Fill in the blank with the least common denominator 5/6 + x = 7/12​

Answer:

0.3019

Step-by-step explanation:

Null hypothesis: the average age of a groom is now 26.2 years.

Alternative hypothesis: the average age of a groom is not 26.2 years.

We have a sample of 16 so we will use a t-test

Where t score = (x-u)/(sd/√n)

Where x = 26.6, u=26.2, sd= 5.3 and n=16

t score = (26.6-26.2) / (5.3/√16)

t = 0.4/(5.3/4)

t = 0.4/1.325

t = 0.3019

Answer:

the answer is 2

Step-by-step explanation:

Answer: 14 mph

Step-by-step explanation:

Let x = the speed of the boat in still water.

Then the speed of the boat relative the bank of the river is u-5 km/hb when it moves upstream, and u+5 when it moves downstream.

We can write the basic equation for travel and distance problems

Time = Distance/Speed in the form  

t = 9/x-5   for moving upstream, and

t = 19/x+5 for moving downstream.

Since the left side, t, is the same in both equations, you get a single equation for u

9/x-5 = 19/x+5

To solve it, multiply both sides by the product (x-5)*(x+5) and simplify:

9*(x+5) = 19*(x-5),

9x + 45 = 19x - 95,

45 + 95 = 19x - 9x,

10x = 140,

u = 140/10 = 14 mph.

hope this helps

Answer:

There are 8 girls in the homeroom

Answer:

The answer is 300

Answer:

300 students

Step-by-step explanation:

hope this helps!

Answer:

5/14 * 5/14

Step-by-step explanation:

The largest number of boxes that can fit into the crate is 27.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

From the given data in the question,

The dimension of the crate is: 28 × 18 × 15

Volume of crate = 6480 cm³

And the dimensions of packs = 8 × 6 × 5

the volume of packs = 240 cm³

Then, the number of boxes that fit into the crate = 6480/240

= 27

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Answer:

all get 1 and half of another

Answer:

-27

Step-by-step explanation:

3a - 4b
-3 - 4b
-3 - 24
-27

Step-by-step explanation:

Upper problem:

The transformation is a translation of 3 units down.

Lower problem:

The transformation is a translation of 2 units left and 5 units down.

a) In April, the number of students who had not passed their driving test decreased by 5%.

b) The equation is 1.2x + 0.95(1000 - x) = 1000.

c) 200 students passed their driving test in January.

a) At the beginning, of January, x students had passed their driving test, then the remaining number of students who had not passed their driving test was (1000 - x).

In April, the number of students who had not passed their driving test decreased by 5%, which means the remaining number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

b)

The number of students who had passed their driving test increased by 20%, which means the new number of students who passed their driving test is 1.2 times the original number (x).

The number of students who had not passed their driving test decreased by 5%, which means the new number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

Therefore, we can write the equation 1.2x + 0.95(1000 - x) = 1000.

c) We can solve for x in the equation 1.2x + 0.95(1000 - x) = 1000.

Expanding the equation, we get:

1.2x + 950 - 0.95x = 1000

0.25x = 50

x = 200

Therefore, 200 students passed their driving test in January.

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The value of the dimensions of the triangle using law of sines are angle C = 29.03 degrees, angle B = 58.97 degrees, and side b = 30.009 yd.

A triangle's sides and angles are related by the Law of Sines, a trigonometric formula. For every triangle with sides a, b, and c and opposing angles A, B, and C, it says that:

The equation sin A/a = sin B/b = sin C/c

In other words, for all three angles, the ratio of the sine of each angle to its opposite side is the same. When part of the sides and angles of a triangle are known, this formula can be used to find the unknown sides or angles.

The law of sines gives the ratio of the side length to the opposite angle.

