The rate of increasing the area of the rectangle is 72cm²/s
We have, The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 13 cm and the width is 4 cm, we have to find how fast is the area of the rectangle increasing.
The area of a rectangle is given by, A = l × w
Where l is the length and w is the width.
Now we will differentiate the equation with respect to time t.
dA/dt = d/dt (l × w)
dA/dt = l(dw/dt) + w(dl/dt)
We can use this formula to calculate how fast the area of the rectangle increases when the length is 13 cm and the width is 4 cm.
Substituting the given values, l = 13 cm and dl/dt = 5 cm/s w = 4 cm and dw/dt = 4 cm/s
dA/dt = 13(4) + 4(5)
dA/dt = 72 cm²/s
Therefore, the area of the rectangle increasing at a rate of 72 cm²/s.
To know more about the "area of the rectangle": https://brainly.com/question/24571594
#SPJ11
work out the value of
(2.92 x 10^6) ÷ (4 x 10^-2)
give your answer in standard form
???
Answer:
7.3*10^7
Step-by-step explanation:
Find the common ratio of the geometric sequence -7, -42, -252,. −7,−42,−252,
the common ratio of the geometeric sequence -7, -42, -252 is 6.
A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed non-zero constant, called the common ratio. We can find the common ratio (r) of the sequence -7, -42, -252 by dividing any term by its previous term. For example:
-42 / (-7) = 6
-252 / (-42) = 6
Since the ratio is the same for both, we can conclude that the common ratio is 6. Therefore, each term is obtained by multiplying the previous term by 6.
To check, we can multiply any term by 6 to obtain the next term in the sequence. For example:
-7 * 6 = -42
-42 * 6 = -252
So, the common ratio of the sequence -7, -42, -252 is 6.
To learn more about geometric sequence refer to:
brainly.com/question/13008517
#SPJ4
Helpppppppppppppppppppp
Answer:
SAS proves that these triangles are congruent.
The owner of a produce stand is selling bunches of grapes, priced by the pound. She rounded each measurement to the nearest
1/8
start fraction, 1, divided by, 8, end fraction of a pound.
Answer: 1 1/4
Step-by-step explanation:
the heaviest bunch of grapes weights 1 7/8 pounds
A line plot labeled 0 to 2 with tick marks every one-eighth unit. Above the tick mark at five-eighths is one dark blue dot. Above the tick mark for six-eighths is a column of two light blue dots. Above the tick mark at 1 there is a column of three light blue dots. Above the tick mark at one and four-eighths is a column of two light blue dots. Above the tick mark for one and five-eighths is a column of four light blue dots. Above the tick mark for one and seven-eighths is one light blue dot.
Please help me answer my homework in the image
Using distance formula, the triangle ABC is a scalene triangle
What is triangle ABCTo classify the triangle, we need to determine whether its sides are equal in length (in which case it's equilateral or isosceles), or whether they are all different lengths (in which case it's scalene). We can use the distance formula to calculate the length of each side of the triangle, as follows:
The distance formula gives us the distance between two points (x1, y1) and (x2, y2) in the coordinate plane:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Using this formula, we can find the length of each side of triangle ABC:
AB = √[(4-1)^2 + (4-0)^2] = √(9 + 16) = √25 = 5
BC = √[(6-4)^2 + (2-4)^2] = √(4 + 4) = 2√2
AC = √[(6-1)^2 + (2-0)^2] = √(25 + 4) = √29
We can see that AB = 5, BC = 2√2, and AC = √29. Since all three sides have different lengths, the triangle is scalene.
Note that the midpoints of the sides AB and BC are not relevant for determining the type of triangle. Also, it's not accurate to say that the midpoint of AB is (4/3, 2), as the coordinates of the midpoint are actually ((1+4)/2, (0+4)/2) = (2.5, 2), and similarly for the midpoint of BC.
Learn more on distance formula here;
https://brainly.com/question/28551043
#SPJ1
If the triangle within the circle is a RIGHT triangle, find the length of the
diameter to find the circumference. Round to the nearest tenth. (Remember, your
answer is the CIRCUMFERENCE!)
