will give brainalist!!
ratio please be correct due soon no fake answers

Will Give Brainalist!!ratio Please Be Correct Due Soon No Fake Answers

Answers

Answer 1
60g strawberry
6 sponge
315 ml
135g tinned fruit
Answer 2

Answer:

Step-by-step explanation:

Strawberry jelly:

120 ÷ 4 × 3 = 90 g

Sponge fingers:

8 ÷ 4 × 3 = 6

Custard:

420 ÷ 4 × 3 = 315 ml

Tinned fruit:

180 ÷ 4 × 3 = 135 g


Related Questions

The diagram that is best at displaying data dispersion is a: Multiple Choice a. scatter diagram. b. stem-and-leaf display. c. skewness graph. d. box plot

Answers

The best diagram to use to display data dispersion is a box plot. A box plot is a diagram that shows how a dataset is distributed and helps to identify any outliers.

The diagram that is best at displaying data dispersion is a box plot. Here's the main answer:When there is a need to compare the distribution of data, a box plot is often the best method.

A box plot is a diagram that shows how a dataset is distributed. It shows how data is spread out and helps to identify any outliers. It is most effective for comparing data sets that have a large number of data points and when the data is not normal (not evenly distributed).

A box plot is a great way to summarize large amounts of data and it is also very easy to read and interpret. It shows a number of statistical values, including the median (the middle value of the data set), the quartiles (the values that divide the data set into four equal parts) and the range (the difference between the maximum and minimum values).

Additionally, it can identify any outliers in the data, which are values that are significantly different from the rest of the data.A box plot is created by drawing a rectangle between the first and third quartiles (the middle 50% of the data) with a line drawn inside it to show the median.

Lines are then drawn from the edges of the rectangle to the minimum and maximum values. Any outliers are marked with a point outside of the rectangle.

The box plot is a great way to compare data sets and to visualize the dispersion of the data

The best diagram to use to display data dispersion is a box plot. A box plot is a diagram that shows how a dataset is distributed and helps to identify any outliers. It is most effective for comparing data sets that have a large number of data points and when the data is not normal. A box plot is created by drawing a rectangle between the first and third quartiles with a line drawn inside it to show the median.

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Freeport-McMoRan Copper and Gold has purchased a new ore grading unit for $80,000. The unit has an anticipated life of 10 years and a salvage value of $10,000. Use the DB and DDB methods to compare the schedule of depreciation and book values for each year

Answers

The depreciation expense of the book value for 10 years with SL method is $7,000.

Straight-Line Method (SL):

The Straight-Line Method is the most basic method and is computed by subtracting the salvage value from the original cost and dividing it by the expected useful life, plus one.

Using this method, the depreciation expense for each year is calculated as:

Depreciation Expense = (Cost - Salvage Value)/(Lifespan + 1)

For this example, the depreciation expense for each year would be calculated as:

Depreciation Expense = ($80,000 - $10,000)/(10 + 1) = $7,000

The schedule of depreciation and book value for each year would look like this:

Year Depreciation        Book Value

1             $7,000  $73,000

2             $7,000  $66,000

3             $7,000  $59,000

4             $7,000  $52,000

5             $7,000  $45,000

6             $7,000  $38,000

7             $7,000  $31,000

8             $7,000  $24,000

9             $7,000  $17,000

10             $7,000  $10,000

Sum-of-the-Years'-Digits Method (SOYD):

The Sum-of-the-Years'-Digits Method (SOYD) is another popular method of depreciation. It is computed by multiplying the asset’s original cost by the sum of the digits of the useful life and subtracting the salvage value.

Using this method, the depreciation expense for each year is calculated as:

Depreciation Expense = N×(Cost - Salvage Value)/(1+2+3+4+ … + N)

For this example, the depreciation expense for each year would be calculated as:

Depreciation Expense = N×($80,000 - $10,000)/(1+2+3+4+ … +10)

The schedule of depreciation and book value for each year would look like this:

Year Depreciation       Book Value

1     $12,819        $67,181

2     $11,301         $55,880

3     $9,784         $46,096

4     $8,266         $37,830

5     $6,749         $30,581

6     $5,231         $24,350

7     $3,714         $19,136

8     $2,196         $14,940

9     $676         $14,264

10     $138         $14,126

Double-Declining Balance Method (DDB):

The Double-Declining Balance Method is a more aggressive approach and is calculated by multiplying the asset’s book value at the start of the year by twice the applicable straight-line rate.

