Skylar Had 12 Sphere-shaped Pool Toys That Each Have Radius Of 2 Inches. If The Toys Fill Water, How (2024)

The inequality is represented as -2x >-14

How to determine the inequality

It is important to note that inequalities are described as unequal comparison between two variables, numbers or expressions.

Inequalities are represented with the signs;

< represents the sign for less than> represents the sign for greater than≤ represents the sign for less than or equal to≥ represents the sign for greater than or equal to

From the information gibe, we have;

x>7 by -2

Multiply both sides by -2, we have;

2 × - x > 7(-2)

multiply the values, we have;

-2x >-14

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The cost of the building per square foot is approximately $9.74.

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

The area of a 36-ft by 36-ft square is:

Area = (36 ft) x (36 ft) = 1,296 square feet

To find the cost per square foot, we divide the total cost by the area:

Cost per square foot = Total cost / Area

Total cost = $12,619

Substituting these values, we get:

Cost per square foot = $12,619 / 1,296 sq ft

Cost per square foot ≈ $9.74

Therefore, the cost of the building per square foot is approximately $9.74.

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Answer:

9/8

Step-by-step explanation:

3/4 ÷ 8/12 = 3/4 · 12/8 = 36/32 = 9/8

So, the answer is 9/8

Answer:

9/8

Step-by-step explanation:

a/b ÷ c/d = (a/b) x (d/c) = ad / bc

we can simplify 3/4 ÷ 8/12 as :

3/4 ÷ 8/12 = (3/4) x (12/8) = (3 x 3) / (4 x 2) = 9/8

Therefore, 3/4 ÷ 8/12 simplifies to 9/8.

a) The vertex of a quadratic function is a maximum point if the coefficient a is negative, and a minimum point if the coefficient a is negative.

b) A quadratic function in which the vertex is a maximum is given as follows: y = -2x².

c) A quadratic function in which the vertex is a minimum is given as follows: y = 2x².

How to obtain the vertex of a quadratic function?

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The leading coefficient a determines if the vertex of the quadratic function is a maximum point or a minimum point, as follows:

a > 0: minimum point.a < 0: maximum point.

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Answer:

The slope is 5/3.

Step-by-step explanation:

Slope intercept equation format;

y = mx + b

- m slope

b y-intercept

Answer:

5/3 is the slope

Step-by-step explanation:

You need to find the slope of y = 5/3x - 4.

Notice how the equation is written in slope-intercept form: y = mx + b.

Whereas:

m = slopeb = y-intercept

In slope-int. form, the slope is always the number in front of x.

Therefore, the slope is 5/3

The equation has one valid solutions and one extraneous solution and a valid solution for x is 5.

Solving the equation for x

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

√(x-1) - 5 = x - 8

So, we have

√(x-1) = x - 3

Using a graphing tool, we have

x = 5

This means that it has one valid solution and the solution is x = 5

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the measure of Angle D in the given triangle is 45 degrees, which is option B.

what are angles?

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's faces, that converge upon the vertex, and center, within its shape. A surface angle may be created by the configuration of two rays. Additionally, when two planes collide, an angle is created. Dihedral angles are what they are called. An angle is a possible shape for two lines or rays without a common termination in planar geometry. The English term "angle" derives from the Latin term "angulus," which meaning "horn." The intersection of both of the rays' common endpoints is called the vertex, which is sometimes referred to as either side of an angle.

given,

In a triangle, the sum of the angles is always 180 degrees. Therefore, to find the measure of angle D in the given triangle, we can use the fact that:

Angle A + Angle B + Angle D = 180 degrees

We are given that Angle A is 45 degrees. We can see from the diagram that Angle B is a right angle, which means it measures 90 degrees. As a result, we may enter the following numbers into the formula above to obtain:

45 + 90 + Angle D = 180

Simplifying the equation, we get:

135 + Angle D = 180

Subtracting 135 from both sides, we get:

Angle D = 45 degrees

Therefore, the measure of Angle D in the given triangle is 45 degrees, which is option B.

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After answering the presented question, we can conclude that Hence surface area option A) [tex]928 inches^{2}[/tex] is the correct answer.

What is surface area ?

The surface area of an object indicates the overall space occupied by its surface. The surface area of a three-dimensional shape is the entire amount of space that surrounds it. The surface area of a three-dimensional shape refers to its full surface area. By adding the areas of each face, the surface area of a cuboid with six rectangular faces may be computed. As an alternative, you can use the following formula to name the box's dimensions: [tex]2lh + 2lw + 2hw = surface (SA)[/tex]. Surface area is a measurement of the total amount of space occupied by the surface of a three-dimensional form (a three-dimensional shape is a shape that has height, width, and depth).

To get the surface area of a rectangular prism, sum the areas of all six faces.

