50 pounds of pet food for $37.99? what is the unit rate?

Answer:

width = 6 ft

length = 21 ft

Step-by-step explanation:

Forming algebraic expressions and finding the dimensions of a rectangle:

 Width = w ft

 length =  3*w + 3 = (3w + 3) ft

              2l +2w = P

 2(3w + 3) + 2w = 54

Use distributive property to open the brackets,

 2*3w + 2*3 + 2w = 54

        6w + 6 + 2w = 54

Combine like terms,

          6w + 2w + 6 = 54

               8w   + 6   = 54

Subtract 6 from both sides,

                      8w    = 54 - 6

                         8w = 48

Divide both sides by 8

                           w = 48 ÷ 8

                           [tex]\sf \boxed{\bf w = 6 \ ft}[/tex]

l = 3w + 3

 = 3*6 + 3

 = 18 + 3

l = 21 ft

The equation of the line with slope −6 which goes through the point (−9,−6) = y = -6x + 9.

When you know the slope of something like the line to be investigated and the point given also contains the y-intercept, you can utilize the slope-intercept formula y = MX + b. (0, b). The y value of the y-intercept  point is represented by b in the formula.

A line's slope is the ratio of how much y grows as x increases by a certain amount. The slope of a line indicates how steep it is, or how much y grows as x increases.

The slope of the line = -6  = m

The points (−9,−6). x = -9 , y = -6

Find the y-intercept.

y=mx+b

Substituting the value we get:

-6 = (-6 x -9) + b

-6 = -54 x b

b = 54/6

b = 9.

The equation in slope intercept form as:

y=mx+b

y = (-6)x + 9

y = -6x + 9

The equation of the line with slope −6 which goes through the point (−9,−6) = y = -6x + 9.

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Using proportions, it is found that the cost per ounce is of $0.8.

The missing information is the number of ounces in the balm, that is of 20.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The cost per ounce is given by the proportion of the cost by the number of ounces, hence:

Then:

$16/20 = $0.8.

The cost per ounce is of $0.8.

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The weight of the fruits in ounces is 40 ounces

The pints of water dispensed after 50 seconds is 56 pints

The mathematical operations that would be used to determine the answer is multiplication. Multiplication is the process of determining the product of two or more numbers. Multiplication is represented with the sign - x.

A mixed fraction is a non-integer that is made up of a whole number and a proper fraction. An example of a mixed fraction is 2 1/2.

Weight of the fruits in ounces = 2 1/2 x 16

5/2 x 16 = 40 ounces

Pints of water dispensed after 50 seconds = gallon per second x 50 x 4 x 2

0.14 x 50 x 4 x 2 = 56 pints

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The original logo is a triangle and measures

1.5in x 1.5in

Magnification is

Original shirt = 1:8

Shirt logo area

A = 1/2bh

A = 1 / 2 * (1.5 * 8) (1.5 * 8) = 72 square inches

The area is a quantity that describes the extent of an area on a plane or curved surface. Planar region or planar region area refers to the area of ​​a shape or planar layer, and surface area refers to the open surface or boundary area of ​​a three-dimensional object.

The area is defined as the total space occupied by a planar (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. A two-dimensional character. The space a shape occupies on paper is called its area. Now imagine that the square is made up of smaller unit squares.

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The function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

We are given the function:

f ( x ) = 2 x² + 5

We need to find the value of f ( -3 ).

We will do this by substituting the value of x = - 3 in the function and then evaluating the expression.

Putting x = -3 in the function, we get that:

f ( x = - 3 ) = 2 (- 3)² + 5

Solving the square, we get that:

f (- 3) = 2 ( 9 ) + 5

Simplifying the expression, we get that:

f (- 3) = 18 + 5

f (- 3) = 23

Therefore, we get that, the function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

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Answer: -8

Step-by-step explanation:

First, you plug -1 in for x

[tex]f(x)=f(-1)=(-1)^2 -9[/tex]

[tex]=1-9=-8[/tex]

The value of d is 18.

