Find all the numbers that satisfy the fol-
lowing descriptions:
The number has seven digits.
The number is between 1,000 and
10,000.
The digit in the tenths place is 150%
of the digit in the thousandths place.
The digit in the hundredths place is
of the sum of the digit in the
tenths place and the digit in the
thousandths place.
The sum of all the digits in the num-
ber is 17.
None of the digits are zero.

The solutions are:

a) y = (lnx + 42 - ln7)/x

b) y = (lnx + 42 - ln6)/x

What are differential equations?
A differential equation is an equation that relates a function to its derivatives.

To verify that every member of the family of functions y=(lnx+C)/x is a solution of the differential equation x^2y' + xy = 1, we can substitute the function into the equation and see if it holds true for all values of x.

y=(lnx+C)/x

y'= (1/x - lnx - C)/x^2

x^2(1/x - lnx - C)/x^2 + x(lnx+C)/x = 1

(1 - xlnx - xC) + (lnx+C) = 1

lnx + C = 1/x

The equation holds true for all x, so it is a solution of the differential equation.

a) To find a solution of the differential equation that satisfies the initial condition y(7)=6, we can use the fact that y=(lnx+C)/x is a solution and plug in the initial condition.

y(7) = (ln7+C)/7 = 6

ln7 + C = 42

C = 42 - ln7

y = (lnx + 42 - ln7)/x

b) To find a solution of the differential equation that satisfies the initial condition y(6)=7, we can use the fact that y=(lnx+C)/x is a solution and plug in the initial condition.

y(6) = (ln6+C)/6 = 7

ln6 + C = 42

C = 42 - ln6

y = (lnx + 42 - ln6)/x

Hence, the solutions are:

a) y = (lnx + 42 - ln7)/x

b) y = (lnx + 42 - ln6)/x

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Answer:$11.5

Step-by-step explanation:

Admission = $9 charged once

each ride = $2.5x (x=number of rides)

Total cost for x rides

=2.5x+9

This function shows a horizontal translation of the parent function to the left and 2 units up.

The parent function of a square root function is expressed as:

f(x) = √x

According to the question, we are to plot the expression f(x) = √x+ 3 - 2

This function shows a horizontal translation of the parent function to the left and 2 units up. The required graph will be in the 2nd quadrant of the graph as shown;

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Answer:

It should be the first one.

Answer:

The value of d is 17.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(d-9)/(10-9)

m=8

8=(d-9)/1

8*1=d-9

8=d-9

d=8+9

d=17

Answer:

I think its 72,000

Step-by-step explanation:

there's 144 months in 12 years and i just multiplied it by 500

Answer:

Step-by-step explanation:

The needed number of days at 10 degrees is given as follows:

11 days.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For this problem, we have that when x decreases by 5, y increases by 2, hence the slope m is given as follows:

m = -2/5

m = -0.4.

Hence the time needed for a temperature of 10 degrees is given as follows:

9 + 2 = 11 days.

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a) The total closing costs are $100,000.

b) The actual amount they financed with the mortgage is $90,000.

a) Total Closing Costs:

To find the total closing costs, we need to calculate 10% of the selling price, which represents the down payment. Additionally, we need to consider the closing costs that are financed as part of the mortgage.

Calculate the down payment:

Down Payment = 10% of Selling Price

Down Payment = 10% of $100,000

Down Payment = $10,000

Calculate the financed amount for closing costs:

Financed Closing Costs = Selling Price - Down Payment

Financed Closing Costs = $100,000 - $10,000

Financed Closing Costs = $90,000

Therefore, the total closing costs are $10,000 for the down payment plus $90,000 for the financed closing costs, resulting in a total of $100,000.

b) Actual Amount Financed with the Mortgage:

To find the actual amount financed with the mortgage, we need to subtract the down payment from the selling price.

Actual Amount Financed = Selling Price - Down Payment

Actual Amount Financed = $100,000 - $10,000

Actual Amount Financed = $90,000

Therefore, Kyung Ja and Hideo Hakola financed $90,000 with the mortgage.

