Ten oranges are to be shared between two boys in the ratio 1:4 how many will each boy get​

Answer:

well for starters

the answer you get when you factor it out is 3(x+3)(x+3)

i know that would mean x=-3 but i dont know how the big 3 would effect anything. hope this helps

The height of water in the cylinder for the second rain gauge, with an opening 10 times the area of the first rain gauge, is 1 cm.

In the second rain gauge, with an opening 10 times the area of the first rain gauge (B: 200 cm^2), and a collection cylinder with the same opening as the rain gauge in (A: 20 cm^2), we need to determine the height of water in the cylinder for a rainstorm of 10 cm.

To find the height of water in the cylinder, we can use the principle of conservation of volume. The volume of water collected in both rain gauges should be the same since it is from the same rainstorm.

The volume of water collected in the first rain gauge (A) can be calculated using the formula:

Volume = Area * Height

Given that the area of the opening is 20 cm^2 and the height of the water collected is 10 cm, we can find the volume of water collected in rain gauge (A).

Now, let's calculate the volume of water collected in the second rain gauge (B). Since the opening is 10 times the area of the first rain gauge (200 cm^2), we need to find the height of water in the cylinder to maintain the same volume as in rain gauge (A).

By using the formula Volume = Area * Height, we can rearrange it to solve for the height:

Height = Volume / Area

Substituting the volume of water collected in rain gauge (A) and the area of the opening in rain gauge (B), we can calculate the height of water in the cylinder for the second rain gauge.

By performing the calculations, we find that the height of water in the cylinder for the same rainstorm of 10 cm is XXX cm in the second rain gauge.

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A professional rain gauge (B) that is more precise has an opening that is 10 times the area (i.e. 200 cm^2  ). The collection cylinder is the same 20 cm^2  opening as the rain gauge in (A) (i.e. 20 cm^2 ) but a funnel ensure all the water ends up in the collection cylinder. In this second rain gauge, what is the height of water in the cylinder for the same rainstorm of 10 cm rain? ( 2 points)

Answer:

A

Step-by-step explanation:

Step-by-step explanation:

A. total mass = 9 + (x × 1.2)

B. 21 - 9 = 12kg

12 ÷ 1.2 = 10 articles.

hope it helps. :)

Answer:

FJ = 15 GH = 15

FG is parallel to HJ

Step-by-step explanation:

There is no any fraction of Pizza left for other toppings, so the required space for other toppings is Zero.

Fractions are used to represent portions of a full or collection of items. There are two parts to every fraction. The number which is at the top of the line is referred to as the numerator. It specifies the number of equal pieces taken from the overall amount or collection. Figure below the line is referred to as the denominator. It shows the number of identical items in a group or the total number of equal parts in a whole.

Ed place mushrooms on Pizza = 5/12

Ed place onions on Pizza = 7/12

Total Fraction of Pizza left = 1 - (5/12 + 7/12)

So Total fraction of Pizza left = 1 - (12/12)

So Total Pizza left = 0

So there is no any more Pizza left for any toppings.

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The complete Question is :

Ed place mushrooms on a 5/12 pizza and onions on a 7/12 pizza. How much more of the pizza is left for other toppings?

Step-by-step explanation:

5n-2

5(4) - 2

20-2=18

A= 18

5n - 2 =48

5n=48+2

5n=50

divide by 5

n= 10

B=10

The statement is not true in general. The correct formula relating the second differential equations of y with respect to x and t is:

(d²y)/(dx²) = [(d²y)/(dt²)] / [(d²x)/(dt²)]

This formula is known as the Chain Rule for Second Derivatives, and it relates the rate of change of the slope of a curve with respect to x to the rate of change of the slope of the curve with respect to t. However, it is important to note that this formula only holds under certain conditions, such as when x is a function of t that is invertible and has a continuous derivative.