Given, the slope of the line is 3.

Slope equals a height change (Change in width) You may also say that a slope is a climb or a run. This formula changes if the graph's horizontal axis is represented by x and the vertical axis by y: Slope is equal to (y-change)/ (Change in x)

Two points which lie are N(₋2 , 3) and D(3,d)

slope of the line = y₂ ₋ y₁/x₂ ₋ x₁

let the points N(₋2 , 3) be (x₁ , y₁)

and D(3,d) be (x₂ , y₂)

therefore, 3 = d ₋ 3/3 ₋ (₋2)

3 = d ₋ 3/3 ₊ 2

3 = d ₋ 3 / 5

15 = d ₋ 3

d = 15₊3

d = 18

Hence we get the value of d as 18.

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Using exponent properties, the equivalent expression is given as follows:

[tex]\left(\frac{2}{3}\right)^14[/tex]

Two thirds to the fourth power is given by:

[tex]\left(\frac{2}{3}\right)^4[/tex]

Two thirds to the third power is given by:

[tex]\left(\frac{2}{3}\right)^3[/tex]

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:

[tex]\left(\frac{2}{3}\right)^4 \times \left(\frac{2}{3}\right)^3 \left(\frac{2}{3}\right)^{4 + 3} = \left(\frac{2}{3}\right)^7[/tex]

Then, this entire expression is raised to the second power, meaning that:

[tex]\left[\left(\frac{2}{3}\right)^7\right]^2 = \left(\frac{2}{3}\right)^7 \times \left(\frac{2}{3}\right)^7 = \left(\frac{2}{3}\right)^{7+7} = \left(\frac{2}{3}\right)^14[/tex]

[tex]\left(\frac{2}{3}\right)^14[/tex] is the equivalent expression.

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The simplified rational number that represents this scenario is 1/4

The given parameters are:

14 programming errors for every 56 programmers

The above means:

Error : Actual = 14 : 56

Express as fraction

Error/Actual = 14/56

Simplify the ratio

Error/Actual = 1/4

Hence, the simplified rational number that represents this scenario is 1/4

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The first integer is 16 and the next two integers are 17 and 18. The largest one is 18

What in math is an integer?

The first integer will be called x. Consequently, the second integer is x+1 and the third is x+2 (this is because they are consecutive integers). The total of these three numbers is 51, so build up the following equation and answer it.

x+(x+1)+(x+2)=51

3x+3=51

3x=48

x=16

Therefore, the first integer is 16 and the next two integers are 17 and 18. The largest one is 18 and this is the answer.

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Answer:

1.3 is the correct answer

Step-by-step explanation:

Answer:

non

Step-by-step explanation:

bc its not a straight line

Answer: Non-linear

Step-by-step explanation:

It’s not a straight line and there is no pattern.

Answer:

+ 1.45

Step-by-step explanation:

the end result is 16.55, therefore you add 1.45 to get $18 again.

Answer:

0.139

Step-by-step explanation:

total = 43 + 56 + 16 = 115

country songs = 16

p(country song) = 16/115 = 0.139

The approximate location of the dolphin is 155 feet as it moves at the rate of 6.2 feet per second.

Rate in defined as the speed or the distance travelled by the dolphin in unit time.

Given the rate of the dolphin is  feet per second .

Time taken by the dolphin is 25 seconds.

∴ distance travelled is given by rate × time

Hence distance travelled is 6.2 × 25 = 155 feet

Therefore the approximate location is given by 155 feet from the starting point.

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There is no solution for the given equation i.e.10[x] =2.5

Equation:

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 two mathematical expressions.

Greatest integer function:

The largest integer function is one that yields an integer that is closest to the specified real value. Additionally known as the step function. The closest integer is used to round off the input using the biggest integer function. Thus, the equation to determine the largest integer is fairly straightforward. It is symbolised by [x]  where x can take on any value.