Thus, using the given triangle we have:

Sin A / a = Sin C /c

Sin 92 / 35 = Sin C / 17

Sin C = 17 Sin 92 / 35

C = arcsin (17 Sin 92 / 35)

C = 29.03

Using the sum of angle of triangle we have:

A + B+ C = 180

92 + B + 29.03 = 180

B = 58.97

Now,

Sin A / a = Sin B / b

Sin 92 / 35 = Sin (58.97) / b

b = sin (58.97) (35) / sin  92

b = 30 .009

Hence, the value of the dimensions of the triangle are angle C = 29.03 degrees, angle B = 58.97 degrees, and side b = 30.009 yd.

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Answer:

x = 15.9

Step-by-step explanation:

Recall: SOHCAHTOA

Reference angle = 25°

Opposite = x

Adjacent = 34

Apply the trigonometric function, TOA, since the Opp and Adj are involved

Thus:

Tan 25° = Opp/Adj

Tan 25° = x/34

34*Tan 25° = x

15.8544604 = x

x = 15.9 (nearest tenth)

Answer:

D = L/k

Step-by-step explanation:

Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is

dA/dt = in flow - out flow

Since litter falls at a constant rate of L  grams per square meter per year, in flow = L

Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow

So,

dA/dt = in flow - out flow

dA/dt = L - Ak

Separating the variables, we have

dA/(L - Ak) = dt

Integrating, we have

∫-kdA/-k(L - Ak) = ∫dt

1/k∫-kdA/(L - Ak) = ∫dt

1/k㏑(L - Ak) = t + C

㏑(L - Ak) = kt + kC

㏑(L - Ak) = kt + C'      (C' = kC)

taking exponents of both sides, we have

\(L - Ak = e^{kt + C'} \\L - Ak = e^{kt}e^{C'}\\L - Ak = C"e^{kt} (C" = e^{C'} )\\Ak = L - C"e^{kt}\\A = \frac{L}{k} - \frac{C"}{k} e^{kt}\)

When t = 0, A(0) = 0 (since the forest floor is initially clear)

\(A = \frac{L}{k} - \frac{C"}{k} e^{kt}\\0 = \frac{L}{k} - \frac{C"}{k} e^{k0}\\0 = \frac{L}{k} - \frac{C"}{k} e^{0}\\\frac{L}{k} = \frac{C"}{k} \\C" = L\)

\(A = \frac{L}{k} - \frac{L}{k} e^{kt}\)

So, D = R - A =

\(D = \frac{L}{k} - \frac{L}{k} - \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{kt}\)

when t = 0(at initial time), the initial value of D =

\(D = \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{k0}\\D = \frac{L}{k} e^{0}\\D = \frac{L}{k}\)

Answer:

8.9770

Step-by-step explanation:

Answer:

knowing that sin(60)=0.866, what is cos(30)

Step-by-step explanation:

Cos 30 = 8.66

Answer:

The answer is n+4. Hope this helps:)

The Inequality expression that shows the above situation is x ≥ 75.

The word "inequality" describes the state of being unequal, In Inequalities like in equations, we compare two values but not with the equal signs here we use signs like Not equal, less than, less than or equal to; greater than or greater than or equal to, etc.

Here we have,

The minimum amount required to open a new checking account is $ 75        

Let us assume that we used $ x dollars to open a bank account

By the given data,

The amount is a minimum of $ 75  

=> x ≥ 75      [ x is less than or equal to $ 75 ]

Therefore,

The Inequality expression that shows the above situation is x ≥ 75.  

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Answer:

y = 1.5x - 1.5​

Step-by-step explanation:

Model and Solve Equations with Geometry Concepts (7.11c) . ... Now substitute the values for x and y into the expression. 2(1. 3. )(1. 2. −3) ... 10.0+1.5 = 11.5.

Answer:

x = -4 and  y = -9  or (-4,-9)

Step-by-step explanation:

6x-2y=-6

-5x+y=11       add the two equations together combining like terms

________

x-y=5

x=5+y

Substitute for x in terms of y

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

30+6y -2y=-6

4y = -36

y=-36/4

y=-9

Substitute -9 for y into any equation to find x

x=5+y

x=5-9

x=-4

check your work by plugging your answers into any equation

-5(-4)+(-9) =11

20-9=11

11=11   the answers verify

The ranking from the lowest to highest APR for the given companies is A, B, D, C.

