I invest $350 in a simple interest account that earns 8%. how much interest will I make after 3.5 years

Answer:

Step-by-step explanation:

In this scenario, the confidence interval represents the possible range of differences in the proportion of employees who skip breakfast when free breakfast is offered and when it's not. A confidence interval that does not include zero indicates that there is statistically significant evidence to suggest a difference in proportions between these two groups.

Therefore, for the first interval (-0.44,-0.16), since it does not include zero, we can be confident that offering free breakfast results in a decrease in the proportion of employees who skip breakfast.

For the second interval (-0.25, 0.05), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

Similarly, for the third interval (-0.23, 0.15), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

So, the correct answer is:

For the interval (-0.44,-0.16), we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.

For the intervals (-0.25, 0.05) and (-0.23, 0.15), our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.

Answer:5

Step-by-step explanation:

Collect like term:

6-3.5=0.5x

2.5=0.5x

Divide both side by 0.5

Ans:5

Therefore x=5

Answer:

51 miles

Step-by-step explanation:

perimeter is distance around the outside of figure.

there are three sides with 17 mi. That means the perimeter is 51 miles

Answer: 240

Step-by-step explanation:

You would multiply each of the sides to get the final answer of 240 (:

The total cupcakes the bakery sell that day is 80

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

Number of sales = 76

Proportion = 95%

This implies that

Number of sales = Proportion * Total number of cupcakes

Substitute the known values in the above equation, so, we have the following representation

76 = 95% * Total number of cupcakes

Divide both sides by 95%

Total number of cupcakes = 80

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Answer:

9

Step-by-step explanation:

5,6,7,8,9

The difference, to the nearest gram, of the masses of the rectangular

prisms  is 1393.2 grams.

The volume of the rectangular prism is the product of the length, breadth, and height of the given prism.

Volume of rectangular prism = (length x width x height)

Joe has a rectangular prism made of aluminum and a rectangular prism made of lead.

Each rectangular prism has a height of 6 cm, length of 9 cm, and width of 3 cm.

The volume of a rectangular prism made of aluminum  = (length x width x height)

= \(6 \times 9\times 3\\\\162\)

The volume of a rectangular prism made of lead= (length x width x height)

= 162 cubic cm

We know that mass = density x volume

The density of aluminum is approximately 2.70.

mass = 2.70 x 162

          = 437.4 grams

The density of lead is approximately 11.3 cm3

mass = 11.3 x 162

          = 1830.6 grams

The difference, to the nearest gram, of the masses of the rectangular

prisms  1830.6 - 437.4  = 1393.2 grams

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We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.

The Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:

1. f(t, y) is continuous in the region.

2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.

then there exists a unique solution to the differential equation that passes through any point in the region.

In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:

f(t, y) = (y cot(2t)) / (t² + y² + 1)

This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.

To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:

∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²

Taking the absolute value and simplifying, we get:

|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|

= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|

Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:

1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1

Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.

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the square root of 598 is 24.4540385

Therefore, the estimated relative error in the calculated surface area is 1.14%.

To estimate the maximum error in the calculated surface area of a sphere, we can use linear approximation.

The surface area of a sphere is given by the formula:

A = 4πr²

where r is the radius of the sphere.

We know that the circumference of the sphere is measured to be 70 cm with a possible error of 0.5 cm. The circumference is related to the radius by the formula:

C = 2πr

Therefore, the radius of the sphere can be approximated as:

r ≈ C/2π

Substituting the given value of the circumference, we get:

r ≈ 70/2π

r ≈ 11.137 cm

To estimate the maximum error in the calculated surface area, we need to find the maximum possible error in the radius. The error in the radius can be approximated as:

Δr ≈ ΔC/2π

Substituting the given value of the possible error in the circumference, we get:

Δr ≈ 0.5/2π

Δr ≈ 0.0796 cm

Therefore, the maximum possible error in the calculated surface area can be estimated as:

ΔA ≈ 2πrΔr

ΔA ≈ 2π(11.137) (0.0796)

ΔA ≈ 5.58 cm² (rounded to two decimal places)

To estimate the relative error in the calculated surface area, we can use the formula:

ΔA/A ≈ 2Δr/r

Substituting the values of Δr and r, we get:

ΔA/A ≈ 2(0.0796)/11.137

ΔA/A ≈ 0.0114

Converting to a percentage, we get:

ΔA/A ≈ 1.14% (rounded to two decimal places)

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Answer:

The table represents a linear function.

