The equation 24b = t is used to find b, the cost of 1 bottle of water when sold in a 24‐pack case with a case price of t dollars. What is the cost of 1 bottle of water when the case price is $7.50?

We can conclude after answering the presented question that As a equation result, the first car's fuel efficiency was 15 miles per gallon, whereas the second car's fuel economy was 35 miles per gallon.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Let's name the first car's fuel efficiency (miles per gallon) x and the second car's fuel efficiency y. We are aware of the following:

The first automobile used 25 gallons of gas and covered 25 miles.

The second automobile used 20 gallons of petrol and drove 20 miles.

The two automobiles went a total of 1075 miles, thus 25x + 20y = 1075.

Their combined fuel economy was 50 miles per gallon, thus x + y = 50/1 = 50.

[tex]25x + 20y = 1075\\x + y = 50\\25x + 20y = 1075\\-20x - 20y = -1000\\5x = 75x = 15\\x + y = 50\\15 + y = 50\\y = 35\\[/tex]

As a result, the first car's fuel efficiency was 15 miles per gallon, whereas the second car's fuel economy was 35 miles per gallon.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

The correct answer is 36π

Step-by-step explanation:

Using mensuration, we can find that the mass of male is greater than that of the female's by 63.507kg.

Mensuration can be defined as a measurement action. Our world is three dimensional. Both elementary school mathematics and secondary school mathematics heavily rely on the idea of measurement. Also, measuring is directly related to our daily life. When we learn to measure items, we practise measuring both 2D and 3D shapes. Both conventional and nonconventional units of measurement can be used to determine the size of objects or quantities.

In the given table,

Height of male = 1.68m.

Mass of male = 158.757kg.

Height of female = 1.448m.

Mass of female = 95.25kg.

Difference between mass of male and female,

= 158.757 - 95.25

= 63.507kg.

The mass of male is greater than that of the female's by 63.507kg.

So, 2nd statement is true.

Rest of the statements are not true.

To know more about mensuration, visit:

https://brainly.com/question/13077063

#SPJ1

Answer:

To work out the probability that Caroline buys fruit or buys a CD or both, you can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are events.

In this case, A is the event that Caroline buys fruit and B is the event that Caroline buys a CD.

The probability that Caroline buys fruit is 0.4 and the probability that Caroline buys a CD is 0.6.

To find the probability that Caroline buys fruit and a CD, you can multiply the probabilities of the two events:

P(A and B) = P(A) x P(B) = 0.4 x 0.6 = 0.24

Therefore, the probability that Caroline buys fruit or buys a CD or both is:

P(A or B) = P(A) + P(B) - P(A and B) = 0.4 + 0.6 - 0.24 = 0.76

So, the probability that Caroline buys fruit or buys a CD or both is 0.76 .

The piecewise function formed by two functions and a point is not continuous at x = 1.

In this problem we find the case of a piecewise function formed by three expressions in three corresponding intervals: two functions and a point. These expressions are defined in the images attached below. The x-value is on the horizontal axis and the y-value is on the vertical axis.

According to the first figure, the y-value of the function is getting closer to 2 as x approaches 1 from the left side.

According to the second figure, the y-value of the function is getting closer to 3 as x approaches 1 from the left side.

According to the third figure, the y-value of the function is equal to 0.5 when x is equal to 1.

Therefore, the piecewise function is not continuous at x = 1.

To learn more on piecewise functions: https://brainly.com/question/28225662

#SPJ1

Answer: Kayla sold 1/12 gallons more than Ethan.

Step-by-step explanation:

Let's start by finding out how much lemonade Kayla sold. We know that together, Ethan and Kayla sold 1 1/4 gallons, which is the same as 5/4 gallons. We also know that Ethan sold 2/3 gallons. Therefore, we can find how much Kayla sold by subtracting Ethan's sales from the total sales:

Kayla's sales = Total sales - Ethan's sales

Kayla's sales = 5/4 - 2/3

To subtract these fractions, we need to find a common denominator. The smallest common multiple of 4 and 3 is 12, so we can rewrite the fractions with 12 as the denominator:

Kayla's sales = (5/4)(3/3) - (2/3)(4/4)

Kayla's sales = 15/12 - 8/12

Kayla's sales = 7/12

Therefore, Kayla sold 7/12 gallons of lemonade. Now, we need to compare this to Ethan's sales. We can convert Ethan's sales to twelfths to make it easier to compare:

Ethan's sales = (2/3)(4/4) = 8/12

Now we can see that Kayla sold more lemonade than Ethan. The difference in sales is:

Kayla's sales - Ethan's sales = 7/12 - 8/12

Kayla's sales - Ethan's sales = -1/12

The result is negative, which means that Ethan sold 1/12 gallons less than Kayla. Therefore, Kayla sold 1/12 gallons more than Ethan.

