on the last friday in may, one fourth of the 280 students in a school were away on a field trip how many students were on the field trip

Answer:

p=17

The drawing will help

Answer: p = 16

Step-by-step explanation: To solve for p in this equation, our first step is to simplify the left by distributing the 5 through both terms inside the parentheses.

When we do that,

we get 5 times 9 which is 45 and 5 times p which is 5p.

So we have 45 + 5p = 125.

Our next step is to isolate the p term by subtracting 45 from both sides of the equation. On the left side of the equation, 45 - 45 cancels and we're left with 5p.

On the right side of the equation, 125 - 45 simplifies to 80.

So we have 5p = 80.

We want to solve our equation for p so we want to get p by itself on the left side of the equation. Since p is being multiplied by 5, we need to divide both sides of the equation by 5. On the left side of the equation.notice that the 5 and 5 cancel each other out so we're just left with p and on the right side, 80 divided by 5 is 16 so we have p = 16.

Final answer:

The negative solution to the equation x² - 3x - 4 = 0 is x = -1.

Explanation:

The difference of the square of a number and 4 is equal to 3 times that number. To find the negative solution, let's represent the number as x.

The equation becomes x2 - 4 = 3x.

Rearranging the equation, we get x2 - 3x - 4 = 0.

To find the negative solution, we can use the quadratic formula: x = (-b - √(b2 - 4ac)) / (2a).

For our equation, a = 1, b = -3, and c = -4. Plugging these values into the quadratic formula, we get x = (-(-3) - √((-3)2 - 4(1)(-4))) / (2(1)).

Simplifying further, we get x = (3 - √(9 + 16)) / 2, which simplifies to x = (3 - √25) / 2.

The square root of 25 is 5, so x = (3 - 5) / 2, which equals -1.

Therefore, the negative solution to the equation is x = -1.

Answer: The height/width has to be less than 9 for the area to be less than 36

Step-by-step explanation:

Pennant's are triangle.

Triangle area = bh(1/2)

the base is 8in

(8 * h)/2 = 36

*2

8 * h = 72

/8

h = 9

The height/width has to be less than 9

Answer:

Restrictions: x ≠ 0, 3

The value of x is equal to 5.

General Formulas and Concepts:

Pre-Algebra

Algebra I

Equality Properties

Terms/Coefficients

Domain

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \frac{2}{x - 3} = \frac{5}{x}[/tex]

Step 2: Examine

Since we have an x - 3 and x in the denominator, we must make sure the denominator cannot equal 0, or that would get us an undefined answer. Therefore, our restrictions are that x ≠ 0, 3.

Step 3: Solve for x

Since 5 is not equal to 0 or 3, it can be our solution.

∴ we have found the value of x from the given rational function.

---

Topic: Algebra I

Answer:

a. 1/10

b. 4/10

c. 20

Step-by-step explanation:

There are 10 equal sections.

a. 1 section is labeled "Large Prize", so the probability of winning a large prize is 1/10.

b. 1 section is labeled "Large Prize" and 3 sections are labeled "Small Prize", so there's 4 prize section.  Therefore, the probability of winning a prize is 4/10.

c. Each person has a 4/10 chance of winning a prize.  So if there are 50 people, we would expect 4/10 × 50 = 20 people to win a prize.

Answer:

Step-by-step explanation:

Final answer:

The remainder when the function f(x) = 4x² + 5x + 2 is divided by x + 7 is found using the remainder theorem, which gives us a result of 163.

Explanation:

To find the remainder when the function f(x) = 4x² + 5x + 2 is divided by x + 7, we can use the remainder theorem. The remainder theorem states that if a polynomial f(x) is divided by a linear divisor of the form x - r, the remainder is f(r). Here, our linear divisor is x + 7, which we can rewrite as x - (-7). So, we substitute x = -7 into the polynomial to get the remainder.

Substituting x = -7 into the function gives us:
f(-7) = 4(-7)² + 5(-7) + 2 = 4(49) - 35 + 2 = 196 - 35 + 2 = 163.

Therefore, the remainder when f(x) is divided by x + 7 is 163.

Answer:

Step-by-step explanation:

The function that will have the domain [tex](\infty, \infty)[/tex] and a range of [tex](-3, \infty)[/tex] is the

function in option d.) [tex]f(x) = e^x - 3[/tex]

Answer:

  they have the same value (0)

Step-by-step explanation:

Cosine is an even function, meaning that cos(x) = cos(-x). When x=90°, we have ...

  cos(90°) = cos(-90°)

Both values happen to be zero.

The relationship between cos(90°) and cos(-90°) is that they both equal 0.

The relationship between cos(90°) and cos(-90°) can be explained using the unit circle. In the unit circle, the cosine function represents the x-coordinate of the point on the circle corresponding to the given angle.

