a) Find the area of each face .
b) Calculate the surface area of this rectangular prism .

Based on the equation given, the values of m and n are:

m = -1, t = 4, and n = sqrt(14)

m = 5, t = -2, and n = sqrt(14)

To find the values of m and n, we can first use the quadratic formula to solve for x:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = 6, and c = -5. Substituting these values, we get:

x = (-6 ± sqrt(6² - 4(1)(-5))) / 2(1)

x = (-6 ± sqrt(56)) / 2

x = -3 ± sqrt(14)

So the solutions for the equation x² + 6x - 5 = 0 are:

x = -3 + sqrt(14) and x = -3 - sqrt(14)

To express these solutions as x = mtn, we can set m and n equal to the factors of the constant term (-5) that add up to the coefficient of the linear term (6). The factors of -5 are -1 and 5, and we can see that:

-1 + 5 = 4

So we can express the solutions as:

x = -3 + sqrt(14) = -1 * 4 * sqrt(14)

x = -3 - sqrt(14) = 5 * (-2) * sqrt(14)

Therefore, the values of m and n are:

m = -1, t = 4, and n = sqrt(14)

m = 5, t = -2, and n = sqrt(14)

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Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

the variance will be 0.6217.

What is frequency distribution?

The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.

A small data analysis class has six computer science majors among the fourteen total students.

Three people are chosen at random to form a group.

here this is hypergeometric distribution with parameter n=sample size =3 ; N =population size =14

and k=computer sience major =6

a) E(X) =nk/N =3*6/14 =18/14 =9/7 =1.2857

b)|varaince =σ²=(nk/N)*(1-k/N)*(N-n)/(N-1)) =(3*6/14)(1-6/14)*(14-3)/(14-1)= 0.6217

Hence, the variance will be 0.6217.

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Answer:

204

Step-by-step explanation:

Answer: Cosec 2 A + Cot 4 A = Cosec 4 A - Cot 2 A

Step-by-step explanation:

Taking LHS  :

⇒Cosec 2 A + Cot 4 A

⇒Cosec 2 A + ( Cot 2 A )2

⇒Cosec 2 A + ( Cosec 2 A - 1 )2  (  we know : 1 + Cot 2 θ =  Cosec 2 θ )

⇒Cosec 2 A +  Cosec 4 A  + 1  - 2 Cosec 2 A

⇒ Cosec 4 A  + 1  - Cosec 2 A

⇒ Cosec 4 A  + 1  - ( 1 + Cot 2 A)

⇒ Cosec 4 A  + 1  -  1 - Cot 2 A

⇒ Cosec 4 A  - Cot 2 A

or cosec2A+cosec4A=cotA-cot4A

Answer: She bought 68 books.

Step-by-step explanation:

Subtract 31 from 99 to find the difference! The difference tells us how many books she bought at the yard sale.

The limit of the composite function is given as follows:

lim x->7 f(g(x)) = 2.

A limit is given by the value of function f(x) as x tends to a value.

From the graph of g(x), we have that the lateral limits at x = 7 are given as follows:

\(\lim_{x \rightarrow 7^-} = \lim_{x \rightarrow 7^+} = -2\)

Hence:

lim x->7 f(g(x)) = f(lim x->7 g(x)) = f(-2).

Looking at the graph of f(x), we have that:

f(-2) = 2.

Hence:

lim x->7 f(g(x)) = 2.

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Answer:

–6x + 15 < 10 – 5x

A number line from negative 3 to 7 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Step-by-step explanation:

\(-3(2x-5) < 5(2-x)\)

Expand the brackets:

\(\implies -6x+15 < 10-5x\)

Add 6x to both sides:

\(\implies 15 < 10+x\)

Subtract 10 from both sides:

\(\implies 5 < x\)

\(\implies x > 5\)

Therefore, x is bigger than 5.

When graphing inequalities on a number line:

To graph the given inequality on a number line:

Therefore, the correct representations of the given inequality are:

\(\\ \rm\leadsto -3(2x-5)<5(2-x)\)

\(\\ \rm\leadsto -6x+15<10-5x\)

Option C

\(\\ \rm\leadsto -x<-5\)

\(\\ \rm\leadsto x>5\)

Rest are wrong

Answer: in the third draw 33.33% people eliminated.

Step-by-step explanation:

Answer:

0.1 = 10% probability that more than 4 people arrive in a vehicle

Step-by-step explanation:

We have these following probabilities:

0.2 probability that 1 people arrive in a vehicle.

