A box contains cards that are numbered from 1 to 100. What is the probability of randomly selecting a number that is less than 12? StartFraction 1 over 100 EndFraction StartFraction 1 over 12 EndFraction StartFraction 11 over 100 EndFraction StartFraction 12 over 100 EndFraction

The (∃E) rule is used to infer P(0) from ∀xP(x), and this conclusion is supported by the existence of an object that satisfies the predicate.

The rule of natural deduction that justifies P(0) from ∀xP(x) is the existential elimination (∃E) rule. This rule allows us to infer a particular instance of an existential quantification based on the existence of an object that satisfies the predicate. In this case, since we have the universal quantification ∀xP(x), we can use (∃E) to conclude P(0) by substituting 0 for x. By doing so, we have shown that there exists an object, namely 0, that satisfies the predicate P(x). Therefore, (∃E) justifies the statement P(0) from the given universal quantification.

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Answer:

Step-by-step explanation:

The goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

Given that the mean number of goals a netball team scores per match in the first 9 matches of a competition is 4.

Thus the average of the goals in 9 matches is 4.

Total number of goals is = 9*4 = 36 goals .

Given that the team scores 3 goals in their next match .

Thus the total number of goals scored in 10 matches is 36 + 3 = 39 goals,

Required mean = Total goals / 10 matches .

∴ Required mean = 39/10 = 3.9 .

Therefore, the goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

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The correct answers are options b. LM ≅ ON and d. ∠L ≅ ∠N as they verify that LMNO is an isosceles trapezoid.

To verify that LMNO is an isosceles trapezoid, we need to check if the following conditions are met:
1. One pair of opposite sides must be parallel (base angles are equal).
2. The non-parallel sides (legs) are congruent.
From the given options:
a. LN ≅ MO - This does not verify LMNO as an isosceles trapezoid, as it only shows congruence between the parallel sides.
b. LM ≅ ON - This verifies LMNO as an isosceles trapezoid, as it shows that the non-parallel sides (legs) are congruent.
c. LO ≅ MN - This does not verify LMNO as an isosceles trapezoid, as it only shows congruence between the diagonals.
d. ∠L ≅ ∠N - This verifies LMNO as an isosceles trapezoid, as it shows that the base angles are congruent, indicating that the opposite sides are parallel.
e. ∠L ≅ ∠M - This does not verify LMNO as an isosceles trapezoid, as it only shows congruence between adjacent angles.
Thus, options b and d are the correct answers that verify LMNO is an isosceles trapezoid.

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Answer:

The mean is,

C) 68

Step-by-step explanation:

The mean is calculated using the formula,

\(m = (sum \ of \ the \ terms)/(number \ of \ terms)\\\)

Now, there are 6 terms (in this case numbers) so,

we have to divide by 6,

and sum them.

\(m = (57+90+70+68+61+62)/6\\m=408/6\\\\m=68\)

Hence the mean is 68

If they work together, they will take 14.3 min to shovel the parking lot.

Provided to us :

time taken by Sebastian to shovel the parking lot = 50 min

time taken by Clair to shovel the parking lot = 20 min

both are doing the same work , so we take work as 1

Now , rate of doing work = work / time

Sebastian's rate of doing work = 1 /50

Clair's rate of doing work =  1/20

If they work together , the rate of doing work will

become = 1/50 + 1/20 = 7/100

So, the time for both to do the same work together will be

time = work / rate

time = 1 / (7/100)

time = 100/7

time = 14.3 minutes

So the time taken by both to work together and clear the parking lot will be 14.3 minutes.

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If g ◦ f = IX and f ◦ g = IY, then f and g are both one-to-one and onto, and g = f⁻¹.

A function is composed when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

The statement is true. Let's prove it.

To prove that f is one-to-one, suppose we have two elements a, b ∈ X such that f(a) = f(b). We need to show that a = b.

Using the composition property, we have (g ◦ f)(a) = (g ◦ f)(b). Since g ◦ f = IX, we can simplify this to IX(a) = IX(b), which gives g(f(a)) = g(f(b)).

