Eli wants to combine 0.5 gallons of a 10% acid solution with a 35% solution to make a 15% acetic acid solution. He needs to determine how many gallons of 35% solution are needed.
Eli decides to let v represent the volume of the 35% solution and makes a table to help solve the problem.
Help Eli by completing the table.
Drag each tile to the correct cell in the table.

The simplified form of the expression (81x⁴y⁹)¹/² is 9x²y⁴√y

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

what is the simplified form of (81x^4y^9)^1/2

Rewrite the superscripts properly

(81x⁴y⁹)¹/²

The above expression is a radical expression

And the radicand is 81x⁴y⁹

The superscript outside the bracket represents square root

So, we have the following representation

(81x⁴y⁹)¹/² = 9x²y⁴√y

Hence, the solution is 9x²y⁴√y

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The measure of angle C in the vertical angles is B. 28.3°.

Vertical angles are the angles formed when two lines intersect. The term "vertical" in this context refers to the fact that they share the same Vertex (corner point), rather than the usual meaning of up-down.

When two lines intersect, vertical angles are formed. Because the angles are opposite each other, they are sometimes referred to as vertically opposite angles. Real-world examples of vertical angles include a railroad crossing sign, the letter "X," open scissors pliers, and so on.

There angles are equal. Therefore, it'll be 28.3°.

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Answer: 28.3 GO GET UR A+ BROSKI

Step-by-step explanation:

They're virtical angles which mean

THEY'RE THE SAME BRO

so just do 28.3 :)

According to the figure, the side congruent to line GK is line HL

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSS

Side - Angle - Side = SAS

Angle - Side - Angle = ASA

Angle - Angle - Side = AAS

Hypotenuse and one leg = HL

The problem requires the prove by Angle - Side - Angle = ASA to ensure that the the triangles are congruent

The Angle and sides used for the proof include

< F = < J

FL = JK

<  L = < K

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Answer:

  A.  HL

Step-by-step explanation:

You want to identify the side corresponding to GK in the figure showing congruent triangles.

The larger triangles on the left and right each have an angle marked with one arc, an angle marked with two arcs, and the segment between those angles marked with one hash mark. This identical marking of two angles and the side between them means you can declare the triangles congruent by the ASA (angle-side-angle) congruence postulate.

When we name the triangles in order of the number of marks on the angles (0–2 arcs), we find the congruence statement to be ...

  ∆HLF ≅ ∆GKJ

The segment of interest is GK, which is identified by the first two letters of its triangle designator in the congruence statement. The corresponding side is identified by the first two letters in the other triangle designator: HL.

  ∆HLF ≅ ∆GKJ

Side HL is congruent to GK.

__

Additional comment

Like a lot of math, this requires you to match patterns.

Answer:

m < 3

Step-by-step explanation:

Writing inequalities

The line is going to the left so we use a less than sign (<)

The circle is open so there is no equal sign

The number is where the circle is

m < 3

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

1 can of paint is used in 2(1/4) hours

4/9 can of paint is used in 1 hour.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

2/3 can of paint = 1(1/2) hours

2/3 can of paint = 3/2 hours

Multiply 2/3 on both sides.

2/3 x 2/3 can of paint = 1 hour

4/9 can of paint = 1 hour

Or

2/3 can of paint = 1(1/2) hours

Multiply 3/2 on both sides.

1 can of paint = 3/2 x 3/2 hours

1 can of paint = 9/4 hours

1 can of paint = 2(1/4) hours

Thus,

We can say that,

1 can of paint is used in 2(1/4) hours

4/9 can of paint is used in 1 hour.

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The pattern that this system detects is a four-digit number that is divisible by 3.

1. The system starts by taking an input of a four-digit number.

2. It then checks if the last digit of the input number is divisible by 3.

3. If it is, the system continues to check if the sum of the remaining three digits is divisible by 3.

4. If this turns out to be true, the system will output a signal indicating that the input number is divisible by 3.

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Answer:

6.64

Step-by-step explanation:

The nearest hundredth is the second digit after the decimal point.

6.6428571 rounded to the nearest hundredth is 6.64

The answer is (76.42 ; 78.17)

Given that:

A botanist is attempting to determine how many seeds are typically present in a particular fruit. She collects 65 samples and counts how many seeds are present in each. Using her sample data, the mean is 77.3 and the SD is 5.5.

