Freshman
Sophomores
Total
Blology
0.15
0.2
0.35
Which statement is false?
Chemistry
0.1
0.25
0.35
Physical
science
0.2
0.1
0.3
OA. 15% of her students are in biology.
OB. 30% of her students are in physical science.
OC. 35% of her students are in chemistry.
OD. 45% of her students are freshmen.
Total
0.45
0.55
1.0

The formula for tension (T) in terms of extension (x) is T = 25x.

The given statement is T = kx, where T is the tension, x is the extension, and k is the proportionality constant.

To solve this problem, we need to find the value of k. We can do that by substituting the given values of T and x into the equation:

T = kx

150 = k×6

k = 25

Therefore, the formula for tension (T) in terms of extension (x) is T = 25x.

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The new mixture contains 34% peanuts.

The correct option is A

We have,

Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts.

First, Total weight = 4 kg + 12 kg = 16 kg

Now, Total weight in kilograms is =  (4 kg) (0.16) + (12 kg) (0.40)

= 0.64 kg + 4.80 kg

= 5.44 kg.

Now, the Percent of peanuts

= (Total amount of peanuts / Total weight) x 100%

= (5.44 kg / 16 kg) x 100

= 34%

Thus, the new mixture contains 34% peanuts.

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Answer:f/g=29

Step-by-step explanation:

Answer: (f/g)=29

Hope this helps

Answer:

yes it is if you bisect 5m on a 12m line

Answer: (440-308) ÷ 22 = The cost of each tool kit is 6 dollars

Step-by-step explanation:

The original price of the field trip was $308 after the price fof each tool kit was added the price was $440.

The total costs of all the tool kits was 132

440-308=132

the total cost of the tool kits divided by the number of kids will get the price of each tool kit

132÷22 =

K=

Part A: A

Part B: Julia collected 18.65, Keller collected 61.15, and Israel collected 45.15

The frequency for the interval 160-169 seconds is 3.

The value that appears the most frequently in a data set is its mode. In the data set, it is the number that appears the most frequently. For instance, in the subsequent data set:

2, 3, 4, 4, 5, 5, 5, 6, 7, 8

Since no other value appears more frequently, the mode is 5, which only appears three times. The data set is considered to have several modes if various values occur with the same greatest frequency. There is no mode if no value appears more than once in the data collection.

From the given table we see that the songs that have the time duration between 160 and 169 is:

162, 168, 165

Hence, the frequency for the interval 160-169 seconds is 3.

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The complete question is:

The number of triangles that are displayed can be found to be 216 triangles.

Each rectangular tile has a decorative pattern of 3 equal-sized squares, and each square is divided into 2 same-sized triangles. Therefore, each tile has 3 squares * 2 triangles per square = 6 triangles.

Marnie uses 36 of these tiles on the wall behind her kitchen stove. To find the total number of triangles displayed, multiply the number of triangles per tile by the total number of tiles:

Total triangles = 6 triangles per tile x 36 tiles = 216 triangles

So, there are 216 triangles displayed on the wall behind Marnie's kitchen stove.

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Answer:

6 and 2/3

Step-by-step explanation:

4 divided by 3/5 is the same as 4 divided by 0.6

4 divided by 0.6 equals 6.6 repeating...

or

6 and 2/3

Answer:

Work smartly not hard.

Step-by-step explanation:

AI

Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

The geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

It should be noted that to find the geometric mean of two numbers, we multiply them together and then take the square root of the result. So, for each pair of numbers, we can follow these steps:

Multiply the two numbers together.

Take the square root of the product.

Using this formula, we get:

7.16 and 27:

Geometric mean = √(7.16 × 27) ≈ 14.85

5 and 36:

Geometric mean = √(5 × 36) = √180 ≈ 13.42

10.8 and 48:

Geometric mean = √(10.8 × 48) ≈ 22.94

Therefore, the geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

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The P-value is between 0.025 and 0.05. and t = -1.85

On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.

Therefore tests the hypotheses:

[tex]H_0[/tex] : μ = 25 versus Ha: μ < 25,

where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.

