In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure how many draws did it take before the person picks

72 squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard

Solution:

Given, 4-inch by 4-inch squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard

Therefore,

Area of square = 4 x 4 = 16

Thus area of square to be cut is 16 square inches

Rectangular piece of leather measuring 4 feet by two-thirds of a yard

Convert feet to inches

1 feet = 12 inch

4 feet = 4 x 12 = 48 inches

Also,

1 yard = 36 inch

Given is a two-thirds of a yard

[tex]\frac{2}{3} \times 36 = 24\ inches[/tex]

Thus area of rectangular piece of leather is:

[tex]Area = 48 \times 24 = 1152\ square\ inches[/tex]

Total number of squares cut is given as:

[tex]\text{Total number of squares cut} = \frac{\text{area of leather}}{\text{ area of square}}[/tex]

Thus we get,

[tex]\text{Total number of squares cut} = \frac{1152}{16} = 72[/tex]

Thus 72 squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard

Answer:

72

Step-by-step explanation:

Answer: the length of the arc is 15.17π feet

Step-by-step explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 13 feet

θ = 210 degrees

Therefore,

Length of arc = 210/360 × 2 × π × 13

Length of arc = 15.167π feet

rounding up to 2 decimal places, it becomes

15.17π feet

Answer:

1 .  60!=8.31*[tex]10^{81}[/tex] ways

The rows and number of barns are related in that if we want to get the number of ways the cows and horse can be arranged

Step-by-step explanation:

At the county fair,animals are judged for the quality of their breeding and health.The animal pens are arranged in an array,with one animal in each pen .A barn can hold at most 10 rows of pens and at most 6 pens in each row ,with room for people to walk around them.What different ways can the planners of county fair arrange the pens for the horses and cows in the same barn? How the quantities given in the problem relate to each other?

if there are 10 ros and 6 barns. the number of ways animsls can be arrganged becomes

10 *6=60

60

look for 60 factorials, the number of ways

60!=8.31*[tex]10^{81}[/tex] ways

2.Permutation means arrangement . The rows and number of barns are related in that if we want to get the number of ways the cows and horse can be arranged , it makes it possible

For example find the number of ways 12 cows and 18 horses can be arranged in the barns.

we have the number of animals to be=12+18=30

60P30=60[tex]\frac{60!}{960-30)!} =\frac{60!}{30!}[/tex]

31.37*10^48 ways

Final answer:

The planners at the county fair can arrange the animal pens in various ways as long as the total number does not exceed 60, based on a maximum of 10 rows and 6 pens per row. This problem is one of combinatorics, requiring the counting and arranging of objects within given constraints.

Explanation:

The question involves arranging animal pens within a barn that can accommodate at most 10 rows of pens and up to 6 pens per row for animals like horses and cows at a county fair. This is fundamentally a problem of combinatorics, a branch of mathematics dealing with the counting, arrangement, and combination of objects. To determine the different arrangements possible for placing the pens, we would consider the combinations that do not exceed the given maximums for rows and pens per row.

The total number of pens that can fit in the barn is found by multiplying the maximum number of rows by the maximum number of pens per row, which gives us 10 rows × 6 pens per row = 60 pens as the upper limit. Therefore, the planners could arrange the pens in a variety of ways, including all rows filled with 6 pens, fewer rows with 6 pens, or more rows with less than 6 pens each, as long as the total number of pens does not exceed 60.

The quantities given in the problem relate to one another as constraints in a two-dimensional array. The planners have the flexibility to decide how many rows and pens per row to use without exceeding the maximum capacity of the structure. This scenario underscores the practical application of mathematical principles in planning and logistics.

Answer: the second one

Step-by-step explanation:

Answer:

The answer to your question is There is only one solution (0, -2)

Step-by-step explanation:

Data

Equation 1     x - y = 2

Equation 2    x + y = -2

Solve for y

Equation 1          y = x -2

                          y = x - 2

Equation 2         y = - x - 2

See the graph below

These lines cross in point (0 ,-2), that is the only solution.