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Answer:

(3, 0 )

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c (a ≠ 0 )

Then the x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

y = 5x² - 30x + 45 ← is in standard form

with a = 5, b = - 30 , then

\(x_{vertex}\) = - \(\frac{-30}{10}\) = 3

Substitute x = 3 into the function for corresponding value of y

y = 5(3)² - 30(3) + 45 = 45 - 90 + 45 = 0

vertex = (3, 0 )

Answer:

Vertex is (3,0)

Step-by-step explanation:

Given y= 5x^2 - 30x + 45

         y    = 5 ( x^2 - 6x + 9)

               = 5 ( x -3 )^ 2 + 0

Standard formula of parabola is y = a(x - k)^2 + k where vertex is (h,k)

Here, h = 3 and k = 0

So,  Vertex is ( 3, 0)

Answer:

\(\frac{3}{8} x+\frac{1}{2} y+\frac{3}{8}\)

Step-by-step explanation:

Gather like terms:

\(\frac{3}{4}y-\frac{1}{4}y=\frac{2}{4}y=\frac{1}{2}y\)

\(\frac{7}{8} -\frac{1}{2}=\frac{7}{8} -\frac{4}{8}=\frac{3}{8}\)

Therefore, equivalent expression = \(\frac{3}{8} x+\frac{1}{2} y+\frac{3}{8}\)

Answer:

Step-by-step Solution:

Hence, Option B is correct.

Answer:

100,000,000

Step-by-step explanation:

Multiply.

10 x 10 x 10 x 10 = 10,000

Then multiply 10,000 to the power of 2

10,000 x 10,000

The answer is 100,000,000

Hope this helped :)

Answer:

The answer is 4.57

Step-by-step explanation:

The scores in the econometrics class were approximately normally distributed in both populations, with unknown but equal variances. A random sample of 23 students from the X population had a mean econometrics score of 80 and a standard deviation of 8.

The study aims to compare the performance of students who took the math course (X population) with those who did not (Y population) in the econometrics class. By selecting random samples from both populations, the researchers can evaluate whether there is a significant difference in their econometrics scores.

The sample of 23 students from the X population had an average econometrics score of 80, with a standard deviation of 8. This information provides an estimate of the mean and variability of the econometrics scores for the X population. However, to draw conclusions about the entire X population, statistical inference techniques can be employed.

A common approach is to conduct a hypothesis test, such as a two-sample t-test, to determine if there is a significant difference in the means of the two populations. The test considers factors like the sample means, sample sizes, and the assumed equal variances of the two populations. The analysis would provide insights into whether the math course in linear algebra has a significant impact on the grades in the econometrics class.

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Answer:

B

Step-by-step explanation:

44/77

=0.55

Answer: The product of two consecutive negative integers is 600. What is the value of the lesser integer?

Step-by-step explanation:

EDGE2021

The 1s in 14.937 and 6.1225 have distinct values. The digit 1 in 14.937 is in the thousandths place, representing a value of 0.001, but the digit 1 in 6.1225 is in the hundredths place, representing a value of 0.01.

When we compare the values of the 1s in these two numbers, we can observe that the 1 in 6.1225 is 10 times bigger than the 1 in 14.937. This is due to the fact that the place value of digit 1 in 6.1225 is ten times bigger than the place value of digit 1 in 14.937. It should be noted that while comparing the values of digits in numbers, their location or place value is a significant consideration. Even the smallest Changes in a digit's location can have a substantial influence on its total value. The variation in place value of the 1s in 14.937 and 6.1225 leads in a considerable disparity in their respective values in this situation.

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Glide reflections or Translations, either can  used to create the pattern below, starting with the top figure.

By a transformation of the plane, we mean a map from the set of points in the plane, into the set of the plane, or more colloquially a map from the plane and into the plane.  By a symmetry of the plane we mean a transformation of the plane, which is a bijection, and which is an isometry. that is, it keeps the distance between any two points fixed. The set of all symmetries of the plane form a group, called the symmetry group of the plane. This group is generated by 3 types of elements. \(R_L\), which is a reflection about some line \(L\) in the plane, \(r_\theta\) a rotation about the origin by an angle \(\theta\), and \(T_v\), a Translation on the plane by a vector \(v\). There is a fourth type of symmetry got by composing a reflection and a translation, called a glide-reflection.\(G_{v,L} = T_v \circ R_L\) Together these give all the rigid symmetries of the plane.

To get the the pattern below from the figure above, we can simply translate the arrow four times, and get the pattern. We can also get the pattern by first  reflecting it about the horizontal line midway between the figure and the pattern, followed by 4 translations. cumulatively translation . reflection = glide-reflection, so by four glide reflections we can get the pattern below.

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The statement that cannot be inferred from the information provided is:

"Since the random sample is collected from less than 10% of the population (1,018 is less than 10% of US population), the margin of error is likely to be much larger than reported."

While the sample size is less than 10% of the US population, the margin of error is reported to be 3% using a 95% confidence level.

This indicates that the pollsters have taken into account the sample size, as well as the level of confidence, when calculating the margin of error.

Therefore, we cannot make any inferences about the size of the margin of error based solely on the fact that the sample size is less than 10% of the population.

The statement that can be inferred from the information provided is:

"The success-failure condition is satisfied.

A 95% confidence interval for the proportion of adults who think that licensed drivers should be required to retake their road test once they reach 65 years of age is (63%, 69%)."

Since the sample size is 1,018, we can assume that the success-failure condition is satisfied if the sample proportion is between 10% and 90%.

In this case, the reported proportion is 66%, which satisfies the success-failure condition.

Using a 95% confidence level, the margin of error is reported to be 3%. Based on this, we can construct a confidence interval for the population proportion:

66% ± 3%

This interval can be simplified to (63%, 69%), which means we can be 95% confident that the true proportion of adults who think licensed drivers should be required to retake their road test once they reach 65 years of age is between 63% and 69%.

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Part A: Width = 9.3 ft; Height = 16.5 ft; Area =  153.45 sq ft.

Part B: Width = 38.25 ft ; Height = 91 ft; Area =  3503.5 sq ft.

Part A: conversion factor: 1 in = 3 ft

Width = 3.1 in

Width = 3.1 x 3

Width = 9.3 ft

Height = 5.5 x 3 ft

Height = 16.5 ft

Area = Width x Height

Area = 9.3 ft x  16.5 ft

Area = 153.45 sq ft

Part B: conversion factor: 1 in = 6.5 ft

Width = 8.5 in

Width = 8.5 x 6.5

Width = 38.25 ft

Height = 14 x 6.5 ft

Height = 91 ft

Area = Width x Height

Area = 38.5 ft x  91 ft

Area =  3503.5 sq ft

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The value of the infinite series as n tends to 0 is: 0

Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.

From the infinite series, we want to find the value of the series as n tends to 0.

We are given the series as:

x/2ˣ

At x = 0, we have:

0/2⁰ = 0/1 = 0

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Answer:

yes, im about to look at it.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

slope('m") = 0     y-intersect ("b") = 6

y= mx + b

y = 0x + 6

y = 6

a. The derivative values f'(0), f'(1), f'(2), and f'(3) of the function f(x) = 4x - x^2 are calculated using the limit definition, resulting in f'(0) = 4, f'(1) = 3, f'(2) = 0, and f'(3) = -3.

b. Based on the calculations, we conjecture that f'(4) and f'(5) will also be equal to 4, as the derivative value is independent of the specific value of 'a'.

c. Conjecturing a formula for f'(a), we observe that f'(a) is always equal to 4, regardless of the value of 'a', leading to the formula f'(a) = 4.

d. To compute f'(1) using the limit definition of the derivative, we substitute x = 1 into the difference quotient formula and simplify, resulting in f'(1) = 3.

a. To compute the derivative values using the limit definition, we need to find the limit of the difference quotient as it approaches the given values.

For f'(0):

f'(0) = lim(h->0) [f(0 + h) - f(0)] / h

      = lim(h->0) [(4(0 + h) - (0 + h)^2) - (4(0) - (0)^2)] / h

      = lim(h->0) [4h - h^2 - 0] / h

      = lim(h->0) (4 - h)

      = 4

Similarly, we can calculate f'(1), f'(2), and f'(3) using the same process.

b. Based on our calculations in part (a), we can observe that the derivative value f'(a) is the same regardless of the value of a. Therefore, we can conjecture that f'(4) and f'(5) will also be equal to 4.

c. From our observations, we can conjecture a formula for f'(a) that depends only on the value a. Since we have found that f'(a) is always equal to 4, regardless of the value of a, we can express the formula as f'(a) = 4.

To compute f'(1) using the limit definition of the derivative, we substitute the value of x as 1 in the difference quotient formula:

f'(1) = lim(h->0) [f(1 + h) - f(1)] / h

      = lim(h->0) [(4(1 + h) - (1 + h)^2) - (4(1) - (1)^2)] / h

      = lim(h->0) [4 + 4h - (1 + 2h + h^2) - 4 + 1] / h

      = lim(h->0) (3 - h)

      = 3

Therefore, using the limit definition of the derivative, we find that f'(1) is equal to 3.

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Answer:

1) c. Use only appliances to do the most important task in the house.

2) b. 112kwh

3) b. 111kwh

Step-by-step explanation:

Energy can be defined as the ability (capacity) to do work and it's measured in Joules. The various forms of energy are solar energy, chemical energy, thermal energy, wind energy, nuclear energy, electrical energy, etc.

Power can be defined as the energy required to do work per unit time.

Mathematically, it is given by the formula;

\( Power = \frac {Energy}{time} \)

Energy consumption is the total amount of power used by an electronic device per unit time and it's measured in Watt-hour or Kilowatt-hour.

Mathematically, it is given by the formula;

\( Energy = power * time \)

Generally, the most economic way to lessen electric consumption is by ensuring only the important electrical appliances are used at all times.

2. Given the following data;

Previous reading = 2156 KWh

Present reading = 2268 KWh

To find how many kilowatt-hour was consumed;

Energy consumption = present reading - previous reading

Energy consumption = 2268 - 2156

Energy consumption = 112 KWh

3. Given the following data;

Previous reading = 5512 KWh

Present reading = 5623 KWh

To find the electrical consumption of Falogme Family;

Electrical consumption = present reading - previous reading

Electrical consumption = 5623 - 5512

Electrical consumption = 111 KWh

a) the expression of P(t) describing the population of crocodiles at any time t is: P(t) = 10 * e\(^{(0.1823t)}\)

b) it would take approximately 4.522 time units (months or years, depending on the unit of t) for the population of crocodiles to reach 30.

a) To determine the expression of P(t) describing the population of crocodiles at any time t, we can use the formula for exponential growth, which states that P(t) = P0 * e\(^{(rt)}\) where P0 is the initial population, r is the growth rate, and t is the time.

Given that the initial population P0 is 10 crocodiles and the population after 6 months is 12 crocodiles, we can use this information to find the value of r.

Using the formula P(t) = P0 * e\(^{(rt)}\) and plugging in the values, we have:

12 = 10 * e\(^{(r * (6/12))}\)

Simplifying further:

12/10 = e\(^{(r/2)}\)

1.2 = e\(^{(r/2)}\)

To find the value of r, we can take the natural logarithm of both sides:

ln(1.2) = r/2

r/2 ≈ 0.1823

Therefore, the expression of P(t) describing the population of crocodiles at any time t is:

P(t) = 10 * e\(^{(0.1823t)}\)

b) To find the population of crocodile species A after 2 years, we substitute t = 2 into the expression we derived in part a:

P(2) = 10 * e\(^{(0.1823 * 2)}\)

P(2) ≈ 10 * e\(^{(0.3646)}\)

P(2) ≈ 10 * 1.4406

P(2) ≈ 14.406

Therefore, the population of crocodile species A after 2 years is approximately 14.406 crocodiles.

c) To determine how long it would take for the population of crocodiles to reach 30, we can set the population P(t) equal to 30 and solve for t in the expression we derived in part a:

30 = 10 * e\(^{(0.1823t)}\)

3 = e\(^{(0.1823t)}\)

Taking the natural logarithm of both sides:

ln(3) = 0.1823t

t = ln(3) / 0.1823

t ≈ 4.522

Therefore, it would take approximately 4.522 time units (months or years, depending on the unit of t) for the population of crocodiles to reach 30.

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Answer:

2 Cups

Step-by-step explanation:

Converting both fractions to have the same denominator, she has 6/10 of a quart, and each cup holds 3/10. Since she only has 6, 6/3 is 2.

The number of cups she can fill will be 2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Holly made 3/5 of a quart of tea for her tea party. She plans to fill small tea cups that hold 3/10 of a quart of tea.

The number of cups will be calculated as follows:-

Number = ( 3 / 5 ) ÷ ( 3 / 10 )

Number = ( 3 / 5 ) ÷ ( 10 / 3 )

Number = 10 / 5 ) = 2

Therefore, the number of cups she can fill will be 2.

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a) Our assumption that there exist integers x and y such that x² - 4y = 2 is false, and we can conclude that for all integers x and y, x² - 4y ≠ 2.

b)  46¹⁰ ≡ 1 (mod 7).

     345 mod 9 ≡ 1 (mod 9).

(a) Proof by contradiction:

Assume that there exist integers x and y such that x² - 4y = 2.

Then x² = 2 + 4y.

Since 2 is an even integer, 4y must also be an even integer, which means that y is an even integer.

Let y = 2k, where k is an integer.

Then x² = 2 + 8k.

If x² is an even integer, then x must also be an even integer (by the given fact).

Let x = 2m, where m is an integer.

Then (2m)² = 2 + 8k.

Simplifying this equation, we get:

4m² = 1 + 4k.

This equation implies that 4m² is an odd integer, which is a contradiction.

Therefore, our assumption that there exist integers x and y such that x² - 4y = 2 is false, and we can conclude that for all integers x and y, x² - 4y ≠ 2.

(b)

(i) 46¹⁰ mod 7:

We can use the property that \(a^{b+c} = (a^b)*(a^c)\) to simplify the exponent:

46¹⁰ = (46⁵)²

To find 46⁵ mod 7, we can reduce the base modulo 7:

46 ≡ 4 (mod 7)

Then, we can use the property that (a*b) mod m = ((a mod m) * (b mod m)) mod m:

46⁵ ≡ 4⁵ (mod 7)

≡ (44444) mod 7

≡ (-1)(-1)(-1)(-1)(-1) mod 7

≡ -1 mod 7

≡ 6 (mod 7)

Substituting this value back into the original expression:

46¹⁰ ≡ (46⁵)²

≡ 6² (mod 7)

≡ 36 (mod 7)

≡ 1 (mod 7)

Therefore, 46¹⁰ ≡ 1 (mod 7).

(ii) 345 mod 9:

We can use the property that \(a^{b+c} = (a^b)*(a^c)\) to simplify the exponent:

345 = (3100 + 410 + 5)

Therefore, we can break down 345 into its digits and calculate each digit modulo 9:

3100 mod 9 ≡ 0 (mod 9)

410 mod 9 ≡ 5 (mod 9)

5 mod 9 ≡ 5 (mod 9)

Then, we can use the property that (a+b) mod m = ((a mod m) + (b mod m)) mod m:

345 mod 9 ≡ (0 + 5 + 5) mod 9

≡ 10 mod 9

≡ 1 (mod 9)

Therefore, 345 mod 9 ≡ 1 (mod 9).

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such pair of equation that have only one pair of solutions which satisfy both equation is linear equation

1. the mechanical advantage of the rake is 0.5. 2. the efficiency of the blade adjuster is approximately 92.73%.

1. The mechanical advantage of a simple machine is determined by the ratio of the output force to the input force. In this case, the woman applies an input force of 32 N to the rake, and the rake exerts an output force of 16 N.

The mechanical advantage (MA) can be calculated as MA = Output Force / Input Force.

Using the given values, we can substitute them into the formula:

MA = 16 N / 32 N = 0.5.

Therefore, the mechanical advantage of the rake is 0.5.

Explanation:

The mechanical advantage represents the amplification of force achieved by using a machine. In this case, the mechanical advantage of 0.5 means that the rake reduces the input force by half to produce the output force. It indicates that for every 1 unit of input force applied by the woman, the rake generates 0.5 units of output force.

2. Efficiency is a measure of how effectively a machine converts input work to output work. It is calculated as the ratio of output work to input work, expressed as a percentage.

The efficiency (η) can be calculated using the formula: Efficiency = (Output Work / Input Work) * 100%.

Given that the input work is 55 J and the output work is 51 J, we can substitute these values into the formula:

Efficiency = (51 J / 55 J) * 100% ≈ 92.73%.

Therefore, the efficiency of the blade adjuster is approximately 92.73%.

Explanation:

Efficiency quantifies the effectiveness of a machine in converting the input energy into useful output energy. In this case, the blade adjuster converts 51 J of input work into 51 J of output work. The efficiency of approximately 92.73% indicates that the blade adjuster is relatively efficient, as a high percentage of the input work is effectively converted into useful output work.

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The coordinate of points A, B, and C will be (0, a), (0, 0), and (a, 0), respectively.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In an isosceles right triangle, the two legs of the triangle are congruent and intersect at right angles and their opposite angles are also equal.

The vertice C lies on the x-axis, then the coordinate of point C will be (a, 0).

The vertice A lies on the y-axis, then the coordinate of point C will be (0, a).

Then the coordinate of B will be at the origin which is (0, 0).

Thus, the coordinate of points A, B, and C will be (0, a), (0, 0), and (a, 0), respectively.

The diagram is attached below.

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