Russo is trying to find the area of the lake in his neighborhood. He sees a duck (point C) and uses a tape measure to find that the duck is 16 feet from the point of tangency (point B). He also measures out that the duck is 8 feet away from the edge of the lake (in the direction of A).



Using this information, what is the radius of the lake?

Answers

Answer 1

The radius of the lake is approximately 17.89 feet.

To find the radius of the lake, we can use the information given and apply the properties of tangents to circles.

Since point B is the point of tangency, the line segment AB is tangent to the circle. A radius drawn to the point of tangency, in this case from the center of the lake (point O) to point B, will be perpendicular to the tangent line (line AB).

Now, let's use the given measurements. The distance from the duck (point C) to the point of tangency (point B) is 16 feet, and the distance from the duck (point C) to the edge of the lake in the direction of A (line AC) is 8 feet. We can form a right-angled triangle OBC with the given information.

Since OB is perpendicular to AB, we have a right-angled triangle with legs CB and OC. Using the Pythagorean theorem, we can find the length of the hypotenuse, which is the radius of the lake:

OC^2 + CB^2 = OB^2
(8 feet)^2 + (16 feet)^2 = OB^2
64 + 256 = OB^2
320 = OB^2
OB = √320
OB ≈ 17.89 feet

So, the radius of the lake is approximately 17.89 feet.

To learn more about radius, refer below:

https://brainly.com/question/13449316

#SPJ11


Related Questions

Your answer should be in the form p(x) +k/x+2 where p is a polynomial and k is an integer of x^2 +7x+12/x+2

Answers

p(x) = x + 5, and k = 2. The expression x^2 + 7x + 12 / (x + 2) can be written in the form p(x) + k / (x + 2) as:

x + 5 + 2 / (x + 2)

To express the given expression x^2 + 7x + 12 / (x + 2) in the form p(x) + k / (x + 2), we will perform polynomial division.

1. Divide the numerator (x^2 + 7x + 12) by the denominator (x + 2):

(x^2 + 7x + 12) ÷ (x + 2)

2. Perform long division:

       x + 5
       ________________
x + 2 | x^2 + 7x + 12
       - (x^2 + 2x)
       ________________
             5x + 12
             - (5x + 10)
       ________________
                 2

3. Write the result:

p(x) + k / (x + 2) = x + 5 + 2 / (x + 2)

So, p(x) = x + 5, and k = 2. The expression x^2 + 7x + 12 / (x + 2) can be written in the form p(x) + k / (x + 2) as:

x + 5 + 2 / (x + 2)

Learn more about polynomial division,

https://brainly.com/question/24662212

#SPJ11

Let x1 > 1 and xn+1 := 2−1/xn for n ∈ N. Show that xn is bounded and monotone. Find the limit. Prove by induction

Answers

We have shown that xn is bounded and monotone increasing, and its limit is √2. First, we will show that xn is bounded and monotone increasing by induction:

Base Case: For n = 1, we have x1 > 1, which is true.

Inductive Hypothesis: Assume that xn > 1 for some n = k and show that xn+1 > xn for n = k.

Inductive Step:

We have xn+1 := 2−1/xn

Since xn > 1, we have 1/xn < 1

Therefore, 2−1/xn > 2−1/1 = 1/2

So, xn+1 > 1/2

Since xn > 1, we have xn+1 = 2−1/xn < 2−1/1/ = 1

So, 1/2 < xn+1 < 1

Therefore, xn is bounded and monotone increasing.

Next, we will find the limit of xn as n → ∞:

Let L = lim xn as n → ∞

Then, taking the limit on both sides of xn+1 = 2−1/xn, we get:

L = 2−1/L

Multiplying both sides by L, we get:

L2 = 2−1

Solving for L, we get:

L = ±√2

Since xn > 1 for all n, we have L > 1. Therefore, L = √2.

Thus, we have shown that xn is bounded and monotone increasing, and its limit is √2.

Learn more about monotone increasing,

https://brainly.com/question/17177037

#SPJ4

Given the following exponential function, identify whether the change represents


growth or decay, and determine the percentage rate of increase or decrease.


y = 660(0. 902)

Answers

The function represents exponential decay with a percentage rate of decrease of 9.8%.

The given exponential function y = 660(0.902) represents decay because the base of the exponent is less than one.

This means that the output value of the function will decrease as the input value increases.

To determine the percentage rate of decrease, we need to find the value of the base of the exponent subtracted from one and then multiply it by 100.

The base of the exponent is 0.902, so we subtract it from one to get 0.098.