The surface area of a rectangular prism is calculated as follows:

[tex]2lw + 2lh + 2wh = 2lw + 2lh + 2wh[/tex]

where l, w, and h denote the rectangular prism's length, breadth, and height.

Substituting the provided values yields:

[tex]surface Area = 2(24* 16) + 2(24 * 2) + 2(24 * 2) + 2 (16 * 2)[/tex]

928 square inches of surface area

As a result, the box's surface area is 928 square inches.

Hence option A) [tex]928 inches ^{2}[/tex] is the correct answer.

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Answer: your answer is 768 in2

Step-by-step explanation:

Answer: $0.15 per pencil

Step-by-step explanation:

1.80 / 12 = 0.15

Given: The cost price of 12 pencils = $1.80

To find the cost of each pencil, we need to divide the total cost by the number of pencils , we get

The cost price of each pencil = [tex]\dfrac{1.80}{12}[/tex]

Therefore, The cost price of each pencil = [tex]\$0.15[/tex]

Hence, the cost price of each pencil = [tex]\bold{\$0.15}[/tex] or 15 cents.

The solution to the inequality -4x - 5 < 3 is x > -2.

What is the solution to the inequality?

Given the inequality in the question;

-4x - 5 < 3

To solve the inequality, we need to isolate the variable "x" on one side of the inequality symbol.

-4x - 5 < 3

Add 5 to both sides of the inequality:

-4x - 5 + 5 < 3 + 5

-4x < 3 + 5

-4x < 8

Divide both sides of the inequality by -4, but remember that when dividing by a negative number, we must reverse the direction of the inequality symbol:

-4x/-4 > 8/-4

x > -2

Therefore, the solution is x > -2.

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Answer:

The options for this quadratic equation are x = -4 + √20 and x = -4 - √20.

Step-by-step explanation:

1. The quadratic equation you furnished is 4(x+4)² - eighty = zero

2. To remedy this equation, we can first simplify it by way of dividing each aspect using 4, which offers us (x+4)² - 20 = zero

3. add 20 to each facet of the equation to get (x+4)² = 20.

4. Take the rectangular root of each facet of the equation to get x+4 = ±√20, which simplifies to x = -4 ± √20.

Answer:

Here you go

Step-by-step explanation:

A

T

F

T

F

AND NOW Ā

Ā

F

T

F

T

FOR B

B

T

T

F

F

FOR B COMPLIMENT

B

F

F

T

T

The truth table for the logic expression is shown below

Drawing truth table for the logic expression

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

________

(A AND B)

When expanded, we have

________ ___ ___

(A AND B) = A + B

So, we have

_______

AB(A AND B)

0 0 0

0 1 1

1 0 1

1 1 1

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Thus, the partial sum of S4 for the very first 4 terms of the sequence is obtained as: 66.67.

Explain about the partial sum:

The total of the terms in a sequence constitutes a series, rather than a list of words like a sequence. Finding the sum of the series via adding the terms is straightforward if the series does have a finite number of terms.

The summation becomes more challenging when the series contains an infinite number of terms, and the series could potentially have a finite total.

An infinite series' partial sum is the total of a finite number of terms, starting with the first term. It is frequently beneficial to look at the behaviour of the partial sums when dealing with infinite series.

Given expression for the number in series is:

[tex]a_{n} = 5(3)^{n-2}[/tex]

Thus, 1st four terms are obtained by putting n = 1,2,3,4.

[tex]a_{1} = 5(3)^{1-2} = 5/3[/tex]

[tex]a_{2} = 5(3)^{2-2} = 5[/tex]

[tex]a_{3} = 5(3)^{3-2} = 15[/tex]

[tex]a_{4} = 5(3)^{4-2} = 45[/tex]

Thus, the sum of all 4 numbers:

S4 = a1 + a2 + a3 + a4

S4 = 5/3 + 5 + 15 + 45

S4 = 66.67

Thus, the partial sum of S4 for the very first 4 terms of the sequence is obtained as: 66.67.

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The correct equation that contains the given elements is:

6 = x + 2 + 4

Note that this equation represents a sum of the variable x and the constants 2 and 4, which equals 6

Answer:

Step-by-step explanation:

The answer includes 6x+4=2, 6x+2=4 and 2+4=6x

Answer:

x<-11 or x>7

Step-by-step explanation:

First, we get the right side to be 0.

[tex]x^2+4x-77 > 0[/tex]

Then we factor the left side.

[tex](x+11)(x-7) > 0[/tex]

Using the Snake Method, we determine the intervals as x<-11 or x>7

First you would identify the sides given. We have 3cm, which is one of the legs, or bases, and 5cm which is the hypotenuse because it is the longest side.