Conve
The required circumference of the given circle is 45.27 cm approx.
What is circumference?In geometry, the perimeter of a circle or ellipse is its circumference. In other words, the circumference would equal the length of the arc if the circle were expanded up and straightened out to a line segment.
The term "perimeter" is most frequently used to describe the radius of any closed shape.
The circumference of a circle is the length around its periphery.
It is similar to the edges of other shapes, including squares.
It can be viewed as the line that defines the shape.
So, calculate the diameter using the Pythagorean theorem as follows:
h² = a² + b²
h² = 8² + 12²
h² = 64 + 144
h² = 208
h = √208
h = 14.42
Now, calculate the circumference as follows:
Radius = 14.42/2 = 7.21
Now,
= 2πr
= 2*3.14*7.21
= 45.2788
Therefore, the required circumference of the given circle is 45.27 cm approx.
Know more about circumference here:
https://brainly.com/question/20489969
#SPJ1
Housing 30%
Gas 8%
Internet 2%
Personal care 5%
Food 25%
Saving 15%
Child 15%Andrew erne $154000 per month he has a small business income of $25000 , create a budget for Andrew to reflect the following
[Andrew needs to buy a refrigerated That cost $95000. How much months will he need to save to buy it
Andrew needs to save money for 3.8 months, or about 4 months (rounded up) to buy that refrigerator.
Based on the given information, Andrew's budget can be broken down as follows:
Housing: $46,200 (30% of $154,000)
Gas: $12,320 (8% of $154,000)
Internet: $3,080 (2% of $154,000)
Personal care: $7,700 (5% of $154,000)
Food: $38,500 (25% of $154,000)
Saving: $23,100 (15% of $154,000)
Child: $23,100 (15% of $154,000)
Small business income: $25,000
To calculate how long it will take for Andrew to save enough money to buy the $95,000 refrigerator, we need to calculate his monthly savings based on his budget.
Andrew's total monthly income (before expenses) is
$154,000 + $25,000 = $179,000.His total monthly expenses (including savings) are
$46,200 + $12,320 + $3,080 + $7,700 + $38,500 + $23,100 + $23,100 = $154,000.Therefore, his monthly savings are $179,000 - $154,000 = $25,000. To save up $95,000, he will need $95,000 / $25,000 = 3.8 months, or about 4 months (rounded up).
Learn more about Budget:
https://brainly.com/question/24940564
#SPJ4
"Jade and Jackson go to Cracker Barrel and order $62.60 worth of food. They want to tip their waiter 20%. They also have to pay a tax of 5% on the original bill. What is the final cost of the meal?"
I just need help please!!!!!!
Answer:
78.25
Step-by-step explanation:
First find the tip.
62.60 * 20%
62.60*.2 = 12.52
Then find the tax
62.60 * 5%
62.60 * .05
3.13
Now add the cost of the food, tip, and tax.
62.60+12.52+3.13
78.25
Find the area of the region bounded by the x-axis, line x=2, line x=6, and lines y=x+3, and y=10-x.
Therefore , the solution of the given problem of area comes out to be region is 24.5 square units in size.
Define area.How much room is needed to fully cover the outside can be used to estimate its overall size. When calculating a trapezoidal shape's surface, the immediate environs are taken into account. The surface area of something determines its overall dimensions. The internal water volume of a cuboid is given by the total of the borders for each of its six rectangular edges.
Here,
We must first calculate the areas of the three shapes in order to add them up to get the area of the territory.
Triangle 1: The height is equal to the distance of the y-coordinates of the x-axis (which is 0) and the y-coordinates of (3,6), which is 6. Consequently, the triangle's size is:
=> 1/2 * base * height
= >1/2 * 3 * 6 = 9
The segment between the x-axis and the location where the line y=10-x meets the x-axis, which is the base in triangle 2 (10,0).
Triangle 2:
=> 1/2 * base * height = 1/2 * 4 * 1 = 2
Trapezoid:
The three shapes' combined regions result in:
=> 9 + 2 + 13.5 = 24.5
The region is 24.5 square units in size and is circumscribed by the x-axis, lines x=2, x=6, lines y=x+3, and y=10-x.