Multiplying by 100 gives us a percentage rate of decrease of 9.8%.

This means that for every unit increase in the input value, the output value of the function will decrease by approximately 9.8%.

For example, if the input value increases from 1 to 2, the output value will decrease by 9.8%, and if the input value increases from 2 to 3, the output value will again decrease by 9.8%.

Learn more about exponential decay here:

https://brainly.com/question/2193820

#SPJ4

Bill needs a table to display his model train set. the table needs to be 2 times longer and 3 inches shorter
than it is wide and have an area of 4,608 square inches. what does x need to be to fit these requirements?
2x-3

Answers

2x - 3 would be 92 - 3 = 89 inches, which is the length of the table

How to find the length?.

The table needs to be 2 times longer than it is wide, so its length is 2 times its width, or 2x.

The table also needs to be 3 inches shorter than it is wide, so its width is x + 3 inches.

The area of the table is 4,608 square inches, so we can set up an equation:

2x(x + 3) = 4,608

Simplifying this equation:

2x²+ 6x = 4,608

Dividing both sides by 2:

x²+ 3x - 2,304 = 0

We can solve for x using the quadratic formula:

x = (-b ±  √(b² - 4ac)) / 2a

In this case, a = 1, b = 3, and c = -2,304. Substituting these values:

x = (-3 ±  √(3² - 4(1)(-2,304))) / 2(1)

Simplifying:

x = (-3 ±  √(9 + 9,216)) / 2

x = (-3 ±  √(9,225)) / 2

x = (-3 ± 95) / 2

x = 46 or x = -49

Since the width of the table cannot be negative, we can ignore the negative solution. Therefore, x needs to be 46 inches to fit the given requirements.

The length of the table is 2x, or 2(46) = 92 inches, and the width is x + 3, or 46 + 3 = 49 inches. The area is 92 * 49 = 4,508 square inches, which matches the given area requirement.

So, 2x - 3 would be 92 - 3 = 89 inches, which is the length of the table.

Learn more about Length

brainly.com/question/9842733

#SPJ11

Alexandra rolls a standard six-sided die, numbered from 1 to 6. which word or phrase describes the probability that she will roll a number between 1 and 6 ( including 1 and 6)?​

Answers

The probability that Alexandra will roll a number between 1 and 6, including 1 and 6, on a standard six-sided die can be described as "certain" or "100%."

Here's a step-by-step explanation:

1. A standard six-sided die has six faces, numbered from 1 to 6.


2. When rolling the die, each face has an equal chance of landing face up.


3. The question asks for the probability of rolling a number between 1 and 6, which includes all the possible outcomes (1, 2, 3, 4, 5, and 6).


4. Since all outcomes are covered, the probability of this event occurring is 100% or certain.


Therefore, the word or phrase that describes this probability is "certain" or "100%."

To know more about probability refer here:

https://brainly.com/question/30034780

#SPJ11

The picture has the instructions.

Answers

The Gross Profit Margin Ratio for Frontier Art Gallery is 69.38%, calculated by dividing the Gross Profit by Net Sales and multiplying the result by 100 to get the percentage.

Gross Profit Margin Ratio is calculated by dividing the Gross Profit by Net Sales and multiplying the result by 100 to get the percentage

Gross Profit = Net Sales - Cost of Merchandise Sold

Gross Profit = $62,481.45 - $19,123.49

Gross Profit = $43,357.96

Gross Profit Margin Ratio = (Gross Profit / Net Sales) x 100

Gross Profit Margin Ratio = ($43,357.96 / $62,481.45) x 100

Gross Profit Margin Ratio = 69.38%

Therefore, the Gross Profit Margin Ratio for Frontier Art Gallery is 69.38%.

To know more about Gross Profit Margin Ratio:

https://brainly.com/question/22718027

#SPJ1

Find the value of x

Hellpppp

Answers

Explanation is in the image!

Mary’s dog weighed 25 kg, but then it got sick and lost 2. 3 kg. A What percentage of body weight did the dog lose? B Mary weighs 58 kg. If Mary lost the same percentage of her body weight as what the dog did, how much would Mary weigh?

Answers

The percentage of body weight the dog lost is 9.2%. Mary would weigh 52.664 kg after losing the same percentage of body weight as her dog.

A) To find the percentage of body weight the dog lost, first, calculate the actual weight loss: 25 kg - 2.3 kg = 22.7 kg. Then, divide the weight loss (2.3 kg) by the original weight (25 kg) and multiply by 100 to get the percentage: (2.3 kg / 25 kg) * 100 = 9.2%.

