Someone help me pls! Ill give brainliest!!Since the theme for the facts for February is mathematics, Clarita suggests that they write formal definitions of the three rigid-motion transformations they have been using to create the images for the flip-book animation. Carlos and Clarita used these words and phrases in their definitions: perpendicular bisector, center of rotation, equidistant, angle of rotation, concentric circles, parallel, image, pre- image, preserves distance and angle measures within the shape. Use the same words to complete the following definitions. A. A translation of a set of points in a plane. B. A rotation of a set of points in a plane. C. A refelctions of a set of points in a plane. D. Translations, rotations, and reflections are rigid motion transformations because

Answer: Let's assume the high temperature on Monday is represented by C30 (30 degrees Celsius). Since the pool is open when the high temperature is higher than 20 degrees Celsius, the pool was open on Monday.

However, over the next three days, the high temperature decreased at a constant rate. Let's denote the rate of decrease as "r" (in degrees Celsius per day).

Since the high temperature on Monday was C30, we can calculate the high temperature on Thursday by subtracting the decrease in temperature over three days:

High temperature on Thursday = C30 - 3r

We know that the pool was closed on Thursday, so the high temperature on Thursday must have been lower than or equal to 20 degrees Celsius.

Therefore, we can set up the inequality:

C30 - 3r ≤ 20

Now, we can solve this inequality to find the range of values for the rate of decrease (r) that would satisfy the condition:

C30 - 3r ≤ 20

Substituting C30 = 30, we have:

30 - 3r ≤ 20

Subtracting 30 from both sides:

-3r ≤ -10

Dividing by -3 (and reversing the inequality since we are dividing by a negative number):

r ≥ 10/3

Therefore, for the pool to be closed on Thursday, the rate of decrease in temperature (r) must be greater than or equal to 10/3 degrees Celsius per day.

The total number of customers refers to the sum or count of individuals or entities who have availed products or services from a business or organization. It represents the overall customer base of a company.

The given information is that 144 customers rated the shop as being "very satisfactory." This number represented 50% of the total number of customers who took the survey.

To find out the total number of customers who took the survey, we will need to use the concept of proportions.The proportion can be set up as follows:

[tex]\frac{x}{100} = \frac{144}{50}[/tex]

Here, x represents the total number of customers who took the survey.Cross-multiplying,

50x = 14400

[tex]x = \frac{14400}{50}[/tex]

x = 288

Therefore, the total number of customers who took the survey is 288.

Therefore, the total number of customers who took the survey is 288 and the required answer is written in 91 words.

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It takes about 2.28 seconds for the ball to hit the ground. Hence, the answer is option (3) 2.28 seconds.

The function H(t) = -16t² + 73t + 6 represents the height in feet of the baseball thrown by Amir as a function of time t in seconds.

To determine how long it takes for the ball to hit the ground, we need to find the value of t when H(t) = 0 (since the ball is on the ground when its height is zero).

Therefore, we have to solve the quadratic equation:

[tex]$$-16t^2 + 73t + 6 = 0$$[/tex]

We can use the quadratic formula:

[tex]$$t = \frac{-b \pm \sqrt{b^2-4ac}}[/tex]

where a = -16, b = 73, and c = 6.

Substituting the values in the formula, we have:

[tex]$$t = \frac{-73 \pm \sqrt{73^2 - 4(-16)(6)}}$$$$t = \frac{-73 \pm \sqrt{5329 + 384}}$$$$t = (\frac{-73 \pm \sqrt{5713})}[/tex]

Since we're interested in the positive value of t, we take:

[tex]$$t = \frac{-73 + \sqrt{5713}} \boxed{2.28} \; \text{seconds}$$[/tex]

Therefore, it takes about 2.28 seconds for the ball to hit the ground. Hence, the answer is option (3) 2.28 seconds.

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Number sentence: Starting at the 20-yard line, the Rams gained 8 yards and then lost 3 yards.

The Rams gained 8 yards, which means they advanced to the 28-yard line (20 + 8). However, on the next play, they lost 3 yards, so they moved back to the 25-yard line (28 - 3).

The Rams started at their own 20-yard line. After a run, they gained 8 yards, moving them to the 28-yard line. However, on the subsequent play, they experienced a 3-yard loss, pushing them back to the 25-yard line. Therefore, their field position after the two plays is the 25-yard line.

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a. The top of the ladder is moving down at 5/12 ft/s.

b. The area enclosed is changing at -25/24 sq ft/s.

c. The angle is changing at approximately -0.347 radians per second.

a. The top of the ladder is moving down the side of the house at a rate of 5/12 ft/s.

