True or False
The formula to calculate average monthly expenditure is the sum of monthly expenditures divided by the number of months.

Answer:

∠2 and ∠5 are corresponding angles

Step-by-step explanation:

Answer:

corresponding angles

Step-by-step explanation:

198 of the 275 customers can be expected to prefer soda

A restaurant manger surveyed a random sample of costumers to determine which drink they prefer. Fourteen chose tea and 36 chose soda.

Based on the results , we have to find how many of the 275 customers can be expected to prefer soda?

total customers x = 275

customers chose soda y= 36

customers chose tea z= 14

therefore out of 275 customer who prefer soda = (x * y)/(y+z)

Based on the given conditions, formulate: \(: \frac{275 * 36}{14+36} \\\\\)

Calculate the product or quotient:\(\frac{9900}{14+36}\)

Calculate the sum or difference:\(\frac{9900}{50}\)

Cross out the common factor: \(198\)

Hence ,198 of the 275 customers can be expected to prefer soda

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Answer:

Divide

Step-by-step explanation:

Divide 24 into how many friends there are.

Answer:

8 * 3 = 24

Step-by-step explanation:

Answer:

The correct options are;

A. Let x equal the cost of a shirt and y equal the cost of a pair pants

B. Solve each equation for y

D. The solution is the point where the lines intersect

Step-by-step explanation:

The cost of two shirts and five pants = $150

Three shirts and four pairs of pants = $190

Let x = The cost of a shirt  and y = the cost of a pair of pants

We have;

2·x + 5·y = 150

3·x + 4·y = 190

We solve each equation for y, to get;

For the first equation, we have;

2·x + 5·y = 150

5·y = 150 - 2·x

y = 150/5 - 2/5·x = 30 - 2/5·x

y = 30 - 2/5·x

For the second equation, we have;

3·x + 4·y = 190

4·y = 190 - 3·x

y = 190/4 - 3/4·x = 47.5 - 3/4·x

y = 47.5 - 3/4·x

The solution is the point where the two lines intersect, which is given as follows;

y = y

47.5 - 3/4·x = 30 - 2/5·x

17.5 = 3/4·x - 2/5·x = 7/20·x

x = 20/7 × 17.5 = 50

The cost of a shirt = x = $50

The cost of a pair of pant = y = 30 - 2/5·x = 30 - 2/5 × 50 = 10

The cost of a pair of pant = $10.

Answer:

Step-by-step explanation:

       56

Answer:

Step-by-step explanation:

so you have 2 rectangles and you first need to find what the area is for the side opposite 25 which is 9 because the 2 9's are the same as the missing number.

now 16x9=144

and 9x9x9=729

725x25=18225

hope that helps

have a great day/night

19NBoli

Answer:

\(\boxed {v = -12}\)

Step-by-step explanation:

Solve for the value of \(v\):

\(v - 15 = -27\)

-Add both sides by \(15\):

\(v - 15 + 15 = -27 + 15\)

\(\boxed {v = -12}\)

Therefore, the value of \(v\) is \(-12\).

Answer:

a) A₁ = 18 unit²

b) A₂ = 20 unit²

c) A₃ = 12 unit²

d) A₄ = 12 unit²

Step-by-step explanation:

a) Given that the side length of square is 6 units, we have;

The height of the square = The height of the triangle = 6 units

The base of the triangle = The side length of the square = 6 units

The area of a triangle A₁ = 1/2×base×height = 1/2×6×6 = 18 unit²

b) The side of the square A₂ forms an hypotenuse side to the side length 2 and 4 on sides of the circumscribing square

The length of the side = √(4^2 + 2^2) = 2·√5

A₂ = The area of a square =Side² = (2·√5)² = 20 unit²

c) The base length of the triangle, A₃ + 2 = The side length of the circumscribing square = 6 units

∴ The base length of the triangle, ₃₂ = 6 - 2 = 4 units

The height of the triangle, A₃ = The  side length of the circumscribing square = 6 units

The area of a triangle A₃ = 1/2×base×height = 1/2×4×6 = 12 unit²

d) Figure, A₄, is a parallelogram;

The area of a parallelogram = Base × Height

The base of the parallelogram, A₄ + 4 = 6 units

Therefore, the base of the parallelogram, A₄ = 6 - 4 = 2 units

The height of the parallelogram = The  side length of the circumscribing square = 6 units

The area of a parallelogram A₄ = 2× 6 = 12 unit².