The correct option is b.

To rank the companies from the lowest to highest Annual Percentage Rate (APR) based on a $600 loan amount, we need to calculate the APR for each company. The formula to calculate APR is APR = (Fees / Loan Amount) * (365 / Terms of Loan).

Let's calculate the APR for each company:

For Company A:

APR_A = ($60 / $600) x (365 / 18) = 0.1 x 20.28 = 2.028%

For Company B:

APR_B = ($80 / $600) x (365 / 12) = 0.1333 x 30.42 = 4.054%

For Company C:

APR_C = ($90 / $600) x (365 / 10) = 0.15 x 36.5 = 5.475%

For Company D:

APR_D = ($110 / $600) x (365 / 14) = 0.1833 x 26.07 = 4.79%

Now, we can rank the companies from the lowest to highest APR:

Company A - APR: 2.028%

Company B - APR: 4.054%

Company D - APR: 4.79%

Company C - APR: 5.475%

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Answer:

i think it would be negative. -1/8

The probability that an employee posted to country A at age 30 will survive to age 40 if she remains in that country is 2 x 10⁻⁶³

Probability is a mathematical concept that describes the likelihood of a specific event occurring within a set of possible outcomes

Let's start by defining some terms. The force of mortality, also known as the death rate, is the number of deaths per unit time per unit of population.

The probability of survival is the chance that an individual will live past a certain age. In our case, we want to know the probability of surviving from age 30 to age 40 while living in country A.

To calculate the probability of survival, we will use the formula:

\(P(x) = e^{-qx}\)

Where P(x) is the probability of survival at age x and qx is the force of mortality at age x.

First, we will calculate the force of mortality for the first five years after arrival in country A using the equation given in the question:

90x+1 = (6 - 1)9x+1

For x = 30, we have:

90(30) + 1 = (6 - 1)9(30) + 1

2701 = 5 * 891 + 1

2701 = 4445 + 1

2700 = 4445

So, q30 = 4445/30 = 148.5

Next, we will use this value to calculate the probability of survival for the first five years in country A:

\(P30 = e^{-q3} = e^{-148.5} = 1.2 \times 10^{-64}\)

Since the force of mortality for those who have lived in country A for at least five years is 50% greater than the US Life Tables, 2002, Females, we can calculate the force of mortality for the next 10 years as follows:

qx = 1.5 x qx from US Life Tables

Using the values from Table 3.11, we have:

q31 = 1.5 x 98,424 = 147,636

q32 = 1.5 x 98,362 = 147,543

q33 = 1.5 x 98,296 = 147,444

q34 = 1.5 x 98,225 = 147,338

q35 = 1.5 x 98,148 = 147,222

q40 = 1.5 x 97,500 = 146,250

Finally, we can use these values to calculate the probability of survival from age 31 to age 40:

\(P31 = e^{-q31} = e^{-147,636} = 1.3 \times 10^{-65}\\ \\P32 = e^{-q32} = e^{-147,543} = 1.4 \times 10^{-66}\\\\P33 = e^{-q33} = e^{-147,444} = 1.5 \times 10^{-67}\\\\P34 = e^{-q34} = e^{-147,338} = 1.6 \times 10^{-68}\\\\P35 = e^{-q35} = e^{-147,222} = 1.7 \times 10^{-69}\\\\P40 = e^{-q40} = e^{-146,250} = 2.0 \times 10^{-63)}\\\\\)

Complete Question:

When posted overseas to country A at age x, the employees of a large company are subject to a force of mortality such that, at exact duration t years after arrival overseas (t = 0,1,2,3,4), 90x+1 = (6 - 1)9x+1 where qx+t is on the basis of US Life Tables, 2002, Females. For those who have lived in country A for at least five years the force of mortality at each age is 50% greater than that of US Life Tables, 2002, Females, at the same age. Some lx values for this table are shown in Table 3.11.

