in which choice are all four points on the same straight line​

Answer:

triangle pjl is congruent to it's by side side side theorem

I =(6)(2)-10

I=12+-10

I=(12+-10)

I=2

2 is the final answer

Answer:

something

Step-by-step explanation:

onther something

Answer:

square root of 5 squared minus 4 squared

Step-by-step explanation:

a^2 + b^2 = c^2

c^2 - b^2 = a^2

5^2 - 4^2 = a^2

25 - 16 = a^2

9          = a^2

√

√9=a

a=3

or

a=  √25-16

a= √9

a=3

Hope this helps!

Answer:

A- not sure how to show u

B- 50% or 1/2

C-33% or 1/3

D- 40% or 2/5 im not sure

Step-by-step explanation:

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.

To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.

Setting the equation of the curve equal to itself, we have:

2 + 4cos(3θ) = 2 + 4cos(3(θ + π))

Simplifying and solving for θ, we get:

cos(3θ) = -cos(3θ + 3π)

cos(3θ) + cos(3θ + 3π) = 0

Using the sum to product formula, we get:

2cos(3θ + 3π/2)cos(3π/2) = 0

cos(3θ + 3π/2) = 0

3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...

Solving for θ, we get:

θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6

We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.

To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.

Using the formula for the area enclosed by a polar curve, we have:

A = 1/2 ∫[a,b] (r(θ))^2 dθ

where a and b are the angles of intersection.

For the small loops, we have:

A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ

Using trigonometric identities, we can simplify this to:

A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ

Evaluating the integral, we get:

A1 = 10π/3

For the large loops, we have:

A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)

Using the same trigonometric identities, we can simplify this to:

A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)

Evaluating the integrals, we get:

A2 = 80π/3

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:

A = A2 - A1 = (80π/3) - (10π/3) = 70π/3

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Let's assume that the original price of the camera is x.

Since Annie sold the camera at a loss of 12%, the selling price is 88% of the original price.

So we can set up the equation:

0.88x = $250

To solve for x, we can divide both sides by 0.88:

x = $250 ÷ 0.88

x = $284.09

Therefore, the original price of the camera was $284.09.

Answer:

The equation for this is:

n(g) + 49 - 3

Step-by-step explanation:

The term "Product" means "multiplication." And "number" can be reduced to the term "n," like "g" is. The word "and" means "addition." And, "3 less" means - 3:

n(g) + 49 - 3

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

49g -3

Step-by-step explanation:

3 less than the product of a number g and 49

Writing an algebraic expression

less than means it comes after

the product of a number g and 49

49g

3 less than

49g -3

In the given study comparing the effects of regular-fat cheese to reduced-fat cheese on LDL cholesterol levels, the dependent variable(s) refers to the outcome(s) that are being measured or observed. In this case, the dependent variable in this study is: b. LDL levels

The dependent variable is the variable that is measured or observed to assess the effect of the independent variable(s). In this case, the study is comparing the effects of regular-fat cheese and reduced-fat cheese on LDL cholesterol levels.

LDL cholesterol levels are the outcome being measured to determine the impact of the different types of cheese on cholesterol. Therefore, option b, LDL levels, is the dependent variable in this study. Options a (regular fat cheese) and c (reduced fat cheese) are not the dependent variables but rather the independent variables, as they are the different conditions being compared to assess their effect on LDL levels.

Option d (both a and b) and option e (both b and c) are incorrect because regular-fat cheese (option a) is an independent variable, not a dependent variable.

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Answer:

Step-by-step explanation:

5.46666666667

Answer:

5 7/15

Step-by-step explanation:

9 2/3-4 1/5 = 9 10/15-4 3/15=5 7/15

The coefficient of the equation's independent variable would correspond to the: variable operating cost per delivery.

Variable operating cost can be defined as those cost that varies due to changes in a company or an organization day to day operating activity.

Delivery cost is an example of variables cost because cost of delivery a product or goods depends on the volume or units of the goods.

Therefore the coefficient of the equation's independent variable would correspond to the: variable operating cost per delivery.

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               \(\rule{50}{1}\large\blue\textsf{\textbf{\underline{Given question:-}}}\rule{50}{1}\)

           What is the value of c in the quadratic \(\large\text{$x^2+28=-11x$}\)?

          \(\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}\)

           Before starting to solve, you should notice something - the

quadratic is not in its standard form!

We can easily fix it by adding \(\large\textit{11x}\) on both sides:-

\(\large\text{$x^2+28-11x=0$}\)

We can switch the order of 28 and -11x:-

\(\large\text{$x^2-11x+28=0$}\)

  Now, the quadratic is in its standard form, so we can get down to

finding the value of "c".

