The larger of two numbers is seven less than three times the smaller number. If the sum is 61, find the numbers.

The value of b, given the lines that are parallel in the figure, would be D. 27. 67.

Given that the lines are parallel, then we can infer that angles 92 degrees and ( 3b + 5 ) degrees are supplementary angles which means that they add up to 180 degrees.

We can therefore solve for b by equating the sum of both angles to 180 degrees as shown in the formula below :

92 + ( 3b + 5 ) = 180

92 + 5 + 3 b = 180

3b = 180 - 92 - 5

b = 83 / 3

b = 27. 67

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Answer:

the two triangles are similar

reasons are

(a) both are right angled triangles

(b) both are scalene triangles

Answer:

there are 431 females and 354 males in the class

Step-by-step explanation:

Let the number of females student in the class be x

Let the males by y

If there are 785 students in the senior class, then;

x+y = 785 .... 1

If there are 77 more females in  the class than males, then;

x = y+77 ....2

Substitute 2 into 1

y+77+y = 785

2y = 785 - 77

2y = 708

y = 708/2

y = 354

Since x = 785 - y

x = 785 - 354

x = 431

Hence there are 431 females and 354 males in the class

Step 1: The greatest common factor (GCF) in this equation is x^3. So we can factor it out:

y = x^3(x - 343)

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Step 2: We can not take root of a³ and b as there is no square term in the equation.

Step 3:

a= x^3

b= - 343

Step 4: Plugging in a and b into the original equation, we get

y = x^3(x - 343)

This is the simplified form of the equation.

So, the equation is a polynomial equation of degree 4, with the leading coefficient a = x^3 and the constant term b = -343, and it can be written as y = a(x-b) which is y = x^3(x-343)

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The bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.

What are scientific notations?

Scientific notations are a way of representing either a very small or a very large number in the powers of 10. Scientific notations comprise digits from 1 to 9 with powers of 10.

Calculation of the amount by which a bacterial cell is smaller than the amoeba cell

Given the length of amoeba cell in scientific notations is 3.5 × 10^(- 4)

The length of a bacterial cell in scientific notations is 5 × 10^(- 6)

To obtain how small the bacterial cell is from the amoeba cell, we need to divide both the lengths i.e.

= 3.5 × 10^(- 4) / 5 × 10^(- 6)

= 0.7 × 10^(2)

= 7 × 10^(1)

Hence, the bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.

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The value of the x is option b. 9√3.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given figure is a right angled triangle because it is marked in the figure.

For right angled triangle, we have the Pythagoras theorem,

Hypotenuse² = Base² +  Altitude²

Given,

Length of hypotenuse = 18

Length of base = 9

Substituting in the Pythagoras theorem,

18² = 9² + x²

x² = 18² - 9²

x² = 243

x² = 81 × 3

x = √(81 × 3)

x = 9√3

Hence the value of the unknown side is 9√3.

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The equation of the parabola in vertex form is y = (-1/12)(x + 3)^2 + 2, which opens downwards since the leading coefficient is negative.

The equation of the given parabola in vertex form is y = a(x + 3)^2 + 2, where a is a constant that depends on whether the parabola opens up or down.

To determine the value of a, we can use the fact that the parabola passes through (-7, 2/3). Substituting these values into the equation, we get:

2/3 = a(-7 + 3)^2 + 2

2/3 = 16a + 2

16a = -4/3

a = -1/12

Therefore, the equation of the parabola in vertex form is

y = (-1/12)(x + 3)^2 + 2.

The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, we are given that the vertex is (-3, 2), so we can write the equation as y = a(x + 3)^2 + 2.

To find the value of a, we use the fact that the parabola passes through (-7, 2/3). Substituting these values into the equation, we get 2/3 = a(-7 + 3)^2 + 2. Simplifying this equation, we get 2/3 = 16a + 2, which we can solve for a to get a = -1/12.

Therefore, the final equation of the parabola in vertex form is y = (-1/12)(x + 3)^2 + 2, which opens downwards since the leading coefficient is negative.

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We wοuld expect tο rοll a 5 apprοximately 500 times

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

The prοbability οf rοlling a 5 οn a fair die is 1/6. We can use this prοbability tο find the expected number οf times we wοuld rοll a 5 in 3000 rοlls.

The expected number οf times we wοuld rοll a 5 is equal tο the prοbability οf rοlling a 5 multiplied by the number οf rοlls. Sο, we have:

Expected number οf 5's = (prοbability οf rοlling a 5) x (number οf rοlls)

Expected number οf 5's = (1/6) x (3000)

Expected number οf 5's = 500

Therefοre, we wοuld expect tο rοll a 5 apprοximately 500 times when the dice is thrοwn 3000 times, based οn the given frequency chart.

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Answer:

My apologies if this is incorrect, but perhaps it is p=4.

3j+1≥10

Subtract 1 from both sides.

3j ≥ 9

Then divide both sides by 3.

j ≥ 3

The required length of the guy wire, to the nearest foot is 15 feet.

We can use the Pythagorean theorem to solve for the length of the guy wire. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we can consider the 7-foot pole, the 4-foot distance from the stake to the pole, and the guy wire as the sides of a right triangle. Therefore, the length of the guy wire (the hypotenuse) can be found using the formula:

c² = a² + b²

Where c is the length of the guy wire, a is the 4-foot distance from the stake to the pole, and b is the 14-foot distance from the pole to the tower. Plugging in the given values, we get:

c² = 4² + 14²

c² = 16 + 196

c² = 212

c = √212

c = 14.6

So, the length of the guy wire is approximately 14.6 feet, rounded to the nearest foot, which is 15 feet.

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Answer:

The answer for the nearest foot is 36ft long.

Step-by-step explanation:

So first we have to find the hypotenuse of the small triangle which is:

                                     \(a^{2}\)+\(b^{2}\)=  \(c^{2}\)

                                     \(7^{2}\)+\(4^{2}\)=\(c^{2}\)

                                     65 = \(c^{2}\)

                                     ±\(\sqrt{65}\)=\(\sqrt{c^{2} }\)​

                                     8.062... = c

Then we compare the small triangle to the big triangle:Compare the small triangle to the big triangle (in the photo link):

After that we set up a proportion and solve for x:Set up a proportion and solve for x which is:

                                     \(\frac{4}{18}\)=\(\frac{8.062}{x}\)

                                    \(4x\)=  145.120

                                    \(\frac{4x}{4}\)=\(\frac{145.120}{4}\)

                                   \(x=36.280\)

                                   \(x\)≈  36

The final answer is the guys wire is 36 ft long.

The table with the scale measurements is given by the image shown at the end of the answer.

The measurements are obtained applying the proportion given for each table.

The symbols are given as follows:

For the first table, we have that every inch on the table represents one feet in real life, hence:

For the second table, we have that every inch on the paper represents two feet in real life, hence the measurements are given as follows:

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Answer:

5/8

Step-by-step explanation:

Answer: The answer is 5/8. Try reducing using 58

Answer:

is approximately 10.092 units long.

Step-by-step explanation:

NM + ML = JL

Substituting the given values:

x + 5 + 6x + 2 = 24

7x + 7 = 24

Subtracting 7 from both sides:

7x = 17

Dividing by 7:

x = 2.43 (rounded to two decimal places)

Now that we know x, we can find the length of segment NM:

NM = x + 5

NM = 2.43 + 5

NM = 7.43

Finally, we can find the length of segment NL by using the Pythagorean theorem:

NL^2 = NM^2 + ML^2

Substituting the given values and the value we found for NM:

NL^2 = (7.43)^2 + (6x + 2)^2

NL^2 = 55.2049 + (6(2.43) + 2)^2

NL^2 = 55.2049 + 46.6564

NL^2 = 101.8613

Taking the square root of both sides:

Answer:

B

Step-by-step explanation:

Answer:

14-5=9, then 34 / 9 x 2, 9x2=18, 34 / 18= 1.888888 orrrr 34 / 9= 3.7777 that x 2 = 7.55555554

Answer:

20$ increasing every month

Step-by-step explanation:

This problem is a slope problem, so his cell phone plan increases by 20$ every month, so solve for slope

\(\frac{120-100}{2-1} =\frac{20}{1} =20\)

Answer:

\(\frac{14}{16}\) simplified to \(\frac{7}{8\\}\)

Step-by-step explanation:

\(\frac{7}{16} times \frac{2}{1} you get \frac{14}{16} \\this \\simplifies \\to \frac{7}{8}\)

Answer: -6x^2 + 3x + 4

Step-by-step explanation:

The result of the expression 4(2m - n) - 3(2m - n) for the variables m= -15 and n= -18 is -12

Given,

The algebraic expression = 4(2m - n) - 3(2m - n)

Expand the terms

4(2m - n) - 3(2m - n)= 8m-4n-6m+3n

Combine the like terms

8m-4n-6m+3n = 2m-n

We know,

m= -15

n= -18

Substitute the values in the expression

2m-n= 2(-15)-(-18)

=-30+18

= -12

Hence, the result of the expression 4(2m - n) - 3(2m - n) for the variables m= -15 and n= -18 is -12

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The variance of z = 3x + 10 is 18.

The variance of z = 3x + 10 can be found by using the formula for variance of a linear transformation of a random variable. The formula is: Var(aX + b) = a^2 * Var(X).

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.

Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value.

In this case, a = 3 and b = 10. Therefore, the variance of z = 3x + 10 is:

Var(z) = 3^2 * Var(x)
Var(z) = 9 * 2
Var(z) = 18.

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Answer:

= 5 ( 12d + 23f )

Step-by-step explanation:

-2(5d-9f)+7f-10(-9f-7d

Open parenthesis

= -10d + 18f + 7f + 90f + 70d

Collect like terms

= -10d + 70d + 18f + 7f + 90f

= 60d + 115f

Factorise

= 5 ( 12d + 23f )

Therefore,

-2(5d-9f)+7f-10(-9f-7d) in its simplest form is 5 ( 12d + 23f )

the answer for 135 times 12 is 1620

Answer:

1620

Step-by-step explanation:

u can time 12 by 135 or divide them

By finding the average rate of change, we can see that:

a) The cost decreases.

b) The cost increases.

To check that, we need to find the average rate of change on the interval.

Remember that for function f(x) on an interval (a, b), the average rate of change is:

R = (f(b) - f(a))/(b - a)

Here the cost function is:

c(n) = 0.25*n² - 10n + 800

a) In the interval [10, 15] the average rate of change is given by:

R = (c(15) - c(10)/(15 - 10)

Where:

c(15) = 0.25*15^2 - 10*15 + 800 = 706.25

c(10) = 0.25*10^2 - 10*10 + 800 = 725

Then the average rate of change is:

R = (706.25 - 725)/(15 - 10) = -3.75

This means that between 10 and 15 light fixtures, the cost is decreasing.

b) Now we have the interval [20, 25], so let's do the same ting:

c(20) = 0.25*20^2 - 10*20 + 800 = 700

c(25) = 0.25*25^2  - 10*25 + 800 = 706.25

Here the average rate of change is:

R = (706.25 - 700)/(25 - 20) = 1.25

It is positive, which means that the cost is increasing.

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The dissociation curve is a graphical representation of the relationship between the fractional saturation of hemoglobin (Y-axis) and the partial pressure of oxygen (X-axis) under specific conditions. It provides important information about the binding and release of oxygen by hemoglobin.

The dissociation curve for hemoglobin exhibits a sigmoidal (S-shaped) shape. At low partial pressures of oxygen, such as in tissues, hemoglobin has a low affinity for oxygen and only binds a small amount. As the partial pressure of oxygen increases, hemoglobin's affinity for oxygen increases, resulting in a rapid increase in the binding of oxygen molecules. However, once the hemoglobin becomes nearly saturated with oxygen, the curve levels off, indicating that further increases in partial pressure have minimal effects on oxygen binding.

To calculate the fractional saturation of hemoglobin at a given partial pressure of oxygen, you can use the Hill equation:

Y = [O2]^n / ([O2]^n + P50^n)

Where:

Y is the fractional saturation of hemoglobin,

[O2] is the partial pressure of oxygen,

P50 is the partial pressure of oxygen at which hemoglobin is 50% saturated,

n is the Hill coefficient, which represents the cooperativity of oxygen binding.

To determine the P50 value experimentally, the partial pressure of oxygen at which hemoglobin is 50% saturated, you can plot the dissociation curve and identify the point where the curve reaches 50% saturation.

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Answer:

y≤-1

Step-by-step explanation:

Subtract 9 from both sides

4-9 = -5

Divide the remainding by 5

-5 / 5 = -1

The correct option is Simple Linear Regression. Simple Linear Regression is NOT considered to be a Time-Series method of forecasting. The other methods are Time-Series method.

Time-Series analysis is a technique for forecasting future values based on previous observations. It includes various methods such as Moving Average, Exponential Smoothing, Seasonality Analysis, and Multiplicative/Additive Decomposition. Simple Linear Regression, on the other hand, is a method of predicting the relationship between two variables through a straight-line equation. Therefore, it is not considered to be a Time-Series method of forecasting.

A moving average is a common Time-Series method that calculates the average of a specific number of past observations to forecast future values. Exponential smoothing, another popular Time-Series method, assigns more weight to recent observations than to older ones. Seasonality analysis and multiplicative/additive decomposition are also Time-Series methods that are used to analyze trends and patterns in data over time.

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Answer:

55

Step-by-step explanation:

bedcause if you add 50 and 5 then it makes yes

The number of papers checked by both becomes equal in 10 hours.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Teacher Malone is reviewing papers in the educators' parlor. She has previously gotten done with reviewing 20 tasks and is evaluating 5 additional tasks each hour. Her showing colleague just came in to help her. He can grade at a pace of 7 tasks consistently.

Let 'x' be the number of hours and 'y' be the number of assignments. Then the equations are given as,

y = 5x + 20        ...1

y = 7x                ...2

At some point, they will be finished and will have graded the same number of papers. Then from equations 1 and 2, we have

7x = 5x + 20

7x - 5x = 20

2x = 20

x = 20 / 2

x = 10

The number of papers checked by both becomes equal in 10 hours.

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