A company is loading recliners and sofas onto a trailer that has a volume of about 3800 cubic feet. Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet. The company wants the shipment to have at least 30 recliners and more than 25 sofas. Identify and interpret the ordered pair in the solution region.

The area of ΔADC is equal to 6 unit².

The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h.

A abc = A adc because the areas of the initial and reflected triangles are equal.

Using the formula area=1/2 base height, determine the area of triangle ABC.

ABC in a triangle:

base = 4 units + AC

height = 3 units + BE

AΔ= abc = 1/2×4×3 =6 unnit²

Hence,

 ΔADC = 6 unit²

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The volume of the cube, given the lengths of the small cubes used to make the larger cube, is 8 cm ³

The surface area of the cube is 24 cm ²

The total length of the edges of the cube is  24 cm

The volume of a cube can be found by the formula :

= Side x Side x Side

This is because all the sides of a cube at the same and so the volume would measure them three - dimensionally.

The side length of this cube is the length of two of the smaller cubes as these make up a side of the cube :

= 2 x 1

= 2 cm

The volume is therefore :

= 2 x 2 x 2

= 8 cm ³

The surface area of a cube is:

= 6 x side ²

= 6 x 2 ²

= 24 cm ²

The total length of the edges would be:

= 12 edges on a cube x length of each edge

= 12 x 2

= 24 cm

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If Andrew takes same amount of time to kayak 4 miles upstream and 9 miles downstream in a river with a 6 mph current, then the speed of Andrew’s kayak in still water is 15.6 miles per hour.

Therefore the answer is 15.6 mph.

We can begin solving the problem by using the equation:

Speed (relative to water) = Speed (in still water) + Speed (of the water)

Let x be the speed of Andrew's kayak in still water.

When kayaking upstream, his speed relative to the water is x - 6 mph (since the current is moving in the opposite direction at 6 mph).

When kayaking downstream, his speed relative to the water is x + 6 mph (since the current is moving in the same direction at 6 mph).

Since the problem states that it takes Andrew the same amount of time to kayak 4 miles upstream as it takes him to kayak 9 miles downstream, we can set up the following equation knowing time = distance/ speed :

4/ (x - 6) = 9/ (x + 6)

Simplifying and solving for x we get

4(x + 6) = 9(x - 6)

4x + 24 = 9x - 54

9x - 4x = 54 + 24

5x = 78

x = 15.6

So, Andrew's kayak speed in still water is 15.6 miles per hour.

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The expression (1/4 - 3/5) is equivalent to the following expressions -

Given is the expression as -

(1/4 - 3/5)

The given expression is -

(1/4 - 3/5)

1/4 - 3/5

(5 - 12)/20

-7/20

We can write the fraction : -7/20 in many ways as given below -

-7/20 = (3/20 - 10/20) = (1/4 - 3/5)

-7/20 = (13/20 - 1) = (1/4 - 3/5)

-7/20 = (23/20 - 3/2) = 1/4 - 3/5)

Therefore, the expression (1/4 - 3/5) is equivalent to the following expressions -

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The graph of a line with a slope of 3/5 has an equation of y = 3/5x + 1 and the graph is attached

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

Graph of a line with a slope of 3/5

This means that

Slope = 3/5

And it also means that the equation is a linear equation

A linear equation is represented as

y = mx + c

Where

m = slope

i.e. m = 3/5

So, we have

y = 3/5x + c

Assume that c = 1

So, we have

y = 3/5x + 1

Hence, the equation is y = 3/5x + 1

See attachment for graph

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    Given ,

To Find : Maximum number of small cube shaped boxes that can fit in the cuboid

Volume of the Cuboid = [tex]2(lb+bh+lh)[/tex]

Volume of the cuboid = [tex]2(70X40+40X40+70X40)[/tex]

                                      = [tex]14400cm^{3}[/tex]

Now to find the volume of a cube,

[tex]V = a^{3}[/tex]

[tex]V = 10X10X10[/tex]

[tex]V = 1000cm^{3}[/tex]

Number of boxes that can fit in a cuboid = [tex]\frac{14400}{1000}[/tex]

                                                                    = [tex]14boxes[/tex]

Hence , the number of cube shaped boxes that can fit in a cuboid are 14

The total amount in the bank after the specific number of years is;

9.  $476. 1

11. $7, 128. 8

The formula for calculating simple interest is expressed as;

I = PRT/100

Where;

From the information given, we have that;

9.Principal amount = $450

Interest rate = 1.45

Time = 5

Substitute the values into the formula

SImple interest = $450 ×1. 45× 5/100

Multiply the values, we get;

Simple interest, I = 2610/100

Divide through

Simple interest = $26. 1

Total amount = $450 + $26.1 = $476. 1

11. Principal amount = $5600

Interest rate = 3.9

Time = 7 years

Substitute the values

Simple interest = $5600× 3. 9 × 7/100

Multiply the values

Simple interest = 152,880/100

Simple interest = $1528. 8

Total amount = $7, 128. 8

Hence, the values are $476. 1 and  $7, 128. 8

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The domain of the function f(x) = log x is (0, ∞). The value of x belongs to (0, ∞).

What is a logarithm?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

The given function is f(x) = log x.

When the value of x is less than or equal to 0, then the value of log x is undefined.

The possible value of x where f(x) exists is the domain of a function.

In the given function the value of x must be greater than zero.

The domain of the function is (0,∞).

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Column A and B matching the results with the operations

The simplified form of the algebraic expression [tex]2c-7c[/tex] is [tex]-15[/tex]

The given algebraic expression is [tex]2c-7c[/tex] and we need to use [tex]c=3[/tex]

Let's substitute the value of [tex]c[/tex] in the given algebraic expression, that is

                      [tex]=2(3)-7(3)\\=6-21\\=-15[/tex]

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Answer:

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

Given expression

Simplify it:

Find its value by plugging in the value of c:

Mrs. Smith will be responsible for paying $75.00

The normal monthly charge is $40.00 and the current balance is $110.00,

so the difference is $110.00 - $40.00 = $70.00.

Mrs. Smith negotiated a 50% credit, so she will receive

$70.00 x 0.50 = $35.00 credit.

To find the amount she is responsible for paying, we subtract the credit from the current balance

$110.00 - $35.00 = $75.00

Thus, the amount Mrs. Smith will be responsible for paying is $75.00

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Since X is an odd number, x+2 is the following odd number. If x is an even number, the subsequent odd number is x + 1.

The vehicles that will travel on the highways on particular days are decided by the Odd-Even rule, a space rationing system. According to the plan, vehicles with odd and even numbers will travel the roads on alternate days.

In jQuery, the odd() method is used to pick elements with odd index numbers (such as 1, 3, 5, etc.). The index begins at zero. It picks odd numbers, unlike the even() function, which is comparable. From the set of chosen items, the odd() method returns the odd indexed elements.

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There is very strong evidence to reject the null hypothesis, and to conclude that the machine gives radiation doses lower than the maximum on the label.

Hypothesis testing is a statistical method used to test a claim or a hypothesis about a population parameter, based on a sample of data. The goal of hypothesis testing is to determine whether there is enough evidence in the sample data to support or reject a claim about a population.

A t-test is a type of statistical hypothesis test that compares the mean of a sample to a known population mean. There are different types of t-tests, depending on the design of the study and the number of samples being compared.

To test the claim that the machine gives a radiation dose lower than the maximum on the label (5.00 milliroentgens), we can use a one-sample t-test. A one-sample t-test compares the mean of a sample to a known population mean (in this case, the maximum on the label). The null hypothesis for this test is that the mean radiation dose given by the machine is equal to or greater than the maximum on the label (5.00 milliroentgens). The alternative hypothesis is that the mean radiation dose given by the machine is less than the maximum on the label.

The test statistic for a one-sample t-test is:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values:

t = (4.23 - 5.00) / (1.91 / sqrt(46)) = -4.05

We can use a t-distribution table to find the p-value associated with this test statistic. With 45 degrees of freedom (sample size - 1), the p-value for t = -4.05 is extremely low, much less than 0.001, the significance level commonly used in hypothesis testing.

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Experimental probablity will be - 12 over 30

Answer: D: 12/60 (12 over 60)

Step-by-step explanation:

Side-Angle-Side (SAS) (SAS), The triangles are congruent if the included angles are also congruent and two sides of one triangle match two sides of another triangle.

Side-Angle-Side (SAS) (SAS), The triangles are congruent if the included angles are also congruent and two sides of one triangle match two sides of another triangle.

The use of labels Triangle ABC is congruent to triangle DEF if the angles of triangles ABC and DEF are AB = DE, AC = DF, and A = D.

ABC=CDE: a) in accordance with the conditions BC=CD and AC=CE; b) BCA=m (DCE).

If ABC = CDE, then m(BAC) = m(DEC), and m(ABC) = m (CDE).

If m(BAC)=m(DEC), then AB || DE, or if m(ABC)=m(CDE), then AB || DE.

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An angle that measures 120 degrees is called an obtuse angle.

An obtuse angle is defined as an angle that measures greater than 90 degrees but less than 180 degrees. It is formed by the intersection of two lines that are not collinear, that is, they do not lie on the same line, and the angle is greater than a right angle but less than a straight angle.

