Two cards are drawn at random from a well shuffled pack of cards. What is the probability that
i)both are spades or both are diamonds?
ii)both are queens or both are red coloured?
iii)both are diamonds or neither is a king?

Answer: Mr. Sink bought 7 calves for a total of $3,500, and he later bought another calf for $600, for a total of $4,100.

In total, Mr. Sink bought 7 + 1 = 8 calves.

The mean cost for all of the calves is equal to the total cost of all of the calves divided by the number of calves.

Therefore, the mean cost for all of the calves is 4,100 / 8 = $512.50.

Step-by-step explanation:

Answer:

[tex]20\ln(5)-16\approx16.18876[/tex]

Step-by-step explanation:

[tex]\displaystyle\int\int\limits^{}_R {\frac{4x}{1+xy} } \, dA\\\\\\=\int\limits^4_0\int\limits^1_0 {\frac{4x}{1+xy} } \, dy \, dx\\\\\\=\int\limits^4_0 {\ln(1+xy)\biggr|_0^1} \, dx\\\\\\=\int\limits^4_0 {\ln(1+x)} \, dx\,\,\,\,\,\,\,\,\,\,\,\,\bigr(u=\ln(1+x),\,dv=dx\bigr)\\\\\\=4\biggr(x\ln(1+x)\biggr|_0^4-\int\limits^4_0 \frac{x}{1+x} \,dx\biggr)\\\\=4\biggr(4\ln(5)-\bigr[x-\ln(1+x)\bigr]\biggr|_0^4\biggr)\\\\=4\biggr(4\ln(5)-\bigr[4-\ln(5)\bigr]\biggr)\\\\=4\biggr(5\ln(5)-4]\biggr)\\\\=20\ln(5)-16[/tex]

Yes, when we connect the points, we get straight line.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Given that, you are at an altitude of 250 feet in a hot-air balloon. You turn the burner on high and rise at a rate of 20 feet per minute for 5 minutes.

Your altitude h after you have risen for t minutes is given by the function h = 250+ 20t.

a) Make a table to show the altitude as a function of the number of minutes you have traveled.

    t         h

    0     250

    1      270

    2     290

    3      310

b) Graph the points, (0, 250), (1, 270), (2, 290) and (3, 310).

c) Yes, when we connect the points, we get straight line.

Hence, graph the points, (0, 250), (1, 270), (2, 290) and (3, 310).

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Answer:

4 7

Step-by-step explanation:

a. The area of the parallelogram ABCD in this problem is given as follows: 24 units squared.

b. The fraction of the area of the parallelogram that is shaded is given as follows: 1/4. (option C).

The area of a parallelogram is given by the multiplication of the length of the base by the height, as follows:

Area = base x height.

The base and the height for this problem are obtained counting the number of dots, hence:

Hence the area is given as follows:

Area = 4 x 6

Area = 24 units squared.

The shaded region is composed by a triangle with base 4 and height 3, hence:

Area shaded = 0.5 x 4 x 3 = 6 units squared.

(formula for the area of the triangle).

Meaning that the fraction is given as follows:

6/24 = 1/4.

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Answer:

Step-by-step explanation:

You want to know if the standard form quadratic equation ax² +bx +c = 0 can be factored when c=0.

When the constant is zero, the equation becomes ...

  ax² +bx = 0

Factoring out x, we have a factored form as ...

  x(ax +b) = 0

showing that the equation can always be factored.

The  linear function is a straight line graph . Consequently, the third graph shows a linear function.

When the independent variable (often 'x') varies by a constant amount and the dependent variable (typically expressed by 'y') changes by a constant amount, the function is said to be linear. To show the relationship between two quantities, a linear graph is a straight line graph. This graph is useful for showing a result as a series of simple straight lines. The phrase "linear" refers to a straight line and excludes the usage of curves, dots, bars, etc. Plot coordinates at positions where x and y are identical in order to draw the line y = x. More points can be plotted even though three are plenty.

given

A linear function has a graph that is a straight line. A nonlinear function, then, has a graph that is not a straight line.

