lee went shopping with $60.50 . he bought 5 boxes of blue berries and 3 watermelons and had $16.50 left each watermelon cost $8.30

The inequality of the change of state of the gas in the driver's truck indicates;

Part A: The inequality  that represents the temperature at which the gas in the truck will be in liquid form is; -40 ≤ T ≤ 140

Part B: The graph is a shaded region bounded by two solid vertical lines at t = -40 and t = 140

Part C: The gas will be frozen because the temperature is below the freezing point temperature of the gas.

An inequality indicates the relationship between two expressions that are not equal

The temperature at which the gas freezes = -40 °F

Temperature at which the gas evaporates = 140 °F

Part A: The inequality that represents the temperature at which the gas in the truck will remain in liquid form, t is; -40 ≤ t ≤ 140

Part B: The description of the graph of the inequality is a region on the coordinate plane bounded by two solid vertical lines at x = -40 and x = 140, the region between the two solid vertical lines is shaded/.

Part C: The temperature of -49 °F obtained in January 1989 in Nome, Alaska is not in the feasible region of the graph of the inequality, therefore, the gas in the driver's truck will not remain in liquid form, and would freeze, such that the driver would not drive on the specified date.

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The area of the painting is 289 [tex]inches^{2}[/tex].

Given:

A square painting has a side length of 17 inches.

we know that,

Area of square = side * side.

= 17 inches * 17 inches

= 289 [tex]inches^{2}[/tex].

Therefore the area of the painting is 289 [tex]inches^{2}[/tex].

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The probability that Halima walks at least one way is 0.64

Calcualting Probability:

Probability is a branch of mathematics which is deals with the occurrence of a random event. The value of probability is expressed from zero to one but not more than 1. It is used to predict how likely events are to happen. The probability of an event 'E' is denoted by P(E).

Here we have

Halima either travels by bus or walks when she visits the town center

The probability that she catches the bus to town = 0.4

The probability that she catches the bus from town = 0.9

Let A and B be the events that she catches the bus to the town and the event that she catches the bus from the town respectively

=> P(A) = 0.4

=> P(B) = 0.9

The above events P(A) and P(B) are two independent events

Then the probability that she catches the bus to and from the town
=> P(A∩B) =  0.4 × 0.9 = 0.36

Therefore,

The Probability she walks at least one way P(A ∪ B) = 1 - P(A∩B)
=> P(A∪B) = 1 - 0.36

=>  P(A∪B) = 0.64

Hence,

The probability that Halima walks at least one way = 0.64

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Answer:

Domain: {7, 8, 9} Range: {2, 3, 4, 5}

Step-by-step explanation:

This relationship is not a function because one input (7) gave two different outputs (2 and 4)

In a binomial experiment, there are two possible results for each trial, which are referred to as "success" and "failure," respectively.

If the following criteria are satisfied, a statistical experimentation can be categorised as a binomial experiment:

Thus, in a binomial experiment, there are two possible results for each trial, which are referred to as "success" and "failure," respectively.

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Answer:

[tex]y=-\frac{1}{4}x-\frac{1}{4}[/tex]

Step-by-step explanation:

To find the equation in slope-intercept form, isolate [tex]y[/tex].

[tex]4y+x=-1 \\ \\ 4y=-x-1 \\ \\ y=-\frac{1}{4}x-\frac{1}{4}[/tex]

By factorizing algebraic expression 30 - [tex]6x^3[/tex] using a common factor, the result will be option (A) 2(15 - [tex]3x^3[/tex])

The expression is given,

30 - [tex]6x^3[/tex]

The expression is the mathematical sentence that consist of different types of variables, numbers and the mathematical operators. The mathematical operators will be addition, subtraction, division and multiplication. The expression does not contains a equal sign or inequality signs

The expression is given,

30 - [tex]6x^3[/tex]

Take a common term outside

Here the common term is 2

30 - [tex]6x^3[/tex]  = 2((30/2) - [tex]6x^3[/tex] /2)

= 2(15 - [tex]3x^3[/tex])

Hence, by factorizing algebraic expression 30 - [tex]6x^3[/tex] using a common factor, the result will be option (A) 2(15 - [tex]3x^3[/tex])

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The probability is 0.1.

acc to our question-

Hence,The probability is 0.1.