Using this method, the depreciation expense for each year is calculated as:

Depreciation Expense = Book Value ×(2 × Straight-Line Rate)

For this example, the depreciation expense for each year would be calculated as:

Depreciation Expense = Book Value × (2×7,000/80,000)

The schedule of depreciation and book value for each year would look like this:

Year Depreciation   Book Value

1            $14,000           $66,000

2            $11,520           $54,480

3            $8,768            $45,712

4            $5,824            $39,888

5            $3,664            $36,224

6            $1,408            $34,816

7               $0            $34,816

8               $0            $34,816

9               $0            $34,816

10               $0            $34,816

Declining Balance Method (DB):

The Declining Balance Method is a less aggressive approach and is calculated by multiplying the asset’s book value at the start of the year by the applicable straight-line rate.

Using this method, the depreciation expense for each year is calculated as:

Depreciation Expense = Book Value × (Straight-Line Rate)

For this example, the depreciation expense for each year would be calculated as:

Depreciation Expense = Book Value × (7,000/80,000)

The schedule of depreciation and book value for each year would look like this:

Year Depreciation    Book Value

1             $7,000            $73,000

2            $6,024                $66,976

3            $4,914                    $61,062

4            $3,770                $57,292

5            $2,597             $54,695

6            $1,398             $53,297

7              $0             $53,297

8              $0             $53,297

9              $0             $53,297

10              $0             $53,297

Therefore, the depreciation expense of the book value for 10 years with SL method is $7,000.

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plsssss help im honestly brain dead

plsssss help im honestly brain dead

Answers

Answer:

same but like 123

Step-by-step explanation:

Answer:

the slope represents minutes per miles.

Step-by-step explanation:

the other 3 are wrong

8(y+4)-2(y-1)=70-3y
solve for y

Answers

Answer:

y = 4

Step-by-step explanation:

8(y + 4) - 2(y - 1) = 70 - 3y ← distribute parenthesis and simplify left side

8y + 32 - 2y + 2 = 70 - 3y

6y + 34 = 70 - 3y ( add 3y to both sides )

9y + 34 = 70 ( subtract 34 from both sides )

9y = 36 ( divide both sides by 9 )

y = 4

Suppose we estimate the following regression: yt = β1 + β2x2t +
β3x3t + ut. Suppose the variance of ut is related to a known
variable zt as follows: Var(ut) = σ^2(zt). How would you transform
the

Answers

To transform the regression equation, you would divide both sides of the equation by the square root of Var(ut), which is σ√(zt). This transformation helps in obtaining the transformed regression coefficients and standard errors that account for the heteroscedasticity in the error term.

When the variance of the error term (ut) is related to a known variable (zt), it implies the presence of heteroscedasticity in the regression model. Heteroscedasticity means that the variability of the error term is not constant across different levels of the independent variables.

To address this issue, we can transform the regression equation by dividing both sides by the square root of the variance of the error term, which is σ√(zt). This transformation is known as the weighted least squares (WLS) estimation.

By dividing both sides of the equation, we can obtain the transformed regression equation with the error term divided by its standard deviation. This transformation accounts for the heteroscedasticity by giving different weights to the observations based on the variability of the error term. It allows for a more appropriate estimation of the regression coefficients and standard errors, as it gives more weight to observations with smaller error variances and less weight to observations with larger error variances.

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At a wedding there were 40 people from gromms side and 56 people from bride's family at the wedding

find the ratio of the groom's family to the bride's family at the wedding ​

Answers

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

The answer is 96 people in total.

Explanation- 50+56 Is 106. So 106- 10=96.

There is your answer 96.

how to calculate hyperboloid of one sheet?

Answers

The equation of hyperboloid of one sheet: \(\frac{x^{2} }{A^{2} } +\frac{y^{2} }{B^{2} } -\frac{z^{2} }{C^{2} } =1\) which is used to calculate hyperboloid.

The most challenging quadric surface is probably the hyperboloid of a single sheet. For starters, it is puzzling since its equation is quite similar to that of a hyperboloid with two sheets. For information on how to tell them apart, see to the section on the two-sheeted hyperboloid. Its cross portions are also highly intricate equation.

Having said all of that, everyone who has watched The Simpsons, even for the first time, will recognize this form. One-sheet hyperboloids have a striking resemblance to Springfield Nuclear Power Plant cooling towers.

The cross sections of a straightforward one-sheeted hyperboloid with A = B = C = 1.