To find X, we would start at the angle we need to find and see that the given values are opposite and hypotenuse. Using SOH CAH TOA we know that we will use sin because sin=opposite divided by hypotenuse

The final calculation is
sin^-1=3/5
Angle X=36.8 degrees

(sin^-1 is just the inverse of sine, which can usually be found on a scientific calculator)

The expression can be simplified to get.

(1/2)*(2x² − 8) + (1/3)*(6x² − 3) = 3x² - 5

So the correct option is B.

How to simplify the expression?

Here we want to simplify the expression below:

(1/2)*(2x² − 8) + (1/3)*(6x² − 3)

To do so, we need to expand the two products, we will get:

(1/2)*(2x² − 8) + (1/3)*(6x² − 3) = (1/2)*2x² − (1/2)*8 + (1/3)*6x² - (1/3)*3

(1/2)*2x² − (1/2)*8 + (1/3)*6x² - (1/3)*3 = x² - 4 + 2x² - 1

Now we can simplify this to get:

x² - 4 + 2x² - 1 = 3x² - 5

Then the correct opion is B.

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The rectangular form of the polar coordinate given is as follows:

[tex]\left(-r\frac{\sqrt{2}}{2}, r\frac{\sqrt{2}}{2}\right)[/tex]

How to convert from polar coordinates to rectangular coordinates?

To convert from polar coordinates to rectangular coordinates, you can use the following formulas:

x = r*cos(θ)y = r*sin(θ)

In which:

r is the distance from the origin to the point, also known as the magnitude or modulus.θ is the angle between the positive x-axis and the line connecting the origin to the point, measured in radians.

The sine and the cosine of the second quadrant angle in this problem are given as follows:

cos(θ) = -cos(45º) = -sqrt(2)/2.sin(θ) = sin(45º) = sqrt(2)/2.

The radius is not given, hence the rectangular coordinates are given as a function of the radius as follows:

[tex]\left(-r\frac{\sqrt{2}}{2}, r\frac{\sqrt{2}}{2}\right)[/tex]

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This is the appropriate set notation for the set R , which includes all integers between -3 and 0.

The set R can be rewritten by listing its elements in the appropriate set notation. Since the set R contains all integers between -3 and zero, we can list the elements as follows:

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

R = {-5, -4}

In set notation, this can be written as:

R = {x | x is an integer and -3≤x≤0}

Therefore, the set R can be rewritten as:

R = {-3, 0}

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There are between 175 and 245 eggs that will be cracked upon packaging in one week.

To find the number of eggs that will be cracked upon packaging in one week, we first need to calculate the daily rate of cracked eggs:

Daily rate of cracked eggs = 0.3% of 10,000 = 0.3/100 x 10,000 = 30

Next, we can find the weekly rate of cracked eggs by multiplying the daily rate by the number of days in a week:

Weekly rate of cracked eggs = 30 x 7 = 210

To determine the margin of error, we can use the formula:

[tex]Margin \ of\ error = z \sqrt(p \times (1 - p) / n)[/tex]

where z is the z-score for the desired confidence level, p is the proportion of cracked eggs, and n is the sample size.

In this case, the number of eggs produced in one week, which is 10,000 x 7 = 70,000.

Assuming a 95% confidence level, the z-score is approximately 1.96. Substituting the given values, we get:

Margin of error = 1.96 x √(0.003 x 0.997 / 70,000) ≈ 0.00040514945

Therefore, the range of possible values for the number of cracked eggs in one week is:

210 ± 0.05% of 70,000 = 210 ± 35.

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Points a, b, and c's translated images would now have new coordinates of (1, 0), (-1, 5), and (4,5), respectively.

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Answer:

$2.0025

Step-by-Step Explanation:

To calculate the player's expected winnings, we need to multiply each outcome by its probability and sum the results.

The spinner has four equally likely outcomes (A, B, C, and D), so each outcome has a probability of 1/4.

The player wins $8 if the spinner lands on A, which has probability 1/4. So the contribution to the expected winnings from this outcome is:

(1/4) * $8 = $2

The player wins a penny if the spinner lands on D, which also has probability 1/4. So the contribution to the expected winnings from this outcome is:

(1/4) * $0.01 = $0.0025

The player wins nothing if the spinner lands on B or C, each of which has probability 1/4. So the contribution to the expected winnings from these outcomes is:

(1/4) * $0 + (1/4) * $0 = $0

Now we can sum the contributions from each outcome to get the player's expected winnings:

$2 + $0.0025 + $0 = $2.0025

Therefore, the player's expected winnings are $2.0025.

Hopefully this helps!

Answer:

The answer is D.

Step-by-step explanation:

To calculate the chances of winning the Mega Bucks prize, we need to first calculate the probability of winning at each stage of the lottery.

