The larger of two numbers is two more than five times the smaller number. If the sum of the two numbers is 80, find both numbers.​

Given phrase as numerical expression: 114 < -49

and the numerical expression is mathematically incorrect.

In this question, we have been given a phrase.

We need to write a numerical expression for the phrase and simplify.

Given phrase is: '114 less than -49'

We can write this in mathematical expression form as,

114 < -49

Now add 49 to both the sides.

114 +49 < -49 + 49

163 < 0

which is False.

Therefore, given phrase as numerical expression: 114 < -49

and the numerical expression is mathematically incorrect.

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Answer:

f=0.03b

Step-by-step explanation:

Amount of balance = b

Fee charged on balance = f = 3%

Amount of fee charged on balance  = 3% of amount of balance

Amount of fee charged = 0.03b

Thus,

f=0.03b

Content area the calculation for annual depreciation using the units-of-output method is yearly output.

What are the output method's units?

What is the annual depreciation formula?

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The probability that the driver has no accidents in the next 365 days, but then has at least one accident in the 365-day period that follows this initial 365-day period, is approximately 0.204.

Let X be the time until the next accident for the driver. We know that X is exponentially distributed with a mean of 200 days, which means that its probability density function (PDF) is:

\($f(x) = \frac{1}{200} e^{-\frac{x}{200}} \text{ for } x > 0$\)

We want to calculate the probability that the driver has no accidents in the next 365 days (i.e., from day 0 to day 365), but then has at least one accident in the 365-day period that follows (i.e., from day 366 to day 730). We can express this probability as:

P(no accidents in first 365 days) * P(at least one accident in next 365 days | no accidents in first 365 days)

The probability of having no accidents in the first 365 days is simply the cumulative distribution function (CDF) of X evaluated at x = 365:

\($F(365) = \int_{0}^{365} f(x) dx = 1 - e^{-\frac{365}{200}} \approx 0.451$\)

The probability of having at least one accident in the next 365 days, given that there were no accidents in the first 365 days, can be calculated using the memoryless property of the exponential distribution:

P(at least one accident in next 365 days | no accidents in first 365 days) = P(X < 365) = F(365) ≈ 0.451

Therefore, the probability we are interested in is:

P(no accidents in first 365 days) * P(at least one accident in next 365 days | no accidents in first 365 days)

= 0.451 * 0.451 ≈ 0.204

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Answer:

second option

Step-by-step explanation:

Given the 2 equations

y = \(\frac{2}{3}\) x + 2 → (1)

6x - 4y = - 10 → (2)

Substitute y = \(\frac{2}{3}\) x + 2 into (2)

6x - 4(\(\frac{2}{3}\) x + 2) = - 10 ← distribute parenthesis and simplify left side

6x - \(\frac{8}{3}\) x - 8 = - 10 ( multiply through by 3 to clear the fraction )

18x - 8x - 24 = - 30

10x - 24 = - 30 ( add 24 to both sides )

10x = - 6 ( divide both sides by 10 )

x = - 0.6

Substitute x = - 0.6 into (1) and evaluate for y

y = \(\frac{2}{3}\) × - 0.6 + 2 = 2x × - 0.2 + 2 = - 0.4 + 2 = 1.6

One Solution is (- 0.6, 1. 6 )

For solving the inequalities, there are more than four steps.

The step to solve given inequalities, the first step is to add the same number to both sides, the second step is to  Subtract the same number from both sides and the third step is to  Multiply both sides by the same positive number, and the fourth step is to  Divide both sides by the same positive number, and the fifth step is to Multiply both sides by the same negative number and reverse the sign and the last step is to Divide both sides by the same negative number and reverse the sign. Out of which steps 2,3,4 and 5 are the most important steps.

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The deposit amount need to be paid in option 1 with 20% of the cost is equal to R10,000.

Cost of a tv = R50,000

Option 1.

Deposit amount = 20% of the cost.

Balance to be paid in 36 months

Simple interest = 12% p.a.

Deposit amount

= 20% of R50,000

= 0.2 x R50,000

= R10,000

Now,

Let x be the balance amount that needs to be paid.

x = R50,000 - R10,000

⇒ x = R40,000

Simple Interest = ( Principal × Rate of interest × time ) / 100

Total amount to be paid = Principal + Simple Interest

= R40,000 + (R40,000 x 0.12 x 3)

= R40,000 + R14,400

= R54,400

Therefore, the deposit amount for option 1 as per the given details is equal to R10,000.