If the lines have not crossed, they were parallel lines.

Answer:

The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are [tex]x=1\pm i\sqrt{7}[/tex].

Step-by-step explanation:

Consider the provided information.

Algebra's fundamental theorem states that: Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.

Now consider the provided equation.

[tex]2x^2-4x+16=0[/tex]

The degree of the polynomial equation is 2, therefore according to Algebra's fundamental theorem the equation have two complex roots.

Now find the root of the equation.

For the quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are: [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Substitute [tex]a=2,\:b=-4,\:\ and \ c=16[/tex] in above formula.

[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:2\cdot \:16}}{2\cdot \:2}[/tex]

[tex]x_{1,\:2}=\frac{4\pm \sqrt{16-128}}{4}[/tex]

[tex]x_{1,\:2}=\frac{4\pm \sqrt{-112}}{4}[/tex]

[tex]x_{1,\:2}=\frac{4\pm 4i\sqrt{7}}{4}[/tex]

[tex]x_{1,\:2}=1\pm i\sqrt{7}[/tex]

Hence, the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are [tex]x=1\pm i\sqrt{7}[/tex].

Answer:

The answer to your question is x = 2.5

Step-by-step explanation:

We know that lines r and s are parallel so angles 1 and 2 are corresponding angles. Corresponding angles measure the same.

                                      m∠1 = m∠2

Substitution

                                40 - 4x = 50 - 8x

Solve for x

                               8x - 4x = 50 - 40

                                       4x = 10

                                         x = 10/4

                                         x = 2.5

Since they are similar both dimensions would have the same ratio. The ratio of 5 and 15 is 3. 15 is 3 times larger than 5, so the unknown dimension is 3 times larger than the known dimension.

3 x 10 = 30

The unknown dimension is 30

Answer:

Z=4

Step-by-step

You just add 2.05 to 1.95 to get z alone

Answer: Z=4

Step-by-step explanation:

Add 2.05 and 1.95 and you get 4.

If you subtract 2.05 from 4 you get 1.95

Answer: he got 297 cards in a year.

Step-by-step explanation:

There are 12 months in a year. Rashaads sister gives him 2 pack of cards per month. This means that in a year, his sister would give him

2 × 12 = 24 packs of cards.

If there are 11 cards in a pack, then the number of cards that his sister gives him in a year would be

24 × 11 = 264 cards.

He also gets 3 extra packs for his birthday. It means that the number of cards that he gets for his birthday would be

3 × 11 = 33 cards.

Therefore, the total number of cards that he gets in a year is

264 + 33 = 297 cards

Answer:

Well this question was hard ngl, but what I have learned in the previous years in 8th grade, the Area ≈93.53ft²

Step-by-step explanation:

If Im wrong I apologize but I believe thats the answer. You have an amazing day, you mean alot too this world, Y.O.L.O

Answer: 53 radical 3 or 93.53

Answer:

B=80 A=40 EFD=60 BCF=120

Step-by-step explanation:

First off chill. Second off B=80  A=40 EFD=60  BCF=120.  It is quite simple. The congruency marks give the first angle away and you solve from there. If you need help I would do more research because this is important for later units. Also the triangles are congruent.

Answer

Angle A = 40 degrees

Angle B = 80 degrees

Measure BCF = 120 degrees

Measure EFD = 60 degrees

Step-by-step explanation:

Angle A:

Ok, so we know angle A is congruent to angle D because of the line. If you make an equation out of it, you get 2x+20 = 3x+10. If you solve this equation:

2x + 20 = 3x + 10

20 = x+10

10 = x

you will get x=10. Plug it into the equation, and Angle A = 40 degrees.

Angle B:

The two lines that are both on angle B and E mean that they are congruent. We know that angle E = 80 degrees, so angle B does too.

Measure BCF:

We know that Angle A = 40 degrees, and angle B = 80 degrees. The degree sum of all angles in a triangle is 180 degrees.