B) If Mary lost the same percentage of her body weight as the dog did, she would lose 9.2% of her weight. To calculate this, multiply her original weight (58 kg) by the percentage (9.2%): 58 kg * 0.092 = 5.336 kg. Now, subtract this weight loss from her original weight to find her new weight: 58 kg - 5.336 kg = 52.664 kg. So, Mary would weigh 52.664 kg after losing the same percentage of body weight as her dog.

More on body weight: https://brainly.com/question/28505958

#SPJ11

Geometry in circle p, m2=m1, m2= 4x + 35, m1= 9x +5 find :
need help!

Answers

Based on the given information, we can set up an equation using the fact that the measures of angles m1 and m2 are equal in circle P.

m1 = m2

Substituting the given values:

9x + 5 = 4x + 35

Solving for x:

9x - 4x = 35 - 5

5x = 30

x = 6

Now that we have found the value of x, we can substitute it back into the expressions for m1 and m2 to find their measures:

m1 = 9x + 5 = 9(6) + 5 = 59

m2 = 4x + 35 = 4(6) + 35 = 59

Therefore, both angles have a measure of 59 degrees.

To know more about angles refer here

https://brainly.com/question/7116550#

#SPJ11

The cost to produce x cases of Thingamabobs is given by the function C = 50x + 1000 where Cis in hundreds of dollars. If production is growing at a rate of 20 cases per day when the production level is x= 50 cases, find the rate at which the cost of production is changing.

Answers

The rate at which the cost of production is changing is 1000 hundred dollars per day or $100,000 per day.

To find the rate at which the cost of production is changing, we'll use the given cost function C = 50x + 1000, and the information that production is growing at a rate of 20 cases per day when x = 50 cases.

First, differentiate the cost function with respect to x to get the rate of change of the cost with respect to the number of cases produced (dC/dx):

dC/dx = 50

The derivative, 50, tells us that the cost increases by 50 hundred dollars for each additional case produced.

Now, we're given that dx/dt = 20 cases per day when x = 50 cases. To find dC/dt, the rate at which the cost of production is changing, multiply the rate of change of the cost with respect to the number of cases (dC/dx) by the rate of change of the number of cases with respect to time (dx/dt):

[tex]dC/dt = (dC/dx) × (dx/dt) = 50 × 20[/tex]

dC/dt = 1000

So, the rate at which the cost of production is changing is 1000 hundred dollars per day or $100,000 per day.

To learn more about cost function, refer below:

https://brainly.com/question/29583181

#SPJ11

Evaluate. (3/5)3 enter your answer by filling in the boxes.

Answers

the final answer is 27/125.

To evaluate [tex](3/5)^3[/tex], we simply need to multiply (3/5) by itself three times:

[tex](3/5)^3 = (3/5) * (3/5) * (3/5)[/tex]

To simplify, we can first multiply the numerators together and the denominators together:

[tex](3/5)^3 = 27/125[/tex]

To know more about multiply  refer here

https://brainly.com/question/10883691#

#SPJ11

A tabletop in the shape of a trapezoid has an area of 7,021 square centimeters. its longer base measures 131 centimeters, and the shorter base is 105 centimeters. what is the height?


urgent

Answers

The height of the trapezoidal tabletop is approximately 59.5 centimeters.

To calculate the height of a trapezoid with the given measurements, we need to use the formula for the area of a trapezoid: A = (b1 + b2)h / 2, where A is the area, b1 and b2 are the lengths of the two bases, and h is the height.

In this problem, the area (A) is 7,021 square centimeters, the longer base (b1) is 131 centimeters, and the shorter base (b2) is 105 centimeters. Our task is to find the height (h).

First, let's plug the given values into the formula:

7,021 = (131 + 105)h / 2

Now, simplify the equation:

7,021 = 236h / 2

To solve for h, multiply both sides of the equation by 2:

14,042 = 236h

Finally, divide both sides by 236:

h ≈ 59.5

Thus, the height is approximately 59.5 centimeters.

To know more about height, refer to the link below:

https://brainly.com/question/29115688#

#SPJ11

The length of the radius of a sphere is 6 inches. The length of the radius of a cone is 3 inches, and the height is 7 inches. What is the difference between the volume of the sphere and the volume of the cone?

Answers

The difference between the volume of the sphere and the volume of the cone is approximately 838.81 cubic inches.

