you buy 15 apples and a $2.75 block of cheese. the bill cost $6.20. write and solve an equation to find "a" the cost of each apple

The original equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. A perpendicular line to Y = -4x + 7 would be Y = 4x + 7.

To find the equation of a line perpendicular to Y = -4x + 7, we need to switch the x and y variables and then change the sign of the slope.

The original equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Since the original equation has a slope of -4, the perpendicular line will have a slope of 4.

Therefore, the equation for the perpendicular line is y = 4x + b.

We can find the y-intercept by plugging in a point from the original equation.

For example, if we plug in (0,7), we get 7 = -4(0) + b, or b = 7.

Therefore, the equation for the perpendicular line is y = 4x + 7.

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The closure property of addition states that the sum of two whole numbers will always be a whole number.

A whole number is a set of all positive integers from 0 to infinity.  Now we all know that if we add two positive numbers up, the sum will either remain constant (if the number is 0) or be greater than both numbers. This means that the sum of two whole numbers has to be a whole number.

Example 1 If we add 0 and 45

0 + 45

= 45

We already know that 45 is a whole number.

Example 2- If we add 486 and 354

486 + 354

= 840

From the definition, we can say that 840 is a whole number.

This is the closure property.

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The required exponent form is obtained as 2 x 2 x 2 x 2 = 2⁴.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

The given expression is 2 x 2 x 2 x 2.

It can be written in exponent form as,

2 x 2 x 2 x 2

The number 2 is multiplied to itself by four times,.

Thus, the exponent form is given as 2⁴.

Hence, the exponent form of the given expression is 2⁴.

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The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process

The t-value will be equal to 1.39 for the given statistics.

To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.

The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:

H0: µ ≤ 5.5

The alternative hypothesis is that the mean processing time is greater than 5.5 hours:

Ha: µ > 5.5

We will use a significance level of 0.05.

The formula for the t-test statistic is:

t = (X - µ) / (s / √n)

Where:

X = sample mean

µ = hypothesized population mean

s = sample standard deviation

n = sample size

Substituting the given values, we get:

t = (6 - 5.5) / (2 / √21) = 1.386

The degree of freedom for the t-test is n-1 = 20.

Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.

Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.

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Answer: nose

Step-by-step explanation:

The value of (x,y) on the given points of the function will be (-2,10),(-1,7),(0,4),(1,1), and (2,-2).

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

As per the given function,

f(x) = 3(2 – x) –2

Put x = -2

f(-2) = 3(2 + 2) - 2 = 10 thus, (-2,10)

Put x = -1

f(-1) = 3(2 + 1) - 2 = 7 thus, (-1,7)

Put x = 0

f(0) = 3(2 - 0) - 2 = 4 thus, (0,4)

Put x = 1

f(1) = 3(2 - 1) - 2 = 1 thus, (1,1)

Put x = 2

f(2) = 3(2 - 2) - 2 = -2 thus, (2,-2)

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Answer:

y=-1.25x+7

Step-by-step explanation:

See the image

[tex]3^4x=9^3x+7[/tex]

Simplify:

[tex]81x=729x+7[/tex]

Subtract 729x from both sides:

[tex]81x-729x=729x+7-729x[/tex]

[tex]-648x=7[/tex]

Divide both sides by -648:

[tex]\dfrac{-648x}{-648} =\dfrac{7}{-648}[/tex]

[tex]\fbox{x = $\dfrac{-7}{-648}$}[/tex]

Answer:

y = 3/5x + 2

Step-by-step explanation:
Parallel lines have the same gradient, so

y = 3/5x + c

Put in your point (-5,-1):

(-1) = 3/5(-5) + c

-1 = -3 + c

-1 + 3 = c

2 = c

So

y = 3/5x + 2

There are 160 possible area codes can be created with this format.

A process determining the number of possible arrangements in a collection of items in which the order of the selection does not matter is called combination.

Given that, When three-digit telephone area codes were first put in place in the United States and Canada, the first number could be any digit from 2 through 9, the second number could only be 0 or 1, and the third number could be any digit from 0 through 9.

So, according to question,

The first digit has about 8 options

The second digit has about 2 options

The third digit has about 10 options

Therefore, the total possible code = 8×2×10=160.

