One cubic foot holds 7.48 gallons of water and one gallon of water weighs 8.33 pounds. How much does a 1.8 cubic foot of water weigh in pounds?

Answer: = 1 (look at the image for the solution)

Step-by-step explanation:

The "value of x" in algebraic expression represented as "3x + 2 = 8" , in decimal form is 2.0   .

We have to solve the algebraic  expression "3x + 2 = 8" for value of x, we first need to separate the "variable x" on one side of the equation.

So , we subtract "2" from both sides of expression  ,

we get ;

⇒ 3x + 2 - 2 = 8 - 2  ;

Simplifying the left hand side, we get:

⇒ 3x = 6 ;

To solve for the variable x, we on divide both sides by 3 ;

⇒ 3x/3 = 6/3  ;

Simplifying, we get:

⇒ x = 6/3 = 2 .

Therefore, the value of x in the algebraic expression "3x + 2 = 8" is 2 , which is 2.0 when expressed as a decimal.

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The given question is incomplete , the complete question is

What is the value of x in the algebraic expression "3x + 2 = 8" ? Enter your answer, as a decimal . Do not round your answer.

We would expect John to weigh approximately 216.4 pounds at the end of week 8.

To answer this question, we need to fit a regression model to the data to determine the relationship between the number of calories burned and John's weight. We can use linear regression to find the line of best fit that represents this relationship.

We can see that there is a negative relationship between the number of calories burned and John's weight, which is consistent with the statement that "the more someone exercises the less they will weigh." We can use linear regression to find the line of best fit that represents this relationship.

Using a linear regression model, we get the following equation:

Weight = 219.9 - 0.0007 * Exercise

We can use this equation to predict John's weight at the end of week 8 based on the number of calories he burned. Plugging in Exercise = 5000, we get:

Weight = 219.9 - 0.0007 * 5000

Weight = 216.4

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1/2a+6 is the simplified form of the expression  3/4a + 8 - 1/4a - 2

An expression is combination of variables, numbers and operators.

The given expression is 3/4a + 8 - 1/4a - 2

Three by four times of a plus eight minus one by four times of a minus 2.

In the given expression a is a variable and plus and minus signs are the operators.

3/4a + 8 - 1/4a - 2

3/4a and  - 1/4a are the like terms

Add the like terms

3/4a   - 1/4a +8 - 2

2/4 a +6

1/2a+6

Hence, 1/2a+6 is the simplified form of the expression  3/4a + 8 - 1/4a - 2

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The number of solutions to the trigonometric equation is; 1 solution which is x = 270°

The trigonometric equation is given as;

sin²x - 2sin x - 3 = 0

Now, factorizing this gives us;

(sin x - 3)(sin x + 1) = 0

Thus, we now have;

sin x - 3 = 0

sin x = 3

At this point, x has no real solution

For the second factor, we have;

sin x + 1 = 0

sin x = -1

x = sin⁻¹ -1

x = 270°

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Answer:

Step-by-step explanation:

To find the distance between a line and a point, we need to find the perpendicular distance from the point to the line. Here's the step-by-step process:

Find the equation of the line perpendicular to ℓ that passes through point F(-1, 7): Since the slope of line ℓ is -1, the slope of the perpendicular line will be the negative reciprocal of -1, which is 1. To find the equation of the line, we need a point and the slope. Point F(-1, 7) will be used, and the slope is 1.

Using the point-slope form of a line, we can write the equation of the perpendicular line passing through point F as: y - 7 = 1(x + 1). Simplifying, we get: y = x + 8.

To find the point of intersection between the two lines, we can substitute the equation of line ℓ into the equation of the perpendicular line:

-x + 4 = x + 8

Solving for x, we get x = 6. Substituting x = 6 into the equation of line ℓ, we get:

y = -6 + 4 = -2

So, the point of intersection between the two lines is (6, -2).

