Martina, Ryan, and Keith sent a total of 77 text messages during the weekend. Ryan sent 7 fewer messages than Martina. Keith sent 2 times as many messages as Martina. How many messages did they each send?

Rounding to the nearest cubic foot, the volume of water that will be in the pool when it is filled is approximately 2713 feet³.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The first step is to find the radius of the cylinder.

Since the diameter is given as 24 feet, the radius is half of the diameter or 12 feet.

Next, we can use the formula for the volume of a cylinder -

V = πr²h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get -

V = π(12)²(6)

= π(144)(6)

= 2712.96

≈ 2713 cubic feet

Therefore, the volume value is obtained as 2713 cubic feet.

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Answer:

g(2) = 20

Step-by-step explanation:

g(x) = 7x + 6                              g(2)

g(2) = 7(2) + 6

g(2) = 14 + 6

g(2) = 20

So, the answer is g(2) = 20

Answer:

I think the answer is 50 pencils

Figure B is the correct option which represents the the contrapositive of the statement "If it is a square, then it is a quadrilateral".

What is a contrapositive statement ?

A contrapositive statement is a statement formed by negating both the hypothesis and the conclusion of the original statement, and then switching them and negating the entire statement.

In other words, if the original statement is of the form "If A, then B", then the contrapositive statement is of the form "If not B, then not A". The contrapositive statement is logically equivalent to the original statement, which means that if the original statement is true, then the contrapositive statement is also true, and if the original statement is false, then the contrapositive statement is also false.

Finding the contrapositive statement -

We are given "if it is a square,then it is a quadrilateral ".

To determine the contrapositive of a conditional statement, we must switch the hypothesis and the conclusion and negate both.

The original statement is "If it is a square, then it is a quadrilateral." The hypothesis is "it is a square," and the conclusion is "it is a quadrilateral."

Contrapositive of our given statement is -

"if it is not a square,then it is not a quadrilateral "

Therefore, figure B is correct option.

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The single equivalent discount rate for Company A is 19.28%, and for Company B is 23.18%.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

We are given;

The measures of company A and B= 8/10/14/4 10/6/16/3

Now,

To calculate the single equivalent discount rate for each company, we can use the following formula:

Single equivalent discount rate = [(1 - (Discount % / 100)) ^ (365 / Average payment period) - 1] x 100

For Company A, the average payment period is:

(8 + 10 + 14 + 4) / 4 = 9

Using the formula, we can calculate the single equivalent discount rate for Company A:

Single equivalent discount rate = [(1 - (8/100)) ^ (365 / 9) - 1] x 100 = 19.28%

For Company B, the average payment period is:

(10 + 6 + 16 + 3) / 4 = 8.75

Using the formula, we can calculate the single equivalent discount rate for Company B:

Single equivalent discount rate = [(1 - (10/100)) ^ (365 / 8.75) - 1] x 100 = 23.18%

Therefore, by percentage the answer will be 19.28% and 23.18%.

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The product of 6 √12 and 2√14 in simplest radical form is 24 √42 .

Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.

We have to find the product of 6 √12 and 2√14 in simplest radical form.

So,   6 √12 x  2√14

= 12 x √12 x √14

= 12 x 2√3 x √14

= 24 x √3 x √14

= 24 √42

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For the triangle which is mentioned above the measurement of the base will be 10 cm.

What is a Triangle?

With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.

    The area of a triangle is A=1/2b*h

Here, A is the area of  triangle =45.5 square units

          b will be the  base(NEED TO FIND)

          h will be  the height = 9.1cm

Substituting,  45.5 = (1/2)×b×9.1

                       b=  (45.5×2)/9.1

                        b=  10 cms

The base value will be: 10cms

The Complete Question: The area of the triangle is 45.5 square units and the height of the triangle is given as 9.1 cm. What is the measurement of the base?

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Answer:

$91

Step-by-step explanation:

bill = $76

tip = 20%

20% of bill = (20/100) * 76

                 = $15.2

total bill = $76 + $15.2

             = $91.2

             = $91

Answer:

x = 13

Step-by-step explanation:

We know that 5x, x+12, and 90 makes a straight line, which is 180 degrees

5x + x+12 + 90 = 180

Combine like terms.

6x+102=180

Subtract 102 from each side.

6x+102-102=180-102

6x = 78

Divide each side by 6

6x/6 = 78/6

x = 13

Answer:

x = 13

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

We know that,

→ The angle of right angle is 90°.

Forming the equation,

→ (x + 12)° + (5x)° = 90°

Then the value of x will be,

→ (x + 12)° + (5x)° = 90°

→ x + 12 + 5x = 90

→ (x + 5x) + 12 = 90

→ 6x + 12 = 90

→ 6x = 90 - 12

→ 6x = 78

→ x = 78 ÷ 6

→ [ x = 13 ]

Hence, the value of x is 13.

Where the graphs intersect or touch, the supplied statement is true, and that is the solution to any system.

