Select the correct expressions.
Which expressions are equivalent to 3x + 2(x - 1) - 4?
3x + 2x - 2 - 4
5x -6
3(x-4)
3(x + 2) - 6
6(x - 1)
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The density in pounds per cubic meter is 83 pounds per cubic metre.

The density is mass of a unit volume of a material substance.

In other words, density is the ratio between mass and volume or mass per unit .

Therefore, density can be represented mathematically as follows:

density = mass / volume

Hence,

mass = 5 ounces

5 ounces = 0.3125 pounds

1 gallon = 0.00378541 pounds

Therefore,

density = 0.3125 / 0.00378541

density = 82.5538052681

density = 83 pounds per cubic metre.

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Using proportions, it is found that the federal tax rate is of 10%.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The tax rate is the proportion that $17.50 is of $175, hence:

r = 17.50/175 = 0.1 = 10%.

The federal tax rate is of 10%.

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Miami gets 6.12 more inches of rainfall more than Tampa.

The annual amount of precipitation that we anticipate is known as normal or typical rainfall (in a given area).

It is calculated and set by estimating the average (mean) of precipitation that has been observed in a region over a long period of time ( at least 30 years). The total amount of daily precipitation in a year is referred to as annual precipitation.

Calculation for the average rainfall-

The average rainfall (in inches) in Miami for 5 months are-

1.61, 2.24, 2.99, 3.15, 5.35, and 9.68,

Thus, the total rainfall in Miami in 5 months,

Total average rainfall = 1.61 +2.24 +2.99 +3.15 +5.35 + 9.68 = 25.02 inches

Similarly,

The average rainfall (in inches) in Tampa for 5 months are-

2.24, 2.8, 3.03, 2.05, 2.09, and 6.69.

Thus, the total rainfall in Tampa in 5 months,

Total average rainfall = 2.24 +2.8 +3.03 + 2.05 + 2.09 + 6.69 = 18.9 inches.

The difference between the total rainfall in Miami and Tampa is

25.02 - 18.9 = 6.12 inches

The total rainfall in Miami is 25.02 inches while the total rainfall in Tampa in the same time period is 18.9 inches.

Therefore, Miami gets 6.12 inches more rainfall during the same time period.

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Answer:

B

Step-by-step explanation:

The missing side of a right triangle x is 24 units.

A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

The side x can be found using similar triangle ratios,

Hence,

x / 400 = 144 / x

cross multiply

x × x = 400 × 144

x² = 57600

square root both sides

√x² = √57600

x = 240

Therefore, the value of x in the right triangle is 240 units.

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The definition of the piecewise function is given as follows:

A piecewise function is a function that has different definitions, depending on the input.

Researching this problem on the internet, for x equal or greater than -3 and less than -1, the function is a line with a slope of 1 that goes through (-3,0), hence the definition is found as follows:

y = x + b

0 = -3 + b

b = 3

Then:

[tex]f(x) = x + 3, -3 \leq x < 1[/tex].

For x between -1 and 1, inclusive, the function is constant at 5, hence the definition is:

[tex]f(x) = 5, -1 \leq x \leq 1[/tex].

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The length of the side of the octagon is 4.142 inches.

Let the length of the congruent sides of the isosceles triangle be x.

The hypotenuse of the triangle is given by:

√x+x = √2x

This is also the length of the sides of the octagon. It is given that the sides of the octagon are equal.

It is also given that the length of the square side is 10 inches.

This means that:

x + √2x + x = 10

2x + √2x = 10

(2 + √2)x = 10

(2 + 1.414)x = 10

3.414x = 10

x = 10/3.414

x = 2.929 inches.

The side of the octagon is given by:

√2 × 2.929 = 4.142 inches

Therefore, we have found that the length of the sides of the octagon is 4.142 inches.

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The surface area of the parallelpiped is equal to 800 square units.

The surface area of the parallelpiped seen in the picture is equal to the sum of the areas of its six faces, which are combination of areas of quadrilaterals and triangles. There are four parallelograms and two squares. Thus, the surface area of the solid is:

A = 2 · 8 · 20 + 2 · 7 · 20 + 2 · 10²

A = 800

The surface area of the parallelpiped is equal to 800 square units.

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The modal and mean mark of the frequency distribution is 5 and 4.83 respectively.

Mode refers to a mark which reoccurs most in a frequency distribution.