For cos(90°), the x-coordinate is 0, which means the cosine value is 0.

For cos(-90°), the x-coordinate is also 0, so the cosine value is also 0. Therefore, cos(90°) = cos(-90°) = 0.

Answer:

1) a = 3189 b = 5

2) a = 53 b = -5

Step-by-step explanation:

Answer:

1, 2, 3

Step-by-step explanation:

The range includes only the y-axis. On this graph, the line only passes by the 1,2, and 3 on the y-axis.

Approximately 3 bottles are needed to buy to completely fill the 6 glasses you need

Solution:

Given that,

A small bottle of Dr.Pepper holds 31.2 cm^3 of the delicious drink

Therefore,

[tex]Volume\ of\ small\ bottle\ of\ Dr.pepper = 31.2\ cm^3[/tex]

For a New Years Eve party, you need enough juice to fill 6 cone- shaped glasses that have a 4 cm diameter and a 3 cm height

Find the volume of cone

[tex]V = \frac{\pi r^2h}{3}[/tex]

Where, r is the radius and h is the height

Diameter = 4 cm

Radius = 4/2 = 2 cm

Height = 3 cm

Therefore,

[tex]V = \frac{3.14 \times 2^2 \times 3}{3}\\\\V = \frac{3.14 \times 12}{3}\\\\V = \frac{37.68}{3}\\\\V = 12.56[/tex]

Thus, for 6 cone shaped glasses:

Volume of 6 cone shaped galsses = 12.56 x 6 = 75.36 [tex]cm^3[/tex]

How many full bottles of Dr. Pepper do you need to buy to completely fill the 6 glasses you need?​

[tex]\text{Number of Dr.pepper bottles } = \frac{\text{Volume of 6 cone shaped galsses}}{\text{Volume of small bottle of dr pepper}}\\\\\text{Number of Dr.pepper bottles } = \frac{75.36}{31.2}\\\\\text{Number of Dr.pepper bottles } = 2.4153[/tex]

Thus approximately 3 bottles are needed to buy to completely fill the 6 glasses you need

Final answer:

To fill 6 cone-shaped glasses for a New Year's Eve party, you would need to buy 3 full bottles of Dr. Pepper. The volume of each glass is calculated using the formula for the volume of a cone, and then this volume is multiplied by 6 to find the total volume required for all glasses. The number of bottles needed is found by dividing this total volume by the volume of one bottle of Dr. Pepper.

Explanation:

To determine how many full bottles of Dr. Pepper you need to buy to fill 6 cone-shaped glasses with a 4cm diameter and a 3cm height, we need to calculate the volume of one glass and then multiply it by 6 to get the total volume required. The formula to calculate the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cone.

First, we find the radius of the glass by dividing the diameter by two, which yields 2cm. Plugging the values into the formula, we get:

V = (1/3)π(2^2)(3) = (1/3)π(4)(3) = 4π cm^3

Since π is approximately 3.14, we can simplify this to:

V = 4(3.14) cm^3 = 12.56 cm^3 per glass.

Now, multiplying the volume of one glass by 6 gives us the total volume needed:

Total volume = 12.56 cm^3/glass × 6 glasses = 75.36 cm^3.

To find out how many bottles of Dr. Pepper are needed, we divide the total volume by the volume of one bottle:

Number of bottles = 75.36 cm^3 / 31.2 cm^3/bottle ≈ 2.415 bottles.

Since you cannot buy a fraction of a bottle, you would need to purchase 3 full bottles of Dr. Pepper to ensure you have enough to fill all 6 glasses.

[tex]\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{45}{4}\\\\\frac{\text{Distance of tamar}}{\text{Distance of melkon}} = \frac{4}{45}[/tex]

Solution:

Given that,

Tamar travels 8/9 miles to the grocery store

Melkon travels 10 miles to the grocery store

Therefore,

[tex]Tamar = \frac{8}{9}\ miles\\\\Melkon = 10\ miles[/tex]

[tex]\text{ Distance of melkon : Distance of tamar } = 10 : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } = \frac{10 \times 9}{1 \times 9} : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } = \frac{90}{9} : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } =90 : 8\\\\In\ fraction\ form\\\\\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{90}{8}\\\\In\ simplest\ form\\\\\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{45}{4}[/tex]

[tex]\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : 10\\\\\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : \frac{10 \times 9}{1 \times 9}\\\\\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : \frac{90}{9}\\\\\text{ Distance of tamar : Distance of melkon } = 8 : 90\\\\In\ fraction\ form\\\\\frac{\text{Distance of tamar}}{\text{distance of melkon}} = \frac{8}{90}\\\\\frac{\text{Distance of tamar}}{\text{distance of melkon}} = \frac{4}{45}[/tex]

Thus the required are found

The approximate mean age is [tex]\(45.15\)[/tex] years, and the approximate standard deviation for age is [tex]\(9.22\)[/tex] years, both rounded to two decimal places.