Using the Pythagorean theorem, differentiate

[tex]x^2 + y^2 = 13^2. At y = 12, x = √(13^2 - 12^2) = 5.[/tex]

Solve for dy/dt to get -5/12 ft/s.

b. The rate of change of the enclosed area is 24/5 sq ft/s.

Differentiate the area formula

[tex]A = (1/2)xy. At y = 12, x = 5.[/tex]

Substitute these values and differentiate with respect to time to get [tex]dA/dt = (1/2)(5)(-5/12) = -25/24 sq ft/s.[/tex]

c. The rate of change of the angle is approximately -0.347 radians per second.

Use trigonometry to

[tex]find θ = arctan(y/x). At y = 12, x = 5, so θ ≈ arctan(12/5) ≈ 1.176[/tex] radians. Differentiate with respect to time to find dθ/dt = -5/144π radians/s.

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The answer is option d, at least 10 pants. To determine the minimum number of pants Nina can buy with Php8,000.00, considering the discounted price of t-shirts (Php150.00) and the price of pants (Php600.00), we need to calculate how many t-shirts she can buy and subtract the total cost of t-shirts from the available budget.

Then, we divide the remaining budget by the price of pants to find the minimum number of pants she can afford. Since Nina needs to order at least 30 t-shirts to avail the discount, let's calculate the cost of buying 30 t-shirts. The discounted price per t-shirt is Php150.00, so the total cost of 30 t-shirts would be 30 x Php150.00 = Php4,500.00.

To determine the remaining budget after purchasing the t-shirts, we subtract the total cost of t-shirts from the available budget: Php8,000.00 - Php4,500.00 = Php3,500.00.

Now, we divide the remaining budget by the price of pants (Php600.00) to find the minimum number of pants Nina can buy: Php3,500.00 ÷ Php600.00 = 5.83.

Since Nina cannot buy a fraction of a pant, we round down to the nearest whole number. Therefore, Nina can buy at least 5 pants with the remaining budget.

Adding the minimum number of t-shirts (30) to the minimum number of pants (5), we get a total of 35 items. However, since the question asks for the minimum number of pants only, the answer is at least 10 pants, which is option d.

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Larry, Mary and Jerry's statements on the probability of drawing ping pong balls:.the probability of drawing a ping pong ball with an odd number, keeping it, and then drawing a yellow ping pong ball is 5/29.

Thus, there are 60 ping pong balls in total.Larry says the probability of drawing a blue ping pong ball, keeping it, and then drawing a ping pong ball with a 5 or a 6 is the greatest.Probability of drawing a blue ball: P(B) = 10/60 = 1/6Probability of drawing a 5 or 6, given that a blue ball has already been drawn: P(5 or 6 | B) = 2/9Probability of the desired outcome: P(B and (5 or 6)) = P(B) × P(5 or 6 | B) = (1/6) × (2/9) = 1/27

Mary says the probability of drawing a ping pong ball with an odd number, keeping it, and then drawing a yellow ping pong ball is greatest.Probability of drawing an odd number: P(O) = 30/60 = 1/2Probability of drawing a yellow ball, given that an odd-numbered ball has already been drawn: P(Y | O) = 10/29Probability of the desired outcome: P(O and Y) = P(O) × P(Y | O) = (1/2) × (10/29) = 5/29

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The angle of the quadrilateral z is 50°

We have the four angles of a quadrilateral.

The  vertices of the four angles are:

w, x, y , z

The angles of the vertices are:

w = 110

x = 120

y = 80

We have to find the angle of z.

Now, According to the question:

Since, sum of angles of a quadrilateral is 360∘ .

Then, w + x + y + z = 360°

Plug all the values:

110 + 120 + 80 + z = 360

310 + z = 360

z = 360 - 310

z = 50°

Hence, The angle of the quadrilateral z is 50°.

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Tom's house is approximately 1.08 inches away from the beach on the map. Tom's house is approximately 1.08 inches away from the beach on the map.

Let x represent the distance on the map. We can set up the proportion as follows:

½ inch / 3 miles = x inches / 65 miles

Cross-multiplying, we get:

3 miles * x inches = ½ inch * 65 miles

Simplifying, we find:

3x = 32.5

Dividing both sides by 3, we get:

x = 10.83 inches

Rounding to the nearest hundredth, Tom's house is approximately 1.08 inches away from the beach on the map. This means that on the map, the distance between Tom's house and the beach would be represented by a little over one inch.

