Write and solve an equation.

A drink and 7 pizzas cost $94.25. The cost of the drink was $1.50. What was the cost, c, of one pizza?

The interest George Jimerson would earn by June 30 be $83368.21

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let y represent the amount of money in Jimerson savings account after x days.

The account pays 5.5% interest compounded daily, hence:

y = 6521.37(1.055)ˣ

In June 30, the number of days from April 11 is 49. Hence;

y = 6521.37(1.055)⁴⁹ = 89889.58

The interest = 89889.58 - 6521.37 = 83368.21

The interest would be $83368.21

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The plumber bought 5 pieces of copper wire and 5 pieces of plastic wire.

What is an equation?

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.

Length of each piece of copper wire = 6 m

Length of each piece of plastic wire = 1 m

Total number of pipes bought = 10

Total length of pipes = 35 m

Let the number of copper pipes be x.

Let the number of plastic pipes be y.

The equation for number of pipes will be -

x + y = 10...(1)

The equation for length of pipes will be -

6x + y = 35...(2)

Subtracting equation (1) from (2) -

5x = 25

x = 5

Substituting the value of x in equation (1) -

5 + y = 10

y = 10 - 5

y = 5

Therefore, the number of copper and plastic wires is 5 each.

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The expression √5x × √30x is simplified using the product rule to give 12.25x

Square root of a number can be defined as the inverse operation of the square of a number.

It is the number obtained by finding a number that when squared would give the original number.

Square root is represented using the symbol '√ '. The symbol is called a radical.

Also, the number under the symbol is called the radicand.

To multiply two square roots, we have to multiply the radicands and leave the radical sign.

From the information given, we have;

√5x × √30x

Multiply the radicands and retain the square root symbol, we have;

√150x²

Find the square root

12.25x

Hence, the value is 12.25x

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Answer:

7x2−4x/5

Step-by-step explanation:

7x2−4x over 5

The cost of labor per hour is $125.

The equation that can be used to solve for the cost of labor per hour is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

The form of the linear equation is:

Total cost = cost of the parts + (cost per hour x total hours worked)

$585.25 = $54 + (4.25 x d)

$585.25 = $54 + 4.25d

In order to determine the value of x, take the following steps:

Combine similar terms:

$585.25 - $54 = 4.25d

Add similar terms

$531.25 = 4.25d

Divide both sides of the equation by 4.24

d = 531.25 / 4.25

d = 125

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The dimensions of the sides of the triangular flower bed are 27ft, 54ft and 52ft.

A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.

Given the data in the question;

Let the shortest side b x.

Since a triangle has three side, the perimeter of the triangle will be;

Perimeter = side 1 + side 2 + side 3

Plug in the values and solve for x

133 = x + 2x + x +25

133 = 4x + 25

133 - 25 = 4x

108 = 4x

4x = 108

x = 108/4

x = 27

Therefore, the dimensions of the flower bed are;

Shortest side = x = 27ft

Second side = 2x = 2( 27) = 54 ft.

Third side = x + 25 = 27 + 25 = 52 ft

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The point at which the perpendicular bisectors of a triangle's sides come together is known as the circumcenter of that triangle. The line's equation is x=-2.5.

The circumcenter is, in other words, the point at which the bisector of a triangle's sides coincides. P serves to indicate it (X, Y).

This intersection represents the point on the triangle's perimeter. Distance d = (a - ax)2 + (b - bx)2 is the geometry formula for distance. "d" represents the separation between a vertex and the circumference, where x = 1, 2, 3.

The junction of the perpendicular bisectors of each side of the triangle, or the lines that are perpendicular to each side's midpoint, is where the triangle's circumcenter can be located.

To determine it, we locate the intersection of the circumcenter and the first name of the triangle, which is the point at which each line intersects the other

(-4,0) B=(-4,-4) C=(-1,-4) (-1,-4) (-4, -2),

y=-2 is the perpendicular line to AB's midpoint.

The intersection of the line at (-2.5,-2) and (-5/2,-2)

where BC's midpoint is located.

The line's equation is x=-2.5.

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a) The 99% confidence interval for the proportion of all adults in the United States who would have chosen the minimum wage statement is given as follows: (0.3926, 0.4474).