Hence, 160 possible codes are there.

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The Question is based on concept of Cost Price and selling Price is 5.2$

What is Cost PRice and Selling PRice?

Cost price is the actual price of an object where as selling price is the price in which seller sells it to customer

Solution

Cost Price of batteries = 4$

and shopkeeper can charge upto 30% interest

hence selling price will be 4$ + 30% of 4$

= 4 + 30/100(4)

= 4 + 1.2

5.2$

Hence answer to this Question is 5.2$

and this 5.2$ is the selling price of duracell batteries whereas 4$ was the cost price for the same

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The probability that there is at least two 4s in the three throws is [tex]\frac{2}{27}[/tex]

Permutations and combinations

permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor

given that

we throw a fair die three times

Due to the fact that each die has a 4 on it, the equation would be [tex]\frac{1}{6}[/tex]+ [tex]\frac{1}{6}[/tex]+ [tex]\frac{1}{6}[/tex]=[tex]\frac{1}{2}[/tex] if all the dice were added together.

(There are fifteen ways to get 2 fours: 441,414,144,442,424,244.. and so on until 446,464,644; another way to get the solution is using permutations and combinations:

=(1[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])(5[tex]C_{1}[/tex])+1[tex]C_{1}[/tex])(5[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])+(5[tex]C_{1}[/tex](1[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])/[tex](6C_{1} )^{3}[/tex]

=  [tex]\frac{1+15}{216}[/tex]

=[tex]\frac{2}{27}[/tex]

The probability that there is at least two 4s in the three throws is [tex]\frac{2}{27}[/tex]

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The terminal ray of an angle measuring negative startfraction 10 over 9 endfraction pi lies in the Second quadrant. this angle measures 200°.

The standard Cartesian coordinate plane is divided into four quadrants as shown in the figure above.

Angle measure: This is the unit of measure used to determine the distance between two lines joined at a common vertex. Subtract 360 to find the quadrant in degree units.

We have given that,

the angle = - 10π/9°

As we know that , π = 180°

so, - 10π/9° = (-10×180/9)° = - 200°

Now, we check the quadrant for angle - 200°

For this follow the above steps,

So, the required quadrant is second .

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The negation of the given statement " Everyone failed the quiz today " is given by " No one failed the quiz today."

As given in the question,

Given statement is written as:

S : Everyone failed the quiz today.

Negation of the given statement represent the conversion of true statement into false statement or conversion of false statement into true statement.

Here given statement is true statement.

Convert the given statement into false statement.

So Negation of statement S is represented by ~ S.

~S : No one failed the quiz today.

Therefore, the negation of the given statement is equal to " No one failed the quiz today".

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Answer:

Irrational

Step-by-step explanation:

An irrational number added to any other real numbers still keep its infinitely long and never repeating decimals, leaving it still irrational.

Answer:

The conclusion is incorrect because there is exactly one solution to the equation.

Step-by-step explanation:

8x - 12 = 4(12x - 6)

4 x 12x = 48x    4 x -6 = -24

8x - 12 = 48x - 24

Move the terms

8x - 12 - 48x = -24

Move the constant to the right-hand side and change its sign

8x - 48x = -24 + 12

-40x = -24 + 12

-40x = -12

Divide both sides by -40

40x  =  -12

40    =   40

x = [tex]\frac{3}{10}[/tex]  or, alternate form, x = 0.3

Answer: 7w + 6

Step-by-step explanation:

Your question was "7w + 6". When we simplify this, we get 7w + 6. So your answer is 7w + 6.

Answer:

25

Step-by-step explanation:

Answer:25

Step-by-step explanation:

Answer:

Step-by-step explanation:

g

Step-by-step explanation:

16.            +.        5

__.                    ____
7(x+4).                7 (x-3)

The shortest length of fence that the rancher can use is 6000ft

Given that

x = width of rectangle

y = length of rectangle

A = area of rectangle = x*y = 1500000 [tex]ft^{2}[/tex]

L = length of fencing needed = 2(x + y) + x = 3x + 2y

L = 3x + 2([tex]\frac{1500000}{x}[/tex]) = 3x + 3([tex]10^{6}[/tex])[tex]x^{-1}[/tex]

As x –> 0+, L –> +inf.

