Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?
A. 1/24
B. 1/8
C. 1/4
D. 1/3
E. 3/8

To determine the length of an unknown side in a right triangle, we can use the sin, cos, tan ratios or the Pythagorean theorem, depending on which sides and/or angles we already know. However, the specific information about measures and sides in the two right triangles in the question is not clear, hence a specific answer cannot be provided.

The subject of this question is trigonometry, a branch of mathematics that studies relationships involving lengths and angles of triangles. As the triangles are right-angled, we can use properties specific to this type of triangle. When given the measure of an angle in a right triangle, we can find the lengths of the sides using trigonometric ratios such as sine, cosine, and tangent.

In this particular problem, we're given the measure of an angle and lengths of some sides but the information about the measures of the triangles and their sides are not clearly mentioned. To provide an answer, we'd need clear information on which triangle contains the given angle and sides.

However, to give you an idea of how this type of problem can be solved, let's consider that the measure of the angle α is 30 degrees, the measure of side a is 6 units, the measure of side b is 3 units, and the measure of side c (the hypotenuse) is 12 units (These are just hypothetical names to represent the sides). If we are asked to find the length of an unknown side, we can use the Sin, Cos or Tan ratios or even the Pythagorean theorem (a² + b² = c²), depending on the sides that we know.

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Answer:

download photomath

Step-by-step explanation:

I swear it would help you because it always help me.. just look carefully

Answer: x = 1,

y = 5

z = 2

Step-by-step explanation:

Answer:

There are 436937109262510348800 ways to selected 12 countries.

Step-by-step explanation:

Let [tex]x_1, x_2, x_3, x_4,x_5[/tex] the countries selected from the block of 45. For [tex]x_1[/tex] there are 45 options of countries to select. For [tex]x_2[/tex] there are 44 options of countries to select because there can be no repeated countries. With the same reasoning, for [tex]x_3[/tex] there are 43 options, for [tex]x_4[/tex] there are 42 options and for [tex]x_5[/tex] there are 41 options.

Let [tex]x_6, x_7, x_8, x_9[/tex] the countries selected from the block of 57 countries. For [tex]x_6[/tex] there are 57 options of countries to select. For [tex]x_7[/tex] there are 56 options of countries to select because there can be no repeated countries. With the same reasoning, for [tex]x_8[/tex] there are 55 options and for [tex]x_9[/tex] there are 54 options.

Let [tex]x_{10}, x_{11}, x_{12}[/tex] the countries selected from the block of 69 remain countries. For [tex]x_{10}[/tex] there are 69 options of countries to select. For [tex]x_{11}[/tex] there are 68 options of countries to select because there can be no repeated countries and for [tex]x_{12}[/tex] there are 67 options.

For find the total of options o ways to select 12 countries we multiply the above options.

[tex]45*44*43*42*41*57*56*55*54*69*68*67= 436937109262510348800[/tex]

Final answer:

The number of ways to select 12 countries from the United Nations to serve on a council is determined by calculating the combinations for each block of countries and then multiplying these values together.

Explanation:

The student question deals with determining the number of ways to select 12 countries from the United Nations to serve on a council, given specific blocks of countries to choose from. To calculate this, we use the principles of combinations, as the order of selection does not matter. The number of ways to select 5 countries from the first block of 45 is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and '!' denotes factorial. Applying this to the first block:

C(45, 5) = 45! / (5! * (45-5)!) = 1,221,759 ways

Similarly, for the second block of 57 countries, from which 4 must be chosen:

C(57, 4) = 57! / (4! * (57-4)!) = 496,674 ways

For the remaining 3 countries from the last block of 69:

C(69, 3) = 69! / (3! * (69-3)!) = 54,834 ways

To find the total number of combinations, we multiply the number of ways for each block, as each selection is independent of the others:

Total ways = C(45, 5) * C(57, 4) * C(69, 3) = 1,221,759 * 496,674 * 54,834

After calculating this product, we obtain the total number of ways to select 12 countries from the United Nations for the council.