Since g ◦ f = IX, we can apply the property of the identity function to get f(a) = f(b). Since f is one-to-one, this implies that a = b. Therefore, f is one-to-one.

To prove that f is onto, let y be an arbitrary element in Y. We need to show that there exists an element x in X such that f(x) = y.

Since g ◦ f = IX, for any y ∈ Y, we have (g ◦ f)(y) = IX(y). Simplifying, we get g(f(y)) = y.

This shows that for any y ∈ Y, there exists an x = f(y) in X such that f(x) = y. Therefore, f is onto.

Now, to prove that g = f⁻¹, we need to show that for every x ∈ X, g(x) = f⁻¹(x).

Using the composition property, we have (f ◦ g)(x) = (f ◦ g)(x) = IY(x) = x.

Since f ◦ g = IY, this implies that f(g(x)) = x.

Therefore, for every x ∈ X, we have f(g(x)) = x, which means that g(x) = f⁻¹(x). Hence, g = f⁻¹.

In conclusion, if g ◦ f = IX and f ◦ g = IY, then f and g are both one-to-one and onto, and g = f⁻¹.

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Stabilizing selection is a type of natural selection that favors the average phenotype over extreme variants, leading to a reduction in genetic diversity.

Directional selection is a type of natural selection that favors one extreme phenotype over others, leading to a shift in allele frequency in one direction, often in response to a changing environment or new selective pressure.

Stabilizing selection is a type of natural selection that favors the average phenotype over extreme variants. This type of selection occurs when the existing phenotype is well adapted to a stable environment, and individuals with extreme phenotypes are less fit. As a result, the genetic diversity of a population is reduced, and the population becomes more homogeneous over time.

Directional selection, on the other hand, favors one extreme phenotype over others, leading to a shift in allele frequency in one direction. This type of selection often occurs in response to a changing environment or new selective pressure, and can lead to the evolution of a new trait or the adaptation of a population to a new environment.

Overall, natural selection plays a critical role in shaping the genetic makeup of populations and driving the process of evolution.

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Answer:

-2(9x-8)

Step-by-step explanation:

We are to simplify the expression -3.1x+7-7.4x-1.5x-6(x-3/2)

Open the parenthesis

-3.1x+7-7.4x-1.5x-6(x-3/2)

= -3.1x+7-7.4x-1.5x-6x+6(3/2)

= -3.1x+7-7.4x-1.5x-6x+9

Collect like terms

= -3.1x-7.4x-1.5x-6x+7+9

= -12x-6x+16

= -18x+16

= -2(9x-8)

Hence the simplified form of the expression is -2(9x-8)

The volume of water in the ocean is estimated to be approximately 1,332,000,000,000,000,000 liters.

The Earth's oceans cover about 71% of the planet's surface and contain a vast amount of water. To calculate the volume of water in the ocean, we need to consider the average depth and the total surface area of the oceans.

The average depth of the ocean is estimated to be around 3,800 meters. The total surface area of the oceans is approximately 361,900,000 square kilometers. By multiplying the average depth by the surface area, we can find the volume of water.

Volume = Average Depth × Surface Area

Using the given values, we have:

Volume = 3,800 meters × 361,900,000 square kilometers

To convert this volume to liters, we need to consider that 1 cubic meter is equal to 1,000 liters. Therefore, we can multiply the volume in cubic meters by 1,000 to obtain the volume in liters.

Calculating the above expression, we find that the volume of water in the ocean is approximately 1,332,000,000,000,000,000 liters. This is an estimation and may vary slightly depending on the sources and assumptions used for average depth and surface area calculations.

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The length of AB in simplest radical form is 8.06.

We can find the length of AB using the principle of similar triangles on the triangles ABD and ABC.

Considering triangle ABD, given that AD = 5 then

Cos A = AD/AB

Also,

Cos A = AB/AC

Given that AD = 5, AC = 13, AB = x

therefore,

x/13 = 5/x

x² = 65

x = √65

= 8.06

Hence, the length of AB in simplest radical form is 8.06.

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Answer:

Step-by-step explanation:

i think b because it is going across the 5 but i'm not sure.

