A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:
f(t) = −16t2 + 48t + 100
The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____ feet per second.
Christina goes to the market with $50. She buys one papaya for $20 and spends the rest of the money on bananas. Each banana cost $6. Write an inequality for the number of bananas purchased
The height of a triangle is increasing at a rate of 2 2 centimeters/minute while the area of the triangle is increasing at a rate of 3.5 3.5 square centimeters per minute. at what rate is the base of the triangle changing when the height is 10 10 centimeters and the area is 80 80 square centimeters?
Kevin rolled two number cubes each numbered 1 to 6.
what is the probability that both number cubes land on 3?
Q # 17 please solve the figures
A triangle has side lengths 4, 7 and 9. What is the measure of the angle across from the longest side?
92 = 42 + 72 − 2g4g7cos(A)
81 = 16 + 49 − 56cos(A)
81 = 9cos(A)
9 = cos(A)
A cannot exist!
Gabe tried to use the law of cosines to find an unknown angle measure in a triangle. His work is shown. What is Gabe’s error?
Gabe reversed the order of the 9 and the 4.
Gabe squared the numbers incorrectly.
Gabe should not have subtracted 56 from
16 + 49.
Gabe incorrectly stated that cos–1(9) is not defined.
Answer:
Step-by-step explanation:
Given that a triangle has sides 4,7 and 9
A student Gabe tried to use law of cosines to find unknown angle measure
The angle is opposite side 9 because angle across the longest side is given
He used cosine formula for triangles
[tex]a^2=b^2+c^2-2bccosA\\9^2 = 4^2+7^2-2(4)(8) cosA\\81-65 =-56 cosA\\[/tex]
But instead he adjusted -56 with 16 +49 which is wrong
Because -56 has product as cosA it is not like term as other constants
So correct step should be
81 = 65-56 Cos A
Gabe should not have subtracted 56 from
16 + 49.
This is the correct answer
Paige rides her bike around town. She can ride one half of a mile in 1 30 ith of an hour. If she continues to ride at the same pace, how many miles could she travel in 1 hour?
We have been given that Paige can ride one half of a mile in 1/30 th of an hour. And we have to found the distance traveled in 1 hour if she continues to ride at the same pace.
Let d be the distance traveled in 1 hour.
In 1/30 th of an hour distance traveled is 0.5 mile
Hence, in 1 hour the distance traveled is given by
[tex]d=\frac{0.3}{1/30} \\ \\ d=0.5\times 30\\ \\ d=15[/tex]
Therefore, she will travel 15 miles.
Using what you know about angles and triangles, what is the measure of angle 6?
Answer:158
Step-by-step explanation:∠6 = 68 + 90 = 158°
hello can you please help me posted picture of question
which of the following are geometric sequences?
A. 1,3,9,27,81
B. 10,5,2.5,1.25,0.625, 0.3125
C. 3,6,9,12,15,18
D. 5,10,20,40,80,160
Final answer:
Options A, B, and D are geometric sequences because they have a constant ratio between successive terms. Option A has a ratio of 3, option B has a ratio of 0.5, and option D has a ratio of 2. Option C is an arithmetic sequence and not geometric.
Explanation:
The question asks which of the listed sequences are geometric sequences. A geometric sequence is characterized by a constant ratio between successive terms. Let's analyze each option:
A. 1,3,9,27,81 - Each term is multiplied by 3 to get the next term, hence it is a geometric sequence with a common ratio of 3.
B. 10,5,2.5,1.25,0.625, 0.3125 - Each term is multiplied by 0.5 (or divided by 2) to get the next term, hence it is a geometric sequence with a common ratio of 0.5.
C. 3,6,9,12,15,18 - The difference between successive terms is constant (+3), making it an arithmetic sequence, not geometric.
D. 5,10,20,40,80,160 - Each term is multiplied by 2 to get the next term, hence it is a geometric sequence with a common ratio of 2.
Therefore, options A, B, and D are geometric sequences, while option C is not.
What is the area of the region between the graphs of y=x^2 and y=-x from x=0 to x=2?
The area between [tex]\( y = x^2 \)[/tex] and [tex]\( y = -x \) from \( x = 0 \) to \( x = 2 \) is \( \frac{14}{3} \)[/tex] square units, found by integrating [tex]\( x^2 + x \)[/tex] from 0 to 2.
Intersection Points: To find the area between [tex]\( y = x^2 \)[/tex] and [tex]\( y = -x \)[/tex] from [tex]\( x = 0 \) to \( x = 2 \)[/tex], first find their intersection points by setting [tex]\( x^2 = -x \)[/tex]. This gives [tex]\( x^2 + x = 0 \)[/tex], which factors to [tex]\( x(x + 1) = 0 \)[/tex], yielding [tex]\( x = 0 \)[/tex] and [tex]\( x = -1 \)[/tex] as the intersection points.
Limits of Integration: We are interested in the area between these curves from [tex]\( x = 0 \) to \( x = 2 \)[/tex]. Since[tex]\( x = -1 \)[/tex] lies outside this interval, we only consider [tex]\( x = 0 \)[/tex].
