You have some baseball trading cards. You give 21 baseball
cards to a friend and have 9 left for yourself. How many
.
baseball cards were in your original deck? Write and solve
an equation to find t, the number of baseball cards in
your original deck.

Answer:

Answer:17 (I think)

Because if you look at the problem below Y u can see the patter 5+3=8 8+3=11 contiously adding 3 you get 17

Answer:

The angle between the diagonal of the rectangle is \(\frac{\pi }{2}\).

Given:

The vertices of the rectangle are

a = (1, 0), b = (0, 3), c = (3, 4), and d = (4, 1)

To find:

The objective is to find the angle between the diagonals.

Step 1 of 3

Consider the diagram attached.

Step 2 of3

The position vector of diagonal AC is-

=(3-1)î+(4-0)j=2î+4j

And the position vector of diagonal BD is-

=(4-0)î+(1-3)j=4î-2j

Step 3 of 3

cosθ=\(\frac{AC.BD}{|AC|.|BD|}\)

cosθ=\(\frac{(2i-4j)(4i-2j)}{\sqrt{2^2+4^2} \sqrt{4^2+(-2)^2\\} }\)

=\(\frac{8-8}{\sqrt{20}.\sqrt{20} }\)

=0

θ=\(cos^{-1}\)(0)

θ=\(\frac{\pi }{2}\)

Therefore the angle between the diagonal of the rectangle is \(\frac{\pi }{2}\)

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The angle between the diagonals of a rectangle is π/2

The vertices of the rectangle are

a = (1, 0), b = (0, 3), c = (3, 4),  d = (4, 1)

The diagonal position vector AC  

=(3-1)î+(4-0)j=2î+4j

And the diagonal position vector BD  

=(4-0)î+(1-3)j=4î-2j

cos Ф = (AC.BD) / (|AC| . |BD|)

cos Ф = (8-8) / (root20 -roo20)

= 0

Ф = π/2

Therefore the angle between the diagonals of the rectangle is π/2

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Answer:

150.31

Step-by-step explanation:

First, use Order of Operation to multiply.

16.55(8) + 5.97(3)​

= 132.4 + 17.91

= 150.31

Answer

132.4+17.91

Step-by-step explanation:

16.55*8=132.4

5.97*3=17.91

The length of the arc intercepted by the given central angle of 60° in a circle with a radius of 13.74 mi is approximately 4.63 mi when rounded to the nearest hundredth.

To find the length of an arc intercepted by a given central angle in a circle, we can use the formula:

Arc Length = (Central Angle / 360°) × (2πr),

where r is the radius of the circle.

In this case, the radius of the circle is given as 13.74 mi, and the central angle is 60°

Substituting these values into the formula, we have:

Arc Length = (60° / 360°) × (2π × 13.74 mi).

Simplifying the expression, we get:

Arc Length = (1/6) × (2π × 13.74 mi),

Arc Length = (π / 3) × 13.74 mi.

Approximating the value of π as 3.14, we have:

Arc Length ≈ (3.14 / 3) × 13.74 mi,

Arc Length ≈ 4.63 mi.

Therefore, the length of the arc intercepted by the given central angle of 60° in a circle with a radius of 13.74 mi is approximately 4.63 mi when rounded to the nearest hundredth.

To summarize, the length of the intercepted arc is approximately 4.63 mi.

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The experimental probability of spinning a number less than 5 is 60%, while the theoretical probability is also 60%.

Experimental probability is determined by conducting actual experiments or observations and counting the favorable outcomes. In this case, the relative frequency of spinning a number less than 5 is given as 0.6, which translates to 60%.

Theoretical probability, on the other hand, is calculated based on the assumption of equally likely outcomes. Since there are 10 equally likely outcomes when spinning a number, out of which 6 are less than 5 (i.e., 1, 2, 3, and 4), the theoretical probability can be calculated as the ratio of favorable outcomes to the total number of outcomes:

Theoretical probability = (Number of favorable outcomes) / (Total number of outcomes)

Theoretical probability = 6 / 10 = 0.6 = 60%

Therefore, both the experimental and theoretical probabilities for spinning a number less than 5 are 60%.

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Answer:

  you need to show the number is prime

Step-by-step explanation:

To show 2^7 -1 is prime, you have to show it is not divisible by any prime less than its square root. That root is approximately 2^(7/2) = 2^3×√2 ≈ 11.3.