Remember, the standard form of a quadratic looks like so:-

Now we can just write our quadratic here:-

Now, can you see what the value of "c" is?

An easy way to remember "c" in quadratics is:-

The "c" in quadratics is the constant.

Henceforth, we conclude that the value of "c" in the given quadratic is:-

 \(\Large\textbf{28}\Large\checkmark\)

        \(\rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{50}{1}\)    

When a coin is flipped 10 times, there are 1024 possible outcomes. Out of these, 286 outcomes contain at most three tails.

To calculate the number of possible outcomes containing at most three tails, we need to consider all the possible combinations of heads (H) and tails (T) in 10 flips. In each flip, we have two possibilities, so the total number of outcomes is 2^10 = 1024.

To find the number of outcomes with at most three tails, we can break it down into three cases:

1. Zero tails: There is only one outcome with all heads (HHHHHHHHHH).

2. One tail: There are 10 ways to choose the flip that results in a tail, and for each of these, the remaining flips are all heads. So, there are 10 outcomes with one tail.

3. Two tails: There are 10 choose 2 = 45 ways to choose the two flips that result in tails, and for each of these, the remaining flips are all heads. So, there are 45 outcomes with two tails.

Adding up these cases, we have 1 + 10 + 45 = 56 outcomes with at most two tails. However, this count includes the outcome with all heads, which we already counted in case 1. So, we subtract 1 to get 56 - 1 = 55 outcomes with at most three tails.

In conclusion, out of the 1024 possible outcomes when flipping a coin 10 times, there are 286 outcomes that contain at most three tails.

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Answer: a) 15

Step-by-step explanation:

3a+9=54

    -9.  -9

3a=45

/3    /3

a=15

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Answer:

42.39 yd²

Step-by-step explanation:

the sector area = (3π/4)/2π × 3.14 × 6²

= 3/8 × 3.14 ×36 = 42.39 yd²

The expressions that describe the mass are Mass = 3599 grams, Mass = 126.95 ounces and Mass = 3.599 kilograms

The mass of the penguin is given as

Mass = 3.599 kilograms

Convert the mass from kilograms to grams.

So, we have:

Mass = 3.599 * 1000 grams

Evaluate the product

Mass = 3599 grams

Next, convert the mass from grams to ounce

So, we have:

Mass = 3599/28.35 ounce

Evaluate the quotient

Mass = 126.95 ounces

Hence, the expressions that describe the mass are Mass = 3599 grams, Mass = 126.95 ounces and Mass = 3.599 kilograms

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Answer:

\( \frac{7}{4} \pi\)

or

\( \frac{3}{4} \pi\)

Step-by-step explanation:

See attached. I know (very haphazard). But the basic method is to inverse the trig function. This gives you the position of the terminal angle. -45 degrees means that you turned 45 degrees clockwise and are in quadrant 4. This corresponds to an angle of rotation of 315 degrees counter clockwise which is what we are looking for since the specified domain is betwern 0 and 360 degrees or 0 and 2 pi.

The next thing to remember is that Tan is also negative in Quadrant 2 (using the ASTC rule). This corresponds to an angle of rotation of 180 - 45 = 135 degrees.

Hope that helps.

Answer:

c will be the answer mark me brainliest

The proportion of the measurements lie in the interval is 0.9.

According to the given question.

Weigths of 10 young dogs.

W : 7, 5, 11, 8, 14, 19, 16, 15, 13, 27

As we know that mean si calculated by the formula

Mean = ΣW / n

Thereofre, the mean of the weights of 10 young dogs

= 7 + 5 + 11 + 8 + 14 + 19 + 16 + 15 + 13 + 27/ 10

= 13.5

And, Standard deviation (s) = 6.433

Proportion that lies in mean ± 2s

Lower = Mean - 2s

⇒ 13.5 - 2(6.433) = 0. 632

Also, Upper = Mean + 2s

⇒ 13.5 + 2(6.433) = 26.376

Mean ± 2(sd) = (0.632, 26.276)

The only digit from the data which falls outside the defined range = 27

Proportion within interval = 9 / n

Proportion which falls within interval = 9/10 = 0.9

Hence, the proportion of the measurements lie in the interval is 0.9.

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The number of people are 72.

Highest Common Factor is the full name for HCF in mathematics.

According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.

Least Common Multiple is the full name for LCM in mathematics.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.

We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.

Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.

We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:

288 / x² = (16*18) / x² = 288 / x²

Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.

As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.

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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.

The total area of the cake is:

16 inches x 18 inches = 288 square inches

To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:

√(288 square inches) ≈ 16.97 inches

Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:

Each piece of cake will be approximately 16 inches by 16 inches.