Something like y equals x cubed or y equals e to the power of x is an illustration of this. Furthermore, if we look closely at our graph, we can see that the line is not vertical.

The graph of a linear function is a straight line. Consequently, the third graph shows a linear function.

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Answer:

To determine which loan will have a higher balance at the time of repayment, we need to calculate the balance of each loan after the interest has been compounded over the repayment period.

The unsubsidized Stafford Loan has an annual interest rate of 3.85% and a grace period of six months from the time of graduation. This means that the loan will accrue interest for a total of 12 months - 6 months = 6 months.

The balance of the unsubsidized Stafford Loan at the time of repayment can be calculated using the following formula:

Balance = Principal * (1 + Interest rate / Number of compounding periods per year)^(Number of compounding periods)

Plugging in the given values, we have:

Balance = $10,958 * (1 + 0.0385 / 12)^(6) = $10,958 * (1.003125)^(6) = $11,283.16

The PLUS loan has an annual interest rate of 4.15% and a balance of $11,421.51 at the time of repayment.

The balance of the PLUS loan at the time of repayment can be calculated using the same formula:

Balance = $11,421.51 * (1 + 0.0415 / 12)^(6) = $11,421.51 * (1.003479)^(6) = $11,973.54

Therefore, the PLUS loan will have a higher balance at the time of repayment, by $11,973.54 - $11,283.16 = $690.38.

Step-by-step explanation:

Answer:

48 ounces of Mixed Nuts

Step-by-step explanation:

You need to convert pounds to ounces to find the answer to this problem.

1 pound is 16 ounces, so multiply 3 by 16 for your answer,

For the given value of domain and range , By observing the figure, The correct answer are options B,C and E.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A function's domain and range are the set of all possible inputs and outputs, respectively. A function's domain and range are crucial components. The range includes all of the function's output values, whereas the domain includes all potential input values from the set of real numbers.

domain : (x | x [tex]\geq[/tex] 3/2)

range : (-∞ , 2)

For these values, Option B , C and E holds that they exists when x [tex]\geq[/tex] 3/2 and it's output that is y exists between  (-∞ , 2).

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The total area of the recreational area can be represented by the polynomial expression 26x² + 57x + 35.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

The area of the rectangular pool is given by its length times its width, so the area of the pool is (3x - 3) meters × (2x + 7) meters = (6x² + x - 21) square meters.

The area of the patio is given by the length of the pool plus twice the extension (x) on each side, times the width of the pool plus twice the extension on each side, so the area of the patio is (3x - 3 + 2x) meters × (2x + 7 + 2x) meters = (5x + 4) × (4x + 14) = 20x² + 56x + 56 square meters.

The total area of the recreational area is the sum of the areas of the pool and the patio, so it can be represented by the polynomial expression:

20x² + 56x + 56 + 6x² + x - 21 = 26x² + 57x + 35

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Answer: 4/27 or 0.148148

First you solve for any grouping symbols ( absolute value, parentheses, brackets, etc.) Since there aren’t any you move on to exponents, 4^3 is the same as 4*4*4 which equals 64. Next you do multiplication 6*2 is 12 so our problem is currently

64-60 over 15+12. Next you simplify, which make the problem 4/27. You can divide which makes your problem 0.148148 but most of the times you keep it as a fraction.

Answer:

-4

Sorry if this is wrong.

The cost of the shirts after the discount is $43.20.

A 5% tax adds an additional $2.16 so the total bill comes to  45.36.

Kayla does not have enough money to buy the three shirts.

The first step is to determine the total cost of the three shirts.