It is impossible to determine if 443 is a plausible value for the true average degree of polymerization.

The interval you mentioned might provide some information about the possible range of values for the true average degree of polymerization. However, it would depend on how the interval was calculated and what assumptions were made in the calculation.

In general, if the interval was calculated using a reliable and appropriate statistical method, and if the underlying data is representative and unbiased, then it is possible that 443 is a plausible value for the true average degree of polymerization. However, without more information about the context and the data, it is difficult to make any definitive conclusions.

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Answer:

The answer is b

Step-by-step explanation:

The distance traveled by the passenger train and the cattle train is equal to the total distance between them, which is 960 miles. Let x be the time (in hours) traveled by the passenger train and cattle train. Then, the equation that represents this situation is:

55x + 65x = 960

Simplifying the left-hand side of the equation, we get:

120x = 960

Dividing both sides by 120, we get:

x = 8

Therefore, the correct equation is:

B - 65x - 55x = 960

You can solve this equation by converting to standard form and using the formula for roots of quadratic equation.

The solution to given equation equation is \(x = \dfrac{-1 + \sqrt{37}}{2}\)

The standard form of quadratic equation is given by:

\(ax^2 + bx + c =0\)

The roots of this equation is obtained by:

\(x =\dfrac{-b \pm \sqrt{b^2 -4ac }}{2a}\)

We can take square on both sides to remove the root.

\(\sqrt{x+10} -1 =x\\ \sqrt{x+10} = x + 1\\ \\ \text{Taking square on both sides}\\ \\ x + 10 = (x + 1)^2\\ x + 10 = x^2 + 1 + 2x\\ x^2 + x - 9 = 0\\ \)

Know that we took square.

Also know that \((\sqrt{x+10})^2 = (-\sqrt{x+10})^2 = x+10\\ \) This is the reason that both roots we will obtain won't belong to our quadratic equation we obtained. Thus, we will have to check which root is correct solution of the obtained quadratic equation.

Now, comparing with standard form, we get a = 1, b = 1, c = -9, thus:
\(x = \dfrac{-1 \pm \sqrt{1 + 36}}{2} = \dfrac{-1\pm\sqrt{37}}{2}\)

x = 2.54 or x = -3.54

Putting both values, we get:

For x  =2.54:

\(\sqrt{x+10} -1 =x\\ \sqrt{2.54+10}-1 = 2.54\\ 2.5411 \approx 2.54\)

For x = -3.54

\(\sqrt{x+10} -1 =x\\\sqrt{-3.54+10}-1 = -3.54\\1.5411 \neq -3.54\)

Thus, the solution to given equation equation is \(x = \dfrac{-1 + \sqrt{37}}{2}\)

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Answer:

C. 500 ft

Step-by-step explanation:

If we want to make it all equal, we can divide the 2,000 ft by 4 because we have 4 equal descents.

2000 ÷ 4 = 500

He should travel 500 feet in each descent.

Answer:

Mia got 8 incorrect. She scored 72/80.

Step-by-step explanation:

On a surface analysis chart, the solid lines that depict sea level pressure patterns are called isobars.

Isobars are lines connecting points of equal atmospheric pressure at sea level. They provide a visual representation of pressure variations across a geographical area.

Isobars are typically displayed on weather maps to illustrate high and low pressure systems, as well as the strength and location of pressure gradients. High-pressure systems are indicated by circular isobars, while low-pressure systems are depicted by oval or elongated isobars.

By examining the spacing and configuration of isobars, meteorologists can interpret weather patterns and make predictions.

Areas with tightly packed isobars indicate strong pressure gradients, which signify strong winds and potentially severe weather conditions. On the other hand, widely spaced isobars suggest weaker pressure gradients and calmer weather.

Overall, isobars on a surface analysis chart are crucial in understanding and analyzing atmospheric pressure patterns and their implications on weather conditions.

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,

The given expression represents the z-score with an area to its right, indicating the probability of observing a value greater than the z-score.

The z-score, also known as the standard score, measures the distance between a given data point and the mean of a distribution in terms of standard deviations. It is calculated by subtracting the mean from the data point and dividing the result by the standard deviation. The resulting z-score represents the number of standard deviations a data point is away from the mean.

When we refer to the expression denoting the z-score with an area to its right, we are essentially talking about the cumulative probability associated with the z-score. This probability represents the area under the normal distribution curve to the right of the given z-score. In other words, it indicates the likelihood of observing a value greater than the z-score.