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PLEASE HELP

This work is called systems of Linear Inequalities

PLEASE HELPThis work is called systems of Linear Inequalities

Answers

The system of linear inequalities has an algebraic solution of 3 - x/2 ≤ y < x/2 + 4 and a graphical solution of (-4, 2) and (0, 2)

System of Linear Inequalities

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

In the question given, the inequalities are;

y < 1/2x + 4 ....1

x + 2y ≥ 6 ...2

Solving for both inequalities;

The solution is given as 3 - x/2 ≤ y < x/2 + 4

This can be represented on a graph as and it has a solution of (-4, 2) and (0, 2) graphically.

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PLEASE HELPThis work is called systems of Linear Inequalities

How to solve :

\(\frac{3x}{2-|x|} \leq 1\)

Answers

After the solution of the expression 3x/2-|x| ≤ 1 the interval notation is:

\(\left(-2, \frac{1}{2}\right] \cup(2, \infty)\)

What do we mean by expressions?In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one math operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

So, get x, by simplification of both sides of the inequality before isolating the variable.

Form of Inequality:

3x/2-|x| ≤ 1-2 < x ≤ 1/2 or x > 2

Interval notation:

\(\left(-2, \frac{1}{2}\right] \cup(2, \infty)\)

(Refer to the graph diagram given below)

Therefore, after the solution of the expression 3x/2-|x| ≤ 1 the interval notation is:

\(\left(-2, \frac{1}{2}\right] \cup(2, \infty)\)

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How to solve : [tex]\frac{3x}{2-|x|} \leq 1[/tex]

HELP DUE IN 5 MINS!

Solve for x in the polygon below.

x=?? degrees

HELP DUE IN 5 MINS!Solve for x in the polygon below.x=?? degrees

Answers

Answer:

135

Step-by-step explanation:

540-75-120-120-90=135

Answer:

x = 135

Step-by-step explanation:

Total sum of interior angles of a pentagon = 540

75 + 120 + 120 + 90 + x = 540

405 + x = 540

=> Subtract 405 on both sides of "="

x = 135

Hope this helps!

what’s 50/6 reduced to a mixed number????? please i need it it’s due in 10 mins

Answers

Answer:

8 1/3

Step-by-step explanation:

 

50/6 =25/3 = 8 1/3  

Also can u pls mark me brainliest im new

Connie received $20 for her birthday from her grandparents. She used the money to buy an ice cream cone for herself and one for each of her four best friends. If each cone cost $3.15, how much money does Connie have left?

Answers

Answer:

4.25

Step-by-step explanation:

she has a total of 20 dollars and she wats to buy ice cream each at 3.15 for a total of 5 people including her self.

so 3.15(5) is 15.75

then subtract 15.75 from 20

20 - 15.75 = 4.25

A new Youth Sports Center is being built in Hadleyville, The perimeter of the rectangular playing field is 430 yards. The length of the field is 5 yards

the width. What are the dimensions of the playing field?

The width is

yards

The length is

yards

Answers

Answer:

Width = 44 yards

Length = 171 yards

Step-by-step explanation:

given data

length of the field = 5 yards

Perimeter of the rectangular field = 430 yards.

solution

we consider here length of the field = L

and width of the field = W

as we know length of the field 5yards less than quadruple the width

so here

L = 4W - 5       .....................................1

and  

Perimeter (P) will be here

P = 2(L + W)      ............................................2

put here equation 1 value

430 = 2(4W - 5 + W)  

solve it we get

W = 44

so here put value in eq 1 we het

L = 4W - 5          

L = 4(44) - 5

L = 171

so, length of the field is 171 yards

Need help asap pleaseeeeeeeeee

Need help asap pleaseeeeeeeeee

Answers

Answer:5.7ft

Step-by-step explanation:

sin = opposite/adjacent

sin 35 = x/10

10 * sin 35 = x

x=5.7

bivariate regression can not demonstrate: question 19 options: a) when the two variables are linear. b) when the two variables are strongly inversely related. c) when the two variables are strongly positively related. d) when the two variables are causally related.

Answers

Bivariate regression can not demonstrate when the two variables are causally related.

The term variables in math means an alphabet or term that represents an unknown number or unknown value or unknown quantity.

Here we have to find the term that must not demonstrate the bivariate in math.

In order to find the resulting term, we must know the definition of bivariate regression.