The primes of in that range are 2, 3, 5, 7, 11. The prime we're testing is ...

  2^7 -1 = 128 -1 = 127

The sum of digits is 10, which is not a multiple of 3: not divisible by 3.

The units digit is 7, not 0 or 5: not divisible by 5.

The test for divisibility by 7 is to subtract twice the units digit from the rest of the number: 12 -2(7) = -2. This is not 0 or a multiple of 7, so 127 is not divisible by 7.

We know that 11² = 121, so 127 is not divisible by 11.

All of the tests for primality pass, so 2^7 -1 is a Mersenne prime.

_____

Additional comment

It is known that 2^n -1 being prime requires n to be prime. (The converse is not true: 2^11 -1 = 2047 = 23×89 is not prime.) The discovery of Mersenne primes is an ongoing process involving thousands of computers around the world. Only about 50 such primes are known.

You will notice that we have made use of some divisibility rules in order to simplify the process of dividing by small numbers. These can be helpful in many situations, so can be useful to learn.

Answer:

50 units²

Step-by-step explanation:

Solve for both long sides:

6² + 8² = x²

36 + 64 = x²

100 = x²

x = 10

Solve for both short sides:

3² + 4² = x²

9 + 16 = x²

25 = x²

x = 5

Area:

5 x 10 = 50

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

the angle that they want you to find is complementary to the angle that equals 40. Complementary means they will add up to equal 90. 90-40=50 so ADB = 50

Answer: x = 2

Step-by-step explanation: the interior angles of a rhombus add to 360 degrees and since half of 360 is 180, create the equation 130 + (36 +7x) and set it equal to 180. when solved 130 + (36 +7x) = 180 you get x =2

answer

1st rearrange the terms. then subtract 36 in both sides.then you will get 94=7x then simplify  by dividing by 7. then you will get 13.4285714286. which if you round up maybe its 94/7.

       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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Answer:

2.25x2+2x1.00+1.50=8, 10-8 =$2.00

Step-by-step explanation:

Answer:

5.5

Step-by-step explanation:

Answer: \(\overline{VW}=15\) units.

Step-by-step explanation:

Since Point W is on line segment \(\overline{VX}\).

That means V,W,X  are collinear such that \(\overline{VX} = \overline{WX}+\overline{VW}\)  (i)

Given\(\overline{ WX}=2\) units. ,  \(\overline{ VX} = 17\) units.

To determine :  length of \(\overline{ VW}\).

Substitute all the given values in (i), we get

\(17=2+\overline{VW}\\\\\Rightarrow\ \overline{VW} =17-2=15\\\\\Rightarrow\overline{VW}=15\)

Hence, the length of \(\overline{VW}=15\) units.

Answer:

huh are u asking to solve it

The number of pages the student can read in a minute is an illustration of rates.

The time left to complete the whole book is 90 minutes

From the complete question, the student's rate is:

\(\mathbf{Rate = 50\ pages/hr}\)

The number of pages is:

\(\mathbf{Total = 100\ pages}\)

First, we calculate the time to read the whole book

\(\mathbf{Total\ Time = \frac{Total\ pages}{Rate}}\)

\(\mathbf{Total\ Time = \frac{100\ pages}{50\ pages/ hr}}\)

\(\mathbf{Total\ Time = 2\ hours}\)

The number of the student has read is:

\(\mathbf{Pages = 25}\)

Next, we calculate the time spent on the 25 pages

\(\mathbf{Time\ Spent = \frac{Pages}{Rate}}\)

\(\mathbf{Time\ Spent = \frac{25\ pages}{50\ pages/hr}}\)

\(\mathbf{Time\ Spent = 0.5\ hr}\)

Convert to minutes

\(\mathbf{Time\ Spent = 30\ minutes}\)

So, the time left is:

\(\mathbf{Time\ Left = Total\ Time - Time\ Spent}\)

This gives

\(\mathbf{Time\ Left = 2\ hours- 30\ minutes}\)

\(\mathbf{Time\ Left = 1\ hour, 30\ minutes}\)

Convert to minutes

\(\mathbf{Time\ Left = 90\ minutes}\)

Hence, the time left is 90 minutes

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Answer:

The correct answer should be the first option.