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius. Thus, for a sphere with a radius of 6 inches, the volume is:

V_sphere = (4/3)π(6³) = 904.78 cubic inches

The volume of a cone is given by the formula V = (1/3)πr[tex]^{2h}[/tex], where r is the radius and h is the height. Thus, for a cone with a radius of 3 inches and a height of 7 inches, the volume is:

V_cone = (1/3)π(3²)(7) = 65.97 cubic inches

Therefore, the difference between the volume of the sphere and the volume of the cone is:

V_sphere - V_cone = 904.78 - 65.97 = 838.81 cubic inches

Hence, the difference between the volume of the sphere and the volume of the cone is approximately 838.81 cubic inches.

To know more about sphere click here

brainly.com/question/30897173

#SPJ11

Dawson, a 42-year-old male, bought a $180,000, 20-year life insurance policy. What is Dawsons annual premium? use the table. $819. 00 $1040. 40 $1859. 40 $2463. 40

Answers

Note that Dawson's annual premium will be $2,462.40.

Why is this so?

Dawson's annual premium will be $2,462.40.

This can be derived by going across from "Male 40-44" over to "20-year coverage" which is $13.68. Since $13.68 is per $1000 of coverage, you would multiply it by 180 to get $2,462.40.

An insurance premium is the amount of money paid by a person, firm, or enterprise to obtain an insurance coverage. The amount of the insurance premium is governed by a variety of factors and varies from one payee to the next.

Learn more about annual premium at:

https://brainly.com/question/9834518

#SPJ4

Full Question:

Although part of your question is missing, you might be referring to this full question:

Solid cylinders A and B are similar and made from metal. 72.8% more metal is used to make cylinder B than cylinder A. The surface area of cylinder A is 700cm². Work out the surface area of cylinder B

Answers

If the surface area of cylinder A is 700cm², the surface area of cylinder B is 1612.8cm².

Since the two cylinders are similar, their dimensions are proportional to each other. Let the height and radius of cylinder A be h and r, respectively, and let the height and radius of cylinder B be kh and kr, respectively, where k is the scale factor.

Since cylinder B uses 72.8% more metal than cylinder A, we have:

Volume of cylinder B = 1.728 times the volume of cylinder A

Using the formula for the volume of a cylinder, we have:

π(kr)²(kh) = 1.728πr²h

Simplifying the equation, we get:

k³ = 1.728

k = 1.2

So the scale factor is 1.2. Therefore, the height and radius of cylinder B are 1.2 times those of cylinder A. Hence, we have:

Surface area of cylinder B = 2π(1.2r)² + 2π(1.2r)(1.2h)

= 2.304(2πrh)

= 2.304(700cm²)

= 1612.8cm²

To learn more about surface area click on,

https://brainly.com/question/11482614

#SPJ1

A book club of 7 members meet at a local coffee shop. One week, 5 of the
members ordered a small cup of coffee and a muffin. The other 2 members
ordered a small cup of coffee and a piece of banana bread. The cost of a muffin,
including tax, is $3.51. The cost of piece of banana bread is $2. 16 more than
the cup of coffee. The total bill for the book club was $48. 60.

Answers

The cost of a small cup of coffee is $2.97, and the cost of a piece of banana bread is $5.13.

How to solve

Let x represent the cost of a small coffee and y represent the cost of a piece of banana bread. We know:

Cost of muffin: $3.51

y = x + $2.16

5(x + $3.51) + 2(x + y) = $48.60

Substitute y with x + $2.16:

5(x + $3.51) + 2(x + (x + $2.16)) = $48.60

Solve for x:

9x + $21.87 = $48.60

9x = $26.73

x = $2.97

Find y:

y = x + $2.16

y = $2.97 + $2.16

y = $5.13

A slice of banana bread costs $5.13, while a small coffee costs $2.97.

Read more about algebra here:

https://brainly.com/question/432678

#SPJ1

An educational psychologist wants to check claims that regular physical exercise improves academic achievement. To control for academic aptitude, pairs of college students with similar GPAs are randomly assigned to either a treatment group that attends daily exercise classes or a control group. At the end of the experiment, the following scores were reported for the six pairs of participants:



GPAs Pair number Physical Exercise No Physical exercise


1 4 3. 75


2 2. 67 2. 74


3 3. 65 3. 42


4 2. 11 1. 67


5 3. 21 3


6 3. 6 3. 25


7 2. 8 2. 65




Using t, test the null hypothesis at the. 01 level of significance Specify the p-value for this test result. If appropriate (because the test result is statistically significant), use Cohen’s d to estimate the effect size. How might this test result be reported in the literature?