Sample size, n = 65

Mean, xbar = 77.3

Standard deviation, s = 5.5

Confidence level, Zcritical at 80% = 1.28

Confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * s/sqrt(n)

Margin of Error = 1.28 * 5.5/sqrt(65)

Margin of Error =0.873

Lower boundary = 77.3 - 0.873 =76.42

Upper boundary = 77.3  + 0.873 = 78.17

Therefore, the answer is (76.42 ; 78.17)

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Answer:

100 pounds

Step-by-Step Explanation:

20+100=120

cat weighs 20

dog weighs 100

dog weighs 80 pounds more than the cat (20) = 100

The value of the formula will be;

⇒ S = 180 (n - 2)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.''

Now,

Since, The algebraic expression is,

''The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.''

Hence, We can formulate the expression as;

⇒ S = 180 (n - 2)

Thus, The value of the formula is,

⇒ S = 180 (n - 2)

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Josiah will take 1.5 hours to travel to work at the speed of 55 miles per hour.

As the speed and time are inversely proportional to each other, we can represent it as -

speed(i)/speed(f) = time(f)/time(i), where I represents initial and f represents final. Now, keep the values in formula to find the time (final).

35/55 = time(f)/2.5

Rewriting the equation according to variable time(f).

time(f) = (35×2.5)/55

Performing multiplication on Right Hand Side of the equation

time(f) = 87.5/55

Performing division on Right Hand Side of the equation

time(f) = 1.59 hours

Hence, it will take 1.59 hours.

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The complete question is -

The speed (or rate) Josiah travels to work is inversely proportional to time it

takes to get there. If he travels 35 miles per hour it will take him 2.5 hours to get to work. How long will it take him if he travels 55 miles per hour?

The system of equations y 2 3x 3 x= -2 has a solution.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

y = -2*2/3+3

y= -4/3+3

now simplifying,

5/3

Hence, The system of equations y 2 3x 3 x= -2 has a solution.

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Complete question-

What is the solution to the system of equations y 2 3x 3 x?

Answer:

-----------------------------------

Slope-intercept form of a line:

The line has points:

The first point represents the y-intercept, b = 2.

The slope is:

The line is:

Answer:

1.d

2.a

3.e

4.g

5.f

6.c

7.b

Step-by-step explanation:

did it already

In picking the smoothing constant for an exponential smoothing model, we should look for a value that produces values which compare well with actual values based on a standard measure of error.

What is exponential smoothing model?

Using the exponential window function, exponential smoothing is a general method for blending time series data. Exponential functions are used to assign exponentially decreasing weights over time, as opposed to the simple moving average, which weights previous observations equally.

The correct answer is, produces values which compare well with actual values based on a standard measure of error.

Quantitative forecasting utilizes a compilation of past performance data of the organization to arrive at an accurate forecast for any given process.

The smoothing constant selected requires to optimize accuracy the unknown parameters and the initial values need to be considered with the implementation of the sum of squared errors providing the required accuracy.

Hence, in picking the smoothing constant for an exponential smoothing model, we should look for a value that produces values which compare well with actual values based on a standard measure of error.

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Complete question:

Complete question is attached below.

Metric tons of soil lost during its formation [tex]2.96*10^-7[/tex]

Gully is 2 meter deep 4 meter wide and 50 meters long.

So we know if Gully length = l width =w height =h

then volume of gully is l*b*h.

by same way volume of gully is 50*4*2 = 200 [tex]m^3[/tex]

Bulk density of this soil is 1.48 mg/m^3.

How many metric tons of soil lost during its formation?

1000kg = 1 metric ton.

density  = 1.48mg/m^3 = [tex]1.48*10^-6[/tex] kg/m^3

means for 1 m^3 volume we lost [tex]1.48*10^-6[/tex] kg of soil.

for 200m^3 volume we lost [tex]200*1.48*10^-6[/tex] kg of soil.

[tex]296*10^-6[/tex] kg of soil.

to convert kg into metric ton we have to divide 1000.

[tex]296*10^-6[/tex]/1000 = [tex]296*10^-9[/tex] = [tex]2.96*10^-7[/tex]

So  Metric tons of soil lost during its formation [tex]2.96*10^-7[/tex]

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Absolute Value: The "unsigned" number that corresponds to the (Positive) distance between a number and zero on the number line. [tex]| - 4| = 4 and | 4| = 4;[/tex]

Positive and negative integers, fractions, rational numbers, including irrational numbers, and negative integers are all examples of real numbers. fictitious numbers,  Real numbers are those that fall between the two extremes,

Absolute Value: The "unsigned" number that corresponds to the (Positive) distance between a number and zero on the number line. | - 4| = 4 and | 4| = 4; The collection of positive numbers used to count items is known as the counting numbers, sometimes known as natural numbers. 1, 2, 3, 4, 5, ...; Fractions and decimals are not integers; rather, integers are the set of all whole numbers, along with their opposites (the positive whole numbers, the negative whole numbers, and zero). -3, -2, -1, 0, 1, 2, 3, ...; Irrational Numbers - The collection of all non-terminating, non-repeating decimal numbers; Natural Integers: The collection of positive numbers utilized in object counting (also called counting numbers). 1, 2, 3, 4, 5, ...; Unfavorable Numbers - the range of numbers on the number line that are less than zero and to the left of zero.; Number Line - a horizontal line with points representing different numbers. In a number line with just whole numbers or integers, the dots are uniformly spaced out according to the value of the number they represent.; Opposite - a number that is on the other side of zero and at the same distance from zero as a given integer. For instance, the opposites of 7 and -7 and 9 and 9 are both 7; positive figures - the group of numbers on the number line that are greater than zero and to the right of zero.

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She needs to bike for 66 miles on the last day so that her mean is 54 miles per day.

Mean, in terms of math, is the total added values of all the data in a set divided by the number of data in the set.

To calculate the miles Marthina needs to bike so that her mean is 54 mile per day, we use the formula below.

Formula:

Where:

Let y be the miles she biked for the last day.

From the question,

Given:

Substitute these values into equation 1 and solve for y

Hence, she needs to bike for 66 miles on the last day.

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Answer:

minus 5 times x and the quantity x squared minus 1.

Step-by-step explanation:

Step-by-step explanation:

???

(x + y) + 3

this is 3 more than the sum of x and y.

The Median age for the Chess Club members is 14 and  the Median age for the Chess Club members is 12.

Option A. The Median age for the Chess Club members is less than the Median age for the Checkers Club members is the correct option of the given figure.

The value that, when a dataset is arranged, lies exactly in the middle is the median. The difference between the lowest 50% and highest 50% of data is a measure of central tendency. Depending on whether you have an odd or an even number of data points, there are several procedures to find the median.

Identifying the median The data points should be arranged from smallest to largest. The median is the middle data point in the list if the number of data points is odd. The median is the average of the two middle data points in the list if the number of data points is even.

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The sigma notation is:

Σ (6 to k=1) k²

Given:

The summation symbol, S, tells us to add up the sequence's components. To the right of the summation sign is a typical component of the sequence that is being summed. An index that appears below the summation sign designates the variable of summation.

Typically, a sum of several terms is represented by the symbol "sigma." Typically, this symbol is accompanied by an index that changes to include all terms that must be taken into account while calculating the sum.

use 1 as the lower limit of summation and k for the index of summation. 1+41+4+9+16+25+36

⇒ 1+4+9+16+25+36

⇒ 1² + 2² + 3² + 4² + 5² + 6²

⇒ Σ (6 to k=1) k²

Hence we get the required answer.

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Answer:

4 is the smallest number

Step-by-step explanation:

4 times 8 is 32. 4 + 8 is 12. 4 is smaller than 8 so it would be the smaller number

The simplified form of function sin(t)sec(t) is tan(t)

The trigonometric functions and identities are the ratio of sides of a right-angled triangle. The sides of a right triangle are the perpendicular side, hypotenuse, and base, which are used to calculate the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas.

sec(t) = 1/cos(t)

replacing sec(t) in the function sin(t)sec(t)

we have sin(t) x 1/cos(t) which  becomes sin(t)/cos(t)

but sin(t)/cos(t) = tan(t)

In conclusion the simplified form of the function is  tan(t)

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The group of symmetries of a regular tetrahedron is known as the tetrahedral group, and is denoted by $T_d$. This group consists of all the symmetries of a regular tetrahedron, including orientation-reversing symmetries.

The regular tetrahedron is a three-dimensional object with four faces that are all equilateral triangles. It is one of the five Platonic solids, which are convex polyhedral with congruent faces and regular polygonal faces. The tetrahedral group $T_d$ contains a total of 24 symmetries, which can be divided into two classes: rotational symmetries and reflection symmetries. The rotational symmetries consist of 8 proper rotations, which are rotations that preserve the orientation of the tetrahedron, and 6 improper rotations, which are rotations that reverse the orientation of the tetrahedron. The reflection symmetries consist of 6 plane reflections that reflect the tetrahedron across one of its faces.

To understand the symmetries of the tetrahedron, it is helpful to think about the symmetries of an individual face. An equilateral triangle has 6 symmetries: 3 rotational symmetries (120 degree rotations about the center of the triangle), and 3 reflection symmetries (across the lines of symmetry of the triangle). The regular tetrahedron has four faces, so these symmetries can be applied to each face independently, resulting in a total of $6^4=1296$ symmetries. However, many of these symmetries are not distinct, and can be generated by combinations of the tetrahedral group's 24 symmetries. Thus, the tetrahedral group $T_d$ is the group of all the distinct symmetries of a regular tetrahedron.

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The average value of the function f(x) on [0, 2] is 3.03515625.

A function is a relationship between the inputs, such that each input is related to one and only one output. If it is related to more than one output, then the relation is not a function.

The question did not specify the value of f(x). Considering the value of f(x) as f(x)= [tex]x^4[/tex] on (0,2)

Now, partitioning the interval into four sub-intervals of equal length, we get,

2-0/4=2/4 or 1/2 or 0.5

Thus, we get the four intervals:

[0, 0.5], [0.5, 1], [1, 1.5], and [1.5, 2].

When finding the mid-points of the intervals, we get the mid-points as:

[0, 0.5] = 0.25

[0.5, 1] = 0.75

[1, 1.5] = 1.25

[1.5, 2] = 1.75

Now, finding the f(x) of each interval, by substituting the value of the mid-point in the place of x we get:

Thus, f(0.25) = [tex]0.25^4[/tex]

f(0.75) = [tex]0.75^4[/tex]

f(1.25) = [tex]1.25^4[/tex]

f(1.75) = [tex]1.75^4[/tex]

Now, find the average value of f(x) =[tex]x^4[/tex]  on [0, 2].

1/2[([tex]0.25^4[/tex]+[tex]0.75^4 +1.25^4+1.75^4[/tex])/2]

= 3.03515625

Thus,

The average value of the function f(x) on [0, 2] is 3.03515625.

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The ΔABC and ΔDEF are congruent by SSS congruent criteria

According to the question,

We have to prove ΔABC and ΔDEF are congruent

Coordinates of ΔABC are given as :

A(-2 , -2) , B(4 , -2) and C(4,6)

By using Distance formula ,

AB = √(-2-(-2))²+ (4 - (-2))²

=> √(-2 + 2)² + (4 +2)²

=> √ 6²

=> 6

AC = √(6-(-2))²+ (4 - (-2))²

=> √(6 + 2)² + (4 +2)²

=> √ 56 + 36

=> √92

BC = √(6-(-2))²+ (4 - 4)²

=> √(6+ 2)²

=> √ 8²

=> 8

Coordinates for ΔDEF,

D(5 , 7) , E(5,1) and F(13 , 1)

By using Distance formula ,

DE = √(1 - 7)²+ (5 -5)²

=> √(-6)²

=> √36

=> 6

DF = √(1-7)²+ (13 - 5)²

=> √(-6)² + (8)²

=> √ 56 + 36

=> √92

EF= √(1 - 1)²+ (13 - 5)²

=> √ 8²

=> 8

Now, two triangles are congruent if they are equal sides or equal angles

Therefore , In ΔABC and ΔDEF

AB = DE

AC = DF

BC =EF

By the SSS criteria , ΔABC and ΔDEF are congruent

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The probability of having a boy when a couple has six ​children is 63 / 64.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

A couple has six ​children, n = 6

The wanted event, p = 1 / 2

Calculate the probability of having a boy given by the following formula,

[tex]P(X) = nC_x px (1-p)n-x[/tex]

Here, [tex]X[/tex] = number of boys,

So,

P(X >= x) = 1 - P(X = 0)

P (X) = 1 - 6C₀ × (1 / 2) 0 × (1/2) 6

P (X) = 63 / 64

Therefore, the probability of having a boy when a couple has six ​children is 63 / 64.

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Answer:A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

A topic sentence is used to bring

to a paragraph.