Math Questions

Find the final amount of money in an account if 3,400 is deposited at 6.5% interest compounded weekly and the money is left for 8 years. The final amount is $ Round the answer to 2 decimal places.

The areas of two similar octagons are 9 m² and 25 m². What is the scale factor of their side lengths?

If $15,000.00 is invested at 10% annual simple interest, how long does it take to be worth $33,000.00. It will take to the nearest whole). years (round

Select the correct answer. Which function displays this end behavior? As x approaches negative infinity, y approaches positive infinity. As x approaches positive infinity, y approaches negative infinity. y = 3(1-1)² y -2³ - 1 y = (¹ + 2)³ - 9 y = -3.x² + 4

Answer the following questions for the price-demand equation. p+0.001x=40 (A) Express the demand x as a function of the price p.

Semielliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 12 meters wide. The center of the arch is 5 meters above the center of the river (see the figure). Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch. Type the left side of the equation below.

A baseball is hit towards the outfield, following the equations x (t) = 51.5t and y(t) = -16t² + 105t +4, where and y are measured in feet and t is time measured in seconds. A. How long does it take for the ball to hit the ground? Round your answer to the nearest second. B. How far has the ball traveled (horizontally) when it hits the ground? Round your answer to the nearest foot. C. Eliminate the parameter by writing the parametric equations as a single rectangular equation. D. 330 feet away the outfield fence stands 20 feet high. Is the ball going to clear the fence? Justify your answer.

An equilateral triangle has symmetry with respect to a line containing an altitude of the triangle. True False

Find the common difference for the given sequence. 1.05, 1.1, 1.15, 1.2, ... 0.5 0.05 0.005

Theodore invests $4,000 at 4% simple interest for 2 years. How much is in the account at the end of the 2 years period?

Which of the following equations could be used to solve for the tenth term of the following sequence? 15, 13, 11, 9, ... A(10) 15+10(-2) A(10) = 15 + 9(2) A(10)=15+ 10(2) A(10)=15+ 9(-2)

Melissa saved $3900. Over the course of 6 years, Melissa ended up earning an additional $2106 in interest. What was the simple interest rate of the loan?

Select the correct answer from each drop-down menu. Mike drove 40 miles from his home to his office, and he then drove back home using the same route. The average speed on his return trip was 10 miles/hour more than the average speed on his trip to the office. The total time for the trip is represented by this expression, where x is the average speed on the trip from his home to his office.

Describe the transformations of the graph of y = 5.2-2 +3 as compared to the graph of y = 2*.

A plane is heading due south with an airspeed of 298 mph. A wind from a direction of 55° (N55°E) is blowing at 20 mph. Find the bearing of the plane. Round to the nearest degree. 178⁰ 92° 1879 183°

Find the common difference of the arithmetic sequence shown. 1/4 , 3/8, 1/2, ...

A ship leaves a pier on a bearing of S62°E and travels for 75 km. it then turns and continues on a bearing of N28°E for 53 km. How far is the ship from the pier? Round your answer to the nearest km.

If a price-demand equation is solved for p, then price is expressed as p = g(x) and x becomes the independent variable. In this case, it can be shown that the elasticity of demand is given by E(x) = - price-demand equation below to find E(x) at the indicated value of x.

Find the area of a regular polygon with 7 sides, an apothem of 8 meters, and a side length of 7.7 meters. Enter your answer to the nearest tenth. [?] m²

Which statement describes the vertical asymptote(s), if any, in the graph of the function f(x)= (2x-4)/(x^2-4) A. The graph has no vertical asymptotes. B. The graph has one vertical asymptote. C. The graph has two vertical asymptotes. D. The number of asymptotes depends on whether the rational expression is simplified.

