a racecar travels around an oval track. let d represent the distance driven by the racecar (in meters) from the starting line, and let t represent the number of seconds since the racecar left the starting line. the function f , defined by the formula f ( t )

The probability that exactly 2 of them are the deluxe model =0.474

given that

there is a shipment of 15 televisions contains 6 regular and 9 deluxe models

now 3 cartons are selected at random

C(15,3) =[tex]\frac{15!}{(15-3)!3!}[/tex]

C(15,3) = [tex]\frac{13*14*15}{3*2*1}[/tex]

C(15,3) = 455

2 out of 9 deluxe models be picked

C(9,2) = [tex]\frac{9!}{(9-2)!2!}[/tex]

C(9,2) = [tex]\frac{8*9}{2*1}[/tex]

C(9,2) = 36

Each of these can be matched with 1 of 6 regular models

36 × 6 = 216

the probability that exactly 2 of them are the deluxe model

= [tex]\frac{216}{455}[/tex]

=0.474

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Answer:

Step-by-step explanation:

domain = all real numbers

x-intercepts (2,0)

y-intercepts (0,-14)

vertex = minimum (-3/1 - 121/8)

Answer: Okay so I got,

1) x intercept = (2, 0), (-7/2, 0) and y intercept (0, -14)

2) 'x' equals to..

-Exact Form: 2, -7/2

-Decimal Form: 2, -3.5

Hope this helps!

The amount of ounces of sugar she added to the new cake is 22 ounces

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the total ounces of ingredients in the cake be = 44 ounces

The ratio of flour to sugar is = 6 : 5

So , the amount of flour in 44 ounces = 6x

The amount of sugar in 44 ounces = 5x

And , the equation is

6x + 5x = 44

On simplifying the equation , we get

11x = 44

Divide by 11 on both sides , we get

x = 4

So , the total amount of sugar in 44 ounces of ingredients = 5x

Substitute the value for x = 4 , we get

Total amount of sugar in 44 ounces of ingredients = 20 ounces

And ,

Let the total ounces of ingredients in the new cake be = 91 ounces

The ratio of flour to sugar is = 7 : 6

So , the amount of flour in 91 ounces = 7y

The amount of sugar in 91 ounces = 6y

And , the equation is

7y + 6y = 91

On simplifying the equation , we get

13y = 91

Divide by 13 on both sides , we get

y = 7

So , the total amount of sugar in 91 ounces of ingredients = 6y

Substitute the value for y = 7 , we get

Total amount of sugar in 91 ounces of ingredients = 42 ounces

Therefore , the extra ounces of sugar the baker added to the new cake is =

Total amount of sugar in 91 ounces of ingredients - Total amount of sugar in 44 ounces of ingredients

The extra ounces of sugar the baker added to the new cake is = 42 - 20

Extra ounces of sugar the baker added to the new cake is = 22 ounces

Hence ,

The amount of ounces of sugar she added to the new cake is 22 ounces

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The term in cell I5 will be for the AVERAGEIFS function:

AVERAGEIF( I11:I67 ,"<3500",J11:J67 ,"E3")

For the given question the termed   AVERAGEIFS  is the function formula in excel which returns the average of all the cells available in the sheet in a range that meets a given condition.the syntax for the term is  AVERAGEIF(range, criteria, [average_range]),  where the range is  Required like  One or more cells to get the average. Criteria os the basically the form of an expression, number, or cell reference, and at last the average range is optional it is just the set of cells to average.

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Answer: x = 10

Step-by-step explanation:

x + 6 + 3x = 5x - 4

First you want to group your like values together

6 +4 = 5x - 3x - x

Note that when any value crosses the = sign, The sign in front of it (+/-) changes. (e.g. -4 changes to +4 after it crosses the = sign)

Then work out your values

10 = x

Also note that x is the same as 1x. So you minus 3x from 5x to get 2x and 2x minus 1x is equal to 1x which is the same as x.

By using multiplication and division of integers, it can be calculated that

Conversion factor of the recipe = [tex]\frac{500}{300}[/tex] = 1.6

What is multiplication and division of integers?

At first it is important to know about integers

Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.

Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

This is a word problem where multiplication and division of integers is required

The original recipe calls for 50 portions, 6oz each

Required yield of the original recipe = 50 [tex]\times[/tex] 6 = 300 oz

The new recipe calls for 100 portions at 5oz each

Required yield of the new recipe = 100 [tex]\times[/tex] 5 = 500 oz

Conversion factor of the recipe = [tex]\frac{500}{300}[/tex] = 1.6

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Kadita has 4 pigs and 26 chickens in on his farm.