By utilizing statistical tables or software, we can determine the exact value of the area or probability associated with a given z-score. This information is useful in various applications, such as hypothesis testing, confidence intervals, and determining percentiles in a distribution. It allows us to make inferences and draw conclusions based on the relative position of a data point within a distribution.

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Answer:

f(x) = { u√(sin(1/x)) for x ≠ 0; 0 for x = 0 is not differentiable at x₀ = 0.

Step-by-step explanation:

To check the differentiability of the given functions at the point x₀ = 0 using the definition of derivative, we need to examine if the limit of the difference quotient exists as x approaches 0.

a) f(x) = x[x]

To check the differentiability of f(x) = x[x] at x₀ = 0, we evaluate the difference quotient:

f'(0) = lim┬(x→0)⁡〖(f(x) - f(0))/(x - 0)〗

      = lim┬(x→0)⁡〖(x[x] - 0)/(x - 0)〗

      = lim┬(x→0)⁡〖x[x]/x〗

      = lim┬(x→0)⁡〖[x]〗

As x approaches 0, the value of [x] changes discontinuously. Since the limit of [x] as x approaches 0 does not exist, the limit of the difference quotient does not exist as well. Therefore, f(x) = x[x] is not differentiable at x₀ = 0.

b) f(x) = |x|

To check the differentiability of f(x) = |x| at x₀ = 0, we evaluate the difference quotient:

f'(0) = lim┬(x→0)⁡〖(f(x) - f(0))/(x - 0)〗

      = lim┬(x→0)⁡(|x| - |0|)/(x - 0)〗

      = lim┬(x→0)⁡〖|x|/x〗

As x approaches 0 from the left (negative side), |x|/x = -1, and as x approaches 0 from the right (positive side), |x|/x = 1. Since the limit of |x|/x as x approaches 0 from both sides is different, the limit of the difference quotient does not exist. Therefore, f(x) = |x| is not differentiable at x₀ = 0.

c) f(x) = √(x)

To check the differentiability of f(x) = √(x) at x₀ = 0, we evaluate the difference quotient:

f'(0) = lim┬(x→0)⁡〖(f(x) - f(0))/(x - 0)〗

      = lim┬(x→0)⁡(√(x) - √(0))/(x - 0)〗

      = lim┬(x→0)⁡〖√(x)/x〗

To evaluate this limit, we can use the property of limits:

lim┬(x→0)⁡√(x)/x = lim┬(x→0)⁡(1/√(x)) / (1/x)

                = lim┬(x→0)⁡(1/√(x)) * (x/1)

                = lim┬(x→0)⁡√(x)

                = √(0)

                = 0

Therefore, f(x) = √(x) is differentiable at x₀ = 0, and the derivative f'(x) at x₀ = 0 is 0.

d) f(x) = { u√(sin(1/x)) for x ≠ 0; 0 for x = 0

To check the differentiability of

f(x) = { u√(sin(1/x)) for x ≠ 0; 0 for x = 0 at x₀ = 0, we evaluate the difference quotient:

f'(0) = lim┬(x→0)⁡〖(f(x) - f(0))/(x - 0)〗

      = lim┬(x→0)⁡{ u√(sin(1/x)) - 0)/(x - 0)〗

      = lim┬(x→0)⁡〖u√(sin(1/x))/x〗

As x approaches 0, sin(1/x) oscillates between -1 and 1, and u√(sin(1/x))/x takes various values depending on the path approaching 0. Therefore, the limit of the difference quotient does not exist.

Hence, f(x) = { u√(sin(1/x)) for x ≠ 0; 0 for x = 0 is not differentiable at x₀ = 0.

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The differential equation y' + 2y = 2ex does not have a solution in the form of y = 23ex - 8e-2x.

To check whether y = 23ex - 8e-2x is a solution of the differential equation y' + 2y = 2ex, we need to substitute y and y' into the differential equation and see if the equation holds.

First, we calculate y':

y' = d/dx (23ex - 8e-2x)

= 2(3ex) - 8(-2e-2x)

= 6ex + 16e-2x

Now, we substitute y and y' into the differential equation:

y' + 2y = (6ex + 16e-2x) + 2(23ex - 8e-2x)

Simplifying this expression, we get:

y' + 2y = 6ex + 46ex - 16e-2x

y' + 2y = 52ex - 16e-2x

So, to determine whether y = 23ex - 8e-2x is a solution of the differential equation y' + 2y = 2ex, we need to check whether y' + 2y = 2ex for all x.