To know more about area visit:
https://brainly.com/question/2835293
#SPJ1
find the area of a circle with a circumference of 11 pi feet 
Answer:
95ft²
Step-by-step explanation:
2πr = 11π
πr = 11π/2
r = 11/2 = 5.5ft
area = πr²
area = π(5.5)² = 95.0331... ≈ 95ft²
A person tosses from atop a cliff a people straight downward with an initial velocity of -9. 0 meters per second, after 50 seconds, how far beneath the cliff is the people?
After 50 seconds, the person has fallen approximately 2252.5 meters below the cliff.
Assuming no air resistance, we can use the formula for distance traveled by an object under constant acceleration:
d = v_i * t + (1/2) * a * t²
where d is the distance traveled, v_i is the initial velocity, t is the time, and a is the acceleration.
In this case, the initial velocity is -9.0 m/s (negative since it is downward), and the time is 50 seconds. The acceleration due to gravity is approximately -9.81 m/s².
Substituting the given values into the formula, we get:
d = -9.0 m/s * 50 s + (1/2) * (-9.81 m/s²) * (50 s)²
≈ -2252.5 m
Therefore, the person is approximately 2252.5 meters beneath the cliff after 50 seconds.
Learn more about velocity here: brainly.com/question/17127206
#SPJ4
the only question i need help is number 48 pleaseee
Therefore, the measure of angle 1 is 40°.
What does a mathematical angle mean?Two rays (half-lines) that share a terminal are combined to form an angle. In contrast, the rays are variously referred to as the angle's legs and its arms, with the latter serving as the angle's vertex.
The measure of an inscribed angle is half the measure of its intercepted arc. Therefore, we can use this property to find the measure of angle 1.
If mAB = 80°, then arc AB is also 80° because an inscribed angle intercepts an arc with the same measure as the angle. Therefore, the measure of arc AB is 80°.
Since angle 1 is an inscribed angle that intercepts arc AB, its measure is half the measure of arc AB. Therefore, we can find the measure of angle 1 as follows:
m∠1 = (1/2) x m arc AB
m∠1 = (1/2) x 80°
m∠1 = 40°
Therefore, the measure of angle 1 is 40°.
To know more about angle visit:
https://brainly.com/question/28451077
#SPJ1
A bottle of apple juice has 25 ounces. Find the number of quarts of apple juice in a case of 24 bottles
There are 18.75 quarts of apple juice in a case of 24 bottles.
To calculate the number of quarts of apple juice in a case of 24 bottles, we must first calculate the number of ounces in the case. To do this, we can use the formula:
Total Ounces = Number of Bottles x Ounces per Bottle
Total Ounces = 24 x 25
Total Ounces = 600
Now that we have the total ounces of apple juice in the case, we can convert this to quarts using the formula:
Quarts = Ounces ÷ 32
Quarts = 600 ÷ 32
Quarts = 18.75
Therefore, there are 18.75 quarts of apple juice in a case of 24 bottles.
Learn more about total ounces here:
https://brainly.com/question/14827945
#SPJ4
a) Show that sin(BAC) = in both drawings. 5 b) Work out angle BAC in the drawing where it is acute. c) Work out angle BAC in the drawing where it is obtuse. Give each angle to 1 d.p. 15 mm B 24 mm 30° B. 15 mm A 24 mm 30° Not drawn accurately
Answer:
Step-by-step explanation:
Which statement best compares and contrasts the two formats?
The infographic shows the movement of water visually, while the text describes it.
The infographic would be less appealing to visual learners than the text.
It is impossible to understand the infographic without the text.
The text is more accurate than the infographic.
need help !!!!!!!!!!
Answer: X: 230
Explanation in image.