The probability of winning $2-$5 in the state lottery is 1 in 3, or 1/3. This means that the probability of not winning $2-$5 is 2 in 3, or 2/3.

The probability of winning the Big Bucks drawing is 1 in 10, or 1/10. This means that the probability of not winning the Big Bucks drawing is 9 in 10, or 9/10.

The probability of winning the Mega Bucks prize is 1 in 50, or 1/50. This means that the probability of not winning the Mega Bucks prize is 49 in 50, or 49/50.

To find the probability of winning the Mega Bucks prize if you buy one lottery ticket, we need to multiply the probabilities of winning at each stage:

P(Mega Bucks) = P(state lottery) x P(Big Bucks) x P(Mega Bucks)

P(Mega Bucks) = (1/3) x (1/10) x (1/50)

P(Mega Bucks) = 1/1,500

Therefore, the chances of winning the Mega Bucks prize if you buy one lottery ticket are 1 in 1,500. The answer is D.

The percentage of the company's shares owned by the mutual fund is 0.4 %

How to calculate percentages?

The percentage is defined as dividing the value by the overall value and multiplying the resulting number by 100.

∴ Percentage = (Value/Total value) × 100

The original number is subtracted from the new number, divided by the original number, and multiplied by 100 to get the increased percentage.The decreased percentage is calculated by subtracting a new number from the original number, dividing that new number by the original number, and multiplying the result by 100.

Given:

The mutual fund owns = 80,000 shares

Total shares = 20 million.

Percentage = fund owns/total shares * 100

= (80000/20000000) * 100

= 8/20

= 0.4 %

Therefore, the percentage of the company's shares owned by the mutual fund is 0.4 %.

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The equation of the exponential growth function is y = 1/20(5/2)^x

Finding the exponential growth function

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

The list of options

An exponential growth function is represented as

y = ab^x

Where

b > 1

Testing option (a), we have

b = 5/2

This gives

b = 2.5

2.5 > 1

So, the function is y = 1/20(5/2)^x

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Part A: length of the shortest colored pencil = 6 inches.

Part B: length is most common colored pencil = 7 1/4 inches. (twice)

Part C: For the pencil of 7 2/4 inches long, Only 1 pencil 7 3/4 is longer than this.

Explain about the mixed fractions:

A mixed number combines an integer (whole number) with a fraction. It is also sometimes referred to as a mixed fraction (section of a whole number).

Mixed numbers can all be written either way, for example, ¾ or 5¾.. The mixed number's fractional component needs to be a legal fraction (less than 1 complete). In a correct fraction, such as 3/7, or 11/ 15., the numerator (top number) is smaller than that of the denominator (bottom number).

The data for the lengths of 8 coloured pencils.

7 1/4, 6 3/4, 7 3/4, 7, 6 2/4, 7 1/4, 6 1/4, 6

Arranging the numbers in ascending order:

6 , 6 1/4, 6 2/4, 6 3/4, 7 , 7 1/4, 7 1/4 , 7 3/4

Part A: length of the shortest colored pencil = 6 inches.

Part B: length is most common colored pencil = 7 1/4 inches. (twice)

Part C: For the pencil of 7 2/4 inches long: Only 1 pencil 7 3/4 is longer than this.

Part D: 3 pencils are between 6 and 7 inches in length, which are- 6 1/4, 6 2/4, 6 3/4 inches length.

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Answer:

C

Step-by-step explanation:

The cost depends on the number of windows. The number of windows is the independent variable.

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

Because all of the numbers have a degree symbol, we know that they all add together to make 360° since that's how many degrees there are a circle.

4x + 6x + 7x + 7x = 360

Then, we solve for x

24x = 360

x = 15

Then, add the two degrees with the red arc.

6(15) + 7(15) = 195°

The length of the red arc is 195°

The location of the image of line AB after the reflection is (d) quadrant IV

Determining the location of the image of line AB

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

The line AB located in the first quadrant

The transformation is given as

Reflection in the x-axis

The quadrant at the x-axis of the first quadrant is the fourth quadrant

This means that the reflection of the line across the x-axis would given an image located in the fourth quadrant

And as such we can conclude that the location is the fourth quadrant

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The area of the sector is 50.24ft² and the length of an arc is 16.75ft

What is area of sector?

The area of a sector of a circle is a fraction of the area of the entire circle, where the fraction is equal to the ratio of the central angle of the sector to the total central angle of the circle (which is 360 degrees or 2π radians).

The formula for the area of a sector of a circle is:

A = (θ/360) × πr²

Substituting the values into the formula;

A = (160/360) * 3.14 * (6)^2

A = 50.24ft²

b. The length of AB can be calculated using formula of length of an arc which is given as;

L = θ/360 * 2 πr

L = 160/360 * 2 * 3.14 * 6

L = 16.75ft

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