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Answer: (a * 50%)^3

Step-by-step explanation:

length = a

(a * 50%)^3

If a would've been the length and would've been decreased to 50%, the volume would be equal to that expression.

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

(a) Mean x = 245.63636363636

(b) Median x = 245

(c) Mode = 207, 255

(d) The mid-range = 252

(e) The results are not likely to be representative because the championship team may not be representative of the entire league.

The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. to find the median first arrange the data points in ascending order.

(a) Mean x = 245.63636363636

(b) Median x = 245

(c) Mode = 207, 255

A. The modes are 201 and 255.

B. There are two modes.

Range = 90

Minimum = 207

Maximum = 297

Count = 11

Sum = 2702

Quartiles Quartiles:

Q1 --> 217

Q2 --> 245

Q3 --> 255

Interquartile Range IQR = 38

Outliers = none

(d) The mid-range = 252

(e) The results are not likely to be representative because the championship team may not be representative of the entire league.

Therefore, all the required values are given above.

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Answer:

2×3³ + 3² - 3 = 60

Answer:

B. Jazz and opra

Step-by-step explanation:

40 percent of 55 is 22. Find whatever is equal to 22

B) Jazz & Opera music combo were chosen by 40% of people surveyed

Given : Total respondents = 55

So, 40% of total respondents = 40% of 55 = 22

County & Opera are chosen by 15 + 10 = total 25 respondents, ie not equal to 40%

Jazz & Opera are chosen by 12 + 10 = total 22 respondents, ie equal to 40%

Jazz, Opera, Rock & Country, Jazz, Rock are totally more respondents.

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Answer:

0.7703

Step-by-step explanation:

The easiest way to calculate this is to find the probability that none of the cubes show a 2. The probability that a cube doesn't show a 2 is 11/12.

\(\frac{11}{12} * \frac{11}{12} * \frac{11}{12} =\) 0.7703. Now we have to subtract this value from one which gives us 0.2297. Hope this helps

Answer:

The correct answer is 0.2297 (B)

Step-by-step explanation:

I just finished the Unit test review on Edge-The other person is wrong!!!

"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

To calculate the scores that are three standard deviations above and below the mean, we use the formula:

Lower limit = Mean - (Standard Deviation * 3)

Upper limit = Mean + (Standard Deviation * 3)

Given:

Mean = 269

Standard Deviation = 33

Using the formula, we can calculate the limits:

Lower limit = 269 - (33 * 3) = 269 - 99 = 170

Upper limit = 269 + (33 * 3) = 269 + 99 = 368

Therefore, the lower limit is 170 and the upper limit is 368.

To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.

Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.

For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:

Percentage = (1 - Probability) * 100

= (1 - 0.9972) * 100

= 0.0028 * 100

= 0.28%

Therefore, approximately 0.28% of the female students have scores below 302.

It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

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9514 1404 393

Answer:

  y = 0.4^(x+3) -2

Step-by-step explanation:

I have chosen the decay function y=0.4^x as the parent function.

Shifting any function f(x) left 3 and down 2 will transform it to ...

  y = f(x+3) -2

So, the shifted parent function is ...

  y = 0.4^(x+3) -2

Answer:

Hi what do you need help with

Answer:

Whats up?

Step-by-step explanation:

Answer:

When you solve it, the leading coefficient is 3.

Step-by-step explanation:

Combine Like Terms:

=5x+4+−2x+−1

=(5x+−2x)+(4+−1)

=3x+3

Hope it helps :)

Answer:

The coefficients are 5, 4, 2 and -1

Step-by-step explanation:

Coefficients are the whole numbers

Answer:

The answer would have came out of 3.84615384615

Then round up the answer to 3.85.  So the unit price is $3.85

The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:

Write the dividend and divisor in polynomial long division format:

_________________________

x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...

Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).

Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).

Subtract the result obtained in step 3 from the original dividend:

x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...

Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.

Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.

-3x^(2n-2) + 0x^(2n-3) + ... = -80

Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.