Answer:

m = -14

Step-by-step explanation:

Answer: 144

Step-by-step explanation:  144 is exactly 4.8 percent of 3000 the poster can not because the answer is not 10 its 144

Answer:

the like terms are -13, 17,-8g, and 6g. the terms are all, coefficents are -8 ang 6. constants are 7h

Step-by-step explanation:

To find the area of the region in the first quadrant that lies under the curve y = ln(x)/x², you need to evaluate the definite integral of the function from the lower bound to the upper bound.

Step 1: Determine the bounds of integration. Since we are looking for the area in the first quadrant, the lower bound is 1, and the upper bound is determined by the intersection of the curve with the x-axis, which is at x = e.

Step 2: Evaluate the definite integral. The integral to calculate is ∫(1, e) ln(x)/x² dx.

Step 3: Use integration by parts with u = ln(x) and dv = 1/x² dx. Then, du = 1/x dx and v = -1/x.

Step 4: Apply the integration by parts formula: ∫udv = uv - ∫vdu.

Step 5: Evaluate the integral: [-ln(x)/x - (-1/x)] from 1 to e.

Step 6: Substitute the bounds: [-(1/e) + 1] - [-(0) + 1] = 1 - 1/e.

Thus, the area of the region in the first quadrant under the curve y = ln(x)/x² is approximately 1 - 1/e.

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Check the picture below.

Answer:

Step-by-step explanation:

x=16 root 3 y is 32 root 3

Answer:

hmmmmm b

Step-by-step explanation:

Answer: Y = -12.25

Step-by-step explanation:

Answer:

-4.75

Step-by-step explanation:

5(-3) - 4y = 34

-15 - 4y = 34

-4y = 19

y = -4.75

Answer:  1) C. Reflexive Property of Congruence

               2) A. MD ≅ SG

               3) C. 5.3

               4) D. LK || MJ & JK ≡ LM

Step-by-step explanation:

1) An angle or side is congruent to itself by the Reflexive Property

2) TM ≡ LG       Sides are congruent (given)

   ∠M ≡ ∠G       Angles are congruent (given)

   MD ≡ SG       Sides are congruent                  

ΔTMD ≡ ΔLGS  Side-Angle-Side (SAS) Theorem

Note: The angle must connect the two sides

3) Use similarity proportion

\(\dfrac{6}{x}=\dfrac{9}{8}\\\\\\48=9x\\\\\\\dfrac{48}{9}=x\\\\\\5.3=x\)

4) In order to prove a polygon is a parallelogram, you must show

As per the graph, the domain and the range of the function is [-3, 6], [-2, 2].

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is indeed the collection of all possible input values.

As per the given graph in the question,

Let's find out the domain first, and it is in the horizontal axis.

As we can see in the graph,

The point follows from -3 to 6. So, the domain of the function is,

= [-3, 6]

Now, let's find out the range, and it is on the vertical axis,

As we can see in the graph,

The point follow from -2 to 2, so the range of the function is,

= [-2, 2]

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Answer:

She can make 20 baskets in 5 hours

(3) Add: Under applied overhead 34,000

(4) Adjusted cost of goods sold 364,000

1 and 2 RAW MATERIAL INVENTORY

Beginning balance 75,000

a 225,000 150,000 b, Ending Balance 150,000

WORK IN PROGRESS INVENTORY

Beginning balance 140,000

b 125,000 352,000 g

c 60,000

f 105,000

j Ending Balance 78,000

FINISHED GOODS INVENTORY

Beginning balance -

g 352,000 330,000 h

Ending Balance 22,000

FACTORY OVERHEAD

b 25,000

c 40,000 105,000 f

d 74,000

Ending Balance 34,000

COST OF GOODS SOLD

h 330,000

Ending Balance 330,000

Factory overhead applied on the basis of direct labor cost .