0.35 probability that 2 people arrive in a vehicle

0.25 probability that 3 people arrive in a vehicle

0.1 probability that 4 people arrive in a vehicle

x probability that more than 4 people arrive in a vehicle.

What is the probability that more than 4 people arrive in a vehicle?

The sum of all probabilities is 1 = 100%. So

0.2 + 0.35 + 0.25 + 0.1 + x = 1

x = 0.1

0.1 = 10% probability that more than 4 people arrive in a vehicle

The value of the house changes by 8% each year.

The percentage that a lender adds to the amount of money lent to them is called an interest rate.

The given function is \(v(t) = 659500(1.08)^t\).

(1)

To find the initial value of the house, substitute t=0 into the function:
\(v(0)=659500(1.08)^0\\= 659500\)

(2)

The general form of an exponential growth function is f(x) = a(1+ r)ˣ.

Since the given function is in the form of growth, it represents growth.

(3)

Comparing the given function with the general form of the exponential growth function, it follows:

1 + r = 1.08

r = 1.08 -1

r = 0.08

r = 8 %

Hence, the value of the house changes by 8% each year.

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The relationship between investments and productivity is that investments can help improve productivity, which is the correct option (C).

Investments can be used to acquire new equipment, hire additional workers, or implement new technologies that can enhance a company's productivity.

In general, corporations' major source of revenue is productivity, which is the economic outcome of the company's specific operations, such as the sale of a certain product, the rental of a certain item, the supply of a certain service, and so on.

By investing in these areas, companies can improve their efficiency, reduce costs, and increase output.

Therefore, the relationship between investments and productivity is that investments can help improve productivity.

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Answer:

y = 5x + 38

Step-by-step explanation:

Slope m = 5

Point (-7 , 3) = (x₁ , y₁)

Equation of line:  y - y₁ = m(x - x₁)

                   y - 3 = 5*(x - [-7])

                  y - 3 = 5*(x + 7)

                 y - 3 = 5x + 5*7

                 y - 3 = 5x + 35

                      y = 5x + 35 + 3

                      y = 5x + 38

Answer:

slope=7x-2

Step-by-step explanation:

none

Answer:

A ) Yes it is possible

B) The color of the most likely taxi to hit the victim is Green in color because

P( Tg / Yb ) = 0.75 = 75%

Step-by-step explanation:

A) Yes it is possible

attached below is a proposition that can be used to calculate the most likely color of the taxi

where: Tg = taxi is green

            Tb = Taxi is blue

            Yg = green taxi is seen

            Yb = blue taxi is seen

B) When 9 out of 10 Athenian taxis are green

The color of the most likely taxi to hit the victim is Green in color because

P( Tg / Yb ) = 0.75 = 75%

Each step of this theorem is proved below.

Given that,

S is finite,

Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).

According to the cancellation rule,

This product is independent of the order of the factors.

As a result, we can define the identity element e as this product.

It is simple to demonstrate that e meets the criteria of an identity element.

Now, let's show that every element of S has an inverse.

Let a be any element of S. Consider the set {a, a, a, ...}.

Since S is finite,

There exist positive integers m and n such that

am = an   for some m > n.

By the cancellation law,

We can cancel a power of a from both sides to get a\({(m-n)}\) = e.

This means that a has an inverse, and we can conclude that S is a group.

Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.

This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.

As a result, this is not a group.

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Answer:

C/95.10

Step-by-step explanation:13.75 x 6 =82.5+12.60=95.1

Answer:

3√10/5

Step-by-step explanation:

\(\frac{3\sqrt{6} }{\sqrt{15} }\)

Rationalize √15

\(\hookrightarrow \frac{3\sqrt{6} }{\sqrt{15}}\times\frac{\sqrt{15} }{\sqrt{15} } \\\\\hookrightarrow \frac{3\sqrt{6} \times\sqrt{15} }{15} \\\\\hookrightarrow \frac{3\sqrt{90}}{15} \\\\\hookrightarrow \frac{3\sqrt{10} }{5} \\\\\)

Answer:

48.668 ≤ μ ≤ 63.332

Step-by-step explanation:

Given the data:

Sample (X) : 71, 45, 54, 75, 50, 49, 63, 55, 48, 50

Number of samples (n) = 10

α = 95% = 0.05

Determine the range within which the true mean of the fluid samples from the day shift will be with a 95% confidence

