The required rate of increasing in volume of a sphere when diameter is 80 mm is equals to 25600π mm^3/s
let 'V' be the volume of the volume of a sphere
'r' be the radius of the sphere.
The formula for the volume of a sphere in terms of its radius,
V = (4/3) × π × r^3
Taking the derivative with respect to time, we get,
dV/dt = 4× π × r^2 × (dr/dt)
where dV/dt is the rate of change of the volume,
dr/dt is the rate of change of the radius,
And π is a constant.
The rate of change of the radius dr/dt is 4 mm/s.
Calculate the rate of change of the volume when the diameter is 80 mm.
Diameter = 2 (radius)
This means the radius is 40 mm.
Substituting the values in the formula above, we get,
⇒dV/dt = 4 × π × (40 mm)^2 ×(4 mm/s)
Simplifying this expression, we get,
⇒ dV/dt = 25600π mm^3/s
Therefore, the volume of the sphere is increasing at a rate of 25600π mm^3/s when the diameter is 80 mm.
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. The balance sheet of Trinagar Company for the subsequent two years is provided to you: Liabilities Year I (Rs.) 50,000 70,000 80,000 50,000 250,000 Share capital. Debentures... Creditors..... Retained earning.. Year I (Rs.) i. ii. iii. iv. 100,000 50,000 40,000 60,000 250,000 Additional information for year II: Sales Rs. 180,000. Cost of goods sold Rs. 100,000. Cash operating expenses Rs. 50,000. Dividend paid Rs. 5,000. V. Interest paid Rs. 5,000. Required: Cash flow statement. Year II (Rs.) 250,000 100,000 80,000 430,000 Assets Fixed assets at cost ... Stock Debtors.. Cash balance. CROA Year II (Rs.) 230,000 100,000 40,000 60,000 430,000
To prepare the cash flow statement, we can use the indirect method, which involves adjusting the net income figure for non-cash items and changes in working capital to arrive at the net cash flow from operating activities. Then, we can account for cash flows from investing and financing activities to arrive at the net change in cash and cash equivalents.
Cash flow statement applying indirect methodHere's the cash flow statement for Year II:
Cash flow from operating activities:
Net income: Rs. 30,000 (180,000 - 100,000 - 50,000 - 5,000 - 5,000)
Adjustments for non-cash items:
Depreciation: Rs. 30,000 (230,000 - 200,000)
Changes in working capital:
Increase in stock: Rs. 10,000 (100,000 - 90,000)
Increase in debtors: Rs. 20,000 (60,000 - 40,000)
Increase in creditors: Rs. 10,000 (80,000 - 70,000)
Net cash flow from operating activities: Rs. 100,000
Cash flow from investing activities:
Purchase of fixed assets: Rs. 30,000 (230,000 - 200,000)
Net cash flow from investing activities: Rs. -30,000
Cash flow from financing activities:
Repayment of debentures: Rs. 20,000 (50,000 - 30,000)
Payment of dividends: Rs. 5,000
Net cash flow from financing activities: Rs. -25,000
Net change in cash and cash equivalents: Rs. 45,000 (100,000 - 30,000 - 25,000)
Cash and cash equivalents at the beginning of the year: Rs. 60,000
Cash and cash equivalents at the end of the year: Rs. 105,000
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The bishop family brought a case of water containing 24 bottles. During one week,Lydia drank 1/8 of the bottles,Mitchell drank 33 1/3% of the bottles,Alexa drank 0.25 of the bottles, and Todd drank the rest.What % did todd drink.
Todd drank 29.17% of the bottles. First, we need to calculate the total number of bottles drank by Lydia, Mitchell, and Alexa.
Lydia = (1/8) x 24 = 3 bottles
Mitchell = (33 1/3%) x 24 = (1/3) x 24 = 8 bottles
Alexa = 0.25 x 24 = 6 bottles
The total number of bottles drank by Lydia, Mitchell, and Alexa is 3 + 8 + 6 = 17 bottles.
Therefore, the number of bottles Todd drank is 24 - 17 = 7 bottles.
To find the percentage of bottles Todd drank, we can use the following formula:
Percentage = (Part/Whole) x 100%
Where the Part is 7 and the Whole is 24.
Percentage = (7/24) x 100% = 29.17%
Therefore, Todd drank 29.17% of the bottles.