Answers

The calculated t-value of 1.100 is less than the critical t-value of 2.718, we fail to reject the null hypothesis.

To test the hypothesis that regular physical exercise improves academic achievement, we will conduct a two-sample t-test for independent samples. The null hypothesis is that there is no difference in the mean academic achievement scores between the treatment group (physical exercise) and the control group (no physical exercise).

Let's calculate the mean and standard deviation for each group:

Treatment group (physical exercise):

mean = (4 + 2.67 + 3.65 + 2.11 + 3.21 + 3.6) / 6 = 3.3833

standard deviation = 0.7589

Control group (no physical exercise):

mean = (3.75 + 2.74 + 3.42 + 1.67 + 3 + 3.25 + 2.65) / 7 = 3.0071

standard deviation = 0.7037

We can now calculate the t-statistic:

t = (3.3833 - 3.0071) / sqrt((0.7589^2 / 6) + (0.7037^2 / 7)) = 1.100

The degrees of freedom for this test are 6 + 7 - 2 = 11 (assuming equal variances).

Using a t-table or a t-distribution calculator with 11 degrees of freedom and a significance level of 0.01, we find that the critical t-value is ±2.718.

Since the calculated t-value of 1.100 is less than the critical t-value of 2.718, we fail to reject the null hypothesis. We do not have enough evidence to conclude that regular physical exercise improves academic achievement.

The p-value for this test can be calculated as the probability of getting a t-value as extreme as 1.100, assuming the null hypothesis is true. Using a t-distribution calculator with 11 degrees of freedom, we find that the p-value is 0.294 (rounded to three decimal places).

Since the test result is not statistically significant (p > 0.01), we do not need to report an effect size using Cohen's d.

This test result could be reported in the literature as follows: "A two-sample t-test for independent samples was conducted to examine the effect of regular physical exercise on academic achievement, while controlling for academic aptitude. Six pairs of college students with similar GPAs were randomly assigned to either a treatment group that attended daily exercise classes or a control group. The mean academic achievement score for the treatment group was 3.3833 with a standard deviation of 0.7589, while the mean academic achievement score for the control group was 3.0071 with a standard deviation of 0.7037. The t-test result was not statistically significant (t(11) = 1.100, p = 0.294), indicating that there is not enough evidence to conclude that regular physical exercise improves academic achievement."

To learn more about null hypothesis visit: https://brainly.com/question/28920252

#SPJ11

Solve the system of equation and explain geometrically how you know that your answers are solutions to the system. x^2+y^2 =100 and 3x - y = 30 how you know

Answers

The solution of the system of equations is given by the ordered pairs [10, 0] and [8, -6].

How to graphically solve this system of equations?

In order to graphically solve the given system of equations on a coordinate plane, we would use an online graphing calculator to create a plot of the system of equations and then determine their point of intersection;

x² + y² = 100   ......equation 1.

3x - y = 30 ......equation 2.

Based on the graph shown in the image attached above, we can reasonably infer and logically deduce that the solution to this system of equations lies in both Quadrant I and Quadrant IV, and it is represented by this ordered pairs (10, 0) and (8, -6).

Read more on solution and equation here: brainly.com/question/25858757

#SPJ1

What is the unknown fraction?

eight tenths plus unknown fraction equals ninety seven hundredths

seventeen hundredths
eighty nine hundredths
one hundred five hundredths
one hundred seventy seven hundredths

Answers

1. Write out the given equation: 8/10 + unknown fraction = 97/100

2. Subtract 8/10 from both sides of the equation to isolate the unknown fraction:

  8/10 + unknown fraction - 8/10 = 97/100 - 8/10

  Simplifying the left side: unknown fraction = 97/100 - 8/10

3. Convert both fractions to have a common denominator of 100:

  97/100 - 8/10 = 97/100 - 80/100

  Simplifying the right side: unknown fraction = 17/100

4. Therefore, the unknown fraction is 17/100.

So, the correct answer is "seventeen hundredths".

To know more about denominator refer here

https://brainly.com/question/19613319#

#SPJ11

Mr carlos family are choosing a menu for their reception they have 3 choices of appetizers 5 choices of entrees 4 choices of cake how many different menu combinations are possible for them to choose

Answers

The number of different menu combinations Mr. Carlos' family can choose is 60.