True mean = μ

Confidence interval :

m ± t(α/2 ; df) * s/√n

m - t(α/2 ; df) * s/√n ≤ μ ≤ m + t(α/2 ; df) * s/√n

m = sample mean ; s = sample standard deviation ; df = degree of freedom =(n - 1) = (10 - 1) = 9

Calculating the sample mean and standard deviation using calculator to save computation time :

71, 45, 54, 75, 50, 49, 63, 55, 48, 50

m = 56 ; s = 10.25

m - t(0.05/2 ; 9) * s/√n ≤ μ ≤ m + t(0.05/2 ; df) * s/√n

From t table : t(0.05/2 ; 9) = t(0.025, 9) = 2.262

56-2.262 * (10.25/√10) ≤ μ ≤ 56+2.262 * (10.25/√10)

48.668 ≤ μ ≤ 63.332

Answer:

After 121 passes, there will be 11 cups facing up

Step-by-step explanation:

Given that:

Peter initially  lines up 121 cups facing down in a straight line from left to right and consecutively labels them from 1 to 121.

We can have an inequality ; i.e 1 ≤ n ≤  121; if n represents the divisor including n itself for which n  = odd number. Thus at the end of this claim, the cup will be facing up.

On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.)

For each divisor on the ith pass of n;

\(i \ th \ pass \ = \ n \ \to \ p |n\)  since we are dealing with possibility of having an odds number:

Thus; \(p =i\) and \(i^2 = n\)  where ; n = perfect square.

Thus ; we will realize that between 1 to 121 ; there exist 11 perfect squares. Therefore; as a result of that ; 11 cups will definitely be facing up after 121 passes

Answer:

Step-by-step explanation:

[4m(2.5m)(100^2cm^2/m^2)]/10^2cm^2=1000 tiles

Answer: 1000

Step-by-step explanation:

10xm×10cm=100cm

400cm×250cm=100000cm

100000cm²÷100cm²=1000

Answer:

x = 8.92 units

Step-by-step explanation:

From the triangle given in the picture,

Missing side of the triangle is the opposite side of the angle measuring 28°

And hypotenuse measuring 19 units has been given.

So, we will use sine ratio for the given angle.

sin(28°) = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

sin(28°) = \(\frac{x}{19}\)

x = 19sin(28°)

x = 8.92 units

Answer:

65 packets and 4 stamps

Step-by-step explanation:

The first thing we see is that the stamps are mixed... which means they must be added.

208 + 186 = 394 stamps total

Now we see that each packet has 6 stamps. So we divide the number of stamps in total by 6.

394/6= 65.66667

Now we see from that number that the stamps can't quite make 66 packets, so there are 65 packets.

Now we find the number of stamps left over by multiplying the number of packets by 6.

65 x 6= 390

Now we take the total number of stamps minus the number of stamps in packets.

394 - 390 = 4

Therefore, there are four stamps left over.

Hope this helps!

The sampling method used in this problem is classified as:

Simple Random Sampling

Samples may be classified as:

In this problem, all the options are assigned a number and then taken, hence a Simple Random Sample is used.

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The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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Answer:

The mid-point of AB is (5,6)

Step-by-step explanation:

The mid-point of two points lies between the middle of two points or divides the line in two equal parts.

The formula for finding mid-point, M, is:

\(M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

Here (x1,y1) are the coordinates of first point and (x2,y2) are coordinates of second point.

Given

(2, 3) and (8,9)

Putting the values in the formula

\(M(x,y) =(\frac{2+8}{2} , \frac{3+9}{2})\\M = (\frac{10}{2}, \frac{12}{2})\\M = (5,6)\)

Hence,

The mid-point of AB is (5,6)

The scale factor of figure B to figure A is 1/2.

To find the scale factor of figure B to figure A, we need to determine how much the corresponding sides of the two figures have been multiplied or divided by.

Looking at the figures, we can see that the corresponding sides of figure B are half the length of the corresponding sides of figure A. For example, the length of side AB in figure A is twice the length of side AB' in figure B, and the length of side BC in figure A is twice the length of side B'C' in figure B.

Since the corresponding sides of figure B are half the length of the corresponding sides of figure A, the scale factor of figure B to figure A is 1:2 or 1/2.

Therefore, the scale factor of figure B to figure A is 1/2.

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Answer:

Karen got $8.00 per hour for babysitting. Find x, the amount she was paid for 8 hours of babysitting.

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

none

Answer:

6+4×3+7=37

Step-by-step explanation:

6+4= 10

3x10=30

30+7=37