Step-by-step explanation:

Answer:

First option. The graphs domain is -∞<x<∞ and its range is -5 ≤ y < ∞

Step-by-step explanation:

I graphed this function

Domain: x ∈ R

Range: y ∈ [-5, + ∞

Minimum (1, -5)

Verticle intercept (0, -4)

Michael’s child is going to college in 13 years. If he saves $ 7,000 a year at 9% compounded annually. Therefore,  the amount available for Peter's child education will be $147,330.55.

Given that Michael is saving $7,000 per year for his child's education which will occur in 13 years. If the interest rate is 9% compounded annually,

The problem of finding the amount of money Michael will have saved in 13 years is a compound interest problem.

In this case, the formula for calculating the future value of the annuity is: $FV = A[(1 + r)n - 1] / r

where: FV is the future value of the annuity, A is the annual payment,r is the annual interest rate, and n is the number of payments.

Using the above formula; the future value of Michael's savings is:

FV = 7000[(1 + 0.09)^13 - 1] / 0.09= 7000(1.09^13 - 1) / 0.09= 147,330.55

Therefore, the amount available for Peter's child education will be $147,330.55.

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A country with little land and few natural resources could make up for such deficits without depending on other countries and having a healthy economy by developing its Human Capital.

Examples of small countries with low natural resources and high GDP are:

It is to be noted that of all the factors of production, (Land, labor, Capital, and Entrepreneurship) Human Capital (Labor and Entrepreneurship) are the most valuable and yield the greatest return on investment.

The Democratic Republic of the Congo is commonly regarded as the world's richest country in terms of natural resources; its undiscovered stockpiles of raw minerals are estimated to be worth more than US $24 trillion.

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To solve the problem, let's go step by step.

1) Draw the K-map and find all prime implicants:

The given function f has 4 variables (d, c, b, a). So, we need to draw a 4-variable Karnaugh map (K-map). The K-map will have 2^4 = 16 cells.

The K-map for f is as follows:

```

        cd

ab     00 01 11 10

00 |   1   2   8   7

01 |   3   4   12 15

11 |   X   5   X   14

10 |   X   9   X   10

```

Now, let's find all the prime implicants:

- A: Group (1, 2, 3, 4) with d = 0.

- B: Group (2, 3, 7, 8) with b = 0.

- C: Group (3, 4, 12, 15) with a = 0.

- D: Group (2, 3, 4, 5) with c = 1.

- E: Group (7, 8, 14, 15) with b = 1.

- F: Group (4, 5, 9, 10) with a = 1.

- G: Group (8, 9, 12, 15) with c = 0.

- H: Group (12, 14, 15, 10) with d = 1.

2) Minimize f:

To minimize f, we need to simplify it by combining the prime implicants.

The minimized form of f can be expressed as the sum of prime implicants A, B, D, and E:

f = A + B + D + E

This can be further simplified, if desired, using Boolean algebra techniques.

Note: Please double-check the given function f and the tabulation method steps to ensure accuracy in the K-map and prime implicant identification.

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Answer:

Distribute the numbers answer: 2m+18

Step-by-step explanation:

2(m+9)

MULTIPLY 2 and m, and MULTIPLY 2 and 9!

Answer:

Step-by-step explanation:

Convert mixed fraction to improper fraction.

Find LCM of the denominators and find equivalent fraction.

Now, subtract

\(7\dfrac{2}{9}=\dfrac{(7*9)+2}{9}=\dfrac{63+2}{9}=\dfrac{65}{9}\)

\(5\dfrac{1}{5}=\dfrac{26}{5}\)

LCM of 9 and 5 = 45

\(\dfrac{65}{9}*\dfrac{5}{5}=\dfrac{325}{45}\)

\(\dfrac{26}{5}*\dfrac{9}{9}=\dfrac{234}{45}\)

\(7\dfrac{2}{9}- 5\dfrac{1}{5}=\dfrac{65}{9}-\dfrac{26}{5}\\\\ =\dfrac{65*5}{9*5}-\dfrac{26*9}{5*9}\\\\\\=\dfrac{325}{45}-\dfrac{234}{45}\\\\\\=\dfrac{325-234}{45}\\\\\\=\dfrac{91}{45}\\\\\\=2\dfrac{1}{45}\)

The scores that separate the middle 60 percent from the extremes are none of the other alternatives are correct. Option D is correct.