The interpretation is that we are 99% sure that the true population proportion is in this interval.

b) The condition has to be satisfied as the confidence interval is constructed considering an assumption of normality, and by the Central Limit Theorem, at least 10 successes and 10 failures are needed for the sampling distribution of sample proportions to be normal.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The sample size and the estimate are given as follows:

[tex]n = 2150, \pi = 0.42[/tex]

Hence the lower bound of the interval is given as follows:

[tex]0.42 - 2.575\sqrt{\frac{0.42(0.58)}{2150}} = 0.3926[/tex]

The upper bound of the interval is given as follows:

[tex]0.42 + 2.575\sqrt{\frac{0.42(0.58)}{2150}} = 0.4474[/tex]

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Answer:

Step-by-step explanation:

640 - 10x^2 = (4x-10)(160 + 4x)

The factors of 640-10x^2 are (4x-10) and (160 + 4x).

Answer:

To solve this problem, we will use the following steps:

Step 1: Let's assume that the number of quarters is x, and the number of dimes is y

Step 2: We know that the number of dimes is three more than four times the number of quarters, so we can write the equation: y = 4x + 3

Step 3: We also know that Chi has $13.30 in dimes and quarters. Since dimes are worth $0.10 and quarters are worth $0.25, we can write the equation: 0.25x + 0.10y = 13.30

Step 4: Now we have two equations with two unknowns, we can substitute one equation into another to find the value of x and y.

y = 4x + 3

0.25x + 0.10(4x + 3) = 13.30

0.25x + 0.40x + 0.30 = 13.30

0.65x = 13

x = 20

Step 5: We can substitute the value of x in one of the equation, to find the value of y

y = 4(20) + 3

y = 83

Final Answer: Chi has 20 quarters and 83 dimes.

Note: We can check our solution by multiplying the number of quarters by $0.25 and the number of dimes by $0.10 to check if the total money is $13.30 which is true.

Answer:

25 median. 29 mean.

Step-by-step explanation:

7, 16, 18, 25, 43, 47, 47

25 is the middle number when ordered by value, so 25 is the median

7 + 47 + 43 + 47 + 25 + 16 + 18 = 203

203 / 7 (amount of numbers in the set) = 29

29 mean

1.600 amps of current flow through resistor r3 are measured.

A resistor is a passive, two-terminal electrical component used in circuits to apply electrical resistance.

Resistors are employed in electronic circuits for a variety of purposes, including reducing current flow, adjusting signal levels, dividing voltages, biassing active devices, and terminating transmission lines.

The parameters are determined by the query:

total current = 2 amperes

Total resistance = 80 ohms

Total current = voltage * Resistance

Total current = 2* 80

= 160V.

Consequently, the current passing through resistor R3 will be

V= IR (Ohms law)

where I (current)= V/R

current = 160/ 100

Current flowing through R3 =1.600  amperes.

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Answer:

no

Step-by-step explanation:

An identity is an equality that is always true. An equation is an equality that is (only necessarily) conditionally true.

That is to say that for any real value inputted into a variable in an identity, an equality will result, whereas only certain values for a variable in an equation will necessarily result in an equality.

If the given equation is an identity, it should result in an equality no matter what the input for k is. So, to prove that it isn't an identity, we simply have to find one value for k that results in an inequality. To do so, we can simply plug in 0 for k and simplify.

[tex]k - 4 = 4 + k[/tex]

[tex]0 - 4 \stackrel{?}{=} 4 + 0[/tex]

[tex]-4 \ne 4[/tex]

We have found one value for k that results in an inequality. Thus, this equation is not an identity.

The regression equation, given the line of best fit and the points on the line, would be F ( x ) = 30x + 685

To find the regression equation, you first need to find two points on the line on the graph. Those two lines would be ( 3, 775) and ( 4 , 805).

The next step would be to find the slope of the line :

= ( Y₂ - Y ₁ ) / ( X ₂ - X  ₁ )

= ( 805 - 775 ) / ( 4 - 3 )

= 30 / 1

= 30

Then use the points to find the y - intercept :

y =  mx + y- intercept

775 = 30 ( 3 ) + y - intercept

y - intercept = 775 - 90

y - intercept = 685

The regression equation is:

F ( x ) = 30x + 685

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Using the above equation 1/i is equal to 2/(9-5j^2+3k)

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given; 2i+5j^2-3k=9

2i+5j^2-3k=9

2i=9-5j^2+3k

i=(9-5j^2+3k)/2

1/i=2/(9-5j^2+3k)

Therefore, the value of 1/i according to the given equation will be

2/(9-5j^2+3k)

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Answer:

1.  Hypothesis: "All 120° angles"

    Conclusion: "are obtuse angles"

    If-then statement: If an angle measures 120°, then it is an obtuse angle.