An obtuse angle is represented by an arc with a curved arrow on one end, pointing in the direction of the other end.

It's important to keep in mind that the term obtuse angle is just a classification based on the measure of the angle, which is greater than 90 degrees but less than 180 degrees, and it's not a specific angle measure, it could be any angle that is in that range.

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The third side of a triangle can be found using the Pythagorean Theorem.

The Pythagorean Theorem states that for a triangle with sides of length a, b, and c (with c being the length of the unknown side) a^2 + b^2 = c^2.

To find the third side of a triangle that is not right, first calculate the lengths of the two known sides. Let's say the lengths of the two known sides are a = 5 and b = 12.

Next, plug the values into the Pythagorean Theorem and solve for c.

[tex]a^2 + b^2 = c^2[/tex]

[tex](5)^2 + (12)^2 = c^2 \\25 + 144 = c^2[/tex]

[tex]169 = c^2[/tex]

Finally, take the square root of both sides to solve for c.

sqrt(169) = c

13 = c

Therefore, the length of the third side is 13.

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The z-score is compared as Test A : 3.25; Test B : 3.5; Test B.

Here given that,

Test A

Jeanette's score 90

Mean score 64

Standard deviation 8

Test B

Jeanette's score 95

Mean score 60

Standard deviation 10

The formula =

z = x - µ / σ

By substituting,

test A : z = (90 - 64) / 8 = 26 / 8 = 3.25

test B : z = (95 - 60) / 10 = 35/10 = 3.5

So Test A : 3.25; Test B : 3.5; Test B

The data of the question is attached below:

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Z-score in test A = 3.25, Z-score in test B = 3.5. She performed better in test B.

Z-score represent the difference between a given value and standard deviation.

given, Jeanette scored 90 in the Test A

 mean score of test A = 64

standard deviation = 8

we know, the Z-score is calculated by the following formula.

Z-score = (X - μ) /σ

where, σ denotes the standard deviation.

          μ denotes the mean value

    X is the actual value

Test A has Z- score = (actual score - mean score) / standard deviation

                             = (90 -64)/8

                           Z = 3.25

In the test B, she scored 95.

actual score = X = 95

mean score in test B = 60

standard deviation in test B = 10

hence, Z-score for test B = (X - μ)/ σ

                                        = (95 -60)/ 10

       Z-score = 3.5

Therefore, Jeanette scored better in her test B.

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Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b

The linear equation f(x) is  4x - 10 and the quadratic equation f(k) is -5/2k^2 + 4k - 1 for the two given points.

The linear equation can be found using the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept. To find the slope (m) we can use the two points given:

m = (y2 - y1) / (x2 - x1) = (18 - 2) / (7 - 3) = 16/4 = 4

The y-intercept (b) can be found using one of the points and the slope:

b = y - mx = 2 - 4(3) = -10

So the linear equation in standard form is:

f(x) = 4x - 10

For the quadratic equation, we know that it's in the form of y = ax^2 + bx + c. We have 2 points, so we have 2 equations with 2 unknowns. We can use this information to solve for a, b and c.

Let's (3,2) point 1 and (7,18) point 2.

f(k) = ak^2 + bk + c....(1)

point 1: f(3) = 2 = 9a + 3b + c...(2)

point 2: f(7) = 18 = 49a + 7b + c...(3)

Now we have 2 equations and 3 unknowns.

using theirs first equation and substitute it in the second and third equation

18 = 49a + 7b + c

2 = 9a + 3b + c

c = 2 - 9a - 3b

18 = 49a + 7b + (2 - 9a - 3b)

18 = 49a + 7b + 2 - 9a - 3b

18 = 40a + 4b + 2

16 = 40a + 4b

now this equation is used to solve for a and b

b = (16 - 40a) / 4

so a,b and c are

a = -5/2

b = 4

c = -1

so the quadratic equation in standard form is:

f(k) = -5/2k^2 + 4k - 1

4x - 10 is the linear equation f(x)  and -5/2k^2 + 4k - 1 is the quadratic equation f(k) for the two given points.

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If their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.

The term taxable income refers to any gross income earned that is used to calculate the amount of tax you owe. Put simply, it is your adjusted gross income less any deductions. This includes any wages, tips, salaries, and bonuses from employers.

The minimum income amount depends on your filing status and age. In 2022, for example, the minimum for single filing status if under age 65 is $12,950. If your income is below that threshold, you generally do not need to file a federal tax return. Review the full list below for other filing statuses and ages.