Let X be the number of successes observed in a sample of n = 4 items selected from a population of N = 8. suppose that of the N=8 items, 5 are considered ''successes''.
a) Find the probability of observing all successes.
b) Find the probability of observing one success.
c) Find the probability of at most two successes.
a)0.1071
b)0.2857
c) 0.3571`.
a) The probability of observing all successes is `(5/8) × (4/7) × (3/6) × (2/5) = 0.1071`b) The probability of observing one success is `(5/8) × (3/7) × (4/6) × (4/5) = 0.2857`c) The probability of at most two successes is equal to `P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)`.The probability of observing zero successes is `(3/8) × (2/7) × (1/6) × (0/5) = 0`.The probability of observing one success is `(5/8) × (3/7) × (4/6) × (4/5) = 0.2857`The probability of observing two successes is `(5/8) × (3/7) × (4/6) × (1/5) = 0.0714`.Therefore, `P(X ≤ 2) = 0 + 0.2857 + 0.0714 = 0.3571`.
Learn more about probability
brainly.com/question/14017353
#SPJ4
i stil dont understand it how you do it please break it down a little on how to increase 80 by25%
Answer:
100
Step-by-step explanation:
25% can also be converted to 0.25
if you want to INCREASE it by 25%, you're adding 25% to your current 100% to get 125% of 80
125% is the same as 1.25, so you multiply 80 by 1.25
80 * 1.25 = 100
Answer:
100
Step-by-step explanation:
To increase 80 by 25%, you need to add 25% of 80 to 80.
First, we find what 25% of 80 is.
To find a percent of a number, multiply the percent by the number.
Change the percent to a decimal by dividing the percent by 100.
25% of 80 = 25% × 80 = 25/100 × 80 = 0.25 × 80 = 20
25% of 80 is 20.
Now we add 20 to 80.
80 + 20 = 100
Answer: 100
10. Kendall drew a right triangle. The tangent value for one angle in her triangle is 1.8750. Which set of side lengths could belong to a right triangle similar to the triangle Kendall drew? A. 16, 30, 35 B. C. 6, 8, 10 D. 1.875, 8, 8.2 8, 15, 17
The sets of side lengths that are similar to the triangle that Kendall drew are; A. 16, 30, 35, and D. 8, 15, 17.
How to obtain the sidesThe tangent of a right triangle is given as the opposite side divided by the adjacent side. Now, we are given the value of the tangent to be 1.8750.
To obtain the tangents, we are going to divide the opposite by the adjacent as follows:
30/16 = 1.875
8/6 = 1.333
8/1.875 = 4.266
15/8 = 1.875.
So, the set of side lengths that are similar to the triangle that Kendall drew are 16, 30, 35, and 8, 15, 17.
Learn more about right triangles here:
https://brainly.com/question/2217700
#SPJ1
What is the value of x.
Answer:
19.8
Step-by-step explanation:
Given: ABCD is a rectangle
AE≅CF
Prove: DE≅BF
(written in a two-column proof please)
Therefore , the solution of the given problem of rectangle comes out to be DE ≅ BF | Corresponding parts of congruent triangles are congruent
What is a rectangle?A rectangle is a cube with four perpendicular sides in the Euclidean plane. It is also known as an equal-sided rectangle or an equiangular trapezoid. Additionally, the trapezoid may have a straight border. A square has four edges that are the same length. Quadrilaterals that are rectangular have four identical sides but instead four 90° edges. As a result, it is sometimes referred to as a "rectangular trapezoid".
Here,
ABCD is a rectangle | Given
=> AE ≅ CF | Given
AEFC is a parallelogram | Definition of parallelogram
=> AC ≅ EF | Opposite sides of a parallelogram are congruent
=> ∠EAF ≅ ∠ACF | Opposite angles of a parallelogram are congruent
=> ∠EAF ≅ ∠CAD | Diagonals of a rectangle bisect each other
=> ∠ACF ≅ ∠CAD | Transitive property of congruence
=> ∆ACF ≅ ∆CAD | ASA (angle-side-angle) congruence
=> DF ≅ DF | Reflexive property of congruence
=> ∆DFC ≅ ∆DFE | SSS (side-side-side) congruence
=> ∠BCF ≅ ∠ADE | Corresponding angles of congruent triangles are congruent
=> ∠BCF ≅ ∠BDF | Diagonals of a rectangle bisect each other
=> ∠ADE ≅ ∠BDF | Transitive property of congruence
=>∆ADE ≅ ∆BDF | ASA congruence
=> DE ≅ BF | Corresponding parts of congruent triangles are congruent
To know more about rectangle visit:
https://brainly.com/question/29123947
#SPJ1
A softball team has 20 players. How many 9 player batting orders are possible?