To find the distance between the point F and the line ℓ, we can use the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the point F(-1, 7) and (x2, y2) is the point of intersection (6, -2).

So, substituting the values into the formula:

distance = √((6 - (-1))^2 + ((-2) - 7)^2) = √((7)^2 + (9)^2) = √(49 + 81) = √(130) = approximately 11.3

Therefore, the distance between the line ℓ and point F is approximately 11.3 units.

To give Tara a lower price, coupon 2 should be applied first.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Tara has two store coupons.

Coupon 1 gives her $10 off on one item.

Coupon 2 gives her 10% off on one item.

Tara can use both coupons together on one item in the store and choose which coupon to apply first.

For an item that has an original price of x dollars,

let f be the function that models the discount price of the item using only coupon 1,

and let g be the function that models the discount price of the item using only coupon 2.

The price of each item in this store is more than $20.

Let the price is $50.

So applying coupon 1 and then coupan2,

we get,

(50 - 10) - ($50 - $10) x 0.10 = $36

Now, apply coupon 2 and then coupon 1,

we get,

$50 x 0.10 - $10 = $35

Therefore, she should apply coupon 2 and then coupon 1.

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The balance will be at least $1200 after 8.18 months, if you deposit $1000 in an account that pays 3.5% annual interest compounded monthly.

The result of earning interest on a principal amount as well as the accumulated interest from earlier periods is known as compound interest. It occurs when money is reinvested rather being paid out, allowing interest to be generated on the principle and accrued interest over the next month.

The balance of an account with an initial deposit of $1000 earning 3.5% annual interest compounded monthly will reach $1200 after 8.18 months.

To find the time it takes for the balance to reach $1200, we can use the formula for compound interest, A = P[tex](1 + r/n)^{nt}[/tex],

where P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = 1000, r = 0.035, n = 12 (because the interest is compounded monthly), and t is the unknown variable. We can rearrange the formula to solve for t:

t = (A/P) / (1 + r/n)

Plugging in the values, we get

t = (1200/1000) / (12(1 + 0.035/12))

which simplifies to

t = 8.18 months

Therefore, it will take 8.18 months for the balance of the account to reach $1200.

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The measure of the angles are 60 degrees each

From the question, we have the following parameters that can be used in our computation:

AOB = 138 degrees

Also, we have:

The line OX bisects the angle AOB

Using the above as a guide, we have the following:

AOX = AOB/2 = 138/2 = 69

Also, we have

XOB = AOB/2 = 138/2 = 69

Hence, the angles are 69 degrees each

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Answer:

0.075 is a hundred times smaller than 7.5

Step-by-step explanation:

The radius of the circle is 7.8 cm.

What is a circle?

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Given that the area of a circle is 192 cm².

The area of a circle is πr², where r is the radius of the circle.

Assume that the radius of the circle is r.

Therefore,

πr² = 192

Divide both sides by π:

r² = 192/π

r² = 61.115

r = 7.817

r  ≈ 7.8 cm

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In order to infuse 0.5 grams of magnesium sulfate, 6.25ml must be administered in 1 hour.

A magnesium salt with the counterion sulfate is known as magnesium sulfate. It functions as a medication called, anaesthetic, tocolytic, anti-arrhythmia, analgesic, fertilizer, anticonvulsant, cardiovascular medication, analgesic, and all of the above. Drug is used to treat constipation temporarily.

Additionally, it is employed as a soaking solution to treat minor sprains, bruises, muscular aches, joint stiffness, and fatigued feet. A cleanse and soaking solution, this medication Magnesium sulfate, also known as Bath, is a natural compound used for a variety of therapeutic and physiological benefits.

xml = 0.5*50     (cross multiplication)

               4

So xml = 6.25ml

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Answer:

[tex]\frac{1}{22}[/tex]

Step-by-step explanation:

For these time of limit problems, we want to try to rewrite the equation in such a way that we can get some value, because in this case plugging in x=121, we simply get 0/0 which is indeterminate.