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Answer:

-1

Step-by-step explanation:

2x² - 5x + 7 is subtracted from x² + 2x - 11, so

(x² + 2x - 11) - (2x² - 5x + 7)

x² + 2x - 11 - 2x² + 5x -7 (Distribute the negative)

-x² + 7x - 18 (Combine like terms)

The leading coefficient is the coefficient of the first term, so it is -1.

Therefore, the arithmetic mean of the four-digit positive integers on Jake's list is 2222.

To find the arithmetic mean of the integers on Jake's list, we first need to determine the integers that satisfy the given property: the product of the four digits is 5.

Let's consider the possible combinations of four digits that multiply to give 5:

1 * 1 * 1 * 5 = 5

1 * 1 * 5 * 1 = 5

1 * 5 * 1 * 1 = 5

5 * 1 * 1 * 1 = 5

We can see that there are four possible combinations that satisfy the given condition. So, the four-digit positive integers that meet the criteria are:

1151, 1115, 1511, and 5111.

To find the arithmetic mean of these integers, we sum them up and divide by the total number of integers:

Arithmetic Mean = (1151 + 1115 + 1511 + 5111) / 4

Arithmetic Mean = 8888 / 4

Arithmetic Mean = 2222

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Answer:

8x-6

12x-9-4x+3

Step-by-step explanation:

12x-4x-9+3

=8x-6

Answer:

\( \sf \: 8x - 6 \)

Step-by-step explanation:

Given expression,

→ 12x - 9 - 4x + 3

Let's simplify the expression,

→ 12x - 9 - 4x + 3

→ (12x - 4x) + (-9 + 3)

→ (8x) + (-6)

→ 8x - 6

Hence, the answer is 8x - 6.

Answer:

here's your answer

Five years hence, A's age will be twice the age of B.. B's age = 10 years

please mark me as brainliest

1. 3 rows with 21 sneakers

2. D. 11*2

Answer:

I think the answer would be \(-\frac{73}{7}\)

Step-by-step explanation:

The expression for the volume of the pyramid is V = 2/9s^3

Volume of a pyramid

To find the volume of a pyramid, we multiply the area of its base with the height of the pyramid, and divide by 3. We express this product with the formula V=(1/3)×B×H, where B is the area of the base of the pyramid, and H is its height.

The volume of a pyramid is:

V=1/3(B)(H)

Where

B:Base = s^2

H:Height = 2/3s

Then:

V=1/3(B)(H) = 1/3(s^2)(2/3s) = 2/9s^3

Hence, the expression for the volume of the pyramid is V = 2/9s^3

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We will have the following equation representing the problem:

This is:

The life length in hours is exceeded by 95/5% of the light bulbs is 1329 hours.

To find the life length in hours that is exceeded by 95% of the light bulbs, we need to determine the corresponding z-score for the 95th percentile and use it to calculate the value.

Since the distribution is assumed to be normal, we can use the standard normal distribution (z-distribution) to find the z-score. The z-score represents the number of standard deviations an observation is above or below the mean.

To find the z-score corresponding to the 95th percentile, we look for the z-value that corresponds to a cumulative probability of 0.95. This value can be obtained from standard normal distribution tables or using a statistical software/tool.

For a cumulative probability of 0.95, the corresponding z-score is approximately 1.645.

Once we have the z-score, we can calculate the exceeded life length as follows:

Exceeded life length = Mean + (Z-score * Standard deviation)

Exceeded life length = 1000 + (1.645 * 200)

Exceeded life length ≈ 1000 + 329

Exceeded life length ≈ 1329 hours

Therefore, approximately 95% of the light bulbs will have a life length that exceeds 1329 hours.

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Using the normal distribution and the central limit theorem, we have that there is a:

a) 0.95 = 0.95% probability that the sample mean hardness for a random sample of 15 pins is at least 61.

b) 0% approximate probability that the sample mean hardness for a random sample of 50 pins is at least 61.

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

                 Z = x-μ/ σ

It measures the number of standard deviations between the measurements and the mean.

Once the z-score is found, we look at the z-score table and find the p-value associated with that z-score, i.e. the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = σ/√n

In this problem:

Mean of 50, hence μ = 6

Standard deviation of 1.2, hence σ = 1.8

Sample of 9, hence n =9, s = 1.8/√9 = 0.6

(i) Item a:

The probability is 1 subtracted by the p-value of Z when X = 51, hence:                                                                          Z = x-μ/ σ

By the Central Limit Theorem:

   Z = 61-60/0.6

⇒ Z = 1.6

⇒ Z = 1.6 has a p value of 0.05

Therefore,

1 - 0.05 = 0.95

There is a 0.95 = 0.95% probability that the sample mean hardness for a random sample of 15 pins is at least 61.

