The sum of two numbers is 25. One number
is twice the second number plus seven.
What are the two numbers?

Answer:

12x -7

Step-by-step explanation:

Answer:

96 hours

Step-by-step explanation:

25 eyes - 2 hours

1200 eyes* - x hours

\(x = \frac{2 \times 1200}{25} \)

\(x = 96\)

*each student has 2 eyes. So 600 students have 600×2=1200 eyes.

It will take the nurse 48 hours to give eye tests to all 600 students in her school.

An expression is combination of variables, numbers and operators.

If the nurse can give 25 eye tests in two hours, then she can give 12.5 tests in one hour (since 25 divided by 2 equals 12.5).

To give eye tests to all 600 students, the nurse will need to give 600 tests in total.

Using the rate of 12.5 tests per hour, we can set up a proportion:

12.5 tests / 1 hour = 600 tests / x hours

Apply Cross-multiplication

12.5 tests ×  x hours = 600 tests

Divide both sides by 12.5 tests

we get,  x hours = 600 tests / 12.5 tests per hour

x hours = 48 hours

Therefore, it will take the nurse 48 hours to give eye tests to all 600 students in her school.

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Therefore, the integral ∫ (3cos(8x) - 2sin(4x) + 2sec(tan(x))) dx cannot be expressed in terms of elementary functions.

To evaluate the integral ∫ (3cos(8x) - 2sin(4x) + 2sec(tan(x))) dx, we can simplify each term and then integrate term by term.

Let's start by simplifying each term:

∫ 3cos(8x) dx - ∫ 2sin(4x) dx + ∫ 2sec(tan(x)) dx

To integrate each term, we can use standard integration formulas:

∫ cos(ax) dx = (1/a) sin(ax) + C

∫ sin(ax) dx = -(1/a) cos(ax) + C

∫ sec²(u) du = tan(u) + C

Applying these formulas, we have:

(3/8) ∫ cos(8x) dx - (2/4) ∫ sin(4x) dx + 2 ∫ sec(tan(x)) dx

= (3/8) (1/8) sin(8x) - (1/2) (-1/4) cos(4x) + 2 ∫ sec(tan(x)) dx

= (3/64) sin(8x) + (1/8) cos(4x) + 2 ∫ sec(tan(x)) dx

Now, we need to evaluate the integral of sec(tan(x)) dx. This integral does not have a simple closed-form expression, so we cannot integrate it directly. It is often denoted as "non-elementary" or "special" integral.

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The cοrrect answer is 18. Ricardο's answer wοuld be incοrrect because he used curly braces instead οf square brackets and ignοred the missing οpening bracket.

Assuming the cοrrect expressiοn is 3x[(2x8)-6-4], we can simplify it using the οrder οf οperatiοns (PEMDAS) tο get:

3x[(16)-6-4]

3x[6]

= 18

Therefοre, the cοrrect answer is 18. Hοwever, if the missing bracket is nοt added and the expressiοn is evaluated as 3x{2x8-6-4], it wοuld be interpreted as: 3x[2x8-6-4] 3x[8] = 24

Thus, Ricardο's answer wοuld be incοrrect because he used curly braces instead οf square brackets and ignοred the missing οpening bracket. It's essential tο fοllοw the cοrrect syntax and οrder οf οperatiοns when evaluating mathematical expressiοns tο οbtain accurate results.

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Step-by-step explanation:

(4sin0 × 4sin0) +(4sin0 × -3cos0)+ (3cos0×4sin0) +(3cos0 × -3cos0)=

16 sin²0 - 12 sin0cos0 + 12 sin0cos0 -

9cos²0

= 16sin²0 - 9 cos²0

\(\\ \sf\longmapsto (4sin\theta+2cos\theta)(4sin\theta-3cos\theta)\)

\(\boxed{\sf (a+b)(a-b)=a^2-b^2}\)

\(\\ \sf\longmapsto (4sin\theta)^2-(3cos\theta)^2\)

\(\\ \sf\longmapsto 16sin^2\theta-9cos^2\theta\)

3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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Answer:

4) -11.3...

Step-by-step explanation:

distribute both sides to get (1/6)x - (4/3) = (4/15)x - (1/5)

move the variables to one side and the constants to the other: ((4/15) - (1/6))x = (-(4/3) + (1/5))

simplify to get (1/10)x = (-17/15) multiply everything by 10 to get x=-34/3 or -11.33333333333333333...

Answer:

option 4

Step-by-step explanation:

\(\frac{2}{3}\) (\(\frac{1}{4}\) x - 2) = \(\frac{1}{5}\) (\(\frac{4}{3}\) x - 1) ← distribute parenthesis on both sides

\(\frac{1}{6}\) x - \(\frac{4}{3}\) = \(\frac{4}{15}\) x - \(\frac{1}{5}\)

Multiply through by 30, the LCM of 6, 3, 15, 5

5x - 40 = 8x - 6 ( subtract 8x from both sides )

- 3x - 40 = - 6 ( add 40 to both sides )

- 3x = 34 ( divide both sides by - 3 )

x = - \(\frac{34}{3}\) = - 11.333..

The number formed by the digits 16, 06, and 68 is 160668, which is determined by concatenating them in the given order.

To determine the number formed by the given digits, we concatenate them in the given order. Starting with the first digit, we have 16. The next digit is 06, and finally, we have 68. By combining these three digits in order, we get the number 160668.

When concatenating the digits, the position of each digit is crucial. The placement of the digits determines the resulting number. In this case, the digits are arranged as 16, 06, and 68, and when they are concatenated, we obtain the number 160668. It's important to note that the leading zero in the digit 06 does not affect the value of the resulting number. When combining the digits, the leading zero is preserved as part of the number.

Therefore, the number formed by the digits 16, 06, and 68 is 160668.

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Answer:

21

Step-by-step explanation:

for the 42.

21×2=42

t t t t t t. t tt. t t t. r r r 4 4 4. r r r t t t t t t t t r r r r r r t. tt t t f f. re enne e r r r

Answer:

130 degrees

Step-by-step explanation:

2x+25+25=180

2x=130

Answer:

65°

Step-by-step explanation:

25+25+2x= 180(sum of all the angles of a triangle)

2x= 180-50

x=130/2= 65

Answer:

$3h

Step-by-step explanation:

w=$44+$12h

w=$35+$15h

$44+$12h=$35+$15h

         -12              -12

$44=$35+$3h

-35    -35

$9=3h

/3   /3

$3=h

Answer:

Step-by-step explanation:

\(A=(3+8)\cdot4+\frac12\cdot3\cdot2+\frac12\cdot3\cdot3=44+3+4,5=51.5\,ft\)

Answer:

17 feet

Step-by-step explanation:

We have to use the pythagorean theorem, this is actually a bit more complicated than it seems at a first glance.

If Tony is 8 feet to Lexi's right, then we can form a triangle as such

I can't paste it (sorry)

but we can use the formula a^2+b^2=c^2, so 15^2=225, and 8^2=64, and 225+64=289, and \(\sqrt289=17\)

so they're 17 feet apart!

A) The matrix equation that represents the given information is;

\(\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right]\) \(\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right]\)

B) The cost of a banana is; $0.05

The cost of an orange is; $0.12

A matrix equation is defined as an equation where a variable stands for a matrix .

Let x represent cost of oranges

Let y represent cost of bananas

5 oranges and 14 bananas cost me $1.30 and 8 oranges and 9 bananas

cost me $1.41. Thus, the equations are;

5x + 14y = 1.30  ----(1)

8x + 9y = 1.41   -----(2)

A) Now, the matrix form of the simultaneous equation above will be;

\(\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right]\) \(\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right]\)

B) Multiply the first equation by 8 and the second one by 5 to get;

40x + 112y = 10.4

40x +   45y = 7.05   Subtract to get;

            67y = 3.35

Divide both sides by 67 to get;

y = $0.05 per banana

Plug in 0.05 for y into eq 1 to get;

5x + 14(0.05) = 1.30

5x + 0.7 = 1.3

5x = 1.3 - 0.7

5x = 0.6

x = 0.6/5

x = $0.12

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The expression that correctly describes completing the square is;

Option C; x² + ax + (a/2)²

Let's say we have an expression;

x² + ax + c = 0

Let us first rearrange to get;

x² + ax = -c

Add (a/2)² to both sides to get;

x² + ax + (a/2)² = -c + (a/2)²

Thereafter, we can simplify the left hand side to give; (x + a/2)² = -c + (a/2)²

But from the given options, the only one with a corresponding step with what we have is option C which is x² + ax + (a/2)²

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A. numerical expression is a mathematical phrase containing numbers, at least one operation, and no variables.

Numerical expressions are those expressions that represent some mathematical process that has already been evaluated. Numeric expressions include only numbers and mathematical operations to perform on those numbers. A numerical expression is a mathematical expression that contains only numbers and arithmetic operations such as addition, subtraction, multiplication, and division.

A numerical expression is simply a combination of numbers and operational symbols that follows a certain pattern or rule. The expression may involve arithmetic operations, such as addition, subtraction, multiplication, or division. The expression may also involve multiple operations, such as the order of operations. A numerical expression cannot have any variables, which are used to represent unknown quantities.

Variables are letters that represent numbers or other values. They can be used in algebraic expressions to represent unknown quantities, such as x + 3 = 10. In contrast, numerical expressions use only numbers and mathematical symbols. An example of a numerical expression is 2 + 3 × 5. This expression evaluates to 17 because multiplication is performed before addition. Another example of a numerical expression is (4 + 6) ÷ 2, which evaluates to 5 because addition is performed before division. Therefore the correct option is  A

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Answer: ales revenue = 1,386,000 dollars Increase sales in percent = 10 percent Increase sales in dollars = 1,386,000 dollars * 0,1 = 138,600 dollars New sales goal in dollars = 1,386,000 dollars + 138,600 dollars = 1,524,600 dollars

New sales goal is 1,524,600 dollars.

Step-by-step explanation:

Answer:

  (b)  4

Step-by-step explanation:

You want the y-coordinate of point C on the line x=-3 so that ∆ABC has area 6 square units with segment AB being 6 units long.

The formula for the area of a triangle is ...

  A = 1/2bh

Given the base of 6 units, and area of 6 square units, we find the height to be ...

  6 = 1/2(6)h

  6/3 = h = 2

The height of the triangle is 2 units.

Point C is given as being on the line x=-3. Its y-coordinate must differ from the y-coordinates of A and B by 2 units. Those y-coordinates are 2, so the y-coordinate of C is ...

  2 ±2 = {4, 0}

Point C may have a y-coordinate of 0 or 4. The appropriate answer choice is 4.

The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

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When testing partial correlation, the impact of a third variable is removed.

Partial correlation is a statistical technique used to measure the relationship between two variables while controlling for the effect of one or more additional variables, known as "covariates" or "control variables." By removing the effect of the covariates, the partial correlation measures the direct relationship between the two variables of interest. This technique is useful when we want to examine the relationship between two variables after accounting for the effect of one or more confounding variables.

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The following a probability model? what do we call the outcome No, the provided information is not sufficient to determine if it is a probability model. The outcome "red" is typically referred to as an event.

A probability model is a mathematical representation of a random experiment, where the sample space is defined, and probabilities are assigned to all possible outcomes. To determine if the given information is a probability model, we would need to know the complete list of possible outcomes, their corresponding probabilities, and ensure that the probabilities meet the necessary conditions (sum up to 1 and are non-negative).

Based on the limited information provided, we cannot determine if it is a probability model. The outcome "red" is called an event in the context of probability.

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The rectangular coordinate for the polar coordinate (4, 210°) is  (-3.46, -2).

The rectangular coordinate for the polar coordinate (4, 210°) is calculated by applying the following formula as shown below;

x = r cos(θ)

y = r sin(θ)

where;

From the given  polar coordinate (4, 210°);

r = 4

θ = 210⁰

The rectangular coordinate is calculated as follows;

x = 4 x cos(210°)

y = 4 x sin(210°)

x = -3.46

y = -2

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A data of cases of diabetes from the centers for disease control and prevention, the probability that the combined sample tests positive with at least 1 of the 10 people having diabetes is equals to 0.04218.

We have a data from the centers for disease control and prevention.

The rate of new cases of diabetes

= 4.3 per 1000

So, probability ( diabetes) =\( \frac{4.3}{1000}\) = 0.0043

Using complement rule, Probability for no diabetes people, P( no diabetes)

= 1 - 0.0043 = 0.9957

Now, blood samples from 10 is randomly selected. It is assumed that each of these different people having diabetes is independent events. Using multiplcation rule for independent events, P( All 10 have no diabetes )

= P( no diabetes)× P( no diabetes)×....× P( no diabetes) ( 10 times)

= ( P( no diabetes))¹⁰ = 0.9957¹⁰

= 0.957823

Using complement rule, P ( atleast 1 the 10 people having diabetes) = 1 - P( All 10 have no diabetes ) = 1 - 0.957823

= 0.04218

Since, probability value is small so it is unlikely that a combined sample test. Hence, required probability is 0.04218.

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1.The machine will have no value after 48 months. 2.The graph of the machine's value over time will be a straight line. 3.The slope of the graph represents the rate of depreciation per month. 4.The intercepts of the graph indicate the initial value and zero value. 5.The expression V = -750x + 28,000 represents the value of the machine. 6.The machine has no value when x = 37 according to the expression. 7.The answer obtained using the expression differs from the answer in 8.question 1 due to possible rounding errors or calculation variations.

To determine when the machine has no value, we observe the pattern of depreciation. Based on the given data, the machine depreciates by $3,500 every 6 months. Therefore, it will take 48 months (8 cycles of 6 months) for the machine to have no value.

The table shows a consistent decrease in value over time with equal intervals of 6 months. This indicates a linear relationship between the number of months and the value. A linear relationship is represented by a straight line on a graph.

The slope of the graph can be determined by calculating the change in value divided by the change in time. In this case, the slope is (-750), meaning the value decreases by $750 per month. It represents the rate of depreciation per month.

The intercepts of the graph are obtained by determining the value of the machine at the start (initial value intercept) and when it reaches zero (zero value intercept). The initial value intercept is $28,000, which represents the starting value of the machine. The zero value intercept occurs when the machine has no value.

The expression V = -750x + 28,000 represents the value of the machine. The coefficient of x (-750) represents the rate of depreciation per month, while the constant term (28,000) represents the initial value.

Using the expression, when x = 37, the machine has no value. This differs from the answer in question 1 (48 months). The discrepancy could be due to rounding errors or variations in the method used to calculate the exact point at which the value reaches zero.

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Answer:

1/3

Step-by-step explanation:

Probability= expected/favored outcomes/total outcomes

there are 5 green marbles, and 15 in total.

So:

5 green (what we want) / 15 total

5/15 can simplify to:

1/3

Answer:

None of the given points satisfy the inequality 2x - 3y < 1.

Step-by-step explanation:

To determine which points satisfy the inequality 2x - 3y < 1, we can substitute the coordinates of each point into the inequality and check if the inequality holds true.

Let's consider the given points:

Point A: (1, 0)

2(1) - 3(0) < 1

2 - 0 < 1

2 < 1 (False)

Point B: (-1, -1)

2(-1) - 3(-1) < 1

-2 + 3 < 1

1 < 1 (False)

Point C: (3, -2)

2(3) - 3(-2) < 1

6 + 6 < 1

12 < 1 (False)

None of the given points satisfy the inequality 2x - 3y < 1.

Therefore, none of the points A, B, or C satisfy the inequality.

Answer:

Step-by-step explanation:

E

Answer:

answer is 32

Step-by-step explanation:

keep adding 3 to the figures and that is how you will get the answer

A triple bond consists of  d)1 sigma bond and 2 pi bonds.

In a triple bond, there is one sigma bond which is formed by the direct overlap of one s-orbital and one p-orbital. The remaining two bonds are pi bonds, formed by the lateral overlap of two p-orbitals. The pi bonds are oriented parallel to each other and perpendicular to the sigma bond.

Therefore, the number of sigma bonds in a triple bond is always 1, and the number of pi bonds is 2. This is true for all molecules that contain a triple bond, such as acetylene (C2H2) or nitrogen gas (N2).

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To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

Rearranging the equation, we get n = PV/RT.

Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.

Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.

To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:

1. Recall the ideal gas equation: PV = nRT

2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).

3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):

  n/V = (1.524 g/L) / (22.4 L/mol)

4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):

  M = (n/V) * (RT/P)

5. Substitute the values and solve for M:

  M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)

6. Calculate the molecular weight of the gas:

  M ≈ 32.0 g/mol

Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

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