This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:

2n-2 = 0

2n = 2

n = 1

Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

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Step-by-step explanation:

y²+5y+6=0

y²+2y+3y+6=0

y(y+2)+3(y+2)=0

(y+2)(y+3)=0

:. y=2,3

option C.

hope this helps you.

Answer:

Step-by-step explanation:

Y^2+5y+6=0

5^2 - 4*2*6

25-48

23 i

-5 +4.79i =>   -0.21  =>      0.5i

2*2                     4

-5 +4.79i =>   -9.79  =>      2.44i

2*2                     4

spellings are incorect

The value of angle x is 161 degree. So the option B is correct.

In the given question, lines h and j are parallel and cut by transversal k.

We have to find the measure of angle x and choose the correct option.

The diagram of the given question is given below:

From the given diagram using the corresponding angle theorem

x = y

As we know that the angle of straight line is 180 degree.

So x+19 = 180

Subtract 19 on both side, we get;

x = 161 degree

Hence, the value of angle x is 161 degree. So the option B is correct.

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The requried, probability that both the first digit in the last digit of the three-digit number is even numbers is 20%.

To count the number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3, 5, 8, and 9, we can use the permutation formula:

P(n, r) = n! / (n-r)!

In this case, we have n = 6 (since we have 6 digits to choose from) and r = 3 (since we want to form three-digit numbers). Using the formula, we get:

P(6, 3) = 120

We can choose the first digit in two ways (2 or 8), and we can choose the last digit in three ways (2, 8, or 6). For the middle digit, we have four digits left to choose from (1, 3, 5, or 9), since we cannot repeat digits. Therefore, the number of three-digit numbers with distinct digits that have an even first and last digit is:

2 x 4 x 3 = 24

The total number of three-digit numbers with distinct digits is 120, so the probability that a randomly chosen three-digit number with distinct digits has an even first and last digit is:

24/120 = 0.2 or 20%

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Answer:

Step-by-step explanation:

3x = 90 + 46 - 14

3x = 122

x=\(\frac{122}{3}\)≈40,7

Answer: 40.6 repeated

Step-by-step explanation: combine -46 and 14 which is -32. then add 32 to 90. then divide 3 on both sides. 122/3 is 40.6 repeated

The order of operations (PEMDAS) states that we should perform multiplication and division before addition and subtraction. Using this order, we get:

244 - (33456 / 3456) * 345 + 13.55 - 2

= 244 - 97.02 * 345 + 13.55 - 2

= 244 - 33494.1 + 13.55 - 2

= -33238.55

Therefore, 244-33456/3456*345+13.55-2 = -33238.55.

Answer: 118

Step-by-step explanation:

Angle ABC and Angle BCD add up to 180 degrees, because Line AB and line CD are parallel. Because of this, Angle BCD can be moved up the the angle above 3n-47. Because the two angles fall on to a straight line, we can say that (3n-47)+(n+7)=180. Solving, n=55, so angle ABC equals 118 degrees.

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According to the given data the value is 22.

Addition is a basic mathematical operation that involves combining two or more numbers to get a total or sum. It is typically denoted by the symbol "+" and can be performed on a variety of numerical values, including whole numbers, decimals, fractions, and even negative numbers.

The value of the addition for 2+4+8+8=22

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Area of A = \(8 \cdot 2x = 16x\)

Area of B = \(8 \cdot x = 8x\)

Area of shape = Area of A + Area of B = \(16x + 8x\)

The area of the figure can be given from the expression 24x

What is the Area of a Rectangle?

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

The entire figure can be split into 2 figures of different length and width

Let the top figure be A and the bottom figure be B

So , Area of the figure = Area of A + Area of B

Now , the Length of B = 16

Width of B = x

Area of B = Length of B x Width of B

So , Area of B = 16x

And from figure , we can conclude that

Length of A = 16 - 8

                          = 8

And Width of B = x

Area of B = Length of B x Width of B

So , Area of B = 8x

Therefore , total area of figure = Area of A + Area of B

                                                   = 16x + 8x

                                                   = 24x

Hence , the area of the figure is 24x

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Answer:25 boys

Step-by-step explanation: look at pic below to see how solved.