Step-by-step explanation:

Graphed, the points go in a straight line, and you are able to draw a line through it. The equation for the line is y = 4x + 4.

The acute angle of intersection is  5.2°.

What is acute angle?

Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Discover the various sorts of angles and examples of each.

The direction vector normal to the plane is ...

 n = (1, 1, 3)

The direction vector of the line is ...

 m = (1, -3, 1)

Then the angle θ between them can be found from the dot product:

 n•m = |n|·|m|·cos(θ)

 (1·1 +1(-3) +3·1) = 1 -3 +3 = 1 = √(1²+1²+3²)·√(1²+(-3)²+1²)·cos(θ)

 1 = 11·cos(θ)

 θ = arccos(1/11) ≈ 84.8°

This is the angle between the line and the normal to the plane, so the angle between the line and the plane will be the complement of this. Since this angle is not 90°, the line and plane must intersect.

 acute angle = 90° -84.8° = 5.2°

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Answer:

724 miles

Step-by-step explanation:

subtract the values(1372-648)

Answer:

\({\dfrac{x^{2}}{9} - \dfrac{y^{2}}{36} = 1}\)

Step-by-step explanation:

The hyperbola has x-intercepts, so it has a horizontal transverse axis.

The standard form of the equation of a hyperbola with a horizontal transverse axis is  \(\dfrac{(x - h)^{2}}{a^{2}} - \dfrac{(y - k)^{2}}{b^{2}} = 1\)

The center is at (h,k).

The distance between the vertices is 2a.

The equations of the asymptotes are\(y = k \pm \dfrac{b}{a}(x - h)\)

1. Calculate h and k. The hyperbola is symmetric about the origin, so  

h = 0 and k = 0

2. For 'a': 2a = x₂ - x₁ = 3 - (-3) = 3 + 3 = 6

a = 6/2 = 3  

3. For 'b': The equation for the asymptote with the positive slope is  

\(y = k + \dfrac{b}{a}(x - h) = \dfrac{b}{a}x\)

Thus,  asymptote has the slope of

\(\begin{array}{rcl}m& =& \dfrac{b}{a}\\\\2& =& \dfrac{b}{3}\\\\b& =& \mathbf{6}\end{array}\)

4.  The equation of the hyperbola is

\(\large \boxed{\mathbf{\dfrac{x^{2}}{9} - \dfrac{y^{2}}{36} = 1}}\)

The attachment below represents your hyperbola with x-intercepts at ±3 and asymptotes with slope ±2.

Answer: c

Step-by-step explanation: edge 23

The expression in terms of q is,

⇒ q = (x - 48,084) / 2.68

We have to given that;

Expression is,

⇒ x = 2.68q + 48,084

Now, We can simplify the expression in terms of q as;

⇒ x = 2.68q + 48,084

Subtract both side by 48,084;

⇒ x - 48,084 = 2.68q + 48,084 - 48,084

⇒ x - 48,084 = 2.68q

Divide both side by 2.68;

⇒ (x - 48,084) / 2.68 = q

⇒ q = (x - 48,084) / 2.68

Thus, The expression in terms of q is,

⇒ q = (x - 48,084) / 2.68

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Answer:

the answer is c. it’s commutative property

Step-by-step explanation:

12-(y•2) is the same as 12-(2•y) 2 and y are just flipped around. hope this helps!

Answer:

B. {robin, sparrow, pelican}

Step-by-step explanation:

hope it helps you...

The outcomes are in A and B is,

⇒  {robin, sparrow, pelican}

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Let event A = The animal is a bird

Let event B = The animal can fly.

Hence, We get;

The outcomes are in A and B in which animal is a bird and also can fly.