Integration: The area can be calculated by integrating the difference between the upper curve [tex]\( y = x^2 \)[/tex] and the lower curve [tex]\( y = -x \) from \( x = 0 \) to \( x = 2 \):[/tex]
[tex]\[ \text{Area} = \int_{0}^{2} (x^2 - (-x)) \, dx \][/tex]
Sure, here is the rewritten line:
[tex]\[ \text{The area can be found by integrating} \, x^2 + x \, \text{from} \, x = 0 \, \text{to} \, x = 2: \, \int_{0}^{2} (x^2 + x) \, dx \][/tex]
Integrating term by term:
[tex]\[ = \left[ \frac{x^3}{3} + \frac{x^2}{2} \right]_{0}^{2} \][/tex]
[tex]\[ = \left( \frac{2^3}{3} + \frac{2^2}{2} \right) - \left( \frac{0^3}{3} + \frac{0^2}{2} \right) \][/tex]
[tex]\[ = \left( \frac{8}{3} + 2 \right) - 0 \][/tex]
[tex]\[ = \frac{8}{3} + 2 \][/tex]
[tex]\[ = \frac{14}{3} \][/tex]
Complete question:
What is the area of the region between the graphs of y=x² and y=-x from x=0 to x=2?
What is the volume of a right circular cylinder with a base diameter of 18yd. And a height of 3yd.
Answer:
[tex]Volume=254[/tex] to the nearest cubic yard.
Step-by-step explanation:
The volume of a right circular cylinder can be calculated using the formula;
[tex]Volume=\pi r^2h[/tex].
The diameter of the base is given to us. We divide it into two to obtain the radius.
[tex]r=\frac{18}{2}=9yd[/tex] and also the height of the cylinder is [tex]h=3yd[/tex].
We substitute these values into the formula to obtain;
[tex]Volume=9^2\times 3\pi yd^3[/tex]
[tex]Volume=243\pi yd^3[/tex]
[tex]Volume=763.4yd^3[/tex]
Answer:
answer= 254
Step-by-step explanation:
Solve for x
in the equation x^2-12x+36=90
Answer:
Using the identity rule:
[tex](a-b)^2 = a^2-2ab+b^2[/tex]
Given the equation:
[tex]x^2-12x+36 = 90[/tex]
Rewrite the above equation as:
[tex]x^2-2 \cdot x \cdot 6+6^2 = 90[/tex]
Apply the identity rule:
[tex](x-6)^2 = 90[/tex]
Take square root to both sides we have;
[tex]x-6 = \pm \sqrt{90}[/tex]
Add 6 to both sides we have;
[tex]x = 6\pm \sqrt{90}[/tex]
or
[tex]x = 6 \pm 3\sqrt{10}[/tex]
Therefore, the value of x are:
[tex]6+3\sqrt{10}[/tex] and [tex]6-3\sqrt{10}[/tex]
PLZ HELP ASAP GRAPH A CIRCLE FROM ITS STANDERED EQUATION
The graph of the circle with the equation (x - 3)² + (y + 3)² = 36, is a circle with center (3, -3) and radius of 6 units
Please find attached the graph of the circle (x - 3)² + (y + 3)² = 36, created with MS Excel
The details of the steps used to graph of the circle are as follows;
The standard form of the equation of a circle is; (x - h)² + (y - k)² = r², where the center of the circle is (h, k)
The equation of the circle in standard form is; (x - 3)² + (y + 3)² = 36
The comparison of the above equation with the form of the general equation of a circle in standard form indicates that the center of the circle is (3, -3)
The comparison of the radius of the circle with equation (x - 3)² + (y + 3)² = 36, with the general form of the equation of a circle in standard form indicates that the radius of the circle is; √(36) = 6
Assume that the population of the world in 2010 was 6.9 billions and is growing at the rate of 1.1 percent a year. (a) set up a recurrence relation for the population of the world n years after 2010 (b) find an explicit formula for the population of the world n years after 2010. (c) what will the population of the world be in 2030
Answer:
a 1=6.9
a an =
(an-1)(1.1)
b an=
(6.9)
(1.1^n-1)
c
46.419
billion
Step-by-step explanation:
Estimate the size of a crowd standing along 1 mile section of parade route that is 10 feet deep on both sides of the street assume that each person occupies 2.5 square feet
A) 21,120
B) 42,240
C) 84,480
D) 168,960
The correct answer is option B). The size of a crowd standing along 1 mile section of parade route that is 10 feet deep on both sides of the street is 42,240.
To estimate the size of the crowd, we need to calculate the total area occupied by the crowd and then divide by the area occupied by each person.
First, let's calculate the total area available for the crowd on both sides of the street:
The length of the parade route is 1 mile. Since there are 5280 feet in a mile, the length in feet is 5280.
The depth of the crowd on both sides of the street is 10 feet.
Therefore, the total area available for the crowd on both sides is:
Total area = 2 [tex]\times[/tex] (Depth of crowd) [tex]\times[/tex] (Length of parade route)
Total area = 2 [tex]\times[/tex] 10 feet [tex]\times[/tex] 5280 feet
Total area = 105,600 square feet
Next, we need to calculate how many people can fit in this area:
Each person occupies 2.5 square feet.
