A Carpenter Is Working With A Beam That Is 10 Feet Long And In The Shape Of A Rectangular Prism. He Cuts (2024)

Ok, so:

Let's make all operations and then choose the equivalent expression for each one.

Let's start in order:

a. 4/12 + 4/12 = 8/12

b. 1/12 + (3/12 + 3/12) = 7/12

c. 4/12 + 5/12 = 9/12

d. 2/12 + 2/12 + 2/12 = 6/12.

Notice that the last operations are the columns of the table.

So, let's do it the same with the upper rows:

e. 5/12 + 4/12 = 9/12

f. (1/12 + 3/12) + 3/12 = 7/12

g. 1/12 + 2/12 + 3/12 = 6/12

h. 15/12 - 7/12 = 8/12.

Now, let me draw the table to make this problem more understandable.

This is the order you have to put the answer:

ANSWER

2/27

EXPLANATION

There are a total of 9 marbles in the bowl. The probability of drawing a red marble is,

[tex]P(red)=\frac{\#red.marbles}{\#total.marbles}=\frac{3}{9}=\frac{1}{3}[/tex]

Then you draw another marble, but you put the first back in the bowl, so the total number of marbles is the same. The probability of drawing a yellow marble is,

[tex]P(yellow)=\frac{\#yellow.marbles}{\#total.marbles}=\frac{2}{9}[/tex]

The probability of drawing a red marble and a yellow marble is,

[tex]P(red.and.yellow)=P(red)\cdot P(yellow)=\frac{1}{3}\cdot\frac{2}{9}=\frac{2}{27}[/tex]

The given table is

Male Female Total

Drive 26 24 50

Did not drive 34 116 150

Total 60 140 200

From the table, total number of males and females = 200

number of guests that are males and did not drive = 34

Recall, Probability is expressed as

number of favorable outcomes/number of total outcomes

Therefore, the chances of choosing a guest who is male and did not drive to the party is

34/200 = 0.17

By converting to percentage, it is

0.17 x 100 = 17%

[tex]\begin{gathered} To\text{ find the missing length, we will use law of cosines.} \\ Co\sin es\text{ rule is-} \\ (L)^2=38^2+42^2-2\times38\times42\times\cos 39^{\circ} \\ L^2=727.35 \\ L=\sqrt[]{727.35} \\ L=26.96 \end{gathered}[/tex]

As per the unitary method, the number of democrats are 53 and the number of republicans are 47.

Unitary method:

Unitary method is the process of finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

The U.S senate has 100 members. after a certain election, there were 6 more democrats than republicans, with no other parties represented.

Here we need to find the number of democrats and the number of republicans.

Let us consider the number of Republican's be "x"

And then the number of Democrats is "x+6".

We know that the total number of members in the senate is 100.

So, it can be written as

x + (x + 6) = 100

2x + 6 = 100

2x = 100 - 6

2x = 94

x = 94/2

Then the value of x is,

x = 47

Therefore, there are 47 republicans in the senate then the number of democrats is

x + 6 => 47 + 6 => 53

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Let x be the required number.

[tex]15\text{ \% of 80 =}60\text{ \% of x}[/tex]

[tex]15\text{ \% }\times\text{ 80 =}60\text{ \% }\times\text{ x}[/tex]

[tex]\frac{15}{100}\text{ }\times\text{ 80 =}\frac{60}{100}\text{ }\times\text{ x}[/tex]

Using the cross-product method, we get

[tex]\frac{15\times80}{100}\times\frac{100}{60}=x[/tex][tex]x=20[/tex]

Hence 15% of 80 is 60% of 20.

The answer is 20.

Check the picture below.

usign the pythagorean theorem let's find the side CD, then let's get the side AC using the same pythagorean threorem.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{16}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{7}\\ \end{cases} \\\\\\ \sqrt{16^2 - 7^2}=CD\implies \sqrt{207}=CD \\\\[-0.35em] ~\dotfill[/tex]

[tex]c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ AC=\sqrt{(\sqrt{207})^2~~ + ~~11^2}\implies AC=\sqrt{207 + 121}\implies \boxed{AC\approx 18.1}[/tex]

Recall that the slope-intercept form of the line equation is of the form y=mx+b, where m is the slope and b is the y-intercept.

To transform the equation 10=-2y-x into the slope-intercept form we should apply algebraic operations so we isolate the y on one side of the equation.

