50 Points! Algebra question. Photo attached. Thank you!

Answer:

Let's call the speed of the bus on the winding road "s". Then we know that the bus traveled at a speed of "s + 20" on the level road. We also know that the time spent on the winding road was 4 hours, so the distance traveled on the winding road is:

distance = speed × time = s × 4

Similarly, the distance traveled on the level road is:

distance = speed × time = (s + 20) × 4

Since the entire trip was 400 miles, we can write:

4s + 4(s + 20) = 400

Simplifying this equation, we get:

8s + 80 = 400

8s = 320

s = 40

Therefore, the speed of the bus on the winding road was 40 mph, and the speed on the level road was 40 + 20 = 60 mph.

To check that this solution is correct, we can calculate the distance traveled on each road:

distance on winding road = 40 × 4 = 160 miles

distance on level road = 60 × 4 = 240 miles

The total distance traveled is indeed 160 + 240 = 400 miles, so our solution is correct.

Therefore, the average speed on the level road was 60 miles per hour.

Answer:

Step-by-step explanation:

substitute:

2(5) + 3(3-5) + 3²     Do PEMDAS  order (parenthesis, exponent, mult/div, add/sub

2(5) + 3(-2) +3²

2(5) + 3(-2) + 9

10 + 3(-2) +9

10-6+9

4+9

13

The sample in this study is D. The students who complete the survey.
This is because the dance committee is only collecting data from those students who are surveyed, which represents a smaller group within the entire population of the school.

The sample in this study refers to the specific group of individuals who are selected to participate in the survey or study.

In this case, the dance committee at Northeast Middle School is choosing the theme for the spring dance and conducts a poll to ask students about their choices.

They ask every 10th student entering the cafeteria to complete a survey.

Therefore, the sample in this study is the students who complete the survey.

They are the specific group of individuals who are selected to participate in the survey and provide information about their preferences for the spring dance theme.

D. The students who complete the survey.

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Answer:

The students who complete the survey

Step-by-step explanation:

Wesley's class collected 253/18 pounds of clothing, which can also be written as 14 1/18 pounds (rounded to the nearest hundredth).

Whole numbers include natural numbers that begin from 1 onwards. Let us look at some examples of whole numbers. The set of whole numbers is denoted by the alphabet 'W'. W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,.…}

Jada's class collected 7 2/3 kilograms of clothes. Wesley's class collected 15/6 times as many clothes as Jada's class, which means they collected:

1 5/6 x (7 2/3) pounds of fabric

To multiply fractions, you can first convert the mixed numbers to improper fractions, then multiply the numerators and denominators separately and simplify if possible.

Convert mixed numbers to improper fractions:

7 2/3 = (37 + 2)/3 = 23/3

1 5/6 = (61 + 5)/6 = 11/6

Multiply Fractions:

(11/6) * (23/3) = (1123)/(63) = 253/18

Therefore, Wesley's class collected 253/18 pounds of clothing, which can also be written as 14 1/18 pounds (rounded to the nearest hundredth).

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The best method to ensure an unbiased sample is to randomly select parents from the entire population of parents with enrolled students at the school.

To ensure an unbiased sample for the survey, the method used should not favor any particular group or exclude any group from the population.

Option A: Surveying all parents attending the next PTO meeting would not be an unbiased sample as not all parents attend PTO meetings.

Option B: Surveying every fifth person on a list of parent volunteers would also not be an unbiased sample as it may exclude parents who are not on the list.

Option C: Surveying all parents waiting in the pick-up line after school may not be an unbiased sample as it may exclude parents who do not pick up their children from school.

Option D: Surveying all parents of students whose birthdays are on even-numbered days may not be an unbiased sample as it excludes parents whose children's birthdays are on odd-numbered days.

Therefore, the best method to ensure an unbiased sample is to randomly select parents from the entire population of parents with enrolled students at the school.

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There are 715 ways to select four people from a group of six men and seven women to attend a conference.

Combinations in mathematics relate to the various ways that a group of things can be chosen, regardless of the order in which they are chosen. Combinations are a form of counting problem where a smaller subset of the objects in the bigger set are selected.