To find the total menu combinations, you need to use the multiplication principle. Since there are 3 choices of appetizers, 5 choices of entrees, and 4 choices of cake, you simply multiply these numbers together. Here's the step-by-step explanation:

1. Multiply the number of appetizer choices (3) by the number of entree choices (5): 3 x 5 = 15
2. Multiply the result (15) by the number of cake choices (4): 15 x 4 = 60

So, there are 60 different menu combinations possible for Mr. Carlos' family to choose for their reception.

To know more about multiplication principle click on below link:

https://brainly.com/question/17514196#

#SPJ11

You travel east 10 miles on an adventure, then south 14 miles. You realize you don't want to go on an adventure, so you decide to go directly back where you started your adventure. Assuming the most direct path is walking in a straight line back home, how many miles will you have to walk back home.


Round to the nearest tenth.

Answers

you will have to walk approximately 17.2 miles back home.

A right triangle is a triangle in which one of the angles measures 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.  the length of the hypotenuse. Right triangles have many important applications in mathematics, science, and engineering, particularly in trigonometry, which is the study of the relationships between the sides and angles of triangles.

You have formed a right triangle with legs of length 10 and 14. To find the length of the hypotenuse, which is the distance back to your starting point, we can use the Pythagorean theorem:

[tex]c^2 = a^2 + b^2[/tex]

[tex]c^2 = 10^2 + 14^2[/tex]

[tex]c^2 = 100 + 196[/tex]

[tex]c^2 = 296[/tex]

c = sqrt(296)

c ≈ 17.2

Therefore, you will have to walk approximately 17.2 miles back home.

To learn more about right triangle visit: https://brainly.com/question/6322314

#SPJ11

Luis tiene una mochila de ruedas que mide 3.5 pies de alto cuando se extiende el mango. Al hacer rodar su mochila, la mano de Luis se encuentra a 3 pies del suelo. ?Qué ángulo forma su mochila con el suelo? Aproxima al grado más cercano.

Answers

The backpack forms an angle of approximately 15 degrees with the ground.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in mathematics that relates to the lengths of the sides of a right triangle.

To find the angle that Luis's backpack forms with the ground, we can use the inverse tangent function.

The height of the backpack when the handle is extended is 3.5 feet, and the distance from the ground to Luis's hand is 3 feet. So the opposite side of the triangle is 3.5 - 3 = 0.5 feet, and the adjacent side is the distance from Luis's hand to the backpack, which we can call x.

Using the tangent function, we have:

tan(theta) = opposite/adjacent

tan(theta) = 0.5/x

To solve for x, we can use the Pythagorean theorem:

x² + 3² = (3.5)²

x² = 3.5² - 3²

x² = 3.25

x = sqrt(3.25)

x ≈ 1.8 feet

Now we can substitute x into our tangent equation and solve for theta:

tan(theta) = 0.5/1.8

theta = arctan(0.5/1.8)

theta ≈ 15 degrees

Therefore, the backpack forms an angle of approximately 15 degrees with the ground.

To learn more about Pythagorean theorem from the given link:

https://brainly.com/question/14930619

#SPJ1

A credit card had a APR of 33. 01% all of last year and compounded interest daily. What was the credit card’s effective interest rate last year?

Answers

The credit card's effective interest rate for the year is [tex]40.51%.[/tex]%

To solve this problem

We can use the following formula:

Effective annual interest rate is calculated as[tex](1 + APR/365)365 - 1.[/tex]

The interest is compounded everyday in this case and the APR is 33.01 percent. When we enter these values into the formula, we obtain:

Effective annual interest rate =[tex](1 + 0.3301/365)^365 - 1[/tex]

Effective annual interest rate =[tex]1.4051 - 1[/tex]

Effective annual interest rate =[tex]1.4051 - 1[/tex]

So the credit card's effective interest rate for the year is[tex]40.51%.[/tex]%

Learn more about interest rate here : brainly.com/question/30512587

#SPJ4

Prove that U(1, 1), Q(4,4), and A(6, 2) are the vertices of a right triangle.   Use the following as a guide. Find the slopes of sides UQ, QA, and UA. Which segments are perpendicular? How do you know the segments are perpendicular? What are the lengths of each side? Use the Pythagorean Theorem to show that it is a right triangle. â

Answers

U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.

How do we know that UQ and QA are perpendicular?

To determine whether U(1,1), Q(4,4), and A(6,2) form a right triangle, we will follow the given guide:

Find the slopes of sides UQ, QA, and UA:

Slope of UQ: (4-1)/(4-1) = 1Slope of QA: (2-4)/(6-4) = -1Slope of UA: (2-1)/(6-1) = 1/5

Determine which segments are perpendicular and how we know they are perpendicular:

To determine if two lines are perpendicular, we need to check if their slopes are negative reciprocals of each other.

