Each triangle weighs 8 grams. Each circle weighs 3 grams. Each trapezoid weighs x grams.

Flo ate more of the sandwich than Arnie.

Option A is the correct answer.

We have,

We need to compare the values 3/4 and 2/3 to determine which fraction represents a larger amount of sandwiches eaten.

To make the fractions comparable, we need to find a common denominator.

The least common multiple of 4 and 3 is 12.

So we can rewrite 3/4 and 2/3 with 12 as the denominator:

3/4 = 9/12

2/3 = 8/12

Comparing these fractions, we see that 9/12 (or 3/4) is greater than 8/12

(or 2/3).

Therefore,

Flo ate more of the sandwich than Arnie.

Learn more about fractions here:

https://brainly.com/question/24370499

#SPJ1

The series [infinity]Σ n=1 (4^n * x^(2n))/n converges conditionally when x is in the interval: (c) x = ±1/2

To determine when the series [infinity]Σ n=1 (4^n * x^(2n))/n converges conditionally, we can use the ratio test. Let's apply the ratio test to the series:

lim(n→∞) |(4^(n+1) * x^(2(n+1)) / (n+1)) / (4^n * x^(2n) / n)|

Simplifying this expression:

lim(n→∞) |(4^(n+1) * x^(2(n+1)) * n) / (4^n * x^(2n) * (n+1))|

Simplifying further:

lim(n→∞) |4 * x^2 * n / (n+1)|

Taking the absolute value and applying the limit:

lim(n→∞) |4 * x^2 * n / (n+1)| = |4 * x^2|

Now, for the series to converge conditionally, the ratio |4 * x^2| must be less than 1. Therefore, we have:

|4 * x^2| < 1

Solving this inequality:

-1 < 4 * x^2 < 1

Dividing all terms by 4:

-1/4 < x^2 < 1/4

Taking the square root of all terms:

-1/2 < x < 1/2

Hence, the series [infinity]Σ n=1 (4^n * x^(2n))/n converges conditionally when x is in the interval: (c) x = ±1/2

To learn more about series click here:

brainly.com/question/31062040

#SPJ11

Option(C),  the approximate standard deviation of X is 7.59. The sample size increases, the standard deviation of X will decrease, making it a more reliable estimate of the population proportion.

To find the approximate standard deviation of X, we can use the formula:
σ = √(np(1-p))
Where n is the sample size (1500 in this case), p is the probability of success (0.04 in this case), and (1-p) is the probability of failure (0.96 in this case).
Substituting the values, we get:
σ = √(1500 x 0.04 x 0.96)
σ = √57.6
σ ≈ 7.59
Therefore, the approximate standard deviation of X is 7.59. Option C is the correct answer.
The standard deviation is a measure of how spread out a set of data is from the mean. In this case, the standard deviation of X represents how much the number of people who support the increase in the state sales tax varies from sample to sample.
As per the given information, 4% of all adults in Ohio support the increase. We can assume that this is the population proportion. Since we are dealing with a sample of 1500 adults in Ohio, we need to calculate the standard deviation of the sample proportion (X), which is an estimate of the population proportion.
Using the formula σ = √(np(1-p)), we find that the standard deviation of X is approximately 7.59. This means that if we were to take multiple random samples of 1500 adults from Ohio and ask them about their support for the sales tax increase, we can expect the number of supporters to vary by about 7.59 on average.
It's important to note that this is only an estimate, and the actual standard deviation of X may differ slightly from 7.59 due to sampling error. However, as the sample size increases, the standard deviation of X will decrease, making it a more reliable estimate of the population proportion.

To know more about  standard deviation visit :

https://brainly.com/question/29115611

#SPJ11

Answer:

she bought 7 packs of paper

Step-by-step explanation:

12.74/p = 7

Points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.

Every triangle has inner angles that add up to 180 degrees. A right angle and a right triangle are both formed when one of their internal angles is 90 degrees.

Given coordinates :

a(5,2) , b(2,-3) and c(-8,3).

Find the distance between the points using the distance formula:

d = √[(x2 - x1)² + (y2 - y1)²]

ab = √[(2 - 5)² + (- 3 - 2)²]

ab = √[(-3)² + (- 5)²]

ab = √[9 + 25]

ab = √34

ab² = 34

bc = √[(2 + 8)² + (- 3 - 3)²]

bc  = √[(10)² + (- 6)²]

bc  = √[100 + 36]

bc  = √136

bc²  = 136

ac = √[(-8 - 5)² + (3 - 2)²]

ac = √[(-13)² + (1)²]

ac = √[169 + 1]

ac = √170

ac² = 170

Now,

(ac)² = (bc)² + (ab)²

170 = 136 + 24

170 = 170

This, points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.

know more about the right angled triangle

https://brainly.com/question/64787

#SPJ1

The two expressions (with at least two terms each) that when added together have a sum of -4n + 6 will be (n + 4) + (2 -5n)

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

A mathematical expression is a phrase with at least two variables or numbers and one math operation. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

The expressions will be:

(n + 4) + (2 -5n)

= n - 5n + 4 + 2

= -4n + 6

Learn more about expressions:

brainly.com/question/723406

#SPJ1

To show h(t) = |r(t)|², where r(t) is a complex-valued function, we need to first find the magnitude of r(t) and then square it.

Let r(t) = x(t) + i y(t) be a complex-valued function, where x(t) and y(t) are the real and imaginary parts of r(t), respectively. The magnitude of r(t) is given by |r(t)| = √(x(t)² + y(t)²), which is the distance of the point (x(t), y(t)) from the origin in the complex plane.

To find |r(t)|², we simply square the magnitude, i.e., |r(t)|² = (x(t)² + y(t)²).

Therefore, h(t) = |r(t)|² = (x(t)² + y(t)²),

which is the sum of the squares of the real and imaginary parts of r(t).

In the case where r(t) is a real-valued function, i.e., y(t) = 0, then h(t) reduces to h(t) = r(t)².

To know more about complex-valued function, refer here:
https://brainly.com/question/30612470#
#SPJ11

Answer: C. 15x + 12y = 489

Step-by-step explanation: Got it right on edge test

Answer:

C

Step-by-step explanation:

15x+12y=489

Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

To learn more about the mean and standard deviation visit:

brainly.com/question/475676

#SPJ4

After the raise, the salary of woman becomes $2700.

The answer was determined through simple arithmetic calculations.

This method of calculation can be applied to any similar scenario where an initial salary is reduced by a certain percentage and then increased by another percentage. The formula used can be generalized as:

Final Salary = (Initial Salary - Initial Salary * Reduction Percentage) * (1 + Raise Percentage)

It's a simple and straightforward method that can be easily applied to find the final salary in similar cases.

Learn more about Salary Reduction and Raise here:

https://brainly.com/question/15997856

#SPJ4

Answer:

100

Step-by-step explanation:

Givens

WX = 4 + 3 = 7

ZY = 7 + 6 = 13

Height = 4 + 6 = 10

Formula

Area = (WX + ZY ) * height /2

Solution

Area = (7 +13)*10 / 2

Area = 20*10/2

Area = 200/2

Area = 100

Answer:

71.7

Step-by-step explanation:

If you draw out a picture and visualize it, you will be able to see that you need to use inverse cosine to solve this. Plug in cos^-1 (2.2/7) and you will get 71.7 as your answer.

Answer:

71.7 degrees

Step-by-step explanation:

The sum of the two number is 23.

Let's call the two numbers x and y. We know that:

x^2 + y^2 = 327

xy = 101

We want to find x + y.

We can start by squaring the equation x + y:

(x + y)^2 = x^2 + 2xy + y^2

Substituting in the values we know:

(x + y)^2 = x^2 + y^2 + 2xy

(x + y)^2 = 327 + 2(101)

(x + y)^2 = 529

Taking the square root of both sides:

x + y = ±23

Since both x and y are non-negative, we know that x + y must be positive. Therefore:

x + y = 23

So the sum of the two numbers is 23.