Thus, The outcomes are in A and B is,

⇒  {robin, sparrow, pelican}

Hence, The outcomes are in A and B is,

⇒  {robin, sparrow, pelican}

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Answer:

6 minutes

Step-by-step explanation:

The ant can crawl 40 cm per minute but is pushed back 5 cm every minute aswell. In total the ant will crawl 35 cm per minute (40 - 5 = 35).

In order to find how long it will take for the ant to reach the hole we divide 210 by 35 (210/35) to get the answer of 6, therefore it takes the ant 6 minutes to reach the hole.

A tree diagram to calculate the probability of each of the four possible outcomes are 0.8, 0.8, 0.1, 0.06.

Bag A contains one red ball and one blue ball, whereas bag B contains two white balls and three black balls.

P(A) = 0.2

P(B) = 0.8

Probability of getting one red is 1/1 = 1

Probability of getting one blue is 1/1 = 1

Probability of getting one white ball is 1/2

Probability of getting 1 black ball is 1/3

Therefore, by tree diagram we get four possible probability that is  

0.8, 0.8, 0.1, 0.06.

A probability tree illustration is used to represent the probability of circumstance of events without using complicated formulas. It displays all the possible issues of an event. The purpose of a probability tree is that it shows all the possible issues of an event and calculates the probability of these issues. A probability tree illustration can either represent a series of independent events or it can be used to denote tentative chances.

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The insect measurement that was the most frequent is given as follows:

1 and 1/4 inches.

A dot plot is a simple graphical display that uses dots to represent data values. It is also sometimes called a dot chart or a scatterplot. In a dot plot, each data point is represented by a dot along a number line or axis, where the position of the dot corresponds to the value of the data point.

Hence, a dot plot shows the number of times that each observation appeared in the data-set.

The observation with the most dots is the observation 2/8 of the way between 1 and 2, hence the most frequent observation is given by the following mixed number:

1 and 2/8 = 1 and 1/4 inches.

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Answer:

$54

Step-by-step explanation:

10% of $60 is $6

$60-$6=$54

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The speed is the independent variable because when it changes all the others change because it changed

The correct option is D. speed.

Given, As a person increases cycling speed, the rate of calorie burned, distance traveled, and energy also increase.

We have to find the Independent variable.

Since, Calories burned, distance traveled and Energy generated all are dependent on the speed of cycling. As the speed increases calories burned will be more.So speed is the independent variable here and the other variables all are dependent variable.

Hence the correct option is D. speed.

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Answer:

honestly I don't know 5

Step-by-step explanation:

Answer:

The number is 500.

Step-by-step explanation:

Let n be the number

Convert percent to decimal

20% = 0.20

0.20n = 100

Divide both sides of the equation by 0.20

0.20n/0.20 = 100/0.20

n = 500

Answer:

I believe it is 200. Forgive me if its wrong-

A .The canoe left the campsite did the motorboat catch up with it 3 hrs and 40 minutes

B . The motorboat travel at 1 hr 40 minutes

A group of campers and one group leader left a campsite in a canoe.

They traveled at an average rate of 10 km/h.

1st Group DATA:

rate = 10 km/h ; distance = x km ; time = d/r = x/10 hrs

Two hours later, the other group leader left the campsite in a motorboat.

He traveled at an average rate of 22 km/h.

Group Leader DATA:

rate = 22 km/h ; distance = x km ; time = d/r = x/22 hrs

A. How long after the canoe left the campsite did the motorboat catch up with it?

Group time - Leader time = 2 hr

x/10 - x/22 = 2

Multiply thru by 110 to get:

11x - 5x = 220

6x = 220

x = 110/3 = km

canoe total time = x/10 = (110/3)/(10) = 11/3 = 3 hrs and 40 minutes

B. How long did the motorboat travel?

motorboat time = x/22 = (110/3)/22 = 1 hr 40 minutes

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Answer:

81.20

Step-by-step explanation:

I took the test and got it right

Answer:

157,500

Step-by-step explanation:

45,000 x 3.5$= 157,500

Lolz i' wrong prolly cuh so my bad g