One thing you may or may not notice is that 11 and 121 are closely related, as 121 is just the square of 11... something important to solving this.

We have the fraction: [tex]\sqrt{x}-11[/tex], we want to possibly rewrite this into the denominator (x-121) to cancel out the two... well we can use the difference of squares. [tex](\sqrt{x}-11)(\sqrt{x}+11)=x-121[/tex] and we want to multiply the bottom by this amount as well, giving us the fraction:

[tex]\frac{x-121}{(x-121)(\sqrt{x}+11}[/tex]

Now we can cancel out the x-121 from the numerator and denominator, leaving us with:

[tex]\frac{1}{\sqrt{x}+11}[/tex]

and now we can directly plug in 121

[tex]\frac{1}{\sqrt{121}+11}=\frac{1}{11+11}=\frac{1}{22}[/tex]

Answer:

9.5

Step-by-step explanation:

Law of sine:

[tex]\frac{SideXY}{sinZ^{o}} = \frac{SideZY}{sinX^{o}} = \frac{SideXZ}{sinY^{o}}[/tex]

Sum of interior angles = 180°:
∴∠Z° = 180° - 63° - 41°

 ∠Z° = 76°

∴[tex]\frac{14}{sin76^{o}}[/tex]= [tex]\frac{x}{sin41^{o}}[/tex]

Cross- multiplication is applied:

(x)(sin76°) = (14)(sin41°)

x has to be isolated and made the subject of the equation:

x = [tex]\frac{[(14)(sin41^{o})]}{sin76^{o}}[/tex]

x = 9.466

x = 9.5 (Rounded to the nearest tenth)

Answer: That’s easy… The answer is -13

Step-by-step explanation: -2 x 3 + -7 = ?

-2 x 3 = -6

-6 + -7 = -13

Answer:

∠1 and ∠3

Step-by-step explanation:

The other pair of vertical angles are ∠2 and ∠4

Answer:

284 + 28d

Step-by-step explanation:

Because she has 284 it is known

She plans to obtain 28/day

Therefor, it should be 248+28d

Answer:

1,800 lbs of sand

900 lbs of gravel

600 lbs of cement

Step-by-step explanation: 11*300=3,300. 300*6=1,800, 300*3=900, and 300*2=600. This is correct because if you add 1,800+900+600 you get 3,300.

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image. Resizing an object is accomplished through the transformation of dilation. The objects can be enlarged or shrunk using dilation. The result of this transformation is an image that has the same shape as the original shape. The size of the shape varies, though. A dilation should either stretch or contract the original shape. The term "scale factor" describes this transformation.

From the diagram:

Scale factor = A'B' / AB = 6/3 = 2

Center = (6, -6)

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

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The system of equations which has infinitely many solutions as required to be determined is; Choice D; 2x + y = 5 and 4x + 2y = 10.

By the standards of linear geometry, two equations have infinitely many solutions when their graphs coincide and in which case, they have the same slope and y-intercept.

Therefore, the system of equations which satisfy the said criterion is; 2x + y = 5 and 4x + 2y = 10.

Ultimately, the correct answer is; Choice D; 2x + y = 5 and 4x + 2y = 10.

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If sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18

A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. Thus inequality emerges from an imbalance.

Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >, <, ≤ or ≥.

An inequality symbol represents that the expressions on each side are not equal. It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa.

Let the given sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18

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The solution to each of the exponent problems are;

a) 10¹¹

b) 10²

c) 10⁴

d) 10¹²

The seven laws of exponents are;

1) Product of powers rule.

2) Quotient of powers rule.

3) Power of a power rule.

4) Power of a product rule.

5) Power of a quotient rule.

6) Zero power rule.

7) Negative exponent rule.

