The Wood family bought 6 crates of eggs last week. Each crate had 12 eggs. Since then, they have eaten 27 of the eggs. How many eggs are left?

Answer:

  y = -5/8(x -8)²

Step-by-step explanation:

You want the function of the form y = a(x -h)² that passes through the points (12, -10) and (8, 0).

The vertex form of the equation of a quadratic is ...

  y = a(x -h)² +k . . . . . . quadratic with vertex (h, k)

Comparing this to the given equation, we see that k=0. This means the point (8, 0) is the vertex and h = 8.

The value of 'a' can be found using the other point.

  (x, y) = (12, -10)

  -10 = a(12 -8)²

  -10 = 16a

  -5/8 = a . . . . . . divide by 16 and reduce the fraction

The quadratic function is y = -5/8(x -8)².

__

Additional comment

The equation can also be found using technology to do a quadratic regression with the constraint that the vertex is on the x-axis.

The required equation of the line is given as y = -14x + 45.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

Given that,

The slope of the line is -14.

And, the point it passes through is (3, 3).

The equation of the line for given data can be written as follows,

(y - 3)/(x - 3) = -14

=> y - 3 = -14(x - 3)

=> y = -14x + 42 + 3

=> y = -14x + 45

Hence, the equation of the line for the given point and slope can be written as y = -14x + 45.

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The probability for observing the expected count will be given by [tex]E_i = nP_i[/tex]

Consider an experiment with n independent trials and k > 3 mutually incompatible outcomes.

Where [tex]P_i[/tex] stands for the likelihood of seeing the i-th result.

Hence for the nth expected result on i will be given by multiplying the i-th probability with the expected variable n.

Hence [tex]E_i = n\times P_i[/tex]

∴ [tex]E_i = nP_i[/tex]  provides the predicted numbers for each potential outcome.

where pi is the likelihood of seeing the i-th result.

The predicted count of the i-th result is called [tex]E_i[/tex].

When two events cannot occur concurrently at the same moment, they are said to be mutually exclusive in accordance with probability theory. Or, to put it another way, discontinuous events are said to be mutually exclusive.

There is no possibility of two occurrences occurring simultaneously if they are viewed as separate events. If two events do not take place at the same time, they are said to be mutually exclusive. If a coin is tossed, the outcome will always be either head or tail; we cannot get both.

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The error that Bobby most likely made in verifying if the relation is a function is given as follows:

C. Bobby drew the incorrect arrow diagram. The correct arrow diagram of the relation is a function. Bobby's arrow diagram is not a function.

A relation represents a function if each value of the input is mapped to only one value of the output.

The ordered pairs from this data-set are given as follows:

(​4,​5), ​(​9,​15), ​(14​,​22), ​and (​18,​37).

The input and the output for the pairs are given as follows:

Each value of the input is mapped to only one value of output, hence the relation represents a function.

However, Bobby made a mistake, in mapping the point (9, 15), as he mapped an input of 14 to an output of 9, and thus it would not represent a function. Hence the correct statement is given by option C.

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Lexi drinks 3/10 gallon of water in one hour.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Lexi drinks water in 50 minutes = 1/4 gallon

To find water that Lexi drinks in one hour,

Use ratio property,

50 minutes = 1/4 gallon

1 minute = 1/(4 x 50)

60 minutes = 60/(4 x 50)

60 minutes = 3/10 gallon

Lexi drinks 3/10 gallon of water in 1 hour.

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The total number of possible strings that can be chosen is 4^13, since there are 13 characters and 4 possible choices for each character, b, c, d). Now, we need to determine the number of strings that contain at least one pair of adjacent characters that are the same in this probability.

To do this, we'll consider each letter in the string and calculate the number of possible strings that contain at least one pair of adjacent characters that are the same for that letter. For the first letter in the string, there are 4 strings that contain at least one pair of adjacent characters that are the same (aa, bb, cc, dd).For the second letter in the string, there are 4 strings that contain at least one pair of adjacent characters that are the same (ab, be, cd, dc).For the third letter in the string, there are 4 strings that contain at least one pair of adjacent characters that are the same (ac, bd, ca, db.).For the fourth letter in the string, there are 4 strings that contain at least one pair of adjacent characters that are the same (ad, bc, da, cb).