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The height of the trees in the year 2010, given their average rate of growth will be 21 foot

The trees are said to grow at a rate of 3/4 foot per year. In decimals this is:

= 3 / 4

= 0.75

The number of years between 1990 and 2010 is:

= 2010 - 1990

= 20 years

The height of the trees in 2010 would be:

= Current height x ( Rate of growth x number of years)

= 6 x (0.75 x 20)

= 21 foot

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The equation of the line parallel to 3x+3y=6 that passes through the point (7,-1) is  y = -x + 8

The equation of a line can be represented as follows:

y = mx + b

where

The lines that are parallel have the same slopes.

Therefore, let's find the slope of the equation 3x+3y=6.

3x + 3y = 6

3y = - 3x + 6

divide through by 3

y = - x + 2

Therefore, the slope is - 1.

Let's find the y-intercept of the equation using (7, 1)

y = - x + b

1 = - 7 + b

b = 8

Therefore, the equation of the line is y = -x + 8

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Answer:

$1.80

Step-by-step explanation:

The money left with Dan is £30  .

In the question ,

it is given that

the amount of money earned by Dan in a week is = £240  .

amount of money spent by Dan on rent is = 3/4 wage

amount of money spent by Dan on food is = 1/8 of wage

So ,

the total amount spent = amount spent on food + amount spent on rent

Substituting the values ,

we get ,

= 3/4 + 1/8 = 7/8 of his wage = (7/8)*240

= 210

so , total amount spent is £210 .

Amount left = amount earned - amount spent

= 240 - 210
= 30

Therefore ,The money left with Dan is £30  .

The given question is incomplete , the complete question is

Dan spends 3/4 of his wages on rent and 1/8 on food. If he makes £240 per week, how much money does he have left?

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The expression 11! / 9!(11-9)! evaluates to 55

The symbol ! is called factorial in mathematics.

Factorial can be defined as the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point.

Thus, factorial five is written as 5! meaning 5×4×3×2×1

It can also be written in shortened form as 5×4! or 5×4×3!

Let's evaluate  11! / 9!(11-9)!  now:

11! / 9!(11-9)! =  11! / 9!(2)!

                    = 11×10×9! / 9!2!

                    = 11×10/ 2                   (Note: 2! = 2×1 =2 )

                    = 110/2

                   =  55

Note: We shortened 11! to 11×10×9! because we want the 9! to cancel out each other. This is usually done to ease the evaluation. Also, note that 0! = 1

Therefore,  the result of the evaluation of the expression 11! / 9!(11-9)! is 55

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The required equation is 20 + 2m = 15 + 4m. The number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.

Uber charges a flat rate of $20 plus $2 per mile. Lyft charges a flat rate of $15 plus $4 per mile. We need to find out the equation and the number of miles for which Uber and Lyft would charge the same amount for the ride.

Let the charge of Uber and Lyft be represented by the variables C1 and C2. We can write the equations given below.

C1 = 20 + 2m

C2 = 15 + 4m

We need the charge for both companies to be equal.

C1 = C2

20 + 2m = 15 + 4m

Hence, the required equation is 20 + 2m = 15 + 4m. Now we will solve this equation to find the number of miles.

2m = 5

m = 2.5

Hence, the number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.