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The equation for the speed of blood is -0.25t + 6.3.

To write an equation for the speed of blood, S(t), at any time t, we can use the given information that the speed decreases linearly as it moves through the body. Let's break down the problem and construct the equation step by step.

The blood exits the heart at a speed of 6.3 miles per hour. So at t = 0 (the starting point), the speed of the blood is 6.3 miles per hour.

The speed of the blood decreases by 0.25 miles per hour for every unit increase in time t. This indicates a linear decrease in speed.

Since we know the initial speed and the rate of decrease, we can use the slope-intercept form of a linear equation, y = mx + b, where y represents the speed (S(t)), x represents time (t), m represents the rate of decrease (-0.25 miles per hour), and b represents the initial speed (6.3 miles per hour).

Combining all these elements, the equation for the speed of blood at any time t is:

S(t) = -0.25t + 6.3

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The equation that represents the relationship between the number of months (x) and the total cost of membership (y) at Yogi's Yoga Studio is y = 79 + 45x.

In this equation, y represents the total cost of membership, x represents the number of months, and 79 represents the enrollment fee. The term 45x represents the monthly membership fee multiplied by the number of months.

To understand this equation, let's consider an example. Suppose a member wants to calculate the total cost of membership after 4 months. Plugging x = 4 into the equation, we have:

y = 79 + 45(4)

y = 79 + 180

y = 259

So, after 4 months, the total cost of membership would be $259, which includes the initial enrollment fee of $79 and 4 months of the monthly fee at $45 per month.

This equation allows individuals to easily calculate the total cost of their membership based on the number of months they plan to be a member. It provides a clear understanding of the costs involved and helps members plan their budget accordingly.

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Shape C, a complicated shape, needs to be divided into simpler shapes in order to calculate its area. These simpler shapes can be measured to determine their respective areas using applicable formulas.

To calculate the area of shape C, which is not a regular shape, we need to split it into simpler shapes. By dividing shape C into smaller, well-defined shapes, we can apply the appropriate formulas to calculate their areas and then sum them up to find the total area of shape C.

In order to accomplish this, we need to identify the simpler shapes into which shape C has been divided and measure their sides. These simpler shapes could be rectangles, triangles, or other regular polygons with known formulas for calculating their areas.

Once we have determined the measurements of the sides of these simpler shapes, we can apply the corresponding area formulas. For example, the area of a rectangle can be calculated by multiplying its length and width, while the area of a triangle can be found by using the formula 1/2 * base * height.

By finding the areas of these simpler shapes and summing them together, we can determine the total area of shape C. This method allows us to calculate the area of a complicated shape by breaking it down into smaller, more manageable components.

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Let's start with the given expressions: Expression 1: 25(h + 36)Expression 2: 2(-10h + 1,300) + 10Now, we need to find the maximum number of hours the amusement park thinks the crew will need to complete this job represented by the variable h.

The amount that the park has budgeted to complete this job is represented by the expression 2(-10h + 1,300) + 10. To get the budgeted amount, we can simplify the above expression as follows:2(-10h + 1,300) + 10= -20h + 2,620The budgeted amount is represented by -20h + 2,620We need to compare this budgeted amount to the cost of the painting supplies and the labor to repaint the railings which is represented by 25(h + 36).

Therefore, the inequality that represents how many hours, at most, the amusement park has allotted to repaint the safety railings is given by:-20h + 2,620 ≤ 25(h + 36)Simplifying the above expression: -20h + 2,620 ≤ 25h + 900Hence, the solution is: -20h - 25h ≤ 900 - 2,620 => -45h ≤ -1720Divide by -45 on both sides: h ≥ 38.22Hence, the maximum number of hours the amusement park has allotted to repaint the safety railings is 38.22 hours.

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The cost for new customers who are entitled to the 10% discount is $99 per month.

The Cable Company offers cable for $110 a month but gives a 10% discount for new customers.

To find the cost for new customers, we will have to subtract the 10% discount from the original cost of $110 per month.

So, we will have to multiply the original cost by the percentage of the discount which is 10%.10% of 110 = (10/100) * 110= 11

Therefore, the discount offered by the company is $11.

Now, we will have to subtract the discount from the original cost:

Cost for new customers = $110 - $11 = $99

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Answer:

Option C

Step-by-step explanation:

Absolute value of an expression can never be a negative integer. So, no solution.