We can continue this process for each letter

We get probability as 83.3%

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Answer:

(-15x^3 -12x^2 -5x-3)

Step-by-step explanation:

You can't add/subtract numbers that have different exponent numbers so you have to stick with the ones that have the same number

So then the coefficients would be:

x^3 : -9 - 6 = -15

x^2 : -7 -5 = -12
x: -3 -2 =-5
0: -1 - 2 = -3

Answer:

Step-by-step explanation:

Using system of linear equations, the number of cars and trucks that parked are 950 and 150 respectively.

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

To solve this problem, we have to write out two equations and solve the unknown variable.

x + y = 1100 ...eq(i)

0.75x + 1.25y = 900 ...eq(ii)

From equ(i)

x = 1100 - y ..eq(iii)

Put eq(iii) into eq(ii)

0.75(1100 - y) + 1.25y = 900

y = 150

Put y = 150 in equation (i)

x + 150 = 1100

x = 1100 - 150

x = 950

x = 950, y = 150

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9514 1404 393  each kind of ticket were sold  if 550 tickets were sold for a game for a total of $687.50. if adult tickets sold for $1.50 and children's tickets sold for $1.00,

adult: 325

children's: 225

It usually works well to let a variable represent the higher-value item in the mix. Here, we can let 'a' represent the number of adult tickets sold. Then the total revenue is ...

 1.50a +1.00(550 -a) = 687.50

 0.50a = 162.50 . . . . . . . . . . . . . subtract 550 and collect terms

 a = 325

 c = 550 -325 = 225

325 adult and 225 children's tickets were sold

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Using the system of equations we get the values of 3 digit number as:

238

Given:

The sum of the digits of a three-digit number is 13.

The tens digit, t, is 1 more than the hundreds digit, h. The units digit, u, is 3 more than the sum of the tens and hundreds digits.

we are asked to determine each digit of the given number:

we frame the equation as:

tens digit (t) = 1+h

hundreds digit (h) = h

units digit (u) = 3+(t+h)

hence,

h + (1+h) + (3+(t+h)) = 13

open the brackets.

h+1+h+3+(t+h)=13

substitute t value from the above mentioned state.

h+1+h+3+((1+h)+h)=13

h+1+h+3+1+h+h=13

arrange the like terms and add.

4h + 5 = 13

4h = 13-5

4h=8

h = 8/4

h = 2

hence we get the hundreds digit as 2.

now substitute it to get t and u value.

t = 1+h

t = 1+2

t = 3

tens digit = 3

u = 3+(t+h)

u = 3+(3+2)

u = 3+5

u = 8

units digit = 8

Hence we get the number as 238 whose sum is 13 when added.

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There is significant relation between price and overall score.

Given that,

Following are details on the cost ($) and final rating for the six stereo headphones that Consumer Reports examined. ($) brand price Score: Bose 180, 72 Scullcandy 150, 78 Koss, 96, 54 Phillips/O'Neill, 72, 42 Denon, 48, 24.

a) t =3.54

The P value is less than 0.2

There is significant relation between price and overall score.

P value is between 0.01 and 0.025.

Because p value is less than or equal to 0.05 , we reject H₀ : β₁ is equal to zero.

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A certain bacteria strain needs 4 hours to double its population. If in the beginning there are 45 bacteria, after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.

The problem can be solved using the exponential growth model.

In the given problem, the formula for the growth model is given, that is:

f(x) = 45 (64)^(x)

Where:

f(x) = total number of bacteria present after x days

To find f(x) for 1 day, 2 days, and 3 says, substitute x = 1, x = 2, and x = 3 into the formula.

f(1) = 45 (64)¹ = 2,880

f(2) = 45 (64)² = 184,320

f(3) = 45 (64)³ = 11,796,480

Hence,

after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.

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The value of r is r = -8/3, for a line that has slope -12, passes through points (-3, -6) and (r, -10)

Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.

Slope formula = (y₂-y₁)/(x₂-x₁)

Given that,

A line that has slope -12, passes through points (-3, -6) and (r, -10).