Total cost of the three shirts = cost of one shirt x total number of shirts

$18 x 3 = $54

Cost of the shirt after the sale = (1 - discount/100) x total cost of the shirt

(1 - 20/100) x $54

(1 - 0.2) x $54

= 0.8 x $54

= $43.20

Price after the tax : (1 + tax/100) x cost of the shirt after the discount

(1 + 5/100) x $43.20

(1 + 0.05) x $43.20

1.05 x $43.20 = 45.36

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On solving the question, we can say that y using the given information we can prove that similar angle m ∠ABC = m ∠EDC.

Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.

Given:

m ∠1 = m ∠2

m ∠2 = m ∠4

We have to prove that m ∠ABC = m ∠EDC

∠EDC = ∠3 + ∠4

m ∠ABC = m ∠1 + m ∠2

m ∠EDC = m ∠3 + m ∠4

m ∠1 + m ∠2 = m ∠3 + m ∠4      

m ∠ABC = m ∠EDC

Hence, by using the given information we can prove that  

m ∠ABC = m ∠EDC.

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Answer: 4.8

Step-by-step explanation: By using the intersecting chords theorem, we know that 10 * x = 6 * 8

This simplifies to 10x = 48

After dividing both sides by 10 we get x = 4.8

Answer:

To calculate the percent of change, you will need to find the difference between the original score and the revised score and divide that by the original score. Then, multiply the result by 100 to express the answer as a percentage.

In this case, the difference between the original score (5 questions right) and the revised score (15 questions right) is 10 questions. Dividing this by the original score of 5 questions gives you a result of 2. Multiplying this by 100 gives you a percent of change of 200%. This means that your revised score is 200% higher than your original score.

Step-by-step explanation:

Using the values for x and y and substituting these values in the expression of equations provided, The answer is 23 and 1728.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.

When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated.

x=3 and y=4

[tex]x^2 + 2(x+y)\\=3^2 + 2* (3+4)\\=9+2*7\\=9+14\\=23[/tex]

[tex](xy)^3\\=(3*4)^3\\=12^3\\=1728[/tex]

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Answer:

x = 55

Step-by-step explanation:

Since the sides of the shape are parallel, AngleC and AngleD will add up to 180° (see "parallel lines cut by a transversal" or maybe you have learned a big pile of parallelogram theorems)

Use this relationship to set up an equation.

2x + 20 + 50 = 180

combine like terms

2x + 70 = 180

subtract 70

2x = 110

divide by 2

x = 110/2

x = 55

x is 55

Answer:

The value of x is 55°

Step-by-step explanation:

Since we know that opposite angles of a parallelogram are equal

The sum of any two adjacent angles is supplementary. This means, ∠A + ∠B = 180°, ∠B + ∠C = 180°, ∠C + ∠D = 180°, and ∠D + ∠A = 180.

So,

∠C + ∠D = 180°

(2x + 20)° + 50° = 180°

2x + 70° = 180°

2x + 70° - 70° = 180° - 70°

2x = 110°

2x/2 = 110°

x = 55°

Thus, The value of x is 55°

The best price for her to purchase ice cream is given as follows:

D. $49.60 / five gallon tub.

The best price is obtained applying the proportions in this problem, dividing the price by the volume of the cartoon/tub, in ounces.

For item a, the price per ounce is calculated as follows:

3.99/24 = $0.16625 per ounce.

The ratios for the remaining items are given as follows:

Hence the prices for items b, c and d are given as follows:

Due to the lower cost per ounce, the option D represents the best option for her to purchase ice cream.

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Her class of 30 pupils can be divided into 10 groups using 5 groups of 2 students and 5 groups of 4 students each.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle.

given

10 groups of 3 students = 30 students :

5 groups of 2 students + 5 groups of 4 students = 30 students : 7 groups of 3 students + 3 groups of 3 students = 30 students

so Her class of 30 pupils can be divided into 10 groups using 5 groups of 2 students and 5 groups of 4 students each.