To find the scores that separate the middle 60% from the extremes, we need to find the z-scores that correspond to the 20th and 80th percentiles, which will give us the values that separate the middle 60%.

Using a standard normal distribution table or calculator, we can find that the z-score that corresponds to the 20th percentile is -0.84, and the z-score that corresponds to the 80th percentile is 0.84.

We can then use the formula z = (x - mu) / sigma to convert these z-scores back to raw scores:

For the 20th percentile: -0.84 = (x - 32) / 3

x - 32 = -2.52

x = 29.48

For the 80th percentile: 0.84 = (x - 32) / 3

x - 32 = 2.52

x = 34.52

Therefore, the scores that separate the middle 60% from the extremes are approximately 29.48 and 34.52.

Hence, D. none of the other alternatives are correct is the correct option.

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Given:    \(\frac{1}{3}x + 5x = -6\)

To find: x = ?

Solution:  

\(\frac{1}{3}x + 5x = -6\\ \\\frac{x+15x}{3} = -6\\\\\ 16x = -18\\\\x= \frac{-18}{16}\\ \\x = \frac{9}{8} \\\\x = 1.125\)

Answer:

1) 1 * 10^5    2) 3.5 * 10^3

Step-by-step explanation:

A parabola with a vertical axis of symmetry is graphed at the end of the answer.

The equation of a quadratic function, of vertex (h,k), with a vertical axis of symmetry, is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

The most simple example of this is the parabola y = x², which is graphed at the end of the answer.

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the formula for the equation of the line is ,

y-y1 = m (x-x1 )

2)

for point .( -5,-6), and slope m = 2

put x1 = -5 and y1 = -6

the equation of the line is,

y - (-6) = 2 (x -(-5) )

y +6 = 2(x + 5)

thus, the answer is point slope equation is y + 6 = 2(x + 5)

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3)

for point .( -7,2), and slope m = 3

put x1 = -7 and y1 = 2 and m = 3

the equation of the line is,

y - 2 = 3 (x -(-7) )

y - 2 = 3(x + 7)

thus, the answer is point slope equation is y - 2 = 3(x + 7)

Answer:

x = 2 + √2

x = 2 - √2

Step-by-step explanation:

- x² + 2x + 1 = 0

x² - 2x - 1 = 0

Here,

a = 1

b = - 2

c = - 1

Now,

Discriminant

D = b² - 4ac

= (-2)² - 4(1)(-1)

= 4 + 4

= 8

=2√2 > 0

Real and Distinct roots

x = - b +- √b² - 4ac/2a

= - (-2) +- √ = (-2)² - 4(1)(-1)/2(1)

= 2 +- √4 + 4/2

= 2 +- √8/2

= 2 +- 2√2/2

= 2 +- √2

x = 2 + √2 or x = 2 - √2

Answer:

x = 2 + √2 or x = 2 - √2

Step-by-step explanation:

Edge 2021

The equation that represents Grant’s path is; y = 4 - ¹/₂x

A slope of a line is defined as the change in y coordinate with respect to the change in x coordinate.

In geometry, a coordinate system is defined as a system that utilizes one or more numbers, or even  coordinates, to specifically determine the position of the points or perhaps other geometric elements.

We are given that a line segment drawn from Point A at (8, 0), passing through (0, 4) to Point B at (negative 4, 6).

The slope of the line with coordinates (8, 0) and (0, 4) is gotten by the formula;

m = (y₂ - y₁)/(x₂ - x₁)

m = (4 - 0)/0 - 8)

m = -¹/₂

Thus, equation of line is;

y - 6 = -¹/₂(x - (-4))

y - 6 = -¹/₂x - 2

y = -¹/₂x - 2 + 6

y = 4 - ¹/₂x

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Complete Question is;

A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend who is located at point B. A coordinate plane with a circle drawn. The center of the circle is the origin, (0, 0). The circle has a diameter of 16 units. There is a line segment drawn from Point A at (8, 0), passing through (0, 4) to Point B at (negative 4, 6). Which equation represents Grant’s path? y = 2 – 4x y = 4 – y = 6 – y = 8 – 2x