Answer:

C. g(0)=8; g(1)=12

Step-by-step explanation:

Answer:

The answer to your question is g(0) = 12; g(1) = 8. Letter D

Step-by-step explanation:

  g(x) = 12(2/3)[tex]^{x}[/tex]

a) Substitute 0 in the equation and simplify

   g(0) = 12(2/3) ⁰

   g(0) = 12(1)

   g(0) = 12

b) Substitute 1 in the equation and simplify

   g(1) = 12(2/3)¹

   g(1) = 12(2/3)

   g(1) = 24/3

   g(1) = 8

Answer:

c) 2.415

Step-by-step explanation:

Given that X represent the number on the face that lands up when a fair six-sided number cube is tossed.

The expected value of X is 3.5, and the standard deviation of X is approximately 1.708.

When another die is rolled let Y represent the number on the face that lands up when a fair six-sided number cube is tossed.

The expected value of Y is 3.5, and the standard deviation of Y is approximately 1.708.

Also we find that X and Y are independent

Let U = X+Y

Then we have U as the random variable representing the sum shown by two dice

Since X and Y are independent

[tex]Var(x+y) = Var(x) +Var(y)\\= 1.708^2 *2\\= 5.83333[/tex]

Std dev for sum

= [tex]\sqrt{5.8333} \\=2.4152[/tex]

Hence option C 2.415 is correct

Answer:

2.415

Step-by-step explanation:

Its not as complicated as that other response. You never subtract standard deviations, you always add them, and you don't add them directly, you have to square them to make them variances, add them, and find the square root of it.

In this problem, you do [tex]\sqrt{(1.708^{2}) + (1.708^{2})}[/tex]

Put it in the calculator and you get 2.415

Answer:

  2.  100°              22.  7

  18.  6                  23.  9

  19.  8                  24.  65°

  20.  55°             25.  AB = (1/2)DF

  21.  6                 26.  AB ║ DF

Step-by-step explanation:

Please be aware that the triangle measurements shown for problems 18–20 and 22–24 cannot exist. In the first case, the angle is closer to 48.6° (not 35°), and in the second case, the angle is closer to 51.1°, not 25°. So, you have to take the numbers at face value and not think too deeply about them. (This state of affairs is all too common in geometry problems these days.)

_____

2. You have done yourself no favors by marking the drawing the way you have. Look again at the given conditions. You will find that x+2x must total a right angle, so x=30°. Angle P is the complement of 40°, so is 50°. Then the sum of x and angle P is 30° +50° = 80°, and the angle of interest is the supplement of that, 100°.

__

18–20. Perpendicular bisector NO means  ∆NOL ≅ ΔNOM. Corresponding parts have the same measures, and angle L is the complement of the marked angle.

__

21. ∆ODA ≅ ∆ODB by hypotenuse-angle congruence (HA), so corresponding parts are the same measure. DB = DA = 6.

__

22–24. ∆VPT ≅ ∆VPR by LL congruence, so corresponding measures are the same. Once again, the angle in question is the complement of the given angle.

__

25–26. You observe that A is the midpoint of DE, and B is the midpoint of FE, so AB is what is called a "midsegment." The features of a midsegment are that it is ...

Answer:

  -5/4

Step-by-step explanation:

See the attachment for rise and run lines. The slope is the ratio ...

   slope = rise / run = -5/4

In mathematics, 'rise' and 'run' are used to find the slope of a line. They represent vertical and horizontal distances respectively between two points. Slope, represented as 'm' is calculated as 'rise/run' which gives the ratio of the vertical change to the horizontal change.

In Mathematics, specifically in Algebra and Geometry, the terms 'rise' and 'run' refer to the vertical and horizontal distances between two points on a line, respectively. In the context of a line on a graph, the 'run' corresponds to the difference in the x-values of the points (horizontal change), while the 'rise' corresponds to the difference in the y-values of the points (vertical change). These terms are crucial when calculating the slope of a line.

The slope of a line, also often represented by the letter 'm', is computed as 'rise/run', giving us the ratio of the vertical change to the horizontal change between two points on the line. If for instance, the rise is 4 units and the run is 2 units, your slope or 'm' would be 4/2 which simplifies to 2. This means that for every step you move horizontally (run), you move two steps vertically (rise).