UQ and QA: Since the slope of UQ is 1 and the slope of QA is -1, we know that UQ and QA are perpendicular.UQ and UA: The slopes of UQ and UA are both positive, so they cannot be perpendicular.QA and UA: The slope of QA is -1, and the slope of UA is 1/5. Their product is -1/5, which is not -1, so QA and UA are not perpendicular.

Find the lengths of each side:

Length of UQ: √[(4-1)² + (4-1)²] = √27Length of QA: √[(6-4)² + (2-4)²] = √8Length of UA: √[(6-1)² + (2-1)²] = √26

Use the Pythagorean Theorem to show that it is a right triangle:

Since we have determined that UQ and QA are perpendicular, we can use the Pythagorean Theorem to show that it is a right triangle.

(Length of UQ)² + (Length of QA)² = (√27)² + (√8)² = 27 + 8 = 35(Length of UA)² = (√26)² = 26

Since (Length of UA)² + (Length of QA)² = (Length of UQ)², we know that the triangle is a right triangle.

U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.

Learn more about UQ and QA

brainly.com/question/27157027

#SPJ11

What’s the answer? I need help:)

Answers

Answer:

x=180-90-54, y=180-x,z=90

Step-by-step explanation:

the sum of the degree of a triangle will equal 180. the sum of the degree of a line will equal 180.

Use tha appropriate compound interest formula to find the amount that will be in each account, given the stated conditions. $26,000 invested at 3.65% annual interest
for 2 years compounded
(a) daily (n = 365); (b) continuously

Answers

Amount that will be in the account after 2 years with daily compounding is $28,484.03.

Amount that will be in the account after 2 years with continuous compounding is $28,498.84.

What is appropriate proceedure to calculate annual interest?

The appropriate compound interest formula is:

[tex]A = P(1 + r/n)^{nt[/tex]

A is the amount.

P is the principal.

r is the annual interest rate.

n is the number of times the interest is compounded all year.

t is the number of years.

(a) For daily compounding (n = 365), we have:

A = 26000(1 + 0.0365/365)³⁶⁵*²
A = 26000(1 + 0.0001)⁷³⁰
A = 26000(1.0001)⁷³⁰
A = 28,484.03

Therefore, the amount that will be in the account after 2 years with daily compounding is $28,484.03.

(b) For continuous compounding, we have:

A = P[tex]e^{rt[/tex]

e is the mathematical constant almost equal to 2.71828.

A = 26000[tex]e^{0.0365*2[/tex]
A = 26000[tex]e^{0.073[/tex]
A = 28,498.84

Therefore, the amount that will be in the account after 2 years with continuous compounding is $28,498.84.

Learn more about appropriate compound interest.

brainly.com/question/18722904

#SPJ11

I need help with this problem.
Please and thank you.

Answers

Answer:

Step-by-step explanation:

Solve for X
[tex]\frac{3x-2}{3x+1} =\frac{1}{2}[/tex]

Answers

The value of x is 5/3.

What is a fraction in math?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

We have equation in fraction are:

[tex]\frac{3x-2}{3x+1} = \frac{1}{2}[/tex]

To solve the value of x

In the above equation, Solve by cross multiplication:

2(3x - 2) = 3x + 1

Open the bracket and multiply by 2 :

6x - 4 = 3x +1

Combine the like terms:

6x - 3x = 1 + 4

Add and subtract the terms:

3x = 5

x = 5/3

Learn more about Fraction at:

https://brainly.com/question/10354322

#SPJ1

Question 2 of 10
What are the dimensions of AB?
A. 3x2
B. 3x3
C. 2x3
D. 2 x 2

Answers

Answer:

Based on the image, we can see that matrix A is a 3x2 matrix, and matrix B is a 2x3 matrix. In order to multiply matrices A and B, the number of columns in matrix A must match the number of rows in matrix B.

Since matrix A has 2 columns and matrix B has 2 rows, we can multiply them together, resulting in a 3x3 matrix. Therefore, the answer is B. The dimensions of AB are 3x3.

I DONT NEED BRAINLEST JUST STAY FUN AND SAFE

Ans. (c) 2X3

Dimension of matrix is given by row x column

Convert the number 35/4 into decimal form rounded to the nearest hundred. ​

Answers

Answer: 8.75

Step-by-step explanation:

We know that 4 goes into 35 eight times.

        35 - (4 * 8) = 3

Next, we know that 3/4 is equal to 0.75 by dividing.