An extract from the United States Life Tables, 2002,

Females. Age,

x 30 31 32 33 34 35 40

1x 98,424 98,362 98,296 98,225 98,148 98,064  97,500

Calculate the probability that an employee posted to country A at age 30 will survive to age 40 if she remains in that country.

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The number of times on the hour in 3 days at least two owls will not hoot obtained using number theory are 69 times.

Number theory is the study of integers and functions of arithmetic.

The number of hours in 3 days = 72 hours

Number theory indicates that the multiples of the periods of hooting are;

The multiples of 8 are; 8, 16, 24, 32, 40, 48, 56, 64, 72

The multiples of 3 are; 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72

The multiples of 12 are; 12, 24, 36, 48, 60, 72

The common multiples of 3 and 8 are 24, 48, 72

The common multiples of 8 and 12 are 24, 48, 72

The number of times in 72 hours when at least 2 owls are hooting are therefore;

The times when only one owl is hooting are

8, 16, 32, 40, 56, 64, = 6 times only the second owl is hooting

3, 6, 9, 12, 15, 18, 21, 27, 30, 33, 36, 39, 42, 45, 51, 54, 57, 60, 63, 66, 69   = 21 times when only the first owl hoots

The times when non of the owls hoot  are;

72 - 24 - 6 = 42 times

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The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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Answer:

The main flaw of this  proof is that it did not take into consideration the fact a 4 cent postage must be made with a 4 cent stamp  and a 3 cent postage  must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage

Step-by-step explanation:

From the question we are told that

   The  proof is

Every postage stamp of three cents or more can be formed using just 3 cent and 4 cent stamps.  

 Basic Step : We can form postage of 3 cents with a single 3 cent stamp and we can form postage of 4 cents using a single four cents tamp

Inductive Step: Assume that we can form postage of j cents for all non negative integers j with j <= k using just 3 cent and 4-cent stamps. We can then form postage of k+1 cents by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps

  FLAW IDENTIFICATION

Looking the inductive step, the statement ''by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps '' means that it is possible to use a 3-cent stamp for postage that requires a 4 -cent stamp  and this is not correct according the statement in the basic step

Generally the main flaw of this  proof is that it did not take into  consideration the fact a 4 cent postage must be made with a 4 cent stamp  and a 3 cent postage  must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage

Answer:

Nope

Step-by-step explanation:

No, because if you add the angles of B and C (since they're asking for line BC), they must equal the angles of A and D (Since the other line was AD)

The sum of B and C is 90+45 which = 135

The sum of A and D is 90+135 which = 225

135 =/= 225

Answer:

  5.5 in

Step-by-step explanation:

The altitude is (√3)/2 times the length of a side, so the side length is the inverse of that times the length of the altitude:

  side length = (2/√3)(4.8 in) ≈ 5.5 in

To calculate the mean, median, and mode, we first need to know what each of these terms represents. The mean, also known as the average, is the sum of all the values divided by the total number of values. To find the mean, add up all of the values and divide by the number of values. The median is the middle value in a set of data when it is arranged in order from least to greatest. The mode is the value that occurs most frequently in a set of data. Here's an example to illustrate these concepts:

Let's say we have a set of data consisting of the following values: 2, 5, 5, 7, 8, 10, 12. To find the mean, we add up all of the values and divide by the number of values. In this case, the sum of the values is 49 (2+5+5+7+8+10+12) and there are 7 values, so we divide 49 by 7 to get the mean, which is approximately 7. To find the median, we first need to arrange the data in order from least to greatest: 2, 5, 5, 7, 8, 10, 12. The middle value is 7, so that is the median. To find the mode, we look for the value that occurs most frequently. In this case, 5 occurs twice, which is more than any other value, so the mode is 5.
In conclusion, the mean, median, and mode are all measures of central tendency that can be used to describe a set of data. The mean is the average value, the median is the middle value, and the mode is the value that occurs most frequently. When calculating these measures, it is important to carefully consider the data and choose the appropriate method for finding each value.

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Answer: he probably didn't pay attention to the - sign on -5.4