The combination is given by the formula:

C(n,r) = n!/(r!(n-r)!)

The total number of people = 13.

The number of ways we can choose 4 people from the given 13 people are:

C(13,4) = 13!/(4!9!) = (13x12x11x10)/(4x3x2x1) = 715

Hence, there are 715 ways to select four people from a group of six men and seven women.

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The complete question is:

Answer:

63

Step-by-step explanation:

given the sight of the angle it should be 63, correct me if I'm wrong.

The statement that must be true is c is the least common multiple of A and B, is D. c ≥ b and c ≥ a.

The rationale behind this lies in the fact that finding the least common multiple (LCM) of two numbers necessitates determining a value that is commensurate with both figures, yet simultaneously represents their most diminutive shared multiple.

To expound further, It is the minimal positive integer among all feasible ones that can be divided entirely without any leftover remainder by all supplied integers. Thus, this computation allows you to determine the minimum possible factorization required to obtain each number while preserving its numerical integrity.

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Step-by-step explanation:

(x-3)(x-1 +2i)(x-1-2i)        The imaginary roots always come in pairs :   1+- 2i

Answer:

Step-by-step explanation:

It is given that length and width of a rectangle is 11 cm and 10 cm.

We know the formula of Perimeter of rectangle

[tex]:\implies \: [/tex] Perimeter = 2(L + B)

Where 'L' denote the length of the rectangle and 'B' denotes the breadth of the Rectangle.

Now Let's substitute the value of Length= 11 cm and Breadth = 10 cm in the above formula .

[tex]:\implies \: [/tex] 2(11 + 10)

[tex]:\implies \: [/tex] 2 × 21

[tex]:\implies \: [/tex] 42 cm

Henceforth The perimeter of the rectangle is 42 cm

The perimeter of a rectangle is calculated by multiplying by 2 the sum of its length and width. So, in this case, the rectangle's perimeter is 42 cm.

The subject of this question is on calculating the perimeter of a rectangle. The formula for finding the perimeter of a rectangle is 2*(length + width). Applying the values given, that is length = 11 cm and width = 10 cm.

So, the perimeter of a rectangle = 2*(11 + 10) cm = 2*21 cm = 42 cm

Therefore, the correct option is OC. 42 cm.

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Answer:

its 32 square units

Step-by-step explanation:

The Shape is a rectangle. Area of a rectangle is Length x Width

8 x 4 = 32

Answer:

32 Square units

Step-by-step explanation:

You can see that there are 8 spaces of width by using the graph. And 4 spaces of height. So, assuming each space is 1 Square unit. All you have to do is 8×4 which is 32.

According to probability, the answer to the question is that an average surgeon performs 8 operations, of which 5 are successful. 18.9%.

In a fixed number of independent trials, each of which can only have one of two outcomes—success or failure—the number of successes is expressed as a probability distribution known as a binomial probability. Additionally, it is presummated that each trial has an equivalent chance of success.

The binomial probability formula can be used to determine the likelihood that a surgeon will perform 5 successful operations out of 8 given that each operation has a 92% chance of being successful.

You may find the binomial probability formula by using:

[tex]P(X = k) = C(n, k)*p^k*(1 - p)^{(n - k)}[/tex]

Where:

P(X = k) is the likelihood that, out of n surgeries, exactly k will be successful.

The binomial coefficient, C(n, k), is defined as the number of ways to select k successful operations among n surgeries C(n, k) = n! / (k! * (n - k)!), where ! denotes factorial.

p is the likelihood that a single surgery will succeed (92% in this case, or 0.92).

The number of successful operations that interests us is k.

The total number of operations is n, which in this case is 8.

By entering the values, we can determine the probability using the formula below:

P(X = 5) = C(8, 5) * 0.92⁵ * (1 - 0.92)⁽⁸⁻⁵⁾

C(8, 5) = 8! / (5! * (8 - 5)!) = 56

0.92⁵ = 0.659

(1 - 0.92)³ = 0.512

P(X = 5) = 56 * 0.512 * 0.659 = 18.89 or 18.9%

Given a 92% success rate for each surgery, the likelihood that a surgeon will perform 5 successful operations out of 8 is roughly 18.9%.