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The area, a, of an ellipse can be determined using the formula a = Ï€xy, where x and y are half the lengths of the largest and smallest diameters of the ellipse. which is an equivalent equation solved for y? y = a · Ï€x y = a (Ï€x) y = a â€" Ï€x y = a ÷ (Ï€x)
The correct equivalent equation solved for y is y = a ÷ (πx).
The equivalent equation solved for y in the given formula
a = πxy is y = a ÷ (πx).
1. Start with the original formula:
a = πxy
2. To solve for y, we need to isolate y on one side of the equation.
3. Divide both sides of the equation by πx:
a ÷ (πx) = (πxy) ÷ (πx)
4. The πx terms cancel out on the right side of the equation, leaving:
y = a ÷ (πx).
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Please show working out.
A line has the equation y = 3x + k. What is the gradient of the line?
3
when the line is at the y=ax+b form the gradient is equal to a
a swimming pool can hold 2,376 m3 of water. its length is 33 meters and its width is 9 meters. calculate the height of the pool. what is the answer
Answer: 8 meters
Step-by-step explanation:
33x9=297
2376 divided by 297= 8
The height of the swimming pool is approximately 2.6 meters. This can be answered by the concept of Surface Area.
To calculate the height of the swimming pool, we can use the formula for the volume of a rectangular prism, which is V = lwh, where V is the volume, l is the length, w is the width, and h is the height. We know that the volume of the pool is 2,376 m3, the length is 33 meters, and the width is 9 meters.
Plugging these values into the formula, we get 2,376 = 33 x 9 x h. Solving for h, we get h = 2.6 meters.
Therefore, the height of the swimming pool is approximately 2.6 meters, which can be calculated by using the formula for the volume of a rectangular prism and plugging in the known values of length, width, and volume.
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Help me solve e this question?
The correct statement regarding the transformations is given as follows:
g(x) is stretched vertically by a factor of 5 and translated 3 units to the right.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The transformations to the parent function in this problem are given as follows:
Multiplication by 5 -> vertical stretch by a factor of 5.x -> x - 3: translation right 3 units.More can be learned about translations at brainly.com/question/28174785
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MAKE SURE TO SAY HOW TO GOT THE ANSWER SO I CAN HELP OTHERS AND SHOW MY MOM THIS!
1. By simplifying and comparing, the value of x is 4
2. By simplifying and comparing, the value of x is 6
3. By simplifying and comparing, the value of x is 0.53 and the value of y is 4
Simplifying an expressionFrom the question, we are to simplify the given expressions
1.
(4.2 × 10⁷) / (2 × 10³)
This can be expressed
(4.2 / 2) × (10⁷ / 10³)
Simplifying and applying the division law of indices
= 2.1 × 10⁷⁻³
= 2.1 × 10⁴
By comparison, the value of x is 4
2.
(7.2 × 10⁻⁸) ÷ (1.2 × 10⁻³)
This can be expressed as
(7.2 ÷ 1.2) × (10⁻⁸ ÷ 10⁻³)
Simplifying and applying the division law of indices
6 × 10⁻⁸ ⁻ ⁻³
6 × 10⁻⁸ ⁺ ³
6 × 10⁻⁵
By comparison, the value of x is 6
3.
(4.24 × 10⁶) ÷ (8 × 10²)
This can be expressed as
(4.24 ÷ 8) × (10⁶ ÷ 10²)
Simplifying and applying the division law of indices
= 0.53 × 10⁶ ⁻ ²
= 0.53 × 10⁴
By comparison, the value of x is 0.53 and the value of y is 4
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An ant carries a piece of leaf home that is 1.25 x 10-2 grams and his partner carries home a piece of leaf that is 2.3 x 10-3 grams. What is the combined weight of their pieces of leaf?
the combined weight of the two pieces of leaf is 1.47 x 10⁻²grams.
HOW TO FIND WEIGHT ?
To find the combined weight of the two pieces of leaf, we simply need to add the weights of the individual pieces of leaf. We are given that one piece of leaf weighs 1.25 x 10⁻² grams and the other piece of leaf weighs 2.3 x 10⁻³ grams.
Adding these two weights, we get:
1.25 x 10⁻²grams + 2.3 x 10⁻³ grams = 1.47 x 10⁻² grams
Therefore, the combined weight of the two pieces of leaf is 1.47 x 10⁻²grams.
It's important to note that when working with scientific notation, we need to pay attention to the exponents and perform the operations according to the rules of exponents. In this case, we add the numbers in front of the exponent (1.25 and 2.3) and keep the exponent (10⁻²) the same.