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Answer:

Step-by-step explanation:

Answer:

A. A - 0.2, B - 0.3, C - 0.2, D - 0.15, E - 0.15

B. Grade B

Step-by-step explanation:

A. Total number of students = 4 + 6 + 4 + 3 + 3 = 20

So the relative frequency of each grade can be computed as the ratio of number of students with the grade and the total number of students.

A : 4/20 = 0.2

B : 6/20 = 0.3

C : 4/20 = 0.2

D : 3/20 = 0.15

E : 3/20 = 0.15

B. Among the grades, grade B has the highest relative frequency of 0.3. Hence Grade B received the most number of students.

Answer:

Step-by-step explanation:

Factor the given function:

        (x + 2)(x + 5)

f(x) = --------------------

         (x + 5)(x + 4)

The factor (x + 5) can be crossed out in numerator and denominator.  There is a 'hole' at x = -5 (which comes from setting (x + 5) = 0 and solving for x).

If we do cancel the (x + 5) factors, we are left with

           (x + 2)

f(x) =  ------------- .  We can't just substitute x = -5 because the original

           (x + 4)         function is not defined for that x value.  However, we

can locate the hole by letting x have the value of a litle more than -5, obtaining:

           ( -5+ + 2)

f(-5+) =  -------------, which comes out to approx. -3/-1, or +3 .  

            (-5+ + 4)    

So the hole location is (-5, 3).

f(x) = --------------------

         (x + 5)(x + 4)

Answer:

[tex]cos^{-1} (\frac{8}{[tex]\sqrt{113}[/tex]} )[/tex]

Step-by-step explanation:

Given two vectors a and b,we are rquired to find the angle between them.

a=(8,7);b=(7,0).

Angle between two vectors can be found by dot product of them.

If a and b are two vectors then the dot product of them is given by|a||b|cos(α).

Where α is the angle between the vectors a and b.

Now [tex]|a|=\sqrt{113}\text{ } and\text{ } |b|=\sqrt{49}[/tex]. and [tex]a.b=8\ times 7+7\times 0[/tex] =56.

Now cosα=[tex]\frac{8}{\sqrt{113} }[/tex] so α= cosine inverse of that.

∴α=

[tex]cos^{-1} (\frac{8}{[tex]\sqrt{113}[/tex]} )[/tex]

Answer:

$ 55135.978

Step-by-step explanation:

At most, the present value of annuity must be paid. So we must find the present value of the annuity

Given in the problem, we have:

Periodic Payment = PMT = $10000

Rate of interest annually = i = 6.35 %= [tex]\frac{6.35}{100}[/tex]=0.0635

no. of periods= n=7

So to solve this, we need to use the present value formula:

Present Value = Periodic payment [tex]\frac{1-(1+rate.of.interest)^{-n} }{rate.of.interest}[/tex]

Present Value = PMT [tex]\frac{1-(1+i)^{-n} }{i}[/tex]

Present value = 10000[tex]\frac{1-(1+0.0635)^{-7} }{0.0635}[/tex]

Present Value =10000[tex]\frac{0.35011}{0.0635}[/tex]

Present Value =10000 (5.5135978)

Present value= $ 55135.978

Which is the amount that must be paid at most to get annuities such that $10,000 annually over the 7-year period are to be received.

You should pay approximately $55,598 for a 7-year ordinary annuity with a guaranteed 6.35% annual interest rate to receive annual payments of $10,000.

To find out how much you should pay for a 7-year ordinary annuity with a guaranteed rate of 6.35% compounded annually to receive payments of $10,000 annually, we can use the present value of an annuity formula:

PV = PMT × [(1 - (1 + r)⁻ⁿ) / r]

Substituting the values into the formula:

PV = $10,000 × [(1 - (1 + 0.0635)⁻⁷) / 0.0635]

PV = $10,000 × [(1 - (1 / (1.0635)⁷)) / 0.0635]

PV = $10,000 × [(1 - (1 / 1.545677)) / 0.0635]

PV = $10,000 × [0.353032 / 0.0635]

PV = $10,000 × 5.5598

PV ≈ $55,598

Therefore, you should pay approximately $55,598 for this annuity to receive payments of $10,000 annually over 7 years.