One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The above is sometimes referred to as "linear equation of two variables," where y and x are the variables.

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The arc length of a single section on a dartboard rounded to the nearest millimeter is 53 mm.

In mathematics, an equation is a statement that two expressions are equal. It typically involves one or more variables that can take on different values, and the goal is often to solve for the value(s) of the variable(s) that make the equation true.

The total circumference of the dartboard is given by:

C = 2πr

where r is the radius of the dartboard.

Substituting the given values, we get:

C = 2π(170 mm)

C = 1068.18 mm

Dividing the circumference by the number of sections, we get the arc length of a single section:

Arc length = C/20

Arc length = 1068.18 mm/20

Arc length ≈ 53.41 mm

Rounding this to the nearest millimeter, we get:

Arc length ≈ 53 mm

Therefore, the arc length of a single section on a dartboard rounded to the nearest millimeter is 53 mm.

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In response to the query, we have that The Pythagorean identity for theta = 30° is therefore confirmed since sin(30°) + cos(30°) = 1.

The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.

This trigonometric identity is valid for all theta values. Because it is connected to the geometry-related Pythagorean theorem, it is known as the Pythagorean identity.

According to Pythagorean theory,

[tex]Cos(theta)^2 + Sin(theta^)2 = 1[/tex]

So, you can easily include that value into the equation and simplify it if you need to assess sin(theta) + cos(theta) for a certain value of theta:

[tex]Cos(theta)2 + Sin(theta)2 = 1\\Sin(2) + Cos(30)\\If theta = 30, then 2(30) = 1.\\(1/2)\\c^2 + (√3/2)\\c^2 = 1 \s1/4 + 3/4 = 1 \s1 = 1[/tex]

The Pythagorean identity for theta = 30° is therefore confirmed since sin(30°) + cos(30°) = 1.

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Answer:

36 Units

Step-by-step explanation:

The circumference (C) of a circle is related to its diameter (d) by the formula:

C = πd

We can rearrange this formula to solve for the diameter:

d = C / π

In this case, the circumference of the circle is C = 113.04 units and π is approximately 3.14. Substituting these values into the formula, we get:

d = 113.04 units / 3.14

d ≈ 36 units (rounded to the nearest unit)

Therefore, the diameter of the circle is approximately 36 units.

Answer:36 units

Step-by-step explanation:

[tex]x + (x+1) + (x+2) + (x+3) = -326\\[/tex]

[tex]4x + 6 = -326[/tex]

[tex]4x = - 326-6[/tex]

[tex]4x = -332[/tex]

[tex]x = -332/4 \implies x = - 83[/tex]

the integers are:

[tex]-83 < -82 < -81 < -80[/tex]

the largest integer is: -80

55.0% of the people surveyed were satisfied with the car.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Formula for percentages is (Value/Total value) x 100.

If two values are presented to us, we must determine the percentage difference between them.

Given that, 1,705 said they would buy that type of car again.

Thus, to find people who were satisfied with the car:

Percentage = (Number of satisfied people / Total number of people) x 100%

Percentage = (1,705 / 3,100) x 100% = 55.0%

Hence, 55.0% of the people surveyed were satisfied with the car.

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The number of square feet of wallpaper that Austin will need for the large wooden storage boxes would be = 1,296 ft².

To calculate the amount of wallpaper needed, we should find the area of the rectangular prism.

The formula for the area of rectangular prism = 2 (lh +wh + lw ).

Where;

Length (l) = 6ft

width (w) = 3ft

Height (h) = 6ft

area = 2( 6×6 + 3×6 + 6×3)

= 2( 36+18+18)

= 2( 72)

= 144 ft²

Therefore the amount of wallpaper needed = 144× 9 = 1296 ft².

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The x-coordinate at which F(x) = G(x) is 0.667. By graphing the functions, the answer has been discovered.

Making a graph of the pertinent function is the first step in graphing a function. The function equation will be satisfied by a curve if it reflects the function at that location.

We are given two functions as f(x) = log (2x) and g(x) = 3x - 2

The graph of the given functions has been plotted and attached below.

In the graph, the red line represents the log function i.e. f(x) and the blue line represents the linear function i.e. g(x).

From the graph, we can observe that the two functions meet at two points which are (0.667, 0) and (0, -2).

Hence, the x value where F(x) = G(x) is 0.667.

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Answer:

Before Tax Price: $40.00

Sale Tax: 5.00% or $2.00

After Tax Price: $42.00

Step-by-step explanation:

Answer:

42 dollars

Step-by-step explanation:

When doing tax problems, we need to memorize the formula of:

price + tax • price = price with sales tax.

This formula works because you have the initial percentage of the cost, with the added tax, which gives the extra value--then added together it gives the sales cost price.

So let's plug our numbers in

40 + (0.05 or 5%) • 40 = price with sales tax

40 + 2 = price with sales tax

42 = price with sales tax

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Answer:

the full numbers is 9, 27, 81, 243.