Answer:

6+20

Step-by-step explanation:

Answer:

The formula for the surface area of a rectangular prism is:

Surface Area = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively.

Since the length, width, and height of the prism in this case are all x inches, we can substitute x for l, w, and h in the formula to get:

Surface Area = 2(x)(x) + 2(x)(x) + 2(x)(x)

Simplifying the equation, we get:

Surface Area = 2x^2 + 2x^2 + 2x^2

Surface Area = 6x^2

Therefore, the equation for the surface area of a prism with a length, width, and height of x inches is:

Surface Area = 6x^2 square inches

The length of the unknown leg of the right triangle is 6.2 ft rounded to one decimal place, using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

we shall represent the unknown leg of the right triangle with the letter "x" so that by Pythagoras rule we can evaluate for x as follows:

8² = 5² + x²

x = √(8² - 5²) {make TV the subject}

x = √(64 - 25)

x = √39

x = 6.2450

Therefore, the length of the unknown leg of the right triangle is 6.2 ft rounded to one decimal place, using the Pythagoras rule.

Know more about Pythagoras here:https://brainly.com/question/343682

#SPJ1

Answer:

34 ft.²

Step-by-step explanation:

We can find the area of this polygon by splitting it into two rectangles.

We can find the area of each individual rectangle, then add their areas to get the area of the entire polygon.

See the attached image for a diagram.

First, we can find the area of the smaller rectangle.

length × width

5 ft. × 2 ft. = 10 ft.²

Next, we can find the area of the larger rectangle.

4 ft. × 6 ft. = 24 ft.²

Finally, we can add the two rectangles' areas together to get the area of the entire polygon.

10 ft.² + 24 ft.² = 34 ft.²

Answer:

165inch^3

Step-by-step explanation:

4×7×3=84inch^3

9×3×3=81inch^3

84+81=165inch^3

Answer: 6 songs.

Step-by-step explanation:

Each song is $2 dollars. $12 divided by $2 equals 6.

So he can download 6 songs.

The probability of getting a '1' on the first roll and '2' on the second roll for the given expression is [tex]\frac{1}{18}[/tex] .

What about probability?

In mathematics and statistics, probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

The probability of an event A is denoted by P(A) and is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In other words, it is the number of ways that event A can occur divided by the total number of possible outcomes.

For example, if you roll a fair six-sided die, the probability of rolling a 4 is 1/6, since there is only one favorable outcome (rolling a 4) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

Probability is used in many different fields, such as gambling, statistics, and science, to make predictions about the likelihood of different outcomes. It is also used to model complex systems and to test hypotheses in scientific experiments.

According to the given information:

When a die is rolled 2 times, the output we get

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Total no of getting '1' on first roll and '2' on second roll = 2

Total outcomes = 36

⇒ [tex]\frac{2}{36}[/tex]

⇒ [tex]\frac{1}{18}[/tex]

To know more about probability visit:

https://brainly.com/question/22983072

#SPJ1

Answer: 120

Step-by-step explanation:

The angle measures should add up to 360

110+130+x=360

240+x=360

x=120

b) Scatter plot chart would indicate a positive correlation

c) Candidate D would be the most cost-effective choice, as their expected salary would increase the most. Candidate F would also be a good choice, as their expected salary would increase by £1,000.

A scatter plot chart can be used to plot the data of the two variables on a two-dimensional graph, and the data points can be connected with a line or a curve.

a) The weights of the attributes in this case seem to be appropriate for the purpose of selecting a Regional Officer for the Western Region.

This data shows that the charity is placing a greater emphasis on the candidate's commitment, managerial experience and ideas, as these are likely to be the most important factors in selecting a successful Regional Officer.

Additionally, Education has the lowest weight at 10, indicating that this is not a major factor in consideration.

Overall, the weight of each criteria reflects the importance of the criteria to the charity and is appropriate for this case.

b) The scatter plot chart would indicate a positive correlation between the two variables, with the higher aggregate score corresponding to the higher expected salary.

Based on this chart, candidates A, D and F would be the best 2-3 candidates, with the highest aggregate scores of 50, 90 and 62 respectively.

c) If the charity is prepared to pay £1,000 for each additional aggregate score, then candidate D would be the most cost-effective choice, as their expected salary would increase the most (from £60,000 to £61,000). Candidate F would also be a good choice, as their expected salary would increase by £1,000 (from £52,000 to £53,000).

Candidate A would not be recommended, as their expected salary would increase by only £500 (from £46,000 to £46,500).

For more questions related to attributes

https://brainly.com/question/30295887

#SPJ1

Answer:september

Step-by-step explanation:

Using the sum-to-product formula we get the value as √2 cos(2α)

What is the sum-to-product formula?