Answer:

9/49

Step-by-step explanation:

For the first die, probability of obtaining 4= 2/7

For the second die, the probability of obtaining 3= 2/7

Other outcomes for each die appear with a probability of 1/7

There are six cases of obtaining the sum of the two die as 7.

E1 = 1 and 6

E2 = 2 and 5

E3 = 3 and 4

E4 = 4 and 3

E5 = 5 and 2

E6 = 6 and 1

Pr(E1) = 1/7*1/7

= 1/49

Pr(E2) = 1/7*1/7

= 1/49

Pr(E3) = 1/7*1/7

= 1/49

Pr(E4) = 2/7*2/7

= 4/49

Pr(E5) = 1/7*1/7

= 1/49

Pr(E6)= 1/7*1/7

= 1/49

P(E) = Pr(E1) + Pr(E2) + Pr(E3) + Pr(E4) + Pr(E5) + Pr(E6)

= 1/49 + 1/49 + 1/49 + 4/49 + 1/49 + 1/49

= 9/49

When rolling loaded dice with particular probabilities of obtaining 3 and 4, the probability of obtaining a sum of 7 when two dice are rolled is 8/49.

Your question pertains to the concept of probability in mathematics, particularly when dealing with loaded dice and the probabilities of certain outcomes. In your scenario, you want to determine the probability of obtaining a sum of 7 given particular probabilities of rolling a 4 on the first die and a 3 on the second die.

In general, obtaining a sum of 7 is possible with the following combinations: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1. With your loaded dice, however, only the combinations 4 and 3 and 3 and 4 are relevant. Given that the probability of rolling a 4 on the first die is 2/7, and the probability of rolling a 3 on the second die is also 2/7, the probability of rolling a 7 is (2/7)*(2/7)=4/49. As you are considering both the combinations 4 and 3, and 3 and 4, you need to multiply this result by 2 which gives a final probability of 8/49.

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Answer:

Sample size should be atleast 617

Step-by-step explanation:

given that a 95% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit.

i.e. margin of error <0.3

Std devition sample = 3.8

For 95% assuming sample size large we can use z critical value

Z critical = 1.96

we have

[tex]1.96 * std error <0.3\\1.96(\frac{3.8}{\sqrt{n} } )<0.3\\\sqrt{n} >24.83\\n>616.3634[/tex]

Sample size should be atleast 617 to get an accurate margin of error 0.3

To construct a 95% confidence interval with an accuracy of 0.3 units, the smallest sample size (n) is 25.

To construct a 95% confidence interval with an accuracy of 0.3 units, we need to determine the sample size (n). We can use the formula:

n = (Z * σ) / E

Where Z is the Z-score corresponding to the desired confidence level (in this case, 95% corresponds to a Z-score of 1.96), σ is the preliminary sample standard deviation (3.8), and E is the desired accuracy (0.3).

Substituting the values into the formula:

n = (1.96 * 3.8) / 0.3 = 24.8

Rounding up to the nearest whole number, the smallest sample size n that provides the desired accuracy is 25.

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Answer:

  the cylinder volume is greater

Step-by-step explanation:

The volume of a cube with x=1 is ...

  V(1) = 1^3 = 1

The graph shows y ≈ 1.5 for x=1. Since 1.5 > 1, the volume of the cylinder is greater.

When x = 1, the volume of the cylinder is greater than the volume of the cube.

To determine which volume is greater when x = 1, we can calculate the volume of the cube and the volume of the cylinder at x = 1 and compare them.

For the cube with side length x, the volume is given by V(x) = x^3. So, when x = 1:

V(cube) = (1)^3 = 1

For the cylinder with radius x and height 0.5x, the volume is given by the formula for the volume of a cylinder: V(cylinder) = πr^2h, where r is the radius and h is the height.