The alternative hypothesis is:

[tex]H_1:\mu < 25[/tex]

The test statistic is given by:

[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }[/tex]

The parameters are:

the values of the parameters are:

x = 23.5 , [tex]\mu=25[/tex] , s = 4.8, n = 35

Plug all the values in above formula of t- statistic is:

[tex]t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }[/tex]

t = -1.85

Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.

t = –1.85; the P-value is between 0.025 and 0.05.

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Thus, new coordinates of A'B'C' after the reflection across the y-axis are-

A'(-5, -1), B'(-3,-4), C'(-3, 0).

The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).

The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).

Given coordinates of ABC.

A(5, -1), B(3,-4), C(3, 0)

Reflection across the y-axis : y coordinates remains same while x coordinate multiplied with -1.

(x,y) -- > (-x, y)

A'(-5, -1), B'(-3,-4), C'(-3, 0)

Thus, new coordinates of A'B'C' after the reflection across the y-axis are-

A'(-5, -1), B'(-3,-4), C'(-3, 0).

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the direction and angle of rotation between the two polygons is 180° clockwise rotation.

How to solve the question?

Based on the given information, we can determine the direction and angle of rotation between the two polygons.

First, let's look at the initial positions of the polygons. The graph of triangle ABC is located in Quadrant 4, which means that it is in the bottom-right portion of the coordinate plane. On the other hand, the second polygon A'B'C' is located in Quadrant 3, which is in the bottom-left portion of the coordinate plane.

To find the direction and angle of rotation between the two polygons, we need to imagine rotating one polygon onto the other. We can see that the two polygons are mirror images of each other across the y-axis. Therefore, we can infer that there is a horizontal line of symmetry between the two polygons.

If we rotate polygon A'B'C' 180 degrees clockwise around the origin, it will overlap perfectly with triangle ABC. This is because a 180-degree rotation is equivalent to a half-turn or a flip, which is exactly what we need to make the two polygons overlap. Therefore, the answer is 180° clockwise rotation.

In summary, the direction and angle of rotation between the two polygons is 180° clockwise rotation.

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Answer: B

Step-by-step explanation:

The word that would indicate that the cat was afraid of the veterinarian is "cowered." "Cowered" means to crouch down in fear or shame. So, the sentence would be: "The cat cowered under the table when the veterinarian came into the examining room."

Answer: 3

Step-by-step explanation:

You would need to use the Pythagorean theorem to solve this equation. 6 is the hypotenuse and 3[tex]\sqrt{3}[/tex] is the longer leg.  

a^2+b^2=c^2

c= hypotenuse

6^2=3[tex]\sqrt{3}[/tex]^2 + a^2

36=27+a^2

36-27=9

[tex]\sqrt{9}[/tex] = 3

Answer:

Step-by-step explanation:

The value of the variable is 3/2

A fraction cam simply be described as an expression that is being used to represent the part of a whole number, a whole variable or element.

There are different types of fractions. They are listed as;

From the information given, we have that;

-7 4/5 divided by X = -5 1/5

convert to improper fractions, we have;

-39/5/x = -26/5

Now, cross multiply the values, we have;

-39/5 = -26x/5

cross multiply

-130x = -195

Divide both sides

x = -195/-130

x = 39/26 = 3/2

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From the calculation, g increases on the interval [-3, 6) and for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)^2.

To determine where g is increasing, we need to find where its derivative, g'(x), is positive. We can find g'(x) by differentiating g(x) with respect to x:

g'(x) = f(x)

Since f(x) is a piecewise-defined function, we need to consider each interval separately.

Therefore, g is increasing on the interval [-3, 6).

To justify this, note that g'(x) = 0 at x = 0 and x = 6, where g has local maxima. This means that g is increasing on the intervals (-3, 0) and (0, 6) and decreasing on (6, 9]. Since g is continuous, it cannot have any jumps, so it must be increasing or decreasing on each of these intervals. Since g(-3) = 0 and g(6) = 9, we know that g is increasing on the interval [-3, 6).