There are 184,756 possible 9 player batting orders for a softball team with 20 players.
The formula to calculate the combination number of possible batting orders for a team with n players is n!/(n-r)! where n = the total number of players, and r = the number of players in the batting order. Therefore, for a softball team with 20 players, the number of possible 9 player batting orders is 20!/(20-9)! = 184,756.
20! = 20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
(20-9)! = (20 - 9) × (19 - 9) × (18 - 9) × (17 - 9) × (16 - 9) × (15 - 9) × (14 - 9) × (13 - 9) × (12 - 9) × (11 - 9) × (10 - 9) × (9 - 9)
20!/(20-9)! = 184,756
Therefore, there are 184,756 possible 9 player batting orders for a softball team with 20 players.
Learn more about combination here:
https://brainly.com/question/20211959
#SPJ4
It’s a solve for why problem pls help me
The exponential function in the given table is:
y = 0.02*(1/2)^x
How to get the function in the table?This seems to be an exponential function of the form:
y = a*b^x
Using the points in the table we can try to find the values of a and b.
for the first point we can write:
0.02 = a*b^0
0.02 = a
Then the function is:
y = 0.02*b^x
Now the second point, (1, 0.01), replacing that we will get:
0.01 = 0.02*b^1
0.01 = 0.02*b
0.01/0.02 = b
1/2 = b
The function is:
y = 0.02*(1/2)^x
Learn more about exponential functions at:
https://brainly.com/question/2456547
#SPJ1
Mufasa, Heloise, Angie, I have written more than a combined total of 22 articles for the school newspaper.Heloise has written 1/4 as many articles does Mufasa has. Gia has written 3/2 as many articles as Mufasa has.
If we are aware that Mustafa, Heloise, or Gia have penned more than [tex]22[/tex]pieces altogether. [tex]M > 8[/tex] This is the number of articles Mustafa might have written.
How to explain number?A numeric is a mathematical number which can be utilized to compute and describe a quantity. Numerical symbols, such as "3," are written to represent numbers. A counting system is a logical way of expressing numbers that uses digits or symbols to represent them.
How come 100 is a number?The fact that we use a decimal (base 10) mathematical notation system for numbers gives the number 100 importance that it probably wouldn't otherwise have. It is a circular numeral with undertones of excellence.
[tex]M + H + A > 22[/tex]
We also know that:
[tex]H = 1/4M[/tex]
[tex]A = 3/2M[/tex]
We can substitute these expressions into the first equation:
[tex]M + 1/4M + 3/2M > 22[/tex]
Multiplying everything by the common denominator of 4:
[tex]4M + M + 6M > 88[/tex]
[tex]11M > 88[/tex]
[tex]M > 8[/tex]
So, Mufasa has written more than [tex]8[/tex] articles.
Using the equation [tex]H = 1/4M[/tex], we can find that Heloise has written:
[tex]H = 1/4(8) = 2[/tex]
Using the equation [tex]A = 3/2M[/tex], we can find that Angie has written:
[tex]A = 3/2(8) = 12[/tex]
Therefore, Mufasa has written more than [tex]8[/tex] articles, Heloise has written [tex]2[/tex]articles, and Angie has written [tex]12[/tex] articles.
To check if their combined total is more than [tex]22[/tex]:
[tex]M + H + A = 8 + 2 + 12 = 22[/tex]
So, their combined total is exactly [tex]22[/tex], which means that they have not written more than [tex]22[/tex] articles for the school newspaper.
To know more about number visit:
https://brainly.com/question/12077473
#SPJ1
Two sides of a triangle have lengths 9 and 14. Which inequalities represent the possible lengths for the third side, x?