The total number of students who wrote the test = 2 + 3 + 4 + 6 + 10 + 4 + 3 + 2 + 1 + 1

= 36 students

Mean mark = Total mark / Total students

= (2×1) + (3×2) + (4×3) + (6×4) + (10×5) + (4×6) + (3×7) + (2×8) + (1×9) + (1×10) / 36

= (2+6+12+24+50+24+21+16+9+10 / 36

= 174/36

= 4.83333333333333

Approximately,

Mean mark = 4.83

If 25% of students failed,

Number of students who failed = 25% of 36

= 25/100 × 36

= 0.25 × 36

= 9 students.

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The probability that Ron will get by a pitch exactly once is 0.351912.

Given that out of 596 plate appearance Ron was hit 19 times from pitches.

We have to find the probability that ron was hit by pitches in 22 plate appearances.

The value of probability lies between 0 and 1. The formula of calculating proabability is number of items/ total items.

We can find the required probability through binomial distribution which is

n[tex]C_{r}p^{r} (1-p)^{n-r}[/tex] where n is the number of trials and r is the successes.

Probability that Ron will be hit =19/596

=0.031

Probability that Ron will get hit by a pitch exactly once =P(X=1)

=[tex]22C_{1}(0.031)^{1} (1-0.031)^{21}[/tex]

=22!/1!21!*0.031*[tex](0.969)^{21}[/tex]

=22*0.031*0.516

=22*0.015996

=0.351912

Hence the probability that Ron will get hit by a pitch exactly once is 0.35.

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Answer:

x = -4/3 or x = 3/2

Step-by-step explanation:

Let's solve your equation step-by-step.

6x^2−x−12=0

Step 1: Factor left side of equation.

(3x+4)(2x−3)=0

Step 2: Set factors equal to 0.

3x+4=0 or 2x−3=0

x = -4/3 or x = 3/2

Answer:

x = -4/3 or x = 3/2

(p p) would produce Tautology.

Tautology:

It is needless repetition of an idea, statement, or word Rhetorical repetition, tautology ('always and for ever'), banal metaphor, and short paragraphs are part of the jargon.— Philip Howard. b : an instance of such repetition The phrase "a beginner who has just started" is a tautology.

A tautology is an expression or phrase that says the same thing twice, just in a different way. For this reason, tautology is usually undesirable, as it can make you sound wordier than you need to be and make you appear foolish.

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The time restriction faced by ABC Corporation for it to buy back its newly issued shares is 4 weeks

What is share buyback?

Share buyback means that the company would repurchase its own shares in the stock market by paying investors holding the shares, then reduce its number of shares outstanding by the number of shares bought back.

The shares repurchased are known as Treasury stocks, which are held until the company decides to reissue them or cancel them.

The restriction placed on a company before it can repurchase its shares is that the shares must be in issue 4 weeks, in other words, the new issued shares through Initial Public Offer(IPO) must be existence for 4 weeks before being repurchased by the company after having issued an IPO.

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Answer:

23.53

Step-by-step explanation:

OK so we got sin 52°=0.8 and the cos 52°=0.6

but we need tan 52° because we don't want to spend our time on calculating hypothenuse so

[tex] \frac{ \sin(52) }{ \cos(52) } = 1.3 = \tan(52) [/tex]

so

[tex]1.3 = \frac{x}{18.1} = = = > x = 23.53[/tex]

Answer:

[tex]\sf Equation: \quad \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]

The number is 2.

Step-by-step explanation:

The reciprocal of a number is simply 1 divided by the number.

The reciprocal of a fraction is where the numerator and denominator are swapped (so the fraction is turned upside down).

Let x be the positive number.

The reciprocal of the positive number x:

[tex]\sf \implies \dfrac{1}{x}[/tex]

The reciprocal of 3 more than the number x:

[tex]\sf \implies \dfrac{1}{x+3}[/tex]

The sum of the reciprocal of a positive number and the reciprocal of 3 more than the number is 7/10:

[tex]\implies \sf \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]

To solve, make the denominators of the two fractions on the left side the same by multiplying them.

Multiply the numerator of the first fraction by the denominator of the second fraction to get the new numerator of the first fraction.

Multiply the numerator of the second fraction by the denominator of the first fraction to get the new numerator of the second fraction.