We can evaluate g(x) on the interval [0, 6] by integrating f(x) with respect to t from -2 to x:

g(x) = ∫_{-2}^{x} f(t) dt

On the interval [-3, 0), f(t) = 3, so we have:

g(x) = ∫_{-2}^{0} 3 dt + ∫_{0}^{x} (-t + 3) dt

Simplifying the integrals, we get:

g(x) = 6 - 1/2(x-2)^2, for 0 ≤ x ≤ 6

(Note that we can drop the "+C" since it's being evaluated at the limits of integration.)

Therefore, for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)^2.

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Answer:

3016 centímetros cúbicos.

Step-by-step explanation:

El radio del cilindro es de 8 cm y la altura es de 15 cm. Sustituya 8 por r y 15 por h en la fórmula . Simplifique. Por lo tanto, el volumen del cilindro es de alrededor de 3016 centímetros cúbicos.

The distance Ben travels to get to the park is approximately 2.21 times greater than the distance David travels. This is found by using the distance formula to calculate the distances each person travels and then comparing the results.

To solve this problem, we need to find the distance between each person's house and the park using the distance formula

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

For Ben

distance = √((-2 - 4)² + (-2 - 6)²) = √((-6)² + (-8)²) = √(100) = 10

For David

distance = √((-2 - (-7))² + (-2 - (-6))²) = √((5)² + (4)²) = √(41)

So the ratio of Ben's distance to David's distance is

10 / √(41) ≈ 2.21

Therefore, Ben's distance is about 2.21 times greater than David's distance.

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With additive inverse and by grouping like terms the simplified form of the expression is 6a²-13ab-b².

The given expression is 3a²-5ab+b²-(-3a²+2b²+8ab).

Here,

3a²-5ab+b²+3a²-2b²-8ab

Group like terms, that is

(3a²+3a²)+(-5ab-8ab)+(b²-2b²)

= 6a²-13ab-b²

Therefore, with additive inverse and by grouping like terms the simplified form of the expression is 6a²-13ab-b².

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Answer:

Step-by-step explanation:

The distance from the top of the flagpole to the end of its shadow is approximately 10.02 feet.

Explain the term distance

Distance refers to the measurement of the space between two objects or points. It is typically measured in units such as meters, kilometres, miles, or feet. The distance can be calculated using various methods, including using maps, GPS technology, or mathematical formulas.

According to the given information

We can set up the following proportion:

h / 12 = d / 11

We can cross-multiply to get:

h x 11 = 12 x d

Simplifying further:

d = (h x 11) / 12

We need to solve for d, so we need to find the value of h. Using the Pythagorean theorem, we can set up the following equation:

h² + d² = 12²

Substituting d = (h x 11) / 12, we get:

h² + ((h x 11) / 12)² = 12²

Simplifying:

h² + (121h²) / 144 = 144

Multiplying both sides by 144/265:

265h² / 144 = 144

Solving for h:

h² = (144 x 144) / 265

h = √(20736 / 265)

h = √(78.113)

Now we can substitute this value into our earlier equation to find d:

d = (√(78.113) x 11) / 12

d ≈ 10.02 feet

Therefore, the distance from the top of the flagpole to the end of its shadow is approximately 10.02 feet.

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Applying the intersecting secants theorem, the value of x is calculated as: x = 5.

According to the intersecting secants theorem, if two secant lines intersect outside of a circle, then the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.

Using the theorem, the equation below is created to find the value of x:

4(4 + 5) = (x - 2)(x - 2 + x + 4)

4(9) = (x - 2)(2x + 2)

36 = 2x² - 2x - 4

2x² - 2x - 4 - 36 = 0

2x² - 2x - 40 = 0

Factorize:

(x + 4)(x - 5) = 0

x = -4 or x = 5

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number one take the second

The percentage of the people that preferred cooking who where surveyed would be = 87.2%

The total number of people surveyed = 8

The total number of people that preferred cooking = 7

The percentage of people that preferred cooking;

= 7/8×100/1

= 700/8

= 87.2%

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Answer: 300

Step-by-step explanation:

10*8*6=480-6*6*5=180=300