To know more about non-negative

https://brainly.com/question/16155009

#SPJ4

Answer:

The first pair.

Step-by-step explanation:

3 corresponding parts must be congruent for two triangles to be congruent. The first pair has 3 congruence markings; two angles and one side are congruent. Additionally, they are congruent by the ASA postulate because two angles and the included side are congruent.

Answer:10

Step-by-step explanation:

8+2=10

Answer: yes it is

Step-by-step explanation:

The value of f(-2) is -2 and the function f in the slope intercept form is y = (1/2)x - 1.

From the graph, we can observe that, the x-intercept is 2 and the y-intercept is -1.

Hence,

Coordinates of x-intercept = (0,-1)

Coordinates of y-intercept = (2,0)

Slope, m of the line = (-1-0)/(0-2) = -1/(-2) = 1/2.

General equation of the line in the slope intercept form :-

y = mx + c

Putting (0,-1) in the equation, we get,

-1 = (1/2)*(0) + c

-1 = 0 + c

c = -1

Hence, the equation of the function will be:-

y = (1/2)x - 1.

Now, value of f(-2) = (1/2)(-2) - 1 = -1 - 1 = -2.

To learn more about slope intercept form, here:-

https://brainly.com/question/9682526

#SPJ1

Using the straight angles we know that the following angles are: ∠a=54°, ∠b=47°, and ∠c=89°

In Mathematics, a straight angle is an angle equal to 180 degrees. Because it resembles a straight line, it is called straight.

Straight angles are those that have a 180-degree ( = 180°) angle.

Reflex angles are those with a value between 180 and 360 degrees (180° 360°).

Whole turns ( = 360°) are angles that are 360 degrees in length.

So, we now know that:

a + b + c = 180

3x+5 + 5x-18 + 7x-2 = 180

15x -15 = 180

15x = 180+15

15x = 195

x = 195/15

x = 13

Now,

∠a=3x+5

∠a=3(13)+5

∠a=54°

∠b=5x-18

∠b=5(13)-18

∠b=47°

c=7x-2

c=7(13)-2

∠c=89°

Therefore, using the straight angles we know that the following angles are: ∠a=54°, ∠b=47°, and ∠c=89°

Know more about straight angles here:

https://brainly.com/question/24024505

#SPJ1

Answer:

C

Step-by-step explanation:

If you draw a straight line through all the corresponding vertices, where the three vertices meet up at is the center of dilation, they all meat up at point C so C is the center of dilation.

Answer: 804.25 yards3

Step-by-step explanation: : Explanation We have height (H) = 4 yards Diameter = 4x4 = 16, Radius (r) = 16/2 = 8, volume and cylinder V = nr2h. V= 3.14 x 8x8x4, V= 804.25 yards 3

Answer:

This is not a function

Step-by-step explanation:

take your pencil, place it vertically. If it lines up with two coordinates on top of eachother, it is not a function.

Answer:

20

Step-by-step explanation:

that is right...........

The correct interpretation of the 95% confidence interval is:

"We estimate with 95% confidence that the true population mean height of orangutans is between 52 and 58 inches."

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

The confidence interval provides a range of values within which the true population mean height is likely to fall with a 95% level of confidence. It does not provide information about individual orangutans' heights or the sample mean's precise location within the interval.

Therefore, The correct interpretation of the 95% confidence interval is:

"We estimate with 95% confidence that the true population mean height of orangutans is between 52 and 58 inches."

To learn more about statistics from the given link:

https://brainly.com/question/28053564

#SPJ1

If isosceles trapezoid ABCD has a median XY then CD = 8 .

What is trapezoid?