[tex]\implies \sf \dfrac{1(x+3)}{x(x+3)}+\dfrac{1(x)}{(x+3)(x)}=\dfrac{7}{10}[/tex]

[tex]\implies \sf \dfrac{x+3}{x(x+3)}+\dfrac{x}{x(x+3)}=\dfrac{7}{10}[/tex]

Add the numerators and keep the denominator so that there is now one fraction:

[tex]\implies \sf \dfrac{2x+3}{x(x+3)}=\dfrac{7}{10}[/tex]

Cross multiply:

[tex]\implies \sf 10(2x+3)=7x(x+3)[/tex]

Expand:

[tex]\implies \sf 20x+30=7x^2+21x[/tex]

Rearrange so the equation is equal to zero:

[tex]\implies \sf 7x^2+x-30=0[/tex]

Split the middle term:

[tex]\implies \sf 7x^2+15x-14x-30=0[/tex]

Factor the first two terms and last two terms separately:

[tex]\implies \sf x(7x+15)-2(7x+15)=0[/tex]

Factor out the common term (7x + 15):

[tex]\implies \sf (x-2)(7x+15)=0[/tex]

Apply the zero product property:

[tex]\sf (x-2)=0 \implies x=2[/tex]

[tex]\sf (7x+15)=0 \implies x=-\dfrac{15}{7}[/tex]

As x is a positive number, x = 2.

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Considering the definition of an inequality, the inequality that expresses the previous relationship is 12 < x ≤ 12.2

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that to fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm.

It means that the length has to be strictly greater than 12 cm but less than or equal to 12.2 cm. In other words, length of frame must be longer than 12 cm means that x>12, while ength of frame not longer than 12.2 cm means x≤12.2

Finally, the inequality that expresses the previous relationship is

12 < x ≤ 12.2

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Answer:

x = 20°

f = 40°

Step-by-step explanation:

4x + 5x = 180°

because a straight line is 180°

so 9x = 180°

1x = 180 ÷ 9

1x = 20

all angles in a triangle add together is 180°

so 7x + f = 180°

1x = 20

7x = 20 × 7

7x = 140°

f = 180° - 140 °

f = 40°

Answer:

x = 20 , f = 40

Step-by-step explanation:

4x and 5x are a linear pair and sum to 180° , then

4x + 5x = 180

9x = 180 ( divide both sides by 9 )

x = 20

then

5x = 5 × 20 = 100° and 3x = 3 × 20 = 60°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

5x is an exterior angle of the triangle , then

f + 3x = 5x , that is

f + 60 = 100 ( subtract 60 from both sides )

f = 40

The cost of kilograms of almonds is $8.5 if 4 kilograms of almonds cost $34.

According to the questions,

4 kilograms of almonds cost $34. In order to find one kilograms of almonds  only if we divide 34 by 4.

= [tex]\frac{34}{4}[/tex] = 8.5

Hence, the cost of kilograms of almonds is $8.5 if 4 kilograms of almonds cost $34.

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Answer: [tex]m\angle 1=82^{\circ}, m\angle 2=128^{\circ}[/tex]

Step-by-step explanation:

By the same-side interior angles theorem,

[tex]m\angle 1=180^{\circ}-98^{\circ}=82^{\circ}\\\\m\angle 2=180^{\circ}-52^{\circ}=128^{\circ}[/tex]

The first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}

Given the nth term of a recursive expression shown below

an =an-1 - 1.4

where

an-1 is the preceding term

a1 is the first term

an is the nth term

an-1 is

Given the following

a1 = 0

For the second term a2

a2 = 0 - 1.4

a2 = -1.4

For the third term a3

a3 = -1.4 - 1.4

a3 = -2.8

For the fourth term a4

a4 = -2.8 - 1.4

a4 = -4.2

For the fifth term a2

a5 = -4.2 - 1.4

a5 = -5.6

Hence the first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}

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Option A is correct. If segment DC bisects segment AB, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. This can be obtained using perpendicular bisector theorem.

Perpendicular bisector theorem : In a plane, if we choose a point, say D, on the perpendicular bisector,say PQ, drawn from segment, say AB, then the point D is equidistant from the endpoints, that is A and B, of the segment.

That is, perpendicular bisector PQ of line segment AB is the line with         Q = 90° and Q is the midpoint of AB ⇒ AQ = BQ. A point on PQ say D is equidistant from A and B ⇒AD and BD.

Thus in the given question we can use perpendicular bisector theorem.

Here DC is the perpendicular bisector of the line segment AB and therefore AD and BD are equal.

Hence it is clear that Option A is correct.

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The quadrilateral is a parallelogram because both pairs of opposite sides are parallel and since the product of the slopes of both pairs of adjacent segments is -1, the quadrilateral is a rectangle

Answer:

The guy above is somewhat right.