Let's add x on both sides, we get

[tex]-2y=10+x[/tex]

Now, lets divide by -2 on both sides, we get

[tex]y=\frac{10}{-2}+\frac{x}{-2}=-\frac{1}{2}\cdot x-5[/tex]

we see that this now has the slope-intercept form, where the slope is m=(-1/2) and b=-5

-27/9 = -3

answer is -3

The Solution:

Given:

Required:

To find the perimeter (in inches) of the floor in the scale drawing.

Step 1:

Find the value of x.

By the similarity theorem:

[tex]\frac{14}{x}=\frac{28}{30}[/tex]

Cross multiplying, we get:

[tex]\begin{gathered} 28x=14\times30 \\ \\ Dividing\text{ both sides by 28, we get} \\ \\ x=\frac{14\times30}{28}=\frac{30}{2}=15\text{ in.} \end{gathered}[/tex]

Step 2:

Find the perimeter, in inches, of the floor in the scale drawing.

By formula, the perimeter is:

[tex]\begin{gathered} P=2(L+W) \\ \text{ Where:} \\ L=14\text{ inches} \\ W=x=15\text{ inches} \\ P=perimeter=? \end{gathered}[/tex]

Substituting these values in the formula, we get:

[tex]P=2(14+15)=2\times29=58\text{ inches}[/tex]

Therefore, the correct answer is 58 inches.

As given by the question

There are given that the graph of the line.

Now,

To find the slope and y-intercept of the line, first select two intersect point from the graph.

Then,

The points are:

[tex](0,\text{ 5) and (5, 0)}[/tex]

Then,

First find the slope,

So,

From the formula of slope,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where,

[tex]x_1=0,y_1=5,x_2=5,y_2=0[/tex]

Then,

Put all the value into the given formula.

So,

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0_{}-5_{}}{5_{}-0_{}} \\ m=-\frac{5}{5} \\ m=-1 \end{gathered}[/tex]

Now,

From the standard form of the line,

[tex]y=mx+b[/tex]

Then,

Put y is 5, x is 0 and m is -5 into the above equation to find the y-intercept

So,

[tex]\begin{gathered} y=mx+b \\ 5=-1(0)+b \\ b=5 \end{gathered}[/tex]

Hence, the value of the y-intercept is 5.

Now,

The line equation is shown below:

[tex]\begin{gathered} y=mx+b \\ y=-1x+b \\ y=-x+5 \end{gathered}[/tex]

Hence, the slope of the line is -1, y-intercept of the line is 5 and the equation of line is y = -x + 5.

We want to find the x and y-intercepts of

[tex]3x+8y=24[/tex]

The x-intercept is where the graph cuts the x-axis, when y = 0. To find this in our equation, we just need to evaluate it at y = 0.

[tex]\begin{gathered} 3x+8\times0=24 \\ 3x=24 \\ x=\frac{24}{3}=8 \end{gathered}[/tex]

Then, the x-intercept is (8, 0).

The y-intercept is where the graph cuts the y-axis, when x = 0. To find this in our equation, we just need to evaluate it at x = 0.

[tex]\begin{gathered} 3\times0+8y=24 \\ 8y=24 \\ y=\frac{24}{8}=3 \end{gathered}[/tex]

The y-intercept is (0, 3).

In order to find the value of a composition of functions at x = a, (f º g)(a), we first find the value of g(a), then find the value of f(x) at x = g(a).

(f º g)(a) = f(g(a))

In this problem, the values of f(x) and g(x) are shown in the table, for integer values of x from 0 to 9.

So, we have:

1. (f º g)(8) = f(g(8))

From the table, we see that

g(8) = 4 (value of g(x) in the line corresponding to x = 8)

Then:

f(g(8)) = f(4) = 4 (value of f(x) in the line corresponding to x = 4)

Thus:

[tex]\mleft(f\circ g\mright)\mleft(8\mright)=4[/tex]

2. g(f(3))

f(3) = 8

g(8) = 4

Thus:

[tex]g(f(3))=4[/tex]

3. f(f(1))

f(1) = 6

f(6) = 2

Thus:

[tex]f(f(1))=2[/tex]

4. (g º g)(6) = g(g(6))

g(6) = 7

g(7) = 3

Thus:

[tex]\mleft(g\circ g\mright)\mleft(6\mright)=3[/tex]

Answer:

Step-by-step explanation:

0.776 in decimal form.

The radical expression √108 is not equivalent to the expression √5√21 .

Given the radical expression as √108 .

Now the number 108 can be broken down into factors as

108 = 54 × 2 , 36 × 3 , 18×6

therefore we can see that the radical expression is equivalent to

√108 = √54 × √2

√108 = √36 × √3

√108 = √18 × √6

But 21 × 5 = 105 ≠ 108.

Therefore the radical expression √108 is not equivalent to √5√21 .

Expressions in mathematics are statements with variables, numbers, or both, and at least two terms joined by an operator. Mathematical operations include addition, subtraction, multiplication, and division.

In mathematics, there are two types of expressions: numerical expressions, which only contain numbers, and algebraic expressions, which also contain variables.

A symbol with an unknown value is called a variable. A term can be made up of a single constant, a single variable, or a group of variables and constants multiplied or divided. A number that has been further multiplied by a variable serves as the coefficient in an equation.

Disclaimer: The complete question is :

Which of the following is not a radical expression that is equivalent to √108?

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Given:

The population P of a city is given by,

[tex]P=115600e^{0.024t,}[/tex]

To find:

The time taken for the population to reach 130,000.

Explanation:

Substituting P = 130,000 in the given function, we get

[tex]\begin{gathered} 130000=115600 \\ e^{0.024t}=\frac{130000}{115600} \\ e^{0.024t}=1.1245 \\ 0.024t=\ln1.1245 \\ 0.024t=0.1174 \\ t=4.891 \\ t\approx4.89years \end{gathered}[/tex]

Therefore, the number of years required for the population to reach 130,000 is 4.89years.

Final answer:

The number of years required is 4.89years.

Given data:

The expression for the given statement is,

[tex]0.9x+5=75[/tex]

Thus, the option (C) is correct.

Given data;

The area in which cucumbers usually grown are 2/3 x.

Here, x is the total area of the garden.

The area of the cucumber taken to grow raddish are,

[tex]\begin{gathered} R=\frac{3}{4}\times\frac{2}{3}x \\ =\frac{1}{2}x \end{gathered}[/tex]

Thus, the area of the raddish is 50% of the total area of the garden sfter the changes.

Answer

[tex]y=2x+5[/tex]

SOLUTION

Problem Statement

The question wants us to model the distance Jane is from her home given her initial starting point (5 miles from home) and her speed (2 mph)

Explanation

To solve the question, we simply need to model her jogging using the equation of a line.

The general equation of a line is given as:

[tex]\begin{gathered} y=mx+c \\ \text{where,} \\ m=\text{slope}=\text{this represents Jane's speed} \\ c=y-\text{intercept}=\text{this represents her initial position from her home} \\ x=\text{time taken for Jane to move} \\ y=\text{Jane's final position after moving for time, x} \end{gathered}[/tex]

We have been told that her speed is 2 mph. Thus, m = 2. We have also been given her initial position from her house to be 5 miles.

Jane starts jogging 5 miles from her home, thus, her position relative to her home will continue to increase as she jogs on at 2 mph. Thus, c = 5 and NOT -5.

This means we can write the equation for her position is:

[tex]\begin{gathered} m=2,c=5 \\ \therefore y=2x+5 \end{gathered}[/tex]

Final Answer

[tex]y=2x+5[/tex]

Given the next equation

2900 = 250 + 132.5T

its solution is:

2900 - 250 = 132.5T

2650 = 132.5T

2650/132.5 = T

T = 20

Given that W is weigth and T is t-shirts, the solution tell us that a box with 20 t-shirts weights 2900 grams

For the inequality 1 ≤ x ≤ 4 given by Felipe the domain of the function is stated as {1,2,3,4} which shows the error of x belongs to which set of numbers is not specified.

As given in the question,

Given inequality is equal to :

1 ≤ x ≤ 4

Domain of the given inequality function is given by :

x belongs to all real numbers as it is not specified which set of numbers x belongs.

Consider x as set of real numbers

Given domain is {1,2,3,4}

Error is Felipe needs to specify x must belongs to integers or natural numbers then only domain is {1,2,3,4} for the given inequality else there are infinite many numbers between 1 to 4.

Therefore, for the inequality 1 ≤ x ≤ 4 given by Felipe the domain of the function is stated as {1,2,3,4} which shows the error of x belongs to which set of numbers is not specified.

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In the given figure, line LP is lie on the line RE, thus from the linear property

Angle LPR + Angle LPE = 180°

It is given that Angle LPR = 3z, angle LPE = 2z

Angle LPR + Angle LPE = 180°

3z° + 2z° = 180°

5z° = 180°

z = 180/5

z=36

Substitute the value of z = 36 in the angle LPR;

Angle LPR = 3z

= 3(36)

=108°

Angle LPE = 2z

= 2(36)

= 72°

Answer : B) 108 and 72

Answer:

Explanation:

Option A

[tex]\begin{gathered} \text{One wager jug hold 5 quarts} \\ y=kx \\ 5=1k \\ y=5x \end{gathered}[/tex]

Option B

[tex]\begin{gathered} 1\text{ banana costs \$}$0.20$ \\ y=0.20x \\ y=\frac{1}{5}x \end{gathered}[/tex]

The correct choice is B.