To find the slope of the line that passes through points (-3, -6) and (r, -10),

Use slope formula,

m =  (y₂-y₁) / (x₂-x₁)

m = (-10 + 6) / r - (-3)

m = -4 / (r+3)

Since a line that has slope -12 passes through the points (-3, -6) and (r, -10),

Therefore, both will have the same slope,

-4 / (r+3) = -12

r + 3 = 1/3

r = 1/3 - 3

r = -8/3

The required value of r is -8/3.

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$2.50 is found to be the proportionality constant for the relationship between the length of track (in inches) and the cost in dollars.

Direct proportionality is represented by the equation y = kx.

Where:

The price of the track is the dependent variable in this situation.

The tracks' length is an independent variable.

$16 = 6.4k

k = 16 / 6.4

k = $2.5

Thus, the constant of proportionality for the relationship between the length of track (in inches) and the cost in dollars is found as $2.5.

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The width of a confidence interval except increased sample size.

What is the Confidence Interval?

An area surrounding a measurement that indicates how accurate it is is called a confidence interval.

The following points clear the answer of given question:

Hence, The width of a confidence interval except increased sample size.

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He needs 2.5 pounds of ground turkey.

Given,

In the question:

Ben wants to triple his spaghetti sauce recipe, which calls for 2 pound 8 ounces of ground turkey.

To find the how much pounds ground turkey will he need?

Now, According to the question:

Let's know:

How do you convert ounces to pounds formula?

In other words, dividing a number of ounces by 16 will get you an answer in pounds. In our example, dividing the baby's weight in ounces by 16 gets us 160/16 = 10 lbs.
We know that there are 16 ounces in 1 pound,

It is meaning that 8 ounces is half a pound.

Adding this to the 2 pound gives 2 + 1/2 = 2.5 pounds of ground turkey.

Hence, 2.5 pounds of ground turkey.

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If a measurement was not sensitive, and resulted in everyone scoring high, then this is called a ceiling effect

Given,

Ceiling effect;-

When a large percentage of study participants get the highest scores on the observable variable, it is said that a ceiling effect has occurred. Discrimination between subjects at the top end of the scale is therefore impossible. For instance, a test could result in, say, 50% of the students receiving a perfect score.

Here,

To be able to measure participant differences, variables must be measured with sufficient sensitivity. However, if a test was insensitive and everyone received good scores, this is known as ceiling effect

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Hence, the negative solution is [tex]x=-3[/tex].

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

When [tex]27[/tex] is subtracted from the square of a number, the result is [tex]6[/tex] times the number.

So we can write the equation is

[tex]x^2-27=6x\\x^2-6x-27=0\\x^2-9x+3x-27=0\\x(x-9)+3(x-9)=0\\(x+3)(x-9)=0\\x=-3,9[/tex]

Hence, the negative solution is [tex]x=-3[/tex].

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The correct option is the standard deviations of the variables.

What is correlation?

Any statistical relationship between two random variables or bivariate data, whether causal or not, is referred to in statistics as correlation or dependence.

Correlation is a term used to describe the linear relationship between two entities. When using a correlation tool, the variables must be present in quantities of two or more to test their relationship (degree of association).

In order to scale the measurement between two variables connected to a similar sample, the standard deviation measures dispersion.

The variables' standard deviations are the best choice as a result.

Option involving the standard errors of the variables is incorrect because standard error, which stands for standard deviation, determines the relationship between dependent and independent variables.

Option involving the coefficients of variation of two variables is incorrect because the coefficient expressing standard deviation and mean ratio determines how much variation there is.

Option The means of the variables are incorrect because they are not a scale for determining the correlation between two variables.

Hence, the correct option is the standard deviations of the variables.

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Complete question:

The correlation between two variables related to the same sample is a scaled quantitative measure. What is used to scale this measurement?