Answer:

243

Step-by-step explanation:

After the pumping of Container A's water into Container B, the volume of water in Container B is 6,286 feet³.

The volume refers to the amount of space in a container.

The volume of a container can be determined using the following formula: πr²h, where:

Diameter = 26 feet

Height = 20 feet

The volume of water in Container A = πr²h

r = radius = diameter/2

= 20/2 = 10 feet

Volume = 22/7 x 10 x 10 x 20

= 22/7 x 100 x 20

=6,285.7

= 6,286 feet³

Diameter = 36 feet

Height = 19 feet

Thus, the volume of Container B after the pumping, which is equal to the volume of water in Container A, is 6,286 feet³.

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After the pumping of Container A's water into Container B, what is the volume of water in Container B?

Answer:

32 : 1

Step-by-step explanation:

dimensions of the parts of the ratio must be in the same units

convert 9 feet to inches

1 foot = 12 inches

then

9 feet = 9 × 12 = 108 inches

then ratio

9 feet : 3 [tex]\frac{3}{8}[/tex] inches

= 108 inches : 3 [tex]\frac{3}{8}[/tex] inches ( change mixed number to improper fraction )

= 108 : [tex]\frac{27}{8}[/tex] ( multiply both parts by 8 to clear the fraction )

= 864 : 27 ( divide both parts by 27 )

= 32 : 1

Answer:

Believe it's just a

Step-by-step explanation:

Because

This is an observational study because the researchers do not attempt to modify or apply a treatment to the individuals. Major problem with the study is A.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

This is a convenience sample with voluntary response, which has a high chance of leading to bias.

The survey relies on self-selection, meaning that only those who were interested in responding to the question chose to do so.

This can result in a biased sample that does not accurately represent the population of all internet users.

Additionally, the sample size is not known to be representative or sufficient for generalization, and there is no control group or experimental design to establish cause and effect.

Hence, this is an observational study because the researchers do not attempt to modify or apply a treatment to the individuals.

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480 m³ is the volume of the given solid.

What is Volume?

The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

The dimensions of the trapezoidal prism are given in the diagram.

The dimensions of the cuboidal cavity are also given.

Volume of the solid = Volume of trapezoidal prism - Volume of cuboidal cavity

Volume of trapezoidal prism = (1/2)[Sum of parallel sides][h]×length

= (1/2)×[13+8]×[5]×10

= 525 m³

Volume of cuboidal cavity = l×b×h

= 10×3×1.5

= 45 m³

Volume of the solid = 525 - 45 m³

= 480 m³

The volume of the solid is 480 m³.

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Noah missed 7 points on the test. And Gabe missed 2x - 3 = 2(7) - 3 = 11 points on the test. So, Gabe missed 11 points on the test.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let x be the number of points that Noah missed on the test.

Then, the number of points that Gabe missed is 2x - 3, according to the problem.

The total number of points missed by both of them is given as 18.

So, we can write an equation based on the problem statement:

x + (2x - 3) = 18

Simplifying the equation, we get:

3x - 3 = 18

Adding 3 to both sides of the equation, we get:

3x = 21

Dividing both sides of the equation by 3, we get:

x = 7

Therefore, Noah missed 7 points on the test. And Gabe missed 2x - 3 = 2(7) - 3 = 11 points on the test. So, Gabe missed 11 points on the test.

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The tangent of angle Z is given as follows:

tan(Z) = length of opposite side/length of adjacent side.

The three trigonometric ratios are defined as follows:

Hence the tangent for angle Z is given by the ratio between the length of the opposite side to angle Z and the length of the adjacent side to angle Z.

The problem is incomplete, hence the general procedure to obtain the tangent of angle Z is presented.

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The mean of the data is 1097.5

A mean in math is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers. For example, with the data set: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.

Mean = summation of item /number of items

summation of item = 4390

number of items = 4

therefore mean = 4390/4

= 1,097.5

therefore the mean if the data is 1,097.5

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Answer:

1 and 7/8.

Step-by-step explanation:

Two and a half= 5/2

5/2 x 3/4 = 15/8 = 1 7/8

Answer: 205

Step-by-step explanation:

ok, the height of this thing is 22 so lets start whit the top. So the height of this thing is 17 not including the triangles at the top. And 22-17=5 so the height of these triangles is 5 and the base is 10 because if you dd the two 5s and subtract it from the whole base you get 10 and 10 x 7 is 70 /2 is 35 now for the rectangle in the middle the height is 7 and we alr know the base which is 10 so 7x10 is 70 70+35=105 ok now the last one 10 x 20= 200 +105= 205

Answer:

Area=295cm²

Step-by-step explanation:

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The value of x for the given cone will be 4. The correct option is C.

The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.

Given that the volume of the cone is V = 128π and the height of the cone is h = 24 units.

The value of the radius x will be calculated as,

V = ( 1 / 3 )πr²h

128π = ( 1 / 3) π x r² x 24

r² = 16

r = 4 units

Therefore, the value of x will be 4 units.

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