Hope this helps!

Step-by-step explanation:

The quadrilateral is a rectangle.

Considerando la definición de una ecuación, el número desconocido es 50.

Una ecuación es la igualdad existente entre dos expresiones algebraicas conectadas a través del signo de igualdad en la que figuran uno o varios valores desconocidos, llamadas incógnitas, además de ciertos datos conocidos.

Los miembros de una ecuación son cada una de las expresiones que aparecen a ambos lados del signo igual.

En este caso, "La suma de un número con su mitad es igual a 75" puede ser expresado mediante una ecuación, donde consideras que "x" es la incógnita, que representa el número desconocido.

Teniendo en cuenta que la mitad de un número se calcula dividiendo el número por 2, entonces la ecuación queda expresada como:

x + x÷2= 75

O lo que es lo mismo

x + [tex]\frac{1}{2}[/tex]x= 75

Resolviendo:

[tex]\frac{3}{2}[/tex]x= 75

x= 75 ÷[tex]\frac{3}{2}[/tex]

x= 75×[tex]\frac{2}{3}[/tex]

x=50

Finalmente, el número desconocido es 50.

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The graphs of the reciprocal functions are related to their corresponding original functions based on the information illustrated below.

It should be noted that the trigonometric functions are the real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are six functions of an angle. They are sine (sin), cosine (cos), tangent (tan), cotangent, secant, and cosecant (csc).

It should be noted that all the y-coordinates of a reciprocal function will be the reciprocals of the y-coordinates of the original function. Then, the graph of a reciprocal function has a vertical asymptote at each zero of the original function. For example, y=arcsinx reflects against y=sinx.

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All the events in the sample space that are not part of the specified event are called Complement of Event.

Complement of event:

The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event. The complement of an event A is denoted as A c A^c Ac or A′. An event and its complement are mutually exclusive and exhaustive.

Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less.

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Answer: 18 years

Work Shown:

[tex]f(\text{x}) = 2.56(1.04)^\text{x}\\\\5 = 2.56(1.04)^\text{x}\\\\5/2.56 = (1.04)^\text{x}\\\\1.953125 = (1.04)^\text{x}\\\\\log(1.953125) = \log(1.04^\text{x})\\\\\log(1.953125) = \text{x}*\log(1.04)\\\\\text{x} = \frac{\log(1.953125)}{\log(1.04)}\\\\\text{x} \approx 17.0682937693249\\\\[/tex]

The steps above show f(x) replaced with 5. Then you'd use logarithms to isolate the variable x. The relevant useful log rule is [tex]\log(A^B) = B\log(A)[/tex] so we can pull down the exponent.

From here it seems your teacher wants you to round up to the nearest integer.

If we plugged in x = 17, then f(x) = 4.99 which is one cent too small.

While x = 18 leads to f(x) = 5.19

Therefore, x = 18 has the price reach or exceed $5

Answer:

Step-by-step explanation:

 5x² - 6x - 2 = 0

a = Coefficient of x² = 5

b = coefficient of x = -6

c = constant = -2

Discriminant = D = b² - 4ac

                           = (-6)² - 4 * 5 * (-2)

                           = 36 +  40

                           = 76  > 0

So, the quadratic equation has two distinct real roots.

[tex]\sf \boxed{\bf x = \dfrac{-b \± \sqrt{D}}{2a}}\\\\[/tex]

     [tex]\sf = \dfrac{-[-6] \± \sqrt{76}}{2*5}\\\\= \dfrac{6 \±8.7}{10}\\\\=\dfrac{6+8.7}{10} \ ; \ or \ x =\dfrac{6-8.7}{10}\\\\=\dfrac{14.7}{10} \ ; \ or \ x = \dfrac{-2.7}{10}[/tex]

x = 1.47  or x = -0.27

Answer: x = 1.5 or (-0.3)

b) x² + 3x = 40

x² + 3x - 40= 0

We can solve the quadratic equation using factor method.

Sum = 3

Product = -40

Factors = 8 , (-5)

 When we add, 8 + (-5) = 3 , we get 5and when we multiply 8 *(-5) = -40, we get -(-40).

Rewrite the middle term of the quadratic equation using the factors.

 x² + 8x - 5x - 40 = 0

x(x + 8) - 5(x + 8)= 0

 (x + 8) (x - 5)    = 0

 x + 8 = 0   or x - 5 = 0

     x = -8   or       x = 5

Answer : x = -8 , 5