R 0,-180 is the same rotation as R 0,180 R.90, 180 R 90,180 R 0,90

The average distance from the planet Venus to the Sun is 6.7 x 10 mi. What is the area of the planar region swept by the line segment from the center of Venus to the center of the sun in one orbit around the sun? Assume a circular orbit. (Area Epts of circle: A=m², circumference of a circle: C= 2)

A population grows according to an exponential growth model, with Po = 80 and P₁ = 96 Complete the recursive formula: Pn= x Pn-1 Write an explicit formula for Pn

A hot-air balloon is rising vertically 12 ft/sec while the wind is blowing horizontally at 6 ft/sec. Find the angle that the balloon makes with the horizontal. Round to the nearest tenth of a degree, if necessary. 52.1° 50.3° 26.6° 63.4°

While the majority of people who are color blind are male, an institute reports that 0.3% of women with Northern European ancestry have the common form of red-green color blindness. Suppose a random sample of 100 women with Northern European ancestry is selected. Can we find the probability that less than 0.2% of the sample is color blind? If so, find the probability. If not, explain why this probability cannot be calculated. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. This probability cannot be calculated because the sample is too small to satisfy the conditions of the Central Limit Theorem. B. This probability cannot be calculated because the sample does not satisfy the Central Limit Theorems conditions for randomness and independence. C. This probability can be calculated, the sample meets all of the conditions of the Central Limit Theorem. The probability is %. (Type an integer or decimal rounded to one decimal place as needed.) D. This probability can be calculated, the sample meets enough of the conditions of the Central Limit Theorem. The probability is (Type an integer or decimal rounded to one decimal place as needed.) E. This probability cannot be calculated because the population size is too small to satisfy the conditions of the Central Limit Theorem. %.

Given the exponential growth function f(x) = 77(1.0275)* What is the initial value of the function? Enter an integer or decimal number [more..] What is the growth factor, or growth rate of the function (as a percent)?%

Javier purchased a digital camera for $384. The value of the camera depreciates by 25% every year. This situation represents ... The rate of growth or decay, r, is equal to ... So the value of the camera each year is ... times the value in the previous year. It will take ... years for the value of the

Fill in the blank in the following statement. The wholesale price of a TV is 10% less than retail price. Therefore, the wholesale price is times the retail price. The wholesale price is times the retail price.

A retiree invests $9,000 in a savings plan that pays 6% per year. What will the account balance be at the end of the first year?

Which of these steps will eliminate a variable in this system? 4x9y = 8 2x + 3y = 24 A. Multiply the first equation by 3. Then subtract the second equation from the first. B. Multiply the second equation by 3. Then subtract the second equation from the first. C. Multiply the second equation by 2. Then subtract the second equation from the first. D. Multiply the second equation by 2. Then add the equations.

A reflection maps the point (2, 3) to the point (-2, 3). It is a reflection over the x-axis y-axis line y = x

The distribution of weights (rounded to the nearest whole number) of all boxes of a certain cereal is approximately normal with mean 25 ounces and standard deviation 2.5 ounces. A sample of the cereal boxes was selected, and the weights of the selected boxes are summarized in the histogram shown. Which of these values is the best estimate of the number of boxes in the sample with weights that are more than 2 standard deviations above the mean?

Solve the equation by using the quadratic formula: 3x² + x = 4 x=-1 or x=-4/3 x=1 or x = 4/3 x=1 or x=-4/3 x = -1 or x = 4/3

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (5.-6) and perpendicular to the line whose equation is y=x+2 Write an equation for the line in point-slope form. (y+6)= -2(x-5).

The length, I, that a spring is stretched varies directly as the amount of force, F, applied to the end of the spring. When a force of 10 pounds is applied to a spring, it stretches 3 inches. How much will the same spring stretch if the force is increased to 15 pounds? A. 8 inches B. 7.5 inches C. 4.5 inches D. 2 inches

The revenue, in thousands of dollars, that a company earns selling lawnmowers can be modeled by R(x) = 90x-x^2 and the company's total profi in thousands of dollars, after selling x lawnmowers can be modeled by P(x) = -x^2 +30x - 200. Which function represents the company's cost, in thousands of dollars, for producing lawnmowers? (Recall that profit equals revenue minus cost.) A. C(x) = 60x+ 200 B. C(x) = -60ײ - 200 C. C(x) = -2x² - 60x-200 D. C(x) = 2x² +60x+200

Write the point-slope form of the line's equation satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Slope = 4, passing through (3,2) What is the point-slope form of the equation of the line? (Simplify your answer. Use integers or fractions for any numbers in the equation.) What is the slope-intercept form of the equation of the line? (Simplify your answer. Use integers or fractions for any numbers in the equation.)