80 + 40 = 120

180 - 120 = 60

So measure BCA = 60 degrees.

That angle is on a straight line. Two angles on a straight line add up to 180 degrees.

180 - 60 = 120.

So, Measure BCF = 120 degrees.

Measure EFD:

We already found measure BCA while finding measure BCF, and that is just congruent to EFD.

So, measure EFD = 60 degrees

Answer:

There are 5 apples in the best bundle Charlie can afford

Step-by-step explanation:

If the utility function is u(xa, xb) , where xa represent the quantity of apples and xb is the quantity of bananas then we want to choose the quantity of bananas and apples that maximises the utility of Charlie for the same budget restriction ( get the most benefit for the same money).

The budget restriction is

$4* xa + $2* xb = $40

then

u(xa, xb) =xa*xb

4*xa + 2*xb = 40  → xb = (40 - 4*xa)/2 = 20 - 2*xa

replacing in the utility function

u(xa, xb) =xa* (20 - 2*xa) = 20*xa - 2*xa²

the maximum of this function is obtained when the derivative of the utility function with respect to xa is 0 . Thus

du/dxa = 20 - 4*xa = 0 → xa = 20/4 = 5

then for

xa=5 apples

xb=20 - 2*xa = 20 - 2*5 = 10 bananas

Charlie maximises his utility  . Therefore there are 5 apples in the best bundle Charlie can afford

To determine the best bundle Charlie can afford, we need to maximize his utility function u(xa, xb) = xaxb subject to his income and the prices of apples and bananas. The maximum value of xa represents the number of apples in the best bundle Charlie can afford, which is 5.

To determine the best bundle Charlie can afford, we need to maximize his utility function u(xa, xb) = xaxb subject to his income and the prices of apples and bananas. Let's denote the quantity of apples as xa and the quantity of bananas as xb. Since Charlie's income is $40, we have 4xa + 2xb ≤ 40. Using this inequality, we can find the maximum value of xa, which represents the number of apples in the best bundle Charlie can afford.

To solve for xa, we rearrange the inequality:

Now, let's look at the utility function u(xa, xb) = xaxb. To maximize the utility function, we take the derivative of u with respect to xa and set it equal to zero.

Since xb is in the denominator, its value should be greater than zero. Therefore, the best bundle Charlie can afford will have the maximum value of xa such that 4xa + 2(could be anything greater than 0) ≤ 40. Solving for xa, we get xa ≤ 5.

Hence, Charlie can afford a maximum of 5 apples in the best bundle.

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Final answer:

Explaining the calculation of different starting lineups with and without a versatile player X on a college team roster.

Explanation:

The total number of different starting lineups can be created by considering various scenarios:

To get the final count, add up the lineups from each scenario: 45 (without X) + 54 (X as guard) + 60 (X as forward) = 159 different starting lineups.

Therefore, as per the above explaination, the correct answer is 159 different lineups

The length of AE is [tex]18in[/tex]

Explanation:

From the figure, we can see that the two triangles ΔAED and ΔACB are similar. Thus, the legs of the triangle are proportional to each other.

Thus, we have,

[tex]\frac{EC}{DB} =\frac{AE}{AD}[/tex]

Substituting the values of the sides from the image, we get,

[tex]\frac{3}{1} =\frac{AE}{6}[/tex]

Multiplying both sides of the equation by 6, we get,

[tex]6(3)=AE[/tex]

Multiplying, we have,

[tex]18=AE[/tex]

Thus, the length of AE is [tex]18in[/tex]

Answer:

the answer is 18 inches.

Step-by-step explanation:

Answer:

$4200

Step-by-step explanation:

450 - 240 = 210 this is the amount of her commissions for the week.

we are looking for x = sales for the week

x * .05 = 210

x = 210/.05

x = 4200

Answer:c 4200

Step-by-step explanation:

Answer:

His average this season is 154 yards a game.

Step-by-step explanation:

This question can be solved by a simple rule of three.