Hence applied overhead = 60,000 x 175% = $105,000Step: 2

3)

Computation of under /(over) applied OH

Actual OH($) Applied OH ($) Under /(over) applied OH ($)

139,000 105,000 34,000

Actual manufacturing overhead:

$

Indirect material 25,000

Indirect Labour 40,000

Other manufacturing overhead 74,000

139,000

4)

Cost of goods sold (Unadjusted) 330,000

Add: Under applied overhead 34,000

Adjusted cost of goods sold 364,000

Actal manufacturing overhead is more than applied overhead,it means factory overhead under applied and it will be added in unadjusted cost of goods sold to ascertain adjused cost of goods sold.

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Answer:

A=16, the formula to find the area of a kite is A=pq/2

Step-by-step explanation:

A=pq/2 = 4×8/2=16

Chelsea has 15 dimes and 20 nickels in her pocket. She has a total of $2.50 in dimes and nickels. The number of nickels is five more than the number of dimes.

1. Let's assume that Chelsea has x dimes. According to the problem, she has five more nickels than dimes, which means she has x + 5 nickels. The value of x dimes is $0.10x, as each dime is worth $0.10. The value of (x + 5) nickels is $0.05(x + 5), as each nickel is worth $0.05.

Since the total value of the coins is $2.50, we can set up the equation:

$0.10x + $0.05(x + 5) = $2.50

2. Simplifying the equation, we get:

$0.10x + $0.05x + $0.25 = $2.50

$0.15x + $0.25 = $2.50

$0.15x = $2.50 - $0.25

$0.15x = $2.25

3. Dividing both sides by $0.15, we find:

x = 15

Therefore, Chelsea has 15 dimes and 15 + 5 = 20 nickels in her pocket.

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Answer:

21

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

AD        AH

-----  =  ---------

AB         AH +y

3        9

---- = ------

10         9+y

Using cross products:

3(9+y) = 9*10

27+3y = 90

3y = 90-27

3y =63

y = 63/3

y = 21

Answer:

y = 21

Step-by-step explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, according to the Side Splitter Theorem:

\(\boxed{\sf AD : DB = AH : HC}\)

From inspection of the given triangle, the lengths of the line segments are:

To find the value of y, substitute the given line segment lengths into the proportion and solve for y:

\(\begin{aligned}\sf AD : DB &=\sf AH : HC\\\\3:7&=9:y\\\\\dfrac{3}{7}&=\dfrac{9}{y}\\\\3 \cdot y&=9 \cdot 7\\\\3y&=63\\\\\dfrac{3y}{3}&=\dfrac{63}{3}\\\\y&=21\end{aligned}\)

Therefore, the value of y is 21.

We can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.

Based on the line of best fit for the data, we can estimate the number of servings of kakigori Cho will sell on a day when the high temperature is 29° Celsius.

From the scatter plot, we can see that the line of best fit is increasing as the temperature increases.

By estimating the value on the line of best fit for the temperature of 29° Celsius, we can approximate the number of servings sold. Based on the scatter plot, it appears that the number of servings sold is around 100 when the temperature is 29° Celsius.

Therefore, we can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.

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Answer:

1). g(x) = \(5^{3x}\)

2). g(x) = \(\frac{1}{3}5^{x}\)

3). g(x) = \(3(5)^{x}\)

4). g(x) = \(5^{\frac{1}{3}x}\)

Step-by-step explanation:

Parent function f(x) = \(a^{x}\) when transformed in the form of  \(g(x)=h(a^{\frac{x}{k} })\)

1). If h > 1, function is vertically stretched.

2). If 0 < h < 1, function is vertically compressed.

3). If k > 1, function is horizontally compressed.

4). If 0 < k < 1, function is horizontally stretched.

Parent function of the given functions in the question is f(x) = \(5^{x}\)

g(x)= \(\frac{1}{3}(5^{x})\), parent function is vertically compressed by a factor of \(\frac{1}{3}\).

g(x) = \(5^{3x}\), parent function 'f' is horizontally stretched by a factor of 3.

g(x) = \(5^{\frac{x}{3}}\), parent function 'f' is horizontally compressed by a factor of \(\frac{1}{3}\).

g(x) = \(3(5^{x})\), parent function 'f' is vertically stretched by a factor of 3.