- the standard deviations of the variables

- the standard errors of the variables

- the coefficients of variation of the two variables

- the means of the variables

The order of H can be 84 , 210 or 420

One of the key theorems in abstract algebra is the Lagrange theorem. According to the Lagrange Theorem , In group theory, for any finite group say G, the order of subgroup H of group G is the divisor of the order of G. The order of the group represents the number of elements

According to the question,

Group G has order 840

Also , By Lagrange's theorem

|K| divides |H| , so order of h should be multiple of 42

|H| = 42k ------(1)  (for some k)

And , H is subgroup of G

|G| should divides |H|

=> 42k should divides 840

=> k = 840/42 = 20

Since , H is proper subgroup of G

K < 20

So, either k =2 , 5 or 10

Hence , order of H can be 84 , 210 or 421

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The measure of the ∠1 for the given angles of the triangle are found as 1162/13.

The given angles are-

∠1 = 7x - 7.

∠2 = 4x + 2

∠3 = 2x + 6

By the angle sum property of the triangle.

∠1 + ∠2 + ∠3 = 180

Thus,

7x - 7 + 4x + 2 +  2x + 6 = 180

Simplifying,

13x = 179

x = 179/13

So, ∠1 becomes-

∠1 = 7x - 7

∠1  = 7(179/13)- 7

∠1  = 1162/13

Thus, the measure of the ∠1 for the given angles of the triangle are found as 1162/13.

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the sample proportion under probability has a mean sampling distribution of 82.

The population percentage is the major variable in the sampling distribution of this proportion, which has a quarter-um normal distribution. Variants include population proportion times one and population proportion divided by sample size. Additionally, we are aware that the population proportion is under the null hypothesis. 200 is the sample soil. When we enter the value of P into this calculation without normalisation, we can obtain the standing ovation as the variance's root. 025 in excess. The probability that we got a sample result of 188/58 or less is then calculated. We simply need to determine this left tail probability after that.

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Answer:

Since it appears that you are talking about a triangle, if the third side that you are looking for is the hypotenuse, then you can use the Pythagorean theorem, a^2 + b^2 = c^2. In this case, the length of the side, if it would be the hypotenuse, would be approximately 21.63.

Step-by-step explanation:

Hope this helped! :D

If you have been asked to assemble a two person team from among your five person team, then there are 10 different teams

Total number of members for the team = 5

Number of members that we need to assemble = 2

Here we have to use the combination

The combination is defined as the number of ways of selecting samples from the collection and the order of the collection does not matter

The number of combination of 2 members from a 5 member team = [tex]5C_2[/tex]

= 5! / 2!(5-2)!

= 5! / 2! × 3!

= (5 × 4 × 3!) /(2! × 3!)

= (5 × 4) / 2

= 20 / 2

= 10

Therefore, there are 10 different teams

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The original Price of a case of scented candles was 8.5

A percent increase refers to how much a percentage has gone up over time.

In order to reach this number, you would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease.

The formula for calculating Percentage increase is:

(ΔPrice/Original price) × 100

change in price (new price - original price)/original price) × 100

From the question:

Percentage increase = 110%

New price = 17.85

Original price = X

so it  we can substitute in the formula

((17.85 - X)/X) * 100 = 110%

Opening brackets

(17.85*100 - X*100)/ X =110

1785 - 100X = 110X (we balance the equation)

(we collect like terms)

1785 = 210X

to find X we divide both sides by 210

1785/210 = X

8.5

The original Price was $8.5

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The interest estimated by compounding methods are-

(a) Annual: n = 1; CI = $860

(b) Semiannual: n = 2; CI = $862.

(c) Monthly: n = 12; CI = $865

(d) Daily: n = 365; CI = $855

The formula for computing the compound interest is -

CI = A - P

A = P(1 + r/100nt)∧rt

In which,

(a) Annual: n = 1

A = 10,400(1 + 8/500)∧5

A = 10,400 x 1.08

A = 11,260

CI = 11,260 - 10,400

CI = $860

(b) Semiannual: n = 2

A = 10,400(1 + 8/1000)∧10

A = 10,400 x 1.089

A = 11,262

CI = $862.

(c) Monthly: n = 12

A = 10,400(1 + 8/6000)∧60

A = 10,400 x 1.083

A = 11,265

CI = $865

(d) Daily: n = 365

A = 10,400(1 + 8/182500)∧1825

A = 10,400 x 1.0832

A = 11,255

CI = $855

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Answer:

Obtuse

Step-by-step explanation:

Obtuse because one angle is more than 90 degrees.

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