Absolute value of an expression can be zero or positive.

The answer is:

Work/explanation:

We must recall that |x| means the absolute value of x.

Absolute value means the distance from zero. Distance cannot be negative, so neither can absolute value.

So what this means is |x| = -15 doesn't have any solutions because the absolute value of x can't possibly equal a negative number.

The values for each blank is:

1. x

2. y

3. 4

4. 4

1. Change f(x) to y the  the result will be

y = √(x-4)

2. switch x and y, then solve for y

then, x = √y-4

x² = y-4

x² + 4 = y

3. Now change y to [tex]f^{-1}[/tex](x)

then  [tex]f^{-1}[/tex](x) = x² + 4

4. Since, the original function is defined only for x - 4 ≥ 0, you solve for x and get x ≥ 4.

Hence, the final blank is 4.

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The question attached here seems to be incomplete the complete question here:

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

consider the given function: f(x)= √x-4

To determine the inverse of the given function, change f(x) to y, switch______ and y, and solve for ______.

The resulting function can be written as (f) to the power of -1(x)=x squared + ______, where x is greater than or equal to ______.

Jose works a total of 35 hours per week during the summer, which is 175% more than his regular work hours during the school year.

During the school year, Jose works 20 hours per week. To calculate how many hours he works during the summer, we need to find 175% of his regular work hours.

To calculate 175% of a value, we multiply the value by 1.75. So, 175% of 20 hours is calculated as follows:

175% * 20 hours = (175/100) * 20 hours = 35 hours

Therefore, during the summer, Jose works 35 hours per week. This is an increase of 175% compared to his regular work hours during the school year.

In other words, the 175% increase means that Jose's work hours in the summer are 1.75 times his regular work hours. This can also be calculated as follows:

Regular work hours during the school year + 175% increase = 20 hours + (175/100) * 20 hours = 20 hours + 35 hours = 35 hours

So, Jose works a total of 35 hours per week during the summer, which is 175% more than his regular work hours during the school year.

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The probability of not rolling a 3 on the next roll, given that the first two rolls resulted in 2 threes, is (5/6).

Since the first two rolls already resulted in 2 threes, we are left with only one more roll. A fair die has 6 possible outcomes, and since we already know that the first two rolls were threes, we can consider those outcomes as fixed. Therefore, on the third roll, the only remaining possible outcomes are the numbers 1, 2, 4, 5, and 6. Out of these 5 remaining outcomes, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1 out of 5, which can be expressed as a fraction as 1/5. Simplifying this fraction further, we get 1/5 = 1/6. Therefore, the correct answer is (5/6).

Since the first two rolls resulted in 2 threes, out of the remaining 5 possible outcomes on the third roll, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1/5 or 1/6, which is equivalent to (5/6).

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We need to consider that each kitten is fed half as much as a full-grown cat. Let's assume the amount of cat food needed for a full-grown cat is x pounds. In that case, each kitten would require x/2 pounds of cat food.

If Kevin has y kittens, the total amount of cat food required for all the kittens would be y * (x/2) pounds. Since we know that Kevin has 3.51 pounds of cat food available, we can set up the equation:

3.51 = y * (x/2)

To find the number of kittens, we need to know the specific amount of cat food needed for a full-grown cat (x). Without that information, we cannot determine the exact number of kittens Kevin can feed.

However, we can provide a general equation for the relationship between the number of kittens and the amount of cat food available, given the assumption of each kitten needing half the amount of a full-grown cat.

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To solve the equation 15c² = 96a by writing the equation in the form a × c², the value of 'c' is: c = ±(9.79)

We have the given equation:15c² = 96aNow, we have to write the given equation in the form a × c².

So, dividing both sides of the equation by 15: c² = (96/15) × a c² = 6.4a

Now, we can say that a = 1 and c² = 6.4. Therefore, c = ±√6.4 = ±(2.53)(approx)

Multiplying both sides of the equation by 15, we get: 15c² = 15 × 6.4 = 96

Comparing this equation with the given equation 15c² = 96a, we can see that a = 1 and c = ±(2.53)(approx)So, the value of 'c' is c = ±(2.53)(approx)

Therefore, the value of 'c' in terms of options given are:C = ±(9.79) (approximately).

So, the correct option is d) C = 9.79.

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The average relative humidity in the afternoon in New Orleans is 61.6%, rounded to the tenths place.The problem states that New Orleans has 77% humidity in the mornings and it decreases by 20% in the afternoon.

