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, how fast is the area of the rectangle increasing (in cm2/s)?

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.

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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.

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]

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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

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.

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Therefore , the solution of the given problem of rectangle comes out to be  DE ≅ BF | Corresponding parts of congruent triangles are congruent

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

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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.

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.

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.

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Answer:

19.8

Step-by-step explanation:

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).

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).

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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.

The sets of side lengths that are similar to the triangle that Kendall drew are; A. 16, 30, 35, and D. 8, 15, 17​.

The 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​.

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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.

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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

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]

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

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

His total monthly expenses (including savings) are

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).

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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.

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Answer: X: 230

Explanation in image.

Answer:

7.3*10^7

Step-by-step explanation:

Therefore, the measure of angle 1 is 40°.

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°.

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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`.

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Answer:

SAS proves that these triangles are congruent.

The required circumference of the given circle is 45.27 cm approx.

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.

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Using distance formula, the triangle ABC is a scalene triangle

To 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.

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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.

Therefore , the solution of the given problem of area comes out to be  region is 24.5 square units in size.

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.

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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.

The exponential function in the given table is:

y = 0.02*(1/2)^x

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

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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.

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

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.