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The expression can be rewriten as a single radical as:

[tex]\sqrt[5]{4} *\sqrt{2} = \sqrt[10]{2^9}[/tex]

We want to rewrite the expression below as a single radical:

[tex]\sqrt[5]{4} *\sqrt{2}[/tex]

First remember that 4 = 2², then we can replace that to get:

[tex]\sqrt[5]{4} *\sqrt{2} = \sqrt[5]{2^2} *\sqrt{2}[/tex]

Converthing the roots to exponents we will get.

[tex]\sqrt[5]{2^2} *\sqrt{2} = 2^{2/5}*2^{1/2}[/tex]

Now the exponents are just added:

[tex]2^{2/5}*2^{1/2} = 2^{2/5 + 1/2} = 2^{4/10 + 5/10} = 2^{9/10} = \sqrt[10]{2^9}[/tex]

That is the correct option.

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The surface area covered with stickers is 169.4 cm².

How to calculate the surface area of the paperweight?

We need to find the area of each face and then add them up for calculate the surface area of the paperweight,

We know,

Area of the rectangular base [tex]= length \times breadth = 17 cm \times 11 cm = 187 \: {cm}^{2} [/tex]

Area of the triangular top = (1/2) x base x height = (1/2) × 15 cm × 8 cm × 7 cm / √((15/2)² - (8/2)²) = 42 cm²

Area of the front and back faces (which are rectangles) [tex]= 2 \times length \times height = 2 \times 17 cm \times 10 cm = 340 \: cm²[/tex]

Area of the left and right faces (which are trapezoids) [tex]= ( \frac{1}{2} )(a+b) \times h \times 2 = ( \frac{1}{2} )(15 cm + 8 cm) \times 7 cm \times 2 = 91 {cm}^{2} [/tex]

Area of the bottom face (which is a rectangle) [tex]= length \times breadth = 17 cm \times 11 cm = 187 cm²[/tex]

Total surface area = 187 cm² + 42 cm² + 340 cm² + 91 cm² + 187 cm² = 847 cm²

To find the surface area covered with stickers, we need to calculate 20% of the total surface area:

Surface area covered with stickers [tex]=20\% \: of \: 874 \: {cm}^{2} = 0.2 \times 847 \: {cm}^{2} = 169.4 \: {cm}^{2} [/tex]

Therefore, the surface area covered with stickers is 169.4 cm² approximately.

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Answer: 7

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The unit of measurement that would typically be used to weigh an elephant is the ton. Elephants are very large animals, and they can weigh several tons, depending on their species and size. While other units of measurement like pounds, kilograms, or ounces could also be used to measure the weight of an elephant, the ton is the most appropriate unit for such a large animal.

Therefore, there are approximately 889 faculty members at the college.

Ratio is a mathematical concept that expresses the relationship between two or more quantities or values. It is a way to compare the size of two numbers, by dividing one number by the other. The result of this division is a numerical expression of the relative size of the two numbers.

Ratios are often expressed as a fraction or a colon (:) between the two numbers. For example, if there are 4 red balls and 6 blue balls in a bag, the ratio of red balls to blue balls can be expressed as 4/6 or 4:6. This means that for every 4 red balls in the bag, there are 6 blue balls.

Ratios are commonly used in various fields, such as finance, statistics, and science, to compare different values and make meaningful interpretations.

To solve this problem, we need to use the ratio between faculty members and students, which is given as 1:18. This means that for every one faculty member, there are 18 students.

If there are 16000 students in the college, we can find the number of faculty members by dividing the number of students by the ratio of students to faculty members:

Number of faculty members = 16000 / 18

This gives us 888.888, but since we are asked to round to the nearest whole number, we should round up to 889. Therefore, there are approximately 889 faculty members at the college.

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The answer of the given question based on the image transformation is , (a) reflection over line BC⎯.