[tex]\begin{gathered} C(1,9) \\ D(4,9) \\ E\left(0,3\right) \\ Rotation\text{ of 90\degree counterclockwise} \\ The\text{ new coordinates will be \lparen-y,x\rparen} \\ Hence \\ C^{\prime}(-9,1) \\ D^{\prime}(-9,4) \\ E^{\prime}(-3,0) \end{gathered}[/tex]

We have a system of 2 equation (Eq):

y = 3x + 7 (Eq 1)

y = 2x + 8 (Eq 2)

To solve the system, we can match both equations.

3x + 7 = 2x + 8

3x - 2x = 8 - 7

x = 1

The Solution:

Given:

[tex]y=7x^2+bx+c[/tex]

Given that the points: (-1,4) and (2,13) are on the graph of the given equation,

We are required to find the values of a and b.

Substitute (x= -1, y = 4) in the equation, we get:

[tex]\begin{gathered} 4=7(-1)^2+b(-1)+c \\ 4=7-b+c \\ -3=-b+c...eqn(1) \end{gathered}[/tex]

Substitute (x= 2, y = 13) in the equation, we get:

[tex]\begin{gathered} 13=7(2)^2+b(2)+c \\ 13=28+2b+c \\ -15=2b+c...eqn(2) \end{gathered}[/tex]

Solving eqn(1) and eqn(2) simultaneously by the elimination method:

Subtract eqn(1) from eqn(2):

[tex]\begin{gathered} -15--3=2b--b+c-c \\ -12=3b \end{gathered}[/tex]

Divide both sides by 3.

[tex]b=\frac{-12}{3}=-4[/tex]

Substitute -6 for b in eqn(1).

[tex]\begin{gathered} -3=-b+c \\ -3=-(-4)+c \\ \\ -3=4+c \\ -3-4=c \\ -7=c \\ c=-7 \end{gathered}[/tex]

Therefore, the correct answers are:

b = -4

c = -7

Since both variables are equal (b) we can add them:

[tex]4b+9b[/tex][tex]13b[/tex]

Solution:

Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood, and each repetition is known as a trial.

[tex]\begin{gathered} P(E)=\frac{n(E)}{n(T)} \\ \\ Where; \\ n(E)=\text{ number of event} \\ \\ n(T)=\text{ total outcome} \end{gathered}[/tex]

If 219 of the first 264 customers have not received a star on the receipt, then a customer that would win a free gallon of milk would be among (264 - 219) customers. Thus;

The experimental probability of winning a free gallon of milk is;

[tex]\begin{gathered} =\frac{264-219}{264} \\ \\ =\frac{45}{264} \\ \\ =\frac{15}{88} \end{gathered}[/tex]

CORRECT OPTION:

[tex]\frac{15}{88}[/tex]

The coordinates of the images are;

[tex]undefined[/tex]

Here, we want to translate the given triangle

The translation is in the units of (10,2)

What this mean is that we are going to make a translation of 10 in the x-axis direction and 2 units in the y-axis direction

Hence, we are having a unit of 10 rightwards (positive x-axia) and 2 unit of 2 units upwards (vertically on the y-axis)

So what we do now in respective cases is add 10 to the x-axis values of each point and add 2 to the y-axis values of each point

Thus, we have;

[tex]\begin{gathered} A(-1,6)\text{ to A'(-1+10, 6+2)= A'(9,8)} \\ B(0,4)\text{ to B'(0+10, 4+2) = B'(10,6)} \\ C(-6,1)\text{ to C'(-6+10,1+2) = C'(4,3)} \end{gathered}[/tex]

The given expression is:

[tex]\frac{10^4}{10^6}[/tex]

Exapanding the above expression,

[tex]\frac{10\times10\times10\times10}{10\times10\times10\times10\times10\times10}[/tex]

(The number of 10s are the same as the power of 10).

Now, cancel out the common terms in the numerator and the denominator of the above expression.

[tex]\frac{1}{10\times10}[/tex]

The denominator of the above expression can now be expressed as the power of 10 as,

[tex]\frac{1}{10^2}[/tex]

According to the law of exponents,

[tex]\frac{1}{x_{^{^m}}}=x^{-m}[/tex]

Hence, we can write

[tex]\frac{1}{10^2}=10^{-2}[/tex]

Therefore, 10^4 divided by 10^6 can be expressed as a term with a single power as,

[tex]10^{-2}[/tex]