Substituting x = 0, we get:

y'(0) + 2y(0) = (6e0 + 16e0) + 2(23e0 - 8e0) = 52 - 16 = 36

2ex(0) = 2e0 = 2

Since y'(0) + 2y(0) is not equal to 2ex(0), y = 23ex - 8e-2x is not a solution of the differential equation y' + 2y = 2ex.

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The system of equations that represent the situation are 1.20R + 2B = 70, and R + B = 90.

The system of equations are sets of equations that have to be solved simultaneously in order to determine their required values. They are often referred to as simultaneous equations.

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Answer:

6x + 25 ≤ 135

Step-by-step explanation:

Maximum amount to spend = $135

Boxes of popcorn = 2

Boxes of candy = 3

Cost per box of popcorn = $6

For 3 boxes = $6 * 3 = $18

Cost per box of candy = $3.50

For 2 boxes = $2 * 3.50 = $7

Item cost = Cost of candy and popcorn = $18 + $7 = $25

Ticket price = $6

Inequality to find number of friends ;

Let number of friends = x

Ticket cost = 6x

Hence ;

Ticket cost + item cost ≤ 135

6x + 25 ≤ 135

Answer:

6/9

Step-by-step explanation:

6 numbers including 29 are odd

The different ways that the students can elect a president and a vice president will be 13110.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

Given data;

Total no of students =  115

The total number of ways to elect a president = 115

If one person is elected as the president the total number of ways to elect a president  = 114

The different ways that the students can elect a president and a vice president are found as;

⇒ 115 ways × 114 ways

⇒ 13110 ways

Hence the different ways that the students can elect a president and a vice president will be 13110.

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Answer:

Step-by-step explanation:

See image

The points that has same quadrant as (2, –10) could Tamara use a number line to find the distance are (2, -9), (10, -10) and (7, -10)

The coordinates of the first point = (2, -10)

Using the number line we can only find the distance when the y coordinates or the x coordinates of the lines are equal

Here the first point is (2, -10)

The next point should be same quadrant, then the x coordinate will be positive and y coordinate will be negative

The points with same x coordinates = (2, -9)

The points with same y coordinates = (10, -10) and (7, -10)

Hence, the points that has same quadrant as (2, –10) could Tamara use a number line to find the distance are (2, -9), (10, -10) and (7, -10)

The complete question is

Tamara wants to find the distance from (2, –10) to other points. For which points in the same quadrant as (2, –10) could Tamara use a number line to find the distance? Check all that apply. (10, –10) (3, –2) (2, –9) (7, –10) (9, –2) (10, –2) (12, –1)

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Answer:

31.33 degrees

Step-by-step explanation:

The question is asking to find angle x.  You can use sine to find out x because sine is opposite/hypotenuse but since you are finding an angle measurement, it would be to the power of -1.  So:

sine^-1=13/25

31.33

Answer:

180 units

Step-by-step explanation:

In order to solve this, we need to find the length of the missing side of the triangle using the Pythagorean theorem.

a²+b²=c²

a= 7

b=x

c= 25

7²+x²=25²

49+x²=625

Subtract 49 from both sides

x²=576

x=24

The length of the missing side of the triangle is 24, which is also the base of the triangle. We need to find the area of the triangle so we use the formula for the area of a triangle, A=1/2bh.

A= 1/2 (24 x 7)

A=84

Now, we need to find the area of the rectangle.

Formula for area of rectangle: A= bh

A= bh

A= 4 x 24

A= 96

Next, we add the areas of both shapes to get the area of the entire figure.

96+84=180

Area of figure= 180

Answer:

area = 180

Step-by-step explanation:

will make it simple and short

area of a trapezoid = (a + b) h/2

h = sqrt(25² - 7²) = 24

Area = (4 + 11) * 24/2

area = 180

Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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Answer:

  a = -5

Step-by-step explanation:

You want the solution to the equation a -6/3 = -7.

The improper fraction -6/3 can be written as -2, so the equation is ...

  a -2 = -7

  a = -5 . . . . . . . add 2 to both sides

__

Additional comment

If you intend the equation to be ...

  (a -6)/3 = -7

The first step can be multiplication by 3:

  a -6 = -21

  a = -15 . . . . . . . add 6 to both sides

If the equation is typeset as ...

  \(\dfrac{a-6}{3}=-7\)

the fraction bar serves the purpose of grouping the terms of the numerator. When this is written in plain text, the typographic grouping clues are lost, and parentheses are needed.

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