Last season's numbers(110 yards a game) is 100% = 1 decimal

This season number(x yards a game) is an increase of 40% over last season, so 40% + 100% = 140% = 1.40 decimal.

So

110 yards a game - 1

x yards a game - 1.40

[tex]x = 110*1.40 = 154[/tex]

His average this season is 154 yards a game.

Answer:

Ben

Step-by-step explanation:

Ben has an absolute advantage in making of pizza because he can make five pizzas in one hour which is a greater quantity compared to Sam that makes four pizzas in one hour.

The surface area of the cone is [tex]266.9cm^2[/tex]

Explanation:

The diameter of the cone is 10 cms

Thus, the radius of the cone is given by

[tex]r=\frac{d}{2} =\frac{10}{2} =5[/tex]

The slant height of the cone is 12 cms

The formula for surface area of the cone is given by

[tex]$S A=\pi r^{2}+\pi r l$[/tex]

Substituting the values, we get,

[tex]$S A=(3.14)(5)^{2}+(3.14)(5)(12)$[/tex]

[tex]$S A=(3.14)25+(3.14)(60)$[/tex]

[tex]SA=78.5+188.4[/tex]

[tex]SA=266.9cm^2[/tex]

Thus, The surface area of the cone is [tex]266.9cm^2[/tex]

The surface area of the cone is approximately 268 square centimeters.

To find the surface area of a cone, we need to know the slant height and the radius of the base. The slant height is given as 12 centimeters. Since the diameter is 10 centimeters, we can find the radius by dividing the diameter by 2, which is 5 centimeters. Now we can use the formula for the surface area of a cone:

A = πr(r + l), where A is the surface area, r is the radius, and l is the slant height.

Plugging in the values, we get: A = 3.14 * 5(5 + 12) = 3.14 * 5 * 17 = 268.1 square centimeters. Rounding to the nearest whole number, the surface area of the cone is approximately 268 square centimeters.

Your Question is incomplete, here is the complete statement of the question with the box plots in the attached file.

Question statement:

The box plots show the target heart rates of men 20-40 years old and men 50-70 years old.

Which statement is best supported by the information in the box plots?

A)

The range of the data for men 20-40 years old is less than the range of the

data for men 50-70 years old.

B)

The median of the data for men 20-40 years old is less than the median of

the data for men 50-70 years old.

o

The minimum target heart rate for men 20-40 years old is less than the

minimum target heart rate for men 50-70 years old.

D)

The interquartile range of the data for men 20-40 years old is greater than

the interquartile range of the data for men 50-70 years old.

Answer:

D

Step-by-step explanation:

please find the box plots in the file attached below.

looking at the box plots we can say that the answers is D due to following reasons:

Option A is incorrect:

The range of the data for men 20-40 years old is not less than the range of data for men 50-70 years old because  for men 20-40 years old range is 80 and for men 50-70 years old range is 70.

Option B is incorrect:

The median of the data for men 20-40 years old is not less than the range of data for men 50-70 years old because  for men 20-40 years old median is 130 and for men 50-70 years old median is 110.

Option C is incorrect:

The minimum target heart rate for men 20-40 years old is not less than the minimum target heart rate for men 50-70 years old because  for men 20-40 years old the minimum target heart rate is 90 and for men 50-70 years old the minimum target heart rate is 75.

Option D is correct:

The interquartile range of the data for men 20-40 years old is greater than the interquartile range of data for men 50-70 years old because  for men 20-40 years old interquarile range is  [tex]Q_{3}-Q_{1}=152.5-107.5=45[/tex] and for men 50-70 years old interquartile range is [tex]Q_{3} -Q_{1} =130-90=40[/tex].

Answer:

20 square units

Step-by-step explanation:

The figure shows a triangle whose;

We are supposed to get its area;

Area of a triangle is given by the formula;

Area = 0.5×b×h

Thus;

Area = 0.5 × 8 units × 5 units

        = 20 square units

Hence, the area of the figure is 20 square units

Answer: I will pick B

Step-by-step explanation:

Because it's a logical explanation

Answer:

Room 1.