When x = 1:

r = 1 (radius)

h = 0.5(1) = 0.5 (height)

V(cylinder) = π(1^2)(0.5) = π(0.5) = 0.5π

Now, we need to compare the volumes.

V(cube) = 1

V(cylinder) = 0.5π ≈ 1.57 (rounded to two decimal places)

So, when x = 1, the volume of the cylinder is greater than the volume of the cube.

for such more question on volume

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Answer:

  4.47 years

Step-by-step explanation:

Fill in the numbers and solve for t.

  P = a·b^t

  15390 = 19000·0.954^t

  15390/19000 = 0.954^t . . . . . divide by 19000

  0.81 = 0.954^t . . . . . . . . . . . . . simplify

  log(0.81) = t·log(0.954) . . . . . . take the log

  t = log(0.81)/log(0.954) . . . . . . divide by the coefficient of t

  t ≈ 4.47

It will take about 4.47 years for the population to drop to 15390 organisms.

_____

A graphing calculator can be another way to solve a problem like this.

Answer:

  • 80%

Step-by-step explanation:

Consult your course reference materials.

Advice found on the Internet varies from 70% to 90%, depending on a number of factors. 70% has been a guide historically, but more recent advice favors higher numbers, it seems.

For this case we must find the solution of the following quadratic equation:

[tex]x ^ 2 + 5x + 7 = 0[/tex]

Where:

[tex]a = 1\\b = 5\\c = 7[/tex]

Then, the solution is given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

Substituting the values:

[tex]x = \frac {-5 \pm \sqrt {5 ^ 2-4 (1) (7)}} {2 (1)}\\x = \frac {-5 \pm \sqrt {25-28}} {2}\\x = \frac {-5 \pm \sqrt {-3}} {2}[/tex]

By definition we have:[tex]i ^ 2 = -1[/tex]

[tex]x = \frac {-5 \pm \sqrt {3i ^ 2}} {2}\\x = \frac {-5 \pm i \sqrt {3}} {2}[/tex]

Thus, we have two complex roots.

Answer:

The equation has no real roots.

Answer:

3/5

Step-by-step explanation:

Out of the 10 times flipped, you got heads 6 times

That is 6/10 or 3/5

Answer:3/5

Step-by-step explanation:took the test and got right

Answer:

230.

Step-by-step explanation:

You have a 50% chance to get heads or tails. So that's half of 490, which is 245. It says estimate, so that means a relative guess. 230 would be the closest.

Final answer:

To estimate the number of times a coin flipped 490 times lands on heads, one should expect approximately half of the flips to be heads, which is about 245. Thus, option B. 230 is the closest estimation.

Explanation:

The question deals with the probability of outcomes when flipping a coin multiple times. When you flip a coin, the probability of it landing on heads is 50 percent each time, irrespective of previous outcomes. Thus, if you flip a coin 490 times, a good estimate for the number of times it will land on heads is roughly half of 490, which is 245. Therefore, the best estimate from the given options would be B. 230, as it is the closest to 245.

Answer:

(a) [tex]y = 83 (1.048)^x[/tex]

(b) 2020

Step-by-step explanation:

(a) Let the exponential equation that shows the population in thousand after x years,

[tex]y = ab^x[/tex]

Also, suppose the population is estimated since 2010,

So, x = 0, y = 83 thousands,

[tex]83 = ab^0[/tex]

[tex]\implies a = 83[/tex]

Again by 2015 the population had grown to 105 thousand,

i.e. y = 105, if x = 5,

[tex]\implies 105 = ab^5[/tex]

[tex]\implies 105 = 83 b^5[/tex]

[tex]\implies b = (\frac{105}{83})^\frac{1}{5}=1.0481471103\approx 1.048[/tex]

Hence, the required function,

[tex]y = 83 (1.048)^x[/tex]

(b) if y = 135,

[tex]135 = 83(1.048)^x[/tex]

[tex]\implies x = 10.375\approx 10[/tex]

Hence, after approximately 10 years since 2010 i.e. in 2020 the population would be 135.

Final answer:

By assuming exponential growth, we derived the equation P = 83,000 * e^(0.048t) and determined that the town's population would exceed 135,000 around the year 2021.

