

PV = PMT x (1 - 1 / (1 + r)ⁿ) / r

The formula for weighted average is:

Weighted average = (Cash flow 1 x Probability 1) + (Cash flow 2 x Probability 2) + (Cash flow 3 x Probability 3)

PV = (700,000 x 0.25 x (1 - 1 / (1 + 0.08)⁵) / 0.08) + (750,000 x 0.4 x (1 - 1 / (1 + 0.08)⁵) / 0.08) + (850,000 x 0.35 x (1 - 1 / (1 + 0.08)⁵) / 0.08)

PV = $2,317,283.36

Since this is the end of the first year, the accumulated depreciation and amortization is simply the present value of the estimated cash flows for the first year:

Accumulated depreciation and amortization = (700,000 x 0.25 / (1 + 0.08)) + (750,000 x 0.4 / (1 + 0.08)) + (850,000 x 0.35 / (1 + 0.08))

Accumulated depreciation and amortization = $1,830,532.21

Finally, we can calculate the book value of the ARL at the end of one year:

Book value of ARL = Present value of estimated cash flows for ARL - Accumulated depreciation and amortization

Book value of ARL = $2,317,283.36 - $1,830,532.21

Book value of ARL = $486,751.15

Therefore, the book value of the asset retirement liability at the end of one year is $486,751.15.

Loss = Actual restoration costs - Book value of ARL

Loss = $796,000 - $486,751.15

Loss = $309,248.85

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Answer: first one is 700

Step-by-step explanation:

Triangle ABC's longest side is found as 4 units. Thus, Triangle DEF has a 100-times larger area than triangle ABC.

A ratio is a tool being used compare the sizes of two or more quantities with relation to one another in mathematics. By making amounts easier to understand, ratios enable us to evaluate and express quantities.

Given that both triangles remain similar, triangle DEF is 10 times larger than triangle ABC according to the ratio 1:10.

Thus, Triangle DEF has a 100-times larger area than triangle ABC.

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1. The two triangles are congruent, ASA criteria. angle H ≅ angle M, HY ≅ MN and EY ≅ AN using CPCT. 2. The two triangles are congruent, ASA criteria. AT ≅ AP, by CPCT. Angle T ≅ angle P. CT ≅ RP, by CPCT.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.

1. For the given triangle HEY and triangle MAN we see that,

angle E ≅ angle A

angle Y ≅ angle N

and HE ≅ AM

Thus, the two triangles are congruent using the ASA criteria.

Also angle H ≅ angle M (CPCT)

HY ≅ MN

EY ≅ AN using CPCT.

2. For triangle CAT and PAR we have:

angle A ≅ angle A (vertically opposite angles)

Angle C ≅ angle R

AC ≅ AR

Thus, the two triangles are congruent using the ASA criteria.

Also, AT ≅ AP, by CPCT

Angle T ≅ angle P, by CPCT

CT ≅ RP, by CPCT.

3. For the triangles ACL and triangle ARS:

AC ≅ AR and angle 1 ≅ angle 2 (Given)

Also, angle A = angle A (Vertically opposite angle)

Thus, the two triangles are congruent using ASA criteria.

Now, angle 3 ≅ angle 4 using CPCT.

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Thus, the surface area of the rectangular prism is found as : S = 275 ¹/₈ cm².

A rectangular prism is one of the more usual shapes for prisms. One definition of a rectangular prism is a prism with rectangle-shaped bases. An other faces also were rectangles because the bases are rectangles. These are a rectangular prism's characteristics:

Given dimensions for the rectangular prism :

Then ,

surface area of the prism S = 2(lw + wh + hl)

Put the values:

S = 2(11.75*5.75 + 5.75*4 + 4*11.75)

S = 2*137.5625

S = 275.125

S = 275 ¹/₈ cm²

Thus, the surface area of the rectangular prism is found as : S = 275 ¹/₈ cm².

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An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. Equations can be used to model a wide range of real-world situations, and they are an essential tool in many fields of study, including physics, engineering, and economics.

To solve for y, we need to isolate y on one side of the equation. We can do this by first distributing the 3 on the right-hand side:

24 = 3y + 18

Next, we can isolate 3y by subtracting 18 from both sides:

24 - 18 = 3y

6 = 3y

Finally, we can solve for y by dividing both sides by 3:

y = 2

Therefore, the solution to the equation 24 = 3(y + 6) is y = 2.

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