The number of people that can fit in the total area is:
Number of people = Total area / Area per person
Number of people = 105,600 square feet / 2.5 square feet per person
Number of people = 42,240.
What are the zeros of the polynomial function f(x)=x^2+5x+6
Simon has a scale model of the Concorde airplane. The actual length of the Concorde is approximately 200 feet. If the ratio of the actual length in feet to the length of the model in centimeters is 5 : 1, what is the approximate length of Simon's model?
Answer:
yur
Step-by-step explanation:
Juan is spinning a wheel with 4 unequal spaces marked with values of $200, $300, $400, and $600. The probability of landing on $200 is 2/9 . The probability of landing on $300 is 4/9 . The probability of landing on $400 is 2/9. The probability of landing on $600 is 1/9 . The expected value of spinning the wheel once is $, and the expected value of spinning the wheel three times is
Answer:
333 and 1000
Step-by-step explanation:
A company has a minimum required rate of return of 9% and is considering investing in a project that costs $350,000 and is expected to generate cash inflows of $140,000 at the end of each year for three years. the net present value of this project is
two dice are tossed what is the probability of obtaining a sum greater than 6
Mary has three baking pans. Each pan is 8" × 8" × 3". Which expression will give her the total volume of the pans?
8^2 × 3
8 × 3^2
(8 × 2 × 3) × 3
(8^2 × 3) × 3
Answer:
D. (8^2 × 3) × 3
Step-by-step explanation:
its d on plato
-4 × 7 with an absolute value is?
how can you write the expression with a rationalized denominator? √3/√4
Please do not answer unless you are pretty sure. Thanks!
Using a rain gauge, Gerry determined that 1/2 inch of rain fell during 3/4 of an hour. What is the unit rate of rainfall in inches per hour?
Final answer:
To calculate the unit rate of rainfall in inches per hour, divide the amount of rainfall (1/2 inch) by the duration (3/4 hour), which gives 2/3 inches per hour.
Explanation:
The student is asking how to find the unit rate of rainfall in inches per hour when given that 1/2 inch of rain fell during 3/4 of an hour. To find the unit rate, divide the total amount of rainfall by the total time to get the amount of rain per one hour.
Step-by-step calculation:
Amount of rainfall: 1/2 inch
Duration of rainfall: 3/4 hour
To find inches per hour, divide the amount of rainfall by the duration:
(1/2 inch) / (3/4 hour) = (1/2) / (3/4) = (1/2) * (4/3) = 4/6 = 2/3 inches per hour.
Therefore, the unit rate of rainfall is 2/3 inches per hour.
In 1983, a year-long newspaper subscription cost $12.75. Today, a year-long newspaper subscription costs $28.50. If the CPI is 193, what is the relation of the actual price of a year-long newspaper subscription to the expected price, to the nearest cent? a. The actual price is $14.79 higher than the expected price. b. The actual price is $3.89 higher than the expected price. c. The actual price is $9.20 lower than the expected price. d. The actual price is $11.86 lower than the expected price
Answer:
Option b - The actual price is $3.89 higher than the expected price.
Step-by-step explanation:
Given : In 1983, a year-long newspaper subscription cost $12.75. Today, a year-long newspaper subscription costs $28.50. If the CPI is 193
To find : What is the relation of the actual price of a year-long newspaper subscription to the expected price, to the nearest cent?
Solution :
CPI is the consumer price index.
The formula of CPI is
[tex]\text{CPI}=\frac{\text{Cost of newspaper subscription in Given Year}}{\text{Cost of newspaper subscription in Base Year}}\times 100[/tex]
We have given CPI = 193
Cost of newspaper subscription in Base Year = $12.75
We have to find cost of newspaper subscription in Given Year
[tex]193=\frac{\text{Cost of newspaper subscription in Given Year}}{12.75}\times 100[/tex]
[tex]\text{Cost of newspaper subscription in Given Year}=\frac{193\times12.75}{100}[/tex]
[tex]\text{Cost of newspaper subscription in Given Year}=\frac{2460.75}{100}[/tex]
[tex]\text{Cost of newspaper subscription in Given Year}=24.61[/tex]
The actual price of newspaper subscription = $28.50
The expected price of newspaper subscription = $24.61
Now, to find how much higher they expected is
$28.50 -$24.61 = $3.89
Therefore, Option b is correct.
The actual price is $3.89 higher than the expected price.
AB is tangent to circle O at B. Find the length of the radius, r, for AB = 5 and AO = 13.
the radius is twelve
Clabber company has bonds outstanding with a par value of $113,000 and a carrying value of $105,100. if the company calls these bonds at a price of $101,500, the gain or loss on retirement is:
Which of the following shows the correct evaluation for the exponential expression 6 over 7 to the power of 2?
6 over 7 plus 2 equals 2 and 6 over 7
6 over 7 times 2 equals 12 over 7 which equals 1 and 5 over 7
6 over 7 times 6 over 7 equals 36 over 49
6 over 7 divided by 2 equals 6 over 14