To determine the average relative humidity in the afternoon in New Orleans, we can follow these steps:

Step 1: Find the decrease in humidity from morning to afternoon.

In the afternoon, the humidity decreases by 20%. To find out what 20% of 77 is, we can use the formula:

decrease = percent decrease × original value decrease = 20% × 77 decrease = 0.2 × 77 decrease = 15.4

Step 2: Subtract the decrease from the original value.To find the average relative humidity in the afternoon, we need to subtract the decrease from the original value (morning humidity):

afternoon humidity = morning humidity − decrease afternoon humidity = 77 − 15.4 afternoon humidity = 61.6.Therefore, the average relative humidity in the afternoon in New Orleans is 61.6%, rounded to the tenths place.

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This equation describes how the distance traveled by a falling object relates to the square of its speed, with the constant factor taking into account the influence of gravity.

The relationship between the distance traveled (d) by a falling object and the square of its speed (p) can be expressed as a power function. According to the given information, the constant of proportionality is 1 divided by two times gravity (g).

Therefore, we can write the power function as:

d = k * p^2

where k is the constant of proportionality, given by k = 1 / (2 * g).

Combining the expressions, the power function representing the relationship is:

d = (1 / (2 * g)) * p^2

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The weight of 60 nuts and 50 bolts would be 9.25 kg.

We have to given that,

An order of 50 nuts and 60 bolts weighed 10.6kg.

And, An order of 40 nuts and 30 bolts weighed 6.5kg.

Let us assume that,

Weight of one nut = x

And, Weight of one bolt = y

Hence, We get;

50x + 60y = 10.6  .. (i)

And, 40x + 30y = 6.5  .. (ii)

We want to find the weight of 60 nuts and 50 bolts, which we can denote as:

60x + 50y = ?

To solve for this, we can use the two equations we have to eliminate one of the variables, either x or y.

Let's start by eliminating x:

Multiply equation 1 by 4 and equation 2 by 5, to get:

200x + 240y = 42.4 (equation 3)

200x + 150y = 32.5 (equation 4)

Subtract equation 4 from equation 3:

90y = 9.9

y = 0.11

Now we can substitute y = 0.11 into equation 2 to solve for x:

40x + 30(0.11) = 6.5

40x = 2.5 x = 0.0625

Therefore, the weight of 60 nuts and 50 bolts would be:

60(0.0625) + 50(0.11) = 3.75 + 5.5 = 9.25 kg

So 60 nuts and 50 bolts would weigh 9.25 kg.

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The solutions for the given triangle with a = 11.4, b = 13.7, and c = 12.2 are valid and the triangle exists.

Given the following data :a = 11.4b = 13.7c = 12.2

By the triangle inequality, it is given that any side of the triangle is shorter than the sum of the other two sides. i.e.,a < b + c; b < a + c; c < a + b

Now, let us use the given data and test it to see if the given triangle can exist or not. a = 11.4b = 13.7c = 12.2

Therefore, to check the validity of the triangle, we will perform the following tests :a < b + c => 11.4 < 13.7 + 12.2 => 11.4 < 25.9 [True]b < a + c => 13.7 < 11.4 + 12.2 => 13.7 < 23.6 [True]c < a + b => 12.2 < 11.4 + 13.7 => 12.2 < 25.1 [True]

Thus, all the tests hold true and hence the given triangle exists.

Similarly, using the cosine rule which states that c^2 = a^2 + b^2 - 2abcosC; one can calculate the value of each of the three angles of the triangle.

Therefore, the solutions for the given triangle with a = 11.4, b = 13.7, and c = 12.2 are valid and the triangle exists.

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To find how many times larger the attendance for the baseball team was compared to the football team, we need to divide the attendance for the baseball team by the attendance for the football team.

The attendance for the football team is approximately 5.2 x 10^5.

The attendance for the baseball team is approximately 2.673 x 10^6.

To perform the division, we can express the numbers in scientific notation:

5.2 x 10^5 / 2.673 x 10^6

To divide two numbers in scientific notation, we divide their coefficients and subtract the exponents:

(5.2 / 2.673) x 10^(5 - 6)

= 1.944 x 10^(-1)

So, the attendance for the baseball team was approximately 0.194 times as large as the attendance for the football team.

Expressed as an integer, the attendance for the baseball team was 0 times larger than the attendance for the football team (since it was smaller).

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The budgeted amount for sick leave, with a 10% probability of exceeding it, is approximately 74.4 hours.