As x –> +inf, L –> (3x)+.

There will be a minimum in Quadrant I.

dL/dx = 3 - 3([tex]10^{6}[/tex])[tex]x^{-2}[/tex]

dL/dx = 0:

3 - 3([tex]10^{6}[/tex])[tex]x^{-2}[/tex] = 0

3([tex]10^{6}[/tex])[tex]x^{-2}[/tex]= 3

([tex]10^{6}[/tex])[tex]x^{-2}[/tex] = 1

[tex]x^{2}[/tex] = [tex]10^{6}[/tex]

x > 0, so x = 1000 feet for shortest length.

Shortest L = 3000 + 3([tex]10^{6}[/tex])([tex](10^{3} )^{-1}[/tex])= 6000 feet.

The shortest length of fence that the rancher can use is 6000ft

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There are two ways to find the remainder when a polynomial in x is divided by a binomial of the form x-r, the use of synthetic division or calculate P(r).

Synthetic division

The Synthetic division is a shortcut way of polynomial division, especially if we need to divide it by a linear factor. It is generally used to find out the zeroes or roots of polynomials and not for the division of factors.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

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By using Pythagoras' theorem the required length of the cable  is 85 feets.

The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem. Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case because it is opposite the angle of 90°.

The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of a right-angled triangle. Alternatively, the sum of the squares of a right triangle's two legs equals the square of its hypotenuse.

Given:

Height of the tower = 68 feet = perpendicular

distance of box form tower = 51 feet = base

Let's assume lenght of the cable = L = hypotenous

Acoording to the question by using Pythagoras' theorem,

[tex]hyp^{2}= perpendicular^{2} +base^{2} \\(L)^2 = (68)^2 + (51)^2\\L^2 = 4624 + 2601\\L^2 = 7225\\L =\sqrt{7225}\\L = 85 feet[/tex]

Hence by using Pythagoras' theorem the required length of the cable  is 85 feets.

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Answer:

Step-by-step explanation:

0.0154, I think, I apologize if this is wrong.

1/5 or -1/9 would both be correct

The total urine patient/client has been measuring at home is 2.838 liters.

Given that,

the patient/client has been measuring urine at home with a quart milk carton and states voiding 1 quarts 2 days ago and 2 quarts yesterday.

We know that 1 quart = 0.946 litre

and 2 quarts = 1.892 litre

Therefore total amount = 0.946 + 1.892

                                       = 2.838

Hence the total urine patient/client has been measuring at home is 2.828 litres.

What is Quart?

The quart is an English unit of volume equal to a quarter gallon. It is a quarter of a gallon. Measurement of volume, capacity. Its unit of measurement for liquids, equal to approximately 1.14 litres in the UK, or 0.95 litrs in the US.

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The formula is = 7 and 3. It may be used to calculate the number regular mall boxes as well as the number of big boxes.

What is the world's most difficult arithmetic problem? A mathematical conundrum that has baffled mathematicians over decades is finally solved earlier this week. Diophantine Equation, sometimes referred to as the "sum of three cubes," is what it is: Find x, y, & z such that, for any k between 1 and 100, x3+y3+z3=k.

Let x= Number of small boxes , y = Number of large boxes.

As per given , 30x+55y=375 (i)

x+y=10 (ii)

Multiply (ii) by 30, we get

30x+30y=300 (iii)

Eliminate (iii) from (i), we get

25y=75

⇒ y= 3

Put y=3 in (ii), we get

x+3=10 ⇒ x=7

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The first term of the geometric progression= 1/5

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

Given:

The second term = 3/10

The sixth term = 243/ 160

The formula for the nth term of geometric sequence is given by

an = a1 r^(n-1 ) , a1 = first term , r= common ratio

Substitute n=2

a2 = a1 r^(2-1 ) ..................(1)

3/10 = a1* r

Substitute n=6

243 / 160 = a1 r^5 ..............(2)

dividing equation 2 by 1 , we get

r^4 = 5.0625

=> r = 1.5

Substitute this value of r into equation 1

3/10 = a1 * (1.5)

a1 = 0.2

So, the first term = 1/5

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Answer: 4:5

Step-by-step explanation: The lowest form

Answer:

Step-by-step explanation:

4:5