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The synthetic division (x²+9) by (x-3) has a quotient of x+3 and the remainder of 18

Synthetic division is a way of performing the division of polynomials, with less writing and fewer calculations than the long division method

Given: (x²+9) ÷ (x-3)

The numerator can be written as p(x)= x²+9

The zero of the denominator g(x) is 3         (Note: the sign changed)

The coefficients of p(x) are arranged as follows, with the zero of g(x) on the left:    

           3 |   1   0    9    

              |________

The first coefficient after the bar is "dropped" to the last row.

           3 |   1    0    9      

              |___________

              | 1  

The dropped number is multiplied by the number before the bar, and placed in the next column

          3  |   1     0    9  

              |          3  

              |___________

              | 1  

An addition is performed in the next column

           3 |   1     0    9  

              |          3  

              |___________

              | 1        3

The previous two steps are repeated and the following is obtained:

           3 |   1    0    9  

              |         3    9

              |___________

              | 1      3    18

Here, the last term (18) is the remainder while the rest are the coefficients of the quotient

The terms are written with increasing degree from right to left beginning with degree zero for the remainder and the result

1x + 3 | 18

Where the quotient q(x) = x+3 and the remainder r(x) = 18

Therefore, the quotient is  x+3 and the remainder is 18

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Answer:

Step-by-step explanation: 1 is the mode it has the most numbers that repeat

Answer:

The mode is 1.

Step-by-step explanation:

The mode is the number that occurs in a set the most. You can remember this as the word "most" and "mode" sounding similar.

Answer:

A

Step-by-step explanation:

Domain is the set of x values, so we can cross off C and D as answer choices as those would be possible answer choices for range. Looking at the graph, you can see the graph continues infinitely. The domain of the function is all real numbers, or A.

The absolute value of the difference between the first and second numbers is 5.

Here we have to find the difference between the first and the second numbers.

There are three statements.

Let a, b, and c be the first, second, and third numbers respectively.

The first statement is that the sum of the three number is 96.

The second statement is that the first number is 6 times the third number.

a = 6c

The third statement is that the third number is 40 less than the second number.

c = b - 40

b = c + 40

The sum of the three numbers is 96.

a + b + c = 96

6c + c + 40 + c = 96

8c = 96 - 40

8c = 56

c = 7

As a = 6c and b = c + 40

Now put the value of c as 7 we have:

a = 6 × 7

= 42

b = 7 + 40

= 47

Difference between the first and second numbers= 47 - 42

= 5

Therefore the difference is 5.

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The distance between the two points is 8.25 units

The distance between two points in a plane is the length of the line segment separating the two locations. Typically, the equation d=((x2 - x1)2 + (y2 - y1)2) is used to calculate the distance between two locations. You may use this formula to get the separation between any two points on an x-y plane or coordinate plane.

The following is the formula for the separation between two points:

d= √(x₁-x₂)²+(y₁-y₂)²

Points (x1, Y1) and (x2, Y2)

As given in the question, the points are (-6, -6) and (-8, 2)

The distance between the two points is,

d= √(-6+8)²+(-6-2)²

d=√4+64

d=√68 units= 8.25 units

Therefore, the distance between the two points is 8.25 units

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The equation which passes through (3,2) and slope 1/3 is:

y - 2 = 1/3 (x - 3)

Given, we have:

slope (m) = 1/3

Point = (3,2) = (x₁,y₁)

we are asked to determine the point slope form :

we know that:

point slope form:

y-y₁ = m(x-x₁)

substitute the above values in the formula:

y - 2 = 1/3 (x - 3)

Hence the correct option is B.

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Answer:

The answer is 33,710 euros.

Step-by-step explanation:

Start by multiplying 45,550 by 6%. This will give 2,730. over the next three years the price decreases, so multiply 2,730 by 3, which is 8,190. Finally, subtract 45,550 by 8,190 to get 33,710.

Answer:

m∠DGB = 108°

Step-by-step explanation:

          If the non-common arms of two adjacent angles form a straight line, then the adjacent angles are called linear pair and they add up to 180°.

m∠AGD + m∠DGB = 180°   {Linear pair}

      72    + m∠DGB = 180

                 m∠DGB = 180 - 72

                 m∠DGB = 108°

The researcher was using Investigator triangulation quality-enhancement strategy.