The sum-to-product formula is a trigonometric identity that expresses the sum or difference of two trigonometric functions as a product of two trigonometric functions. There are several versions of this formula, depending on the specific functions involved.

We can use the sum-to-product formula to simplify the expression:

cos(2α - π/16) + cos(9π/16 - 2α)

= cos(2α)cos(π/16) - sin(2α)sin(π/16) + cos(9π/16)cos(2α) + sin(9π/16)sin(2α)

= cos(2α)(cos(π/16) + cos(9π/16)) + sin(2α)(-sin(π/16) + sin(9π/16))

= cos(2α)(2cos(5π/16)cos(3π/16)) - sin(2α)(2cos(7π/16)sin(π/16)) (using the sum-to-product formula again)

= 2cos(2α)cos(5π/16)cos(3π/16) - 2sin(2α)cos(7π/16)sin(π/16)

= 2cos(2α)(cos(5π/16)cos(3π/16) - sin(5π/16)sin(3π/16)) (using the product-to-sum formula)

= 2cos(2α)cos(π/4)

= 2cos(2α)/√2

= √2 cos(2α)

To know more about the sum-to-product formula visit:

brainly.com/question/15270433

#SPJ1

Answer:

To write the equation of the parabola in vertex form, we use the standard form:

y = a(x - h)^2 + k, where (h, k) is the vertex.

Given that the vertex is (-4, -6), we have:

h = -4 and k = -6

Now, we need to find the value of "a" using the point (-14, 13/2) which lies on the parabola.

Substituting the values in the standard form, we get:

13/2 = a(-14 - (-4))^2 - 6

Simplifying, we get:

13/2 = 100a - 6

100a = 13/2 + 6

a = 19/200

Therefore, the equation of the parabola in vertex form is:

y = (19/200)(x + 4)^2 - 6

Step-by-step explanation:

Answer: Your answer should be

               D

Step-by-step explanation: this is because absolute value makes a number positive, no matter the scenario as long as the number(s) are in the absolute value sign (indicated basically by straight lines) this makes it to where the number can never be negative within the lines.

Given the above circles,

1) x = 42°

2) x = 29°

3) x = 101°

4) x = 37°

5) x = 31°

6) x = 120°

1) x = 42° because the Angles at the circumference of a circle

subtended by the same arc are equal. Since 35° and 103° are two of the three angles in a triangle whose third angle subtends the circumference of the circle along with ∠x, and the third angle = 180 - 35 - 103 = 42° therefore,  x = 42°

2) x = 29° because according to the central angle theorem, the angle at the circumference is double the one at the center. Since the angle at the circumference is 61°, the one at the center is 122°. Since the line from the center that couches on both sides of the circumference is the radius, they are equal. Hence, the angles formed at their bases are equal.

Thus, x = (180-122)/2

x = 29°

3) 3) x = 101° because the opposite angles of a cyclic quadrilateral are supplementary.

4) x = 37° based on the angle in the alternate segment theorem.

5) x= 31° is based on the "inscribed angle theorem" or the "theorem of the intercepted arc".

This theorem states that if an angle is inscribed in a semicircle, then the angle is a right angle (i.e., it measures 90 degrees). In other words, if you draw any two chords from the ends of the diameter to any point on the arc of the semicircle, then the angle formed by these two chords at the point on the arc will always be 90 degrees.

6) x = 120° on the basis of  the "Tangent-Secant Angle Theorem" or "Tangent-Chord Angle Theorem".

In the problem given above, the angle x is formed by two tangents intersecting at the vertex outside the circle, and the Tangent-Secant (or Tangent-Chord) Angle Theorem is used to find its measure.

The arc formed at the points where the two tangents meet is twice the angle formed inside the circle which is = 30°
Thus, where the rest of the arc traced from the upper point of tangency  is traced back to the lower point of tangency is called A,

The measure of arc A is 360° - 60° = 300°.

The measure of angle x is half the difference between the measures of the intercepted arcs, which is (300° - 60°)/2 = 120°.

Therefore, the measure of angle x would be 120°.


Learn more about circle theorems:
https://brainly.com/question/19906313
#SPJ1

Recording the customer billing using (a) accrual-basis accounting and (b) cash-basis accounting is as follows:

Customer Billing:

Debit Accounts Receivable $3,200

Credit Service Revenue $3,200

(To record the performance of services for customers during the month.)

Customer Billing:

No Record during the current month.

Cash-basis accounting recognizes expenses and revenues when cash exchange takes place.

Accrual-basis accounting matches expenses and revenues to the month or period when the transaction occurs, whether there is a cash exchange or not.