The given expressions are;

a) 10⁵ × 10⁶

= 10⁵⁺⁶

= 10¹¹

b) 10⁴ × 10⁻²

= 10⁴⁻²

= 10²

c) 10⁸/10⁴

= 10⁸⁻⁴

= 10⁴

d) 10⁹/10⁻³

= 10⁹⁻⁽⁻³⁾

= 10⁹⁺³

= 10¹²

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When a = 9, b = -12. However, this result is not physically meaningful in this context because it implies that Monica signed up for a gym membership 12 weeks after Victoria, which contradicts the original statement.

What is algebraic expression ?

An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.

If Victoria signed up for a gym membership 21 weeks after Monica and we let a represent the number of weeks Victoria has been a member and b represent the number of weeks Monica has been a member, then we have a = b + 21.

Substituting a = 9, we get:

9 = b + 21

Solving for b, we subtract 21 from both sides:

b = 9 - 21

b = -12

Therefore, when a = 9, b = -12. However, this result is not physically meaningful in this context because it implies that Monica signed up for a gym membership 12 weeks after Victoria, which contradicts the original statement.

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Answer:

To find the final price for the jacket, we need to first calculate the amount of the discount and then add the sales tax.

The amount of the discount is $65.00 * 40% = $26.00. So the price after the discount is $65.00 - $26.00 = $39.00.

The sales tax is $39.00 * 5% = $1.95. So the final price for the jacket is $39.00 + $1.95 = $40.95.

Step-by-step explanation:

Answer:

he final price for the jacket is $40.95.

Step-by-step explanation:

First, let's calculate the discount for the jacket:

Discount = $65.00 * 40% = $26.00

The price of the jacket after the discount is:

$65.00 - $26.00 = $39.00

Next, let's calculate the sales tax:

Sales tax = $39.00 * 5% = $1.95

Finally, let's add the sales tax to the discounted price to find the final price:

Final price = $39.00 + $1.95 = $40.95

So, the final price for the jacket is $40.95.

Answer:

Step-by-step explanation:

Cardinality of a set refers to the number of elements in the set. There are two types of cardinality: finite and infinite. A set is considered to have finite cardinality if it has a finite number of elements, meaning that the elements can be counted. A set is considered to have infinite cardinality if it has an infinite number of elements and cannot be counted.

In the case of the set B = {x | x ∈ N and x > 5}, the set is comprised of all natural numbers greater than 5. The set of natural numbers is infinite, meaning that there are an infinite number of elements in the set B. As a result, the cardinality of the set B is also considered to be infinite.

The symbol "ℵ0" is used to represent the cardinality of the set of natural numbers, and it is often used to indicate the cardinality of infinite sets with the same size as the set of natural numbers. In this case, we can say that the cardinality of the set B is ℵ0, meaning that the set B has the same size as the set of natural numbers and therefore has infinite cardinality.

Answer:

3/400 per min

Explanation:

Divide the rate at which he can walk by the number how mins he can walk at that rate

The summary of the given data is Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56  . So option C is correct.

The middle  number of data in a collection is known as the median. Three alternative metrics are employed in mathematics to determine the average value for a given group of integers. They are the median,  mode, and mean. The measures of central tendency are this trio of measurements.

Median = [(n/2)th term + {(n/2)+1}th term]/2 (for even)

Median = {(n+1)/2}th term (for odd)

Based on the given information,

we can see that the box plot shows the values of 44, 48, 50.5, 53, and 56.

These values represent the minimum, lower quartile (Q1), median, upper quartile (Q3), and maximum, respectively.

Therefore, the five-number summary for this data is:

Min = 44,

Q1 = 48,

Median = 50.5,

Q3 = 53,

Max = 56

So the answer is: Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56

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Equations 4 and 5 are not equivalent to any of the other equations.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The equations that are equivalent are:

2 + x = 5

Negative 5 + x = negative 2

x + 1 = 4

Subtracting 2 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.

Adding 5 to both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.

Subtracting 1 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.

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