It's also worth mentioning that this problem involves very small weights, as the values are expressed in grams using scientific notation. This is a common approach when dealing with very large or very small values in scientific contexts, as it allows us to easily express and compare values using a standardized format
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miss america winners from the 1920's and 1930's had a average bmi of 19.2. a sample of recent winners had reported bmis of 18.3, 19.6, 19.9, 18.8, 18.2, 18.1, 18.1, 18.3, 18.3, 18, and 19.8 . do recent winners appear to be significantly different from those in the 1920s and 1930s? (assume normality)
A one-sample t-test is conducted to determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s. The test results fail to reject the null hypothesis, indicating that recent winners do not appear to be significantly different from those in the 1920s and 1930s.
To determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s, a one-sample t-test can be conducted. Using the given sample, the sample mean BMI is calculated to be 18.5.
The null hypothesis is that the population mean BMI of recent winners is equal to 19.2. The alternative hypothesis is that the population mean BMI of recent winners is different from 19.2.
Assuming a significance level of 0.05 and using a two-tailed test, the calculated t-value is -2.08 and the corresponding p-value is 0.057.
Since the p-value is greater than the significance level, we fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that recent Miss America winners have significantly different BMI compared to winners from the 1920s and 1930s.
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Two corners of the backyard are right angles. The third corner forms an obtuse angle measuring 127°. The fourth corner forms an acute angle measuring 53°. When transferring these angle measurements from the real world to the scale drawing, will their measures increase, decrease or stay the same?
Answer:
The angle measurement will stay the same.
Step-by-step explanation:
When you scale a figure the angle measurements stay the same.
Helping in the name of Jesus.
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 12 N acts on a certain object, the acceleration
of the object is 4 m/s². If the acceleration of the object becomes 10 m/s², what is the force?
ON
Answer: [tex]F=30N[/tex]
Step-by-step explanation:
1. You know that the force acting on the object varies directly with the object's acceleration. Then, by definition, you have:
[tex]F=ka[/tex]
Where [tex]F[/tex] is the force acting on the object, [tex]a[/tex] is the object's acceleration and [tex]k[/tex] is the constant of proportionality.
2. Keeping this on mind, you can calculate the constant of proportionality by substituting [tex]F=12[/tex] and [tex]a=4[/tex] into the equation and solving for [tex]k[/tex]:
[tex]12=k4[/tex]
[tex]k=\dfrac{12}{4}[/tex]
[tex]k=3[/tex]
3. Now, you can calculate the force when the acceleration of the object becomes 10 m/s², as following:
[tex]F=3(10)[/tex]
[tex]F=30[/tex]
3. The result is:
[tex]F=30N[/tex]
find the length of SU is S is -15 and U is 10
The requried length of the line segment on number line SU is 25 units.
To find the length of the line segment SU, we need to subtract the coordinates of S from the coordinates of U and take the absolute value. So we have:
|SU| = |U - S| = |10 - (-15)| = |25| = 25
Therefore, the length of the line segment on number line SU is 25 units.
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the surface area of a rectangular prism is 1300 square inches. find the surface area of a similar solid that is larger by a scale factor of 3.
The surface area after larger by scale factor is 11700 [tex]in^2[/tex].
What is surface area?The surface area οf an οbject refers tο the οverall space filled by its surfaces. Many 3D shapes in geοmetry have variοus surface areas, which may be quickly estimated using the fοrmulas we shall learn in this lessοn. Twο categοries are used tο classify the surface area:
Curved surface area οr Lateral surface areaSurface area in tοtalHere the given rectangular prism ,
Surface area = 1300 square inches
Here the given prism is larger by scale factor of 3 then,
=> surface area = 1300[tex]\times3^2[/tex] = 1300[tex]\times9[/tex] = 11700 [tex]in^2[/tex].
Hence the surface area after larger by scale factor is 11700 [tex]in^2[/tex].
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A number gives a remainder of 5 when divided by 10. Another number gives a remainder of 4 when divided by 10. The sum of these two numbers is multiplied by 3 to give the third number. What is the remainder when this third number is divided by 10?
Answer:
The remainder is 7.
Step-by-step explanation:
Let's pick 15 and 14. The sum of these two numbers is 29. Multiplying 29 by 3, we have 87. 87 divided by 10 is 8 with a remainder of 7.