2.  It is not raining.

Step-by-step explanation:

Conditional statement

"If this happens, then that will happen."

For the statement "All 120° angles are obtuse angles":

Therefore, the statement written in the if-then form is:

Given statement:

The definition of a negation of a statement is the opposite of the given statement.  For example, the negation of statement "p" is "not p."

Therefore, the negation of the given statement is:

Answer: The probability that a waitress will refuse to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students from among ten students of which four are not of legal age is 0.288 or 28.8%.

Step-by-step explanation:

he probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated using the binomial probability formula.

The binomial probability formula is: P(x) = (n choose x) * p^x * (1-p)^(n-x)

Where:

x = the number of successful outcomes (in this case, the number of minors refused service)

n = the total number of trials (in this case, the number of IDs checked)

p = the probability of a successful outcome in a single trial (in this case, the probability that a randomly chosen student is a minor)

In this case:

x = 3 (the number of minors refused service)

n = 5 (the number of IDs checked)

p = 4/10 (the probability that a randomly chosen student is a minor)

So, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated as:

P(3) = (5 choose 3) * (4/10)^3 * (6/10)^2 = (10/3) * (0.16) * (0.36) = 0.288

Therefore, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students is 0.288 or 28.8%.

It's worth noting that this problem assumes that the waitress randomly chooses the 5 students, if the waitress doesn't pick them randomly the result may be different.

Step-by-step explanation:

For 60 muffins sold there are 3 boxes, because there are 20 muffins per box.

For 600 muffins sold there are 30 boxes, because there are 20 muffins per box.

For 6000 muffins sold there are 300 boxes, because there are 20 muffins per box.

Because 2×3=6

A quadratic equation, or second-order polynomial equation with a single variable, has the form ax^2 + bx + c = 0. The solution to the given equation is v = 7, -5 and 3

The form ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given the quadratic expression below:

(v-7)(v+5)(v-3)=0

Required

The solution to the system of equation

Equate each expression to zero calculate the value of 'v' as shown:

v - 7 = 0

v = 0 + 7

v = 7

Also, v + 5 = 0

v = 0 - 5

v = -5

Similarly, v - 3 = 0

v = 0 + 3

v = 3

Hence the solution to the given equation is v = 7, -5 and 3

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[tex] \sf {x}^{2} + 5x - 14 \\ \sf {x}^{2} - 2x + 7x - 14 \\ \sf x(x - 2) + 7(x - 2) \\ \sf \: (x - 2)(x + 7) = 0 \\ \sf \: x = 2 \: and \: x = - 7[/tex]

Answer:

1.6 g/cm³

Step-by-step explanation:

230g = 0.23 kg

0.23 kg x 8 = 1.84 kg

So, the weight of chutney in the 8 jars is 5.68kg - 1.84kg = 3.84kg or 3840g.

So, 1 jar weight is 3840g/8 or 480g of chutney.

Density = 480/300 or 1.6 g/cm³

Answer:

2.36

Step-by-step explanation:

5.68 kg into grams = 5680 and 300*8 is 2400

5680/2400 is 2.36

Answer:

Step-by-step explanation:

The problem can be solved by using the information provided to set up a system of equations and then solving for the unknown variable, which in this case is the fixed charge.

Let x be the fixed charge.

We know that the total cost of the 11-mile trip is the fixed charge plus the charge for the distance covered, so we can write the equation:

x + 11y = 88 (1)

We also know that the total cost of the 16-mile trip is the fixed charge plus the charge for the distance covered, so we can write the equation:

x + 16y = 108 (2)

Where y is the cost per mile

We can solve for y by subtracting equation (1) from equation (2), so:

16y - 11y = 108 - 88

5y = 20

y = 4

Now we know that cost per mile is 4$, we can substitute it in equation (1)

x + 11(4) = 88

x = 24

Now we know the fixed charge is 24$ and cost per mile is 4$, we can calculate the fare for 6 miles

24 + 6(4) = $48

Therefore, Linus would have to pay $48 to travel 6 miles.