The Investigator triangulation strategy make use of more than one researcher, investigator or interviewer to study the data.This research strategy can help you improve the credibility and the validity of your findings.

Including the Investigator triangulation strategy , there are basically four types of triangulation strategies . The other three are listed below :

- Data Triangulation

- Theory Triangulation

- Methodological Triangulation

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If the degree of the polynomial is 3 with zeros 7i and 9/5, then the polynomial f(x) = [tex]5x^3-9x^2+245x-441[/tex]

The zeros of the polynomial = 7i and 9/5

Here the degree of polynomial is 3, therefore there will be three zeros in polynomial, here only 2 zeros are given. We have to find the third zero of the polynomial.

Here one of the polynomial is complex number, therefore another zero will be the conjugate of the complex zero

Therefore the equation will be

(x+7i)(x-7i)(5x-9) = 0

We have to solve the equation

([tex]x^2[/tex] -7ix+7ix+49)(5x-9) = 0

([tex]x^2[/tex] + 49)(5x - 9) = 0

[tex]5x^3-9x^2+245x-441 =0[/tex]

Therefore

f(x) = [tex]5x^3-9x^2+245x-441[/tex]

Hence, if the degree of the polynomial is 3 with zeros 7i and 9/5, then the polynomial f(x) = [tex]5x^3-9x^2+245x-441[/tex]

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The solution of the algebraic equation is x = -2. The proof is elaborated below.

The algebraic equation given to us is 14(x + 1) = -7(4 + x). An equation is a mathematical statement that proves the equality of two mathematical expressions. The first step is to simplify the brackets. The equation becomes 14x + 14 = -28 - 7x. Now, we will add 7x to both sides of the equation. The equation is modified as 21x + 14 = -28. Now, we will subtract 14 from both sides of the equation. The equation is modified as 21x = -42. Now, we will divide both sides of the equation by 21. The equation is modified as x = -2.

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Answer:

128

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]14^2+x^2=18^2 \\ \\ 196+x^2=324 \\ \\ x^2=128 \\ \\ x=\sqrt{128}[/tex]

Answer: y intercept is -1

Step-by-step explanation:

Using mathematical operations, we know that temperature after 6 p.m. will be -22.7°F.

So, the temperature after 6 p.m. will be:

The temperature at different times:

Now, calculate to get the temperature after 6 p.m. as follows:

Therefore, using mathematical operations, we know that the temperature after 6 p.m. will be -22.7°F.

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Answer:

EGFB

Step-by-step explanation:

PQ= (105)^2 + (208)^2

PQ=233

Area = b*h

Area = 21840

RS = (210)^2 + (120)^2

RS = 241.87

Area = 1/2bh

Area = 1/2 (210)(120)

Area = 12600

The length of the rectangle is 7 centimeter and the width of the rectangle is 4 centimeter

A rectangle has length 3 cm greater than it’s width

Consider the width of the rectangle = x

The length of the the rectangle = x + 3

The area of the rectangle = 28 square centimeter

The area of the rectangle = The length of the the rectangle × The width of the rectangle

Substitute the values in the equation

x(x+3) = 28

Apply the distributive property

[tex]x^2[/tex]  + 3x = 28

[tex]x^2[/tex] + 3x -28 = 0

Split the middle term and solve the equation

[tex]x^2[/tex] -4x + 7x -28 = 0

Take common term outside

x(x-4) + 7(x-4) =0

Take common term outside

(x+7) (x-4) = 0

x = -7, 4

The length cannot be negative value

x = 4 centimeter

Then the length of the rectangle = x + 3

= 4 +3

= 7 centimeter

Hence, the length of the rectangle is 7 centimeter and the width of the rectangle is 4 centimeter

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