Taxable income

a. Taxable income:

Taxable income=Gross income - Total taxes due

Taxable income=$63,000-$6,847.50

Taxable income=$56,152.5

b. The marginal tax rate for taxable income  under the income bracket of of $40,526 to $86,375 is 22%.

c. Effective tax rate:

Effective tax rate = Total taxes due/ Taxable income×100

Effective tax rate =$6,847.50/$56,152.5×100

Effective tax rate =10.869%

Effective tax rate =10.87% (Approximately)

Inconclusion if their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.

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Explanation:

The equation y = 5x^2+3x^6-10x-8 is not in standard form.

Why not? Because the term with the largest exponent (6) isn't listed first.

The standard form would be y = 3x^6+5x^2-10x-8; note the exponents decrease (6, 2, 1, then 0).

After the polynomial is in standard form, we can read off the leading coefficient to be 3. This is the coefficient of the first term 3x^6.

Side note: The degree is 6 as it's the largest exponent.

The fast of the radius of balloon increasing is 480 cm³ / sec.

Given data :

V = [tex]\frac{4}{3}[/tex] π r³

we know [tex]\frac{dr}{dt}[/tex] = 30 cm/ sec

we want [tex]\frac{dV}{dt}[/tex] when r = 2cm

Differentiate V = [tex]\frac{4}{3}[/tex] π r³ implicitly with respect to t

[tex]\frac{dV}{dt}[/tex] (V) = [tex]\frac{dr}{dt}[/tex] ( [tex]\frac{4}{3}[/tex] π r³ )

[tex]\frac{dV}{dt}[/tex] = [tex]\frac{4}{3}[/tex] π x 3r² [tex]\frac{dr}{dt}[/tex] = 4 π r² [tex]\frac{dr}{dt}[/tex]

Plug in what you know and solve for what you don't know.

[tex]\frac{dV}{dt}[/tex] = 4π ( 2 )² ( 30 / sec ) =

= 120 x 4 .π cm³ / sec

= 480 cm³ / sec

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Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Given that, Manuel says [tex]25\frac{5}{8}[/tex] feet of fencing is enough for a rectangular flower bed that measures [tex]9\frac{7}{8}[/tex] feet by [tex]15\frac{3}{4}[/tex] feet

Here, perimeter =2([tex]9\frac{7}{8}[/tex] +  [tex]15\frac{3}{4}[/tex]) feet

= 2(79/8 + 63/4)

= 2(79/8 + 126/8)

= 2(205/8)

= 410/8

= [tex]51\frac{1}{4}[/tex] feet

Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.

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Answer: -1/4

Step-by-step explanation:

Rate of change is just another term for slope. To calculate slope, we just need any 2 points on the graph and apply the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

[tex]m=\frac{1-2}{4-0} =\frac{-1}{4} =-\frac{1}{4}[/tex]

This means -1/4 is the rate of change.

There are 3 terms in expression 7[tex]x^{2}[/tex]-5x+5.

Monomials, binomials, trinomials, and polynomials are all examples of algebraic expressions in mathematics. Algebraic expressions are those that are modeled utilizing unknowable constants, coefficients, and variables. A variable can have any value because it is not fixed, unlike a constant, which has a definite value. Monomials, binomials, trinomials, and polynomials are examples of algebraic expressions that are created by combining variables and constants using arithmetic operations. Terms are the components of algebraic expressions that are separated by addition or subtraction. The type of expression—monomial, binomial, trinomial, or polynomial—depends on the number of terms.

An algebraic expression with three terms is called a trinomial.

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Real value numbers are both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc are all real numbers.

The real number that consist of different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures.Any number that we can think except complex numbers is a real number.

Real numbers encompass three classifications of numbers.Whole numbers, rational numbers, and irrational numbers are all real numbers.Even counting and natural number are all real numbers.

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On solving the provided question, we can say that In light of this, the lowest common denominator of the equation is (x - 4)(x + 1)(x - 2) (x - 2)

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

equation is given as:

x2 — 3x — 4 = x2 — Ox + 8

x2 — 4x + x — 4 =

x(x — 4) + I(x — 4)

Factor out x - 4

(x + I)(x — 4) = x-2(x-4)

The common factor between the two sides of the equation is x – 4.

In light of this, the lowest common denominator is (x - 4)

(x + 1)(x - 2) (x - 2)

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Answer: Jesus will have 36 dollars after 8 days

Step-by-step explanation: 8 x 8= 64

100-64=36

Answer:

8.66 years

Step-by-step explanation:

F = Pe^(rt)

2 = e^(0.08t)

ln 2 = ln [e^(0.08t)]

ln 2 = 0.08t

t = (ln 2)/0.08

t = 8.66

Answer: 8.66 years