The term bivariate regression in statistics is defined as the simple linear regression model which is used to predict one variable referred to as the outcome, criterion, or dependent variable from one other variable referred to as the predictor or independent variable.

Based on these definition we have identified that if the two variables are related then the regression process is not possible.

Therefore, option (d) is correct.

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Connor has made deposits of $125.00 into his savings account at the end of every three months for 15 years. If interest is 10% per annum compounded monthly and he leaves the accumulated balance for another 5 ​years, what would be the balance in his account​ then?

Answers

You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

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Which ordered pair would form a proportional relationship with the point graphed below?


On a coordinate plane, a line goes through points (0, 0), (10, 40) and (negative 10, negative 40).

Answers

Answer:

the answer is c

Step-by-step explanation:

HOPE THIS HELPS

Answer:

The answer is c

Step-by-step explanation:

I did the test on edge

An artist creates a​ cone-shaped sculpture for an art exhibit. If the sculpture is 8 feet tall and has a base with a circumference of 23.236 ​feet, what is the volume of the​ sculpture? Use 3.14 for pi .

Answers

Answer:

The volume of the cone-shaped sculpture is equal to 114.631 ft³.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Geometry

Circumference Formula:
\(\displaystyle C = 2 \pi r\)

r is radius

Volume Formula [Cone]:
\(\displaystyle V = \frac{\pi r^2 h}{3}\)

r is radiush is height

Step-by-step explanation:

Step 1: Define

Identify given.

h = 8 ft

C = 23.236 ft

Step 2: Find Radius r

[Circumference Formula] Substitute in variables:
\(\displaystyle \begin{aligned}C = 2 \pi r & \rightarrow 23.236 \ \text{ft} = 2(3.14)r \\\end{aligned}\)Solve [Equality Properties]:
\(\displaystyle \begin{aligned}C = 2 \pi r & \rightarrow 23.236 \ \text{ft} = 2(3.14)r \\& \rightarrow r = 3.7 \ \text{ft} \\\end{aligned}\)

Step 3: Find Volume

[Volume Formula - Cone] Substitute in variables:
\(\displaystyle \begin{aligned}V = \frac{\pi r^2 h}{3} & \rightarrow V = \frac{(3.14)(3.7 \ \text{ft})^2(8 \ \text{ft})}{3} \\\end{aligned}\)Evaluate:
\(\displaystyle \begin{aligned}V = \frac{\pi r^2 h}{3} & \rightarrow V = \frac{(3.14)(3.7 \ \text{ft})^2(8 \ \text{ft})}{3} \\& \rightarrow V = \boxed{ 114.631 \ \text{ft}^3 } \\\end{aligned}\)

∴ the volume of the artist-created sculpture is 114.631 ft³.

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Topic: Geometry

please help!!
I attached a picture!

please help!!I attached a picture!

Answers

1-
sides that are proportional
LM ~ ZY
MN ~ YX
NL ~ XZ

angles that are congruent (equal)
L = Z
M = Y
N = X

2-

RQ/PR = ZX/YZ



What is the correct equation to solve for x ?

cos (58) = x/11
tan (58) = 11/x
tan (58) = x/11
sin (58) = x/11

Answers

Answer:

\(x=11cos(58)\)

Step-by-step explanation:

Solve cos(58)=x/11 to find angles

\(x=11cos(58)\)

I hope this helps you

:)

What point is a solution to both equations: y = x - 8 and y = -3x + 16 ?

Answers

Answer:

(6,-2)

Step-by-step explanation:

graph and see the point where they cross and that is the solution

(-6,2) is the answer

What is 1/root 2
Give me that ans asap

Answers

Answer:

1/√2

Approximate numerical value

1/√2 = 0.707106781186548

---------------------------

Rationalize the denominator

(1/√2) * (√2 / √2) = √2 / 2

(37x+9)+(32x+2) whats the answer

Answers

Answer:

69x+11

Step-by-step explanation:

If f(x)= 3x2 +x-2. then f(-2) =

Answers

Your answer be 8 I do believe

The value of function f (- 2) is,

⇒ f (-2) = 8

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Function is,

⇒ f (x) = 3x² + x - 2

Now, We can plug x = - 2;

⇒ f (x) = 3x² + x - 2

⇒ f (-2) = 3(-2)² + (-2) - 2

⇒ f (-2) = 12 - 2 - 2

⇒ f (-2) = 8

Thus, The value of function f (- 2) is,

⇒ f (-2) = 8

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Report the following: (a). At what value does the CDF of a N(0,1) take on the value of 0.3? (b). At what value does the CDF of a N(0, 1) take on the value of 0.75? (c). What is the value of the CDF of a N(-2,5) at 0.8? (d). What is the value of the PDF of a N(-2,5) at 0.8? (e). What is the value of the CDF of a N(-2,5) at -1.2?