A trapezοid is alsο knοwn as a trapezium is a fοur-sided pοlygοn οr a quadrilateral. It has οne set οf οppοsite sides which are parallel and a set οf nοn-parallel sides. The parallel sides are knοwn as the bases and the nοn-parallel sides are knοwn as the legs οf the trapezοid. A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Given AX = 4

Now, AX = BX as XY is the meridian

i.e.

AB = 2AX

AB = 2(4)

AB = 8

We have given that the trapezoid is an isosceles trapezoid, which means

AB = CD

i.e.

CD = 8

Thus, If isosceles trapezoid ABCD has a median XY then CD = 8.

To learn more about trapezoid from the given link:

https://brainly.com/question/8643562

#SPJ1

Scheduling court hearings is a linear optimization problem with judge hours and available hours as constraints. The given set of vectors form a basis for R³ and the matrices have rank 3.

1. a) The linear program for scheduling court hearings can be formulated as follows:

Minimize Z = 0

Subject to:

∑_j (x_ij) * (h_i) <= (Δ_j) for all i = 1,2,...,n

x_ij >= 0 for all i = 1,2,...,n and j = 1,2,...,m

Where x_ij is the number of hearings of class i processed at period j, h_i is the number of judge-hours required to process a hearing of class i, and Δ_j is the available judge-hours at period j.

b) To prevent hearings from being delayed for too long, the linear program can be modified by adding a constraint that ensures that the number of hearings of class i processed at each period is at least a minimum value. For example:

x_ij >= minimum value for all i = 1,2,...,n and j = 1,2,...,m

2. a) The vectors ???? = (1 2 1), ???? = (-1 0 -1), ???? = (0 0 1) form a basis of R^3 because they are linearly independent and span the entire space R^3.

b) The vectors ???? = (-1 2 3), ???? = (0 1 0), ???? = (1 2 3), ???? = (-3 2 4) form a basis of R^3 because they are linearly independent and span the entire space R^3.

c) The vectors ???? = (1 2 1), ???? = (-3 -1 2), ???? = (8 -1 7) form a basis of R^3 because they are linearly independent and span the entire space R^3.

3. The vectors ???? = (1 0 0), ???? = (0 1 0), ???? = (1 5 3) form a basis of R^3. If ???? is replaced by (0 1 1), the new set of vectors do not form a basis of R^3 because they are linearly dependent.

4. The rank of a matrix is the number of linearly independent rows or columns. The rank of a matrix is equal to the number of non-zero rows in the row echelon form of the matrix or the number of non-zero columns in the column echelon form of the matrix. By inspection, the rank of the matrices is 3, which is the number of non-zero rows or columns in either form.

To learn more about the matrix, visit:

brainly.com/question/29132693

#SPJ4

Answer:

the answer is D.

Answer:

x=18

Step-by-step explanation:

Hey There!

So if you did not know all of the angles in a triangle will add up to equal 180

So we use the equation

180=2x+3x+5x

and solve for x

step 1 combine like terms

2x+3x=5x

5x+5x=10x

so now we have

180=10x

step 2 divide each side by 10

180/10=18

therefore x = 18

hope this helps and if you have any more questions feel free to ask :)

Margo is raising money for her club by selling boxes of nuts. She discovers that cashews are sold in three out of every seven cartons of nuts. The ratio, y=3/7, is the proportion of cashew boxes sold to all boxes sold.

Describe ratio:

A relationship between two quantities is called a ratio, and it is expressed as one quantity divided by the other. A ratio between two quantities, let's say 'a' and 'b,' is typically expressed as a: b.

Three out of every seven boxes of nuts, according to Margo, are cashews. These steps can be used to determine the ratio of two quantities: Before we can calculate the ratio, we must first figure out the values for both instances. There are three cashews and seven boxes present in this scenario. As a fraction, write it as a/b. Therefore, we express it as y= 3/7. As a result, the ratio of the number of cashew boxes to the total number of boxes sold is given as y=3/7.

Learn more about the equation here: brainly.com/question/2972832

#SPJ4