This leaves us with 8.75. Eight wholes and a part of 0.75.

Other Questions
1. From the chemicals listed on your lab handout, write down the weak acid (with its pKa) and its conjugate base that would create a buffer that best fits your protein. Would you expect for your buffer to have more acid or more base?My assigned protein is Xylanase and has an optimum pH of 5. 5. 2. Buffers are used to the inhibit the change of pH upon the addition of strong acids and bases. If you were to add 0. 1 M HCl to your buffer, would you expect the pH to change? If so, would the pH increase or decrease? What would happen if 0. 1M NaOH were to be added instead? 3. Keeping your buffer composition from question 1 in mind, would you expect to use a larger volume of HCl or NaOH to change the pH of the buffer solution by one unit? Explain Find the measure of angle D. Whats the answer? I need help please two riders on bicycles, 100 miles apart. o each of these series. o begin traveling toward each other at the same time, one traveling at 10 miles a) acbdfe gal per hour and the other at is miles per hour. a fly named paul revere begins b) b~dwf fly~ng between the bicycles, starting from the front wheel of the slower c) h~f~dc~ beycle. if the fly travels at 20 miles per hour flying back and forth between 2 adam dropped a rubber ball from a bicycles, being able to reverse o window 40 feet above the sidewalk. directions without losing any time. how the ball always bounces half of the far will paul revere travel before the height that it drops. how far will the ball bicycles meet? 3. The insurance company also offers safety glass coverage. There is a 50% chance of no repairs ($0), a 30% chance of minor repairs ($50), and a 20% chance of full replacement ($300). Which plan for optional safety glass coverage has the lower expected cost?Enter your answer. Why did militarism erode diplomacy The outside of a closed glass display case measures 22" x 15" x 12". The glass is half inch thick. How much air is contained in the case All of the training times of which person had the greatest spread? Explain how you know. (b) The middle 50% of the training times of which person had the least spread? Explain how you know. (c) What do the answers to Parts 2(a) and 2(b) tell you about Adams and Miguels training times? Called by some "the new Dance Rock Diva," ____________ also served as a cohost on TV's American Idol and appeared on shows such as X Factor and So You Think You Can Dance Customers arrive at a busy food truck according to a Poisson process with parameter . If there are i people already in line, the customer will join the line with probability 1/(i +1). Assume that the chef at the truck takes, on average, a minutes to process an order. Required:a. Find the long-term average number of people in line. b. Find the long-term probability that there are at least two people in line expliquer Le rle de l'association pour la protection de l'environnement et de l'unesco I need to find the missing angle and arc measures. please answerStep by step Plot all of the existing five features of the following rational function (some may notbe needed). if you get a fraction or decimal then plot as close to the true location aspossible.f(x)5x + 20x2- - 20plot rational functionvertical asymptotehorizontal asymptotex-intercept y-intercept holeclick on a feature then drag it into place,to54589 10 A table titled inequality symbols contains the symbols for less-than and greater-than. Check all that are inequalities. -3 = yt > 0-4. 3 < ag = 5 and one-halfk less-than Negative Start Fraction 5 Over 7 End Fractionx = 1 Why is jerusalem the "thorniest" obstacle to peace? I need done asap I have 1 min Can someone please answer these 2 questions asap and please show me the breakdown of it so I learn a better way of doing it. The following information pertains to Rainey Inc. For 2020. Jan. 1Number of common share issued and outstanding, 200,000Feb. 1Number of new common shares issued, 8,000July 31100% common stock dividendDec. 31Reported net income of $560,000What is the companys earnings per share reported in its financial statements for the year ended December 31, 2020?Select one:a. $1. 35b. $1. 90c. $1. 45d. $1. 3 A candlemaker prices one set of scented candles at $10 and sells an average of 200 sets each week. He finds that when he reduces the priceby $1, he then sells 50 more candle sets each week. A function can be used to model the relationship between the candlemaker's weeklyrevenue, R(x) after xone-dollar decreases in price. R(x)R(x)6,000+4,000+6,000+1,000+2. 0002,000+2,0002,000+-4,0004,0006,000+-6,000Graph wR(x)Graph XR(x)6,000+1,000+6,000+1,000+2,000+2,000-2,000+2,0001,000+4,000-6,0006,000Graph YGraph ZThis situation can be modeled by the equation y =x +x +and by graphNext What are the possible blood types for children of a man that has blood type AB and a female that has blood type O? Give probabilities for each.Type A Type BType ABType O