Reflection is a transformation in which a figure or an object is flipped across a line or a plane. The line or plane across which  figure is flipped is called line or plane of reflection. In two-dimensional geometry, a reflection can be thought of as a "flip" of the figure over the line of reflection. Any point on the figure that lies on the line of reflection will remain fixed, while all other points will be reflected across the line.

The pre-image ABC was transformed to create image A′B′C′ through a reflection over line BC⎯.

To visualize this transformation, imagine folding the original figure over line BC⎯, so that point A maps to point A′, point B maps to point B′, and point C maps to point C′. The resulting image is the reflection of the original figure over line BC⎯.

The other options listed (90° clockwise rotation around point C, translation up, and translation down) would create different images, but not the image A′B′C′ shown in the diagram.

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Answer :

Angle A = 19.6°

Step-by-step explanation :

According to the question It is given that,

Angle A = x

Angle B = 5x

Angle C = 4x - 16

We will apply angle sum property in the question.

Angle sum property states that sum of all the angles of triangle is 180°

[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180

[tex]\: :\implies [/tex] x + 5x + 4x - 16 = 180

[tex]\: :\implies [/tex] 10x - 16 = 180

[tex]\: :\implies [/tex] 10x = 180 + 16

[tex]\: :\implies [/tex] 10x = 196

[tex]\: :\implies [/tex] x = 196/10

[tex]\: :\implies [/tex] x = 19.6

Hence,

Angle A = x

[tex]\: :\implies [/tex] 19.6 °

Angle B = 5x5 × 19.6

[tex]\: :\implies [/tex] 98

Angle c = 4x - 16

[tex]\: :\implies [/tex] 4 × 19.6 - 16

[tex]\: :\implies [/tex] 78.4 - 16

[tex]\: :\implies [/tex] 62. 4

We must also check our answer.

Sum of all angles = 180°

[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180

[tex]\: :\implies [/tex] 19.6 + 98 + 62.4 = 180

[tex]\: :\implies [/tex] 117.6 + 62.4 = 180

[tex]\: :\implies [/tex] 180 = 180

Hence, Verified.

Therefore, The Measure of Angle A is 19.6°

Answer:

angle A = 19.6°

Explanation:

angle ABC + angle ACB + angle BAC = 180°

5x + (4x - 16)° + x = 180°

Simplifying:

5x + x + (4x + -16) = 180

Reorder the terms:

5x + x + (-16 + 4x) = 180

Remove parenthesis around (-16 + 4x)

5x + x + -16 + 4x = 180

Reorder the terms:

-16 + 5x + x + 4x = 180

Combine like terms: 5x + x = 6x

-16 + 6x + 4x = 180

Combine like terms: 6x + 4x = 10x

-16 + 10x = 180

Solving

-16 + 10x = 180

Solving for variable 'x'.

Add '16' to each side of the equation

-16 + 16 + 10x = 180 + 16

Combine like terms: -16 + 16 = 0

0 + 10x = 180 + 16

10x = 180 + 16

Combine like terms: 180 + 16 = 196

10x = 196

Divide each side by '10'

x = 19.6

The measure of angle A is 19.6°

Answer: the answer is B

Step-by-step explanation:

The average rate of change of a beach ball thrown according to the function[tex]f(x) = 12x - 4.8x^2[/tex] over the interval 0 < x < 2 is -9.6 feet per second.

To find the average rate of change, we need to find the height of the ball at x = 0 and x = 2, and then find the change in height over the time interval.

At x = 0, the height of the ball is:

[tex]f(0) = 12(0) - 4.8(0)^2 = 0[/tex]

At x = 2, the height of the ball is:

[tex]f(2) = 12(2) - 4.8(2)^2 = -19.2[/tex]

The change in height over the time interval 0 < x < 2 is:

-19.2 - 0 = -19.2

Therefore, -19.2/2 = -9.6 feet per second is the average rate of change over the range 0 x 2.

The average change throughout the range of 0 x 2 is therefore -9.6 feet per second.

