For Daniel's lemonade recipe, 4 lemons are required to make 16 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade?

The foot be moving away from the wall when the top is 10 feet above the ground is 2.4077

How to solve word problems?

It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.

The ladder against the wall is a right triangle:

x² + y² = 15²

Top slips down => dy/dt = -2 ft/s. When y = 10 ft.  dx/dt = ?

1) Take the derivative with respect to time:

2x (dx/dt) + 2y (dy/dt) = 0

2) Substitute y = 10, x =sqrt(69) z =15

2(sqrt(69)) (dx/dt) + 2(10) (-2) = 0

dx/dt = 40/2(sqrt(69))

dx/dt = 20/(sqrt(69))

= 20/8.30

=2.4077

Hence, the foot be moving away from the wall when the top is 10 feet above the ground is 2.4077.

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The simplified form of  (m + 3n + 8)(m + 3n - 8) is  m^2 + 3n^2 + 6mn - 64.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given,  (x+2)(x+3) = x^2+5x+6.

∴ (m + 3n + 8)(m + 3n - 8).

= m^2 + 3mn - 8m + 3mn + 3n^2 - 24n + 8m + 24n - 64.

= m^2 + 3n^2 + 6mn - 64.

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The density of the rock with a mass of 39.78 g and volume 12.45 cm³ is 3.2 g/cm³.

Density is simply the mass of a unit volume of a material substance.

It is expressed mathematically as;

p = m / v

Where m is mass and v is volume

Given the data in the question;

Plug the given values into the above formula and solve for p.

p = m / v

p = 39.78g / 12.45 cm³

p = 3.2 g/cm³

Therefore, the density of the rock is approximately 3.2 g/cm³.

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Answer:

1 cm = 20 km

Step-by-step explanation:

Starting with what we know:

2/5 cm = 8 km

Need to change the left side to a 1. So multiply both sides by 5/2

5/2 × 2/5 = 8 × 5/2

1 cm = 40/2 km

1 cm = 20 km

A good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up is count all the bytes of the data in the struct.

Rule:

In math rule refers a numerical pattern is a sequence of numbers that has been created based on a formula or rule called a pattern rule

Given,

Here we need to find a good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up.

According to the rule of thumb, the count all the bytes of the data in the struct.

and then we need to find the nearest power of 2, 4 or 8 based on the largest Data Type in your struct.

So, if the total number of bytes is larger than that power, then the struct will be the next power in size.

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Answer:

33

Step-by-step explanation:

-4(-6) + 9

24 + 9

33

The sample proportion of persons with credit card debts of further than $2,000 has a distribution that is roughly normal;

μ = 0.27 and σ = 0.022.

According to a research conducted in one town, the percentage of persons living there had credit card debt of at least $2,000:

p = 27% = 0.27.

An adult sample from the entire city was gathered: n = 400 adults.

The following two requirements should be used to determine the whether sample is adequate before obtaining a sampling distribution of the probability value p:

       400 x 0.27  = 108

       108 ≥ 10

And,

      400(1 - 0.27)  ≥ 10

      292  ≥ 10

We know that the as being p is nearly normally distributed the by suing  "Central limit theorem."

Mean of a sample proportion

μ = P = 0.27

The standard deviation's sample proportion P:

σ = √(p(1 - p)/n

σ = √(0.27(1 - 0.27)/400

σ = 0.022

Since the sample proportion of persons with credit card debts of further than $2,000 has a distribution that is roughly normal;

μ = 0.27 and σ = 0.022.

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Answer:

Step-by-step explanation: 12

In multiple linear regression analysis, the correlation among independent variables is termed multicollinearity i.e. option C.

Definition:

a) Homoscedasticity: Homoscedasticity, also known as homogeneity of variances, is the presumption that variations in various groups being compared are equivalent or comparable.

b) Linearity: A mathematical relationship (function) that can be graphically represented as a straight line is said to be linear. Proportionality and linearity are closely linked concepts.

c) Multicollinearity: Multiple independent variables in a model that are correlating from a statistical concept known as multicollinearity.

d) Adjusted Coefficient of Determination: The number of variables in a data collection is taken into account when calculating the adjusted coefficient of determination (also known as adjusted R-squared). Additionally, it penalizes you for any points that deviate from the model.

Hence, the required choice is Option C.

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Answer:

x-intercept: (7/5, 0)

y-intercept: (0, 14)

Step-by-step explanation:

The x intercept is when y is equal to 0.

1/2(0) + 5x = 7

5x = 7

x = 7/5

Put this into point form, where x is 7/5 and y is 0.

(7/5, 0)

The y intercept is when x is equal to 0.

1/2y + 5(0) = 7

1/2y = 7

y = 14

Put this into point form, where x is 0 and y is 14.