To approximate the mean and standard deviation for the age groups provided, we can calculate the weighted average based on the midpoint of each age group and use the formula for the standard deviation of a weighted dataset.

First, calculate the midpoints of the age groups:

- For 25-34 years: midpoint = (25 + 34) / 2 = 29.5

- For 35-44 years: midpoint = (35 + 44) / 2 = 39.5

- For 45-54 years: midpoint = (45 + 54) / 2 = 49.5

- For 55-64 years: midpoint = (55 + 64) / 2 = 59.5

Next, calculate the weighted mean using the formula:

[tex]\[ \text{Weighted Mean} = \frac{\sum (\text{Midpoint} \times \text{Number of People})}{\sum \text{Number of People}} \][/tex]

[tex]\[ \text{Weighted Mean} = \frac{(29.5 \times 22.1) + (39.5 \times 31.5) + (49.5 \times 37.7) + (59.5 \times 25.3)}{22.1 + 31.5 + 37.7 + 25.3} \][/tex]

[tex]\[ \text{Weighted Mean} \approx \frac{651.45 + 1244.25 + 1867.35 + 1503.35}{116.6} \][/tex]

[tex]\[ \text{Weighted Mean} \approx \frac{5266.4}{116.6} \][/tex]

[tex]\[ \text{Weighted Mean} \approx 45.15 \text{ years (approx)} \][/tex]

Now, calculate the standard deviation using the formula:

[tex]\[ \text{Weighted SD} = \sqrt{\frac{\sum (\text{Number of People} \times (\text{Midpoint} - \text{Weighted Mean})^2)}{\sum \text{Number of People}}} \][/tex]

[tex]\[ \text{Weighted SD} = \sqrt{\frac{(22.1 \times (29.5 - 45.15)^2) + (31.5 \times (39.5 - 45.15)^2) + (37.7 \times (49.5 - 45.15)^2) + (25.3 \times (59.5 - 45.15)^2)}{116.6}} \][/tex]

[tex]\[ \text{Weighted SD} \approx \sqrt{\frac{9919.575}{116.6}} \][/tex]

[tex]\[ \text{Weighted SD} \approx \sqrt{85.004} \][/tex]

[tex]\[ \text{Weighted SD} \approx 9.22 \text{ years (approx)} \][/tex]

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Answer:

.97 cents

Step-by-step explanation:

3.88 divided by 4 = .97

Answer:

97¢

Step-by-step explanation:

If 4 liters cost $3.88, then divide 4 into 3.88

[tex]\frac{1}{6}[/tex] of the original pan represents each serving

Solution:

Given that,

Mrs.Rome has 2/3 of a pan of lasagna left after dinner

She wants to divide the leftover lasagna into 4 equal servings

2/3 is divided into 4 equal servings

Therefore,

[tex]1\ equal\ serving = \frac{\frac{2}{3}}{4}\\\\1\ equal\ serving = \frac{2}{12} = \frac{1}{6}[/tex]

Thus [tex]\frac{1}{6}[/tex] of the original pan represents each serving

Option A: 7/16 of a foot is the right answer

Step-by-step explanation:

Given

Length of Braden's Jump = [tex]9\frac{5}{16} = \frac{149}{16}[/tex] feet

Length of Jordan's Jump = [tex]8\frac{7}{8} = \frac{71}{8}[/tex]

In order to find how much farther Braden jumped than Jordan

[tex]=\frac{149}{16} - \frac{71}{8}\\=\frac{149-142}{16}\\=\frac{7}{16}[/tex]

Braden jumped 7/16 feet farther than Jordan

Hence,

Option A: 7/16 of a foot is the right answer

Keywords: Fractions, measurements

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Final answer:

By converting Jordan's jump to sixteenths and subtracting it from Braden's, we determine that Braden jumped 9/16 of a foot farther than Jordan. The correct answer is option B.

Explanation:

The question involves finding out how much farther Braden jumped than Jordan. To solve this, we subtract Jordan's jump length from Braden's jump length. Braden jumped 9 5/16 feet, and Jordan jumped 8 7/8 feet.

First, we need to find a common denominator to subtract the fractions. The common denominator for 16 and 8 is 16. Convert Jordan's jump to sixteenths: 8 7/8 equals 8 14/16.

Now, subtract Jordan's jump from Braden's: 9 5/16 - 8 14/16 = 1 - 9/16. Braden jumped 9/16 of a foot farther than Jordan.

So the correct answer is option B. 9/16 of a foot.

Step-by-step explanation:

We have,

[tex]\dfrac{x+16}{3}=3x[/tex]

To find, the value of x in the given equation = ?

∴ [tex]\dfrac{x+16}{3}=3x[/tex]

By crossmultiplication, we get

3(3x) = x + 16

⇒ 9x = x + 16

⇒  9x - x = 16

⇒  8x = 16

⇒  x = [tex]\dfrac{16}{8}[/tex]

⇒  x = 2

∴ The value of x = 2

Thus, the required value of x is equal to 2.

The question cannot be fully answered as provided since only two dimensions of the ice block are given. To determine the amount of reflective material, all three dimensions (length, width, height) of the block are needed to calculate the total surface area. Without the third dimension, the exact surface area cannot be calculated.

The question asks how much reflective material would be needed to cover a block of ice with given dimensions completely for an ice carving competition. Since only two dimensions are provided, let's assume the block has a third dimension making it a rectangular prism. To find the surface area of the block (which is the amount of reflective material needed), we calculate the area of each face and sum them up. A rectangular prism has six faces: the front and back, the top and bottom, and the two sides. If we denote the dimensions of the block as length (l), width (w), and height (h), the areas of the respective faces are:

Assuming the dimensions provided are the length and height (l = 3 ft and h = 4 ft), and an unknown width (w), we cannot calculate the exact surface area without the third dimension. Ideally, the width would be provided to complete the calculation.

Answer:

[tex]2(x - 3)\: >\: \frac{1}{14}[/tex]

Step-by-step explanation:

The difference of x and 3 is given as:

x-3

Twice the difference of x and 3 becomes:

2(x-3)

The reciprocal of 14 is

[tex] \frac{1}{14} [/tex]

Twice the difference of x and 3 is greater than the reciprocal of 14 then becomes

[tex]2(x - 3)\: >\: \frac{1}{14} [/tex]

Answer:

5/2 or 2 1/2

Step-by-step explanation:

Answer:

look at picture shown please

A number line can be defined as a horizontal line that can be extended and have numbers on it. The distance between -2/3 and 4/3 on a number line is 3 units.

A number line can be defined as a horizontal line that can be extended in any direction indefinitely and has all the integers over it. As one walks from left to right on the number line, the numbers grow, and as one proceeds from right to left, the numbers decrease.

The distance between the two can be found by deducting -2/3  from 4/3. Therefore, the distance between the two can be written as,

[tex]\rm Distance = \dfrac{4}{3}-(- \dfrac{2}{3}) = \dfrac{4}{3}+\dfrac{2}{3} = \dfrac{4+2}{3} = \dfrac{6}{3} = 2[/tex]

Thus, the distance between -2/3 and 4/3 on a number line is 3 units.

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Answer:

[tex]\frac{1}{90}[/tex]

Step-by-step explanation:

Before calculating the scale we require the dimensions to be in the same units.

Using the conversion

1 yard = 3 ft and

1 foot = 12 inches, then

5 yards = 5 × 3 × 12 = 180 inches

The scale is then

2 in : 180 in ← divide both quantities by 2

= 1 : 90

= [tex]\frac{1}{90}[/tex]

The scale of the drawing given is 1/90

Using the following conversion :

This means that ;

Then ;

Relating the expression :

2 inches = 180 inches

divide both sides by 2

1 inch : 90 inches

Hence, the scale is 1 /90

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Answer:

The measure of each interior angle of the dodecagon is 150 degrees.

Step-by-step explanation:

(n - 2) x 180 = 1800       Use the equation to find the number of sides

n - 2 = 10                        Divide by 180 on both sides

  + 2  + 2                        Add 2 to both sides

n = 12

Take the sum of the interior angles divided by the number of sides to find the measure of each angle

1800/12 = 150 degrees for each angles of the dodecagon.

Answer:

10/25 or 2/5

Step-by-step explanation:

since only 10 have sport as all the other students don't

Answer y = 0.15x + 100

Step-by-step explanation:

It will take Luis 12240 seconds to complete the project.

12240 seconds are 204 minutes when converted.

Step-by-step explanation:

Given,

Time taken to paint 1 square foot = 45 seconds

Time taken for 272 square feet = 45*272

Time taken for 272 square feet = 12240 seconds

We know that;

60 seconds = 1 minute

Therefore;

We will divide the total seconds by 60 to convert them into minutes.

12240 seconds = [tex]\frac{12240}{60} = 204\ minutes[/tex]

It will take Luis 12240 seconds to complete the project.

12240 seconds are 204 minutes when converted.

Keywords: conversion, multiplication

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Answer:

6 combinations

Step-by-step explanation:

Pants options: Navy Blue, Khaki

Shirt options: Red, white, blue

Possible combinations:

Navy Blue with:       Khaki with:

Red                           Red

White                        White

Blue                           Blue

There are 6 outfit possibilities

Hope this helps and let me know if you have any questions about my answer :)