For instance, the accrual-basis will recognize the receipt of cash as follows:

Next Month:

Debit Cash $3,200

Credit Accounts Receivable $3,200

On the other hand, the cash-basis will recognize revenue with the receipt of cash as follows:

Next Month:

Debit Cash $3,200

Credit Service Revenue $3,200

Learn more about cash-basis and accrual-basis accounting at https://brainly.com/question/30694533.

#SPJ1

The expression that represents the sentence "A number cubed decreased by 24"​ is given as follows:

x³ - 24.

The sentence for this problem is defined as follows:

"A number cubed decreased by 24".

The number is unknown, hence the variable that represents the number is given as follows:

x.

The cube of the number is given as follows:

x³.

The number is then decreased by 24, hence we subtract the expression x³ by 24 to obtain the algebraic expression as follows:

x³ - 24.

More can be learned about algebraic expressions at https://brainly.com/question/4344214

#SPJ1

Answer:

If 60% of the beings surveyed preferred hopt juice and 50 beings were surveyed altogether, then we can calculate the number of beings who preferred hopt juice by multiplying the total number of beings surveyed by the percentage that preferred hopt juice: `50 x 0.60 = 30`. So, **30** beings preferred hopt juice.

Answer:

the answer to the question is B

Step-by-step explanation:

no need for explanation just trust the source

Due to its neighbouring perpendicular sides and opposite parallel and equal-length sides, the quadrilateral ABCD is a rectangle.

a) The opposite sides are parallel and equal.

b) The opposite angles are equal.

c) The consecutive or adjacent angles are supplementary.

d) If any one of the angles is a right angle, then all the other angles will be at right angle.

e) The two diagonals bisect each other.

4. To find the area of a parallelogram, you can follow these steps:

Measure the length of the base of the parallelogram. Let's call this measurement "b".

Measure the height of the parallelogram. Let's call this measurement "h".

Multiply the base length "b" by the height "h" to get the area of the parallelogram.

Therefore, the formula to calculate the area of a parallelogram is:

Area = base length (b) [tex]*[/tex] height (h)

In symbols, this can be written as:

[tex]A = b \times h[/tex]

Alternatively, if the length of both adjacent sides is known, you can use the formula:

A = base length (b) [tex]*[/tex] the length of adjacent [tex]side (a) * sin[/tex](θ)

where theta is the angle between the base and adjacent side.

5.  the given vertices on a coordinate plane and see what kind of figure they form.

The figure formed by the vertices A, B, C, and D is a quadrilateral. To determine the precise classification of the quadrilateral, we can use its properties.

To determine if the parallelogram is a rhombus, rectangle, or square, we need to check if the diagonals bisect each other and if the adjacent sides are perpendicular. We can find the midpoint of AC and BD as:

Midpoint of AC:  [tex]((2 + 8)/2, (3 + 7)/2) = (5, 5)[/tex]

Midpoint of BD: [tex]((7 + 3)/2, (2 + 8)/2) = (5, 5)[/tex]

The diagonals AC and BD intersect at the midpoint [tex](5,5)[/tex], so they bisect each other.

We can also find the slopes of adjacent sides AB and BC, and we find that they are:

AB: [tex]-1/5[/tex]

BC: [tex]5[/tex]

The product of their slopes is [tex]-1[/tex], so the adjacent sides are perpendicular.

Therefore, the quadrilateral ABCD is a rectangle, because it has opposite sides that are parallel and equal in length, and adjacent sides that are perpendicular.

Learn more about parallelogram here:

https://brainly.com/question/29147156

#SPJ1

Answer: there you go :)

Car 1 consumes 30 gallons of gas.

Car 2 consumes 20 gallons of gas.

Step-by-step explanation:

Let x = gallons consumed by car 1

Let y = gallons consumed by car 2

We set up our equations:

35x+40y = 1850        eq1

x+y = 50                   eq2

Substituting eq 2 into eq 1,

35x+40(50-x) = 1850

35x+2000-40x = 1850

-5x+2000 = 1850

-5x = -150

  x = 30

Substitute value of x into eq 2.

x+y = 50

30+y = 50

     y = 20

Car 1 consumes 30 gallons of gas.

Car 2 consumes 20 gallons of gas.

Answer : 10.5

Explanation: Divide 168/16

In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

To find the annual rate of change between 1992 and 2006, we can use the formula:

r = [tex](V_2/V_1)^{1/n}-1[/tex]

where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.

=>r = -0.0839

Therefore, the rate of change between 1992 and 2006 is -0.0839.

To express the rate of change in percentage form, we can multiply the result from part A by 100:

=>r = -0.0839 x 100

=> r = -8.39%

Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.

To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.

From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:

where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.

=>V = 11792.51

Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).

To learn more about exponential decay refer the below link

https://brainly.com/question/12139640

#SPJ1