The variable m varies directly as the cube root of n. When n = 27, m= 216. Which equation can be used to find other combinations of m and n? A m=8n B. m=72³m C m²n=648 D. mn=5,832

More people are purchasing food from farmers' markets around the country. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 2.8% every six months. If there were 7823 farmers' markets in 2019, how many will there be in 4 years? Given the exponential growth scenario above, answer the following questions: What is the initial value, Po in this problem? What is the growth factor or growth rate (as a decimal value)? What is the n value, or number of time periods?

Maria invests $9,000 at 11% simple interest for 1 year. How much is in the account at the end of the 1 year period?

The depth of a pond decreases at a rate of 2% per year. If the pond currently has a depth of 5 feet, in approximately how many years will the depth of the pond fall below 4 feet? A 11 years B. 50 years C 6 years D. 24 years

What are the characteristics of the function f(x) = 2(x-4)^5? A. It is a reflection and a translation to the right of the parent function. B. Both ends of the graph of the function go up. C. It has 4 zeros and at most 5 relative maximums or minimums. D. The left end of the graph of the function goes down, and the right end goes up. E. It has 5 zeros and at most 4 relative maximums or minimums. F. It is a vertical stretch and a translation to the right of the parent function.

Emma says that for f(x)=8,000(0.95), the exponential growth is 0.95 and the y-intercept is 8,000. What is her error? Choose the correct answer below and fill in the answer box(es) to complete your choice. A. In an exponential growth model y=a-b*, the exponential growth is a and the y-intercept is b. So, the exponential growth is and the y-intercept is B. For f(x) to be an exponential growth model, a> and b>1. Since b=0.95, it should be exponential decay, not growth. C. In an exponential growth model y=a-b*, the exponential growth r is found using the equation r=1-b. So, the exponential growth is D. Emma found the x-intercept instead of the y-intercept The x-intercept is 8,000 and the y-intercept is

Francine currently has $75,000 in her 401k account at work, and plans to contribute $8,000 each year for the next 10 years. How much will she have in the account in 10 years, if the account averages a 5% annual return?

Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her own expenses. After a month of driving from neighborhood to neighborhood and walking door-to-door, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks on. She writes the equation of the function like this: E(x) = 20x-50, where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars. What does the slope of Jessica's function represent? A. For each additional door she knocks on, her earnings will increase by $20. B. For each additional set of books she sells, her earnings will increase by $50. C. For each additional set of books she sells, her earnings will increase by $20. D. For each additional door she knocks on, her earnings will increase by $50.

Simplify: 24x4-16x³ +8x²+2/2x² 12x2² - 8x + 4 + 1/x² 20x²-16x³ +2 12x-²8x +6 12x² + 8x + 4 + 1/x2

Assume than men's weights are normally distributed with a mean given by μ = 155 pounds and ad mont standard deviation given by o = 4.4 pounds. If one man is randomly selected, find the probability that his weight is between 152 pounds and 21 91159 pounds.

Which statement is true about the graph of function f? f(3) = log₂ # A The graph has a horizontal asymptote of y = 0 and is decreasing as x approaches positive infinity. B. The graph has a vertical asymptote of = 0 and is increasing as x approaches positive infinity. C The graph has a vertical asymptote of = and is decreasing as x approaches positive infinity. D. The graph has a horizontal asymptote of y = 0 and is increasing as x approaches positive infinity.

If the first step in the solution of the equation -x + 6 = 5 - 3x is "subtract 5," then what should the next step be? add 3x subtract 6 add x

If a translation maps point (3, 2) to (4, 5); or T: (3, 2) (4, 5), indicate the image for (2, 4). (3.7) (2, -1) (5, 3)