Answer:
[tex]5 < x < 23[/tex]
Step-by-step explanation:
Accoriding to the Triangle Inequality Theorem:
9 + x > 14 ------> x > 5
14 + 9 > x ------> x < 23
So we have 5 < x < 23.
Can someone please help me with this asap? I will give brainliest if it’s correct
Show work!!
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
There are a total of 30 number between 1 and 30, so the total events is 30.
Now for the favorable events (A: even and multiple of 3) there's a total of 5 numbers (6,12,18,24,30)
Using classic probability law the probability is given by the favorable events between the total events
[tex]P(A)=\frac{6}{30}=\frac{1}{5}[/tex]
The average cost of a pizza in 2022 is $18. Inflation has been averaging 3.25% for many years. In what year was the average cost of a pizza 9$ (half)? Approximate using rule of 72.
Therefore , the solution of the given problem of average comes out to be the average price of a pizza in 2000 was about $9 (or half of $18).
Explain average.An organised collection's median value is the precise value that makes up the collection's mean. In this case, the ratio between the lowest and highest 50% of the data is a normal but rather probability measure. When finding the middle and mode, a variety of algorithms can be applied in order to identify any unusual or even amounts of values.
Here,
By dividing 72 by the interest rate, we can calculate how many years it will take an investment to double in value at a specific interest rate. This is known as the law of 72. In this instance
With an inflation rate of 3.25 percent, it takes roughly how many years for the price of a pizza to double as a result of inflation:
72 / 3.25 = 22.15 years
In light of this, we can calculate that a pizza cost $9 (half of $18) roughly 22 years ago, which corresponds to the following year:
2022 - 22 ≈ 2000
As a result of inflation running at an average of 3.25% for many years, the average price of a pizza in 2000 was about $9 (or half of $18).
To know more about average , visit
https://brainly.com/question/24057012
#SPJ1
Rob's favorite shampoo is available in two sizes: regular and economy. Each size and its price are shown in the table. Size regular economy Quantity (oz) 20 40 Price ($) $8.00 $10. Which size is the better buy?
Answer:
Step-by-step explanation:
To determine which size of shampoo is the better buy, we need to calculate the unit price, which is the price per ounce for each size.
For the regular size, the unit price is:
$8.00 / 20 oz = $0.40/oz
For the economy size, the unit price is:
$10.00 / 40 oz = $0.25/oz
Since the unit price for the economy size is lower than the unit price for the regular size, the economy size is the better buy.
Therefore, the economy size of shampoo is the better buy.
Which of the following is a rational number?
Answer: D) square root 49
Step-by-step explanation: a rational number is a number that eventually ends. Square root 49 is the answer, because it terminates.
Estimate 12% of 77.
10
8
6
12
Answer:
Step-by-step explanation:
12% of 77 is 10.24 or 10.
Step-by-step explanation:
12/100 * 77
12*77=824
824/100
divide by 2
206/25
use long division method
8.24
questions are in the images attached below :)
Simple interest is calculated as $3000 x 2.5% = $76. Compound interest is added to the principal to determine the balance for the next period.
What is simple interest?Simple interest is a type of interest calculation that only takes into account the principal amount of a loan or investment. It does not include any additional payments (or compounding) of the interest. It is calculated by multiplying the principal amount by the interest rate and the number of periods for which the loan is taken out.
For Suzanne's investment, the annual interest rate is [tex]$2.5 %$[/tex], and the interest is simple. Therefore, the interest she earns each year is [tex]$$ I = P \times r = 3000 \times 0.025 = 75. $$[/tex]
Her balance at the end of each year is the sum of her initial deposit and the interest earned in that year. The completed table is:
For Derek's investment, the annual interest rate is also [tex]$2.5 %$[/tex], but the interest is compounded annually. Therefore, we use the compound interest formula with [tex]P=3000[/tex], [tex]r=0.025$, and $n=1[/tex]:
[tex]$$ A = 3000 \times (1+0.025)^Y. $[/tex]
To know more about principal, visit
brainly.com/question/1173061
#SPJ1