What is the equation of the line that passes through the point ( 2 , − 3 ) and has a slope of 2?
Answer:
y = 2x - 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 2 , then
y = 2x + c ← is the partial equation
to find c substitute (2, - 3 ) into the partial equation
- 3 = 2(2) + c = 4 + c ( subtract 4 from both sides )
- 7 = c
y = 2x - 7 ← equation of line
The price of buying x boxes of cereal at the Corner Store is shown by the graph below. The advertisement shows the cost of buying x boxes of cereal at Bargain World.
(graph shown in picture attache)
A. Determine the costs when a family buys 1, 2, 3, and 4 boxes of cereal at each store.
Show your work.
B. Explain when a family should buy cereal at the Corner Store and when they should buy cereal at Bargain World.
The cost of the cereals and where the family should buy, obtained by simple arithmetic operations are;
A. The cost of 1, 2, 3, and 4 boxes of cereals are;
Corner Store; $4.5, $9, $13.5, $18
Bargain World; $6, $9.5, $13, $16.5
B. When the number of boxes of cereals bought are less than 3, the family shoulds buy from the Bargain World, when the number of cereals bought are more than 3, the family should buy from the Bargain World Store
What are simple arithmetic operations?Simple arithmetic operations are addition, subtraction, division and multiplication operations.
A. The cost of the boxes of cereal obtained by arithmetic operations are as follows;
The cost of buying 1, 2, 3, and 4 boxes at the Corner store obtained from the graph are;
1 box costs $4.5
2 boxes costs $9
3 boxes costs $13.5
4 boxes costs $18
The cost of buying 1, 2, 3, and 4 boxes at the Bargain World are;
Cost of buying the first box = $6
Cost of buying 2 boxes = $6 + $3.5 = $9.5
Cost of buying 3 boxes = $6 + $3.5 + $3.5 = $13
Cost of buying 4 boxes = $6 + $3.5 + $3.5 + $3.5 = $16.5
B. Based on the costs which is initially higher at the Bargain World store, a family.
The cost of 3 boxes at the Bargain World is $13, while at the Corner Store, it is $13.5
The higher number of boxes are more expensive at the Corner Store than the Bargain Worldstore
Therefore, a family should buy from the Corner Store when they are buying less than 3 boxes of cereal and they should buy from the Bargain World when they are buying more than 3 boxes of cereal
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Which transformation maps quadrilateral ABCD onto quadrilateral HGFE?
The correct answer to the given question about mapping quadrilateral ABCD onto quadrilateral HGEF is option D Translation 6 units left and 2 units down
To determine the transformation that maps quadrilateral ABCD onto quadrilateral HGFE, we need to compare the corresponding sides and angles of the two quadrilaterals.
Option 1: Rotation of 180° about the origin
A rotation of 180° about the origin would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, side AB of ABCD would not match side HG of HGFE after the rotation. Therefore, option 1 is incorrect.
Option 2: Reflection across the y-axis
A reflection across the y-axis would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, angle A of ABCD would not match angle H of HGFE after the reflection. Therefore, option 2 is incorrect.
Option 3: Reflection across the x-axis
A reflection across the x-axis would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, side BC of ABCD would not match side GF of HGFE after the reflection. Therefore, option 3 is incorrect.
Option 4: Translation 6 units left and 2 units down
A translation 6 units left and 2 units down would map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are congruent. Each point of ABCD would move left by 6 units and down by 2 units to reach its corresponding point in HGFE. Therefore, option 4 is the correct transformation that maps quadrilateral ABCD onto quadrilateral HGFE.
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Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits x days to pick up the motorcycle.
Answer:
Step-by-step explanation:
1200x5= it is 6000
Answer:
900=5x + 1200
Step-by-step explanation:
What is the axis of symmetry of the graph of the function f(x) = 2x^2 + 8x − 5?
Answer:
The axis of symmetry is at x = -2.
Step-by-step explanation:
To find the axis of symmetry of a quadratic function in the form of f(x) = ax^2 + bx + c, you can use the formula x = -b / (2a).
In the function f(x) = 2x^2 + 8x − 5, a = 2 and b = 8, so we can plug those values into the formula and get:
x = -b / (2a) = -8 / (2 * 2) = -2
Therefore, the axis of symmetry of the function f(x) = 2x^2 + 8x − 5 is located at x = -2.
This means that the graph of the function is symmetric with respect to the vertical line x = -2. Any point on the graph that is a distance of t from the line x = -2 will have a corresponding point on the graph that is also a distance of t from the line.