Explanation:

To find an exponential equation for the town's population and determine in what year the population will exceed 135 thousand, we start by assuming the population growth follows the form P = P0 * e^(rt), where P is the final population, P0 is the initial population, r is the rate of growth, and t is the time in years. For this town, in 2010 (t=0), the population was 83,000 (P0=83,000), and by 2015 (t=5), the population grew to 105,000.

Substituting these values into the formula, we have 105,000 = 83,000 * e^(5r). Solving for r, we find that r ≈ 0.048. Thus, the exponential growth equation is roughly P = 83,000 * e^(0.048t).

To determine when the population will exceed 135,000, we set P > 135,000 and solve for t. This gives us the inequality 135,000 < 83,000 * e^(0.048t). Solving this, we find that t ≈ 10.24 years after 2010, which rounds up to the year 2021 when the population will exceed 135 thousand.

Answer:

Option d

Step-by-step explanation:

given that a, b, c, and d be non-zero real numbers.

[tex]ax(cx + d) = -b(cx+d) \\acx^2+x(ad+bc)+bd =0[/tex]

we can factorise this equation by grouping

[tex](acx^2+xad)+)xbc+bd) =0\\ax(cx+d) +b(cx+d) =0\\(ax+b)(cx+d) =0[/tex]

Equate each factor to 0 to get

[tex]x=\frac{-b}{a} , \frac{-d}{c}[/tex]

Ratio of one solution to another would be

[tex]\frac{-b}{a} / \frac{-d}{c} \\=\frac{ad}{bc}[/tex]

So ratio would be ad/bc

Out of the four options given, option d is equal to this

So option d is right

Answer:

[tex]x^2 + x - 72 = 0[/tex]

Explanation:

We are given product of two consecutive odd integers is equal to 72.

Let one integer be x , then since these are consecutive and odd so the other integer will be equal to x + 1.  

Their product is equal to 72. So,

x * (x + 1) = 72

=> [tex]x^2 + x = 72[/tex]

=>  [tex]x^2 + x - 72 = 0[/tex] is the required quadratic equation.

Answer:

Value of x is 20 and y is 120.

Step-by-step explanation:

Given,

m∠A = 70°, m∠B = 60°, m∠C = 50°,m∠D = (3x + 10)°, m∠E= (1/3y + 20)°, and m∠F = (z² + 14)°

Also,

ΔABC ≅ ΔDEF,

Since, the corresponding parts of congruent triangles are always congruent or equal.

⇒ m∠A = m∠D, m∠B = m∠E and m∠C = m∠F

When m∠A = m∠D

[tex]\implies 70 = 3x + 10[/tex]

[tex]70 - 10 = 3x[/tex]

[tex]60 = 3x[/tex]

[tex]\implies x =\frac{60}{3}=20[/tex]

When, m∠B = m∠E,

[tex]\implies 60 = \frac{1}{3}y + 20[/tex]

[tex]60 - 20 =\frac{1}{3}y[/tex]

[tex]40 =\frac{1}{3}y[/tex]

[tex]\implies y =3\times 40=120[/tex]

Answer:

The  equation  7 m + 15  m = 44 is the equation that can be used to determine the number of small cars rented and the number of large cars rented.

where, m : Number of large cars rented

Step-by-step explanation:

The number of people small car can hold  = 5

The number of people large car can hold  = 7

Let us assume the number of large cars rented  = m

So, the number of smaller cars rented = 3 x ( Number of large cars rented)

= 3 m

Now, the number of people in m large cars  = m x ( Capacity of 1 large car)

= m x ( 7)  = 7 m

And, the number of people in 3 m small  cars  = 3 m x ( Capacity of 1 small car) = 3 m x ( 5)  = 15  m

Total people altogether going for the plan = 44

⇒ The number of people in ( Small +Large) car  = 44

or, 7 m + 15  m = 44

Hence,  the equation  7 m + 15  m = 44 is the equation that can be used to determine the number of small cars rented and the number of large cars rented.