The perimeter of the parallelogram is greater than the perimeter of the square.

What is a perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. The perimeter of a shape is obtained by adding up the length of all the sides and edges of the shape. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

Now, let's assume a geometric system of a square and a parallelogram having the same base and equivalent side of the square " a ".

Therefore, the respective two parallel sides of the Parallelogram will also be equal to " a ".

Now, let's rotate the one of the parallel lines with angle Φ clockwise then, the side lengths which aren't equal and parallel to the first set will get increased and it's incremental rate will be responsible for the increase in perimeter of the figures aslike , perimeter is the sum of the sides of the figure.

Now let's rotate alternate side length at maximum at angle θ , aslike it should touch the square at diagonally opposite angles ,

Now, let's calculate perimeters of both the figures -

Square of side length " a " = a + a + a + a = 4a

Parallelogram of two base side length " a " and two parallel set lines of length √2a

= a + a + √2a + √2a

= 2a + 2√2a

= 2a [ 1 + √2 ]

Hence, the acquired perimeter of Parallelogram is greater than that of square

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Answer: The formula for the mathematical function that takes as input an RGB color vector ⟨r,g,b⟩ and yields as output the RGB color vector that is the unique shade of gray whose total amount of light (r+g+b) is equal to that of the input is:

(r+g+b)/3, (r+g+b)/3, (r+g+b)/3

Step-by-step explanation: RGB color space is a way to represent colors digitally, where each color is represented by a combination of red, green, and blue values ranging from 0 to 255. To obtain a unique shade of gray whose total amount of light (r+g+b) is equal to that of the input color, we have to set all three color channels to the average value of the red, green and blue values.

To calculate this average value we use the formula: (r+g+b)/3

So the output of the function is ⟨(r+g+b)/3, (r+g+b)/3, (r+g+b)/3⟩ which is the unique shade of gray whose total amount of light is equal to that of the input color.

Note: This is one way to convert color to gray, other methods exist like using luminosity or other weights to RGB channels.

If Just before Henderson Laboratories opened for business. The totals that would appear in the firm’s fundamental accounting equation is $96,875

Using this formula

Assets = Liabilities + Owner’s Equity

Total Owners Equity = Assets - Liabilities

Where:

Assets:

Assets = Laboratory Equipment + Laboratory supplies+ Cash

Assets=$75,000 + $6,200 + $39,900

Asset= $121,100

Liabilities:

Liabilities= Loan Payable+ Accounts Payable

Liabilities = $14,500 + $9,725

Liabilities= $24,225

Let plug in the formula

Total Owners Equity = Assets - Liabilities

Total Owners Equity =$121,100 - $24,225

Total Owners Equity= $96,875

Therefore the totals that would appear in the firm’s fundamental accounting equation is $96,875.

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The complete question is:

Just before Henderson Laboratories opened for business, Eugene Henderson, the owner, had the following assets and liabilities. Cash $ 39,900 Laboratory equipment 75,000 Laboratory supplies 6,200 Loan payable 14,500 Accounts payable 9,725. Determine the totals that would appear in the firm’s fundamental accounting equation (Assets = Liabilities + Owner’s Equity).

Given a set A={1,2,3,4,5,6,7}, a relation induced by the partition of set A is

(1,2,3) -> {1,2,3}, (4,5) -> {4,5}, (6,7)-> {6,7}

Generally, A set comprises elements or members that may be mathematical objects of any sort, including numbers, signs, points in space, lines, other geometric forms, variables, or even other sets. A set is a mathematical formula for a collection of various things.

A relation induced by a partition of a set is a relation that defines a way of grouping elements in the set into subsets, called "blocks" or "cells". In this case, the set

A={1,2,3,4,5,6,7}

can be partitioned into at least 3 subsets. For example, one possible partition is

A={1,2,3}, {4,5}, {6,7}.

The relation induced by this partition is a relation that assigns to each element in one of the 3 subsets, i.e.

(1,2,3) -> {1,2,3}, (4,5) -> {4,5}, (6,7)-> {6,7}

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