Given, Kadita counted 30 pigs and chickens on the farm. Jack counted a total of 68 legs for the animals.

Let the number of pigs be, x

and the number of chickens be, y

x + y = 30

4x + 2y = 68

Now, we have to two equations,

x + y = 30

2x + y = 34

On subtracting both the equations, we get

x = 4

and y = 30 - 4

y = 26

So, Kadita has 4 pigs and 26 chickens in on his farm.

Hence, Kadita has 4 pigs and 26 chickens in on his farm.

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The new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4),  (-5, 3).

A function, f, that maps to itself are known as a transformation, or f: X → X. The transformation results in the pre-image X becoming the picture X. This transformation can utilize any operation, or a combination of operations, including translation, rotation, reflection, and dilation.

Given, the triangle vertices (-3, 1) (2, 4), and (5, -3).

When the triangle turned 180 degrees counterclockwise, we must determine the new coordinates;

When we rotate 180 degree counterclockwise, the plane changes not the point.

That is,

(-3, 1) becomes (3, -1)

(2, 4) becomes (-2, -4)

(5, -3) becomes (-5, 3)

Therefore, the new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4),  (-5, 3).

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The mean of the decrease in rounded percentage of home is 7.14 which would used as misleading the about  data as raw data very far away from 7.14.

As given in the question,

Given rounded percentage decrease in home price is:

3, 3, 5, 6, 7, 7, 19

Mean of the rounded percentage

= ( Sum of all the values)/ (Number of values)

= ( 3 + 3 + 5 + 6 + 7 + 7 + 19) / 7

= 50 /7

=7.1428

= 7.14

7.14 is very far away from 3 and 19.

Mean is not representing  the correct information of the home price.

Using mean is misleading the correct information about percentage decrease.

Therefore, value of the mean is equal to 7.14 which mislead the decrease percentage.

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The sum of the indicated variable is 23.

What is variable?

A variable is an  alphabet or term that represents an unknown variety or unknown worth or unknown amount. The variables are specially employed in the case of pure mathematics expression or pure mathematics.

MAIN body:

the correct expression is as follows :

1(1!) +2(2!) +3(3!)+ 4(4!) ........+ m(m!)   where m = 3

for m= 3

the expression becomes:

=1(1!) +2(2!) +3(3!)

factorial means we need to multiply the number until it reaches 1.

= 1*1 + 2*2*1 + 3*3*2*1

= 1+ 4+ 18

= 23

Hence the sum of expression is 23.

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Step-by-step explanation:

55.7% of fire station response times are between 4 and 6 minutes. This can be calculated using the z-score formula, which is (x-μ)/σ, where x is the value of interest (in this case, 4 and 6 minutes), μ is the mean (4.5 minutes), and σ is the standard deviation (1.2 minutes). The z-score for 4 minutes is -0.42 and the z-score for 6 minutes is 0.42. Using a standard

Answer:

y=-1/2x-5

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

0.9 times 0.3 equals 0.27

In the following passage we have proven the Pythagoras' theorem.

What is Pythagoras' theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

So the hypotenuse of the triangle is 13 feet

Now using the Pythagoras theorem we can find out the length of the other wall

b²=h²-p²

AB² + BC² = AD × AC + CD × AC

AB² + BC² = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC² = AB² + BC²

So we have p² + b² = h².

Hence, we prove the Pythagoras theorem using two triangle.

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9 appears in all integers from 1 to 500, 95 times.

9 total from

1-9: 1 time

10-19: 1 time

20-29: 1 time

30-39: 1 time

40-49: 1 time

50-59: 1 time

60-69: 1 time

70-79: 1 time

80-89 : 1 time

among 90 and 99

Between 1991 and 1998, one will occur.

then in 1999, 2 9.

9 from 90 to 99 is 10, thus

9+10 = 19 is the total number of 9s from 1 to 99.

In 1 to 99, there are so 19 9s.

similarly

the following:

19 9's in 100 to 199

19 9's in 200 to 299

19 9's in 300 to 399

19 9's in 400 to 499

Total 9s will therefore be

19+19+19+19+19+19 = 95 times

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The pValue is 0.15625 > 0.05 when  brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.

Let A represent the new pesticide and B be the Ant Killer. Then, you are given that

Brand1 kills ants in 65 of 100 containers:

Xa = 65/100 = 0.65

Brand2 kills ants in 58 of 100 containers:

Xb = 58/100 = 0.58

You know need to find sample variance for both,

s²A =∑(Xi - Xa)

= 65(1-0.65)² + 35(0 - 0.65)²

= 22.7

s²B =∑(Xi - Xb)²

= 59(1-0.59)² + 41(0 - 0.59)²

= 24.19

You can know do a test for significance

t = (Xa - Xb) / √(sA /nA) +(sB/nB)

and derive the conclusion from there

Here, Null and alternative hypothesis are generally,

Alternative hypothesis

Here, there are three samples are assumed. They are:

i) Samples are taken independently

ii) Samples must be selected randomly

iii) n₁p₁ ≥ 5 , n₁q₁ ≥ 5, n₂p₂ ≥ 5, n₂q₂ ≥ 5

i.e., p₁ = 0.65 ; p₂ = 0.58 , n₁= 100

q₁ = 0.35 ; q₂ = 0.42 , n₂=100

Corresponding p-value at Z = 1.01722

p-value = 0.15625 > 0.05

Hence, the pValue is 0.15625 > 0.05 when  brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.

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Answer:

y

=

−

3

2

x

+

13

Explanation:

First write it using point-slope form:

y

−

7

=

−

3

2

(

x

−

4

)

Now simplify to slope-intercept:

Add 7 to each side:

y

=

−

3

2

(

x

−

4

)

+

7

Distribute

−

3

2

to each term in the parentheses:

y

=

−

3

2

x

+

6

+

7

y

=

−

3

2

x

+

13

hope I helped you:)

Answer:

it would be CD or 50%

Step-by-step explanation:

Answer:  The correct answer is 5a^3b^3 − 4a^2b^4 + ab^5

Step-by-step explanation:

ab^3 (5a^2 − 4ab + b^2)

Multiply together:

(ab^3)*(5a^2 + −4ab + b^2)

(ab^3)*(5a^2) + (ab^3)*(−4ab) + (ab^3)*(b^2)

= 5a^3b^3 − 4a^2b^4 + ab^5

Answer:

[tex]5a^3b^3-4a^2b^4+ab^5[/tex]

Step-by-step explanation:

Given expression:

[tex]ab^3(5a^2-4ab+b^2)[/tex]

Apply the distributive property  a(b - c + d) = ab - ac + ad :

[tex]\implies ab^3 \cdot5 a^2-ab^3 \cdot 4ab+ab^3 \cdot b^2[/tex]

Collect like terms:

[tex]\implies 5aa^2b^3-4aabb^3+ab^2b^3[/tex]

Apply the exponent rule  a = a¹ :

[tex]\implies 5a^1a^2b^3-4a^1a^1b^1b^3+a^1b^2b^3[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 5a^{(1+2)}b^3-4a^{(1+1)}b^{(1+3)}+a^1b^{(2+3)}[/tex]

Simplify:

[tex]\implies 5a^3b^3-4a^2b^4+ab^5[/tex]

Answer:

Step-by-step explanation:

You want the statements that describe the function f(x) = 2(x -4)⁴.

The degree of the function is the exponent: 4. This means the function has 4 zeros.

The maximum number of relative extrema is 1 less than the degree. The function has at most 3 relative maximums or minimums.

The even degree means both ends of the graph go in the same direction.

The leading coefficient of 2 is positive, so the ends of the function will go up.

In the parent function f(x) = x⁴, the value of x has been replaced by (x-4). This causes the graph to be translated 4 units to the right.

__

Additional comment

This function has a zero at (4, 0) with multiplicity 4. There is a flat spot where the graph touches, but does not cross, the x-axis. As a consequence, there is only one minimum and no relative maximums.

<95141404393>

Answer:

Step-by-step explanation:

What are you supposed to do?

0.00305 moles of sodium hypochlorite are present in a 4.00 ml sample.

A mole is the mass of a substance made up of the same number of fundamental components. Atoms in a 12-gram example are identical to 12C. Depending on the substance, the fundamental units may be molecules, atoms, or formula units.

A mole fraction shows how many chemical elements are present. The value of 6.023 x 1023 is equal to one mole of any substance (Avagadro number). It can be used to quantify the chemical reaction's byproducts. The symbol for the unit is mol.

The number of moles formula is denoted by the following expression.

The mass of material / Mass of one mole equals the number of moles.

moles of NaClO = mass of sample×density of bleach solution×mass of                bleach solution×1 mol/ mass of NaClO

= 4.00×1.08×0.0525/74.4 g of NaClO

= 0.00305.

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The expression x^2 + 22x + c becomes a perfect square trinomial if the value of c is 121, so the correct option is A.

A perfect square trinomial is written as:

(a + b)^2 = a^2 + 2ab + b^2

Here we have the expression:

x^2 + 22x + c

We can rewrite the second term in such a way that we get:

x^2 + 2*11*x + c

comparing this with the form of the general perfect square trinomial we can see that:

a = x

b = 11

Then the value of c must be 11^2 = 121

Then we have:

x^2 + 2*11*x + 121 = (x + 11)^2

The correct option is A.

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Answer:

see explanation

Step-by-step explanation:

given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 21 when x = 14 , then

21 = 14k ( divide both sides by 14 )

[tex]\frac{21}{14}[/tex] = k , that is

k = [tex]\frac{3}{2}[/tex] = 1.5

y = 1.5x ← equation of variation

when x = 40 , then

y = 1.5 × 40 = 60

Answer:

$12.50

Step-by-step explanation:

Look at the graph down below \/

U can also mark where the pounds is so right at 25 pounds it would be about $12~

Using unit I, calculate the average waiting time of customers in the wash line (μ for unit I = 12 per unit).

For unit II at 15 per hour

if waiting time is the only criterion, unit II should be purchased. But before we make the final decision, we must look at the profit differential between both units.

With unit I, some customers would balk and renege because of the 5 minute wait. And, although this greatly complicates the mathematical analysis, we can gain some estimate of lost sales with unit I by increasing Wq = 5 minutes and solving for λ. This would be the effective arrival rate of customers.

Therefore, because the original estimate of λ was 10 per hour, an estimated 2 customers per hour will be lost.

Lost profit of 2 costumers per hour × 14 hours × 1/2 ($0.70 fill-up profit + $0.40 wash profit) = $15.40 per day.

Because the additional cost pf unit II over unit I is only $4 per day, the loss of $15.40 profit obviously warrants installing unit II.

The original five-minute maximum wait constraint is satisfied by unit II.

Therefore, unit III is not considered unless the arrival rate is expected to increase.

Given question is incomplete.

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Solving the equation using quadratic formula the value of y in the quadratic equation is y= 0.675 or y= -3.11

Mathematically, quadratic formula can be written as

[tex]y= \frac {-b + or - \sqrt{b^{2}-4ac } }{2a}[/tex]

from the expression, a= 3.9 , b=9.5, c= -8.2

substitute the value into the quadratic equation

[tex]y= \frac{-b^{} + or -\sqrt{b^{2}- 4ac } }{2a}[/tex]

y= [tex]\frac{-9.5^{} + or - \sqrt{9.5^{2}-4(3.9)(-8.2) } }{2(3.9)}[/tex]

y= [tex]\frac{-9.5^{} + or -\sqrt{90.25+127.92} }{7.8}[/tex]

y=  [tex]\frac{-9.5^{} + \sqrt{218.17} }{7.8}[/tex] or y= [tex]\frac{-9.5^{} - \sqrt{218.17} }{7.8}[/tex]

y =   [tex]\frac{-9.5 + {14.77} }{7.8}[/tex] or y= [tex]\frac{-9.5 - {14.77} }{7.8}[/tex]

y =   [tex]\frac{5.27}{7.8\\}[/tex] or  y= [tex]\frac{-24.27}{7.8}[/tex]

y= 0.67 or y= -3.11

Therefore the value of y in the quadratic equation is y= 0.67 or y= -3.11

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The difference between these distances on the Earth is 3.32 × 10⁴.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.

The difference will be:

= 4.00x10^4 km - 6.8x10^3 km.

= 3.32 × 10⁴

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In a regression analysis, a(n) is used to predict a(n) is known as option (b).independent variable, dependent variable.

Regression analysis:

In the concept of statistics, the regression analysis is useful to come up with a predictive model consisting of dependent and independent variables. And the R-squared value for a regression equation indicates the percentage of variability in the dependent variable being expressed by the variability in the independent variables.

Given,

Here we need to find the type of variable for  a regression analysis, a(n) is used to predict a(n).

As per the definition of regression analysis, in the given question, we have two variable there are

=> a(n)

After prediction, the predicted value of a(n).

Here the first one is the independent variable because the this value is the based to predict the value of the other one is the dependent variable.

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