(0, 14)

In linear equation, the solution of equations is ( -2 , 1)

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

y = 2x + 5

y = 1/2x + 2

the solution of equations is ( -2 , 1)

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Answer: 8 phones sold and 24 accessories

The correct expression that is equivalent to the algebraic expression -5x - 15 + 25x - 30 is -5(-4x + 9).

We shall simplify the given algebraic expression by carrying out basic mathematics operations as follows;

Given: -5x - 15 + 25x - 30

we group like terms together

25x - 5x - 15 - 30

20x - 45

the number 5 is a common factor of 20x and 45, so we have that;

5 × 4x - 5 × 9

by factoring out 5

5(4x - 9)

also;

5(4x - 9) = -5(-4x + 9)

Therefore, -5(-4x + 9) is an equivalent expression to the algebraic expression -5x - 15 + 25x - 30

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Answer:

55°

Step-by-step explanation:

Assuming the angle is at 180°

180° - 125° = 55°

SCl2 has a Bent molecular geometry and a tetrahedral shape in nature. SCl2 consists of a single Sulfur atom surrounded by two Chlorine atoms. In its most stable state, Sulfur acts as the central atom and forms two covalent bonds with the Chlorine atoms. It also possesses two lone pairs.

The three-dimensional configuration of the atoms that make up a molecule is known as molecular geometry. In addition to bond lengths, bond angles, torsional angles, and any other geometrical factors that affect each atom's location, it also contains the molecule's overall structure. The arrangement of atoms in a molecule in three dimensions is known as molecular geometry, commonly referred to as the molecular structure. A compound's polarity, reactivity, phase of matter, color, magnetism, and biological activity can all be determined by knowing its molecular structure.

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The cost of a racket and a  ball  is equal to $3.21 and  $4 as per the given data .

As given in the question,

Let us consider cost of a racket is equal to $x

Let us consider cost of a ball is equal to $y.

Equation formed using the given data we have,

3x + 3y = $21.63  ____(1)

3x + 10y = $49.63 ____(2)

Subtract equation (2) from (1) to eliminate x

3x + 10y = $49.63

3x + 3y = $21.63

0x + 7y = $28.00

⇒7y = 28.00

⇒ y = 28 / 7

⇒ y = $4

Substitute the value of y in (1) we get,

3x + 3(4) = 21.63

⇒3x = 21.63 -12

⇒3x = 9.63

⇒ x = $3.21

Therefore, from the given relation the cost of a racket and a ball is equal to $3.21 and $4.00.

The complete question is:

The cost of 3rackets and 3 balls cost $21.63.

The cost of 3rackets and 10 balls is $49.63.

Work out the cost of

a) a ball.

b) a racket

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Answer:

x= –2

Step-by-step explanation:

y = 2

just substitute for y

2 = x + 4

2 – 4 = x

–2 = x

or x = –2

check

y=-2+4

y=2

so our answer is correct.

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Answer:  The correct answer is b = √13 or b = −√13

Step-by-step explanation:

When factoring squared variables or numbers, use the square root

b^2 = 13

Take the square root of both sides

√b^2 = √13

b = √13 or b = −√13

Answer:0.56

Step-by-step explanation:

First multiply $3.92 from 1 pound

Next dived the answer by 7 which will give you 0.56

It has been suggested that 4% of all cars on the freeway are going 70 mph. If 4 cars are examined, the probability that at least 1 is going 70 miles per hour is 0.151.

A probability is a numerical representation of the likelihood or possibility that a particular event will occur. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, it is said that 4% of all vehicles on the roadway are going more than 70 mph.

P(speed excess of 70 mph) = 0.04. Radar is used to determine the speeds of four random cars. Then, n = 4. Then, X = the number of cars going over 70 mph.

Then, the probability that at least one car is going over 70 mph

= P(x = 1, 2, 3, 4)

= 1 - P(x = 0)

= [tex]1 - 4_{C}_{0} (0.04)^{0} (1 - 0.04)^{4-0}[/tex]

= 1 - 0.849

= 0.151

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Answer:

2 cm and 6 cm

Step-by-step explanation:

x = first leg

y = second leg

y = 4 + x

xy/2 = 6

y = 4 + x

xy = 12

x(4+x) = 12

x²+4x - 12 = 0

(x+6)(x-2) = 0

x = -6 (impossible because a length can’t be negative)

x = 2 cm

y = 2 + 4 = 6 cm

Answer:

250.32 dollars

Step-by-step explanation:

The given loan amount is equal to 8,700 dollars and the number of years is 3 years and the a p r is equal to 2.31 percentage. The formula for monthly payment is a is equal to p into or divided by 12 into 1 plus or divided by 12 points the whole power and whole divided by 1 plus r divided by 12 points.The whole power n minus 1 in this formula, p is the lown amount and r is the well interest rate and n is the number of payments here. We have the number of years is 3, so the number of payments will be 36 points. Then, by this formula we have the monthly payment: a is equal to 8700 into 0.0231, divided by 12 into 0.0231 divided by 12 plus 1. The whole power 36 whole divided by 0.0231, divided by 12 plus 1, the whole power 36 minus 1, and it will be equal to 250.32 dollars. Therefore, the monthly payment is equal to 250.32 dollars.

The required function of the line would be y = 2x + 1.

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.

The slope-intercept form is one rule to represent linear function rules. f(x)=mx + b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.

According to the given figure,

We clearly see that the coordinates of the y-intercept would be (0, 1).

The value of the x-coordinate is 1 when y-coordinate is 3.

Here the line passes through points (0, 1) and (1, 3).

Let the required linear function would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]

x₁ = 0, y₁ = 1

x₂ = 1, y₂ = 3

⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]

⇒ y - 3 = (2)[x -1]

⇒ y - 3 = 2x - 2

⇒ y = 2x - 2 + 3

⇒ y = 2x + 1

Therefore, the required function of the line would be y = 2x + 1 .

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There are 62 number of ways in which classes to these students can be assigned. It can be solved by using the fomula of combination.

What is the formula of combination?

Following is the fomula of combination:

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Here, n is the total objects available and r is the number of object need to choose from n objects.

Let six friends are A, B, C, D, E, and manoj.

Consider all 6 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_6[/tex]

Consider 5 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_5[/tex]

Consider 4 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_4[/tex]

Consider 3 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_3[/tex]

Consider 2 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_2[/tex]

Consider 1 friend is in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_1[/tex]

Consider no friend is in chemistry class all are in biology class. Hence, number of ways in which it can be is,

[tex]^6C_0[/tex]

Hence, total number of ways in which classes can be assigned to 6 students is,

[tex]^6C_6+^6C_5+^6C_4+^6C_3+^6C_2+^6C_1+^6C_0=64[/tex]

Now, the number of ways in which mnoj is alon. There are two ways. Either he will be in the chemistry class or he will be in the physics class.

Hence, subtract 2 from 64 to get the answer.

[tex]64-2=62[/tex]

Hence, there are 62 number of ways in which classes to these students can be assigned.

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Answer:

y = 5 + 3/5x

Step-by-step explanation:

We need to isolate y to get it in slope-intercept form. Let's subtract 12x from both sides, which gives us [tex]-20y=-100-12x[/tex]. Then, we can negate both sides, and then divide by 20, which results in [tex]y = (100+12x)/20[/tex], which we can further simplify to [tex]y=5 + 3/5x[/tex], which gives us our answer.

Investigating an outlier that a data analyst has found is the best course of action.

To find the solution to a problem or provide an answer to a question, a data analyst gathers, purifies, and analyzes data sets.

They work in a variety of fields, including as government, business, finance, law enforcement, and science.

Depending on the question you're attempting to answer, data analysis might take on various shapes.

More information on different data analysis types is available here.

In a nutshell, descriptive analysis explains what happened, diagnostic analysis explains why it occurred, predictive analytics offers future projections, and prescriptive analysis generates actionable recommendations for what to do.

Hence, Investigating an outlier that a data analyst has found is the best course of action.

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Answer: Tyler has 22 cards

Step-by-step explanation:

To begin, we know that Morgan has 12 less than 5x Tyler's cards, so...

12+98=110

Now that we had 110, we then read that it is the PRODUCT of 5 and the number that Tyler has, so we will show that algebraically.

110=5x

Now, divide 110 by 5 to find X.

110/5=22

Tyler has 22 cards.

The number of sequence of 0s and 1s of length 19 are there that begin with a 0, end with a 0 are 65 .

In the question ,

After any particular 0, the next 0 in sequence must appear exactly 2 or 3 positions down.

In this case, we start at position 1 and end at position 19,

that is , we move a total of 18 positions down the line.

So , we must add the series of 2s and 3s to get 18.

There are several number of ways to do this:

Case 1: nine 2s - there is only 1 way to arrange them.

Case 2: two 3s and six 2s - there are ⁸C₂ ways = 28 ways

Case 3: four 3s and three 2s - there are ⁷C₄ ways = 35 ways

Case 4: six 3s - there is only 1 way to arrange them.

So , the number of sequences is = 1 + 28 + 35 + 1 = 65 .

Therefore , the total number of sequence is = 65 .

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The number of ways to paint the pots can be found using permutations and is found to be 15120 ways.

What are permutations?

An arrangement of all or a portion of a collection of items, taking into account the arrangement's order, is referred to as a permutation.

Here, we know that there are 9 different paints to choose from, so we are required to find the number of ways we can paint 5 pots without repeating any color.

This can be given by [tex]9P_{5}[/tex] ways.

[tex]=\frac{9!}{(9-5)!} \\=\frac{9!}{4!} \\=15120\space\ ways[/tex].

Therefore, the number of ways to paint the pots is 15120 ways.

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