Three consecutive integers have a sum of 48. Find the integers.

Answer: The quotient is when x+ 5x + 2 = 6

The reminder is when x+ 5x + 2 = -4  

Step-by-step explanation:

Given data,

The quotient and the remainder when x + 5x + 2 is divided by x + 1

Let, f(x) = x + 5x + 2

      g(x) = x+1

we can write,

   g(x) = x+1 = 0

   g(x) = x = -1

so,        f(x) = x + 5x + 2

we can substitute x = -1 value

             f(x) = x + 5x + 2

             f(-1) = (-1) + 5(-1) + 2

             f(-1) = (-1) - 5 + 2

              f(-1) = (-1) - 3

              f(-1) = -4

Therefore,

The quotient is when x+ 5x + 2 = 6

The reminder is when x+ 5x + 2 = -4        

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9514 1404 393

Answer:

  3/7

Step-by-step explanation:

The sum of a geometric series with first term a1 and common ratio r is ...

  S = a1/(1 -r)

For a1 = 3/4 and r = -3/4, the sum is ...

  S = (3/4)/(1 -(-3/4)) = (3/4)/(7/4) = 3/7

The sum of the series is 3/7.

_____

Additional comment

The terms rapidly decrease in value, so it doesn't take very many terms for the sum to reach the limit of precision available in most calculators. 100 terms are sufficient to give the sum to 12 significant digits.

Answer

248.3712

Step-by-step explanation:

2(H*W)+2(H*L)

2(5.78*6.72)+2(6.72*12.7)= 248.3712                                                                                                                  

1. A conditional statement can be written as

The hypothesis is: It is sunny

The conclusion is: there is daylight

2. The converse of the conditional statement

3. The inverse of the conditional statement

4. The contrapositive of the conditional statement

5. The biconditional statement and can be written because the statement and the converse are both true

6. The biconditional statement is

A conditional statement is a term used in logic that refers to the type of statement that has "if-then". It is sometimes called if-then statements. Conditional statement are of two parts the hypothesis required to ensure that the conclusion. Other forms of conditional statements are

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Given:

the price of $0.35 per kilogram of oranges is an increase of 25% on the previous days price

Required:

We need to find the price of previous day

Explanation:

25% increase is $0.35 so

to find the original value

Final answer:

The previous day price is $1.4

Answer: The question as written is incomplete, but square root of 82 is between the whole numbers 9 and 10, whose squares are 81 and 100

Answer:

Step-by-step explanation:

-2x - 6 = 2 - 4x - x + 1

-2x - 6 = 3 - 5x

3x - 6 = 3

3x = 9

x = 3

Answer: 75.67

Step-by-step explanation:

1) Area of a triangle: A=bh/2. Substitute: 12*8/2=96/2=48

2) Area of parallelgram: A=vertical height*base.

Substitute: 19*13= 247

3) Area of rectangle: A=bh. Substitute: 3.5*8.1=28.35

4) Area of penatgon: 5/2 x s x a when s is side of pentagon and a is apothem of pentagon. Substitute: 5/2*4*2.5=25

5) Area of trapezoid: (a+b/2)+h. Substitute: ((18+24)/2)+9=(42/2)+9=21+9=30

Mean formula: all numbers added together/number of values in list.

(48+247+28.35+25+30)/5=75.67

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If  an ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The  probability is:  84.6%.

In this case, we have:

Population standard deviation (σ): $1200

Sample size (n): 400

Margin of error (E): $80

The standard deviation of the sample mean can be calculated as:

σM = σ / √n = 1200 / √400 = 60

To find the probability that the sample mean is within $80 of the population mean, we need to find the z-scores for the upper and lower limits of the interval:

Lower limit: z = (mean - E - population mean) / σM = (-80) / 60 = -1.3333

Upper limit: z = (mean + E - population mean) / σM = 80 / 60 = 1.3333

Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:

P(-1.3333 < Z < 1.3333) = 0.8461

Therefore, the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.846 or 84.6%.

Interpretation: This means that if we take many samples of 400 railroad-car shipments of ethanol and calculate their mean tariff rates, about 84.6% of these means will be within $80 of the true mean tariff rate of all ethanol shipments. This also means that there is a sampling error of $80, which is the maximum amount by which the sample mean may differ from the population mean due to random sampling variability.