Answers

The values are as follows: (a) -0.52, (b) 0.68, (c) 0.7764, (d) the value of the PDF at 0.8 using the given parameters, and (e) 0.3300.

(a) The value at which the cumulative distribution function (CDF) of a standard normal distribution (N(0,1)) takes on the value of 0.3 is approximately -0.52.

(b) The value at which the CDF of a standard normal distribution (N(0,1)) takes on the value of 0.75 is approximately 0.68.

(c) The value of the CDF of a normal distribution N(-2,5) at 0.8 can be calculated by standardizing the value using the formula Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation. After standardizing, we find that Z ≈ 0.76. Using a standard normal distribution table or calculator, we can determine that the CDF value at Z = 0.76 is approximately 0.7764.

(d) The value of the probability density function (PDF) of a normal distribution N(-2,5) at 0.8 can be calculated using the formula f(x) = (1 / (σ * √(2π\(^(-(x -\) μ)))) * e² / (2σ²)), where x is the given value, μ is the mean, σ is the standard deviation, and e is Euler's number (approximately 2.71828). Plugging in the values, we can compute the PDF at x = 0.8.

(e) The value of the CDF of a normal distribution N(-2,5) at -1.2 can be calculated in a similar manner as in part (c). After standardizing the value, we find that Z ≈ -0.44. Using a standard normal distribution table or calculator, we can determine that the CDF value at Z = -0.44 is approximately 0.3300.

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The dimension of the row space of a 3 x 3 matrix A is 2. (a) What is the dimension of the column space of A? (b) What is the rank of A? (c) What is the nullity of A? (d) What is the dimension of the solution space of the homogeneous system Ax = 0?

Answers

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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What is the difference?

5−(−6)

answers
−11

−1

1

11

Answers

5-(-6)…a negative sign multiplied by a negative sign gives you a positive
5+6
11

The difference between the numbers 5 and −6 will be 11. Then the correct option is D.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The numbers are given below.

5 and −6

Then the difference between the numbers 5 and −6 will be

⇒ 5 − (−6)

Simplify the expression, then the value of the expression will be

⇒ 5 + 6

⇒ 11

The difference between the numbers 5 and −6 will be 11.

Then the correct option is D.

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solve for x : 15x - 3(3x+4)=6

Answers

The answer would be 20 if I’m correct
so brainly needs this to be 20 characters long but answer is x=3
solve for x : 15x - 3(3x+4)=6

54Find the exact value of x.

Answers

5/x = x/ 9

Cross-multiply

x² =45

Take the square root of both-side

x = 3√5 or 6.7082039325

Suppose a random sample of 35 cars are observed and their waiting time is recorded. What is the probability that the sample mean of the waiting times is less than 1.5 minutes

Answers

The probability that the sample mean of the waiting times is less than 1.5 minutes is approximately 0.0057, or 0.57%.

To calculate the probability that the sample mean of the waiting times is less than 1.5 minutes, we can use the Central Limit Theorem (CLT) since we have a large enough sample size (n = 35) and the waiting times are uniformly distributed.

According to the CLT, the sample mean of a sufficiently large sample size will follow an approximately normal distribution, regardless of the underlying distribution. In this case, the population mean is E(X) = 2 (the midpoint of the uniform distribution between 0 and 4), and the population standard deviation is σ(X) = √(4²/12) = √(16/12) = √(4/3) ≈ 1.155.

The standard deviation of the sample mean (also known as the standard error) is given by σ(X)/√(n), which in this case is approximately 1.155/sqrt(35) ≈ 0.196.

To calculate the probability that the sample mean is less than 1.5 minutes, we can standardize the value using the z-score formula:

z = (sample mean - population mean) / standard error

z = (1.5 - 2) / 0.196 ≈ -2.551

Next, we can look up the probability corresponding to this z-score in the standard normal distribution table.

From the table, we find that the probability of obtaining a z-score less than -2.551 is approximately 0.0057.

Therefore, the probability that the sample mean of the waiting times is less than 1.5 minutes is approximately 0.0057, or 0.57%.

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