⇒10[x] =2.5

⇒[x] =[tex]\frac{2.5}{10}[/tex]

⇒[x] =0.25

⇒[x] will be always a interger.As a result there is no solution for the given equation.

Therefore,There is no solution for the given equation i.e.10[x] =2.5

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The raw score from the given table that corresponds with the 20th and 30th percentiles are;

First distribution;

Second distribution;

The Z–Score percentile normal distribution table can be used to find the Z–Score that gives the percentile value of a raw score.

The Z–Score, also known as the standard score, gives the number of standard deviations, a raw score is far from the mean.

The mathematical equation for the Z–Score is as following; [tex]Z = \frac{x - \mu}{ \sigma} [/tex]

Therefore, a positive value of Z is obtained when the raw score, x, is larger than the mean, [tex] \mu[/tex]

and negative Z value is given by raw scores lower than the mean.

Using the standard normal distribution table, raw score corresponds to the 1th percentile when the Z–Score = -2.326, while the Z–Score for the 99th percentile is 2.326.

The Z–Score of the 20th percentile is -0.842, while for the 30th percentile it is -0.524

Comparing the standard values with the values in the given table, we have;

First distribution;

-0.91960-(-0.842) = -0.0776

-0.71082 -(-0.842) = 0.13118

The smaller difference is given by -0.91960.

Similarly;

Second distribution;

While;

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The expression that best compares the minimum temperature of the two planets is -195 > -275

From the question, we are to determine which of the given options best compares the minimum temperature of the two planets

From the given information,

"The minimum temperature of mercury is approximately -275 F"

and

"The minimum temperature of Mars is approximately -195 F"

NOTE: The number -195 is greater than the number -275

Thus,

The minimum temperature of Mars is greater than the minimum temperature of Mercury

Hence, the expression that best compares the minimum temperature of the two planets is -195 > -275

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Answer:

6.7

Step-by-step explanation:

√45 = 6.7

.................

The interval(s) for which f(x) ≥ 0. is x ≥ 2

The function is given as:

f(x) = x - 2

Also, we have:

f(x) ≥ 0

This means that

x − 2 ≥ 0

Add 2 to both sides of the inequality

x ≥ 2

Hence, the interval(s) for which f(x) ≥ 0. is x ≥ 2

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Answer: 6.7% 0.67 6
                                 -
                                9

Step-by-step explanation:

Answer:

[tex]\sf 6.7\% < 6/9 < 0.67[/tex]

Explanation:

You would think 6.7% is a lot bigger than both, but it is not. Remember 6.7 is a percentage out of 100, thus, 6.7% actually is 0.067.

58, 62 and 74 are the numbers between 50 and 80 that has exactly 4 factors with 2 being one of them 4.

As per the question statement, we are required to find out the numbers between 50 and 80 that has exactly 4 factors with 2 being one of the factors.

To solve this question, we need to know that every or any number in the number system as has at least 2 factors: 1 and the number itself.

Since we are to find numbers with exactly 4 factors, 2 being one of the factors and as per the above mentioned concept, two of the remaining three factors will be 1 and the number itself, the fourth factor has to be a prime number as prime numbers have no other factors than 1 and itself.

That is, we will have to find prime numbers (say "n") which when multiplied by 2 lies within the range of 50 and 80,

[tex]or, 50\leq (n*2) \leq 80\\or, \frac{50}{2}\leq n\leq \frac{80}{2}\\ or, 25\leq n\leq 40[/tex]

That is, we will need to find the prime numbers between 25 and 40; They are 29, 31 and 37.

Hence, our required numbers are [(29 * 2) = 58], [(31 * 2) = 62] and

[(37 * 2) = 74]. They lie between 50 and 80 that has exactly 4 factors with 2 being one of them.

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Answer:

Step-by-step explanation:

2(4x-3)≥-3(3x)+5x

8x-6≥-9x+5x

8x≥-4x+6

8x+4x≥6

12x≥6

x≥6/12

or

x≥1/2

Answer: 32604

Step-by-step explanation: