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16 cups of water using 1/2 cup of measuring cup will fill a gallon of water.

To find the number of 1/2 cups that will fill a gallon, we simply need to know how many cups are in one gallon.

[tex]1cup = 0.0625 gallon[/tex]

This implies that

[tex]\frac{1}{2} cup = 0.03125 gallon[/tex]

Let's equate this and find how many cups are in one gallon.

[tex]\frac{1}{2} cup = 0.03125 gallon\\x cup = 1 gallon\\[/tex]

cross multiply both sides and make x the subject of formula

[tex]x = \frac{0.5}{0.03125}\\x = 16 cups[/tex]

The number of 1/2 cups that will fill 1 gallon will be 16 cups.

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Although part of your question is missing, you might be referring to this complete question "Translate the sum of m and 2.33 multiplied by s is 77.77 into an algebraic equation. Do not solve the equation."

Translated equation is m + 2.33s = 77.77

An algebraic equation is the equality of two expressions formulated by applying a set of variables such as addition, subtraction, multiplication, division, raise to power, etc. The phrase " the sum of a and b" into an algebraic expression is determined as a+b. It deals with symbols and these symbols deal with each other through variants.

Hence, the equation translated is a linear equation of algebraic equations.  m+ 2.33s = 77.77

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We have a rectangular slab.

The volume of concrete is equal to the volume of this rectangular prism.

The volume of this prism is equal to the product of its length, width and thickness.

Then, we can write:

We convert the thickness from inches to feet by multiplying it by a unit ratio 1 ft / 12 inches, which has a value of 1, as 1 ft = 12 inches, but let us change the units from inches to feet.

When we have all the measures in feet we can have the volume in cubic feet.

Answer: 232 cubic feet.

Given that 3 unit factor growth is 1.65

Then 1 unit growth factor = (1.65)^1/3 = 1.181

2 unit growth factor of F  = 1.396

And 1/2 unit growth factor = (1.65)^0.5/3 = (1.65)^0.53/3 = (1.65)^1/6

                                              = 1.0875

or 1/2 unit growth of factor f = 1.0875

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Answer:

6 and 8

Step-by-step explanation:

x =     one integer

x+2 = other integer

Pythagorean Theorem:

x^2   +   ( x+2)^2 = 10^2

x^2 + x^2 + 4x + 4 = 100

2x^2 + 4x - 96 = 0

x^2 + 2x -48 = 0           Use factoring   ( or Quadratic Formula)

(x+8)(x-6) = 0     shows x = 6     the other integer is 8

If line m is parallel to line n then determine the value of x= 65°

2x+50° = 180°

2x = 180° - 50°

2x = 130°

x = 130°÷2

x = 65°

Parallel lines are  lines that do not cross or meet  at any point in the plane. They are always parallel and  equidistant from each other. Parallel lines are non-intersecting lines. We can also say that parallel lines meet at infinity.

Properties of Parallel Lines

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The value of x is 25. It states that when two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent.

Parallel lines are coplanar straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

Parallels, paralleling, and paralleled are all word forms. a countable noun A parallel is something that is similar to something else but exists or occurs in a different place or at a different time.

Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that intersect at a right angle (90 degrees).

Two different interior angles.

- (2x - 10)°

- (65 - x)°

Because lines m and n are parallel and because of the alternate angles theorem.

We can see that.

2x - 10 = 65 - x

2x + x = 65 + 10

3x = 75

x = 75/3

x = 25

Hence, the value of x is 25.

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[tex]5.51134751094269\times10^8[/tex] transistors could fit on a microchip [tex]19[/tex] years later.

Moore's law predicts that the number of transistors that can be fit on a microchip will increase 40% every year.

So the expected increment every year [tex]40\%[/tex].

Microchips from a given year could hold about [tex]922,200[/tex] transistors.

We have to find ow many transistors could fit on a microchip [tex]19[/tex] years later.

From the question total years are [tex]19[/tex].

Since the number of transistors is increased every year so number of transistors of previous year added. So we can see that  the number of transistors that can be fit on a microchip is increased compound. We can find the total number of transistors by multiplying number of transistors with the rate assembled by one. So we can use the formula

So the number of transistors could fit on a microchip 19 years later.

Number of transistor = Microchips from a given year could hold about transistors(1 + increment rate)^total years

Number of transistor [tex]=922,200(1+\frac{40}{100})^{19}[/tex]

Number of transistor [tex]=922,200(1+\frac{2}{5})^{19}[/tex]

Number of transistor [tex]=922,200(\frac{5+2}{5})^{19}[/tex]

Number of transistor [tex]=922,200(\frac{7}{5})^{19}[/tex]

After evaluating the expression using the calculator we get

Number of transistor [tex]=551134751.094269[/tex]

Number of transistor [tex]=5.51134751094269\times10^8[/tex]

Hence, [tex]5.51134751094269\times10^8[/tex] transistors could fit on a microchip [tex]19[/tex] years later.

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Answer:

-2

Step-by-step explanation:

PT = TQ

3x + 4 = 5x - 8

-3x         -3x

4 = 2x - 8

-8          -8

-4 = 2x

÷2   ÷2

x= -2      

sooo

3 times -2 +4 = -2

An expression which shows the order the numbers would appear on a number line from least to greatest is: A. 17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3.

A number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.

In Mathematics, a number line typically increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In order to arrange the given numbers in order from least to greatest, we would convert them into a decimal number as follows:

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The measure of the angle y is 49 degrees if AB=AD and BC=DC; the answer is 49 degrees.

It is defined as a four-sided polygon in geometry having four edges and four corners. The kite is quadrilateral, having two pairs of congruent sides and it has one pair of opposite congruent angles.

The kite is given in the picture.

AB = AD

BC = DC

∠DBC + ∠CBD +  ∠C = 180  

From the property of kite: ∠DBC = ∠CBD

y + y + 82 = 180

y = 98/2

y = 49 degrees

Thus, the measure of the angle y is 49 degrees if AB=AD and BC=DC; the answer is 49 degrees.

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Answer:

Evaluate

18p

3

−6p

2

+3p−1

Rewrite the expression

18p

3

+3p−6p

2

−1

Factor out 3p from the expression

3p(6p

2

+1)−6p

2

−1

Factor out −1 from the expression

3p(6p

2

+1)−(6p

2

+1)

Solution

(3p−1)(6p

2

+1)

Leah can run 320 yards in 2 minutes at the same rate as she can run 720 yards in 4.5 minutes. The correct option is B. 320.

To find out how many yards Leah can run in 2 minutes at the same rate, we can use the concept of proportionality.

Let's set up a proportion based on the information given:

720 yards / 4.5 minutes = x yards / 2 minutes

To find the value of x, we can cross-multiply:

4.5 minutes × x yards = 720 yards × 2 minutes

Now, divide both sides by 4.5 to solve for x:

x yards = (720 yards × 2 minutes) / 4.5 minutes

x yards = 320 yards

So, Leah can run 320 yards in 2 minutes at the same rate.

The correct answer is B. 320.

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Answer:

A is correct.

[tex]g = \frac{p}{6} - 15[/tex]

Step-by-step explanation:

[tex]p = 6g + 90[/tex]

[tex]6g = p - 90[/tex]

[tex]g = \frac{p}{6} - 15[/tex]

So A is correct.

The covariance value between two variables says, days to 230 lbs and backfat thickness, is 0.48..

The covariance value between any two variables is used to determine whether the variables are changing in the same direction. It relates the two variables if they are from different data sets.

Let X and Y be two data sets with different values. Then the covariance between X and Y is given by

Cov ( X,Y) = ∑ ( X ᵢ– u) ( Yⱼ-v ) /n

Where are Xᵢ's elements in the X data set

Yⱼ→ elements of the Y set

μ → mean of X data set

ν→ mean of Y set

n→ total number of observations

As we have given two sets of data, let days to 230 lbs and backfat thickness be sets X and Y, respectively.

Now, we shall calculate the mean value for X and Y sets.

Mean of X set = (164+158+180 + +160+198+172+186+178+178+186)/10= 176

The mean of Y set =

 (1.0+ 1.1+ 1.2+ 1.4+1.2+1.3++1.1+1.3+1.4+1.0)/10 = 1.2

Xᵢ– μ - 12 -18 4 -16 22 -4 10 2 2 10

Yⱼ– ν -.2 - .1 0 .2 0 .1 -.1 .1 .2 -.2

(Xᵢ - μ)(Yⱼ- ν) 2.4 1.8 0 - 3.2. 0 0.4 1 4.4 -2

∑ (Xᵢ - μ ) ( Yⱼ - ν) = 4.8

put all the values of variables in above formula we get,. Cov( X, Y) = 4.8 / 10 = 0.48 ..

So, the Covariance between the days of 230lb and backfat thickness is 0.48 ..

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I will plug in the POINTS including k in the equation each point in its place either x or y.

[tex]( - 2)^{2} +( {k})^{2} = 20 \\ 4 + {k}^{2} = 20 \\ k^{2} + 4 - 20 = 0 \\ {k}^{2} - 16 = 0 \\ (k + 4)(k - 4) = 0 \\ \\ k + 4 = 0 \\ \\ or \\ \\ k - 4 = 0 \\ \\ k = 4 \\ or \\ k = - 4[/tex]

ATTACHED IS THE SOLUTION

Answer:

x = 9

Step-by-step explanation:

3(x - 5) = 12 ← distribute the parenthesis on the left by 3

3x - 15 = 12 ( add 15 to both sides )

3x = 27 ( divide both sides by 3 )

x = 9

The actual closet has a length of 6 feet

The scale of the drawing is given as

Scale = 8 inches : 3 feet.

Also, we have the length of the closet to be

Length = 16 inches

So, we have

16 inches : Actual length = 8 inches : 3 feet.

Multiply the ratio by 2

So, we have

16 inches : Actual length = 16 inches : 6 feet.

By comparison, we have

Actual length = 6 feet

Hence, the length of the actual closet is 6 feet

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Answer:

-4/5 > -8/

-4/5 greater than -8/

Answer:

" > "

Step-by-step explanation:

-4/5=4x9 5×9

-4/5 = - 36/ 45

-8/9=8×5 9×5

-8/9 =-40/45

-36/ 45 > -40/45

-4/5 > -8/9

in this case - 4/5 is closer to 0

Answer:

domain -2<x<2

range -2<y<2

not a function

[tex]\frac{v}{8} -3.1=-15.9[/tex]

Simplify equation:

[tex]\frac{1}{8}v+-3.1=-15.9[/tex]

[tex]\frac{1}{8} v-3.1=-15.9[/tex]

Add 3.1 to both sides:

[tex]\frac{1}{8} v-3.1+3.1=-15.9+3.1\\[/tex]

[tex]\frac{1}{8} v=-12.8[/tex]

Multiply both sides by 8:

[tex]8\times(\frac{1}{8} v)=(8)\times(-12.8)\\-102.4[/tex]

[tex]\fbox{v=-102.4}[/tex]

Solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1

Algebraic equations are defined as mathematical statements in which two algebraic expressions are set equal to each other. An algebraic expression usually consists of  variables,  coefficients and  constants. Algebraic equations can be of many types, such as monomial algebraic equations, binomial algebraic equations, quadratic algebraic equations, polynomial equations.  

Given in the question that the value of f(x) is equal to 4x³+6x²-3x-4

and the value of g(x) is equal to 4x-3.

Subtracting g(x) from f(x) we get,

(f-g)(x)= 4x³+6x²-3x-4-4x+3

4x³+6x²-7x-1

Therefore, solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1.

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In order to find the proportion of disks that are defective, we can divide the number of defective disks by the total number of disks in the sample:

Therefore the proportion is 35/881.

for the function

f(x) = (x -g)(x - h)

To get the x-intercept, we can equate the function to zero

f(x) = (x -g)(x - h) = 0

so (x - g) = 0

which gives x = g

And (x - h) = 0

which gives x = h

Since we have been told that g and h are positive, then it follows that both intercepts are positive