We define variable as

Let x be the number of small cars and y be the number of large cars.

Since ,

Each small car can hold 5 people and each large car can hold 7 people.

i.e. Number of people in x cars = 5x

Number of people in y cars = 7y

The students rented 3 times as many small cars as large cars, implies

y=3(x)

They altogether can hold 44 people.

i.e. 5x+7y=44

Thus , the system of equations that could be used to determine the number of small cars rented and the number of large cars rented :

[tex]y=3(x)[/tex]

[tex]5x+7y=44[/tex]

Answer:

a and b both are true.

Step-by-step explanation:

Given : A coin is tossed 10 times.

To find : True or false, and explain ?

Solution :

(a) The chance of getting 10 heads in a row is [tex]\frac{1}{1024}[/tex]

Coin has two face head and tail.

The probability of getting head is [tex]P(H)=\frac{1}{2}[/tex]

The probability of getting 10 heads in a row is

[tex]P=(P(H))^{10}[/tex]

[tex]P=(\frac{1}{2})^{10}[/tex]

[tex]P=\frac{1}{1024}[/tex]

The chance of getting 10 heads in a row is [tex]\frac{1}{1024}[/tex] is true.

(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is [tex]\frac{1}{2}[/tex].

The probability of getting 10 heads in a row is [tex]P_1=(\frac{1}{2})^{10}[/tex]

The probability of getting 9 tosses were heads is [tex]P_2=(\frac{1}{2})^{9}[/tex]

Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is given by,

[tex]P=\frac{P_1}{P_2}[/tex]

[tex]P=\frac{(\frac{1}{2})^{10}}{(\frac{1}{2})^{9}}[/tex]

[tex]P=(\frac{1}{2})^{10-9}[/tex]

[tex]P=\frac{1}{2}[/tex]

Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is [tex]\frac{1}{2}[/tex] is true.

(a) True: The chance of getting 10 heads in a row is [tex]\( \frac{1}{1024} \)[/tex].

(b) True: Given 9 heads, the chance of the 10th being heads remains [tex]\( \frac{1}{2} \).[/tex]

Step 1:

(a) The chance of getting 10 heads in a row:

The probability of getting heads on a single toss of a fair coin is [tex]\( \frac{1}{2} \).[/tex]

Since each toss is independent, the probability of getting 10 heads in a row is calculated by multiplying the individual probabilities:

[tex]\[ \left( \frac{1}{2} \right)^{10} = \frac{1}{1024} \][/tex]

Step 2:

(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row:

Since each toss is independent, the probability of getting heads on the 10th toss is still  [tex]\( \frac{1}{2} \).[/tex]

So, the chance of getting 10 heads in a row given the first 9 were heads remains [tex]\( \frac{1}{2} \).[/tex]

Therefore, the calculations support the statements:

(a) The chance of getting 10 heads in a row is indeed [tex]\( \frac{1}{1024} \)[/tex].

(b) Given the first 9 tosses were heads, the chance of getting 10 heads in a row is still [tex]\( \frac{1}{2} \).[/tex]

Answer:

c. Stdev

Step-by-step explanation:

Excel stdev function is not appropriate to construct confidence interval estimate, because the estimation of the proportion of defective items that are produced by a certain machine has binomial distribution.

stdev fuction is used for calculating standard deviations where sample has more than two different values. (multinomial)

Norm.s.inv function calculates inverse of the standard normal cumulative distribution, and countif counts the number of cells that meet a criterion. Both functions are used to construct confidence interval estimate

Answer:

8. [tex]\displaystyle \frac{9[x + 5]}{x - 14}[/tex]

7. [tex]\displaystyle -\frac{2x - 1}{2[3x - 5]}[/tex]

6. [tex]\displaystyle \frac{2[x - 4]}{5[x + 3]}[/tex]

5. [tex]\displaystyle \frac{2x + 7}{x + 3}[/tex]

4. [tex]\displaystyle 3x^{-1}[/tex]

Step-by-step explanation:

All work is shown above from 8 − 4.

I am joyous to assist you anytime.

Answer:

A youre welcome

Step-by-step explanation: