Match the terms to their definition.
1. the constant preceding the variables in a product

2. a mathematical phrase that cannot be determined true or false

3. a numerical value expression

4. a mathematical expression containing one or more variables algebraic

5. a letter or symbol used to represent an unknown

1. variable
2. coefficent
3. expression
4. algebraic expression
5. constant​

(a) Isla's trading cards are 125% of Lily's trading cards.

(b) Lily's trading cards are 80% of Isla's trading cards.

Given that,

There are 225 trading cards and Lily has 180 trading cards.

To calculate the percentage of Isla's trading cards compared to Lily's,

We can use this formula:

⇒ Isla's trading cards / Lily's trading cards x 100%

Plugging in the values we get:

⇒ (225 / 180) x 100% = 125%

Therefore,

Isla's trading cards are 125% of Lily's trading cards.

b) To calculate the percentage of Lily's trading cards compared to Isla's, we can use the formula:

⇒ Lily's trading cards / Isla's trading cards x 100%

Plugging in the values we get:

(180 / 225) x 100% = 80%

Therefore,

Lily's trading cards are 80% of Isla's trading cards.

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Answer:

well 126/3 is 42. if 1/6 of those 42 kids that coach B had, 7 of those kids had medication. because 42 divided by 6 is 7 and only 1/6 of the kids had medication. (didn't understand exactly what you meant, hope this helps)

Step-by-step explanation:

6 chewy toys and 6 cat collars are needed to have the same amount or price at both stores.

An equation is an expression used to show the relationship between two or more angles and variables.

Let x represent the number of dogs and y represent the number of cats collars. Hence:

At Marco's market:

2x + 6y = 48 (1)

At Sonia's superstore:

4x + 4y = 48  (2)

Graphing both equations, the solution is at (6,6)

6 chewy toys and 6 cat collars are needed to have the same amount or price at both stores.

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Answer:

Confidence Level z*-value

90% 1.645 (by convention)

95% 1.96

98% 2.33

99% 2.58

Step-by-step explanation:

the difference in sample means is 0.1, and the upper end of the confidence interval is 0.1 + 0.1085 = 0.2085 while the lower end is 0.1 – 0.1085 = –0.0085.

Answer:

7

Step-by-step explanation:

66+(4x-4)=90

66+4x-4=90

62+4x. =90

4x. =28

x. =7

Answer:

18

Step-by-step explanation:

for f(3), x = 3

We should use the one where x ≥ 3

f(x) = 2x²

f(3) = 2 * 3²

= 2*9

=18

The best estimate of Joe's average speed is 4.125 meters per second (m/s).

To find the runner's average speed in meters per second, we need to divide the total distance he covered by the total time taken.

The total distance covered by Joe is 9.25 times the length of the track, which is 9.25 x 502.3 = 4646.775 meters (rounded to 3 decimal places).

The total time taken by Joe is 1,125.803 seconds.

Therefore, the average speed of Joe can be estimated as:

Average speed = Total distance covered / Total time taken

Average speed = 4646.775 / 1125.803

Average speed = 4.125 m/s (rounded to 3 decimal places)

So the best estimate of Joe's average speed is 4.125 meters per second (m/s).

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Euler's formula can be used to derive the trigonometric identities.

Euler's formula states that for any real number x, the complex exponential function can be represented as follows:

\(\[e^{ix} = \cos(x) + i\sin(x)\]\)

where \(e\) is the base of the natural logarithm, \(i\) is the imaginary unit, \(\cos(x)\) represents the cosine function, and \(\sin(x)\) represents the sine function. This formula provides a powerful connection between exponential functions and trigonometric functions.

To derive trigonometric identities using Euler's formula, we can start with the exponential form of Euler's formula and manipulate it algebraically. Let's consider the complex exponential function for two angles, \(x\) and \(y\):

\(\[e^{ix} \cdot e^{iy}\]\)

Using the properties of exponents, we can simplify this expression:

\(\[e^{ix} \cdot e^{iy} = e^{i(x + y)}\]\)

Now, applying Euler's formula to both sides, we get:

\(\[\cos(x) + i\sin(x) \cdot \cos(y) + i\sin(y) = \cos(x + y) + i\sin(x + y)\]\)

By comparing the real and imaginary parts of this equation, we obtain the sum and product formulas for cosine and sine:

\(\[\cos(x) \cdot \cos(y) - \sin(x) \cdot \sin(y) = \cos(x + y)\]\[\sin(x) \cdot \cos(y) + \cos(x) \cdot \sin(y) = \sin(x + y)\]\)

These are known as the angle addition formulas, and they form the basis for deriving other trigonometric identities. By manipulating and applying these formulas, we can establish relationships such as double-angle formulas, half-angle formulas, and more.

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Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

Answer:

c) x<2

Step-by-step explanation:

2x-1<3

add 1 to both side gets 2x<4

divide 2 to both sides gets x<2

Answer:

volume

of course, how much water is asking about the capacity of cylinder, meaning it's volume in this case.

For the system to have infinitely many solutions, the values of a and b must be a = 2 and b = 7 - 9x,

where x is any real number.

For the system to have infinitely many solutions, the equations must be dependent, which means that one equation can be obtained by multiplying the other equation by a constant and adding the two equations.

Let's start by multiplying the second equation by (2a-1)/3:

\((2a-1)/3 \times (3x + (b-1)y - 2) = (2a-1)/3 \times 0\)

This simplifies to:

\((2a-1)x + ((2a-1)(b-1))/3 y - (2a-1)(2/3) = 0\)

Now we can compare this equation with the first equation:

(2a-1)x + 3y - 5 = 0

We can see that the coefficients of x and y in both equations are equal if:

2a - 1 = (2a-1)(b-1)/3

3 = 2a - 1

Solving for a, we get a = 2.

Substituting a = 2 in the first equation, we get:

3y - 1 = 0

Solving for y, we get y = 1/3.

Substituting a = 2 and y = 1/3 in the second equation, we get:

3x + (b-1)(1/3) - 2 = 0

Simplifying, we get:

3x + (b-1)/3 - 2 = 0

Multiplying by 3 to eliminate the fraction:

9x + b - 1 - 6 = 0

9x + b - 7 = 0

Solving for b, we get b = 7 - 9x.

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To determine the values of a and b so that the system of linear equations has infinitely many solutions, we need to check whether the equations are dependent or independent. If the determinant is zero, then the equations are dependent.

     To have infinitely many solutions for this system of linear equations, both equations must represent the same line. Therefore, the ratios of the coefficients must be equal.

(1) (2a - 1) / 3 = 3 / (b - 1)
(2) 3 / (b - 1) = -5 / -2

Solve equation (2) for b:
3 / (b - 1) = 5 / 2
2 * 3 = 5 * (b - 1)
6 = 5b - 5
b = 11 / 5

Substitute b into equation (1):
(2a - 1) / 3 = 3 / (11 / 5 - 1)
(2a - 1) / 3 = 3 / (6 / 5)
(2a - 1) / 3 = 5 / 2

Solve for a:
2a - 1 = 5
2a = 6
a = 3

So, a = 3 and b = 11/5 for the system to have infinitely many solutions.

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Answer:

all you do is add

Step-by-step explanation:

Answer:

if u need to write an equation for it, it would be |2x-11| =7

Answer:

The gum returns to the wall each time the graph shows a minimum value of 6 (the height of the wall).

Count the number of minimums that occur between x = 0 ft and x = 60 (but omit the first time when x = 0).

The gum returns to the wall 9 times while traveling a distance of 60 feet.

edge2022 answer

hope it helps :)

mark brainliest!!

The graph is a periodic function that oscillates between 5 and 7.

The function completes about 9.55 cycles (or oscillations) as it travels a distance of 60 feet.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The graph is a periodic function that oscillates between 5 and 7.

Now,

To find the number of times the graph returns to the wall (i.e. the x-axis) as it travels a distance of 60 feet, you need to find the period of the function.

The period of the cosine function is 2π, which means the function completes one full cycle (i.e. one oscillation) every 2π units of x.

In the equation,

y = -cos(x) + 7, the coefficient of x is 1, which means that the function has not been horizontally compressed or stretched.

So the period of the function is still 2π.

To find the number of cycles completed in 60 feet, you need to find how many periods of the function fit in a distance of 60 feet.

And,

If you know the wavelength of the function, you can use that to find the number of cycles.

So,

The wavelength is the distance between two consecutive points on the graph that have the same value, such as two consecutive peaks or troughs.

To find the wavelength of y = -cos(x) + 7, you can use the fact that the amplitude (the distance between the peak and the trough) is 1.

So the distance between two consecutive peaks (or troughs) is 2.

The wavelength of the function is 2π, which means that the function completes one cycle every 2π units of x.

To find the number of cycles completed in 60 feet, you need to convert 60 feet to units of x.

Since the wavelength is 2π, one cycle corresponds to 2π units of x.

cycles = 60 / (2π) = 9.55

Thus,

The function completes about 9.55 cycles (or oscillations) as it travels a distance of 60 feet.

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∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Given:

Three lines AD, CF, and BE are intersecting each other at the midpoint O.

To prove:

∠CFA ≅ ∠EDA

Proof:

Given that AD, CF, and BE intersect at the midpoint O.

By definition of a midpoint, OA ≅ OD, OB ≅ OE.

OA = OD and OB = OE.

Triangle OAD ≅ Triangle OBE (By Side-Side-Side congruence).

∠OAD ≅ ∠OBE (By Corresponding Parts of Congruent Triangles are Congruent).

∠CFA and ∠EDA are vertical angles.

∠OAD ≅ ∠CFA and ∠OBE ≅ ∠EDA (By Vertical Angles are Congruent).

Therefore, ∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Hence, it is proven that ∠CFA ≅ ∠EDA.

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True response is that the function represented by the graph is Increasing on (-∞, 0) and decreasing on (0, ∞)

A function is said to be increasing in its domains if the value of its range is increasing in that domain.

Similarly, if the function is decreasing in its domain then it's range must be decreasing with the domain.

When the value of x(domain) is increasing on the left side. The value of y(range) is increasing constantly. But when the value of x increases further after 0, then the value of y is decreasing constantly.

So we can say, the following function represented on the graph is increasing in the interval of ( -∞,0) and decreasing in (0,∞).

As per the situation described in the graph the option third which say increasing on (×,0) and decreasing on (0,×).

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Yes, the figure shown in the xy-coordinate plane is a parallelogram because side OP is parallel to side TS and side OT is parallel to side PS

In order for any quadrilateral to be considered a parallelogram, two pairs of its parallel sides must be equal (congruent). Therefore, we would determine the slope of each side by using this mathematical equation:

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

For side OP, the slope is given by:

Slope (m) = (b - 0)/(a - 0)

Slope (m) = b/a.

For side TS, the slope is given by:

Slope (m) = (0 - )/(c - (a + c))

Slope (m) = -b/-a = b/a

Therefore, side OP is parallel to side TS.

For side OT, the slope is given by:

Slope (m) = (0 - 0)/(c - 0)

Slope (m) = 0.

For side PS, the slope is given by:

Slope (m) = (b - b)/((a + c) - c)

Slope (m) = 0

In conclusion, the figure shown above is a parallelogram because side OT is parallel to side PS and side OP is parallel to side TS.

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Answer:

1. 4

2. 11

3. 18

4. 25

Step-by-step explanation:

Answer:

The price of a child ticket in dollars $8.00

Step-by-step explanation:

Answer: 60

Step-by-step explanation:

From the question, we are informed that the ratio of BMX bikes in a sporting goods store to mountain bikes is 3 to 2 and that the store has 90 BMX bikes .

To calculate the number of mountain bikes that the store has goes thus:

= 2/3 × 90

= 2 × 30

= 60 mountain bikes

The probability is 0.96 that a randomly selected camper does not like to have a cookout, based on the given information and the complement rule of probability.

To determine the probability that a randomly selected camper does not like to have a cookout, we need to find the complement of the event C (the event that the camper likes to have a cookout).

Looking at the Venn diagram, we see that the probability of event C is 0.04 (represented by the intersection of circles C and A). Therefore, the probability of the complement of event C (not liking to have a cookout) is equal to 1 minus the probability of event C.

1 - 0.04 = 0.96

Hence, the probability that a randomly selected camper does not like to have a cookout is 0.96.

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To determine whether the number of customers, which is expected to be 15 each day, follows a uniform distribution, a chi-square test for goodness of fit should be performed with a specified significance level (alpha).

The chi-square test for goodness of fit is used to determine if observed data follows an expected distribution. In this case, we want to test whether the number of customers each day, which is expected to be 15, follows a uniform distribution.

To perform the test, we need to collect data on the number of customers over a period of time and compare it to the expected uniform distribution. The observed frequencies for each category (e.g., the number of days with 0 customers, 1 customer, 2 customers, etc.) would be obtained.

Then, the chi-square test statistic can be calculated based on the observed and expected frequencies. The test statistic measures the discrepancy between the observed and expected distributions.

To interpret the test results, we compare the calculated chi-square value to the critical chi-square value at the chosen significance level (alpha). If the calculated chi-square value exceeds the critical value, we reject the null hypothesis and conclude that the number of customers does not follow a uniform distribution. Conversely, if the calculated chi-square value does not exceed the critical value, we fail to reject the null hypothesis, indicating that the number of customers can be considered to follow a uniform distribution.

Please note that the specific calculations and decision-making process require additional data and the use of statistical software or tables to obtain the critical chi-square value.

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According to the tangent-chord theorem, when a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency.  The measure of CD is 60 degrees.

In the given diagram, we can observe that AB is a tangent to the circle at point B. According to the tangent-chord theorem, when a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency. Therefore, angle BCD is a right angle, measuring 90 degrees.

Since BCD is a right angle and angle ACD is given as 30 degrees, we can determine the measure of angle BCA by subtracting the sum of angles ACD and BCD from 180 degrees.

Angle BCA = 180 degrees - (30 degrees + 90 degrees) = 180 degrees - 120 degrees = 60 degrees.

Therefore, the measure of CD is 60 degrees.

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Enthalpy change (∆H) of the given reaction is -300 kJ/mol.

Let's discuss it further below.

In the given equation, 2 Xm3(g) reacts to produce 2 Xm2(g) and M2(g). The symbol "X" represents the element and "M" represents an inert gas like helium or neon.

The question is asking about the enthalpy change (∆H) of the given chemical reaction. The enthalpy change (∆H) is the amount of energy released or absorbed during a chemical reaction.

It can be calculated using the difference in the energy of the reactants and the products. If the enthalpy change is negative, the reaction is exothermic, and if the enthalpy change is positive, the reaction is endothermic. If the enthalpy change is zero, the reaction is said to be in equilibrium.

To determine the enthalpy change of the given reaction, we need to know the enthalpy of the reactants and the products. The enthalpy of a substance is its heat content at constant pressure.

The standard enthalpy of formation (∆H°f) is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states (∆H°f of the elements is zero).

The standard enthalpy of formation (∆H°f) of the reactants and products are given below:

∆H°f (Xm3(g)) = -300 kJ/mol∆H°f (Xm2(g)) = -450 kJ/mol∆H°f (M2(g)) = 0 kJ/mol

Now we can calculate the enthalpy change (∆H) of the given reaction using the formula:

∆H = Σ∆H°f (products) - Σ∆H°f (reactants)

where Σ represents the sum of the values.

∆H = [2(-450 kJ/mol) + 0 kJ/mol] - [2(-300 kJ/mol)]∆H = -900 kJ/mol + 600 kJ/mol∆H = -300 kJ/mol

Therefore, the enthalpy change (∆H) of the given reaction is -300 kJ/mol. This means that the reaction is exothermic, and energy is released during the reaction.

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\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the mirror reflection.

Since the image of triangle is reflected along Y-axis,hence the coordinates of N after 270° rotation are

N ==> ( 3,0)

===> Option D.) is correct

Answer:(3,0)

Step-by-step explanation:

D

For path A, the total distance traveled is 480 meters. The magnitude of displacement from start to finish is 240 meters, and the direction of the displacement is southeast.

To determine the total distance traveled along path A, we add up the lengths of all the individual segments. Path A consists of two horizontal segments followed by two vertical segments, each of which is 120 meters long.  the total distance is 2 * 120 + 2 * 120 = 480 meters.

To calculate the magnitude of the displacement, we consider the straight-line distance from the starting point to the ending point. In this case, the displacement is equal to the length of the hypotenuse of a right triangle formed by the horizontal and vertical segments of path A. Using the Pythagorean theorem, we find the displacement to be sqrt((120)^2 + (120)^2) ≈ 169.7 meters.

The direction of the displacement can be determined by finding the angle between the displacement vector and the positive x-axis. In this case, the angle can be determined using trigonometry as arctan(120/120) ≈ 45 degrees. Since the displacement is in the southeast direction, the direction can be stated as 45 degrees southeast.

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The confidence interval for estimating the mean sale price of homes in the neighborhood is made at a 95% level of reliability.

The confidence level for the given interval is 95%. This means that if the sampling and estimation process is repeated many times, the calculated interval will contain the true mean sale price of homes in the neighborhood 95% of the time.

The given printout already indicates a confidence level of 95%, which means that you can be 95% certain that the true mean sale price falls within the range of the lower limit (38,886.4) and the upper limit (54,113.6).

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Step-by-step explanation:

4^2+9^2=97

Magnitude=sqrt(97)

In simplified radical form, the magnitude of the vector (4, 9) is represented as √97.

To find the magnitude of a vector (a, b), you can use the formula which is expressed as:

Magnitude = √(a² + b²)

Given the vector (4, 9), let's calculate its magnitude as shown below:

Magnitude = √(4² + 9²)

Magnitude = √(16 + 81)

Magnitude = √97

So, the magnitude of the vector (4, 9) is √97 in simplified radical form.

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