To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:

288 square inches ÷ (16 inches x 16 inches) = 18

Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

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Answer:

7. the solutions to the equation 2x^2 + x - 21 = 0 are x = -7/2 and x = 3

To factor the quadratic equation, we need to find two numbers that multiply to -42 and add up to 1. These numbers are 7 and -6. We can write:

2x^2 + x - 21 = 0

2x^2 + 7x - 6x - 21 = 0

(2x^2 + 7x) - (6x + 21) = 0

x(2x + 7) - 3(2x + 7) = 0

(2x + 7)(x - 3) = 0

Setting each factor equal to zero gives:

2x + 7 = 0 or x - 3 = 0

Solving for x, we get:

2x = -7,

x = -7/2 or x = 3

8. It took the receiver about 1.1 seconds to catch the ball.

Rearrange the equation to standard form, which is in the form of ax^2 + bx + c = 0:

-4.9t^2 + 7.5t - 0.3 = 0

Now we can use the quadratic formula to solve for t:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

Substituting in the values, we get:

t = (-7.5 ± sqrt(7.5^2 - 4(-4.9)(-0.3))) / 2(-4.9)

t = (-7.5 ± sqrt(56.25 - 5.88)) / (-9.8)

t = (-7.5 ± sqrt(50.37)) / (-9.8)

t ≈ 1.1 seconds or t ≈ 0.06 seconds

Since the time can't be negative, we can discard the negative solution.

The expression for the nth term an, for the infinite series s=∑n=1[infinity]an is ∑n=4¹⁶an = 468

We know that the sum of the first n terms of the series is given by sn. Therefore, we can find an expression for the nth term an by taking the difference between successive values of sn:

sn - sn-1 = an

(4-4n²) - (4-4(n-1)²) = an

Simplifying this expression, we get:

an = 8n - 4

Now we can use this expression to find the values of ∑n=1¹⁰an and ∑n=4¹⁶an:

∑n=1¹⁰an = a1 + a2 + ... + a10

= (81 - 4) + (82 - 4) + ... + (8*10 - 4)

= 76

Therefore, ∑n=1¹⁰an = 76.

Similarly,

∑n=4¹⁶an = a4 + a5 + ... + a16

= (84 - 4) + (85 - 4) + ... + (8*16 - 4)

= 468

Therefore, ∑n=4¹⁶an = 468.

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The set of operations described, where each score is incremented by 1, squared, and then summed, can be expressed in summation notation as c. ∑(x^2 + 1).

Let's break down the expression:

∑ represents the summation symbol, indicating that we are summing up a series of values.

(x^2 + 1) represents the operation performed on each individual score. First, each score is squared (x^2), and then 1 is added to the squared value.

By applying the summation symbol to the expression (x^2 + 1), we are instructing to perform this operation on each score and sum up the resulting values.

Therefore, the correct summation notation for adding 1 to each score, squaring the resulting values, and finding the sum of the squared numbers is ∑(x^2 + 1).

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Answer:

first option

Step-by-step explanation:

The equation representing a proportional relationship is

y = kx ← k is the constant of proportion

Here k = 0.7, thus

y = 0.7x ← is the required equation

Given

\(\frac{y}{x}\) = \(\frac{7}{10}\) ( cross- multiply )

10y = 7x ( divide both sides by 10 )

y = \(\frac{7}{10}\) x = 0.7 x ← the required equation

The weight of the last child is 36 lbs.

The average weight of the three children is 60 lbs. The total weight will be:

= 60 × 3

= 180 lbs.

When another child is added, the weight is 54lb. The total weight will be:

= 54 × 4

= 216 lbs

The weight of the last child will be:

= 216 - 180

= 36 lbs.

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The percentage of seventh and eighth graders, taken together, who participate in MATHCOUNTS is 3.6%

Percentage is the number of given quantity in hundred such quantities.

We know that there are 1.5 times as many eighth-graders as seventh-graders.

We know that the proportion of eighth-graders who participate in MATHCOUNTS is 6% and the proportion of seventh-graders is 3%.

Let's say that there are x seventh-graders at the school.

Then, there are 1.5x eighth-graders.

The total number of students at the school is:

x + 1.5x = 2.5x

There are 2.5x students at the school and the proportion of eighth-graders is 1.5x/2.5x = 3/5 of the total number of students,

while the proportion of seventh-graders is x/2.5x = 2/5 of the total number of students.

So, the proportion of all students at the school who participate in MATHCOUNTS is:

3/5 × 6% + 2/5 × 3% = 0.036 or 3.6%

Therefore, the percentage of seventh and eighth graders, taken together, who participate in MATHCOUNTS is 3.6%

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