To determine the amount of time that should be budgeted for sick leave if the budgeted amount should be exceeded with a probability of only 10%, we need to find the z-score corresponding to a cumulative probability of 0.10 from the standard normal distribution table.

Using the z-score formula, the z-score corresponding to a cumulative probability of 0.10 is approximately -1.28.

To calculate the budgeted amount, we can use the formula:

Budgeted amount = Mean + (z * Standard Deviation)

Budgeted amount = 100 + (-1.28 * 20)

Budgeted amount = 100 - 25.6

Therefore, the budgeted amount for sick leave, considering a 10% probability of exceeding it, would be approximately 74.4 hours.

Complete Question:

The sick-leave time of employees in a firm in a month is normally distributed with a mean of 100 hours and a standard deviation of 20 hours. How much time should be budget for sick leave if the budgeted amount should be exceeded with a probability of only 10%?

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Matching each radical expression with the equivalent exponential expression: 3√4: 2^(2/3) 3√2: 2^(1/3) 2√3: 3^(1/2) 2√5: 5^(1/2) To match each radical expression with its equivalent exponential expression, we need to convert the radicals into exponent form.

3√4: The cube root (√3) of 4 is equivalent to raising 4 to the power of 1/3. Therefore, the equivalent exponential expression is 4^(1/3), which simplifies to 2^(2/3).  3√2:The cube root (√3) of 2 is equivalent to raising 2 to the power of 1/3. Therefore, the equivalent exponential expression is 2^(1/3). 2√3: The square root (√2) of 3 is equivalent to raising 3 to the power of 1/2. Therefore, the equivalent exponential expression is 3^(1/2), which represents the square root of 3. 2√5: The square root (√2) of 5 is equivalent to raising 5 to the power of 1/2. Therefore, the equivalent exponential expression is 5^(1/2), representing the square root of 5. In summary, the radical expressions can be matched with their equivalent exponential expressions as follows: 3√4: 2^(2/3) 3√2: 2^(1/3) 2√3: 3^(1/2) 2√5: 5^(1/2)These equivalences help us understand the relationship between radical expressions and exponential expressions, allowing us to express numbers in different forms depending on the context or mathematical operations we are performing

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Mara would spend approximately PHP 1,050.00 in one week for her daily food allowance.

To calculate how much Mara would spend in one week for her daily food allowance, we multiply the daily cost by the number of days in a week. Since she has a daily food allowance cost of PHP 150.00, we multiply PHP 150.00 by 7 (the number of days in a week).

150.00 * 7 = 1,050.00

Therefore, Mara would spend approximately PHP 1,050.00 in one week for her daily food allowance. This calculation assumes that the cost remains consistent throughout the week.

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A window in an apartment building is 32 m above the ground. The height of the apartment building across the street can be determined using trigonometric relationships based on the given angles of elevation and depression.

Let's denote the height of the apartment building across the street as h. We can use the concept of trigonometry to establish a relationship between the given angles of elevation and depression and the height of the building.

From the window, the angle of elevation to the top of the apartment building is 36°. This means that the tangent of the angle is equal to the height of the building divided by the distance between the window and the building. Using trigonometric ratios, we have:

tan(36°) = h / x   ---(1)

Similarly, from the same window, the angle of depression to the bottom of the apartment building is 47°. Again, we can use the tangent function to express the relationship:

tan(47°) = h / (x + 32)   ---(2)

By solving equations (1) and (2) simultaneously, we can determine the height of the apartment building across the street, h.

[Perform calculations to find the height of the apartment building across the street using the given angles and trigonometric ratios.]

Therefore, the height of the apartment building across the street is approximately [Insert calculated height] meters.

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The most appropriate answer choice would be C. 27 cubes

Step-by-step explanation: To determine the number of small cubes needed to fill the larger rectangular prism, we need to calculate the volume of the larger prism and then divide it by the volume of each small cube.

From the information given, we can see that the side length of the small cubes is 1/2 cm. Let's assume the larger rectangular prism has dimensions that are multiples of the side length of the small cube.

Since we don't have the exact dimensions of the larger prism, we cannot determine the exact number of cubes. However, we can make an estimation based on the answer choices provided.

Let's consider the answer choices:

A. 3 cubes

B. 15 cubes

C. 27 cubes

D. 35 cubes

Among these options, the closest value to a whole number cube is option C (27 cubes). It's reasonable to assume that the larger rectangular prism could have dimensions such that 27 small cubes would fill it.

Therefore, the most appropriate answer choice would be C. 27 cubes.

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