Kirk made a cake for his mother's birthday. He started making the cake batter at 3:48 P.M. It took 1 hour and 3 minutes to make the batter. Then, the cake baked in the oven for 1 hour and 8 minutes. What time did the cake come out of the oven?
Answer:
Kirk started making the cake batter at 3:48 P.M. and it took him 1 hour and 3 minutes to make the batter. So he finished making the batter at 3:48 P.M. + 1 hour and 3 minutes = 4:51 P.M.
Then, the cake baked in the oven for 1 hour and 8 minutes. So the cake came out of the oven at 4:51 P.M. + 1 hour and 8 minutes = 5:59 P.M.
deena has pairs of white socks, pairs of black socks, pair of red socks, and pairs of navy socks in her sock drawer. each pair of socks is folded together. if she pulls a pair of socks out of her drawer in the morning without looking, what is the probability that she will choose a pair of navy socks?
The final answer is 1 / 11
Deena has a total of 11 pairs of socks in her sock drawer. One pair of those 11 pairs is navy socks. Therefore, the probability that she will choose a pair of navy socks is 1/11.What is probability? Probability is the numerical measure of the possibility of an event taking place. Probability is calculated by dividing the number of successful outcomes by the total number of possible outcomes.The probability of Deena picking navy socks is calculated as:Probability of selecting navy socks = Number of pairs of navy socks/ Total number of pairs of socks in the drawerNumber of pairs of navy socks = 1Total number of pairs of socks in the drawer = 1 /11Probability of selecting navy socks = 1/11Therefore, the probability that Deena will select a pair of navy socks is 1/11.
Therefore, the answer is 1 / 11.
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The perimeter of a rectangle is 66, and the length is 1 more
than 3 times the width. What is the length?
O 25
O24
O 35
O 30
Ignore the graph it’s for a different question
Answer:
35. Radius= 12 cm
36. (B) 50 cm
Step-by-step explanation:
35.
TSA = 2πr(h+r)
Expanding the brackets, we get:
TSA = 2πrh + 2πr^2
Rearranging the equation, we get:
TSA - 2πrh = 2πr^2
Dividing both sides by 2π, we get:
r^2 = (TSA - 2πrh) / 2π
Taking the square root of both sides, we get:
r = √[(TSA - 2πrh) / 2π]
We need to simplify the given equation to solve for r.
r = √[(905.143) - 2(22/7)r(14)) / 2(22/7)]
r = √[(905.143) - (88/7)r] / (44/7)
Squaring both sides, we get:
r^2 = [(905.143) - (88/7)r] / (44/7)
Multiplying both sides by (44/7) and simplifying:
7r^2 - 88r - 905.143 = 0
Using the quadratic formula:
r = [88 ± √(88^2 - 4(7)(-905.143))] / (2(7))
r ≈ 12.009 or r ≈ -12.892
Since r represents the radius of a circle, which cannot be negative, we ignore the negative solution.
Therefore, the solution is r ≈ 12.009.
36.
We can use the formula for the volume of a cylinder:
volume = πr^2h
where r is the radius and h is the height of the cylinder.
First, we need to find the radius of the drum. The diameter is given as 56 cm, so the radius is half of that, or 28 cm.
Next, we can use the given volume of 123.2 liters. However, we need to convert liters to cubic centimeters (cm^3) since the dimensions are in centimeters.
1 liter = 1000 cm^3
So, 123.2 liters = 123,200 cm^3.
Now we can plug in the values:
123,200 cm^3 = π(28 cm)^2h
Simplifying:
123,200 cm^3 = 2464π cm^2h
Dividing both sides by 2464π cm^2:
50 cm = h
Therefore, the height of the drum is 50 cm.
help i am stuck in this question.
The proof of the sum of the triangles ΔPMS + ΔMQT and ΔSOR + ΔNRT is shown below
Proving the sum of the triangles are equalGiven that
PQRS and MNOP are parallelograms
We have the following congruent sides by the theorem of CPCTC
QT = RT and MQ = NR
PM = SO and MS = SR
This is alse true because of the SSS congruent theorem
When the sides are added, we get
PMS + MQT = SOR + NRT
So, we have
ΔPMS + ΔMQT = ΔSOR + ΔNRT
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a bug travels from a to b along the segments in the hexagonal lattice pictured below. the segments marked with an arrow can be traveled only in the direction of the arrow, and the bug never travels the same segment more than once. how many different paths are there? (2012amc10b problem 25 or 2012 amc12b problem 22)
There are 20,149 different paths from A to B in the given hexagonal lattice, satisfying the given conditions.
To solve this problem, we can use the Principle of Inclusion-Exclusion (PIE). We start by counting the total number of paths from A to B without any restrictions, which is simply 6!/(3!3!) = 20,160. This is the number of ways to arrange 3 up arrows and 3 right arrows.
Next, we count the number of paths that violate the restriction on the middle segment. There are two cases to consider, The bug travels the middle segment from left to right: There are 3 choices for the path of the bug on the top half of the hexagon and 2 choices for the path on the bottom half, for a total of 3*2 = 6 paths.
The bug travels the middle segment from right to left: This is the same as case 1, so there are another 6 paths. However, we have counted some paths twice, namely those that violate both restrictions on the middle segment. There is only one such path, which is the one that starts with the up arrow, goes left on the top half of the hexagon, and goes right on the bottom half.
Thus, the total number of valid paths is 20,160 - 6 - 6 + 1 = 20,149.
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Jesse bought 2 pickles and 2 popcorn boxes for $10. Ronnie
bought 4 pickles and 2 popcorn boxes for $13.50 How
much does the Pickel cost?
O $1.25
O $1.50
O $2.00
O $1.75
Step-by-step explanation: To find the cost of one pickle, we can use a system of equations. Let x be the cost of one pickle and y be the cost of one popcorn box. Then we have:
2x + 2y = 10 4x + 2y = 13.50
Subtracting the first equation from the second, we get:
2x = 3.50 x = 1.75
So one pickle costs $1.75.
Exit Ticket
Draw the 2 dimensional cross section that is perpendicular to the
base of the pyramid.
b. Draw the 2 dimensional cross section that is parallel to the
base of the pyramid.
An exit ticket is an informal assessment tool used by educators to gauge student understanding of the content taught during a lesson. It is typically a brief activity, such as a short questionnaire or problem-solving task, that students complete at the end of the class.
This helps the teacher identify areas where students may need additional support or review. Exit tickets provide valuable insights into students' learning progress and inform future instruction.
The base of a pyramid refers to the flat surface on which the pyramid rests. In geometry, a pyramid is a polyhedron composed of a base and triangular faces that converge at a single vertex (the apex). The base can be a variety of shapes, including triangles, squares, rectangles, or other polygons.
The properties of the base, such as its area and perimeter, play a crucial role in determining the volume and surface area of the entire pyramid.
To connect these concepts, you could use an exit ticket to assess students' understanding of pyramids, specifically focusing on the properties and importance of the base. This could include questions related to calculating the area, perimeter, or identifying different types of pyramid bases.
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HELP PLEASE!!!
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
A- 14 and 1 over 7 in2
B -23 and 4 over 7 in2
C -47 and 1 over 7 in2
D - 84 and 6 over 7 in2
A,B,C,D which one
Therefore, the answer is option B 23 and 4/7 inch² that is at least 23 and 4/7 inch² paper is needed to wrap 6 mini muffins.
What is total surface area?Total surface area refers to the sum of the areas of all the faces or surfaces of a three-dimensional object. It includes the areas of the base, top, and lateral faces of the object. For example, the total surface area of a cube is the sum of the areas of all six faces, while the total surface area of a cylinder includes the areas of both circular bases and the lateral surface area.
Here,
The surface area of each mini muffin can be calculated by finding the lateral surface area of the cylinder and adding the surface area of its circular bases. The diameter of each mini muffin is 2 inches, so the radius is 1 inch. The height is 1 and 1/4 inches. The lateral surface area of each mini muffin is given by:
Lateral surface area = height x circumference
Lateral surface area = (5/4) x 2 x πr
Lateral surface area = (5/4) x 2 x (22/7) x 1
Lateral surface area = 11/2 cm²
The surface area of each circular base is given by:
Surface area of base = πr²
Surface area of base = (22/7) x 1²
Surface area of base = 22/7 cm²
The total surface area of each mini muffin is given by:
Total surface area = Lateral surface area + 2 x Surface area of base
Total surface area = (11/2) + 2 x (22/7)
Total surface area = 69/14 cm²
To wrap 6 mini muffins, we need to multiply the surface area of one mini muffin by 6. So the total surface area needed is:
Total surface area = 6 x (69/14)
Total surface area = 207/7 cm² (approx.)
Converting to square inches and simplifying, we get:
Total surface area = 23 and 4/7 inch²
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Josiah is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 12 in and the height of the pyramid is 14in. To get the wax for the candle, Josiah melts cubes of wax that are each 6 in by 6 in by 6 in. How many of the wax cubes will Josiah need in order to make the candle? Show your work.
Answer:
13
Step-by-step explanation:
The volume of the pyramid can be calculated using the formula:
Volume = (1/3) * base area * height
The base area of the pyramid is equal to the area of one of the square sides, which is:
Base area = 12 in * 12 in = 144 in^2
Therefore, the volume of the pyramid is:
Volume = (1/3) * 144 in^2 * 14 in = 2,688 in^3
Each wax cube has a volume of:
Volume of a wax cube = 6 in * 6 in * 6 in = 216 in^3
To find out how many wax cubes Josiah needs, we can divide the volume of the pyramid by the volume of each wax cube:
Number of wax cubes = Volume of pyramid / Volume of each wax cube
Number of wax cubes = 2,688 in^3 / 216 in^3 = 12.4444...
Since we can't use a fraction of a wax cube, Josiah will need to use 13 wax cubes to make the candle.
please help! it has to be at least 5 paragraphs ! all the instructions are in the photo!
Paragraph - 1: Introduction: A mathematical function called a logarithmic function uses logarithms, which are exponential functions' inverses. A logarithmic function has the generic form f(x) = loga(x).
What is a logarithmic function?A mathematical function called a logarithmic function uses logarithms, which are exponential functions' inverses. A logarithmic function has the generic form f(x) = loga(x). An essential mathematical topic, logarithmic functions are employed in many disciplines including physics, chemistry, biology, economics, and engineering. Using the pH scale to determine a solution's acidity and alkalinity is one practical use of logarithms.
Paragraph - 1: Introduction:
A mathematical function called a logarithmic function uses logarithms, which are exponential functions' inverses. A logarithmic function has the generic form f(x) = loga(x), where an is the base of the logarithm. The bases 10 and e are the most popular. The mathematical constant e, sometimes referred to as Euler's number, is roughly equal to 2.71828. A logarithm with base e is the natural logarithm, abbreviated as ln(x). A logarithmic function's parent function is f(x) = loga(x), where an is a real number with a positive sign. When the argument of the logarithm equals 1, the point where the function's graph crosses the x-axis is known as the x-intercept of a logarithmic function. There isn't a y-intercept. The graph of a logarithmic function has a vertical asymptote at x = 0.
Paragraph 2: Characteristics:
Logarithmic function f(x) = -log(x-7)-9 is provided. Any real integers bigger than 7 fall into the domain of the function since the logarithm's argument must be positive. Due to the fact that the logarithm approaches negative infinity as x approaches 7 from the right, the function's range includes any real integers that are less than or equal to -9. The function's final behaviour is that it approaches negative infinity as x approaches 7 from the right. The function's x-intercept is (8, 0), indicating that it crosses the x-axis at x = 8. Since the function approaches negative infinity as x moves away from 7 to the right, it has a vertical asymptote at x = 7.
Paragraph 3: Transformations:
The parent function, f(x) = log(x), which has a vertical asymptote at x = 0 and a y-intercept at 0, is transformed into the supplied function, f(x) = -log(x-7)-9) (1, 0). The provided function is created by taking the negative of the logarithm, moving it 7 units to the right on the horizontal axis, and 9 units downward on the vertical axis. The resulting function would be f(x) = -1/4 * log(1/8(x+3))+11 if we shift the provided function left by 3 units, reflect it over the y-axis, shift it down by 2 units, compress it by a factor of 8, and reflect it over the x-axis.
Paragraph 4: Evaluation:
For f(x) = -log(x-7)-9 let x = 8:
f(x) = -log(1)-9 = -9
For x = 10, f(x) = -log(3)-9 = -7.52288.
Paragraph 5 - conclusion:
An essential mathematical topic, logarithmic functions are employed in many disciplines including physics, chemistry, biology, economics, and engineering. Using the pH scale to determine a solution's acidity and alkalinity is one practical use of logarithms. My favourite aspect of logarithms is how they help us simplify complex calculations by reducing big numerical values into more comprehensible forms. Understanding how to employ logarithmic characteristics to simplify complex statements and solve problems was the most difficult part of studying logarithms.
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