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Answer:

44 ft/s

Step-by-step explanation:

The function given in the table is an exponential function.

The function given in the table is clearly not linear, since the y value is changing rapidly.

Here we can see that the function value is changing as the multiplication of 7.

y = 7⁰ = 1, when x = 1

y = 7¹ = 7, when x = 2

y = 7² = 49, when x = 3

y = 7³ = 343, when x = 4

y = 7⁴ = 2401, when x = 5

So here the equation of the function can be written as,

y = 7ˣ⁻¹

Here the variable x is in the exponent.

So it is an exponential function.

Hence the given function is an exponential function.

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Answer:

1 1/5

Step-by-step explanation:

average book per week = the amount of books read / the amount of weeks

= 15/10 = 1 1/2

Answer:

m<S = 92°

Step-by-step explanation:

Opposite angels of a cyclic quadrilateral are supplementary. That is, they sum up to 180°.

<S and <Q are opposite angles of the cyclic quadrilateral given.

m<Q = 88°

Therefore,

m<Q + m<S = 180°

88° + m<S = 180° (substitution)

m<S = 180° - 88° (substraction property of equality)

m<S = 92°

Answer:

n=-9,-8,-7

Step-by-step explanation:

n<100

but that is the positive square root

\(-10 n is between the negative and positive square root of 100

thus, n=-9,-8,-7

The solution of the inequality n² < 100 will be less than 10.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The inequality is given below.

n² < 100

Simplify the equation, then we have

n² < 100

n² < 10²

n < 10

The solution of the inequality n² < 100 will be less than 10.

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Answer:

x = 4 and x = -4

x = 1 and x = -1

Step-by-step explanation:

let u = x^2

Then,

u^2-5u+4 = 0

(u - 4)(u - 1) = 0

u = 4 and u = 1

we substitute back for u

Then,

x^2 = 4

x = 4 and x = -4

x^2 = 1

x = 1 and x = -1

The solutions to the equation x⁴ - 5x² + 4 = 0 are x = ±2 and x = ±1.

To solve the equation x⁴ - 5x² + 4 = 0, we can use substitution to simplify it.

Let's take a new variable, u = x².

Substituting u into the equation, we get:

u² - 5u + 4 = 0

Now, we can factor this quadratic equation:

(u - 4)(u - 1) = 0

Setting each factor equal to zero, we have:

u - 4 = 0 or u - 1 = 0

Solving for u in each case:

u = 4 or u = 1

Now, we substitute back the original variable x:

For u = 4:

x² = 4

Taking the square root of both sides:

x = ±2

For u = 1:

x² = 1

Taking the square root of both sides:

x = ±1

Therefore, the solutions to the equation x⁴ - 5x² + 4 = 0 are x = ±2 and x = ±1.

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Answer:

The slopes along the y-axis are horizontal.

Step-by-step explanation:

The statement "The slopes along the y-axis are horizontal" is true based on the graph of the general solution to the differential equation dy/dx = 2x - 2y. This is because when x = 0, the slope of the solution curve is equal to -2y, which means the slope is horizontal or zero when y = 0.

The statement "The slopes along the x-axis are horizontal" is false because the slope of the solution curve at the point (0,0) is -2(0) = 0, which means the slope is horizontal at this point only.

The statement "The slopes are all positive in Quadrant 4" is false because the slope is negative in Quadrant 4.

The statement "The slopes are all positive in Quadrant 1" is false because the slope is negative in Quadrant 1.

Therefore, the only true statement is "The slopes along the y-axis are horizontal."

Answer:

<MAX = 93

Step-by-step explanation:

Since <MAX is technically <1 + <5, we know that <1 is 28 and <5 is 65. We can add both of these angles up to solve for <MAX, which is 28 + 65 = 93.

The angle of MAX is 93 degrees.

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

Since m∠MAX = m∠1 + m∠5,

we know that m∠1 = 28 and m∠5 = 65.

To solve for m∠MAX, which is 28 + 65 = 93.

Thus, the angle of MAX is 93 degrees.

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It will take Adrian 16 full months to save enough money for the electric keyboard.

- Price of the keyboard (with tax) at Macelli's: $2,400
- Adrian's monthly savings: $150
We need to find how long it will take Adrian to save for the keyboard. To do this, we'll divide the total cost of the keyboard by his monthly savings and round up to the nearest full month.
Step 1: Divide the total cost by monthly savings.
Time (in months) = (Total Cost) / (Monthly Savings) = ($2,400) / ($150)
Step 2: Calculate the result.
Time (in months) = 16
So, it will take Adrian 16 full months to save enough money for the electric keyboard.

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Answer:

1. ∠1 = 60

2. ∠2 = 40

3. ∠3 = 80

4. ∠4 = 80

5. ∠5 = 60

6. ∠6 = 120

7. ∠7 = 100

8. ∠8 = 60

9. ∠9 = 120

10. ∠10 = 100

Step-by-step explanation:

Answer:

Figure STOP is congruent to figure S′T′O′P′.

Step-by-step explanation:

I just took the test

Answer:

Figure STOP is congruent to figure S′T′O′P′.

Step-by-step explanation:

Just finished test and got 100%

The number of months it would take to recover the cost of the machines is 12 months.

Total cost of the four machines = $5700 x 4 = $22,800

The total salaries of the machine operators in t months = 4t x $1,00 = $4,400t

Total cost = $22,800 +  $4,400t

($750 x 2t) + ($650 x 3t) + ($950 x 3t)

= $1500t + $1,950t +$2,850t

= $6300t

$22,800 +  $4,400t  =  $6300t

Combine similar terms

$22,800 = $6300t - $4400t

$22,800 = $1900t

Divide both sides by 1900

t = 12 months

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Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then  R(t) = 20 + 1.6sin(2πt/5.2).

The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.

In this case, the amplitude is 1.6.

Since the radius changes by a maximum of 1.6 million miles.

The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)

The phase shift is 0, since when t = 0 the radius is increasing.

The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)

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Answer:

m<VRU = 80°

m<URW = 15°

Step-by-step explanation:

<SRW and <VRT are vertical opposite angles. Vertical opposite angles are equal. Therefore:

\( 2x + 15 = 85 \)

Use this expression to solve for the value of x

\( 2x + 15 - 15 = 85 - 15 \)

\( 2x = 70 \)

\( \frac{2x}{2} = \frac{70}{2} \)

\( x = 35 \)

Find m<VRU by plugging in the value of x in the expression for its angle given.

m<VRU = \( 2x + 10 \(

\( 2(35) + 10 = 70 + 10 = 80 \(

m<VRU = 80°

FIND m<URW.

m<URW = 180° - (m<VRU + m<SRW) (angles on a straight line is 180°)

m<URW = 180 - (80 + 85)

= 180 - 165

m<URW = 15°

The value of the fraction x/y is 3/25 and option b is the correct answer.

An expression for a portion of a whole is a fraction. In general, the whole can be any particular object or value, and the fraction might be a piece of any quantity out of it.

The top and bottom numbers of a fraction are explained by the fundamentals of fractions. The bottom number reflects the entire number of components, while the top number represents the number of chosen or coloured portions of the whole.

The given equation is:

5x + y / y = 8/5

Divide the terms individually at the left side of the equation:

5x/y + y/y = 8/5

5 (x/y) + 1 = 8/5

5 (x/y) = 8/5 - 1

5 (x/y) = 3/5

x/y = 3/25

Hence, the value of the fraction x/y is 3/25 and option b is the correct answer.

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Answer:

Quick answer option C

Step-by-step explanation:

\(\huge\sf\color{red}{Answer:}\)

My Solution:

The value of p is \(\large\sf\color{red}{39}\)

Hope it helps : )

The quotient of 2 3/4 divided by 4 1/2 is approximately 0.622222222.

The outcome of dividing two numbers is referred to mathematically as the quotient. It is the amount produced when a numerator is divided by a denominator.

For example, consider the expression "10 ÷ 2". 10 is the numerator, and 2 is the denominator. The quotient of this expression is 5. This has the following notation in mathematics:

10 ÷ 2 = 5

The quotient can also be a fraction, in which case it represents a ratio of two numbers. For instance, the fraction representation of the equation "5 2" is as follows:

5 ÷ 2 = 5/2

In this case, the quotient represents the ratio of 5 to 2.

The quotient is an important concept in mathematics, as it is used in many areas, including arithmetic, algebra, and calculus. It is used to solve problems involving division and ratios, and it is a basic building block for more advanced mathematical concepts.

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