(ii) Item b:

Even though the distribution is not normal, the sample size is of

n = 61 > 50 , hence the Central Limit Theorem can be applied.

S = 1.8/√40

  = 0.28

Based on: Z = x-μ/ σ

Z = 61 - 60/ 0.19

Z = 5.26

Z = 5.26  has a p-value of 1.

Now,

1 - 1 = 0

0% approximate probability that the sample mean hardness for a random sample of 50 pins is at least 61.

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Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.

Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:

160B + 256C ≤ 6400c

Inequality stating that the engineer has at least 12 million pesos to spend for materials:

600B + 800C ≤ 12000d

. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C

Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.

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9514 1404 393

Answer:

  5 cups and 4 tbsp

Step-by-step explanation:

Double the quantity (2 c, 10 T) is ...

  2 × (2 c, 10 T) = (4 c, 20 T)

A cup is equal to 16 tablespoons, so this quantity can be rewritten as ...

  (5 c, 4 T)

Five cups and four tablespoons of flour are needed for the double recipe.

A relation R on Z is an equivalence relation if and only if it is reflexive, symmetric, and transitive. Specifically, in this case, xRy if and only if x^2+y^2 is even.

Reflexive: for any x in Z, x^2+x^2 is even, thus xRx. So, R is reflexive.

Symmetric: for any x,y in Z, if xRy, then x^2+y^2 is even, which implies y^2+x^2 is even, thus yRx. So, R is symmetric.

Transitive: for any x,y,z in Z, if xRy and yRz, then x^2+y^2 and y^2+z^2 are both even, thus x^2+z^2 is even, thus xRz. So, R is transitive.

Therefore, R is an equivalence relation.

To describe the equivalence classes, we need to find all the integers that are related to a given integer x under the relation R.

Let [x] denote the equivalence class of x.

For any integer x, we can observe that xR0 if and only if x^2 is even, which occurs when x is even.

Therefore, every even integer is related to 0 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any even integer x.

Similarly, for any odd integer x, we can observe that xR1 if and only if x^2 is odd, which occurs when x is odd. Therefore, every odd integer is related to 1 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any odd integer x.

In summary, the equivalence classes of R are of the form {x + 2k: k in Z}, where x is an integer and the parity of x determines whether the class contains all even or odd integers.

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Calculator with inverse tangent is a calculator with  four basic arithmetic operations and variety of functions such as logarithms, exponents, trigonometric functions etc.

A calculator with inverse tangent, commonly known as a scientific calculator, is a type of electronic calculator designed to perform mathematical calculations beyond basic arithmetic. In addition to the four basic arithmetic operations (addition, subtraction, multiplication, and division), it includes a variety of functions such as logarithms, exponents, trigonometric functions (sine, cosine, tangent), and their inverse functions (arcsine, arccosine, and arctangent).

The inverse tangent function, also known as arctangent, is one of the trigonometric functions that is commonly included in scientific calculators. It is used to determine the angle between the x-axis and a line drawn between the origin and a point on the graph of a function. In other words, it helps to find the angle whose tangent is a given number.

To use the inverse tangent function on a calculator, you will typically need to press the "tan^-1" or "arctan" button, followed by the number you want to find the arctangent of. The calculator will then display the angle in radians or degrees, depending on the mode it is set to.

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When two opposite sides of a rectangle increase in length, the other two opposite sides decrease in length if the area of the rectangle is to remain constant. Thus, option (B) is the correct answer.

How do I find the length of opposite sides of a rectangle?

In a rectangle, the opposite sides are of equal length. As a result, if you have the length of one side of a rectangle, you can find the length of the opposite side. Furthermore, if you know the length and width of a rectangle, you can find the area, perimeter, and diagonal of the rectangle.

The area of a rectangle is given by A = l × w,

where A represents the area, l represents the length, and w represents the width.

To find the length and width of a rectangle, use the formula A = l × w.

If you know the length of one side of a rectangle, you can calculate the length of the opposite side because the opposite sides of a rectangle are equal in length.

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Answer:

She is correct.

Step-by-step explanation:

She is correct.

Triangles QPS and QRS are congruent by SSS since all sides of one triangle are congruent to corresponding sides of the other triangle. Two pairs of sides are marked as congruent, and the third side, QS, is congruent to itself.

Then by CPCTC, angles P and R are congruent.

the derivative is 0, the slope of the tangent line is 0 at any point on the curve. Therefore, the equation of the tangent line at x = 1 is simply y = (-3)(-9+1) = 24.

To compute the derivative of y = (-3)(-9+1) using the product rule, we first label the two factors as u and v. Let u = -3 and v = -9+1 = -8. Then, we have:

y = u*v

y' = u*v' + u'*v

Using the chain rule, we can compute v' as the derivative of -8 multiplied by the derivative of (-9+1) with respect to x, which is 0. Therefore, v' = 0. We can also compute u' as the derivative of -3 with respect to x, which is also 0. Therefore, u' = 0.

Substituting these values into the product rule formula, we have:

y' = -3*0 + 0*(-8)

y' = 0

Thus, the derivative of y = (-3)(-9+1) is 0.

To find the equation of the tangent line at x = 1, we need to find the slope of the tangent line at that point. Since the derivative is 0, the slope of the tangent line is 0 at any point on the curve. Therefore, the equation of the tangent line at x = 1 is simply y = (-3)(-9+1) = 24.

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Answer:

178 m^2 first question answer by adding area of 2 rectangles,triangle

2nd question answer is x = 18 by using  similarity formula

and last one answer is 11 ft which is obtained by finding circumference of wheel pi * Diameter = 3.14*140 and then divided by (3.14*140)/40 cars = 10.99 ft == 11 ft

Step-by-step explanation:

Answer:

All your answers were correct!

Step-by-step explanation:

For the first problem, find the area of each part. The area of the rectangles would be (16m*8m) + (5m*6m) = 128m²+30m² = 158m². Next, tacking on the area of the triangle, then we have 158m² + (8m*5m)/2 = 158m²+20m² = 178m², so the first option is correct. Good job on getting it right!

For the second problem, assuming the parallelograms are similar, then we can set up a proportional equation to find the missing side, x:

12/x = 16/24

12*24 = 16x <-- Cross-Multiply

288 = 16x

18 = x

Looks like you got it correct again, good job!

For the third problem, it helps to first find the circumference of the Ferris wheel, which would be 2πr = 2(3.14)(140ft/2) = 439.6ft approximately. Now, since there are 40 cars, then the circumference can be split into 40 equal parts, so the distance between each one would be 439.6ft/40 = 10.99ft, which is basically 11ft. Hence, you got this one correct too, good job!

Hope the answers and explanations helped!

Answer:   \(d \ge 1 \ \text{ or } \ d \le -3\\\\\)

Both parts are needed to form the full solution set.

=============================================

Work Shown:

\(3|d+1|-7 \ge -1\\\\3|d+1| \ge 6\\\\|d+1| \ge 2\\\\d+1 \ge 2 \ \text{ or } \ d+1 \le -2\\\\d \ge 1 \ \text{ or } \ d \le -3\\\\\)

In the second step, I added 7 to both sides. In the third step, I divided both sides by 3. Afterward, I used the rule that \(|x| \ge k\) breaks down into \(x \ge k \ \text{ or } \ x \le -k\) for some positive value k. The last thing to do is to subtract 1 from both sides to fully isolate d.

An r value of 0 in a correlation analysis indicates that there is no linear relationship between the two quantities being analyzed.

This means that there is no correlation between the two variables, and any observed pattern or association between them is likely due to chance. In other words, the values of one variable do not predict the values of the other variable. However, it is important to note that a correlation analysis only measures linear relationships, and there may still be other types of relationships between the variables that are not captured by the r value.

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Answer:

7 2's

Step-by-step explanation:

2*2*2*2*2*2*2=128

Answer:

20.5 in.

Step-by-step explanation:

Just divide 82 by 4 to get the answer since  1 inch equals to 4 feet.

The graph shows the tides' behavior within a 24-hour period. Two high tides are visible with different amplitudes, and the relative height above the MLLW is not the same. Similarly, two low tides can be observed, with the lowest amplitude and lower amplitude having relative heights of 1 foot and 3.7 feet above the MLLW.

The tidal pattern in this graph is a mixed one, with two high and two low tides of different sizes. The maximum tidal range observed in this period is calculated as 5.2 feet by subtracting the height of the lower low tide from that of the higher high tide.

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Complete Question:

the chart below shows the predicted tide level during a 2-day period of time for crescent city, ca on july 24 and 25, 2007. answer the questions below based on the chart. how many high tides (or peaks) are there each day?