Step-by-step explanation:

The note on room 3 is true.  So The notes on room 1 and room 2 are untrue.

If the lion is in  room 1 that would make the note on room 1 untrue  - so both room 1 and room 2 notes would be untrue.

Also if the lion  is in room 2  that would make both room 1 and room 2 notes true.

So the lion must be in room 1.

Answer:

COPD

Step-by-step explanation:

COPD is a lung disease caused by tobacco use and other factors

Answer:

50 miles per hour

Step-by-step explanation:

500 miles in 10 hours

= 500/10

= 50 miles per hour

Answer:

probability is 671 out of 1296 or 51.8 %.

Step-by-step explanation:

When we roll 4 fair 6-sided dice total outcomes are

 6^4 = 1296

The outcomes where no dice show greater than 5, the dice can show numbers 0,1,2,3,4,5

So the no of these outcomes where no dice show greater than 5 can be found by

5^4 = 625

No of outcomes where at least one dice will show number greater than 5 are

1296-625 = 671

Or in percentage,the probability is (671/1296)*100 = 51.8%

Answer:

Less

Step-by-step explanation:

The closer e is to 0, the more the ellipse will resemble a circle

Answer:

A) zero; cannot

Step-by-step explanation:

In line with the principle of rational expectations, expectation errors are unpredictable. The expectations of all available information will not differ from the optimal projections.The word optimal projection is inexorably intertwined with the best guess in rational expectations theory.

Answer:

Step-by-step explanation:

Assuming the rate of increase in the cost of tuition fee per year is linear. We would apply the formula for determining the nth term of an arithmetic sequence which is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = $20500(amount in 2000)

From 2000 to 2018, the number of terms is 19, hence,

n = 19

T19 = 454120

Therefore,

454120 = 20500 + (19 - 1)d

454120 - 20500 = 18d

18d = 433620

d = 433620/18

d = 24090

Therefore, the equation that can be used to find the tuition y for x years after 2000 is expressed as

y = 20500 + 24090(x - 1)

To to estimate the tuition at this college in 2020, the number of terms between 2000 and 2020 is 21, hence

x = 21

y = 20500 + 24090(21 - 1)

y = 20500 + 481800

y = $502300

Using linear interpolation, the yearly increase of tuition was calculated and an equation was formed. Substituting the year 2020 into the equation gave an estimated tuition of $47,855.60.

To write an equation that represents the tuition cost y for x years after 2000, we use two given data points: in 2000, tuition was $20,500 (which means when x=0, y=$20,500), and in 2018, tuition was $45,120 (when x=18, y=$45,120). To find the rate of change, we calculate the slope by finding the difference in tuition and dividing it by the difference in years:

Slope (m) = (Y2 - Y1) / (X2 - X1) = ($45,120 - $20,500) / (18 - 0) = $24,620 / 18 ≈ $1,367.78

Now we can write the equation of the line in slope-intercept form (y = mx + b), where b is the initial tuition in the year 2000:

Equation: y = 1367.78x + 20,500

To estimate the tuition in 2020, set x to 20:

y = 1367.78(20) + 20,500 = $27,355.60 + 20,500 = $47,855.60

Therefore, the estimated tuition in 2020 is $47,855.60.

Step-by-step explanation:

[tex]PV = FV \div (1+i)^n[/tex]

Here FV = $83870

i = 6.8% = 0.068

[tex]n = \frac{226}{365}[/tex] =0.62

Therefore,

[tex]PV=\frac{83870}{(1+0.068)^{0.62}}[/tex]

     =$80517.91

Therefore the present value = $ 80517.91

The true statement is: d. The conclusion is incorrect because the range is limited to the set of positive real numbers.

The function is given as:

[tex]\mathbf{f(x) =2x}[/tex]

The above function implies that:

The above highlights mean that: Geraldine's claims are incorrect.

Because y increases or decreases by 2, when x increases or decreases by 1

In other words, the value of y does not get doubled or halved.

Hence, both statements are incorrect

Read more about range at:

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