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Answer:

125.54%

Step-by-step explanation:

160.7/128 = 1.2554

1.2554 *100 = 125.54%

Therefore , the solution of the given problem of circle comes out to be Area = 154 meter square  or 49π meter square option 1 is correct.

A moving point on a plane is followed so that its distance from a specific point remains constant to produce the circular form known as a circle. The English term circle derives from the Greek word kirkos, which meaning hoop or ring. Area of circle= πr²

Here,

Given :

Diameter of circle : 14

Radius =14/2 =  7 meters

and

Using formula

Area= πr²

=> Area = π7²

=>Area = 22/7 * 7²

=> Area = 22*7

=> Area = 154 meter square or 49π meter square

Therefore , the solution of the given problem of circle comes out to be Area = 154 meter square  or 49π meter square option 1 is correct.

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Answer: A the first one 49π square meters

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

Explanation:

I'm assuming your teacher meant to say "same number or letter" instead of "same number of letter" at the very end of the problem.

The best case scenario is that the person selecting the cards is very lucky to select say a king of hearts and king of clubs. This shows that 2 cards is the lowest amount of cards to select here.

----------

Of course, such a scenario is not that likely. That person is likely to get some other card compared to the 1st selection.

Let's assume the person selecting the cards has the worst luck possible. This means they select each card 1,2,3,...,10,J,Q,K exactly once in any order. If this happens, then the person does not have any pairs just yet. The person has selected 13 cards so far with this worst case scenario.

The 14th card is guaranteed to pair up with some other card previously chosen. There simply aren't any other options left once you've exhausted all possibilities. See the pigeonhole principle for more information.

So this is why you would need to select 14 cards to guarantee having at least two pair up together (i.e. you would have 2 or more pairs).

On solving the provided question, we cans ay that By unitary method, the amount to be removed = original - shortened = 3/9 - 2/9 = 1/9

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

By unitary method,

original length of pipe = 3/9 inch

shortened length of pipe = 2/9

so, the amount to be removed = original - shortened = 3/9 - 2/9 = 1/9

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Therefore , the solution of the given problem of percentage comes out to be time n = 3 years.

A figure or ratio that is stated as a percentage of 100 is referred to as a percentage in mathematics.  However, the percent symbol ("%) is usually used to denote it." The percent amount is flat. When the numerator is 100, percentages are really just fractions. Put the standard form (%) next to a number to show that it is a percentage. For instance, if you correctly respond to 75 out of questions in total on a test, you receive a 75% (75/100).

Here,

Given: 1757600 more people overall

Population as of now: 1562500

According to the issue,

=> 1562500[tex](1 + 4/100 )^{n}[/tex] = 1757600

=> [tex](26/25)^{n}[/tex] =  1757600/ 1562500

=>  [tex](26/25)^{n}[/tex]=  [tex](26/25)^{3}[/tex]

On comparing,

n=3

Therefore , the solution of the given problem of percentage comes out to be time n = 3 years.

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If the amount of time in seconds, t, it takes for a bungee jumper to free fall is given by the function t equals the square root of the quantity d over 16. The distance the jumper fall is: A 400 feet.

Using this formula to find the distance by solving for d

t=√d/q

Where:

t = Time = 5 seconds

d = Distance = ?

q = Quantity = 16

So,

5 seconds=√d/16

d=16x5²

d=16 × 25

d= 400 feet

Therefore we can conclude that the correct option is A.

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Answer: To find out how much medication the patient receives each day, you need to determine the patient's weight in kilograms and then calculate the total dosage per day.

You can convert the patient's weight from pounds (lb) to kilograms (kg) by dividing the weight by 2.2.

So,

315/2.2 = 142.72 kg

Next, we can use this weight to determine the dosage per day:

3 mg/kg * 142.72 kg = 428.16 mg

Now, since the physician ordered twice a day, we will multiply the dosage per day with 2:

428.16 mg * 2 = 856.32 mg

So the patient receives 856.32 mg of medication each day.

Step-by-step explanation: