What is the reciprocal of 3 ⅞

The conic equation 16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0 is equivalent to (x + 3)² / 4.75 + (y - 2)² / 19 = 1, that represents an ellipse.

Mathematically speaking, conics are described by quadratic equations of the form A · x² + B · y² + C · x + D · y + E = 0, where A, B, C, D, E are real coefficients of the conic.

We can infer if a conic is a circle, a parabola, an ellipse or a hyperbola by modifying the expression into its standard form by algebra properties. First, write the equation of the conic:

16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0

Second, complete the square in the equation of the previous step:

16 · (x² + 6 · x) + 4 · (y² - 2 · y) = - 84

16 · (x² + 6 · x + 9) + 4 · (y² - 2 · y + 4) = - 84 + 16 · 9 + 4 · 4

16 · (x² + 6 · x + 9) + 4 · (y² - 2 · y + 4) = 76

Third, factor the polynomial and simplify the expression until standard form is derived:

16 · (x + 3)² + 4 · (y - 2)² = 76

(x + 3)² / 4.75 + (y - 2)² / 19 = 1

The conic equation represents an ellipse.

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The confidence interval form of the given question will be (783.4,522.4).

What is a confidence interval?

A confidence interval (CI) in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 96%, but other values, such 90% or 99%, are occasionally used. The confidence level is the percentage of corresponding CIs over the long run that actually contain the parameter's true value. As an illustration, 96% of all intervals produced at the 96% level should have the parameter's actual value.

Here this question, it is given in the interval form.

Now we can find out the minimum and maximum value of the value.

Maximum value is 653.1+130.3 = 783.4

Minimum value is 653.1 - 130.3 = 522.4

So The confidence interval can be written as (783.4,522.4).

Hence the answer will be (783.4,522.4).

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The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.

Now when no letters are repeated:

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.

So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes

if letters can be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.

So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes

if adjacent letters cannot be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.

So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes

Hence the total number of codes as calculated by permutation and combination is 1280.

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Answer:

  c.  71°

Step-by-step explanation:

You have isosceles triangle XYZ with a.pex angle Y = 38°. You want to know the measure of angle Z.

The base angles of the triangle are X and Z, which are congruent. The sum of all angles is 180°:

  X +Y +Z = 180°

  2Z +38° = 180° . . . . . . substitute for X and Y

  2Z = 142° . . . . . . . . . subtract 38°

  Z = 71° . . . . . . . . . . divide by 2

The measure of angle Z is 71°.

Answer:

x=58

Step-by-step explanation:

The new form of 11^0.3^(-5) is 1/3^5 with positive exponent.

What is exponent of a number?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For example: a^b, where b is the exponent of a.

What is negative exponent?

The negative exponent indicates how many times the base number must be divided. In other words, the negative exponent indicates how many times the reciprocal of the base must be multiplied.

If the exponent of a number is zero, then the value of the number is 1.

Given expression is

11^0.3^(-5)

The value of 11^0 is 1.

Rewrite 3^(-5) into positive exponent 1/3^5.

The new form of 11^0.3^(-5) is 1×(1/3^5) = 1/3^5.

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The rectangular crate will be able to carry a maximum of 27 boxes

The crate carries a shape of a cuboid which can be said to be a rectangle in three-dimensional side. To solve this problem, we have to find the volume of the crate and then the volume of the box and divide the volume of the crate by the volume of box.

The volume of a cuboid = L * W * H

This can be calculated as V = 24 * 18 * 15 = 6480cm³

The volume of the box = 8 * 6 * 5 = 240cm³

Number of boxes that can fit in the cuboid = 6480 / 240

Number of boxes = 27 boxes

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Answer:

[tex]y=\left(x^2-\dfrac{9}{2}\right)^2-\dfrac{65}{4}[/tex]

Step-by-step explanation:

To put this in vertex form, we need to create a perfect square polynomial within the right side of the equation.

[tex]y=x^2-9x+4[/tex]

[tex]y=\left(x^2-9x + \left(-\dfrac{9}{2}\right)^2\right)+4 - \dfrac{81}{4}[/tex]

[tex]y=\left(x^2-\dfrac{9}{2}\right)^2+4 - \dfrac{81}{4}[/tex]

[tex]y=\left(x^2-\dfrac{9}{2}\right)^2-\dfrac{65}{4}[/tex]

Answer:

The mean is 6

Step-by-step explanation:

To find the mean, add all the numbers and then divide by the number of data points

( 7+5+4+5+6+9)/ 6

36/6

6

The mean is 6

(9) The triangle ABD ≅ triangle CDB by SAS Congruence Postulate ,

(10) The triangle EFG ≅ triangle LNM by SAS Congruence Postulate .

In the question ,

(9)

a figure is given where AD = CB

In the Triangle ABD and triangle CDB ,

side AD = CB   ....given

angle ADB = angle CBD     .... given

side AB = CD .......because opposite sides of parallelogram are equal .

hence ΔABD ≅ ΔCDB by SAS Congruence Postulate .

(10)

a figure is given where EF = LN

In the Triangle EFG and triangle LNM ,

side EF = LN   ....given

angle G = angle M        .... because both are 90°

side FG = NM       .....given

hence ΔEFG ≅ ΔLNM by SAS Congruence Postulate .

Therefore , (9) The triangle ABD ≅ triangle CDB by SAS Congruence Postulate ,

(10) The triangle EFG ≅ triangle LNM by SAS Congruence Postulate .

The given question is incomplete , the complete question is

Complete the Congruence Statement for the figure given below , If possible . If so , state the Postulate / Theorem you used .

(9) ΔABD ≅                                               (10) ΔEFG ≅                    .

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The percent of its flights that do not arrive on time is 9.3%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, the airlines reports that 90.7 percent of its flights arrive on time.

The percent of its flights which do not arrive on time will be:

= 1 - Those who came in time

= 1 - 90.7

= 9.3%

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The probability of randomly picking a green marble, a marble that is not red and 2 blue marbles in a row is 0.03 approximately to 2 decimal places

Probability of an event is the fraction of the required outcome of event divided by the number of possible outcomes of events. The probability that an event will not occur is one minus the probability of the event occurring.

The total marbles are 21 in number with;

the probability of picking a green marble = 4/21

the probability of picking a marble that is not red = 1 - (7/21) = 14/21

the probability of picking two blue marbles = (10/21) × (10/21)

probability of randomly picking a green marble, a marble that is not red and 2 blue marbles in a row = (4/21) × (14/21) × (10/21) × (10/21)

probability of randomly picking a green marble, a marble that is not red and 2 blue marbles in a row = 5600/19481 = 0.03

Therefore, considering it is a random pick without replacement, the probability of the event for picking a green marble, a marble that is not red and 2 blue marbles in a row is approximately 0.03.

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The equation that models the balance y after x​ months will be: y = -115x + 1600.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that Zachary purchased a computer for ​$1600 on a payment plan.

Then two months after he purchased the​ computer, his balance was ​$1255. Three months  after  his balance was ​$1140.  

Initial cost = 1600

Difference in balance = 1,255 - 1,140 = 115

Number of months used = 3 months - 2 months = 1 month1

Therefore, the equation that models the balance b after m months will be:

= - (115/1)x + 1600

y = - 115x + 1600

Hence, The equation that models the balance y after x​ months will be: y = -115x + 1600.

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The associations that best describe the scatter plot is Option A and C

When below-average values also tend to occur together and above-average values of one variable tend to be accompanied by below-average values of the other, there is a positive association between the two variables. When the average values of two variables tend to be below average, two variables have a negative connection.

Note that a statistical term used to describe a straight-line relationship between two variables is a linear relationship (or linear association).

Additionally, a straight line connecting the spots indicates a linear association. As a result, the scatter plot indicates that as practice time increases,  giving off also rise.

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The association that describe the scatter plot is

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events (called variables).

The connection is positive if the variables tend to rise and fall together. When one variable tends to rise while the other falls, there is a negative connection.

The connection between the variables demonstrates a straight line in the positive direction. hence the option having linear and positive association is the correct choice

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Answer:

20

Step-by-step explanation:

we turn 5 into a fraction to make it easier

[tex]\frac{5}{1}[/tex]÷[tex]\frac{1}{4}[/tex]

Now to figure it out we keep the first fraction 5/1 the same and then flip the second one 1/4 to make it 4/1 and multiply

[tex]\frac{5}{1}[/tex]×[tex]\frac{4}{1}[/tex]

[tex]\frac{20}{1}[/tex]

20

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The drug has a half-life of 5 hours

Half-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.

The formula is given as;

T1/2 = ln2 / λ

Where;

But λ = 15% = 0.15/hr

t1/2 = ln2 / 0.15

T1/2 = 0.693/0.15

T1/2 = 4.62 = 5 hours.

The half-life of the drug is 5 hours

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The coach expects each player to make a fraction of 3/4 of their shot which is 75 percent in order to make starting team.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

In this case, if the coach wants each player to make 75% of their shot, it implies that each player must make a certain fraction of their total shot.

Converting percentage to fraction, we will have

75% = 3/4

Each player must make at least 3/4 of their shot to make her starting team,

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The probability of getting at least one Canadian quarter is 0.6

This is a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:

P(x = r) = nCr . p^r . q^n-r

Where n = number of trials, p =  probability of success and q = probability of failure,  x = number of Canadian quarters

39 U.S. quarters  + 11 Canadian quarters coins = 50 coins

Given: n = 4 (four quarters picked), p = 11/50  = 0.22, q = 1-p =1-0.22 = 0.78

Probability at least one Canadian quarter  = 1 - Probability of no Canadian quarter

P(x≥1) = 1 - P(x = 0)          

         = 1 - (4C0×0.22⁰× 0.78⁴⁻⁰ )

        = 1 - 0.4

        = 0.6

Therefore, the probability of getting at least one Canadian quarter is 0.6

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Answer:

Step-by-step explanation:

X+Y = 50

0.13X + 0.18Y = 0.16*50 = 8

0.13X + 0.18(50-X) = 8

0.13X + 9 - 0.18X = 8

-0.05X = -1

5x = 100

x=20

20 mL of the 13% salt solution

30 mL of the 18% salt solution

Arithmetic proportions are those whose means are not equal and are called discrete arithmetic proportions. On the contrary, if the means of the arithmetic proportion are equal, it is called continuous.

[tex]\bf\large{\underline{\fcolorbox{blue}{aqua}{Problem:}}}[/tex]

[tex]\sf 20 : x :: x : 5 [/tex]

Since the unknown term is an extreme and as we have seen, it is equal to the product of the means divided by the other extremes, we will have:

[tex]\sf x = \sqrt{20 \times 5} = \sqrt{100} = 10[/tex]

Therefore, the resulting geometric proportion would be:

[tex] \: \: \: \: \: \: \: \: \: \: \: \red\longmapsto \sf \orange{20 : 10 ::10: 5 }[/tex]

Arithmetic proportions are those whose means are not equal and are called discrete arithmetic proportions. On the contrary, if the means of the arithmetic proportion are equal, it is called continuous.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \Rightarrow \bold{x :: x : 5 }[/tex]

Since the unknown term is an extreme and as we have seen, it is equal to the product of the means divided by the other extremes, we will have:

[tex]\bold{ x = \sqrt{20 \times 5} = \sqrt{100} }[/tex]

[tex]\therefore[/tex] The resulting geometric proportion would be:

[tex] \Rightarrow \bold{20 : 10 ::10: 5 }[/tex]

Answer: No, the answer is not reasonable because 3,627/9 doesn’t equal 43, it equals 387.

Answer:

No, you friend's answer is not reasonable.

Step-by-step explanation:

3,627 x 9 does not equal 43

3,627 x 9 =32643

Therefore your friend is incorrect

The Speed of the plane in still air is 165 miles per hour.

What is speed?

 The rate that an object travels a certain distance is what is meant by the speed formula. The amount of distance a body moves in a certain amount of time is referred to as speed. The metric unit of speed is the m/s. For example, m/s, km/hr, miles/hr, and other units can be used to express speed.

Let x be the speed of the plane in the still air, and w be the wind speed.

Using speed formula Balancing by the time,

=> Time = Distance/ Speed

=> 420/(x+w) = 350/(x-w)

Then ,

=>420/(x+15)=350/(x-15)

=> 420(x-15)=350(x+15)

=> 420x-6300=350x+5250

=> 420x-350x=5250+6300

=>70x=11550

=>x=11550/70

=>x=165mph.

Hence speed of the plane in still air is 165 miles per hour.

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Solving a system of equations we can see that she bought 3 bags of popcorn and 6 drinks.

We can define the two variables:

Knowing that each bag of popcorn costs $5 and each drink costs $6, and the total cost was $51, we can write:

x*$5 + y*$6 = $51

And we also know that she bought twice as many drinks as bags of popcorn, then:

y = 2x

So we have a system of equations:

y = 2x

x*$5 + y*$6 = $51

Replacing the first equation into the second one:

x*$5 + (2x)*$6 = $51

x*$17 = $51

x = $51/$17 = 3

So she bought 3 bags of popcorn and 2*3 = 6 drinks.

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The number of hours per year that the equipment be used to justify purchasing it rather than renting it is 2125 hours.

It should be noted that an expression is used to illustrate the relationship between the variables.

Let the number of hours be illustrated as h.

The landscaper can rent a backhoe for $45,000 a year and he could purchase the equipment for

monthly costs of $2,500 plus $20 for each hour it is used.

This will be:

2500 + 20h = 45000

Collect like terms

20h = 45000 - 2500

20h = 42500

Divide

h = 42500 / 20

h = 2125

The number of hours is 2125 hours.

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Answer:

it should round up to 36000

In general, “degrees of freedom is most clearly related to the sample size.

Degrees of freedom are frequently discussed in statistics in relation to various types of hypothesis testing, such as chi-square. When attempting to understand the significance of a chi-square statistic and the validity of the null hypothesis, it is critical to calculate degrees of freedom.

Degrees of freedom refer to the maximum number of logically independent values in a data sample, which are values with the freedom to vary. Because the degrees of freedom are so closely related to sample size, the effect of sample size can be seen. The t-distribution has thicker tails as the DF decreases. This property allows for the higher level of uncertainty that comes with small sample sizes.

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If two names are given for the same quantity then we can use algebra

to solve the equation thus option (C) is correct.

There are many different ways to define an equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In another word, the equation must be constrained with some constraints.

If we have a problem in word formate.

And the same quantity is used two times with two different names.

Then by algebra, the variable defines the quantity remains the same but the value of the variable changes according to the given value.

By this the problem can be easily solved.

Hence "If two names are given for the same quantity then we can use algebra to solve the equation".

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Answer: (-2m)-10

3x+11

9xy+2z-16

-7x-11

6m^2-m+8

Step-by-step explanation:

×= 5484883929292922882829

Answer:

Your right it's C

Step-by-step explanation:

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