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The calculated value of the rocket’s greatest height is 324 feet

From the question, we have the following parameters that can be used in our computation:

h(t) = -16t² + 144t

Differentiate the height function and set the differentiated equation to 0

So, we have

32t = 144

This gives

t = 144/32

So, we have

t = 4.5

Substitute t = 4.5 in the above equation, so, we have the following representation

h(4.5) = -16(4.5)^2 + 144(4.5)

Evaluate

h(4.5) = 324

Hence, the rocket’s greatest height is 324 feet

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Complete question

A rocket is launched in the air. Its height in feet is given by h(t) = −16t² + 144t where t represents the time in seconds after launch.

What is the rocket’s greatest height?

Formula for the concentration after n steps is [tex]C(n) = C(0) * (0.86)^n[/tex] and

after 11 steps, the mixture contains less than 9% vinegar.

What is concentration?

Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.

a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:

[tex]C(1) = C(0) * \frac{1 - 0.14}{1}[/tex]

where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:

C(2) = C(1) * [tex]\frac{1 - 0.14}{1}[/tex]

Substituting the formula for C(1), we get:

C(2) = C(0) * [tex](\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})[/tex]

or, more generally:

[tex]C(n) = C(0) * (0.86)^n[/tex]

b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:

[tex]C(0) * (0.86)^n < 0.09[/tex]

Dividing both sides by C(0), we get:

[tex](0.86)^n < 0.09[/tex]

Taking the natural logarithm of both sides, we get:

n * ln(0.86) < ln(0.09)

Dividing both sides by ln(0.86), we get:

n > ln(0.09) / ln(0.86)

Using a calculator, we get:

n > 10.7

Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.

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Answer:

Step-by-step explanation:

7k+8=71

7k=71-8

7k=63

k=63/7

k=9

-9=3-y

-9+3=y

-6=y

y=-6

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Salut! Comment allez-vous? Comment s'est passée ta journée?

Answer:

A. When x = 3, h(x) = 16 is false.

B. When x = 4, h(x) = 8 1/3 is true.

C. When x = 9, h(x) = 10 is true.

D. When x = 10, h(x) = 10 1/3 is true.

E. When x = 12, h(x) = 12 is false.Therefore, the true statements are B, C, and D.

The direction of the vector is 27 degrees

The vector is the hypotenuse and the angle showing magnitude and direction.

To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem.

hypotenuse^2 = opposite^2 + adjacent^2

hypotenuse^2 = 88.4^2 + 174^2

hypotenuse ≈ 195.17 m

Therefore, the magnitude of the vector (hypotenuse of the right triangle) is approximately 194.8 m.

The direction

We can use the trigonometric function of tangent to find the angle between the opposite and adjacent sides of a right triangle.

tan(θ) = opposite/adjacent

We are given

so we can use these values to find the angle θ:

tan(θ) = 88.4/174

θ = arc tan (88.4/174)

θ ≈ 26.93 degrees

Therefore, the angle between the opposite and adjacent sides of the right triangle is approximately 27 degrees.

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the total cost for a Mug Club member who refills their cup 120 times in one year is $309.

How to solve?

If a customer purchases a Mug Club membership, they pay $75 for the mug and then refill it for $1.95 per refill. If they refill their mug 120 times in one year, the total cost would be:

$75 (for the initial purchase of the mug) + $1.95 x 120 (for the 120 refills)

= $75 + $234

= $309

Therefore, the total cost for a Mug Club member who refills their cup 120 times in one year is $309.

Cost refers to the amount of money or resources that are required to produce or obtain a good or service. It can include expenses such as materials, labor, rent, utilities, and other expenses incurred in the production or acquisition of a product or service.

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Answer:

Step-by-step explanation:

You take items out of a square root if you have a pair of numbers or if you know the square root.  

[tex]\sqrt{48b^{7} }[/tex]=[tex]\sqrt{4*4*3*bbbbbbb}[/tex]

So I know the [tex]\sqrt{4}[/tex]=2 so i can take both out so outside the root will be 2*2 and inside the root will be 3

Now for the b's for every pair there are, you can take that out.  There are 3 pairs of b's so b³ is outside and one b is left inside.

Answer:

4b³[tex]\sqrt{3b}[/tex]